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Artist 52 [7]
3 years ago
10

F(x)=3x and g(x)=x+2 find fog(x),gof(x),fog(2),gof(2)

Mathematics
1 answer:
Gala2k [10]3 years ago
8 0

Answer:

Step-by-step explanation:

fog(x)=f(g(x)) =f(x+2) =3⋅(x+2) =3x+6

gof(x)=g(f(x))=g(3x) =3x+2

gof(2)=3⋅2+2 =6+2 =8

fog(2)=3⋅(2+2) =3*2+6=12

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Answer:

Step-by-step explanation:

0.5-8y= 72

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3 years ago
Sin (x/2)= √2- sin (x/2) solve for the exact solutions in the interval (0, 2π)
serg [7]

sin\left( \frac{x}{2} \right)=\sqrt{2}-sin\left( \frac{x}{2} \right)\implies sin\left( \frac{x}{2} \right)+sin\left( \frac{x}{2} \right)=\sqrt{2}\implies 2sin\left( \frac{x}{2} \right)=\sqrt{2} \\\\\\ sin\left( \cfrac{x}{2} \right)=\cfrac{\sqrt{2}}{2}\implies sin^{-1}\left[ sin\left( \cfrac{x}{2} \right) \right]=sin^{-1}\left( \cfrac{\sqrt{2}}{2} \right) \implies \cfrac{x}{2}= \begin{cases} \frac{\pi }{4}\\\\ \frac{3\pi }{4} \end{cases} \\\\[-0.35em] ~\dotfill

\cfrac{x}{2}=\cfrac{\pi }{4}\implies \boxed{x=\cfrac{\pi }{2}}~\hfill \cfrac{x}{2}=\cfrac{3\pi }{4}\implies \boxed{x=\cfrac{3\pi }{2}}

5 0
2 years ago
Complete the problem to represent the situation given by the equation 0.40e + 10 + 15 = 0.20e + 5 + 25. At one store a trophy co
olganol [36]

Answer: The number of letters that must be engraved for the costs to be the same is 125.

Step-by-step explanation:

Since we have given that

0.4e+10+15=0.20e+5+25

We need to find the number of letters.

0.4e+25=0.2e+30\\\\0.4e-0.2e=30-25\\\\0.2e=25\\\\e=\dfrac{25}{0.2}\\\\e=125

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Read 2 more answers
Write the null and alternative hypotheses in words and then symbols for each of the following situations.
Marrrta [24]

Answer:

A) the hypothesis in words and symbols are;

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Alternative hypothesis: Grades have improved for most students

Null hypothesis; H0: p^ = 0.5

Alternative hypothesis; Ha: p^ > 0.5

B) Null hypothesis: During march madness, employees averaged 15 minutes per day on non - business activities

Alternative hypothesis: During march madness, employees averaged more than 15 minutes per day on non-business activities

Null hypothesis; H0: μ = 15

Alternative hypothesis; Ha: μ > 15

Step-by-step explanation:

A) We are told that they sampled 200 of the students who used their service in the past year and ask them if their grades have improved or declined from the previous year. Thus, there will be a 50% chance of success for their grades to have improved and a 50% chance for it to remain the same.

Thus; p^ = 0.5

So the hypothesis in words and symbols are;

Null hypothesis: Grades have not improved for most students

Alternative hypothesis: Grades have improved for most students

Null hypothesis; H0: p = 0.5

Alternative hypothesis; Ha: p > 0.5

B) We are told that they estimate that on a regular business day employees spend on average 15 minutes of company time checking personal email, making personal phone calls, etc

Also, They also collect data on how much company time employees spend on such non-business activities during March Madness.

The hypotheses in words and symbols are;

Null hypothesis: During march madness, employees averaged 15 minutes per day on non - business activities

Alternative hypothesis: During march madness, employees averaged more than 15 minutes per day on non-business activities

Null hypothesis; H0: μ = 15

Alternative hypothesis; Ha: μ > 15

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Answer:

10 1/2

Step-by-step explanation:

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