16. A multiple-choice test question is considered easy if at least 80% of the responses are correct. A sample of 6503 responses to one question indicates that 5463 of those responses were correct. a) What is the best point estimate for the true proportion of correct answers? (2) b) What is the margin of error of the estimate of p with 99% confidence? (5) c) Construct the 99% confidence interval for the true proportion of correct responses. (2) d) Is it really likely that this question is really easy? Why, or why not? (3)

The graph is a downward-opening parabola opening downward with its vertex at (2,0). Therefore, the correct option is C.

The equation y = -16t^2 + 64t + 16 represents the path of a projectile launched from a 16-ft-tall tower. To determine the correct graph, we can analyze the equation. The coefficient of t^2 (-16) is negative, indicating a downward-opening parabola. The coefficient of t (64) determines the horizontal shift of the graph, and in this case, t = 4 represents the maximum height of the projectile. The constant term (16) represents the initial height of the tower.

Considering these factors, we find that the correct graph of the equation is option C. It depicts a downward-opening parabola with its vertex at (2,0). The parabola starts at an initial height of 16 ft (the tower's height) and descends symmetrically from its vertex.

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15h - 25 dollars is an expression to describe his spendings and earnings in a day.

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

Peter makes 15 dollars an hour, so if he works for h hours, he earns:

15h dollars

Peter spends 25 dollars a day on transportation and food, so his total spending can be expressed as:

25 dollars

Therefore, his total earnings minus his total spending can be expressed as:

15h - 25 dollars

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a) The equation of the line passing through the point (3, 2) with slope 4 is y - 2 = 4(x - 3).

b. The equation of the line passing through (4, -2) and (5,6) is y + 2 = 8(x - 4).

c) The slope of the line 6x +2y +4 is -3.

a. To derive the equation, we use the point-slope form of a linear equation: y - y₁ = m(x - x₁), where (x₁, y₁) represents the given point and m represents the slope.

Substituting the given values into the equation, we have:

y - 2 = 4(x - 3)

This equation can be further simplified if required.

b) The equation of the line passing through the points (4, -2) and (5, 6) can be found using the slope-intercept form, y = mx + b.

First, we calculate the slope (m) using the formula: m = (y₂ - y₁) / (x₂ - x₁).

m = (6 - (-2)) / (5 - 4) = 8.

Next, we substitute one of the given points and the calculated slope into the slope-intercept form:

y - y₁ = m(x - x₁).

y - (-2) = 8(x - 4).

Simplifying the equation:

y + 2 = 8(x - 4).

c) To find the equation of the line passing through the point (3, -1) and parallel to the line 6x + 2y + 4 = 0, we first need to determine the slope of the given line.

Rearranging the equation 6x + 2y + 4 = 0, we have:

2y = -6x - 4,

y = -3x - 2.

The given line has a slope of -3.

Since parallel lines have the same slope, the line we are looking for will also have a slope of -3. Using the point-slope form with the given point (3, -1), the equation becomes:

y - (-1) = -3(x - 3).

Simplifying:

y + 1 = -3(x - 3).

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Answer:

Step-by-step explanation:

a = 32 ÷ 4

a = 8

The 99% confidence interval of the true mean is given as follows:

8.56 million < μ < 16.78 million.

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the equation presented as follows:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

The variables of the equation are listed as follows:

The critical value, using a t-distribution calculator, for a two-tailed 99% confidence interval, with 10 - 1 = 9 df, is t = 3.2498.

The parameter values for this problem are given as follows:

[tex]\overline{x} = 12.67, s = 4, n = 10[/tex]

The lower bound of the interval is then given as follows:

[tex]12.67 - 3.2498 \times \frac{4}{\sqrt{10}} = 8.56[/tex]

The upper bound of the interval is then given as follows:

[tex]12.67 + 3.2498 \times \frac{4}{\sqrt{10}} = 16.78[/tex]

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Answer:

3. The equivalent fractions are presented as follows;

[tex]\dfrac{2}{3} = \dfrac{2 \times 2}{3 \times 2} =\dfrac{4}{6}[/tex]

4.  The equivalent fractions are presented as follows;

[tex]\dfrac{2}{3} = \dfrac{4 \times 2}{4 \times 3} =\dfrac{8}{12}[/tex]

5. The reason why it works is because [tex]\dfrac{1}{8} + \dfrac{1}{8} = \dfrac{1}{4}[/tex]

Step-by-step explanation:

3. Based on the shaded region of the given figures, the two fractions are equivalent

Mathematically, we can show the equivalency of the two fractions as follows;

