A bag contains 10 marbles: 2 are green, 4 are red, and 4 are blue. Tammy chooses a marble at random, and without putting it back, chooses another one at random. What is the probability that both marbles she chooses are blue?

The function that represents the number of comic book as a function of the number of years, t is expressed as y = 30x or f(t) = 30t.

We can use the given data to create a linear equation of the form y = mx + b, where y represents the number of comic books and x represents the number of years.

To find the equation, we can use any two pairs of (x, y) values. Let's use the first and fourth years:

First year: (1, 30)

Fourth year: (4, 120)

The slope, m, of the line can be calculated using the formula:

m = change in y / change in x = (120 - 30) / (4 - 1)

m = 90 / 3

m = 30

The y-intercept, b, can be found by substituting one of the (x, y) values and the slope into the linear equation, y = mx + b:

30 = 30(1) + b

b = 0

Therefore, the equation that represents the number of comic books, y, as a function of the number of years, x, is:

y = 30x

or

f(t) = 30t [where t represents the number of years.]

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Answer:

The answer is 8

Step-by-step explanation:

/x/ // /8/

x=8

The output of the program for the variable z is -22 or it returns an error if z = x - 25y

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

x = 1

x = 3

z = x - 25y

print(z)

The value of the variable y is not given

So, the program would return an error

However, if the complete program is as follows (removing the variable y)

x = 1

x = 3

z = x - 25

print(z)

Using the above as a guide, we have the following:

The final value of x is 3

So, we have

z = 3 - 25

Evaluate

z = -22

This means that the output of the program for z is -22

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Answer:

D

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 3x + 4 ← is in slope- intercept form

with slope m = - 3

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-3}[/tex] = [tex]\frac{1}{3}[/tex] , then

y = [tex]\frac{1}{3}[/tex] x + c ← is the partial equation

to find c substitute (- 1, 5 ) into the partial equation

5 = - [tex]\frac{1}{3}[/tex] + c ( add [tex]\frac{1}{3}[/tex] to both sides )

5 [tex]\frac{1}{3}[/tex] = c ⇒ c = [tex]\frac{16}{3}[/tex]

y = [tex]\frac{1}{3}[/tex] x + [tex]\frac{16}{3}[/tex] ( multiply through by 3 to clear the fractions )

3y = x + 16

The volume of the triangular prism is V = 18ft³

The volume of the prism is equal to the area of the triangular face, times the length of the prism, which is 9ft.

Remember that the area of a triangle of base B and height H is:

A = B*H/2

Here we can see that the base is 2ft and the height is 2ft, then the area of the triangular face is:

A = 2ft*2ft/2 = 2ft²

And thus, the volume of the prism is:

V = 2ft²*9ft

V = 18ft³

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Answer:

10

Step-by-step explanation:

300 plus 200 is 500

80 minus 30 is 50

500 divided by 50 is 10

The probability that in a sample of 200 Americans, the proportion that uses CNN as their primary news source is at least 0.21 is 49.6%.

The probability is determined using the normal approximation to the binomial distribution.

Given that the sample size is large (n = 200) and the probability of success (p = 0.15) is not too close to 0 or 1, the mean (μ) and standard deviation (σ) of the binomial distribution, will be:

μ = n * p

μ = 200 * 0.15

μ = 30

σ = √(n * p * (1 - p))

σ = √(200 * 0.15 * (1 - 0.15))

σ ≈ 4.29

Then, the z-score corresponding to the proportion of 0.21 is:

z = (x - μ) / σ

z = (0.21 - 0.15) / 4.29

z ≈ 0.014

Using a calculator, the probability of a z-score of 0.014 is approximately 0.504.

Hence, the probability of obtaining a proportion at least 0.21, is:

Probability = 1 - 0.504

Probability ≈ 0.496

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The equation shows that the point total in the 10th level is predicted to be 514.4.

The equation given is: y= 48.2x + 32.4

where y is the point total and x is the level.

In order to predict the point total in the 10th level, I will substitute x=10 into the equation:

y=48.2(10) + 32.4 = 482 + 32.4 = 514.4

Therefore, the point total in the 10th level is predicted to be 514.4.

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Answer:

A. Using the commutative property

Step-by-step explanation:

Because there is no use of commutative property in the solution process.

Answer:

A) Using Commutative property

Step-by-step explanation:

In step 1, it used distributive property when the number 5 is distributed inside of the equation in the parenthesis.

In Step 4, dividing both sides by 10 to further simplify the equation

In step 2, you combined like terms and it results to the equation in step 3

The number of ways to draw the socks in each case is given as follows:

a) 90 ways.

b) 48 ways.

c) 42 ways.

The Fundamental Counting Theorem states that if there are m ways for one trial and n ways for another trial, then there are m x n ways in which the two trials can happen simultaneously.

This can be extended to more than two trials, where the number of ways in which all the trials can happen simultaneously is the product of the number of outcomes of each individual trial, according to the equation presented as follows:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

For item a, we have that there are no restrictions, hence there are 10 options for the first sock and 9 for the second, hence:

10 x 9 = 90.

