What is 2008 AP Multiple Choice AB answers and solutions?

Answer:

Step-by-step explanation:

Let's start by translating the given sentence into an equation:

2x + 29 ≥ -25

To solve for x, we can isolate x on one side of the inequality:

2x ≥ -25 - 29

2x ≥ -54

x ≥ -27

Therefore, the solution to the inequality is x ≥ -27.

The value of f(1) will be 45.

A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.

Given a function f(n) = 45.(4/5)ⁿ⁻¹

To calculate the value of f(1) we will substitute the value of the n by 1.

f(1) = 45.(4/5)¹⁻¹

f(1) = 45.(4/5)⁰

f(1) = 45

To calculate the value of f(n -1) we will substitute the value of the n by

n - 1.

f(n -1) = 45.(4/5)ⁿ⁻¹⁻¹

that can also be written as, from the rule of power

f(n -1) = (45.(4/5)ⁿ⁻¹)/4/5

f(n -1) = (45.(4/5)ⁿ⁻¹) * 5/4

f(n -1) = f(n) * 5/4

so,

f(n) = f(n-1) * 4/5

Therefore, the value of f(1) will be 45, and the value of f(n) = f(n-11)*4/5.

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Answer:

[tex]\frac{2}{30}[/tex]

Step-by-step explanation:

[tex]\frac{4}{6}-\frac{3}{5} \\ \\ =\frac{2}{3}-\frac{3}{5} \\ \\ =\frac{10}{15}-\frac{9}{15} \\ \\ =\frac{1}{15} \\ \\ =\frac{2}{30}[/tex]

It would be 1/15 but thats not an option, if you need help try math  way doht  com, thats the best thing u can use for math problems

In statistics, p represents the true proportion p hat represents the sample proportion

p represents population that has a certain characteristic or falls into a certain category. It is a fixed, unknown value that we are trying to estimate.

p hat represents the sample proportion, which is an estimate of the true proportion based on a sample of the population. It is calculated by dividing the number of individuals in the sample with the characteristic or in the category by the total sample size.

For example, if we want to estimate the proportion of students who prefer chocolate ice cream, we could take a sample of 100 students and find that 60 of them prefer chocolate.

In this case, p hat would be 60/100 or 0.6. This is our estimate of the true proportion, p, of all students who prefer chocolate ice cream.

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Answer:A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

Step-by-step explanation:

A scale factor in math is the ratio between corresponding measurements of an object and a representation of that object. If the scale factor is a whole number, the copy will be larger. If the scale factor is a fraction, the copy will be smaller.

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To convert 0.1667 to a fraction, we write it as 1667/10000, and simplify it to 1/6. Hence, the fraction of .1667 is 1/6.

To convert the decimal number 0.1667 to a fraction, we can write it as 1667/10000. This fraction can be simplified by dividing both the numerator and the denominator by their greatest common factor, which is 167.

1667 ÷ 167 = 10

10000 ÷ 167 = 60 + 40/167

So, the fraction equivalent to 0.1667 is 1667/10000, which can be simplified to 10/60 + 40/167.

10/60 can be simplified to 1/6, so the final simplified fraction is:

0.1667 = 1/6 + 40/167

Therefore, the fraction equivalent to 0.1667 is 1/6.

Converting a decimal to a fraction involves expressing a decimal number as a ratio of two integers. To convert a decimal to a fraction, the decimal is written in the form of a fraction, with the decimal value as the numerator and a power of 10 as the denominator. The resulting fraction can be simplified by finding the greatest common factor between the numerator and denominator, and then dividing both by that factor. For example, to convert 0.1667 to a fraction, we write it as 1667/10000, and simplify it to 1/6.

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Question: A line passes through the point (9, 5) and has a slope of -4/3. Write an equation in slope-intercept form for this line.

Answer:

[tex]y=-\frac{4}{3}x+17[/tex]

Given:

x = 9

y = 5

m = -4/3

Step-by-step explanation:

Slope intercept form is y = mx+b

Plug in x, y, and m to solve for b.

