Express your answer as a polynomial in standard form.
f(x)=
f(x)=
\,\,-3x+5
−3x+5
g(x)=
g(x)=
\,\,x^2+2x+15
x
2
+2x+15
\text{Find: }(g\circ f)(x)
Find: (g∘f)(x)

Answer:

The number is -36 or x = -36

Step-by-step explanation:

2x + 16 = -56
       2x = -72
         x = -36

The solution to the difference 20 4/10 - 3 1/10 is 17 3/10

We have been given two fractions.

20 4/10 and 3 1/10

We need to find the difference 20 4/10 - 3 1/10

First we write improper fraction as a proper fraction.

20 4/10 = 204/10

3 1/10 = 31/10

So, the difference would be,

20 4/10 - 3 1/10

= 204/10 - 31/10

= 173/10

= 17 3/10

Therefore, the solution to the difference 20 4/10 - 3 1/10 is 17 3/10

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In the given triangle KLM with coordinates K(0,2) ,L(2 ,9) ,M(4,2), the sets of points which represent the dilation from the origin is K'(0,8), L'(8, 36) , M'(16, 8) multiply by scale factor 4.

As given in the question,

In the given triangle KLM,

Coordinates of the triangle KLM are given by :

K(0,2) ,L(2 ,9) ,M(4,2)

Dilation from the origin is represented by:

a. K'(0,2) , L'(8,9) , M'(16, 2)

Dilation scale factor does not effect on all the coordinates .

Not a correct option.

b. K'(0,2) , L'(2,36) , M'(16, 2)

Dilation scale factor does not effect on all the coordinates .

Not a correct option.

c. K'(0,8) , L'(8,36) , M'(16, 8)

Multiply by scale factor 4.

Dilation exist.

d. K'(4,6) , L'(6,13) , M'(8, 6)

Scale factor of addition of 4.

Dilation does not exist.

Therefore, in the given triangle KLM with coordinates K(0,2) ,L(2 ,9) ,M(4,2), the sets of points which represent the dilation from the origin is K'(0,8), L'(8, 36) , M'(16, 8) multiply by scale factor 4.

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The sequence has the 10th term of 15625000

The sequence is given as:

8,40,200,...

The above sequence has the following parameters

First term, a = 8

Common ratio, r = 5 i.e. 40/8 = 5

Number of terms , n = 10

This means that the sequence is a geometric sequence

The nth term of an geometric sequence is calculated as

f(n) = ar^(n - 1)

Substitute the known values in the above equation

So, we have the following equation

f(10) = 8 * 5^(10 - 1)

Evaluate

f(10) = 15625000

Hence, the 10th term for the sequence is 15625000

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The option(1) that is  g(1) is 3 is True and remaining are false.

Function of a variable is when a change in one is accompanied by a change in the other. The graph's x-axis denotes the function's domain, and the y-axis its range.

Eight distinct types of regularly used functions correspond to eight distinct types of function graphs. They include linear, power, quadratic, polynomial, rational, exponential, logarithmic, and sinusoidal function graphs.

we have,

g(x) = f(x - 3)

As graph in question,

g(1) = f(1-3) = f(-2) = 3

This option is true.

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The total time it took Jace to out home and return home is 21 minutes and the graph represents that the total distance was 8 blocks.

So, the total number of minutes Jace takes to get back home after going out:

Total minutes:

(Refer to the graph attached below)

Therefore, the total time it took Jace to out of home and return home is 21 minutes and the graph represents that the total distance was 8 blocks.

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The probability that it toys will be shipped is option b ) 0.6691 .

Hypergeometric Distribution will be used

P ( X = x ) = h ( x , N , n , k ) = [tex]C_{k,x}[/tex][tex]C_{N-k,n-x}[/tex] / [tex]C_{N,n}[/tex]

[tex]C_{n,x}[/tex] = n! / [ x! ( n - x ) !

According to question,

N = 17

k = 2

n = 3

To find : P ( X = 0 ) ,

P ( X = 0 ) = h ( 0 , 17 , 3 , 2 )

                = [tex]C_{2,0} C_{15,3} / C_{17,3}[/tex]

                 = 455 / 680

         = 0.6691

So there is 66.91 % probability that toys will be shipped .

