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spayn [35]
3 years ago
13

What is the value of r? Round your final answer to the nearest whole number.

Mathematics
2 answers:
vaieri [72.5K]3 years ago
8 0

Answer:

r = 13

Step-by-step explanation:

Hypotenuse is the side opposite to 90 degree angle, so hypotenuse is r.

Also, with respect to the angle given, the side "12" is the opposite.

So we have opposite side to angle and we need hypotenuse. Which trigonometric ratio related opposite with hypotenuse? It is SINE.

So we can write:

Sin(67.4)=\frac{Opposite}{Hypotenuse}=\frac{12}{r}\\rSin(67.4)=12\\r=\frac{12}{Sin(67.4)}\\r=12.99

Rounded to nearest whole number, r = 13

Len [333]3 years ago
6 0

<u>Answer:</u>

r = 13

<u>Step-by-step explanation:</u>

We are given a right angled triangle with one known angle and two side lengths (12 and r) and we are to find the value of r (which is the hypotenuse).

For that, we can use sine.

sin ( 67.4 ) = \frac {12} {r}

0.923 = \frac {12} {r}

r = \frac {12} {0.923}

r = 12.9

r ≈ 13

Therefore, the value of r is 13.

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a) The mean age of graduate students at a University is at most 31 y ears with a standard deviation of two years. A random sampl
kari74 [83]

Answer:

A.)

H0: μ ≤ 31

H1: μ > 31

B.)

H0: μ ≥ 16

H1: μ < 16

C.)

Right tailed test

D.)

If Pvalue is less than or equal to α ; we reject the Null

Step-by-step explanation:

The significance level , α = 0.01

The Pvalue = 0.0264

The decision region :

Reject the null if :

Pvalue < α

0.0264 > 0.01

Since Pvalue is greater than α ; then, we fail to reject the Null ;

Then there is no significant evidence that the mean graduate age is more Than 31.

B.)

H0: μ ≥ 16

H1: μ < 16

Null Fluid contains 16

Alternative hypothesis, fluid contains less than 16

One sample t - test

C.)

Null hypothesis :

H0 : μ ≤ 12

. The direction of the sign in the alternative hypothesis signifies the type of test or tht opposite direction of the sign in the null hypothesis.

Hence, this is a right tailed test ; Alternative hypothesis, H1 : μ > 12

d.)

If Pvalue is less than or equal to α ; we reject the Null.

3 0
3 years ago
Mrs. Bonilla is a saleswoman at a furniture store. Her commission on rugs is 10% and her commission on furniture is 15%. Her goa
lara31 [8.8K]
<span>so here is how you can answer this: 

Your commission must be equal to the sum of the 10% of the value of the rug and the 15% of the value of the furniture and equate this to the value of your commission. Translate this to a mathematical equation, you would get, 

Commission = (10%) (value of rugs) + (15%) (value of furniture).
substituting the known values, 
 
5000 =.1 * x + .15 * 12500.

Now it's a matter of finding for x. You should get, 

 x = $31,250.</span>
8 0
3 years ago
Given the equation y = |x| - 2 and the x values of -2, -1, 0, 1, 2, substitute x and choose the correct set of y values below.
Marat540 [252]

Answer:

y = {0, -1, -2}

3 0
3 years ago
1) Which of the following does not show the Commutative Property of Addition ?
Luda [366]

Answer:

I think it would be c.ab=ba but im not 100% sure

Step-by-step explanation:

4 0
3 years ago
A recipe calls for 1 ½ cups of flour, 2/3 cup of white sugar, and 1/3 cup of brown sugar. The recipe makes 6 servings. A) How ma
Goryan [66]
<span>A) How many cups of flour are there per serving? 

</span>1 ½ cups of flour --------<span>6 servings
?     cups of flour ------- 1 serving

      </span>1 ½ 
------------ 
        6 

= 3/2 x 1/6
= 1/4

answer: 1/4 cups of flour per serving

<span>B) how many total cups of sugar(white and brown) are there per serving?
</span>total white and brown: <span>2/3 + 1/3 = 3/3 = 1 cups (combine)

1 cup of sugar (white and brown) </span>--------6 servings
? cups of sugar (white and brown) ------ 1 serving

  1
-----  = 1/6
  6
answer: 1/6 cups of sugar (white and brown) per serving

<span> (c) Suppose you modify the recipe so that it makes 9 servings. How much more flour do you need for the modified recipe than you need for the original recipe?
</span>
3/2  cups of flour --------6 servings
? cups of flour -----------9 servings


  9 * 3/2             
-----------  
      6

= (13 1/2) / 6
= 2 1/4

2 1/4 ( 9 servings) - 1 1/2(6 servings) = 3/4 cups

answer: you need 3/4 more cups of flour

6 0
3 years ago
Read 2 more answers
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