Fall Math Benchmark
1. For the scenario given, explain in words your process for solving the problem.
Two rectangular walls need to be painted. They are each 12 feet high and 23 feet
wide. It costs $1.50 per square foot for paint. How much will it cost to paint the
walls?

Answers

Answer 1

The amount that it will cost to paint the walls, given the cost per square foot and the dimensions of the rectangular walls is $828

How to find the cost?

First, find the area of the rectangular walls by the formula for the area of a rectangle which is:

= Length x Width

The area of the rectangles is therefore:

= 12 x 23

= 276 feet ²

The area of the two rectangular walls is:

= 276 + 276

= 552 feet ²

The cost to paint the walls is:

= Area of walls x cost per square feet to paint

= 552 x 1.50

= $828

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Related Questions

What is the next fraction
in this sequence?
Simplify your answer

5/14, 3/7, 1/2, 4/7 …

Answers

Closed form:
an=n+4/14 (for all terms given)

Next fraction would be 9/14.

Between which two integers does the square root of 92 lie?

Answers

The square root of 92 lies between 9 and 10.

According to the question,

We have the following information:

Square root of 92

Now, we have to find the two integers between which its square root lie.

So, we will first find the perfect squares of positive integers to get an idea where the square root of 92 lies.

Perfect squares are given below:

1 = 1

2 = 4

3 = 9

4 = 16

5 = 25

6 = 36

7 = 49

8 = 64

9 = 81

10 = 100

Now, the square of 10 is greater than 92 and square of 9 is less than 92. So, it will lie between these two integers.

Hence, the square root of 92 lies between 9 and 10.

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for each pair of points, find the slope of the line that passes through both points. If you get stuck, try plotting the points on graph paper and drawing the line thoruhg them wiht a ruler

Answers

The slope of points (1,3) and (4,5) will be 2/3.

What is a slope?

Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line. The slope is also defined as the ratio of the rise and the run of the line.

Given that the line is passing through points (1,3) and (4,5). The slope of the line will be calculated as,

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope = ( 5 - 3 ) / ( 4 - 1)

Slope = 2 / 3

Therefore, the slope of points (1,3) and (4,5) will be 2/3.

The complete question is given below.

Find the slope of the line that passes through both points (11,3) and (4,5).

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Please help
What equation is represented by the values in this table

Answers

Answer:

y=2x-2

Step-by-step explanation:

use y2-y1/x2-x1 to find slope

4-2/3-2

2/1

2 is the slope

A and B are the only possible answers so far

Now to find y intercept

We know it can’t be +2 because at 2 x is equal to 2 so -2 is the only option

Hopes this helps please mark brainliest

rohit studies 5⅖ hrs daily. He devotes 1¼ hrs of his time for English abd 1½ hrs for Mathematics. How much time does he devote for other subjects​

Answers

Answer:3 1/2 hours

Step-by-step explanation: 5 2/5 - 1 1/4 -1 1/2= 3 1/2

How do this?Help pls give answer

Answers

Answer:

Step-by-step explanation:

Ok! So apparently I think you are learning about pre algebra. So the questions are saying what times 1/4=8 in that case it would be x = 32. x is just a fancy way to say you don’t know what it is.

A retailer needs to purchase 12 printers. The first printer costs $54, and each additional printer costs 5% less than the price of the previous printer, up to 15 printers. What is the total cost of 12 printers?.

Answers

The total cost of 12 printers is; $493.41

Cost of first printer; C1 = $54

Cost of second printer is; 95% × 54 = $51.3

Cost of third printer is; 0.95 × 51.3 = $48.735

Cost of fourth printer = 0.95 × 48.735 = $46.298

Now, let us apply same pattern using a calculator for the remaining costs and we will have them as follows;

Cost of 5th printer = $43.983

Cost of 6th printer = $41.784

Cost of 7th printer = $39.695

Cost of 8th printer = $37.710

Cost of 9th printer = $35.825

Cost of 10th printer = $34.033

Cost of 11th printer = $32.332

Cost of 12th printer = $30.715

Total cos is; 54 + 51.3 + 48.735 + 46.298 + 43.983 + 41.784 + 36.695 + 37.710 + 35.825 + 34.033 + 32.332 + 30.715 = $493.41

Therefore, the total cost of 12 printers is $493.41

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STATISTICS The most familiar statistical measure is the arithmetic mean, or average. A second important statistical measure is the standard deviation, which is a measure of how far the individual scores are from the mean. For example, the mean score on the Wechsler IQ test is 100 and the standard deviation is 15. This means that people within one deviation of the mean have IQ scores that are 15 points higher or lower than the mean.

