Is it true that If B is formed by adding to one row of A a linear combination of the other rows, then detB = detA.

Answer:

The answer to your problem is, 149.5

Step-by-step explanation:

How to find our number from the problem, 115% of 130.

Calculate:

[tex]\frac{115}{100}[/tex] of 130 = [tex]\frac{115}{300}[/tex] × 130

= 149.5

The new snowboard is 149.5 centimeters now.

Thus the answer to your problem is, 149.5

a) The sample mean years to maturity for corporate bonds = 16.9625

and the sample standard deviation =  8.2232

b) A 95% confidence interval for the population mean years to maturity: (14.4141, 19.5112)

c) The sample mean yield on corporate bonds is 4.5405

and the sample standard deviation = 2.3082

d) A 95% confidence interval for the population mean yield on corporate bonds:  (3.825, 5.256)

a) The mean of the sample would be,

[tex]\bar{x}[/tex] = (10.25 + 28 +  23 + 13.25 + 3, 7.5 + 26.5 + 21.25 + 3.25, 19 + 9.25 + 28.75 + 1.75 + 17 + 8.75 + 24 + 24.5 + 18+ 11.75 + 22 + 22.75 + 27.75 + 16.75 + 12 + 16.5 + 23.75 + 25.25 + 25.75 + 22.5 + 1.25 + 19.5 + 12.5 + 27.25 + 19.5 + 17.75 + 11.5+ 3.5 + 20 + 25.25 + 6.75) / 40

[tex]\bar{x}[/tex] = 678.5 / 40

[tex]\bar{x}[/tex] = 16.9625

And  the sample standard deviation would be,

s = √(67.6203)

s =  8.2232

b)

We know that the formula for the confidence interval is,

CI = [tex]\bar{x}[/tex] ± (z × s/√n)

Here, n = 40, [tex]\bar{x}[/tex] = 16.9625, s = 8.2232 and z = 1.9600

Using above formula the 95% confidence interval for the population mean years to maturity would be,

CI = 16.9625 ± (1.9600 × 8.2232/√40)

CI = (16.9625 ± 2.548)

CI =  (16.9625 - 2.548,  16.9625 + 2.548)

CI = (14.4141, 19.5112)

c) Consider sample yield on corporate bonds.

The mean would be,

[tex]\bar{x}[/tex] = 181.62 / 40

[tex]\bar{x}[/tex] = 4.5405

And the standard deviation would be,

s = √(5.327594)

s = 2.3082

d) Now we construct a 95% confience interval.

Here, n = 40, s = 2.3082, [tex]\bar{x}[/tex] = 4.4505, and z = 1.9600

Using above formula the 95% confidence interval for the population mean years to maturity would be,

CI =  4.4505 ± (1.9600 × 2.3082/√40)

CI = (4.5405 ± 0.716)

CI = (4.5405 - 0.716, 4.5405 + 0.716)

CI = (3.825, 5.256)

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Find the complete question below.

Answer:

1. 75%

2. 0%

3. 0.1

4. one half

5. six tenths

6. 0.75

7. 64%

Step-by-step explanation:Answer 1:

The spinner has a total of 8 sections, out of which there are 2 yellow sections. Therefore, the probability of not getting a yellow section when the spinner is spun once is 6/8 or 3/4, which is equal to 75%.

Answer 2:

The spinner has only three sections and none of them is colored yellow. Therefore, the probability of getting a yellow section when the spinner is spun once is 0%.

Answer 3:

The total number of students surveyed is:

1 + 3 + 2 + 5 + 9 + 7 + 3 = 30

The number of students who studied for 1 hour is 3. Therefore, the probability of a student studying for 1 hour is 3/30, which simplifies to 1/10 or 0.1.

Answer 4:

Since the coin is fair and has one side colored yellow and the other side colored green, the probability of getting a yellow side when the coin is tossed is 1/2 or one half.

Answer 5:

The set of cards has 10 letters, out of which 4 are vowels (A, I, U). Therefore, the number of consonants in the set is 10 - 4 = 6. The probability of drawing a consonant is therefore 6/10, which simplifies to 3/5 or 0.6.

Answer 6:

The number cube has 8 sides, numbered 1 through 8. The probability of getting a number greater than 2 is the same as the probability of getting any number from 3 to 8. There are 6 such numbers out of 8 total numbers, so the probability is 6/8 or 3/4, which is equal to 0.75.

