1 If a line segment joins the midpoints of two sides of a triangle, then it is _____slot 1_____ to the third side and _____ slot 2 _____ of the third side.

The probability that a randomly selected shirt has loose threads or crooked stitching is 8%.

To find the probability that a randomly selected shirt has loose threads or crooked stitching, we can use the principle of inclusion-exclusion.

P(A or B) = P(A) + P(B) - P(A and B)

Given:

P(loose threads) = 5%

P(crooked stitching) = 9%

P(loose threads and crooked stitching) = 3.5%

P(loose threads or crooked stitching) = P(loose threads) + P(crooked stitching) - P(loose threads and crooked stitching)

P(loose threads or crooked stitching) = 5% + 9% - 3.5%

P(loose threads or crooked stitching) = 11.5% - 3.5%

P(loose threads or crooked stitching) = 8%

Therefore, the probability that a randomly selected shirt has loose threads or crooked stitching is 8%.

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The percent markup on cost can be calculated by finding the difference between the selling price and the cost, dividing it by the cost, and then multiplying by 100 to express it as a percentage.

In this case, the selling price of the Kindle E-readers is $79.99 and the cost to the store is $16.9. To calculate the percent markup on cost, we can use the following formula:

Percent Markup on Cost = ((Selling Price - Cost) / Cost) * 100

Plugging in the values:

Percent Markup on Cost = (($79.99 - $16.9) / $16.9) * 100

Simplifying the expression:

Percent Markup on Cost = ($63.09 / $16.9) * 100

Calculating this expression gives us the percent markup on cost for the Kindle E-readers sold at Best Buy.

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The percent markup on cost, given that the E-reader costing $16. 9 was sold for $79. 99 is 373.31%

From the question given above, the following data were obtained:

The percent markup on cost can be obtain as illustrated below:

Percent markup on cost = (Gain / cost prize) × 100

= (63.09 / 16.9) × 100

= 373.31%

Thus, we can conclude from the above calculation that the percent markup on cost is 373.31%

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The appropriate null hypothesis is the proportion of defective products produced by this machine is equal to 0.20.

The appropriate null hypothesis is B. The proportion of defective products produced by this machine is equal to 0.20.What is a Null Hypothesis?A null hypothesis is a statistical hypothesis that is tested to determine whether it is statistically significant.

The null hypothesis is typically represented by the symbol H0. It is the hypothesis that there is no statistical significance between two variables. If there is statistical significance, then the null hypothesis is rejected.T

he appropriate null hypothesis in the given case is that the proportion of defective products produced by this machine is equal to 0.20. The machine is known to produce 20% defective products before it was sent for repair. After the repair, the manager of the factory wants to ensure that the machine is functioning correctly.

400 products produced by the machine are chosen at random, and 64 of them are found to be defective. We will use a hypothesis test to determine whether the repair was effective or not. In hypothesis testing, the null hypothesis is the hypothesis of no effect, while the alternative hypothesis is the hypothesis of an effect.

Therefore, the appropriate null hypothesis is B. The proportion of defective products produced by this machine is equal to 0.20.

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The appropriate null hypothesis in this case is "The proportion of defective products produced by this machine is equal to 0.20". Hence the correct option is B.

The null hypothesis is a statement that assumes there is no effect or difference.

In this scenario, it assumes that after the machine is repaired, it will continue to produce defective products at the same rate as before, which is 20%.

The alternative hypothesis would suggest that there is a difference in the proportion of defective products produced after the repair.

By choosing option B as the null hypothesis, the manager is testing whether the repair has effectively fixed the machine and brought its production of defective products back to the expected rate of 20%.

The alternative hypothesis would indicate that the repair has not been successful in reducing the proportion of defective products.

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The term "dependent variable" refers to a variable that is affected by another variable. The correct option is d.

A variable that is influenced by another variable is known as the dependent variable. Hence, the correct answer is option d) dependent variable. What is a variable? A variable is a characteristic or phenomenon that can take on various values.

