The following is the (edited) output for the test: A Two-sample T-Test and CI for the data. Sample 1(M) has N=112, Mean=7.38, StDev=6.95, SE Mean=0.66. Sample 2 (F) has N=101, Mean=7.15, StDev=6.31, SE Mean = 0.63. The difference is mu (1) - mu (2) and its estimate is 0.230000. The 95% lower bound for difference is -1.271079. The T-Test of difference: T-Value = 0.25, P- Value =0.400, DF=210. From the output we learn that: (i) The data provide sufficient evidence to reject H0 and to conclude that the mean depression score for male teens is larger than that of female teens. (ii) The data provide sufficient evidence to conclude that male and female teens do not differ in mean depression score. (iii) The data do not provide sufficient evidence to conclude that the mean depression score of male teens is larger than that of female teens. (iv) The data do not provide sufficient evidence to reject H0, so we accept it, and conclude that male and female teens do not differ in mean depression score.

Answer:

2 seconds and 38 seconds

Step-by-step explanation:

h=-16t²-vot

1,200=-16t²-640t

turn this into standard form

16t²-640t+1200=0

now plug thes numbers into the quadratice formula

a 16 b -640 c 1200

solve with quadratic formula to get ≅2 and ≅38 seconds

Answer:

t≈2 seconds,t≈38 seconds

Step-by-step explanation:

h=−16t2+ v0t

Step 1. Solve the equation.

1,200= −16t^2+ 640t

We know the velocity, v0, is 640 feet per second.

The height is 1,200 feet. Substitute the values.

This is a quadratic equation. Rewrite it in standard form. Solve the equation using the quadratic formula.

ax^2 +   bx  +      c .   = 0

16t^2 −640t +  1,200 = 0

Identify the values of a, b, and c.

a=16,  b=−640, c=1,200

Write the quadratic formula.

t=−b± √b2−4ac‾‾‾‾‾‾‾‾

               2a

640+ √332,800‾‾‾‾‾‾‾‾   t= √640− √332,800‾‾‾‾‾‾‾

             32                                           32

Rewrite to show two solutions.

t=640+332,800‾‾‾‾‾‾‾‾√32,t=640−332,800‾‾‾‾‾‾‾‾√32

Approximate the answer with a calculator.

t≈2 seconds,t≈38 seconds

Step 2. Check the answer. The check is left to you.

Step 3. Answer the question.

The firework will go up and then fall back down. As the firework goes up, it will reach 1,200 feet after approximately 2 seconds. It will also pass that height on the way down at 38 seconds.

Answer:

[tex]\frac{1}{6}[/tex]

Step-by-step explanation:

The factors of 15 are numbers that can divide even through 15 without any remainders.

  These numbers are 1, 3, 5 and 15;

When we roll two fair dice once, there are about 36 possible out comes and this is the sample space of rolling this fair dice.

          1       2             3              4             5                6

1       (1, 1) (1, 2)         (1, 3)         (1, 4)   (1, 5)          (1, 6)

2 (2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)

3 (3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)

4 (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)

5 (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)

6 (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)

The total that will give a factor of 15;

  (1, 2)  (2, 3)   (1, 4)    (2, 1)   (3, 2)      (4, 1)

Out of the 36 possible outcomes, we have 6 whose sum will give a factor of 15;

  Probability of this  = [tex]\frac{6}{36}[/tex]   = [tex]\frac{1}{6}[/tex]

Answer:

a) MSE = 61.33

Forecast for 8th month = 15

b) MSE = 34.51

Forecast for 8th month = 18

c) The average method provides a better forecast because of its low MSE

Explanation:

Check the attached file for the solvings.

To answer this two-part question, you'll need to calculate the mean square errors (MSE) using two different forecasting methods: using the most recent value as a forecast and using the average of all data for a forecast. The one with lower MSE is the correct prediction. The forecast for the next month is always based on the previous value or average value depending on the method.

To answer this question, you need to understand how mean square error (MSE) and forecasting work. For (a), we use the last value as the forecast for the next value and compute MSE. For (b), we use the average of all data as the forecast for the next value and calculate the MSE. Finally, we compare which method gives a lower MSE, therefore better forecasting.