Answer 7:

The total number of marbles in the bag is:

2 + 4 + 10 + 9 = 25

The number of marbles that are not purple is:

2 + 4 + 10 = 16

Therefore, the probability of not getting a purple marble when one marble is chosen from the bag is 16/25, which is equal to 64%.

The expressions are subtracted to give -a⁴ + a²b² + 4b⁴

It is important to note that algebraic expressions are described as expressions that are made up of terms, variables, constants, coefficients and factors.

These expressions are also identified with arithmetic operations. These operations are;

From the information given, we have that;

4a⁴ + 4a²b² - 2b⁴

3a⁴ + 5a²b² + 2b⁴

Now, subtract the expressions;

3a⁴ + 5a²b² + 2b⁴ - (4a⁴ + 4a²b² - 2b⁴)

expand the bracket

3a⁴ + 5a²b² + 2b⁴ - 4a⁴ - 4a²b² + 2b⁴

add  the  values

-a⁴ + a²b² + 4b⁴

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To model the decrease in the value of the car over time, we can use an exponential function of the form:

V(t) = V(0) * e^(-rt)

where:

V(0) is the initial value of the car (in this case, $20,000).

r is the annual rate of depreciation, expressed as a decimal (in this case, 0.103).

t is the number of years since the car was purchased.

Plugging in the given values, we get:

V(t) = $20,000 * e^(-0.103t)

This is the exponential function that models the value of the car in t years.

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Answer:

On x < -5, the function is increasing.

Based on the given side lengths a=3.5 cm, b=√18 cm (which is approximately 4.24 cm), and c=6 cm, the triangle is an scalene triangle.

Triangles are described in terms of their sides and angles in geometry. A closed planar three-sided polygon shape with three sides and three angles is known as a triangle. The lengths of the sides of a scalene triangle vary. They are not equal, and the angles have three measurements. However, it still has a 180° angle sum, just like all triangles.

A scalene triangle is a triangle with three different side lengths and three different angle measurements. The total of all internal angles, however, is always equal to 180 degrees. As a result, it satisfies the triangle's condition of angle sum.

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The points that belong to the image of the equation of a line are (4, - 8) and U' = (1, 4).

In this question we find the definition of the equation of a line, whose image must be found by a kind of rigid transformation known as dilation:

U'(x, y) = O(x, y) + k · [U(x, y) - O(x, y)]

Where:

If we know that O(x, y) = (5, - 8), k = 1 / 4 and y = - 4 · x - 4, then the image of the point:

U'(x, y) = (5, - 8) + (1 / 4) · [(x, - 4 · x - 4) - (5, - 8)]

U'(x, y) = (5, - 8) + (1 / 4) · (x - 5, - 4 · x + 4)

U'(x, y) = (5, - 8) + (x / 4 - 5 / 4, - x + 1)

U'(x, y) = (x / 4 + 15 / 4, - x - 7)

Now we evaluate the expression at each x-value:

x = 1

U' = (1 / 4 + 15 / 4, - 1 - 7)

U' = (4, - 8) (YES)

x = - 11

U' = (- 11 / 4 + 15 / 4, - (- 11) - 7)

U' = (1, 4) (YES)

x = - 23

U' = (- 23 / 4 + 15 / 4, - (- 23) - 7)

U' = (- 2, 16) (NO)

x = 17

U' = (17 / 4 + 15 / 4, - 17 - 7)

U' = (8, - 24) (NO)

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Answer:

Both shots good: .8(.8) = .64 = 64%

Exactly one shot good: 2(.2)(.8) = .32 = 32%

Neither shot good: .2(.2) = .04 = 4%

If a model predicting minutes includes "ftmade" as an explanatory variable, the model would have two parameters: the intercept and the slope of "ftmade." The intercept represents the expected minutes when "ftmade" is zero, and the slope represents the expected increase in minutes for every one-unit increase in "ftmade."

The number of parameters in a model that predicts mins by including ftmade as an explanatory variable depends on the type of model being used.

If a simple linear regression model is used, the model would have two parameters: the intercept and the slope coefficient for the ftmade variable.

If a multiple linear regression model is used, which includes more than one explanatory variable, the model would have additional parameters for each additional explanatory variable included.

For example, if the model also included the variables age and gender, the model would have four parameters: the intercept, the slope coefficient for ftmade, the slope coefficient for age, and the coefficient for gender (assuming gender is coded as a binary variable).

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The length of the sides are

AC = 5.4

BC = 10.5

To determine the value, we need to know the different trigonometric identities.

