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DIA
2 months ago
5

A map of Colorado says that the scale is 1 inch to 20 miles or 1 to 1,267,200. Are these two ways of reporting the scale the sam

e? Explain your reasoning.
Mathematics
1 answer:
Leona [12.6K]2 months ago
4 0

Response:

1,267,200

Step-by-step explanation:

Considering the map indicates a scale of 1 inch equals 20 miles.

Keep in mind, there are 63,360 inches in a mile, therefore for 20 miles, it calculates to 20 x 63,360 = 1,267,200.

Consequently, a scale of 1 inch to 20 miles can also be represented as 1 to 1,267,200

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A small-appliance manufacturer finds that the profit P (in dollars) generated by producing x microwave ovens per week is given b
PIT_PIT [12445]

Answer:

The amount of ovens that must be produced in a week to earn a $1610 profit is 70.

Step-by-step explanation:

Given:

A small-appliance manufacturer determines the profit P (in dollars) from producing x microwave ovens weekly by the formula:

P=\frac{1}{10}x(300-x)

with 0 ≤ x ≤ 200.

The target profit is $1610

So, set P = 1610, then solve for x:

1610=\frac{1}{10}x(300-x)

Multiply both sides by 10:

1610\cdot \:10=\frac{1}{10}x\left(300-x\right)\cdot \:10

16100=x\left(300-x\right)

16100=300x-x^2

-x^2+300x-16100=0

Next, factor the quadratic:

(x-70)(x-230)=0

Solving for x gives:

x=70,x=230

Since x=230 is outside the domain 0 ≤ x ≤ 200, we discard it.

Hence, the valid solution is x=70.

Therefore, to achieve a $1610 profit, the manufacturer must produce 70 ovens weekly.


7 0
3 months ago
The volume of a packing box is 5 – x cubic feet. The width of the box is x feet and the length is x – 2 feet. The height is give
Zina [12379]
According to the definition, the volume is indicated by
V = h * w * l
where
V: Volume
h: height
w: width
l: length
By solving for height, we get:
h = V / (w * l)
h = (5 - x) / ((x) * (x - 2))
The expression is undefined for x values that cause the denominator to equal zero:
((x) * (x - 2)) = 0
x = 0
x = 2
Answer
h = (5 - x) / ((x) * (x - 2))
x = 0
x = 2
4 0
1 month ago
casey bought sandwiches and a bag of chips. Each sandwich cost three times as much as bag of chips. She bought 5 sandwiches for
AnnZ [12381]

Answer:

4

Step-by-step explanation:

Each sandwich costs 6 dollars, while chips sell for 3 dollars. She purchased 5 sandwiches at 6 dollars each, amounting to 30 dollars (5*6=30). This leaves her with 12 dollars to use since her total expenditure was 42 dollars. Given that chips are 3 dollars each, with 12 dollars left, 4 bags could be bought (4 * 3 = 12).

3 0
2 months ago
Read 2 more answers
If Sam has 6 different hats and 3 different scarves, how many different combinations could he wear
tester [12383]
18

He can combine one hat with a scarf, resulting in 18 different combinations for Sam when multiplying 6 by 3.
6 0
3 months ago
Read 2 more answers
Last week, your delivery runs took 7 hours 12 minutes on Monday, 6 hours 46 minutes on Wednesday, and 6 hours 53 minutes on Frid
zzz [12365]
7 hours 12 minutes
6 hours 46 minutes
6 hours 53 minutes
--------------------------sum
Total: 19 hours 111 minutes, which converts to (19 × 60) + 111 = 1140 + 111 = 1251 minutes

Calculate average time by dividing by 3: 1251 / 3 = 417 minutes, equivalent to 6 hours 57 minutes, which is the average delivery duration.
7 0
3 months ago
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