a bookcase is to be constructed as shown in the figure below. the height of the bookcase is 2 feet longer than the length of a shelf. if 22 feet of lumber is available for the entire unit including the shelves but NOT the back of the bookcase find the length and height of the unit.

Answers

Answer 1

The length of the shelf is 10 feet while its height is 10 feet.

Equation

Equation is an expression used to show the relationship between the sides and angles of a right angled triangle.

Let x represent the shelf length and y represent the shelf height.

The height of the bookcase is 2 feet longer than the length of a shelf. hence:

y = x + 2-x + y = 2 (1)

Also, 22 feet of lumber is available:

x + y = 22 (2)

From equation 1 and 2:

y = 12, x = 10

The length of the shelf is 10 feet while its height is 10 feet.

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Related Questions

7
5
3
10
Find the perimeter.
8
2
8

Answers

The perimeter of the figure is 43 units.

How to find the perimeter of a figure?

The perimeter of a figure is the sum of the whole sides of the figure. Therefore, the figure above is a composite figure, let's find the perimeter of the shape as follows:

Hence,

Perimeter of the figure = 8 + 3 + 5 + 7 + 10 + 2 + 8

Therefore,

Perimeter of the figure = 11 + 12 + 12 + 8

Perimeter of the figure = 23 + 20

Perimeter of the figure = 43 units

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how do you
Evaluate 11/6 - 2/8

Answers

Answer:

1 7/12

Step-by-step explanation:

two alarms are set to go off in the morning. one alarm will buzz every 6 minutes and the other will beep every 9 minutes. if both alarms go off 6:15 am what is the next time the both alarms will go off at the same time

Answers

Answer = 6:33 AM

=========================================================

Explanation:

The LCM of 6 and 9 is 18. We can see that by listing out the multiples

multiples of 6 = {6,12,18,24,30,...}

multiples of 9 = {9,18,27,36,45...}

Or we could multiply 9*6 = 54, and divide by the GCF 3 getting 54/3 = 18. There are a few options to find the LCM.

The LCM being 18 means that every 18 minutes, both alarms will go off. If they both sound off at 6:15 AM, then the next time they trigger together is 6:33 AM since 15+18 = 33, and there is no carry over to the next hour.

You can think of the time values adding like this

6:15 + 0:18 = (6+0):(15+18) = 6:33

Select the correct answer. Maria donates a fixed amount, a, to a charity each month. If she donates $300 in 12 months, what is the equation for a? A. a + 300 = 12 B. a × 300 = 12 C. a × 12 = 300 D. a + 12 = 300 E. a + 32 = 100

Answers

Answer: C

she donates a for 12 months, the 12 in the a * 12=300. the a is the fixed amount, meaning she will donate a 12 times in a year.

Consider the binary operation table on set A ={1,2,3,6}
* 1 2 3 6
13 1 2 6
21 2 3 6
32 3 1 6
61 6 6 3
i) Find 2*6 , 6*1,2*(1*6), 6*(2*3)
ii) Is * commutative ? justify
iii) Find the identity element if exists.
iv) Find the elements which has inverse
*
PLEASE ANSWER THIS FASSSTT!!
I need this now as this is my assignment question!!

Answers

(i)

2 * 6 = 6

6 * 1 = 1

2 * (1 * 6) = 2 * 6 = 6

6 * (2 * 3) = 6 * 3 = 6

(ii) * is commutative if for any a, b ∈ A, we have a * b = b * a. You can verify this visually by checking for symmetry in the table along the main diagonal (going from top left to bottom right).

* is not commutative because

6 * 1 = 1

while

1 * 6 = 6

(iii) If e is the identity, then for any a ∈ A, we have a * e = e * a = a.

Here, 2 is the identity element because 1 * 2 = 1 and 2 * 1 = 1, and the same is true if we replace 1 with 2, 3, or 6.

(iv) Let a ∈ A. a has an inverse a ⁻¹ if a * a ⁻¹ = a ⁻¹ * a = e.

