Mathematics High School

## Answers

**Answer 1**

The **other angle **of the **triangle **is 65°.

We know that

Exterior Angle = Sum of two angles **opposite **to the **exterior angle**

Here, 145° = 80° + x°

=> x° = (145 – 80)°

=> x° = 65°

Therefore, the **value **of x in the given figure is 65°

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**Complete question:**

## Related Questions

a table or spreadsheet used to systematically evaluate options according to specific criteria is a ________.

### Answers

A table or **spreadsheet** used to systematically evaluate options according to specific criteria is a decision matrix.

A decision matrix is a table or spreadsheet used to systematically evaluate options based on specific criteria. It is a tool commonly used in decision-making processes to objectively assess and compare different **choices**.

The **decision matrix** organizes the criteria in rows and the options in columns. Each cell in the matrix represents the evaluation or score of an option based on a particular criterion. The criteria can be weighted to reflect their relative importance in the decision-making process.

By filling out the decision matrix with scores or ratings for each option and criterion, a comprehensive evaluation can be performed. The matrix allows decision-makers to **visualize** and compare the performance of different options against the criteria, helping them make more informed and structured decisions.

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The formula for the materials price variance is a. (AQ x SP) - (SQ SP). b. (AQ X SP) - (SQ X AP). c. (AQ X AP) - (AQ X SP). d. (AQ X AP) - (SQ x SP)

### Answers

The correct formula for the **materials price** variance is:

b. (AQ x SP) - (SQ x AP)

Find out the correct formula of materials price?

These are the formula for finding the following.

AQ = Actual quantity of materials **purchased**

SP = Standard price per unit of materials

SQ = Standard quantity of materials allowed for actual output

AP = Actual price per unit of materials

This formula calculates the difference between the actual cost of materials purchased (AQ x AP) and the **standard cost **of materials that should have been used for the actual output (SQ x SP). The variance shows whether the actual price paid for materials is higher or lower than the standard price, and the difference is attributed to the materials price variance.

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what are the minors of this matrix?

### Answers

The **minors** of the given **matrix** are:

6 -24 60

-93 0 -93

6 10 -27

We have,

To find the **minors** of a **matrix**, we calculate the determinants of each of the 2x2 submatrices formed by removing one row and one column from the original matrix.

Given the matrix:

-5 8 5

4 -1 0

6 9 -6

Let's calculate the **minors**:

- For the element in the first row, the first column (-5):

Remove the first row and first column to obtain the submatrix:

-1 0

9 -6

The determinant of this 2x2 submatrix is (-1 x -6) - (0 x 9) = 6.

Therefore, the minor for the element -5 is 6.

- For the element in the first row, second column (8):

Remove the first row and second column to obtain the submatrix:

4 0

6 -6

The determinant of this 2x2 submatrix is (4 x -6) - (0 x 6) = -24.

Therefore, the minor for the element 8 is -24.

- For the element in the first row, third column (5):

Remove the first row and third column to obtain the submatrix:

4 -1

6 9

The determinant of this 2x2 submatrix is (4 x 9) - (-1 x 6) = 54 + 6 = 60.

Therefore, the minor for the element 5 is 60.

- For the element in the second row, first column (4):

Remove the second row and first column to obtain the submatrix:

8 5

9 -6

The determinant of this 2x2 submatrix is (8 x -6) - (5 x 9) = -48 - 45 = -93.

Therefore, the minor for the element 4 is -93.

- For the element in the second row, second column (-1):

Remove the second row and second column to obtain the submatrix:

-5 5

6 -6

The determinant of this 2x2 submatrix is (-5 x -6) - (5 x 6) = 30 - 30 = 0.

Therefore, the minor for the element -1 is 0.

- For the element in the second row, third column (0):

Remove the second row and third column to obtain the submatrix:

-5 8

6 9

The determinant of this 2x2 submatrix is (-5 x 9) - (8 x 6) = -45 - 48 = -93.

Therefore, the minor for the element 0 is -93.

- For the element in the third row, first column (6):

Remove the third row and first column to obtain the submatrix:

-1 0

9 -6

The determinant of this 2x2 submatrix is (-1 x -6) - (0 x 9) = 6.

Therefore, the minor for the element 6 is 6.

- For the element in the third row, second column (9):

Remove the third row and second column to obtain the submatrix:

-5 5

4 -6

The determinant of this 2x2 submatrix is (-5 x -6) - (5 x 4) = 30 - 20 =

Therefore, the minor for the element 9 is 10.

- For the element in the third row, third column (-6):

Remove the third row and third column to obtain the submatrix:

-5 8

4 -1

The determinant of this 2x2 submatrix is (-5 x -1) - (8 x 4) = 5 - 32 = -27.

Therefore, the minor for the element -6 is -27.

Thus,

The **minors** of the given **matrix** are:

6 -24 60

-93 0 -93

6 10 -27

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yearly income of a married proprietor of a firm was Rs 675000 and 4% of his yearly income was invested in CIF which was also tax free If 10% tax was levied on the rest of his income.

