Find (f + g)(x) when f(x) = x - 2 and g(x) = 2x - 7.

Answers

Answer 1

Answer:

3x-9

Step-by-step explanation:

Just add the two together. (x-2) + (2x-7)= 3x-9


Related Questions

4) Evelyn used the proportion y/x = 5/3
when deriving the equation of a line with similar triangles. Which of these statements about the line are correct? Select two.

Answers

Using the slope-intercept form of the equation of a line, the correct statement are:

The slope of the line is 5/3

The y-intercept of the line is 0

Slope-intercept form of the equation of a line

From the question, we are to determine the statements about the given line that are correct

The given equation is

y/x = 5/3

To determine the statements that are correct, we will write the equation of the line the slope-intercept form of a line

The slope-intercept form of a line is given by

y = mx + b

Where m is the slope

and b is the y-intercept

Writing the equation in the slope-intercept form

y/x = 5/3

y = 5/3(x)

By comparing with the slope-intercept form of a line,

m = 5/3

c = 0

Thus,

The slope is 5/3

and the y-intercept is 0

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help please! will give brainlest

Answers

Answer: 20°

Step-by-step explanation:

The sum of all the interior angles of a triangle is 180°

So to find the missing angle you just need to subtract 25° and 135° from 180°, which equals 20°

All three angles in a triangle must add up to 180 degrees. So first, you add 135 and 25 which equals 160. Then to find the missing angle you subtract 160 from 180 to get 20 degrees as your final answer.

x + 25 + 135 = 180
x + 160 = 180
x = 180-160
x = 20

Help please i am stuck! More points!

Answers

Answer:

I belive it would be 102

Step-by-step explanation:

Answer:

306 cm

Step-by-step explanation:

the opposite side is the same as the shaded side

18 x 17 = 306 cm

a newsletter publisher believes that over 62% of their readers own a rolls royce. for marketing purposes, a potential advertiser wants to confirm this claim. after performing a test at the 0.02 level of significance, the advertiser decides to reject the null hypothesis. what is the conclusion regarding the publisher's claim?\

Answers

There is sufficient evidence at the 0.02 level of significance that the percentage is over 62% for hypothesis.

Given that,

Over 62% of a newsletter publisher's subscribers, in their estimation, own a Rolls-Royce. A potential advertiser wants to verify this claim for marketing purposes. The advertiser decides to reject the null hypothesis following a test with a significance threshold of 0.02 after executing the analysis.

We have to find what is the verdict in relation to the publisher's assertion.

We know that,

First we have to write the null hypothesis and alternative hypothesis for the hypothesis test.

H₀:P=0.62

H₁:P>0.62

At 0.02 level of significance, rejecting H₀ then accepting H₁.

That is sufficient evidence that percentage over 62%.

Therefore, there is sufficient evidence at the 0.02 level of significance that the percentage is over 62% for hypothesis.

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he production costs, P , for a band to have a concert can be modeled by the equation P=850+5x , where x is the number of concert tickets sold. The band earns $50 for each ticket sold. The band’s goal is for the amount earned on ticket sales minus production costs to equal $5,000 per concert. How many tickets does the band have to sell

Answers

Therefore they have to sell 130 concert tickets to equal $5,000 per concert.

What is equation?

Equations are logical statements in mathematics with two algebraic expressions on either side of the equals (=) symbol. The expressions on the left and right are demonstrated to be equal in relation to one another. All mathematical equations start with LHS = RHS (left hand side = right hand side). To find the value of an unknown variable, or unknown quantity, you can solve equations. If the statement does not contain an "equal to" sign, it is not an equation. As an expression, it will be considered. An explanation of the differences between an expression and an equation will be provided later in this essay.

Here,

P=850+5x

so the band’s goal is for the amount earned on ticket sales minus production costs to equal $5,000 per concert.

So new equation formed is

50x-P=5000

50x-(850+5x)=5000

50x-5x-850=5000

45x=5850

x=5850/45

x=130

Therefore they have to sell 130 concert tickets to equal $5,000 per concert.

