The volume, V, of a cube with edge length s cm is given by the equation V=s3.Is the volume of a cube with edge length s=3 greater or less than the volume of a sphere with radius 3?If a sphere has the same volume as a cube with edge length 5, estimate the radius of the sphere?Compare the outputs of the two volume functions when the inputs are 2?

we have the exponential formula

so

we have

A=182 million ------> initial value (value of P when the value of t=0)

The year 1994 is when the value ot t=0

so

year 2002 -----> t=2002-1994=8 years

For t=8 years, P=186 million

substitute the value of A in the formula

Now

substitute the values of t=8 years, P=186 million

the formula is equal to

Estimate the population in 2004

t=2004-1994=10 years

substitute the value of t in the formula

therefore

The percentage change can be found below

Since the percentage is negative, this means there is a 60% decrease.

Given the equation:

Multiplying both sides by 2

So, the answer will be option B) 12

We have the next system of equations

We can sum both equations we can eliminate one variable

then we isolate the x

Therefore x=-1 then we substitute the value of x in order to find the value of y in the second equation

Then we simplify

Then we isolate the y

ANSWER

x=-1

y=0

The inverse function table of the function is given by the image at the end of the answer.

A function y = f(x) is composed by the following set of cartesian points:

(x,y).

In the inverse function, the input of the function represented by x and the output of the function represented by y are exchanged, meaning that the coordinate set is given by the following rule:

Thus, the points that will belong to the inverse function table are given as follows:

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Answer:

[tex]\begin{array}{|c|c|c|c|c|}\cline{1-5} \vphantom{\dfrac12} x &-8 &-4.5 & -4&0 \\\cline{1-5} \vphantom{\dfrac12} f^{-1}(x) &-2 & -1& 0&2 \\ \cline{1-5}\end{array}[/tex]

Step-by-step explanation:

The inverse of the graph of a function is its reflection in the line y = x.

Therefore, the mapping rule to find the inverse of the given ordered pairs is:

Therefore:

Completed table:

[tex]\begin{array}{|c|c|c|c|c|}\cline{1-5} \vphantom{\dfrac12} x &-8 &-4.5 & -4&0 \\\cline{1-5} \vphantom{\dfrac12} f^{-1}(x) &-2 & -1& 0&2 \\ \cline{1-5}\end{array}[/tex]

Given:

The number of quarters = 27

The number of dimes = 21

The number of Nickels = 24

The number of Pennies = 28

Required:

Find the probability to obtain a penny.

Explanation:

The total number of coins = 27 + 21 + 24 +28 = 100

The probability of an event is given by the formula:

The number of penny = 28

Final Answer:

The probability of obtaining Penny is 0.28.

Input data

7h + 3

Procedure

A term is a single mathematical expression.

3 = is a single term.

It is simply a numerical term called a constant.

7h = is also a single term. , The coefficient of the first term is 7

For the given polynomial the roots can't have multiplicity, and the polynomial is:

p(x) = (x - 2)*(x - 3)*(x - 5).

Here we know that we have a cubic polynomial (of degree 3) with the following zeros:

2, 3, and 5.

Can any of the roots have multiplicity?

No, because a cubic polynomial can have at maximum 3 zeroes, and here we already have 3.

Now let's get the polynomial

Remember that a cubic polynomial with zeros a, b, and c can be written as:

p(x) = (x - a)*(x - b)*(x - c)

Then the polynomial in this case is:

p(x) = (x - 2)*(x - 3)*(x - 5).

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Consider the given function,

Solve for x=-3 as,

Thus, the value of f(-3) is 0.2987 approximately.

Solve for x=-1 as,

Thus, the value of f(-1) is 2.2073 approximately.

Solve for x=0 as,

Thus, the value of f(0) is 6 .

Solve for x=1 as,

Thus, the value of f(1) is 16.3097 approximately.

Solve for x=3 as,

Thus, the value of f(3) is 120.5132 approximately.

we have:

general members are excluded then

answer: 330

Add the two expressions together;

The first option is the correct answer

Part 1:

The probability that a single randomly selected value is greater than 231.1 equals one minus the probability that it is less or equal to 231.1:

P(x > 231.1) = 1 - P(x ≤ 231.1)

Now, to find P(x ≤ 231.1), we can transform x in its correspondent z-score, and then use a z-score table to find the probability:

x ≤ 231.1 => z ≤ (231.1 - 203.6)/35.5, because z = (x - mean)/(standard deviation)

z ≤ 0.775 (rounding to 3 decimal places)

Then we have:

P(x ≤ 231.1) = P( z ≤ 0.775)

Now, using a table, we find:

P( z ≤ 0.775) ≅ 0.7808

Then, we have:

P(x > 231.1) ≅ 1 - 0.7808 = 0.2192

Therefore, the asked probability is approximately 0.2192.

Part 2

For the next part, since we will select a sample out of other samples with size n = 16, we need to use the formula:

z = (x - mean)/(standard deviation/√n)

Now, x represents the mean of the selected sample, which we want to be greater than 231.1. Then, we have:

z = (231.1 - 203.6)/(35.5/√16) = 27.5/(35.5/4) = 3.099

P(x > 231.1) = 1 - P(x ≤ 231.1) = 1 - P(x ≤ 231.1) = 1 - P( z ≤ 3.099) = 1 - 0.9990 = 0.0010

Therefore, the asked probability is approximately 0.0010.

Given:-

A survey on the nationality of the student in the St Thomas international school is conducted and the results are shown.

To find if two students are randomly selected, what is the probability that both of them are European and if one student is randomly selected, what is the probability that a student is not Asian.

So now the total number of students are,

So now the probability of getting European is,

So the probability is,

So now the probability is asian is,

So the probability that it is not asian is,

so the required probability is,

Answer: We have to find three unknown asked quantities, before we could do that we must find the g(x) from the coordinate points:

The answers are as follows:

The last answer is:

start identifying the slope and y-intercept for each high school.

The slope represents the growth for each year, in this case for high school A is 25 and for high school B is 50.

The y-intercept is the number of students that are enrolled currently, in this case for A is 400 and for B is 250.

The complete equations in the slope-intercept form are

Continue to graph the equations

High school B is projected to have more students in 8 years.

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

Line A:

point 1 (2,7)

point 2 (-1,10)

Line B:

point 1 (-4,7)

point 2 (-1,6)

Line C:

point 1 (6,5)

point 2 (7,9)

Step 02:

perpendicular lines:

slope of the perpendicular line, m’

m' = - 1 / m

Line A:

slope:

Line B:

slope:

Line C:

slope:

m' = - 1 / m ===> none of the slopes meet the condition

The answer is:

there are no perpendicular lines

Answer:

9x+b

Step-by-step explanation:

First, we need to calculate the total earned during the three days, so we need to sum 20.56, 32.90, and 20.78 as:

So, the total earned is 74.24, then half of 74.24 is calculated as:

If he spends the half, he has left the half. Therefore, he has left 37.12

Answer: 37.12

The next figure illustrates the problem

x is computed as follows:

tan(12°) = opposite/adjacent

tan(12°) = 2/x

x = 2/tan(12°)

x = 9.4 ft

y is computed as follows:

sin(12°) = opposite/hypotenuse

sin(12°) = 2/y

y = 2/sin(12°)

y = 9.6 ft

Given:

There are given the function:

Explanation:

According to the question:

We need to draw the graph of the given equation:

So,

The graph is:

vertical asymptotes are (-1,1)

And,

The horizontal asymptotes is

y = 0.

Hey there!

[tex]g+6g\\g=9,h=4[/tex]

[tex]4(h)+6(9(g))[/tex]

[tex]4+6(9)[/tex]

[tex]=58[/tex]

Hope this helps!

Answer:-0.4545555...,-0.453333...,-0.45222.....

hope i helped

Step-by-step explanation:

Answer: D(12)

Step-by-step explanation: To find the opposite it the number you would do -12= -12 x -1 = 12

Given two matrices

We will solve for the resultant matrix -B - 1/2A.

This operation is represented as

Let's simplify the matrices further based on scalar operations that can be done here. The B matrix will be multiplied by -1 while the A matrix will be multiplied by 1/2. We now have

Now, we apply the subtraction of matrices to the simplified matrix operation above. We have

Hence, the resulting matrix for the operation -B - 1/2A is

Step 1

Given;

Required; To find the zeroes by factoring

Step 2

Find two factors that when added gives -5x and when multiplied give -6x

Factoring we have and replacing -5x with -6x and x we have

Graphically the x-intercepts are;

The x-intercepts are;-1/3,2

Hence, the answer is the zeroes and x-intercepts are the same, they are;

Answer: serbia

Step-by-step explanation:

According to the problem, the length is 60 cm and the width is 450 mm.

Let's transform 450mm to cm. We know that 1 cm is equivalent to 10 mm. So,

Then, we use the perimeter formula for rectangles.

Where w = 45 cm and l = 60 cm.

However, we know that 1 meter is equivalent to 100 centimeters.

Hence, the perimeter, in meters, is 2.1 meters long.

The scale factor is basically by what we need to multiply the original to get the dilated one.

Simple.

We can see that the original one is Trapezoid WXYZ and the dilated one is W'X'Y'Z'.

THe dilated trapezoid is definitely bigger than original. So the scale factor should be larger than 1.

One side of original is "6" and the corresponding side of dilated trapezoid is "14".

So, what we have to do to "6", to get "14"??

This is the scale factor!

To get 14, we have to multiply 6 with, suppose, "x", so:

Hence, SF is 7/3