MATHEMATICS COLLEGE

What is the perimeter of a square with s = 8 centimeters?

Answers

Answer 1

Answer:

Answer:

32centimeters

Step-by-step explanation:

4 sides are in a sqaure and all of them are equal so

8 times 4 is 32

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Will a truck that is 10 feet wide carrying a load that reaches 12 feet above the ground clear the semielliptical arch on the one-way road that passes under the bridge shown in the figure on the right? 13 ft --- 52 ft It will clear the arch because the height of the archway of the bridge 5 feet from the center is approximately (Round to two decimal places as needed.) feet.

Answers

Height of the archway 5 feet from the center is required.

The height of the archway 5 feet away from the center is 12.757 feet.

Semi-major axis = $a=(52)/(2)=26\ \text{feet}$

Semi-minor axis = $b=13\ \text{feet}$

The formula for ellipse is

$(x^2)/(a^2)+(y^2)/(b^2)=1\n\Rightarrow (x^2)/(26^2)+(y^2)/(13^2)=1$

At 10 feet is the width of the truck.

The truck is passing through the center so the $x=(10)/(2)=5$

$(5^2)/(26^2)+(y^2)/(13^2)=1\n\Rightarrow y=\sqrt{(1-(5^2)/(26^2))* 13^2}\n\Rightarrow y=12.757\ \text{feet}$

Now $y=12.757\ \text{feet}>12\ \text{feet}$

So, the height of the archway 5 feet away from the center is 12.757 feet.

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Figure is missing, so i have attached it.

Answer:

it will clear the arch because the height of the archway of the bridge 5 feet from the center is approximately 12.76 ft

Step-by-step explanation:

The standard form of equation of an ellipse is;

x²/a² + y²/b² = 1

From the figure in the image attached, we can see that the radius is; a = 52/2 = 26 ft

While the value of b = 13 ft

Thus;

x²/26² + y²/13² = 1

x²/676 + y²/169 = 1

We want to find the height of the archway of the bridge 5 feet from the center.

Thus, we will plug in 5 for x to get;

5²/676 + y²/169 = 1

(25/676) + (y²/169) = 1

Multiply through by 676 to get;

25 + 4y² = 676

4y² = 676 - 25

y² = 651/4

y² = 162.75

y = 12.76 ft

Thus height of the truck is 12 ft and so it will clear the arch because the height of the archway of the bridge 5 feet from the center is approximately 12.76 ft

In the first quadrant you start at (7,4) and move 4 units left and 3 units up.

Answers

Answer:

(3,7)

Step-by-step explanation:

(7,4)

Moving left and right relates to x

Moving up and down relates to y

When you move to the left, you subtract

When you move to the right, you add

When moving up, you add

When moving down you subtract

X= 7-4 = 3

x=3

Y= 4+3 = 7

y = 7

(3,7)

Each prize for a carnival booth costs $0.32. How many prizes can you buy with $96?

Answers

Answer: 96 divided by 0.32 is 300, so it's 300.

Solve the equation −11=−3m+7

Answers

Answer:

m = 6

Step-by-step explanation:

Step 1: Write out equation

-11 = -3m + 7

Step 2: Subtract 7 on both sides

-18 = -3m

Step 3: Divide both sides by -3

6 = m

Step 4: Rewrite

m = 6

Answer:

m = 6

Step-by-step explanation:

-11 = -3m + 7

Multiply -1 on both sides

11 = 3m - 7

11 + 7 = 3m

18 = 3m

18/3 = m

m = 6

A high school student took two college entrance exams, scoring 1070 on the SAT and 25 on the ACT. Suppose that SAT scores have a mean of 950 and a standard deviation of 155 while the ACT scores have a mean of 22 and a standard deviation of 4. Assuming the performance on both tests follows a normal distribution, determine which test the student did better on.

Answers

Answer:

Due to the higher z-score, he did better on the SAT.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = (X - \mu)/(\sigma)$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Determine which test the student did better on.

He did better on whichever test he had the higher z-score.

SAT:

Scored 1070, so $X = 1070$

SAT scores have a mean of 950 and a standard deviation of 155. This means that $\mu = 950, \sigma = 155$ .

$Z = (X - \mu)/(\sigma)$

$Z = (1070 - 950)/(155)$

$Z = 0.77$

ACT:

Scored 25, so $X = 25$

ACT scores have a mean of 22 and a standard deviation of 4. This means that $\mu = 22, \sigma = 4$

$Z = (X - \mu)/(\sigma)$

$Z = (25 - 22)/(4)$

$Z = 0.75$

Due to the higher z-score, he did better on the SAT.

Trevor is preparing dinner plates. He has 18 pieces of chicken and 14 rolls. If he wants to make all the plates identical without any food left over, what is the greatest number of plates Trevor can prepare?

Answers

Answer:

split the four extra pieces into smaller pieces to were it will give each plate the same amount.

Step-by-step explanation:

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