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alexdok [17]
3 years ago
11

Make r the subject of the formula

20%20%5Cfrac%7Bh%7D%7B3%7D%29" id="TexFormula1" title="v = \pi \: h {}^{2}(r - \frac{h}{3})" alt="v = \pi \: h {}^{2}(r - \frac{h}{3})" align="absmiddle" class="latex-formula">
​
Mathematics
1 answer:
Vaselesa [24]3 years ago
8 0

Answer:

\boxed{r =  \frac{h}{3}  +  \frac{v}{\pi {h}^{2} } }

Step-by-step explanation:

Solve \:  for \:  r:  \\  =  >   v= \pi {h}^{2}(r -  \frac{h}{3}  ) \\  \\  v=\pi {h}^{2}(r -  \frac{h}{3}  )is \:  equivalent  \: to   \:   {h}^{2}\pi(r -  \frac{h}{3}  ) = v: \\  =  >  {h}^{2}\pi(r -  \frac{h}{3}  ) = v \\  \\ Divide  \: both \:  sides  \: by  \: \pi  {h}^{2} :  \\  =  > r -  \frac{h}{3}  =  \frac{v}{\pi {h}^{2} }  \\  \\ Add \:   \frac{h}{3}  \:  to  \: both \:  sides:  \\  =  > r =  \frac{h}{3}  +  \frac{v}{\pi {h}^{2} }

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James earned a total of $900 this week. this total was $20 less than four times the amount he earned last week. how much money d
Vladimir [108]
<span>4x – 20 = 900
4x = 900+20
4x = 920
x = 920/4
x = 230
he earned $230
                                   </span>
7 0
3 years ago
27. The average hourly wage of workers at a fast food restaurant is $7.25/hr
morpeh [17]

Answer:

0.0668 = 6.68% probability that the worker earns more than $8.00

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

The average hourly wage of workers at a fast food restaurant is $7.25/hr with a standard deviation of $0.50.

This means that \mu = 7.25, \sigma = 0.5

If a worker at this fast food restaurant is selected at random, what is the probability that the worker earns more than $8.00?

This is 1 subtracted by the pvalue of Z when X = 8. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{8 - 7.25}{0.5}

Z = 1.5

Z = 1.5 has a pvalue of 0.9332

1 - 0.9332 = 0.0668

0.0668 = 6.68% probability that the worker earns more than $8.00

8 0
3 years ago
Solve the system of equations by graphing: -1/3x + y=-1, y=4+1/3x
Arada [10]

-\frac{1}{3}x + y = -1   ⇒   y = \frac{1}{3}x - 1

To graph this line, plot a point at the y-intercept (0, -1), than plot the next point using the rise over run from the slope (\frac{1}{3}) by counting up 1 and to the right 3 of the y-intercept.  This gives you a second point of (3. 0).  Draw a line through those two coordinates.

Answer: Plot (0, -1) and (3, 0) and draw a line through them.

***************************************************************************************

y = 4 +  \frac{1}{3}x    ⇒   y =  \frac{1}{3}x  + 4

Same as above.  Plot the y-intercept (0, 4) and then use rise over run from the slope to plot (3, 5).

Answer: Plot (0, 4) and (3, 5) and draw a line through them.

***********************************************************************************

You should end up with two PARALLEL lines.  Since the lines never intersect, there are no solutions to this system of equations.

Answer: No Solution

3 0
3 years ago
What is the distance, in units, between the points (-4,5) and (8,0) in the
Anna71 [15]
Answerrrrrrrrrrrrrrrr isssssssss: 5.38
8 0
3 years ago
Please help me with this
Alexxandr [17]

If the perimeter is 98 cm, the sum of the lengths of two adjacent sides is 49 cm.

... (2x -1) + (3x +5) = 49 . . . . use the given information and relation

... 5x +4 = 49 . .  . . . . . . . . . simplify

... 5x = 45 . . . . . . . . . . . . . . . subtract 4

... x = 9 . . . . . . . . . . . . . . . . . divide by 5

The left side dimension is then

... 2x -1 = 2·9 -1 = 17 . . . . cm

The top dimension is

... 3x +5 = 3·9 +5 = 32 . . . . cm

The rectangle is 17 cm by 32 cm.

5 0
3 years ago
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