### Answers

The yearly** income tax **for the proprietor is Rs 64,800.

Let's break down the calculations step by step.

The **amount invested** in CIF (tax-free) is 4% of the yearly income.

CIF investment = 4% of Rs 675,000 = (4/100) × 675,000 = Rs 27,000.

The remaining **income** after deducting the CIF investment is:

Remaining **income** = Yearly income - CIF investment

= Rs 675,000 - Rs 27,000

= Rs 648,000.

The tax is **levied** on the remaining income at a rate of 10%.

Tax on remaining **income** = 10% of Rs 648,000

= (10/100) × 648,000

= Rs 64,800.

Therefore, the yearly **income tax** for the proprietor is Rs 64,800.

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find an equation of the tangent line to the graph of the function at the given point. y = 5 ln ex e−x 2 , (0, 0) y =

### Answers

the **equation** of the tangent line to the graph of the **function** at the point (0, 0) is y = 5x.

To find the equation of the tangent line to the **graph** of the function at the point (0, 0), we need to find the derivative of the function and evaluate it at x = 0.

The given function is y = 5 ln(exe^(-x^2)).

To find the derivative, we can use the **chain rule** and the properties of logarithmic and exponential functions. The **derivative** of y with respect to x can be calculated as follows:

dy/dx = 5 * (1/exe^(-x^2)) * (d/dx(exe^(-x^2)))

Applying the chain rule, we have:

dy/dx = 5 * (1/exe^(-x^2)) * (e^(-x^2) * d/dx(ex) + ex * d/dx(e^(-x^2)))

Simplifying further, we get:

dy/dx = 5 * (1/exe^(-x^2)) * (e^(-x^2) * 1 + ex * (-2x))

dy/dx = 5 * (e^(-x^2) - 2xex) / (ex * e^(-x^2))

Now, we can evaluate the derivative at x = 0 to find the slope of the tangent line at the point (0, 0).

dy/dx = 5 * (e^0 - 2(0)e^0) / (e^0 * e^0) = 5 * (1 - 0) / 1 = 5

Therefore, the slope of the tangent line at the point (0, 0) is 5.

Using the point-slope form of a linear equation (y - y1 = m(x - x1)), where m is the slope and (x1, y1) is the given point, we can substitute the values to find the equation of the **tangent** line:

y - 0 = 5(x - 0)

Simplifying, we get:

y = 5x

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-1 greater or less than -6

### Answers

greater

because -1 is closer to zero than -6 so that means that it is greater

**Answer: -1 is greater than -6**

**Step-by-step explanation:**

It is greater because it is closer to 0 than -6 therefore it is greater to becoming a positive number so it is greater than -6.

a graph from a rational function cannot cross a horizontal asymptote true or false

### Answers

**Answer:**

False

**Step-by-step explanation:**

You want to know if it is **true** that the **graph** of a **rational function** **cannot** **cross a horizontal asymptote**.

Asymptote

Once a function is on its final approach to an asymptote, it will approach, but not cross, that asymptote.

The function may have a variety of behaviors prior to that point, so may cross the horizontal asymptote one or more times before its final behavior is established.

An example with the asymptote y = 0 is attached.

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find the unit tangent vector to the space curve described by the given vector function, at the point t = 2. ⇀ r ( t ) = t ⇀ i − t 2 ⇀ j ( 2 t − 1 ) ⇀ k

### Answers

The unit tangent vector to the space curve at **time t = 2** is therefore [tex]\(\vec{T} = \frac{1}{\sqrt{21}}\vec{i} - \frac{4}{\sqrt{21}}\vec{j} + \frac{2}{\sqrt{21}}\vec{k}\)[/tex]

**What is a Unit tangent vector?**

The direction of a curve at a particular point is depicted by the unit tangent vector, which is a vector. The direction the curve is traveling in at that location is shown by a vector of length 1. The unit tangent vector is frequently represented by the letters[tex]\(\vec{T}\) or \(\hat{T}\)[/tex]

Using the given vector function, we can get the unit tangent vector to the space curve at the point (t = 2) by doing the following steps:

1. To get the velocity vector, calculate the derivative of the vector function.

2. Calculate the velocity vector at time t = 2 to determine the tangent vector.

The unit tangent vector is produced by normalizing the **tangent vector.**

The derivative of the vector function [tex]\(\vec{r}(t) = t\vec{i} - t^2\vec{j} + (2t-1)\vec{k}\)[/tex] is found as follows:

[tex]\(\vec{v}(t) = \vec{r}'(t) = \frac{d\vec{r}}{dt} = \vec{i} - 2t\vec{j} + 2\vec{k}\)[/tex]

We may calculate the **velocity vector** at time t by using the formula: [tex]\(\vec{v}(2) = \vec{i} - 2(2)\vec{j} + 2\vec{k} = \vec{i} - 4\vec{j} + 2\vec{k}\)[/tex]

The curve at (t = 2) is represented by the tangent vector in this vector.

