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I am Lyosha [343]
3 years ago
14

Find the 72nd term of the arithmetic sequence -27, -11, 5, ...

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

Step-by-step explanation:

first identify the common difference

The first term which i will define by u⁰=-27

u¹=u⁰+(1)d where d is the common difference and u¹ is the second term

u¹=-27+d

-11=-27+d

d=27-11=16

The 72nd term would be u⁷¹ since we started from u⁰ as our first term:

Use the explicit relation given by:

u(n)=u⁰+(n)d

u(71)=-27+71(d)

u⁷¹=-27+71(16)

u⁷¹=-27+1136

u⁷¹=1109

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What is the correlation coefficient between the variables? Round to three decimal places. Enter your answer in the box. r≈ Age S
Free_Kalibri [48]

There are two data sets x and y.

X includes = 14 25 19 35 20 12 5

Y includes = 360 293 315 212 315 331 404

 to solve for the correlation coefficient, we need to get the following values step by step

Step 1: Find the mean of each set.

The mean of X = 18.571

The mean of Y = 318.571

 

Step 2: Subtract the mean of X from every value X value (denote this with letter a). Do the same for y (denote this with letter b).

The mean of X subtracted from every X value (a):

14 - 18.571 = -4.571

25 - 18.571 = 6.429

19 - 18.571 = 0.429

35 - 18.571 = 16.429

20 - 18.571 = 1.429

12 - 18.571 = -6.571

5 - 18.571 = -13.571

The mean of Y subtracted from every value of Y (b):

360 - 318.571 = 41.429

293 - 318.571 = -25.571

315 - 318.571 = -3.571

212 = 318.571 = -106.571

315 - 318.571 = -3.571

331 - 318.571 = 12.429

404 - 318.571 = 85.429

 

Step 3: Calculate: a *  b, a^2 and b^2 of every value.

For a*b

-189.388

-164.388

-1.531

-1750.816

-5.102

-81.673

-1159.388

Sum: -3352.286


For a²

20.898

41.327

0.184

269.898

2.041

43.184

184.184

Sum: 561.714


For b²

1716.327

653.898

12.755

11357.469

12.755

154.469

7298.041

Sum: 21205.714


Step 4: Solve using this formula

r = ∑a * b / √((a²)(b²))

r = -3352.286 / √((561.714)(21205.714))

 = -0.9713


The correlation coefficient is -0.971

8 0
3 years ago
Read 2 more answers
Please help solve 20 points.
Bond [772]

Answer: scroll down to find out :)

Step-by-step explanation:

This isn't a hard equation, so I would just use the points and figure something out.

Some obvious points are (3, 6), (6, 12), and (7, 14). Immediately, we notice that the y coordinate is 2 times the x coordinate.

So, the equation would be y = 2x.

<em>P.S. Let me know if I got it wrong! I'll be more than happy to fix it :)</em>

7 0
3 years ago
How high is a tree that casts a 25 ft shadow at the same time a 7ft pole casts a shadow which is 4 ft long?
Olegator [25]

Answer:

x=12

Step-by-step explanation:

height of tree)/(shadow length of tree) = (height of pole)/(shadow length of pole)

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13x = 26*6

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4 0
3 years ago
3/8 to 7/8 find the percent of change and is it decrease or increase
mote1985 [20]

Answer:133.33%


Step-by-step explanation:

For given change in fractions from \frac{3}{8} to \frac{7}{8}

The initial fraction=\frac{3}{8}

New fraction= \frac{7}{8}

Change in fractions= New fraction-Initial fraction

=\frac{7}{8}-\frac{3}{8}\\\\=\frac{7-3}{8}\\\\=\frac{4}{8}\\=\frac{1}{2}

As change in fraction is positive thus it is an increase.

\text{Percent of increase=}\frac{\text{increase in fraction}}{\text{initial fraction}}\times100\\\\=\frac{\frac{1}{2}}{\frac{3}{8}}\times100\\\\=\frac{1}{2}\times\frac{8}{3}\times100\\\\=\frac{400}{3}=133.33\%

4 0
4 years ago
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A vet borrows $12,000 for 4 years. The total interest paid was $960. What was the interest rate on the loan?
Alchen [17]

Answer:

2% per year.

Step-by-step explanation:

Solving our equation

r = 960 / ( 12000 × 4 ) = 0.02

r = 0.02

converting r decimal to a percentage

R = 0.02 * 100 = 2%/year

The interest rate required to

accumulate simple interest of $ 960.00

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over 4 years is 2% per year.

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3 years ago
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