Hence , option b ) 0.6691 is the correct answer .

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ΔBGC is right because Line EG is perpendicular-to CC'.

A reflection image or reflection point is the mirror image of a figure in the axis or plane of reflection.

Each point of the original figure (the pre-image) has an image that is the same distance from the reflection line as the original point, but is on the other side of the line. This transformation is known as a reflection over line. The size and form of the image in a reflection are identical to those of the pre-image.

Given:

On the line of reflection will be the midpoints of the segments connecting a triangle vertex with its reflected image. The segment will be parallel to the reflection's line.

A triangle will be considered correct in this situation if it has a leg that is a part of the segment connecting the reflected points and a leg that is on the line of reflection. Such a triangle is the BGC.

Hence, BGC is right triangle.

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Answer: D

Step-by-step explanation: Trust

Answer:

m=2

Step-by-step explanation:

-16=m-18

-16+18=m

2=m

The simple interest earned on a 2,000 principal at 8% interest for 5 years is I = $1,937.50.

Therefore,

I = Prt

First, converting R percent to r a decimal

r = R/100 = 3.875%/100 = 0.03875 per year,

then, solving our equation

I = 10000 × 0.03875 × 5 = 1937.5

I = $ 1,937.50

The simple interest accumulated

on a principal of $ 10,000.00

at a rate of 3.875% per year

for 5 years is $ 1,937.50.

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Mr. Harrington will need $510.75  to buy the TV

The correct answer is an option (a)

In this question, Mr. Harrington wants to buy a new TV for $500

He has a 10% off coupon.

After applying this coupon, the cost of TV would be,

500 - (10 percent of $500)

= 500 -[ (10/100) * 500]

= 500 - 50

= 450

He knows the tax be 13.5%.

13.5 percent of 450 would be,

(13.5/100) * 450

= 60.75

So, the amount he will need to save to buy the TV,

$450 + $60.75 = $510.75

Therefore, Mr. Harrington will need $510.75  to buy the TV

The correct answer is an option (a)

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The equation of a line is the mathematical function of a line thus the equation of the line that passes through the points (-4, -6) and (2, 8) will be y = (14/6)x + 10/3.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

A linear equation or function is given as ;

y = mx + c

Here, m is the slope and is given as (y₂ - y₁)/(x₂ - x₁).

The slope of the line passing through (-4, -6) and (2, 8) will be,

m = (8 + 6)/(2 + 4)

m = 14/6

So, y = (14/6)x + c

Substitute,  (2, 8)

8 =  (14/6)2 + c

c = 8 - 14/3 = 10/3

Therefore, y = (14/6)x + 10/3

Hence "The equation of a line is the mathematical function of a line thus the equation of the line that passes through the points (-4, -6) and (2, 8) will be y = (14/6)x + 10/3".

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Answer:

Step-by-step explanation:

b) The value of 12⁰ will be?

→ 12⁰ = ?

→ 12⁰ = 1

Hence, the solution is 1.

c) The value of (3)^(-2) will be?

→ (3)^(-2) = ?

→ (3)^(-2) = 0.1

Hence, the solution is 0.1.

Answer:

Y = 2x+8

Step-by-step explanation:

Y=mx=b equations

The probability of workers who earn between rs. 35,000 and rs. 52,000 is 99.62 %.

A data set with a normal distribution has the majority of its values clustered in the middle of the distribution and the remaining values tapering off symmetrical toward either end.

For the given question;

z = (x - μ)/σ

In which,

x = sample mean

μ = mean  (48,000)

σ = standard deviation (1500)

x = 35,000 and x = 52,000

For x = 35,000.

z = (35,000 - 48,000)/1500

z = -8.66

Check the p value from table

p(z = -8.66) = 0

For x = 52,000

z = (52,000 - 48,000)/1500

z = 2.66

p(z = 2.66) = 0.99617

P(35,000 < x < 52,000) = 0.99617 - 0

P(35,000 < x < 52,000) = 0.99617

Thus, the probability of workers who earn between rs. 35,000 and rs. 52,000 is 99.62 %.

