Mathematics High School

## Answers

**Answer 1**

If Mr. Garcia checked at 5 minute intervals to see if Jane was playing appropriately in the small group. he was using **time **Sampling .

The **time sampling **is a systematic observation method used in behavioral research to record occurrences of a behavior over a specified period of time.

This method involves dividing the observation period into **equal intervals** of time and observing the behavior during those intervals.

Mr. Garcia was using a **fixed interval **time sampling method, where he observed Jane's behavior at fixed intervals of time (every five minutes).

Therefore , Mr. Garcia used time sampling method .

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The given question is incomplete , the complete question is

Mr. Garcia checked at five-minute intervals to see if jane was playing appropriately in a small group. he was using ______ Sampling .

## Related Questions

Can someone help with these 3 problems!

### Answers

Using the sum of angles of a **triangle **formula we get,

10. ∠J = 127°, ∠K = 20°, ∠L = 33°

11. ∠W = 77°, ∠X = 62°, ∠Y = 41°

12. ∠F = 16°, ∠E = 49°, ∠D = 115°

What do you mean by triangles?

Basic three-sided polygons with three internal angles are triangles. The symbol represents one of the fundamental geometric shapes with three **vertex **connections. According to their sides and angles, triangles can be divided into several different types.

The three inner angles of a triangle can never add up to more than 180 degrees, which is known as the "**angle sum property**" of triangles.

Using the same principle in the question 10 we get,

∠L = 13° + ∠K

∠J = 7° + 6∠K

Now we know,

∠L + ∠J + ∠K = 180°

Substituting the values of L and J we get,

∠K = 20°

Putting the value of ∠K in ∠L and ∠J,

we get: ∠J = 127°, ∠K = 20°, ∠L = 33°

Similarly in question 11,

∠W = 2∠Y - 5°

∠X = 21 + ∠Y

Substituting the values of W and X,

∠Y = 41°

So, we are putting the value of ∠Y in ∠X and ∠W and we get:

∠W = 77°, ∠X = 62°, ∠Y = 41°

Again, in question 12,

∠E = 3∠F + 1

∠D = 7∠F + 3

Substituting the values of E and D,

∠F = 16°

Putting the value of ∠F in ∠E and ∠D, we get:

∠F = 16°, ∠E = 49°, ∠D = 115°

Therefore, through the sum of the angles in a triangle theorem we can get the angles of the triangles.

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original dixieland one step this piece is in 3 sections like a ragtime piece. how many times does the third section repeat?

### Answers

The third section of the Original **Dixieland **One Step typically repeats **twice.**

The first **section **is usually composed of 8 bars of music, the second section is usually 16 bars, and the third section is 8 bars in length. After the first 8 bar section, the second section is then repeated.

This is followed by the third section which will **repeat **twice. This means that the entire composition is made up of three 8 bar sections and two 16 bar sections of music.

This is a common **structure **for ragtime pieces as the 8 bar sections provide a contrast to the longer 16 bar sections. This creates a distinctive sound that is unique to ragtime and the Original Dixieland One Step.

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STAT 3090 Lecture NotesChapter 459Practice Exercises for Chapter 41.Wanda works in the Botanical Gardens and is studying how to best care for the rose bushes.One of the ways she evaluates how the bushes are doing is by observing how many flowers asingle bush produces. The number of roses she finds on each of 20 bushes are given below.9, 2, 5, 4, 12, 7, 8, 11, 9, 3, 7, 4, 6, 5, 4, 10, 9, 6, 7, 4(a)Find the mean number of roses per bush.(b)Find the median of the dataset.(c)Find the mode of the dataset.(d)Find the variance of the dataset.(e)Find the standard deviation of the dataset.2.The lifespans of tigers in a particular zoo have a normal (bell-shaped) distribution. Theaverage tiger lives 17 years with a standard deviation of 2.5 years. Use the Empirical Rule toestimate the proportion of tigers at this zoo that live 14.5 years or longer.6.646.584%

### Answers

For the given number of roses that **Wanda **finds on each 20 bushes , the **mean **number of roses per bush is 6.6 .

