The longer leg of a right triangle is 3 inches longer than the shorter leg. The hypotenuse is 6 inches longer than the shorter leg. Find the side lengths of the triangle.

The surface area of circle of radius 3 cm and cube of edge length x cm being equal implies [tex]x = \sqrt{k\pi}[/tex] integer (k = 6).

Suppose that radius of the considered sphere is of 'r' units.

Then, its surface area S would be:

[tex]S = 4\pi r^2 \: \rm unit^2[/tex]

Given that:

Finding the surface area of the considered cube and sphere:

Thus, we get:

[tex]6x^2 = 36\pi\\\\\text{Dividing both the sides by 6}\\\\x^2 = 6\pi\\\\\text{Taking root of both the sides}\\\\x = \sqrt{6\pi} \: \rm cm[/tex]

(took positive value out of the root since x cannot be negative as it represents length of the edge of a cube which cannot be a negative quantity).

Thus, the surface area of circle of radius 3 cm and cube of edge length x cm being equal implies [tex]x = \sqrt{k\pi}[/tex] integer (k = 6).

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[tex]\\\text{Side length of square A = a \text{ft}}\\\\\text{Side length of square B = b \text{ft}}\\\\ \text{Side length of square C = c \text{ft}}\\\\ \text{Given that,}\\\\\text{Area of square C} = 400 ~ \text{ft}^2\\\\\implies c^2=400~~~~~~......(i)\\\\\\\text{Perimeter of square B } = 64~ \text{ft}\\\\\implies 4b = 64\\\\\implies b = \dfrac{64}4\\\\\implies b = 16\\\\\implies b^2 = 256~~~~~~~.....(ii)\\\\\\[/tex]

[tex]\text{Applying Pythagorean theorem,}\\ \\~~~~~c^2 =a^2 +b^2\\\\\implies a = \sqrt{c^2 - b^2}\\ \\\implies a = \sqrt{400-256}\\\\\implies a = \sqrt{144}\\\\\implies a = 12[/tex]

[tex]\text{Hence, the side length of square A is 12 ft.}[/tex]

Answer:

3.4cm

Step-by-step explanation:

Multiply the 2 numbers 5x24=120 then u will solve trhe surface and V=bxh  so then u U will get that

Answer:

1/6

Step-by-step explanation:

Using proportions, it is found that the amount owed for each bill are given as follows:

$31.33 for food $9.90 for alcohol.

A proportion is a fraction of a total amount.

In this problem, each of the bills are split equally among the five people, hence the fraction is 1/5.

Thus:

1/5 x 156.65 = $31.33

1/5 x 49.50 = $9.90.

Hence the amount owed for each bill are given as follows:

$31.33 for food $9.90 for alcohol.

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The number of people at the party now is 23.

The percentage of a number is the fraction of that number multiplied by 100. Percentages are represented with this sign: %.

3 friends arrive at a party. The percentage of people increase by 20%.This can be represented with this equation:

p x 20% = 3 people

where p is the number of people at the party before the friends arrived.

p = 3 / 20%

p = 3 / 0.20

p = 15 people

The total number of people at the party now : 15 + 8 = 23.

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Answer:

-5,-4.9,-4.35,-4.3,-4

Step-by-step explanation:

Hope this helps :)

Answer:

0** (READ BELOW)

Step-by-step explanation:

First, solve for g(0). Since g(0) = 3x +2, we plug in 0 for x.

So,

g(0) = 3(0) + 2  = 0 + 2 = 2.

Now that we have an answer for g(0), we can plug it into f(x).

So,

f(x) = (x-2)/3

f(x) = f(g(0)) = f(2).

f(2) = (2-2)/3 = 0/3 = 0.

Thus, f(g(0)) = 0.

Essentially, you first solve for g(0) and use the answer from that to solve for f(x) where x is your answer from g(0).

**I was unsure of what the equation was for f(x) based on how you wrote it in the question, but I assumed it was f(x) = (x-2)/3.

The square cake can be distributed in such a way that each person out of 15 guest may get 8  [tex]inch^{3}[/tex], with the least amount left over .

The Correct option is (1).

The volume of an object is the amount of space occupied by the object or shape, which is in three-dimensional space. It is usually measured in terms of cubic units.