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The equation 2.5x + 2y = 225 represents the total cost and 2.5x  represents the cost of dried fruit when its quantity is x.

A health food business prepares trail mixes out of dried fruit and nuts. The dried fruit costs $2.50 per pound, while the nuts cost $2.00 per pound. The overall cost of making the trail mix is $225.

Let the quantity of the dried fruit is x,

And the quantity of nuts is y,

As per the given question, the equation would be as:

2.5x + 2y = 225

The above equation represents the total cost and 2.5x  represents the cost of dried fruit when its quantity is x.

Thus, 2.5x  represents the cost of dried fruit when its quantity is x.

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Coppinger Corp is using Scenario Analysis.

Given, that Coppinger Corp is considering the use of a computer to assign probability distributions to the input variables used in the analysis.

The computer would then randomly select input variables from their distributions and calculate npvs based on those selections

Now, A scenario analysis consists of multiple inputs. For eg. a Company may consider how an increase in available fuel can impact their number of goods sold etc.

Here, also Coppinger Corp is assigning multiple values to the computer and getting outputs.

So, this can be the Scenario Analysis.

Hence, Coppinger Corp is using Scenario Analysis.

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Completely random design is used in this experiment.

In the given question,

A business wants to investigate the efficacy of a novel painkiller.

100 participants who suffer from chronic discomfort are enlisted.

Each participant takes the brand-new painkiller for two weeks before switching to a placebo for an additional two weeks.

The order of the tablets is chosen at random for each participant, and the subjects are unaware of which pill contains the actual medication.

Each subject's variance in total pain will be measured by researchers.

We have to check what type of experiment design is this.

As we can see in the question that they recruit 100 volunteers with chronic pain and each subject they use new pain relief medicine for a 2-week period and a placebo for another 2-week period.

They assign each subject randomly.

As we know that in a completely random design, treatments are randomly assigned to sampling material. The usual method for doing this is to make a list of the treatments and give each one a random number.

So we can see that completely random design is used in this experiment.

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The remainder of the long division problem (x + 1)/x is given as follows:

1.

The representation of a long division problem is given as follows:

di(x)/d(x) = q(x) + (r(x)/b(x))

In which the meaning of each symbol is listed as follows:

In the context of this problem, the operation is presented as follows:

(x + 1)/x.

This division can be separated into two divisions that are added, hence:

(x + 1)/x = x/x + 1/x = 1 + 1/x.

Comparing to the standard symbols, we have that:

The expression is:

(x + 1)/x.

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Answer:

B 1

Step-by-step explanation:

After using proportion method 325 calories will she get if she drinks the larger 20 oz. size.

What is proportion?

 Ratio and fractions are the main bases on which proportion is explained. Two ratios are equal when they are expressed as a fraction in the form of a/b, ratio a:b, and then a proportion. In this case, a and b can be any two integers. The ratio and proportion are important building blocks for understanding the numerous ideas in science and mathematics. Numerous challenges in daily life can be solved with proportion, including those in business when handling transactions or in the kitchen, among other situations. It creates a relationship between two or more quantities and aids in comparing them.

Here 16 oz medium size has 260 calories.

Then

=> [tex]\frac{size of coffee}{ calories}[/tex]

=>[tex]\frac{16}{260}=\frac{20}{x}[/tex]

=>x=[tex]\frac{20*260}{16}[/tex]

=> x = 325

Hence 325 calories will she get if she drinks the larger 20 oz. size.

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Ruth must have an initial deposit of $12000 in order to have the same simple interest at the same rate within the same time as Carter

Simple Interest (S.I) is the method of calculating the interest amount for some principal amount of money. Simple interest is a quick and easy method of calculating the interest charge on a loan. Simple interest is determined by multiplying the daily interest rate by the principal by the number of days that elapse between payments.

The formula of simple interest is given as

S.I = PRT

We can set up equivalent equations since both interest are equal.

