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# College Algebra 7th

## Educators

AG

### Problem 1

The model $L=4 S$ gives the total number of legs that $S$ sheep have. Using this model, we find that 12 sheep have $L=$____ legs.

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Suppose gas costs $\$ 3.50$a gallon. We make a model for the cost$C$of buying$x$gallons of gas by writing the formula$C=$____ . Check back soon! ### Problem 3 Use the model given to answer the questions about the object or process being modeled. The sales tax$T$in a certain county is modeled by the formula$T=0.06 x$. Find the sales tax on an item whose price is$\$120 .$

AG
Ankit G.
Numerade Educator

### Problem 4

Use the model given to answer the questions about the object or process being modeled.
Mintonville School District residents pay a wage tax $T$ that is modeled by the formula $T=0.005 x$ Find the wage tax paid by a resident who earns $\$ 62,000$per year. AG Ankit G. Numerade Educator ### Problem 5 Use the model given to answer the questions about the object or process being modeled. The distance$d$(in mi) driven by a car traveling at a speed of$v$miles per hour for$t$hours is given by $$d=v t$$ If the car is driven at$70 \mathrm{mi} / \mathrm{h}$for$3.5 \mathrm{h}$, how far has it traveled? AG Ankit G. Numerade Educator ### Problem 6 Use the model given to answer the questions about the object or process being modeled. The volume$V$of a cylindrical can is modeled by the formula $$V=\pi r^{2} h$$ where$r$is the radius and$h$is the height of the can. Find the volume of a can with radius 3 in. and height 5 in. AG Ankit G. Numerade Educator ### Problem 7 Use the model given to answer the questions about the object or process being modeled. The gas mileage$M$(in mi/gal) of a car is modeled by$M=N / G$, where$N$is the number of miles driven and$G$is the number of gallons of gas used. a. Find the gas mileage$M$for a car that drove 240 mi on 8 gal of gas. b. A car with a gas mileage$M=25$mi/gal is driven 175 mi. How many gallons of gas are used? AG Ankit G. Numerade Educator ### Problem 8 Use the model given to answer the questions about the object or process being modeled. A mountain climber models the temperature$T$(in$^{\circ} \mathrm{F}$) at elevation$h$(in$\mathrm{ft}$) by $$T=70-0.003 h$$ a. Find the temperature$T$at an elevation of$1500 \mathrm{ft}$. b. If the temperature is$64^{\circ} \mathrm{F}$, what is the elevation? Check back soon! ### Problem 9 Use the model given to answer the questions about the object or process being modeled. The portion of a floating iceberg that is below the water surface is much larger than the portion above the surface. The total volume$V$of an iceberg is modeled by $$V=9.5 S$$ where$S$is the volume showing above the surface. a. Find the total volume of an iceberg if the volume showing above the surface is$4 \mathrm{km}^{3}$. b. Find the volume showing above the surface for an iceberg with total volume$19 \mathrm{km}^{3}$. AG Ankit G. Numerade Educator ### Problem 10 Use the model given to answer the questions about the object or process being modeled. The power$P$measured in horsepower (hp) needed to drive a certain ship at a speed of$s$knots is modeled by $$P=0.06 s^{3}$$ a. Find the power needed to drive the ship at 12 knots. b. At what speed will a 7.5 -hp engine drive the ship? a. Find the power needed to drive the ship at 12 knots. b. At what speed will a 7.5 -hp engine drive the ship? AG Ankit G. Numerade Educator ### Problem 11 An ocean diver models the pressure$P (\text { in } 1 b / \text { in }^{2} \text { ) at depth } d$(in ft) by $$P=14.7+0.45 d$$a. Make a table that gives the pressure for each$10-\mathrm{ft}$change in depth, from a depth of$0 \mathrm{ft}$to 60 ft.. b. If the pressure is$30 \mathrm{lb} / \mathrm{in}^{2},$what is the depth? AG Ankit G. Numerade Educator ### Problem 12 Arizonans use an average of 40 gal of water per person each day. The number of gallons$W$of water used by$x$Arizonans each day is modeled by$W=40 x$a. Make a table that gives the number of gallons of water used for each 1000 -person change in population, from 0 to 5000. b. What is the population of an Arizona town whose water usage is 120,000 gal per day? AG Ankit G. Numerade Educator ### Problem 13 Write an algebraic formula that models the given quantity. The number$N$of cents in$q$quarters AG Ankit G. Numerade Educator ### Problem 14 Write an algebraic formula that models the given quantity. The average$A$of two numbers$a$and$b$AG Ankit G. Numerade Educator ### Problem 15 Write an algebraic formula that models the given quantity. The cost$C$of purchasing$x$gallons of gas at$\$3.50$ a gallon

AG
Ankit G.
Numerade Educator

### Problem 16

Write an algebraic formula that models the given quantity.
The amount $T$ of a $15 \%$ tip on a restaurant bill of $x$ dollars

AG
Ankit G.
Numerade Educator

### Problem 17

Write an algebraic formula that models the given quantity.
The distance $d$ in miles that a car travels in $t$ hours at $60 \mathrm{mi} / \mathrm{h}$

AG
Ankit G.
Numerade Educator

### Problem 18

Write an algebraic formula that models the given quantity.
The speed $r$ of a boat that travels $d$ miles in $3 \mathrm{h}$

AG
Ankit G.
Numerade Educator

### Problem 19

A pizza parlor charges $\$ 12$for a cheese pizza and$\$1$ for each topping.
a. How much does a 3 -topping pizza cost?
b. Find a formula that models the cost $C$ of a pizza with $n$ toppings.
c. If a pizza costs $\$ 16,$how many toppings does it have? AG Ankit G. Numerade Educator ### Problem 20 a. How much does it cost to rent a car for 3 days if the car is driven$280 \mathrm{mi} ?$b. Find a formula that models the cost$C$of renting this car for$n$days if it is driven$m$miles. c. If the cost for a 3 -day rental was$\$140$, how many miles was the car driven?

AG
Ankit G.
Numerade Educator

### Problem 21

The cost of the electricity needed to drive an all-electric car is about 4 cents per mile. The cost of the gasoline needed to drive the average gasoline-powered car is about 12 cents per mile.
a. Find a formula that models the energy cost $C$ of driving $x$ miles for
i. the all-electric car and
ii. the average gasoline-powered car.
b. Find the cost of driving 10,000 mi with each type of car.

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### Problem 22

A fruit crate has square ends and is twice as long as it is wide.
a. Find the volume of the crate if its width is 20 in.
b. Find a formula for the volume $V$ of the crate in terms of its width $x$

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### Problem 23

In many universities students are given grade points for each credit unit according to the following scale:
A 4
points
B 3
points
C 2
points
$D \quad 1$ point
$F \quad 0$ point
For example, a grade of A in a 3 -unit course earns $4 \times 3=12$ grade points and a grade of $\mathrm{B}$ in a 5-unit course earns 3 $\times 5=15$ grade points. A student's grade point average (GPA) for these two courses is the total number of grade points earned divided by the number of units; in this case the GPA is $(12+15) / 8=3.375$
a. Find a formula for the GPA of a student who earns a grade of A in $a$ units of course work, $\mathrm{B}$ in
$b$ units, $\mathrm{C}$ in $c$ units, $\mathrm{D}$ in $d$ units, and $\mathrm{F}$ in $f$ units.
b. Find the GPA of a student who has earned a grade of A in two 3 -unit courses, $\mathrm{B}$ in one 4 -unit course, and C in three 3-unit courses.

AG
Ankit G.
Numerade Educator