MATHEMATICS COLLEGE

2Viviana is ordering carpet

for 16 square rooms in a

hotel. Each room will need

100 square feet of

carpet. What is the

length of 1 room?

Answers

Answer 1

Answer:

Answer:

Length of a room is 10ft

Step-by-step explanation:

Given

$Rooms = 16$

$Carpet\ Area = 100ft^2$

Required

Determine the length of each room

Here, we'll assume that the carpet will cover each room completely.

If so:

$Carpet\ Area = Length * Length$

$100ft^2 = Length * Length$

$100ft^2 = Length^2$

Take square root of both sides

$√(100ft^2) = √(Length^2)$

$√(100ft^2) = Length$

Take positive square root

$10ft = Length$

$Length = 10ft$

Hence, the length of a room is 10ft

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Two equal rectangular lots are enclosed by fencing the perimeter of a rectangular lot and then putting a fence across its middle. If each lot is to contain 2,700 square feet, what is the minimum amount of fence (in ft) needed to enclose the lots (include the fence across the middle)

Answers

Answer:

360 feet

Step-by-step explanation:

Area = 2XY = 2 · 2,700 = 5,400

Perimeter = (2 · 2X) + 3Y = 4X + 3Y

Y = 5,400 / 2X = 2,700 / X

Perimeter = 4X + 8,100/X

P'(x) = 4 - 8,100/X² = 0

4 = 8,100/X²

X² = 8,100 / 4 = 2,025

X = √2,025 = 45

Y = 2,700 / 45 = 60

Perimeter = (4 · 45) + (3 · 60) = 180 + 180 = 360 feet

According to a government study among adults in the 25- to 34-year age group, the mean amount spent per year on reading and entertainment is $1,999. Assume that the distribution of the amounts spent follows the normal distribution with a standard deviation of $574. (Round your z-score computation to 2 decimal places and final answers to 2 decimal places.) What percent of the adults spend more than $2,550 per year on reading and entertainment?

Answers

Answer:

The probability is $P(X > x ) = 0.19215$

Step-by-step explanation:

From the question we are told that

Th The population mean $\mu = \$ 1,999$

The standard deviation is $\sigma = \$ 574$

The values considered is $x = \$ 2,500$

Given that the distribution of the amounts spent follows the normal distribution then the percent of the adults spend more than $2,550 per year on reading and entertainment is mathematically represented as

$P(X > x ) = P(( X - \mu)/(\sigma ) > ( x - \mu)/(\sigma ) )$

Generally

$X - \mu}{\sigma } = Z (The \ standardized \ value \ of \ X )$

$P(X > x ) = P(Z > ( x - \mu)/(\sigma ) )$

substituting values

$P(X > 2500 ) = P(Z > ( 2500 - 1999)/(574 ) )$

$P(X > 2500 ) = P(Z >0.87 )$

From the normal distribution table the value of $P(Z >0.87 )$ is

$P(Z >0.87 ) = 0.19215$

Thus

$P(X > x ) = 0.19215$

Final answer:

We calculate the z-score for the amount $2,550 using the given mean and standard deviation. The z-table gives us the percentage of people who spend less than this, which we subtract from 1 to find the percentage who spend more. Approximately 16.85% of adults in the 25- to 34-year age group spend more than $2,550 on reading and entertainment each year.

Explanation:

To compute the percentage of adults spending more than $2,550 per year, we must first find the z-score associated with this value. The z-score is a measurement of how many standard deviations a particular data point is from the mean.

The formula for calculating the z-score is: Z = (X - μ) / σ.

Where:
- X is the value we are interested in.
- μ is the mean.
- σ is the standard deviation.

Using this formula, the z-score for $2,550 is:
Z = ($2,550 - $1,999) / $574 = 0.96.

Next, we need to use a z-table or a standard normal distribution table to find out the probability that lies below the calculated z-score. Looking this up on a z-table, we get a value of 0.8315, meaning that 83.15% of the population will spend $2,550 or less per year on reading and entertainment. Since we want to know the percentage spending more than $2,550, we subtract this value from 1: 1 - 0.8315 = 0.1685.

Therefore, based on the given mean and standard deviation, about 16.85% of adults in the 25- to 34-year age group spend more than $2,550 on reading and entertainment each year.

Learn more about Z-Score here:

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Answers

Answer:

fx =1; then fx =2; then fx =4

Step-by-step explanation:

then plug the coordinates in as x is horizontal bar in top right then the fx

A ladder leans against a building that angle of elevation of the latter is 70° the top of the ladder is 25 feet from the ground. to the nearest 10th of a foot how far from the building is the base of the ladder a. 20.5 feet b. 30.5 feet C.32.3’ or D.39.5 feet

Answers

Answer:

a. 20.5

Step-by-step explanation:

because this will form a right triangle we can use tan (opposite over adjacent) so an equation we could set up would be tan(70)=25/x

therefore we can just solve the equation which would give us 20.45. so if we round it the answer would be a

Answer:

The correct answer option is a. 20.5 feet.

Step-by-step explanation:

We are given that the angle of elevation of the ladder is 70° and the height of the ladder is 25 feet from the ground.

We are to find the distance of the building from the base of the ladder.

For this, we will use tan:

$tan 70 = \frac { 2 5 } { x }$

$x = \frac { 2 5 } { tan 7 0 }$

x = 20.5 feet

Find the perimeter of the following polygon. Be sure to include the correct unit in your answer.15 m
1
mm
15 m
17 m
km
9 m
12 m

Answers

Answer:

489 km is the perimeter

Step-by-step explanation:

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The formula for the volume of a cylinder is V 7r²h, where r is the radius of the cylinder and his the
height of the cylinder. Rewrite the formula to solve for h in terms of r and V.
G

Answers

Final answer:

To solve for the height of a cylinder in terms of its radius and volume, rewrite the formula as h = V/(7r²).

Explanation:

To rewrite the formula to solve for h in terms of r and V, we need to isolate h on one side of the equation. The given formula is V = 7r²h. To isolate h, we divide both sides of the equation by 7r². This gives us the formula: h = V/(7r²). This formula allows us to calculate the height of a cylinder given its radius and volume.