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3 years ago

Which function is the inverse of f(x) = 2x + 3

Mathematics

1 answer:

Marizza181 [45]3 years ago

5 0

Answer:

$\displaystyle f^{-1}(x)=\frac{x-3}{2}$

Step-by-step explanation:

<u>The Inverse of a Function</u>

The procedure to find the inverse of the function is:

* Write the function as a two-variable equation:

y = 2x + 3

* Solve the equation for x.

y - 3 = 2x

$\displaystyle x=\frac{y-3}{2}$

* Swap the variables:

$\displaystyle y=\frac{x-3}{2}$

Write back into function form. This is the inverse function:

$\mathbf{\displaystyle f^{-1}(x)=\frac{x-3}{2}}$

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According to the last census (2010), the mean number of people per household in the United States is LaTeX: \mu = 2.58 Assume a

Veseljchak [2.6K]

Answer:

P(2.50 < Xbar < 2.66) = 0.046

Step-by-step explanation:

We are given that Population Mean, $\mu$ = 2.58 and Standard deviation, $\sigma$ = 0.75

Also, a random sample (n) of 110 households is taken.

Let Xbar = sample mean household size

The z score probability distribution for sample mean is give by;

Z = $\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

So, probability that the sample mean household size is between 2.50 and 2.66 people = P(2.50 < Xbar < 2.66)

P(2.50 < Xbar < 2.66) = P(Xbar < 2.66) - P(Xbar $\leq$ 2.50)

P(Xbar < 2.66) = P( $\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }$ < $\frac{2.66-2.78}{\frac{0.75}{\sqrt{110} } }$ ) = P(Z < -1.68) = 1 - P(Z 1.68)

= 1 - 0.95352 = 0.04648

P(Xbar $\leq$ 2.50) = P( $\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }$ $\leq$ $\frac{2.50-2.78}{\frac{0.75}{\sqrt{110} } }$ ) = P(Z $\leq$ -3.92) = 1 - P(Z < 3.92)

= 1 - 0.99996 = 0.00004

Therefore, P(2.50 < Xbar < 2.66) = 0.04648 - 0.00004 = 0.046

7 0

3 years ago

In a logistic regression model, the predictor _________

Sonbull [250]

Answer:

B. must undergo a logarithmic transformation before undergoing logistic regression.

Step-by-step explanation:

A logistic regression model allows us to establish a relationship between a binary outcome variable and a group of predictor variables. It models the logit-transformed probability as a linear relationship with the predictor variables.

5 0

3 years ago

The number of students who ride the school bus is 110% of the number of students who walk. How many students ride the school bus

Mama L [17]

Answer:

506

Step-by-step explanation:

5 0

3 years ago

what equation would represent the same linear relationship for the points (40,80) (80,115) (120,140) (160,165)

tiny-mole [99]

You can use the formula y1-y2=m(x1-x2)

to find m, you just do (y2-y1)/(x2-x1) so....

(115-80)/(80-40)= 35/40= 7/8

then plug it into the point slope equation:

y-115=7/8(x-80)

y-115=7/8x-70
y= 7/8 x + 45

5 0

3 years ago

Read 2 more answers

If = u2 + 2as, evaluate a when v - 5.<br>= 2 and s = 7.

adell [148]

Answer:

75a

Step-by-step explanation:

2(vas)

2(35a)

75a

Hope this helps plz hit the crown :D

3 0

3 years ago