What is the inverse of the function f(x) = 2x
10?

Answer:

24

Step-by-step explanation:

Sara = x age

Amy = x+2        when Sara  x = 22    Amy is x + 2 = 24

Product of ages = 528 so............

    x(x+2) = 528

    x² + 2x - 528 = 0     solve for x         I did it graphically first to get x = -24, 22

    (x+24) (x-22)  = 0

   (x+24) = 0         (x-22) = 0

           x = -24             x = 22        since you really can't have a negative age

Answer:

As the pvalue of the test is 0.02097 < 0.1, using a .10 significance level, he can conclude that the average trunk diameter of a pine tree is greater than the average diameter of a spruce tree.

Step-by-step explanation:

Using a .10 significance level, can he conclude that the average trunk diameter of a pine tree is greater than the average diameter of a spruce tree

The null hypothesis is that they are equal(that is, subtraction between the means is 0), while the alternate hypothesis is that they are greater(that is, subtraction between the means is larger than 0). So

[tex]H_0: \mu_1 - \mu_2 = 0[/tex]

[tex]H_a: \mu_1 - \mu_2 > 0[/tex]

In which [tex]\mu_1[/tex] is the mean pine trees height while [tex]\mu_2[/tex] is the mean spruce trees height.

The test statistic is:

[tex]z = \frac{X - \mu}{s}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis and s is the standard error.

0 is tested at the null hypothesis:

This means that [tex]\mu = 0[/tex]

Mean trunk diameter (cm) 35 30:

Pine trees - 35

Spruce trees - 30

The sample mean is given by the subtraction of the means. So

[tex]X = 35 - 30 = 5[/tex]

Sample Size 40 80

Population variance 160 160

This means that the standard error for each sample is given by:

[tex]s_1 = \frac{\sqrt{160}}{\sqrt{40}} = 2[/tex]

[tex]s_1 = \frac{\sqrt{160}}{\sqrt{80}} = \sqrt{2}[/tex]

The standard error of the difference is the square root of the sum squared of the standard error of each sample.

[tex]s = \sqrt{2^2 + (\sqrt{2})^2} = \sqrt{6} = 2.4495[/tex]

Test statistic:

[tex]z = \frac{X - \mu}{s}[/tex]

[tex]z = \frac{5 - 0}{2.4495}[/tex]

[tex]z = 2.04[/tex]

Pvalue of the test:

Probability of a sample mean larger than 5, which is 1 subtracted by the pvalue of Z when X = 5.

Looking at the z-table, z = 2.04 has a pvalue of 0.9793.

1 - 0.9793 = 0.0207

As the pvalue of the test is 0.02097 < 0.1, using a .10 significance level, he can conclude that the average trunk diameter of a pine tree is greater than the average diameter of a spruce tree.

Answer:

- The population in 2001 is 23.1 million

- It will reach 28.3 million in 2013

Step-by-step explanation:

Given

[tex]A =23.1e^{0.0152t}[/tex]

Solving (a): Population in 2000.

This implies that

[tex]t = 2000 - 2000[/tex]

[tex]t = 0[/tex]

So, we have:

[tex]A =23.1e^{0.0152t}[/tex]

[tex]A =23.1e^{0.0152*0}[/tex]

[tex]A =23.1e^{0}[/tex]

Solve the exponent

[tex]A =23.1*1[/tex]

[tex]A =23.1[/tex]

The population in 2001 is 23.1 million

Solving (b): When will it reach 28.3 million

This implies that:

[tex]A =28.3[/tex]

So, we have:

[tex]A =23.1e^{0.0152t}[/tex]

[tex]28.3 = 23.1e^{0.0152t}[/tex]

Divide both sides by 23.1

[tex]1.225 = e^{0.0152t}[/tex]

Take natural logarithm of both sides

[tex]ln\ 1.225 = ln(e^{0.0152t})[/tex]

Rewrite as:

[tex]ln\ 1.225 = 0.0152t\ ln(e)[/tex]

[tex]ln(e) = 1[/tex]

So:

[tex]ln\ 1.225 = 0.0152t*1[/tex]

[tex]ln\ 1.225 = 0.0152t[/tex]

Make t the subject

[tex]t = \frac{ln\ 1.225}{0.0152}[/tex]

[tex]t = \frac{0.2029}{0.0152}[/tex]

[tex]t \approx 13[/tex]

Add the value of t to 2013 to get the actual year

[tex]Year = 2000 +13[/tex]

[tex]Year = 2013[/tex]

It will reach 28.3 million in 2013

Answer: 90 degrees to 120

Step-by-step explanation:

The probability of a temperature from 90 degrees to 120 degrees.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.

