True or False?
"Studying for the exam is a necessary condition for passing" means: If you studied for the exam, then you will pass. True False

The required sample size is 907.

We have,

To determine the required sample size for estimating the fraction of new car buyers who prefer foreign cars over domestic with a 95% confidence level and an error of at most 0.03, we'll use the following formula:
n = (Z² x p  (1 - p)) / E²
Where:
- n is the required sample size
- Z is the Z-score for the desired confidence level (1.96 for a 95% confidence level)
- p is the estimated population proportion (0.31)
- E is the margin of error (0.03)

Step-by-step calculation:
1. Calculate Z²: 1.96² = 3.8416
2. Calculate p (1 - p): 0.31 x (1 - 0.31) = 0.2139
3. Calculate E²: 0.03² = 0.0009
4. Substitute these values into the formula: n = (3.8416 x 0.2139) / 0.0009 = 906.92

Since we need to round up to the next integer, the required sample size is 907.

Thus,

The required sample size is 907.

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Answer:

a. -5x³ + 29x² - 56x + 15

b. 8x² + 9x + 5

c. 18t³ - 42t² - 14t - 30

d. x³ - 2x² - 5x + 6

e. -2b⁴ + a² + 6b² - 24a

Step-by-step explanation:

a. 3(x³ − x² + 5) − 8(x³ − 4x² + 7x)

3x³ - 3x² + 15 - 8x³ + 32x² - 56x

-5x³ + 29x² - 56x + 15

b. 7x² + 2x + 5 + x(x + 7)

7x² + 2x + 5 + x² + 7x

8x² + 9x + 5

c. 10(t³ − 4t² + 1) − t(2t + 6) + 8(t³ − t − 5)

10t³ - 40t² + 10 - 2t² - 6t + 8t³ - 8t - 40

18t³ - 42t² - 14t - 30

d. (x − 1)(x + 2)(x − 3)

(x - 1)(x + 2)

x(x + 2) - 1(x + 2)

x² + 2x - x - 2

x² + x - 2(x - 3)

x(x² + x - 2) - 3(x² + x - 2)

x³ + x² - 2x - 3x² - 3x + 6

x³ - 2x² - 5x + 6

e. (3a − 2b²)(3a + 2b²) − 3(4a − b²)2 + 2(−2a − b²)(2a − b²)

3a(3a - 2b²) + 2b²(3a - 2b²)

9a² - 6ab² + 6ab² - 4b⁴ - 3(4a − b²)2 + 2(−2a − b²)(2a − b²)

9a² - 4b⁴ - 24a + 6b² + 2(−2a − b²)(2a − b²)

                                                               (−2a − b²)(2a − b²)

                                                              -2a(2a - b²) - b²(2a - b²)

                                                               -4a² + 2ab² - 2ab² + b⁴

                                                                -4a² + b⁴

                                                                 2(-4a² + b⁴)

                                                                  -8a² + 2b⁴

9a² - 4b⁴ - 24a + 6b² - 8a² + 2b⁴

-2b⁴ + a² + 6b² - 24a

The statement that "a surface generated by a closed plane curve rotated about a line that lies in the same plane as the curve but does not intersect" is true.

The surface generated by a closed plane curve rotated about a line that lies in the same plane as the curve but does not intersect it is called a torus. The torus is a three-dimensional surface that can be thought of as a doughnut shape. The curve that generates the torus is called the generator, and the line about which the curve is rotated is called the axis of rotation. The torus has the interesting property that it has a hole in the center, and the distance from any point on the surface to the center of the torus is constant.

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Answer:

804, the second one depends how many chips the chocolate chip cookies have in each

Step-by-step explanation:

Factors of 6mn are: 6, m and n.

Factors of 24\(m^{4}\)np³q are: 24, \(m^{4}\), n, p³ and q.

Factorization, also known as identifying two or more expressions whose product is the given expression, is the process of determining the factors of an algebraic expression. Finding two or more expressions whose product is the given expression is the process of factoring algebraic expressions.

