Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 decade ago

Plss help to solve maths problems?

Hi Friends, Im very weak in maths. Pls help me to solve the below 2 problems with explaination how to solve. (Short cuts if any)...

1) In a box containing Z pens, S pens contain red lead and the rest contain blue lead. Which of the following expressions indicates the exact percent of the pen containing blue lead?

a) [100 (Z – S) ] / Z

b) 100 – (Z/S)

c) S / (Z-S)

d) (Z-S) / (Z+S)

e) 100s / (Z-S)

2) The formula for Area of a circle A=πr^2 If Circle X has 3 times as large a radius (r ) as the circle Y, the area of circle X equals.

a) 3 times the area of circle Y

b) Twice the area of circle Y

c) 8 times the area of circle Y

d) 6 times the area of circle Y

e) None of the above

3) S dollars are divided amongst 3 persons so that the first person receives $20 less than the 2nd person, and the 2nd person receives $20 less than the 3rd person. What does the last person receive?

a) S – 60

b) S – 40

c) S/3 – 20

d) S/3 +20

None of the above

4) A department store offers a discount of X % off the list price of an item. It also offers

Y % off the discount price for immediate cash payment. The net amount due for a cash purchase of an item with list price L would be?

a) L – (X / 100) – (Y / 100)

b) L* (1-(X / 100) – (Y / 100))

c) L – [ (X – Y) / (100 * L)]

d) L* [1 – (X / 100)]*[1 – (Y /100)]

e) None of the above

4 Answers

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  • Karl
    Lv 6
    1 decade ago
    Favorite Answer

    1) Percent is the fraction of the total, times 100. "Percent" is from Latin meaning "out of a hundred"

    The total number of pens is Z. The number that contain blue ink is (Z - S)

    The fraction that contain blue ink is (Z - S) / Z

    To express it as a percentage, multiply by 100.

    % = [100 (Z - S)]/Z

    2) The formula for the area of a circle is A=πr^2 If Circle X has 3 times as large a radius (r ) as the circle Y, the area of circle X equals...

    The area of a circle increases as the square of r. That means, if you double the radius, you increase the area by a factor of the square of 2, a four-fold increase. If you triple it, you increase the area by the square of 3, which is 9. Answer = none of the above.

    3) S dollars are divided amongst 3 persons so that the first person receives $20 less than the 2nd person, and the 2nd person receives $20 less than the 3rd person. What does the last person receive?

    Call the amount the first person receives R.

    The second person receives R+20, the third receives R+40.

    The total amount of money handed out is

    R + R+20 + R+40 = 3R+60 = S

    Solving for R, we get

    3R = S - 60

    R = S/3 - 20

    The last person receives R+40 = S/3 + 40 -20 = S/3 + 20 (d)

    4) A department store offers a discount of X % off the list price of an item. It also offers

    Y % off the discount price for immediate cash payment. The net amount due for a cash purchase of an item with list price L would be?

    Percentages are fractions times 100.

    The discount price is X%. That means, the purchase price is

    L - L * X/100 = L (1 - X/100)

    The discount for immediate cash payment is Y%

    If only the cash payment discount applied to L, the amount due would be

    L - L * Y/100 = L (1 - Y/100)

    Multiplication is commutative. It doesn't matter in what order you do it. So we can just multiply the list price with the discount terms:

    Due = L *(1 - X/100) * (1 - Y/100) which happens to be (d)

  • Anonymous
    1 decade ago

    1) You want to find 100 * (#blue lead pens/ total pens)

    Note, the 100 just makes it a percentage value i.e. => .15(100) = 15%

    So, If there are Z pens total and S are Red then (Z-S) is the number of Blue pens.

    Answer: a) 100*[(Z-S)/Z) = [100 (Z – S) ] / Z

    2) For this one we know that (pi) is constant so area only changes with change in radius (r)

    So, if we put in test values.

    R=1 and 3

    R^2 = 1 and 9

    OR

    R=2 and 6

    R^2 = 4 and 36

    Either way the area of the circle Y is 9 times larger than X for all positive values of X.

    Answer: e) None of the above

  • 1 decade ago

    I'll help you on the first one:

    blue pens = total minus red ones = z-s

    percent blue is number blue divided by total:

    (z-s)/z times 100 to get percent instead of a decimal.

  • Anonymous
    5 years ago

    Hi, If A^-1 is (3, 4, -1, -1), then A is its inverse: [.-1..-4.] [...1...3.] If this is A, then 2A - 3B = [.-5..-26.] [..-4..15.] rref [ 3..4..2.] ......[.-1.-1..4.] gives an answer of: [1..0..-18.] [.0.1....14.] so x = -18 and y = 14. Matrix A + B = [..0..2.] [..3..0.] That matrix cubed is: [.0..12.] [.18..0.] Its determinant is -216. On the other hand, matrix A + B = [..0..2.] [..3..0.] so its determinant is -6 and that determinant cubed is also -216. This was verified by use of the calculator. I hope that helps!!

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