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garri49 [273]
3 years ago
15

Dean Halverson recently read that full-time college students study 20 hours each week. She decides to do a study at her universi

ty to see if there is evidence that students study an average of more than 20 hours each week. A random sample of 35 students were asked to keep a diary of their activities over a period of several weeks. It was found that the average number of hours that the 35 students studied each week was 21.1 hours. The sample standard deviation of 4.3 hours.
Find the p-value.
The p-value should be rounded to 4-decimal places.
Mathematics
1 answer:
Ann [662]3 years ago
3 0

Answer:

0.0698

Step-by-step explanation:

Given :

Population mean, μ = 20

Sample mean, xbar = 21.1

Sample standard deviation, s = 4.3

Sample size, n = 35

The hypothesis :

H0 : μ = 20

H0 : μ > 20

The test statistic :

(xbar - μ) ÷ (s/√(n))

T = (21.1 - 20) ÷ (4.3/√(35))

T = 1.1 ÷ 0.7268326

Test statistic = 1.513

Using the Pvalue calculator :

df = n - 1 = 35 - 1 = 34

Pvalue(1.513, 34) = 0.06976

Pvalue = 0.0698 (4 decimal places)

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The ratio of SAMs age to hank is 5 to 3. If the sum of their age is 24. How old is is hank?
Serggg [28]
Lets consider SAM's age is 'x'  and Hank's age is 'y'
So as per given data Sam's age is 5/3 times of Hank's age
so x = 5/3 * y
3x = 5y --> equation 1
 and also sum of their ages is 24
so, x + y = 24
we need to find Hank's age (y)
so x = 24 - y
Now replace x value in equation 1
3(24-y) = 5y
72-3y = 5y
72 = 3y+5y
8y= 72
y= 72/8
y = 9 years.

So the Hank's age is 9 years

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3 0
3 years ago
Given sinx= −3/5 when 3π/2 < x < 2π, find tan x/2
GarryVolchara [31]

Answer:

B -⅓

Step-by-step explanation:

sinx = -3/5

Adjacent² = 5² - 3² = 16

Adjacent = 4

tan(x) = -3/4

-¾ = 2tan(½x)/[1 - tan²(½x)]

-3 + 3tan²(½x) = 8tan(½x)

3tan²(½x) - 8tan(½x) - 3 = 0

tan(½x) = 3, -⅓

5 0
3 years ago
Read 2 more answers
Please Help ! Will give brainliest!
sveta [45]

Answer:

D: I and IV only.

Step-by-step explanation:

We can go through each statement and examine its validity.

I) All congruent triangles are similar.

For congruent triangles, all of its corresponding sides and angles are congruent.

Since all angles are congruent, this fulfills the AA Similarity criterion. Thus, I is true.

II) All similar triangles are congruent.

Congruence guarantees similarity, but similarity does not guarantee congruence.

Two triangles need only two congruent angles to guarantee similarity, while two congruent angles does guarantee congruence. II is false.

III) All right triangles are similar.

Triangles are similar through the AA criterion. One angle of a right triangle must be 90, so this leaves 90 for the two remaining angles. Since these two angles can be anything that sum to 90, we are not guaranteed similarity. For example, 20 - 70 - 90 and 30 - 60 - 90 triangles. They are both right triangles, but are not similar. III is false.

IV) All isosceles right triangles are similar.

Again, since we have a right triangle, one angle is 90, which leaves two remaining angles that must sum to 90.

However, since it is isosceles, the two remaining angles must measure the same. Only one solution exists then: both angles must be 45.

Since all angles must be 45 - 45 - 90, it fulfills the AA Criterion. Thus, all isosceles right triangles are similar. IV is true.

The correct statements are I and IV.

3 0
3 years ago
I NEED ANSWER SUPER BAD PLEASE!!!!!!!!!!!What is the greatest integer less than 100 for which the greatest common divisor of tha
PtichkaEL [24]

Answer:

92

Step-by-step explanation:

We will list out the numbers which are factors of 12. They include:

1, 2, 3, 4, 6, 12.

We need to get the highest number that has its greatest factor to be 4. It means that 6 and 12 cannot divide it.

To do this, we will write out the multiples of 4. They include:

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We will have to choose the highest number which only 4  can divide and  6 and 12 cannot divide.

Since we are looking for the largest, We can try dividing all the numbers by 4, 6, and 12 starting from 96.

We will quickly see that 4 can divide 92 but 6 and 12 cannot.

This gives us 92 as the answer.

4 0
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your friends says that an exterior angle can never be complementary to any of the interior angles in a triangle?
rusak2 [61]
Exterior angles are complementary to the opposite interior angle 

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3 years ago
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