4 pts
John makes $2,800 per month and has an opportunity to invest $150 per month at an APR of 4.5% in a 401K plan through work. He plans to retire in 30 years.



Type in the EXACT formula you would use in excel (no spaces) to find the amount in the account after he has invested for 30 years.



Using excel, what is the answer to the formula from the previous part?



How much money will he deposit into the 401K over the 30 years?



How much total interest will he earn on his 401K over the 30 years?

Answer:

[tex]3 \sqrt{2} [/tex]

Step-by-step explanation:

[tex] \sqrt{(9 \times 2)} [/tex]

Take the square root of 9 out of the square root and leave the 2 in.

Answer:

3[tex]\sqrt{2}[/tex]

Step-by-step explanation:

Using the rules of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex] , then

[tex]\sqrt{3}[/tex] × [tex]\sqrt{6}[/tex]

= [tex]\sqrt{3(6)}[/tex]

= [tex]\sqrt{18}[/tex]

= [tex]\sqrt{9(2)}[/tex]

= [tex]\sqrt{9}[/tex] × [tex]\sqrt{2}[/tex]

= 3[tex]\sqrt{2}[/tex]

15,068 mi/hr

Step-by-step explanation:

[tex]22100\:\frac{\text{ft}}{\text{s}}×\frac{1\:\text{mi}}{5280\:\text{ft}}×\frac{60\:\text{s}}{1\:\text{min}}×\frac{60\:\text{min}}{1\:\text{hr}}[/tex]

[tex]=15,068\:\text{mi/hr}[/tex]

The speed of 22100 feet per second will be 15068.18 miles per hour.

Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure.

Unit conversion is the expression of the same property in a different unit of measurement. Time, for example, can be expressed in minutes rather than hours, and distance can be converted from miles to kilometres, feet, or any other length measurement.

Given that the speed of the satellite is 22100 feet per second. The speed in miles per hour will be calculated as,

22100 ft /s = ( 22100 x 3600 ) / 5280

22100 ft/s = 79560000 / 5280

22100 ft/s = 15068.18 miles per hour

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The exact amount of oil that leaks out for 0 ≤ t ≤ 10 is given by the integral,

[tex]\displaystyle\int_0^{10}r(t)\,\mathrm dt[/tex]

Then the upper and lower estimates of this integral correspond to the upper and lower Riemann/Darboux sums. Since r(t) is said to be decreasing, this means that the upper estimate corresponds to the left-endpoint Riemann sum, while the lower estimate would correspond to the right-endpoint sum.

So you have

• upper estimate:

(8.8 L/h) (2 h - 0 h) + (7.6 L/h) (4 h - 2h) + (6.8 L/h) (6 h - 4h) + (6.2 L/h) (8 h - 6h) + (5.7 L/h) (10 h - 8 h)

= (2 h) (8.8 + 7.6 + 6.8 + 6.2 + 5.7) L/h)

= 70.2 L

• lower estimate:

(7.6 L/h) (2 h - 0 h) + (6.8 L/h) (4 h - 2h) + (6.2 L/h) (6 h - 4h) + (5.7 L/h) (8 h - 6h) + (5.3 L/h) (10 h - 8 h)

= (2 h) (7.6 + 6.8 + 6.2 + 5.7 + 5.3) L/h)

= 63.2 L

9514 1404 393

Answer:

  y = -9x +49

Step-by-step explanation:

The slope of line b is the same as the slope of line a. That can be found using the slope formula:

  m = (y2 -y1)/(x2 -x1)

  m = (-1 -8)/(2 -1) = -9

The y-intercept can be found from the given point using the formula ...

  b = y - mx

  b = 13 -(-9)(4) = 13 +36 = 49

Then the slope-intercept equation of line b is ...

  y = -9x +49

Answer:

The slope is undefined.

Step-by-step explanation:

The line must pass through the points (10,-3) and (10,-8), meaning that it must be vertical. The slope of a line is undefined if the line is vertical.

9514 1404 393

Answer:

  (b)  x = -2

Step-by-step explanation:

The graph shows the lines intersect at (x, y) = (-2, 3).

The x-coordinate of the solution is x = -2.

9514 1404 393

Answer:

  382 cm²

Step-by-step explanation:

The side facing is a trapezoid with bases 8 and 14 cm, and height 7 cm. Its area is ...

  A = 1/2(b1 +b2)h

  A = (1/2)(8 +14)(7) = 77 . . . . cm²

The perimeter of the face is ...

  7 cm + 8 cm + 9 cm + 14 cm = 38 cm

The total surface area is the sum of the lateral area and the base area.

