Regina is buying a new car. She sees two advertisements in the paper for the same car at two different prices from two different dealerships. Both dealers are offering a simple-interest loan for the price of the car. A photo of car includes two ads. Ad A shows the vehicle priced at twenty-four thousand two hundred dollars at six point five percent interest and an unknown number of years. Ad B shows an unknown price, at a five point three percent interest over nine years. Question 1 Part A Regina calculates that to buy the car in Ad A, the loan would ultimately cost her $41,503. Over how many years is the loan in Ad A to be paid back?

Answer:

5:2

Step-by-step explanation:

Answer:

The answer is below

Step-by-step explanation:

Find the dimensions of the rectangle of maximum area with sides parallel to the coordinate axes that can be inscribed in the ellipse 4x² + 16y² = 16

Solution:

Given that the ellipse has the equation: 4x² + 16y² = 16

let us make x the subject of the formula, hence:

4x² + 16y² = 16

4x² = 16 - 16y²

Dividing through by 4:

x² = (16 - 16y²)/4

x² = 4 - 4y²

Taking square root of both sides:

[tex]x=\sqrt{4-4y^2 }\\[/tex]

The points of the rectangle vertices is at (x,y), (-x,y), (x,-y), (-x,-y). Hence the rectangle has length and width of 2x and 2y.

The area of a rectangle inscribed inside an ellipse is given by:

Area (A) = 4xy

A = 4xy

[tex]A=4(\sqrt{4-4y^2} )y\\\\A=4y\sqrt{4-4y^2}=4\sqrt{4y^2-4y^4} \\\\The\ maximum\ area\ of\ the\ rectangle\ is\ at\ \frac{dA}{dy}=0\\\\ \frac{dA}{dy}=4(\frac{4-8y^2}{\sqrt{4-4y^2} } )\\\\4(\frac{4-8y^2}{\sqrt{4-4y^2} } )=0\\\\4-8y^2=0\\\\8y^2=4\\\\y^2=1/2\\\\y=\frac{1}{\sqrt{2} }\\\\x=\sqrt{4-4(\frac{1}{\sqrt{2} })^2}=\sqrt{2}[/tex]

Therefore the length = 2x = 2√2, the width = 2y = 2/√2

1n=n Answer:

Step-by-step explanation:

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The required measure of the radius inscribed in the triangle RST is 11.

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°

Here,
The incenter of the triangle will be the center of the circle inscribed in the triangle. and radius will be the perpendicular distance from the incenter to the sides.
So,
XU = XW,
-2y + 15 = 3y +5
5y = 10
y = 2

Now,
Radius = XU
          = -2(2) + 15
          = 11

Thus, the required measure of the radius inscribed in the triangle RST is 11.

Learn more about triangles here:
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1452 is 33x44’s sum

  33

x 44

____

 132

1320

1452

Answer:

1452

Step-by-step explanation:

33 * 44 = 1452

Answer:

Step-by-step explanation:

Many points lie circle O

The points with a distance of 10 units will be on the circle

eg. (8,-2) or (4,6) both lie on the circle as they have a distance of 10 units from the center.

Complete question :

A college football coach wants to know if the is a correlation between his players' leg strength and the time it takes for them to sprint 40 yards. he sets up the following test and records the data:

Every day for a week, he counts how many times each player can leg press 350 pounds. The following week, he has each player sprint 40 yards every day. The tables shows the average number of leg-press repetitions and the average 40-yard dash time (in seconds) for seven randomly selected players. What is the equation of the line of best fit? How many seconds should he expect a player to take to run 40 yards if that player can do 22 leg-press repetitions?

Leg Press (reps)|40-yard Dash (s)

15 |5.2

18 |6.3

8 |6.8

30 |8.2

26 |8.0

12 |5.3

21 |5.9

Answer:

ŷ = 0.1073X + 4.5365

6.9

Step-by-step explanation:

Leg Press (reps)X:

15

18

8

30

26

12

21

Y:

5.2

6.3

6.8

8.2

8.0

5.3

5.9

Using a regression calculator :

The equation of line of best fit is :

ŷ = 0.1073X + 4.5365

Slope or gradient = 0.1073

Intercept = 4.5365

X = independent or predictor variable (leg press)

Y = predicted variable (40 yard dash)

B)

X = 22

Y = 0.1073(22) + 4.5365

Y = 6.8971

Y = 6.9

Answer:

-4 and any number above.

Answer:

162,811

Step-by-step explanation:

Answer:

Step-by-step explanation:

f(7) = 32

f(-9) = 32

f(s) = 32

f(s-t) = 32

g(7) = 10·7+4 = 74

g(-9)  = 10(-9)+4 = -86

Answer:

The variance of this distribution is 42353.2

Step-by-step explanation:

For each visitor, there are only two possible outcomes. Either they clicked on the button, or they did not. Visitors are independent of each other. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The variance of the binomial distribution is:

[tex]V(X) = np(1-p)[/tex]

In this question:

226977 visitors, so [tex]n = 226977[/tex]

56330 clicked, so [tex]p = \frac{56330}{226977} = 0.2482[/tex]

Then

[tex]V(X) = 226977*0.2482*(1 - 0.2482) = 42353.2[/tex]

The variance of this distribution is 42353.2

Answer:

3rd is the answer

Step-by-step explanation:

caculator duhhhhhhhhhh

Answer:

Answer is (4+3i)+(5-6i)=(9-3i)

Step-by-step explanation:

I hope it's helpful!

