Write y=2x^2+8x+11 in vertex form

Suppose the life of a particular brand of calculator battery is approximately normally distributed with a mean of 75 hours and a

shepuryov [24]

Answer:

a) $P(X$

And we can find this probability using the normal standard table or excel:

$P(z$

b) $P(X>77)=P(\frac{X-\mu}{\sigma}>\frac{77-\mu}{\sigma})=P(Z>\frac{77-75}{10})=P(z>0.2)$

And we can find this probability using the complement rule and the normal standard table or excel:

$P(z>0.2)=1-P(Z$

c) $z = \frac{70-75}{\frac{10}{\sqrt{16}}}= -2$

$z = \frac{80-75}{\frac{10}{\sqrt{16}}}= 2$

And we can find this probability with this difference:

$P(-2$

Step-by-step explanation:

Previous concepts

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 Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the life of a particular brand of a population, and for this case we know the distribution for X is given by:

$X \sim N(75,10)$

Where $\mu=75$ and $\sigma=10$

Part a

We are interested on this probability

$P(X$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(X$

And we can find this probability using the normal standard table or excel:

$P(z$

Part b

$P(X>77)=P(\frac{X-\mu}{\sigma}>\frac{77-\mu}{\sigma})=P(Z>\frac{77-75}{10})=P(z>0.2)$

And we can find this probability using the complement rule and the normal standard table or excel:

$P(z>0.2)=1-P(Z$

Part c

For this case we select a sample size of n =16. and we want this probability:

$P(70 < \bar X$

We know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

And we can find the z scores for the limits like this:

$z = \frac{70-75}{\frac{10}{\sqrt{16}}}= -2$

$z = \frac{80-75}{\frac{10}{\sqrt{16}}}= 2$

And we can find this probability with this difference:

$P(-2$

6 0

4 years ago

If 1 = 35°, then 4 =

vodomira [7]

Answer:

140 degrees

Step-by-step explanation:

im basing it off of the fact that 1 is equal to 35 and so 4 must be 4 times 35 degrees

6 0

4 years ago

Read 2 more answers

[(y+4)/(y+7)]+1=(y+3)/(y+1)

Sunny_sXe [5.5K]

<span>First note that y cannot equal -7 or -1 as division by zero is undefined. So that if it comes up in our solution we know that it is not a real solution.

[(y+4)/(y+7)]+1=(y+3)/(y+1) make the left side have a common denominator

(y+4+y+7)/(y+7)=(y+3)/(y+1) combine like terms on left side

(2y+11)/(y+7)=(y+3)/(y+1) cross multiply

(2y+11)(y+1)=(y+3)(y+7) expand

2y^2+13y+11=y^2+10y+21 subtract y^2 from both sides

y^2+13y+11=10y+21 subtract 10y from both sides

y^2+3y+11=21 subtract 21 from both sides

y^2+3y-10=0 expand so factoring is easier

y^2-2y+5y-10=0 factor

y(y-2)+5(y-2)=0 which is equal to

(y+5)(y-2)=0

y=-5 or 2</span>

6 0

3 years ago

Can someone help me?

frutty [35]

To multiply a fraction with another fraction, we multiply the numerators the denominators:

(5/2) x (2/3) = (5 x 2) / (6 x 3) = 10/18 = 5/9

8 0

3 years ago

After plotting the data where x represents the length of the side of a polygon, and f(x) represents the area of the polygon, Jac

garri49 [273]

Answer:

C. 19

Step-by-step explanation:

$f(x) = x {}^{2} + 3x + 1 \\ f(3) = 3 {}^{2} + 3(3) + 1 \\ = 19$

7 0

3 years ago