What are the solutions to the absolute value inequality |x − 70| ≤ 3?

Remember, the inequality can be written as −3 ≤ x − 70 ≤ 3

or as x − 70 ≤ 3 and x − 70 ≥ −3.

Answers

Answer 1

Answer:

67 ≤ x ≤ 73

Step-by-step explanation:

The absolute value of a real number x is the non negative value of x. Therefore the absolute value of x (|x|) = x for x ≥ 0 and -x for x < 0.

An expression |x - a| = b signifies that x - a = b or -(x - a) = b

Given that |x − 70| ≤ 3, hence:

|x − 70| ≤ 3

x - 70 ≤ 3 or -(x - 70) ≤ 3

x ≤ 3 + 70 or x - 70 ≥ -3

x ≤ 73 or x ≥ -3 + 70

x ≤ 73 or x ≥ 67

67 ≤ x ≤ 73

Hence the solution of |x − 70| ≤ 3 is 67 ≤ x ≤ 73


Related Questions


A carpenter takes one day to complete 1/2 a set of cabinets. What fraction is complete in a 1/4 of a day

Answers

1/2 / 4 = 1/8

1/8 is the answer

In a sample of 528 customers, 237 say they are happy with the service. If you select three customers without replacement for a commercial, what is the probability they will all say they are happy with the service

Answers

Answer: 0.0898

Step-by-step explanation:

Probability = [tex]\dfrac{favorable\ outcomes}{Total\ outcomes}[/tex]

Given : Sample size : 528

Number pf customers say they are happy = 237

Probability of getting one happy customer= [tex]\dfrac{237}{528}[/tex]

Probability of getting second happy customer= [tex]\dfrac{236}{527}[/tex]  [subtract 1 from both numbers]

Probability of getting third happy customer= [tex]\dfrac{235}{526}[/tex]  

If 3 customers are elected without replacement

The probability they will all say they are happy with the service  = [tex]\dfrac{237}{528}\times\dfrac{236}{527}\times\dfrac{235}{526}[/tex]  

[tex]\approx0.0898[/tex]

Hence, the required probability = 0.0898

I need help is this right

Answers

Answer:

it's D

Step-by-step explanation:

it said that its more then which equals to a greater sign (>).

What is the solution of the proportion 13/y = 3/8?

Answers

Answer:

y =  34 [tex]\frac{2}{3}[/tex]

Answer:

Step-by-step explanation:

if you have

13/y=3/8

y=(13*8)/3=104/3=34 2/3

6(4-1)? - 5(2) =
ILL MAKE BRAINLYIST

Answers

63-52
11!
Hope this helps
Answer:
8
Explanation:
You have to do the parentheses first(4-1), then you have to multiply both sides(separately) and subtract

A study of 40 English composition professors showed that they spent, on average, 13 minutes correcting a student's term paper. The standard deviation was 2 min. a. Find and the 90% confidence interval for the mean grading time of all composition papers. < μ < b. intrepret the meaning of the confidence interval you found in part a. b. Does the confidence interval, at 90% confidence level, provide sufficient evidence that the mean time English composition professors spend on grading term papers exceeds 11 minutes? Write an appropriate inequality to justify your answer.

Answers

Answer:

a)

90% confidence interval for the mean grading time of all composition papers.

(12.47981 , 13.52019)

b)

Appropriate inequality

The interval is  ( 12.47981 < μ < 13.52019)

Step-by-step explanation:

Explanation:-

a)

Given sample size 'n' = 40

Mean of the sample = 13 minutes

standard deviation = 2 min

level of significance = 0.10 or 90%

90% confidence interval for the mean grading time of all composition papers.

[tex]( x^{-} - Z_{0.1} \frac{S.D}{\sqrt{n} } , x^{-} + Z_{0.10} \frac{S.D}{\sqrt{n} } )[/tex]

 [tex]( 13 - 1.645 \frac{2}{\sqrt{40} } , 13 +1.645 \frac{2}{\sqrt{40} } )[/tex]

( 13 - 0.52019 , 13 + 0.52019)

(12.47981 , 13.52019)

b)

The interval is  ( 12.47981 < μ < 13.52019)

Six out of the 12 members of the school choir are boys. In simplest form, what fraction of the choir is boys?

