michelle ran 1/2 of a mile in 1/8 of an hour. How many miles can she run in one hour?​

a. The explanatory variable in this study is insomnia and the response variable is the likelihood of experiencing heart problems. b. Amount of caffeine consumed could be a confounding variable in this study because it fits the two properties of confounding variables.

In this study, the explanatory variable is "insomnia" and the response variable is "heart problems." A confounding variable, such as "amount of caffeine consumed," might affect the relationship between insomnia and heart problems. Caffeine consumption fits the two properties of confounding variables as it is related to both the explanatory variable (insomnia) and the response variable (heart problems). Consuming more caffeine can lead to insomnia, and it can also increase the risk of heart problems independently. Therefore, caffeine consumption could be a confounding variable in this study, potentially influencing the observed relationship between insomnia and heart problems.

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158,400 people will fit into an area with a dimension of 30feets by 2 miles.

The area of the street can be calculated thus :

Area = Length × width

Converting the width to feets :

1 mile = 5280 feets

2 miles = x

Cross multiply :

x = 5280 × 2 = 10560 feets

Area = 10560 ft × 30ft = 316800 ft²

Since 15 people fit into an area with dimension which is 6 ft by 6ft

Area = 6 × 6 = 36 ft²

Let x = number of people

15 people = 36 ft²

x people = 316800 ft²

Cross multiply :

x = (316800 × 15) / 36

x = 158,400 people

Hence 158,400 people will fit in.

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Answer:

1/10

Step-by-step explanation:

;)

Lines l and m are parallel; line l will map onto line m with a 90° rotation; line l can map onto line m with a vertical line of reflection.

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Answer:

1/27

Step-by-step explanation:

I believe the answer to your question is 1/27

I hope this helps you!

We can compute various descriptive statistics such as the mean, median, mode, range, variance, standard deviation, sum of values, and sum of squared deviations.

The sample mean, also known as the average, provides information about the central tendency of the variable X. It represents the typical or average number of coupons used by the shoppers in the sample. In this case, calculating the mean of the given data would provide an estimate of the average number of coupons used over the 6-month period.

The sample standard deviation measures the dispersion or variability of the data points around the mean. It indicates how much the individual observations deviate from the mean value. A higher standard deviation implies greater variability, indicating a wider range of coupon usage among the shoppers in the sample.

By computing the sample mean and standard deviation, we can understand the average coupon usage and the degree of variability in the data. These statistics help us summarize and interpret the characteristics of the variable X, allowing us to make comparisons, identify outliers, assess the spread of the data, and make inferences about the larger population from which the sample was drawn.

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Answer:

Step-by-step explanation:

b) x=-1

c) x=-4, x=2, y = 8

d) (-1,9)

Answer:

C: 8 weeks

Step-by-step explanation:

Using the information provided in the question we can create the following model for this scenario. We have the total amount needed, an initial starting point of money he had already saved and the amount he is able to save each week which is multiplied by the variable number of weeks (x) which we need to solve for...

565.95 = 205.00 + 46.00x  ... subtract 205.00 from both sides

360.95 = 46.00x ... divide both sides by 46.00

7.84 = x

We can now see that it would take Sayir a total of 7.84 weeks to save that money but since he gets paid on a weekly basis we would need to round up to 8 weeks.

Answer:

1040

Step-by-step explanation:

P=$20000

T=1 year

R=5.2%

we know that ,

I=PTR/100

I=$20000*1*5.2/100

I=1040

Answer:

(A) - B

(B) - DC

Answer:

9

Step-by-step explanation:

x − 3y

Let x =3 and y = -2

3 -3(-2)

3 + 6

9

 The limit, as n approaches infinity, of the summation of cos(xi)∆x / xi from i = 1 to n over the interval [2π, 5π], can be expressed as the definite integral of cos(x)/x from 2π to 5π.

To express the given limit as a definite integral, we need to recognize that the limit is equivalent to the Riemann sum of the function cos(x)/x over the interval [2π, 5π]. The Riemann sum approximates the area under the curve of the function by dividing the interval into smaller subintervals and summing the values of the function at each subinterval.
In this case, as n approaches infinity, the interval [2π, 5π] is divided into n subintervals, each with width ∆x = (5π - 2π)/n = 3π/n. The xi values represent the endpoints of these subintervals. The function cos(xi)∆x / xi is evaluated at each xi, and the sum is taken over all the subintervals from i = 1 to n.
As n tends to infinity, the Riemann sum converges to the definite integral of cos(x)/x over the interval [2π, 5π]. Therefore, the given limit can be expressed as the definite integral from 2π to 5π of cos(x)/x.

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the complete question is:
Express the limit as a definite integral on the given interval. lim n→[infinity] summation i is from 1 to n cos(xi)∆x /xi [2π, 5π] = integral 2π to 5π ???

Answer:

The answer is $66.95

Step-by-step explanation:

First you multiply the Principle (1300) Rate (in decimal form which is 0.118) Time (2 years = 24 months). 1300(0.118)(2) = 306.8 add principle (1300) = $1606.8 divide by 2 years in month form (24) = $66.95

Comment if confusing.

Answer:

\(3 \times \frac{1}{3 } + \frac{1}{2} \times - 12( \frac{1}{3} ) = \frac{1}{3} \)

Selecting all students with last names beginning with the letter M would not produce a random sample of a school population of 1000 students. Hence the answer is no.

A random sample is obtained by selecting individuals from a population in a way that ensures every member of the population has an equal chance of being included in the sample.

By choosing only students with last names beginning with the letter M, you are introducing a bias and not providing an equal chance for all students to be selected.

To obtain a random sample of 1000 students from a school population, you would need to use a random selection method that ensures each student has an equal probability of being chosen.

This could be achieved through techniques such as random number generators, random sampling software, or random sampling techniques like stratified or cluster sampling.

Selecting all students with last names beginning with the letter M would not meet the requirements of a random sample, as it would not provide an equal chance for all students in the population to be included.

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Answer:

13×1/4

Step-by-step explanation:

turn into improper fraction

Answer:

45

Step-by-step explanation:

25 plus 7 is 32

32 minus 3 is 29

29 plus 16 is 45

hmmm well that's a  lil too hard for my smol brain to process but hmmm well when I think about it, it really gets my brain thinking and ummm well you see it's uh hmm you add the yeah to that and hmmmm well ahhh that looks to be about right uuuuuuuuuh

45....

.....or is it?

hmmmmmmmmmmmmmmm

The value of alpha is 0.025. The Z-value is 1.96. The P(z) is 0.5. The effect size is 0.05. The Sample size for the study is 384.

An area created using fixed-size samples of data from a population (sample space) that follows a certain probability distribution is known as a confidence interval. A selected population statistic is built into the interval with a specified probability. An estimate's level of uncertainty is described by a confidence interval, which is a range of numbers. The 68-95-99.7 Rule states that 95% of values lie within two standard deviations of the mean, hence to get the 95% confidence interval, you add and subtract two standard deviations from the mean.

Here,

All the calculations attached in image.

z= 1.96

p = 0.5

q = 1-p = 0.5

E = 0.05

sample size =

(z^2).(pq)=(1.96^2).(0.5)(.0.5)

384.16,

round up

n for study =385

Alpha has a value of 0.025. There is a 1.96 Z-value. P(z) equals 0.5. The impact factor is 0.05. The Sample size for the study is 384.

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When performing a statistical test, such as the Chi-Square test, the p-value is a crucial component in determining the significance of the data compared to the null hypothesis. The p-value represents the probability of observing the given data, or more extreme results, assuming the null hypothesis is true. In general, a p-value threshold of 0.05 is used to determine statistical significance.

If the calculated p-value is less than or equal to 0.05, it indicates that the observed data significantly differ from what is expected under the null hypothesis. This means that there is a less than 5% chance of obtaining the observed data if the null hypothesis were true. Consequently, researchers often reject the null hypothesis in favor of the alternative hypothesis when the p-value is less than or equal to 0.05.

However, it is essential to note that the choice of the significance level is subjective and may vary depending on the field or specific study. In some cases, a more stringent threshold, such as 0.01, might be required to minimize the chances of false positives, while in other situations, a more lenient threshold, such as 0.10, may be acceptable.

In summary, a p-value of 0.05 or less typically indicates that the data differ significantly from what is expected under the null hypothesis in a statistical test like the Chi-Square test. However, the chosen threshold for significance may vary depending on the specific context and research objectives.

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The solutions to the equation are x = -1, x = -8, and x = 1/2.

The equation 4x³ + 32x² + 42x - 16 = 0 can be divided throuh by 2 as follows:

2x³ + 16x² + 21x - 8 = 0

We can test each of these possible roots by substituting them into the equation and seeing if we get 0. When we substitute -1, we get 0, so -1 is a root of the equation. We can then factor out (x + 1) from the equation to get:

(x + 1)(2x² + 15x - 8) = 0

We can then factor the quadratic 2x² + 15x - 8 by grouping to get:

(x + 8)(2x - 1) = 0

This gives us two more roots, x = -8 and x = 1/2.

Therefore, the solutions to the equation are x = -1, x = -8, and x = 1/2.

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Step-by-step explanation:

\(11=8+2+1=2^3+2^1+2^0=\bold1\cdot2^3+\bold0\cdot2^2+\bold1\cdot2^1+\bold1\cdot2^0\\\\11_{10}=\bold{1011}_2\)

The p-value is a statistical measure used to determine the likelihood of observing a particular result or more extreme results, given the null hypothesis is true.

In this case, the null hypothesis is that the average amount Bob makes in tips per table is indeed $9.60, as claimed by the restaurant.

The p-value of 0.13 indicates that there is a 13% chance of observing an average tip amount as low as $8.95 or lower, assuming the null hypothesis is true.

In other words, if the restaurant's claim is accurate and Bob is just experiencing natural variation, there is a 13% probability of seeing an average tip amount as low as $8.95 or even lower.

Since the p-value is greater than the commonly used significance level of 0.05, which represents a 5% chance of seeing such a result due to random variation alone, we fail to reject the null hypothesis.

This means that the evidence does not provide strong enough support to conclude that Bob's average tip amount is significantly different from the claimed average of $9.60.

However, it is important to note that the p-value does not provide information on the direction of the difference.

It only tells us the likelihood of observing a result as extreme or more extreme than the one observed. So, even though Bob's average tip amount is lower than the claimed average,

the p-value alone does not determine whether the difference is statistically significant.

In summary, a p-value of 0.13 suggests that there is not enough evidence to conclude that Bob's average tip amount is significantly different from the claimed average of $9.60.

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Answer:

21.17 to 2d.p.

Step-by-step explanation:

Using Pythagoras rearrage to find b c^2-a^2 = b^2

c= hypothenuse

32^2 = 1024 and 24^2 = 576

1024 -576 = 448

\(\sqrt{448}\) = 21.1660105

21.17 to 2d.p.

Answer:

x=12

Step-by-step explanation:

\(x^{2}\)=\(15^{2}\)-\(9^{2}\)

\(x^{2}\)=225-81

\(x^{2}\)=144 /sqrt

x=12

If the volume of three rectangular pyramids is equal to the volume of a rectangular prism, it implies that the three pyramids can be combined to form the rectangular prism.

In a rectangular prism, the volume is given by the formula V = lwh, where l is the length, w is the width, and h is the height.

Since the three pyramids have equal length, width, and height, let's denote them as x.

The volume of one rectangular pyramid is given by V = (1/3) ×  (x ×  x ×  x) = (1/3) × x³

The combined volume of the three pyramids is (3/3)× x³

= x³

To constitute the volume of the rectangular prism, the volume of the three pyramids should be equal to the volume of the prism, so we have:

x³ = lwh

Therefore, the length, width, and height of the rectangular prism are all equal to x.

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Answer:

∠ P ≈ 46.9°

Step-by-step explanation:

The area (A) of Δ PST is calculated as

A = \(\frac{1}{2}\) × PS × PT × sinP

Here A = 71.24 , then

\(\frac{1}{2}\) × 15 × 13 × sinP= 71.24 , that is

97.5 × sinP = 71.24 ( divide both sides by 97.5 )

sinP = \(\frac{71.24}{97.5}\) , then

∠ P = \(sin^{-1}\) (\(\frac{71.24}{97.5}\) ) ≈ 46.9° ( to the nearest tenth )

Answer:

7

Step-by-step explanation:

The middle 2 numbers are 6 and 8. Add them both up and divide them by 2. Gets you 7.

The zeros of the polynomial function

1.0,3,-1

2.3,-2,+1

3.2,-3,0

The zeros of a polynomial are the x values that satisfy the equation f(x) = 0. In this case, f(x) is a function of x, and the polynomial zeros are the x values for which the f(x) value is zero. The number of zeros in a polynomial is determined by the degree of the equation f(x) = 0. The polynomial zeros are all domain values of the function whose range is equal to zero.

The polynomial zeros are the points on the graph where y = f(x) touches the x-axis. More on this in the page below on expressing polynomial zeros on a graph.

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