The tangent vector is normalized as follows to produce the unit tangent [tex]\(\vec{T} = \frac{\vec{v}(2)}{|\vec{v}(2)|}\)[/tex]

Using the Euclidean norm, determine the size of [tex]\(\vec{v}(2)\)[/tex]:

[tex]\(|\vec{v}(2)| = \sqrt{\vec{v}(2) \cdot \vec{v}(2)} = \sqrt{1^2 + (-4)^2 + 2^2} = \sqrt{1 + 16 + 4} = \sqrt{21}\)[/tex]

The unit tangent vector is thus:[tex]\(\vec{T} = \frac{1}{\sqrt{21}}\vec{i} - \frac{4}{\sqrt{21}}\vec{j} + \frac{2}{\sqrt{21}}\vec{k}\)[/tex]

The unit tangent vector to the space curve at time **t = 2 is therefore **[tex]\(\vec{T} = \frac{1}{\sqrt{21}}\vec{i} - \frac{4}{\sqrt{21}}\vec{j} + \frac{2}{\sqrt{21}}\vec{k}\)[/tex]

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Consider the set of vectors B = {(3,4),(1,2)} in R2. (a) Prove that B is a basis for R2. Eupe Rolo bi (b) Perform the Gram-Schmidt orthonormalization to make B an orthonormal basis for R2.

### Answers

The values of all **sub-parts **have been obtained.

(a) The prove that B is a basis for R2 Eupe Rolo bi has been proved.

(b) The Gram-Schmidt orthonormalization to make B an orthonormal basis for R2 has been proven.

What is **set of vectors**?

A vector **space,** also known as a** linear** space, is a set-in mathematics and physics made up of **variables **that can be added to and multiplied ("scaled") by scalar values.

As given,

Suppose that the **set of vectors **B = {(3,4), (1,2)} in R².

(a)

Let V1 = (3,4), V2 = (1,2)

Then a (3,4) + b (1,2) = (0,0)

Simplify values as follows:

3a + b = 0 ......(1)

4a + 2b = 0 ......(2)

**Divide **2 in equation (2),

2a + b = 0

**Subtract** equation (2) from equation (1) respectively,

a + 0 = 0

a = 0

Substitute value of **a** to evaluate the value of **b**,

4(0) + 2b = 0

b = 0

So {V1, V2} is a L.S. set ......(3)

Now let (p, q) = a V1 + b V2

Then

3a + b = p ......(4)

4a + 2b = q ......(5)

Divide 2 in equation (5),

2a + b = q/2

Subtract equation (5) from equation (4) respectively,

a + 0 = p - q/2

a = (2p - q) / 2

Similarly, substitute value of **a** to evaluate the value of **b**,

4(p - q/2) + 2b = q

4p - 2q + 2b = q

2b = 3q - 4p

b = (3q - 4p)/2

Hence, every (p, q) is a linear combination of V1 and V2 ......(6)

From equation (3) and equation (6), {V1, V2} is a basis of IR².

(b) Perform the **Gram-Schmidt orthonormalization** to make B an orthonormal basis for R²

Let U1 = V1 = (3, 4), and U2 = V2 - proj (V2 and U1)

Simplify value,

U2 = V2 - (V1 - U1)/(U1 · U1) U1

Substitute values,

U2 = (1, 2) - (3 + 8)/(9 + 16) (3, 4)

U2 = (1, 2) - (11)/(25) (3, 4)

U2 = (-8/25, +6/25)

So, U1 and U2 are **orthogonal** i.e. U1 · U2 = 0.

Now we normalize them to make then **unit vector**.

So, U1/IUI = 1/√(3² + 4²) U1 = (3/5, 4/5) and

U2/IUI = 1/√((-8/25)² + (6/25)²) U2

U2/IUI = 25/√(64 + 36) U2

U2/IUI = 25/10 U2

U2/IUI = 5/2 U2

U2/IUI = (-4/5, 3/5)

Hence, {(3/5,4/5), (-4/5, 3/5)} is an orthogonal basis of IR².

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A rocket is launched from the top of a 60 foot cliff with an initial velocity of 150 feet per second. The height, h, of the rocket after t seconds is given by the equation h = - 16t² + 150t + 60. How long after the rocket is launched will it be 10 feet from the ground?

### Answers

The rocket will be 10** feet** from the ground approximately 9.15 seconds after it is launched, and this can be found by solving the equation -16t^2 + 150t + 60 = 10.