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These cones are similar. Find the volume
of the smaller cone. Round to the
nearest tenth.
2 cm
Volume = [?] cm³
3 cm
Volume = 66 cm³

Answers

The volume of the smaller cone is 19.6cm³

How to determine the volume of the smaller cone

From the question, we have the following parameters that can be used in our computation:

Side length = 2 cmVolume = [?] cm³Side length = 3 cmVolume = 66 cm³

The above parameter mean that

Smaller cone

Side length = 2 cm

Volume = [?] cm³

Large cone

Side length = 3 cm

Volume = 66 cm³

The ratio of the cones can be represented as

Ratio = Side length³ : Volume

So, we have

2³ : Volume of smaller cone = 3³ : 66

Evaluate the exponents

8 : Volume of smaller cone = 27 : 66

Express as fraction

Volume of smaller cone/8 = 66/27

So, we have

Volume of smaller cone = 8 * 66/27

Evaluate

Volume of smaller cone = 19.6

Hence, the volume is 19.6cm³

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a pollster wishes to estimate the true proportion of u.s. voters who oppose capital punishment. what is the smallest number of voters that should be surveyed in order to be 95% confident that the true proportion is estimated to within 2%? (hint: use a 'worst case scenario' of p

Answers

To be 95% confident that the true proportion is calculated to within 2%, 62 voters must be questioned.

Given,

A pollster wishes to estimate the true proportion of US. voters who oppose capital punishment.

We have to find the smallest number of voters that should be surveyed in order to be 95% confident that the true proportion is estimated to within 2%

Here,

To obtain the sample size,

n = z² pq / ME²

Where,

P is the proportion of voters

M. E is the margin of error.

q is the proportion of non-voters

z is the corresponding z score

The z score for the 95% confidence interval is 1.96.

n = 1.96² pq / 0.05²

n = 1536.64 pq

If 0.2 is the proportion of voters, then 0.2 is the fraction of non-voters.

n = 1536.64 pq = 61.42

≈ 62 voters

Therefore,

62 voters can be surveyed in order to be 95% confident that the true proportion is estimated to within 2%

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What are all the prime fractions of 84?

Answers

Answer:

these are the prime factors of 84

6² subtracted 4 divided 2

Answers

Answer: For problem a is 16 and problem b is 34 i wasn't sure which problem it was so i did both

Step-by-step explanation:

problem a                                                    problem b

(6²-4)/2                        or                              6²-4/2

     |                                                                      |

[tex]6^2=36\\[/tex]                                                            [tex]6^2=36[/tex]

36-4=32                                                         36-4/2

32/2=16                                                          36-2=34

   16                                                                    34

can someone please help?
does it represent a function
yes or no

Answers

Answer:

No

Step-by-step explanation:

Functions must have only one answer for each x. However, in all the x values in this graph there are two answers.

No since there are 2 answers

4. suppose ches tahoe restaurant is one of the 7 largest restaurants in x city. a. you would like to choose two different restaurants from them. how many different ways are there? (5 points) b. you would like to choose two different restaurants. one is for your lunch and the other one is for your dinner. how many different ways are there? (5 points) c. you would like to choose two restaurants. one is for your lunch and the other one is for your dinner. you are ok for going to the same restaurants. how many different ways are there? (5 points)

Answers

(a) There are 21 different ways to choose two different restaurants.

(b)There are 42 different ways to choose two different restaurants.

(c) There are 49 different ways to choose two different restaurants.

In the given question,  suppose Ches Tahoe restaurant is one of the 7 largest restaurants in x city.

a. We would like to choose two different restaurants from them. So we have to find how many different ways are there.

There are total 7 largest restaurants in x city.

We have to choose two different restaurants.

So different ways:

n = [tex]^{7}C_{2}[/tex]

Using, [tex]^{n}C_{r} = \frac{n!}{r!(n-r)!}[/tex]

n = [tex]\frac{7!}{2!(7-2)!}[/tex]

After solving

n = 21

There are 21 different ways to choose two different restaurants.

b. We would like to choose two different restaurants. one is for our lunch and the other one is for our dinner. We have to find how many different ways are there.

There are total 7 largest restaurants in x city.

We have to choose two different restaurants one for our lunch and the other one for our dinner.

So different ways:

n = [tex]^{7}P_{2}[/tex]

Using, [tex]^{n}P_{r} = \frac{n!}{(n-r)!}[/tex]

n = [tex]\frac{7!}{(7-2)!}[/tex]

After solving

n = 42

There are 42 different ways to choose two different restaurants.

c. We would like to choose two restaurants. one is for your lunch and the other one is for your dinner. We are OK for going to the same restaurants. We have to find how many different ways are there.

