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rjkz [21]
2 years ago
14

Able is carving a rectangular pyramid clock out of green quartz. The length of the rectangle base is 14 cm and the height of the

clock is 9cm. If the clock needs to have a volume of 168cm3 what is the width of the base
Mathematics
1 answer:
andrezito [222]2 years ago
7 0

Answer:

14cm

Step-by-step explanation:

Volume of the pyramid = Base area × height/3

V = BH/3

Base area = 14×width

Height= 9cm

Volume = 168cm³

Substitute into the formula

168 = 4w×9/3

36w = 168×3

36w = 504

w = 14cm

Hence the width of the pyramid is 14cm

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Step-by-step explanation:

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A researcher claims that the mean cost of raising a child from birth to age 2 by husband­wife families in the U.S. is $13,960. A
irina1246 [14]

Answer:

Yes, there enough evidence to reject the claim.

Step-by-step explanation:

Here we need to perform a test for single mean to determine whether the  mean cost of raising a child from birth to age 2 by husband-wife families in the U.S. is $13,960.

The hypothesis is:

<em>H₀</em>: The  mean cost of raising a child from birth to age 2 by husband-wife families in the U.S. is $13,960, i.e. µ = $13,960.

<em>Hₐ</em>: The  mean cost of raising a child from birth to age 2 by husband-wife families in the U.S. is different from $13,960, i.e. µ ≠ $13,960.

The information provided is:

\ar x=13725\\\sigma=2345\\n=500\\\alpha =0.10

The test statistic is:

z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}=\frac{13725-13960}{2345/\sqrt{500}}=-2.24

The test statistic value is -2.24.

Compute the <em>p</em>-value for this test statistic value at 10% level of significance as follows:

p-value=2\times P(Z

               =2\times 0.01255\\=0.0251

Use the <em>z</em>-table.

The calculated <em>p</em>-value is, 0.0251 < 0.10, therefore the null hypothesis will be rejected.

<u>Conclusion</u>:

As the null hypothesis is rejected at 10% level of significance it can be concluded that there enough evidence to reject the claim.

The  mean cost of raising a child from birth to age 2 by husband-wife families in the U.S. is different from $13,960.

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Step-by-step explanation:

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Philip ran out of time while taking a multiple-choice test and plans to guess on the last 4 questions. Each question has 5 possi
belka [17]

Answer:

There is a 40.96% probability that he answers exactly 1 question correctly in the last 4 questions.

Step-by-step explanation:

For each question, there are only two possible outcomes. Either it is correct, or it is not. This means that we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which  is the number of different combinatios of x objects from a set of n elements, given by the following formula.

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In this problem we have that:

There are four questions, so n = 4.

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This is

There is a 40.96% probability that he answers exactly 1 question correctly in the last 4 questions.

My guess...

⊕⊕⊕

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