Answers

An absolute value equation that can be used to find the maximum and minimum scores within one standard deviation of the mean is |x - 20.9| = 5.3.

The minimum score that is within one standard deviation of the mean is equal to 15.6.

What is an absolute value function?

In Mathematics, an absolute value function can be defined as a type of function that consist of an algebraic expression, which is placed within absolute value symbols and measures the distance of a point on the x-coordinate to the x-origin (0).

Mathematically, an absolute value function can be represented by this mathematical expression:

|x| = x, x ≥ 0.|x| = x, x < 0.

Since the standard deviation is 5.3 and the mean is 20.9, an absolute value equation for the scores that is within one standard deviation of the mean is given by:

|x - 20.9| = 5.3.

x - 20.9 = ±5.3

Evaluating the absolute value function, the maximum score is given by:

x - 20.9 = 5.3

x = 20.9 + 5.3

x = 26.2.

Evaluating the absolute value function, the minimum score is given by:

x - 20.9 = -5.3

x = 20.9 - 5.3

x = 15.6.

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Complete Question:

The most familiar statistical measure is the arithmetic mean, or average. A second important statistical measure is the standard deviation, which is a measure of how far the data are from the mean. For example, the mean score on the Wechsler IQ test is 100 and the standard deviation is 15. This means that people within one standard deviation of the mean have IQ scores that are 15 points higher or lower than the mean. One year, the mean mathematics score on the ACT test was 20.9 with a standard deviation of 5.3. Write an absolute value equation to find the maximum and minimum scores within one standard deviation of the mean. Use your equation to find the minimum score that is within one standard deviation of the mean

Valentina measured a kitchen and made a scale drawing. She used the scale 1 inch : 2 feet. A countertop in the kitchen is 2 inches wide in the drawing. How wide is the actual counter?

Answers

The actual width of the countertop is 4 feet

Given,

Valentina measured a kitchen and made a scale drawing;

The scale she used for the drawing = 1 inch ; 2 feet

The width of countertop of kitchen in drawing = 2 inches.

We have to find the actual width of the countertop;

Here,

The scale factor used in the drawing = 1 inch = 2 feet

1 inch  = 2 feet

2 inch = 2 x 2 = 4 feet

Now,

The actual width of the countertop = Width in drawing x 2

= 2 x 2 = 4 feet

That is,

The actual width of the countertop is 4 feet

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if -3 + i is a root of the polynomial function f(x), which of the following must also be a root of f(x)?

Answers

Answer:

-3 - i

Step-by-step explanation:

This is true, because when solving for an imaginary solution through a polynomial, the form A ± Bi will always be adhered. A and B are both constants.

(Constants are just any real number, like 1, 2.35, or [tex]\frac{1}{2}[/tex].)

what is 6,000 lb/day = ____ t/wk?

Answers

Answer: 21 tons/wk

Step-by-step explanation:

6000 lb/day = 3 tons/day

3 t/day * 7 = 21 t/wk

A car moves at a speed of 80km/h from P at 0800 hours and reaches Q at 0930 hours. A lorry takes the same route from Q at 0800 hours to P at a speed of 70km/h. At what time do both vehicles meet?​

Answers

The vehicles will meet at 0845 at a distance of 64 km from P when they move at the respective speeds.

The car moves at a speed of 80km/h from P to Q and it takes time t

t = 9.30 - 8.00 = 1 hour 30 minutes or 1.5 hours

Distance covered = speed × time

Distance = 80 × 1.5 = 120 km

Now et the cars meets at a distance of x km from P.

times taken by the car to cover x km = x/80 hours

The lorry travels 120 - x in that same time.

time taken = 70/(120 - x)

Now the time taken must be equal.

Therefore we will form an equation to calculate x.

(120 - x) / 70 = x / 80

or, 960 - 8x = 7x

or, 15x = 960

or, x = 64

Therefore the cars will meet at 64 km from P.

Now time taken by the car to cover 64 km = 64/80 = 0.8 hours = 48 minutes

Hence the cars will meet at 0845 hours.

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8x1 4* 28 × +8 help me ​

Answers

Answer:

8x1 4* 28 × +8 = 28x + 12

8x^1 + 4 times 28 + 8

Add common Factors which are 8x and 28x added they equals 36x and 4 and 8 which equals 12 so now we got 28x + 12 and that is the answer

PLEASE GIVE BRAINLIEST THANK YOU!!!

Greg mow and rakes lawn to earn extra money He makes 45 for every lawn he mows and an extra 15 for raking his goal is to earn at least 250 per week

Answers

The inequality is 45m + 14 n ≥ 250.