==============================================

Work Shown:

(4+3i) + (5-6i)

4+3i + 5-6i

(4+5) + (3i-6i)

9 + (3-6)i

9 + (-3)i

9 - 3i

As the steps above show, we treat the 'i' as a variable. So we could think of the expression as (4+3x)+(5-6x) and simplify to get 9-3x. Though we use ''i' instead of x.

Answer:

1) The expected value of the number of moving violations for which the individual was cited during the last 3 years is 1

2) The expected amount of surcharges is $250

Step-by-step explanation:

Given that;

Y      0           1       2        3         4

p(y) 0.50   0.20   0.15   0.10   0.05

1)

Value of E(Y)

E(Y) = (0×0.50) + ( 1×0.20) + ( 2×0.15) + (3×0.10) + (4×0.05)

= 0 + 0.20 + 0.3 + 0.3 + 0.2

E(Y) = 1

Therefore, The expected value of the number of moving violations for which the individual was cited during the last 3 years is 1

b)

Suppose an individual with Y violations incurs a surcharge of $100Y² , the expected amount of the surcharge is given by,

E($100Y²) = 100E(Y)²

= 100∑Y²P(y)

= 100(0²×0.50) + ( 1²×0.20) + ( 2²×0.15) + (3²×0.10) + (4²×0.05)

= 100( 0 + 0.2 + 0.6 + 0.9 + 0.8 )

= 100(2.5)

= $250

Therefore; The expected amount of surcharges is $250

Answer:

4/3

Step-by-step explanation:

because it is just that

Answer:

0.11111111111

Step-by-step explanation:

Answer:

Step-by-step explanation: Explanation:

If

L

,

H

and

W

represent the length, height and width of the prism, then the volume of the rectangular prism is :

V

=

L

.

H

.

W

............. (1)

Given :

V

=

x

3

+

11

x

2

+

20

x

−

32

;

............... (2)

W

=

(

x

−

1

)

;

H

=

(

x

+

8

)

.

Let

L

=

(

x

+

l

0

)

be the expression for the length, then the RHS of equation (1) becomes

L

.

H

.

W

=

(

x

−

l

0

)

(

x

+

8

)

(

x

−

1

)

,

=

(

x

+

l

0

)

(

x

2

+

7

x

−

8

)

=

(

x

+

l

0

)

(

x

2

+

7

x

−

8

)

=

x

3

+

(

7

+

l

0

)

x

2

+

(

7

l

0

−

8

)

x

−

8

l

0

..... (3)

Comparing this to the LHS of equation (1), we get the following set of equations to solve for

l

0

,

7

+

l

0

=

11

;

7

l

0

−

8

=

20

;

8

l

0

=

32

;

l

0

=

4

Therefore

L

=

(

x

+

4

)

answer is 13

I hope it helpful

Answer:

The value of p² + r³, when p = 2 & r = 3

(2)²+(3)³=4+27=31

Answer:

7 to 10 or 70%

Step-by-step explanation:

Answer:

abc

Step-by-step explanation:

Answer:

216 m

Step-by-step explanation:

12/4= x/6

3=x/6

x=3x6

length= 18

area=length x width

12x18=216

Answer:

I think it's the 3 one if in wrong I'm sorry

Answer:

3/24 + 4/24 = 7/24

Step-by-step explanation:

Find a common denominator then multiply the numerator by how many times you multiplied the denominator and add them to get your answer and you may simplify.

Answer:

2

Step-by-step explanation:

Answer:

The volume is: [tex]V = \frac{\pi}{3}[/tex] cubic units

Step-by-step explanation:

Volume of a solid:

The volume of a solid, given by the function f(x), over an interval between a and b, is given by:

[tex]V = \pi \int_{a}^{b} (f(x))^2 dx[/tex]

y = x, y =1, x = 0

This means that the upper function is y = 1, and the lower function is y = x. So

[tex]f(x) = (1 - x)[/tex]

The lower limit of integration is x = 0.

The upper limit is y = x when y = 1, so x = 1.

Then

[tex]V = \pi \int_{a}^{b} (f(x))^2 dx[/tex]

[tex]V = \pi \int_{0}^{1} (1-x)^2 dx[/tex]

[tex]V = \pi \int_{0}^{1} (1-2x+x^2) dx[/tex]

[tex]V = \pi (x-x^2+\frac{x^3}{3})|_{0}^{1} dx[/tex]

[tex]V = \pi(1 - (1^2) + \frac{1^3}{3})[/tex]

[tex]V = \frac{\pi}{3}[/tex]

Answer:

2x+2x2=32

2x+4=32

Step-by-step explanation:

Answer:

A(n) = a + (n - 1)d is the correct formula for an arithmetic sequence.

Step-by-step explanation:

Answer:

A) 1000/1 = x/2500 is the answer