How do I calculate the volume of this pyramid?

Answer:

The expression [tex](x+1)^2[/tex] represents the radius of the soap dispenser.

The expression [tex]4x+1[/tex] represents the height of the soap dispenser.

Step-by-step explanation:

The question says that the soap dispenser is in the form of a cylinder.

Now, we find the volume of the cylinder by using the given formula:

[tex]V= \pi r^2 h[/tex], where V represents the volume, 'r' represents the radius, and 'h' represents the height of the cylinder.

Now, the volume is the product of radius squared and the height, if they both are functions of [tex]x[/tex], then the function to represent the volume must have cubic exponents.

Since, the radius is squared in the formula and it is a function of [tex]x[/tex] that implies that the function of radius must have square as the exponent of [tex]x[/tex], therefore, the expression [tex](x+1)^2[/tex] will represent the radius of the soap dispenser and the expression [tex](4x+1)[/tex] represents the height of the soap dispenser.

Answer:

D

Step-by-step explanation:

10(1/2x + 6) = 8

Distributive property.

5x + 60 = 8

Subtract 60 from both sides.

5x = -52

Divide both sides by 5.

x = -10.4 (This is your answer.)

135 is a composite number.

135 = 1 x 135, 3 x 45, 5 x 27, or 9 x 15.

Factors of 135: 1, 3, 5, 9, 15, 27, 45, 135.

Prime factorization: 135 = 3 x 3 x 3 x 5, which can also be written 135 = 3³ x 5

The prime factorization of 135 is 3^3 × 5.

The prime factorization of 135 is obtained by finding the prime numbers that divide 135 evenly, repeatedly dividing until the quotient is no longer divisible by any prime numbers.

Starting with the number 135, we can see that it is divisible by 3, so we divide 135 by 3:

135 ÷ 3 = 45

Now, we repeat the process with 45. It is also divisible by 3:

45 ÷ 3 = 15

Continuing, we divide 15 by 3:

15 ÷ 3 = 5

Now we have reached a quotient of 5, which is a prime number. We cannot divide it any further, so we have obtained the prime factorization of 135 as follows:

135 = 3 × 3 × 3 × 5

Therefore, the prime factorization of 135 is 3³ × 5.

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Answer:

39.66

Step-by-step explanation:

If the divisor is not a whole number, move decimal point to right to make it a whole number and move decimal point in dividend the same number of places.

Divide like you usually do

Put decimal point directly above decimal point in the dividend.

Check your answer.

Answer:

39.66

Hope this helps :-)

Answer:

Option B

Step-by-step explanation:

h(x) =  x             if  x <  -1

         -x             if  x ≥  -1

Here piece wise function is given.

Firstly we graph the line h(x)  = x .

Remember that, this line start from x = -1 to -infinite , because x is less than -1.

Here we can not include the point x=-1. This situation represent with the help of circle at x = -1.

Now we graph the line h(x)  = -x .

Remember that, this line start from x = -1 to infinite , because x is greater  than equal to -1.

Here we  include the point x=-1. This situation represent with the help of solid circle at x = -1..

So, option 2 is correct answer.

Answer:

the numerator is 12

Step-by-step explanation:

since 48 is a percent, it would be put as 48/100 as a fraction. since both the numerator and denominator are divisible by 4, you can reduce the fraction into 12/25. Since the question is asking what the numerator was when the denominator was 25, the answer is 12.

Answer:

A=12

Step-by-step explanation:

Emily's clothing store sold 138 short sleeve shirts, calculated by dividing the total shirts by the sum of the ratio parts (10) and multiplying the result by the short sleeve part of the ratio (3).

The question asks how many short sleeve shirts were sold if the ratio of short sleeve to long sleeve shirts is 3:7 and a total of 460 shirts were sold. To find the answer, first calculate the total parts of the ratio by adding both parts of the ratio together, which is 3+7=10.

Then, divide the total number of shirts by the total parts of the ratio to find out how many shirts each part of the ratio represents: 460/10=46. Since the ratio of short sleeve shirts is 3 parts, multiply the number each part represents by 3 to get the number of short sleeve shirts: 46*3=138. Therefore, Emily's clothing store sold 138 short sleeve shirts.

There are 126 possible selections of collars for Tony's 4 dogs if repetitions of colors are not allowed.

The number of selections of collars possible if repetitions of colors are not allowed, we can use the concept of permutations.

Using the formula for permutations without repetition, we can calculate this as:

9P4 = 9! / (9 - 4)!

= 9! / 5!

= (9 * 8 * 7 * 6) / (4 * 3 * 2 * 1)

= 3024 / 24

= 126

This shows that  126 possible selections of collars for Tony's 4 dogs if repetitions of colors are not allowed.

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Here is you're answer:

In order to solve this equation you have to remember that a negative divided by a positive is a negative then just solve the equation.

Therefore you're answer is "-17."

Hope this helps!

