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4 years ago

Walter takes 7/10 of an hour to mow 2/5 of an acre of lawn. At this rate, how many acres will he mow in an hour?

1 answer:

7 0

$\bf \begin{array}{ccll}
hours&\stackrel{lawn}{acre}\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
\frac{7}{10}&\frac{2}{5}\\\\
1&a
\end{array}\implies \cfrac{\frac{7}{10}}{1}=\cfrac{\frac{2}{5}}{a}\implies \cfrac{\frac{7}{10}}{\frac{1}{1}}=\cfrac{\frac{2}{5}}{\frac{a}{1}}\implies \cfrac{7}{10}\cdot \cfrac{1}{1}=\cfrac{2}{5}\cdot \cfrac{1}{a}
\\\\\\
\cfrac{7}{10}=\cfrac{2}{5a}\implies 35a=20\implies a=\cfrac{20}{35}\implies a=\cfrac{4}{7}$

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If r=10 and s=31 find R. Round to the nearest tenth

Vsevolod [243]

Answer: option c.

Step-by-step explanation:

You need to remember the identity:

$tan\alpha=\frac{opposite}{adjacent}$

The inverse of the tangent function is arctangent. You need to use this to calculate the angle "R":

$\alpha =arctan(\frac{opposite}{adjacent})$

You know that you need to find the measure of "R" and $r=10$ (which is the opposite side) and $s=31$ (which is the adjacent side), you can sustitute values into $\alpha =arctan(\frac{opposite}{adjacent})$

Then, you get:

$R=arctan(\frac{10}{31})\\\\R=17.9\°$

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4 years ago

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3 years 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) = $1.96 \times \sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} }$

= $1.96 \times \sqrt{\frac{0.011(1-0.011)}{2823}+\frac{0.002(1-0.002)}{7765} }$

= 0.00397

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3 years ago

angelique says that finding the absolute value of a number is the same as finding the opposite of the number. For example |-5|=5

olga2289 [7]

So, Angelique took away a a number from the two numbers and did not replace it with the correct number. So, this should be 1-51=50. Hope I helped! :)

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3 years ago