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3 years ago

An acute angle θ is in a right triangle with sin θ = one half. What is the value of cot θ?

Mathematics

1 answer:

MrMuchimi3 years ago

7 0

Answer:

√3

Step-by-step explanation:

cot²(θ) = csc²(θ) -1 . . . . . a relevant identity

= 1/sin²(θ) -1

= (1/(1/2))² -1 = 2² -1 = 3

Then ...

cot(θ) = √3 . . . . . . . . take the square root

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A rectangular cake pan has a volume of

enot [183]

Step-by-step explanation:

volume of a rectangular pan = length of the pan × width of the pan × height of the pan

V=l.b.h

234=9.13.h

h=234/9×13

h= 2in.

hope this helps you.

7 0

3 years ago

Read 2 more answers

Stevens school is selling chocolate bars to earn money for new band instrument The school will receive 33% of total sales; given

LiRa [457]

Given that the amount Steven will collect is given by the model y=0.33x, where x is represents the total number of sales:
The x-intercept will represent the minimum amount of sales that Steven will be able to make initially.

4 0

3 years ago

According to the U.S. Census Bureau, 11% of children in the United States lived with at least one grandparent in 2009 (USA TODAY

Yakvenalex [24]

Answer:

The decision rule is

Fail to reject the null hypothesis

The conclusion is

There is no sufficient evidence to show that the proportion of all children in the United States who currently live with at least one grandparent is higher than 11%

Step-by-step explanation:

From the question we are told that

The population proportion is $p = 0.11$

The sample size is n = 1640

The number found to be living with at least one grandparent is $k = 225$

The level of significance is $\alpha = 0.02$

The null hypothesis is $H_o : p = 0.11$

The alternative hypothesis is $H_a : p > 0.11$

Generally the sample proportion is mathematically represented as

$\^ p = \frac{ k }{n}$

=> $\^ p = \frac{ 225 }{1640 }$

=> $\^ p = 0.1372$

Generally the test statistics is mathematically represented as

$z= \frac{\^ p - p }{ \sqrt{\frac{p(1- p)}{n} } }$

=> $z = \frac{ 0.1372 - 0.11 }{ \sqrt{\frac{0.11(1- 0.11)}{1640} } }$

=> $z = 0.0077$

From the z table the area under the normal curve to the left corresponding to 0.0077 is

$p-value = P(Z > 0.0077) = 0.4969$

From the value obtained we see that $p-value > \alpha$ hence

The decision rule is

Reject the null hypothesis

The conclusion is

There is no sufficient evidence to show that the proportion of all children in the United States who currently live with at least one grandparent is higher than 11%

3 0

3 years ago

A number greater than -5 as an inequality

charle [14.2K]

Answer:

n > -5

Step-by-step explanation:

8 0

3 years ago

Amy and Margaret has stopped at the bottom of one of the highest waterfalls in Cascade State Park as any looked up at the waterf

melisa1 [442]

1. You have to make a system of equations.

2. The problem gives the following information:

- <span>. Emi said wow I think the top of that waterfall is about 20 ft more than three times the height of a young Redwood.

- Margaret had a different opinion she said no I think it's about 50 ft less than 4 times the height of the Redwood.

3. So, you have:

y: the height of the waterfall.
x: </span>the height of the Redwood

4. The equations are:

y=3x+20 (i)
y=4x-50 (ii)

3x+20=4x-50
x=70 ft

y=3x+20
y=230 ft

H<span>ow tall is the Redwood and how high is the waterfall?
</span>
The Redwood: 70 ft
The waterfall: 230 ft

5 0

3 years ago