For this type of question, you have to use the Pythagorean Theorem:

[tex]a^{2} +b^{2} = c^{2}[/tex]

In the theorem, a and b are the legs. To find the length of the hypotenuse, you have to square the lengths of the two legs and add it together. Then, find the square root of the sum.

First square both numbers.

[tex]a=12 \\ a^{2} = 12 \times 12 = 144[/tex]

[tex]b = 16 \\b^{2} = 16 \times 16 = 256[/tex]

Now that you have the numbers, you need to add them.

[tex]144+256=400[/tex]

Now you need to find the square root of 400 to find the length of the htypotenuse.

[tex]\sqrt{400} = 20[/tex]

The length of the hypotenuse is 20 cm, which is the 3rd choice

a. 15 cm x

b. 17 cm x

c. 20 cm ✔

d. 28 cm x

If you have any questions, feel free to ask in the comments! :)

Answer:

the answer is C

Step-by-step explanation:

That's a really good positive correlation pictured.  The line fits the data very well.  The slope of the line is positive, meaning as x increases so does y.  I'd choose a big positive value.

Answer: 0.872

The correlation coefficient for the set of data is 0.872.

A correlation coefficient exists as a number between -1 and +1 that represents the linear dependence of two variables or groups of data

Using the process CORREL in the Excel tool, find the correlation coefficient

see the attached table

the correlation coefficient is equal to

r = 0.872373

Therefore, the correlation coefficient for the set of data is option D. 0.872.

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Answer: 36 degrees

Step-by-step explanation:

subtract 5 from 30=25

add 11 to 25

25+11=36

Considering the temperature changes throughout the day, the temperature at noon was 36 degrees F.

If the temperature started at 30 degrees F at midnight, and it dropped 5 degrees by 6:00 a.m, the temperature at 6:00 a.m. was 30 - 5 = 25 degrees F. Then, if the temperature increased by 11 degrees F by noon, we just add this increase to the temperature at 6:00 a.m. This results in 25 + 11 = 36 degrees F. So, the temperature at noon was 36 degrees F.

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You multiply by 1.12 to find your answer

Answer: 1.12

To get this answer, you would represent 12% as 0.12 (move the decimal point 2 spots to the left to go from 12.0% to 0.12) then you add on 1 to get 1+0.12 = 1.12

Another way to think about it is to have 100% + 12% = 112%, so the new price is 112% of the old price. For example, if the car was $100 and you increase the price by 12%, then it jumps to $112. Notice how 1.12*(old price) = 1.12*100 = 112 = new price

3x + 5x = 8x

2n - 3n = - n

4c + c - 7c = 5c - 7c = - 2c

4x - 6x + x - 5x = - 2x + x - 5x = - x - 5x = - 6x

3a + 2a + 7a - 5 = 5a + 7a - 5 = 12a - 5

235$ and if you withdraw 20$ on three days thats 60$ so if we remove that from the account we have 175$ left.

Then on Friday when he got paid he put 130$ into the bank he has 175+130=305$

If he wrote a check 1 for 167$ and 1 for 212$ thats his account balance - 212 then -167 = 305 -378 so he has a balance of -73

The checking balance after writing the checks is -$74.

To calculate the checking balance after writing the checks, we need to keep track of George's transactions:

To find the final balance, we add the positive values (deposits) and subtract the negative values (withdrawals and checks):

Starting balance ($235) + Deposits ($130) - Withdrawals ($60) - Checks ($167 + $212) = $235 + $130 - $60 - $167 - $212 = -$74

Therefore, the checking balance after writing the checks is -$74.

That's a trap ezoid , lower base b = 4 - -4 = 8, upper base B = 3 - -3 = 6 and height h = 2 - -2 = 4.

[tex]A = \frac 1 2 (b+B) h = \frac 1 2 (8 + 6)(4) = 28[/tex]

Answer: 28

The number of cabinets he must sell to breakeven is 9.

Breakeven is when the total cost and the revenue is zero. At the breakeven point, profit is zero.

Breakeven : total cost = revenue

1800 + 400x = 600x

In order to determine the value of x, take the following steps:

Combine similar terms:

1800 = 600x - 400x

Add similar terms together

1800 = 200x

Divide both sides of the equation by 200

x = 1800 / 200

x = 9

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To break-even, John Thunderhawk must sell 9 cabinets. After selling 9 cabinets, his revenue will start exceeding his costs, allowing him to make a profit.

The break-even point occurs when the total cost is equal to the total revenue.

We can find this point by setting the cost equation and the revenue equation equal to each other and solving for x :

Set the cost and revenue equations equal :

  Given that the cost equation is y = 1,800 + 400x, and the revenue equation is y = 600x , set these two equations equal to find the break-even point:

[tex]\[ 1,800 + 400x = 600x. \][/tex]

Rearrange the equation :

  Subtract 400x from each side:

 [tex]\[ 1,800 = 200x. \][/tex]

Solve for x :

  Divide by 200 to isolate x :

 [tex]\[ x = \frac{1,800}{200} = 9. \][/tex]

Therefore, to break-even, John Thunderhawk must sell 9 cabinets. After selling 9 cabinets, his revenue will start exceeding his costs, allowing him to make a profit.

