Suppose a young couple deposits $1000 at the end of each quarter in an account that earns 7.6%, compounded quarterly, for a period of 8 years. After the 8 years, they start a family and find they can contribute only $200 per quarter. If they leave the money from the first 8 years in the account and continue to contribute $200 at the end of each quarter for the next 19 years, how much will they have in the account (to help with their child’s college expenses)?

Answer:

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Number of marbles:

Total number:

Probability of getting a blue marble:

Since the second marble is selected with replacement, the probability of the second blue marble is same, so the probability of two blue marbles is:

[tex] \sf \: Probability _{(Blue)}=2/10×2/10 \\ \\ \sf Probability _{(Blue)}= \frac{1}{25} [/tex]

Answer:

x = 15

Step-by-step explanation:

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

x² = 9² + 12² = 81 + 144 = 225 ( take square root of both sides )

x = [tex]\sqrt{225}[/tex] = 15

Answer:

x = 15

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]

From inspection of the given right triangle:

Substitute the given values into Pythagoras Theorem and solve for x:

[tex]\implies 9^2+12^2=x^2[/tex]

[tex]\implies 81+144=x^2[/tex]

[tex]\implies 225=x^2[/tex]

[tex]\implies \sqrt{x^2}=\sqrt{225}[/tex]

[tex]\implies x=15[/tex]

Step-by-step explanation:

I'm pretty sure it's 19200? or maybe im writing is wrong

Answer:

After 24 years population of the city will be 27000.

exponential function.

Step-by-step explanation:

in picture

Answer: -3√3

Step-by-step explanation: Factor out the square roots from each term

2√54 -> 6√6

√27 -> 3√3

3√24 -> 6√6

The equation becomes 6√6 - 3√3 - 6√6

By combining like terms we can eliminate 6√6

This leaves us with -3√3 as the simplified solution

Answer:

-3√3

Step-by-step explanation:

do the hcf method to get all the values outside

hcf of 54= 2, 3, 3, 3

hcf of 27 = 3, 3, 3

hcf of 24 = 2,2,3,3

2✓2×3×3×3 - √3,3,3 - 3√2,2,3,3

take out the common factor and multiply it with the value we have outside leave it if it doesnt have a number

2×3√2×3 - 3✓3 -3×2×3

6√6 - 3√3 - 3×2×3

6×3 - 3√3 - 3×2×3

18-18 - 3✓3

-3√3

Linear function Is a function that can be graphed as a solid line discrete or continuous

Linear functions are simply known as functions whose graph is a straight line.

They have one dependent variable and one independent variable.

These functions have either one or two variables without exponents.

Continuous graphs are used to represent functions that are continuous along their entire or whole domain.

Whereas, discrete graphs are used to represent values at specific points along the number line from different directions.

Types of the linear function;

Hence, it is a linear function

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Step-by-step explanation:

that is a college level question ? and you don't know the answer ?

that is basic, basic, basic ...

you go on the x-axis to -2.

from there you go either up or down and look at what y-value are you crossing the functional curve.

it is -1.

so, the "output" for x = -2 is y = -1. or simply -1.

The cost of renting the car for one day and driving 200 miles is $54.

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, In some cities you can rent a car for $18 per day and $0.20 per miles.

Establishing the equation for finding total cost y for x miles and d days

y = 18d + 0.2x

For 200 miles, the cost =

y = 18×1+0.20×200

y = 18+40

y = $54

Hence, the cost of renting the car for one day and driving 200 miles is $54.

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The MIRR statistic for the project I given the cost of capital and the reinvestment rate, is 7. 43 %.

A monetary indicator of an investment's allure is the modified internal rate of return or MIRR. Ranking equivalent alternative investments is done in capital budgeting.

You can use a spreadsheet to find the MIRR by first ordering the cash flows as shown in the attached image. Then use the = MIRR function.

The cost of capital is the finance charge which is 11 %. The reivestment rate will be the same as the finance charge if not given so it will be 11 % as well.

The MIRR is therefore 7 .43 %.

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Therefore , the solution of the problem of probability comes out to be  

Probability = 0.25 or 25% that he will pass using this random option picking method.

Probability is the likelihood or potential for something to event.  For instance, there is only one way to get a head and a total of two possible outcomes, hence the probability of flipping a coin and getting heads is 1 in 2. (a head or tail). P(heads) must equal 12. Classical: (equally likely results) (equally probable outcomes) S, the sample location (the collection of all distinct outcomes that could occur), Definition of Relative Frequency and Subjective Probability.

Here,

Given : t the end of each week there is a 5 questions multiple choice test.

and

Has 4 options.

Probability that he will pass using this random option picking method.

