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3 years ago

7

Scientists predict that there is a 0.8 chance that there will be an earthquake in San Francisco this year. How likely is that th

ere will be an Earthquake?

1 answer:

Firlakuza [10]3 years ago

8 0

Answer:

80%

Step-by-step explanation:

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If U={1,2,3,4,5,6,7,8}, M={1,2,3,5} and N={2,4,6} find MUN compliment

nydimaria [60]

$M\cup N=\{1,2,3,4,5,6\}\\\\\overline{M\cup N}=\{7,8\}$

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3 years ago

What is a quartic function with only the two real zeros given?

VashaNatasha [74]

The right answer is B

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4 years ago

Find the cost price of an article sold at $360 with a profit of 20%.

FinnZ [79.3K]

Step-by-step explanation:

360÷100×20

=72

so 360+72

=432

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3 years ago

A balloon is blowing up at a constant rate of 9 cubic centimeters per second. When the volume of the balloon is 2048/3 pi cubic

jekas [21]

Answer:

$\displaystyle \frac{dr}{dt}\approx 0,0112\ cm/sec$

Step-by-step explanation:

<u>Rates of Change as Derivatives</u>

If some variable V is a function of another variable r, we can compute the rate of change of one with respect to the other as the first derivative of V, or

$\displaystyle V'=\frac{dV}{dr}$

The volume of a sphere of radius r is

$\displaystyle V=\frac{4}{3}\pi r^3$

The volume of the balloon is growing at a rate of $9\ cm^3/sec$ . This can be written as

$\displaystyle \frac{dV}{dt}=9$

We need to compute the rate of change of the radius. Note that both the volume and the radius are functions of time, so we need to use the chain rule. Differentiating the volume with respect to t, we get

$\displaystyle \frac{dV}{dt}=\displaystyle \frac{dV}{dr}\displaystyle \frac{dr}{dt}$

$\displaystyle \frac{dV}{dt}=4\pi r^2 \frac{dr}{dt}$

solving for $\displaystyle \frac{dr}{dt}$

$\displaystyle \frac{dr}{dt}=\frac{\frac{dV}{dt}}{4\pi r^2}$

We need to find the value of r, which can be obtained by using the condition that in that exact time

$\displaystyle V=\frac{2048}{3}\pi\ cm^3$

$\displaystyle \frac{2048}{3}\pi=\frac{4}{3}\pi r^3$

Simplifying and isolating r

$\displaystyle r^3=512$

$\displaystyle r=\sqrt[3]{512}=8\ cm$

Replacing in the rate of change

$\displaystyle \frac{dr}{dt}=\frac{9}{4\pi 8^2}$

$\displaystyle \frac{dr}{dt}=\frac{9}{256\pi }$

$\displaystyle \frac{dr}{dt}\approx 0,0112\ cm/sec$

8 0

3 years ago

On a recent trip to the convenience store, you picked up 2 gallons of milk, 6 bottles of water, and 7 snack-size bags of chips.

pshichka [43]

Answer:

The water costs $1.90, the chips are $.95 and the milk is $3.80.

Step-by-step explanation:

Let m = milk

Let w = water

Let c = chips

2m+6w+7c =25.65 w = 2c m = w + 1.90

For the first equation, substitute w for 2C and m for w + 1.90 to get:

2(w+1.90) +6(2c) + 7c = 25.65

2w+3.8+12c+7c=25.65

2w+19c = 21.85

Now substitute 2c for w:

2(2c)+19c =21.85

4c + 19c = 21.85

23c = 21.85

c = .95 Now that we know the cost of the chips we can use that to find the water and the milk for the original equations that we wrote at the top.

w = 2c

w=2(.95) = 1.90

m = w + 1.90 = 1.90+1.90 = 3.80

5 0

2 years ago