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2 years ago

If the retail price of an item is $65, and the markup is 50%, find the wholesale price.

Mathematics

1 answer:

Montano1993 [528]2 years ago

8 0

Answer:

32.5

Step-by-step explanation:

% over 100 = is/ of

50% over 100 = x / 65

cross multiply

3250/ 100x = 32.5

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Jose can read 7 pages of his book in5 minutes. at this rate, how long will it take him to read the entire 175-page book?

Lera25 [3.4K]

Since 7 pages could be in 5 min.
So time required by 1 page 5/7 min.
So time required by 175 pages =175×5/7=125 min.
= 2 hours and 5minutes

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3 years ago

Choose the scatter plot that shows a negative correlation.

Alenkinab [10]

Negative correlation between two variables means when x is increasing but y is decreasing or vice versa.

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Second graph of survey of adults doesn't represnt any distinct relationship as the data scattered randomly everywhere in the graph. So, it's showsa very week correlation.

Third graph of speed and MPG shows a negative slope as speed is increasing then MPG is decreasing. So, the third graph (speed and MPG) shows a negative correlation.

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2 years ago

Read 2 more answers

A rock thrown vertically upward from the surface of the moon at a velocity of 36m/sec reaches a height of s = 36t - 0.8 t^2 met

Verdich [7]

Answer:

a. The rock's velocity is $v(t)=36-1.6t \:{(m/s)}$ and the acceleration is $a(t)=-1.6 \:{(m/s^2)}$

b. It takes 22.5 seconds to reach the highest point.

c. The rock goes up to 405 m.

d. It reach half its maximum height when time is 6.59 s or 38.41 s.

e. The rock is aloft for 45 seconds.

Step-by-step explanation:

Velocity is defined as the rate of change of position or the rate of displacement. $v(t)=\frac{ds}{dt}$
Acceleration is defined as the rate of change of velocity. $a(t)=\frac{dv}{dt}$

The rock's velocity is the derivative of the height function $s(t) = 36t - 0.8 t^2$

$v(t)=\frac{d}{dt}(36t - 0.8 t^2) \\\\\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'\\\\v(t)=\frac{d}{dt}\left(36t\right)-\frac{d}{dt}\left(0.8t^2\right)\\\\v(t)=36-1.6t$

The rock's acceleration is the derivative of the velocity function $v(t)=36-1.6t$

$a(t)=\frac{d}{dt}(36-1.6t)\\\\a(t)=-1.6$

b. The rock will reach its highest point when the velocity becomes zero.

$v(t)=36-1.6t=0\\36\cdot \:10-1.6t\cdot \:10=0\cdot \:10\\360-16t=0\\360-16t-360=0-360\\-16t=-360\\t=\frac{45}{2}=22.5$

It takes 22.5 seconds to reach the highest point.

c. The rock reach its highest point when t = 22.5 s

Thus

$s(22.5) = 36(22.5) - 0.8 (22.5)^2\\s(22.5) =405$

So the rock goes up to 405 m.

d. The maximum height is 405 m. So the half of its maximum height = $\frac{405}{2} =202.5 \:m$

To find the time it reach half its maximum height, we need to solve

$36t - 0.8 t^2=202.5\\36t\cdot \:10-0.8t^2\cdot \:10=202.5\cdot \:10\\360t-8t^2=2025\\360t-8t^2-2025=2025-2025\\-8t^2+360t-2025=0$

For a quadratic equation of the form $ax^2+bx+c=0$ the solutions are

$x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\mathrm{For\:}\quad a=-8,\:b=360,\:c=-2025:\\\\t=\frac{-360+\sqrt{360^2-4\left(-8\right)\left(-2025\right)}}{2\left(-8\right)}=\frac{45\left(2-\sqrt{2}\right)}{4}\approx 6.59\\\\t=\frac{-360-\sqrt{360^2-4\left(-8\right)\left(-2025\right)}}{2\left(-8\right)}=\frac{45\left(2+\sqrt{2}\right)}{4}\approx 38.41$

It reach half its maximum height when time is 6.59 s or 38.41 s.

e. It is aloft until s(t) = 0 again

$36t - 0.8 t^2=0\\\\\mathrm{Factor\:}36t-0.8t^2\rightarrow -t\left(0.8t-36\right)\\\\\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}\\\\t=0,\:t=45$

The rock is aloft for 45 seconds.

5 0

3 years ago

There are 24 pizzas. each person gets 1/3 of a pizza. how many people can be fed from the 24 pizzas?

ValentinkaMS [17]

Hello there.

<span>There are 24 pizzas. each person gets 1/3 of a pizza. how many people can be fed from the 24 pizzas?

Answer: There are 3 thirds in a whole.
Therefore 3 people could be fed by 1 pizza.
Since there are 24 , multiply 3 by 24.
3 x 24 = 72.
The number of people that could be fed from the 24 pizzas is 72.

Hope This Helps You!
Good Luck Studying ^-^</span>

6 0

2 years ago

Solve the system of equations. y = 2x y = x 2 – 15

inn [45]

Answer:

D. (–3, –6) and (5, 10)

Step-by-step explanation:

The system has equations:

$y=2x$ ...(1)