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what is a 4 dimention hypercube     

Look up tesseract for an interesting description.     

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4 pencils and 3 crayons are 20.9 inches. 5 pencils and 4 crayons are 26.5 inches. Each pencil isthe same length as the other pencils, and each crayon is the same length as the other crayons. What is the length of 1 pencil? What is the length of 1 crayon?     

4P + 3C  =  20.9     both sides x4  —>  16P + 12C  =  83.6     (eq 1)     

5P + 4C  =  26.5     both sides x3  —>  15P + 12C  =  79.5     (eq 2)     

subtract (eq 2) from (eq 1)                        P             =    4.1     

substitute 4.1 back into (eq 1)            (4)(4.1) + 3C  =  20.9     

                                                                16.4 + 3C  =  20.9     

                                                                           3C  =    4.5     

                                                                             C  =    1.5     

check answer     

substitute both back into (eq 2)     

Does (5)(4.1) + (4)(1.5)  =  26.5   ?     

           20.5    +    6.0      =  26.5   ?     

                              26.5  =  26.5   True     

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Alice gave Betty as many cents as Betty had. Betty then gave Alice as many cents as Alice had. Then, each of them had 12 cents. How much did Alice start with?     

Start at the end and work backward.     

Remember, the total is always 24 ¢.     

       A     B      

      12    12     after B doubled A's     

        6    18     after A doubled B's     

      15      9     before A doubled B's     

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A pyramid has a square base which has an area of 1440 . Each of the pyramid’s triangular faces is identical and each has an area of 840.  Find the height of the pyramid.     

sqrt(1440)  =  37.95      This is the side of the square base.     

Area_triangle  =  (1/2) • base • height     

            840  =  (1/2) • 37.95 • h     

                h  =  840 / 18.98     

                h  =  44.27     This is the slant height.     

       c²  =  a² + b²     

44.27²  =  18.98² + b²     

   1960  =  360 + b²     

        b²  =  1600     

        b¹  =  40                This is the height from the center of the base to the apex.     

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Hi Kitty,

I used Coordinate geometry as shown in the diagram and then solved the bottom circle equation (centred at A) with x=0 and then y=0 respectively to find the points I and H.

Then just find the distance between them.

I will leave the rest to you,

To find the radius of a quarter-circle, we need either the arc length or the area.

From arc length (L): (r = \frac{2L}{\pi})

From area (A): (r = \sqrt{\frac{4A}{\pi}})

Give me one of these, and I can compute it exactly.

Kate Alexander worked 40 hours last week. Her pay rate is $8.50 per hour. Assuming 7.65% social security withholding, how much should her employer withhold from her check for social security?     

(40 hrs) • (8.50 $/hr)  =  340.00 $     

(0.765) • (340.00 $)  =  26.01 $     

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Mileage between Webster,ky and Arthur Il     

Per the website google maps, the shortest route     

between Webster KY and Arthur IL is 261 miles      

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  Disregarding air resistance, what is the speed of a ball dropped from 12 feet just before it hits the ground?     

  (Use 1 ft = 0.30 m, and use g = 9.8 m/s2.)     

  S  =  (1/2) a t²     

  (12 ft) • (0.30 m/ft)  =  (1/2) • (9.8 m/sec²) • t²     

  3.6 m  =  (4.9 m/sec²) • t²     

  t²  =  (3.6 m) / (4.9 m/sec²)     

  t²  =  0.735 sec²     

  t¹  =  0.857 sec     

  V  =  a t     

  V  =  (9.8 m/sec²) • (0.857 sec)     

  V  =  8.34 m/sec     

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wat is the definition of the community prop of multiplication     

The commutative property of multiplication states that changing the order     

of the factors in a multiplication problem does not change the final product.     

Expressed as a×b = b×a, this rule means that swapping the position of the     

numbers always results in the same answer (e.g., 4×6 = 6×4 = 24 ).     

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In an alloy of 150 pounds of zinc and copper, there are 100 pounds of copper.     

How much copper must be added so that alloy may be 10% zinc??      

Since there are 100 lb copper, the other 50 lb are the zinc.     

You want that 50 lb to be 10% so the alloy must total 500 lb.     

There's already 100 lb copper so add another 350 lb copper.     

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228 miles on 12 gallons of fuel;240 miles on 10 gallons of fuel     

228 mi on 12 gal  =  19 mi/gal     

240 mi on 10 gal  =  24 mi/gal     

Conclusion:  Either two different vehicles     

                     or a very strong head wind.

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x=1/2(120-45)     

x=-104?     

 Is this right answer? where is wrong?      

  x  =  (¹/₂) (120 – 45)     

  x  =  (¹/₂) (75)     

  x  =  37.5     

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The number of allowable doubtful digits in a measurement or     

the result of mathematical operations with measurements is _____________ .     

A properly recorded measurement or calculation should     

contain only one doubtful (estimated or uncertain) digit,     

which is always the last significant figure. This last digit     

represents the limit of the instrument's precision, with all     

preceding digits assumed to be certain.     

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The lateral area of a right cylinder having a base diameter of 10 units and a height of 10 units is:     

Area_lateral  =  Circumference x Height     

                  =  π d h     

                  = (3.14) (10) (10)     

                  =  314 units²     

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Assume that the moon is a sphere.     

What is the volume of the moon if its diameter is 3,476 km?     

Express your answer in scientific notation to two significant digits.     

Volume_sphere  =  (4/3) π r³     

                        =  (4/3) (3.1416) (1738³)     

                        =  (4/3) (3.1416) (5,249,879,272)     

                        =  21,990,694,294.6  rounds to  2.20 x 10¹⁰ km³     

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