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## Bill bought a new cellular phone. His monthly bill will be \$34.99 each month which includes 100 minutes of use. Additional minutes will cost \$0.23 per minute. Write an equation that represents the cost of the bill C in terms of m, which is the number of minutes used ABOVE the 100 that are included in the base price. a. C = 34.99(m – 100) + 0.23 c. C = 0.23m b. C = 0.23m + 34.99 d. C = 0.23(m – 100) + 34.99

d. C = 0.23(m – 100) + 34.99

Step-by-step explanation:

Let C = X + Y, where

C = Cost of the bill in terms of m

X = First term of the equation

Y = Second term of the equation

X = add additional minutes to \$ 0.23 minus the 100 minutes of use allocated.

X = 0.23 (m – 100)

Y = Base price monthly will be \$ 34.99

Y = 34.99

C = X + Y

C = 0.23 (m – 100) + 34.99

Note: The only possible answer is 0.23 (m – 100) + 34.99, but we must assume that “m” is greater than or equal to 100, that is, Bill consumes at least his 100 minutes assigned by the base price.

Hope this helps!

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## For jacobs company, the predetermined overhead rate is 70% of direct labor cost. during the month, \$600,000 of factory labor costs are incurred of which \$140,000 is indirect labor. actual overhead incurred was \$320,000. the amount of overhead debited to work in process inventory should be:

First find the amount of direct labor cost by subtracting the amount of indirect labor cost from the amount of factory labor cost
Direct labor cost is
600,000−140,000=460,000

The amount of overhead debited to work in process inventory should be
460,000×0.7=322,000

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## The property taxes on a house that Alan owns and rents out to have increased. to balance his monthly budget, he decides to increase his talents rent by \$10 per month. he will use extra money to pay his property tax. in this scenario, what type of tax do his tenants pay?

The property taxes on a house that Alan owns and rents out to have increased. to balance his monthly budget, he decides to increase his talents rent by \$10 per month. he will use extra money to pay his property tax. in this scenario, what type of tax do his tenants pay?

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## Franklin deposited \$75 in a no-interest bank account when he opened it. After that, he deposits \$50 per month in the account. Assume he makes no other withdrawls or deposits. The equation below can be used to find m, the number of months it take him to save a total of \$175 . What number should he use as the coefficient of m ??

Franklin deposited \$75 in a no-interest bank account when he opened it. After that, he deposits \$50 per month in the account. Assume he makes no other withdrawls or deposits. The equation below can be used to find m, the number of months it take him to save a total of \$175 . What number should he use as the coefficient of m ??

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## In the old Roman calendar, December was the _____ month.

In the old Roman calendar, December was the _____ month.

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## There are 150 marigold plants in a back yard. Each month, the number of marigold plants decreases by 15%. There are 125 sunflower plants in the back yard. Each month, 8 sunflower plants are removed. Part A: Write functions to represent the number of marigold plants and the number of sunflower plants in the back yard throughout the months. (4 points) Part B: How many marigold plants are in the back yard after 3 months? How many sunflower plants are in the back yard after the same number of months? (2 points) Part C: After approximately how many months is the number of marigold plants and the number of sunflower plants the same? Justify your answer mathematically. (4 points)

If a quantity A is decreased by 15%, it means that what is left is 85% of it.

85%A=

Part A.

Consider the 150 marigolds.

After the first month, 0.85*150 are left
After the second month, 0.85*0.85*150=
After the third month, 0.85*0.85*0.85*150 =
.
.
so After n months,  marigolds are left.

in functional notation:  is the function which gives the number of marigolds after n months

consider the 125 sunflowers.

After 1 month, 125-8 are left
After 2 months, 125-8*2 are left
After 3 months, 125-8*3 are left
.
.
After n months, 125-8*n sunflowers are left.

In functional notation: S(n)=125-8*n is the function which gives the number of sunflowers left after n months

Part B.

marigolds are left after 3 months.

S(3)=125-8*3=125-24=121 sunflowers are left after 3 months.

Part C.

