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Y_Kistochka [10]
3 years ago
13

Please help. I just am I bit confused..

Mathematics
1 answer:
8_murik_8 [283]3 years ago
8 0

Answer:

add tjem all up and fid the outnumber one

Step-by-step explanation:

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A go-cart with a mass of 200 kg is pushed with a force of 1000 N (1000 kg m/s2). What is the acceleration of the go-cart? ​
Hunter-Best [27]

Answer:

Acceleration=5m/s^2

Step-by-step explanation:

F=ma

1000=200xa

a=1000/200

a=5m/s^2

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
Wade borrowed $12,500 from his uncle at 4.5% simple interest to use for travel and repaid the loan in 4 years. How much did he p
natali 33 [55]
12,500 / 100 = 125    125 x 4.5 = 562.5      562.5 x 4 = 2250
2250 + 12,500 = 14,750       He paid back a total of $14,750. Hope this helps :)
7 0
3 years ago
F(n+1)=f(n)-5. If f(1)=100, what is f(6)
PilotLPTM [1.2K]

Answer:

<em>75</em>

Step-by-step explanation:

Given:

f(1) = 100

f(n+1) = f(n) - 5

Solve for:

f(6)

Solution:

f(1) = 100

f(2) = f(1) - 5 = 100 - 5 = 100 - 1 x 5 = f(1) - 1 x 5

f(3) = f(2) - 5 = 100 - 5 - 5 = 100 - 2 x 5 = f(1)  - 2 x 5

...

f(n) = f(n - 1) - 5 = 100 - (n-1) x 5 = f(1) - (n-1) x 5

=> f(6) = f(1) - (6-1) x 5 = 100 - 5 x 5 = 100 - 25 = 75

Hope this helps!

8 0
3 years ago
Find the average rate of change.
alina1380 [7]

The average rate of change = 1.59 ≈ 2

The average rate of change can be calculated by

1) The first one = \frac{3 + 0}{2} = 1.5

2 ) the second can also be solved by ; 8 + 2/ 2 = 5

3 ) the third one will be 20 + 6 / 2 = 13

4) 8.5

5) 12.5

To calculate the average rate of change

we will first add all the distance

Adding all the distance we will get the sum = 3 + 8 + 20 + 10 + 10 = 51

The total time = 2 + 6 + 9 +15 = 32

Thus the average rate of change = 51 / 32 = 1.59

To know more about average rate of change you may visit the link which is mentioned below;

brainly.com/question/28744270

#SPJ13

5 0
1 year ago
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