To find out when the rocket will be 10 feet from the ground, we need to find the value of t that makes h equal to 10 feet. Given that the** height** of the rocket at time t is h = -16t^2 + 150t + 60, we can set this equal to 10 and solve for t:

-16t^2 + 150t + 60 = 10

Simplifying the equation by** subtracting **10 from both sides:

-16t^2 + 150t + 50 = 0

Dividing both sides by -2, we get:

8t^2 - 75t - 25 = 0

To solve this quadratic equation, we can use the quadratic formula:

t =[tex][-b \± \sqrt(b^2 - 4ac)] / 2a[/tex]

where a = 8, b = -75, and c = -25. Substituting these values, we get:

t =[tex][75 \±\ sqrt(75^2 - 4(8)(-25))] / 2(8)[/tex]

t = [tex][75 \± \sqrt(7145)] / 16[/tex]

t ≈ 9.15 seconds or t ≈ 0.41 seconds

Since the rocket is launched from the top of a 60-foot cliff, it will be 10 feet above the ground only after it has fallen below the level of the cliff. Therefore, we can ignore the** solution** t ≈ 0.41 seconds and conclude that the rocket will be 10 feet from the ground approximately 9.15 seconds after it is launched.

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pls help

How does 8 × 2 13 compare to 8? Responses

A Greater than 8 because you are multiplying by a number greater than 1.Greater than 8 because you are multiplying by a number greater than 1.

B Greater than 8 because you are multiplying by a number less than 1.Greater than 8 because you are multiplying by a number less than 1.

C Less than 8 because you are multiplying by number less than 1.Less than 8 because you are multiplying by number less than 1.

D Less than 8 because you are multiplying by a number greater than 1.Less than 8 because you are multiplying by a number greater than 1.

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### Answers

A Greater than 8 because you are multiplying by a number **Greater **than 1.

The expression 8 × 2 13 can be simplified using the **order **of operations (PEMDAS/BODMAS) which states that we should perform the multiplication before the exponentiation. Let's simplify the expression:

8 × 2 13 = 8 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

Now, we can calculate the value of the expression:

8 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 8 × 8192 = 65536

So, the **expression **8 × 2 13 simplifies to 65536.

Comparing this value to 8, we can see that 65536 is much greater than 8. Therefore, the correct response is:

A Greater than 8 because you are multiplying by a **number** greater than 1.

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Which of the following holds for all events A and B in a uniform probability space? a.If A כ B, then P (A) > P (B) b.If P (A) P (B), then A B c.If A2B, then P (A) 2 P (B) d.If P(A) 2 P (B), then AB

### Answers

b. **If** P(A) > P(B), **then** A ⊂ B.

This means that if the **probability** of event A is greater than the probability of event B, then event A is a subset of event B.

The statement "If P(A) > P(B), then A ⊂ B" means that if the probability of event A is greater than the probability of event B, then event A is a **subset** of event B. In other words, if event A is more likely to occur than event B, then it implies that event A is included within event B.

This statement reflects the relationship between the probabilities of two events and their corresponding subsets. It highlights that the likelihood of an event occurring can determine its **relationship** with another event in terms of inclusiveness.

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A car travels from city a to b 120 km apart at an average speed of 50 kmph. It then makes a return trip at an average speed of 40kmph. The average speed over the entire 360 km will be

### Answers

The **Average speed **over the entire 360 km journey is approximately 66.67 kmph.

The average speed over the entire 360 km journey, we can use the formula:

Average Speed = Total **Distance **/ Total Time

In this case, the total distance is 360 km (120 km from A to B and 120 km back from B to A).

Let's calculate the **total time** for the journey:

Time taken for the first leg (from A to B):

Distance = 120 km

Speed = 50 kmph

Time = Distance / Speed = 120 km / 50 kmph = 2.4 hours

Time taken for the return leg (from B to A):

Distance = 120 km

Speed = 40 kmph

Time = Distance / Speed = 120 km / 40 kmph = 3 hours

Total time for the journey = Time for the first leg + Time for the return leg = 2.4 hours + 3 hours = 5.4 hours

Now we can calculate the average speed:

Average Speed = Total Distance** **/ Total Time = 360 km / 5.4 **hours **= 66.67 kmph

Therefore, the average speed over the entire 360 km journey is approximately 66.67 kmph.

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The graphs of f(x)=2x+2 and g(x)=2(2)^x are shown. What are the correct solutions to the equation 2x+2=2(2)^x? Select each correct answer. A. 0, B. 1, C. 2, D. 4

### Answers

The correct **solutions **to the **equation **2x + 2 = 2(2)ˣ are (a) 0 and (b) 1

How to determine the correct solutions to the equation

From the question, we have the following **equations** that can be used in our computation:

2x + 2 = 2(2)ˣ

**Divide **through by 2

So, we have

x + 1 = (2)ˣ

Set x = 0

So, we have

0 + 1 = 1

1 = 1

Set x = 1

So, we have

1 + 1 = 2

2 = 2

Hence, the correct **solutions **to the **equation **are (a) 0 and (b) 1

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parallelogram calc: find p, b=n/a, a=n/a

### Answers

Therefore, the **perimeter** can be calculated by **adding** up all four sides: p = 2b + 2n.

To find the perimeter (p) of a **parallelogram**, you need to know the length of all four sides. However, in this case, you are given the ratio of the base (b) to one of the sides (a), which is n/a.

