Matt has $550 in his savings account. He is eager to know how much interest the bank will pay him for the whole year. He knows that the bank pays a 3 percent interest rate. He sits down with a pen, paper, and calculator to find out the simple interest

The ratio of the volume of the smaller sphere to the volume of the larger sphere, given their surface areas are 256 ft² and 576 ft², is 8:27.

The student has asked about finding the ratio of the volumes of two similar spheres given their surface areas. The surface areas are 256 ft² and 576 ft². To find the volume ratio, we need to use the fact that the ratio of the surface areas of similar spheres is the square of the ratio of their radii, and thus the ratio of the volumes will be the cube of the ratio of their radii.

Let's denote the surface areas as S₁ and S₂, and the volumes as V₁ and V₂. Then, S₁:S₂ = (radius of smaller sphere)² : (radius of larger sphere)² and V₁:V₂ = (radius of smaller sphere)³ : (radius of larger sphere)³.

First, we find the square root of the surface area ratios: [tex]\sqrt{\frac{256}{576} }[/tex] = [tex]\frac{16}{24}[/tex] = [tex]\frac{2}{3}[/tex]. Then, taking the cube of [tex]\frac{2}{3}[/tex] gives us the volume ratio V₁:V₂ = [tex](\frac{2}{3} )^3[/tex] = [tex]\frac{8}{27}[/tex].

Therefore, the ratio of the volume of the smaller sphere to the volume of the larger sphere is 8:27.

1. Changing f(x) to f(x) + 1 adds 1 to every output value of the function, moving that value "1 space higher". This is true for the y-intercept, too.

___

2. The rules of exponents apply:

You apparently want to simplify ...

... 9^(1/4) × 9^(1/2) / 9^(5/4)

... = 9^(1/4 + 1/2 - 5/4)

... = 9^((1+2-5)/4)

... = 9^(-2/4) = 9^(-1/2)

The first step is calculate the surface area of the flat surface shown

Surface area of the rectangle = length * width = 25*12.9 = 322.5 square feet

Surface area of the triangle = 1/2 *base*height = 1/2*25*7.2 = 90 square feet

Total surface area = 322.5 +90 = 412.5 square feet

Total force = 0.004*a*v^2 = 0.004*412.5*81^2 = 10,825.65 pounds

Answer:

The correct option is B.

Step-by-step explanation:

A function is called an exponential function if it has common ratio.

A function is called an linear function if it has common difference.

In option A.

[tex]\frac{f(2)}{f(1)}=\frac{6}{3}=2[/tex]

[tex]\frac{f(3)}{f(2)}=\frac{9}{6}=\frac{3}{2}[/tex]

[tex]2\neq \frac{3}{2}[/tex]

Since the given table has different ratio, therefore it is not an exponential function. Option A is incorrect.

In option B.

[tex]\frac{f(2)}{f(1)}=\frac{6}{2}=3[/tex]

[tex]\frac{f(3)}{f(2)}=\frac{18}{6}=3[/tex]

[tex]3=3[/tex]

Since the given table has common ratio, therefore it is an exponential function. Option B is correct.

In option C.

[tex]\frac{f(2)}{f(1)}=\frac{22}{10}=\frac{11}{5}[/tex]

[tex]\frac{f(3)}{f(2)}=\frac{34}{22}=\frac{17}{11}[/tex]

[tex]\frac{11}{5}\neq \frac{17}{11}[/tex]

Since the given table has different ratio, therefore it is not an exponential function. Option C is incorrect.

In option D.

[tex]\frac{f(2)}{f(1)}=\frac{8}{7}[/tex]

[tex]\frac{f(3)}{f(2)}=\frac{9}{8}[/tex]

[tex]\frac{8}{7}\neq \frac{9}{8}[/tex]

Since the given table has different ratio, therefore it is not an exponential function. Option D is incorrect.

Answer:

Table B represents an exponential function.

Step-by-step explanation:

An exponential function is a function which has common ratio. Using this fact we will evaluate the functions given in the form of a table.

Table A.

f(1) = 3

f(2) = 6

f(3) = 9

Now [tex]\frac{f(2)}{f(1)}=\frac{6}{3}=\frac{2}{1}[/tex]

[tex]\frac{f(3)}{f(2)}=\frac{9}{6}=\frac{3}{2}[/tex]

Ratios are not equal so it's not an exponential function.

Table B.

f(1) = 2

f(2) = 6

f(3) = 18

[tex]\frac{f(2)}{f(1)}=\frac{6}{2}=\frac{3}{1}[/tex]

[tex]\frac{f(3)}{f(2)}=\frac{18}{6}=\frac{3}{1}[/tex]

Here ratios are same therefore it's an exponential function.

Table C.

f(1) = 10

f(2) = 22

f(3) = 34

[tex]\frac{f(2)}{f(1)}=\frac{22}{10}=\frac{11}{5}[/tex]

[tex]\frac{f(3)}{f(2)}=\frac{34}{22}=\frac{17}{11}[/tex]

Ratios are not equal therefore it's not an exponential function.

Table D.

f(1) = 7

f(2) = 8

f(3) = 9

[tex]\frac{f(2)}{f(1)}=\frac{8}{7}[/tex]

[tex]\frac{f(3)}{f(2)}=\frac{9}{8}[/tex]

Ratios are not equal so it's not an exponential function.

Therefore Table B is the correct option.

