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2 years ago

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

Mathematics

1 answer:

MAXImum [283]2 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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3 8/20 in simplest form

daser333 [38]

It would be: 3 8/20 = 68/20 = 34/10 = 17/5

In short, Your Answer would be 17/5

Hope this helps!

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3 years ago

Jon earned $38,000 last year. He paid $6,840 for entertainment. What percent of his earnings did Jon pay in entertainment expens

marysya [2.9K]

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3 years ago

How many times can 4 go into 75

Arisa [49]

Answer:

solve using long division.

75/4

what is the largest whole number smaller than 75 that 4 can go into?

72.

how many times can 4 go into 72?

18.

so then subtract 72 from 75 to get 3.

the new equation is

3/4

how many times can 3 go into 4?

0.75 times.

so add the 2 answers to get

18.75

4 can go into 75 18.75 times.

8 0

3 years ago

Read 2 more answers

A researcher wishes to estimate, with 9090% confidence, the proportion of adults who have high-speed Internet access. Her es

Sunny_sXe [5.5K]

Answer: a) Required minimum sample size= 219

b) Required minimum sample size= 271

Step-by-step explanation:

As per given , we have

Margin of error : E= 5% =0.05

Critical z-value for 90% confidence interval : $z_{\alpha/2}=1.645$

a) Prior estimate of true proportion: p=28%=0.28

Formula to find the sample size :-

$n=p(1-p)(\dfrac{z_{\alpha/2}}{E})^2\\\\=0.28(1-0.28)(\dfrac{1.645}{0.05})^2\\\\=218.213856\approx219$

Required minimum sample size= 219

b) If no estimate of true proportion is given , then we assume p= 0.5

Formula to find the sample size :-

$n=0.5(1-0.5)(\dfrac{z_{\alpha/2}}{E})^2\\\\=0.25(\dfrac{1.645}{0.05})^2\\\\=270.6025\approx271$

Required minimum sample size= 271

8 0

3 years ago

algebraically determine the values of h and k to correctly complete the identity stated below : 2 x cubed - 10x squared + 11x -

11Alexandr11 [23.1K]

Answer:

The values for expression is h = - 2 and k = 5

Step-by-step explanation:

Given algebraic expression can be written as :

2 x³ - 10 x² + 11 x - 7 = ( x - 4 ) × ( 2 x² + h x + 3 ) + k

Now opening the bracket

Or, 2 x³ - 10 x² + 11 x - 7 = x × ( 2 x² + h x + 3 ) - 4 × ( 2 x² + h x + 3 ) + k

Or, 2 x³ - 10 x² + 11 x - 7 = 2 x³ + h x² + 3 x - 2 x² - 4 h x - 12 +k

Or , 2 x³ - 10 x² + 11 x - 7 = 2 x³ + ( h - 2 ) x² + ( 3 - 4 h ) x - 12 + k

Now, equating the equation both sides

I.e - 10 = ( h - 2 )

Or , h - 2 = - 10

I.e , h = - 10 + 2

∴ h = - 2

Again , 11 = ( 3 - 4 h )

or, 11 = 3 - 4 h

or, 11 - 3 = - 4 h

or, 8 = - 4 h

∴ h = $\frac{-8}{4}$

I.e h = - 2

Again

- 7 = - 12 + k

Or, k = - 7 + 12

∴ k = 5

Hence The values for expression is h = - 2 and k = 5 . Answer

5 0

3 years ago