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A six-sided die is rolled 50 times.

The number 4 appears 18 times.

What is the experimental probability

of getting a four?

A .08

B 17

C.32

D.36

Answer:

Step-by-step explanation:

Let the subscripts d and n represent day and night respectively

The null hypothesis is

H0 : μd ≥ μn

The alternative hypothesis is

H1 : μd < μn

it is a one-tailed and also a right left test because of the greater than symbol in the alternative hypothesis.

The decision rule is to reject H0: μd ≥ μn If 0.10 > p value

Since the population standard deviations are known, we would use the formula to determine the test statistic(z score)

z = (xd - xn)/√σd²/nd + σn²/nn

Where

xd and xn represents sample means for day and night respectively.

σd and σn represents population standard deviations for day and night respectively.

nd and nn represents number of samples

From the information given,

xd = 334

xn = 341

σd = 23

σ2 = 28

nd = 60

nn = 68

z = (334 - 341)/√23²/60 + 28²/68

= - 7/√20.34607843138

z = - 1.55

From the normal distribution table, the probability value corresponding to the z score is 0.061

Since the level of significance, 0.1 > 0.061, we would reject H0

Therefore, there is enough evidence to conclude that there are more units produced on the night shift than on the day shift.

Final answer:

Clark Heter is conducting a one-tailed test to compare the mean production of day and night shifts. The decision to reject the null hypothesis that day shift production is greater or equal to night shift production is based on a critical value of -1.28 linked to a significance level of 0.10. The test statistic is computed from the given means and standard deviations for both samples.

Explanation:

Conducting a Two-Sample Z-Test

Clark Heter wants to determine if more units are produced on the night shift than on the day shift. Given the samples:
- Day-shift (n=60): mean = 334, population standard deviation = 23.
- Night-shift (n=68): mean = 341, population standard deviation = 28.
The significance level is 0.10.

Answer:

8.5

Step-by-step explanation:

To find mean, we simply take the average of all the numbers in the data set, and divide in by the amount of values!

[tex]8+10+6+4+12+6+8+14= 68\\[/tex]

68 ÷ 8 = 8.5!

Answer:

[tex]8\frac{1}{2}[/tex]

Step-by-step explanation:

First add up all the numbers:

8+10+6+4+12+6+8+14=68

Now you have to divide the sum by the amount of numbers. There are 8 numbers.

[tex]\frac{68}{8}=\frac{34}{4}=\frac{17}{2}[/tex]

[tex]\frac{17}{2}=8\frac{1}{2}[/tex]

Answer:

Proposal B

Step-by-step explanation:

This problem can be solved by comparing the expected returns on both options.

The expected return is the sum of the possible outcomes multiplied by its probabilities of occurrence.

For proposal A, the net profits are $20,000, $30,000 and $50,000, with respective probabilities 0.2, 0.4 and 0.4. Then, the expected return can be calculated as:

[tex]E(A)=\sum_{i=1}^3p_iR_i\\\\E(A)=p_1R_1+p_2R_2+p_3R_3\\\\E(A)=0.2*20,000+0.4*30,000+0.4*50,000\\\\E(A)=4,000+12,000+20,000\\\\E(A)=36,000[/tex]

The proposal A has a expected net profit of $36,000.

The proposal B has a 50% chance of having a net profit of $100,000 and a 50% of break even (zero net profit). We applied the same calculation for the expected profit and we have:

[tex]E(B)=\sum_{i=1}^2p_iR_i\\\\E(B)=p_1R_1+p_2R_2\\\\E(B)=0.5*100,000+0.5*0\\\\E(B)=50,000[/tex]

The proposal B has a expected net profit of $50,000.

Assuming that each proposal requires the same investment, the proposal B has more expected monetary return (GHȼ 50,000) than proposal A (GHȼ 36,000).

Answer:

6/25 probability

Step-by-step explanation:

We have 5 marbles total,   3 + 2  = 5

Find P(  white marble, yellow marble with replacement)

= P(white, yellow) = (2/5)*(3/5) =  6 / 25

There are 32,760 ways to select 4 winners from 15 participants in a local raffle where the order of prizes matters according to permutation.