We know that e = 2, so look for any pairs that map to 2. The table shows that

1 * 3 = 2 and 3 * 1 = 2

2 * 2 = 2

so 1 has an inverse of 3, 3 has an inverse of 1, and 2 has itself as its inverse (which is to be expected for the identity).

Please help me and thanks in advance

Thompson Middle School is painting a circle on their playground with a radius
of 14 feet. What will be the total area of the circle, in square feet?
Use t = 3.14, and round your answer to the nearest hundredth.

Answers

Answer:

The answer will be 615.4

Step-by-step explanation:

What you have to do is multiply 3.14 to 14 square and you round it.

QUICK 100 Points, What is the standard portion cost for a 1-ounce portion of parmesan cheese purchased a pound for $14.60 per pound? (There are 16 ounces in a pound.)

$0.53
$0.68
$0.91
$1.02

Answers

Answer:

$0.91

Step-by-step explanation:

Given:

1 pound = 16 ounces$14.60 = 1 lb Parmesan cheese

If one pound of Parmesan cheese costs $14.60, to find the cost of a one-ounce portion, simply divide the cost of one pound by 16:

$\implies \textsf{1 ounce portion}=\dfrac{\$14.60}{16}=\$0.9125=\$0.91\;\sf (nearest \; cent)$

Therefore, the standard portion cost for a one-ounce portion of Parmesan cheese is $0.91 (nearest cent).

The graph shows the ratio of goals attempted to goals made for two soccer players, Andres and Deyvi. Which player has a better record of making goals? Explain how you know.

Answers

Answer: Andres

Explanation:

y = goals made

x = goals attempted

For Andres, his ratio is y/x = 4/8 = 1/2 = 0.50 meaning that he made 50% of his attempts

For Deyvi, the ratio is y/x = 9/20 = 0.45 = 45%

Andres has the better record.

2 3/4 of 500grams in step by step calculator

Answers

Answer:

To calculate 2 3/4 of 500 grams, follow these steps:

1. Convert the mixed number to an improper fraction:

2 3/4 = (2 x 4 + 3)/4 = 11/4

2. Multiply the improper fraction by 500:

11/4 x 500 = (11 x 500)/4 = 2,750/4

3. Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is 2:

2,750/4 = (2 x 1,375)/(2 x 2) = 1,375/2

Therefore, 2 3/4 of 500 grams is equal to 1,375/2 grams or 687.5 grams.

Step-by-step explanation:

What is the difference between the expression -4 - 4 and -4 + -4 ?

Answers

Answer:

the difference is that one equation has 2 signs while the other equation has 3

Step-by-step explanation:

the volume of a rectangle prism is 8cm height 4 width.

Answers

Answer:

Step-by-step explanation:

6% pay increases 62,900 thanks i look forward to the additional _ per month

Answers

Answer:

Step-by-step explanation:

$314.50

To calculate the additional pay per month, we need to multiply the current salary by the percentage increase and divide by 12 (months).

The pay increase is 6% of $62,900, which is:

0.06 x $62,900 = $3,774

Therefore, the additional pay per month is:

$3,774 / 12 = $314.50

So, Ciara can look forward to an additional $314.50 per month.

Solve: (x - 10)² + 10 = 100

Square Roots and Completing the Square.

Answers

Answer:

Below

Step-by-step explanation:

(x-10)^2 = 90 sqrt both sides

x-10 = ± sqrt (90)

x = 10 ± sqrt (90)

A friend recently planned a camping trip. He had two flashlights, one that required a single 6-V battery and another that used two size-D batteries. He had previously packed two 6-V and four size-D batteries in his camper. Suppose the probability that any particular battery works is p and that batteries work or fail independently of one another. Our friend wants to take just one flashlight. For what values of p should he take the 6-V flashlight

Answers

Answer:

The values of p = 0 < p ≤ 2/3

Step-by-step explanation:

First we write the probability of 6V flashlight working representing it as a binomial mass function of a binomial random variable

P ( 6v flashlight working ) = P ( at least one 6V battery works )

= P ( 1 6v battery work ) + P ( 2 6v battery work )