The Mean is defined as a measure of **central tendency** of a set of numerical data. It is calculated by adding up all the values in the data set and dividing by the total number of values.

To find the mean number of roses per bush, we add up the number of roses and divide by the number of **bushes** ,

So , Mean = (9+2+5+4+12+7+8+11+9+3+7+4+6+5+4+10+9+6+7+4)/20

= 132/20

= 6.6

Therefore, the mean number of **roses **per bush is 6.6.

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The given question is incomplete , the complete question is

Wanda works in the Botanical Gardens and is studying how to best care for the rose bushes. One of the ways she evaluates how the bushes are doing is by observing how many flowers a single bush produces.

The number of roses she finds on each of 20 bushes are given as 9, 2, 5, 4, 12, 7, 8, 11, 9, 3, 7, 4, 6, 5, 4, 10, 9, 6, 7, 4 .

Find the mean number of roses per bush.

Complete the steps for the single variable linear equation below.

9x + 5 = 10 ( x + 3 ) - x

1. Solve for x. Be sure to show your work.

2. State whether the single variable linear equation has a solution, no solution, or infinitely many solutions.

3. Explain your answer in step 2.

### Answers

Answers

1. Solution is 5 = 3

2. No solution

3. 5 = 3 is a false statement so there are no solutions

Step by step

9x + 5 = 10 ( x + 3 ) - x

Distribute

9x + 5 = 10x + 30 -x

combine like terms

9x + 5 = 9x + 30

Subtract 9x from both sides to isolate variables

9x - 9x + 5 = 9x - 9x + 30

Simplify

5 = 30

This is a false statement so there are no solutions

the probability of failure of a wastewater treatment facility is normally 0.02. during significant power outages, the probability of failure of the system is 0.28. the probability of significant power outage in the area is 0.04. what is the total probability of failure of the facility?

### Answers

The total **probability **of failure of the wastewater treatment facility is 0.0304 or about 3.04%.

To calculate the total probability of failure of the facility, we can use the **law of total probability**:

P(failure) = P(failure | no power outage) * P(no power outage) + P(failure | power outage) * P(power outage)

We are given:

P(failure | no power outage) = 0.02 (probability of failure when there is no power outage)

P(failure | power outage) = 0.28 (probability of failure when there is a power outage)

P(power outage) = 0.04 (probability of a power outage)

To find P(no power outage), we can use the fact that the sum of the probabilities of all **possible outcomes** must be 1. So:

P(no power outage) = 1 - P(power outage) = 1 - 0.04 = 0.96

Now we can plug in the values:

P(failure) = 0.02 * 0.96 + 0.28 * 0.04 = 0.0192 + 0.0112 = 0.0304

Therefore, the total **probability **of failure of the wastewater treatment facility is 0.0304 or about 3.04%.

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The baseball player Ichiro Suzuki gets a hit about 33.1% of the time over an entire season. After he failed to hit safely in nine straight at-bats, the TV commentator says ‘Ichiro is due for a hit by the law of averages.’ IS that right? Why? This error is so common it has its own name: The Gambler’s Fallacy.

### Answers

The TV **commentator's** statement is **wrong**, and it is important to understand that the outcome of a single event is not influenced by previous outcomes of independent events.

The TV commentator is incorrect when he says that "Ichiro is due for a hit by the law of **averages**."

This is an example of the **Gambler's** Fallacy, which is the mistaken belief that if something happens more frequently than usual during a certain period, then it will happen less frequently in the future to "balance out" the **probabilities**.

The concept of the "law of averages" is also a misconception. There is no physical law that governs the probability of independent events like baseball hits, and the idea that past events will somehow **balance** out in the future is simply a **fallacy**.

