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3 years ago

Instructions: Use the ratio of a 30-60-90 triangle to solve for the variables.

Mathematics

1 answer:

Pepsi [2]3 years ago

8 0

Answer:

$x=20$

$y=10\,\sqrt{3}$

Step-by-step explanation:

In the triangle we have the following trigonometric equations:

$tan(60^o)=\frac{opposite}{adjacent} \\\sqrt{3} =\frac{y}{10} \\y=10\,\sqrt{3}$

and also:

$cos(60^o)=\frac{adjacent}{hypotenuse}\\\frac{1}{2} =\frac{10}{x}\\x=20$

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Talamunda to velcratia is 70 miles the train takes 5 hours to travel the distance at what unit rate is the train travilining

garri49 [273]

Your answer would be 14 because 70÷5= 14

3 0

3 years ago

With double-digit annual percentage increases in the cost of health insurance, more and more workers are likely to lack health i

Dahasolnce [82]

Answer:

1. χ² = 15.3902

2. The p value is :_____.a. less than .005

3. Conclusion

a. health insurance coverage is not independent of the size of the company

4. The percentages of employees

Small %= 33/50= 0.66

Medium %= 68/75 = 0.91

Large %= 88/100= 0.88

Step-by-step explanation:

1) We set up our null and alternative hypothesis as

H0: the employee health insurance coverage is independent of the size of the company

against the claim

Ha: the employee health insurance coverage is not independent of the size of the company

2) the significance level alpha is set at 0.05

3) the test statistic under H0 is

χ²= ∑ (O - E)²/ E where O is the observed and E is the expected frequency

which has an approximate chi square distribution with ( 3-1) (2-1)= 2 d.f

4) Computations:

Under H0 , the observed frequencies are :

Observed Expected E (O-E) (O-E)² (O-E)²/E

33 42 -9 81 1.928

68 63 5 25 0.3968

88 84 4 16 0.1904

17 8 9 81 10.125

7 12 -5 21 1.75

12 16 -4 16 1

15.3902

Expected Values are calculated using the formula :

Row Total * Column Total / sample size

E1= (33+17) (33+ 68+88)/ 50+75+100= 42

E4= (33+17) (17+ 7+ 12)/ 50+75+100=8

E2= (68+7) (33+ 68+88)/ 50+75+100= 63

E5= (68+7) (17+ 7+ 12)/ 50+75+100= 12

E3= (88+12) (33+ 68+88)/ 50+75+100= 84

E6= (88+12) (17+ 7+ 12)/ 50+75+100= 16

5) The critical region is χ² ≥ χ² (0.05)2 = 5.99

6) Conclusion:

The calculated χ² = 15.3902 falls in the critical region χ² ≥ 5.99 so we reject the null hypothesis that the employee health insurance coverage is NOT independent of the size of the company.

2. The p value is :_____.

a. less than .005

The p-value is .000385.

3. Conclusion

a. health insurance coverage is not independent of the size of the company

4. The percentages of employees

Small %= 33/50= 0.66

Medium %= 68/75 = 0.91

Large %= 88/100= 0.88

3 0

3 years ago

What values of a and b would make the equation shown have infinitely many solutions? 3x=ax+b

Wittaler [7]

Infinitely many solutions means that you have the same thing on both sides of the equation no matter what value of x you plug in, right?

We just need both sides to be 3x then, correct?

If a were equal to 3 and b were equal to 0, we'd have

3x = (3)x + 0

Which is essentially 3x = 3x

So that means a = 3 and b = 0 must work!
Let's say x = 5

3(5) = 3(5) + 0

15 = 15 + 0

15 = 15

That means that a = 3 and b = 0 is your final answer :)

7 0

3 years ago

You are trying to heat up a cup of water with a butane lighter.

algol13

Answer:

Step-by-step explanation:

Remark

The formula for this is

Heat = m * c * Δt

Givens

Heat = unknown

m = 200 grams

c = 4.184 Joules / grams oC

Δt = the change in temperature = 35.7 - 22.3 = 13.4

Solution

Heat = 200 * 4.184 * 13.4

Heat = 11213 Joules

Heat = 11.2 Kj

It's hard to get the correct number of sig digs because the 200 is not qualified in any way.

Part 2.

This can really puzzle you until you know that heat given up = the heat taken on. The heat taken on was 11.2 Kj. The Butane lighter must have given that heat on.

Heat of Combustion = Heat Given Up / Number grams burned.

Heat of Combustion = 11.2 Kj / 0.23 grams

Heat of Combustion = 48.8 Kj / gram

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3 years ago

choose all of the terms that describe the set of lines. transversal parallel lines perpendicular lines intersecting lines

Greeley [361]

Answer:

C. Perpendicular Lines

D. Intersecting Lines

Step-by-step explanation:

Intersecting lines are a pair of lines, line segments or rays are intersecting if they have a common point.

Perpendicular lines are a point where two city roads intersect.

Hope this helps. I am sorry if you get it wrong.

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3 years ago