If f(x)=x²+5 and g(x)=3x, find (f . g)(x) and (g . f)(x).

(f . g)(x)= _____ (Simplify your answer.)

x = 1/2, x = -1/2

Simplify:

4|x| + |-4| = |-6|

4|x| + 4 = 6

4|x| = 2

|x| = 1/2

Solutions:

1) x = 1/2

2) x = -1/2

Answer:

Step-by-step explanation:

Linear functions are represented by the following expression:

m is the constant rate of change of the function, and it's calculated as the change in y over the change in x:

The y-intercept of a linear function is when the line crosses the y-axis, which means when x=0.

Therefore, the y-intercept of the line is 15.

a. 20.31% of New York's high school teachers earn between 83,000 and 88,000

b.  18.49% of New York teachers earn between 88,000 and 103,000

c. 1.19%  of New York’s state high school teachers earn less than 73,000

Given,

The salary for high school teachers in 2017 = 97010

Standard deviation = 9540

Consider salaries as normal distribution.

Here,

Mean, μ = 97010, Standard deviation, σ = 9540

a. Percentage of New York's high school teachers earn between 83,000 and 88,000

The proportion is the p-value of Z when X = 88,000 subtracted by the p-value of Z when X = 83,000.

That is,

X = 88,000

Z = (X - μ) / σ = (88,000 - 97010) / 9540 = -9010/9540 = -0.944

The p value of z score - 0.944 is 0.3452

Next,

X = 83,000

Z = (X - μ) / σ = (83,000 - 97010) / 9540 = -14010/9540 = -1.468

The p value of z score - 1.468 is 0.1421

Then,

0.3452 - 0.1421 = 0.2031 = 20.31%

That is,

20.31% of New York's high school teachers earn between 83,000 and 88,000

b. Percentage of New York teachers earn between 88,000 and 103,000

The proportion is the p-value of Z when X = 103,000 subtracted by the p-value of Z when X = 88,000

X = 103,000

Z = (X - μ) / σ = (103,000 - 97010) / 9540 = 5990/9540 = 0.6279

The p value of z score 0.6279 is 0.5301

Next,

X = 88,000

Z = (X - μ) / σ = (88,000 - 97010) / 9540 = -9010/9540 = -0.944

The p value of z score - 0.944 is 0.3452

Then,

0.5301 - 0.3452 = 0.1849 = 18.49%

That is,

18.49% of New York teachers earn between 88,000 and 103,000

c.  Percentage of new York’s state high school teachers earn less than 73,000

The proportion is the p-value of Z when X = 73000

X = 73,000

Z = (X - μ) / σ = (73,000 - 97010) / 9540 = -24010/9540 = -2.516

The p value of z score - 2.516 is 0.0119

That is,

1.19%  of New York’s state high school teachers earn less than 73,000

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The fisrt part is the divide your angle into two angles, could be 6/12π and 5/12π

For the sum formula:

For the difference formula:

Both methods work and result in the same answeer

The monthly rate of change in demand is -$40.7.

The slope of a graphed function is determined using the average rate of change formula. The method for finding the slope is differentiation.

A price-demand relation equation is given.

2x²-5xp + 55p²=23,200.

Differentiate the given equation with time

[tex]\begin{aligned}&4 x \frac{d x}{d t}-5\left(x \frac{d p}{d t}+p \frac{d x}{d t}\right)+110 p \frac{d p}{d t}=0 \\&4 x \frac{d x}{d t}-5 p \frac{d x}{d t}=5 x \frac{d p}{d t}-110 p \frac{d p}{d t} \\&(4 x-5 p) \frac{d x}{d t}=(5 x-110 p) \frac{d p}{d t} \\&\frac{d x}{d t}=\frac{(5x-110 p)}{(4 x-5p)} \frac{d p}{d t}\end{aligned}[/tex]

Put the value of p in the original equation.

For p=20

[tex]2x^{2} -5x\times 20+ 55\times20^{2}=23200\\2x^{2}-100x+22000=23200\\2x^{2}-100x-1200=0\\x^{2}-50x-600=0\\x=60 \text{ or }-10[/tex]

Since the price can not be negative, x=60.

Putting these values in the differential equation.

[tex]\frac{d x}{d t}=\frac{(5 x-110 p)}{(4 x-5 p)} \frac{d p}{d t}\\=\frac{(5\times60-110\times 20)}{(4\times60-5 \times20)} \times3\\=\frac{300-2200}{140}\times3\\ =-40.7[/tex]

So, the monthly rate of change in demand is -$40.7.

