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Norma-Jean [14]
3 years ago
10

The simplest form of 18/37 & 33/44, no mixed numbers please, thanks

Mathematics
1 answer:
Luden [163]3 years ago
8 0
37 is prime so it is reduced to its lowest form.

33/44 simplifies to 3/4
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Put the fraction in least to greatest 1/5, 5/5 ,4/5
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Divide. −425÷(−5) −2225 −825 825 2225
Alex17521 [72]

Answer: The correct answer would be -85.


Step-by-step explanation: This is because the -5 becomes positive because it is inside parentheses.

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3 years ago
Find the tenth term in the following geometric sequence. 8, 4, 2, 1, . . .
Marrrta [24]

Answer:

  c)  0.0156

Step-by-step explanation:

The general term a[n] of a geometric sequence is given in terms of the first term a[1] and common ratio r as ...

  a[n] = a[1]r^(n-1)

The given sequence has an initial term of a[1]=8 and a common ratio of 4/8=1/2. Then the general term is ...

  a[n] = 8(1/2)^(n-1)

The 10th term is then ...

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7 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
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