= b( 2; 2, p ) + b( 1; 2, p )

write out a formula of b( 2; 2, p ) + b( 1; 2, p )

P ( 6v flashlight working ) = p^2 + 2p( 1 - p )

Next we write the probability of D flashlight working representing it as a binomial mass function of a binomial random variable

P ( D flashlight works ) = p ( at least two D batteries works )

= b( 4; 4, p ) + b(3;4, p ) + b(2; 4, p )

write out a formula of b( 4; 4, p ) + b(3;4, p ) + b(2; 4, p )

P ( D flashlight works ) = $P^4 + 4p^3 ( 1- p ) + 6p^2 ( 1- p)^2$

attached below is the remaining solution

A friend recently planned a camping trip. He had two flashlights, one that required a single 6-V battery

"What are the coordinates of your reflected triangle A’B’C’?"
Please help! Thank you!

Answers

A' - (-1,4)

B' - (-1,8)

C' - (-5,4)

hope this helps

Ivan is saving money to buy a game. So far he has saved 8, which is one-fourth of the total cost of the game. How much does the game cost?

Answers

Answer:

$\$32$

Step-by-step explanation:

Let the cost of the game be $x$. Since one-fourth of the cost of the game is equal to 8 dollars, we have the following equation:

$\frac{1}{4}x=8$

Multiply both sides by 4 to isolate and solve for $x$:

$x=8\cdot 4=\boxed{\$32}$

Mrs.Leitz spent $8.75 on new folders, f, for the 25 students in her class. Which equation shows how to find the cost of each folder

Answers

Answer:

each folder costed 0.35

Step-by-step explanation:

8.75 divided by 25 would have given you the answer

A venture capitalist, willing to invest $1,000,000, has three investments to choose from. The first investment, a software company, has a 8% chance of returning $8,000,000 profit, a 21% chance of returning $2,500,000 profit, and a 71% chance of losing the million dollars. The second company, a hardware company, has a 5% chance of returning $8,000,000 profit, a 30% chance of returning $500,000 profit, and a 65% chance of losing the million dollars. The third company, a biotech firm, has a 10% chance of returning $10,000,000 profit, a 28% of no profit or loss, and a 62% chance of losing the million dollars.

Order the expected values from smallest to largest.

second, third, first
third, second, first
third, first, second
first, second, third
second, first, third
first, third, second

Answers

Answer:

I don't know..........

Step-by-step explanation:

I'm sorry..........

find the surface area of the prism

Answers

Answer: 132 cm cubed

Step-by-step explanation:

0.5*3*4*2=12

10*5=50

4*10=40

3*10=30

30+40+50+12=132 cm cubed

write and solve an inequality to find the possible values of x

Answers

The inequality that represents the value of x is (b) x > 80

Writing and solving the inequality for x

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

The figure

The general rule is that

The larger the side length, the larger the angle opposite it

using the above as a guide, we have the following:

1/8x > 10

So, we have

x > 80

Hence, the inequality is x > 80

Answers

Answer:

There were 4 thieves. They went off to steal from the king, hearing about the great treasure he kept locked in his vault. They managed to break in and sneak out without any of the guards even noticing them. They rode back to their run down hide out and opened the treasure, only to find it was a tarp. They decided they would sell it to the highest bidder, but there was four of them and they all wanted the profits. They couldn't decide who would sell it so the leader sliced it with his sword into four equal pieces, each person getting 1. How much of the tarp did each thief get?

The division story will be that there are 16 boys who want to share 4 oranges. What fraction will each person get?

Number of boys = 16Number of oranges = 4

Fraction that each person will get will be:

= Number of oranges / Number of boys

= 4/16

= 1/4

Each boy gets 1/4.

