Katie received a speeding ticket that incurred a $125 fine. After one month, she will also
be charged late fees for every month that she is delinquent. The amount she pays is
modeled by an exponential function, and the following table reflects the amount she will
have to pay each month.
Month Paid
Amount Paid
$125
1
2
3
$137.50
$151.25
$166.38
4
a. Write a function that models the fine Katie will pay in terms of the month it is paid. (5
points)
b. Using your function, predict how much Katie will pay if she waits until month 12 to pay
her fine. (5 points)

Answer:

A. 5(1 + 3x)

Step-by-step explanation:

5(1 + 3x)

(5 × 1) + (5 × 3x)

5 + (5 × 3x)

5 + 15x

A works. Let's check the rest.

1(5 + 3x)

(1 × 5) + (1 × 3x)

5 + (1 × 3x)

5 + 3x

B does not work.

3(5 + х)

(3 × 5) + (3 × x)

15 + (3 × x)

15 + 3x

C doesn't work.

5(3x)

5 × 3x

15x

B, C, and D do not work.

Answer:

YES X=3

Step-by-step explanation:

10x=3x+21

-3x    -3x

7x=21

________ . *DIVIDE BY 7 on each side

7     7

X=3

Answer:

11. 78

12. 4x² - 3x - 1

Step-by-step explanation:

11. Sum of n whole numbers = ½(n² + n)

Multiply

½*n² + ½*n

= n²/2 + n/2

To find the sum of the first 12 whole number, substitute 12 for n into the equation.

= 12²/2 + 12/2

= 144/2 + 12/2

= 72 + 6

= 78

12. Area of trapezoid = ½(a + b)*h

Where,

a = 5x - 4

b = 3x + 2

h = x + 1

Area = ½(5x - 4 + 3x + 2)*(x + 1)

Area = ½(8x - 2)*(x + 1)

Area = ½[8x(x + 1) -2(x + 1)]

= ½[8x² + 8x - 2x - 2]

Add like terms

= ½(8x² - 6x - 2)

= ½(8x²) - ½(6x) - ½(2)

= 4x² - 3x - 1

Answer:

Step-by-step explanation:

a+b=58 and 4a-2b=28 is the system of equations

solving the first for a, a=58-b, using this value for b in second equation is

4(58-b)-2b=28

232-4b-2b=28

232-6b=28

-6b=-204

b=34, and since a=58-b

a=58-34

a=24

So the two numbers are 24 and 34

Answer:

The last one, 81000 sq ft.

Step-by-step explanation:

To find area, you do length times width.

81,000 ft. squared

Answer:

a) 0.1536 = 15.36% probability that exactly two of the four components last longer than 1000 hours.

b) 0.9728 = 97.28% probability that the subsystem operates longer than 1000 hours.

Step-by-step explanation:

For each component, there are only two possible outcomes. Either they fail in less than 1000 hours, or they do not. The probability of a component failing in less than 1000 hours is independent of any other component. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

And p is the probability of X happening.

One subsystem has four identical components, each with a probability of 0.2 of failing in less than 1000 hours.

Four components means that [tex]n = 4[/tex]

Probability of 0.2 of failling means that 1 - 0.2 = 0.8 probability of not failling, so [tex]p = 0.8[/tex]

a) Find the probability that exactly two of the four components last longer than 1000 hours.

This is [tex]P(X = 2)[/tex]. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{4,2}.(0.8)^{2}.(0.2)^{2} = 0.1536[/tex]

0.1536 = 15.36% probability that exactly two of the four components last longer than 1000 hours.

b) Find the probability that the subsystem operates longer than 1000 hours.

It will operate if at least two compoents last longer than 1000 hours. So

[tex]P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{4,2}.(0.8)^{2}.(0.2)^{2} = 0.1536[/tex]

[tex]P(X = 3) = C_{4,3}.(0.8)^{3}.(0.2)^{1} = 0.4096[/tex]

[tex]P(X = 4) = C_{4,4}.(0.8)^{4}.(0.2)^{0} = 0.4096[/tex]

[tex]P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4) = 0.1536 + 0.4096 + 0.4096 = 0.9728[/tex]

0.9728 = 97.28% probability that the subsystem operates longer than 1000 hours.