  SA = LA + BA

  SA = (38 cm)(6 cm) + 2×(77 cm²) = 228 cm² + 154 cm²

  SA = 382 cm²

The surface area of the composite figure is 382 square centimeters.

_____

Additional comment

The lateral area is the width of a rectangular face (6 cm) times the total of all of the lengths of those faces. That total is the perimeter of the trapezoidal base (38 cm).

There are two trapezoidal bases that contribute area. The first calculation figured the area of one of them.

Answer:

Always. Always.

Step-by-step explanation:

All circles conform to the same equations such as using pie to calculate circumference. Unlike a rectangle, for example, all ratios used in a circle are the same.

Answer: I believe that you have to do e^3 to find the volume of a cube.

If you had the side, you would do a^3 (a stands for the side length)

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

Explanation:

Focus entirely on the triangle on the right side. The other parts of the drawing are not necessary. In my opinion, they are distracting filler.

Refer to the diagram below.

We have an unknown adjacent side, let's call it x, that's along the horizontal part of the triangle.

The hypotenuse however is known and it is 19 ft

We use the cosine ratio to tie the two sides together

cos(angle) = adjacent/hypotenuse

cos(75) = x/19

19*cos(75) = x

x = 19*cos(75)

x = 4.9175618569479 which is approximate

x = 4.9

The base of the ladder is roughly 4.9 feet away from the base of the house.

Side note: make sure your calculator is in degree mode.

Answer:

180000 people

1 : 2

$40

80 stores

Step-by-step explanation:

1.)

Population in 2020 are equal : Let population =

City A increased by 20% From 120,000 in 2015

(1 + 0.2) * 120,000 = (1.2 * 120,000) = 144,000

Hence, city A = 144,000.

Since, city A and B have equal population ; city B also has a population of 144000 in 2020.

Let population in 2015 = x

(1 - 0.2) * x = 144000

0.8x = 144000

x = 144000/0.8

x = 180,000

2.)

Let proportion of 20% butter = x and proportion of 50% butter = 1 - x

0.2x + 0.5(1 - x) = 0.4

0.2x + 0.5 - 0.5x = 0.4

-0.3x + 0.5 = 0.4

-0.3x = 0.4 - 0.5

-0.3x = - 0.1

x = 0.1/0.3

x = 0.3333

(1-x) = 1 - 0.33333 = 0.6666%

0.3333% of 20% butter

0.6666% of 50% butter

Hence ;

0.3333 : 0.6666

1 : 2

3.)

Let original price of book = x

Discount on sale = 30%

Sale price = $28

Sale price = original price * (1 - discount)

$28 = (1 - 0.3) * x

$28 = 0.7x

x = $28/0.7

x = $40

4.)

Let total number of stores = x

Store surveys needed = 32

40% of total stores = 32 stores

0.4x = 32

x = 32 / 0.4

x = 80

9514 1404 393

Answer:

  6 units

Step-by-step explanation:

The dilation factor is 2, so the length of A'B' will be 2 times the length of AB.

AB can be seen to be 3 units, so A'B' will be 2×3 = 6 units.

Answer:

The point is a solution

Step-by-step explanation:

y = x^2

Substitute the point into the equation and see if it is true

0 = 0^2

0=0

True

Answer:

{(121, 63), (180, 71), (140, 67), (108, 65), (165, 72)}

Step-by-step explanation:

We have:

Weight as a function of height.

Give the points for these students that represent height as a function of weight:

Inverse of the input, that is, in the (x,y) format, (x,y) -> (y,x), the coordinates are exchanged, and thus, the correct option is:

{(121, 63), (180, 71), (140, 67), (108, 65), (165, 72)}

Answer:

8 minuets

Step-by-step explanation:

24min/3miles = 8

Answer:

8 minutes.

Step-by-step explanation:

If we divide 24 minutes by 3 miles, your answer will be 8 minutes.

Answer:

It cannot be 0

Step-by-step explanation:

it can also be positive number :2/4

it can be odd number too:3/9

it is bigger than numerator bcoz we have to divide it for numerator

So, 0 number cannot be put as denominator in fraction is true statement

Answer:

what are the answers

Step-by-step explanation:

If y (0) = -1/3, then

-1/3 = 1 / (1 + C e ⁻⁰)

Solve for C :

-1/3 = 1 / (1 + C )

-3 = 1 + C

C = -4

So the particular solution to the DE that satisfies the given initial condition is

[tex]\boxed{y=\dfrac1{1-4e^{-x}}}[/tex]

Answer:

90

Step-by-step explanation:

The sum of the angles of a triangle is 180 degrees

x+x+10 +x+50 = 180

3x+60= 180

3x = 180-60

3x = 120

Divide by 3

3x/3 = 120/3

x = 40

The largest angle is

x+50

40+50 = 90

We have to,

find the measure of the largest angle.

