Find the number of years it would take for $1200 to earn simple interest of $324 at an annual interest rate of 6% per year

f(x) + n - shift a graph n units up

f(x) - n - shift a graph n units down

f(x + n) - shift a graph n units left

f(x - n) - shift a graph n units right

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We have:

[tex]y=\dfrac{1}{x}\to y=\dfrac{1}{x+4}\\\\f(x)=\dfrac{1}{x}\to f(x+4)=\dfrac{1}{x+4}[/tex]

In order to turn a ratio into a percentage, you have to turn the given fraction into an equivalent fraction with denominator 100. So, you have

[tex] \dfrac{3500}{5000}=\dfrac{x}{100} [/tex]

Solving for x, you get

[tex] x=\dfrac{3500\cdot 100}{5000} = \dfrac{3500}{50} = \dfrac{350}{5} = 70 [/tex]

So, they achieved the 70% of their goal.

Answer:

The statement is false because the conclusion is false.

Step-by-step explanation:

"then it is 0" is the conclusion. This is false because not all integers are 0.

Remark

Usually this is written in very simple terms. You could do it as a proportion, but it might be easier to see if you used Newton's formula twice.

Formula

F = m * a

m = mass, F = force, a = accelerationn

Givens

F1 = 70 N

a1 = 6.5 m/s^2

m = ?

F2 = ??

m = ?

a2 = 8 m/s^2

Step One

Solve for m

F1 = m * a1              Substitute the values

70 = m *  6.5           Divide by 6.5

70/6.5 = m

10.77 kg = m

Step Two

Solve for F2

m = 10.77 kg

a = 8

F2 = ??

F2 = m * a2

F2 = 10.77 * 8

F2 = 86.154

Answer: C rounded to the nearest 1/100

Answer:

D

Step-by-step explanation:

Start by subtracting 64 from both sides:

[tex]25x^2=225[/tex]

Factor this by taking roots.  Divide both sides by 25 first:

[tex]x^2=9[/tex]

We "undo" a square by taking the square roots of both sides.  Taking the square root leaves the possibilities of both the positive and negative roots of 9.  Therefore, the solutions to this are

[tex]x=\sqrt{3},-\sqrt{3}[/tex]

The value of f(12) which represents the amount of interest he will receive after 12 months is; $120.

Evidently, the sequence is an arithmetic progression;

As such, we must evaluate the common difference, d as follows;

The first term, a = $10

Therefore; From the nth term formula for an arithmetic progression;

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Consider the parrent function [tex]y=\sqrt{x}.[/tex] The graph of this function you can  see in the attached diagram (red line).

1. Reflect this graph about the x-axis, then the function becomes [tex]y=-\sqrt{x}[/tex] (blue line).

2. Translate the reflected graph 2 units up, then the function becomes [tex]y=-\sqrt{x} +2[/tex] (green line).

Answer: correct choice is B.

Let us check the slope of y-intercepts of the given lines in the graph first.

The y-intercept of above line is 1 and slope of

Rise/run = 2/1 (Moving 2 units up and 1 unit right).

So, the equation should be

y=2x+1

Y-intercept of second line is -2 and slope is

Rise/run = -1/1 (Moving 1 unit down and 1 unit right).

So, the equation should be

y=-x-2.

Now, we need to check the shaded portion for inequality signs.

We have both lines dotted.

So, the inequality signs would be just < or >.

For y=2x+1 line : Shading is on the left side.

On the left side of the line y=2x+1, the y-values are greater than on right side.

Therefore, we got first inequality y>2x+1

For y=-x-2 line : Shading is on the down of the line.

On the down of the line y=-x-2, the y-values are less than up side of the line.

Therefore, second inequality would be

y<-x-2 or y+x<-2

Therfore, correct option is first option y>2x+1 and y+x<-2.

Answer:

A was the answer.

Step-by-step explanation:

i took the test.

The 8 is in the hundredths place.

Hope this helps & good luck. :)

Answer:  The correct option is  (C) [tex]2x+5y=-15.[/tex]

Step-by-step explanation:  Given that the equation of the line that passes through (-5, -1) and (10, -7) in point-slope form is given by

[tex]y+7=-\dfrac{2}{5}(x-10)~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We are to find the standard form of the equation for the above line.

