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3 years ago

8

A teacher has 4 packs of pencils to share equally between 12 students. What fraction of a pack of pencils will each student rece

ive?

1 answer:

mariarad [96]3 years ago

7 0

Answer:

1/3

Step-by-step explanation:

4 divided by 12 is 1/3

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If f(x)=x-5, find x when f(x)=15

Leya [2.2K]

Answer:

x = 20

Step-by-step explanation:

we are given the value of f(x), replace it in the first equation

15 = x - 5

solve for x by adding 5 on both sides

15 + 5 = x

20 = x or x = 20

5 0

3 years ago

Two lines are parallel to each other if they have the same slope. True or false?

wariber [46]

Answer:

true

Step-by-step explanation:

8 0

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 :

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

5 0

3 years ago

Jack and Jill live 126 km apart. They want to leave their homes at the same time,

Digiron [165]

Answer:

Both will leave their homes to meet on time at 9 am

Step-by-step explanation:

Given as, Distance between Jack and Jill = 126 km

Speed of Jack rides = 18 kilometers per hours

Speed of Jill rides = 24 kilometers per hours

Let the distance travel by Jack = x km

And the distance travel by Jill = (126 - x ) km

Time taken by Jack and Jill = T hours

Now , Distance = Speed × Time

So, x = 18 × T

And 126 - x = 24 × T

Or, 126 - x = 24 × $\frac{x}{18}$

Or, 126 - x = x × $\frac{4}{3}$

Or, 378 - 3x = 4x

Or, 378 = 7x

i.e x = $\frac{378}{7}$ = 54 km

And distance travel by Jill = 126 - 54 = 72 km

So, time taken by Jack = $\frac{x}{18}$ = $\frac{54}{18}$

Or, Time taken by Jack = 3 hours

Similarly Time take by Jill = $\frac{72}{24}$ = 3 hours

∵ Both Jack and Jill will take 3 hours to meet at 12 : 00 pm

Hence, Both will leave their homes to meet on time at 9 am Answer

7 0

4 years ago

I need this quick pls will mark brainliest <br>write in slope intercept

gayaneshka [121]

Answer:

-5,3,4

Step-by-step explanation:

6 0

3 years ago