2x + 9
8x + 1
Solve for x

Answer:

9-8 = 1  and 7 times 2 = 14

Step-by-step explanation:

Answer:

[tex](f\ o\ g)(x) = 3x[/tex]

[tex]-\infty < x < \infty[/tex]

Step-by-step explanation:

See comment for right presentation of question

Given

[tex]f(x) = ln(x^2)[/tex]

[tex]g(x)=\sqrt{e^{3x}}[/tex]

Solving (a): (f o g)(x)

This is calculated as:

[tex](f\ o\ g)(x) = f(g(x))[/tex]

We have:

[tex]f(x) = ln(x^2)[/tex]

[tex]f(g(x)) = \ln((g(x))^2)[/tex]

Substitute: [tex]g(x)=\sqrt{e^{3x}}[/tex]

[tex]f(g(x)) = \ln(\sqrt{e^{3x}})^2[/tex]

Evaluate the square

[tex]f(g(x)) = \ln(e^{3x})[/tex]

Using laws of natural logarithm:

[tex]\ln(e^{ax}) = ax[/tex]

So:

[tex]f(g(x)) = \ln(e^{3x})[/tex]

[tex]f(g(x)) = 3x[/tex]

Hence:

[tex](f\ o\ g)(x) = 3x[/tex]

Solving (b): The domain

We have:

[tex]f(g(x)) = 3x[/tex]

The above function has does not have any undefined points and domain constraints.

Hence, the domain is: [tex]-\infty < x < \infty[/tex]

Answer:

a

Step-by-step explanation:

Answer: three dimensional figure and plane.

Step-by-step explanation:

A cross section is the intersection between a (three dimensional figure) and also a (plane).

When an object is being cut straight, the shape that we get is referred to as the cross section. We should note that several parallel cross sections will be firmed when we cut a particular object into slices.

Answer:

56.0625

Step-by-step explanation:

5 3/4x 9 3/4=56.0625

Answer:

Area = 7 km x 5 km = 35 km2 ... by either an addition, subtraction, or some other combination of operations to find the required area. ... ½ x base x height ½ x 9 x 4 = 18. Area of rectangle part: width x height 9 x 6 = 54.

Step-by-step explanation:

Answer:

1. The 90% confidence interval for the true difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2 is (-2411.84, -1332.16).

2. The point estimate for the true difference between the population means is of -1872.

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem and subtraction between normal variables.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Subtraction of Normal Variables:

When two normal variables are subtracted, the mean is the subtraction of the means while the standard deviation is the square root of the sum of the variances.

A sample of 212 brakes using Compound 1 yields an average brake life of 47,895 miles. The population standard deviation for Compound 1 is 1590 miles.

This means that [tex]\mu_1 = 47895, \sigma_1 = 1590, n = 212, s_1 = \frac{1590}{\sqrt{212}} = 109.2[/tex]

A sample of 180 brakes using Compound 2 yields an average brake life of 49,767 miles. The population standard deviation for Compound 2 is 4152 miles.

This means that [tex]\mu_2 = 49767, \sigma_2 = 4152, n = 180, s_2 = \frac{4152}{\sqrt{180}} = 309.47[/tex]

True difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2.

This is the distribution 1 - 2. So

[tex]\mu = \mu_1 - \mu_2 = 47895 - 49767 = -1872[/tex]

This is also the point estimate for the true difference between the population means, which is question 2.

[tex]s = \sqrt{s_1^2+s_2^2} = \sqrt{109.2^2+309.47^2} = 328.17[/tex]

90% confidence interval

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.

Now, find the margin of error M as such

[tex]M = zs = 1.645*328.17 = 539.84[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is -1872 - 539.84 = -2411.84

The upper end of the interval is the sample mean added to M. So it is -1872 + 539.84 = -1332.16.

The 90% confidence interval for the true difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2 is (-2411.84, -1332.16).

Answer:

[tex] m\widehat {MP} =46\degree [/tex]

Step-by-step explanation:

By inscribed angle theorem:

[tex] m\angle MQP=\frac{1}{2} \times \widehat {MP} [/tex]

[tex] 23\degree =\frac{1}{2} \times m\widehat {MP} [/tex]

[tex] 23\degree \times 2= m\widehat {MP} [/tex]

[tex] m\widehat {MP} =46\degree [/tex]

Answer:  the correct answer should be 160 but you said that didnt work so try 480

Step-by-step explanation:  

I just did base times Hight 8*10 which is 80*6=480

hoped this helps:))

Answer:

80

Step-by-step explanation:

V= Bh/3

Area of base= (L × W) ÷2

(8×6)÷2 = 24

Multiply by height

24×10=240

Divide by 3 (since its a pyramid therefore has 3 sides)

240/3=80

80 is your answer

Answer:

hey here the link it.ly/3dXyuz8

Answer: Hello, your Answer is Below ^^

Your Answer Is 6

Step-by-step explanation:

I Got the answer 6 Because 6 x 2 = 12

Tina Walked 12 blocks and Half of 12 Is 6

Hope this helps  you!