[tex]5=-\frac{4}{3}(9)+b[/tex]

[tex]b=5+\frac{4}{3}(9)=17[/tex]

Now that you have b, plug in m and b back into the equation

[tex]y=-\frac{4}{3}x+17[/tex]

The answer is 36. you basically add and subtract to the left and right.

32+8= 40

40-4=36

(you get the 8 because 2 x 2 x 2 = 8)

Answer:

12.5 in²

Step-by-step explanation:

The equations in the slope-intercept form are

p = 3b + 2 and p = (5/2)b + 15/2.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction

From the table and scatter plot;

(a). The line for 'Build it' passes through (1, 10) and (3, 15),

then the equation of the line is,

p = (5/2)b + 15/2

Similarly, the equation of the line-'All things home' is,

p = 3b + 2.

(b) the graphs of the lines are given in the attached image.

(c) The equation in the slope-intercept form;

p = 3b + 2 and p = (5/2)b + 15/2.

(d) When b = 65,

then p = 3(65) + 2 and p = (5/2)(65) + 15/2.

So, p = 197 and p = 170

Therefore, all the required values are given above.

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When performing a t-test assuming unequal variances, the test statistic is a t-value, which is calculated by dividing the difference between the means of the two groups by the standard error of the difference.

To see if the difference in mean mpg between 4 and 8 cylinder cars is statistically significant, compare the estimated t-value to a critical t-value based on degrees of freedom and desired level of significance. The difference is regarded statistically significant if the estimated t-value is bigger than the crucial t-value.

As a result, the right response depends on the estimated t-value, the crucial t-value, and the level of significance utilized in the test.

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Answer: The student correctly wrote an expression to find the total cost of downloading "s" songs. The expression is: 0.99s + 7.99. However, they made a mistake when they simplified the expression to 8.98s. The expression should have remained as 0.99s + 7.99, because the $7.99 membership fee does not change regardless of how many songs are downloaded.

In Part B, the student correctly used the expression to find the cost of downloading 12 songs. They multiplied 8.98 by 12 and got the correct answer of 107.76.

Step-by-step explanation:

The distance between the points -3,-8, and 6,-8 is 3 units.

The length of the line segment bridging two points on a plane is known as the distance between the points.

Look at the provided points.

Calculate the distance between the points using the given formula.

Given points are -3,-8 and 6,-8

Given two points lies the parallel to X-axis

The distance between the two points is

A (-3,-8) and B(6,-8) =  X₂ - X₁

6 - 3  = 3 units.

Therefore, the distance between two points -3,-8 and 6,-8 is 3 units.

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The equation of parabola in vertex form is [tex]$$\boxed{x^2 - 6x + 9 = 0}$$[/tex]

To write the equation of a parabola in vertex form, we use the following formula:

[tex]$$(x-h)^2=4p(y-k)$$[/tex]

where (h,k) is the vertex and p is the distance between the focus and the vertex.

Given that the focus of the parabola is at (3, 2.5), we can determine that the vertex of the parabola is also at (3, 2.5). Let's substitute these values into the formula:

[tex]$$(x-3)^2=4p(y-2.5)$$[/tex]

To find the value of p, we need to use the fact that the distance between the focus and vertex is p. The distance formula is:

[tex]$$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$[/tex]

Substituting the values we know:

[tex]$$\begin{aligned} d &= \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \ &= \sqrt{(3 - 3)^2 + (2.5 - 2.5)^2} \ &= 0 \end{aligned}$$[/tex]

Since d = 0, we know that p = 0 and the equation simplifies to:

[tex]$$(x-3)^2=0$$[/tex]

Expanding the left side:

[tex]$$x^2 - 6x + 9 = 0$$[/tex]

So the equation of the parabola in vertex form is:

[tex]$$\boxed{(x-3)^2=4 \cdot 0 (y-2.5)}$$[/tex]

Or

[tex]$$\boxed{x^2 - 6x + 9 = 0}$$[/tex]

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Answer: The word "BASKETBALL" has 2 B's and 3 vowels (A, E, A). The probability of choosing the letter B, not replacing it, and then choosing a vowel is:

(2/10) * (2/9) * (3/8) = 6/90 = 1/15

So, the probability of choosing the letter B, not replacing it, and then choosing a vowel is 1/15.