Since a parallelogram has two pairs of parallel sides, the opposite sides are equal in **length**. Therefore, if the base is b, then the opposite side is also b. Using the given ratio, you can find the length of the other side (n) by **multiplying** a by n/a, which is n.

So, the length of the other side is also n, and the **perimeter** can be calculated by adding up all four sides: p = 2b + 2n.

However, if given the ratio of the base to one of the sides, you can use this to find the length of the other side. For this problem, if the base is b, then the opposite side is also b, and the length of the other side is n (where n/a = b/a).

Therefore, the **perimeter** can be calculated by **adding** up all four sides: p = 2b + 2n.

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solve the ode combined with an initial condition in matlab. plot your results over the domain [0, 5]. dy/dt=2y 5y(5)=3

### Answers

The solution to the given ODE dy/dt = 2y with the initial condition y(5) = 3 over the **domain** [0, 5] is y(t) = (3 / exp(10)) × exp(2t).

How we solve the ode combined with an initial condition?

The ODE dy/dt = 2y represents a simple **exponential **growth equation. The general solution to this ODE is given by y(t) = y0 × exp(2t), where y0 is the constant determined by the initial condition. In this case, the initial condition is y(5) = 3.

To find the **specific** solution, we substitute the initial condition into the general solution and solve for y0. Substituting y(5) = 3 into y(t) = y0 × exp(2t), we get 3 = y0 × exp(2 × 5), which simplifies to y0 = 3 / exp(10).

Thus, the solution to the ODE with the given initial condition is y(t) = (3 / exp(10)) × exp(2t).

This solution describes the behavior of the function y(t) over the interval [0, 5], showing exponential growth with a rate determined by the coefficient 2 in the **ODE**.

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Find parametric equations and a parameter interval for the motion of a particle in the xy plane that traces the ellipse 16x^2+9y^2=144 once counterclockwise.

### Answers

The** parametric** equations for the motion of the particle in the xy plane that traces the counterclockwise ellipse are x = 6cos(t) and y = 4sin(t), where t is the parameter. The parameter **interval **for the motion is 0 ≤ t ≤ 2π.

To find the parametric equations for the **counterclockwise **motion of the particle along the given ellipse, we can start by parameterizing the ellipse equation [tex]16x^2 + 9y^2 =[/tex] 144. We divide both sides of the equation by 144 to normalize it, giving us [tex](x^2/9) + (y^2/16[/tex]) = 1. By comparing this equation with the standard form of an **ellipse**, we can see that a = 3 and b = 4.

We can then use the **trigonometric** parametrization of an ellipse to obtain the parametric equations. Letting x = acos(t) and y = bsin(t), where t is the parameter, we substitute the values for a and b, resulting in x = 6cos(t) and y = 4sin(t). These equations represent the motion of the particle along the ellipse.

Since we want the particle to trace the ellipse counterclockwise, we need to cover the full circumference of the ellipse. This corresponds to a parameter interval of 0 ≤ t ≤ 2π, which completes one full** revolution **around the unit circle. Therefore, the parametric equations for the motion of the particle are x = 6cos(t) and y = 4sin(t), with a parameter interval of 0 ≤ t ≤ 2π.

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What is the interval being used in this table

A,4 B,5 C,6 D,7

### Answers

The **interval** being used in this table is 4.

The correct option is A.

Given information:

Minutes Tally

1 to 5 3

6 to 10 8

11 to 15 11

16 to 20 4

21 to 25 1

To determine the **interval** being used in the given table, we can observe the differences between **consecutive** **tally** ranges.

The **differences** between the **lower** and **upper** limits of each tally range are as follows:

5 - 1 = 4

10 - 6 = 4

15 - 11 = 4

20 - 16 = 4

25 - 21 = 4

As we can see, the **differences** between consecutive tally ranges are all 4. Therefore, the **interval** being used in this table is 4.

Based on the provided options:

A. 4: The correct answer.

B. 5: Incorrect, as the interval is 4.

C. 6: Incorrect, as the interval is 4.

D. 7: Incorrect, as the interval is 4.

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Find the sum of the first 70 terms of the arithmetic sequence: 22, 19, 16, 13,... Find the sum of the first 95 terms of the arithmetic sequence: -17, -12, -7, -2,... Find the sum of the f irst 777 terms of the arithmetic sequence: 3, 9, 15, 21, ...

### Answers

The sum of the first 777 terms of the **arithmetic sequence** is 1,814,383.

To find the sum of an arithmetic sequence, we can use the formula for the sum of n terms:

Sn = (n/2)(a1 + an)

where Sn represents the **sum **of the first n terms, a1 is the first term, and an is the nth term.

