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Veseljchak [2.6K]

3 years ago

12

Janine has job offers at two companies. one company offers a starting salary of $28,000 with a raise of $3000 each year . the ot

her company offers a starting salary of $36,000 with a raise of $2000 each year. ? after how many years would janine's salary be the same with both ccomanies?

1 answer:

ollegr [7]3 years ago

7 0

After nine years the salaries will be the same
28000 3600031000 3800034000 4000037000 4200040000 4400043000 4600046000 4800049000 5000052000 52000

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A box with a rectangular base and open top must have a volume of 128 f t 3 . The length of the base is twice the width of base.

noname [10]

Answer:

$Width = 4ft$

$Height = 4ft$

$Length = 8ft$

Step-by-step explanation:

Given

$Volume = 128ft^3$

$L = 2W$

$Base\ Cost = \$9/ft^2$

$Sides\ Cost = \$6/ft^2$

Required

The dimension that minimizes the cost

The volume is:

$Volume = LWH$

This gives:

$128 = LWH$

Substitute $L = 2W$

$128 = 2W * WH$

$128 = 2W^2H$

Make H the subject

$H = \frac{128}{2W^2}$

$H = \frac{64}{W^2}$

The surface area is:

Area = Area of Bottom + Area of Sides

So, we have:

$A = LW + 2(WH + LH)$

The cost is:

$Cost = 9 * LW + 6 * 2(WH + LH)$

$Cost = 9 * LW + 12(WH + LH)$

$Cost = 9 * LW + 12H(W + L)$

Substitute: $H = \frac{64}{W^2}$ and $L = 2W$

$Cost =9*2W*W + 12 * \frac{64}{W^2}(W + 2W)$

$Cost =18W^2 + \frac{768}{W^2}*3W$

$Cost =18W^2 + \frac{2304}{W}$

To minimize the cost, we differentiate

$C' =2*18W + -1 * 2304W^{-2}$

Then set to 0

$2*18W + -1 * 2304W^{-2} =0$

$36W - 2304W^{-2} =0$

Rewrite as:

$36W = 2304W^{-2}$

Divide both sides by W

$36 = 2304W^{-3}$

Rewrite as:

$36 = \frac{2304}{W^3}$

Solve for $W^3$

$W^3 = \frac{2304}{36}$

$W^3 = 64$

Take cube roots

$W = 4$

Recall that:

$L = 2W$

$L = 2 * 4$

$L = 8$

$H = \frac{64}{W^2}$

$H = \frac{64}{4^2}$

$H = \frac{64}{16}$

$H = 4$

Hence, the dimension that minimizes the cost is:

$Width = 4ft$

$Height = 4ft$

$Length = 8ft$

8 0

2 years ago

Can you help me simplify this expression 16d + 20c + 5d -7 - 8c - 7d + 3?

dimulka [17.4K]

Answer:

12c + 14d - 4

Step-by-step explanation:

16d + 20c + 5d -7 - 8c - 7d + 3

Simplify the expression

__________________________

To solve, we need to first take in mind the fact that there are different like terms within this expression. Like terms are numbers or values that end in different symbols, such as variables or exponents. Since we are filled with variables such as c and d. We can do as followed :

Combine the "d" like terms :

16d + 5d - 7d

21d - 7d

14d

Combine the "c" like terms :

20c - 8c

12c

Combine the constants :

-7 + 3

-4

Now add all of the values together to get the final expression.

12c + 14d - 4

6 0

2 years ago

Read 2 more answers

In New York City at the spring equinox there are 12 hours 8 minutes of daylight. The

slamgirl [31]

Answer:

independent: day number; dependent: hours of daylight

d(t) = 12.133 +2.883sin(2π(t-80)/365.25)

1.79 fewer hours on Feb 10

Step-by-step explanation:

a) The independent variable is the day number of the year (t), and the dependent variable is daylight hours (d).

__

b) The average value of the sinusoidal function for daylight hours is given as 12 hours, 8 minutes, about 12.133 hours. The amplitude of the function is given as 2 hours 53 minutes, about 2.883 hours. Without too much error, we can assume the year length is 365.25 days, so that is the period of the function,

March 21 is day 80 of the year, so that will be the horizontal offset of the function. Putting these values into the form ...

d(t) = (average value) +(amplitude)sin(2π/(period)·(t -offset days))

d(t) = 12.133 +2.883sin(2π(t-80)/365.25)

__

c) d(41) = 10.34, so February 10 will have ...

12.13 -10.34 = 1.79

hours less daylight.

5 0

2 years ago

You need a 35% alcohol solution. On hand, you have a 715 mL of a 20% alcohol mixture. You also have 90% alcohol mixture. How muc

asambeis [7]

Answer:

90% Solution

Step-by-step explanation:

5% of 90 + 90% of x = 75% of (90 + x)

5×90/100 + 90x/100 = 75×90/100 + 75x/100

Or 90x/100 - 75x/100 = 75×90/100 - 5×90/100

Or 15x/100 = 90×70/100

Or X = 420ml

You Will Need ML Of The 90% Solution To Obtain ML Of The Desired 75% Solution.

6 0

2 years ago

Read 2 more answers

Choose the type of function that is represented in each table below. (pic)

Vlada [557]

A.Linear B.Linear C.Exponential D.Other

5 0

3 years ago