There are total 7 largest restaurants in x city.

We have to choose two different restaurants one is for your lunch and the other one is for your dinner OK to the same

So different ways:

n = (7)^2

n = 49

There are 49 different ways to choose two different restaurants.

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The solution of the equation 2x+4=3x-62x+4=3x−6 is x =

Answers

the answer , answer :45xy

Which equation has the same solution as 4-2(x-5)=x-19
(A) 2(x+5)= -8.
(B) 3(x-3)=9
(C) x+2=2x-3
(D) 3x-4=2x+7

Answers

Answer:

3x-4=2x+7 thus: (D)

x = 11

Step-by-step explanation:

Solve for x:

3 x - 4 = 2 x + 7

Subtract 2 x from both sides:

(3 x - 2 x) - 4 = (2 x - 2 x) + 7

3 x - 2 x = x:

x - 4 = (2 x - 2 x) + 7

2 x - 2 x = 0:

x - 4 = 7

Add 4 to both sides:

x + (4 - 4) = 4 + 7

4 - 4 = 0:

x = 7 + 4

7 + 4 = 11:

Answer: x = 11

___________________________

Solve for x:

4 - 2 (x - 5) = x - 19

-2 (x - 5) = -2 x + 10:

(-2 x + 10) + 4 = x - 19

Add like terms. 4 + 10 = 14:

-2 x + 14 = x - 19

Subtract x from both sides:

(-2 x - x) + 14 = (x - x) - 19

-2 x - x = -3 x:

-3 x + 14 = (x - x) - 19

x - x = 0:

-3 x + 14 = -19

Subtract 14 from both sides:

(14 - 14) - 3 x = -14 - 19

14 - 14 = 0:

-3 x = -14 - 19

-14 - 19 = -33:

-3 x = -33

Divide both sides of -3 x = -33 by -3:

(-3 x)/(-3) = (-33)/(-3)

(-3)/(-3) = 1:

x = (-33)/(-3)

The gcd of -33 and -3 is -3, so (-33)/(-3) = (-3×11)/(-3×1) = (-3)/(-3)×11 = 11:

Answer: x = 11

Answer:3x-4=2x+7

Step-by-step explanation:

first,  4-2x+10=x-19

        14+19 =x+2x

           33=3x

               x=11

A. 2x+10=8

    2x= -18

      x=-9

B. 3x-9=9

       3x=18

         x=6

C. x+2=2x-3

      3x = 5

         x = 5/3

D. 3x-4 = 2x+7

    3x-2x=7+4

          x=11

evaluate √24−x when x = 6. write the answer in simplified radical form.

Answers

Given √24−x when x = 6 in simple radical form is 3*√2.

What is radical form?

Simply put, simplifying a radical eliminates the need to find any further square roots, cube roots, fourth roots, etc.

Additionally, it entails eliminating any radicals from a fraction's denominator.

The square root of 2 or root 2 is represented using the square root symbol √ and written as √2 whose value is 1.414.

So, we have:

√24−x when x = 6
Thus we must now calculate the square root of 18.

The square root, if you're allowed to use a calculator, is 4.242.

If not, however, let's come as close as we can:

√(9 * 2)

Since 3 is the square root of 9:

3*√2

Therefore, given √24−x when x = 6 in simple radical form is 3*√2.

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Find the value of x so that the ratios are equivalent.
x: 5/2 and 8:10

Answers

The value of x in the given ratio is 2.

What is ratio?

The relationship in quantity, amount, or size between two or more things.

Given is a ratio, x:5/2 = 8:10

x/5/2= 8/10

2x/5 = 8/10

2x = 40/10

2x = 4

x = 2

Hence, The value of x in the given ratio is 2.

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many states run lotteries, giving away millions of dollars if you match a certain set of winning numbers. how are those numbers determined? do you think this method guarantees randomness? explain.

Answers

The method to determine the numbers is random only if the balls generate numbers in equal frequencies.

The entire process is random and is not generated by a computer or humans.