Probability(Event) = Favorable Outcomes/Total Outcomes = x/n

Experiment: A trial or an operation conducted to produce an outcome is called an experiment.

Sample Space: All the possible outcomes of an experiment together constitute a sample space. For example, the sample space of tossing a coin is head and tail.

Favorable Outcome: An event that has produced the desired result or expected event is called a favorable outcome. For example, when we roll two dice, the possible/favorable outcomes of getting the sum of numbers on the two dice as 4 are (1,3), (2,2), and (3,1).

Trial: A trial denotes doing a random experiment.

Given:

Temperatures from 60 degrees to 160 degrees.

As, per the situation the probability will lie between 60 degree to 160 degree.

Hence, The probability of a temperature from 90 degrees to 120 degrees.

Learn more about probability here:

https://brainly.com/question/11234923

#SPJ2

Answer:

A = $10,441.68

A = P + I where

P (principal) = $10,400.00

I (interest) = $41.68

Step-by-step explanation:

First, convert R as a percent to r as a decimal

r = R/100

r = 0.02/100

r = 0.0002 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 10,400.00(1 + 0.0002/2)(2)(20)

A = 10,400.00(1 + 0.0001)(40)

A = $10,441.68

Summary:

The total amount accrued, principal plus interest, with compound interest on a principal of $10,400.00 at a rate of 0.02% per year compounded 2 times per year over 20 years is $10,441.68.

The total amount , with compound interest on a principal of $10,400.00 at a rate of 0.02% per year compounded 2 times per year over 20 years is $10,441.68.

Compound interest is a method of calculating the interest charge. In other words, it is the addition of interest on interest.

Compound Interest =[tex]P(1+r/n)^rt[/tex]

Given that

A = $10,441.68

A = P + I

P (principal) = $10,400.00

I (interest) = $41.68

First, we need to convert R as a percent to r as a decimal

r = R/100

r = 0.02/100

r = 0.0002 rate per year,

Then we will solve the equation for A

A = [tex]P(1+r/n)^rt[/tex]

[tex]A = 10,400.00(1 + 0.0002/2)^{(2)(20)}[/tex]

A = 10,400.00(1 + 0.0001)

A = $10,441.68

Hence, The total amount , with compound interest on a principal of $10,400.00 at a rate of 0.02% per year compounded 2 times per year over 20 years is $10,441.68.

Learn more about interest here;

https://brainly.com/question/1548909

#SPJ2

Answer:

d=11.2

Step-by-step explanation:

[tex]d=\sqrt{(x2-x1)^{2}+(y2-y1)^{2} \\ }[/tex]

[tex]d=\sqrt{(6-(-4)^{2}+(-3-2)^{2} }[/tex]

[tex]d=\sqrt{10^{2}+5^{2} }[/tex]

[tex]d=\sqrt{100+25}[/tex]

[tex]d=\sqrt{125}[/tex]

[tex]d=11.18[/tex]

[tex]d=11.2[/tex]

Answer:

12345678910

Step-by-step explanation:

CHARRRRRRRRR joke lang bestie

Answer:

A) £650 = $1053

B) $405 = £250

Step-by-step explanation:

For a) Since £1 is equal to $1.62 you would just do £650 times 1.62 to get $1053

For b) Since £1 is equal to $1.62 you would do $405 divided by 1.62 to get £250

Answer:

1086ft squared

Step-by-step explanation:

Answer:

if you have the value of x then y =x +7

Answer:

We are missing a picture, we can't see the dilation they are referring to. The photo is just showing the answer options, so without the dilation it can't be answered.

