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insens350 [35]
3 years ago
5

A group of people were given a personality test to determine if they were Type A or Type B. The results are shown in the table b

elow: Male Female Type A 65 85 Type B 38 12 Compare P(Male or Type B) with P(Male | Type B). P(Male or Type B) > P(Male | Type B) P(Male or Type B) = P(Male | Type B) P(Male or Type B) < P(Male | Type B) There is not enough information.
Mathematics
1 answer:
boyakko [2]3 years ago
8 0

Answer:

Step-by-step explanation:

Yeah

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maxonik [38]

(9\sin2x+9\cos2x)^2=81

Taking the square root of both sides gives two possible cases,

9\sin2x+9\cos2x=9\implies\sin2x+\cos2x=1

or

9\sin2x+9\cos2x=-9\implies\sin2x+\cos2x=-1

Recall that

\sin(\alpha\pm\beta)=\sin\alpha\cos\beta\pm\cos\alpha\sin\beta

If \alpha=2x and \beta=\dfrac\pi4, we have

\sin\left(2x+\dfrac\pi4\right)=\dfrac{\sin2x+\cos2x}{\sqrt2}

so in the equations above, we can write

\sin2x+\cos2x=\sqrt2\sin\left(2x+\dfrac\pi4\right)=\pm1

Then in the first case,

\sqrt2\sin\left(2x+\dfrac\pi4\right)=1\implies\sin\left(2x+\dfrac\pi4\right)=\dfrac1{\sqrt2}

\implies2x+\dfrac\pi4=\dfrac\pi4+2n\pi\text{ or }\dfrac{3\pi}4+2n\pi

(where n is any integer)

\implies2x=2n\pi\text{ or }\dfrac\pi2+2n\pi

\implies x=n\pi\text{ or }\dfrac\pi4+n\pi

and in the second,

\sqrt2\sin\left(2x+\dfrac\pi4\right)=-1\implies\sin\left(2x+\dfrac\pi4\right)=-\dfrac1{\sqrt2}

\implies2x+\dfrac\pi4=-\dfrac\pi4+2n\pi\text{ or }-\dfrac{3\pi}4+2n\pi

\implies2x=-\dfrac\pi2+2n\pi\text{ or }-\pi+2n\pi

\implies x=-\dfrac\pi4+n\pi\text{ or }-\dfrac\pi2+n\pi

Then the solutions that fall in the interval [0,2\pi) are

x=0,\dfrac\pi4,\dfrac\pi2,\dfrac{3\pi}4,\pi,\dfrac{5\pi}4,\dfrac{3\pi}2,\dfrac{7\pi}4

5 0
3 years ago
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Use the given domain to find the range of function: f(x)=−2x²+7, D={2, −3, 0}
soldi70 [24.7K]

Answer:

R={-1, -11, 7}

Step-by-step explanation:

-2(2)^2+7=

-2(4)+7=

-8+7=

-1

-2(-3)^2+7=

-2(9)+7=

-18+7=

-11

-2(0)^2+7=  

-2(0)+7=

0+7=

7

5 0
3 years ago
BRAINLIST WILL BE GIVEN TO THE PERSON WHO GIVES THE CORRECT ANSWER​
hjlf

Answer:

25pi. 36pi

10pi. 12pi

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9pi. 49pi

6pi. 14pi

6 0
3 years ago
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Landon scored an 85% on his test. If he got 34 problems correct, how many were on the test?
Sergeu [11.5K]

Answer:

There are 40 problems on the test

Step-by-step explanation:

Let p = the number of problems on the test

The number of problems on the test times the percent correct is the number correct

p * 85% = 34

p * .85 = 34

Divide each side by .85

p * .85/.85 = 34/.85

p = 40

There are 40 problems on the test

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3 years ago
The solutions to a certain quadratic equation are x = -4 and x = 3. Write the equation in standard form below.
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3 years ago
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