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tres enteros pares consecutivos tienen una suma de 24. hallar los enteros

### Answers

Los tres **enteros pares consecutivos** son 6, 8, y 10.

¿Como encontrar los 3 enteros consecutivos?

Sabemos que 3 enteros** pares consecutivos** tienen una suma de 24.

Recordar que dos pares consecutivos se escribe como x y x + 2.

Entonces la **suma **de 3 pares consecutivos son:

x + (x + 2) + (x + 4)

Y eso es igual a 24, entonces podemos escribir:

x + (x + 2) + (x + 4) = 24

Ahora podemos resolver esto para x.

x + (x + 2) + (x + 4) = 24

3x + 6 = 24

3x = 24 - 6

3x = 18

x = 18/3

x = 6

Los enteros son:

x = 6

x + 2 = 8

x + 4 = 10

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Allied receives payment from Macy for the amount old on the May 5 purchase; payment is net of returns, allowances, and any cash discount.

### Answers

The amount of the **discount **is calculated as 2% of the net amount due ($22,500 - $2,250 - $1,050 = $19,200).

Journal Entries for Sales, Sales Returns, and Sales Allowances Using Perpetual Inventory System and Gross Method for Allied Merchandisers.

May 3:

**Inventory** purchase:

Inventory (Dr) $33,000

Cash (Cr) $33,000

May 5:

**Sale **of inventory to Macy Company:

**Accounts **Receivable - Macy Company (Dr) $22,500

Sales (Cr) $22,500

Cost of **goods **sold:

Cost of Goods Sold (Dr) $16,500

Inventory (Cr) $16,500

May 7:

Return of inventory by Macy Company:

Accounts Receivable - Macy Company (Cr) $2,250

Sales **Returns** and Allowances (Dr) $2,250

**Cost **of goods sold (restored units):

Inventory (Dr) $1,650

Cost of Goods Sold (Cr) $1,650

May 8:

**Allowance** given to Macy Company:

Sales Returns and Allowances (Dr) $1,050

Accounts Receivable - Macy Company (Cr) $1,050

May 15:

**Receipt **of payment from Macy Company:

Cash (Dr) $21,450

Sales Discount (Dr) $450

Accounts Receivable - Macy **Company** (Cr) $22,500

The Sales Discount account is used to record the amount of the discount given to Macy Company for paying within the discount period (2/10, n/60). The **amoun**t of the discount is calculated as 2% of the net amount due ($22,500 - $2,250 - $1,050 = $19,200).

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Let f(x)= -3x² - 6x + 2.

a. Find the maximum value of f.

b. Find the axis of symmetry of the parabola.

c. Find The x - intercepts, if they exist.

### Answers

**a) **The **maximum value **of f is given as follows: y = 5.

**b) **The **axis of symmetry** of the parabola is given as follows: x = -1.

**c) **The **x-intercepts** of the parabola are given as follows: x = -0.29 and x = 2.29.

How to obtain the features?

The quadratic function is **defined **as follows:

f(x) = -3x² - 6x + 2.

The **coefficients **are given as follows:

a = -3, b = -6, c = 2.

Hence the **axis of symmetry**, which is the x-coordinate of the vertex, is given as follows:

x = -b/2a

x = 6/-6

x = -1.

The** maximum value** is the numeric value at the axis of symmetry, hence:

f(-1) = -3(-1)² - 6(-1) + 2

f(-1) = 5.

The **x-intercepts** are the roots of the quadratic function, obtained with a calculator, as follows:

x = -0.29 and x = 2.29.

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Simplify

cos(x-(pi )/(4))+cos(x+(pi )/(4))

### Answers

The simplified **value **of the **trigonometric **expression "Cos(x - π/4) + Cos(x + π/4)" is √2cos(x).

An "Algebraic-**Expression**" is mathematical phrase which includes numbers, variables and mathematical-operations, such as addition, subtraction, multiplication, and division.