Answer : equalizing M(n) to S(n) produces an equation which is very complicated to solve algebraically.

A much better approach is to graph both functions and see where they intersect.

Another approach is by trial, which gives 14 months

which are close numbers to each other.

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## One month Henry rented 3 movies and 8 video games for a total of \$58 . The next month he rented 5 movies and 2 video games for a total of \$23 . Find the rental cost for each movie and each video game. Rental cost for eachmovie:\$___ Rental costfor each video game:\$____

Henry rented 3 movies and 8 video games for a total of \$58
3m + 8v= \$58
The next month he rented 5 movies and 2 video games for a total of \$23.
5m + 2v = \$23.

Grab an equation and solve it for one of the variables:
3m + 8v= \$58
3m=58-8v
m=19.333-2.6666v

Then sub that result in for the variable in the other equation:
5(19.333-2.666666v )+ 2v = \$23.
96.666 – 13.333v + 2v = \$23.
96.666 – 11.333v = \$23.
-11.333v = \$23-96.666
-11.333v = -73.666
v=6.50

Now sub back in v in one of the equations:
5m + 2v = \$23.
5m + 2(6.50) = \$23.
5m+13 = 23
5m=10
m=2

The video games cost \$6.50 and the Movies cost \$2.00.

3(\$2.00) + 8(\$6.50) = \$58
5(\$2.00) + 2(\$6.50) = \$23.

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## One month Linda rented 3 movies and 5 video games for a total of \$38 . The next month she rented 6 movies and 2 video games for a total of \$26 . Find the rental cost for each movie and each video game. Rentalcostforeachmovie:\$ Rentalcostforeachvideogame:\$ One month Linda rented 3 movies and 5 video games for a total of \$38 . The next month she rented 6 movies and 2 video games for a total of \$26 . Find the rental cost for each movie and each video game. Rentalcostforeachmovie:\$ Rentalcostforeachvideogame:\$

X=cost of movie
y=cost of game

3x+5y=38
6x+2y=26

we can eliminate x’s
times firs equation by -2 and add to 2nd

-6x-10y=-76
6x+2y=26 +
0x-8y=-30

-8y=-50
divide both sides by -8
y=6.25

sub back

3x+5y=38
3x+5(6.25)=38
3x+31.25=38
3x=6.75
divide both sides by 3
x=2.25

each movie costs \$2.25 to rent
each game costs \$6.25 to rent

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## For her cellular service, Vera pays \$32 a month, plus \$0.75 for each minute over the allowed minutes in her plan. Write an expression that shows how much Vera’s bill will be for one month.

Well, “m” represent \$32 she spends a month and “t” be the \$0.75 for each minute will be.

First, since the bill is for one month, we can place “m” by itself with no add-ons to it since it’s been stated only a month is going by and it stays \$32. However, depending of “t” the price can change without the original monthly plan changing, so we write it like m + (t . x). “x” represent every minute spent over the time limit, so it’s “t” times “x” since whatever “t” is is determined by “x”. If “x” is 0, then “t” is 0 since nothing is added and it’d remain \$32. If say “x” was 10 however, that would mean 10 minutes have gone over the limit, so 0.75 x 10 would be \$7.50 + \$32 making it \$39.50.
Note: “m” and “t” can be different if you choose.

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## A company's monthly profit increases by \$1,000 each month. In January, the profit of the company was \$25,000. If x = 0 represents January, which of the following equations represents the profit as a function of time (in months)? A. y = 25,000x + 1,000 B. y = 1,000x C. y = 1,000x – 25,000 D. y = 1,000x + 25,000

A company’s monthly profit increases by \$1,000 each month. In January, the profit of the company was \$25,000. If x = 0 represents January, which of the following equations represents the profit as a function of time (in months)? A. y = 25,000x + 1,000 B. y = 1,000x C. y = 1,000x – 25,000 D. y = 1,000x + 25,000

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## Qs 14-2 fixed and variable costs lo c2 a cell phone company offers two different plans. plan a costs \$80 per month for unlimited talk and text. plan b costs \$0.20 per minute plus \$0.10 per text message sent. you need to purchase a plan for your 14-year-old sister. your sister currently uses 1,700 minutes and sends 1,600 texts each month. (1) what is your sisters total cost under each of the two plans

Plan A: Post paid plan

Total cost A = \$80 per month

Plan B: Pre paid plan

Total cost B = \$0.20 per
minute * 1,700 minutes + \$0.10 per text message * 1,600 texts

Total cost B = \$340 + \$160

Total cost B = \$500 per month

Therefore it is better to get
the post paid plan, plan A.