One of the most important requirements for a random number is independence, as this aids in the establishment of no correlations between successive numbers. It must be ensured that the frequency of occurrence of these random numbers is roughly the same. As a result, it is theoretically difficult to generate a long random number.

The frequency of a repeating event is the number of occurrences per unit of time. It is distinct from angular frequency and is sometimes referred to as temporal frequency. The frequency is expressed in hertz (Hz), which equals one event per second. Because the period is the time interval between events, it is the reciprocal of the frequency.

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Solve for y

6/8 = 15/y

Answers

Answer:

The answer is 20

Step-by-step explanation:

6/8 = 15/y

(6) × y = (8) × (15)

6y = 120

6y/6 = 120/6

y = 20

Thus, The value of y is 20

Answer:

[tex] \sf \: y = 20[/tex]

Step-by-step explanation:

Given equation,

[tex] \sf \rightarrow \: \frac{6}{8} = \frac{15}{y} [/tex]

Now the value of y will be,

[tex] \sf \rightarrow \: \frac{6}{8} = \frac{15}{y} [/tex]

[tex] \sf \rightarrow \: 6y = 15 \times 8[/tex]

[tex] \sf \rightarrow \: 6y = 120[/tex]

[tex] \sf \rightarrow \: y = \frac{120}{6} [/tex]

[tex] \sf \rightarrow \boxed{ \sf y = 20}[/tex]

Hence, the value of y is 20.

Which graph represents the solution set to 2x+3y<6

Answers

On solving the provided graph question, we got to know that - the area below the line will be taken into account.

what are graphs ?

Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph.

Given : equation  2x + 3y ≤ 6

Out of the options provided, we must select the graph that displays the graph of the solution set for the equation 2x + 3y 6.

Consider the given equation   2x + 3y ≤ 6

We first find the points where the equation cut x- axis and y-axis.

Thus,

[tex]For x - axis put y = 0 ,\\We get 2x + 3(0) \leq 6 =2x \leq 6 x \leq 3\\Thus, point (3,0)\\For y - axis put x = 0 ,\\We get 2(0) + 3y \leq 6 = 3y \leq 6 = y \leq 2\\Thus, point (0,2)[/tex]

For each region, we select a test point, determine the values of x and y there, and then determine whether or not the inequality is satisfied.

Take into account the point (0, 0), and inequality becomes,

[tex]2(0) + 3(0) \leq 6 = 0 \leq 6 (true)\\[/tex]

So, the area below the line will be taken into account.

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10. Olive Street crosses two parallel railroad tracks, as shown below
Railroad tracks
30°
Answer
What is the measure of Z1? [2 pts]
Show your work.
2
degrees
1
-Olive Street

Answers

The measure of angle 1 is given as follows:

m < 1 = 150º.

How to obtain the measure of angle 1?

From the image given at the end of the answer, we have that two Railroad tracks are transversal to the Olive Street.

Considering that Olive Street is transversal to the parallel lines, we have that the angle 2 forms a linear pair with the angle of 30º.

Linear pairs are supplementary angles, meaning that the sum of their measures is of 180º, hence the measure of angle 2 is given as follows:

m < 2 + 30º = 180º

m < 2 = 180º - 30º

m < 2 = 150º.

Now we have that angles 1 and 2 are alternate interior angles, as they are between the two parallel lines, on the opposite side of the transversal.

Alternate interior angles are congruent, meaning that the measure of angle 1 is given as follows:

m < 1 = 150º.

Missing Information

The diagram is given by the image shown at the end of the answer.

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a survey of middle school students asked: what is your favorite winter sport? the results are summarized below. using these 545 students as the sample space, a student from this study is randomly selected. if the student selected is an 8th grade student, what is the probability that the student prefers skiing or ice-skating?

Answers

The probability that the chosen student, a grade 8 student, likes skiing over ice skating is 53.89%.

Given that,

A survey of middle school students asked what is your favorite winter sport so they have given the result in the table we can see.

Below is a summary of the findings. A participant from this study is chosen at random from among these 545 students, who serve as the sample space.

We have to find what is the probability that the chosen student, a grade 8 student, likes skiing over ice skating.

The total 8th grade are 180

The skiing are 171

The ice skating are 163

Probability = 180/(171+163) = 0.5389 = 53.89%

Therefore, the probability that the chosen student, a grade 8 student, likes skiing over ice skating is 53.89%.