The expression to be **simplified **is : Cos(x - π/4) + Cos(x + π/4);

We simplify the expression using the trigonometric **identity**:

⇒ cos(a + b) = cos(a)cos(b) - sin(a)sin(b) and cos(a - b) = cos(a)cos(b) + sin(a)sin(b);

Applying these identity on the expression,

We get,

⇒ cos(x - π/4) + cos(x + π/4);

⇒ [cos(x)cos(π/4) + sin(x)sin(π/4)] + [cos(x)cos(π/4) - sin(x)sin(π/4)];

⇒ cos(x)cos(π/4) + cos(x)cos(π/4) + sin(x)sin(π/4) - sin(x)sin(π/4);

⇒ 2cos(x)cos(π/4);

⇒ 2cos(x)(1/√2);

⇒ √2cos(x),

Therefore, the simplified expression is √2cos(x).

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The given question is incomplete, the complete question is

Simplify the following expression : Cos(x - π/4) + Cos(x + π/4);

42,23,65,88,153,?,?,?

What are the next three numbers in the sequence? What type of sequence is this

### Answers

The next **three numbers **in the sequence are 241, 394 and 635

What are the next three numbers in the sequence?

The **definition **of the **function **is given as

42,23,65,88,153,?,?,?

The above **definitions **imply that we simply add the previous two terms to get the **current term**

Using the above as a guide,

So, we have the following representation

Next term = 88 + 153 = 241

Next term = 153 + 241 = 394

Next term = 241 + 394 = 635

What type of sequence is this

The sequence is a **fibonacci sequence**

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a researcher recorded reaction time to respond to a sound. if the data of the research subjects are presented in a frequency distribution graph, what type of graph should be used?

### Answers

If the data of the research subjects are presented in a **frequency** distribution graph, a **histogram-type **graph should be used.

If the data are presented in a frequency **distribution** graph, then the type of graph that should be used is a histogram. A histogram is a type of bar graph that displays the distribution of a continuous **variable** by dividing the range of values into intervals, and bins, and counting the number of **observations** that fall within each bin.

If the academic majors were **nominal** a bar graph could also be used to display the frequency of each major. In a bar graph, each category would be plotted on the **horizontal** axis, and the frequency of students in each category would be plotted on the** vertical axis**.

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Express 3 2/3 as a decimal correct to 2 decimal places

### Answers

**Answer: 3.67**

**Step-by-step explanation:**

3 2/3 is 3 + 2/3 (as a fraction is 0.66 recurring which is rounded to 0.67)

Bilquis owns a food truck that sells tacos and burritos. She sells each taco for $4 and each burrito for $6.25. Bilquis must sell a minimum of $630 worth of tacos and burritos each day. Write an inequality that could represent the possible values for the number of tacos sold, t, and the number of burritos sold, b, that would satisfy the constraint.

Will give barinlest

### Answers

The inequality representing the possible values for the number of tacos sold (t) and the number of burritos sold (b) that would satisfy the constraint of selling a minimum of $630 worth of tacos and burritos each day is:

4t + 6.25b ≥ 630

This inequality states that the total revenue from tacos (4t) and burritos (6.25b) must be greater than or equal to $630. So, the number of tacos and burritos sold can vary as long as the inequality is satisfied.

**Answer:You can graph these equations as you would a normal linear equation. For the first equation, you can shade in the area under the line, and for the other 2 shade in the are above the line. Whatever area of the graph all three shaded areas overlap gives us our possible range of answers, with each point in said area read as (x,y), with x the number of tacos sold and y the number of burritos sold.**

**Step-by-step explanation:**

Let's refer to the number of burritos sold as B and the number of tacos sold as T.

We can go through statements one by one and write an inequality for each, then see if there's any that we can consolidate.