To find out how many ways 4 winners can be selected from 15 participants in a local raffle with given prizes, we can use the concept of permutation because the order in which the prizes are awarded matters (i.e., the prizes are not identical).

The total number of different ways to select 4 winners from 15 participants is represented by the permutation of 15 things taken 4 at a time (since the order of selection matters for different prizes).

The formula for permutation is: P(n, k) = n! / (n-k)! where n is the total number of items, k is the number of items to choose, and '!' represents a factorial.

For this problem, we calculate P(15, 4):

Therefore, there are 32,760 ways to select 4 winners from 15 participants.

Answer:

The train ride is 3.5 hours

Step-by-step explanation:

We know that distance is equal to rate times time

d = rt

We know the distance and the rate

420 = 120*t

Divide each side by 120

420/120 = 120t/120

3.5 =t

The train ride is 3.5 hours

Answer:

3.5 hrs

3 hrs and 30 min

210 min

Answer: -28

Step-by-step explanation: Since x is being divided by -4, to solve for x, multiply both sides of the equation by -4.

On the left side, the -4's will cancel

and on the right side, 7(-4) is -28.

So x = -28.

Please do not try to do this problem in your head.

Show the work that it takes to get x by itself.

Answer:

x= - 28

Step-by-step explanation:

-4/1[x/-4 = 7]

x = -28

Rejection region(s)

t > 2.998

Test statistic value

t = 2.89

Fail to reject H0. The data does not suggest a significant mean difference in breaking load for the two fabric load conditions. Option B is the right choice.

State the hypotheses

H0: μD = 0

Ha: μD > 0

State the rejection region

Since the alternative hypothesis is one-sided, we use a one-tailed test. The rejection region for a one-tailed t-test with significance level 0.01 and 7 degrees of freedom is:

t > 2.998

Compute the test statistic

The test statistic for a paired t-test is calculated as follows:

t = ([tex]\bar x[/tex]D - μD) / (sdD / √n)

where:

[tex]\bar x[/tex]Dis the mean difference between the unabraded and abraded breaking loads

sdD is the standard deviation of the difference between the unabraded and abraded breaking loads

n is the sample size

Calculating the mean difference:

[tex]\bar x[/tex]D = (36.3 - 28.5) + (55.0 - 20.0) + (51.2 - 46.0) + (38.6 - 34.0) + (43.2 - 36.5) + (48.8 - 52.5) + (25.6 - 26.5) + (49.6 - 46.5) = 6.85

Calculating the standard deviation of the difference:

sdD = √[((36.3 - 28.5)^2 + (55.0 - 20.0)^2 + (51.2 - 46.0)^2 + (38.6 - 34.0)^2 + (43.2 - 36.5)^2 + (48.8 - 52.5)^2 + (25.6 - 26.5)^2 + (49.6 - 46.5)^2) / 7] = 10.87

Calculating the test statistic:

t = (6.85 - 0) / (10.87 / √8) = 2.89

Make a decision

Since the test statistic (2.89) is less than the critical value (2.998), we fail to reject the null hypothesis.

The correct choice is option d. Fail to reject H0. The data does not suggest a significant mean difference in breaking load for the two fabric load conditions.

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Question:-

Consider the accompanying data on breaking load (kg/25 mm width) for various fabrics in both an unabraded condition and an abraded condition. Use the paired t test to test H0: ?D = 0 versus Ha: ?D > 0 at significance level 0.01. (Use ?D = ?U ? ?A.)
State the rejection region(s). (If the critical region is one-sided, enter NONE for the unused region. Round your answers to three decimal places.)

t ? _______

t ? ________

Compute the test statistic value. (Round your answer to three decimal places.)

t = _____

State the conclusion in the problem context.

a.Reject H0. The data suggests a significant mean difference in breaking load for the two fabric load conditions.Fail to b.reject H0. The data suggests a significant mean difference in breaking load for the two fabric load conditions. c.Reject H0. The data does not suggest a significant mean difference in breaking load for the two fabric load conditions.

d.Fail to reject H0. The data does not suggest a significant mean difference in breaking load for the two fabric load conditions

Answer:

7

Step-by-step explanation:

formula for circumference of a circle is [tex]\pi[/tex]d

7[tex]\pi[/tex] = [tex]\pi[/tex]d

d = 7

Answer:bruh

Step-by-step explana

The radius of the table, rounded to the nearest half-foot, is 3.5 feet.