Question :

John Thunderhawk is making furniture. He finds that to design a particular cabinet and set up his shop to produce it costs $1,800. Then the labor and supplies to build each one are $400. So his cost, y, for x items is represented by y=1,800 + 400x. He can sell the cabinets for $600. So his revenue, y, is represented by y=600x. The solution to this system of equations is his break-even point, the point beyond which he starts making a profit. How many cabinets must he sell to break-even?

[tex]y^2-16=y^2-4^2=(y-4)(y+4)\\\\\text{used}\ a^2-b^2=(a-b)(a+b)[/tex]

Givens

The cost of one piece of new equipment = 400

The number of new items needed = 4

Cost of one month's use = 35 dollars.

Income from 1 month's use = y

Number of members = x

Problem

Robert, the owner of a gym on the coast of Louisiana, has to replace 4 machines after a hurricane came through. Each machine costs 400. The gym cannot operate without these 4 machines. The gym will be be down for 1 month. He has x members who each pay 35 dollars for the use of the gym for a month. What is the total amount (y), that he is "out" for the month.

y = 35x + 400*4.

find c when D=12: First you have to plug in the number so if d=12 the you do c=12(1.5) which equals 18. C=18

Find d if C=15: you now have to do the inverse operation. if c=d1.5 then d= c/1.5 Then plug in the numbers again, d=15/1.5  it equals 10, so d=10

I hope this helps (:

5.93 * 10^(-5) Hope this Helps

0000593

thats the answer

Answer:

The inequality will be:  [tex]x<560[/tex] , where [tex]x[/tex] is the distance of the retail outlets from the warehouse.

Step-by-step explanation:

For a one-way trip, the trucking company charges a flat rate of $250 per truck, plus $1.25 for every mile driven.

Suppose, the number of miles driven is  [tex]x[/tex]

So, the charge for  [tex]x[/tex] miles will be:  [tex]\$1.25x[/tex]

and the total charge for a one-way trip will be:  [tex]\$250+\$1.25x[/tex]

Given that, the apparel company has a budget of less than $950 per trip.

So, the inequality will be.........

[tex]250+1.25x<950\\ \\ 1.25x<950-250\\ \\ 1.25x<700\\ \\ x<\frac{700}{1.25}\\ \\ x< 560[/tex]

Thus, the retail outlets which are less than 560 miles away from warehouse can be serviced with the given requirements.

Answer:

7719 = 3*31 * 83

Step-by-step explanation:

Because 93 can be factored down further. It is 31*3. So the prime factorization of

7719: 83 * 31 * 3

83 is a prime. It cannot be broken down any further.

To solve this problem you must apply the proccedure shown below:

1. You have the following formula given in the problem above:

[tex]PV=nRT[/tex]

3. Then, to solve for P you only need to move V  from the left member to the right member. V is multiplying P, therefore, it will divide [tex]nRT[/tex], as you can see below:

[tex]PV=nRT\\P=\frac{nRT}{V}[/tex]

Therefore, the answer is: [tex]P=\frac{nRT}{V}[/tex]

the answer is 2362 1/2 minutes

To find out how long each member of the committee will have to spend making flowers, we need to divide the total time needed to make the flowers by the number of committee members.

To find out how long each member of the committee will have to spend making flowers, we need to divide the total time needed to make the flowers by the number of committee members.

Each flower takes 4 1/2 minutes to make, so the total time needed is 525 * 4 1/2 minutes. We can convert 4 1/2 minutes to 4.5 minutes, and then multiply it by 525 to get the total time needed.

Finally, we can divide the total time by the number of committee members (6) to find out how long each member will have to spend making flowers.

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Answer:

1)[tex]10^{-1}[/tex]

2)[tex]2^{-2}[/tex]

3)[tex]12^{-2}[/tex]

Step-by-step explanation:

Using negative exponent rule:

1) one -tenth of kilometer =.1 =[tex]\frac{1}{10}=10^{-1}[/tex]

Using negative exponent rule:

2) [tex]\frac{1}{4} =\frac{1}{2^{2} }=2^{-2}[/tex]

Using negative exponent rule:

3)[tex]\frac{1}{144} =\frac{1}{12^{2} }= 12^{-2}[/tex]

Answer is -23

Add 4 from both sides

Subtract 5 from both sides

Then divide 7

To get rid of the parantheses we must multiply -4 times anything inside the parantheses.

-4(7x+5)=-160

-28x-20=-160

Add 20 to both sides of the equation.

-28x-20=-160

-28x=-140

Divide both sides by -28

-28x/-28=-140/-28

x=5

Our final answer is 5

Hope this helps!