First find the volume of square cake,

= 8 x 8 x 2

=128 [tex]inch^{3}[/tex]

Now there are total 15 guests, Each of get

=[tex]\frac{128}{15}[/tex]

=  8.533 [tex]inch^{3}[/tex]

 2.Volume of round cake (d= 6 inch, r=3 inch, h= 3 inch)

Volume= [tex]\frac{1}{3} \pi r^{2} h[/tex]

= [tex]\frac{1}{3} *3.14 *3^{2}* 3[/tex]

=[tex]3.14*9[/tex]

=28.26  [tex]inch^{3}[/tex]

Now there are total 15 guests, Each of get

=[tex]\frac{28.26}{15}[/tex]

= 1.884[tex]inch^{3}[/tex]

 3.Volume of round cake (d= 8 inch, r=4inch, h= 3 inch)

Volume= [tex]\frac{1}{3} \pi r^{2} h[/tex]

= [tex]\frac{1}{3} *3.14 *4^{2}* 3[/tex]

=[tex]3.14*16[/tex]

=50.24   [tex]inch^{3}[/tex]

Now there are total 15 guests, Each of get

=[tex]\frac{50.24}{15}[/tex]

=  3.349 [tex]inch^{3}[/tex]

 4. Volume = l x b x h

= 6 x 9 x 2

=108 [tex]inch^{3}[/tex]

Now there are total 15 guests, Each of get

=[tex]\frac{108}{15}[/tex]

=  7.2[tex]inch^{3}[/tex]

According to question each person may get 8 [tex]inch^{3}[/tex].

Only the square cake can be distributed in such a way that each person may get 8 [tex]inch^{3}[/tex], with the least amount left over .

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The linear regression equation that estimates the heart rate per number of jumping jacks is: y=1.72x + 69.4; the correlation coefficient of the linear regression equation is 0.97.

a. Linear regression equation:

We would make used of graphing calculator in order to determine the linear regression equation by plugging the below given data and then  click on stats  so as to perform a linear regression.

Given table:

(x, y), (0, 68), (10, 84), (15, 104), (20, 100), (30, 120)

Hence:

a = 1.72

b = 69.4

Equation

y = ax + b

y = 1.72x + 69.4

b. Correlation coefficient :

Correlation coefficient = 0.967

Correlation coefficient=0.97  (nearest hundredth)

Analysis:

The above correlation coefficient shows a strong positive correlation between the number of jumping jacks and the heart rate.

Therefore the linear regression equation that estimates the heart rate per number of jumping jacks is: y=1.72x + 69.4; the correlation coefficient of the linear regression equation is 0.97.

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Answer:

I really don't know happy

Answer:

single payment variable annuity

Step-by-step explanation:

Given : ABC Insurance offers an annuity with 4.5% APR for the next 5 years. You decide to invest $1000 each year into this account.

To find : What type of annuity is this?

Solution :

Annuity is the form of insurance in which some of the money is paid each year to secure for future.

There are two types of annuity:

Single payment variable annuity - In this annuity the payment is made at the end of each period  over a fixed length of time. Also in this annuity payments are made monthly, quarterly, semi-annually or annually.

Annuity due - is the opposite of single payment variable annuity as in this the payment is made at the beginning of each period.

In the given situation the annuity is single payment variable annuity because the investment is done each year for 5 years.

Answer: 2.5$

Step-by-step explanation: Since 1 hour is half of 2 hours and the price to park for 2 hours is 5. We can take half of the 2 hour parking price to find the 1 hour price.

5$/2 Hours = 2.5$ per hour

Answer:

Find each product.

1. (q + 6)(q + 5) 2. (x + 7)(x + 4)

q2 + 11q + 30 x2 + 11x + 28

3. (n - 4)(n - 6) 4. (a + 5)(a - 6)

n2 - 10n + 24 a2 - a - 30

5. (4b + 6)(b - 4) 6. (2x - 9)(2x + 4)

4b2 - 10b - 24 4x2 - 10x - 36

7. (6a - 3)(7a - 4) 8. (2x - 2)(5x - 4)

42a2 - 45a + 12 10x2 - 18x + 8

9. (3a - b)(2a - b) 10. (4g + 3h)(2g + 3h)

6a2 - 5ab + b2

8g2 + 18gh + 9h2

11. (m + 5)(m2 + 4m - 8) 12. (t + 3)(t2 + 4t + 7)

m3 + 9m2 + 12m - 40 t

3 + 7t

2 + 19t + 21

13. (2h + 3)(2h2 + 3h + 4) 14. (3d + 3)(2d2 + 5d - 2)

4h3 + 12h2 + 17h + 12 6d3 + 21d2 + 9d - 6

15. (3q + 2)(9q2 - 12q + 4) 16. (3r + 2)(9r2 + 6r + 4)

27q3 - 18q2 - 12q + 8 27r3 + 36r2 + 24r + 8

17. (3n2 + 2n - 1)(2n2 + n + 9) 18. (2t2 + t + 3)(4t2 + 2t - 2)

6n4 + 7n3 + 27n2 + 17n - 9 8t

4 + 8t

3 + 10t

2 + 4t - 6

19. (2x2 - 2x - 3)(2x2 - 4x + 3) 20. (3y2 + 2y + 2)(3y2 - 4y - 5)

4x4 - 12x3 + 8x2 + 6x - 9 9y4 - 6y3 - 17y2 - 18y - 10

GEOMETRY Write an expression to represent the area of each figure.