Answer:

Perpendicular bisector theorem

Step-by-step explanation:

The illustration of the theorem is:

If point B is a perpendicular bisector of Line AC and the length of AC is 10cm

Then

[tex]AB + BC = 10[/tex]

Where

[tex]AB = BC[/tex] --- Perpendicular bisector

So, the equation becomes

[tex]AB + AB =10[/tex]

[tex]2AB =10[/tex]

[tex]AB = 5[/tex]

Recall: [tex]AB = BC[/tex]

[tex]AB = BC = 5[/tex]

Answer:

The answer is B 200

Step-by-step explanation:

i just took the test so yah :)

Answer:

02920

Step-by-step explanation:

92823

Answer: Compounded quarterly, 350, 420, 25, the account pays interest on both the principal and the interest accumulated.

Step-by-step explanation:

Question 1: Compounded quarterly is growing fastest because it's broken down more than what simple interest does and therefore is faster instead.

Question 2: Account A in 30 years would be 350, I did this problem and eyeballed it. Trust me.

Question 3: Account B in 30 years would be 420.

Question 4: The approximate difference between the two accounts in 20 years would be 25.

Question 5: If the rate of interest is annual and the interest is compounded quarterly then the number of years is 4 times and the rate of annual interest is one-fourth. Therefore, the account pays interest on both the principal and the interest accumulated.

Hope this helps

The simple interest and compound interest are solved for both the curves

a) The compound interest is growing fastest

b) the amount in Account A in 30 years A = $ 350

c) The amount in Account B in 30 years is B = $ 420

d) The difference between the two accounts in 20 years = $ 25

Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.

The formula for calculating Compound Interest is

A = P ( 1 + r/n )ⁿᵇ

where A = Final Amount

P = Principal

r = rate of interest

n = number of times interest is applied

b = number of time periods elapsed

Given data ,

a)

Let the 2 curves be represented as A and B

Now , the amount invested by A = $ 200

The rate of simple interest = 2.5 %

And , the amount invested by B = $ 200

The rate of compound interest = 2.5 %

So , we can say that since it is more thoroughly broken down than basic interest is, compounded quarterly growth is the quickest.

b)

The amount for A in 30 years is given in the graph

A = $ 350

c)

The amount for B in 30 years is given in the graph

B = $ 420

d)

The amount for A in 20 years is given in the graph = $ 300

The amount for B in 20 years is given in the graph = $ 325

The difference between the two accounts in 20 years = $ 325 - $ 300

The difference between the two accounts in 20 years = $ 25

Hence , the compound interest is solved

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A trapezoid consists of two triangles.

A trapezoid does indeed contain two triangles within its structure. A trapezoid is a quadrilateral with one pair of parallel sides.

The other two sides, known as the legs, are not parallel and meet at a point. These legs, along with the two parallel sides, form two triangles within the trapezoid.

One triangle is formed by connecting the two legs and one of the parallel sides. The other triangle is formed by connecting the two legs and the other parallel side.

So, a trapezoid consists of two triangles.

Learn more about Trapezoid here:

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Answer:

5.34 pages/h

Step-by-step explanation:

4/45 = p/60

p ≈ 5.34

Answer:

Step-by-step explanation:

3/4 of an hour is the same as 0.75

Write a proportion.

4 (pages)/0.75 (hours)=p(pages)/1 hour

Cross multiply and divide

(4x1)÷0.75=5.33 (rounded to the nearest hundred)

p=5.33

Marcia can type 5.33 pages per hour.

Answer:

0.345

Step-by-step explanation:

hits/at-bats = 345/1000 = 0.345

The probability of a hit, any particular time he goes to bat. is 0.345.

The problem does not request any particular format, so 0.345 is a perfectly good answer.

In baseball, that is called a 'batting average', and is actually expressed that way - as a decimal - in a player's statistics.

