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2 years ago

Drag each equation to show if it could be a correct first step to solving the equation 8(x + 5) = 56.

Mathematics

2 answers:

lana66690 [7]2 years ago

5 0

8(x + 5) = 56

first step id to distribute the 8 through the parenthesis

8x + 40 = 56

Varvara68 [4.7K]2 years ago

4 0

Answer:

Distribute 8 to all terms within the parenthesis

Step-by-step explanation:

Remember to follow PEMDAS. The steps are:

1) Distribute 8 to all terms within the parenthesis

8(x + 5) = 8(x) + 8(5) = 8x + 40

2) Isolate the x. Do the opposite of PEMDAS

8x + 40 = 56

2.5) Note the equal sign. What you do to one side, you do to the other

8x + 40 (-40) = 56 (-40)

8x = 56 - 40

8x = 16

(8x)/2 = (16)/2

x = 16/2

x = 8

8 is your answer

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Suppose a random sample of 100 observations from a binomial population gives a value of pˆ = .63 and you wish to test the null h

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We conclude that the population proportion is equal to 0.70.

Step-by-step explanation:

We are given that a random sample of 100 observations from a binomial population gives a value of pˆ = 0.63 and you wish to test the null hypothesis that the population parameter p is equal to 0.70 against the alternative hypothesis that p is less than 0.70.

Let p = population proportion.

(1) The intuition tells us that the population parameter p may be less than 0.70 as the sample proportion comes out to be less than 0.70 and also the sample is large enough.

(2) So, Null Hypothesis, $H_0$ : p = 0.70 {means that the population proportion is equal to 0.70}

Alternate Hypothesis, $H_A$ : p < 0.70 {means that the population proportion is less than 0.70}

The test statistics that would be used here One-sample z-test for proportions;

T.S. = $\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }$ ~ N(0,1)

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The value of z-test statistics is -1.528.

Now at 0.05 level of significance, the z table gives a critical value of -1.645 for the left-tailed test.

Since our test statistics is more than the critical value of z as -1.528 > -1.645, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that the population proportion is equal to 0.70.

(c) The observed level of significance in part B is 0.05 on the basis of which we find our critical value of z.

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3 years ago