To determine the radius of the circular dining room table, we can use the formula for the circumference of a circle, which is:

C = 2 π r

where:

C - circumference

r - radius

Given that each person has about 2 feet of space along the edge of the table, the circumference of the table must be able to accommodate the seating for 11 people. Each person occupies 2 feet of space, so the total space needed around the edge of the table is:

11 × 2 = 22 feet

We can set up an equation using the circumference formula:

C = 2 π r = 22

To find the radius (r), we divide both sides of the equation by 2π:

r = [tex]\frac{22}{2 \pi}[/tex]

Now, let's calculate the value:

r = [tex]\frac{22}{2 \pi}[/tex] = [tex]\frac{22}{2 \times 3.14}[/tex] = [tex]\frac{22}{6.28}[/tex] = 3.503

Rounding to the nearest half-foot, we get:

r = 3.5 feet

Answer:

120.

Step-by-step explanation:

This is the number of combinations of 3 from 10.

This = 10C3

= 10! / 3! (10-3)!

= 10*9*8 / 3*2*1

= 120 combinations.

Answer:

120

Step-by-step explanation:

Answer:

is there more to the question?

Step-by-step explanation:

Answer:

1. is 56

2. is 82

Step-by-step explanation:

Just took the quiz and got it right (Like it please so people know its the correct answer)

Answer:

t = 17.5°

f = 12°

Step-by-step explanation:

MNOP is a square  and the angle M is (4t + 20)° and the angle N is (7f + 6)°. The value of t and f can be calculated below.

A square is a quadrilateral and all the sides are equal. Opposite sides are parallel to each other . Each angle of a square is equal to 90°.  

Since ∠M = 4t + 20

This means ∠M

4t + 20 = 90

4t = 90 - 20

4t = 70

t = 70/4

t = 17.5°

∠N = 7 f + 6

7 f + 6 = 90

7f = 90 -6

7f = 84

f = 84/7

f = 12°

Answer:

t=17.5

f=12

Step-by-step explanation:

Answer:

[tex] (x - 9)^2 + y^2 = 36 [/tex]

Step-by-step explanation:

The equation of a circle in standard form is

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

You are given

[tex] x^2 + y^2 - 18x + 45 = 0 [/tex]

In order to put the equation in standard from, we need to complete the square. Since there is no y term, the y part is simply y^2, and there is no need to complete the square for y. For x, we do have an x term, so we must complete the square in x.

Start by grouping the x terms and subtracting 45 from both sides.

[tex] x^2 - 18x + y^2 = -45 [/tex]

Now we need to complete the square for x.

[tex] x^2 - 18x ~~~~~~+ y^2 = -45 [/tex]

The number that completes the square will go in the blank above, and it will also be added to the right side of the equation.

To find the number you need to add to complete the square, take the coefficient of the x term. It is -18. Divide it by 2. You get -9. Now square -9 to get 81. The number that completes the square in x is 81. Now you add it to both sides of the equation.

[tex] x^2 - 18x + 81 + y^2 = -45 + 81 [/tex]

[tex] (x - 9)^2 + y^2 = 36 [/tex]

Answer: [tex] (x - 9)^2 + y^2 = 36 [/tex]

Answer:

A, B, and D.

Step-by-step explanation:

The absolute value function is V shaped, goes through the origin, and never dips below the x axis, meaning that it is in the 1st and 2nd quadrants. The left side resembles a line with slope -1, which means that choice C is incorrect. Hope this helps!

Answer:

  ∠3 = ∠4 = 60°

Step-by-step explanation:

Angles 1 and 3 are "remote interior angles" with respect to angle 2, so ...

