Use a t-distribution to answer this question. Assume the samples are random samples from distributions that are reasonably normally distributed, and that a t-statistic will be used for inference about the difference in sample means. State the degrees of freedom used. Find the endpoints of the t-distribution with 5% beyond them in each tail if the samples have sizes ni = 8 %3D and 11 n2 Enter the exact number for the degrees of freedom and round your answer for the endpoints to two decimal places. degrees of freedom = endpoints

Answer:54.9

Step-by-step explanation:

Answer:

[tex]\rm\implies y = 4x + 3 [/tex]

Step-by-step explanation:

Given :-

And we need to find the equation of the line. On looking at the graph we see that , it cuts y axis at (0,3) .So the y Intercept of the equation is 3 .

Slope Intercept Form :-

[tex]\rm\implies y = mx + c[/tex]

Substituting the respective values :-

[tex]\rm\implies y = 4*x + 3 \\\\\rm\implies y = 4x + 3 [/tex]

Hence the equation of line is y = 4x + 3

Answer:

B. Combination; number of ways = 15

Step-by-step explanation:

Since order doesn't matter, this is a combination:

6 choose 2 = 6 nCr 2 = 6!/(6-2)!2! = 720/(24)(2) = 720/48 = 15

Therefore, there are 15 possible ways to choose 2 co-captains out of 6.

Combination; the number of ways = 15.

Option B is the correct answer.

It is an arrangement of a set of numbers from a total set where the order of the set is not relevant.

We have,

The problem involves selecting two seniors out of a group of six seniors, which is a combination problem.

The number of ways to choose two seniors out of six seniors is given by the formula:

C(6,2) = 6! / (2! * 4!) = 15

Therefore,

Combination; the number of ways = 15.

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Answer:

The answer is A. The product is greater than 12

Answer:

(B) The cost to rent a bike

Answer: the cost to rent a bike

Step-by-step explanation:

Answer:

According to the histogram, the data points from 15-29 would be 12.

Step-by-step explanation:

No explanation needed.

Answer:

12

Step-by-step explanation:

Add the number of data points that are greater or equal to 15 (4+2+6) = 12.

Answer:

a) 0.4772 = 47.72% probability that the average is between 1,142 and 1,150.

b) 0.0228 = 2.28% probability that the average is greater than 1,158.

c) 0 = 0% probability that the average is less than 950.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

A certain type of automobile battery is known to last an average of 1,150 days with a standard deviation of 40 days.

This means that [tex]\mu = 1150, \sigma = 40[/tex]

Sample of 100:

This means that [tex]n = 100, s = \frac{40}{\sqrt{100}} = 4[/tex]

(a) The average is between 1,142 and 1,150.

This is the pvalue of Z when X = 1150 subtracted by the pvalue of Z when X = 1142. So

X = 1150

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

By the Central Limit Theorem

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

[tex]Z = \frac{1150 - 1150}{4}[/tex]

[tex]Z = 0[/tex]

[tex]Z = 0[/tex] has a pvalue of 0.5

X = 1142

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

[tex]Z = \frac{1142 - 1150}{4}[/tex]

[tex]Z = -2[/tex]

[tex]Z = -2[/tex] has a pvalue of 0.0228

0.5 - 0.0228 = 0.4772

0.4772 = 47.72% probability that the average is between 1,142 and 1,150.

(b) The average is greater than 1,158.

This is 1 subtracted by the pvalue of Z when X = 1158. So

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

[tex]Z = \frac{1158 - 1150}{4}[/tex]

[tex]Z = 2[/tex]

[tex]Z = 2[/tex] has a pvalue of 0.9772

1 - 0.9772 = 0.0228

0.0228 = 2.28% probability that the average is greater than 1,158.

(c) The average is less than 950.

This is the pvalue of Z when X = 950. So

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

[tex]Z = \frac{950 - 1150}{4}[/tex]

[tex]Z = -50[/tex]

[tex]Z = -50[/tex] has a pvalue of 0

0 = 0% probability that the average is less than 950.

Answer:

Step-by-step explanation:

The original angle of 30° is in a linear pair on a straight angle with ∠1. So since straight angles equal 180 subtract 30 from 180 to find m∠1, which is 150°.

The original angle of 30° is a vertical angle with ∠3, the same goes for ∠1 and ∠2. So those angles will be congruent. ∠1 = 30° and ∠2 = 150°

Lastly use corresponding angles to find out the values of ∠4, ∠5, ∠6, ∠7.

∠4 is corresponding to 30° so ∠4 is 30°

∠5 is corresponding to ∠1 so ∠5 is 150°

∠6 is corresponding to ∠2 so ∠6 is 150°

∠7 is corresponding to ∠3 so ∠7 is 30°

Hope this helps :)

Answer:

The original angle of 30° is in a linear pair on a straight angle with ∠1. So since straight angles equal 180 subtract 30 from 180 to find m∠1, which is 150°.

The original angle of 30° is a vertical angle with ∠3, the same goes for ∠1 and ∠2. So those angles will be congruent. ∠1 = 30° and ∠2 = 150°

Lastly use corresponding angles to find out the values of ∠4, ∠5, ∠6, ∠7.