For (a), the forecast values would be the previous month's data, i.e., forecast for month 2 is 23, month 3 is 14 and so on. To calculate MSE, you subtract each monthly value from its forecast, square the result and find the average of these squares. The forecast for month 8 would be the value of month 7 which is 15.

For (b), you calculate the average of all the data available and use it as a forecast for all the next periods. The MSE and forecast for month 8 can be calculated in a similar manner as in (a).

In step (c), compare the MSE calculated in step (a) and step (b). A lower MSE indicates a better forecast and consequently represents an accurate choice for a predictive model.

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Answer:

[tex]t=\frac{255.8-270.74}{\sqrt{\frac{(8.215)^2}{6}+\frac{(11.903)^2}{8}}}}=-2.788[/tex]  

[tex]p_v =2*P(t_{(12)}<-2.788)=0.0164[/tex]

So the p value is a very low value and using any significance level for example [tex]\alpha=0.05, 0,1,0.15[/tex] always [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and there is enough evidence to conclude that we have significant difference in the means of the two groups

Step-by-step explanation:

Data given and notation

Disk:[269.0 249.3 255.2 252.7 247.0 261.6]

Oval:[ 268.8 260.0 273.5 253.9 278.5 289.4 261.6 280.2]

[tex]\bar X_{D}=255.8[/tex] represent the mean for the sample Disk

[tex]\bar X_{O}=270.74[/tex] represent the mean for the sample Oval

[tex]s_{D}=8.215[/tex] represent the sample standard deviation for the sample Disk

[tex]s_{O}=11.903[/tex] represent the sample standard deviation for the sample Oval

[tex]n_{D}=6[/tex] sample size for the group Disk

[tex]n_{O}=8[/tex] sample size for the group Oval

t would represent the statistic (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to check if the means are different, the system of hypothesis would be:

Null hypothesis:[tex]\mu_{D} = \mu_{O}[/tex]

Alternative hypothesis:[tex]\mu_{D} \neq \mu_{O}[/tex]

If we analyze the size for the samples both are less than 30 and the population deviations are not given, so for this case is better apply a t test to compare means, and the statistic is given by:

[tex]t=\frac{\bar X_{D}-\bar X_{O}}{\sqrt{\frac{s^2_{D}}{n_{D}}+\frac{s^2_{O}}{n_{O}}}}[/tex] (1)

t-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

Calculate the statistic

We can replace in formula (1) the results obtained like this:

[tex]t=\frac{255.8-270.74}{\sqrt{\frac{(8.215)^2}{6}+\frac{(11.903)^2}{8}}}}=-2.788[/tex]  

Statistical decision

For this case we don't have a significance level provided [tex]\alpha[/tex], but we can calculate the p value for this test. The first step is calculate the degrees of freedom, on this case:

[tex]df=n_{D}+n_{O}-2=6+8-2=12[/tex]

Since is a bilateral test the p value would be:

[tex]p_v =2*P(t_{(12)}<-2.788)=0.0164[/tex]

So the p value is a very low value and using any significance level for example [tex]\alpha=0.05, 0,1,0.15[/tex] always [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and there is enough evidence to conclude that we have significant difference in the means of the two groups

Answer:

Expected number of matches that occur = 4 matches

Step-by-step explanation:

First of all, let X_i be the event that when we turn over card i if it matches the required cards face.

Thus, for example X_1 is the event that turning over one card results in an ace while X_2 is the event that turning over second card reveals a deuce.

The number of matched cards "N" is given by the sum of this indicator random variable as shown in the attached file;

The expected number of matches when cards are drawn from a standard 52-card deck is 4.

We define a match for each card position as X_i = 1 if a match occurs, and X_i = 0 otherwise. The expectation E(X_i) for each card is 1/13 because the probability of the ith card being an i-matched card (Ace in the 1st position, Two in the 2nd position, and so on up to King in the 13th, then repeat with Ace) is 1/13.

Given there are 52 cards, each having the same pattern of matching, the expected number of matches is computed as:

E(X) = E(X_1 + X_2 + ... + X_52) = E(X_1) + E(X_2) + ... + E(X_52)

Since E(X_i) = 1/13 for all i:

E(X) = 52 * (1/13) = 4

Therefore, the expected number of matches is 4.