They include;

These identities also have their ratios;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

From the information given, we have;

tan 31 = AC/9

cross multiply the values

AC = 5. 4

sin 59 = 9/BC

cross multiply the values

BC = 10. 5

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(L2) The Incenter Theorem states that the incenter of a triangle is equidistant from each incenter of a triangle.

The Incenter Theorem is a fundamental result in geometry that describes a unique point within a triangle known as the incenter. The incenter is the point at which the angle bisectors of a triangle intersect.

The Incenter Theorem states that the incenter of a triangle is equidistant from each side of a triangle.

To understand this theorem, consider an arbitrary triangle ABC. Let I be the incenter of the triangle. The angle bisectors of the triangle, AI, BI, and CI, intersect the opposite sides at points D, E, and F, respectively.

According to the angle bisector theorem, these points divide the sides of the triangle into segments that are proportional to the adjacent sides.

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Answer:

$2560 is the total amount to be paid back

Step-by-step explanation:

This is Simple interest described in the question

P = Principal amount

  = Amount of money borrowed

  = $1600  

R = Rate of interest

  = 10% per year

  = 10% per annum

T = Time period

  = 6 years

Make sure the base units of R and T are the same:

S.I. = Simple Interest = [tex]\frac{PRT}{100}[/tex]

                                    = [tex]\frac{(1600 Dollars)(10\frac{Percent}{Year})(6Years)}{(100 Percent)}[/tex]

                                    = $960

This means:

Total amount to be paid back = P + S.I.

                                                   = $1600 + $960

                                                   = $2560                

The system has a unique solution, and therefore, there is only one solution to the system of equations.

Given the system of equation in the question:

x + y = 7

2x - 3y = -21

First, solve one of the equations for one of the variables and substitute it into the other equation.

From equation (1), we can solve for y in terms of x as follows:

x + y = 7

y = 7 - x --- equation (3)

Now we can substitute equation (3) into equation (2) and solve for x:

2x - 3y = -21

Plug in y = 7 - x

2x - 3(7 - x) = -21

Simplifying the above equation, we get:

2x - 21 + 3x = -21

5x - 21 = -21

5x = 0

x = 0

Now we can substitute x = 0 into equation (1) to find y:

x + y = 7

Plug in x = 0

0 + y = 7

y = 7

Therefore, the solution to the system of equations is x = 0, y = 7.

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The power series approximation of f(x)g(x) up to order 3 is:

[tex]e^56 sin 8x - 22(5x)sin 8x - 2e^56(5x) + 22(5x)^2 sin 8x[/tex]

To find the power series expansion of the product f(x)g(x), we need to multiply the power series expansions of f(x) and g(x) and collect like terms.

First, let's find the power series expansion of f(x):

[tex]f(x) = e^56 - 2(5x)^"[/tex]

Using the formula for the power series expansion of e^x:

[tex]e^x = 1 + x + (x^2)/2! + (x^3)/3! + ...[/tex]

We can write the power series expansion of f(x) as:

[tex]f(x) = e^56 - 2(5x)^"[/tex]

[tex]= (1 + 56 + (56^2)/2! + (56^3)/3! + ...) - 2(5x)^(1)[/tex]

= [tex]1 - 5x + (56 - 25x^2) +[/tex]...

Now let's find the power series expansion of g(x):

g(x) = sin 8x

= (8x) - (8x)^3/3! + (8x)^5/5! - ...

Finally, we can multiply the power series expansions of f(x) and g(x) to get the power series expansion of f(x)g(x):

[tex]f(x)g(x) = (1 - 5x + (56 - 25x^2) + ...) * ((8x) - (8x)^3/3! + (8x)^5/5! - ...)[/tex]

[tex]= (8x) - (40x^2) + (568x^2)/2! + ((56-8*8)/2!)x^4 + ...[/tex]

Collecting like terms up to order 3, we get:

[tex]f(x)g(x) = (8x) - (40x^2) + (224x^3)/3! + ...[/tex]

Therefore, the power series approximation of f(x)g(x) up to order 3 is:

[tex]e^56 sin 8x - 22(5x)sin 8x - 2e^56(5x) + 22(5x)^2 sin 8x[/tex]

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Based on the data provided, we can conduct a hypothesis test to determine if there is a difference in the median delivery times for the two services. We can use the Wilcoxon rank-sum test, also known as the Mann-Whitney U test, since the data is not normally distributed.