  ∠2 = ∠1 + ∠3

  120° = 60° + ∠3 . . . fill in known values

  60° = ∠3 . . . . . . . . . subtract 60°

__

Since two of the interior angles in the triangle ABC are 60°, the third one is also. The interior angle at B (supplementary to angle 2) is corresponding to ∠4, so has the same measure as angle 4.

  ∠4 = 60°

Answer:b

Step-by-step explanation:

a. The point estimate of the mean price of college textbooks is $145. b. A 90% confidence interval for the mean price is ($133.49, $156.52).

Given a sample of 25 comparable textbooks with a mean price of $145 and a known population standard deviation of $35, the following steps will help answer the questions:

a. Point Estimate:

The point estimate of the mean price of all such college textbooks is simply the sample mean, which is $145.

b. 90% Confidence Interval:

To construct a 90% confidence interval for the mean price of college textbooks, we follow these steps:

Thus, the 90% confidence interval for the mean price of all college textbooks is ($133.49, $156.52).

To prove that the sequence defined by the recurrence relation satisfies the formula sn = 3 + n(n + 1), we need to show that the base case holds and then prove the inductive step.

To prove that the sequence defined by the recurrence relation satisfies the formula , we need to show that the base case holds and then prove the inductive step.

Base case:

When , we have . This matches the formula, so the base case holds.

Inductive step:

Assume that the formula holds for some . We want to show that it holds for .

Using the recurrence relation, we have:

sn+1 = sn + 2(n+1)

Using the induction hypothesis, we can substitute  in the expression:

sn+1 = (3 + n(n + 1)) + 2(n+1)

Expanding the expression:

sn+1 = 3 + n(n + 1) + 2n + 2

Combining like terms:

sn+1 = 3 + n(n + 1) + 2(n+1)

sn+1 = 3 + (n+1)((n + 1) + 1)

This matches the formula for , so the inductive step holds. Therefore, the formula holds for all integers .

Answer:

Used car have the highest range of 75

Step-by-step explanation:

Yeah the type of car that have the highest range In monthly sales.

we know that

The range is the difference between the highest and the lowest value

First we,

calculate the range in monthly sales for the new car

highest value=51

lowest value=20

range=51-20

range=31

Secondly,we

calculate the range in monthly sales for used car

highest value=87

lowest value=12

range=87-12

range=75

Answer:

My answer: "The car that had the largest range in monthly sales was a used. Through finding the range by subtracting the highest and lowest data points, i was able to find the range for used cars being 75, and for new cars was 31. 75 is larger then 31, so therefore the used cars have the largest monthly range in sales. "

Their sample answer: Sample Response: I subtracted the highest and lowest numbers. The range for new cars was 31. The range for old cars was 75. The range for used cars was much bigger."

Select all that you included in your explanation.

The range for new cars was 31.

The range for used cars was 75.

Subtract the highest and lowest numbers.

Step-by-step explanation:

edg2020

Answer:

x = -2

Step-by-step explanation:

subtract the 6 from 22

then divide -8x and 16 by -8

then you get your anser

The solution to the equation 6 - 8x = 22 is x = -2. The equation was solved by rearranging and isolating 'x', and then dividing by the coefficient -8.

The question is a simple linear equation. Let's solve it step by step:

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Answer:

Answer is 2

Step-by-step explanation:

If it shows a graph with Frog Population on top

Answer:

4 / 9  probability of getting a red

Step-by-step explanation:

How many marbles are there total?

4 red + 2 yellow + 3 green = 9 marbles total

P( red marble) = 4 red / 9 total = 4/9

Answer:

Step-by-step explanation:

Red marbles- 4

Yellow marbles-2

Green marbles-3

Total marbles=9

Probability= 4/9

=0.4444

Answer:

The attendance on tuesday, october 4, is of 144 people.

Step-by-step explanation:

The attendance after t days is given by the following equation:

[tex]A(t) = A(0)(1-r)^{t}[/tex]

In which A(0) is the attendance on the first day and r is the daily decrease rate.

Premieres on saturday, october 1, and 420 people attend.

