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3 years ago

????????????????????????

Mathematics

1 answer:

gavmur [86]3 years ago

3 0

Answer:

$P(Sum = 9) = \frac{1}{9}$

Step-by-step explanation:

Given

Outcomes of rolling two dice

Required

P(Sum = 9)

From the given outcomes, we have:

$n(S) = 36$ -- the sample size

$Sum = 9:=\{(3,6),(4,5),(5,4),(6,3)\}$

So.

$n(Sum = 9) = 4$

The probability is:

$P(Sum = 9) = \frac{n(Sum = 9)}{n(S)}$

$P(Sum = 9) = \frac{4}{36}$

Simplify

$P(Sum = 9) = \frac{1}{9}$

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Answer:

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Step-by-step explanation:

Data given and notation

$\bar X=3.8$ represent the sample mean

$s=0.5$ represent the sample standard deviation for the sample

$n=15$ sample size

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$\alpha$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

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We need to conduct a hypothesis in order to check if the mean weight is less than 4 ounces, the system of hypothesis would be:

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Alternative hypothesis: $\mu < 4$

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{3.8-4}{\frac{0.5}{\sqrt{15}}}=-1.549$

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Below!

Step-by-step explanation:

Using Pythagoras theorem, I will solve all of the problems.

<u>Question 9:</u>

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<u>Question 10:</u>

26² = 24² + x²
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<u>Question 11:</u>

15² = 12² + x²
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<u>Question 12:</u>

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<u>Question 13:</u>

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<u>Question 14</u>

First, let's solve for the variable x using Pythagoras theorem.

=> 5² = 3² + x²
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Now, let's solve for the variable y using Pythagoras theorem.

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Answers (Nearest tenth):

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