A sofa is on sale for 27% off. The sale price is $511. What is the regular price?

kvasek [131]

To find the 20th term in this sequence, we can simply keep on adding the common difference all the way until we get up to the 20th term.

The common difference is the number that we are adding or subtracting to reach the next term in the sequence.

Notice that the difference between 15 and 12 is 3.

In other words, 12 + 3 = 15.

That 3 that we are adding is our common difference.

So we know that our first term is 12.

Now we can continue the sequence.

12 ⇒ 1st term

15 ⇒ 2nd term

18 ⇒ 3rd term

21 ⇒ 4th term

24 ⇒ 5th term

27 ⇒ 6th term

30 ⇒ 7th term

33 ⇒ 8th term

36 ⇒ 9th term

39 ⇒ 10th term

42 ⇒ 11th term

45 ⇒ 12th term

48 ⇒ 13th term

51 ⇒ 14th term

54 ⇒ 15th term

57 ⇒ 16th term

60 ⇒ 17th term

63 ⇒ 18th term

66 ⇒ 19th term

69 ⇒ 20th term

This means that the 20th term of this arithemtic sequence is 69.

5 0

3 years ago

X^2+ 6x - 4 = 3x + 6

jolli1 [7]

Answer:

x=2

x=-5

Step-by-step explanation:

You need to get everything on one side to have a quadratic equation:

x^2+6x-4 -(3x+6) = x^2+3x-10

All factors of 10 are 1*10 and 2*5.

5-2 = 3 and 5*-2 = -10

Factoring x^2+3x-10 gives us (x-2)(x+5)

x=2

x=-5

4 0

3 years ago

Read 2 more answers

A certain high school has 1,488 students. If you subtract the number of girls from boys you get 78. Let x be the number of boys

Dahasolnce [82]

Answer:

boys = 705

girls = 783

Step-by-step explanation:

We are to find the number of boys and girls in the school

the answer can be determined using simultaneous equation

x = boys

y = girls

y - x = 78 equation 1

y + x = 1488 equation 2

subtract equation 1 from 2

2x = 1410

x = 1410/2 = 705

Substitute for x in equation 1

y - 705 = 78

y = 705 + 78 = 783

3 0

2 years ago

You are asked to do a study of shelters for abused and battered women to determine the necessary capacity in your city to provid

ohaa [14]

Answer:

Using the normal probability distribution, with a capacity of 350, it is enough for all abused on 90.82% of nights.

274 shelters will be needed.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 250, \sigma = 75$