The minus sign indicates that demand is decreasing.

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Explanation:

We are told that the rate at which the pump dumps the pollutant per day to be

To solve the question, let us assume that t is the number of days

So, to find the amount dumped after 3 days, we will put t =3 into the equation

Therefore, the answer is 0.115

2x=-1+6

2x=5

x=3

so the answer is 3

P(A∪B) = P(A) + P(B) - P(A∩B)

where P(A) is the probability of A happening

P(B) is the probability of B happening

P(A∪B) is the probability of A or B happening

P(A∩B) is the probability of A and B happening

P(A) = 0.5, P(B) = 0.65 and P(AUB) = 0.75

.75 = .5+ .65 - P(A∩B)

.75 =1.15 - P(A∩B)

.75 - 1.15 = -P(A∩B)

-.4 = -P(A∩B)

.4 =P(A∩B)

P(A∩B) = .4

Given:

GCF of 24 and 12.

Given

To find:

Explanation:

It is given that,

That implies,

Answer:  600 divided by 2 + 40

Step-by-step explanation:

Answer:

2x + 40 = 600

2x = 560

x = 280.

Your friends guitar costs $280.

Step-by-step explanation:

Set the equation equal to $600, the cost of the new guitar. Let the variable, x, represent the cost of your friends guitar. Since your guitar was + 40 more than double the cost of your friend’s, this can be written as an equation:

2x + 40 = 600

Using the z-distribution, it is found that the 95% confidence interval is (0.45 , 0.52), and it does not provide strong evidence against that belief.

A confidence interval of proportions is given by:

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

where [tex]\pi[/tex] is the sample proportion, z is the critical value and n is the sample size.

In this problem, we have 95% confidence level, hence [tex]\alpha[/tex] = 0.95, z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2}[/tex] = 0.975, so the critical value is z = 1.96

We have that a random sample of 860 births in a state included 423 boys, hence the parameters are given by:

n = 864, [tex]\pi =\frac{423}{860}[/tex] = 0.49

Then the bounds of the interval are given by:

[tex]\pi[/tex] + [tex]z\sqrt{\frac{\pi (1-\pi )}{n} }[/tex] = 0.49 + [tex]1.96\sqrt{\frac{0.49(0.513)}{860} }[/tex] = 0.52

[tex]\pi[/tex] - [tex]z\sqrt{\frac{\pi (1-\pi )}{n} }[/tex] = 0.49 - [tex]1.96\sqrt{\frac{0.49(0.513)}{860} }[/tex] = 0.45

The 95% confidence interval estimate of the population of boys in all births is (0.45 , 0.52). Since the interval contains 0.513, it does not provide strong evidence against that belief.

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Answer:

28.26 square inches.

Explanation:

Given a waffle cone with the following properties:

• Height = 6 inches

• Volume = 56.52 cubic inches.

Note that the base of the cone is a circle and the area of a circle:

Substitute the given values:

The area​ of the base is 28.26 square inches.

The given scatter plot points are increasing, indicating a rise in data points, direction oriented to the right and the strength of scatter plot points correlation is moderately strong.

A graph with dots is shown to indicate the relationship between two sets of data.

According to the given scatter plot, the scatter plot points are increasing, indicating a rise in data points, and we may conclude that the correlation is positive.

The scatter plots are now oriented to the right. As a result, we may claim that the correlation is moderately strong.

Thus. the given scatter plot points are increasing, indicating a rise in data points, direction oriented to the right and the strength of scatter plot points correlation is moderately strong.

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We are asked to determine the probability of rolling a 6 and then rolling a number less than 2. To do that we will use the product rule probabilities since we want to find the probability of two independent events happening:

Where:

To determine the probability of rolling a 6 we need to have into account that there are 6 possible outcomes out of which only one is a 6. Therefore, the probability is:

To determine the probability of B we need to have into account that in a 6-sided die the numbers that are less than 2 are (1), this means that there is only one number less than 2 out of 6 possible numbers. Therefore, the probability is:

Now, we substitute in the product rule:

Solving the product:

Therefore, the probability is 1/36.

SOLUTION

Notice that line BA is a radius of the circle.

