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Naddika [18.5K]
4 years ago
7

(08.06)

Mathematics
1 answer:
Greeley [361]4 years ago
6 0

Answer:

(x-7)(x+7)

Step-by-step explanation:

x^2 -49

This is the difference of squares

x^2 -7^2

We know that a^2 -b^2 = (a-b)(a+b)

(x-7)(x+7)

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Amy was scheduled for 12 intervals this week. One her first interval, she had a technical issue that prevented her from working
ad-work [718]

Based on the total of intervals vs the number of intervals Amy attended her CA percentage is 75%

<h3>What is the CA percentage?</h3>

The CA percentage measures the commitment of an employee to be logged in during the intervals that were assigned to him/her to work.

In this way, the CA percentage is equal to 100% if the employee worked as scheduled. Moreover, this percentage can be affected by factors such as:

  • Technical issues.
  • Human errors.

In the case of Amy, there is a total of 12 intervals and it is known:

  • She had a technical issue that prevented her from working, but this was reported so it is unlikely this is considered in her CA.
  • She missed three intervals because she looked at her schedule wrong.

Based on this information, let's calculate her CA:

  • 12 intervals = 100%
  • 9 intervals =  x

  • x = 9 x 100 / 12
  • x = 900 / 12
  • x = 75%

Learn more about percentage in: brainly.com/question/8011401

6 0
3 years ago
Farmer George is painting 3 chicken coops. He started painting this morning. Now he only has 3/4 of a chicken coop left to paint
mariarad [96]
If Farmer George starts painting in the morning, and only has 3/4 of a chicken coop left to paint:
3-3/4=
12/4-3/4=9/4 painting in the morning
To put it in a mixed number,  2 1/4 (aka 2.25)
3 0
3 years ago
Read 2 more answers
John's mother is three less than four times John's age. Their combined age is 37. What is John's age?
Komok [63]
I think the answer is 8
6 0
3 years ago
For waht values of x do the vectors -1,0,-1), (2,1,2), (1,1, x) form a basis for R3?
DaniilM [7]
<h2>Answer:</h2>

The values of x for which the given vectors are basis for R³ is:

                        x\neq 1

<h2>Step-by-step explanation:</h2>

We know that for a set of vectors are linearly independent if the matrix formed by these set of vectors is non-singular i.e. the determinant of the matrix formed by these vectors is non-zero.

We are given three vectors as:

(-1,0,-1), (2,1,2), (1,1, x)

The matrix formed by these vectors is:

\left[\begin{array}{ccc}-1&2&1\\0&1&1\\-1&2&x\end{array}\right]

Now, the determinant of this matrix is:

\begin{vmatrix}-1 &2 & 1\\ 0& 1 & 1\\ -1 & 2 & x\end{vmatrix}=-1(x-2)-2(1)+1\\\\\\\begin{vmatrix}-1 &2 & 1\\ 0& 1 & 1\\ -1 & 2 & x\end{vmatrix}=-x+2-2+1\\\\\\\begin{vmatrix}-1 &2 & 1\\ 0& 1 & 1\\ -1 & 2 & x\end{vmatrix}=-x+1

Hence,

-x+1\neq 0\\\\\\i.e.\\\\\\x\neq 1

4 0
3 years ago
The distribution of lifetimes of a particular brand of car tires has a mean of 51,200 miles and a standard deviation of 8,200 mi
Orlov [11]

Answer:

a) 0.277 = 27.7% probability that a randomly selected tyre lasts between 55,000 and 65,000 miles.

b) 0.348 = 34.8% probability that a randomly selected tyre lasts less than 48,000 miles.

c) 0.892 = 89.2% probability that a randomly selected tyre lasts at least 41,000 miles.

d) 0.778 = 77.8% probability that a randomly selected tyre has a lifetime that is within 10,000 miles of the mean

Step-by-step explanation:

Problems of normally distributed distributions 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 question, we have that:

\mu = 51200, \sigma = 8200

Probabilities:

A) Between 55,000 and 65,000 miles

This is the pvalue of Z when X = 65000 subtracted by the pvalue of Z when X = 55000. So

X = 65000

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

Z = \frac{65000 - 51200}{8200}

Z = 1.68

Z = 1.68 has a pvalue of 0.954

X = 55000

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

Z = \frac{55000 - 51200}{8200}

Z = 0.46

Z = 0.46 has a pvalue of 0.677

0.954 - 0.677 = 0.277

0.277 = 27.7% probability that a randomly selected tyre lasts between 55,000 and 65,000 miles.

B) Less than 48,000 miles

This is the pvalue of Z when X = 48000. So

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

Z = \frac{48000 - 51200}{8200}

Z = -0.39

Z = -0.39 has a pvalue of 0.348

0.348 = 34.8% probability that a randomly selected tyre lasts less than 48,000 miles.

C) At least 41,000 miles

This is 1 subtracted by the pvalue of Z when X = 41,000. So

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

Z = \frac{41000 - 51200}{8200}

Z = -1.24

Z = -1.24 has a pvalue of 0.108

1 - 0.108 = 0.892

0.892 = 89.2% probability that a randomly selected tyre lasts at least 41,000 miles.

D) A lifetime that is within 10,000 miles of the mean

This is the pvalue of Z when X = 51200 + 10000 = 61200 subtracted by the pvalue of Z when X = 51200 - 10000 = 412000. So

X = 61200

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

Z = \frac{61200 - 51200}{8200}

Z = 1.22

Z = 1.22 has a pvalue of 0.889

X = 41200

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

Z = \frac{41200 - 51200}{8200}

Z = -1.22

Z = -1.22 has a pvalue of 0.111

0.889 - 0.111 = 0.778

0.778 = 77.8% probability that a randomly selected tyre has a lifetime that is within 10,000 miles of the mean

4 0
3 years ago
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