Answer:

Whats on the list?????

Step-by-step explanation:

Answer:

You dont multiply anything, you just round

Step-by-step explanation:

basically, you round the 2.3 to the nearest whole number which is most likely 2 because 3 is under five so it doesnt round up

Answer:

3x√x²y, –12x√x²y, x√yx², 2√x²y. or on Edge is A,B,D,F

Step-by-step explanation:

Got 100% on edge...

Answer:

32¾

Step-by-step explanation:

1 pound (lb) = 16 ounces

12 oz = 12/16 = 3/4 lb

32 pounds 12 oz

32 ¾ lb

Answer:

A = 81 pi ft^2

Step-by-step explanation:

The area of a circle is found by

A = pi r^2

The radius is 9

A = pi 9^2

A = 81 pi ft^2

Answer:

x ≤-9/4

Step-by-step explanation:

x/3-x-1/2≥1

Multiply each side by 6 to get rid of the fractions

6(x/3-x-1/2)≥1*6

2x -6x -3≥6

Combine like terms

-4x-3≥6

Add 3 to each side

-4x-3+3≥6+3

-4x ≥9

Divide each side by -4, remembering to flip the inequality

-4x/-4 ≤9/-4

x ≤-9/4

On solving the inequality x/3 - x - 1/2 ≥ 1, we get x ≤ -3. Hence the correct option is A.

Solve the inequality: x/3 - x - 1/2 ≥ 1

Combine like terms: x/3 - (2x + 1)/2 ≥ 1

Get a common denominator: 2x/6 - 3(2x + 1)/6 ≥ 6/6

Simplify the equation: -4x - 3 ≥ 0

Solve for x: x ≤ -3

Answer:

30

Step-by-step explanation:

Everything has to add up to 90.

Add EVERYTHING together.

3x + 33

3x + 33 = 90

90 - 33 = 57

57 / 3 = 19

19 = x

19 x 2 = 38

38 - 8 = 30

Answer:

The answer for ∠CDF is 30°.

Step-by-step explanation:

It ia given that complemetary angle is 90° so we can make an expression in terms of x :

It ia given that complemetary angle is 90° so we can make an expression in terms of x :∠AFB + ∠BFC + ∠CFD = 90°

32° + (x+9)° + (2x-8)° = 90°

In order to find ∠CFD, we have to find the value of x first so we have to move all the like-terms to one side :

32° + x + 9° + 2x - 8° = 90°

2x + x = 90° - 32° - 9° + 8°

3x = 57°

Then divide both sides by 3 :

3x ÷ 3 = 57° ÷ 3

x = 19°

We have already found the value of x. Now, the question ask us to find ∠CDF, (2x-8)°. We just have to substitute x value into the expression :

Let x = 19,

∠CDF = 2x - 8

= 2(19) - 8

= 30°

Answer:

Step-by-step explanation:

Answer:

28 or 29%

Step-by-step explanation:

There are 7 days total, 2 of which start with “S”, divide the 2 by 7 to get your percentage of 28-29%

The probability of picking a day that begins with the letter s is 2/7.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

Example:

The probability of getting a head in tossing a coin.

P(H) = 1/2

We have,

There are seven days in a week, and two of them start with the letter s: Sunday and Saturday.

Now,

The probability of picking a day that begins with the letter s.

= 2/7

Or,

= 0.2857

Or,

= 0.2857 x 100%

= 28.57%.

Thus,

The probability of picking a day that begins with the letter s is 2/7.

Learn more about probability here:

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Answer:

1/12

Step-by-step explanation:

1/6 * 3/6 (First roll has a one in 6 chance, second 3 in 6)

1*3 / 36 =

3 / 36 =

1/12

Answer:

3.8

Step-by-step explanation:

Answer:

Yes, there are only 676 different possibilities, which is less than the number of people in the group.

Step-by-step explanation:

Assuming that the English alphabet has 26 different letters, the number of possible combinations of first and last name initials is:

[tex]n = 26*26\\n=676[/tex]

If we try to assign a different combination to each person in the group, it would only be possible to do it for the first 676 people, while the remaining 24 would have a repeated first and last initial. Therefore, the answer is yes, there must be 2 people who have matching first and last initials.