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Find the slope and the y-intercept of the line. 3x -4y = -12

Answers

$\\ \sf\longmapsto 3x-4y=-12$

Convert to y=mx+b form

$\\ \sf\longmapsto 3x+12=4y$

$\\ \sf\longmapsto y=\dfrac{3x+12}{4}$

$\\ \sf\longmapsto y=\dfrac{3}{4}x+\dfrac{12}{4)$

$\\ \sf\longmapsto y=\dfrac{3}{4}+3$

Slope=3/4

Hurry u need help who ever answers first get more points and NO LINKS

Answers

Answer:

20%

Step-by-step explanation:

Question is in the image

Answers

Answer:

Step-by-step explanation:

y = -2x + 3

-1 = -2(2) + 3

-1 = -4 + 3

-1 = -1

y = x - 3

-1 = 2 - 3

-1 = -1

Can someone tell me this one?

Answers

j = 35 + 10 since 35 is 10 less than j just add 10 to 35 to get j :^)

Answer:

The answer is 45

Step-by-step explanation:

35+10=45

Trucks in a delivery fleet travel a mean of 120 miles per day with a standard deviation of 18 miles per day. The mileage per day is distributed normally. Find the probability that a truck drives between 150 and 156 miles in a day. Round your answer to four decimal places.

Answers

The probability that a truck drives between 150 and 156 miles in a day is 0.0247. Using the standard normal distribution table, the required probability is calculated.

How to calculate the probability distribution?

The formula for calculating the probability distribution for a random variable X, Z-score is calculated. I.e.,

Z = (X - μ)/σ

Where X - random variable; μ - mean; σ - standard deviation;

Then the probability is calculated by P(Z < x), using the values from the distribution table.

Calculation:

The given data has the mean μ = 120 and the standard deviation σ = 18

Z- score for X =150:

Z = (150 - 120)/18

= 1.67

Z - score for X = 156:

Z = (156 - 120)/18

= 2

So, the probability distribution over these scores is

P(150 < X < 156) = P(1.67 < Z < 2)

⇒ P(Z < 2) - P(Z < 1.67)

From the standard distribution table,

P(Z < 2) = 0.97725 and P(Z < 1.67) = 0.95254

On substituting,

P(150 < X < 156) = 0.97725 - 0.95254 = 0.02471

Rounding off to four decimal places,

P(150 < X < 156) = 0.0247

Thus, the required probability is 0.0247.

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The expression 81 √ ⋅ 100√ represents the number of feet between home plate and first base. What is the distance, in feet, between home plate and first base? Answers are 19 30 80 and 810.

Answers

The distance between home plate and first base is -1 feet

what is distance ?

Distance is a numerical or occasionally qualitative measurment of how far apart objects or point are . in physics or everyday usage , distance may refer to a physical length.

How to determine the number

From the information given, we have that;

The expression for the number of feet between home plate and first base is given as;

√81-√100

Where;

√81 is the number of feet at home plate

√100 is the number of feet at the first base

To determine the distance, we take find the square root of the numbers and substitute, we have;

9 - 10 Find the difference

-1 feet

Thus, the distance between home plate and first base is -1 feet

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Levi spends all of his free time surfing. Today he was out on the waves for 7.1 hours. That is 0% more time than yesterday. How many hours did he spend surfing yesterday?

Round your answer to the nearest tenth.

HELPPPP IVE BEEN STUCK ON THIS FOREVER!!

Answers

Is it not 7.1 hours since the difference is 0%?

Suppose that you are taking a course that has 4 tests. The first three tests are each worth 20% of your final grade, and the fourth test is worth 40% of the final grade. To get a B in the course, you must have an average of at least 80 percent on the 4 tests. Your scores on the first 3 tests were 63.5 %, 76 %, and 87 %. What is the minimum score you need on the fourth test to get a B for the course?. Don't round your answer.

Answers

Answer:

86.75

Step-by-step explanation:

Given test scores of 63.5, 76, and 87 that each count for 20% of your grade, you want to know the fourth test score needed for an average of 80, if the fourth test is worth 40% of your grade.

Course grade

The grade for the course, with fourth test score x, will be ...

0.20(63.5 +76 +87) +0.40x = 80

0.40x +45.3 = 80

Solving for x, we get ...

0.40x = 34.7 . . . . subtract 45.3

x = 86.75 . . . . . . . divide by 0.4

The minimum score you need on the fourth test is 86.75.