Since line BC is a tangen then the measure of angle ABC is:

Using Triangle Angle-Sum Theorem, it follows:

This gives:

Solving the equation gives:

Therefore the required answer is:

Quadratic formula

Where a is the coefficient of the first term, b the coefficient of the second term and c the coefficient of third term

a)

replacing on the quadratic formula

simplify

x has two solutions

b)

rewrite on general form

raplace on quadratic formula

simplify

x has two solutions

A graph's domain, which is defined as the entire set of input values visible on the x-axis, refers to the set of possible input values. The possible output values are displayed on the y-axis and make up the range.

Asymptotes are a distinctive feature of the graphs of rational functions. When a curve is nearing the edges of a coordinate plane, it is said to be asymptote. A rational function's vertical asymptotes happen as its denominator gets closer to zero.

In order to cross a vertical asymptote, a rational function must divide by one, which is impossible. When the x-values increase significantly in size, either positively or negatively, horizontal asymptotes develop. You can pass through horizontal asymptotes.

A vertical asymptote of a graph is a vertical line with the equation x = a, where the graph tends toward positive or negative infinity as the inputs get closer to a.

A graph's horizontal asymptote is a horizontal line, y = b, where the graph moves toward the line as the inputs move toward ∞+ or ∞-.

Three problem about finding DOMAIN, X-intercept, Y-intercept, Vertical Asymptote, Horizontal asymptote

1) Determine the vertical asymptote(s), horizontal or slant asymptote, x-intercept(s), y-intercept, and domain. Then, sketch a graph of the function on the given set of axes. Label all asymptotes and intercepts.

[tex]m(x) = \frac{3x^2 -12}{x^2 -7x + 6}[/tex]

2) Determine the Domain, Y-intercept, x-intercept(s), Vertical Asymptote(s), and Horizontal Asymptote, if the exist: Include the multiplicity of the x-intercepts if the multiplicity is greater than 1. Then graph the ratio function.

[tex]v(x) = \frac{3x - 1}{x^2+5x +6}[/tex]

3) What are the Domain, x-intercept, y-intercept, vertical asymptote and horizontal asymptote of the rational function [tex](x^3-x+12/x^2-3x-4)[/tex]?

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We are required to write the expression:

Without exponents. First, we operate the parentheses:

This is the simplified expression. If we wanted to avoid the exponents, then we have to express the exponents as products:

This is the required expression

$12180 the insurance company must set aside now at 6% interest compounded semiannually to pay this obligation to Apollo.

This is a problem from the compound interest system. We can solve this problem by following a few steps.

Apollo Enterprises has been awarded an insurance settlement of $6,000 at the end of each 6-month period for the next 12 years with a 6% interest rate. We have to calculate the total amount after 12 years.

To solve this problem we should know the formula for the compound interest method.

Formula:-

A = P {(1 + r/n)^(n.t)}

Here,

Now, we can calculate the value of A.

A = 6000 {( 1 + 6/200 )^2.12} = 6000 ( 1 + 6/200 )^24 = 6000 × 2.03 = 12180

Therefore, the total amount after 12 years is $12180

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Answer:

To get the additive inverse of a positive number you put a minus in front of it and to get the additive inverse of a negative number, you remove the minus to make it a positive number.

Answer:

4

Step-by-step explanation:

By the exterior angle theorem,

[tex]27x+2=65+10x+5 \\ \\ 27x+2=10x+70 \\ \\ 17x=68 \\ \\ x=4[/tex]

In order to find the new bank account balance, we can do a sum of all the deposits and subtraction of all withdrawals to the old balance account,

Mark's height last year was 46 inches.

Mark definitely grows over the past year. Let the height he grew be x.

Then, Mark's new height will be

Let us represent Mark's height with M and Peter's height with P.

This means that

and, from the question, Peter's height is

The question says that Mark's height is 3 inches less than Peter's height. This we can write as

Therefore, if we put Mark's and Peter's ages into equation c, we can find a value for x as follows:

Since 46 + x = M, then Mark's height is 48 inches

Step-by-step explanation:

this is very much doing the exact same things as the previous question, just with a little bit different numbers.

remember, gradient = slope.

the slope is always the factor of x in the slope-intercept form

y = ax + b

our in the point-slope form

y - y1 = a(x - x1)

"a" is the slope, b is the y-intercept (the y- value when x = 0).