Answers

Answer:

1/2

Step-by-step explanation:

The​ _______ for a procedure consists of all possible simple events or all outcomes that cannot be broken down any further.

Answers

Answer:

Sample space

The _______ for a procedure consists of all possible simple events or all outcomes that cannot be broken down any further.

Help I don’t understand the question

Answers

Answer:

g=8

Step-by-step explanation:

games to wins are the same

g:4=6:3

g=8

Answer:

2

Step-by-step explanation:

the answer is

Got an easy one for you guys

Answers

Answer:

x=17

Step-by-step explanation:

The exterior angle theorem states that one exterior angle of a triangle is equal to the sum of its opposite interior angles. Knowing this, we can set up the following equation:

(8x-11)=(5x)+(2x+6)

Open up the parentheses

8x-11=5x+2x+6

8x-11=7x+6

Add 11 to both sides

8x-11+11=7x+6+11

8x=7x+17

Subtract both sides by 7x

8x-7x=7x+17-7x

x=17

I hope this helps!

Answer:

7x+6=8x-11

17=x

Step-by-step explanation:

Gasoline costs 1.83 euro per liter in France. What is the price in dollars per​ gallon?

Answers

Answer:

€1.85= $2.22

1 Liter= 0.264172 US liquid gallon

$8.40 per gallon

Step-by-step explanation:

Can someone help me??

Answers

Answer:

[tex]1. \: y = - x + 3[/tex]

[tex]2. \: y = x - 3[/tex]

4 The expression (2x² + 6x + 5)-(6x² + 3x + 5) is
equivalent to
1) 4x2 + 3x
2) 4x2 – 3x
3) 4x2 – 3x + 10
4) 4x2 + 3x - 10

Answers

Answer:

1) 4x² + 3x

Step-by-step explanation:

Add/Combine like terms:

2x² - 6x² = -4x²

6x - (+3x) = 3x

5 - (+5) = 0

Simplify: -4x² + 3x

14
1 point
4-32.
Use what you know about the sum of the angles of a triangle to find mZABC and mLBAC. Are these angles acute or obtuse?
2x +2°
6x + 8°
B
They are both acute.
They are both obtuse.
One is obtuse and the other is acute.

please help asap! thank you

Answers

Answer:

alam ko sagot pero mataas lang

Answer:

I am not sure if my answer is yes. .

Mr Rumpole believes that the mean income of lawyers is now more than $65 thousand per year. Which is the correct set of hypotheses to test this belief?

Answers

Answer:

d. Hо:μ ≤ 65,000; H1:μ > 65,000

Step-by-step explanation:

Note: The multiple option to the question is attached as picture below

Null Hypothesis ----> Hо:μ ≤ 65,000

Alternate Hypothesis ----> H1:μ > 65,000

So, option D is correct.

The set of hypotheses that Mr. Rumpole can use to test the stated belief is:

D. H0:μ ≤ 65,000; H1:μ > 65,000

Recall:

We have two types of hypothesis, which are, the null hypothesis and the alternative hypothesis.

The null hypothesis states no statistical relationship or difference exist between two variables. It is denoted by the sign, H0.The alternative hypothesis states there is statistical relationship or difference that exist between two variables. It is denoted by the sign, H1.

Therefore, the set of hypotheses that Mr. Rumpole can use to test the stated belief is:

D. H0:μ ≤ 65,000; H1:μ > 65,000

Learn more here:

https://brainly.com/question/15238661

Find the slope of each line

Answers

Answer:

The slope is 1/2

Step-by-step explanation:

Factor the trinomial. Factor out the GCF first.
5h^2k^2 – 15hk^3 – 200k^4

Answers

Answer:

The factored form is: [tex]5k^2(h^2 - 3hk - 40k^2)[/tex]

Step-by-step explanation:

The factorization of the trinomial is given by the multiplication of the greatest common factor of each coefficient(numeric, h and k), put it in front, and divide each term by it.

Numeric:

GCF between 5, 15 and 200.

We keep dividing while all factors can be divided by the same number

5 - 15 - 200|5

1 - 3 - 40

No other possible division, so the numeric GCF is 5.