Let's calculate the sums for the given arithmetic sequences:

Arithmetic sequence: 22, 19, 16, 13, ...

a1 = 22 (first term)

d = 19 - 22 = -3 (common difference)

n = 70 (number of terms)

Using the formula, we have:

S70 = (70/2)(22 + a70)

To find a70, we can use the formula for the **nth term** of an arithmetic sequence:

an = a1 + (n - 1)d

a70 = 22 + (70 - 1)(-3) = 22 - 207 = -185

Substituting the values back into the sum formula:

S70 = (70/2)(22 - 185)

= 35(-163)

= -5,705

Therefore, the sum of the first 70 terms of the arithmetic sequence is -5,705.

Arithmetic sequence: -17, -12, -7, -2, ...

a1 = -17

d = -12 - (-17) = 5

n = 95

Using the sum formula:

S95 = (95/2)(-17 + a95)

To find a95:

a95 = -17 + (95 - 1)(5) = -17 + 470 = 453

Substituting the values back into the sum formula:

S95 = (95/2)(-17 + 453)

= (95/2)(436)

= 20,740

Therefore, the sum of the first 95 terms of the arithmetic sequence is 20,740.

Arithmetic sequence: 3, 9, 15, 21, ...

a1 = 3

d = 9 - 3 = 6

n = 777

Using the sum **formula**:

S777 = (777/2)(3 + a777)

To find a777:

a777 = 3 + (777 - 1)(6) = 3 + 4,656 = 4,659

Substituting the values back into the sum formula:

S777 = (777/2)(3 + 4,659)

= (777/2)(4,662)

= 1,814,383

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What is not true about any right angle

### Answers

**Answer:**

**Step-by-step explanation:**

Not true: Right angle is not 90 degrees because all right angles must be 90 degrees

sick leave time used by employees of a firm in the course of 1 month has approximately a normal distribution with a mean of 190 hours and a variance o. Find the probability that the total sick leave for next month will be less than 150 hours.

### Answers

if we assume a standard deviation of 20 hours, the probability that the total sick leave for the next month will be less than 150 hours is approximately **0.0228 or 2.28%. **

**What is Probability?**

Probability is a branch of mathematics concerned with numerical descriptions of how likely an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates a certainty

To solve this problem, we can use the properties of the normal distribution. Given that the sick leave time used by employees in a month follows a normal distribution with a mean of 190 hours and a variance of "o" (which is not specified), we need the value of the standard deviation to proceed with the calculations.

Let's assume the standard deviation is represented by σ (sigma). Without the specific value of "o," we cannot determine the exact probability. However, we can still provide a solution using the general formula and any arbitrary value for σ.

The probability of the total sick leave for the next month being less than 150 hours can be calculated by standardizing the value and then looking it up in the standard normal distribution table.

**Z = (X - μ) / σ**

Where:

Z is the standardized value,

X is the desired sick leave value (150 hours in this case),

μ is the mean (190 hours), and

σ is the standard deviation (unknown).

Once we have Z, we can find the corresponding probability from the standard normal distribution table or use a calculator.

Let's assume σ is equal to 20 (this is an arbitrary value for demonstration purposes). Plugging the values into the formula, we get:

Z = (150 - 190) / 20

**Z = -2**

Now, we need to find the probability associated with Z = -2. Using the standard normal distribution table or a calculator, we find that the probability corresponding to Z = -2 is approximately **0.0228.**

Therefore, if we assume a standard deviation of 20 hours, the probability that the total sick leave for the next month will be less than 150 hours is approximately 0.0228 or 2.28%. Please note that this value may vary depending on the actual value of the standard deviation "o."

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In regression analysis, which of the following assumptions is NOT true about the error term E?

a) the expected value of the error term is one

b) the variance of the error term is the same for all values of x

c) te values of the error term are independent

d) the error term is normally distrubuted

### Answers

The **assumption** that is NOT true about the error term E in regression analysis is (a) the expected value of the error term is one. The correct statement is that the expected value of the error term is zero.

How we get the following assumptions is NOT true about the error term E?

The assumption that is NOT true about the error term E in regression analysis is (a) the expected value of the error term is one.

In **regression analysis**, the error term E, also known as the residual or the disturbance term, represents the unexplained variation in the dependent variable. The assumptions about the error term in regression analysis are as follows:

a) The expected value of the error term is zero, not one. This assumption is known as the zero conditional mean assumption or the assumption of no systematic bias. It states that, on average, the error term does not have a systematic relationship with the independent variables.

b) The variance of the error term is the same for all values of x. This assumption is called homoscedasticity. It means that the spread or dispersion of the error term is constant across different levels of the independent **variables**.

c) The values of the error term are independent. This assumption implies that the errors for different observations in the dataset are not correlated or dependent on each other. Each observation's error term is assumed to be unrelated to the errors of other observations.

d) The error term is normally distributed. This assumption, known as normality, states that the errors follow a normal **distribution**. It is important for various statistical tests and estimation methods used in regression analysis.

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1) I am standing at the edge of a 72 meter tall building with a ball in my hand. Consider my hand to

be even with the building top. I throw a ball out at some angle with a force of 45meters/second. I

do the math and find the vertical force is 30 meters/second and the horizontal force is 20

meters/second. Since I threw the ball on an angle, I can't catch it so it falls to the ground.

a) How far does it land from the base of the building?

b) How long does it take from the time it leaves my hand until it hits the ground?