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## Optimization problem:A manufacturer determines that x employees on a certain production line will produce y units per month where . To obtain the maximum monthly production, how many employees should be assigned to the production line?**It is NOT sufficient to find an answer that you think is a max or a min without testing for relative extrema. You MUST test relative extrema at all times by using either the first or second derivative test even if you only have one critical value/point.

Cal problem!

given production
P(x)=75x^2-0.2x^4

To find relative extrema, we need to find P'(x) and solve for P'(x)=0.

P'(x)=150x-0.8x^3    [by the power rule]

Setting P'(x)=0 and solve for extrema.
150x-0.8x^3=0  =>
x(150-0.8x^2)=0 =>
0.8x(187.5-x^2)=0
0.8x(5sqrt(15/2)-x)(5sqrt(15/2)+x)=0
=>
x={0,+5sqrt(15/2), -5sqrt(15/2)}   by the zero product rule.
[note: eqation P'(x)=0 can also be solved by the quadratic formula]

Reject negative root because we cannot hire negative persons.

So possible extrema are x={0,5sqrt(15/2)}

To find out which are relative maxima, we use the second derivative test.  Calculate P”(x), again by the power rule,
P”(x)=-1.6x
For a relative maximum, P”(x)<0, so
P”(0)=0  which is not <0  [in fact, it is an inflection point]
P”(5sqrt(15/2))=-8sqrt(15/2) < 0, therefore x=5sqrt(15/2) is a relative maximum.

However, 5sqrt(15/2)=13.693 persons, which is impossible, so we hire either 13 or 14, but which one?

Let’s go back to P(x) and find that
P(13)=6962.8
P(14)=7016.8

So we say that assigning 14 employees will give a maximum output.

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## Inez Alexander has a car loan of \$425 per month at 5.5% annual interest rate. She would like to pay off the car one year early. About how much will her payoff be

Inez Alexander has a car loan of \$425 per month at 5.5% annual interest rate. She would like to pay off the car one year early. About how much will her payoff be

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## Bryan’s Bakery kept track of their March and April sales of all of their bakery products and noticed there was a definite relationship between the two. Based on the graph, if 50 Lipsmacking Butter Biscuits were sold in the month of April, how many were sold in the month of March? I don’t understand the chart.

The basis to respond this question are:

1) Perpedicular lines form a 90° angle between them.

2) The product of the slopes of two any perpendicular lines is – 1.

So, from that basic knowledge you can analyze each option:

a.Lines s and t have slopes that are opposite reciprocals.

TRUE. Tha comes the number 2 basic condition for the perpendicular lines.

slope_1 * slope_2 = – 1 => slope_1 = – 1 / slope_2, which is what opposite reciprocals means.

b.Lines s and t have the same slope.

FALSE. We have already stated the the slopes are opposite reciprocals.

c.The product of the slopes of s and t is equal to -1

TRUE: that is one of the basic statements that you need to know and handle.

d.The lines have the same steepness.

FALSE: the slope is a measure of steepness, so they have different steepness.

e.The lines have different y intercepts.

FALSE: the y intercepts may be equal or different. For example y = x + 2 and y = -x + 2 are perpendicular and both have the same y intercept, 2.

f.The lines never intersect.

FALSE: perpendicular lines always intersept (in a 90° angle).

g.The intersection of s and t forms right angle.

TRUE: right angle = 90°.

h.If the slope of s is 6, the slope of t is -6

FALSE. – 6 is not the opposite reciprocal of 6. The opposite reciprocal of 6 is – 1/6.