We know that the STANDARD form of the equation of a line is given by

[tex]ax+by=c,~~~~~\textup{[a and b cannot be zero at the same time]}.[/tex]

From equation (i), we have

[tex]y+7=-\dfrac{2}{5}(x-10)\\\\\Rightarrow 5(y+7)=-2(x-10)\\\\\Rightarrow 5y+35=-2x+20\\\\\Rightarrow 2x+5y=20-35\\\\\Rightarrow 2x+5y=-15.[/tex]

Thus, the required standard form is [tex]2x+5y=-15.[/tex]

Option (C) is CORRECT.

Final answer:

To create an alloy with 4.9 lb of zinc based on the nickel to zinc ratio of 2:7, about 1.4 pounds of nickel is required.

Explanation:

To determine how many pounds of nickel have to be used to create an alloy that contains 4.9 lb of zinc, we must first understand the given ratio of nickel to zinc to copper in the alloy, which is 2:7:9. Since zinc's ratio is 7 and we have 4.9 lb of it, we can calculate the amount of nickel by setting up a proportion.

We use the proportion 2/7 = x/4.9, where x represents the pounds of nickel. By cross-multiplying and solving for x, we get x = (2 * 4.9) / 7, which simplifies to x = 9.8 / 7. This gives us the result x ≈ 1.4 lb.

Therefore, to create an alloy with 4.9 lb of zinc, approximately 1.4 pounds of nickel are needed.

Charity donated by Tillman = $3540

Number of employees who donated = 118

Contribution of Tillman = 40%

Let the average contribution of employees be = x

Then the amount contributed by employees = 118x

Then contribution of Tillman = [tex]\frac{40}{100}\times118x[/tex]

As Tillman donated 3540 , then

[tex]3540=\frac{40}{100}\times118x[/tex]

[tex]3540=47.20x[/tex]

[tex]x=75[/tex]

Hence, average contribution by each employee is $75.

Option C is correct.

Answer:

$75

Tillman's donation = .40(total employees' donations)

$3540 = .40x

x = 8850

8850

118

= $75 for each employeeep explanation:

$75

Tillman's donation = .40(total employees' donations)

$3540 = .40x

x = 8850

8850

118

= $75 for each employee

Since you are solving for a, you want to have a on one side of the equation and the other terms on another side of the equation. It would be easiest to have all the terms with a on the left side of the equation, so that is what we will do.

Subtract 9a from both sides to get a on the left side of the equation.

5 + 5a = -5

Subtract 5 from both sides of the equation to isolate the term with a.

5a = -10

Divide both sides of the equation by 5 to solve for a.

a = -2

The result to the equation is a = -2.

To break for a in the equation 5 + 14a = 9a - 5, we can start by simplifying both sides of the equation.

Adding 5 to both sides

5 + 14a + 5 = 9a - 5 + 5

10 + 14a = 9a

Next, we can insulate the variable a by abating 9a from both sides

14a - 9a + 10 = 9a - 9a

5a + 10 = 0

To break for a, we'll abate 10 from both sides

5a + 10 - 10 = 0 - 10

5a = -10

Eventually, we divide both sides by 5 to break for a

5a/ 5 = -10/ 5

a = -2

Thus, the result to the equation is a = -2.

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For this one, find out how many hour have passed per day with 6 pm Friday being where you start.  

6 pm Friday- 6 pm Saturday =24

6 pm Saturday - 6 pm Sunday= 24

6 pm Sunday - 6 am Monday = 12 hours

6 am Monday until 8 am Monday= 2 hours

Now just add the amount of hours together

24+24+12+2= 62 hours

Now convert that to minutes.

There are 60 minutes in 1 hour.  You multiply the amount of hours by 60 to get the minutes.

62 hours times 60 minutes in 1 hour

62*60= 3720.

So you will have a total of 3,720 minutes of tape to review.

Answer: 3,720

Step-by-step explanation:

Answer: Option 'D' is correct.

