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3 years ago

Using trig ratios to find the missing side or angle of a right triangle

Mathematics

2 answers:

goldfiish [28.3K]3 years ago

5 0

$\\ \sf\longmapsto cos31=\dfrac{12}{x}$

$\\ \sf\longmapsto 0.85=\dfrac{12}{x}$

$\\ \sf\longmapsto x=\dfrac{12}{0.85}$

$\\ \sf\longmapsto x=14.11$

Lilit [14]3 years ago

3 0

<h2>>> Answer </h2>

________

$\:$

cos (31°) = 12/x

0.85 = 12/x

x = 12/0.85

x ≈ 14.1

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A survey of 85 families showed that 36 owned at least one DVD player. Find the 99% confidence interval estimate of the true prop

attashe74 [19]

Answer:

$0.424 - 2.58\sqrt{\frac{0.424(1-0.424)}{85}}=0.286$

$0.424 + 2.58\sqrt{\frac{0.424(1-0.424)}{85}}=0.562$

The 99% confidence interval would be given by (0.286;0.562)

Step-by-step explanation:

Information given:

$X= 36$ represent the families owned at least one DVD player

$n= 85$ represent the total number of families

$\hat p=\frac{36}{85}= 0.424$ represent the estimated proportion of families owned at least one DVD player

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 $\alpha/2 =0.05$ . 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 obtained we got:

$0.424 - 2.58\sqrt{\frac{0.424(1-0.424)}{85}}=0.286$

$0.424 + 2.58\sqrt{\frac{0.424(1-0.424)}{85}}=0.562$

The 99% confidence interval would be given by (0.286;0.562)

8 0

3 years ago

A 9x - 40 B 3x + 20 x = [?]

Mrrafil [7]

Answer:

x = 10

Step-by-step explanation:

9x - 40 = 3x + 20

9x - 3x - 40 = 3x - 3x + 20

6x - 40 = 20

6x - 40 + 40 = 20 + 40

6x = 60

6x / 6 = 60 / 6

x = 10

Now plug the x value in the equation to make the statement true that A is parallel to B.

9x - 40

9(10) - 40

90 - 40

3x + 20

3(10) + 20

30 + 20

Therefore, x = 10 making the statement true that A is parallel to B. Hope this helps and stay safe, happy, and healthy, thank you :) !!

7 0

3 years ago

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Find the area of a circle with a circumference of 31.5 units

Westkost [7]

Answer:

79 units²

Step-by-step explanation:

The area of a circle is found by using the formula A = π x r². Since we are not given the radius we can use the formula r = C / (2π). Substituting in the given values, we get r = 31.5/(2π). 2 times pi is 6.283185307. 31.5 divided by this will get you 5.013380707. Now, put that value in for r in the area equation. A = π x 5.013380707². Pi times 5.013380707² equals 78.96074613. This can be rounded to 79. (Or 80 if you need to the nearest whole number.)

6 0

3 years ago

X-2y=4 How to solve this

WARRIOR [948]

Since x does not contain the variable to solve for, move it to the right side of the equation by subtracting x from both sides
.−2y=−x+4
divide each term by −2 and simplify.
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3 years ago

How do you simplify 5/7/15

Natali [406]

Answer:

10 5/7.

Step-by-step explanation:

In words we say this is ' 5 divided by 7/15'.

5 / 7/15

= 5 * 15/7

= 75/7

= 10 5/7

8 0

4 years ago

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