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Your older sister is getting married and to save money she is making her own cylinder shaped cake with three layers. Top layer: Radius= 3cm Height = 3 cm Middle Layer: Radius= 6cm Height = 4 cm Bottom layer: Radius = 10cm Height= 5cm If each tub of frosting costs $6.99 and a each tub of frosting covers 120 cm^2 of cake, figure out how much money your sister will have to spend on frosting
.
Surface Area = Area of top +Area of the side
.
Surface Area = (Area of top) + (perimeter of top)* height
.
Surface Area = (pi r^2) + (2 pi r)* h
.
Top layer:
Surface Area = (3.14*3^2) + (2*3.14*3)* 3
Surface Area = (3.14*9) + (6*3.14)* 3
Surface Area = 84.78 cm^2
.
Middle layer:
Surface Area = (3.14*6^2) + (2*3.14*6)* 4
Surface Area = (3.14*36) + (12*3.14)* 4
Surface Area = 263.76 cm^2
.
Bottom layer:
Surface Area = (3.14*10^2) + (2*3.14*10)* 5
Surface Area = (3.14*100) + (20*3.14)* 5
Surface Area = 628 cm^2
.
Total area = 976.54 cm^2
.
Deciding how many tubs:
976.54/120 = 8.14 tubs
.
Since you can't buy a partial tub, you must buy the next whole number up:
9 tubs of frosting
.
Total cost:
9 * 6.99 = $62.91

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a cyclist leaves his training base for a morning workout riding at a rate of 18mph. one hour later, is support staff leaves the base in a car going 45mph in the same direction. how long will it take the support staff o catch up with the cyclist?
.
Let t = hours it takes staff to catch up
then
"cyclist distance traveled" = "distance staff traveled"
(t+1)18 = t(45)
18t+18 = 45t
18 = 27t
18/27 = t
2/3 hours = t
or
40 minutes = t

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find two numbers whose sum is 108 and whose difference is 54
.
Let x = one number
and y = second number
.
x+y = 108 (equation 1)
x-y = 54 (equation 2)
.
Using the "elimination method" we add the two equations together:
x+y = 108
x-y = 54
-----------
2x = 162
x = 81
.
To find y, we can plug the above into equation 1 and solve for y:
x+y = 108
81+y = 108
y = 108-81
y = 27
.
The two numbers are 27 and 81

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5. Mary can clean an office complex in 5 hours.Working together John and Mary can clean the office complex in 3.5 hours.How long would it take John to clean the office complex by himself?
.
Let x = time it would take for John to clean office alone
then
3.5(1/5 + 1/x) = 1
Multiplying both sides by 5x:
3.5(x + 5) = 5x
3.5x + 17.5 = 5x
17.5 = 1.5x
17.5/1.5 x
175/15 = x
35/3 = x
11 2/3 hours = x
or
11 hours and 40 minutes = x
.
6. Working alone,Maria can complete a task in 100 minutes.Nora can complete the same task in two hours.They work together for thirty minutes when Cita,the new employee,joins and begin helping.They finished the task 20 minutes later.How long would it take Cita to complete the task alone?
.
First, convert the 2 hours into minutes:
2*60 = 120 minutes
.
Let x = time it takes Cita to complete task alone
then
30(1/100 + 1/120) + 20(1/100 + 1/120 + 1/x) = 1
Multiplying both sides by (100)(120)x:
30(120x + 100x) + 20(120x + 100x + 12000) = 12000x
Divide both sides by 10:
3(120x + 100x) + 2(120x + 100x + 12000) = 1200x
360x + 300x + 240x + 200x + 24000 = 1200x
1100x + 24000 = 1200x
24000 = 100x
240 minutes = x
or
4 hours = x
So Cita can do the task alone in 4 hours.

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Write the equation of the line that passes through the given point and is parallel to the given line. Give the answer in slope-intercept form. (-7,4) y+5x =-11
.
First, determine the slope of the "given line":
y+5x =-11
y = -5x-11
Because the above is in the "slope-intercept" form we see that the slope is -5.
.
For two lines to be parallel, they must have the same slope.
.
Therefore, our new line has a slope of -5 and passes through (-7,4).
.
Use the "point-slope" form:
y-y1 = m(x-x1)
y-4 = -5(x-(-7))
y-4 = -5(x+7)
y-4 = -5x-35
y = -5x-31 (this is what they're looking for)

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Think of it as the special condition of "difference of squares".
.
We could rewrite:
49a^2-(5a-4b)^2
as
(7a)^2-(5a-4b)^2
.
Now, we can factor as:
(7a - (5a-4b))(7a + (5a-4b))
.
(7a - 5a+4b)(7a + 5a-4b)
.
(2a+4b)(12a-4b)
2(a+2b)4(3a-b)
8(a+2b)(3a-b)

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If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?
.
Let x = hours it takes for both
then
x(1/4 + 1/6) = 1
.
Multiplying both sides by 24 we get:
x(6 + 4) = 24
x(10) = 24
x = 2.4 hours
.
or
2 hours and 24 minutes

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.
Group terms:

.
Factor out what is common in each group:

.
Factor out what is common for each term:

.
You could stop there. However, you can consider factoring the second term as a the special case of "difference of squares":

.

