2x - 4 = 2(x - 2)<br> solve the following problem and identify the type of equation

Patrick wanted to gather data about the cost of joining a community pool in his area. He plotted the data and determined that th

ohaa [14]

Answer:

The y-intercept is 40. This is the cost of registration ⇒ last answer

Step-by-step explanation:

* Lets explain how to solve the problem

- Patrick wanted to gather data about the cost of joining a community

pool in his area

- He plotted the data and determined that the average community

pool membership cost consists of a one-time registration fee and

a monthly fee

∴ The cost consists of two parts:

# Part A: one-time registration fee, it is a fixed amount not depend on

any other condition

# Part B: monthly fee, it depends on the number of months

- He modeled that by the equation y = 15 x + 40, where

# y is the cost for the membership

# 15 is the monthly fee

# x is the number of months

# 40 is the one-time registration

- The form of the equation is y = mx + c, where c is the y-intercept

∴ The y-intercept in the equation y = 15 x + 40 is 40

∴ The y-intercept is the one-time registration fee

* The y-intercept is 40. This is the cost of registration

4 0

3 years ago

A maker of a certain brand of low-fat cereal barsclaims that the average saturated fat content is 0.5gram. In a random sample of

finlep [7]

Answer:

$t=\frac{0.475-0.5}{\frac{0.183}{\sqrt{8}}}=-0.386$

$p_v =2*P(t_{(7)}$

If we compare the p value and the significance level assumed $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the true mean is different from 0.5 at 5% of signficance. So then the claim makes sense

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

Solution to the problem

In order to calculate the mean and the sample deviation we can use the following formulas:

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$ (2)

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$ (3)

The mean calculated for this case is $\bar X=0.475$

The sample deviation calculated $s=0.183$

We need to conduct a hypothesis in order to check if the true mean is 0.5 or no, the system of hypothesis would be:

Null hypothesis: $\mu = 0.5$

Alternative hypothesis: $\mu \neq 0.5$

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{0.475-0.5}{\frac{0.183}{\sqrt{8}}}=-0.386$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=8-1=7$

Since is a two sided test the p value would be:

$p_v =2*P(t_{(7)}$

Conclusion

If we compare the p value and the significance level assumed $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the true mean is different from 0.5 at 5% of signficance. So then the claim makes sense

4 0

3 years ago

Read 2 more answers

100 POINTS 10 QUESTIONS PLEASE HELP PICTURES BELOW PLEASE SPECIFY WHICH QUESTION YOU ARE ANSWERING

Semenov [28]

Answer:

The answers are $\frac{2}{5}, \frac{1}{4}, \frac{1}{10}, \frac{5}{2}, \frac{5}{8}, \frac{4}{1}, \frac{8}{5},$ and $\frac{10}{1}$ .

Step-by-step explanation:

Proportions are fractions that can be made by using the given numbers, which in this case are 2, 5, 8, and 20. Let's pair each one with the other three and then simplify if possible.

First, let's begin with 2:

$\frac{2}{5} = \frac{2}{5}$

$\frac{2}{8} = \frac{1}{4}$

$\frac{2}{20} = \frac{1}{10}$

Then, let's do 5:

$\frac{5}{2} = \frac{5}{2}$

$\frac{5}{8} = \frac{5}{8}$

$\frac{5}{20} = \frac{1}{4}$

Note that we already have $\frac{1}{4}$ , so we do not need to include an additional one.

Now, let us do 8:

$\frac{8}{2} = \frac{4}{1}$

$\frac{8}{5} = \frac{8}{5}$

$\frac{8}{20} = \frac{2}{5}$

See how we already have $\frac{2}{5}$ , so we won't have to include that as well.

Finally, let's do 20:

$\frac{20}{2} = \frac{10}{1}$

$\frac{20}{5} = \frac{4}{1}$

$\frac{20}{8} = \frac{5}{2}$

Now see that we already have both $\frac{4}{1}$ and $\frac{5}{2}$ , so we won't have to include both of them, as they are both extras.

Hence, the answers are $\frac{2}{5}, \frac{1}{4}, \frac{1}{10}, \frac{5}{2}, \frac{5}{8}, \frac{4}{1}, \frac{8}{5},$ and $\frac{10}{1}$ .

<h2><u><em>PLEASE MARK AS BRAINLIEST!!!!!</em></u></h2>

8 0

3 years ago

Read 2 more answers

Determine whether f(x)=5x+1/x and g(x)= x/5x+1 are inverse functions. Explain how you know.

vladimir1956 [14]

A property of inverse functions is that if f(x) = a, g(a) = x

F(x) = (5x+1)/x
G(x) = x/(5x+1)

Plug in x = 3.
F(3) = 16/3
G(16/3) = 16/83. Since it doesn’t equal 3, it’s not an inverse function

4 0

4 years ago

Read 2 more answers

Bill found a pair of running shoes for $57. The regular price was $68.99. He also found a sweat suit that was originally $37.80.

mestny [16]

Answer: i believe bill saved $21.44

Step-by-step explanation: 68.99-57=11.99

37.80-25%=28.35

37.80-28.35=9.45

9.45+11.99=21.44

8 0

3 years ago

2x - 4 = 2(x - 2) solve the following problem and identify the type of equation