Have a great Day!

~Rainbow~

Answer:

the correct answer is 6

Step-by-step explanation:

since twice = 2 you'll need to do 12 divided by 2

which is equal to 6.

or you can simply just think what number is twice in 12.

Answer:  Le preguntaste a tu maestro?

Step-by-step explanation:

9514 1404 393

Answer:

  60

Step-by-step explanation:

Gavin has 20/4 = 5 times as many sweets as his corresponding number of ratio units. The total number of ratio units is 4+5+3 = 12, so the total number of sweets is 5×12 = 60.

There are 60 sweets altogether.

_____

They are divided as ...

9514 1404 393

Answer:

  after 2 seconds

Step-by-step explanation:

We want to find t such that h = 0.

 0 = -16t² +8t +48

  0 = 2t² -t -6 . . . . . . . divide by -8

  0 = (t -2)(2t +3) . . . . factor

The only positive solution is t = 2, which makes the first factor zero.

Stella will land in the water at t = 2 seconds.

Answer:

[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

1/3 is the fraction form of 33.3% or 0.333

Answer:

63°

Step-by-step explanation:

i=62° f+i=125° 125-62=63

Complete option:

The sample size is less than 10 percent of the population size. A. II onlyB. III onlyC. II and III onlyD. I, II, and III

Answer:

D.) I, II, and III

Step-by-step explanation:

The sample are not well randomly selected as the samples were only selected from a single source, the environmental club in the school.

Similarly only 20 samples were chosen, these 20 samples are not enough to assume normality as the minimum number of samples required to assume normality according to the Central limit theorem is 30 samples or more.

10% of the population size is :

Population size = 5000

0.10 * 5000 = 500 samples

Hence, sample size used is less than 10% of population size.

Answer:

  24 ft³

Step-by-step explanation:

The volume formula for a rectangular prism is ...

  V = LWH

  V = (4 ft)(2 ft)(3 ft) = 24 ft³

The volume of the fish tank is 24 cubic feet.

Answer:

I think the answer for the first one would be 32^2 meters for 4m × 4m and 13m. The 6m and 8m would be 48^2 meters. The second one would be 5in × 5in would be 25in and 2in × 4in would be 8in. The third one would be 6ft × 6ft × 6ft would be 48ft.

Step-by-step explanation:

To find area, you have to multiply the sides of each figure.

I hope this helps your question!

Answer:

1,863

Step-by-step explanation:

Answer:

The height is 13.3 in

Step-by-step explanation:

Pythagorean Theorem

23.5²+b²=27²

552.25+b²=729

b²=729-552.25

b²=176.75

b=√176.75

13.2947

Answer:

A,B,C

Step-by-step explanation:

Answer:

496000

Step-by-step explanation:

Did you mean milimeters? mm? if it is then it is 496 mm

9514 1404 393

Answer:

  193.5 square units

Step-by-step explanation:

The area formula for this situation is ...

  A = 1/2Pa

where P is the perimeter of the regular polygon, and 'a' is its apothem. For a pentagon, the perimeter is 5 times the side length, so the area is ...

  A = (1/2)(5×10.6)(7.3) = 193.45

To the nearest tenth, the area is 193.5 square units.

Answer:

The equation of the circle is [tex]x^2 + y^2 = \frac{1}{4}[/tex]

Step-by-step explanation:

Equation of a circle:

The equation of a circle with center [tex](x_0,y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

Centered at the the origin

Center (0,0), which means that [tex]x_0 = 0, y_0 = 0[/tex]

radius of 1/2

This means that [tex]r = \frac{1}{2}[/tex]

Equation:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

[tex](x - 0)^2 + (y - 0)^2 = (\frac{1}{2})^2[/tex]

[tex]x^2 + y^2 = \frac{1}{4}[/tex]

The equation of the circle is [tex]x^2 + y^2 = \frac{1}{4}[/tex]

Answer:

B

Step-by-step explanation:

Answer:

x^2 = -20

Step-by-step explanation:

Answer:

$17,440

Step-by-step explanation:

the interest every year

=$16,000×3%

=$16,000×3/100

=$480

the balance after 3 years

=$16,000+3($480)

=$16,000+$1,440

=$17,440