### Answers

a) The ball will land approximately 61.2 meters from the base of the building.

b) The **time **it takes for the ball to hit the ground is approximately 3.06 seconds

a) To determine how far the ball lands from the base of the building, we need to find the horizontal **distance **traveled by the ball. Since the horizontal force is 20 meters/second, we can use this value to calculate the distance.

The time it takes for the ball to hit the ground can be found using the vertical force and the **acceleration **due to gravity. Let's assume the acceleration due to gravity is approximately 9.8 meters/second². Since the initial vertical force is 30 meters/second, we can calculate the time it takes for the ball to reach the ground using the following formula:

time = vertical force / acceleration due to gravity

time = 30 m/s / 9.8 m/s² ≈ 3.06 seconds

Now, we can calculate the **horizontal **distance using the time and horizontal force:

distance = horizontal force × time

distance = 20 m/s × 3.06 s ≈ 61.2 meters

Therefore, the ball will land **approximately **61.2 meters from the base of the building.

b) The time it takes for the ball to hit the ground is approximately 3.06 seconds, as calculated in part a).

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If you can buy four bulbs of garlic for $8, then how many can you buy with $32

### Answers

**Answer:**

If you can buy four bulbs of garlic for $8, then with $32, you can buy 4 times as many bulbs. That means buying 4 * 4 = **16 garlic bulbs for $32**.

**Answer:**

16 garlic bulbs for 32

**Step-by-step explanation:**

you can buy 4 times as many

√3/√5

what is the answer?

A. √15/5

B. √5/2

C. 2√15/3

D. √3/3

I need this as soon as possible

### Answers

**Answer:**

**Step-by-step explanation:**

After conducting a comprehensive analysis, it becomes apparent that option D emerges as the most appropriate and suitable resolution. The remaining choices, including a, b, and c, do not fulfill the requirements for a satisfactory outcome. Therefore, I strongly advise selecting option D as the optimal decision.

Solve: x² + 18x = - 31

○ x = −9+5√√/2

O x = 9 ± √√√50

O x = −9+ √50

O x = 5√√√2+9

### Answers

The correct solution to the **Quadratic equation** x² + 18x = -31 is:

x = -9 ± 5√2

The quadratic equation x² + 18x = -31, we can follow these steps:

1. Move all the terms to one side of the equation to set it **equal **to zero:

x² + 18x + 31 = 0

2. Since the equation is not easily factorable, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In this equation, a = 1, b = 18, and c = 31.

Substituting these **values **into the quadratic formula, we get:

x = (-18 ± √(18² - 4(1)(31))) / (2(1))

Simplifying further:

x = (-18 ± √(324 - 124)) / 2

x = (-18 ± √200) / 2

x = (-18 ± √(100 * 2)) / 2

x = (-18 ± 10√2) / 2

Now we can simplify the **expression**:

x = (-18/2) ± (10√2/2)

x = -9 ± 5√2

Therefore, the correct solution to the equation x² + 18x = -31 is:

x = -9 ± 5√2

Among the given options, the correct solution is:

x = -9 ± 5√2

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Question

Based on a survey of 100 people who work 60 or more hours a week, a magazine article reported that a person working 60 or more hours a week sleeps on average 6.2 hours each night with a margin of error of 0.6 hours.

Between what range of values does a person working 60 or more hours a week sleep in a week?

### Answers

**Answer: **Based on the survey, a **person working **60 or more hours a week can expect to sleep between approximately 39.2 and 47.6 hours in a week.

**Step-by-step explanation: **To determine the **range **of values for the amount of sleep a person working 60 or more hours a week gets in a week, we need to consider the margin of error and calculate the upper and** lower bounds.**

Given that the average sleep per night is 6.2 hours with a margin of error of 0.6 hours, we can calculate the upper and **lower limits** for a week of sleep as follows:

Lower bound: (Average sleep per night - Margin of error) * 7

= (6.2 - 0.6) * 7

= 5.6 * 7

= 39.2 hours

Upper bound: (Average sleep per night + Margin of error) * 7

= (6.2 + 0.6) * 7

= 6.8 * 7

= 47.6 hours

Therefore, based on the **survey**, a person working 60 or more hours a week can expect to sleep between approximately 39.2 and 47.6 hours in a week.

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calculate the five-number summary and construct a box plot of the following data set: 1.7 3.2 7.6 1.6 2.6 7.5 1.6 2.2 5.5 1.5 2.1 4.9 1.5 2.0 4.0

### Answers

The five**-number **summary for the given data set is:

Minimum: 1.5

Q1: 1.6

Median (Q2): 2.6

Q3: 4.0

Maximum: 7.6

To calculate the **five-number **summary and construct a box plot for the given data set:

Step 1: Arrange the** data** in ascending order:

1.5, 1.5, 1.6, 1.6, 1.7, 2.0, 2.1, 2.2, 2.6, 3.2, 4.0, 4.9, 5.5, 7.5, 7.6

Step 2: Find the minimum and maximum values:

Minimum value: 1.5

Maximum **value: 7.6**

Step 3: Find the median (Q2):

Since the data set has an odd number of values, the median is the middle **value.**

Median (Q2): 2.6

Step 4: Find the lower** quartile (**Q1):

The lower quartile is the median of the lower half of the data set.

