Eleanor can drive an average of 374 Miles on one tank of gas. How many miles can she drive on 15 tanks of gas

Answer:

80% confidence interval of the true average number of hours of TV watched per week is [8.28 hours, 11.02 hours].

Step-by-step explanation:

We are given that a college student is interested in investigating the TV-watching habits of her classmates and surveys 20 people on the number of hours they watch per week. The results are provided below;

Hours of TV per week (X): 6, 14, 13, 6, 16, 10, 19, 4, 5, 5, 18, 8, 7, 14, 8, 8, 9, 12, 6, 5.

Firstly, the Pivotal quantity for 80% confidence interval for the true average is given by;

                                P.Q. =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean number of hours of TV watched per week = [tex]\frac{\sum X}{n}[/tex] = 9.65

            s = sample standard deviation = [tex]\sqrt{\frac{\sum (X -\bar X)^{2} }{n-1} }[/tex]  = 4.61

            n = sample of people = 20

           [tex]\mu[/tex] = true average number of hours of TV watched per week

Here for constructing 80% confidence interval we have used One-sample t-test statistics as we don't know about population standard deviation.

So, 80% confidence interval for the true average, [tex]\mu[/tex] is ;

P(-1.33 < [tex]t_1_9[/tex] < 1.33) = 0.80  {As the critical value of t at 19 degrees of

                                               freedom are -1.33 & 1.33 with P = 10%}  

P(-1.33 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 1.33) = 0.80

P( [tex]-1.33 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]1.33 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.80

P( [tex]\bar X-1.33 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+1.33 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.80

80% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-1.33 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+1.33 \times {\frac{s}{\sqrt{n} } }[/tex] ]

                                         = [ [tex]9.65-1.33 \times {\frac{4.61}{\sqrt{20} } }[/tex] , [tex]9.65+1.33 \times {\frac{4.61}{\sqrt{20} } }[/tex] ]

                                         = [8.28 hours, 11.02 hours]

Therefore, 80% confidence interval of the true average number of hours of TV watched per week is [8.28 hours, 11.02 hours].

Answer:

4 ft

Step-by-step explanation:

288=16 * 18

12+4=16

14+4=18

The dimensions increased by 4 feet.

The area of the rectangle is the product of the length and width of a given rectangle.

The area of the rectangle = length × Width

Given;

Dimensions of rectangle = 12 + x and 14 + x

The area of the rectangle= (12 + x) (14 + x) = 288

x² + 26x + 168 = 288

x² + 26x - 120 = 0

(x + 30) (x - 4) = 0

x=-30, x =4

Hence, The dimensions increased by 4 feet.

Learn more about the area;

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Answer:

13.125 or 105/8u^3

Step-by-step explanation:

To find the volume of the box, you can use the formula of length times width time height.

3 * 5 = 15

2*2=4

15/4*7/2=105/8      which can be divided to become 13.125

Answer:

x = -7.33        OR         x = [tex]\frac{-22}{3}[/tex]

y = 13

Step-by-step explanation:

→You can use the substitution method. First, make y by itself in (-2 + 2y = 24):

-2 + 2y = 24

2y = 26

y = 13

→Then, plug in 13 for y into the other equation:

3x + 2y = 4

3x + 2(13) = 4

3x + 26 = 4

3x = -22

x = -7.33        OR         x = [tex]\frac{-22}{3}[/tex]

Answer:

[tex]81\pi[/tex]

Step-by-step explanation:

[tex]Area = \pi * r^{2} \\\pi *9^{2} =81\pi[/tex]

Answer:

81 π

Step-by-step explanation:

formula is radius squared times pi or π so the answer would be 9x9=81 and you said to leave in terms of π so the answer is 81 π.

Answer:

20%

Step-by-step explanation:

Use the table provided... it says -10 is .2 which is the same as 20%

Answer:

0.20

Step-by-step explanation:

requires decimal not percentage

Answer:

C is the correct answer.

Step-by-step explanation:

The reason it is C is because pi/the symbol on top is irrational.

Hope you have a good rest of your day :)

Answer:

The diameter of the smallest circular opening through which the box will fit  is 5.7 cm to the nearest tenth

Step-by-step explanation:

The dimensions of the rectangle are :

height: 4 cm

length: 10 cm

breadth: 4 cm

The diameter of the smallest circular opening through which the box will fit will be equals to the diagonal of a face of the rectangular box.

The face we will try to fit in first will determine the diagonal that we will calculate.