For item b, we need one of each, hence the possible combinations are:

Hence:

6 x 4 + 4 x 6 = 48.

For item c, we can take 6 then five(two blue) or 4 then 3(two white), hence:

6 x 5 + 4 x 3 = 42.

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For the function  [tex]A(t)=4000e^0^.^0^4^t[/tex] the value of A'(8) is $220 and the value of [tex]A'(t)=160e^0^.^0^4^t[/tex]

The given function is [tex]A(t)=4000e^0^.^0^4^t[/tex] gives the balance after t years.

The initial investment is 8000

4% is the compounded interest.

Now differentiate with respect to t

[tex]A'(t)=0.04(4000)e^0^.^0^4^t[/tex]

[tex]A'(t)=160e^0^.^0^4^t[/tex]

Now let us find the value of A'(8)

Plug in t as 8

[tex]A'(8)=160e^0^.^0^4^(^8^)[/tex]

A'(8)=220.3

Hence, the value of A'(8) is $220 and the value of [tex]A'(t)=160e^0^.^0^4^t[/tex]

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Answer: b: 58-22=36

A=37 68-22-9

d=99 37+62

c=29 34-9

Step-by-step explanation:

The point that lies in the solution set of (x - 2)²/25 + (y + 3)²/4 < 1 is B. (3, –2.5)

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

(x - 2)²/25 + (y + 3)²/4 < 1

Also, we have

A. (4, –0.5)

B. (3, –2.5)

C. (–2.5, 4)

D. (–4.5, –3)

Next, we test the options as follows

A. (4, –0.5)

(4 - 2)²/25 + (-0.5 + 3)²/4 < 1

1.7225 < 1  -- false

B. (3, –2.5)

(3 - 2)²/25 + (-2.5 + 3)²/4 < 1

0.1025 < 1   -- true

Hence, the point that lies in the solution set is B. (3, –2.5)

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The expected value of the given variable with the probability distribution is 7

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

The probability distribution on the table of values

The expected value of the variable is calculated as

Expected value = ∑x * P(x)

Using the above as a guide, we have the following:

Expected value = 2 * 1/36 + 3 * 1/18 + 4 * 1/12 + 5 * 1/9 + 6 * 5/36 + 7 * 1/6 + 8 * 5/36 + 9 * 1/9 + 10 * 1/12 + 11 * 1/18 + 12 * 1/36

Evaluate

Expected value = 7

Hence, the expected value of the variable is 7

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The estimated population of the town in 2023 is 57,344.

(a) Let P be the population in t years after 2014.

Since the population doubles every year, we can use the formula :

P = P₀(2)ⁿ, where P₀ is the initial population in 2014.

We have P₀= 112, so the equation is P = 112(2)ⁿ.

(b) To find the population in 2023, we need to find t when t + 2014 = 2023.

So t = 2023 - 2014 = 9.

Substituting t = 9 into the equation from part (a), we get:

P = 112(2)⁹

P ≈ 57,344

Therefore, the estimated population of the town in 2023 is 57,344.

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The z-score is calculated as z-score.

The score x = 33 is 1.5 standard deviations above the mean of 27.

To find the z-score for x = 33 in a normal distribution with a mean of 27 and a standard deviation of 4, we can use the formula for calculating the z-score:

z = (x - μ) / σ

where in this case, x = 33, μ = 27, and σ = 4. Plugging these values into the formula, we can calculate the z-score:

z = (33 - 27) / 4

z = 6 / 4

z = 1.5

The z-score for x = 33 is 1.5.

The z-score represents the number of standard deviations that a given value (x) is away from the mean (μ) in a normal distribution. It indicates how many standard deviations a data point is above or below the mean.

In this context, a z-score of 1.5 for x = 33 means that the value 33 is 1.5 standard deviations above the mean of 27.

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Answer: A) [tex]f(x)=\frac{6x^2-x+4}{2x^2-1}[/tex]

Step-by-step explanation:

Line [tex]y=L[/tex] is a horizontal asymptote of the function [tex]y=f(x)[/tex], if either [tex]\lim_{x \to \infty} f(x)=L[/tex] or [tex]\lim_{x \to \infty} f(x)=L[/tex], and [tex]L[/tex] is finite.

calculate the limits:

[tex]\lim_{x \to \infty} (\frac{6x^2-x+4}{2x^2-1})=3[/tex]

[tex]\lim_{x \to -\infty} (\frac{6x^2-x+4}{2x^2-1})=3[/tex]

Thus, the horizontal asymptote is [tex]y=3[/tex]

The equation for each circle is given as follows:

36) (x - 2)² + (y - 15)² = 4.

37) (x + 8)² + (y + 18)² = 25.

38) (x - 11)² + (y + 9)² = 49.

39) (x - 13)² + (y + 8)² = 36.

