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gregori [183]
3 years ago
6

If cscθ = 1 1/4, cosθ = a. 3/4 b. 1 2/3 c. 3/5 d. 4/5

Mathematics
1 answer:
madam [21]3 years ago
4 0

Answer:

we have

cscθ =1 \frac{1}{4}

\frac{h}{p}=\frac{5}{4}

h=5

p=4

b=\sqrt{11 {}^{2}  - 4 {}^{2} }

b=3

now

cosθ=\frac{b}{h}=\frac{3}{5}

<u>c. 3/5</u>

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The Patels took out a 15-year mortgage. How many monthly payments will they have to make on this mortgage?
VikaD [51]
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3 years ago
Use a sample n=1400 , p=0.20 and a 99% confidence level to construct a confidence interval estimate of the population proportion
saul85 [17]

Answer:

0.2 - 2.58\sqrt{\frac{0.2(1-0.2)}{1400}}=0.172

0.2 + 2.58\sqrt{\frac{0.2(1-0.2)}{1400}}=0.228

The 99% confidence interval would be given by (0.172;0.228)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

The population proportion have the following distribution

p \sim N(p,\sqrt{\frac{p(1-p)}{n}})

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by \alpha=1-0.99=0.01 and \alpha/2 =0.005. And the critical value would be given by:

z_{\alpha/2}=-2.58, z_{1-\alpha/2}=2.58

The confidence interval for the mean is given by the following formula:  

\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}

If we replace the values given we got:

0.2 - 2.58\sqrt{\frac{0.2(1-0.2)}{1400}}=0.172

0.2 + 2.58\sqrt{\frac{0.2(1-0.2)}{1400}}=0.228

The 99% confidence interval would be given by (0.172;0.228)

7 0
3 years ago
What is the value of the fourth term in a geometric sequence for which a1 =<br> 30 and r= 1/2
Tcecarenko [31]

Answer:

3¾

Step-by-step explanation:

Geometric sequence also known as geometric progression, can be said to be a sequence with a constant ratio between the terms.

Formula for geometric sequence:

a^n = a ( n-1 ) * r

Given:

First term, a1 = 30

ratio, r = ½

Required:

Find the fourth term

Where, the first term, a¹ = 30

Second term: a² = 30 * ½ = 15

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Fourth term: a⁴ = 7.5 * ½ = 3.75 = 3¾

Therfore the fourth term of the geometric sequence is 3¾

6 0
3 years ago
In triangle FGH, if the measure of angle G is five less than twice the measure of angle F and the measure of angle H is eighteen
tigry1 [53]

Answer:

The measure of angle G is 53\°

Step-by-step explanation:

Let

F ----> the measure of interior angle F of the triangle FGH

G ---> the measure of interior angle G of the triangle FGH

H ---> the measure of interior angle H of the triangle FGH

we know that

The sum of the interior angles in a triangle must be equal to 180 degrees

so

F+G+H=180\° ----> equation A

G=2F-5 ----> equation B

H=4F-18 ----> equation C

Solve the system of equations by substitution

substitute equation B and equation C in equation A

F\°+(2F-5)\°+(4F-18)\°=180\°

Solve for F

7F-23=180

7F=180+23

F=29\°

Find the measure of angle G

G=2F-5

substitute the value of F

G=2(29)-5=53\°

8 0
3 years ago
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