Find f(x) and g(x) so that the function can be described as y = f(g(x)).

Can any number be written in scientific notation

choli [55]

Yes, I'm relatively sure any number can be written in scientific notation.

5 0

2 years ago

The difference of two numbers is 16 the greater number is five less than four times a small number find the two numbers

Elis [28]

Answer:

The numbers are 23 and 7

Step-by-step explanation:

1. Set up the equations

Let x = the greater number

and y = the smaller number. Then

(1) x - y = 16

4y = 4 times the smaller number and

4y - 5 = 5 less than 4 times the smaller number. Then

(2) x = 4y - 5

You have a system of two equations:

$\begin{cases}(1) & x - y = 16\\(2) & x = 4y - 5\end{cases}$

2. Solve the equations

$\begin{array}{lrcll}(3) & 4y - 5 - y & = & 16 &\text{Substituted (2) into (1)}\\& 3y - 5 & = & 16 &\text{Simplified}\\ & 3y & = & 21 &\text{Added 5 to each side}\\(4) &y & = & \mathbf{7} &\text{Divided each side by 3} \\& x - 7 & = & 16 & \text{Substituted (4) into (1)}\\& x& = & \mathbf{23} & \text{Added 7 to each side}\\\end{array}$

The larger number is 23; the smaller number is 7.

3. Check

$\begin{array}{rclcrcl}23 - 7& = & 16 & \qquad &23&=&4(7) - 5\\16 & = & 16 & \qquad &23& = &28 - 5\\&&& \qquad &23& = &23\\\end{array}$

OK.

3 0

2 years ago

Use the given information to find the p-value. Also, use a 0.05 significance level and state the conclusion about the null hyp

Hatshy [7]

Answer:

We can assume that the statistic is $z_{calc}=0.78$

$p_v = 2* P(z>0.78) = 0.435$

So the p value obtained was a very high value and using the significance level given $\alpha=0.05$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the true proportion of interest is not different from 3/5

Step-by-step explanation:

Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the true proportion is equal to 3/5 or not.:

Null hypothesis: $p=3/5$

Alternative hypothesis: $p \neq 3/5$

When we conduct a proportion test we need to use the z statistic, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

Calculate the statistic

We can assume that the statistic is $z_{calc}=0.78$

Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided $\alpha=0.05$ . The next step would be calculate the p value for this test.

Since is a bilateral test the p value would be:

$p_v = 2* P(z>0.78) = 0.435$

So the p value obtained was a very high value and using the significance level given $\alpha=0.05$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the true proportion of interest is not different from 3/5

7 0

2 years ago

Which two activities are examples of data collecting?

Ganezh [65]

Hello!

The 2 activities which represent data collecting are :