So, the right choices are a, c and g.

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## Marie has \$830 in her bank account and withdraws \$60 each month. Denise has \$970 in her bank account and withdraws \$80 each month. In how many months will Marie and Denise have equal amounts of money in their accounts? A. 4 B. 5 C. 7 D. 9

The basis to respond this question are:

1) Perpedicular lines form a 90° angle between them.

2) The product of the slopes of two any perpendicular lines is – 1.

So, from that basic knowledge you can analyze each option:

a.Lines s and t have slopes that are opposite reciprocals.

TRUE. Tha comes the number 2 basic condition for the perpendicular lines.

slope_1 * slope_2 = – 1 => slope_1 = – 1 / slope_2, which is what opposite reciprocals means.

b.Lines s and t have the same slope.

FALSE. We have already stated the the slopes are opposite reciprocals.

c.The product of the slopes of s and t is equal to -1

TRUE: that is one of the basic statements that you need to know and handle.

d.The lines have the same steepness.

FALSE: the slope is a measure of steepness, so they have different steepness.

e.The lines have different y intercepts.

FALSE: the y intercepts may be equal or different. For example y = x + 2 and y = -x + 2 are perpendicular and both have the same y intercept, 2.

f.The lines never intersect.

FALSE: perpendicular lines always intersept (in a 90° angle).

g.The intersection of s and t forms right angle.

TRUE: right angle = 90°.

h.If the slope of s is 6, the slope of t is -6

FALSE. – 6 is not the opposite reciprocal of 6. The opposite reciprocal of 6 is – 1/6.

So, the right choices are a, c and g.

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## How do I calculate say if I was saving \$60 a month for 5 years how do I calculate that

How do I calculate say if I was saving \$60 a month for 5 years how do I calculate that

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## Employees earn vacation pay at the rate of one day per month. during the month of july, 32 employees qualify for one vacation day each. their average daily wage is \$107 per day. what is the amount of vacation benefit expense to be recorded for the month of july?

Employees earn vacation pay at the rate of one day per month. during the month of july, 32 employees qualify for one vacation day each. their average daily wage is \$107 per day. what is the amount of vacation benefit expense to be recorded for the month of july?

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## Which of the following is the best example of making a financial mistake? Select the correct answer below. A. Running up credit card bills and not being able to afford to pay them off B. Going into debt to get a mortgage for a new home C. Going into debt to pay for your undergraduate degree at a university D. Charging an item on your credit card but waiting until the bill is due to pay it off the same month

In the first part, where Bill tells Matt that he has three kids and the product of their ages as well as the sum, there are two possible combinations of ages that have the same sum; 3, 3, and 8, as well as 2, 6, and 6. However, once Bill says that he only has a youngest child, no two youngest children, we can eliminate 3, 3, and 8, and the ages are 2, 6, and 6.

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## A video store charges a monthly membership fee of \$7.50,but the charge to rent each movie is only \$1.00 per movie. Another store has no member fee, but it costs \$2.50 to rent each movie. How many movies need to be rented each month for the total fees to be the same from either company?

A video store charges a monthly membership fee of \$7.50,but the charge to rent each movie is only \$1.00 per movie. Another store has no member fee, but it costs \$2.50 to rent each movie. How many movies need to be rented each month for the total fees to be the same from either company?

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## System of Equations 8th grade 30 points Bhavik bought 3 liters of milk and 5 loaves of bread for a total of \$11. A month later, he bought 4 liters of milk and 4 loaves of bread at the same prices, for a total of \$10. How much does a liter of milk cost, and how much does a loaf of bread cost?

You need to determine the number of ways in which 30 competitors from 50 can qualify. First, you have to realize that the order is irrelevant, that is: it is the same competitor_1, competitor _2, competitor _3 than competitor_3, competitor_2, competitor_1, or any combination of those three competitors.

So, the number of ways is which 30 competitors from 50 can qualify is given by the formula of combinations, which is:

C (m,n) = m! / (n! * (m -n)! )

=> C (50,30) = 50! / (30! (50 – 30)! ) = (50!) / [30! (50 – 30)!] = 50! / [30! 20!] =

= 47,129,212,243,960 different ways the qualifiying round of 30 competitors can be selected from the 50 competitors.