She has enough supplies to make 130 tacos or burritos gives us the equation:

B+T < 130

She sells each taco for $3.75 and each burrito for $6. Ava must sell a minimum of $600 worth of tacos and burritos each day. These statements can be combined to give us the following:

3.75T+6B > 600

She must sell a minimum of 80 burritos gives us:

B > 80

Because the number of burritos sold is going to be our y value, we can rearrange all of these to be in terms of the number of tacos sold. This gives us the following system of equations:

B < 130-T

B > 100-0.625T

B > 80

What is the next number in the arithmetic sequence below?

27, 15, 3, -9,-...

о

OA. -3

O B. -20

O C. 12

OD. -21

### Answers

Steps:

-9+(-12)

Solution

-21

It took Ryan less time to hike down than it did to hike up. Ernest thinks that was

because Ryan jogged down the same trail he went up. Emma thinks the trail down

was steeper than the trail up. Whose hypothesis is valid: Ernest's, Emma's, or both?

Write a detailed explanation of whether each hypothesis is an acceptable

interpretation of the graph.

### Answers

We can infer that one or both of Ernest's and Emma's **theories **could account for Ryan's quicker hike down than up.

what is hypothesis ?

A hypothesis in mathematics is a claim or** presumption** made regarding a mathematical idea or connection between mathematical objects. A hypothesis is typically founded on findings or prior knowledge and is frequently used as the basis for an inquiry or proof. For instance, a hypothesis about the characteristics of a specific shape or the connections between various shapes might be developed in geometry. A hypothesis about the **dispersion of prime numbers** and the behavior of a specific sequence of numbers may be stated in number theory.

given

Emma's theory is that because the path down was steeper than the trail up, Ryan could have hiked down more quickly and easily.

The amount of time it takes to hike can also be significantly influenced by other elements like trail length, elevation increase, and terrain.

Therefore, without more information, we cannot tell for sure whether Emma's hypothesis is a valid interpretation of the graph.

We can infer that one or both of Ernest's and Emma's theories could account for Ryan's quicker hike down than up.

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What is the y coordinate of the point in the standard (x,y) coordinate plane at which the 2 lines y=x/2 =3 and y=3x-2

### Answers

The intersection of the two lines has a** y-coordinate** of 4. In the conventional (x,y) coordinate plane, the meeting point is at (2,4).

To find the point of **intersection **between the lines y = x/2 + 3 and y = 3x - 2, we can set their equations equal to each other and solve for x:

x/2 + 3 = 3x - 2

Simplifying this equation, we get:

5/2 x = 5

x = 2

Now that we have found the x-coordinate of the **intersection point**, we can substitute it into either of the two equations to find the corresponding y-coordinate. Let's use the equation y = 3x - 2:

y = 3(2) - 2

y = 4

Therefore, the **y-coordinate** of the point of intersection of the two lines is 4. The intersection point is (2, 4) in the standard (x,y) **coordinate plane.**

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in which figure do <1 and <2 represent a pair of alternate exterior angles?

### Answers

The **figure **that ∠ 1 and ∠ 2 are a pair of **alternate exterior angles** is Figure A.

What are alternate exterior angles?

**Alternate exterior angles** are a pair of angles that are formed by two parallel lines and a transversal line intersecting them. Alternate exterior angles are located on opposite sides of the transversal line and outside of the two parallel lines.

When two parallel lines are intersected by a **transversal line**, eight angles are formed. These angles can be divided into pairs based on their location and relationship to each other.

In **Figure **1, ∠ 1 and ∠ 2 are a pair of alternate exterior angles as they form due to two parallel lines.

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**Answer: The first one (A)**

**Step-by-step explanation:**

I did the Iready.

What is 5/32 divided by 25/4? simplified answer

### Answers

**Answer: 0.025**

**Step-by-step explanation:**

**5/32 divided by 25/4=**

**Keep 5/32.**

**Change 'divided' into times.**

**Swap 25/4 into 4/25.**

**5/32 x 4/25 = **

**(5 x 4 = 20)**

**(32 x 25 = 800)**

**(800/20 = 400/10 = 200/5 = 0.025)**

**Hope this helped!**

You need 34

cup of yogurt for 1

smoothie.