Let us try to fit in the right side of the rectangular box. The face we will have at that side is a square of 4 cm by 4 cm which is formed by the height and the width of the box.

We can calculate the diagonal using Pythagoras Theorem:

diagonal = [tex]\sqrt{height^{2}+ breadth^{2}}= \sqrt{4^{2}+4^{2}}=5.657 \approx 5.7cm[/tex] to the nearest tenth

Answer:

18 meters.

Step-by-step explanation:

There is a constant acceleration for 3 seconds, reaching 4 m/s. This, when drawn on a velocity/time graph, creates a diagonal line. The area underneath this line, which is the distance it travels, is found by the following: 0.5(l*h), the formula used to find the area of a triangle.

0.5(3*4)=6m

There is then a constant deceleration of 0.5m/s for 4 seconds. This does also create a diagonal line on a velocity/time graph, but it doesn't go down to 0. What I do is split it up so that a triangle and a rectangle are created from the shape made. The triangle has a height of 2, and a length of 4, so we use the same formula used before.

0.5(2*4)=4m

Now, all that remains is a rectangle of height 2 and a length of 4, so we find the area of it.

2*4=8m

Finally, we add each of these up.

6m+4m+8m=18m

Sorry if the step by step process was poorly explained, I'm not the best at explaining. Hope this helped, though. :^)

The total distance traveled by the toy car is 18 meters.

Acceleration of any object is defined as the variation in the speed of the object with the variation of time. Acceleration is a vector term and to define it we require both the magnitude and the direction. The unit of acceleration can be m / sec², miles / sec², etc.

For three seconds, there is a steady acceleration that reaches 4 m/s. This yields a diagonal line when drawn on a velocity/time graph. The following formula can be used to determine the region beneath this line, or the distance it travels:

The triangle area is calculated using the formula:-

A = 0.5(l x h).

A = 0.5(3 x 4)=6m

There is then a constant deceleration of 0.5m/s for 4 seconds. This does also create a diagonal line on a velocity/time graph, but it doesn't go down to 0. What I do is split it up so that a triangle and a rectangle are created from the shape made. The triangle has a height of 2, and a length of 4, so we use the same formula used before.

0.5(2 x 4)=4m

Now, all that remains is a rectangle of height 2 and a length of 4, so we find its area of it.

2 x 4 = 8m

Finally, we add each of these up.

6m+4m+8m=18m

Therefore, the total distance traveled by the toy car is 18 meters.

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Answer:

P=80

Step-by-step explanation:

R= 10  

P = R*2 *4

P of a square = 10*2 *4 = 80

Just divide by any fraction of the squares ratio.

ie) if square = 2/3 of the length of the circle then 80 x 2/3 = 53.333...

ie) if square = 3/4 of the length of the diameter of the circle then 80 x 3/4 = 60

As 3/4 pf 10 = 7.5

7.5 * 2  = 15

15* 4 = 60

Howver the square is outside of the circle as described circle inscribed exactly how much if it fits exactly then the length will be same as circles diameter = 10*2 = D;20.

20 *4 = 80. P;80

Etc.

Answer:

p-value (0.0208) is less than alpha = 0.05 reject H0.

Step-by-step explanation:

we have the following data:

sample size = n = 75

x, the number to evaluate is 45

the sample proportion would be: x / n = 45/75

p * = 0.6

Now, the null and alternative hypotheses are:

H0: P = 0.72

Ha: P no 72

two tailed test

statistic tes = z = (p * - p) / [(p * (1-p) / n)] ^ (1/2)

replacing we have:

z = (0.6 - 0.72) / [(0.72 * (1-0.72) / 75)] ^ (1/2)

z = -2.31

p-vaule = 2 * p (z <-2.31)

using z table, we get:

p-vaule = 2 * (0.0104)

p-vaule = 0.0208

Therefore, p-value (0.0208) is less than alpha = 0.05 reject H0.

Answer:

108 pages

Step-by-step explanation:

Angelina read 30% of the book that contains 360 pages.

30% of 360 pages

"of" also means multiply, so we must multiply 30% and 360.

30% * 360

Convert 30% to a decimal. Divide 30 by 100, or move the decimal place 2 spots to the left.

30/100=0.30

or

30.0---> 3.0---> 0.30

Plug the decimal in for the percent.

0.30*360

Multiply the 2 numbers together

108

Angelina has read 108 pages so far.

Answer:

3¹²

Step-by-step explanation:

Move 3⁻² to the numerator using the negative exponent rule

1/b-n = bⁿ

(3⁵)² ⋅ 3²

Multiply the exponents

3¹⁰ · 3²

Multiply by adding the exponents

3¹⁰⋅ 3²

3¹²

Answer:

432

Step-by-step explanation:

l x w

4x3

4x19

8x24

8x19

432

Answer:

q < 11

Step-by-step explanation:

Distribute the -3

23 - q > 12

Add q and subtract 12

q < 11

Step-by-step explanation:

the answer is

q<11

23-q>12

Answer:

The Answer is C: Yes, △EFG~ △KLM by SSS or SAS

Step-by-step explanation:

SSS is for side-side-side

Both triangles have all three sides given, so the SSS similarity theorem is one way to prove these triangles are similar.

SAS is for side-angle-side

Both triangles have one angle measurement given, and two side lengths given, therefore we can also use the SAS similarity theorem to prove the two triangles are similar.  

Since both SSS and SAS work to prove the triangles are similar, the correct answer is C: Yes, △EFG~ △KLM by SSS or SAS

(I also just answered this question on the assignment and got it correct)

Answer:

Answer is C

Step-by-step explanation:

Took it on Edg

Answer:

2

Step-by-step explanation:

1. Divide by four

2. two of the fours will cancel out leaving you to divide 4 by - 2 which is 2

Answer:

|5| = 5 and |2| = 2 and because 5 > 2, our answer is |5| > |2|.

Answer:

|5|

Step-by-step explanation:

5 is greater than 2

Answer:

a. The mean would be 0.067

The standard deviation would be 0.285

b. Would be of 1-e∧-375

c. The probability that both of them will be gone for more than 25 minutes is 1-e∧-187.5

d. The likelihood of at least of one of the taxis returning within 25 is 1-e∧-375

Step-by-step explanation:

a. According to the given data the mean and the standard deviation would be as follows:

mean=1/β=1/15=0.0666=0.067

standard deviation=√1/15=√0.067=0.285

b. To calculate How likely is it for a particular trip to take more than 25 minutes we would calculate the following:

p(x>25)=1-p(x≤25)

since f(x)=p(x≤x)=1-e∧-βx

p(x>25)=1-p(x≤25)=1-e∧-15x25=1-e∧-375

c. p(x>25/2)=1-p(x≤25/2)=1-e∧-15x25/2=1-e∧-187.5

d. p(x≥25)=1-e∧-15x25=1-e∧-375

Answer:

Step-by-step explanation:

a) The probability of a Type I error in a lie detection test would be the probability that the lie detection machine incorrectly detected lie for the truth tellers. This is already given in the problem as 0.07.

Therefore,

[tex]P(Type-I) = 0.07[/tex]

Therefore 0.07 is the required probability here.

b) The probability of a Type II error in a lie detection test would be the probability that the lie detection machine incorrectly detected truth for the the people who are actually liars. This is thus 1 - reliability.

[tex]P(Type-II) = 1 - Reliability = 1- 0.86 = 0.14[/tex]

Therefore 0.14 is the required probability here.

Answer:

a) 0.070

b) 0.14

Step-by-step explanation:

Given that the tests are 86% reliable, i.e a probability of 0.86 a lie would be detected.

Probability of error = 0.070

a) For type I error, we have:

The probability of a type I error in this lie detector is the probability that the test erroneously detects a lie even when the individual is actually telling the truth, i.e

P(type I error) = P(rejecting true null)

= 0.070

b) The probability of a Type II error this lie detectot is the probability that the test erroneously detected truth insteax of lie.

i.e = 1 - reliability

P (Type II error) = P(Failing to reject false Null)

= P(Not detecting a lie)

= 1-0.86

= 0.14

Answer:

1674 ft²

Step-by-step explanation:

Area S = 65*30

Area A = (65 - x)(30 - x) = (65 - 3)(30 - 3) = 62*27= 1674 ft²

Answer:

The answer is C.

Step-by-step explanation:

You have to divide it by 2 :

∠XYZ = 148° ÷ 2

= 74°

Here is the correct question.