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

5x/2 = -5

5 x/2=2 (-5)

5x= 2 (-5)

5x= -10

5x/5=-10/5

x=-10/5

x=-2

True. A simple random sample is a type of sampling method that is used to select a subset of observations from a larger population.

The key characteristic of a simple random sample is that each observation in the population has an equal probability of being selected to be part of the sample.

Mathematically, this can be expressed as follows: Let N be the population size, and let n be the sample size. Then, the probability of any specific sample of n observations being selected from the population is given by the formula:

P(Sample) = (n!/N!)/(N-n)!

where n! represents the factorial of n (n factorial), and (N-n)! represents the factorial of N-n.

This means that if we were to draw multiple simple random samples of the same size from the same population, each sample would have an equal probability of being selected.

In conclusion, a simple random sample is a method of selecting a subset of observations from a population that ensures that each observation has an equal probability of being selected, and that each sample has an equal probability of being selected.

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Answer:

1. Kevin has 12 pieces of paper.

2. Including Sybill and her friends, each person will get 1/8 of the 1/2 slice.

Step-by-step explanation:

1. This is because if 1 piece of paper turned divided into fourths would 4/1 or 4 “fourths” of paper. So multiply that by 3 since there is 3 pieces of paper and we are following the same steps. 3 x 4 = 12. Hence if you divide 3 pieces of paper into fourths, you will have 12 fourths.

2. Since we are splitting the 1/2 piece four (which includes sybill and her 3 friends) ways, the equation would be: 1/2 divided by 4

Divide:

1/2 divided by 4-

 1/2 : 4 = 1/2 · 1/4 = 1 · 1/2 · 4 = 1/8 

Hence, each friend and Sybill her self will receive a 1/8 piece.

Barbara will therefore shell out $171.36 for the cost of shipping and handling.

The amount of money, or its equivalent, for which anything being offered for sale, purchased, or otherwise transacted. A price on someone's head is a sum provided for their capture, whether they are alive or dead.

We must calculate 28% of the chandelier's original purchase price in order to calculate the value Sarah will charge for shipping and handling.

Step 1

Calculate 28% of $612

We can multiply a value by 0.28 to get 28% of it, or reduce it by 100 & then multiply the result by 28. So:

28% of $612 = 0.28 x $612 = $171.36

Step 2

Add the cost of shipping and handling to the purchase price.

Simply include the shipping & handling fee to the original price to get the chandelier's total cost with shipping and handling included:

Total cost = $612 + $171.36 = $783.36

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The value of c lies in the interval [tex](-\infty, -1.5)[/tex]

Inequality is a statement that shows the relationships the two expressions are not equal. It is defined by the symbols like <, >, ≤, ≥.

[tex]\frac{c}{2} < -0.75[/tex]

To find the value of c:

[tex]\frac{c}{2} < -0.75[/tex]

Multiply both sides by 2 we get,

[tex]2\frac{c}{2} < (-0.75)*2[/tex]

⇒c < -1.5

Therefore c<-1.5 is the solution for the given inequality.

It can also be represented in the interval form.

This is given in the interval notation [tex](-\infty, -1.5)[/tex]

Hence, the value of c lies in the interval [tex](-\infty, -1.5)[/tex]

Complete question:

What is the values that c can take when  [tex]\frac{c}{2} < (-0.75)[/tex]?

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Answer:

Slope: 1

Y-Intercept: -2

y=x-2

Graph it by plotting a point at (0,-2) and then by going up one to the right. One up and then one to the right and repeat twice. Now you can graph this easily. Hope this helped!!

Step-by-step explanation:

Answer:

a: 30%

b: 5%

Step-by-step explanation:

a: (42,000/140,000)*100

b: (7,000/140,000)*100

Answer:

To convert 2 pints into milliliters, we need to use the conversion rate that 1 pint equals 473.176 milliliters.

Therefore, we can calculate that 2 pints is equal to 946.352 milliliters. Rounded to the nearest whole number, this would be 946 milliliters.

