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SVETLANKA909090 [29]

3 years ago

7

Drag the expressions to the correct functions. Not all expressions will be used. Consider the functions f and g. f(x)=4x^2+1 g(x

)=x^2-3 Perform the function compositions.

1 answer:

bagirrra123 [75]3 years ago

5 0

Answer:

(f o g)(x) = 4x⁴ - 96x + 37

(g o f)(x) = 16x⁴ + 8x² - 2

Step-by-step explanation:

Since, the given functions are,

f(x) = 4x² + 1

g(x) = x² - 3

(f o g)(x) = f[g(x)]

f[g(x)] = 4(x² - 3)² + 1

= 4(x⁴ - 24x + 9) + 1

= 4x⁴ - 96x + 36 + 1

= 4x⁴ - 96x + 37

(g o f)(x) = g[f(x)]

= (4x² + 1)²- 3

= 16x⁴ + 8x² + 1 - 3

= 16x⁴ + 8x² - 2

Therefore, out of the given options only two expressions are correct.

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3 years ago

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Anestetic [448]

First we distribute $\frac{1}{5}$ into $n$ and $-\frac{1}{7}$ .

$\frac{1}{5} * n = \frac{1}{5} n$
$\frac{1}{5} * -\frac{1}{7} = - \frac{1}{35}$

That makes the left side of the equation

$\frac{1}{5} n - \frac{1}{35} = \frac{1}{6} n$

Now we subtract $\frac{1}{5}n$ from $\frac{1}{6} n$ , which makes $\frac{1}{30}$

Now the equation is

$-\frac{1}{35} = -\frac{1}{30n}$

Our goal is to isolate $n$ , so we both sides by 30

$30* -\frac{1}{35} = - \frac{1}{30}n * 30$

That will make the equation

$- \frac{30}{35} = -n$

We multiply -1 on both sides of the equation:

$\frac{30}{35} = n$

Finally we simplify $\frac{30}{35}$ , which makes $\frac{6}{7}$

So the answer is $n = \frac{6}{7}$

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erik [133]

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7 0

3 years ago

A TV report conducted a survey of 947 people in New York City and found that 35% of the population believe that the Yankees will

garik1379 [7]

Answer:

$35\%$ represents the sample proportion of the population

Step-by-step explanation:

From the question we are told that

The sample size is n = 947

The proportion of the population that believes that the Yankees will miss the playoffs this year is $k = 35\% = 0.35$

From the question we are told the confidence level is 97%

The lower limit of the confidence level is a = 28%

The upper limit of the b = 42%

Generally the sample proportion of this population is mathematically represented as

$\^ p = \frac{a+ b}{2}$

=> $\^ p = \frac{28 + 42 }{2}$

=> $\^ p = 35\%$

Hence $35\%$ represents the sample proportion

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7 0

3 years ago

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