=> Probability = Favourable events / Total no of outcomes

=>  Probability = 1 /4

=> Probability = 0.25 or 25%

Therefore , the solution of the problem of probability comes out to be  

Probability = 0.25 or 25% that he will pass using this random option picking method.

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Answer:

no solutions

Step-by-step explanation:

   -9x-2y=5

- (-9x-2y=11)

-9x-(-9x) - 2y-(-2y) = 5 - 11  ==> subtract the top two equations

-9x + 9x - 2y + 2y = -6  ==> subtracting by a negative number is equivalent

                                       to adding by a positive number

(-9x + 9x) - 2y + 2y = -6

0 - 2y + 2y = -6

0 - 0 = -6

0 [tex]\neq[/tex] -6  ==> Hence, there is no solutions.

Answer:

Below

Step-by-step explanation:

Each PERIOD is 3 months     there is   4 periods per year

  periodic interest =  .055/4

   effective interest per year would then be

       (1 + .055/4)^4  - 1  = .056144  = ~ 5.61%

Answer:

8.20

Step-by-step explanation:

8.20 is greater than 8.002 due to 0.20 being greater than 0.002

As determined in part, the ball reaches its highest point at time t is 2 seconds

S(t) = 32t - 16t2 is the formula for the displacement s(t) as a function of time t. We presume that the upward motion began at this altitude above the earth.

The ball's starting speed is 64 feet per second.

(A) The velocity is the displacement's first time derivative: v(t) = ds/dt = 32t – 16t. We are just deriving the function s for the first time (t).

(B) v(t = 3) = 32t– 16(3) = –32 feet per second. The ball is currently travelling downhill, according to the negative indication.

(c) The ball briefly pauses as it reaches its highest height before dropping. By setting the velocity to zero to symbolise this halt, we can calculate how long it will take the ball to reach its highest point.

v(t) = 32 - 16t = 0

or 16t = 32

out = 2 seconds.

As determined in part, the ball reaches its highest point at t = 2 seconds (c).

s(t = 2) = 32(2) - 16(2) (2)

2

or 32 feet if s(t = 2).

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Answer:

62 degrees.

Step-by-step explanation:

I think this because it appears that ABC makes a 90 degree angle and I would think that you would just subtract 28 from 90 and get 62.

Hope it helps! =D

The piecewise-defined function for this graph will be y = -(3/5)x - 4/5 for x < 2 and y = (5/2)x - 7 for x ≥ 2.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The equation of the line that passes through (-3, 1) and (2, -2) is given as,

(y + 2) = [(- 2 - 1) / (2 + 3)](x - 2)

y + 2 = - (3/5)x + 6/5

y = -(3/5)x - 4/5

The equation of the line that passes through (2, -2) and (4, 3) is given as,

(y + 2) = [(3 + 2) / (4 - 2)](x - 2)

y + 2 = (5/2)x - 5

y = (5/2)x - 7

The piecewise-defined function for this graph will be y = -(3/5)x - 4/5 for x < 2 and y = (5/2)x - 7 for x ≥ 2.

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Tasha, because she has the lowest ratio since 0.7 < 0.625

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

The ratio of hits compared to total attempts is their batting average

Each player on the team wants to have the highest batting average to help their team the most.

Jana has hit the ball 7 times out of 10 attempts.

Average is 7/10=0.7

Tasha has hit the ball 10 times out of 16 attempts.

Tasha Average is 10/16=0.625

We need to find the player who has better batting average

Tasha, because she has the lowest ratio since 0.7 < 0.625

Hence, Tasha, because she has the lowest ratio since 0.7 < 0.625

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The next step in the series is, shown in Option C.

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

There are three steps are shown.

Now, In first step, only one line shown.

In second line the line is left to first line.

And, So on.

Hence, The next step in the series is, shown in Option C.

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Answer:

[tex]\dfrac{1}{a^{20}c^2d^2e^{6}}[/tex]

Step-by-step explanation:

Given expression:

[tex](a^{10}b^{0}cde^{3})^{-2}[/tex]

[tex]\textsf{Apply the exponent rule} \quad a^{-n}=\dfrac{1}{a^n}:[/tex]

[tex]\implies \dfrac{1}{(a^{10}b^{0}cde^{3})^{2}}[/tex]

[tex]\textsf{Apply the exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies \dfrac{1}{a^{(10 \times 2)}b^{(0 \times 2)}c^2d^2e^{(3 \times 2)}}[/tex]

Simplify:

[tex]\implies \dfrac{1}{a^{20}b^{0}c^2d^2e^{6}}[/tex]

[tex]\textsf{Apply the exponent rule} \quad a^0=1:[/tex]

[tex]\implies \dfrac{1}{a^{20}(1)c^2d^2e^{6}}[/tex]

[tex]\implies \dfrac{1}{a^{20}c^2d^2e^{6}}[/tex]

Answer:316.8

Step-by-step explanation:

Answer:316.8

Step-by-step explanation:

UV is a segment Bisector.