The solution for r in the equation is 428.43

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

100000 = 8000(1+ r/12000)^72

Divide through by 8000

So, we have

12.5 = (1+ r/12000)^72

Take the 72th root of both sides

So, we have

1 + r/12000 = 1.03570211065

Subtract 1

r/12000 = 0.03570211065

So, we have

r = 428.4253278

Hence, the value of r is 428.43

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The total volume of milk would be 1/2 gallons.

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.

Given that,

Volume = 1/4 gallons

The number of weeks = 2

So, the total volume =

1/4 × 2 = 1/2 gallons

Hence, the total volume of milk would be 1/2 gallons

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Answer:

Step-by-step explanation:

X axis intercept (y=0)

3x+2(0)=5

3x=5

x=5/3

Y axis intercept (x=0)

3(0)+2y=5

2y=5

y=5/2

so, the interception points are: (5/3,0) and (5/2,0)

With the thickness of a flange on an aircraft component is uniformly distributed between 0.95 and 1.05 millimeters.

a) 40% of the flanges exceeds 1.01 millimeters.

b) 1.04 millimeters is the thickness that is exceeded by 90% of the flanges.

c) The mean of flange thickness is 1 millimeters and the variance of flange thickness is 0.01 millimeters^2.

a) To determine the proportion of flanges that exceeds 1.01 millimeters, we need to find the area under the probability density function (pdf) of the thickness that is greater than 1.01 millimeters.

Let's call the random variable X representing the thickness of the flange. The pdf of X is uniform, so it has constant value over the interval [0.95, 1.05]. Therefore, the proportion of flanges that exceeds 1.01 millimeters can be found as follows:

P(X > 1.01) = (1.05 - 1.01) / (1.05 - 0.95) = (1.05 - 1.01) / 0.1 = 0.04 / 0.1 = 0.4

So, 40% of the flanges exceed 1.01 millimeters.

b) To find the thickness that is exceeded by 90% of the flanges, we need to solve for X in the following equation:

P(X > X) = 0.9

Substituting the values for the pdf, we get:

(X - 0.95) / (1.05 - 0.95) = 0.9

Solving for X, we get:

X = 0.95 + 0.9 * (1.05 - 0.95) = 0.95 + 0.9 * 0.1 = 0.95 + 0.09 = 1.04

So, 1.04 millimeters is the thickness that is exceeded by 90% of the flanges.

c) The mean of X can be calculated as follows:

Mean = (0.95 + 1.05) / 2 = 1

The variance of X can be calculated as follows:

Variance = (1.05 - 0.95)^2 / 12 = 0.01

So, the mean and variance of flange thickness are:

Mean = 1 millimeters

Variance = 0.01 millimeters^2

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To calculate the percent change in renewable energy investment in the US from 2005 to 2018, you can use the following formula:

Percent change = ((Final value - Initial value) / Initial value) * 100%

In this case, the initial value is $11.4 billion in 2005 and the final value is $46.5 billion in 2018. Plugging these values into the formula, we get:

Percent change = (($46.5 billion - $11.4 billion) / $11.4 billion) * 100%

= ($35.1 billion / $11.4 billion) * 100%

= 3.085 * 100%

= 308.5%

So, the percent change in renewable energy investment in the US from 2005 to 2018 was 308.5%, a substantial increase over the 13-year period.

Yes You can buy 24 apples for $0.125 per pound. This price will not available except in festival or discounts sale.

what are ounces ?

An ounce is a unit of weight or mass commonly used in the United States and other countries. It is usually abbreviated as oz. One ounce is equal to 1/16th of a pound or approximately 28.35 grams. Ounces are often used to measure small quantities of food or ingredients in recipes, as well as for measuring the weight of small objects.

According to the question:

To determine whether you can buy 24 apples for $9, we need to find the cost per apple.

If 24 apples cost $9, then the cost per apple is:

$9 / 24 apples = $0.375 per apple

Since each apple weighs about 5 ounces, there are about 3 apples per pound:

16 ounces / 5 ounces per apple ≈ 3.2 apples per pound

Therefore, the cost per pound of apples is:

$0.375 per apple / 3 apples per pound = $0.125 per pound

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