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Lerok [7]
2 years ago
14

Consider the following function: f(x)=-3/4x+9

Mathematics
2 answers:
miv72 [106K]2 years ago
8 0

Answer:

f^{-1}(x) =  ( \frac{4y - 36}{-3} )

Step-by-step explanation:

f(x)=-3/4x+9

let f(x) be y .......................to find inverse we have making x the subject.

y = -3/4x+9

y - 9 = -3/4 x

-3x = 4y - 36

x = (4y - 36)/-3

so, f^{-1}(x) =  ( \frac{4y - 36}{-3} )

rusak2 [61]2 years ago
8 0
  • Let y=f(x)

\\ \tt\hookrightarrow y=\dfrac{-3}{4}x+9

\\ \tt\hookrightarrow y-9=\dfrac{-3x}{4}

\\ \tt\hookrightarrow -3x=4y-36

\\ \tt\hookrightarrow x=\dfrac{-4}{3}y+12

Now

\\ \tt\hookrightarrow f^{-1}x=\dfrac{-4}{3}x+12

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4m+5+5m+40=180 Help!!!
OLEGan [10]

First, let's put all of the variables together.

4m + 5m + 5 + 40 = 180.

Add them.

M is the same multiplier, so we can add 4 and 5 together to make 9m.

Add 5 and 40.

9m + 45 = 180.

From here, we can go two ways. I will show the first way, which is my personal  preference.

We want to get rid of the coefficient on m to isolate it, so we must divide it by its coefficient. The coefficient on m is 9. So, divide m by 9. We must also divide everything else by 9.

9m/9 = 1m

45/9 = 5

180/9 = 20

Plug it in--

m + 5 = 20.

Subtract the 5 from both sides to isolate m.

m = 15.

4 0
3 years ago
Read 2 more answers
Dan buys a car for £2200.
KatRina [158]

Answer:

The worth of the car after 6 years is £2,134.82

Step-by-step explanation:

The amount at which Dan buys the car, PV = £2200

The rate at which the car depreciates, r = -0.5%

The car's worth, 'FV', in 6 years is given as follows;

FV = PV \cdot \left ( 1 + \dfrac{r}{100} \right )^n

Where;

r = The depreciation rate (negative) = -0.5%

FV = The future value of the asset

PV = The present value pf the asset = £2200

n = The number of years (depreciating) = 6

By plugging in the values, we get;

FV = 2200 \times \left ( 1 + \dfrac{-0.5}{100} \right )^6 \approx 2,134.82

The amount the car will be worth which is its future value, FV after 6 years is FV ≈ £2,134.82 (after rounding to the nearest penny (hundredth))

8 0
3 years ago
1/2(8x-6) = x + 9 solve ... hurry
QveST [7]

Answer:

x=4

Step-by-step explanation:

4x-3=x+9

4x-x-3=9

4x-x=9+3

3x=9+3

3x=12

3/3

12/3=4

x=4

5 0
3 years ago
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. Exam scores for a large introductory statistics class follow an approximate normal distribution with an average score of 56 an
Andru [333]

Answer:

0.1% probability that the average score of a random sample of 20 students exceeds 59.5.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean \mu and standard deviation \sigma, a large sample size can be approximated to a normal distribution with mean \mu and standard deviation \frac{\sigma}{\sqrt{n}}

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 56, \sigma = 5, n = 20, s = \frac{5}{\sqrt{20}} = 1.12

What is the probability that the average score of a random sample of 20 students exceeds 59.5?

This is 1 subtracted by the pvalue of Z when X = 59.5. So

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

Z = \frac{59.5 - 56}{1.12}

Z = 3.1

Z = 3.1 has a pvalue of 0.9990.

So there is a 1-0.9990 = 0.001 = 0.1% probability that the average score of a random sample of 20 students exceeds 59.5.

3 0
3 years ago
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fiasKO [112]

Answer:

y = -7/2x+3

Step-by-step explanation:

The slope intercept form of a line is

y = mx+b  where m is the slope and b is the y intercept

y = -7/2 x+b

Substitute the point into the equation

-4 = -7/2(2) +b

-4 = -7+b

Solving for b

-4+7 = -7+b+7

3 = b

The equation is y = -7/2x+3

5 0
2 years ago
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