S.I = P(1 + RT)

S.I = 12000(1 + 0.019 * 1)

S.I = 12228

But since they earned the same interest at the same rate within the same period, their principal or initial amount invested must be equal

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Answer:

A

Step-by-step explanation:

using the rule of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex] , then

[tex]\sqrt{12}[/tex]

= [tex]\sqrt{4(3)}[/tex]

= [tex]\sqrt{4}[/tex] × [tex]\sqrt{3}[/tex]

= 2[tex]\sqrt{3}[/tex]

Then

[tex]\sqrt{144}[/tex] + 18[tex]\sqrt{12}[/tex] - 5[tex]\sqrt{64}[/tex]

= 12 + 18(2[tex]\sqrt{3}[/tex] ) - 5(8)

= 12 + 36[tex]\sqrt{3}[/tex] - 40

= - 28 + 36[tex]\sqrt{3}[/tex]

Answer:

Step-by-step explanation:

You have a square with sides labeled (y-4), (3x-8), (2y-12), and you want to know the values of the variables as well as the side length.

All sides of the square are the same length. Equating two different y-expressions, we get ...

  y -4 = 2y -12

We can use the solution to that to find x:

  y -4 = 3x -8

Adding 12-y to the first of these equations gives us ...

  8 = y

Using this value in the second equation, we have ...

  8 -4 = 3x -8

  12 = 3x . . . . . . add 8

  4 = x . . . . . . . . divide by 3

The side length is ...

  y -4 = 8 -4 = 4

The values of the variables are x = 4, y = 8, and the side length of the square is 4.

There are 45 yards of cable that will be required.

Since we have given that

Height of cable = 15 yards - 3 yards = 12 yards

Distance from pole = 9 yards

cable is the hypotenuse of the right-angled triangle.

So, it becomes,

[tex]c^{2} = b^{2}+p^{2}[/tex]

[tex]c^{2} = 12^{2}+9^{2}[/tex]

[tex]c^{2} = 144+81[/tex]

[tex]c^{2} = 225[/tex]

[tex]c = \sqrt{225}[/tex]

c=15 yards

Since the number of cables supported = 3

So, the number of yards of cable that will be required would be

= 3  x 15 = 45

Hence, there are 45 yards of cable will be required.

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The Equation of line is y= -1/3x + 5/3

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx

where, m is the slope

Given:

x-intercept = (3,0) and y-intercept =  (0,1).

slope, m= 0-1/ 3-0= -1/3

so, The slope-intercept form of the equation of a line is

y= mx + b

y= -1/3x +b

Now, the passes through (-1, 2) we get

2= -1/3(-1) + b

2- 1/3= b

b= 5/3

So, the Equation of line is y= -1/3x + 5/3

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The equation of line k is y = 1/2x - 1.

The equation y = mx + c is the general equation of any straight line, where m is the gradient of the line and c is the y -intercept.

Given that, the equation for line j can be written as y=1/2x-4. Parallel to line j is line k which passes through the point (-8, -5)

When two lines are parallel their slope are equal, so solving for c,

-5 = 1/2*-8 + c

c = -1

The equation will be,

y = 1/2x - 1

Hence, The equation of line k is y = 1/2x - 1.

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Using simplification, the equations that are equivalent to [tex]\frac{(6x+2)}{3} =2-(3x+14)[/tex] are [tex]\frac{(6x+2)}{3 } = -3x-12[/tex] and 6x + 2 = -9x - 36

Two systems of equations are equivalent if they have the same solution(s)

In a simpler term, two equations are equivalent if they have the same solution.

Therefore, let's simplify the equation to find the equivalent solutions.

[tex]\frac{(6x+2)}{3} =2-(3x+14)[/tex]

let's open the brackets of the right side of the equation.

[tex]\frac{(6x+2)}{3}=2-(3x+14)[/tex]

[tex]\frac{(6x+2)}{3} = 2-3x-14[/tex]

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

Therefore, let's cross multiply

6x + 2 = 3(-3x - 12)

6x + 2 = -9x - 36

Therefore, the equivalent equation are as follows:

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Answer: 81

Step-by-step explanation:

[tex]v=\sqrt{2gh}\\\\g=32, v=72\\\\\implies 72=\sqrt{2(32)h}\\\\5184=64h\\\\h=81[/tex]