Which number line shows how many cups of yogurt you need for 3

smoothies?

### Answers

The **number **of **cups **of **yogurt **needed for 3 **smoothies **is 102 cups. The **number line** that shows the number of cups of yogurt needed is the **number line** marked at 102

Determining the number of cups of yogurt needed for smoothies

From the question, we are to determine the **number **of **cups **of **yogurt **needed for 3 **smoothies**

Let he **number **of **cups **of **yogurt **required be x

From the given information, we have that

"*You need 34 *cup of yogurt for 1 smoothie"

Now,

If 34 cups of yogurt are required for 1 smoothie

Then,

x cups of yogurt will be required for 3 smoothies

x × 1 = 34 × 3

x = 102 cups

Hence, the **number **of **cups **required is 102 cups.

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Faith and Kaj are both driving along the same highway in two different cars to a

stadium in a distant city. At noon, Faith is 293 miles away from the stadium and Kaj

is 329 miles away from the stadium. Faith is driving along the highway at a speed of

47 miles per hour and Kaj is driving at speed of 59 miles per hour. Let F represent

Faith's distance, in miles, away from the stadium t hours after noon. Let K represent

Kaj's distance, in miles, away from the stadium t hours after noon. Write an equation

for each situation, in terms of t, and determine whether Faith or Kaj is closer to the

stadium 4 hours after noon.

F =

>

is

K =

miles closer to the stadium than

4 hours after noon.

Please send help.

### Answers

The equation for each **situation**, in terms of t are F = 293 - 47t and K = 329 - 59t.

Kaj is closer to the **stadium** 4 hours after noon.

How to write the required linear equation?

In order to write a system of **linear equations** that could be used to model the situation, we would assign variables to **Faith's **distance and Kaj's distance respectively as follows:

Let the variable F represent **Faith's **distance away from the stadium t hours after noon.Let the variable K represent Kaj's distance away from the stadium t hours after noon.

Since **Faith** is 293 miles away from the stadium and is driving at a speed of 47 miles per hour, a **linear equation** that models the situation is given by;

F = 293 - 47t

For Kaj's distance, in miles, we have the following:

K = 329 - 59t

At t = 4 hours, we have:

**Faith's** distance, F = 293 - 47(4)

Faith's distance, F = 105 miles.

Kaj's distance, K = 329 - 59(4)

Kaj's distance, K = 93 miles.

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MODELING REAL LIFE A city dumps plastic shade balls into a reservoir to prevent water from evaporating during a drought. It costs $5760 for

16,000 shade balls. How much does it cost for 12,000 shade balls?

It costs

### Answers

**Answer:**

$4320

**Step-by-step explanation:**

5760 / 16000 = $0,36 for each shade ball. So...

12000 * 0.36 = 4320

PLEASE, I NEED HELPPPP, I'LL GIVE YOU 15 POINTS AND BRAINLIEST

A scatter plot is shown on the coordinate plane.

scatter plot with points plotted at 1 comma 7, 1 comma 8, 2 comma 5, 3 comma 6, 4 comma 4, 5 comma 5, 5 comma 6, 6 comma 3, 7 comma 5, 8 comma 2, 9 comma 4, and 10 comma 2

Which of the following graphs shows a line on the scatter plot that fits the data?

scatter plot with points plotted at 1 comma 7, 1 comma 8, 2 comma 5, 3 comma 6, 4 comma 4, 5 comma 5, 5 comma 6, 6 comma 3, 7 comma 5, 8 comma 2, 9 comma 4, and 10 comma 2, with a line drawn through about 1 comma 7 and 3 comma 6

scatter plot with points plotted at 1 comma 7, 1 comma 8, 2 comma 5, 3 comma 6, 4 comma 4, 5 comma 5, 5 comma 6, 6 comma 3, 7 comma 5, 8 comma 2, 9 comma 4, and 10 comma 2, with a line drawn through about 1 comma 8 and 5 comma 6

