If m 27 = 55°, which of the following statements are true? Select all that apply.

Convergent or divergent?

navik [9.2K]

Answer:

Convergent

Step-by-step explanation:

This is an alternating series where bn = 2n / eⁿ. Apply the alternating series test:

lim(n→∞) bn

= lim(n→∞) (2n / eⁿ)

Use L'hopital's rule:

= lim(n→∞) (2 / eⁿ)

= 0

For n ≥ 1, the series is decreasing. 2(n+1) / eⁿ⁺¹ < 2n / eⁿ.

Therefore, the series converges.

6 0

4 years ago

This week, we are covering relationships that can be approximated by linear equations. For instance, y = 453x + 3768 represents

lana [24]

Answer:

See explanation below.

Step-by-step explanation:

We assume that the data is given by :

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.

Where X represent the cost for scholarships in thousands of dollars and y represent the cost of life for an academic semester (The data comes from the web)

We can 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:

$y=-0.317 x +46.02$

We have an inverse linear relationship since the slope is negative between the variables of interest.

8 0

4 years ago

How many numbers have an absolute of 5/4

Andrews [41]

A4

Step-by-step explanation:

1/2

1/3

1/5

1/4

5 0

3 years ago

A cylinder with a radius of 1 cm and a height of 21 cm has the same volume as a cone with a height of 7 cm. What is the radius o

kolbaska11 [484]

The volume of cylinders. In the earlier lesson, you learned that the volume of the rectangular prism is found by multiplying the area of the base by the height of the prism. ... Example 1. This cylinder has a radius of 4 cm and a height of 10 cm. Find its volume. V = B • h. V = (π • r • r) • h. V = (3.14 • 4 • 4) • 10. V = 502.4 cm^3

8 0

4 years ago

What could I say for this question anybody who answers this gets brainlist Answer ASAP!

QveST [7]

Well simply just state ur learning goals are. In my opinion I would keep it short and simple but give a bit of detail to it. At most like 6 sentences should be ok and should work as an answer

7 0

3 years ago