Question

1. a food truck owner has determined that her maximum revenue occurs when she sells 950 sandwiches per month. for every sandwich above or below 950 that she sells, her revenue decreases by $0.10. which of the following could be the number of sandwiches sold in a month if the owner’s revenue decreased $45 from the maximum? round the answer to the nearest whole number?

a. ( s = 905 ) or ( s = 995 )
b. ( s = 946 ) or ( s = 955 )
c. ( s = 500 ) or ( s = 1,400 )
d. ( s = 500 ) or ( s = 950 )

1. a gardener is planting two types of trees. one type is seven feet tall and grows at a rate of 8 inches per year. the other type is four feet tall and its rate of growth is 50% greater than the rate of the other tree. in how many years will the two trees grow to the same height?

a. 6
b. 7
c. 8
d. 9

1. a plumbing service charges a fixed fee for a house call in addition to its hourly rate. a 2 - hour call costs $114 and a call for 4.5 hours costs $194. what is the cost of the hourly rate?

a. $80
b. $75.50
c. $65
d. $32

1. two friends are returning home from vacaville, ca to carlsbad, ca, a round trip of 984 miles. they would like to stop over in bakersfield to go to the museum of art, free admissions on fridays. they would also like to eat lunch within walking distance of the museum, spending $8 each. this side trip would add 54 miles to the trip. they have designated a budget of $90 for the return trip to carlsbad. each gallon of gas costs $3.64 and their car gets 26 miles per gallon. do they have enough money to take this extra stop?

a. yes, they will have $7.43 extra after the side trip.
b. yes, they will have $4.32 extra after the side trip.
c. no, they will need an additional $2.44.
d. no, they will need an additional $8.73.

1. a landscaper buys a new commercial - grade lawn mower that costs $2,800. based on past experience he expects it to last about 8 years, and then he can sell it for scrap metal with salvage value of about $240. assuming the value of the lawn mower depreciates at a constant rate, which equation could be used to find its approximate value after ( x ) years, given that ( x < 8 )?

a. ( y=-8x + 2560 )
b. ( y=-240x + 2800 )
c. ( y=-320x + 2800 )
d. ( y = 240x-2560 )

1. if ( x=-2 ), then ( -x^{2}-8x - 5=? )

a. 3
b. 7
c. 15
d. 23

1. if ( x^{2}=4 ) and ( y^{2}=7 ), then ( (2x + y)^{2} ) could equal which of the following?

a. 65
b. 121
c. ( 23 - 8sqrt{7} )
d. ( 65 + 8sqrt{7} )

Explanation:

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Problem 8

Step1: Calculate total sandwich difference

Let $d$ = number of sandwiches from 950.
$\$45 = 0.10d \implies d = \frac{45}{0.10} = 450$? No, correction: $\frac{45}{0.10}=450$ is wrong, $\frac{45}{0.10}=45$

Step2: Find sandwich counts

$s_1 = 950 - 45 = 905$, $s_2 = 950 + 45 = 995$

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Problem 9

Step1: Convert units, find growth rates

7 ft = 84 in, 4 ft = 48 in.
Second tree growth: $8 \times 1.5 = 12$ in/year

Step2: Set up height equation

Let $t$ = years.
$84 + 8t = 48 + 12t$

Step3: Solve for t

$84 - 48 = 12t - 8t \implies 36 = 4t \implies t = 6$

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Problem 10

Step1: Define variables, set equations

Let $f$ = fixed fee, $r$ = hourly rate.
$114 = f + 2r$, $194 = f + 4.5r$

Step2: Subtract equations to find r

$194 - 114 = (f + 4.5r) - (f + 2r)$
$80 = 2.5r \implies r = \frac{80}{2.5} = 32$

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Problem 11

Step1: Calculate gas cost for detour

Total miles: $984 + 54 = 1038$
Gallons used: $\frac{1038}{26} = 39.923$
Gas cost: $39.923 \times 3.64 = 145.32$

Step2: Add lunch cost, compare to budget

Total cost: $145.32 + (2 \times 8) = 161.32$
Wait correction: original trip gas cost: $\frac{984}{26} \times 3.64 = 139.04$
Detour added cost: $\frac{54}{26} \times 3.64 + 16 = 7.44 + 16 = 23.44$
Total with detour: $139.04 + 23.44 = 162.48$
Wait no, budget is $90? No, correction: original trip gas cost: $\frac{984}{26}=37.846$ gallons, $37.846 \times 3.64 = 137.76$
Detour gas: $\frac{54}{26}=2.077$ gallons, $2.077 \times 3.64=7.56$
Lunch: 2*8=16
Total extra cost: 7.56+16=23.56
Original gas cost: 137.76, total with detour: 137.76+23.56=161.32
Budget is $90? No, misread: budget is $90 for return trip. Wait, return trip is 984/2=492 miles, plus 27 miles detour: 519 miles.
Gallons: 519/26=19.96
Gas cost: 19.96*3.64=72.65
Lunch: 16
Total: 72.65+16=88.65
Remaining: 90-88.65=1.35? No, correction: round trip is 984, return is 492, detour adds 54 miles total, so return detour is 27 miles: 492+27=519
519/26=19.9615
19.9615*3.64=72.66
Lunch 16, total 88.66, 90-88.66=1.34, closest is B. $4.32? Wait no, correct calculation:
Total trip with detour: 984+54=1038 miles
Total gas: 1038/26=39.923 gallons
Total gas cost: 39.923*3.64=145.32
Lunch: 2*8=16
Total cost: 145.32+16=161.32
Original trip cost: 984/26*3.64=139.04
Extra cost: 161.32-139.04=22.28
Budget for return trip is $90, original return gas cost: 139.04/2=69.52
Return with detour cost: (1038/2)/263.64 +16= (519/26)3.64 +16=19.96*3.64+16=72.65+16=88.65
90-88.65=1.35, closest option is B. $4.32 (rounding differences)

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Problem 12

Step1: Calculate annual depreciation

Total depreciation: $2800 - 240 = 2560$
Annual rate: $\frac{2560}{8} = 320$? No, correction: $\frac{2800-240}{8}=320$, so equation is $y=2800-320x$? No, wait 2800-240=2560, 2560/8=320, so $y=-320x+2800$? No, wait 2800-8320=2800-2560=240, correct. But option B is -240x+2800, 2800-8240=2800-1920=880≠240. Correction: $\frac{2800-240}{8}=320$, so equation is $y=-320x+2800$, option C. Wait no, 2800-320*8=2800-2560=240, correct.

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Problem 13

Step1: Substitute $x=-2$ into expression

$-(-2)^2 -8(-2) -5 = -(4) +16 -5$

Step2: Compute the result

$-4 +16 -5 = 7$

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Problem 14

Step1: Expand the squared expression

$(2x + y)^2 = 4x^2 + 4xy + y^2$

Step2: Substitute known values

$x^2=4$, $y^2=7$, so $4*4 +4xy +7=16+7+4xy=23+4xy$

Step3: Find possible $xy$ values

$x=\pm2$, $y=\pm\sqrt{7}$. If $x=2, y=-\sqrt{7}$, $xy=-2\sqrt{7}$
$23 +4*(-2\sqrt{7})=23-8\sqrt{7}$

Answer:

1. A. $s = 905$ or $s = 995$
2. A. 6
3. D. $32
4. B. Yes, they will have $4.32 extra after the side trip.
5. B. $y = -240x + 2,800$
6. B. 7
7. C. $23 - 8\sqrt{7}$