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Suppose that you are taking a course that has 4 tests. The first three tests are each worth 20% of your

On a map, 1 inch equals 25 miles. Two cities are 3 inches apart on the map. What is the actual distance between the cities?

Answers

Answer:

75 Miles apart

Step-by-step explanation:

I = inches on a map

I=25

3I=75

75 miles apart

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HELPPPP!I get confused :\ The Smith family was one of the first to come to the U.S. They had 9 children. Assuming that the probability of a child being a girl is .5, find the probability that the Smith family had: at least 7 girls ? at most 8 girls? In which region would you find the most hardwood forests? You invest $60,000 in the stock market. Since you are a math genius, you have found the secret keyto great returns. You average 22% return on your money. Assume daily compounding (n=365).Using the compound interest equation: A = P(1 + )"ntHow much money will be in the account in 15 years? Describe the houses the Anasazi lived in. How were their villages organized? A restaurant manager suspects that service declines during off-peak hours. To investigate, he selects a random sample of 100 customers who dined in his restaurant during peak hours and a random sample of 70 customers who dined in his restaurant during off-peak hours. Each customer rated the service on a scale of 1 to 5, where 1 = highly dissatisfied and 5 = highly satisfied. The results are displayed in the table.The manager would like to test these hypotheses:H0: There is no difference in the distribution of service ratings among all customers who dine at this restaurant during peak and off-peak hours.Ha: There is a difference in the distribution of service ratings among all customers who dine at this restaurant during peak and off-peak hours.The conditions for inference are met. The test statistic is 2 = 13.88 and the P-value is between 0.005 and 0.01. What conclusion should be made using = 0.05?Because the P-value is less than = 0.05, there is convincing evidence of a difference in the distribution of service ratings among all customers who dine at this restaurant during peak and off-peak hours.Because the P-value is less than = 0.05, there is convincing evidence of no difference in the distribution of service ratings among all customers who dine at this restaurant during peak and off-peak hours.Because the P-value is less than = 0.05, there is not convincing evidence of a difference in the distribution of service ratings among all customers who dine at this restaurant during peak and off-peak hours.Because the P-value is less than = 0.05, there is not convincing evidence of no difference in the distribution of service ratings among all customers who dine at this restaurant during peak and off-peak hours. True or False. Alfred Wegener contributed greatly to the theory of plate tectonics by collecting and analyzing fossil, glacial and geologic evidence. Need 13&14!! ASAP, will put Brainliest In a Command Economy blank makes the basic decisions Consider the following implementation of hashCode(), in a class where str is a String:public int hashCode () {int hash = 0;int n = str.length; for (int i=0; hash = (hash * 31) charat(i); return hash; }if str = new; what does hash code (0 return? Can somebody solve this to be considered a holder in due course, four (4) requirements must be met. which of the following is not one of those requirements? Read the passage to answer the question that follows.What might have happened if Robin Hood had refused to prove his shooting skill in the royal preserve? it is ultmately up to the buyer to avoid fraud Explain how business news items can prove to be a valuablesource of job prospects. Q5- Brainliest to correct answer where installed in a 3-pole, 600-volt fused safety switch, the minimum number of fuses required to protect a 120-volt, 1-ph, 2-wire branch circuit is . A farmer sells 7.2 kilograms of pears and apples at the farmer's market. 3 4 of this weight is pears, and the rest is apples. How many kilograms of apples did she sell at the farmer's market? Are heated air and wind shear the cause for severe storms? Explain. Bill Clinton reportedly was paid an advance of $10.0 million to write his book My Life.Suppose the book took three years to write. In the time he spent writing, Clinton could have been paid to make speeches. Given his popularity, assume that he could earn $7.9 million a year (paid at the end of the year) speaking instead of writing. Assume his cost of capital is 9.8% per year.a. What is the NPV of agreeing to write the book (ignoring any royalty payments)?b. Assume that, once the book is finished, it is expected to generate royalties of $4.7 million in the first year (paid at the end of the year) and these royalties are expected to decrease at a rate of 30% per year in perpetuity. What is the NPV of the book with the royalty payments?