A segment bisector is a line, ray, or segment that splits another line segment in half evenly at its center. The midpoint of the line segment is always bisected by the line, which divides it into two equally sized parts.

The angle bisector theorem states that a triangle's opposite side is divided into two parts by an angle bisector that is proportional to the triangle's other two sides.

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The three ways to purchase a vehicle include: (1) On lease  (2) On hire purchased and (3) On cash basis

A vehicle can be purchased on the following ways:

Lease:  This involves granting the user access on the property over a period of time before he could make payment

Hire purchase:  In this method, the buyer deposits first initial money while he agrees with the seller to make the payment of the balance on installment basis

Cash:  In this method the buyer pays cash at prompt or on the point of purchase

Advantages include:

It places the buyer on good life without cash

He enjoys the luxurious life

Disadvantages:

He can run away with the vehicle

The seller looses in cash of accident taking the life of the buye

Additional expenses include

Cost of maintenance

Repairs

Fueling

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Answer:

6/7

Step-by-step explanation:

36/42 = 36:6/42:6 = 6/7

Therefore ,the value of a given fraction is equal to 10/12, which equals 5/6, after resolving the given problem.

To represent a whole, divide it into any number of comparable parts, or fractions. How many units of a particular size there are is expression using fractions in standard English. 8, 3/4. Parts of a whole are included. Numbers in mathematics are stated as a ratio of the excess to the denominator. These are each simple fractions that represent an integer. A fraction is contained in the fraction or reduction of a complex fraction. When a fraction is true, its numerators are less than its denominators. An amount that makes up a fraction of a whole is called a fraction. You can assess the whole by dissecting it into smaller pieces.

Here,

Given : 5/8 X 4/3

=> 5/8 X 4/3 = 20/24

on condensing,

10/12 = 5/6

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Therefore , the solution of the given problem of equation comes out to be  x = 38.

Equivalent is the meaning of the Latin term equ. A lot of variable words in the English language, such as adequate, equator, and equality, have Latin roots as their root words. Since both side of an equations are, by definition, "equal" to one another, the Latin root term equ makes its way into our vocabulary quite simply.

Here,

Given : m m/MTU = 38°, and m/STU = 2x + 88.

thus,

x + 50 = 2x + 88

To find the value of x:

We do,

=> x + 50 = 2x +88

=> x -2x  = 88 -50

=> -x = -38

=> x = 38

Therefore , the solution of the given problem of equation comes out to be x = 38.

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Answer:

45.5km

Step-by-step explanation:

AREA= base x height

So with this equation, we know that 5km is the height, and 9.1km is the base.

So to find out the area all we have to do is 9.1x5 which equals 45.5

The rate based on the information will be 590 kilometers per hour and 1010 kilometers per hour

Rate in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that rate contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).

Since the an airplane travels 4720 kilometers in 8 hours. The rate is:

= 4720 / 8

= 590 kilometers per hour

Flying with the wind, the same plane travels 4040 kilometers in 4 hours. The rate will be:

= 4040 / 4

= 1010 kilometers per hour

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Answer:

b

Step-by-step explanation:

i think i say c because a is 30 degrees and c is 90 the whole triange needs to be 180 so b would be 60 also you see one side is 10 the other side also known as b is also 10 they have to be the same length and a is five because half of 10 is 5

The Value for x and y as follow:

A) x=2 and y=-8

B) x = -2 and y = 5

C) x = -9/4 and y= -5/2

The elimination approach involves taking one variable out of the system of linear equations by utilising addition or subtraction together with multiplication or division of the variable coefficients.

Given:

A) 9x- 2y = 34...............(1)

5x+ 2y = -6..............(2)

Adding equation (1) and (2) we get

9x -2y = 34

5x + 2y = -6

_____________

14x = 28

x= 28/14

x= 2

and, 5x +2y= -6

5(2) + 2y= -6

2y = -6 -10

y = -8

B) x+ 6y = 28.....................(3)

2x -3y = -19................(4)

Multiply equation (2) by 2 we get

4x - 6y = -38.......................(5)

Adding equation (3) and (5), we get

x + 6y = 28

4x- 6y = -38

___________

5x = -10

x= -2

and, x+ 6y= 28

-2 +6y= 28

6y= 30

y=5

C) 8x -6y = -3................(6)

6x -5y = -1......................(7)

Multiply equation (6) by 5 and equation by (6), we get

40x - 30 y = -15

36 x - 30y = -6

-       +           +

____________

4x = -9

x= -9/4

and, 8x - 6y = -3

8(-9/4) - 6y = -3

-18 - 6y= -3

-6y = 15

y = -5/2

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