Step-by-step explanation:

Since we have given that

Event A: You get a red car

and

[tex]P(A)=0.20[/tex]

Similarly,

Event B: You get a convertible

and

[tex]P(B)=0.40[/tex]

So, if A and B are independent , then they must satisfy,

[tex]P(A).P(B)=P(A\cap B)[/tex]

So,

[tex]P(A\cap B)=0.4\times 0.2=0.08[/tex]

Hence, Option 'D' is correct, which states that the probability of getting a red convertible is 0.08.

Answer:

D.The probability of getting a red convertible is 0.08

Step-by-step explanation:

ap3x

If you borrowed $100, then your monthly payment is $2.44

If you borrowed $200, then your monthly payment is 2*2.44 = 4.88

etc etc

We can set up a proportion

2.44/100 = x/13300

to figure out the monthly payment x. Cross multiply and solve for x

2.44*13300 = 100*x

100x = 2.44*13300

100x = 32452

x = 32452/100

x = 324.52

So the monthly payment is $324.52

An alternative way to get this monthly payment is to apply 2.44% to 13300, which is another way to view the phrase  "monthly payment per $100 is 2.44"

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

There are 48 months in 4 years (start with 12 mon = 1 yr, then multiply both sides by 4) so we multiply 48 by the monthly payment to get the result 48*324.52 = 15,576.96. This is the total amount you have to pay back which is the principal plus interest.

Subtract off the principal (amount borrowed) to find the interest or finance charge: 15,576.96 - 13,300 = 2,276.96

Answer: Choice B

The finance charge on $13,300 financed at 7.9 percent for 4 years is $12,975.48.

To calculate the finance charge, we need to first find the total amount financed. We can do this by multiplying $13,300 by the monthly payment per $100, which is $2.44. $13,300 divided by 100 is 133, so we multiply 133 by 2.44 to get $324.52. Now, we can calculate the finance charge by subtracting the total amount financed from the original loan amount. $13,300 minus $324.52 is $12,975.48. Therefore, the finance charge is $12,975.48.

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m = [tex]\frac{5}{6}[/tex] , y - 7 = [tex]\frac{5}{6}[/tex] ( x - 12), y = [tex]\frac{5}{6}[/tex] x - 3

(a) calculate the slope using the gradient formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 6, - 8) and (x₂, y₂) = (12, 7)

m = [tex]\frac{7+8}{12+6}[/tex] = [tex]\frac{15}{18}[/tex] = [tex]\frac{5}{6}[/tex]

(b) the equation of a line in point-slope form is

y - b = m(x - a )

where m is the slope and (a, b) a point on the line

using m = [tex]\frac{5}{6}[/tex] and (a , b) = (12, 7 )

y - 7 = [tex]\frac{5}{6}[/tex] (x - 12)

(c) the equation of a line in slope-intercept form is

y = mx + c ( m is the slope and c the y-intercept )

rearrange (b ) into this form

y - 7 = [tex]\frac{5}{6}[/tex] - 10

y = [tex]\frac{5}{6}[/tex] x - 3

Remark

First of all you have to declare the meaning of g(f(x)) After you have done that, you have to make the correct substitution.

Givens

f(x) = 4x^2 + x + 1

g(x) = x^2 - 2

Discussion

What the given condition g(f(x)) means is that you begin with g(x). Write down g(x) = x^2 -  2

Wherever you see an x on either the left or right side of the equation, you put fix)

Then wherever you see f(x) on the right you put in what f(x) is equal to.

Solution

g(x) = x^2 - 2

g(f(x)) = (f(x))^2 - 2

g(f(x)) = [4x^2 + x + 1]^2 - 2

f(x)^2 =

4x^2 + x + 1

4x^2 + x + 1

16x^4 + 4x^3 + 4x^2

            4x^3  + x^2 +   x

                        4x^2 + x  + 1

16x^4 + 8x^3 + 9x^2 + 2x + 1

Answer

g(f(x)) = 16x^4 + 8x^3 + 9x^2 + 2x + 1 - 2

g(f(x)) = 16x^4 + 8x^3 + 9x^2 + 2x - 1

ANSWER

The correct answer is D

EXPLANATION

The slope of the given line

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

The line perpendicular to it has slope

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

If the line passes through

[tex](1,27)[/tex]

