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Multiple algebra questions

1. Traffic signs are regulated by the Manual on Uniform Traffic Control Devices (MUTCD). The perimeter of some traffic signs must be 68 Inches. Also, its length is 6 inches longer than its width. Find the dimensions of this sign.
The width of the sign is?
The Length of the sign is?

2. A hardware supplier manufactures three kinds of clamps, types A,B, and C. Production restrictions force it to make 20 more type C clamps than the total of the other types and three times as many type B clamps as type A clamps. The shop must produce 340 clamps per day. How many of each type are made per day?

3. If a car is traveling at 90 miles per hour on a slippery road, then its stopping distance D in feet can be calculated by D=8100/90 time 1/x, where x is the coefficient of friction between the tires and the road and 0<x?1
a. Multiply and simplify the formula for D

b. Compare the stopping distance on an icy road with x=0.2 and on dry pavement with x=0.6
The stopping distance on an icy road is ? feet
The stopping distance on dry pavement is ? feet
When a car is moving at 90 miles per hour, the stopping distance on dry pavement is ? of the stopping distance on an icy road

4. The function f(x)=360x/100-x models the cost, f(x), in millions of dollars, to remove x% of a river's pollutants. If the government commits $540 millions for this project, what percentage of the pollutants can be removed?

5. Find the variation constant in which y varies inversely as x, and the following condition exist.
Y=10 when x=1/2
K=?

6. The current I in an electrical conductor varies inversely as the resistance R of the conductor. The current is 5 ampere when the resistance is 900 ohms. What is the current when the resistance is 560 ohms?

7. The function D(x) models the cumulative number of deaths from a disease x years after 1984. Estimate the year when there were 85,000 deaths. D(x)=3895x^2 +5279x +5500

8. A rectangular pen for a pet is 6 feet longer than it is wide. Give possible values for the width W of the pen if its area must be between 160 and 520 square feet, inclusively.
The width of the pen ranges from the smaller value of the width, ? feet, to the larger value of the width, ? feet , inclusively.

9. If C dollars are deposited in an account paying r percent annual interest, the amount after x years is A=C(1+r)^x. Approximate the amount in the account after x years, when C=$150, r=16%, and X=19 years.
A=? dollars

Solution Preview

Hi there,

1. Traffic signs are regulated by the Manual on Uniform Traffic Control Devices (MUTCD). The perimeter of some traffic signs must be 68 Inches. Also, its length is 6 inches longer than its width. Find the dimensions of this sign.
The width of the sign is 14 in
The Length of the sign is 20 in
If the width is x inches, the length is (x+6) inches.
2x+2(x+6)=68.
X=14 (inches)

2. A hardware supplier manufactures three kinds of clamps, types A,B, and C. Production restrictions force it to make 20 more type C clamps than the total of the other types and three times as many type B clamps as type A clamps. The shop must produce 340 clamps per day. How many of each type are made per day?
Suppose there are x clamps for A, then B type has 3x clamps, C has (4x+20) ...

Solution Summary

The solution provides detailed explanation for multiple algebra questions.

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