What is the vertex and zeros of the function f(x)=x2−4x+3

What are the rational numbers of -12,0,35,4.85,√12,√36,19/6,-10/11,1.4949949994

klemol [59]

All of those numbers are rational, except the square root of 12.

6 0

3 years ago

a bag of potting soil costs $3 less than a flower pot. Ike paid $41 for 3 flower pots and 5 bags of soil. how much does one bag

Arada [10]

Cost of bag of soil = x-3 where x is the price of a flower pot
41=3x + 5(x-3)
41=3x + 5x -15
41=8x -15
41+15=8x
56=8x
56÷8=x
$7.00=x

5 0

3 years ago

A sample survey is designed to estimate the proportion of sports utility vehicles being driven in the state of California. A ran

mart [117]

Answer:

a) The 95% confidence interval would be given (0.070;0.121).

b) "increase the sample size n"

"decrease za/2 by decreasing the confidence"

Step-by-step explanation:

Notation and definitions

$X=48$ number of vehicles classified as sports utility.

$n=500$ random sample taken

$\hat p=\frac{48}{500}=0.096$ estimated proportion of vehicles classified as sports utility vehicles.

$p$ true population proportion of vehicles classified as sports utility vehicles.

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".

The population proportion have the following distribution

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

(a) Use a 95% confidence interval to estimate the proportion of sports utility vehicles in California. (Round your answers to three decimal places.)

The confidence interval would be given by this formula :

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

For the 95% confidence interval the value of $\alpha=1-0.5=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

And replacing into the confidence interval formula we got:

$0.096 - 1.96 \sqrt{\frac{0.096(1-0.096)}{500}}=0.070$

$0.096 + 1.96 \sqrt{\frac{0.096(1-0.096)}{500}}=0.121$

And the 95% confidence interval would be given (0.070;0.121).

We are confident (95%) that about 7.0% to 12.1% of vehicles in California are classified as sports utility .

(b) How can you estimate the proportion of sports utility vehicles in California with a higher degree of accuracy? (HINT: There are two answers. Select all that apply.)

For this case we just have two ways to increase the accuracy one is "increase the sample size n" since if we have a larger sample size the estimation would be more accurate. And the other possibility is "decrease za/2 by decreasing the confidence" because if we decrease the confidence level the interval would be narrower and accurate

7 0

3 years ago

What is the following product?<br> PLEASE HELP,I'M STRUGGLING SO MUCH!

Licemer1 [7]

(x√7 - 3√8 ) (x√7 - 3√8 )

To solve this question you must FOIL (First, Outside, Inside, Last) like so

First:

(x√7 - 3√8 ) (x√7 - 3√8 )

x√7 * x√7

For this you will multiply the numbers/variables on the out side together and separately multiply the values inside the square root together

(x*x)(√7*7)

x²√49

7x²

Outside:

(x√7 - 3√8 ) (x√7 - 3√8 )

x√7 * -3√8

(-3*x)(√7*8)

-3x√56

√56 can be further simplified to: 2√14

Now we have: -3x2√14 ---> -6x√14

Inside:

(x√7 - 3√8 ) (x√7 - 3√8 )

The process is the exact same as in the "outside"

x√7 * -3√8

(-3*x)(√7*8)

-3x√56

√56 can be further simplified to: 2√14

Now we have: -3x2√14 ---> -6x√14

Last:

(x√7 - 3√8 ) (x√7 - 3√8 )

-3√8 * -3√8

(-3*-3)(√8*√8)

9√64

9*8

72

Now combine all the products of the FOIL together like so...

7x² - 6x√14 - 6x√14 + 72

Combine like terms:

7x² - 6x√14 - 6x√14 + 72

^^^When you add together square roots the number inside the radical stays the same, and you combine the numbers/variables attached to the radical on the outside

You selected the correct answer:

7x² -12x√14 + 72

Hope this helped!

~Just a girl in love with Shawn Mendes

5 0

3 years ago

1. In order to get more female customers, a new clothing store offers free gourmet coffee and pastry to its customers. The avera

ioda

Answer:

No, the manager is not correct based on the 95% confidence interval.

Step-by-step explanation:

We are given that the average daily revenue over the past five-week period has been $1,080 with a standard deviation of $260, i.e.; X bar = $1080 and s = $260 and sample size, n = 35 .

The Pivotal quantity for 95% confidence interval is given by;

$\frac{Xbar - \mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, X bar = sample mean = $1080

s = sample standard deviation = $260

n = sample size = 35 {five-week}

So, 95% confidence interval for average daily revenue, $\mu$ is given by;

P(-2.032 < $t_3_4$ < 2.032) = 0.95

P(-2.032 < $\frac{Xbar - \mu}{\frac{s}{\sqrt{n} } }$ < 2.032) = 0.95

P(-2.032 * ${\frac{s}{\sqrt{n} }$ < ${Xbar - \mu}$ < 2.032 * ${\frac{s}{\sqrt{n} }$ ) = 0.95

P(X bar - 2.032 * ${\frac{s}{\sqrt{n} }$ < $\mu$ < X bar + 2.032 * ${\frac{s}{\sqrt{n} }$ ) = 0.95

95% confidence interval for $\mu$ = [ X bar - 2.032 * ${\frac{s}{\sqrt{n} }$ , X bar + 2.032 * ${\frac{s}{\sqrt{n} }$ ]

= [ 1080 - 2.032 * ${\frac{260}{\sqrt{35} }$ , 1080 + 2.032 * ${\frac{260}{\sqrt{35} }$ ]

= [ 990.70 , 1169.30 ]

<em>No, the manager is not correct based on the fact that the coffee and pastry strategy would lead to an average daily revenue of $1,200 because the calculate 95% confidence interval does not include value of $1200.</em>

Therefore, the store manager believe is not correct.

8 0

3 years ago