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3 years ago

What is the inverse of the function f(x) = 2x + 1?

Mathematics

1 answer:

Alexandra [31]3 years ago

6 0

Answer:

$f^{-1}$ (x) = $\frac{x-1}{2}$

Step-by-step explanation:

let y = f(x) and rearrange making x the subject, that is

y = 2x + 1 ( subtract 1 from both sides )

y - 1 = 2 ( divide both sides by 2 )

$\frac{y-1}{2}$ = x

Change y back into terms of x and let x = $f^{-1}$ (x), thus

$f^{-1}$ (x ) = $\frac{x-1}{2}$

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Ms. Williams wanted information about how well her students were

Arturiano [62]

Answer:

https://www.pittsfordschools.org/cms/lib/NY02205365/Centricity/Domain/683/ANSWER%20KEY%20TO%20ALL%20HOMEWORK.pdf

Step-by-step explanation:

If this doesn’t work I’m sorry but that’s the link!

5 0

3 years ago

Complemetary angles are two angles whose measures add up to 90 degrees. The ratio of the measures of two complementary angles is

pochemuha

Let A and B be the two complementary angles.

A = smaller angle = 2x

B = larger angle = 13x

x = some unknown number

Note how the ratio A:B turns into 2x:13x which simplifies to 2:13

A+B = 90 ... because the angles are complementary

2x+13x = 90 ... substitution

15x = 90

x = 90/15

x = 6

A = 2*x = 2*6 = 12 degrees

B = 13*x = 13*6 = 78 degrees

The two angles are 12 degrees and 78 degrees.

Check:

A/B = 12/78 = (2*6)/(13*6) = 2/13, so A:B = 2:13

A+B = 12+78 = 90

3 0

2 years ago

It is known that the life of a particular auto transmission follows a normal distribution with mean 72,000 miles and standard de

scoray [572]

Answer:

a) $P(X$

$P(z$

b) $P(X>65000)=P(\frac{X-\mu}{\sigma}>\frac{65000-\mu}{\sigma})=P(Z>\frac{65000-72000}{12000})=P(z>-0.583)$

$P(z>-0.583)=1-P(Z$

c) $P(X>100000)=P(\frac{X-\mu}{\sigma}>\frac{100000-\mu}{\sigma})=P(Z>\frac{100000-72000}{12000})=P(z>2.33)$

$P(z>2.33)=1-P(Z$

Sicne this probability just represent 1% of the data we can consider this value as unusual.

d) $z=1.28$

And if we solve for a we got

$a=72000 +1.28*12000=87360$

So the value of height that separates the bottom 90% of data from the top 10% is 87360.

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Part a

Let X the random variable that represent the life of a particular auto transmission of a population, and for this case we know the distribution for X is given by:

$X \sim N(72000,12000)$

Where $\mu=72000$ and $\sigma=12000$

We are interested on this probability

$P(X$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(X$

And we can find this probability using excel or the normal standard table and we got:

$P(z$

Part b

$P(X>65000)$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(X>65000)=P(\frac{X-\mu}{\sigma}>\frac{65000-\mu}{\sigma})=P(Z>\frac{65000-72000}{12000})=P(z>-0.583)$

And we can find this probability using the complement rule and excel or the normal standard table and we got:

$P(z>-0.583)=1-P(Z$

Part c

$P(X>100000)$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(X>100000)=P(\frac{X-\mu}{\sigma}>\frac{100000-\mu}{\sigma})=P(Z>\frac{100000-72000}{12000})=P(z>2.33)$

And we can find this probability using the complement rule and excel or the normal standard table and we got:

$P(z>2.33)=1-P(Z$

Sicne this probability just represent 1% of the data we can consider this value as unusual.

Part d

For this part we want to find a value a, such that we satisfy this condition:

$P(X>a)=0.1$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.9 of the area on the left and 0.1 of the area on the right it's z=1.28. On this case P(Z<1.28)=0.9 and P(z>1.28)=0.1

If we use condition (b) from previous we have this:

$P(X$

$P(z$

But we know which value of z satisfy the previous equation so then we can do this:

$z=1.28$

And if we solve for a we got

$a=72000 +1.28*12000=87360$

So the value of height that separates the bottom 90% of data from the top 10% is 87360.

5 0

3 years ago

McKenzie buys 250 shares of stock for $12 a share and pays a 2% commision. She sells the stock 3 years later for $18 a share and

Artemon [7]

250 shares for $ 12 per share......250 * 12 = 3000
plus the 2% commission......3000(1.02) = 3060...so the commission is $ 60

she then sells her stock (250 shares) for $ 18 a share....
250 * 18 = 4500
plus the 1% commission....4500(1.01) = 4545...so the commission is $ 45

net proceeds is the amount received by the seller after all costs and expenses are deducted...

expenses : 3000 + 60 + 45 = 3105
revenue : 4500

net proceeds = 4500 - 3105 = $ 1395 <==

5 0

3 years ago

Which equation has the least steep graph?

MAVERICK [17]

Answer:

$y=\frac{1}{4}x+6$