The Pigeonhole Principle in mathematics implies in a group of 700 people, there must be at least two people who have matching first and last initials.

The concept of this problem involves understanding the Pigeonhole Principle in mathematics. Considering the English alphabet has 26 letters, we can have 26 possible first initials and 26 possible last initials. Therefore, there are 26x26=676 unique combinations of first and last initials. However, we have a group of 700 people which is more than 676. The Pigeonhole Principle states that if you try to distribute more items than there are containers, then at least one container must hold more than one item. Therefore, applying this principle, there must be at least two people among the group of 700 who have matching first and last initials because the number of people (700) is greater than the possible unique combinations of first and last initials (676).

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Answer: The copy machine makes 171 copies in 4 minutes and 45 seconds.

Step-by-step explanation:

Let's dissect the question. The copy machine makes 36 copies per minute.

36 per min.

To see how many copies it makes in 4 minutes and 45 seconds, we multiply 36 * 4.75. 45 seconds is 3/4ths of a minute, or 0.75 of a minute.

[tex]36 * 4.75=171[/tex]

It makes 171 copies in 4 minutes and 45 seconds.

Answer:

Option B is not the most common correct choice.

Step-by-step explanation:

The multiple-choice questions on Advanced Placement exams have five options: A, B, C, D, and E.

The probability that any of these five option is the correct answer is:

[tex]p=\frac{1}{5}=0.20[/tex]

A random sample of 400 multiple-choice questions on Advanced Placement exam are selected.

The results showed that 90 of the 400 questions having B as the answer.

To test the hypothesis that option B is more likely the correct answer for most question, the hypothesis can be defined as:

H₀: All the options are equally probable, i.e. p = 0.20.

Hₐ: Option B is more likely the correct option, i.e. p > 0.20.

Compute the sample proportion as follows:

[tex]\hat p=\frac{90}{400}=0.225[/tex]

The test statistic is:

[tex]z=\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}}=\frac{0.225-0.20}{\sqrt{\frac{0.20(1-0.20)}{400}}}= 1.25[/tex]

The test statistic is 1.25.

Decision rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.

Compute the p-value as follows:

[tex]p-value=P(Z>1.25)\\=1-P(Z<1.25)\\=1-0.89435\\=0.10565\\\approx 0.1057[/tex]

*Use a z-table.

The p-value is 0.1057.

The p-value of the test is quite large. Thus, the null hypothesis was failed to rejected.

Hence, it can be concluded that option B is not  the most common correct choice.

Testing the hypothesis, it is found that since the p-value of the test is of 0.1056 > 0.05, it does not provide evidence that B is more likely to be the correct choice than would be expected if all five options were equally likely.

At the null hypothesis, it is tested if all of them are equally as likely, that is, the proportion of B is [tex]p = \frac{1}{5} = 0.2[/tex]. Thus:

[tex]H_0: p = 0.2[/tex]

At the alternative hypothesis, it is tested if B is more likely, that is, if the proportion of B is more than 0.2. Thus:

[tex]H_1: p > 0.2[/tex]

The test statistic is given by:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which:

In this problem, the parameters are: [tex]p = 0.2, n = 400, \overline{p} = \frac{90}{400} = 0.225[/tex].

The value of the test statistic is:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

[tex]z = \frac{0.225 - 0.2}{\sqrt{\frac{0.2(0.8)}{400}}}[/tex]

[tex]z = 1.25[/tex]

The p-value of the test is the probability of finding a sample proportion above 0.225, which is 1 subtracted by the p-value of z = 1.25.

Looking at the z-table, z = 1.25 has a p-value of 0.8944.

1 - 0.8944 = 0.1056.

Since the p-value of the test is of 0.1056 > 0.05, it does not provide evidence that B is more likely to be the correct choice than would be expected if all five options were equally likely.

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Answer:

80

Step-by-step explanation:

So if 50 tablets are made and 2 are defective then it’s 50:2. That means for every 50 tablets are made 2 are defective. And since 50 goes into 2000 40 times, you would multiply 40 x 2 to get 80, the number defective tablets

Answer:

Country B gaines 2 units of good X , per unit of Good Y sacrifised.