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

For item 36, the center is given as follows:

(-3, 11)

After the translation, the center will be given as follows:

(2, 15)

Hence the equation is given as follows:

(x - 2)² + (y - 15)² = 4.

For item 37, the center is given as follows:

(-3, -14)

After the translation, the center will be given as follows:

(-8, -18)

Hence the equation is given as follows:

(x + 8)² + (y + 18)² = 25.

For item 38, the center is given as follows:

(11, -9).

Hence:

(x - 11)² + (y + 9)² = r².

Point (18, -9) is on the circle, hence the radius squared is obtained as follows:

r² = (18 - 11)² + (-9 + 9)²

r² = 49.

Hence the equation is:

(x - 11)² + (y + 9)² = 49.

For item 39, the center is given as follows:

(13, -8).

Hence the equation is:

(x - 13)² + (y + 8)² = r².

Point (7, -8) is on the circumference of the circle, hence the radius squared is obtained as follows:

r² = (7 - 13)² + (-8 + 8)²

r² = 36.

Hence the equation is given as follows:

(x - 13)² + (y + 8)² = 36.

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Answer:

7/10

Step-by-step explanation:

[tex]1 - \frac{3}{10} \\ = \frac{10}{10} - \frac{3}{10 } \\ = \frac{7}{10} [/tex]

Answer:

27

Step-by-step explanation:

We can solve by using order of operations (PEMDAS), which shows us the order in which we're supposed to perform mathematical operations:

The / comes from the fact that you do these operations from left to right as multiplication and division have the same level of priority in an equation/operation.

Like multiplication/division, the / comes from the fact that you do these operations from left to right as addition and subtraction also have the same level of priority in an equation/operation.

Step 1:  Simplify inside the parentheses:

5 * 4 + (1 + 1) + 5

5 * 4 + 2 + 5

Step 2:  Multiply 5 and 4:

20 + 2 + 5

Step 3:  Add 20 and 2:

22 + 5

Step 4:  Add 22 and 5 to get your answer:

27

Thus, 5 *4 + (1 + 1) + 5 = 27

The given function does not have an end behavior because it is not a polynomial function.

The end behavior of a function refers to how the function behaves or approaches as the input values (x-values) of the function become extremely large (approaching positive infinity) or extremely small (approaching negative infinity).The long term behavior of the function when x moves towards the ends of the coordinate plane can be predicted.

In a polynomial function, the leading coefficient and degree of the function often determine the polynomial function.

The given function is;

f(x) = 2x² - 5 / x² - 1

The end behavior of this function does not exist because this is not a polynomial.

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The length of side CB to one decimal place is 89.3.

To find the length of side CB in the given triangle, we can use the sine rule. The sine rule states that in a triangle, the ratio of the length of a side to the sine of its opposite angle is constant.

In this case, we have the angle C as 53° and the side opposite to it, side CB, as the unknown. Let's denote the length of side CB as x.

According to the sine rule:

sin(C) / x = sin(A) / AB

We know that angle A is 37° and AB is 120 units. Plugging in the values:

sin(53°) / x = sin(37°) / 120

To find x, we can rearrange the equation:

x = (120 * sin(53°)) / sin(37°)

Calculating this expression gives us:

x ≈ 89.32

Rounding this value to one decimal place, the length of side CB is approximately 89.3.

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The function y=x+3 has the greatest y intercept.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The given function is y=x, it has y intercept which is zero

The given function is y=-x, it has y intercept which is zero

Function is y=x+3, it has y intercept which is three

Function is y=2x, it has y intercept which is zero

Hence, the function y=x+3 has the greatest y intercept.

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The ball has traveled approximately 25.24 feet Horizontally.The correct answer is D. 25.2 ft.

The horizontal distance traveled by the soccer ball after 0.9 seconds, we can use the equation:

horizontal distance = initial velocity * time * cos(angle)

Substituting the given values:

initial velocity = 39 ft/s

time = 0.9 s

angle = 44°

horizontal distance = 39 ft/s * 0.9 s * cos(44°)

Calculating:

horizontal distance ≈ 39 ft/s * 0.9 s * 0.71934 ≈ 25.24 ft

Therefore, after 0.9 seconds, the ball has traveled approximately 25.24 feet horizontally.

The correct answer is D. 25.2 ft.

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The probability that exactly 1 buyer would prefer green P ( A ) = 0.1854

Given data ,

A researcher wishes to conduct a study of the color preferences of new car buyers

And , 30 % of this population prefers the color green

where 20 buyers are randomly selected

Now , binomial distribution problem with n = 20, p = 0.30 and we want to find the probability of exactly 1 buyer preferring green.

The formula for the probability mass function of a binomial distribution is:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

where (n choose k) = n! / (k! * (n-k)!)

Plugging in the values, we get:

P(X = 1) = (20 choose 1) * 0.30¹ * 0.70¹⁹

= 20 * 0.30 * 0.70¹⁹

= 0.1854 (rounded to four decimal places)

Hence , the probability that exactly 1 buyer would prefer green is 0.1854

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