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## For her phone service, Kala pays a monthly fee of \$13 , and she pays an additional \$0.05 per minute of use. The least she has been charged in a month is \$63.15 . What are the possible numbers of minutes she has used her phone in a month? Use m for the number of minutes, and solve your inequality for m .

For her phone service, Kala pays a monthly fee of \$13 , and she pays an additional \$0.05 per minute of use. The least she has been charged in a month is \$63.15 . What are the possible numbers of minutes she has used her phone in a month? Use m for the number of minutes, and solve your inequality for m .

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## An obese man sets a long term goal of losing 40 pounds. What’s a reasonable benchmark? a) to start a new diet and exercise plan b) to lose 10 lbs in a month

“Identical twins” who have been raised apart are typically more similar in intelligence level than biological siblings raised together because they have been born with the same genetic code.

Identical twins originate from a single fertilized egg that parts into two. Before it parts, it is either male or female. After it parts, there are either two guys or two females. The two sections of the fertilized egg embed in the uterus and every create one of the twins.

Identical twins have the equivalent hereditary source. No immediate reason for monozygotic twinning has been resolved; it isn’t innate. Monozygotic twins speak to around 33% all things considered. They may look strikingly comparative, and it might be hard to reveal to them separated.

Lawrence Kohlberg felt that one of the only ways individuals will accomplish the objectives in each of his six stages was to participate in “consensus democracy” in small group settings.

Lawrence Kohlberg felt that the best way to support development through these stages was by discourse of good problems and by investment in consensus democracy inside small groups. Consensus democracy was rule by understanding of the gathering, not larger part rule. This would invigorate and widen the reasoning of youngsters and grown-ups, enabling them to advance starting with one phase then onto the next.

3. The answer is “D.  showing a learner how to correct common mistakes”.

The term scaffolding alludes to a procedure in which instructors display or exhibit how to take care of an issue, and afterward venture back, offering support as required. Analyst and instructional architect Jerome Bruner first utilized the term ‘scaffolding’ in this setting, harking back to the 1960s. The hypothesis is that when understudies are given the help they require while discovering some new information, they stand a superior possibility of utilizing that learning freely. Bruner suggests positive association and three methods of portrayal amid educating: activities, pictures, and dialect.

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## Vanya, a newborn going through a growth spurt, grew out of an average of 250 socks per month from January to March, inclusive. He grew out of an average of 300 socks per month in April and May. Find the average amount of socks Vanya grew out of during the 5 months.

Vanya, a newborn going through a growth spurt, grew out of an average of 250 socks per month from January to March, inclusive. He grew out of an average of 300 socks per month in April and May. Find the average amount of socks Vanya grew out of during the 5 months.

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## Marcus employer purchased a health insurance plan that costs \$795 per month and requires that marco pay \$105 toward the plan. What is the annual value of the employers contribution

Marcus employer purchased a health insurance plan that costs \$795 per month and requires that marco pay \$105 toward the plan. What is the annual value of the employers contribution

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## A scatter plot below shows the profit earned each month by a new company over the first year of operation.

Employee                                 Mary      Zoe         Greg         Ann           Tom

Cumulative Pay                       \$6,800   \$10,500  \$8,400    \$66,000   \$4,700

Pay subject to FICA S.S.         \$421.60  \$651.00  \$520.80 \$4092.00 \$291.40
6.2%, (First \$118,000)

Pay subject to FICA Medicare \$98.60 \$152.25    \$121.80    \$957.00    \$68.15
1.45% of gross

Pay subject to FUTA Taxes      \$40.80  \$63.00     \$50.40    \$396.00  \$28.20
0.6%

Pay subject to SUTA Taxes   \$367.20  \$567.00  \$453.60  \$3564.00 \$253.80
5.4% (First \$7000)

Totals                                     \$928.20 \$1,433.25 \$1,146.60 \$9,009.00 \$641.55