This means that [tex]A(0) = 420[/tex]

Attendance then decreases by 30% each day.

This means that [tex]r = 0.3[/tex]

So

[tex]A(t) = A(0)(1-r)^{t}[/tex]

[tex]A(t) = 420(1-0.3)^{t}[/tex]

[tex]A(t) = 420(0.7)^{t}[/tex]

Find the attendance on tuesday , october 4

This is 4-1 = 3 days after saturday. So this is A(3).

[tex]A(3) = 420(0.7)^{3} = 144[/tex]

The attendance on tuesday, october 4, is of 144 people.

To find the attendance on Tuesday, October 4, after a 30% daily decrease from an initial attendance of 420 people on Saturday, October 1, we calculate the exponential decay for three days to get approximately 144 attendees.

The student's question involves an exponential decay math problem where the attendance of a play decreases by a percentage each day. To calculate the attendance on Tuesday, October 4, we begin with the initial attendance of 420 people on Saturday, October 1. We then apply a 30% decrease for each subsequent day:

Since we cannot have a fraction of a person attending, we would generally round to the nearest whole number, which means about 144 people attended the play on Tuesday, October 4.

Answer:

A: 6 Units

Step-by-step explanation:

Answer:

13 meters

Step-by-step explanation:

The perimeter is the sum of all the sides.

As a square has four identical sides, to calculate the length of one side you would simply divide 52 by 4,which gives you 13.

1) Divide 52 by 4.

[tex]52/4=13meters[/tex]

Answer:

13m

Step-by-step explanation:

52/4 = 13

Answer: =x2+7x+5

Step-by-step explanation:

−3x2+2x−4+4x2+5x+9

=−3x2+2x+−4+4x2+5x+9

Combine Like Terms:

=−3x2+2x+−4+4x2+5x+9

=(−3x2+4x2)+(2x+5x)+(−4+9)

=x2+7x+5

Answer:

=x2+7x+5

Answer:

x^2+7x+5

Step-by-step explanation:

Remove parentheses: -3x^2+2x-4+4x^2+5x+9

Group like terms: -3x^2+4x^2+2x+5x-4+9

Add similar elements: x^2+2x+5x-4+9

Add/subtract the numbers: x^2+7x+5

To construct a 95% confidence interval for the difference between the average number of daily intrusion attempts before and after changing firewall settings, you determine the standard deviation and mean for both periods. Use these in the formula for the confidence interval. If the interval doesn't include zero, it indicates a significant difference in the average number of daily intrusion attempts, and thus, potentially a significant reduction in intrusion attempts.

To perform this analysis, we first need to calculate the mean of the numbers of intrusion attempts for both periods - before and after the change of firewall settings. Then, we need to calculate the standard deviation for the numbers of intrusion attempts for both periods. The formula for the confidence interval is Mean Difference ± (Z*Standard Error). Where Z is a standard score value retrieved from the Z distribution table for a particular confidence level, in this case, 95%. The confidence levels you will be working with depend on the number of samples, in this case 14 and 20 respectively.

Once you have the confidence interval, it will give you the range in which the actual difference between the two means lies with 95% certainty. If the interval does not include zero, it indicates a significant difference between the means. By observing whether the values are predominantly positive or negative, we can infer about the significant reduction in the rate of intrusion attempts.

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Answer: A) 32÷6x5=S

B) 30 sheets of chart paper.

Step-by-step explanation:

we have 32 students.

he puts 6 students into each group.

he gives each group 5 pieces of chart paper.

32/6 will give us the number of groups

32/6 = 5.33

This means that we have 5 complete groups 6 students, and one group with 2 students. (a total of 6 groups)

And each of these groups need 5 pieces of paper, so we have the equation:

(32/6)*5 = S

and S = 26.66

now, for the 5 complete groups we need 5 pieces of paper for each, and 5*5 = 25 pieces of papper.

For the group of 2 persons we have the oter 1.66 ( or 2 if we round up) pieces of papper.

but this is a group, so they also should receive 5 pieces of papper regardless that they are only 2 integrants, then the total number of paper pieces is 30.