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VikaD [51]
3 years ago
14

1. The hypotenuse of a right triangle measures 2 sqrt 15 centimeters and its shorter leg measures 2 sqrt 6

Mathematics
2 answers:
Dominik [7]3 years ago
8 0

Answer:

<h2>50.8°</h2>

Step-by-step explanation:

First, we need to use the Pythagorean Theorem to find the third side. We will then use the law of cosines to find the angle.

2√15² = 2√6² + b²

60 = 24 + b²

Subtract 24

36 = b²

b = 6

Now, that we have all three sides, we will use the law of cosines to figure out the angle.

c² = a² + b² - 2abCosC°

Substitute the values in.

6² = 2√15² + 2√6² - 2(2√15)(2√6)CosC°

36 = 60 + 24 - 2(37.947331922)CosC°

36 = 60 + 24 - 75.894663844CosC°

36 = 84 - 75.894663844CosC°

Subtract 84

-48 = -75.9CosC°

0.63241106719 = CosC°

Arccos (0.63241106719) = 50.77176844°

The largest acute angle is approximately 50.8°

strojnjashka [21]3 years ago
8 0

Answer:

50.8 degrees

Step-by-step explanation:

cos^(-1)(sqrt(6)/sqrt(15)) = 50.8

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How many pairs of whole numbers have the Sum of 12
nataly862011 [7]
Thanks for the question!

Don't forget 0 is a whole number:

0 + 12
1 + 11
2 + 10
3 + 9
4 + 8
5 + 7
6 + 6

Hope this helps!
8 0
3 years ago
Write an equation for the line in slope- intercept form. 2. Х -4 -2 o 2 4. -2 4​
Alla [95]

Answer:

y= -2x-3

Step-by-step explanation:

this is because the y intercept is at negative 3 and the rise over run is down 1 over 2

3 0
2 years ago
Given 6 terms what is the sum of 10+25+40+...+85
sdas [7]
Sn = n/2 ( a1+an)
= 6/2 (10+85)
= 3 (95)
= 285
3 0
3 years ago
Suppose that each observation in a random sample of 100 fatal bicycle accidents in 2015 was classified according to the day of t
liraira [26]

Answer:

The calculated χ² =  0.57   does not fall in the critical region χ² ≥  12.59  so we fail to reject the null hypothesis and conclude the proportion of fatal bicycle accidents in 2015 was the same for all days of the week.

Step-by-step explanation:

1) We set up our null and alternative hypothesis as

H0:  proportion of fatal bicycle accidents in 2015 was the same for all days of the week

against the claim

Ha:  proportion of fatal bicycle accidents in 2015 was not the same for all days of the week

2) the significance level alpha is set at 0.05

3) the test statistic under H0 is

χ²= ∑ (ni - npi)²/ npi

which has an approximate chi square distribution with ( n-1)=7-1=  6 d.f

4) The critical region is χ² ≥ χ² (0.05)6 = 12.59

5) Calculations:

χ²= ∑ (16- 14.28)²/14.28 + (12- 14.28)²/14.28 + (12- 14.28)²/14.28 + (13- 14.28)²/14.28 + (14- 14.28)²/14.28 + (15- 14.28)²/14.28 + (18- 14.28)²/14.28

χ²= 1/14.28 [ 2.938+ 5.1984 +5.1984+1.6384+0.0784 +1.6384+13.84]

χ²= 1/14.28[8.1364]

χ²= 0.569= 0.57

6) Conclusion:

The calculated χ² =  0.57   does not fall in the critical region χ² ≥  12.59  so we fail to reject the null hypothesis and conclude the proportion of fatal bicycle accidents in 2015 was the same for all days of the week.

b.<u> It is r</u>easonable to conclude that the proportion of fatal bicycle accidents in 2015 was the same for all days of the week

6 0
3 years ago
in the classroom there are 60 student among them the ratio of boys and girls is 2:3 find the number of boys and girl​
ra1l [238]

Answer:

boys = 24 \\ girls = 36

Step-by-step explanation:

2 : 3 \\ 2 + 3 = 5 \\  \\  \frac{60}{5}  = 12 \\  \\  \: boys \:  \:  \:  : girls\\ \:  2 \:  \:  \:  \:  \:  \:  \:  \:   \:  \:  \:  \: :  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: 3 \\ 12 \times 2 : 12 \times 3 \\  \:  \: 24 \:  \:  \:  \:  \:  \:  \:  \:  :  \:  \:  \: 36

6 0
3 years ago
Read 2 more answers
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