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yan [13]
3 years ago
5

Paige has 3 coats: a pink one, a red one, and a white one. She has a black scarf, a gray scarf and 1 set of white gloves. Determ

ine the different combinations Paige has for staying warm if she always wears a coat, a scarf, and gloves. For your answer, list the total number of possibilities and all possible combinations she has.

Mathematics
2 answers:
IRISSAK [1]3 years ago
5 0

Hi there, again! Hopefully this helps, again!

------------------------------------------------------------------------------------------------------------

<em>Since she has </em><u><em>3 coats</em></u><em>, </em><u><em>2 scarfs</em></u><em>, and 1</em><u><em> glove</em></u><em>:</em>

<em />

<em />

<em>She has </em><u><em>6 ways</em></u><em> to </em><u><em>choose a coat, a scarf, and a glove(s)</em></u><em>.</em>

<em />

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

My <u>6 combinations:</u>

<em />

<em><u>1.) </u></em><em><u>Red coat</u></em><em>, </em><em><u>black scarf</u></em><em>, </em><em><u>white glove</u></em><em>(s).</em>

<em />

<em />

<em><u>2.) </u></em><em><u>White coat</u></em><em>, </em><em><u>grey scarf</u></em><em>, </em><em><u>white glove</u></em><em>(s).</em>

<em />

<em />

<em><u>3.)</u></em><em> </em><em><u>Pink coat</u></em><em>, </em><em><u>black scarf</u></em><em>, </em><em><u>white glove</u></em><em>(s).</em>

<em />

<em />

<em><u>4.)</u></em><em> </em><em><u>Red coat</u></em><em>, </em><em><u>grey scarf</u></em><em>, white glove(s).</em>

<em />

<em />

<em><u>5.)</u></em><em><u> White coat</u></em><em>,</em><em><u> black scarf,</u></em><em> </em><em><u>white glove</u></em><em>(s).</em>

<em />

<em />

<em><u>6.)</u></em><em> </em><em><u>Pink coat</u></em><em>, </em><em><u>grey scarf</u></em><em>, </em><em><u>white glove</u></em><em>(s).</em>

andreev551 [17]3 years ago
4 0
Answer:
Paige has 6 possible combinations.

Working out:
In photo.

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Answer:

Step-by-step explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ = 7463

For the alternative hypothesis,

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This is a 2 tailed test

Since the population standard deviation is given, z score would be determined from the normal distribution table. The formula is

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From the information given,

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x = 7163 hours

σ = 1080 hours

n = 81

b) z = (7163 - 7463)/(1080/√81) = - 2.5

Looking at the normal distribution table, the probability corresponding to the z score is 0.02

Recall, population mean is 7463

The difference between sample sample mean and population mean is 7463 - 7163 = 300

Since the curve is symmetrical and it is a two tailed test, the x value for the left tail is 7463 - 300 = 7163

the x value for the right tail is 7463 + 300 = 7763

These means are higher and lower than the null mean. Thus, they are evidence in favour of the alternative hypothesis. We will look at the area in both tails. Since it is showing in one tail only, we would double the area. We already got the area below z as 0.02

We would double this area to include the area in the right tail of z = 2.5. Thus

p = 0.02 × 2 = 0.04

It means that in a sample of size 81 light bulbs, we would observe a sample mean of 300 hours or more away from 7463 about 4% of the time by chance alone.

c) Confidence interval is written in the form,

(Sample mean - margin of error, sample mean + margin of error)

The sample mean, x is the point estimate for the population mean.

Margin of error = z × σ/√n

To determine the z score, we subtract the confidence level from 100% to get α

α = 1 - 0.95 = 0.05

α/2 = 0.05/2 = 0.025

This is the area in each tail. Since we want the area in the middle, it becomes

1 - 0.025 = 0.975

The z score corresponding to the area on the z table is 1.96. Thus, z score for 95% confidence level is 1.96

Margin of error = 1.96 × 1080/√81

= 235.2

Confidence interval = 7163 ± 23.2

a) Since alpha, 0.05 > than the p value, 0.04, then we would reject the null hypothesis. Therefore, at a 5% level of significance, there is evidence that the mean life is different from 7463 hours

Comparing the results of a and c, it is true that the population mean life is not 7463 hours.

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