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2 years ago

A furniture factory can box a desk chair in 15 seconds. what is the rate per minute

Mathematics

1 answer:

kvasek [131]2 years ago

5 0

Answer:

It is important to carefully look at all the information's that are given in the question. based on those information's the answer to the question has to be deduced. One important aspect for doing this problem is converting 1 minute into 60 seconds and then start solving.

In 15 seconds a the number of desk chairs a furniture factory can box = 1

In 60 seconds a the number of

desk chairs a furniture factory can box = (1/15) * 60

= 4 chairs

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A minor league baseball team plays 72 games in a season. If the team won 15 more than twice as many games as they lost, how many

Alina [70]

X = games won
y = games lost

x + y = 72
x = 2y + 15

2y + 15 + y = 72
3y + 15 = 72
3y = 72 - 15
3y = 57
y = 57/3
y = 19 <=== lost games

x = 2y + 15
x = 2(19) + 15
x = 53 <=== won games

3 0

3 years ago

At 2 PM, a thermometer reading 80°F is taken outside where the air temperature is 20°F. At 2:03 PM, the temperature reading yiel

Alexeev081 [22]

Use Law of Cooling:
$T(t) = (T_0 - T_A)e^{-kt} +T_A$
T0 = initial temperature, TA = ambient or final temperature

First solve for k using given info, T(3) = 42
$42 = (80-20)e^{-3k} +20 \\ \\ e^{-3k} = \frac{22}{60}=\frac{11}{30} \\ \\ k = -\frac{1}{3} ln (\frac{11}{30})$

Substituting k back into cooling equation gives:
$T(t) = 60(\frac{11}{30})^{t/3} + 20$

At some time "t", it is brought back inside at temperature "x".
We know that temperature goes back up to 71 at 2:10 so the time it is inside is 10-t, where t is time that it had been outside.
The new cooling equation for when its back inside is:
$T(t) = (x-80)(\frac{11}{30})^{t/3} + 80 \\ \\ 71 = (x-80)(\frac{11}{30})^{\frac{10-t}{3}} + 80$
Solve for x:
$x = -9(\frac{11}{30})^{\frac{t-10}{3}} + 80$
Sub back into original cooling equation, x = T(t)
$-9(\frac{11}{30})^{\frac{t-10}{3}} + 80 = 60 (\frac{11}{30})^{t/3} +20$
Solve for t:
$60 (\frac{11}{30})^{t/3} +9(\frac{11}{30})^{\frac{-10}{3}}(\frac{11}{30})^{t/3} = 60 \\ \\ (\frac{11}{30})^{t/3} = \frac{60}{60+9(\frac{11}{30})^{\frac{-10}{3}}} \\ \\ \\ t = 3(\frac{ln(\frac{60}{60+9(\frac{11}{30})^{\frac{-10}{3}}})}{ln (\frac{11}{30})}) \\ \\ \\ t = 4.959$

This means the exact time it was brought indoors was about 2.5 seconds before 2:05 PM

8 0

3 years ago

A manufacturer has been selling 1400 television sets a week at $450 each. A market survey indicates that for each $21 rebate off

GuDViN [60]

Correct question is;

A manufacturer has been selling 1400 television sets a week at $450 each. A market survey indicates that for each $21 rebate offered to a buyer, the number of sets sold will increase by 210 per week

A) Find the demand function (price p as a function of units sold x).

p(x)=______

(B) How large a rebate should the company offer the buyer in order to maximize its revenue?

$=_____

Answer:

A) p(x) = (-1/10)x + 590

B) Rebate = $170

Step-by-step explanation:

A) We are told that p(x) is the demand function and x is the number of TV sets sold per week.

Now, since for each $21 rebate offered, the number of sets sold increases by 210 per week, it means that the slope here of this demand function is; m = -21/210 = -1/10

Now, he has been selling 1400 TV sets a week at $450 each. This means; p(1400) = $450

Thus, the demand function will be;

p(x) - 450 = (-1/10)(x - 1400)

Expanding the RHS;

p(x) - 450 = (-1/10)x + 140

Add 450 to both sides to get;

p(x) = (-1/10)x + 140 + 450

p(x) = (-1/10)x + 590

B) Formula for revenue is;

R = price × quantity sold

Our demand function is p = (-1/10)x + 590

Making x the subject, we have;

x = 5900 - 10p

x is quantity sold.

Thus,

R = p(5900 - 10p)

R = 5900p - 10p²

Maximum price will occur at dR/dP = 0

Thus;

dR/dP = 5900 - 20p

At dR/dP = 0,we have;

20p = 5900

p = 5900/20

p = $280

Thus, rebate = 450 - 280 = $170

6 0

2 years ago

To simplify the following expression, which operation would you complete second?

Bingel [31]

Divide, the first operation is the parentheses and then division

3 0

2 years ago

Can someone please answer this !?!!

snow_tiger [21]

Answer:

midpoint is the answer.....

4 0

3 years ago

Read 2 more answers