[tex]\dfrac{2}{3} =\dfrac{2}{3} \times 1 = \dfrac{2}{3} \times \dfrac{2}{2} = \dfrac{2 \times 2}{3 \times 2} =\dfrac{4}{6}[/tex]

Therefore;

[tex]\dfrac{2}{3} = \dfrac{2 \times 2}{3 \times 2} =\dfrac{4}{6}[/tex]

4. From the shaded region of the given figure, the fractions are equivalent

Mathematically, we have;

[tex]\dfrac{2}{3} =\dfrac{2}{3} \times 1 = \dfrac{4}{4} \times \dfrac{2}{3} = \dfrac{4 \times 2}{4 \times 3} =\dfrac{8}{12}[/tex]

Therefore;

[tex]\dfrac{2}{3} = \dfrac{4 \times 2}{4 \times 3} =\dfrac{8}{12}[/tex]

5. The amount of salt required by the recipe = 1/4 teaspoon of salt

The measure of the spoon Jonas has = 1/8 teaspoon

When Jonas adds two 1/8 teaspoons, he gets;

[tex]\dfrac{1}{8} + \dfrac{1}{8} = \dfrac{1 + 1}{8} = \dfrac{2}{8} = \dfrac{2 \times 1}{2 \times 4} = \dfrac{2}{2} \times \dfrac{1}{4} = 1 \times \dfrac{1}{4} = \dfrac{1}{4}[/tex]

Therefore;

[tex]\dfrac{1}{8} + \dfrac{1}{8} = \dfrac{1}{4}[/tex]

Two 1/8 measuring teaspoons are equivalent to one 1/4 teaspoons and therefore Jonas is able to get the 1/4 teaspoons of salt the recipe asks for b combining two 1/8 measuring teaspoons of salt he has because 1/8 + 1/8 = 1/4.

Answer:

however much the Child's pass is x 3 = Adult Pass cost

Step-by-step explanation:

a. Using intersection of events probability of FUA is 0.0165

b. Using complement rule, the probability of F'UA is 0.9835

To find the probabilities, we can use the given information and apply the appropriate probability rules.

(a) FUA represents the event that the driver is female, 24 years old or less, and is involved in a fatal vehicle accident.

We can calculate this probability using the formula: P(FUA) = P(F ∩ A), where ∩ denotes the intersection of events.

P(FUA) = P(F) * P(A|F)

Given information:

P(F) = 0.2868 (probability that the driver is female)

P(A) = 0.1828 (probability that the driver is 24 years old or less)

P(A|F) = 0.0576 (probability that the driver is 24 years old or less given that the driver is female)

P(FUA) = 0.2868 * 0.0576 ≈ 0.0165

Therefore, the probability of FUA is approximately 0.0165.

(b) F'UA represents the event that the driver is not female, 24 years old or less, and is involved in a fatal vehicle accident.

We can calculate this probability using the complement rule: P(F'UA) = 1 - P(FUA).

P(F'UA) = 1 - P(FUA) ≈ 1 - 0.0165 ≈ 0.9835

Therefore, the probability of F'UA is approximately 0.9835.

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Both the classical method and the p-value method lead to the conclusion that the average distance cars travel per year is less than 20,000 kilometers,

a) t =  -2.564

b)  t = -2.564

To test the claim that the average distance cars travel per year is less than 20,000 kilometers, we can conduct a hypothesis test using the classical method and the p-value method.

a) The steps we need to follow are:

Step 1: Formulate the null and alternative hypotheses:

Null hypothesis (H₀): The average distance cars travel per year is 20,000 kilometers.

Alternative hypothesis (H₁): The average distance cars travel per year is less than 20,000 kilometers.

Step 2: Determine the test statistic:

Since we know the sample size (n = 100), the sample mean (x = 19,000 kilometers), and the sample standard deviation (s = 3900 kilometers), we can use the t-test statistic.

t = (x - μ₀) / (s / √n)

where μ₀ is the assumed population mean under the null hypothesis.

Step 3: Set the significance level:

The significance level is given as 0.05, which means we want to be 95% confident in our conclusion.

Step 4: Calculate the critical value:

Since the alternative hypothesis is one-tailed (less than), we need to find the critical t-value corresponding to a 0.05 significance level and degrees of freedom (df) = n - 1 = 99. From the t-distribution table or calculator, the critical t-value is approximately -1.660.

