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Agata [3.3K]
2 years ago
5

A sprinter can run 319 feet and 11 seconds find the sprinters unit rate of feet per second

Mathematics
2 answers:
Brilliant_brown [7]2 years ago
7 0
The answer is 29 ft per second. Just divide 319 by 11
Naddik [55]2 years ago
4 0

Answer:28 feet per second

Step-by-step explanation:

Given : The distance traveled by sprinter = 319 feet

The time taken by sprinter = 11 seconds

We know that the formula to calculate the unit rate of distance per time is given by :_

r=\dfrac{\text{Distance}}{\text{Time}}\\\\\Rightarrow\ r=\dfrac{319}{11}\\\\\Rightarrow\ r=29\text{ feet per second}

Hence, the sprinters unit rate = 28 feet per second

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The ratio of students who wear glasses to the total class is 2:5
Taya2010 [7]

Answer:

a. 2:3, b. 25 students, c. 3:2

Step-by-step explanation:

a. 5 (total) - 2 (with glasses) = 3 (without glasses), making the ratio 2:3.

b. We can assign the total students with the variable x. 3:5=15:x, 75=3x, x=25. 25 total students.

c. 25 (total students) - 15 (without glasses) = 10 (with glasses). (10+5):(15-5) is 15:10, which, when simplified, equals to 3:2.

4 0
2 years ago
Demand for Tablet Computers The quantity demanded per month, x, of a certain make of tablet computer is related to the average u
soldier1979 [14.2K]

x = f ( p ) = \frac { 100 } { 9 } \sqrt { 810,000 - p ^ { 2 } } } \\\\ \qquad { p ( t ) = \dfrac { 400 } { 1 + \dfrac { 1 } { 8 } \sqrt { t } } + 200 \quad ( 0 \leq t \leq 60 ) }

Answer:

12.0 tablet computers/month

Step-by-step explanation:

The average price of the tablet 25 months from now will be:

p ( 25) = \dfrac { 400 } { 1 + \dfrac { 1 } { 8 } \sqrt { 25 } } + 200 \\= \dfrac { 400 } { 1 + \dfrac { 1 } { 8 } \times 5 } + 200\\\\=\dfrac { 400 } { 1 + \dfrac { 5 } { 8 } } + 200\\p(25)=\dfrac { 5800 } {13}

Next, we determine the rate at which the quantity demanded changes with respect to time.

Using Chain Rule (and a calculator)

\dfrac{dx}{dt}= \dfrac{dx}{dp}\dfrac{dp}{dt}

\dfrac{dx}{dp}= \dfrac{d}{dp}\left[{ \dfrac { 100 } { 9 } \sqrt { 810,000 - p ^ { 2 } } }\right] =-\dfrac{100}{9}p(810,000-p^2)^{-1/2}

\dfrac{dp}{dt}=\dfrac{d}{dt}\left[\dfrac { 400 } { 1 + \dfrac { 1 } { 8 } \sqrt { t } } + 200 \right]=-25\left[1 + \dfrac { 1 } { 8 } \sqrt { t } \right]^{-2}t^{-1/2}

Therefore:

\dfrac{dx}{dt}= \left[-\dfrac{100}{9}p(810,000-p^2)^{-1/2}\right]\left[-25\left[1 + \dfrac { 1 } { 8 } \sqrt { t } \right]^{-2}t^{-1/2}\right]

Recall that at t=25, p(25)=\dfrac { 5800 } {13} \approx 446.15

Therefore:

\dfrac{dx}{dt}(25)= \left[-\dfrac{100}{9}\times 446.15(810,000-446.15^2)^{-1/2}\right]\left[-25\left[1 + \dfrac { 1 } { 8 } \sqrt {25} \right]^{-2}25^{-1/2}\right]\\=12.009

The quantity demanded per month of the tablet computers will be changing at a rate of 12 tablet computers/month correct to 1 decimal place.

8 0
2 years ago
What is the simplified form of the equation fraction 4 over 5 n minus fraction 1 over 5 equals fraction 2 over 5 n
liubo4ka [24]
4/5n – 1/5 = 2/5n
Add 1/5 to both sides
4/5n = 2/5n + 1/5
Subtract 2/5n from both sides
2/5n = 1/5
Divide both sides by 2/5

n = 1/2
8 0
3 years ago
Simplify 30x-140-(x-4)
balu736 [363]

Answer:

x = 4.7

Step-by-step explanation:

30x - 140 -(x - 4)

Multiply the -1 into (x - 4)

30x - 140 - x + 4

Add/subtract

29x - 136 = 0

      +136

29x = 136

\frac{29x}{29} = \frac{136}{29}

x = 4.689655172413793

8 0
3 years ago
On which number line are −4 and its opposite shown?
Natasha2012 [34]

Answer:

it is D because it is asking for the opposite of -4 so it would be the tick mark on -4 and 4

Step-by-step explanation:

5 0
2 years ago
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