Tell me basic arithmetic topics

Mathematics

2 answers:

AlexFokin [52]3 years ago

8 0

Step-by-step explanation:

whole numbers, place values etc.

Maurinko [17]3 years ago

6 0

Addition, subtraction, multiplication, division, factoring, fractions etc

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Algebra is hard <br><br>6-9y > 30-5y

igomit [66]

Answer:

y=6

Step-by-step explanation:

6-9y>30-5y,-9y+5y>30-6, -4y>24,-4y/-4so -will concel -and 4 will cancel 4>24/4=y=6

5 0

3 years ago

Differentiate <br> 1/√x^2-1

xz_007 [3.2K]

The function is $f(x)= \frac{1}{ \sqrt{ x^{2} -1}}$

write f again as $f(x)= (x^{2} -1)^{- \frac{1}{2} }$

(the power -1 takes the expression to the denominator, and the power 1/2 is square root)

writing rational expressions as power expressions, generally makes differentiation more practical.

In $f(x)= (x^{2} -1)^{- \frac{1}{2} }$ we notice 2 functions:

the outer function $u^{ -\frac{1}{2} }$ , where $u=x^{2} -1$ , and the inner, u itself , which is a function of x.

So we differentiate by using the chain rule:

$f'(x)= -\frac{1}{2}u^{- \frac{1}{2}-1 }*u'= -\frac{1}{2}u^{- \frac{3}{2} }*(2x)=- \frac{x}{ \sqrt{ u^{3} } } =- \frac{x}{ \sqrt{ (x^{2} -1)^{3} } }$

Answer: $- \frac{x}{ \sqrt{ (x^{2} -1)^{3} } }$

3 0

3 years ago

The amount of time that a 4th grader reads comic books in a week is normally distributed with a mean of 6 hours and a standard d

KATRIN_1 [288]

Answer:

0.9544 = 95.44% probability that the sample mean time for reading comic books per week is between 5 and 7 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 normally distributed samples 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.

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 $s = \frac{\sigma}{\sqrt{n}}$ .