Coefficient h

To the 2, to the 1, and does not appear(to the 0). So the GCF is 0.

Coefficient k

2, 3 and 4. The GCF is 2.

So

[tex]5k^2(\frac{5h^2k^2}{5k^2} - \frac{15hk^3}{5k^2} - \frac{200k^4}{5k^2}) = 5k^2(h^2 - 3hk - 40k^2)[/tex]

The factored form is: [tex]5k^2(h^2 - 3hk - 40k^2)[/tex]

What is the solution to x+1<9?

Answers

Answer:

x < 8

Step-by-step explanation:

x + 1 < 9

x < 9 - 1

x < 8

or

x ∈ 《-∞ , 8》

140% of what number is 39?
Provide an exact fraction answer.

Answers

Answer:

27.86 or 27 wholes 6/7

Step-by-step explanation:

Let the number be x

140% of x = 39

140x/100 = 39

140x = 3900

x= 3900/140

x = 27  wholes 6/7 or 27.86

The answer should be 23.4

75 points if answered corectly and brainlyist
A farm is to be built in the shape of quadrilateral ABCD, as shown below. All four sides are equal.

A rhombus ABCD is shown with diagonal AC equal to 16.8 feet and diagonal BD equal to 11.9 feet

What is the area of the farm?

57.4 square feet
99.96 square feet
114.8 square feet
133.28 square feet

Answers

Answer:

99.96 square feet

Step-by-step explanation:

The formula for the area of a rhombus is (pq)/2, where p and q represent the two diagonals:

A=pq/2

=(16.8)(11.9)/2

=199.92/2

=99.96 square feet

Answer:

99.96

Step-by-step explanation:

Adam wants to mix 10 cups of fertilizer from concentrate. He needs to mix one part of fertilizer concentrate with 4 parts of water. He wrote the system of equations to represent the amount fertilizer concentrate and water needed and then graphed the first line. y = one-fourth x. x + y = 10. A graph titled Fertilizer from Concentrate has cups of water needed on the x-axis and cups of concentrate needs on the y-axis. A line goes through (0, 0) and (4, 1). Graph the second line. What is the solution to the system? (0, 2.5) (4, 6) (5, 5) (8, 2)

Answers

Answer:

8,2

Step-by-step explanation:

Answer:

D.

Step-by-step explanation:

A train travels 250 miles (m) in 5 hours (h) . Calculate the average speed the train was traveling

Answers

Answer50 mph

Step-by-step explanation:

help please ill give brainlyest​

Answers

I would say b if I’m not wrong

Answer:

Step-by-step explanation:

(-1 - 4)/(-8 - 0) = -5/-8 = 5/8

hope this helps


Solve and show steps please please please I NEED HELP ASAP ILL MARK AS Brainlsit plsss

Answers

ANSWER : x>-2


Subtract one from both sides
-3x < 6
Divide both sides by negative 3
-3x/3 < 6/-3

Then you get the answer x>-2

Identify a , r, n, and S,
11-1
M=
63
0 24 = 4, r= 1, n= 6, Sn =
O =-4,r= , n= 6, S.-
-63
00
1
-31
• =-4, r= 5, n=5, 5,-
4
THE

Answers

The answer is B hope this helped

4. The car ride will be no more than 8 hours.

Answers

Answer:

This doesn't really make sense, could you post the whole question?

Can u help me find the E ?

Answers

I don’t think so bc I don’t like math

Steps to answerjamie just bought a box

Answers

Answer:

Steps:

Step-by-step explanation:

1: Jamie had the money

2: Jamie went to the store

3: Jamie picked out the box

4: Jamie bought the box

Hope this helped uwu

Find the lengths of the missing sides in the pairs of similar triangles

Answers

Answer:

x = 4

Step-by-step explanation:

The inner and outer triangles are similar, thus the ratios of corresponding sides are equal, that is

[tex]\frac{x}{5}[/tex] = [tex]\frac{8}{10}[/tex] ( cross- multiply )

10x = 40 ( divide both sides by 10 )

x = 4

2 divided by 9/10
(i know this is simple but I need help ASAP)

Answers

Answer:

2.22

Step-by-step explanation:

Answer:

the answer is 2.22

Step-by-step explanation:

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