What is Inequality?

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

He makes 45 for every lawn he mows

and an extra 15 for raking

His goal earning= at least 250 per week

let the number of lawn he mow is m and the number of lawn rakes is n.

Then the inequality is

45m + 14 n ≥ 250

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write a linear function f with the given values. f(-10) = 4, f (8) = -5 Can someone please help me with this question​

Answers

Answer: y=-0.5x-1

Step-by-step explanation:

                                              y=mx+b

Convert the given values f(-10) = 4, f (8) = -5 to coordinates (-10,4)  (8,-5)

Hence we use the formula for finding the slope m:

[tex]\displaystyle\\\boxed{m=\frac{y_2-y_1}{x_2-x_1} }\\\\x_1=-1\ \ \ \ \ x_2=8\ \ \ \ \ \ y_1=4\ \ \ \ \ y_2=-5\\\\m=\frac{-5-4}{8-(-10)}\\\\m=\frac{-9}{8+10} \\\\m=\frac{-9}{18} \\\\m=-0.5\\\\Thus, y=-0.5x+b\ \ \ \ (1)\\\\[/tex]

We substitute the value of (-10,4) into equation (1):

[tex]4=-0.5(-10)+b\\\\4=5+b\\\\-1=b\\\\Thus, b=-1[/tex]

Hence, y=-0.5x-1

On a math quiz, Tatiana earns 5 points for each question she answers correctly. She wrote this
equation to find how many points she earns (p) based on how many questions she answers
correctly (g):
p = 5q
Identify the dependent and independent variables.
Points earned (p)
Questions correct (g)
Dependent variable Independent variable

Answers

Answer:

For points earned (p), the button should be on the left, and for questions correct (q), its on the right.

Step-by-step explanation:

me not know how to speak English!

In the given equation p = 5q, p is the dependent variable and g is the independent variable.

Given that Tatiana earns 5 points for each question she answers.

So, the equation is p = 5q

The above equation explains that for every question she answers, she earns 5 points. That means answering questions which is "q" is an independent variable as it is not depending on any other factor.

The points earned which is "p", is completely depending on answering questions, so the "p" which is points earned is a dependent variable.

From the above explanation, we can conclude that p is dependent variable and q is independent variable.

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What is the angle of elevation of the sun when a 47-ft mast casts a 14 ft
shadow?
O
The angle of elevation is
(Simplify your answer. Type an integer. Round to the nearest degree.)
***

Answers

The sun's angle of elevation when a 47-foot mast casts a 14-foot shadow 73.4127

What is the angle of elevation ?

At the foot of the mast, place the 90 degree (right) angle of a right triangle. When the sun hits the mast, it casts a 47-foot shadow. Consider the mask's height to be on the "opposite side" of the elevation angle, and this shadow to be on the "adjacent side."

The "tangent" trig function includes the following variables:

Tan = (opposite side) (elevation angle) (adjacent side).

In this case, tan (angle of elevation) equals opposing side / adj opposing side.

is used for

radians, or tan (angle of elevation)

= 47/14 = 3.3571

3.3571 is equal to 73.4127 degree.

The angle of elevation of the sun when a 47-ft mast casts a 14 ft

shadow 73.4127 degree

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Change the following problem to an addition problem.
-5-4

Answers

Answer:-9

Step-by-step explanation:

-(5+4)

-(9)

The answer is -1
-5+4
Will be -1

Beatrice makes a jar of dry soup mix. The ingredients are:

1 3/4 = 7/4cups uncooked rice

1/2 cup dry lentils

1 2/3 = 5/3 cups uncooked pasta

1/3 cup beef bouillon

1/4 cup dried onion flakes

1/2cup dried peas

How much soup mix does this recipe make?

Answer the questions to find out.

The sum 7/4+ 1/2+5/3 +1/3 +1/4 +1/2 gives the amount of mix.


1. Which property could you use to change the grouping of the addends?

Answers

The soup mix that this recipe makes is 5.

The property could you use to change the grouping of the addends is the associative property of addition.

How to calculate the value of the mix?

From the information, the following can be deduced:

7/4cups uncooked rice

1/2 cup dry lentils

1 2/3 = 5/3 cups uncooked pasta

1/3 cup beef bouillon

1/4 cup dried onion flakes

1/2cup dried peas

The soup mix that this recipe make will be the addition of all the values. This will be:

= 7/4+ 1/2+5/3 +1/3 +1/4 +1/2

= 5

The associative property of addition can change the grouping.