Then the equation is given by

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

[tex]\Rightarrow y-27=3(x-1)[/tex]

[tex]\Rightarrow y=3x-3+27[/tex]

[tex]\Rightarrow y=3x+24[/tex]

Equation of the required line which is perpendicular to this line and passes through (1, 27) is y= 3x+24

The equation of the given line is y = -1/3x - 24

Comparing it with the standard form i.e y=mx+c

where 'm' is the slope of the line

and 'c' is the y-intercept of the line

we get 'm=-1/3' and 'c=-24'

Now if two lines are perpendicular the relation between their slopes  'm1' and 'm2' is given as

m1*m2=-1

Thus here m1=-1/3;

(-1/3)*m2=-1

m2=3

Therefore slope of any line perpendicular to  y = -1/3x - 24 would be m2=3

Also given that the line passes through the point  (1, 27)

Thus if a line having slope as 'm' and passing through the point (x1,y1) its equation is given as:

[tex]y-y_{1}=m(x-x_{1})[/tex]

here [tex](x1,y1)=(1,27)[/tex]

and [tex]m=3[/tex]

Thus required equation would be:

y-27 = 3*(x-1)

y-27 = 3x-3

y = 3x-3+27

y= 3x+24

Answer:

26% increase

Step-by-step explanation:

Answer:

26% increase

Step-by-step explanation:

If f(x) varies directly with  [tex]x^2[/tex]

If f(x) varies directly with x then we use equation f(x) = kx

where k is the constant of proportionality

So equation becomes [tex]f(x) = kx^2[/tex]

We use the information and find out k

f(x)= 10

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

[tex]10= kx^2[/tex]

[tex]k = \frac{10}{x^2}[/tex]

now we use the value of k and find the value of f(x) when x=3

[tex]f(x) = \frac{10}{x^2}*x^2[/tex]

f(x) = 10

The value of f(x) = 10 when x= 3

The value of f(x) when x=3 is 90.

If f(x) varies directly with x2 and is given that f(x)=10 when x=1 (since 1 squared is 1), we can express the direct variation as f(x) = k × x2, where k is the constant of variation. To find the value of k, we use the information that f(1)=10. Thus, 10 = k × 12, which means k=10.

Now that we know k=10, we can find f(x) when x=3. We substitute x with 3 in the equation f(x) = 10 × x2, yielding f(3) = 10 × 32 = 10 × 9 = 90. Therefore, the value of f(x) when x=3 is 90.

when rounded to the tenths place it would be 9.3

Answer:

The first and third one

Step-by-step explanation:

Answer:

[tex]\frac{7y^{2} +9x}{4}[/tex] and 6y²+5x

Step-by-step explanation:

Polynomials are algebraic expressions involving one, or even more than one variables raised to any power summing each other. Generally speaking, in other words an one variable Polynomial is

[tex]a_{0}+a_{1} x+a_{2} x^{2}...a_{n} x^{n}[/tex]

So a multivariate polynomial expression are [tex]\frac{7y^{2} +9x}{4}[/tex] and 6y²+ 5x.

Because in the other options:

We have a Radical of an Irrational number[tex]\sqrt{3} =3^{\frac{1}{3}}[/tex] times x (2nd option) what does not configure a polynomial.

And a Polynomial Quotient with a variable on the denominator, described by:

[tex]P(x)=\frac{Q(x)}{R(x)} \\ P(x)=q(x)*Q(x)+R(x)[/tex]

Like the last option:

[tex]\frac{7x^{2}+8}{4x}[/tex]

if x can be 2-5 and y can be 1-6, c=3(5)+4(6)

which would turn out to be c=39

The maximum value of C will be equal to 39.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

Given constraints are:-

x  ≥   2

x  ≤   5

y  ≥   1

y  ≤  6

Here maximum value of x = 5 and for y = 6

Putting the maximum values of x and y to calculate the maximum value of C.

C  =  3x  +  4y

C  = ( 3 x 5 )  +  (  4  x  6 )

C  =  15  +  24

C   =  39

Therefore the maximum value of C will be equal to 39.

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The range = [0 , ∞)

We read from the y axis.  The graph exists from y = 0 to infinity.

You could buy 8 lemons for 60 cents.