The table shows the percentage of students in each of three grade levels who list soccer as their favorite sport. Soccer Sophomores (35%) 50%
Juniors (33%) 45%
Seniors (32%) 30%
Total (100%) (0.5)(0.35) + (0.45)(0.33) + (0.32)(0.3) = 0.4195 or about 42%
Find the probability that the student is a junior, given that soccer is the favorite sport listed.
P(junior | soccer) = ???%

Answer: [tex] fg(x)=4x^3+12x^2-5x-15[/tex]

Step-by-step explanation:

Given: [tex]f(x)=4x^2-5\text{ and } g(x)=x+3[/tex]

We know that for any function f(x) and g(x), the multiplication function (fg) (x) is given by :-

[tex]fg(x)=f(x)g(x)[/tex]

Now, for the given functions, we have

[tex]fg(x)=(4x^2-5)(x+3)\\\\\Rightarrow\ fg(x)=4x^2(x+3)-5(x+3)\\\\\Rightarrow\ fg(x)=4x^3+12x^2-5x-15[/tex]

Answer: V = 2712.94 cubic inches.

Step-by-step explanation: The prop is formed with two objects: cone and half of a sphere. To calculate the volume, find the volume of the cone and the half-sphere and add them together.

Volume of Cone:

V₁ = [tex]\frac{1}{3}.B.h[/tex]

B is area of the base

h is height

Since the cone has its base as a circle, the volume will be:

V₁ = [tex]\frac{1}{3}[/tex].π.[tex]r^{2}[/tex].h

V₁ = [tex]\frac{1}{3}[/tex] . 3.14 . [tex]9^{2}[/tex] . 14

V₁ = 1186.9 cubic inches

Volume of Half-Sphere:

V₂ = [tex]\frac{2}{3}[/tex].π.[tex]r^{3}[/tex]

V₂ = [tex]\frac{2}{3}[/tex] . 3.14 . [tex]9^{3}[/tex]

V₂ = 1526.04 cubic inches

Total Volume:

V = V₁ + V₂

V = 1186.9 + 1526.04

V = 2712.94 cubic inches

The volume of the prop is V = 2712.94 cubic inches

To find the number of students in a group who spent a total of $15.20, with each student spending $1.90, divide the total amount by the amount each student spent, resulting in 8 students.

The question asks how many students were in a group if they spent $15.20 altogether, with each student spending $1.90. To find the number of students, divide the total amount spent by the amount each student spent. This calculation is performed by dividing $15.20 by $1.90.

Calculation: $15.20 ÷ $1.90 = 8 students

Therefore, there were 8 students in the group.

Answer:

[tex]\texttt{Probability}=\frac{3}{25} [/tex]

Step-by-step explanation:

Probability is the ratio of number of favorable outcome to total number of outcomes.

Total number of socks = 4 + 3 + 3 = 10

Number of blue socks = 3

Number of red sock = 4

[tex]\texttt{Probability of selecting blue sock}=\frac{3}{10} \\ [/tex]

[tex]\texttt{Probability of selecting red sock}=\frac{4}{10} \\ [/tex]

For finding the combined probability we need to multiply both the values

[tex]\texttt{Probability that the first sock is blue and the second sock is red}=\frac{3}{10}\times \frac{4}{10}=\frac{12}{100}=\frac{3}{25} \\ [/tex]

[tex]\texttt{Probability}=\frac{3}{25} [/tex]

The average rate of change of the function over the interval is 3

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

f(x) = 6 + 3x

The interval is given as

From x = 1 to x = 8

The function is a linear function

This means that it has a constant average rate of change

So, we have

f(1) = 6 + 3(1) = 9

f(8) = 6 + 3(8) = 30

Next, we have

Rate = (30 - 9)/(8 - 1)

Evaluate

Rate = 3

Hence, the rate is 3

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Question

Find the average value gave of the function g on the given interval. g(x) = 6 + 3x , [1, 8]

Answer:

the correct answer is 18 i hope this helps you

The length of each edge of a cube with a total surface area of 486 square units is 9 units, obtained by dividing the total surface area by 6 to get the area of one face and then taking the square root.

To find the length of each edge of a cube when you have the total surface area, you need to understand that a cube has 6 faces that are all squares of the same size. Since the total surface area of the cube is given as 486 square units, we can find the area of one face by dividing the total surface area by 6. Once we have the area of one face, we can find the length of one edge by taking the square root of that area because the area of a square is equal to the length of one side squared (Area = side x side).

Let's calculate:

Therefore, the length of each edge of the cube is 9 units.

Answer:

The answer is C: rw ◦ RM,180°

Step-by-step explanation:

I had this question on edge

Answer:

One of this ordered pairs: [tex]\left ( 1,3 \right )\,,\,\left (1 ,-2 \right )[/tex] should be removed

Step-by-step explanation:

A relation f is said to be a function if for each and every element of it's domain there exists a unique image in it's codomain.

As per the graph, ordered pairs are [tex]\left ( 1,3 \right )\,,\,\left ( 2,1 \right )\,,\,\left ( -2,2 \right )\,,\,\left (1 ,-2 \right )\,,\,\left ( 5,-4 \right )\,,\,\left ( -4,-4 \right )\,,\,\left ( -5,-3 \right )[/tex]

Here,  all the ordered pairs have unique image except [tex]\left ( 1,3 \right )\,,\,\left (1 ,-2 \right )[/tex]

Here , element 1 of domain has two images 3 and - 2 .

We know that as per definition for each and every element of the domain there should be a unique image in the codomain.

So, one of this ordered pairs: [tex]\left ( 1,3 \right )\,,\,\left (1 ,-2 \right )[/tex] should be removed in order to make it a function.

The correct step in the expansion of (x+y)^4 is to determine the coefficients for each term using the binomial formula.

The correct step in the expansion of (x+y)^4 using the binomial formula is to determine the coefficients for each term.

In this case, the coefficients can be found using the formula n choose k, where n is the exponent (4) and k is the power of either x or y in each term.

For example, the term with x^3*y would have a coefficient of 4 choose 3, which is equal to 4.

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The best answer for these question would be:

A. Flipping two coins and having one show a head and the other show a head

D. Rolling a 4 on one die and rolling a 2 on another die

E. Seeing clouds and winning the lottery

Independent events in math means that the first situation does not affect the other variable. It is generally the individual probability that will happen to the solution. Which means that you have to determine whether the first situation will be affected on the second events that will happen. While the dependent events, have the opposite effect.

Answer:

(1 pt) ~2,6,7~

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

Given : The supply function for baseball caps is P=Q-6, where P is the price and Q is the quantity of baseball caps.

To Find: If Michelle sells the baseball caps for $19 apiece, how many baseball caps will the store make?

Solution:

The supply function for baseball caps is P=Q-6

where P is the price

Q is the quantity of baseball caps.

Now we are given that Michelle sells the baseball caps for $19 a piece.

So, P = 19

Substitute the value in the function:

19=Q-6

19+6=Q

25 =Q

Thus If Michelle sells the baseball caps for $19 apiece, the store make will make 25 baseball caps .

The original problem is translated into a quadratic equation. By following the process of expanding, moving all terms to one side and solving the resulting equation yield the overall possible solutions x = 4 or x = 1.

The question is asking to solve for a number based on a given condition. In this case, let's symbolize this unknown number with x. The problem can be written as an algebraic equation which is (x-9)^2 = x-3. You solve it first by expanding the equation, then move all terms to one side of the equation, to get a quadratic equation. Then, solve the quadratic equation to get the possible values of x. If you follow these steps, you will find that the possible solutions for this equation are x = 4 or x = 1.

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