Step-by-step explanation:

9514 1404 393

Answer:

  1. f^-1(x) = 4/(x+2) -2

  2. f^-1(x) = (-(x+3)/2)^(1/5)

Step-by-step explanation:

1. As with all "inverse function" problems, solve for y:

  x = f(y)

  x +2 = 4/(y +2) . . . . add 2

  y +2 = 4/(x +2) . . . . . multiply by (y+2)/(x+2)

  y = 4/(x+2) -2 . . . . . subtract 2

We see that this function is its own inverse. The attached graph shows it is symmetrical about the line y=x.

  f^-1(x) = 4/(x+2) -2

__

2. x = f(y)

  x +3 = -2y^5 . . . . add 3

  -(x +3)/2 = y^5 . . . . . divide by 2

  (-(x +3)/2)^(1/5) = y . . . . take the 5th root

  f^-1(x) = (-(x +3)/2)^(1/5)

In typeset form, that is ...

  [tex]\displaystyle f^{-1}(x)=\sqrt[5]{\frac{-(x+3)}{2}}\\\\\text{or}\\\\f^{-1}(x)=-\frac{1}{2}\sqrt[5]{16x +48}[/tex]

This last version is with the denominator "rationalized" and the contents of the radical "simplified." It may be a preferred form.

_____

The graphs show the function and inverse are symmetrical about the line y=x, as they should be.

Answer:

[tex]96 - 14[/tex]

Step-by-step explanation:

Given

[tex]Digits: 6\ 1\ 9\ 4[/tex]

Required

Fill in the blanks to get the largest subtraction

The largest subtraction is the difference between the highest possible value and the least possible value.

From the 4 given digits.

We have:

[tex]Highest = 96[/tex]

[tex]Least = 14[/tex]

So, the blanks become:

[tex]96 - 14[/tex]

And the difference is:

[tex]82[/tex] --- possible largest

Answer:

137/1000

Step-by-step explanation:

Because we have 3 numbers after 0....

hope it helps

Answer:

5^3 = 125

Step-by-step explanation:

5^3

5 x 5 x 5

=125

Answer:

[tex]5^{3} = 125[/tex]

Step-by-step explanation:

Mark me brainllest

Answer:

here's the graph

Step-by-step explanation:

Answer:(125-81.25)/125 = 0.35 = 35%

Step-by-step explanation:

Answer:

[tex]\sqrt{43}[/tex]

Step-by-step explanation:

9514 1404 393

Answer:

  90°

Step-by-step explanation:

The inscribed angle is half the measure of the arc it subtends. A semicircle is an arc of 180°. Half that is 90°.

  ? = 90°

Answer:

D

Step-by-step explanation:

This is a pythagoream thereom question, the area of a square can be found by multiplying the sides. All the sides of a sqaure are the same so we are basically sqauring the side lengths. That is where the [tex]BE^{2}[/tex] and [tex]BH^{2}[/tex] come from. The problem tells us that the area of the two small squares are equal to the one bigger square. And the area of the bigger sqaure can be found by squaring that side EH. So [tex]BE^{2}[/tex]+[tex]BH^{2} =EH^{2}[/tex].

Answer:

X = 5.9 (in degree mode)

Step-by-step explanation:

Do the following:

12(tan26) = X

Plugging this into a calculator, you will get:

X = 5.9 (in degree mode)

Answer:

3:00 p.m. in Houston.

Step-by-step explanation:

Answer: 2756 cubic inches

Step-by-step explanation:

Well, first calculate the rectangular prism: 11 x 11 x 16 = 2304

Then the cylinder: pi x 4(sqrd) x 9 = about 452

then add them together

I hope this helps! :)

Step-by-step explanation:

the last one is the answer

Answer:

1: mean equals 17.417, median is 12.75, mode is 8.2, range is 33, the minimum is 8.2 the maximum is 41.2. The IQR is 16.55, the quartiles is q1: 8.95, q2: 12.75, q3 is 25.5, there are no outliers.

2: the best middle is 12.75 because the median is usually the middle number but if you orgainze the numbers there will be two but you will end up getting 12.75 as your median. take the two middle number add together then divide by 2 then that is your answer.

Step-by-step explanation:

GOOD LUCK

Answer:

A is 14 and P is 17

Step-by-step explanation:

working is above mentioned