Researchers measure them to see if they are linked to one another or to find out if one causes another. The characteristics that the researchers seek to measure can be tangible, such as the length of a telephone line, or intangible, such as the number of times a person smokes cigarettes.

The different types of variables are Independent variable Dependent variable Controlled variableWhat is an independent variable?An independent variable is a variable that isn't affected by anything in the experiment except for the introduction of the independent variable.

The experimenter selects it and manipulates it.In an experiment, an independent variable is a variable that causes a change in the dependent variable when it is altered. This is the variable that the experimenter changes to test its impact on the dependent variable.

What is a dependent variable?A dependent variable is the variable that is affected by the independent variable. It's what you measure in the experiment and what is affected by the introduction of the independent variable. The dependent variable is the response that is measured in the experiment.

A variable that is influenced by another variable is known as the dependent variable. Hence, the correct answer is option d) dependent variable.

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In order to carry out a legitimate statistical test of the nutritionists’ claim, we must assume that the observations come from a normally distributed population and that the mean content of the sample follows the normal distribution.

The observations must also be from a normally distributed population. Hence, the correct option is:We must assume that the observations come from a normally distributed population AND that the mean content of the sample follows the normal distribution AND that the population variance is known. To test whether the mean protein content of the soy compound is greater than that of roast beef, we need to carry out a hypothesis test. Since the sample size is less than 30, we need to assume that the population is normally distributed.The assumption that the mean content of the sample follows the normal distribution is necessary to apply the Central Limit Theorem (CLT) and the assumption that the observations are from a normally distributed population is necessary to carry out the hypothesis test.

Finally, in the assumption, the population variance is known, but it is not actually necessary since we can estimate the variance using the sample variance. Therefore, the correct option is:We must assume that the observations come from a normally distributed population AND that the mean content of the sample follows the normal distribution.

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1. The alternative hypothesis ([tex]H_a[/tex]) is that the percentage is actually more than the reported percentage [tex]H_a[/tex]: p > 0.41. 2. The test statistic is 2.89. 3. Since the alternative hypothesis states that the percentage is "more than" the reported percentage, the test is one-tailed. 4. The critical value for a one-tailed z-test with a significance level of 0.01. 5. The test statistic (2.89) is greater than the critical value (2.33). 6. A laptop is more than the reported percentage of 41%.

Step 1 of 6: State the null and alternative hypotheses.

The null hypothesis (H₀) is that the percentage of readers who own a laptop is 41% (reported percentage):

H₀: p = 0.41

The alternative hypothesis (Ha) is that the percentage is actually more than the reported percentage:

[tex]H_a[/tex]: p > 0.41

Step 2 of 6: Find the value of the test statistic. Round your answer to two decimal places.

To find the test statistic, we can use the formula for the z-test for proportions:

z = ([tex]\hat p[/tex] - p) / √(p * (1 - p) / n)

Where:

[tex]\hat p[/tex] is the sample proportion (50% = 0.50)

p is the hypothesized proportion (41% = 0.41)

n is the sample size (260)

Calculating the test statistic:

z = (0.50 - 0.41) / √(0.41 * (1 - 0.41) / 260)

z ≈ 2.89

Step 3 of 6: Specify if the test is one-tailed or two-tailed.

Since the alternative hypothesis states that the percentage is "more than" the reported percentage, the test is one-tailed.

Step 4 of 6: Determine the decision rule for rejecting the null hypothesis, H0.

To determine the decision rule, we compare the test statistic to the critical value at a given significance level (α). In this case, the significance level is 0.01.

Looking up the critical value for a one-tailed z-test with a significance level of 0.01, we find it to be approximately 2.33.

Step 5 of 6: Make the decision to reject or fail to reject the null hypothesis.

Since the test statistic (2.89) is greater than the critical value (2.33), we can reject the null hypothesis.

Step 6 of 6: State the conclusion of the hypothesis test.

Based on the sample data, there is sufficient evidence at the 0.01 level to support the marketing executive's claim that the percentage of readers who own a laptop is more than the reported percentage of 41%.

