All categories

3 years ago

Which is the best interpretation of the solution set for the compound inequality?

Mathematics

1 answer:

andriy [413]3 years ago

7 0

Answer:

all real numbers

Step-by-step explanation:

Here is the solution to the first inequality:

3(2x +1) > 21 . . . . . . given

6x +3 > 21 . . . . . . . . eliminate parentheses

6x > 18 . . . . . . . . . . .subtract 3

x > 3 . . . . . . . . . . . . divide by 6

This is all numbers to the right of 3 on the number line.

The solution to the second inequality is ...

4x +3 < 3x + 7 . . . . given

x < 4 . . . . . . . . . . . . subtract 3x+3

This is all numbers to the left of 4 on the number line.

The conjunction in the system of inequalities is "or", so we are looking for values of x that will satisfy at least one of the conditions. <em>Any value of x</em> will satisfy one or the other or both of these inequalities. The solution is all real numbers.

You might be interested in

Andre and Elena are reading the same book over the 1 summer. Andre says he has read of the book. Elena ! says she has read 20 mo

ddd [48]

Answer: There are 175 pages in the book.

Step-by-step explanation:

If Elena read 20 more pages than Andre and she read 55 pages, to find out how much Andre read you have to:

55-20= the pages Andre read

55-20=35

Andre read 35 pages.

If Andre read 1/5 of the book, then to find how many pages are in the book, you have to multiply 35 x 5. (Multiply by the reciprocal)

35 x 5= 175

There are 175 pages in the book.

7 0

2 years ago

Identify the area of the figure rounded to the nearest tenth. PLEASE HELP!!

kirill115 [55]

Split it up into 3 separate shapes.

Rectangle 1 = 15 x 3 = 45

Rectangle 2 = 3 x 5 = 15

Triangle = 1/2 x 5 x 3 = 7.5

Total area = 45 + 15 + 7.5 = 67.5 cm²

5 0

2 years ago

Can someone help me, please???

jasenka [17]

What are you even supposed to do

5 0

3 years ago

A meteor crater is 3900 feet in diameter. Approximate the distance around the crater. Use 3.14 for pi.

AveGali [126]

"<em>The distance around a circle"</em> = Circumference

Circumference = 3.14 * diameter

3900 * 3.14 = 12246

The circumference (distance around the crater) is equal to 12,246 feet

7 0

2 years ago

A random sample of 200 voters in a town is selected, and 114 are found to support an annexa- tion suit. Find the 96% confidence

EastWind [94]

Answer:

a) 96% CI: $0.51\leq\pi\leq 0.63$

b) If we estimate that the fraction of voters is 0.57, we can claim with 96% confidence that the error is equal or less than 0.06 from the estimated proportion.

Step-by-step explanation:

The proportion of the sample is

$p=\frac{114}{200}=0.57$

The standard deviation of the sample proportion is

$\sigma=\sqrt{\frac{p(1-p)}{n} } =\sqrt{\frac{0.57(1-0.57)}{200} } =\sqrt{\frac{0.2451}{200} } =0.035$

For a 96% CI, the z-value is z=1.751.

Then, the 96% CI can be written as:

$p-z\cdot \sigma\leq\pi\leq p+z\cdot \sigma\\\\0.57-1.751*0.035\leq\pi\leq 0.57+1.751*0.035\\\\0.57-0.06\leq\pi\leq 0.57+0.06\\\\0.51\leq\pi\leq 0.63$

b) If we estimate that the fraction of voters is 0.57, we can claim with 96% confidence that the error is equal or less than 0.06 from the estimated proportion.

6 0

3 years ago