Let f (x) = x^2 + 3x + 2, and g (x) x - 6. Find and simplify: (f • g) (x)

Answer:

The possible values are a = -2.5 or a = 4.5.

Step-by-step explanation:

Composite function:

The composite function of f(x) and g(x) is given by:

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

In this case:

[tex]f(x) = 4x^2 - 8x - 20[/tex]

[tex]g(x) = 2x + a[/tex]

So

[tex](f \circ g)(x) = f(g(x)) = f(2x + a) = 4(2x + a)^2 - 8(2x + a) - 20 = 4(4x^2 + 4ax + a^2) - 16x - 8a - 20 = 16x^2 + 16ax + 4a^2 - 16x - 8a - 20 = 16x^2 +(16a-16)x + 4a^2 - 8a - 20[/tex]

Value of a so that the y-intercept of the graph of the composite function (fog)(x) is (0, 25).

This means that when [tex]x = 0, f(g(x)) = 25[/tex]. So

[tex]4a^2 - 8a - 20 = 25[/tex]

[tex]4a^2 - 8a - 45 = 0[/tex]

Solving a quadratic equation, by Bhaskara:

[tex]\Delta = (-8)^2 - 4(4)(-45) = 784[/tex]

[tex]x_{1} = \frac{-(-8) + \sqrt{784}}{2*(4)} = \frac{36}{8} = 4.5[/tex]

[tex]x_{2} = \frac{-(-8) - \sqrt{784}}{2*(4)} = -\frac{20}{8} = -2.5[/tex]

The possible values are a = -2.5 or a = 4.5.

Answer:

(1) -10, 34 and 3105

(2) 0

Step-by-step explanation:

Solving (a): Select all integers

The integers are numbers without decimal.

So, we have: -10, 34 and 3105

Other options are not integers

Solving (b): Select all integers between -3 and 4

Using the same explanation in (1) but with the range of -3 and 4. the integer is 0.

Other options are not integers

Answer:

(x+5)(x-3) / (x+5)(x+1)

Step-by-step explanation:

A removeable discontinuity is always found in the denominator of a rational function and is one that can be reduced away with an identical term in the numerator.  It is still, however, a problem because it causes the denominator to equal 0 if filled in with the necessary value of x.  In my function above, the terms (x + 5) in the numerator and denominator can cancel each other out, leaving a hole in your graph at -5 since x doesn't exist at -5, but the x + 1 doesn't have anything to cancel out with, so this will present as a vertical asymptote in your graph at x = -1, a nonremoveable discontinuity.

Answer:

1.8574 hours

Step-by-step explanation:

Solve for t.

Take the natural log of both sides.

[tex] 3000 = 75000e^{-1.733t} [/tex]

[tex] 1 = 25e^{-1.733t} [/tex]

[tex] \dfrac{1}{25} = e^{-1.733t} [/tex]

[tex] \ln \dfrac{1}{25} = \ln (e^{-1.733t}) [/tex]

[tex] -3.218875 = -1.733t [/tex]

[tex] t = 1.8574[/tex]

Answer:

Peter is a-8 in 9 years, (a-8)+ 9+ a+ 9= 76

Answer:

P = 25

A = 33

Step-by-step explanation:

P + 8 = A

P + 9 + A + 9 = 76

P + A = 58

~~~~~~~~~~~~~~

P = 58 - A

P = 58 - P - 8

2 P = 50

P = 25

A = 33

Answer:

the result gaven by dividing one number by another

Answer:

78.81%

Step-by-step explanation:

We are given;

Population mean; μ = 149

Sample mean; x¯ = 147.8

Sample size; n = 88

standard deviation; σ = 14

Z-score is;

z = (x¯ - μ)/(σ/√n)

Plugging in the relevant values;

z = (147.8 - 149)/(14/√88)

z = -0.804

From z-distribution table attached, we have; p = 0.21186

P(X > 147.8) = 1 - 0.21186 = 0.78814

In percentage gives; p = 78.81%

Answer:

14=-2x-4

18=-2x

x=-9

Hope This Helps!!!

Answer:

Call More is cheaper at 50 minutes

The two companies would charge the same for 60 minutes of use.

Talk Now is cheaper the more minutes you talk. At some point the rate of change of Call More makes it more expensive. That point is just after their costs are even.

Step-by-step explanation:

Step-by-step explanation:

SAVE

HOME HACKS & ANSWERSBUILDING & REMODELINGWALLS

How to Calculate How Many Bricks to Build a Wall

By KELVIN O'DONAHUE

Hunker may earn compensation through affiliate links in this story.

...

To estimate the number of bricks needed to build a wall, first measure a single brick.

A wall built from brick not only adds security and strength to your property, it also provides a pleasing geometric backdrop for the landscaping. Because of the bricks' size and weight, homeowners generally arrange to have the amount needed for a large project delivered by the masonry company or lumberyard. Doing so requires that you estimate the number of bricks needed before placing the order.

Step 1

Measure the length and thickness of one of the bricks that will be used in the wall. A standard brick is 2-1/4 inches wide and 7-1/2 to 8 inches long. Add 1/2 inch to both the length and thickness to account for the mortar joint between adjacent bricks. For example, a brick that is 2-1/4 inches by 7-1/2 inches, plus mortar joints, will occupy 2 3/4 inches by 8 inches.

Step 2

Measure the length of the space for the wall and convert the number to inches. Divide the length in inches by the length of a brick plus mortar joint. For example, a wall 36 feet, 8 inches long is 440 inches long (36 X 12 = 432 + 8 = 440). Each course (single layer) of bricks will need 440 / 8 = 55 bricks.

SAVE

HOME HACKS & ANSWERSBUILDING & REMODELINGWALLS

How to Calculate How Many Bricks to Build a Wall

By KELVIN O'DONAHUE

Hunker may earn compensation through affiliate links in this story.

...

To estimate the number of bricks needed to build a wall, first measure a single brick.

A wall built from brick not only adds security and strength to your property, it also provides a pleasing geometric backdrop for the landscaping. Because of the bricks' size and weight, homeowners generally arrange to have the amount needed for a large project delivered by the masonry company or lumberyard. Doing so requires that you estimate the number of bricks needed before placing the orderStep 3

Determine the desired height of the wall in inches, and divide the height by the thickness of a brick and mortar joint. For example, a wall 72 inches tall requires 26.18 courses of 2-3/4-inch-wide bricks; rounded up to 27 courses.

Step 4

Multiply the number of bricks per course (55) by the number of courses (27) to obtain the number of bricks in a single-thickness wall or veneer. For our example, the number is 1,485 bricks. Double that number for a double-thickness wall. Bricklayers generally add 5 percent to the estimate to cover broken or wasted bricks, for about 1,560 bricks in this case

Answer:

the probability that I chose red or blue is 75%

75%

Answer:

The 96% CI on the death rate from lung cancer is (0.4177, 0.4823).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

Of 1000 randomly selected cases of lung cancer, 450 resulted in death within 5 years.

This means that [tex]n = 1000, \pi = \frac{450}{1000} = 0.45[/tex]

96% confidence level

So [tex]\alpha = 0.04[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.04}{2} = 0.98[/tex], so [tex]Z = 2.054[/tex].  

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.45 - 2.054\sqrt{\frac{0.45*0.55}{1000}} = 0.4177[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.45 + 2.054\sqrt{\frac{0.45*0.55}{1000}} = 0.4823[/tex]

The 96% CI on the death rate from lung cancer is (0.4177, 0.4823).

Answer:

Answer to the first question is D. Answer to the second question is also D.

Step-by-step explanation:

First question:

All the sides of the square are equal meaning you just have to multiply 1 side by 4 to get the perimeter(all the sides added together.) If one side is (s+3) then you either add that to itself 4 times or multiply it by 4. It's the same thing so it's 4(s+3) and (s+3)+(s+3)+(s+3)+(s+3).

Second question:

Adding a negative number is equivalent to subtracting a positive number. In this case, 59.2-84.7 = 59.2+(-84.7)

Answer:

J

Step-by-step explanation:

Answer: 748,000

Step-by-step explanation: Multiply 850,000 by 0.12 and you would get 102,000 then you would subract 102,000 from 850,000 getting 748,000

Answer:

Step-by-step explanation:

This is a differential equation problem most easily solved with an exponential decay equation of the form

[tex]y=Ce^{kt}[/tex]. We know that the initial amount of salt in the tank is 28 pounds, so

C = 28. Now we just need to find k.

The concentration of salt changes as the pure water flows in and the salt water flows out. So the change in concentration, where y is the concentration of salt in the tank, is [tex]\frac{dy}{dt}[/tex]. Thus, the change in the concentration of salt is found in

[tex]\frac{dy}{dt}=[/tex] inflow of salt - outflow of salt