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Amadou and his children went into a grocery store and he bought $9 worth of apples and bananas. Each apple costs $1 and each banana costs $0.50. He bought 4 times as many apples as bananas. By following the steps below, determine the number of apples, x, and the number of bananas, y, that Amadou bought.

Determine THREE ways to have 4 times as many apples as bananas.

There are 3 other ways so please try to answer them!

Answers

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The number of apples is 8.

The number of bananas is 2.

What is an expression?

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Total cost = $9

Cost of one apple = $1

Cost of one banana = $0.50

The number of bananas = x

The number of apples:

y = 4x

Now,

1y + 0.50x = 9

4x + 0.50x = 9

4.50x = 9

x = 9/4.50

x = 2

Now,

y = 4 x 2 = 8

Thus,

The number of apples 8.

The number of bananas is 2.

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Really need help!
Graph the equation y =x²
+ 4x - 5 on the accompanying set of axes. You must plot 5 points including the roots and the vertex. Using the graph, determine the roots
of the equation x² + 4x − 5 = 0.

Answers

Answer:

See picture below

Step-by-step explanation:

Use Desmos the free calcualtor.

Mrs. Nicholas baked two batches of cookies. The first batch consisted of 120 gingerbread cookies and the second batch consisted of 150 shortbread cookies. Mrs. Nicholas saved the same fraction of cookies from each batch. If Mrs. Nicholas saved 20 more shortbread cookies than gingerbread cookies, what fraction of the cookies did she save?

Answers

Answer:

i think 2/15 of the cookies

Step-by-step explanation:

hope this helps

What are the coordinates of the point on the directed line segment from (-9, -10)
to (1,5) that partitions the segment into a ratio of 2 to 3?

Answers

The coordinates of the point on the directed line segment from (-9, -10) to (1,5) that partitions the segment into a ratio of 2 to 3 is (-5,-4)

The end points of the line segment = (-9, -10) and (1, 5)

The partition ratio = 2 : 3

According to the partition rule

The x coordinate of the point = [tex]x_1+\frac{A(x_2-x_1)}{A+B}[/tex]

A = 2

B = 3

Substitute the values in the equation

The x coordinate of the point = -9 + [2(1--9) / 2+3]

= -9 + [2×10 / 5]

= -9 + [20/5]

= -9 + 4

= -5

Similarly,

The y coordinate of the point = [tex]y_1+\frac{A(y_2-y_1)}{A+B}[/tex]

= -10+[2(5--10)/2+3]

= -10+[2×15/5]

= -10+[30/5]

= -10 + 6

= -4

Hence, the coordinates of the point on the directed line segment from (-9, -10) to (1,5) that partitions the segment into a ratio of 2 to 3 is (-5,-4)

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Solve this system of equations using the SUBSTITUTION method, then answer the questions below.

x + 2y = 4
3x + 6y = 18

What did you get for the (x, y) solution to this system? If you were to graph these equations, would their lines cross? Explain why or why not.

Answers

The x and y do not have the values in the equation because both the equations don't intersect each other.

given that the equation,

x + 2y = 4 ..........i

3x + 6y = 18 ...........ii

now multiply i with 3 and subtract with from ii,

3x + 6y = 18

-(3x + 6y ) = 12

0x + 0y = 6

which is not possible so x and y do not have the values at the intersection of the both equations which states that both the equation do not intersect at each other.

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4. Find x.

78°
65°

This is problem number 4

I will mark brainless if I get this question right when I turn it in

Answers

The answer would be 78 degrees, or 70 degrees

a wheat farmer is investigating the effectiveness of a treatment for controlling a pest. a random sample of 500 plants shows that 47 of them are infected by the pest. what does this sample indicate about the claim that 20% of the plants are infected?

Answers

The sample indicates that the data does not provide sufficient evidence to support the claim that 20% of plants are infected.

This given test is a test for single sample proportion

The test hypothesis are:

[tex]H_{o} :p=0.20[/tex], null hypothesis

[tex]H_{1} :p\neq 0.20[/tex], alternative hypothesis

The test statistic fallows a standard normal distribution and is given by:

[tex]Z=\frac{x-p}{{\sqrt{p(1-p)/n} } }[/tex]

p=0.20

X=47 plants

Sample size, n=500

x, is the sample mean:

x=X/n=47/500

x=0.094

So, test statistic is calculated as:

[tex]Z=\frac{0.094-0.20}{\sqrt{0.20(1-0.20)/500} }[/tex]

Z=-5.93

From the z-table, the p-value associated with Z=-5.93 is approximately 0

The decision rule based on p-vale, is to reject the null hypothesis if p-value is less than confidence level

In this case, the p-value is very small and less than confidence level of 0.20, we therefore reject the null hypothesis or the claim

So we conclude that the data does not provide sufficient evidence to support the claim that 20% of plants are infected.

