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3 years ago

During a thunderstorm, 600 millimeters of rain fell in 30 minutes. How fast did the rain fall, in millimeters per minute?

Mathematics

2 answers:

madreJ [45]3 years ago

5 0

20 milliliters per minute

N76 [4]3 years ago

4 0

The rain fell 20 millimeters per minute.

Explanation:

To find the answer, we must divide the amount of rain by the number of minutes it took to fall.

600 divided by 30 = 20 millimeters.

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Write and equation based on the graph. Please help me 20 points!

zaharov [31]

Answer:

y = 3/5x - 1

Step-by-step explanation:

The slope found from counting the units is 3/5, and the y-intercept is -1, hence 3/5x - 1

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2 years ago

The ratio of marbles to stones is 5 to 7 if there are 35 marbles how many stones is there?

icang [17]

5 : 7
Marbles : Stones

35/5 = 7
So stones
= 7 * 7
49

=35 : 49

3 0

3 years ago

Read 2 more answers

When designing a study to determine this population proportion, what is the minimum number of drivers you would need to survey t

Vlada [557]

Answer: 601

Step-by-step explanation:

The formula to find the minimum sample size(n) , if the prior population proportion is unknown:

$n=0.25(\dfrac{z^c}{E})^2$ , where E = margin of error , $z^c$ = critical z-value for confidence level c.

Given : E = 0.04

Z-value for 95% confidence = 1.96

So, the minimum sample size required = $0.25(\dfrac{1.96}{0.04})^2=0.25(49)^2$

$= 0.25\times 2401=600.25\approx601$

Hence, the minimum sample size required = 601

6 0

2 years ago

Find the maximum and minimum values of the function f(x,y)=2x2+3y2−4x−5 on the domain x2+y2≤100. The maximum value of f(x,y) is:

ryzh [129]

First find the critical points of f :

$f(x,y)=2x^2+3y^2-4x-5=2(x-1)^2+3y^2-7$

$\dfrac{\partial f}{\partial x}=2(x-1)=0\implies x=1$

$\dfrac{\partial f}{\partial y}=6y=0\implies y=0$

so the point (1, 0) is the only critical point, at which we have

$f(1,0)=-7$

Next check for critical points along the boundary, which can be found by converting to polar coordinates:

$f(x,y)=f(10\cos t,10\sin t)=g(t)=295-40\cos t-100\cos^2t$

Find the critical points of g :

$\dfrac{\mathrm dg}{\mathrm dt}=40\sin t+200\sin t\cos t=40\sin t(1+5\cos t)=0$

$\implies\sin t=0\text{ OR }1+5\cos t=0$

$\implies t=n\pi\text{ OR }t=\cos^{-1}\left(-\dfrac15\right)+2n\pi\text{ OR }t=-\cos^{-1}\left(-\dfrac15\right)+2n\pi$

where n is any integer. We get 4 critical points in the interval [0, 2π) at

$t=0\implies f(10,0)=155$

$t=\cos^{-1}\left(-\dfrac15\right)\implies f(-2,4\sqrt6)=299$

$t=\pi\implies f(-10,0)=235$

$t=2\pi-\cos^{-1}\left(-\dfrac15\right)\implies f(-2,-4\sqrt6)=299$

So f has a minimum of -7 and a maximum of 299.

4 0

3 years ago

A company that teaches self-improvement seminars is holding one of its seminars in Lancaster. The company pays a flat fee of $98

alukav5142 [94]

Answer:

Step-by-step explanation:

Let x represent the number of attendees that it will take the company to break even.

The company pays a flat fee of $98 to rent a facility in which to hold each session. Additionally, for every attendee who registers, the company must spend $16 to purchase books and supplies. This means that the total cost that the company would pay for x attendees is

16x + 98

Each attendee will pay $65 for the seminar. This means that the total revenue that the company would generate from x attendees is 65x.

At the break even point,

total cost = total revenue

Therefore,

16x + 90 = 65x

65x - 16x = 98

49x = 98

x = 98/49

x = 2

It will take 2 attendees and the total expenses and revenues is

2 × 65 = $130

4 0

3 years ago