21.

4x + 2

2x - 2

22.

3x + 2

5x - 4

x + 1

23. NUMBER THEORY Let x be an even integer. What is the product of the next two

consecutive even integers?

24. GEOMETRY The volume of a rectangular pyramid is one third the product of the area of

its base and its height. Find an expression for the volume of a rectangular pyramid

whose base has an area of 3x2 + 12x + 9 square feet and whose height is x + 3 feet.

x3 + 7x2 + 15x + 9 ft3

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

Yes, since 21 has more than two factors i.e. 1, 3, 7, 21. In other words, 21 is a composite number because 21 has more than 2 factors.

Answer: 54 inch²

Step-by-step explanation:

The total surface area of the cube can simply be found by finding the area of one face and multiplying by 6 because the cube has 6 faces

Area of one face = 3 inch x 3 inch = 9 inch²

Total surface area of the cube = 9 inch² x 6 = 54 inch²

Answer:

28.9 units²

Step-by-step explanation:

The area of a rectangle formula with L being 8.5 units and B being 3.4 units, is 28.9 units². make sure to add the units squared, otherwise, it's wrong.

Always remember for area:

Hope this helps, if it is the best, mark brainliest, if not, hope it helps anyway.

Answer:

D. $17.28

Step-by-step explanation:

Multiply the price of gas per gallon by the number of gallons purchased to get your answer

2.469 x 7 = 17.28

Answer:

7 1/2 cups

Step-by-step explanation:

First, convert the measure of ice cream from pints to cups:

1 pint = 2 cups

⇒ 4 pints = 4 × 2 = 8 cups

Therefore,

Milkshake = 8 cups of ice cream + 1 1/2 cups of milk

                 = 9 1/2 cups

If he drinks 2 cups of milkshake:

Remaining milkshake = 9 1/2 - 2

                                    = 7 1/2 cups

1pint=2cups

Total cups:-

Cups left:-

Answer:

The nth terms: 15,24,33,42,51,60,69,78,87,96,105...

Step-by-step explanation:

The nth term of an arithmetic sequence is given by an = a + (n – 1)d. So, to find the nth term, substitute the given values a = 2 and d = 3 into the formula

Answer:

10 1/2 gallons = 42 quarts:)

Answer:

12.5

Step-by-step explanation:

25% means the 1/4th part of the whole number and in the case if 50 it's 1/4th part is 12.5

The total area of cardboard needed is equal to 121.34 square centimeters.

This is equal to the surface of the given chocolate.

First, we will have two sides that are rectangles measuring 16cm by 2.6cm, so the area is:

[tex]A = 16cm*2.6cm = 41.6cm^2[/tex]

Then we have another rectangular side which is the bottom one, that is a rectangle of 2.2cm by 16cm, so the are is:

[tex]A' = 2.2cm*16cm = 35.2cm^2[/tex]

Finally, we have the areas of the two triangular faces, the areas of these are:

[tex]A'' = 2.2cm*3cm/2 = 1.47cm^2[/tex]

Then the total area of cardboard needed is:

[tex]area = 2*A + A' + 2*A'' = 2*41.6cm^2 + 35.2cm^2 + 2* 1.47cm^2 = 121.34 cm^2[/tex]

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Answer:

Anything known? I mean the lenght of bottle or anything like that?

Answer:

option b is the correct answer of given statement

Step-by-step explanation:

percent of SSSSD strings

Answer:

step 1: 45:82, unsimplified

step 2: 67:90, unsimplified

Step 3: 1:10 simplified

Step-by-step explanation: Using the property of retrostatistical Ratios, we understand that the answers above are correct.

Answer:

The answer is 404

Step-by-step explanation:

multiply 36 by 6= 216

add 188= 404

she got $404.00

Answer: hii

Its A. x2−x+2−5x−1

Step-by-step explanation:

Divide using polynomial division.

Hopefully this helps you

- Matthew

Answer:

270

Step-by-step explanation: