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Assoli18 [71]
3 years ago
12

Write an absolute value inequality to represent each situation.

Mathematics
1 answer:
Minchanka [31]3 years ago
6 0

Answer:

║ x - 231 ║ ≤ 459

Step-by-step explanation:

Since we have 228 ft below sea level, this is x' = -228 ft. Also,  we have 690 ft above sea level, this is x" = 690 ft.

Since x is our elevation in feet, x ranges from -228 ≤ x ≤ 690.

To write an absolute value equation for x, we first take the average of the two values for the ranges to obtain the ideal value of x.

So, ideal value = [690 + (-228)]/2 = 462/2 = 231.

We also find the tolerance by taking the difference of both values and dividing by 2. So tolerance = [690 - (-228)]/2 =  [690 + 228)]/2 = 918/2 = 459.

Subtracting 231 from each value of the inequality we have

-228 - 231 ≤ x - 231 ≤ 690 - 231

-459 ≤ x - 231 ≤ 459

Since we have in magnitude the values on the left and right side of the inequality,

So ║ x - 231 ║ ≤ 459

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A rectangle flower bed is 9 feet wide and 12 feet long .what is the length of the diagonal?​
BigorU [14]

Answer:

15 feet

Step-by-step explanation:

The question talks about;

  • A rectangular flower bed whose dimensions are 12 ft by 9 ft

We are required to determine the length of the diagonal

To answer the question, we need to know the following;

  • All the angles in a rectangle are right angles
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  • The dimensions of the rectangle acts as the legs of right angled triangle.

Therefore;

Using Pythagoras theorem;

a² + b² = c²

Where, c is the hypotenuse (in this case the diagonal)

a and b are the shorter sides of the right-angled triangle

Therefore;

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c = √225

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5 0
3 years ago
A researcher claims that the average annual salary of part-time community college instructors is at least $45,000. To test this
Doss [256]

Answer:

See explanation

Step-by-step explanation:

Solution:-

- The researcher claims :

" the average annual salary of part-time community college instructors is at least $45,000 "

- We will extract the claim made by the researcher to be the Null hypothesis:

                     Null Hypothesis : μ ≥ $45,000

- Any statement otherwise, or point of rejection criteria will denote the Alternate hypothesis that disbands the claim that:

" the average annual salary of part-time community college instructors is less than $45,000 " :

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- This type of test with a sample size of n = 25 < 30 and population standard deviation is also not given hints the use t-test statistics and t-critical value reject the claim.

                     Lower tail - one sample - T-test.

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cluponka [151]

Answer:

There are infinity equivalent fractions to 3/9

Step-by-step explanation:

1 /3, 2 /6, 3/ 9, 4 /12, 5/ 15, 6 /18, 7/ 21, 8/ 24, 9 /27, 10/ 30, 11/ 33, 12/ 36, 13/ 39, 14 /42, 15 /45..........

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