Questions:
1. Translate the sentence to an equation and solve it
Six less than eight times a number is equal to that number added to one.
Choose the equation that represents the sentence.
A. (6-8)x = 1 + x
B. (8-6)x = x + 1
C. 6-8x = x + 1
D. 8x-6 = x + 1
2. The length of a rectangular mailing label is 3 centimeters less than twice the width. The perimeter is 54 centimeters. Find the dimensions of the label.
The width is centimeters.
The length is n centimeters.
3. The perimeter of a rectangular park is 22,735.8 inches. The length of the park is 9,890.1 inches longer than the width. What is the length of the park?
The length is inches.
(Round to the nearest tenth.)
4. A student needs 10% hydrochloric acid for a chemistry experiment How much 2% acid should be mixed with 200 ml of 30% acid to get a 10% solution?
ml of 2% hydrochloric acid must be added. (Round to the nearest tenth.)
5. A student needs 20% hydrochloric acid for a chemistry experiment How much 3% acid should be mixed with 200 ml of 30% acid to get a 20% solution?
ml of 3% hydrochloric acid must be added. (Round to the nearest tenth.)
6. How many gallons of a 90% antifreeze solution must be mixed with 80 gallons of 20% antifreeze to get a mixture that is 80% antifreeze? Use the six-step method.
You need gallons.
(Round to the nearest whole number.)
7. Students stuff envelopes for extra money. Their initial cost to obtain the information for the job was $600. Each envelope costs $0.02 and they get paid $0.08 per envelope stuffed. Let x represent the number of envelopes stuffed.
(a) Express the cost C as a function of x.
(b) Express the revenue R as a function of x.
(c) Determine analytically the value of x for which revenue equals cost
(a) C(x) = (C in dollars)
8. Find the constant of variation k and the undetermined value in the table if y is directly proportional to x.
x 4 9 12 14
y 28 63 84 ?
What is the constant of variation? k=
10. The pressure excited by a certain. liquid at a given point varies directly as the depth of the point beneath the surface of the liquid. The pressure at 80 feet is 560 pounds per square inch. What is the pressure at 30 feet?
11. A person 4-ft tall casts a shadow 3-ft long. At the same time, a nearby tree casts a shadow 22-ft long Find the height of the tree.
The tree's height is ft.
(Round to the nearest tenth.)
12. Hooke's Law. The distance d when a spring is stretched by a hanging object varies directly as the weight w of the object. If the distance is 61 cm when the weight is 3 kg, what is the distance when the weight is 9 kg?
The distance is CM.
(Simplify your answer. Type an xi. teger or a fraction.)
13. To determine the number of trout in a lake, a conservationist catches 115 trout, tags them and throws them back into the lake. Later, 26 trout are caught; 13 of them are tagged. How many trout are in the lake? There are 111 trout in the lake.
14. A company finds it can produce 25 heaters for $6100, while producing 30 heaters costs $7200. Express the cost, y, as a linear function of the number of heaters, x. Determine the cost to produce 40 heaters.
Express the cost, y, as a linear function of the number of heaters, x_
y=
(Simplify your answer.)
15. Cost for copies is a linear function of the number of copies. If 200 copies cost $4100, and 125 copies cost $30.25, write a formula for copy cost as a linear function of the number of copies. Then find how much it would cost to make 200 copies.
If x is the number of copies made and y is the amount charged For the copies, what is the formula for the amount charged?
The formula is y = E.
(Type an expression using x as the variable. Use integers or decimals for any numbers in the expression)
16. A 20 year old woman whose resting heart rate is 65 beats per minute should not exceed a maximum heart rate of 173.
A 20 year old woman whose resting heart rate is 90 beats per minute should not exceed a maximum heart rate of 178.
a) List the data points (r,M), with r =resting heart rate and M =maximum. heart rate.
b) Find the linear equation which fits the data.
c) Use the equation to predict the maximum heart rate for a woman whose resting heart rate is 70 beats per minute.
What is the data point for the first woman?
17. In the 1990s, a comp any had a profit per share given by the equation P =0.30x+ 4.50, where x ranges from 0 to 9 corresponding to the years 1990 to 1999. What was the profit per share in 1996?
The profit per share in 1996 was P = $
Solve for g. The solution is g =
q=3g+3w
18. Solve the formula for the indicated variable.
P=a+4b+4c, for a
a =
19. Solve for a.
The solution is a =.
1 (Simplify your answer.)
D = 1/5 h(a - b)
20. Solve for a.
The solution is a=
D = -1/5 h(a - b) (Simplify your answer.)
21. Salve for u
k = 11+ unk
The solution is u=
22. Solve each formula for indicated variables.
S = 2∏h + 2∏2 for h.
Choose the correct expression for h.
A. h = S-2∏2/2∏r
B. h = S - r
C. h = S-2∏/2∏2
23. Solve for m. m =
b = 1/2mv
24. Bill invests in a plan that has an APR of 3%. He ill. vests four times as much in a plan that has an APR of 8%. If the total interest from the investments is $805 after one year, how much was invested in each plan?
Bill invested $ F in the plan earning 3% interest.
Bill invested $ in the plan earning 8% interest.