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2 years ago

If f(x) = 4 – x2 and g(x) = 6x, which expression is equivalent to (g – f)(3)?

2 answers:

5 0

First of all, you can distribute ( g - f ) 3 which gives you g (3) - f (3) . Now we know what to find. You plug in 3 to g (x) and f (x) .

f (3) = 4 - 2 (3)f (3) = 4 - 6f (3) = -2
g (3) = 6 (3)g (3) = 18
Now since we know what f (3) and g (3) is, we can plug it in to ( g - f ) 3 which I simplifed at the beginning to g (3) - f (3) .

g (3) - f (3)= (18) - ( -2)= 18 + 2
= 20
Now since we know what it equals, we have to simplify all the answer choices to see which one is equal.
A:6 - 3 - ( 4 + 3) 2 = 6 - 3 - ( 8 + 6)= 6 - 3 - 14= 3 - 14= -11
B:6 - 3 - ( 4 - 32 )
=6 - 3 - ( -28 )
= 6 - 3 + 28= 3 + 28= 31
C:( 6 ) ( 3 ) - 4 + 32
= 18 - 4 + 32= 14 + 32= 46
D:6 ( 3 ) - 4 - 32= 18 - 4 - 32= 14 - 32= -18
Wow, would you look at that. None of the expressions are equal to 20. There is probably an error in the question. See if you made a typo or if it is written/typed like this, ask your teacher or whoever you got it from. I hope this helped you. :D

allochka39001 [22]2 years ago

5 0

Answer:

$6(3)-4+3^2$

Step-by-step explanation:

Given functions,

$f(x) = 4 - x^2------(1)$

$g(x)=6x---------(2)$

Now,

$(g-f)(3)=f(3)-g(3)$ ( Subtracting functions )

$=6(3)-[4-(3)^2]$ ( From equations (1) and (2) )

$=6(3)-4+3^2$ ( Associative property )

Third option is correct.

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WX = WY
4x+3 = 7x-66
3x = 69
x = 23
WX = 95 = WY
XY = 5*23-7 = 108

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2 years ago

Aramp is 17 feet long, rises 8 feet above the floor, and covers a horizontal distance of 15 feet, as shown in the figure.

bonufazy [111]

Answer:

The ratio of Tan B is

$\tan B= \dfrac{AC}{BC}=\dfrac{8}{15}$

$\tan A= \dfrac{BC}{AC}=\dfrac{15}{8}$

Step-by-step explanation:

In Right Angle Triangle ABC

angle C = 90°

AB = Ramp = 17 feet

BC =Horizontal distance = 15 feet

AC = Height from floor = 8 feet

To Find:

Ratio of Tan B = ?

Solution:

In Right Angle Triangle ABC By Tangent Identity we have

$\tan B= \dfrac{\textrm{side opposite to angle B}}{\textrm{side adjacent to angle B}}$

Substituting the given values we get

$\tan B= \dfrac{AC}{BC}=\dfrac{8}{15}$

$\tan A= \dfrac{BC}{AC}=\dfrac{15}{8}$

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2 years ago

Suppose Kay inherits $250,000, which she invest today at a rate of return of 9% compounded annually. How much will Kay's investm

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Answer:

D.$2,155,770,17

Step-by-step explanation:

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2 years ago

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The Wall Street Journal reports that 33% of taxpayers with adjusted gross incomes between $30,000 and $60,000 itemized deduction

Len [333]

Answer:

(a) n : 20 50 100 500

P (-200 < X - μ < 200) : 0.2886 0.4444 0.5954 0.9376

(b) The correct option is (b).

Step-by-step explanation:

Let the random variable X represent the amount of deductions for taxpayers with adjusted gross incomes between $30,000 and $60,000 itemized deductions on their federal income tax return.

The mean amount of deductions is, μ = $16,642 and standard deviation is, σ = $2,400.

Assuming that the random variable X follows a normal distribution.

(a)

Compute the probability that a sample of taxpayers from this income group who have itemized deductions will show a sample mean within $200 of the population mean as follows:

For a sample size of n = 20

$P(\mu-200$

$=P(-0.37$

For a sample size of n = 50

$P(\mu-200$

$=P(-0.59$

For a sample size of n = 100

$P(\mu-200$

$=P(-0.83$

For a sample size of n = 500

$P(\mu-200$

$=P(-1.86$

n : 20 50 100 500

P (-200 < X - μ < 200) : 0.2886 0.4444 0.5954 0.9376

(b)

The law of large numbers, in probability concept, states that as we increase the sample size, the mean of the sample ( $\bar x$ ) approaches the whole population mean ( $\mu_{x}$ ).

Consider the probabilities computed in part (a).

As the sample size increases from 20 to 500 the probability that the sample mean is within $200 of the population mean gets closer to 1.

So, a larger sample increases the probability that the sample mean will be within a specified distance of the population mean.

Thus, the correct option is (b).

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2 years ago

A weather station in a major city in the Northwest kept data about the weather conditions over the past year. The probabilities

Black_prince [1.1K]

It is important to note that all the information's required are already given in the question

Probability that a day will be hot = 0.15 + 0.10
= 0.25
Probability that a day will be sunny = 0.15 + 0.30 + 0.10
= 0.55
Adding the above two probabilities, we get = 0.25 + 0.55
= 0.80
Now
Probability that a day will be both hot and sunny = 0.15
So
Probability that a day was hot or sunny = 0.80 - 0.15
= 0.65
I hope the procedure is clear enough for you to understand.

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2 years ago

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