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2 years ago

When lit, a candle loses 5% of its original height every hour. Jennifer lit a candle with an original height of 8 inches.

Mathematics

1 answer:

Margarita [4]2 years ago

3 0

0.05*8 = 0.4 inches = 5% of its original height

As a result, the candle's height decreases by 0.4 inches per hour.

The height will be 7.6 in after 1 hour. It will be 7.2 in about 2 hours. It will be 6.8 after 3 hours, and so forth.

We must determine when the height will be 7 inches. This happens when the candle height has shrunk by one inch (from 8 in to 7 in). As we can see from the estimates above, this will happen between 2 and 3 hours. After 1/0.4 = 2.5 hours, the height will have decreased by 1 inch.

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2 years ago

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To rent a jet ski at Sam’s costs $25 plus $3 per hour. At Claire’s, it costs $7 plus $6 per hour. At how many hours will the ren

skad [1K]

Answer:

The number of hours that the cost of renting a ski jet will become equal in both shops is 6(hours)

Step-by-step explanation:

Extracting the key information from the question:-

*** Renting a jet ski at Sam's establishment costs $25 and additional $3 per hour.

*** Again, it costs $7 and additional $6 per hour to rent a jet ski at Claire's establishment.

*** We are required to find out the number of hours that the rental cost of jet ski at both shops will be the same.

What we are basically required to do is to find that number of hours that you can rent a jet ski and you wouldn't need to worry about the shop that renting it's jet ski will be more affordable in because the cost will be the same in both establishment when renting the jet ski at a particular number of hours.

For example, in that number of hours, the cost in Sam's shop and Claire's shop will now both be say, $50.

Since it costs a down payment of $25 plus additional $3 for each hour we make use of the jet ski at Sam's establishment, then the cost of renting a jet ski at Sam's shop for that number of hours that the cost will become equal in both shops is:

= 25 + 3x

Again, we are informed that it costs $7 down payment and additional $6 per hour that a jet ski from Claire's establishment will b rented and used. Then the cost of renting a jet ski at Claire's establishment for that number of hours that the cost will become equal in both shops is:

= 7 + 6x

Since at this unknown number of hours (x hours) the cost of renting a jet ski at Sam's shop will be equal to the cost of renting a jet ski at Claire's establishment, then marrying the equations, we will have:-

25 + 3x = 7 + 6x

We now pair like terms

6x - 3x = 25 - 7

3x = 18

x = 18/3

x = 6

Therefore, that number of hours that the cost of renting a jet ski will become equal in both Sam's and Claire's establishment is 6 hours.

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3 years ago

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Answer:

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Step-by-step explanation:

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2 years ago

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Answer:

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Step-by-step explanation:

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3 years ago

An experiment was conducted to observe the effect of an increase in temperature on the potency of an antibiotic. Three 1-ounce p

ludmilkaskok [199]

Answer:

a) $y=-0.317 x +46.02$

b) Figure attached

c) $S^2=\hat \sigma^2=MSE=\frac{190.33}{10}=19.03$

Step-by-step explanation:

We assume that th data is this one:

x: 30, 30, 30, 50, 50, 50, 70,70, 70,90,90,90

y: 38, 43, 29, 32, 26, 33, 19, 27, 23, 14, 19, 21.

a) Find the least-squares line appropriate for this data.

For this case we need to calculate the slope with the following formula:

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

So we can find the sums like this:

$\sum_{i=1}^n x_i = 30+30+30+50+50+50+70+70+70+90+90+90=720$

$\sum_{i=1}^n y_i =38+43+29+32+26+33+19+27+23+14+19+21=324$

$\sum_{i=1}^n x^2_i =30^2+30^2+30^2+50^2+50^2+50^2+70^2+70^2+70^2+90^2+90^2+90^2=49200$

$\sum_{i=1}^n y^2_i =38^2+43^2+29^2+32^2+26^2+33^2+19^2+27^2+23^2+14^2+19^2+21^2=9540$

$\sum_{i=1}^n x_i y_i =30*38+30*43+30*29+50*32+50*26+50*33+70*19+70*27+70*23+90*14+90*19+90*21=17540$

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=49200-\frac{720^2}{12}=6000$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}=17540-\frac{720*324}{12}{12}=-1900$

And the slope would be:

$m=-\frac{1900}{6000}=-0.317$

Nowe we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{720}{12}=60$

$\bar y= \frac{\sum y_i}{n}=\frac{324}{12}=27$

And we can find the intercept using this:

$b=\bar y -m \bar x=27-(-0.317*60)=46.02$

So the line would be given by:

$y=-0.317 x +46.02$

b) Plot the points and graph the line as a check on your calculations.

For this case we can use excel and we got the figure attached as the result.

c) Calculate S^2

In oder to calculate S^2 we need to calculate the MSE, or the mean square error. And is given by this formula:

$MSE=\frac{SSE}{df_{E}}$

The degred of freedom for the error are given by:

$df_{E}=n-2=12-2=10$

We can calculate:

$S_{y}=\sum_{i=1}^n y^2_i -\frac{(\sum_{i=1}^n y_i)^2}{n}=9540-\frac{324^2}{12}=792$

And now we can calculate the sum of squares for the regression given by:

$SSR=\frac{S^2_{xy}}{S_{xx}}=\frac{(-1900)^2}{6000}=601.67$

We have that SST= SSR+SSE, and then SSE=SST-SSR= 792-601.67=190.33[/tex]

So then :

$S^2=\hat \sigma^2=MSE=\frac{190.33}{10}=19.03$

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3 years ago