∠4 is corresponding to 30° so ∠4 is 30°

∠5 is corresponding to ∠1 so ∠5 is 150°

∠6 is corresponding to ∠2 so ∠6 is 150°

∠7 is corresponding to ∠3 so ∠7 is 30°

Hope this helps :)

Step-by-step explanation:

Answer:

142.5 cm2

Step-by-step explanation:

The small markings create a new height, so that would be 9.5 cm.

Multiply:

9.5x15=142.5

Therefore, the area is 142.5 cm2

Answer:

1/3[tex]\pi r[/tex]²[tex]h[/tex]

Step-by-step explanation:

Answer:

i believe the answer is 03.028.68

Step-by-step explanation:

hope this helps

Answer:

105°

Step-by-step explanation:

The sum of all the interior angles of a triangle is equal to 180°. With that I. mind, we can write

(6x + 5) + (11x - 5) + x = 180

Collecting all similar terms, we get

18x = 180 or x = 10

They, the measure of angle Q is

Angle Q = 11x - 5 = 11(10) - 5

= 105°

Answer:

False

Step-by-step explanation:

Answer:

B. 240 sq. ft

Step-by-step explanation:

I calculated it logically

Answer:

is the answer 200/3 Or 66.667 ft

Answer:

The first and last set

y = (-1/2) + 10

Step-by-step explanation:

Two points form a line

The first and last set have a slope of -1/2

and b intercept of 10

х|у

4|8

6|7

y = (-1/2) + 10

and

x|y

2|9

8|6

y = (-1/2) + 10

The requried, tables that represent the same function are tables 1 and 3.

In mathematics, a function is a relationship between two sets of numbers, known as the domain and range, in which each element in the domain is associated with exactly one element in the range.

Here,
The tables that represent the same function are:

x|y

4|8

6|7

x|y

2|8

8|5

For two tables to represent the same function, they must have the same output for the same input. In the first table, input 4 gives output 8 and input 6 gives output 7. In the second table, input 2 gives output 8 and input 8 gives output 5. Therefore, these two tables represent the same function.

The other tables do not represent the same function, as they have different outputs for the same input values.

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Answer:

I think the answer it b and a

Answer:

si

Step-by-step explanation:

si

Answer:

the equation will be

Step-by-step explanation:

2x+y+5=0

Answer:

2x + y + 5 = 0

Step-by-step explanation:

The equation of line is x-2y = 14 and we need to find the equⁿ of line which passes through (-1,-3) and is perpendicular to given line.

=> x - 2y = 14

=> 2y = x - 14

=> y = x-14/2

=> y = x/2 - 7

=> Slope (m) = 1/2 .

Now the slope of line perpendicular to it , will have a slope ,

=>[tex] m_{perp}[/tex] = -1/m

=>[tex] m_{perp}[/tex] = -1/½

=> [tex] m_{perp}[/tex] = -2

=> m = (y - y₁) / ( x - x₁)

=> -2 = { y - (-3) } / { x - (-1) }

=> -2 = y + 3/x + 1

=> -2(x + 1) = y + 3

=> -2x -2 = y + 3

=> y + 2x +3+2 = 0

=> 2x + y + 5 = 0

9514 1404 393

Answer:

  A)  54.4

Step-by-step explanation:

The perimeter of a circumscribing quadrilateral is twice the sum of the lengths of opposite sides.

  P = 2(17.6 +(2.9 +6.7)) = 2(27.2)

  P = 54.4

Answer:

perimeter of each polygon

Answer:

B. x = 0.14

Step-by-step explanation:

Inx = -2

x = e^(-2)

x = 0.135

x = 0.14 (to two d.p)

The solution of the equation ln x =-2 is 0.14

The correct option is (D)

Logarithms are the inverse of exponents.

Given that:

ln x =-2

Shifting the log on the right side, it will become exponential

x = [tex]e^{-2}[/tex]

x = 0.135

x = 0.14 (two decimal places)

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Answer:

h = 4cm

b = 9cm

Step-by-step explanation:

Answer:

No, the 6 servings of soup is 1675 milliliters, which is greater than 1.5 liters.

Step-by-step explanation:

So we already know that 1 surving of soup is 275 milliliters.

We have 6 survings of this soup.

We need to see if these 6 servings will fit in a 1.5 liter jar.

To find the total amount of mililers, we must multipy this by 6:

275*6

=

1650

Remember that 1 liter is equal to 1000 mililiters. To find the 1650 mililliters in liters, we must divide by 1000:

1650/1000

=

1.65

This number is greater than 1.5 liters, which is how much soup the jar can store.

So the answer is no, the 6 servings of soup cannot fit in the jar.

Answer:

12 inches

Step-by-step explanation:

Find the square root

144² ÷ 2 = 12

Therefore, the length of one of the sides of the board with an area of 144 sq. in is 12 inches.

Answer:

D) y=-5/2x; y=-20

Step-by-step explanation:

If y varies directly with x, then y=kx where k is our proportionality constant

Therefore, since y=-5 when x=2, we have -5=k(2) where k=-5/2

This means that when x=8, y=(-5/2)(8)=-20, making choice D correct

Step-by-step explanation:

8(m + 2)= 16

8m + 16 = 16

8m = 0

m = 0

Step-by-step explanation:

the base is 5unit and the height is 9unit

Answer:

The base is 5 units the height is 9 units

Step-by-step explanation:

Just count the blocks in the diagram

base  = 5

Height = 9

Answer:

Step-by-step explanation:

-7m-8=m-4