scatter plot with points plotted at 1 comma 7, 1 comma 8, 2 comma 5, 3 comma 6, 4 comma 4, 5 comma 5, 5 comma 6, 6 comma 3, 7 comma 5, 8 comma 2, 9 comma 4, and 10 comma 2, with a line drawn through about 2 comma 5 and 4 comma 4

scatter plot with points plotted at 1 comma 7, 1 comma 8, 2 comma 5, 3 comma 6, 4 comma 4, 5 comma 5, 5 comma 6, 6 comma 3, 7 comma 5, 8 comma 2, 9 comma 4, and 10 comma 2, with a line drawn through about 1 comma 4.5 and 2 comma 4.5

### Answers

A **graph** that shows a line on the **scatter plot** that fits the data include the following: B. **scatter plot** with points plotted at 1 comma 7, 1 comma 8, 2 comma 5, 3 comma 6, 4 comma 4, 5 comma 5, 5 comma 6, 6 comma 3, 7 comma 5, 8 comma 2, 9 comma 4, and 10 comma 2, with a line drawn through about 1 comma 8 and 5 comma 6.

What are the characteristics of a line of best fit?

In Mathematics, there are different characteristics that are used for determining the **line of best fit** on a scatter plot and these include the following:

The line should be very close to the **data points** as much as possible.The number of data points that are above the line should be equal to the number of **data points** that are below the line.

By critically observing the scatter plot using the aforementioned characteristics, we can reasonably and logically deduce that line B represents the **line of best fit** because the **data points** are in a linear pattern.

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A rectangular gift box is 6 feet long. The width is x feet shorter than the length, and the height is the length plus twice the distance x.

Which equation models the area, A, of one of the sides of the box that has the width and height as its dimensions?

A

A = -x² +36

B

A = -x² + 12x +36

A = -2r² + 18x +36

D A = -2r² + 6x +36

C

### Answers

The **equation **of the **area **is A = 36 + 6x - 2x^2

How to determine the equation of the area

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

**Length **= 6

Width = x feet shorter than length

Height = length plus twice x

From the problem statement, we know that:

**Width **= 6 - x feet

Height = 6 + 2x feet

So, the **area** of one of the sides of the box is:

A = (width) * (height)

A = (6 - x) * (6 + 2x)

Expanding the **brackets**, we get:

A = 36 + 12x - 6x - 2x^2

A = 36 + 6x - 2x^2

So the **equation **that models the area, A, of one of the sides of the box that has the width and **height **as its dimensions is: A = 36 + 6x - 2x^2

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2 3 4

Select from the drop-down menus to correctly complete each statement.

(A) The value of the 8 in 0.28 is Choose...

(B) The value of the 8 in 0.85 is Choose...

(C) The value of the 8 in 0.28 is Choose... the value of the 8 in 0.85.

### Answers

The place values of 8 in 0.28 is 8 **hundredths **and the place value of 8 in 0.85 is 8 tenths.

What is meant by Place Value of a Digit?

Place value of a digit in a number is the value of that particular **digit **according to the position where it stands.

Place value of a **whole number **of digits can be expressed as ones, tens, hundreds, thousand, etc. from right to left.

Place value of a **decimal number **can be expressed as tenths, hundredths, thousandths, etc. from left to right after the decimal point.

(A) The **number **is 0.28

Here 8 is the hundredths place.

Place value of 8 = 8 × [tex]\frac{1}{100}[/tex] = 0.08 = 8 hundredths

(B) The number is 0.85.

Here 8 is in the **tenths **place.

Place value of 8 = 8 × [tex]\frac{1}{10}[/tex] = 0.8 = 8 tenths

Hence the place values of 8 in both numbers are found.

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Your question is incomplete. The complete question with the options is given below.

Select from the drop-down menus to correctly complete each statement.

(A) The **value **of the 8 in 0.28 is Choose...