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Consider w₁ = -3i and w₂ = -2. What is the result of subtracting w₂ from w₁?

Answers

The result after subtracting w2 from w1 is -3i+2

Given that,

w1=-3i

w2=-2

So,

w1 -w2= -3i-(-2)

         =-3i+2

Here w1 is a complex number and w2 is a normal number. And we know that we can add or subtract a complex number only with a complex number only. And a normal number with a normal one only.

Therefore, the result after subtracting  w2 from w1 is -3i+2.

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Equation for

You have c pieces of candy to share equally among 5 people. If
each person gets 32 pieces of candy, how much candy did you start
with?

Answers

Answer:

53 candy

Step-by-step explanation:

Spontaneous dental hydroplosion is a disease makes your teeth spontaneously turn into liquid. To investigate whether a new drug can prevent the onset of this disease, Jim Halpert decided to perform a study in which half of the fourteen employees at Dunder Mifflin Scranton received the drug and the other half received a placebo. Neither Jim nor the employees were told who received which treatment, and the number of times a subjectâs teeth turned into liquid was recorded. This is an example of (A) A double-blind experiment. (B) A matched-paired experiment. (C) An experiment, but neither double-blind or matched-pair. (D) An observational study. In order to make thorough conclusions, the most important condition for statistical inference is usually that (A) the population distribution follows a Normal distribution exactly. (B) the data does not contain outliers. (C) the data follows the asymmetric, single-peaked distribution. (D) the data can be treated as a random sample from the population of interest. A study was taken at the large senior living retirement community, The Senior Living Community, found that the average age of residents is 73 years with a standard deviation of 6.1 years. A simple random sample of 100 residents is selected and the sample mean age !Ì("x-bar") of these residents is calculated. you know that the random variable X has approximately a normal distribution because of (A) the central limit theorem. (B) the 68-95-99.7 rule. (C) the population that youâve sampled from does not have a Normal distribution. (D) the law of large numbers.

Answers

For the study for investing the result of drugs in a particular diseases,

(1)This is an example of double blind experiment. So,correct option is option A

(2) The Correct option is option (C) i.e. the data can be treated as a random sample from the population of interest.

(3) The random variable X has approximately a normal distribution because of Central Limit Theorem i.e the Correct option is option (A).

Here , Spontaneous hydrostatic collapse is a disease in which teeth spontaneously turn into fluid. Jim Halpert decided to perform a study to find out if new drugs can prevent the development of this disease.

1. Since, neither researcher nor the employees were told who received which treatment, this is an example of a double-blind experiment.

2. In order to make thorough conclusions, the most important condition for statistical inference is usually that data can be treated as a random sample from the population of interest.

3. The sample mean age, X-bar of these residents has approximately a normal distribution because of the central limit theorem. Hence, we get all required answers for asking questions.

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cs 2050 has 9 recitation sections. 6 of the recitation sections are led by a pair of tas, and 3 recitation sections are led by a trio of tas. there are also 5 tas who do not teach recitation. how many ways are there to line up all of the tas such that each ta with recitation partner(s) is standing next to them?

Answers

504 ways are there to line up all of the tas such that each tas with recitation partner(s) is standing next to them

Given :

cs 2050 has 9 recitation sections. 6 of the recitation sections are led by a pair of tas, and 3 recitation sections are led by a trio of tas. there are also 5 tas who do not teach recitation.

Number of ways = 9P6 * 9C3 * 1 / 5!

= 9! / ( 9 - 6 ) ! * 9! / ( 9 - 3 ) ! * 1 / 5!

= 9! / 3! * 9! / 6! * 1/5!

= 9 * 8 * 7 * 6 / 3 * 2 * 9 * 8 * 7

= 9 * 8 * 7

= 504 ways

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(9x-6)ln(3)=(12x-8)ln(4)
solve for x with steps

Answers

Answer:

x = 2/3

Step-by-step explanation:

ln3^(9x-6)  = ln4^(12x-8)

9x - 6 = 12x - 8

12x - 9x = -6 + 8

3x = 2

3/3 x = 2/3

x = 2/3

you are selling tickets for a high school play. student tickets cost $4 and general admission tickets cost $6. you sell 31 tickets and collect $170. write the system of equations that could be used to determine the number of student tickets, s, and the number of general admission tickets, g, were sold for the high school play. how many student tickets did you sell?

