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3 years ago

What will be the length of third side of a right angled triangle whose hypotenuse is 13cm and

Mathematics

2 answers:

Anna71 [15]3 years ago

5 0

Answer:

Step-by-step explanation:

Pythagorean theorem:

a^2 + b ^2 = c ^2

side^2 + side^2 = hypotenuse^2

5^2 + x^2 = 13^2

25 + x ^2 = 169

subtract 25

x^2 = 144

√ each side

x= √144 = 12

ch4aika [34]3 years ago

4 0

Answer:

12 cm

Step-by-step explanation:

let call hypotenuse a

and the other 2 sides are b, c respectively

have a = 13 cm and b = 5 cm

Follow Pythagorean theorem for Right triangle

$a^{2} = b^{2} +c^{2} \\c^{2} = a^{2} - b^{2}$

$c^{2} = 13^{2} -5^{2} \\c^{2} = 144\\c = 12$

The length of third side is 12 cm

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What eqauls to 31.25

RSB [31]

125 = 5^3 = 25 * 5

$4 \cdot \sqrt{125} = 4 \sqrt{25 \cdot 5} = 4 \cdot 5 \sqrt{5} = 20\sqrt{5}$

The simplification you are trying to do involves finding the prime factorization of a number. Since 125 is not divisible by 2, move on to 3. 125 is also not divisible by 3, so move on to 5. Then 125/5 = 25, and 25/5 = 5, so 125 = 5^3. The prime factorization of 125 is 5^3.

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Answer:

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Step-by-step explanation:

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1 year ago

2. The National Safety Council routinely analyzes the benefit of seat belt use on driver safety. Their data showed that among 28

JulijaS [17]

Answer:

We conclude that there is difference in the proportion of deaths between the 2 groups.

Step-by-step explanation:

We are given that among 2823 drivers not wearing seat belts, 31 died as a result of injuries, and among 7765 drivers wearing seat belts 16 were killed.

Let $p_1$ = proportion of deaths when drivers were not wearing seat belts.

$p_2$ = proportion of deaths when drivers were wearing seat belts.

So, Null Hypothesis, $H_0$ : $p_1=p_2$ {means that there is no difference in the proportion of deaths between the 2 groups}

Alternate Hypothesis, $H_A$ : $p_1\neq p_2$ {means that there is difference in the proportion of deaths between the 2 groups}

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

T.S. = $\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }$ ~ N(0,1)

where, $\hat p_1$ = sample proportion of deaths when drivers were not wearing seat belts = $\frac{31}{2823}$ = 0.011

$\hat p_2$ = sample proportion of deaths when drivers were wearing seat belts = $\frac{16}{7765}$ = 0.002

$n_1$ = sample of drivers not wearing seat belts = 2823

$n_2$ = sample of drivers wearing seat belts = 7765

So, the test statistics = $\frac{(0.011-0.002)-(0)}{\sqrt{\frac{0.011(1-0.011)}{2823}+\frac{0.002(1-0.002)}{7765} } }$

= 4.438

The value of z test statistics is 4.438.

Now, at 5% significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test.

Since our test statistic doesn't lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that there is difference in the proportion of deaths between the 2 groups.

Also, Margin of error (E) = $1.96 \times \sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} }$