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maksim [4K]
3 years ago
5

Five times Carl's age plus three times Jill's age equals 110. Jill's age is also two times Carl's age. How old is Carla ?

Mathematics
1 answer:
aleksklad [387]3 years ago
6 0
X - Carl's age
y - Jill's age

5x+3y=110 \\
y=2x \ \ \ |\times (-3) \\ \\
5x+3y=110 \\
\underline{-3y=-6x} \\ 5x+3y-3y=110-6x \\ 5x=110-6x \\ 5x+6x=110 \\
11x=110 \\
x=10

Carl is 10 years old.
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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

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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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For this case we have the following equations:

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