The null hypothesis is that there is no difference in the median delivery times between the two services, while the alternative hypothesis is that there is a difference. We can set the level of significance at 0.05.

Using the data provided, we can calculate the median delivery time for each service:

- Service 1: Median delivery time = 24.5 + 26.0 + 28.0 + 21.0 + 18.0 + 36.0 + 25.0 + 21.0 + 24.0 + 26.0 + 31.0 / 11 = 25.5 hours
- Service 2: Median delivery time = 28.0 + 25.5 + 32.0 + 20.0 + 19.5 + 28.0 + 29.0 + 22.0 + 23.5 + 29.5 + 30.0 / 11 = 27.0 hours

To conduct the Wilcoxon rank-sum test, we need to calculate the U statistic. We can use Table 1 in Appendix B to find the critical values for U.

The U statistic is calculated as follows:

- Rank all the observations together from lowest to highest, ignoring which service they belong to.
- Assign ranks to each observation, with the lowest observation receiving a rank of 1 and so on.
- Add up the ranks for each service separately.
- Calculate the U statistic using the following formula: U = n1n2 + n1(n1 + 1) / 2 - R1, where n1 is the sample size for Service 1, n2 is the sample size for Service 2, and R1 is the sum of the ranks for Service 1.

Using the data provided, we can calculate the U statistic as follows:

- Ranks for Service 1: 1, 3, 4, 5, 6, 11, 8, 2, 7, 9, 10
- R1 = 1 + 3 + 4 + 5 + 6 + 11 + 8 + 2 + 7 + 9 + 10 = 66
- U = n1n2 + n1(n1 + 1) / 2 - R1 = 11 x 11 + 11(11 + 1) / 2 - 66 = 35

Using Table 1 in Appendix B with a sample size of 11 for both services and a level of significance of 0.05, we find the critical value of U to be 19. Since our calculated U of 35 is greater than the critical value of 19, we can reject the null hypothesis and conclude that there is a significant difference in the median delivery times for the two services.

In conclusion, the data provided suggests that there is a difference in the median delivery times for the two services. The Wilcoxon rank-sum test was used to determine this, and the critical value of U was found to be 19. Since our calculated U was greater than 19, we can reject the null hypothesis and conclude that there is a significant difference in the median delivery times.

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a. Probability of a standard normal variable being between 0 and 0.60 is 0.2257.

b. Probability of a standard normal variable being between -1.65 and 0 is 0.4505.

c. Probability of a standard normal variable being greater than 0.30 is 0.3821.

d. Probability of a standard normal variable being greater than or equal to -0.35 is 0.6368.

e. Probability of a standard normal variable being less than 2.03 is 0.9798.

f. Probability of a standard normal variable being less than or equal to -0.80 is 0.2119.

Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.

a. P(0 ≤ z ≤ 0.60) = 0.2257

Using a standard normal table or calculator, we can find that the probability of a standard normal variable being between 0 and 0.60 is 0.2257.

b. P(-1.65 ≤ z ≤ 0) = 0.4505

Using a standard normal table or calculator, we can find that the probability of a standard normal variable being between -1.65 and 0 is 0.4505.

c. P(z > 0.30) = 0.3821

Using a standard normal table or calculator, we can find that the probability of a standard normal variable being greater than 0.30 is 0.3821.

d. P(z ≥ -0.35) = 0.6368

Using a standard normal table or calculator, we can find that the probability of a standard normal variable being greater than or equal to -0.35 is 0.6368.

e. P(z < 2.03) = 0.9798

Using a standard normal table or calculator, we can find that the probability of a standard normal variable being less than 2.03 is 0.9798.

f. P(z ≤ -0.80) = 0.2119

Using a standard normal table or calculator, we can find that the probability of a standard normal variable being less than or equal to -0.80 is 0.2119.

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Answer:

the answer is symmetry.

The addition of the surds is determined as 11√19 + 38√71 + 51√13.

The surds can be added by simplifying each term as follows;

11√19 + 38√71 + 19√13 + 16√52

= 11√19 + 38√71 + 19√13 + 16(2√13)

= 11√19 + 38√71 + 19√13 + 32√13

So we will the similar terms as follows;

= 11√19 + 38√71 + (19√13 + 32√13)

= 11√19 + 38√71 + 51√13

Thus, the addition of the surds is determined by simplifying complex term to the lowest possible term.

