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4 years ago

Fred decides to think about retirement and invests at the age of 26. He invests $15,000 and hopes the investment will be

Mathematics

2 answers:

fgiga [73]4 years ago

6 0

Answer:

Step-by-step explanation:

Future value with continuous compounding ; FV = $Pe^{rt\\ } \\ 900,000 = 15,000e^{38r} \\ \\ \frac{900,000}{15,000} =e^{38r\\ }\\ \\ \\ 60 =e^{38r}$

Introduce <em>ln </em>on both sides of the equation

ln 60 = ln $e^{38r}$

note: ln $e^{x} = x$

Next, solve the equation;

4.09 = 38r

Divide both sides by 38 to solve for r;

4.09/38 = r

r= 0.107746 or 10.7746%

Therefore the rate would be 10.775% to the nearest a tenth of a percent.

Eddi Din [679]4 years ago

5 0

Answer:

10.8%

Step-by-step explanation:

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A family plans to have the hardwood floors in their square dining room re-finished, and new baseboards installed. The cost of re

Alexus [3.1K]

Answer:

Dimension of room = 18 foot x 18 foot

Step-by-step explanation:

Let the square room is of side a foot,

The cost of re-finishing the hardwood floors is $2.25 per square foot and the cost of purchasing and installing the new baseboards $14.5 per linear foot

Total cost is $1773.

Cost for re-finishing the hardwood floors = Area x 2.25

Area = a²

Cost for re-finishing the hardwood floors = 2.25 a²

Cost of purchasing and installing the new baseboards = Perimeter x 14.5

Perimeter = 4a

Cost of purchasing and installing the new baseboards = 4a x 14.5 = 58 a

Total cost = Cost for re-finishing the hardwood floors + Cost of purchasing and installing the new baseboards

1773 = 2.25 a² + 58a

2.25 a² + 58a - 1773 = 0

a = 18 or a = -43.77(not possible)

Dimension of room = 18 foot x 18 foot

7 0

4 years ago

Suppose a principal amount of $2079 were invested into a simple interest account that pays an annual rate of 2.31% then the amou

Anna35 [415]

Answer:

The amount of interest earned at the end of 14 years would be $672.3486

Step-by-step explanation:

This is a simple interest problem.

The simple interest formula is given by:

$E = P*I*t$

In which E are the earnings, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.

In this problem, we have that:

$P = 2079, I = 0.0231, t = 14$

$E = 2079*0.0231*14 = 672.3486$

The amount of interest earned at the end of 14 years would be $672.3486

4 0

3 years ago

11. What is the location of the vertex of the parabola defined by f(x) = −3x2 − 18x − 35 and in what direction does the parabola

lbvjy [14]

11. The given parabola has equation: $f(x)=-3x^2-18x-35$

We complete the square to have the function in the vertex form: $f(x)=-3(x^2+6x)-35$

$f(x)=-3(x^2+6x+9)+3*9-35$

$f(x)=-3(x^2+6x+9)+27-35$

$f(x)=-3(x+3)^2-8$

The vertex is (-3,-8), the graph opens down because a=-3<0

Ans: B. Vertex: (−3, −8), opens downward

12. We know the graph of $y=x^2$ is a parabola that opens up and has its minimum point at the origin.

The range of this function is $y\ge 0$

A straight line that has its y-intercept below the x-axis (y=3x-6) will not intersect $y=x^2$ and hence will form a system with no solution.

Ans: D. y equals x squared, y equals 3x minus 6

14. We want to find the zeros of $x^2+21x=5x-63$

$x^2+21x-5x+63=0$

$x^2+16x+63=0$

The factored form is $(x+7)(x+9)=0$

$x=-7\:or\: x=-9$

Ans: C. x = −7, −9

15. The given quadratic expression is $6x^2-17x+10$

We split the middle term to obtain:

$6x^2-12x-5x+10=0$

We factor by grouping to get:

$6x(x-2)-5(x-2)=0$

$(x-2)(6x-5)=0$

Ans: D. 6x − 5

8 0

4 years ago

Read 2 more answers

Joseph Bettino purchased an 11.5-ounce box of cereal for $3.99. What is the unit price of the cereal?

jok3333 [9.3K]

Answer:

$0.35 per ounce. (rounded.)

Step-by-step explanation:

you just divide.

8 0

3 years ago

Read 2 more answers

Write the equation of a circle givin by (x-3)^2+(y+7)^2=4

Ostrovityanka [42]

Answer:8

Step-by-step explanation:(

)

(

−

)

This is the form of a circle. Use this form to determine the center and radius of the circle.

(

−

)

(

−

)

Match the values in this circle to those of the standard form. The variable

represents the radius of the circle,

represents the x-offset from the origin, and

represents the y-offset from origin.

−

The center of the circle is found at

(

)

Center:

(

−

)

These values represent the important values for graphing and analyzing a circle.

Center:

(

−

)

Radius:

6 0

3 years ago