(x1, y1) is a point on the line.

the slope is the ratio (y coordinate change / x coordinate change) when going from one point on the line to another.

a)

y = 2x + 7

b)

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

y = -2x + 8

c)

going from (2, 3) to (-1, 2)

x changes by -3 (from 2 to -1)

y charges by -1 (from 3 to 2)

the slope is -1/-3 = 1/3

we use one of the points, e.g. (2, 3)

y - 3 = (1/3)×(x - 2) = x/3 - 2/3

y = x/3 - 2/3 + 3 = x/3 - 2/3 + 9/3 = x/3 + 7/3

d)

y = 5

this is a horizontal line (parallel to the x-axis) and represents every point on the grid, for which y = 5.

the slope is 0/x = 0, as y never changes at all.

the y- intercept is 5, of course.

Answer:

[tex]\textsf{a) \quad $y=2x+7$}[/tex]

[tex]\textsf{b) \quad $y=-2x+8$}[/tex]

[tex]\textsf{c) \quad $y=\dfrac{1}{3}x+\dfrac{7}{3}$}[/tex]

[tex]\textsf{d) \quad $y=5$}[/tex]

Step-by-step explanation:

Slope-intercept form of a linear equation:

[tex]y=mx+b[/tex]

where:

Given values:

Substitute the given values into the formula to create the equation of the line:

[tex]\implies y=2x+7[/tex]

---------------------------------------------------------------------------

Point-slope form of a linear equation:  

[tex]y-y_1=m(x-x_1)[/tex]

where:

Given:

Substitute the given values into the formula to create the equation of the line:

[tex]\implies y-4=-2(x-2)[/tex]

[tex]\implies y-4=-2x+4[/tex]

[tex]\implies y=-2x+8[/tex]

---------------------------------------------------------------------------

Slope formula:

[tex]\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

where (x₁, y₁) and (x₂, y₂) are points on the line.

Given points:

Substitute the points into the slope formula to calculate the slope of the line:

[tex]\implies m=\dfrac{2-3}{-1-2}=\dfrac{-1}{-3}=\dfrac{1}{3}[/tex]

Substitute the found slope and one of the points into the point-slope formula to create the equation of the line:

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-3=\dfrac{1}{3}(x-2)[/tex]

[tex]\implies y-3=\dfrac{1}{3}x-\dfrac{2}{3}[/tex]

[tex]\implies y=\dfrac{1}{3}x+\dfrac{7}{3}[/tex]

---------------------------------------------------------------------------

Slope-intercept form of a linear equation:

[tex]y=mx+b[/tex]

where:

If the line is parallel to the x-axis, its slope is zero.

If the line intersects the y-axis at y = 5, then its y-intercept is 5.

Therefore:

Substitute the given values into the formula to create the equation of the line:

[tex]\implies y=0x + 5[/tex]

[tex]\implies y=5[/tex]

The Scalar and Cross Product of Vectors

Given two vectors:

The scalar product is defined as:

The cross product is the result of computing the following determinant:

Where i, j, and k are the unit vectors in each of the directions x, y, and z, respectively.

This concept will be applied to the following physics problem.

Given a force F= (2, 3, 0) and the distance vector d = (4, 0, 0), the torque is defined by:

Calculating:

Calculating the determinant:

Expressing in vector form τ = (0, 0, 12) <= should use angle brackets

The magnitude of the torque is:

The power P is equal to the scalar product of the torque by the angular velocity w. We are given the angular velocity w = (3, 3, 2), thus:

P = 24

Answer:

813.75  can you have .75 of a real?  if not, then 813

Step-by-step explanation:

175 x 4.65 = 813.75

Answer: {(1,3),(1,4),(2,3),(2,4)}

Step-by-step explanation:

Step -1: Define the Cartesian product.

              Cartesian product: If A and B are two non empty sets, then  

              Cartesian product A×B is set of all ordered pairs (a,b) such that a∈A and b∈B.

Step -2: Find the Cartesian product of given sets.

              We have given,

              A={1,2} and B={3,4}

              So, A×B={(1,3),(1,4),(2,3),(2,4)}

Hence, option A. {(1,3),(1,4),(2,3),(2,4)} is correct answer.

The graph's range is 0 to M plus or minus 5.5.

The set of graph output values that make up a function's range.

This means that the set of y values in the graph is the range of a function.

The domain

We can observe the following on the function's graph:

The x values range from zero to seven and a half.

This indicates that the domain is 0=x=7.5.

The range

We can observe the following on the function's graph:

Beginning at 0, the x values go all the way up to 5.5.

In other words, the range is 0 = M = 5.5.

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Okay, here we have this:

Considering the provided expression, we are going to identify to which is equivalent, so we obtain the following:

We obtain that the correct answer is the option C, because: