william won 50 tickets at the arcade. he redeemed 30 tickets for a prize and gave 5 tickets to ketelyn. which expression can william use to find how many tickets he has left

The volume of the solid generated is 218.01 cubic units

The curves are given as:

[tex]y = 9x^3[/tex], y = 9

[tex]x = 0[/tex]

Start by calculating x at [tex]y = 9x^3[/tex]

Substitute 9 for y

[tex]9x^3 = 9[/tex]

Divide both sides by 9

[tex]x^3 = 1[/tex]

Take the cube roots of both sides

[tex]x = 1[/tex]

So, the equation of the volume is then represented as:

[tex]V = \pi \int\limits^a_b {9^2 - (9x^3)^2} \, dx[/tex]

[tex]V = \pi\int\limits^a_b {81 - 81x^6} \, dx[/tex]

Where [a,b] = [1,0]

So, we have:

[tex]V = \pi\int\limits^1_0 {81 - 81x^6} \, dx[/tex]

Factor out 81

[tex]V = 81\pi\int\limits^1_0 {1 - x^6} \, dx[/tex]

Integrate

[tex]V = 81\pi [x - \frac 17x^7]|\limits^1_0[/tex]

Expand

[tex]V = 81\pi ([1 - \frac 17(1)^7] - [0 - \frac 17(0)^7] )[/tex]

[tex]V = 81\pi ([1 - \frac 17] )[/tex]

[tex]V = 81\pi * \frac 67[/tex]

So, we have:

[tex]V = 81 * 3.14 * \frac 67[/tex]

[tex]V = 218.01[/tex]

Hence, the volume of the solid generated is 218.01 cubic units

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The answer should look something like this:

Answer:

She sent 8 more postcards last week.

Step-by-step explanation:

Consider the provided information.

Megan sent 12 postcards last week. This week she sent 4 postcards.

We need to find How many more postcards did she sent last week?

To find this simply subtract the numbers as shown:

12-4 = 8

Hence, she sent 8 more postcards last week.

Answer:

150 lbs

Step-by-step explanation:

set up proportion

400/120 = 500/x

cross multiply
120x500 = 400x

then simplify

60000 = 400x

solve for x

60000/400 = x

x = 150

The length of the shorter piece of wire is 12 cm, which is found by setting up the equation x + (x + 6) = 30, where x is the length of the shorter piece.

The student has asked to find the length of the shorter piece of wire when a 30 cm long wire is cut into two pieces, with the longer piece being 6 cm longer than the shorter piece. To solve this, we need to set up a simple equation based on the information given.

Let's represent the length of the shorter piece as x cm. Since the longer piece is 6 cm longer than the shorter piece, we can represent the longer piece as (x + 6) cm

We are told that the total length of the wire before it was cut was 30 cm. Therefore, the sum of the lengths of both pieces must equal 30 cm. This gives us the equation:

x + (x + 6) = 30

Simplifying the equation, we get:

2x + 6 = 30

Subtracting 6 from both sides of the equation gives us:

2x = 24

Dividing both sides by 2 to solve for x gives us:

x = 12

Answer:

Y-4 =2/5(x-(-2)) is answer on edge

Step-by-step explanation:

Use point slope equaction y-y1=m(x-x1)

y1= 4 x1= -2 and m= 2/5 just plug in numbers

The probability of drawing a green card on both the first and second draw, with replacement, is 25/64, as each draw is an independent event with the same probability of 5/8 for drawing a green card.

The problem is asking us to compute the probability of drawing two green cards in succession, with replacement, from a deck that contains eight cards of which five are green and three are yellow. Since the draws are independent and with replacement, the probability of an event occurring on the first draw is not affected by the second draw, and vice versa.

To calculate the probability of drawing a green card on the first draw, denoted as P(G₁), we look at the number of green cards and the total number of cards. There are 5 green cards out of 8 total cards, so P(G₁) = 5/8.

Because we are replacing the drawn card before the second draw, the probability of drawing a green card on the second draw, denoted as P(G₂), remains the same as for the first draw, thus P(G₂) = 5/8.

The probability of both events happening, denoted as P(G₁ and G₂), is the product of the individual probabilities since the draws are independent. Therefore, we have:

P(G₁ and G₂) = P(G₁) * P(G₂) = (5/8) * (5/8) = 25/64.

Yes, the equation has no answer, I took this and there was no solution. hope this helped

Option C correctly applies the Law of Syllogism. By combining the hypothesis from the first statement, 'If it is springtime, you will plant flowers in the garden' with the conclusion of the second, 'If you plant flowers in the garden, your yard will smell good' we form 'If it is springtime, then your yard will smell good'.

The question deals with logical reasoning, specifically the laws of syllogism and detachment. The Law of Syllogism takes two conditional statements and forms a conclusion by combining the hypothesis of one statement with the conclusion of another. The Law of Detachment, also known as Modus Ponens, applies when a single conditional statement and the affirmation of its hypothesis lead to the affirmation of its conclusion.

Looking at the options:
A. The statement does not apply the law of syllogism.
B. The statement does not apply the law of detachment.
C. This statement correctly applies the Law of Syllogism. We have two statements: 'If it is springtime, you will plant flowers in the garden' and 'If you plant flowers in the garden, your yard will smell good'. Combining the hypothesis of the first with the conclusion of the second gives us 'If it is springtime, then your yard will smell good'.
D. This accurately applies the law, but the law it uses is not mentioned.

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Answer:

[tex]y=\frac{a}{(9+3x)}[/tex]

Step-by-step explanation:

we have

[tex]a=9y+3yx[/tex]

Solve for y

That means -----> isolate the variable y

Step 1

Factor the variable y in the right side

[tex]a=y(9+3x)[/tex]

Step 2

Divide by [tex](9+3x)[/tex] both sides

[tex]a/(9+3x)=y(9+3x)/(9+3x)[/tex]

Step 3

Simplify

[tex]y=\frac{a}{(9+3x)}[/tex]

The correct answer is that Jenny's ball bounced 32 inches.

To solve the problem, let's denote the distance that Clark's ball bounced as [tex]\( d \)[/tex] inches. According to the problem, Jenny's ball bounced 8 times farther than Clark's ball, so the distance Jenny's ball bounced is [tex]\( 8d \)[/tex] inches.

The total distance bounced by both balls is the sum of the distances each ball bounced, which is given as 36 inches. Therefore, we can set up the following equation:

[tex]\[ d + 8d = 36 \][/tex]

Combining like terms, we get:

[tex]\[ 9d = 36 \][/tex]

To find the value of [tex]\( d \)[/tex], we divide both sides of the equation by 9:

[tex]\[ d = \frac{36}{9} \][/tex]

[tex]\[ d = 4 \][/tex]

Now that we have the distance Clark's ball bounced, which is 4 inches, we can find the distance Jenny's ball bounced by multiplying [tex]\( d \)[/tex] by 8:

[tex]\[ 8d = 8 \times 4 \][/tex]

[tex]\[ 8d = 32 \][/tex]

So, Jenny's ball bounced 32 inches.