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which choice does not determine the sampling distribution? the population size the population variance the population mean the sample size

Answers

The population size does not determine the sampling distribution.

In the give question we have to find which choice does not determine the sampling distribution.

We firstly learn more about sampling distribution

A sampling distribution is a probability distribution of a statistic that is derived from a bigger sample size of individuals chosen at random from a given population. The sampling distribution of a particular population is the distribution of frequencies of a variety of potential outcomes for a population statistic.

So, the population size does not determine the sampling distribution.

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What does 25 DIVIDE by 3 equal?

Answers

Step-by-step explanation:

25/3 = 8.33

hope it's helpful

25 divided by 3 equals

8.3333
OR
8 1/3
OR
8 remainder 1

find the growth or decay rate: y=2.5(0.72)^x

Answers

Answer: decay

Step-by-step explanation: decay is when the input is less than 1 and greater than 0. 0.75 falls in between these numbers

the tell-tale factor is the value inside the parenthesis, if that's less than 1 is Decay, if more than 1 is Growth

[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &2.5\\ r=rate\to \text{\LARGE 28\%}\to \frac{28}{100}\dotfill &0.28\\ t=\textit{elapsed time}\dotfill &x\\ \end{cases} \\\\\\ A=2.5(1 - 0.28)^{x} \implies A = 2.5(0.72)^x\hspace{5em}y= 2.5(0.72)^x[/tex]

Which of the following is not an isometry
A). Translation
B). Line reflection
3). Point reflection
4). Rotation

Answers

The option that is not an isometry from the given transformations is 3). Point reflection.

What is an isometry?

An Isometry refers to a transformation that leads to the distance and length  of a shape being preserved when it is transformed.

Translations and rotations preserve the shape of a figure during transformation which means they preserve length which makes them an isometry. The same is true of line reflections.

Point reflections on the other hand, will lead to a change in dimensions for the figure being transformed.

In conclusion, `a point reflection is not an isometry.

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a mass of 2kg is supported by two cords which makes angle 30 degree and 50 degree with the vertical. calculate the tension in the two cords What is the measure of ZD in the parallelogram below? Which of the following principles emphasizes that actions should make the community as a whole better off?A. The Rights PrincipleB. The Fairness PrincipleC. The Virtue PrincipleD. The Common Good PrincipleE. The Utilitarian Principle Every complex number can be written in the form a+bi. For the complex numbers 8-4i, identify the values of a and b Concerning incremental project cash flow, which of these is a cost one would never count as an expense of the project?. Which of the following illustrates that infants have natural strategies for coping with their emotions?a) negative affect systemb) positive affect systemc)still-face paradigmd) baseline episode on november 1, alice co. accepted a 90-day, 6%, $2,000 note due january 30. on december 31, the appropriate adjusting entry was made. on january 30 of the next year, the note was honored and paid in full. the entry to record receipt of payment on january 30 would include a credit to: (check all that apply.) Solve by multiplying digits of value and filling in zeros: 25 x 10 What kind of sugar is in dna triose or Penros or hexose Solve each equation. 9^(x+2)=2^(5x-4) a pole that is 3m tall casts a shadow that is 1.4m long. at the same time, a nearby tower casts a shadow that is 39.5m long. how tall is the tower? round your answer to the nearest meter. What is the value of (13)4? 52 52 28,561 28,561 Assume you are performing the calibration step of experiment 8 and you begin with 30 g of water at 20 oc and 30 g of water at 80 oc. After adding the two portions of water into your calorimeter setup and following the procedure outlined in the experiment, you determine the temperature of the mixed portions of water to be 45 oc. What is the heat capacity of the calorimeter?. I need the answer to 1,4 thank you a nurse is assessing a client's surgical wound and sees drainage that is pale pink-yellow and thin and contains plasma and red cells. what is this type of drainage? What is the net force in this image? On a straight road, Jorge is 7 kilometers east of Peter, Jason is10 kilometers west of Juan, and Juan is 13 east of Peter. howmany miles is Jorge from Jason? a curette with ____ is recommended for use by nail technicians. If f (x) = 2x2 + 4x 3, then the quantity f of the quantity x plus h end quantity minus f of x end quantity all over h is equal to which of the following? PLEASE HELP ME I FEEL LIKE THIS SHOULD BE SUPER EASY BUT MY BRAIN CAN NOT RN