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A square light-switch plate is made which measures 6 inches on each side. A square hole measuring 1 inch on each side is left in the center. If the cost to construct the plate is $3.50 per square inch, what is the construction cost? (Hint: Use A = s2)
.
It would be:
3.50("area of plate" - "area of hole")
.
"area of plate" = s^2 = 6^2 = 36
.
"area of hole" = s^2 = 1^2 = 1
.
That is:
3.50(36-1)
= 3.50(35)
= $122.50
.
Wow, that is one expensive light-switch plate.

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The Nutty Professor sells cashews for $6.75 per pound and Brazil nuts for
$5.00 per pound. How much of each type should be used to make a 50-lb
mixture that sells for $5.70 per pound?
.
Let x = pounds of $6.75 per pound cashews
then
50-x = pounds of $5.00 Brazil nuts
.
6.75x + 5(50-x) = 5.70(50)
6.75x + 250-5x = 285
1.75x + 250 = 285
1.75x = 35
x = 35/1.75
x = 20 pounds (cashews)
.
Brazil nuts:
50-x = 50-20 = 30 pounds (Brazil nuts)

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Let ƒ(x) = 3x^2 – 2x and g(x) = x – 6. Find each value.
(ƒ – g)(2)
.
Start with f(x)
3x^2 – 2x
Subtract g(x):
3x^2 – 2x - (x-6)
3x^2 – 2x - x + 6
3x^2 – 3x + 6
.
Now, plug in x=2:
3(2)^2 – 3(2) + 6
3(4) – 6 + 6
12
.
Therefore:
(ƒ – g)(2) = 12

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How would I find the points at which the parabola formed y=x^2 and the line formed by y=2x+3 intersect?
.
Set them equal to each other and solve for x:
x^2 = 2x + 3
x^2 -2x = 3
x^2 -2x -3 = 0
(x-3)(x+1) = 0
x = {3,-1}
.
To find the corresponding y, plug into either of the two equations and solve for y:
when x=3
y=x^2=3^2 = 9
y=x^2=(-1)^2 = 1
.
Therefore, the points are
(3, 9)
and
(-1, 1)

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How much water must be added to 3 gallons of a 4% insecticide solution to reduce the concentration to 3%?
.
Let x = gallons of water to be added
then
.04(3) = .03(3+x)
.12 = .09+.03x
.03 = .03x
1 gallon = x

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On the purchase of a plasma TV, the total cost to the customer (including 6% GST and 7% PST) came to $2822.74. How much GST and how much PST did the customer pay?
.
Let x = cost of plasma tv
then
.06x = GST cost
.07x = PST cost
.
x + .06x + .07x = 2822
x(1 + .06 + .07) = 2822
x(1.13) = 2822
x = 2822/1.13
x = $2497.35
.
GST cost:
.06x = .06(2497.35) = $149.84
PST cost:
.07x = .07(2497.35) = $174.81

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There are 200 questions on a 3 hr examination.Among these questions are 50 mathematics problems.It is suggested that twice as much time be spent on each maths problem as for each other question.How many minutes should be spent on mathematics problems
.
First, since we're talking about minutes, convert 3hr into minutes:
3*60 = 180 minutes
.
Let x = minutes spent on a non-math problem
then
2x = minutes spent on a math problem
.
x(200-50) + 2x(50) = 180
x(150) + 2x(50) = 180
150x + 100x = 180
250x = 180
x = 0.72 minutes
.
Time to spend on math problems:
2x(50)=100x = 100(0.72) = 72 minutes

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three consecutive odd integers such that the product of the first and second exceeds the third by 8
.
Let x = first consecutive odd integer
then
x+2 = second consecutive odd integer
x+4 = third consecutive odd integer
.
x(x+2) = (x+4) + 8
x^2 + 2x = x + 12
x^2 +x -12 = 0
(x-3)(x+4) = 0
x = {3,-4}
.
Since -4 is an even number toss out the solution.
.
The three odd integers:
3,5,7

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v^2+8v+15=0
.
Factoring we get:
(v+5)(v+3) = 0
v = {-5, -3}

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.