Step 5: Calculate the test statistic:

t = (19,000 - 20,000) / (3900 / √100)

t = -10 / (3900 / 10)

t ≈ -2.564

Step 6: Compare the test statistic with the critical value:

Since -2.564 is less than -1.660, the test statistic falls in the rejection region. We reject the null hypothesis.

Step 7: Make a conclusion:

Based on the classical method, since the test statistic falls in the rejection region, we conclude that the average distance cars travel per year is significantly less than 20,000 kilometers.

b) The P-value method:

Using the same test statistic t = -2.564 and the degrees of freedom (df) = 99, we can calculate the p-value. The p-value is the probability of observing a test statistic as extreme as the one obtained, assuming the null hypothesis is true.

From a t-distribution table or calculator, the p-value corresponding to t = -2.564 and df = 99 is approximately 0.0075 (or 0.75% if multiplied by 100).

Since the p-value (0.0075) is less than the significance level (0.05), we reject the null hypothesis. This suggests strong evidence that the average distance cars travel per year is significantly less than 20,000 kilometers.

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Answer:

2,125,760

Step-by-step explanation:

The first term (a) is 8

The fourth term is 216

Hence the sum of the first 12 term can be calculated as follows

= 8-8(3)^12/1-3

= 8-24^12/-2

= 2,125,760

The sum of first 12 terms is 2,125,760

Sum of the first 12 term  =  2,125,760

For geometric sequence,

aₙ = arⁿ⁻¹

where

a = first term

r = common ratio

n = number of terms

Therefore,

a = 8

a₄ = 216

let's find the common ratio

216 = 8 × r⁴⁻¹

216 = 8 × r³

r³ = 216 / 8

r³ = 27

r = [tex]\sqrt[3]{27}[/tex]

r = 3

Let's find sum of the first 12 terms.

Sₙ = a (rⁿ - 1) / r - 1

S₁₂ = 8(3¹² - 1) / 3 - 1

S₁₂ = 8(531440) / 2

S₁₂ = 4251520 / 2

S₁₂ = 2,125,760

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Answer:

E

Step-by-step explanation:

Answer:

Step-by-step explanation:

59 apples two times = 59 x 2 = 118 apples

Total apples = 118 + 60 = 178 apples

Answer:

area = 164.52 cm²

Step-by-step explanation:

area = (12x6) + (12x3x0.5x2) + (3.14)(0.5)(6²) = 164.52 cm²

Answer:

Maximum, and (0, -2)

Step-by-step explanation:

Answer:

27.

Step-by-step explanation:

3^3 = 3 * 3 * 3

= 9 * 3

= 27.

Answer:

IMAO YOU GAVE UP, PSY

Step-by-step explanation:

Answer: 140,  220,  220,  140

Step-by-step explanation:

All you have to do is double the numbers.

all i know is that it would not be 13.9

Answer:

12in

Step-by-step explanation:

this is the only subject i'm good at in math XDDD.

Answer:

5/11 is 0.4555555555555555555555555

so basically the first option out of the two.

U do know you can just calculate this with the calculator right?

By applying the principle of inclusion-exclusion, we can show that for any events E1, E2,..., EM, the inequality P(E1 or E2 or ... or EM) < P(EM) holds. This result holds true for any integer M ≥ 1.

To prove the statement by induction, we will assume that for M = 1, the inequality holds true. Then we will show that if the statement holds for M, it also holds for M + 1.

Base case (M = 1):

For M = 1, we have P(E1) ≤ P(E1), which is true.

Inductive step:

Assuming that the inequality holds for M, we need to show that it holds for M + 1. That is, we need to prove P(E1 or E2 or ... or EM or EM+1) < P(EM+1).

Using the principle of inclusion-exclusion, we can express the probability of the union of events as follows: P(E1 or E2 or ... or EM or EM+1) = P(E1 or E2 or ... or EM) + P(EM+1) - P((E1 or E2 or ... or EM) and EM+1). Since events E1, E2, ..., EM, and EM+1 are mutually exclusive, the last term on the right-hand side becomes zero: P(E1 or E2 or ... or EM or EM+1) = P(E1 or E2 or ... or EM) + P(EM+1)

Since we assumed that P(E1 or E2 or ... or EM) < P(EM), we can rewrite the inequality as: P(E1 or E2 or ... or EM or EM+1) < P(EM) + P(EM+1)

Now we need to show that P(EM) + P(EM+1) < P(EM+1) for the inequality to hold. Simplifying the expression, we have: P(EM) + P(EM+1) < P(EM+1)

Since P(EM+1) is a probability and is always non-negative, this inequality holds true. Therefore, by the principle of mathematical induction, we have shown that for any integer M ≥ 1, the inequality P(E1 or E2 or ... or EM) < P(EM) holds.