A factor is a number that divides the entered amount in half. It simply means to show a number as the result of multiplying it by two additional integers. Algebraic expressions are written in a manner similar to this by using the product of their factors. The only difference is because in this case, an algebraic statement combines addition or subtraction with arithmetic operations involving variables and numbers.

Factors of 6mn are: 6, m and n.

Factors of 24\(m^{4}\)np³q are: 24, \(m^{4}\), n, p³ and q.

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Answer:

55°,90°,35°

Step-by-step explanation:

the sum of interior in a triangle is 180° and 55 +90+35=180

Given dataAn element with mass 310 grams decays by 5.7% per minute. We need to find how much of the element is remaining after 9 minutes, to the nearest 10th of a gram.Solution

Let P be the amount of the element remaining after 9 minutes. Then, the amount of the element that decayed in 9 minutes is:Q = 310(1 - 0.057)^9= 310(0.943)^9≈ 174.24 gramsTherefore, the amount of the element remaining after 9 minutes is:P = 310 - Q≈ 135.76 grams.So, the amount of the element remaining after 9 minutes is approximately 135.76 grams, rounded to the nearest 10th of a gram.

Let x be the number of ounces of the 40% alloy Dr. Hamilton used.Then (80 - x) would be the number of ounces of the 60% alloy he used. Therefore, the equation is:0.4x + 0.6(80 - x) = 0.45(80)Simplify this equation to solve for x as follows:0.4x + 48 - 0.6x = 36Add like terms:-0.2x + 48 = 36Subtract 48 from both sides of the equation:-0.2x = -12Solve for x by dividing both sides of the equation by -0.2:x = 60Therefore, Dr. Hamilton used 60 ounces of the 40% alloy.

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Answer:

x = - 4

\(g(x) = 8 {x}^{2} + 4x\)

g(- 4) =?

\(g( - 4) = 8( { - 4)}^{2} + 4( - 4) \\ g( - 4) = 8 \times 16 - 16 \\ g( - 4) = 128 - 16 \\ g( - 4) = 112\)

=> g (- 4) = 112.

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

If Kim has health insurance with a deductible of $500 and 80/20 coinsurance then amount she pay if she incurs a loss of $1500 is (c)$700 .

In an 80/20 coinsurance, the insurance company pays 80% of covered expenses after the deductible has been met, and the policyholder is responsible for paying the remaining 20%.

So , if Kim incurs a loss of $1500, she first needs to pay the $500 deductible before her insurance kicks in. After that, she will pay for 20% of the remaining $1000 in covered expenses:

⇒ 20% of $1,000 = $200

So, in total, Kim will pay $500 for the deductible plus $200 in coinsurance, for a total of:

⇒ $500 + $200 = $700

Therefore, If Kim will pay (c) $700.

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Based on the given data the standard score (z-score) of the given sample mean is approximately 0.55.

The standard score (z-score) is a measure of how many standard deviations a given sample mean is away from the population mean. It is calculated using the formula: z = (x - μ) / (σ / √n), where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

In this case, the population mean (μ) is given as 48, the population standard deviation (σ) is given as 12, the sample size (n) is 47, and the sample mean (x(bar)) is 51. Plugging these values into the formula, we get: z = (51 - 48) / (12 / √47) ≈ 0.55.

Therefore, the standard score (z-score) of the given sample mean is approximately 0.55.

The z-score provides a standardized measure of how far a given sample mean deviates from the population mean, in terms of standard deviations. In this case, a z-score of 0.55 indicates that the sample mean of 51 is approximately 0.55 standard deviations above the population mean of 48.

By calculating the z-score, we can compare the sample mean to the population mean in a standardized way, regardless of the specific values of the population mean and standard deviation. It allows us to determine the relative position of the sample mean within the distribution of the population. Positive z-scores indicate that the sample mean is above the population mean, while negative z-scores indicate that the sample mean is below the population mean.

The z-score can also be used to determine the proportion of data points that fall below or above a given sample mean. By referring to a standard normal distribution table or using statistical software, we can find the corresponding proportion or percentile associated with a specific z-score.

