How is scientific notation used in the real world?

How to factor this problem with negative exponents? -4x^-4-3x^-2+1=0

Nat2105 [25]

$-4x^{-4}-3x^{-2}+1=0\\
-4x^{-4}-4x^{-2}+x^{-2}+1=0\\
-4x^{-2}(x^{-2}+1)+1(x^{-2}+1)=0\\
-(4x^{-2}-1)(x^{-2}+1)=0\\
4x^{-2}-1 =0 \vee x^{-2}+1=0\\
4x^{-2} =1 \vee x^{-2}=-1\\
x^{-2}=\frac{1}{4} \vee \frac{1}{x^2}=-1\\
\frac{1}{x^2}=\frac{1}{4}\\
x=-2 \vee x=2
$

7 0

3 years ago

As part of a study on pulse rates, a random sample of 10 study participants had their pulse rate taken and asked to sit quietly

Ivahew [28]

Answer:

$t = \frac{-1.2-0}{\frac{2.97}{\sqrt{10}}}= -1.278$

The degrees of freedom are :

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

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

Since the p value is a very high value is higher than the typical values for the significance level (0.05,0.1) so then we have enough evidence to FAIL to reject the null hypothesis and there is no enough evidence to conclude that the true difference in the means is different from 0. And the best conclusion would be:

d. There is not enough evidence to conclude the mean difference in pulse rates before and after the 5 minute waiting period is different from 0.

Step-by-step explanation:

We are interested to check if the true difference in pulse rates before and after after 5 minute waiting period is 0 or no so then the system of hypothesis are:

Null hypothesis: $\mu_d =0$

Alternative hypothesis: $\mu_d \neq 0$

We have the following data given:

$\bar X_d = -1.2$ sample mean for the difference

$n =10$ the sample size

$s_d = 2.97$ sample standard deviation

The statistic is given by:

$t= \frac{\bar X -\mu}{\frac{s}{\sqrt{n}}}$

And replacing we got:

$t = \frac{-1.2-0}{\frac{2.97}{\sqrt{10}}}= -1.278$

The degrees of freedom are :

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

Since we are conducting a bilateral test te p value would be given by:

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

Since the p value is a very high value is higher than the typical values for the significance level (0.05,0.1) so then we have enough evidence to FAIL to reject the null hypothesis and there is no enough evidence to conclude that the true difference in the means is different from 0. And the best conclusion would be:

d. There is not enough evidence to conclude the mean difference in pulse rates before and after the 5 minute waiting period is different from 0.

7 0

4 years ago

Judith has already taken 93 quizzes during past quarters, and she expects to have 5 quizzes

lara [203]

Answer:

103

Step-by-step explanation:

93 + 5 + 5 = 103

6 0

3 years ago

I think of a number, double it and the result is 15

melisa1 [442]

The number in question is 7.5

Step-by-step explanation:

15 ÷ 2 = 7.5

Why divide by 2? Because dividing by 2 is the <u>inverse</u> of multiplying by 2. To double-check our solution, just multiply 7.5 by 2... and 15!!

8 0

3 years ago

00:00

Furkat [3]

Answer:

-2

Step-by-step explanation:

Subtracting a negative number is the same as adding it, so this is basically just negative 8 plus 6, which is -2. Don't know who was right though, you kinda left that part of the question out.

5 0

4 years ago