The complete question is:

A publisher reports that 41% of their readers own a laptop. A marketing executive wants to test the claim that the percentage is actually more than the reported percentage. A random sample of 260 found that 50% of the readers owned a laptop. Is there sufficient evidence at the 0.01 level to support the executive's claim?

Step 1 of 6: State the null and alternative hypotheses.

Step 2 of 6: Find the value of the test statistic. Round your answer to two decimal places.

Step 3 of 6: Specify if the test is one-tailed or two-tailed.

Step 4 of 6: Determine the decision rule for rejecting the null hypothesis, H₀.

Step 5 of 6: Make the decision to reject or fail to reject the null hypothesis.

Step 6 of 6: State the conclusion of the hypothesis test.

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The standard order of transformations for describing a transformation is dilation, rotation, and translation.

When there are several possible sequences of transformations that could be used to place one figure on top of another, there is one sequence that is logically more efficient than the others.

This sequence is called the standard order of transformations.

What is the standard order of transformations?

The standard order of transformations is defined as follows:

Start with a dilation, which changes the size of the figure but leaves it in the same position.

Then, perform a rotation, which changes the orientation of the figure.

Finally, perform a translation, which moves the figure to its final location.

Thus, the standard order of transformations for describing a transformation is dilation, rotation, and translation.

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The smallest positive integer n such that n/2 is a perfect square, n/3 is a perfect cube, and n/5 is a 5th power is 120.

Let's consider the prime factorization of each number.

[tex]n/2 = 2^x * 3^y * 5^z,[/tex] where x, y, and z are non-negative integers.

[tex]n/3 = 2^x * 3^(y+1) * 5^z[/tex], where x, y, and z are non-negative integers.

[tex]n/5 = 2^x * 3^y * 5^(z+1),[/tex]where x, y, and z are non-negative integers.

For n/2 to be a perfect square, x must be even. For n/3 to be a perfect cube, y must be even. For n/5 to be a 5th power, z must be even.

The smallest possible values of x, y, and z are x=2, y=2, and z=2. This gives us n =[tex]2^2 * 3^2 * 5^2[/tex] = 120.

Any smaller value of n will not satisfy all of the conditions. For example, if n=60, then n/2 is a perfect square, but n/3 is not a perfect cube and n/5 is not a 5th power.

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The new limits of integration after applying the substitution u = 4x + π to the integral ∫π to 0 sin(4x + π) dx are π to 5π.

To find the new limits of integration after applying the substitution u = 4x + π to the integral ∫π to 0 sin(4x + π) dx, we need to determine the values of x that correspond to the original limits π and 0.

Let's start by solving the substitution equation for x:

u = 4x + π

Rearranging the equation to solve for x, we have:

x = (u - π)/4

Now we can find the new limits of integration by substituting the original limits into the equation for x:

For the lower limit, when x = 0:

x = (u - π)/4

0 = (u - π)/4

Solving this equation for u, we have:

(u - π)/4 = 0

u - π = 0

u = π

Therefore, the lower limit of integration remains unchanged, and it is still π.

For the upper limit, when x = π:

x = (u - π)/4

π = (u - π)/4

Solving this equation for u, we have:

(u - π)/4 = π

u - π = 4π

u = 5π

Therefore, the upper limit of integration becomes 5π.

The new limits of integration after applying the substitution u = 4x + π to the integral ∫π to 0 sin(4x + π) dx are π to 5π.

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The researcher used cluster sampling, where high schools were chosen as clusters and all administrators from the selected schools were included in the sample.

The sampling technique used by the researcher is known as cluster sampling.

Cluster sampling involves dividing the population into groups or clusters and randomly selecting entire clusters to be included in the sample.

In this case, the high schools are considered the clusters, and the researcher randomly chose five high schools from her list.

Once the clusters are selected, all administrators from the chosen schools are included in the sample.