Given that,

The angles in a triangle are represented by x, x+10, and x+50.

Let's start to solve,

→ x+ (x+10) + (x+50) = 180°

→ x + x + x = 180° (-50-10)

→ 3x = 180° -60

→ 3x = 120

→ x = 120/3

→ [x = 40°]

Then the value of x + 10,

→ x + 10

→ 40 + 10

→ 50°

Then the value of x + 50,

→ x + 50

→ 40 + 50

→ 90°

The measure of the largest angle is,

→ D. 90 degrees

Thus, option (D) is the correct answer.

Answer:

217 is the perfect swuare i think

Answer:

0.055 = 5.5% probability that exactly 5 employees were over 50.

Step-by-step explanation:

The employees are dismissed from the sample without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[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]

In this question:

Total of 7 + 18 = 25 employees, which means that [tex]N = 25[/tex]

7 over 50, which means that [tex]k = 7[/tex]

10 were dismissed, which means that [tex]n = 10[/tex]

What is the probability that exactly 5 employees were over 50?

This is P(X = 5). So

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 5) = h(5,25,10,7) = \frac{C_{7,5}*C_{18,5}}{C_{25,10}} = 0.055[/tex]

0.055 = 5.5% probability that exactly 5 employees were over 50.

Answer: [tex]Rs.3,69,000[/tex]

Step-by-step explanation:

Given

average monthly salary of a worker is [tex]Rs.8200[/tex]

If there are 45 workers in a factory

Total expenditure is calculated by taking the product of Average monthly salary and no of workers in the factory

[tex]\Rightarrow 8200\times 45\\\Rightarrow Rs.3,69,000[/tex]

Answer:

117.8 in.

Step-by-step explanation:

To find the perimeter, add all the side lengths together. If we do that, we get 117.8 in, which is the answer.

Answer:

E

Step-by-step explanation:

Since all the numbers are hundredths decimals, let multiply by the power of 2 of the base 10. So let multiply the equation by

[tex]10 {}^{2} [/tex]

So our new equation is

[tex]3 3{x}^{2} + 71x - 14 = 0[/tex]

Solve by AC method

[tex]ac = - 462[/tex]

[tex]b = 71[/tex]

We must think of two numbers that

Multiply to -462 and Add to 71. Set up equation

The numbers are 77 and -6.

So our new equation is

[tex] {33x}^{2} + 77x - 6x - 14 = 0[/tex]

Solve by factoring by grouping

[tex](33 {x}^{2} + 77x) - (6x - 14)[/tex]

Factor out 11 for the first equation

[tex]11x(3x + 7) - 2(3x + 7)[/tex]

So our factors are

[tex](11x - 2)(3x + 7)[/tex]

Set each equal to zero

[tex]11x - 2 = 0[/tex]

[tex]11x = 2[/tex]

[tex]x = \frac{2}{11} [/tex]

[tex]3x + 7 = [/tex]

[tex]3x = - 7[/tex]

[tex]x = \frac{ - 7}{3} [/tex]

Answer:

[tex](12\frac{1}{3} *2)+(10\frac{3}{4} *2)\\\\=(\frac{12(3)+1}{3} *2)+(\frac{10(4)+3}{4} *2)\\\\=\frac{37*2}{3} +\frac{43*2}{4} \\\\=\frac{74}{3} +\frac{86}{4} \\\\=\frac{74(4)+86(3)}{3*4} \\\\=\frac{296+258}{12} \\\\=\frac{554}{12}[/tex]

Answer:

(-2,2) and (-3,-4)

Step-by-step explanation:

by graphing the line and parabola, you should get this graph

Answer:

sqrt( 150)

Step-by-step explanation:

it can also be 5sqrt(6)

The solution is,  the area of the triangle. ABC is 10 cm^2.

Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.

here, we have,

from the given diagram, we get,

we have to find the area of the triangle. ABC

now, we have,

using the Pythagorean theorem, we get,

BD = √AB² - AD²

     =√50 - 45

     =√5

now, we know that,

area of triangle = 1/2 * base * height

                          = 1/2 * √5 * 4√5

                          = 10

Hence, The solution is,  the area of the triangle. ABC is 10 cm^2.

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Answer:

8 x 9

Have a nice day!