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4 years ago

Which expression shows the result of applying the distributive property to 3(2x−6)3(2x−6) ?

Mathematics

2 answers:

zepelin [54]4 years ago

7 0

Answer:

Option C is correct.

$6x - 18$ is the expression that shows the result of applying the distributive property to $3(2x-6)$

Step-by-step explanation:

Given that: $3(2x-6)$ ......[1]

The distributive property says that:

$a \cdot (b+c) = a\cdot b + a\cdot c$

Apply distributive property on [1] we have;

$3 \cdot (2x) - 3 \cdot (6)$

Simplify:

$6x - 18$

Therefore, the expression that shows the result of applying the distributive property to $3(2x-6)$ is, $6x - 18$

bazaltina [42]4 years ago

4 0

If you are distributing 3(2x-6) then you would do it this way:
(3 x 2x)(3 x (-6))
(6x) (-18)
6x-18 (you can simplify this by dividing by 6)
x-6 would be your answer but I don't see it as one of the options. Are all of these options typed out correctly?

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Approximate cos (12π/ 13) by using a linear approximation with f (x) = cos x.

Katarina [22]

First pick a value of $x$ close to $\dfrac{12\pi}{13}$ . You should be fine with $x=\pi$ .

The linear approximation of $f(x)$ at $x=c$ is given by

$f(c)\approx f(a)+f'(a)(c-a)$

where $x=a$ is some fixed value close to $x=c$ . You have

$f(x)=\cos x\implies f'(x)=-\sin x$

so

$f\left(\dfrac{12\pi}{13}\right)\approx f(\pi)+f'(\pi)\left(\dfrac{12\pi}{13}-\pi\right)$
$\cos\dfrac{12\pi}{13}\approx\cos\pi-\sin(\pi)\left(-\dfrac\pi{13}\right)$
$\cos\dfrac{12\pi}{13}\approx-1$

The actual value is closer to -0.9709, so the approximation is decent.

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3 years ago

How many possible ways are there to get a spare (knock down all pins in two rolls) in bowling? Show work.

dlinn [17]

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3 years ago

Elysse paid for her lunch with a $10 bill and recieved 0.63 in change the lunch special was 7.75 sales tax was 0.47 what was the

adelina 88 [10]

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3 years ago

Read 2 more answers

Suppose that 44% of all Americans approve of the job the President is doing. The most recent Gallup poll consisted of a random s

Novay_Z [31]

Since the possible outcomes of the poll are only two, approve or not, we are dealing with a binomial distribution, where:
n = 1400
p = 44% = 0.44

A) The mean of the sampling distribution is μ = 616
The mean of a binomial distribution can be calculated by the formula:
μ = n · p
 = 1400 · 0.44
 = 616

B) The standard deviation of the sampling distribution is σ = 18.6
The standard deviation of a binomial distribution can be calculated by the formula:
σ = √[n · p · (1 - p)]
 = √[1400 · 0.44 · (1 - 0.44)]
 = √344.96
 = 18.6

C) The normal approximation is N(616, 18.6)

In order to normally approximate a binomial distribution, two conditions must be satisfied:
n · p ≥ 10
n · p · (1 - p) ≥ 10

In our case,
n · p = 616 > 10
n · p · (1 - p) = 344.96 > 10

Since the two conditions are satisfied, the binomial distribution B(n, p) can be approximated with a normal distribution N(μ, σ).
In our case:
B(1400, 0.44) ≈ N(616, 18.6)

D) The probability that the Gallup poll will come up with a proportion within three percentage points of the true 44% is P = 0.98 or 98%

We need to apply the continuity correction to our normal approximation:
P(Y = 0.44) = P(0.44 - 0.03 ≤ Y ≤ 0.44 + 0.03)
= P(0.41 ≤ Y ≤ 0.47)

In order to calculate this probability, we need to calculate mean and standard deviation of the sample proportion:
$\hat{p} = p = 0.44$

$\sigma = \sqrt{ \frac{p(1-p)}{n} } \\ = \sqrt{ \frac{0.44(1-0.44)}{1400} } \\ = 0.013$

Now, we need to calculate the z-score for each Y-value:
z = (Y - p) / σ

z(Y = 0.41) = (0.41 - 0.44) / 0.013 = -2.31
z(Y = 0.47) = (0.47 - 0.44) / 0.013 = 2.31

Therefore, we can say that
P(0.41 ≤ Y ≤ 0.47) = P(-2.31 ≤ z ≤ 2.31)
= P(z ≤ 2.31) - P(z ≤ -2.31)

Looking at a normal standard distribution table, we find
P(z ≤ -2.31) = 0.0104
P(z ≤ 2.31) = 0.9896

Therefore:
P(0.41 ≤ Y ≤ 0.47) = 0.9896 - 0.0104
= 0.9792

Hence, the probability of the poll coming up with a proportion within three percent of the true mean is 0.98 which means 98%

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3 years ago

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ahrayia [7]

Answer:

First question is A.

Second question is C.

Step-by-step explanation:

First question is correct because non-linear graphs look just like that.

Second question is correct because 2 variables cannot equal the same thing in a function.

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3 years ago