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.
To find the inverse:
f(x)=(1/3)x + 3
can be rewritten as
y=(1/3)x + 3
Now, flip all the y's for x's and x's for y's:
x=(1/3)y + 3
Now, solve for y:
x-3 = (1/3)y
3(x-3) = y
3x -9 = y
.
Therefore,
f^-1(x) = 3x -9

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surface area of any sphere is 4(pi)r^2
.
4(pi)r^2 = 28
(pi)r^2 = 7
r^2 = 7/(pi)
r = sqrt(7/(pi))
r = 1.5 inches

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round 2.6666667 to the nearest hundredeth
.
You would look at the digit to the right of the hundreth place -- if it is 5 or greater, increment the digit by one -- otherwise leave it alone.
.
So
2.6666667
would round to
2.67

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If you go 28 minutes to go 50 miles how fast are you going? how do you figure it out?
.
speed = "distance"/"time"
.
In your case: "distance" = 50 miles
and
"time" = 28 minutes
.
So,
Speed = 50/28 but this is miles/min we normally see miles per hour so we need to convert the units:
.
50 miles 60 minutes
----------- * ----------
28 minutes 1 hour
.
Notice the minutes "cancel" leaving:
(50)(60)/28 = 107.14 mph

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The sum of two numbers is 92. One fifth of the first number added to one half of the second number is 34. Find the two numbers.
.
Let x = first number
and y = second number
.
x+y = 92 (equation 1)
(1/5)x + (1/2)y = 34 (equation 2)
.
Solving equation 1 for y:
x+y = 92
y = 92-x
.
Substitute the above into equation 2 and solve for x:
(1/5)x + (1/2)y = 34
(1/5)x + (1/2)(92-x) = 34
Multiplying both sides by 10:
2x + 5(92-x) = 340
2x + 460 - 5x = 340
460 - 3x = 340
-3x = -120
x = 40
.
Substitute back into equation 1 to find y:
x+y = 92
40+y = 92
y = 52
.
Your two numbers sare 40 and 52

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a(a+2)(a-3)-8(a-3)
.
Notice that (a-3) is common to both term. Factor it out:
(a-3)(a(a+2) - 8)

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Your problem is incomplete.
.
Parallel to what line?
Normally, you're given an equation of that line.
Please check and re-enter.

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Josh can deliver his newspapers in 30 minutes. If Amber helps him, it takes 12 minutes working together. How long would it take amber working by herself?
.
Let x = minutes it takes Amber to deliver by herself
then
12(1/30 + 1/x) = 1
Multiply both sides by 30x:
12(x + 30) = 30x
12x + 360 = 30x
360 = 18x
360/18 = x
20 minutes = x

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Winston bakes 4 pies per hour, and Clyde bakes 6 pies per hour. If Winston bakes alone for one hour, and then Clyde joins him, how many minutes will it take them to bake 32 pies?
.
Let x = hours it takes to bake 32 pies
then
1(4) + x(4 + 6) = 32
4 + x(10) = 32
4 + 10x = 32
10x = 28
x = 2.8 hours
.
Converting to minutes:
x = 2.8(60)
x = (2 + .8)(60)
x = 2(60) + .8(60)
x = 120 + 48
x = 168 minutes

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The graph of
y=6
is simply a horizontal line (parallel to the x-axis) that crosses the y-axis at 6. This has a slope of 0 -- since it is horizontal.
.
Therefore, a line parallel to this will have the same slope -- zero (0).

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Strontium–90 has a half-life of 29 years. How long will it take for an initial sample of 10 mg to decay to 1 mg?
.
You can apply the general "exponential decay" modeled by:

Where
A is the final amount
I is the initial amount
k is a constant
t is time
.

Plugging in your given information to first find k:






.
Now, your actual model is:

.
And we can use to to answer your question.
How long will it take for an initial sample of 10 mg to decay to 1 mg?





96.34 yrs = t

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You are both wrong!
.
Your mistake:

x= <--Here -- should be -15
.
Unless your original equation has a typo then the quadratic equation yields:
x = {9.568, -1.568}
Details of quadratic equation follows:
.

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=124 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 9.56776436283002, -1.56776436283002. Here's your graph:

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if a car travels 30 miles in an hour and a half, what is the cars speed?
.
Speed = "distance"/"time"
.
Speed = 30/1.5
Speed = 20 mph