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Step-by-step explanation:

The side opposite to the 4 degree angle is 18 m

The side adjacent the 4 degree angle is x

tan(4) = opposite / adjacent

adjacent = opposite / (tan(4))

adjacent = 18 / tan(4)

adjacent = 257.41

28 is 28.11 percent of 99.6

Percentages are expressed in terms of percent  (%)

Let the required value be x. 28 is what percent of 99.6 is expressed as;

28 = x% of 99.6

28 = x/100. * 99.6

Cross multiply

2800 = 99.6x

Divide both sides by 99.6

x = 2800/99.6

x = 28.11

Hence 28 is 28.11 percent of 99.6

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Answer:

A) congruent

Step-by-step explanation:

because the shapes are the same and congruent but are flipped to trick you.

For the given functions, A is O(B), A is o(B), A is Ω(B), A is ω(B) and A is Θ(B).

To determine the relationship between the functions A and B, we need to analyze their growth rates and compare them using the Big O, little o, Big Omega, little omega, and Big Theta notations.

Let's evaluate each case:

Case 1: A = 4n - 100, B = 50 log n

To determine if A is O(B):

We need to find a positive constant c and a value k such that A <= c * B for all values of n greater than k.

A = 4n - 100

B = 50 log n

Taking the limit as n approaches infinity:

lim(n -> ∞) [(4n - 100) / (50 log n)]

By applying L'Hôpital's rule to the limit, we can find:

lim(n -> ∞) [4 / (50 / (n log(10)))]

Simplifying further:

lim(n -> ∞) [4 / (50 / (n log(10)))]

As n approaches infinity, the limit equals zero. Therefore, A is O(B).

To determine if A is o(B), Ω(B), ω(B), or Θ(B), we would need to go through similar calculations and comparisons, but based on the result that A is O(B), it implies that A is also o(B), Ω(B), ω(B), and Θ(B).

In summary:

A is O(B) (A is Big O of B)

A is o(B) (A is little o of B)

A is Ω(B) (A is Big Omega of B)

A is ω(B) (A is little omega of B)

A is Θ(B) (A is Big Theta of B)

Correct Question:

For each pair of functions (A, B) below, indicate in the table "yes" or "no" to specify whether or not A is O,o,Ω,ω, or Θ of B. Prove the relationships using either the limit approach or the relevant definitions (e.g., where you find values of constants c and k, etc).

A = 4n - 100, B = 50 log n

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Answer: The top 25.

Step-by-step explanation:

Answer:

\(x=-25\)

Step-by-step explanation:

\(-\frac{2}{5}x=10\)

Multiply both sides by 5:-

\(5\left(-\frac{2}{5}x\right)=10\times \:5\)

\(-2x=50\)

Divide both sides by -2:-

\(\frac{-2x}{-2}=\frac{50}{-2}\)

\(x=-25\)

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The given statement is true. The outside bank of a meander that is prone to erosion is known as a cut bank.

As it flows across the land, a river erodes the soil and forms banks. A cut bank is a nearly vertical bank that is also known as a river cliff or river-cut cliff. Cut banks can be found on the river's rim. The river's moving water wears away the earth, resulting in cut banks.

A cut bank, also known as a river cliff or river-cut cliff, is the outside bank of a water channel's constantly eroding curve or meander.

Hence, the given statement is true.

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In response to the query, Line C traverses Point (10, 10) & (1, 5). Line d and line c are parallel, and line d's slope is 5/9.

Parallel in mathematics refers to the different vectors that should never have cross each other with. Parallel relates directly to complementarity or contemporaneous higher incidence.

A straight line's general equation is: y = mx + c [m] where [m] is the slope of the line and represents the unit change rate of [y] without respect to [x].

The y-intercept, or the place where the graph crosses the [y] axis, is represented by [c].

When (x1, y1) and (x2, y2) are really the coordinates of 2 points on the line, m = (y2 - y1) / (x2 - x1).

adding the values we obtain,

m = (5 - 10) / (1 - 10) = -5 / -9 = 5/9

Therefore, the slope of line [d] would be 5/9.

