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Angelina_Jolie [31]
3 years ago
8

matt is standing on top of a cliff 305 feet above a lake. The measurement of the angle of depression to a boat on a lake is 42 d

egrees. how far is the boat from matt

Mathematics
1 answer:
Lyrx [107]3 years ago
3 0

Answer:

So, the distance from boat to matt is 455.81535feet

Step-by-step explanation:

We are given height of a cliff is 305 feet

and the measurement of the angle of depression to a boat on a lake is 42 degrees

so, we can draw diagram

Let's assume

distance from boat to matt is x

We can use trig

sin(42)=\frac{305}{x}

now, we can solve for x

x=\frac{305}{sin(42)}

x=455.81535feet

So, the distance from boat to matt is 455.81535feet

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Answer:

We conclude that this is an unusually high number of faulty modems.

Step-by-step explanation:

We are given that while conducting a test of modems being manufactured, it is found that 10 modems were faulty out of a random sample of 367 modems.

The probability of obtaining this many bad modems (or more), under the assumptions of typical manufacturing flaws would be 0.013.

Let p = <em><u>population proportion</u></em>.

So, Null Hypothesis, H_0 : p = 0.013      {means that this is an unusually 0.013 proportion of faulty modems}

Alternate Hypothesis, H_A : p > 0.013      {means that this is an unusually high number of faulty modems}

The test statistics that would be used here <u>One-sample z-test</u> for proportions;

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where, \hat p = sample proportion faulty modems= \frac{10}{367} = 0.027

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So, <u><em>the test statistics</em></u>  =  \frac{0.027-0.013}{\sqrt{\frac{0.013(1-0.013)}{367} } }

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The value of z-test statistics is 2.367.

Since, we are not given with the level of significance so we assume it to be 5%. <u>Now at 5% level of significance, the z table gives a critical value of 1.645 for the right-tailed test.</u>

Since our test statistics is more than the critical value of z as 2.367 > 1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which <u><em>we reject our null hypothesis</em></u>.

Therefore, we conclude that this is an unusually high number of faulty modems.

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valentina_108 [34]

Answer:

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Step-by-step explanation:

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b - a = 22

(Move variable a to the right side to get the following.)

b = 22 + a

(This way, we can substitute b = 22 + a into the first equation, a + b = 12, and solve.)

a + (22 + a) = 12

a + a + 22 = 12

2a = -10

a = -5

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Hey there!!

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Answer:

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