All categories

3 years ago

Find the value of x for which the graph of y = 3x^2 - 8x + 7 achieves its minimum y-value.

Mathematics

1 answer:

gulaghasi [49]3 years ago

7 0

Answer:

<h3>The y value achieves its minimum at x = 4/3</h3>

Step-by-step explanation:

Given the graph of y to be 3x² - 8x + 7, to get the value of x for which the graph function achieves its minimum y value, we need to find its turning point first.

At the turning point, dy/dx = 0

Given y = 3x² - 8x + 7

$\frac{dy}{dx} = 6x-8\\ at\ turning\ point\ 6x-8 = 0$

$6x = 8\\x = \frac{8}{6}\\ x =\frac{4}{3}$

The y value achieves its minimum at x = 4/3

You might be interested in

50 POINTS!

Hoochie [10]

Answer:

Solution given:

AB=3units

<B=45°

<C=63°

DF=3units

<E=63°

<F=45°

for congruence opposite corresponding angle or side should be equal

∆ABCis congruent to ∆DFE by A.A.S axiom

Similarly

its another name also be

∆BAC=~ ∆FDE

you got it.third one.

7 0

3 years ago

Read 2 more answers

An astronaut inside a spacesuit weighs 300 pounds on Earth. How many pounds does she weigh on the Moon

Alina [70]

She would weigh 48.98
Give Brainly if this helped you

8 0

2 years ago

Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round y

tino4ka555 [31]

Answer:

0.8762 or 87.62%

Step-by-step explanation:

Since our mean is μ=14.3 and our standard deviation is σ=3.7. If we're trying to figure out what percentage is P(10 ≤ x ≤ 26) equal to we must first calculate our z values as such:

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

Our x value ranges from 10 to 26 therefore let x=10 and we obtain:

$z=\frac{10-14.3}{3.7} =-1.16\\$

If we look at our z-table we find that the probability associated with a z value of -1.16 is 0.1230 meaning 12.30%.

Now let's calculate the z value when x = 26 and so:

$z=\frac{26-14.3}{3.7}=3.16\\$

Similarly, we use the z-table again and find that the probability associated with a z value of 3.16 is 0.9992 meaning 99.92%.

Now we want to find the probability in between 10 and 26 so we will now subtract the upper limit minus the lower limit in P(10 ≤ x ≤ 26) therefore:

0.9992 - 0.1230 = 0.8762

or 87.62%

7 0

3 years ago

In a random sample of 80 teenagers, the average number of texts handled in a day is 50. The 96% confidence interval for the mean

Nastasia [14]

Answer:

a) $\bar X =\frac{46+54}{2}=50$

And the margin of error is given by:

$ME= \frac{54-46}{2}= 4$

The confidence level is 0.96 and the significance level is $\alpha=1-0.96=0.04$ and the value of $\alpha/2 =0.02$ and the margin of error is given by:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

We can calculate the critical value and we got:

$z_{\alpha/2} = 2.05$

And if we solve for the deviation like this:

$\sigma = ME * \frac{\sqrt{n}}{z_{\alpha/2}}$

And replacing we got:

$\sigma =4 *\frac{\sqrt{80}}{2.05} =17.45$

b) $ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}=2.05 *\frac{17.45}{\sqrt{160}}=2.828$

And as we can see that the margin of error would be lower than the original value of 4, the margin of error would be reduced by a factor $\sqrt{2}$

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

$\mu$ population mean (variable of interest)

$\sigma$ represent the population standard deviation

n=80 represent the sample size

Solution to the problem

Part a

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

For this case we can calculate the mean like this:

$\bar X =\frac{46+54}{2}=50$

And the margin of error is given by:

$ME= \frac{54-46}{2}= 4$

The confidence level is 0.96 and the significance level is $\alpha=1-0.96=0.04$ and the value of $\alpha/2 =0.02$ and the margin of error is given by:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

We can calculate the critical value and we got:

$z_{\alpha/2} = 2.05$

And if we solve for the deviation like this:

$\sigma = ME * \frac{\sqrt{n}}{z_{\alpha/2}}$

And replacing we got:

$\sigma =4 *\frac{\sqrt{80}}{2.05} =17.45$

Part b

For this case is the sample size is doubled the margin of error would be:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}=2.05 *\frac{17.45}{\sqrt{160}}=2.828$

And as we can see that the margin of error would be lower than the original value of 4, the margin of error would be reduced by a factor $\sqrt{2}$

5 0

3 years ago

Miya went to the bowling alley. There was a $5 shoe rental fee plus $15.0 per game. Which equation models the situation where g

Aloiza [94]

Answer:

$15g + $5 = c

7 0

2 years ago

Find the value of x for which the graph of y = 3x^2 - 8x + 7 achieves its minimum y-value.​

Find the value of x for which the graph of y = 3x^2 - 8x + 7 achieves its minimum y-value.