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3 years ago

11

Diana had a large stack of playing cards. She knew that 17 of them were kings. She took a sample of 30 cards and found 4 kings.

Approximately how many playing card did Diana have?

1 answer:

Mandarinka [93]3 years ago

5 0

Answer:

Diana approximately had 128 cards

Step-by-step explanation:

Let n be the number of cards Diana had. She knows that

there are 17 kings among n cards
4 kings among 30 cards

Write a proportion:

$\dfrac{17}{n}=\dfrac{4}{30}$

Cross multiply:

$4n=17\cdot 30\\ \\4n=510\\ \\n=\dfrac{510}{4}=127.5\approx 128$

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Answer:

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Step-by-step explanation:

54/6=9

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3 years ago

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. $a(t)=\frac{dv}{dt}$

a.

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

4 years ago

A coach jogs 1.8 miles on Monday, 1.3 miles on Tuesday, and 1.2 miles on Wednesday. If the coach's friend jogs twice as far as t

Bond [772]

Answer:

Coach's friend jog <u>8.6 miles</u>.

Step-by-step explanation:

Given:

A coach jogs 1.8 miles on Monday, 1.3 miles on Tuesday, and 1.2 miles on Wednesday.

If the coach's friend jogs twice as far as the coach.

Now, to find the miles the coach's friend jog.

<em>Coach jogs on Monday = 1.8 miles.</em>

<em>Coach jogs on Tuesday = 1.3 miles.</em>

<em>Coach jogs on Wednesday = 1.2 miles.</em>

Total miles coach jog <em>= </em> $1.8+1.3+1.2=4.3\ miles.$ <em />

As, coach's friend jogs twice as coach.

So, to get the miles coach's friend jogs multiply total miles coach jog by 2 we get:

$Total\ miles\ coach\ jog\times 2$

$4.3\times 2\\\\=8.6\ miles.$

Therefore, coach's friend jog 8.6 miles.

4 0

3 years ago

The sum of half of a number and 8 less<br> than the number is 25. Find the number.

LuckyWell [14K]

Answer:

The number is 22

Step-by-step explanation:

let x = the number

$\frac{1}{2} x + x - 8 = 25 \\ \frac{1}{2} x + x - 8 + 8 = 25 + 8 \\ \frac{1}{2} x + x = 33 \\ factor \: out\: x \: on \: the \: left \\ x( \frac{1}{2} + 1) = 33 \\ divide \: both \: sides \: by \: \frac{1}{2} + 1 \\ \frac{x( \frac{1}{2} + 1) }{ \frac{1}{2} + 1} = \frac{33}{ \frac{1}{2} + 1} \\ x = \frac{33}{ \frac{3}{2} } \\ x = \frac{66}{3} \\ x = 22$

let's factor out x from the left hand sid

4 0

3 years ago