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2 years ago

40° 87° Xº Q Image not to scale 38° Calculate the missing internal angle x.

Mathematics

1 answer:

bagirrra123 [75]2 years ago

5 0

Q = 87 + 40

Q = 127

X + 127 + 38 = 180

X = 180 - 127 - 38

X = 15

Therefore we say X is 15

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What is the exact value of cos(7pi/8)

Damm [24]

Answer:

cos ( $\frac{7\pi}{8}$ ) = $-\frac{\sqrt{2+\sqrt{2}}}{2}$

Decimal value: −0.9238795325...

Step-by-step explanation:

Write,

cos $\frac{7\pi}{8}$ = cos $(\pi-\frac{\pi}{8})$ = −cos $\frac{\pi }{8}$

Now using half angle formula, cos(x) = 2 cos²( $\frac{\pi }{2}$ ) − 1, we can write cos $\frac{\pi }{4}$ = 2

cos²( $\frac{\pi }{8}$ ) − 1

This means $\frac{1}{\sqrt{2}}$ + 1 = 2 cos²( $\frac{\pi }{8}$ )

2 cos²( $\frac{\pi }{8}$ ) = $\frac{\sqrt{2}+1}{\sqrt{2}}$

cos²( $\frac{\pi }{8}$ ) = $\frac{\sqrt{2}+1}{2\sqrt{2}}$

cos( $\frac{\pi }{8}$ ) = $\sqrt{\frac{\sqrt{2}+1}{2\sqrt{2}}}$

Simplify,

$\sqrt{\frac{\sqrt{2}+1}{2\sqrt{2}}}$ = $\sqrt{\frac{2+\sqrt{2}}{4}$ = $\frac{\sqrt{2+\sqrt{2}}}{2}$

Hence,

cos ( $\frac{7\pi}{8}$ ) = −cos ( $\frac{\pi }{8}$ ) = $-\frac{\sqrt{2+\sqrt{2}}}{2}$

3 0

3 years ago

Read 2 more answers

) Suppose that a subset of five balls will be randomly selected from an urn containing amber, blue, and green balls. (a) If the

vazorg [7]

Answer:

0.0023 = 0.23% probability that all 5 balls selected will be the same color

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the balls are selected is not important, which means that the combinations formula is used to solve this question.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

Desired outcomes:

Either 5 amber from a set of 6, or 5 blue from a set of 5. So

$D = C_{6,5} + C_{5,5} = \frac{6!}{5!1!} + \frac{5!}{5!0!} = 6 + 1 = 7$

Total outcomes:

5 balls selected from a set of 6 + 5 + 4 = 15. So

$T = C_{15,5} = \frac{15!}{5!10!} = 3003$

Probability:

$p = \frac{D}{T} = \frac{7}{3003} = 0.0023$

0.0023 = 0.23% probability that all 5 balls selected will be the same color

5 0

3 years ago

I have 54 coins in my pocket; some of them are quarters and the rest are nickels. In total, the coins are worth $6.10. How many

ss7ja [257]

Answer:

17 quarters, 37 nickels

Step-by-step explanation:

We just have to set up a system of equations

quarters are x

and nickels are y

x+y=54

0.25x+0.05y=6.10

now we can get ready to substitute

x=54-y

substitute it in

0.25(54-y)+0.05y=6.10

simplify/evaluate

13.5-0.25y+0.05y=6.10

-0.2y=-7.4

y=37

plug it back in

x+37=54

x=17

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3 years ago

Which of the following is most likely the next step in the series?

Delicious77 [7]

it is E20e not e20E

so the answer is A

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3 years ago

Read 2 more answers

40/3 % of 9m Percentage

Yuri [45]

Answer:1.2

Step-by-step explanation:

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3 years ago