Answer:72.03

Step-by-step explanation:

Answer: The probability of hitting an odd number three times is [tex]3\dfrac{3}{8}[/tex] times more than the probability of hitting an even number 3 times.

Step-by-step explanation:

From the given picture , the total total number of sections in the spinner = 5

Sections having Odd numbers = 3

Sections having Even numbers =2

We know that , [tex]\text{Probability}=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]

So , probability of hitting an odd number = [tex]\dfrac{3}{5}[/tex]

Probability of hitting an even number = [tex]\dfrac{2}{5}[/tex]

Since all events are independent of each other ,

So , probability of hitting an odd number three times = [tex](\dfrac{3}{5})^3=\dfrac{27}{125}[/tex]

Probability of hitting an even number three times = [tex](\dfrac{2}{5})^3=\dfrac{8}{125}[/tex]

Divide  [tex]\dfrac{27}{125}[/tex] by [tex]\dfrac{8}{125}[/tex] , we get

[tex]\dfrac{27}{125}\div\dfrac{8}{125}\\\\=\dfrac{27}{125}\times\dfrac{125}{8}=\dfrac{27}{8}=3\dfrac{3}{8}[/tex]

Hence, the probability of hitting an odd number three times is [tex]3\dfrac{3}{8}[/tex] times more than the probability of hitting an even number 3 times.

Answer:

3.375

Step-by-step explanation:

Answer:

  (-5/2, 3/2)

Step-by-step explanation:

The midpoint is the average of the coordinates of the endpoints:

  (P +Q)/2 = ((-2, 1) +(-3, 2))/2 = (-2-3, 1+2)/2 = (-5/2, 3/2)

We have that for the Question "each of 5 boys ate 2/3 of a pizza. what is the total amount of pizza the boys ate?" it can be said that each boy ate

From the question we are told

Generally the equation for the total amount of pizza the boys ate  is mathematically given as

Pt=N*Ratio

Therefore

Pt=5*2/3

Pt=3.333pizza

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The total sum of money will be $320.

Let the total sum of money be represented by x.

Based on the information given, the equation to solve the question will be:

12 1/2% × x = 40

0.125x = 40

Divide by 0.125

x = 40/0.125.

x = 320

Therefore, the total sum of money will be $320.

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Answer: 156 square feet of carpet would be needed to cover the floor in his room.

Step-by-step explanation:

Since we have given that

Dimensions of his room as follows :

Length of his room = 13 feet

Width of his room = 12 feet

We need to find the square feet of carpet which is used to cover the floor of his room.

so, we just need to find the area of his room.

Area of rectangle = Length × Breadth

So, Area of his room becomes

[tex]13\times 12\\\\=156\ sq.\ feet[/tex]

Hence, 156 square feet of carpet would be needed to cover the floor in his room.

Total Members = 15

For electing present number of members = 15

For electing treasurer the numbers of members =14

For electing secretary the numbers of members =13

Find the numbers of possible ways for election of members= ?

Possible ways for election =15*14*13

                                                 =2730

The sum of the series is 28.

The series 13 + 9 + 5 + 1 is an arithmetic series with a common difference of -4. To express this in summation (sigma) notation and find its sum, we first identify the first term (a1) as 13 and the common difference (d) as -4.

Next, we determine the number of terms (n). The series decreases by 4 each time, so we find the number of steps it takes to go from 13 to 1, which are 4 terms in total (13, 9, 5, 1).

We can write the summation formula for an arithmetic series as Sn = n/2 * (2a1 + (n-1)d), where Sn is the sum of the first n terms. With n = 4, a1 = 13, and d = -4, we plug these into the formula:

S4 = 4/2 * (2(13) + (4-1)(-4))

S4 = 2 * (26 - 12)

S4 = 2 * 14

S4 = 28

The sum of the series is 28.

Find the measure of the requested angle. find the complement of 41°.

Solution:

The Sum of Complementary Angles is 90°.

So, Sum of Requested Angle and Given Angle =90°

So,Requested Angle+Given angle=90°

So,Requested Angle+41°=90°

To find, Requested Angle we subtract 41° from both sides,

Requested Angle+41°-41°=90°-41°

Requested Angle+0°=49°

So, Requested Angle=49°

Answer:49°

To get it, combine like terms and restrain the variable. Segregating both sides by 3 gives the solution to the equation as v = -7.

To solve the condition 12 + 5v = 2v - 9, take after these steps:

Step 1: Segregate the variable terms on one side of the condition and the steady terms on the other side.

Subtract 2v from both sides to move the variable term to the cleared outside:

12 + 5v - 2v = 2v - 9 - 2v

Alter both sides of the condition:

12 + 3v = -9

Step 2: Separate the variable term by moving the reliable term to the other side.

Subtract 12 from both sides to move the dependable term to the proper side:

12 + 3v - 12 = -9 - 12

Unwind both sides of the condition:

3v = -21

Step 3: Light up for v by confining both sides of the condition by the coefficient of v, which is 3.

Portion by 3 to clarify for v:

v = -21 / 3

Streamline the division:

v = -7

The solution to the equation is v = -7.

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Answer:

7 ab ( 8 ab² - 5 ) .

Step-by-step explanation:

Given  : 56 a²b³ − 35 ab.

To find : Factor completely.

Solution : We have given 56 a²b³ − 35 ab.

Taking 7ab common form both terms .

7 ab ( 8 ab² - 5 ) .

Therefore, 7 ab ( 8 ab² - 5 ) .