This is known as a "within-cluster" sampling approach, where all individuals within the selected clusters are included, rather than selecting a subset of individuals from each cluster.

Cluster sampling is often employed when it is more practical or cost-effective to sample groups rather than individuals directly.

By randomly selecting high schools as clusters, the researcher can include a representative sample of high school administrators without needing a complete list of administrators.

It is important to note that cluster sampling introduces a potential for within-cluster homogeneity, meaning that individuals within the same cluster may be more similar to each other than to individuals in other clusters.

However, this can be addressed through appropriate statistical analysis techniques that take into account the cluster structure of the data.

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There are 30 different ways to select two items from the given set such that at least one jeans is chosen.

To determine the number of ways to select two items from the given set of shirts and jeans, we can consider the two cases: one where exactly one jeans is chosen and another where both items chosen are jeans.

Case 1: Exactly one jeans is chosen:

In this case, we have 4 options for selecting one jeans, and we need to choose one shirt from the remaining 6 shirts. Thus, the total number of ways to select exactly one jeans and one shirt is 4 * 6 = 24.

Case 2: Both items chosen are jeans:

In this case, we have 4 options for selecting the first jeans and 3 options for selecting the second jeans. The order of selection doesn't matter, so we need to divide the total by 2 to avoid counting duplicates. Thus, the total number of ways to select two jeans is (4 * 3) / 2 = 6.

To find the total number of ways to select two items so that at least one jeans is chosen, we sum up the possibilities from both cases:

Total number of ways = Case 1 + Case 2 = 24 + 6 = 30.

Therefore, there are 30 different ways to select two items from the given set such that at least one jeans is chosen.

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mop ~ ron, and the proof is proved

Proof:

Given:

a // b (Line a is parallel to line b)

In Δmop and Δron:

∠mop = ∠ron [Alternate interior angles]

∠omp = ∠onr [Alternate interior angles]

∠pom = ∠rno [Alternate interior angles]

Therefore, Δmop ~ Δron [By Angle-Angle (AA) similarity]

Therefore, mop ~ ron, and the proof is completed.

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There are a total of 3 batches of fudge, with each batch containing 3/4 of a pound. So, we can multiply the amount of fudge per batch by the number of batches to determine the total amount of fudge that was made:3 batches × 3/4 pound per batch = 9/4 pounds of fudge were made.

Next, we can subtract the amount of fudge that was sold (1 and 1/4 pounds) from the total amount of fudge that was made (9/4 pounds) to determine how much fudge is left:9/4 - 5/4 = 4/4 = 1 pound of fudge is left.

The given problem states that a bakery makes three batches of fudge and each batch contains 3/4 of a pound. They sell 1 and 1/4 pounds of fudge. So, we need to find the amount of fudge they have left. To solve this problem, we will use some simple math.First, let's calculate the total amount of fudge made. We can do this by multiplying the amount of fudge per batch by the number of batches. So, 3 batches x 3/4 pound per batch = 9/4 pounds of fudge were made.Next, we will find out the amount of fudge left by subtracting the amount of fudge that was sold from the total amount of fudge made. They sold 1 and 1/4 pounds of fudge, so we subtract this from 9/4 pounds to get

:9/4 - 5/4 = 4/4 = 1 pound of fudge left. So, the bakery has 1 pound of fudge left. This means that they sold a total of 5/4 pounds of fudge, leaving 1 pound of fudge that they didn't sell.

Therefore, the bakery has 1 pound of fudge left. They sold 1 and 1/4 pounds of fudge and made a total of 9/4 pounds of fudge by using three batches of fudge each containing 3/4 of a pound.

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The amount of fudge that they have left is given as follows:

1 pound.

The amount of fudge that they have left is obtained applying the proportions in the context of the problem.

A bakery makes three batches of fudge. Each batch of fudge contains 3/4 of a pound, hence the total amount is given as follows:

3 x 3/4 = 9/4 pounds.

The amount sold is given as follows:

1 + 1/4 = 5/4 pounds.

Hence the remaining amount is given as follows:

9/4 - 5/4 = 4/4 = 1 pound.

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The Probability of drawing a hand that contains two kings is [tex]\dfrac{6}{1326}[/tex],  if we draw a two-card hand from a standard deck of 52 cards

Total number of ways of drawing 2 cards from a pack of 52 cards  = 5C2.

Probability is the state of possibility of an event occuring. It ranges from 0 to 1

[tex]Probability = \dfrac{number of favourable event}{Total number of event}[/tex]

The Probability of drawing a hand that contains two cards are = [tex]4C2[/tex]

(4-2)[tex]![/tex]

[tex](4-2) ! =\dfrac{4 ! }{2 ! 2 ! }[/tex]

= 6

Total number of ways of drawing 2 cards from a pack of 52 cards [tex]52 C2[/tex]

= (52 - 2) ! = 1326

So, required Probability= [tex]\dfrac{6}{1326}[/tex]

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The level of production that maximizes the manufacturer's total revenue is 220 units per day. The maximum revenue is $78,240 per day.

The manufacturer's total revenue is equal to the price per unit multiplied by the number of units sold. In this case, the price per unit is given by the demand function p = f(q) = -0.16q + 352. To maximize the manufacturer's total revenue, we need to find the value of q that maximizes the function p(q)q.

We can do this by differentiating p(q)q with respect to q and setting the derivative equal to zero. This gives us the equation q(-0.16 + q) = 0. Solving for q, we get q = 220.

Plugging this value of q back into the demand function, we get p(220) = -0.16(220) + 352 = 256.

Therefore, the maximum revenue is 256 * 220 = $78,240 per day.

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For 10% of the normal curve z is 1.28 , and 90% between -z and z = 1.64

For a normal distribution, if z is a z-score or standard score, then the area between the mean and a point that is at a distance of z standard deviations from the mean is the percentage found from the standard normal distribution table.

Here : 10% of the standard normal curve lies to the right of z.

That means, the area to the left of z is 1 - 0.1 = 0.9.Using the z-score table, we find that the z-score corresponding to an area of 0.9 is 1.28.

Therefore, z = 1.28.90% of the standard normal curve lies between -z and z. That means, the area between -z and z is 0.9 or 90%.

Using the z-score table, we find that the z-score corresponding to an area of 0.45 (half of 0.9) is 1.64. Therefore, z = 1.64.

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Statement c. "An interaction effect can only be tested between a continuous variable and a categorical variable" is true. Correct answer is option c.

a. Statement a is false. ANOVA (Analysis of Variance) or ANCOVA (Analysis of Covariance) and multiple linear regression are related but not equivalent. They are different statistical techniques used for different purposes. ANOVA/ANCOVA is typically used to compare means between groups or conditions, while multiple linear regression is used to examine the relationship between multiple predictors and a continuous outcome variable.

b. Statement b is also false. ANOVA/ANCOVA and multiple linear regression can yield different results depending on the research question, data, and assumptions made. While there may be some overlap in certain scenarios, the results are not generally expected to be very different.

d. Statement d is false. An interaction effect can be tested between both continuous and categorical variables, not just between two categorical variables. In statistical analysis, an interaction effect refers to the combined effect of two or more variables on the outcome, where the effect of one variable depends on the level of another variable. These variables can be of different types, such as continuous and categorical, and their interaction can be tested using appropriate statistical techniques.

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Using the fundamental theorem of calculus, we can evaluate the definite integral ∫[1 to 0] (y^2 + y^6) dy exactly.

To evaluate the definite integral ∫[1 to 0] (y^2 + y^6) dy, we can apply the fundamental theorem of calculus. The fundamental theorem states that if F(x) is an antiderivative of a function f(x) on an interval [a, b], then the definite integral of f(x) from a to b is equal to F(b) - F(a).

Let's find the antiderivative of the integrand (y^2 + y^6). The antiderivative of y^2 with respect to y is (1/3)y^3, and the antiderivative of y^6 is (1/7)y^7. Thus, the antiderivative of the integrand is (1/3)y^3 + (1/7)y^7.

Applying the fundamental theorem of calculus, the definite integral becomes [(1/3)(0^3) + (1/7)(0^7)] - [(1/3)(1^3) + (1/7)(1^7)]. Simplifying, we get (0 + 0) - (1/3 + 1/7) = -10/21.

Therefore, the exact value of the definite integral ∫[1 to 0] (y^2 + y^6) dy is -10/21.

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The P-value of drawing a random sample of 50 and getting a mean of 100 or less is approximately 0.1726 (17.26%).

The Z-score formula is given by,

Z = (X - μ)/(σ/√(n))

X = Sample mean (100)

μ = Population mean (102)

σ = Standard deviation (15)

n = Sample size (50)

Let's calculate the Z-score,

Z = (100 - 102)/(15/√(50))

Z = -2 / (15 / 7.071)

Z = -0.9428

To find the P-value, we need to determine the probability of obtaining a Z-score less than or equal to -0.9428 from the standard normal distribution. We can use a Z-table or a statistical calculator to find this probability.

Looking up the Z-score -0.9428 in a standard normal distribution table, we find that the corresponding cumulative probability is approximately 0.1726. Therefore, the P-value of drawing a random sample of 50 and getting a mean of 100 or less is approximately 0.1726, or 17.26%.

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The density of the object is 2.8 g/cm³.

Density is defined as the amount of matter contained in a particular volume.

The formula to calculate the density of an object is given as:

Density = mass/volume

Given, the volume of the object is 20 cm³ and the mass of the object is 56g.

Substituting the values in the formula we get:

Density = mass/volume

Density = 56g/20 cm³

Density = 2.8 g/cm³

Therefore, the density of the object is 2.8 g/cm³.

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The distribution that most likely describes the outcome of the random variable x is Poisson distribution (option b).

The distribution that most likely describes the outcome of the random variable x, the number of cars arriving in any hour, is the Poisson distribution.

The Poisson distribution is commonly used to model the number of events occurring in a fixed interval of time when the events happen at a constant average rate and independently of the time since the last event.

In this case, the average number of cars arriving every hour is given as 6.7. The Poisson distribution is appropriate because it models events occurring over a continuous range (in this case, the number of cars) and is suitable for situations where the events occur independently and at a constant average rate.

Therefore, the answer is b. Poisson distribution.

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We can be 95% confident that the true average amount spent by all students at University XYZ on a date falls within this interval.

To compute a 95% confidence interval for the average amount spent by all students at University XYZ on a date, we can use the formula:

Confidence Interval [tex]= \bar{X} \pm (t \times (s / \sqrt{n} ))[/tex]

Where:

[tex]\bar{X}[/tex] is the sample mean

t is the critical value for the desired confidence level (with n-1 degrees of freedom)

s is the sample standard deviation

n is the sample size

In this case, the sample mean ([tex]\bar{X}[/tex]) is $40.00, the sample standard deviation (s) is $5.00, and the sample size (n) is 30.

Since the sample size is larger than 30 and the distribution is assumed to be normal, we can use a t-distribution to find the critical value.

With 30 degrees of freedom and a 95% confidence level, the critical value (t) can be obtained from a t-distribution table or a statistical software.

Let's assume the critical value is 2.042 (hypothetical value).

Substituting the values into the formula:

Confidence Interval = $40.00 ± (2.042 [tex]\times[/tex] ($5.00 / √30))

Calculating the standard error (s / √n):

Standard Error = $5.00 / √30

Substituting the standard error value:

Confidence Interval = $40.00 ± (2.042 [tex]\times[/tex] [Standard Error])

By evaluating the equation, the confidence interval for the average amount spent by all students at University XYZ on a date is approximately $38.43 to $41.57 (rounded to two decimal places).

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a. The random variable represents the time which takes to completely tune an automobile engine.

b. The probability of tuning an engine is qual to 0.593, or 59.3%.

a. The random variable here is the time it takes to completely tune an engine of an automobile.

b. To find the probability of tuning an engine in 45 minutes or less,

Use the exponential distribution formula.

The exponential distribution is characterized by a rate parameter, which is the reciprocal of the mean.

The mean is 50 minutes,

The rate parameter (λ) can be calculated as λ

= 1/mean

= 1/50.

Using this rate parameter,

The probability of tuning an engine in 45 minutes or less by integrating the exponential probability density function (PDF) from 0 to 45 minutes,

P(X ≤ 45) = [tex]\int_{0}^{45}[/tex]λ × [tex]e^{(-\lambda x)[/tex] dx

Substituting the value of λ = 1/50 into the equation,

P(X ≤ 45) = [tex]\int_{0}^{45}[/tex] (1/50) × [tex]e^{(-x/50)[/tex] dx

Rewrite the integral:

P(X ≤ 45) = (1/50) ×  [tex]\int_{0}^{45}[/tex]  [tex]e^{(-x/50)[/tex] dx

Apply the integral,

P(X ≤ 45) = (1/50) × [-50 × [tex]e^{(-x/50)[/tex]] evaluated from 0 to 45

Plug in the limits of integration,

P(X ≤ 45) = (1/50) × [-50 ×[tex]e^{(-45/50)[/tex] - (-50 × [tex]e^{(-0/50)[/tex])]

Simplify the expression,

P(X ≤ 45) = (1/50) × [-50 × [tex]e^{(-45/50)[/tex]+ 50 × [tex]e^0[/tex]]

Simplify further,

P(X ≤ 45) = -[tex]e^{(-45/50)[/tex] + 1

Evaluate the expression,

⇒P(X ≤ 45) ≈ -[tex]e^{(-0.9)[/tex] + 1

⇒P(X ≤ 45) ≈ -0.407 + 1

⇒P(X ≤ 45) ≈ 0.593

Therefore, the probability of tuning an engine in 45 minutes or less is approximately 0.593, or 59.3%.

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Answer:

1. 790

2 125

3 89

4 1 90

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The parameter of interest is the proportion of smartphone users in the US who have downloaded an app. The notation for the quantity used to make the estimate is p-hat ([tex]\hat{p}[/tex]). The value of the best estimate is 0.769.

(a) The percentage of smartphone users in the US who have downloaded an app is the relevant parameter (a).

(b) The quantity utilized to create the estimate is denoted by the symbol p-hat ([tex]\hat{p}[/tex]), which stands for the sample percentage of smartphone users who have downloaded an app.

(c) The following formula can be used to determine the best estimate of the percentage of smartphone users that have downloaded an app:

[tex]\hat{p}[/tex] = Number of smartphone users who have downloaded an app / Total number of smartphone users

[tex]\hat{p}[/tex] = 355 / 461

[tex]\hat{p}[/tex] ≈ 0.769

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The complete question is:

A random sample of n=461 smartphone users in the US in January 2015 found that 355 of them have downloaded an app.1 Of the n=355 smartphone users who had downloaded an app, the average number of apps downloaded was 19.7.

(a) Give notation for the parameter of interest.

(b) Give the notation for the quantity we use to make the estimate.

(c) Give the value of the best estimate.

Alison has set a goal for herself to complete all of the required trainings in the next 90 days by taking two trainings per week, which is an example of goal setting. Goal setting is the process of deciding what you want to accomplish and devising a plan to achieve it.

It is a critical component of personal and professional development because it allows you to focus your efforts on accomplishing specific objectives that will help you progress in your career or personal life. For instance, Alison sets the goal of completing all of her required training in the next 90 days by taking two trainings per week.

This is an example of goal setting because she has identified a specific objective and established a timeframe and a plan to achieve it.

By doing so, Alison can monitor her progress and adjust her approach as necessary to ensure that she reaches her goal.

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The approximate probability that greater than 99 out of 160 students will pass their college placement exams is 0.2831.