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Answer:

5. B

6. A

7. C

Step-by-step explanation:

Answer:

5.) b. 12 - 2x

6.) a. 8x

7.) c. 5d + 3c = 66

Step-by-step explanation:

uhm, I don't really have proof, i've just been doing this for a long time, you're just gonna have to trust me on this one

Answer:

10

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

The expected number of women in the survey who have group A blood is 48.

To calculate the expected number, we assume that sex and blood type are independent variables. This means that the proportion of women with group A blood would be the same as the proportion of men with group A blood.

Out of 100 men surveyed, 40 had group A blood. This corresponds to a proportion of 40/100 = 0.4.

Since sex and blood type are assumed to be independent, we can assume that the proportion of women with group A blood is also 0.4.

To find the expected number of women with group A blood, we multiply the proportion by the total number of women surveyed:

Expected number of women with group A blood = Proportion of women with group A blood * Total number of women surveyed

Expected number of women with group A blood = 0.4 * 120 = 48

Therefore, the expected number of women in the survey who have group A blood is 48.

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Answer:

8

Step-by-step explanation:

0.20 x 40 = 8

Therefore, 20% of 40 is 8

Answer:

Dining Hall = 24 square meters

Kitchen = 48 square meters

Together = 72 square meters

The sum of given series is infinity ∑(n = 1) sin(nx)/(2n - 1).

What is sum of series?

A series' sum is the sum of the words or list of numbers that make up the series. If a series has a sum, it will be one integer (or fraction), such as 0, 1/2, or 99.

As given series is,

f(x) = sinx + sin(2x)/3 + sin(3x)/5+.....

The series function is trigonometric function such as sinx, sin(2x), sin(3x).

The nth term of series is sin(nx).

The coefficient of series is 1, 1/3, 1/5.

The coefficient of nth terms is 1/(2n - 1).

Sum of series is,

= infinity ∑(n = 1) sin(nx)/(2n - 1).

Hence, the sum of given series is infinity ∑(n = 1) sin(nx)/(2n - 1).

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A method of assigning probabilities based upon personal judgment is referred to as the subjective method. The correct answer is a.

The subjective method of assigning probabilities is based on personal judgment or subjective beliefs about the likelihood of events occurring. It involves incorporating individual knowledge, experience, and intuition to estimate the probabilities of different outcomes.

Unlike the classical method, which assigns probabilities based on equally likely outcomes, or the relative frequency method, which uses observed frequencies to determine probabilities, the subjective method relies on individual opinions and subjective assessments of probabilities.

In the subjective method, probabilities are not determined through mathematical calculations or empirical data. Instead, they are based on an individual's expertise, opinions, and subjective reasoning.

This method is commonly used in situations where objective data or historical information is limited or unavailable, such as in decision-making under uncertainty or when dealing with complex and uncertain scenarios.

The correct answer is a.

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The steps necessary for graphing parametric equations include creating a table, solving the equations for t and plotting those points, connecting the points with a smooth curve, and setting up the coordinate plane with t on the horizontal axis (c, d, f, h).

Create a table: Choose a range of values for t and calculate the corresponding values for x and y using the parametric equations. List these values in a table.

Solve the equations for t and plot those points: Solve the parametric equations separately for t to obtain the x and y coordinates. Plot these points on the coordinate plane.

Connect the points with a smooth curve: Once all the points are plotted, connect them with a smooth curve. This curve represents the graph of the parametric equations.

Set up the coordinate plane with t on the horizontal axis: Label the horizontal axis as t and the vertical axis as either x or y. This allows you to visualize how the x and y values change with respect to the parameter t.

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The the success rate of the student is PHYS>MATH. Therefore, the correct answer is Option A.

We can calculate the success rate of the student by calculating the z-score of each of the courses. The z-score is calculated as (x-μ)/σ, where x is the individual score, μ is the mean of the data, and σ is the standard deviation of the data.

For Physics, we have x=60, μ=49, and σ=11. So the z-score is (60-49)/11=1.09.

For Mathematics, we have x=58, μ=55, and σ=16. So the z-score is (58-55)/16=0.19.

Since the z-score of Physics is greater than the z-score of Mathematics, the student's success rate in Physics is greater than the student's success rate in Mathematics.

Therefore, the correct answer is Option A.

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