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3 years ago

Given the coordinates for the function below, who of the following are coordinates for its inverse?

Mathematics

1 answer:

lapo4ka [179]3 years ago

5 0

Answer:

If we have a function f(x) that has an inverse g(x), we have the relations:

f( g(x)) = x

g( f(x)) = x

Then if the coordinates for the function f(x) are points like (x₁, y₁)

The coordinates for the inverse, g(x), will be (y₁, x₁)

Now let's look at the table, here we can see that the coordinates for f(x) are:

(0, 650)

(100, 550)

(200, 450)

(340, 310)

(650, 0)

Then the coordinates of the inverse function will be:

(650, 0)

(550, 100)

(450, 200)

(340, 310)

(0, 650)

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Two buses leave towns 304 miles apart at the same time and travel toward each other. One bus travels 14 mih slower than the othe

8090 [49]

Answer:

The faster bus moves at 83mi/h and the slower one moves at 69mi/h.

Step-by-step explanation:

Let's define:

R₁ = rate of bus 1, this is the faster one.

R₂ = rate of bus 2, this is the slower one.

We know that one bus travels 14mi/h slower, then:

R₂ = R₁ - 14mi/h.

Now we know that:

Distance = Speed*Time.

If we add the distances that both busses travel in 2 hours, it should be equal to the initial distance between the buses, then:

R₁*2h + R₂*2h = 304 mi

Then we have the two equations:

R₂ = R₁ - 14mi/h

R₁*2h + R₂*2h = 304 mi

The first step is to replace the first equation in the second one, to get:

R₁*2h + (R₁ - 14mi/h)*2h = 304 mi

And now we can solve this for R₁.

R₁*2h + R₁*2h - 14mi/h*2h = 304 mi

R₁*4h - 28mi = 304mi

R₁*4h = 304mi + 28mi = 332mi

R₁ = 332mi/4h = 83mi/h

The faster bus moves at 83mi/h

And we know that the slower one moves at 14mi/h slower than this, then:

R₂ = R₁ - 14mi/h = 83mi/h - 14mi/h = 69 mi/h

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3 years ago

What is the value of

Len [333]

$n-2=10n+42\qquad\text{add 2 to both sides}\\\\n=10n+44\qquad\text{subtract 10n from both sides}\\\\-9n=44\qquad\text{divide both sides by (-9)}\\\\\boxed{n=-\dfrac{44}{9}}$

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3 years ago

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The table shows the total number of student applications to universities in a particular state over a period of 12 semesters. St

ANTONII [103]

5 out of 12 = 5/12

Those are
1 - 106
2 - 137
4 - 120
6 - 195 and
8 - 139

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3 years ago

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Natalie opened a bank account that earns 2.5% simple interest. If her account earned $180 over ten years, how much was Natalie's

Inga [223]

Answer:

i believe your answer is $7,200

Step-by-step explanation:

take 180 and divide it by .025, you should get $7,200.

6 0

3 years ago

Calculate a critical z-score for a left-tailed, right-tailed, or two-tailed test.

muminat

Answer:

a. Z = -1.175.

b. Z = 1.34.

c. |Z| = 2.054.

d. |Z| = 1.28.

Step-by-step explanation:

Z-score:

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

a. The critical z-score for a left-tailed test at a 12% significance level

Left-tailed test: The region of interest is the 12th percentile or below.

Thus, the critical z-score is Z with a p-value of 0.12, so Z = -1.175.

b. The critical z-score for a right-tailed test at a 9% significance level

Right-tailed test: The region of interest is the 100 - 9 = 91th percentile and above.

Thus, the critical z-score is Z with a p-value of 0.91, so Z = 1.34.

c. The critical z-score for a two-sided test at a 4% significance level is 1.75.

Two-tailed test: The region of interest is between the 4/2 = 2th percentile and the 100 - (4/2) = 98th percentile.

Thus, the critical z-score is |Z| with a p-value of 0.02 or 0.98, so |Z| = 2.054.

d. The critical z-score for a two-sided test at a 20% significance level is 0.85.

Region of interest is between the 20/2 = 10th percentile and the 100 - (20/2) = 90th percentile.

Thus, the critical z-score is |Z| with a p-value of 0.1 or 0.9, so |Z| = 1.28.

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3 years ago