Step-by-step explanation:

Country B's production possibilities in form of goods (X,Y) are :

The country can produce 60 units of good X or 30 units of good Y, by complete specialisation in either good & not producing the other good.

The country has more (twice) advantage in producing good X. As, it can produce 2 times more good X, than good Y, from the same available resources.

If it decides to produce at point J, production specialising in Good X:    It will produce only good X, no units of Y. This implies that - it gains 2 units of good X per unit of good Y sacrifised, as per their production potential ratio (60:30)  

Answer:

8 1/3

Step-by-step explanation:

2 1/2 * 3 1/3

Change each to an improper fraction

2 1/2  = (2*2 +1)/2 = 5/2

3 1/3 = (3*3+1)/3 = 10/3

5/2 *10/3 = 50/6

Divide the top and bottom by 2

25/3

Change to a mixed number

3 goes into 25    8 times with 1 left over

8 1/3

Answer:

1/1000

Step-by-step explanation:

Answer:

Binomial probability distribution.

Step-by-step explanation:

For each watch, there are only two possible outcomes. Either it fails within 1 year of purchase, or it does not. The probability of a watch falling within 1 year of purchase is independent of other watches. So the type of of distribution will best model the number of watches out of the 15 sampled that fail within 1 year is the binomial probability distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Answer:

bcd

Step-by-step explanation:

Answer:

B C D

Step-by-step explanation:

Answer:

(4,-4)

Step-by-step explanation:

Diagonals of a rectangle share a common midpoint

(4-6)/2 , (0-4)/2 = (-6+x)/2, (0+y)/2

-2 = -6 + x

x = 4

-4 = y

We determined the fourth point of a rectangle by ensuring that the sides of the rectangle are parallel to the axes and the sides are equal in length. The fourth point of the rectangle formed by the points (4,0), (-6,0), and (-6,-4) is (4,-4).

The fourth point of the rectangle should have the same x-coordinate as the point (4,0) and the same y-coordinate as the point (-6,-4). Therefore, the fourth point is (4,-4)

To better understand the reasoning, let's consider the points on a plane. We recall that rectangles have sides of equal length and parallel to the axes. Therefore, since the line connecting (4,0) and (-6,0) is parallel to the x-axis, the fourth point's x-coordinate has to be the same as the point on the opposite side of the rectangle, which is 4. Similarly, as the line connecting (-6,0) and (-6,-4) is parallel to the y-axis, the fourth point's y-coordinate has to equal the y-coordinate of the point on the opposite side (-6,-4), which is -4. Hence, the fourth point is (4,-4).

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Answer:

Step-by-step explanation:

Hello!

You need to construct a 95% CI for the population variance of the forces the safety helmets transmit to wearers.

The variable of interest is X: Force a helmet transmits its wearer when an external force is applied (pounds)

Assuming this variable has a normal distribution, the manufacturer expects it to have a mean of μ= 800 pounds and a standard deviation of σ= 40 pounds

A test sample of n=40 was taken and the resulting mean and variance are:

X[bar]= 825 pounds

S²= 2350 pounds²

To estimate the population variance per confidence interval you have to use the following statistic:

[tex]X^2= \frac{(n-1)S^2}{Sigma^2} ~~X^2_{n-1}[/tex]

And the CI is calculated as:

[[tex]\frac{(n-1)S^2}{X^2_{n-1;1-\alpha /2}}[/tex];[tex]\frac{(n-1)S^2}{X^2_{n-1;\alpha /2}}[/tex]]

[tex]X^2_{n-1;1-\alpha /2}= X^2_{39;0.975}= 58.1[/tex]

[tex]X^2_{n-1;\alpha /2}= X^2_{39;0.025}= 23.7[/tex]

[[tex]\frac{39*2350}{58.1}[/tex];[tex]\frac{39*2350}{23.7}[/tex]]

[1577.45; 3867.09] pounds²

Using a confidence level of 95% you'd expect that the interval [1577.45; 3867.09] pounds² contains the value of the population variance of the force the safety helmets transmit to their wearers when an external force is applied.

I hope this helps!