(B) The value of the 8 in 0.85 is Choose...

8 tenths

8 hundredths

8 **thousandths**

￼4 units What is the area of the square above? A. 12 square units B. 20 square units C. 24 square units D. 16 square units

### Answers

The **area** of the given **square** with side length 4 units is 16 square units.

The correct answer choice is option D.

What is the area of the square?

The **side length**, a of the square= 4 units

Area of a square= a²

= 4²

= 4 × 4

Area of the square= 16 square units

Therefore, the area of the square is 16 **square units.**

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can someone help me with this question

### Answers

**Answer: - 18**

**Step-by-step explanation:**

Lets just ignore the negative signs since they might make the question confusing, *(**You can only do this when both numbers are negative**)*

Y = 5, W = 31,

X has to be in the exact middle.

(Y+W) / 2 = 36 / 2 = 18

X would have to be at 18 to be in the middle point of W and Y.

We go back to the first thing we did, put the negative sign back,

**X **would be **-18**

Katey has a bag of 4 marbles. There are 2 pink marbles, 1 orange marble, and 1 red marble.

List 1 List 2 List 3 List 4

P1 P1, P2 P1, P2 P1, P2

P2 P1, O P1, O P1, O

O P1, R P1, R P1, R

R P2, O P2, O P2, O

P2, R P2, R P2, R

P2, P2 P2, P2 P2, P2

P1, P1 P1, P1 P1, P1

P2, P1 P2, P1 P2, P1

O, P1 O, P1 O, P1

O, P2 O, P2 O, P2

O, R O, R O, R

O, O O, O O, O

O, P1 R, O

O, P2 R, R

O, R R, P1

R, R R, P2

Which list gives the sample space for pulling 2 marbles from the bag with replacement?

List 4

List 3

List 2

List 1

### Answers

The answer is list 3.

**Answer:**

List 4

**Step-by-step explanation:**

list 4 because 1 bag equals 2 pink which is 4

Write the solution set of the given hom*ogeneous system in parametric vector form.

x^1 + 2x^2-15x^3 = 0 2x^1 + x^2-15x^3=0

-X1+X2=0 where the solution set is x = X1

X2

X3

### Answers

The solution set of the** hom*ogeneous system** can be written in parametric vector form as:

x = t * |-2|

|10|

| 0|

We start by writing the augmented **matrix **for the system:

| 1 2 -15 0 |

| 2 1 -15 0 |

|-1 1 0 0 |

Next, we reduce the matrix to **row echelon form**:

| 1 2 -15 0 |

| 0 -3 15 0 |

| 0 0 1 0 |

The third row tells us that x^3 = 0, so we can set x^3 = t, where t is a **free parameter**. Using the first row, we can express x^1 in terms of x^2 and x^3:

x^1 + 2x^2 - 15x^3 = 0

x^1 = -2x^2 + 15x^3

x^1 = -2x^2 + 15t

Finally, using the second row, we can express x^2 in terms of x^3:

2x^1 + x^2 - 15x^3 = 0

2(-2x^2 + 15t) + x^2 - 15t = 0

-3x^2 + 30t = 0

x^2 = 10t

Therefore, the **solution **set of the** hom*ogeneous system** can be written in parametric vector form as:

x = t * |-2|

|10|

| 0|

where t is a free parameter.

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Do now: Given Sin (2x+11) = Cos (3x+34),

slove for x

### Answers

The **value **of the **variable **x is 9

How to determine the value

It is important to note that the sine and cosine** trigonometric identities **are almost directly opposite to each other.

They are complementary to each.

Then

sin(2x + 11) = sin(90 - 3x + 34)

Factor the like terms

2x + 11 = 90 - 3x - 34

collect the like terms

2x + 3x = 90 -34 - 11

Add or subtract the like terms

5x = 45

Divide by the coefficient of x, we get;

x = 45/5

x = 9

Hence, the **value **is 9

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