All categories

2 years ago

Please answer this question with steps

Mathematics

2 answers:

FromTheMoon [43]2 years ago

6 0

Answer:

Step-by-step explanation:

$\sf \dfrac{1}{3}a^3-\dfrac{3}{4}a^2-\dfrac{5}{2}-\left[\dfrac{5}{2}a^2+\dfrac{3}{2}a^3+\dfrac{a}{3}-\dfrac{6}{5}\right]=$

$\sf = \dfrac{1}{3}a^3-\dfrac{3}{4}a^2-\dfrac{5}{2}-\dfrac{5}{2}a^2-\dfrac{3}{2}a^3-\dfrac{a}{3}+\dfrac{6}{5}\\\\\\( Combine \ like \ terms)\\\\= \dfrac{1}{3}a^3 -\dfrac{3}{2}a^3 -\dfrac{3}{4}a^2-\dfrac{5}{2}a^2-\dfrac{a}{3}-\dfrac{5}{2}+\dfrac{6}{5}\\\\=\left[\dfrac{1*2}{3*2}-\dfrac{3*3}{2*3}\right]a^3 + \left[-\dfrac{3}{4}-\dfrac{5*2}{2*2}\right]a^2-\dfrac{a}{3}+\left[-\dfrac{5*5}{2*5}+\dfrac{6*2}{5*2}\right]\\\\\\$

$\sf ==\left[\dfrac{2}{6}-\dfrac{9}{6}\right]a^3+\left[-\dfrac{3}{4}-\dfrac{10}{4}\right]a^2-\dfrac{a}{3}+\left[-\dfrac{25}{10}+\dfrac{12}{10}\right]\\\\=\dfrac{2-9}{6}a^3+\dfrac{(-3-10)}{4}a^2-\dfrac{a}{3}+\dfrac{(-25+12)}{15}\\\\$

$\sf = \dfrac{-7}{6}a^3+ \dfrac{(-13)}{4}a^2-\dfrac{a}{3}+\dfrac{(-13)}{15}\\\\=-\dfrac{7}{6}a^3-\dfrac{13}{4}a^2-\dfrac{a}{3}-\dfrac{13}{15}$

kobusy [5.1K]2 years ago

6 0

Answer:

see explanation

Step-by-step explanation:

$\frac{1}{3}$ a³ - $\frac{3}{4}$ a² - $\frac{5}{2}$ - ( $\frac{5}{2}$ a² + $\frac{3}{2}$ a³ + $\frac{a}{3}$ - $\frac{6}{5}$ ) ← distribute parenthesis by - 1

= $\frac{1}{3}$ a³ - $\frac{3}{4}$ a² - $\frac{5}{2}$ - $\frac{5}{2}$ a² - $\frac{3}{2}$ a³ - $\frac{a}{3}$ + $\frac{6}{5}$ ← collect like terms

= ( $\frac{1}{3}$ a³ - $\frac{3}{2}$ a³ ) + (- $\frac{3}{4}$ a² - $\frac{5}{2}$ a² ) - $\frac{a}{3}$ + (- $\frac{5}{2}$ + $\frac{6}{5}$ ) ← change to common denominators

= ( $\frac{2}{6}$ a³ - $\frac{9}{6}$ a³ ) + (- $\frac{3}{4}$ a² - $\frac{10}{4}$ a² ) - $\frac{a}{3}$ + (- $\frac{25}{10}$ + $\frac{12}{10}$ ) ← simplify

= - $\frac{7}{6}$ a³ - $\frac{13}{4}$ a² - $\frac{1}{3}$ a - $\frac{13}{10}$

You might be interested in

The following are the average weekly losses of worker-hours due to accidents in 10 industrial plants before and after a certain

soldier1979 [14.2K]

Answer:

$t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{-5.2 -0}{\frac{4.077}{\sqrt{10}}}=-4.0332$

The next step is calculate the degrees of freedom given by:

$df=n-1=10-1=9$

Now we can calculate the p value, since we have a two tailed test the p value is given by:

$p_v =2*P(t_{(9)}$

The p value is lower than the significance level given $\alpha=0.05$ , so then we can conclude that we can reject the null hypothesis that no difference between the two measures. So there is a significant difference between the measurements before and after

The null hypothesis must be rejected at level alpha = 0.05. We conclude that the industrial safety program is effective. The evidence is strong since a computer calculation gives the P value .9985. Enter 0 if this statement is FALSE or 1 otherwise

This STATEMENT is FALSE (1) since the p value is 0.0030 and not 0.9985

Step-by-step explanation:

Previous concepts

We assume that the paired sample data are simple random samples and that the differences have a distribution that is approximately normal. So for this case is better apply a paired t test.

A paired t-test is used to compare two population means where you have two samples in which observations in one sample can be paired with observations in the other sample. For example if we have Before-and-after observations (This problem) we can use it.

Solution to the problem

Let put some notation

x=test value before , y = test value after

x: 45,73,46,124,33,57,83,34,26,17

y: 36,60,44,119,35,51,77,29,24,11

The system of hypothesis for this case are:

Null hypothesis: $\mu_y- \mu_x = 0$