Lower half: 1.5, 1.5, 1.6, 1.6, 1.7, 2.0, 2.1

Median of lower half (Q1): 1.6

Step 5: Find the upper quartile (Q3):

The upper quartile is the median of the upper half of the data set.

Upper half: 2.2, 2.6, 3.2, 4.0, 4.9, 5.5, 7.5, 7.6

Median of upper half (Q3): 4.0

Step 6: Find th**e interquartile **range (IQR):

IQR = Q3 - Q1 = 4.0 - 1.6 = 2.4

Step 7: Calculate the lower and **upper fence:**

Lower fence = Q1 - 1.5 * IQR = 1.6 - 1.5 * 2.4 = -2.1 (Since it is below the minimum value, we ignore it for the box plot)

Upper fence = Q3 + 1.5 * IQR = 4.0 + 1.5 * 2.4 = 7.4

**Step 8: Construct the box plot:**

Using the minimum, Q1, median (Q2), Q3, and maximum, we can construct the box plot. The fences are represented by **whiskers **(lines) outside the box. Any data points beyond the fences are considered outliers.

Box plot:

| o

| o---o---o

| | |

+--+-------+--

**Minimum Maximum**

Q1 Q2 Q3

The five-number** summary** for the given data set is:

Minimum: 1.5

Q1: 1.6

Median (Q2): 2.6

Q3: 4.0

Maximum: 7.6

Note: The box plot** representation **might not be accurate due to the limitations of text formatting.

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A week has 7 days. So in x weeks and 3 days there are 7x + 3 days. In the same way , write an expression for the number of days in y weeks -5 days

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The expression for the **number of days** in **y weeks - 5 days **is **(7*y) -5**.

In x weeks and 3 days there are 7x + 3 days. Following the same pattern, as in a week there are 7 days, so on **multiplying** the **number of weeks(y) by 7**, we get the number of days in y weeks as: **7*y**. On **subtracting 5 **from this number, as per the statement of the question, we get the number of days as: **(7*y) - 5**.

Therefore, the expression for the **number of days** in **y weeks - 5 days **can be written as **(7*y) -5**.

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Integrate f over the given curve.f(x,y)=x2−y,C: x2+y2=4in the first quadrant from (0,2) to (√2,√2)

### Answers

curve C in the first quadrant from **(0, 2) to (√2, √2).**

**What is Quadrant?**

**Quadrant: **Each of the four quarters of a circle or instrument used for angular measurements of altitude in astronomy and navigation, typically consisting of a graduated quarter circle and a sighting mechanism.

To integrate the function f(x, y) = x^2 - y over the given curve C: x^2 + y^2 = 4 in the first quadrant from (0, 2) to (√2, √2), we can parameterize the curve C and then evaluate the line integral.

We can parameterize the curve C as follows:

x = rcos(t)

y = rsin(t)

Since the curve is defined on the circle with radius 2, we have r = 2. Thus, the parameterization becomes:

x = 2cos(t)

y = 2sin(t)

To determine the limits of integration for t, we need to find the values of t that correspond to the given points on the curve.

For the starting point (0, 2), we have:

x = 2*cos(t) = 0

Solving for t, we find t = π/2.

For the ending point (√2, √2), we have:

x = 2*cos(t) = √2

Solving for t, we find t = π/4.

Now we can calculate the line integral of f(x, y) over C using the parameterization:

∫[C] f(x, y) ds = ∫[t=π/2 to t=π/4] (x^2 - y) ||r'(t)|| dt

where ||r'(t)|| represents the magnitude of the derivative of the vector function r(t) = (x(t), y(t)).

Let's calculate the derivatives:

x'(t) = -2sin(t)

y'(t) = 2cos(t)

Therefore, ||r'(t)|| = sqrt(x'(t)^2 + y'(t)^2) = sqrt((-2sin(t))^2 + (2cos(t))^2) = sqrt(4sin(t)^2 + 4cos(t)^2) = sqrt(4) = 2.

Substituting the parameterization, limits of integration, and ||r'(t)|| into the line integral, we have:

∫[C] f(x, y) ds = ∫[t=π/2 to t=π/4] (x^2 - y) ||r'(t)|| dt

= ∫[t=π/2 to t=π/4] ((2cos(t))^2 - 2sin(t)) * 2 dt

= 2∫[t=π/2 to t=π/4] (4cos(t)^2 - 2sin(t)) dt.

Now we can evaluate this definite integral to find the value of the line integral over the given curve C in the first quadrant from (0, 2) to (√2, √2).

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