All categories

3 years ago

Given that x < 5, rewrite 5x - |x - 5| without using absolute value signs.

Mathematics

2 answers:

arsen [322]3 years ago

8 0

For $x$ , $x-5$ , therefore $|x-5|=-(x-5)=-x+5$

So, for $x$ , $5x-|x-5|=5x-(-x+5)=5x+x-5=6x-5$

andriy [413]3 years ago

5 0

So, if we have an arbitrary number under the absolute value, say y, we have |y| to be:

$y0 \implies |y| =y$

Which in plain english means "If y is less than 0, then the absolute value of y is the negation of y, and if y is greater than 0 then the absolute value of y is y."

So, in our above absolute value expression we would have:

$x-5 < 0 \implies |x-5| = -(x-5) \\ x-5>0 \implies |x-5| = x-5$

Since we are given x<5, we know that the absolute value actually negates what's encompassed by it so we have:

$5x-(-(x-5))=\\ 5x-(-x+5)= 5x+x-5= 6x-5$

So our expression without the absolute value signs is simply 6x-5.

You might be interested in

Simplify (3w^2-7w+6)+(-5w^2+2w+1)

leva [86]

Answer:

-2w^2 - 5w + 7

Step-by-step explanation:

Just the values with the same powers of w

(3w^2-5w^2)+(-7w+2w)+(6+1)

-2w^2 - 5w + 7

5 0

2 years ago

What is the missing numbers in this sequence: , 7, 5, 3, , -1

matrenka [14]

Answer:

1 is the missing number.

Step-by-step explanation:

5 0

3 years ago

Assume that P(E) = 0.471 and P(F) = 0.595. If E and F are independent, find P(E and F)

dsp73

The value of the probability P(E and F) is 0.2802

<h3>Independent probability</h3>

Events are known to be independent if the occurrence of one does not affect the other.

Given the following parameters

P (E) =0.471

P(F) = 0.595

If E and F are independent, then;

P(E and F) = P(E)P(F)

P(E and F) = 0.471 * 0.595
P(E and F) = 0.2802

Hence the value of the probability P(E and F) is 0.2802

Learn more on independent events here: brainly.com/question/1374659

#SPJ1

8 0

2 years ago

What is the reciprocal of 4.5? And after I get the reciprocal how did they get 2 over 9 for the answer?

djverab [1.8K]

So 4.5 is equal to 4 and 1/2
u can convert that to 9/2
then to get the reciprocal you flip the denominator and numerator
this gives u 2/9

3 0

3 years ago

The Office of Student Services at a large western state university maintains information on the study habits of its full-time st

Vera_Pavlovna [14]

Answer:

0.8254 = 82.54% probability that the mean of this sample is between 19.25 hours and 21.0 hours

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .