Meta-analysis involves:

a. averaging all the test statistics from every possible study on a given topic.
b. finding all studies published on a topic, calculating the effect size for each of those studies, and averaging the effect sizes together to find the average size of the effect across all studies.
c. finding all studies published on a topic, contacting the authors of the studies to request their original data, and then analyzing all the obtained data in one large analysis of variance.
d. attempting to recreate the experimental conditions of every published study on a given topic.

Answer:

H0 : mu1 = mu2

Ha : mu1 ≠ mu2

Which means

Null hypothesis H0; the true mean price when buying from a friend mu1 and the true mean price when buying from a stranger mu2 is the same/equal

Alternative hypothesis Ha; the true mean price when buying from a friend mu1 and the true mean price when buying from a stranger mu2 is different (not equal)

Step-by-step explanation:

The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean(i.e it tries to prove that the old theory is true). While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.

Therefore, for the case above;

H0 : mu1 = mu2

Ha : mu1 ≠ mu2

Which means

Null hypothesis H0; the true mean price when buying from a friend mu1 and the true mean price when buying from a stranger mu2 is the same/equal

Alternative hypothesis Ha; the true mean price when buying from a friend mu1 and the true mean price when buying from a stranger mu2 is different (not equal)

Answer:

the awnser is c

Answer:

C

Step-by-step explanation:

its on egunity ik u hate it im here for u

Answer:

4.49

Step-by-step explanation:

Answer:

4.49

Step-by-step explanation:

*Imagine it as money, you have $4.25 and you find $0.24

1) 4.25 + 0.24= 4.49

You now have $4.49

Hoped that helped ;)

Answer:

C

Step-by-step explanation:

A cube has 6 faces

Each face is a square of area:

5² = 25

Surface area: 6 × 25

= 150 in²

Answer:

150 in^2

Step-by-step explanation:

The surface area of a cube is given by

SA = 6 s^2 where s is the side length

SA = 6 (5)^2

    = 6 * 25

    = 6*25

    = 150 in^2

Given:

The given figure consists of a triangle, a rectangle and a half circle.

The base of the triangle is 2 mi.

The height of the triangle is 4 mi.

The length of the rectangle is 9 mi.

The diameter of the half circle is 4 mi.

The radius of the half circle is 2 mi.

We need to determine the area of the enclosed figure.

Area of the triangle:

The area of the triangle can be determined using the formula,

[tex]A=\frac{1}{2}bh[/tex]

where b is the base and h is the height

Substituting b = 2 and h = 4, we get;

[tex]A=\frac{1}{2}(2\times 4)[/tex]

[tex]A=4 \ mi^2[/tex]

Thus, the area of the triangle is 4 mi²

Area of the rectangle:

The area of the rectangle can be determined using the formula,

[tex]A=length \times width[/tex]

Substituting length = 9 mi and width = 4 mi, we get;

[tex]A=9 \times 4[/tex]

[tex]A=36 \ mi^2[/tex]

Thus, the area of the rectangle is 36 mi²

Area of the half circle:

The area of the half circle can be determined using the formula,

[tex]A=\frac{\pi r^2}{2}[/tex]

Substituting r = 2, we get;

[tex]A=\frac{(3.14)(2)^2}{2}[/tex]

[tex]A=\frac{(3.14)(4)}{2}[/tex]

[tex]A=\frac{12.56}{2}[/tex]

[tex]A=6.28[/tex]

Thus, the area of the half circle is 6.28 mi²

Area of the enclosed figure:

The area of the entire figure can be determined by adding the area of the triangle, area of rectangle and area of the half circle.

Thus, we have;

Area = Area of triangle + Area of rectangle + Area of half circle

Substituting the values, we get;

[tex]Area=4+36+6.28[/tex]

[tex]Area = 46.28 \ mi^2[/tex]

Thus, the area of the enclosed figure is 46.28 mi²

Answer:

a. 10% - 15%

Step-by-step explanation:

The percentage of a job opening, that gets published, is 15% to 20%,  just since just scarcely any occupations can be seen on a paper, commercials, and employment sheets. A large portion of the employment opportunities can be gotten notification from those representatives that worked inside the organization since there is only two job vacancies.

Answer:

the answer is b

Step-by-step explanation:

Answer:

$7.92

Step-by-step explanation:

110 - ((32 x 2.40) + (32 x 0.79)) = $7.92

Answer:

$7.92 dollars left over

Step-by-step explanation:

32* 2.40= 76.8

32*0.79= 25.28

25.28+ 76.8= 102.08

110-102.08

===========7.92

Answer:

$5,805.92

Step-by-step explanation:

Lets use the compound interest formula provided to solve this:

[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]

P = initial balance

r = interest rate (decimal)

n = number of times compounded annually

t = time

First, change 3% into a decimal:

3% -> [tex]\frac{3}{100}[/tex] -> 0.03

Since the interest is compounded quarterly, we will use 4 for n. Lets plug in the values now:

[tex]A=5,000(1+\frac{0.03}{4})^{4(5)}[/tex]

[tex]A=5,805.92[/tex]

The value of the investment after 5 years will be $5,805.92

Investment value after 5 years, compounded quarterly at 3%, is approximately $5,805.83.

let's calculate step by step.

1. First, let's convert the annual interest rate to decimal form:

 [tex]\[ r = 3\% = \frac{3}{100} = 0.03 \][/tex]

2. Now, let's plug in the given values into the compound interest formula:

[tex]\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \][/tex]

  where:

[tex]- \( P = $5000 \)\\ - \( r = 0.03 \)\\ - \( n = 4 \)\\ - \( t = 5 \)[/tex]

3. Substituting these values into the formula, we get:

[tex]\[ A = 5000 \left(1 + \frac{0.03}{4}\right)^{4 \times 5} \][/tex]

4. Simplifying inside the parentheses:

[tex]\[ A = 5000 \left(1 + 0.0075\right)^{20} \][/tex]

5. Calculating [tex]\( (1 + 0.0075) \):[/tex]

 [tex]\[ 1 + 0.0075 = 1.0075 \][/tex]

6. Now, raise [tex]\( 1.0075 \)[/tex]  to the power of [tex]\( 20 \):[/tex]

[tex]\[ (1.0075)^{20} \][/tex]

  Using a calculator,[tex]\( (1.0075)^{20} \)[/tex] is approximately [tex]\( 1.161166 \).[/tex]

7. Finally, multiply this result by [tex]\( 5000 \):[/tex]

 [tex]\[ A = 5000 \times 1.161166 \]\\ \[ A \approx 5,805.83 \][/tex]

So, the value of the investment in five years, compounded quarterly at a 3% interest rate, would be approximately $5,805.83.

here is complete question:-

"If $5000 is invested at a rate of 3% interest compounded quarterly, what is the value of the investment in five years?"

Answer:

The answer is B.

Step-by-step explanation:

The example given in the question uses the null hypothesis versus the alternative hypothesis. Null hypothesis is the statement that is tested to be true or not and if it is not true, then the alternative hypothesis is accepted.

In the example, it is stated that the hypothesis test for the null hypothesis failed which means that the statement given on the percentage of students who read the book is false.

Then the option b is going to be interpreted which claims that the null hypothesis is false and there is not enough evidence to say that less than 55% of students read the textbook.

I hope this answer helps.

Final answer:

When a hypothesis test does not reject the null hypothesis with a p-value greater than the alpha level of 0.05, it indicates that there is not sufficient evidence to support the claim being tested, in this case, that less than 55% of students read the textbook.

Explanation:

If a hypothesis test is performed and fails to reject the null hypothesis, the interpretation depends on the results related to the alpha level and the p-value. In this case, where the claim is that less than 55% of students read the textbook and the p-value is greater than the alpha level (0.05 or 5%), the correct interpretation is that there is not sufficient evidence to support the claim that less than 55% of students read the text. This means that the sample data does not provide strong enough evidence to infer that the proportion of students who read the textbook is less than 55% for the entire population of students.

Therefore, the correct answer is:

b. There is not sufficient evidence to support the claim that less than 55% of students read this text.

Answer:

9%

Step-by-step explanation:

36/400=9/100=9%

Answer:

5

Step-by-step explanation:

We desire to evaluate the fraction: [tex]\dfrac{15}{k}[/tex] when k=3.

This is a simple substitution, so what is required is

Therefore, when k=3

[tex]\dfrac{15}{k}=\dfrac{15}{3}=5[/tex]

You can try the same for any value of k.

The question requires to evaluate the mathematical expression 15/k when k=3. Substituting k with 3, we get 15/3 which equals to 5.

In the subject of Mathematics, the expression 15/k represents a simple division. The value of this expression changes depending on the value assigned to k. In the case where k = 3, we simply substitute 3 in place of k in the expression. This gives us: 15/3 which equals 5. So, 15/3 = 5. So when k = 3, 15/k equals 5.

Learn more about Mathematical Expression here:

https://brainly.com/question/34902364

#SPJ3

Answer:

  B)  a = 6.7, B = 36°, C = 49°

Step-by-step explanation:

Fill in the numbers in the Law of Cosines formula to find the value of "a".

  a² = b² + c² -2bc·cos(A)

  a² = 4² +5² -2(4)(5)cos(95°) ≈ 44.4862

  a ≈ √44.4862 ≈ 6.66980

Now, the law of sines is used to find one of the remaining angles. The larger angle will be found from ...

  sin(C)/c = sin(A)/a

  sin(C) = (c/a)sin(A)

  C = arcsin(5/6.6698×sin(95°)) ≈ 48.31°

The third angle is ...

  B = 180° -A -C = 180° -95° -48.31° = 36.69°

The closest match to a = 6.7, B = 37°, C = 48° is answer choice B.

Answer:

[tex]P(X\geq 8)=0.0043\\\\[/tex]

It's more likely that  all of the residents surveyed will have adequate earthquake supplies since it has a probability of 98.02% which is very close to 100%.

Step-by-step explanation:

-This is a binomial probability problem with the function:

[tex]P(X=x)={n\choose x}p^x(1-p)^{n-x}[/tex]

-Given p=0.3, n=11, the is calculated as:

[tex]P(X=x)={n\choose x}p^x(1-p)^{n-x}\\\\P(X\geq 8)=P(X=8)+P(X=9)+P(X=10)+P(X=11)\\\\={11\choose 8}0.3^8(0.7)^3+{11\choose 9}0.3^9(0.7)^2+{11\choose 10}0.3^{10}(0.7)^1+{11\choose 11}0.3^{11}(0.7)^0\\\\=0.0037+0.0005+0.00005+0.000002\\\\=0.0043[/tex]

Hence, the probability that at least 8 have adequate supplies 0.0043

#The probability that non has adequate supplies is calculated as;

[tex]P(X=x)={n\choose x}p^x(1-p)^{n-x}\\\\P(X= 0)={11\choose 0}0.3^{0}(0.7)^{11}\\\\=0.0198[/tex]

#The probability that all have adequate supplies is calculated as:

[tex]P(X=x)={n\choose x}p^x(1-p)^{n-x}\\\\P(X= All)=1-{11\choose 0}0.3^{0}(0.7)^{11}\\\\=1-0.0198\\\\=0.9802[/tex]

Hence, it's more likely that  all of the residents surveyed will have adequate earthquake supplies since [tex]P(All)>P(None)\ \[/tex] and that this probability is 0.9802 or 98.02% a figure close to 1

Final answer:

The probability that at least eight California residents have adequate earthquake supplies when surveying 11 can be calculated with the binomial distribution, summing probabilities for exactly 8, 9, 10, and 11. None having adequate supplies is more likely than all, given the 30% success rate. The average number of surveys before finding a resident without supplies is close to 2, and before finding one with supplies, it is approximately 3.

Explanation:

The probability of at least eight California residents having adequate earthquake supplies when surveying 11 residents can be calculated using the binomial distribution formula. Given that the success probability (having adequate supplies) is 30% (0.3), we can calculate the probability for exactly 8, 9, 10, and 11 residents and sum these probabilities to get the total probability for 'at least 8'.

The random variable X can be defined as the number of successes in n independent Bernoulli trials, with success on each trial having probability p. Here, X represents the number of California residents with adequate earthquake supplies in our sample of 11. The values that X can take on are 0, 1, 2, ..., 11.

To find the probability of none or all residents having adequate supplies, we calculate the probabilities for X = 0 and X = 11. The probability of none (X = 0) would be 0.7¹¹, and the probability of all (X = 11) would be 0.3¹¹. Between these, the probability of none is higher due to the lower success probability.

For the expected number of surveys until finding a resident without adequate supplies, we can use the geometric distribution where the expected value E(X) is 1/p. In this case, p = 0.7 (probability of not having adequate supplies), so E(X) would be approximately 1.43, meaning on average we would have to survey close to one or two residents before finding one without adequate supplies.

Conversely, the expected number of surveys until finding one with adequate supplies would be 1/q, where q = 0.3 (probability of having adequate supplies), giving us an expected value of around 3.33 surveys.

Answer:

38755.7

Step-by-step explanation:

The volume of the hemisphere is 55495.5 cubic inches.

To find the volume of a hemisphere, we can use the formula for the volume of a sphere and divide it by 2.

The volume of a sphere can be calculated using the formula:

V = (4/3)πr³

Given that the diameter of the hemisphere is 52.9 inches, we can find the radius by dividing the diameter by 2:

Radius = Diameter / 2 = 52.9 inches / 2 = 26.45 inches

Now we can calculate the volume of the hemisphere:

Volume = (4/3)π(26.45 inches)³ / 2

Using the value of π as approximately 3.14159, we can substitute the values into the formula:

Volume ≈ (4/3) × 3.14159 × (26.45 inches)³ / 2

Simplifying the calculation:

Volume ≈ 55495.5314 cubic inches

Rounding to the nearest tenth of a cubic inch, the volume of the hemisphere is approximately 55495.5 cubic inches.

Answer:

P'(1100)=0.06

(see explanation below)

Step-by-step explanation:

The answer is incomplete. The profit function is missing, but another function will be used as an example (the answer will not match with the options).

The profit generated by a product is given by [tex]P=4\sqrt{x}[/tex].

The changing rate of sales can be mathematically expressed as the derivative of the profit function.

Then, we have to calculate the derivative in function of x:

[tex]\dfrac{dP}{dx}=\dfrac{d[4x^{0.5}]}{dx}=4(0.5)x^{0.5-1}=2x^{-0.5}=\dfrac{2}{\sqrt{x}}[/tex]

We now have to evaluate this function for x=1100 to know the rate of change of the sales at this vlaue of x.

[tex]P'(1100)=\frac{2}{\sqrt{1100} } =\frac{2}{33.16} =0.06[/tex]

Answer: x=35

Step-by-step explanation:

1. Divide both by 3

2. Simplify-x+1=36

3. Subtract 1 form both sides

You answer will be x=35

Answer:

Divide Both Sides by 3

Take the Square Root of Both Sides

Subtract 1 from Both Sides

Step-by-step explanation:

Pray!

Answer:

that a hard question

Step-by-step explanation:

i tried to use a calculator and graphs to solve it but I couldn't

Answer:

Slope = 1.1889. The predicted distance the drivers were able to drive increases by 1.1889 miles for each additional mile reported by the gauge.

Step-by-step explanation:

The slope is the second value under the “Coef” column. The interpretation of slope must include a non-deterministic description (“predicted”) about how much the response variable (actual number of miles driven) changes for each 1-unit increment of change in the explanatory variable (the gauge reading) in context.

Answer:

(E) I, II, and III

Step-by-step explanation:

Suppose the matrix  A has rank 4.

A has 4 linearly independent columns.

As the matrix  A is 4 by 4 matrix so all columns of A are linearly independent.

=> det(A) ≠ 0.

=> A must be invertible.

Suppose A is invertible.

Columns of A are linearly independent.

As A has 4 columns and all columns of A are linearly independent so A has 4 linearly independent columns.

As Rank of A = Number of linearly independent columns of A.

=> Rank of A = 4.

Suppose A is invertible.

=> Rank of A = 4.

By rank nullity theorem,

Rank of A + Nullity of A= 4

=> 4 + Nullity of A= 4

=> Nullity of A= 0.

Hence the nullity of A is 0.

Answer:

242 Full Tickets were sold; and

3008 Student Tickets were sold.

Step-by-step explanation:

Let the number of full tickets sold=x

Let the number of student tickets sold =y

A total of 3250 tickets were sold, therefore:

Cost of a Full Ticket =$58.50.

Cost of a Discounted Ticket=$48.50

Total Amount =(58.50. X Number of Full Tickets sold)+(58.50 X Number of Student Tickets sold)

Total amount of ticket sales was $ 160,045

Therefore:

We solve the two equations simultaneously to obtain the values of x and y.

From the First Equation, x=3250-y

Substitute x=3250-y into the Second Equation.

58.50x+48.50y=160045

58.50(3250-y)+48.50y=160045

Open the brackets

190125-58.50y+48.50y=160045

-10y=160045-190125

-10y=-30080

Divide both sides by -10

y=3008

Recall: x=3250-y

x=3250-3008

x=242

Therefore:

242 Full Tickets were sold; and

3008 Student Tickets were sold.

Final answer:

To solve for the number of full-price and student tickets sold, a system of two linear equations is set up and solved using the elimination method. The solution shows that 242 full-price tickets and 3008 student tickets were sold.

Explanation:

To solve this problem, we will use a system of linear equations. Let's define x as the number of full-price tickets and y as the number of student tickets. The two equations based on the information provided will be:

x + y = 3250 (the total number of tickets sold)

58.50x + 48.50y = 160,045 (the total revenue from ticket sales)

To find the number of full-price and student tickets sold, we need to solve this system of equations. We can do this using either the substitution or elimination method. I'll demonstrate the elimination method.

Step 1: Multiply the first equation by 48.50 to align the y terms.

48.50x + 48.50y = 157,625

Step 2: Subtract this new equation from the second equation.

58.50x + 48.50y = 160,045
- (48.50x + 48.50y = 157,625)

10x = 2,420

Step 3: Solve for x

x = 242

Step 4: Use the value of x to solve for y in the first equation.

242 + y = 3250
y = 3250 - 242
y = 3008

So, 242 full-price tickets were sold, and 3008 student tickets were sold.

Answer:

55

Step-by-step explanation:

Combinations formula is used to make choice of 'R' out of 'N' options =

N(C)R = N ! / [ R ! . (N-R)! ]

Total choices to choose 4 out of 8 friends = 8C4

= 8! / (4! 4!)  

= 70

Choices for calling them 2 together = 2C2 x 6C2

= 1 x [ 6! / (2! 4!)]

= 15

So : Number of choices that the 2 friends are not called together = Total choices - choices they are called together

= 70 - 15 = 55

Answer:

D. Largest p-value

Step-by-step explanation:

P-value assists statistician to know the importance of their result. It assists them in determining the strength of their evidence.

A large P-value which is less than 0.05 depicts that an evidence is week against null hypothesis, therefore the null hypothesis must be accepted.

A small P-value <0.05 depicts a strong evidence against null hypothesis, so the null hypothesis must be rejected.

Answer:

B. Highest increase in the multiple r-squared

Step-by-step explanation:

Forward selection is a type of stepwise regression which begins with an empty model and adds in variables one by one. In each forward step, you add the one variable that gives the single best improvement to your model.

We know that when more variables are added, r-squared values typically increase with probability 1. Based on this and the above definition, we select the candidate variable that increases r-Squared the most and stop adding variables when none of the remaining variables are significant.

Answer: 4.5 pi to this question

Answer:

The minimum score required for a letter of recognition is 631.24.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

[tex]\mu = 493, \sigma = 108[/tex]

What is the minimum score required for a letter of recognition

100 - 10 = 90th percentile, which is the value of X when Z has a pvalue of 0.9. So X when Z = 1.28.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.28 = \frac{X - 493}{108}[/tex]

[tex]X - 493 = 1.28*108[/tex]

[tex]X = 631.24[/tex]

The minimum score required for a letter of recognition is 631.24.

Answer:

[tex]b=493 +1.28*108=631.24[/tex]

The minimum score required for a letter of recognition would be 631.24

Step-by-step explanation:

Let X the random variable that represent the writing scores of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(493,108)[/tex]  

Where [tex]\mu=493[/tex] and [tex]\sigma=108[/tex]

On this questio we want to find a value b, such that we satisfy this condition:

[tex]P(X>b)=0.10[/tex]   (a)

[tex]P(X<b)=0.90[/tex]   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find b.

As we can see on the figure attached the z value that satisfy the condition with 0.90 of the area on the left and 0.1 of the area on the right it's z=1.28. On this case P(Z<1.28)=0.9 and P(z>1.28)=0.1

If we use condition (b) from previous we have this:

[tex]P(X<b)=P(\frac{X-\mu}{\sigma}<\frac{b-\mu}{\sigma})=0.90[/tex]  

[tex]P(z<\frac{b-\mu}{\sigma})=0.90[/tex]

[tex]z=1.28<\frac{b-493}{108}[/tex]

And if we solve for a we got

[tex]b=493 +1.28*108=631.24[/tex]

The minimum score required for a letter of recognition would be 631.24

Answer:

Hence the person stop at floor by at least one person will be

E(X)=(summation from K=1 to k)[1-{(k-1)/k}^n]

Step-by-step explanation:

Given:

There are n peoples and k floors in a building.

Selects floor with 1/k probability .

To find :

Elevator stop at each floor by at least one person.

Solution:

Now

let K= number of floor at which at least one person will be stopping.

For getting E(X)

consider a variable Ak =1 if a least one person get of the elevator

and values for k=1,2,3.....k

K=(summation From k=1 to k)Ak

E(K)=((summation From k=1 to k) E[Ak]

=(summation From k=1 to k)[[tex]1-{(k-1/k)^n[/tex]

Hence the person stop at floor by at least one person will be

E(K)=(summation from K=1 to k)[1-{(k-1)/k}^n]

Answer:

 We are 98% confident interval for the mean caffeine content for cups dispensed by the machine between 107.66 and 112.34 mg .

Step-by-step explanation:

Given -

The sample size is large then we can use central limit theorem

n = 50 ,  

Standard deviation[tex](\sigma)[/tex] = 7.1

Mean [tex]\overline{(y)}[/tex] = 110

[tex]\alpha =[/tex] 1 - confidence interval = 1 - .98 = .02

[tex]z_{\frac{\alpha}{2}}[/tex] = 2.33

98% confidence interval for the mean caffeine content for cups dispensed by the machine = [tex]\overline{(y)}\pm z_{\frac{\alpha}{2}}\frac{\sigma}\sqrt{n}[/tex]

                     = [tex]110\pm z_{.01}\frac{7.1}\sqrt{50}[/tex]

                      = [tex]110\pm 2.33\frac{7.1}\sqrt{50}[/tex]

       First we take  + sign

   [tex]110 + 2.33\frac{7.1}\sqrt{50}[/tex] = 112.34

now  we take  - sign

[tex]110 - 2.33\frac{7.1}\sqrt{50}[/tex] = 107.66

 We are 98% confident interval for the mean caffeine content for cups dispensed by the machine between 107.66 and 112.34 .

Final answer:

A 98% confidence interval for the mean caffeine content of cups dispensed by the machine is calculated using the sample mean, the standard deviation, and the Z-score for a 98% confidence level, leading to an interval of (107.72 mg, 112.28 mg). We can be 98% confident that the true mean caffeine content lies within this range.

Explanation:

To construct a 98% confidence interval for the mean caffeine content of cups dispensed by the machine, we use the provided sample mean (μ), which is 110 mg, and the standard deviation (s), which is 7.1 mg, of the 50 cups sampled. Since the sample size is 50, which is more than 30, we can use the Z-distribution as an approximation of the T-distribution for this confidence interval as the Central Limit Theorem suggests that the distribution of sample means will be normally distributed if the sample size is large enough. Using a Z-score for 98% confidence, which typically is approximately 2.33 (you would obtain the exact value from a Z-table), the margin of error (E) can be calculated using the formula E = Z * (s/√n), where n is the sample size (50 in this case).

The margin of error is then 2.33 * (7.1/√50), which equals approximately 2.28 mg. The 98% confidence interval is therefore the sample mean plus or minus the margin of error, which is 110 mg ± 2.28 mg or (107.72 mg, 112.28 mg).

The interpretation of this confidence interval is that we can be 98% confident that the true mean caffeine content of all cups of coffee dispensed by the machine falls between 107.72 mg and 112.28 mg.

To find the annual interest rate of Nadia’s account, we use the simple interest formula I = PRT. By rearranging the formula and plugging in the known values, we determine that the interest rate is 5.5%.

To determine the interest rate of Nadia’s account, we can use the formula for simple interest I = PRT, where I is the interest earned, P is the principal amount deposited, R is the annual interest rate in decimal, and T is the time in years. In Nadia's case, we know that she earned $990 in interest (I), deposited $3000 (P), over 6 years (T).

We need to solve for R.

The formula thus becomes: $990 = $3000 × R × 6

To find R, we divide both sides of the equation by $3000 × 6:

R = $990 / ($3000 × 6)

R = $990 / $18000

R = 0.055 or 5.5%

Therefore, the annual interest rate Nadia received on her account was 5.5%.