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24 four-digit numbers |
2007-04-21 |
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From Megon:
Of the 24 four-digit numbers formed from the digits 1,2,3,&4 is there an easier way to find their sum other than writing them all out and totaling them by hand?
Answered by Stephen La Rocque. |
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A square contains five circles with the same radius. |
2007-04-21 |
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From Jamie:
A square has a side length on 1 m.
The square contains five circles with the same radius.
The centre of one circle is at the centre of the square and it touches the other four circles.
Each of the other four circles touches two sides of the square and the center circle.
Find the radius.
Answered by Penny Nom. |
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A corny problem |
2007-04-21 |
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From Robby:
My name is Robby and I need help with a problem. I have found at
least 4 correct answers, but I can't figure out how I got the answer or
if there is a formula that I can use. I got my answers by trial and
error. Problem: One hundred bushels of corn are to be divided among
100 men, women, and children. Men get 3 bushels each. Women get two
bushels each. Children get 1/2 bushel each. How can the bushels be
distributed with no leftovers? Is there more than one solution?
So far, I have 4 answers: 8 men,20 women, and 72 children,
2 men, 30 women, and 68 children, 5 men, 25 women, and 70 children, and
11 men, l5 women, and 74 children. I need to know if there is a formula
to use, or if it's just trial and error, or if a pattern is involved.
Answered by Stephen La Rocque and Penny Nom. |
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Constructing an octagonal deck around a circular pool |
2007-04-20 |
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From Cliff:
[I am building an] octagonal desk encompassing 17 foot diameter circle for pool.
I have seen other octagonal calculations but none of these tell me how much allowance for a circle to fit within the octagon without losing the circle edge can anyone help
thanks cliff
Answered by Stephen La Rocque. |
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One equation with two unknowns |
2007-04-20 |
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From Devon:
Solve for y. 3x – 2y = 12
Answered by Penny Nom. |
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Two lines intersect at a right angle |
2007-04-20 |
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From ellen:
The line with the equation 3x + by = 6 intersects with the line 6y + ax = c at right angles at the point
(4,6). Determine the values of a, b & c.
Answered by Stephen La Rocque. |
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A normal distributiion question |
2007-04-20 |
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From Erika:
The amount of time required for a certain type of automobile transmission repair at a service garage is normally distributed with the mean = 45 minutes and the standard deviation =8.0 minutes. The service manager plans to have work begin on the transmission of a customer’s car 10 minutes after the car is dropped off, and he tells the customer that the car will be ready within one hour total time. What is the probability that he will be wrong? Illustrate the proportion of area under the normal curve which is relevant in this case.
What is the required working time allotment such that there is a 75 percent chance that the transmission repair will be completed withing that time? Illustrate the proportion of area that is relevant.
Answered by Penny Nom. |
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Relating volume to depth in a cylindrical container |
2007-04-19 |
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From Dan:
I have a cylindrical polyethylene rain barrel 23" in diameter and 35" high. If I've calculated correctly thus far, its volume is:
14, 547.49 cubic inches (or 8.418686 cubic feet or 0.31 cubic yards)
and could, ideally, contain 62.6 gallons of rain water whose weight would be 525.32 lbs. (62.4 lbs./cubic foot X 8.418686).
I'm having difficulty relating inch depth markings on the side of the barrel to volume capacity; i.e., how many inches in depth
in a cylinder of the size given would = how many gallons (or quarts) of water. The barrel stands upright on its end and is, thus, 35" high
when oriented in this fashion, much as a 55-gallon oil drum appears when similarly stowed.
Dan Watley
Answered by Stephen La Rocque. |
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Two concentric circles |
2007-04-19 |
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From James:
Two concentric circles have a chord running through the outer one. The chord is the tangent of the inner circle and is 14 cm.The outer circle is shaded and the inner circle is not. Find the exact area of the shaded region without using a calculator.
Answered by Stephen La Rocque. |
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I want to mark up a price by 5% |
2007-04-19 |
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From Steve:
ok so i want to mark up a price by 5% or any percentage.
which is correct? ( this is done with a calculator with a % button)
a.
62*5% = 3.1 (3.1 + 62) = 65.1(total)
b.
62+5% = 65.263(total) (rounded to the 3rd decimal)
im trying to wrap my head around this.
the calculator has a button which does % all automatically.
Markup *20 which equal 5%....
Answered by Stephen La Rocque and Penny Nom. |
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Four semi-circles are drawn inside a square |
2007-04-19 |
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From James:
Four semi-circles are drawn inside a square, with the diameter being the length of the square.The overlapping portion of the semicircles are shaded. What fraction is shaded?
Answered by Penny Nom. |
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Liquid is being poured into the top of a funnel |
2007-04-19 |
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From neroshan:
Liquid is being poured into the top of a funnel at a steady rate of 200cm^3/s.
The funnel is in the shape of an inverted right circular cone with a radius
equal to its height. It has a small hole at the bottom where the liquid is
flowing out at a rate of 20 cm^3/s. How fast is the height of the liquid
changing when the liquid in the funnel is 15 cm deep?
At the instant when the height of the liquid is 25cm, the funnel becomes clogged
at the bottom and no more liquid flows out. How fast does the height of the
liquid change just after this occurs?
Answered by Penny Nom. |
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Vertices, edges and faces |
2007-04-19 |
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From Kimberly:
I am trying to help my son find the vertices, edge, and face of a 16 sided figure.
I am not sure of the process to use to find these, could you please tell me
how to do this?
Answered by Penny Nom. |
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All samples of size 3 |
2007-04-19 |
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From Liz:
Consider the population of the first seven integers: 1, 2, 3, 4, 5, 6, and 7; N=7. For this population, mean = 2 and standard deviation = 2.
a. How many samples of size three can be extracted from this population (sampling without replacement)?
b. Form the complete set of samples of size three and for each sample, compute the sample mean and median.
Answered by Penny Nom. |
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Three digit numbers |
2007-04-19 |
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From katelyn:
How many 3 digit numbers can be created if each number is a multiple of 10?
Answered by Penny Nom. |
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