Pure water, what is flowing into the tank, has no salt in it at all; and since we don't know how much salt is leaving (our unknown, basically), the outflow at 3 gal/min is 3 times the amount of salt leaving out of the 400 gallons of salt water at time t:

[tex]3(\frac{y}{400})[/tex]

Therefore,

[tex]\frac{dy}{dt}=0-3(\frac{y}{400})[/tex] or just

[tex]\frac{dy}{dt}=-\frac{3y}{400}[/tex] and in terms of time,

[tex]-\frac{3t}{400}[/tex]

Thus, our equation is

[tex]y=28e^{-\frac{3t}{400}[/tex] and filling in 16 for the number of minutes in t:

y = 24.834 pounds of salt

Answer:

4, 8, 16, 32, ...

Step-by-step explanation:

8 / 4 = 2

16 / 8 = 2

32 / 16 = 2

Common ratio is 2

So, The sequence 4, 8, 16, 32, …. is geometric.

Answer:

a. If the area of the tiles is greater than or equal to the area of all the rooms.

b. 24

c. 360

Step-by-step explanation:

a. Explain how you would estimate whether Ted has enough tiles to cover all the kitchen floors in the entire apartment building?

Ted would have enough tiles if the  area of the tiles is greater than or equal to the area of all the rooms. Since we have 500 one meter square tiles, we have 500 m² of tiles.

Since the rooms are 6 m long and 4 m wide, the area of each room is 6 m × 4 m = 24 m². Since there are 15 rooms, the area of all the rooms is 15 × 24 m² = 360 m².

Since the area of the tiles = 500 m² is greater than the area of the rooms = 360 m², Ted would have enough tiles to cover all kitchen floors in the entire apartment building.

b. How many tiles, each measuring 1 square meter, are needed to cover one room floor?

Since the area of each room floor is 24 m² and the area of each tile is 1 m², so the number of  1 square meter tiles needed to cover each floor is n = area of floor/area of tile = 24 m²/1 m² = 24.

c. How many tiles are needed to cover all the floors in the entire building?

Since 24 tiles are needed to cover each floor and there are 15 rooms in the building, we would require 24 tiles/room × 15 rooms/building = 360 tiles.

So we require 360 tiles.

Answer:

10 degrees

Step-by-step explanation:

The angle bisected so that mean it was divided into 2 parts, so if it's  20 degree angles bisected it's divided by 2:

20/2= 10°

So the measure of the original angle is 10° degrees!

Answer:40

Step-by-step explanation: i took the lesson this was the answer

Step-by-step explanation:

BUC={2,3,4,5,6,7}

An(BUC)={4,6,7}

AnB={4,7},AnC={6,7}

(AnB)U(AnC)={4,6,7}

Au(BnC)={1,4,5,6,7}

(AUB)n(AUC)= {1,4,5,6,7}

Answer:

$375.25

Step-by-step explanation:

[tex]===========================================[/tex]

Withdrew- taking out money (-)

Deposit- putting in money (+)

[tex]===========================================[/tex]

Ray started off with 153.75. He withdraws (-) 71.

[tex]153.75-71=82.75[/tex]

Then he deposits (+) 292.5.

[tex]82.75+292.5=375.25[/tex]

That's your answer!

I hope this helps ❤

Answer:

Yeah the answer is n o .

Answer:

yes i do have but i dont use it

Answer:

39°

Step-by-step explanation:

A radius of a circle (segment CD) drawn to the point of tangency (D) intersects the tangent (line DE) at a 90-deg angle.

That makes m<D = 90.

m<D + m<C + m<E = 180

90 + 51 + m<E = 180

m<E = 39

Answer:

firstly we have to identify the problems, understand carefully and chose the best way to solve problems.

Answer:

5000

Step-by-step explanation:

Add the number of adults first: 27+23=50

Then multiply the number of adults by 100 for the fee.

50*100 = 5000

Answer:

within the two days a total of 5000$ where collected in the two days

Solution:

R= 100 per adult

1 adult = 100

27(R)+ 23(R) = 27(100)+ 23(100)

27(100)+23(100) =5000

or add both 27 and 23 and multiple by 100

50•100 = 5000

Answer:

Give us the picture or numbers please.

Step-by-step explanation:

Answer: add pic pls

Step-by-step explanation:

Answer:

The p-value of the test is 0.0041 < 0.05, which means that there is sufficient evidence at the 0.05 significance level to conclude that the mean cost has increased.

Step-by-step explanation:

The average undergraduate cost for tuition, fees, and room and board for two-year institutions last year was $13,252. Test if the mean cost has increased.

At the null hypothesis, we test if the mean cost is still the same, that is:

[tex]H_0: \mu = 13252[/tex]

At the alternative hypothesis, we test if the mean cost has increased, that is:

[tex]H_1: \mu > 13252[/tex]

The test statistic is:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

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

13252 is tested at the null hypothesis:

This means that [tex]\mu = 13252[/tex]

The following year, a random sample of 20 two-year institutions had a mean of $15,560 and a standard deviation of $3500.

This means that [tex]n = 20, X = 15560, s = 3500[/tex]

Value of the test statistic:

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{15560 - 13252}{\frac{3500}{\sqrt{20}}}[/tex]

[tex]t = 2.95[/tex]

P-value of the test and decision:

The p-value of the test is found using a t-score calculator, with a right-tailed test, with 20-1 = 19 degrees of freedom and t = 2.95. Thus, the p-value of the test is 0.0041.

The p-value of the test is 0.0041 < 0.05, which means that there is sufficient evidence at the 0.05 significance level to conclude that the mean cost has increased.

Answer:

Answer to the following question is as follows.

Step-by-step explanation:

Given:

a = 12500000

b = 0.00125

c = 1120000​

Calculate (ab) ÷ (c)

Given:

d) Express the interval [-1.5, 4] as an inequality and then graph

Computation:

(ab) ÷ (c) = (a)(b) / c

(ab) ÷ (c) = (12500000)(0.00125) / (1120000​)

(ab) ÷ (c) = 25 / 1,792

Express the interval [-1.5, 4]

{x : -1.5 < x ≤ 4}

Graph.

._________._________.

-1.5              0                  4