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free/or 0.5$ |
| m66718 | A rhombus is inscribed in a rectangle that is w meters wide with a perimeter of 40 m. Each vertex of the rhombus is a midpoint of a side of the rectangle. Express the area of the rhombus as a function of the rectangle s width. |
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| m66719 | A right circular cylinder of height h and radius r is inscribed in a right circular cone with a height of 10 ft and a base with radius 6 ft.
(a) Express the height h of the cylinder as a function of r.
(b) Express the volume V of the cylinder as a function of r.
(c) Express the volume V of the cylinder as a function of h. |
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| m66721 | A sack contains 7 dimes, 5 nickels, and 10 quarters. Eight coins are drawn at random. What is the probability of getting 4 dimes, 3 nickels, and 1 quarter? |
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| m66733 | A satellite dish has a parabolic cross section that is 18 in. wide at the opening and 6 in. deep at the vertex. How far from the vertex is the focus? |
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| m66737 | A seamstress is designing a triangular flag so that the length of the base of the triangle, in inches, is 7 less than twice the height h. Express the area of the flag as a function of the height. |
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| m66738 | A seamstress uses 20 ft of lace to trim the edges of a rectangular tablecloth. If the tablecloth is l feet long, express its area as a function of the length. |
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| m66741 | A sequence of payments of $300 is invested over 12 years at the end of each quarter at 5.1%, compounded quarterly. Find the amount of the annuity. Use the formula in Exercise 64(b). |
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| m66742 | A sequence of yearly payments of $750 is invested at the end of each of 10 years at 4.75%, compounded annually. Find the amount of the annuity. Use the formula in Exercise 64(a). |
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| m66743 | A sequence of yearly payments of P dollars is invested at the end of each of N years at interest rate i, compounded annually. The total amount in the account, or the amount of the annuity, is V.
a) Show that
b) Suppose that interest is compounded n times per year and deposits are made every compounding period. Show that the formula for V is then given by |
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| m66763 | A social security number is a 9-digit number like 243-47-0825.
a) How many different social security numbers can there be?
b) There are about 310 million people in the United States. Can each person have a unique social security number? |
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| m66766 | A softball team is designing a triangular pennant such that the height is 6 in. less than four times the length of the base b. Express the area of the pennant as a function of b. |
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| m66767 | A sole proprietorship is worth w dollars. The owner loses a lawsuit against him for y dollars where y is greater than w. Express algebraically the value of the personal property the owner must forfeit to pay the settlement. |
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| m66773 | A spotlight has a parabolic cross section that is 2 ft wide at the opening and 1.5 ft deep at the vertex. How far from the vertex is the focus? |
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| m66774 | A spotlight has a parabolic cross section that is 4 ft wide at the opening and 1.5 ft deep at the vertex. How far from the vertex is the focus? |
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| m66775 | A spreadsheet has been created so that the user enters information in the stated cells.
a. Write a formula to calculate the speed of the car for the trip in cell C1.
b. Write a formula to calculate the number of gallons of gas used in cell C2.
c. Write a formula to calculate the total cost of gas for the trip in cell C3. |
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| m66776 | A spreadsheet user inputs a speed in miles per hour into cell A1.
a. Write a formula that would enter the approximate equivalent of that speed in km/h in cell A2.
b. Write a spreadsheet formula that would enter the approximate total stopping distance in feet in cell A3.
c. Write a spreadsheet formula that would enter the approximate total stopping distance in kilometers in cell A4. |
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| m66779 | A state forms its license plates by first listing a number that corresponds to the county in which the owner of the car resides. (The names of the counties are alphabetized and the number is its location in that order.) Then the plate lists a letter fo the alphabet, and this is followed by a number from to 9999.how many such plates are possible if there are 80 counties? |
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| m66790 | A stone is thrown directly upward from a height of 30 ft with an initial velocity of 60 ft/sec. The height of the stone, in feet, t seconds after it has been thrown is given by the function s(t) = -16t2 + 60t + 30. Determine the time at which the stone reaches its maximum height and find the maximum height. |
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| m66791 | A stone is thrown into a pond, creating a circular ripple that spreads over the pond in such a way that the radius is increasing at a rate of 3 ft/sec.
(a) Find a function r(t) for the radius in terms of t.
(b) Find a function A(t) for the area of the ripple in terms of the radius r.
(c) Find (Aor) (t). Explain the meaning of this function. |
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| m66796 | A student has a total of 226 points on three tests. The sum of the scores on the first and second tests exceeds the score on the third test by 62. The first score exceeds the second by 6. Find the three scores. |
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