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2 years ago

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A dolphin is trying to jump through a hoop that is fixed at height of 3.5m above the surface of her pool. the dolphin leaves the

water at an angle of inclination of 40 degrees. determine the minimum speed the dolphin will need when leaving the water in order to reach the height of the hoop.

1 answer:

frosja888 [35]2 years ago

4 0

40 degrees might be use the question box

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When you have ratios and some unknowns you can create complex fractions from them.Bring them to the same denominator and solve for X.

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Answer:

We conclude that the sample is from a population of songs with a mean greater than 210 seconds.

Step-by-step explanation:

We are given that a simple random sample of 40 current hit songs results in a mean length of 252.5 seconds.

Assume that the standard deviation of song lengths is 54.5 sec.

Let $\mu$ = <u><em>population mean length of the songs</em></u>

So, Null Hypothesis, $H_0$ : $\mu$ $\leq$ 210 seconds {means that the sample is from a population of songs with a mean smaller than or equal to 210 seconds}

Alternate Hypothesis, $H_A$ : $\mu$ > 210 seconds {means that the sample is from a population of songs with a mean greater than 210 seconds}

The test statistics that will be used here is <u>One-sample z-test statistics </u>because we know about population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample mean length of songs = 252.5 seconds

$\sigma$ = population standard deviation = 54.5 seconds

n = sample of current hit songs = 40

So, <u><em>the test statistics</em></u> = $\frac{252.5-210}{\frac{54.5}{\sqrt{40} } }$

= 4.932

The value of z-test statistics is 4.932.

Now, at 0.05 level of significance, the z table gives a critical value of 1.645 for the right-tailed test.

Since the value of our test statistics is more than the critical value of z as 4.932 > 1.645, so <u><em>we have sufficient evidence to reject our null hypothesis</em></u> as it will fall in the rejection region.

Therefore, we conclude that the sample is from a population of songs with a mean greater than 210 seconds.

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Answer:

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Step-by-step explanation:

Given central angle PQR = 45°

Total angle in a circle = 360°

Ratio of the measure of central angle PQR to the measure of the entire circle is $\frac{45}{360} = \frac{1}{8}$ . This shows ratio that <u>the measure of central angle PQR to the measure of the entire circle is one-eighth</u>.

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<u>The ratio of the shaded sector is 4.5πunits² not 4units²</u>

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It is given that $\angle a=135^{\circ}$ .

Now, know that in 180 degrees there are $\pi$ radians. This can be written as:

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Make is a proportion
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