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Kryger [21]
3 years ago
6

A market research company wishes to know how many energy drinks adults drink each week. They want to construct a 80% confidence

interval for the mean and are assuming that the population standard deviation for the number of energy drinks consumed each week is 0.9. The study found that for a sample of 164 adults the mean number of energy drinks consumed per week is 7.9. Construct the desired confidence interval. Round your answers to one decimal place.
Mathematics
1 answer:
Diano4ka-milaya [45]3 years ago
7 0

Answer:

The confidence interval = (7.8 , 8.0)

Step-by-step explanation:

Confidence Interval formula =

Mean ± z × Standard deviation/√n

Mean = 7.9

Standard deviation = 0.9

n = number of samples = 164

z = z score of an 80% confidence interval = 1.282

Confidence Interval = 7.9 ± 1.282 × 0.9/√164

= 7.9 ± 0.0900966432

Confidence Interval

= 7.9 - 0.0900966432

= 7.8099033568

Approximately to 1 decimal place = 7.8

7.9 + 0.0900966432

= 7.9900966432

Approximately to 1 decimal place = 8.0

Therefore, the confidence interval = (7.8 , 8.0)

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Question 13
Mrac [35]

Answer:

71.6 degrees

Step-by-step explanation:

Given the vectors

u= <8,4> v = <9.-9> (5 points)

u*v = (8, 4)*(9, -9)

u*v = 8(9)+(4)(-9)

u*v = 72 - 36

u*v = 36

|u| = √8²+4²

|u| = √64+16

|u| = √80

|v| = √9²+9²

|v|  = √81+81

|v|  = √162

Using the formula

u*v = ||u||v| cos theta

36 = √80(√162)cos theta

36 = √12960 cos theta

cos theta = 36/√12960

cos theta = 36/113.8

cos theta = 0.3162

theta = arccos(0.3162)

theta = 71.56 degrees

Hence the angle between the given vectors to the nearest tenth of a

degree is 71.6 degrees

5 0
2 years ago
Which equation represents the same proportional relationship as the graph? On a coordinate plane, a line goes through points (0,
Misha Larkins [42]

Answer:

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Step-by-step explanation:

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6 0
3 years ago
Read 2 more answers
How Many Pumpkins Did Kate Sell This Weekend
gtnhenbr [62]

Answer:

60 pumpkins

Step-by-step explanation:

Saturday, she sold 6*7 pumpkins. That's 42 pumpkins.

Sunday, she sold 6*3 pumpkins. That's 18 pumpkins.

42+18=60

5 0
3 years ago
Simplify
melomori [17]

Answer: 4\sqrt{3}

Step-by-step explanation:

For this exercise it is important to remember the following:

i=\sqrt{-1} \\\\i^2=-1

Given the following expression:

-2i\sqrt{-12}

You can notice that the radicand (the number inside the square root) is negative. Therefore, in order to simplify the expression, you need to follow these steps:

1. Replace \sqrt{-1} with i and simplify:

(-2i)(i)\sqrt{12}=-2i^2\sqrt{12}=-2(-1)\sqrt{12}=2\sqrt{12}

2. Descompose 12 into its prime factors:

12=2*2*3=2^2*3

3. Substitute into the expression:

=2\sqrt{2^2*3}

4. Since \sqrt[n]{a^n}=a, you can simplify it:

=(2)(2)\sqrt{3}=4\sqrt{3}

4 0
3 years ago
Determine 2nd term and rth term of a.p.whose 6 th term is 12 and 8 th term is 22​
Vanyuwa [196]

Answer:

see explanation

Step-by-step explanation:

The n th term of an arithmetic progression is

a_{n} = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a_{6} = 12 and a_{8} = 22, then

a₁ + 5d = 12 → (1)

a₁ + 7d = 22 → (2)

Subtract (1) from (2) term by term to eliminate a₁

2d = 10 ( divide both sides by 2 )

d = 5

Substitute d = 5 into (1) to find a₁

a₁ + 5(5) = 12

a₁ + 25 = 12 ( subtract 25 from both sides )

a₁ = - 13

Thus

a_{2} = - 13 + 5 = - 8

a_{n} = - 13 + 5(n - 1) = - 13 + 5n - 5 = 5n - 18 ← n th term

8 0
3 years ago
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