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zloy xaker [14]

3 years ago

15

Jodi has two bank accounts. Her parents started Account A for her. It currently has $100 in it, and Jodi deposits $20 into it ea

ch month. Jodi's grandparents started Account B for her. It ccurently has $300 in it, and her grandparents deposit $40 into it each month.
Account A is modeled by the function f(x)=20x+100
and Account B is modeled by the function g(x)=40x+300
, where x
represent the number of months from now.

Write a new function (f+g)(x)
that represents the total amount of money Jodi has in both accounts. Simplify your answer.

1 answer:

marin [14]3 years ago

4 0

Answer: $60x+400$

Step-by-step explanation:

Given

Account A can be modeled by $f(x)=20x+100$ and

Account B can be modeled by $g(x)=40x+300$

So, the function that represents the total amount of money Jodi has can be modeled by

$\Rightarrow (f+g)(x)=20x+100+40x+300\\\Rightarrow (f+g)(x)=60x+400$

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In a survey, the planning value for the population proportion is p* = 0.35. How large a sample should be taken to provide a 95%

lions [1.4K]

Answer:

$n=\frac{0.35(1-0.35)}{(\frac{0.05}{1.96})^2}=349.59$

And rounded up we have that n=350

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".

$p$ represent the real population proportion of interest

$\aht p$ represent the estimated proportion for the sample

n is the sample size required (variable of interest)

$z$ represent the critical value for the margin of error

Solution to the problem

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.05$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

And replacing into equation (b) the values from part a we got:

$n=\frac{0.35(1-0.35)}{(\frac{0.05}{1.96})^2}=349.59$

And rounded up we have that n=350

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3 years ago

Ming plays video games online. When he signed up with the game site, Ming got 200200 points. Ming earns 2020 more points for eac

larisa86 [58]

It will take 148 $\frac{67}{101}$ hours (In decimal form its 148.66336633)

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3 years ago

laiz [17]

Answer:

B) 0.02

Step-by-step explanation:

<u>Use the Binomial Theorem</u>

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We have the probability of success, $p=0.30$ , and the probability of failure, $q=1-0.30=0.70$ . The binomial coefficient, $\binom{n}{k}$ , represents the amount of possible combinations that $k$ items can be chosen out of $n$ items, with its respective formula $\frac{n!}{k!(n-k)!}$ .

Hence, the best choice for the probability that 4 students chosen at random from the class of 30 that want the next test to be on Monday will be option B, 0.02

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Vinvika [58]

Answer:

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Step-by-step explanation:

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