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Answer:

yes it is proportional y is 1.2 times x

not proportional

Step-by-step explanation:

of course the answer is linear

Answer: 10 kg

Step-by-step explanation:

3% = 0.03

First, take 20 times 0.03 = 0.6kg of salt

We know that the 2% solution of seawater

So, we take 100 times 0.6, then divide by 2 = 30kg

Then take 30 - 20 = 10kg

So, to make a solution from 3% to 2%, we have to add  10 kg of water with a 20 kg solution.

If the probability of obtaining a score less than x = 70 is p = 0.0013, the score that corresponds to a probability of 0.0013 is x = 38.2.

We are referring to a normal distribution with a mean (µ) of 100 and a standard deviation (σ) of 20. You want to find the probability of obtaining a score less than x = 70, and you provided that the probability (p) is 0.0013. In a normal distribution with µ = 100 and σ = 20, the probability of obtaining a score less than x = 70 is p = 0.0013. Based on the information given, we know that the probability of obtaining a score less than x = 70 is p = 0.0013. This means that the z-score for x = 70 is -3.09 (found using a standard normal distribution table or calculator).

To find the z-score, we use the formula:

z = (x - µ) / σ

Plugging in the values we know:

-3.09 = (70 - 100) / 20

Solving for x:

-3.09 = (x - 100) / 20

-3.09 * 20 = x - 100

-61.8 + 100 = x

x = 38.2

Therefore, the score that corresponds to a probability of 0.0013 is x = 38.2.

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Using the digits 9, 8, 7, 6, 5, 4, 3, 2, and 1 in that order to create 100 by using the mathematical operations, (9 + 8 + 7) x (6 - 5) x (4 + 3 + 2) - 1 = 100

It is not possible to create 100 using the digits 9, 8, 7, 6, 5, 4, 3, 2, and 1 in that order without using any mathematical operations.

However, it is possible to create 100 by using mathematical operations like addition, subtraction, multiplication, division, and parentheses. One possible way to do this is:

(9 + 8 + 7) x (6 - 5) x (4 + 3 + 2) - 1 = 100

Here, we first add the first three digits (9 + 8 + 7 = 24), subtract the fourth and fifth digits (6 - 5 = 1), add the next three digits (4 + 3 + 2 = 9), and finally multiply all three results and subtract the last digit (24 x 1 x 9 - 1 = 215 - 1 = 100).

So, using this sequence of digits and mathematical operations, we can create 100.

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Answer: 18 inches

Step-by-step explanation:

A triangle with three equivalent angles, because of the properties of triangles, would also be an equilateral triangle. This means each side length is 6 inches. 6+6+6=18 inches.

The Area of triangle with the given height 10 cm and base 6 cm is calculated to be  30 square centimeters.

To calculate the area of a triangle with height 10 cm and base 6 cm, we can use the formula:

Area = (1/2) x Base x Height

Substituting the given values, we get:

Area = (1/2) x 6 cm x 10 cm

Area = 30 square cm

Therefore, the area of the triangle is 30 square centimeters.

We can see that the area of the triangle is calculated by multiplying the base and height and then dividing the result by 2. In this case, the height of the triangle is 10 cm and the base is 6 cm, so the area is 30 square cm. This formula can be used to calculate the area of any triangle, regardless of its size or shape.

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The complete question is :

Calculate the Area of triangle with the height 10 cm and base 6 cm .

By using a system of equations of two variables the number of short answer problems is 10.

Total number of problems in the Test = 30

Maximum points of test = 50

Point of multiple choice = 1

Point of short answer problems = 3

Let the number of multiple choice questions is x and the number of short answer problems is y

So, x + y = 30    - (1)

and 1.x + 3.y = 50 ⇒ x + 3y = 50      -(2)

Equation (2) - Equation (1)

x + 3y - (x + y) = 50 - 30

2y = 20

y = 10

Put y = 10 in equation (1)

x = 30 - 10 = 20

Hence, the number of multiple-choice questions = 20 and the number of short answer problems = 10.

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