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3 years ago

Name 21 and 22 another way.

Mathematics

1 answer:

galben [10]3 years ago

6 0

Answer:

Step-by-step explanation:

You might be interested in

What is the inverse of this function? f(x)=x−7

viva [34]

Answer:

Step-by-step explanation:

Replace f(x) with y. y = x − 7

Interchange the variables. x = y − 7

Solve for y. y = x + 7

Solve for y and replace with f^−1 (x). f^−1(x) = x + 7

I hope this helps have a great day :)

4 0

2 years ago

Aidan drives to school and back each day. The school is 16 miles from his home. He averages 40 miles per hour on his way to scho

yarga [219]

Answer:

26 2/3 mph

Step-by-step explanation:

time = distance/speed

speed = distance/time

Use the first of these relations to find Aidan's time getting to school:

time = 16 mi/(40 mi/h) = 16/40 h = 0.4 h

Then the time Aidan takes to get home is 0.6 hours, and his average speed for that trip home is ...

speed = 16 mi/(0.6 h) = 26 2/3 mi/h

4 0

3 years ago

Read 2 more answers

Consider the computer output below. Fill in the missing information. Round your answers to two decimal places (e.g. 98.76). Test

slamgirl [31]

Answer:

$SE_{Mean}=\frac{s}{\sqrt{n}}=\frac{4.77}{\sqrt{19}}=1.094$

$t=\frac{98.77-100}{\frac{4.77}{\sqrt{19}}}=-1.124$

The 95% confidence interval would be given by (96.625;100.915)

a) $df=n-1= 19-1= 18$

b) $p_v =2*P(t_{18}$

If we compare the p value and a significance level for example $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis.

c) The only thing that changes is the p value and would be given by:

$p_v =P(t_{18}>-1.124)=0.862$

But again since the p value is higher than the significance level we fail to reject the null hypothesis.

Step-by-step explanation:

Previous concepts and data given

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 central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

$\bar X=98.77$ represent the sample mean

$s=4.77$ represent the sample standard deviation

n=19 represent the sample selected

$\alpha$ significance level

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if we have significant difference on the mean of 100, the system of hypothesis would be:

Null hypothesis: $\mu = 100$

Alternative hypothesis: $\mu \neq 100$

From the central limit theorem 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 calculate the Standard error for the mean like this:

$SE_{Mean}=\frac{s}{\sqrt{n}}=\frac{4.77}{\sqrt{19}}=1.094$

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

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

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $z_{\alpha/2}=1.96$

Now we have everything in order to replace into formula (1):

$98.77-1.96\frac{4.77}{\sqrt{19}}=96.625$

$98.77+1.96\frac{4.77}{\sqrt{19}}=100.915$

So on this case the 95% confidence interval would be given by (96.625;100.915)

Part a

The degree of freedom are given by:

$df=n-1= 19-1= 18$

Part b

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

We can replace in formula (1) the info given like this:

$t=\frac{98.77-100}{\frac{4.77}{\sqrt{19}}}=-1.124$

Then since is a two sided test the p value would be:

$p_v =2*P(t_{18}$

If we compare the p value and a significance level for example $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis.

Part c

If the system of hypothesis on this case are:

Null hypothesis: $\mu = 100$

Alternative hypothesis: $\mu > 100$

The only thing that changes is the p value and would be given by:

$p_v =P(t_{18}>-1.124)=0.862$

But again since the p value is higher than the significance level we fail to reject the null hypothesis.

7 0

3 years ago

The tangent to the circle x^2+y^2=18 is parallel to the tangent x+y=6

liubo4ka [24]

Answer:

y = -x - 6

Step-by-step explanation:

If we are looking for the equation of the line tangent to the circle, we have to find the first derivative of the circle function. If that tangent line is to be parallel to the given tangent line, we need to find the slope of the the given tangent line and make sure the slope of the line we are looking for is the same. First let's find the slope of the given tangent. If the given tangent is x+y=6, then to find the slope, solve for y:

y = -x + 6. So the slope of that line, and also the slope of the tangent we are solving for, is -1. Hold that thought while we find the derivative of the function. Using implicit differentiation, we find the derivative to be:

$2x+2y\frac{dy}{dx}=0$

Solving for the slope (dy/dx) gives us:

$2y\frac{dy}{dx}=-2x$ and

$\frac{dy}{dx}=\frac{-2x}{2y}$ so

$\frac{dy}{dx}=-\frac{x}{y}$

Subbing in the value of the slope we found:

$-1=-\frac{x}{y}$ so

-y = -x or, equivalently,

y = x. Now that we know that y and x are the same value, we can go back to the original circle to find out what they both are by substitution. If y = x, we make the substution:

If $x^2+y^2=18$ , then

$y^2+y^2=18$ and

$2y^2=18$ and

$y^2=9$ so

y = ±3

We will choose the negative root (you'll see why in a second) and sub that in for both y and x since y and x are th same number. Going back to the fact that the slope is -1:

y - (-3) = -1(x - (-3)) simplifies a bit to:

y + 3 = -x - 3 which gives us, in slope-intercept form:

y = -x - 6

That is the equation of the tangent to the circle that is parallel to the given tangent.

If we would have chosen the principle (or positive) root of 3, our equation would have looked like this:

y - 3 = -1(x - 3) and

y = -x + 3 + 3 so

y = -x + 6. Notice that that is the EXACT SAME EQUATION as the given tangent. That's why we have to pick the negative 3 as our root.

Good luck in your calculus class! Make sure you post your questions in here! Many of us LOVE the challenge of calculus!

3 0

3 years ago

How is this worked out ? im confused.