The manufacturer of a smart watch claims that individuals who pay attention to how many steps they take per day will inadvertently take more steps per day than individuals who pay no attention to how many steps they take per day. To investigate this claim, the manufacturer conducts a study to estimate the difference in the mean number of steps taken by those that pay attention to how many steps they take per day and those that do not. To do so, 40 volunteers are recruited. Half of the volunteers are randomly assigned to receive a smart watch and are taught how to use it to track their steps. The other half of the volunteers are given a wristband to wear, but are not informed that the wristband is tracking their steps. The volunteers are monitored for 30 days. The mean and standard deviation of the number of steps taken per day are computed for each group. Here are the data:

                                           [tex]n[/tex]                     [tex]\bar x[/tex]                  [tex]S_x[/tex]

Pay attention                    20                 10,244            1,580

Do not pay attention        20                 8.,648            2,350

Which of the following is a 99% confidence interval for the difference in the mean number of steps taken by all people like these that do and do not pay attention to the number of steps they take per day using df - 19 ?

[tex](A) \ 1596 \ \pm 2.861 \sqrt{ \dfrac{1580^2}{20} + \dfrac{2350^2}{20}} \\ \\ \\ (B) \ 1596 \ \pm 2.861 \sqrt{ \dfrac{1580^2}{20} - \dfrac{2350^2}{20}} \\ \\ \\ (C) \ 1596 \pm 2.576 \sqrt{ \dfrac{1580^2}{20} + \dfrac{2350^2}{20}} \\ \\ \\ (D) 1596 \pm 2.576 ( \dfrac{1580^2}{\sqrt{20}} + \dfrac{2350^2}{\sqrt{20}}) \\ \\ \\ (E) 1596 \pm 2.576 ( \dfrac{1580^2}{\sqrt{20}} - \dfrac{2350^2}{\sqrt{20}})[/tex]

Answer:

[tex]\mathbf{(A) \ 1596 \ \pm 2.861 \sqrt{ \dfrac{1580^2}{20} + \dfrac{2350^2}{20}}}[/tex]

Step-by-step explanation:

Given that :

significance level [tex]\alpha = \mathbf{0.01}[/tex]

From the Given data;

Using Excel with the function : TINV(0.01,19);

Critical value t* = 2.861

The margin of error can now be represented by the illustration:

Margin of error = [tex]t^* \sqrt{ \dfrac {s_1 ^2}{n_1} + \dfrac {s_2 ^2}{n_2}[/tex]

Lower Limit =  [tex](\bar x_1 - \bar x_2)- (Margin \ of \ error)[/tex]

Upper Limit =  [tex](\bar x_1 - \bar x_2)+ (Margin \ of \ error)[/tex]

Thus; the confidence interval for the difference in the mean number of steps taken by all people like these that do and do not pay attention to the number of steps they take per day using df - 19 is:

[tex]\mathbf{(A) \ 1596 \ \pm 2.861 \sqrt{ \dfrac{1580^2}{20} + \dfrac{2350^2}{20}}}[/tex]

Answer:

The correct answer is D. The wording of the question is biased to strengthen opposition against a particular candidate. The question wording should be changed to be more neutral.

Step-by-step explanation:

The phrasing and setup of the poll will produce responses that are biased against the candidate. The setup of the poll should be changed to avoid influencing the opinions of the respondents.

Answer:

$61.12

Step-by-step explanation:

Price of the Video game = $69.99

Discount = 18%

Discount price = 18% of $69.99

                         = $69.99*18/100

                         = $12.6

Price after Discount = Price - Discount price

                                  = $69.99 - $12.6

                                  = $57.39

Sales tax = 6.5% applied to the discounted price

                = 6.5% of $57.39

sales tax in dollars = $57.39 * 6.5/100

                               = $3.73

The amount he pays for the game = $57.39 + $3.73

                                                          = $61.12

Answer:

1. Number of classes used are 7 with 5 class interval.

Step-by-step explanation:

Note: See the attached files for the tables and answers to questions 2, 3, 4 and 5.

Answer:

2,748.5

Step-by-step explanation:

Answer:

thank uuu

Step-by-step explanation:

Answer:

The amount remaining in coffee storage bin after making 10cups if coffee = (1500-10n) grams

Step-by-step explanation:

This question is incomplete as we are not told what to determine.

Let's consider the following question:

A coffee storage bin contains 1500 grams of coffee beans. To make a cup of coffee, n grams of coffee beans are removed. How many grams of coffee would be left after making 10 cups of coffee?

Solution:

Total amount of coffee in storage bin = 1500grams

To make one cup of coffee, we need n grams of coffee

The amount remaining for one cup = 1500grams - n grams

To make 10 cups of coffee, we would need = 10× n grams of coffee= 10n grams

The amount remaining in coffee storage bin after making 10cups of coffee = total amount in storage - amount for making 10cups

(1500-10n) grams