Answers

As tickets are selling for a high school play. student tickets cost $4 and general admission tickets cost $6 and sell 31 tickets and collect $170.

Therefore, the system of equation is

8$4 + 23$6 = $32 + $138 = $170 total

A system of equations is a set of one or more equations with many variables. A solution to a system of equations is a variable map such that all component equations are satisfied. That is, the point where all those equations intersect.

Given that :

Ticket cost = $ 4 and $6

and collection = $170.

Now,

        4S+6G = 170                ------------------------ (1)

            S+G = 31                  -----------------------  (2)

Therefore,  subtract from 1st equation to eliminate one variable:

4S+ 4G = 124    ----------------------------- (3)

Now,

  2G = 46

⇒ G = 23 tickets

putting G = 23 in equation(2)

S = 31-23

  = 8 student tickets

The system of equation is:

8$4 + 23$6 = $32 + $138

                    = $170 total

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In AGHI, GI is extended through point I
to point J, m/IGH = (x+16)°,
m/HIJ = (4x – 12)°, and
m/GHI= (x +10)°. Findm/GHI.

Answers

Applying the exterior angles theorem, the measure of angle GHI is: 29°.

What is the Exterior Angle Theorem?

The Exterior Angle Theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.

In other words, if a triangle, for example triangle GHI, has angles G, H, and I, and angle HIJ is the exterior angle formed by extending side GI through point I to point J, then the measure of angle HIJ is equal to the sum of the measures of angles IGH and GHI.

Given the following:

m<IGH = (x+16)°,

m<HIJ = (4x – 12)°,

m<GHI= (x +10)°

Therefore:

m<HIJ = m<IGH + m<GHI

Substitute:

4x - 12 = x + 16 + x + 10

4x - 12 = 2x + 26

4x - 2x = 12 + 26

2x = 38

2x/2 = 38/2

x = 19

m<GHI= (x +10)° = 19 + 10 = 29°

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Select all the coefficients in the simplified form of (4y + 5y2-6) - (5y + 27-2²).
A -1
B. 4
C. 5
D. 6
E. 33

Answers

The coefficient of x²  in simplified form is 5

What is coefficient ?

A coefficient in mathematics is a multiplicative factor in a polynomial term, a series term, or an expression. It is typically a number, but it can also be any expression. They may also be referred to as parameters if the coefficients are variables in and of themselves.

a symbol or number that multiplies another symbol or number (used as a mathematical variable). The coefficient of x in the phrase 3x is 3, and it is a number that represents a quality (such as the metal's coefficient of expansion) of a substance or device.

(4y + 5y² - 6) - (5y + 27 - 2²)

4y + 5y² - 6 - 5y - 27 + 4

5y² - 1y - 29

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(Solving Equations Using Square and Cube Roots LC)

Solve y3 = −1.

y = −0.5
y = 0.5
y = −1
y = ±1

Answers

Answer:

Step-by-step explanation:

J Square Roots and Cube Roots To find the square root of a number, you want to find some number that when multiplied by itself gives you the original number. In other words, to find the square root of 25, you want to find the number that when multiplied by itself gives you 25. The square root of 25, then, is 5. The symbol for square root is equation.

mr. crandall has assigned a term paper due at the end of the semester. he would like to know the average length of the paper. the data below are the numbers of typed pages from a random sample of 10 term papers. what type of critical value is needed to create a 95% confidence interval for the population mean length of all term papers for this class?

Answers

There is a 95% chance that the mean length of all term papers lies between confidence limits (11.58,17.82) for the given data:

14, 20, 25, 10, 16, 8, 15, 12, 18, 9

We assume the length of paper has an approximately normal distribution.

Sample size = 10

The sample mean for the given data = 14.7

The standard deviation for the given data = 5.04

Critical value is obtained from standard normal distribution at the level of significance 0.05.

The critical value is 1.96.

The 95% confidence interval for the mean length of all term papers is calculated as follows:

P(14.7 - (1.96 x (5.04/√10)) < µ < 14.7 + (1.96 x (5.04/√10))) = 0.95

P(11.58 < µ < 17.82) = 0.95

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