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a) The Venn diagram is as follows:

b) After selecting at random a Foster junior for a survey, the probability this student has taken at least 2 out of 3 courses is 0.61

c) After selecting at random a Foster junior for a survey, the probability this student has taken exactly one of the three courses is 0.06.

d) After selecting at random a Foster junior for a survey, the probability this student has taken at the most one course is 0.14.

b) To find the probability that the student has taken at least 2 out of 3 courses, we add the probabilities of the following three events: taking both Finance and Accounting, taking both Finance and Marketing, and taking both Accounting and Marketing, plus the probability of taking all three courses:

Therefore, the probability that the student has taken at least 2 out of 3 courses is 0.61.

c) To find the probability that the student has taken exactly one of the three courses, we add the probabilities of the following three events: taking Finance only, taking Accounting only, and taking Marketing only:

Therefore, the probability that the student has taken exactly one of the three courses is 0.06.

d) To find the probability that the student has taken at most one course, we add the probabilities of the following two events: taking no courses and taking exactly one course:

Therefore, the probability that the student has taken at most one course is 0.14.

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Answer:

The answer is 3x-5y

Step-by-step explanation:

13x+2y-10x-7y

C.L.T.

13x-10x-7y+2y

3x-5y

Answer:

3x - 5y

Step-by-step explanation:

you 1st have to collect like terms which has the same variable

13x + 2y - 10x - 7y

(13x - 10x) + (2y - 7y)

3x - 5y .... is the simplified form of the equation.

The equivalent expression to the -49y - 14 are as follow,

7(-7y -2) , -7(7y + 2) ,-1(49y + 14), -14(3.5y + 1), -98/7 - 49y and -7(7y + k₁) + k₂ where -14 = -k₁ + k₂.

Expression is equal to

-49y - 14

The equivalent expressions are ,

By taking -1 as common factor

-(49y + 14)

By taking -7 as common factor

-7(7y + 2)

By taking 7 as common factor .

7(-7y -2)

By taking -14 as common factor

-14(3.5y + 1)

By replacing -14  as -98/7

-98/7 - 49y

By replacing -14 = -21 + 7

-7(7y + 3) + 7

By replacing -14 = -28 + 14

-7(7y + 4) + 14

By replacing -14 = -35 + 21

-7(7y + 5) + 21

By replacing -14 = -42 + 28

-7(7y + 6) + 4

and many more.

All of these expressions are equivalent to -49y -14.

Therefore, the expression which are equivalent to the given expression are 7(-7y -2) , -7(7y + 2) ,-1(49y + 14), -14(3.5y + 1), -98/7 - 49y and -7(7y + k₁) + k₂ where -14 = -k₁ + k₂.

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The value of angles in inscribed quadrilateral are μ(∠zyx) is 92⁰ and μ(∠yxw) is 65⁰.

An inscribed quadrilateral is a quadrilateral that can be inscribed in a circle, meaning that its vertices all lie on the circumference of a circle. In other words, the four vertices of an inscribed quadrilateral are concyclic.

The opposite angles of an inscribed quadrilateral are supplementary, which means that they add up to 180 degrees. This property is known as the "interior angle sum" of a quadrilateral.

μ(∠zyx) + μ(∠xwz) = 180⁰ (opposite angle of cyclic quadrilateral are supplementary)

μ(∠xwz) = 88⁰

μ(∠zyx) = 180⁰ - 88⁰ = 92⁰

μ(∠yzw) is an inscribed angle that intercepts the arc 112⁰ and 118⁰. Therefore,

μ(∠yzw)

= (112⁰ + 118⁰)/2

= 230⁰/2

= 115⁰

μ(∠yxw) + μ(∠yzw) = 180⁰  (opposite angle of cyclic quadrilateral are supplementary)

μ(∠yxw) = 180⁰ - 115⁰ = 65⁰

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The right response is "the average number of targeted keywords in a website is different than 5 keywords." The website developer asserts that the value of 5 in the article does not accurately reflect the genuine population mean of the number of keywords targeted in a website.

This claim may be one-tailed (if the website developer thinks the true mean is larger or less than 5) or two-tailed (if the website developer thinks the true mean is merely different from 5) in nature. The website developer feels the true mean is different from the value given in the article, without stating whether it is larger or less than 5. As a result, the claim is two-tailed in this instance.

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(a) Using a normal distribution and a 95% confidence interval, the true average failure strain for silicone implant augmentation rhinoplasty to correct congenital nose deformities is estimated to be between 23.83% and 28.17%. This estimate conveys that we are 95% confident that the true average strain falls within this range, and the precision and reliability of this estimate is supported by the sample size and standard deviation.

