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Viktor [21]
3 years ago
12

How do you Rewrite f(x) = −(x + 3)2 − 1 from vertex form to standard form?

Mathematics
1 answer:
wel3 years ago
5 0
Expand it

-(x+3)^2-1
-(x+3)(x+3)-1
-1(x^2+3x+3x+9)-1
-1(x^2+6x+9)-1
-x^2-9x-9-1
-x^2-9x-10

f(x)=-x^2-9x-10
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Suppose that a jewelry store tracked the amount of emeralds they sold each week to more accurately estimate how many emeralds to
RUDIKE [14]

Answer:

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

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)

And for this case the 95% confidence interval is given by (2.13; 2.37)

We have a point of estimate for the sample mean with this formula:

\bar X = \frac{Upper+ Lower}{2}= \frac{3.37+2.13}{2}= 2.75

And for the margin of error we have the following estimation:

ME= \frac{Upper -Lower}{2}= \frac{3.37-2.13}{2}= 0.62

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)

s represent the sample standard deviation

n represent the sample size  

Solution to the problem

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

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)

And for this case the 95% confidence interval is given by (2.13; 2.37)

We have a point of estimate for the sample mean with this formula:

\bar X = \frac{Upper+ Lower}{2}= \frac{3.37+2.13}{2}= 2.75

And for the margin of error we have the following estimation:

ME= \frac{Upper -Lower}{2}= \frac{3.37-2.13}{2}= 0.62

5 0
3 years ago
The mean throwing distance of a football for a Marco, a high school freshman quarterback, is 40 yards, with a standard deviation
Phoenix [80]

Answer:

a) One-tailed t-test about a mean.

b) The null hypothesis would be that there is no significant evidence to conclude that the adjusted grip leads to more distance on the thrown ball.

While the alternative hypothesis is that there is significant evidence to conclude that the adjusted grip leads to more distance on the thrown ball.

Mathematically,

The null hypothesis is represented as

H₀: μ ≤ 40 yards

The alternative hypothesis is given as

Hₐ: μ > 40 yards

c) p-value = 0.00621

d) The graph is presented in the attached image. The p-value obtained is less than the significance level at which the test was performed, hence, we accept the alternative hypothesis and say that there is significant evidence to conclude that the adjusted grip leads to more distance on the thrown ball.

Step-by-step explanation:

a) This test checks if the adjusted grip leads to more distance than before on the ball throws.

So, it is a one tailed test (testing only in one direction), a t-test about a mean.

b) For hypothesis testing, the first thing to define is the null and alternative hypothesis.

The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.

While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.

Since this question aims to test if adjusting the grip leads to more distance on the ball thrown.

The null hypothesis would be that there is no significant evidence to conclude that the adjusted grip leads to more distance on the thrown ball. That is, The adjusted grip leads to a distance lesser than or equal to the previous distance on the thrown ball.

While the alternative hypothesis is that there is significant evidence to conclude that the adjusted grip leads to more distance on the thrown ball.

Mathematically,

The null hypothesis is represented as

H₀: μ ≤ 40 yards

The alternative hypothesis is given as

Hₐ: μ > 40 yards

c) To do this test, we will use the z-distribution because there is information on the population standard deviation.

So, we compute the test statistic

z = (x - μ₀)/σ

x = 45 yards

μ₀ = 40 yards

σ = standard deviation = 2 yards

z = (45 - 40)/2 = 2.50

The p-value for a one-tailed test for z-test statistic of 2.50 is 0.00621

d) The sketch of the graph is presented in the attached image.

The interpretation of p-values is that

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

So, for this question, significance level = 0.05

p-value = 0.00621

0.00621 < 0.05

Hence,

p-value < significance level

This means that we reject the null hypothesis & accept the alternative hypothesis and say that there is enough evidence to conclude that the adjusted grip leads to more distance on the thrown ball.

Hope this Helps!!!

5 0
3 years ago
X2 – 11x + 5 = -2x<br> Solve equation to the nearest tenth
Nataly [62]

Answer:

x = 5/7 -> 0.714285 which to the nearest tenth would be 0.7

Step-by-step explanation:

is it x*2 or x^2?

If it were x to the power of two, then the answer would be about x1 = 0.594875 and x2 = 8.40512

7 0
3 years ago
Please answer quickly. 50 points.<br> Answer 1. and 4. on statements and all of the reasons.
Keith_Richards [23]
1. Is angle 2 and angle 5 are supplementary and the reason is the given
4. The answer is L || M because of the converse of the CIA theorem( corresponding interior angles)

6 0
3 years ago
Work out the area of a circle with radius of 7.5cm
lidiya [134]

Answer:

Area of circle is equal A = πr²

Here r =  7.5 and π = 3.142

so,

A = 3.142(7.5)²

A = 176.17 after rounding off.

3 0
2 years ago
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