To approximate the probability using the normal distribution, we can use the concept of the binomial distribution approximation to the normal distribution. In this case, we have a large sample size (160 students) and a probability of success (passing the exam) that is not extremely small or large (64%).

To calculate the probability that greater than 99 out of 160 students will pass the exam, we can use the normal approximation to the binomial distribution. The mean of the binomial distribution is given by μ = n * p, and the standard deviation is given by σ = sqrt(n * p * (1 - p)), where n is the sample size and p is the probability of success.

In this case, n = 160 and p = 0.64.

Therefore, the mean is μ = 160 * 0.64 = 102.4,

and the standard deviation is σ = sqrt(160 * 0.64 * (1 - 0.64)) ≈ 5.1055.

Now, we can calculate the probability using the normal distribution. We want to find the probability of having more than 99 students pass the exam out of 160, which is equivalent to finding the probability that the number of successes is greater than 99.

We can standardize the value using the z-score formula: z = (x - μ) / σ, where x is the desired number of successes. In this case, x = 99.5 (to account for continuity correction, as we're dealing with a discrete distribution).

z = (99.5 - 102.4) / 5.1055 ≈ -0.565

Using a standard normal distribution table or a calculator, we can find the probability corresponding to the z-score of -0.565, which is the probability of having more than 99 students pass the exam.

Looking up the z-score of -0.565 in the standard normal distribution table, we find that the probability is approximately 0.2831.

Rounding the answer to four decimal places, the approximate probability that greater than 99 out of 160 students will pass their college placement exams is 0.2831.

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Given that students turn in their homework and a teacher rewards them with computer time and the more frequently they turn in their homework, the more they are allowed to use the computers. Students have been turning in their homework with increasing frequency, therefore, the computer time is serving as a POSITIVE REINFORCEMENT.

Positive reinforcement is a behavior modification strategy that entails rewarding or reinforcing a certain action to encourage it to happen again. It is a technique used in operant conditioning, a theory of behavior management that uses rewards and punishments to shape behavior. In other words, positive reinforcement entails the addition of a positive stimulus following a specific action that leads to an increase in the likelihood of that action repeating in the future.

Example, The parents of a child give them $5 for every good grade received, resulting in better grades in the future.

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Linda's walking rate is approximately 4.51 miles per hour.

To calculate Linda's walking rate per hour, we can use the concept of unit conversion.

We know that Linda can walk 6 miles in 80 minutes. To convert this to hours, we need to divide the number of minutes by 60, since there are 60 minutes in an hour.

Walking rate per hour = (Distance walked) / (Time taken in hours)

Time taken in hours = 80 minutes / 60 minutes per hour = 4/3 hours (or 1.33 hours)

Walking rate per hour = 6 miles / 1.33 hours ≈ 4.51 miles per hour

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Null hypothesis (H0): The global mean temperature in the current year is not lower than the global mean temperature in 1998 (μ ≥ 14.3°C).

Alternative hypothesis (H1): The global mean temperature in the current year is lower than the global mean temperature in 1998 (μ < 14.3°C).

As a climatologist, you can formulate the null and alternative hypotheses for testing whether the global mean temperature in the current year is lower than the global mean temperature in 1998. Here are the hypotheses:

Null hypothesis (H0): The global mean temperature in the current year is not lower than the global mean temperature in 1998.

H0: μ ≥ 14.3

Alternative hypothesis (H1): The global mean temperature in the current year is lower than the global mean temperature in 1998.

H1: μ < 14.3

In statistical terms, the null hypothesis assumes that the population mean temperature in the current year is greater than or equal to 14.3 degrees Celsius (or not lower than the temperature in 1998). The alternative hypothesis, on the other hand, suggests that the population mean temperature in the current year is lower than 14.3 degrees Celsius (lower than the temperature in 1998).

To test these hypotheses, you will need to gather more data and conduct appropriate statistical tests. The preliminary sample mean of 15.1 degrees Celsius will serve as a starting point, but further analysis will be necessary to make a conclusive determination.

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