(b) Using a normal distribution and a 95% prediction interval, the strain for a single adult is predicted to fall between 17.72% and 34.28%. This prediction conveys that we are 95% confident that the true strain for a single adult falls within this range, and the precision and reliability of this prediction is supported by the sample size and standard deviation.

The prediction interval in part (b) is much wider than the confidence interval in part (a). This is because the confidence interval in part (a) is estimating the range of the true average failure strain for the entire population, whereas the prediction interval in part (b) is estimating the range of possible failure strains for a single individual. This individual variation results in a wider prediction interval.

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Joan should run 13 times around the park to complete her goal.

Given that, Joan wants to jog in a circular track which 1/4 mile in diameter.

We need to find the circumference of the track and the number of rounds she needs run to complete her goal.

So,

Circumference = π × diameter

= 3.14 × 1/4 = 0.785 miles

Let she runs x rounds to complete her goal,

So,

0.785x = 10

x = 12.73

x ≈ 13

Hence, Joan should run 13 times around the park to complete her goal.

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To investigate whether there is convincing evidence, at a 5 percent level of significance,

that a longer hand length is associated with a decrease in the time to complete the 100-meter freestyle, the researcher should use a two-sample t-test.

The independent variable is hand length, and the dependent variable is time to complete the 100-meter freestyle.

The t-test compares the mean time to complete the 100-meter freestyle for swimmers with longer hand lengths to the mean time for swimmers with shorter hand lengths.

The t-test is appropriate because the sample size is small, and the researcher is comparing two groups.

By conducting a two-sample t-test, the researcher can determine whether the observed difference in mean times is statistically significant or due to chance.

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The distance of the electricity pole from T is 53 km

Given that;

The ST is 54 kilometer long

(180 - 28) + (180 - 70) = 262 degree is the angle PST,

which is the product of the angles at S and T.

S has a 62 degree angle.

The law of sines can be written as:

sin(62)/SP = sin(262/ST)

To find SP, we can rearrange this equation as follows:

SP = sin(62)/sin(262)x(ST)

When we enter the values we are aware of, we obtain:

SP = sin(62)/sin(262)*54 km

We can evaluate this expression to determine that:

SP ≈ 53.5 km Consequently, 53.5 kilometer or so separate T from the electricity pole.

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The probability of P(x < 4) is 0.6922 or approximately 69.22%.

The exponential distribution is often used to model the time between events that occur randomly and independently at a constant rate over time. The probability density function of the exponential distribution with parameter λ is given by f(x) = λe^(-λx) for x ≥ 0.

In this case, X ~ Exp(0.75) means that the parameter λ is 0.75. To find P(x < 4), we need to calculate the area under the curve of the probability density function to the left of 4. This can be done by integrating the function from 0 to 4 as follows

P(x < 4) = ∫₀⁴ λe^(-λx) dx

= [-e^(-λx)]₀⁴

= -e^(-0.75 * 4) + 1

= 0.6922

Therefore, the probability that X is less than 4 is 0.6922 or approximately 69.22%.

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The answer is that the 70% confidence interval for the slope of the regression line using the provided data is between 0.0019 and 0.0037.


To calculate the 70% confidence interval for the slope of the regression line, we need to use the t-distribution with degrees of freedom equal to n - 2, where n is the number of data points. In this case, n = 116, so we have 114 degrees of freedom.

Using a statistical software or calculator, we can find that the t-value for a 70% confidence interval with 114 degrees of freedom is approximately 1.648.

Next, we need to calculate the standard error of the slope, which is given by:

SE =√[ (SS_residuals / (n - 2)) / SS_x ]

where SS_residuals is the sum of squared residuals, SS_x is the sum of squared deviations of x from its mean, and n is the sample size.

Using the regression model provided, we can find that SS_residuals = 6.3574 and SS_x = 1484.9584. Plugging these values into the formula, we get:

SE = √[ (6.3574 / (116 - 2)) / 1484.9584 ] = 0.00044

Finally, we can calculate the confidence interval for the slope using the formula:

slope +/- t * SE

where slope is the estimated slope from the regression model.

Plugging in the values, we get:

slope +/- 1.648 * 0.00044 = 0.0028 +/- 0.0007

Therefore, the 70% confidence interval for the slope of the regression line is between 0.0019 and 0.0037, rounded to 4 decimal places.

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