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4 years ago

Fraction - Multiplication : (a) 2/9 x 1/13 (b) 12/5 x 35/21

Mathematics

2 answers:

anastassius [24]4 years ago

7 0

Answer:

$(a) \frac{2}{117}$

$(b)4$

Step-by-step explanation:

$(a) \frac{2}{9} \times \frac{1}{13} \\ = \frac{2}{117}$

$(b) \frac{12}{5} \times \frac{35}{21} \\ = \frac{84}{21} \\ = \frac{28}{7} \\ = 4$

hope this helps

brainliest appreciated

good luck! have a nice day!

Elena L [17]4 years ago

5 0

$answer \\ a. \frac{2}{117} \\ b. 4 \\ solution \\ a. \: \frac{2}{9} \times \frac{1}{13} \\ = \frac{2 \times 1}{9 \times 13} \\ = \frac{2}{117} \\ b. \: \frac{12}{5} \times \frac{35}{21} \\ = divide \: 35 \: by \: 5 \: it \: becomes \\ = 12 \times \frac{7}{21} \\ divide \: 21 \: by \: 7 \: it \: becomes \\ = 12 \times \frac{1}{3} \\ divide \: 12 \: by \: 3 \: it \: becomes \\ = 4 \times 1 \\ = 4 \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment$

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Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that automobile insurance in Pennsylvania is significantly cheaper than the national average.

Then, the null and alternative hypothesis are:

$H_0: \mu=1503\\\\H_a:\mu< 1503$

The significance level is 0.05.

The sample has a size n=25.

The sample mean is M=1425.

A point estimate of the difference between the mean annual premium in Pennsylvania and the national mean can be calculated with the sample mean:

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As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=160.

The estimated standard error of the mean is computed using the formula:

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Then, we can calculate the t-statistic as:

$t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{1425-1503}{32}=\dfrac{-78}{32}=-2.438$

The degrees of freedom for this sample size are:

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This test is a left-tailed test, with 24 degrees of freedom and t=-2.438, so the P-value for this test is calculated as (using a t-table):

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As the P-value (0.0113) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

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