On the other hand, if we did want to express the probability as a percentage, we would do this:  

0.345 * 100% = (0.345 * 100) % = 34.5 %

Hope this helps

Answer:

x = 60

Step-by-step explanation:

(x + 50)° + (x + 10)° = 180° (interior angles on the same side of transversal)

(2x + 60)° = 180°

2x + 60 = 180

2x = 180 - 60

2x = 120

x = 120/2

x = 60

Answer:

I think the correct answer is $26,843,545.6

Step-by-step explanation:

9514 1404 393

Answer:

  Chun is correct

Step-by-step explanation:

The angle bisector divides the sides of the triangle proportionally. Any proportion that is written should equate ratios of corresponding sides.

Chun's proportion correctly relates the top-side measures to their corresponding bottom-side measures:

  top short : bottom short = top long : bottom long

  5 / 8 = 15 / x

__

Traci's error is that she mixes top-side and bottom-side measures. Her incorrect relation is ...

  top short : bottom long = bottom short : top long

She has used top:bottom for short measures and bottom:top for long measures. This mixing will give Traci an incorrect solution.

__

Chun's proportion correctly gives x=24.

Answer:

Step-by-step explanation:

Chun; by the Triangle Angle Bisector Theorem, the correct proportion is  58=15x.

Answer:

Speed = distance / time

= 6/3 =2 ft/sec

Time = distance / speed

= 60/2

= 30 seconds

Answer:

6+4=10 and 10+5=15

Step-by-step explanation:

Answer:

it is 500500

Step-by-step explanation:

learned this fact a few years ago and it stuck with me.

Answer:19

Step-by-step explanation:perimeter is everything added since it’s a rectangle 10 on both length sides will be 20 so 58-20 is 38 divide that by 2 and that’s your answer.

Answer:

So, the domain are:

[tex]x = 4,1,0,-1[/tex]

The range are:

[tex]y = 2,3,0,-1,-3[/tex]

Step-by-step explanation:

Given:

[tex]\{(4, 2), (1, 3), (0, 0), (-1, -1), (1, -3)\}[/tex]

Required

The domain and the range

In relation, we have:

[tex]\{(x_1, y_1), (x_2, y_2), ......, (x_n, y_n)\}[/tex]

Where the x values are the domain and the y values represent the range.

So, the domain are:

[tex]x = 4,1,0,-1[/tex]

The range are:

[tex]y = 2,3,0,-1,-3[/tex]

Answer:

potential solutions- 1

extraneous solutions- 0

solution to equation- x=3

Step-by-step explanation:

Answer:

x is 44 because

3x+4+x=180

4x=180-4

4x=176

x=44

Answer: 2

Step-by-step explanation:

Answer:

(-1.875, -1.625)

Step-by-step explanation:

We want to find the point on the equation 2*x + 6*y + 1 = 0 which is closest to the point (-5, -3)

Remember that the distance between two points (a, b) and (c, d) is:

D = √( (a - c)^2 + (b - d)^2)

First we can write our equation as a line in the slope intercept form:

y = -(2/6)*x - 1

Now we could minimize the equation:

D = √( (x - (-5))^2 + (y - (-3))^2) = √( (x + 5)^2 + (y + 3)^2)

D = √(  ( x + 5)^2 + (  -(2/6)*x - 1 + 3) ^2)

Then we can minimize:

D^2 = (x + 5)^2 + ( -(2/6)*x + 2)^2

       = x^2 + 10*x + 25  + (4/36)*x^2  - (8/6)*x + 4

       =  (1 + 4/36)*x^2 + (10 - 8/6)*x + 29

        = (40/36)*x^2 + (52/6)*x + 29

This is a quadratic equation whose leading coefficient is positive, then the minimum of this equation is at the vertex.

The vertex is at the x-value such that (D^2)' = 0

Then:

(D^2)' = 2*(40/36)*x + (52/6)

This needs to be zero then:

0 = 2*(40/36)*x + (52/6)

-52/6 = (80/36)*x

(-52/6)*(36/80) = x

-1.875 = x

And the y-value when x = -1.875 is:

y = -(2/6)*-1.875 - 1

y = -1.625

Then the point on the line 2x+6y+1=0 that is closest to (-5,-3) is the point (-1.875, -1.625)

Answer:

Square root of 3

Step-by-step explanation:

Answer:

can you help me with this math am not good enough