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2 years ago

Relative to the graph of y=3sinx what is the shift of the graph of y=3sin(x+pi/3)

1 answer:

4 0

The shifts of the sinus function can be described with the formula:
asin(bx−c)+d, where
a is the amplitude
b is the period
c is the phase shift
d is the vertical shift
So, the graph y=3sinx is phase shifted. The phase shift can be calculated as c/b= pi/3/1=pi/3
So, the function is phase shifted for pi/3.

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Priya tried to translate triangle ABC by the directed line segment from D to E. She knows something went wrong because the image

jeyben [28]

Answer:

When we do a translation, all the translated points must be translated in parallel (between them) lines. (this would mean that all our points suffer the same translation)

Here we can see that the lines BB´ and AA´ are parallel, but the line CC´ is not parallel to the other two. So the distance of the translation is constant, but the direction is not the same for all the points.

Then this is not a translation of all our triangle, because different points suffered different translation operations, this is what caused the triangles ABC and A´B´C´ to not be congruent.

5 0

2 years ago

Last week, your delivery runs took 7 hours 12 minutes on Monday, 6 hours 46 minutes on Wednesday, and 6 hours 53 minutes on Frid

77julia77 [94]

7 hrs 12 minutes
6 hrs 46 minutes
6 hrs 53 minutes
--------------------------add
19 hrs 111 minutes ......... = (19 * 60) + 111 = 1140 + 111 = 1251 minutes

1251 / 3 = 417 minutes <== her average delivery....or 6 hrs 57 minutes

7 0

2 years ago

The following is an incomplete paragraph proving that the opposite sides of parallelogram ABCD are congruent:

OverLord2011 [107]

D) Angles BAC and DCA are congruent by the Alternate Interior Angles Theorem.

8 0

2 years ago

Read 2 more answers

The price of a math book after a discount of 25% is $36. What is the original price of the math book?

UNO [17]

If $36=75%,
That means we can divide both sides by three to get $12=25%,
And because 25x4 is 100, we multiply both sides of the equation by 4 to get $48=100%,
So the answer is $48 dollars.

This also worked for me but I’m not sure it’s the most reliable way:
36 ÷ 0.75 = 48
(amount after discount ÷ percentage that is remaining)

3 0

2 years ago

It is believed that as many as 23% of adults over 50 never graduated from high school. We wish to see if this percentage is the

JulijaS [17]

Answer:

1) n=48

2) n=298

3) n=426

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".

$p$ represent the real population proportion of interest

$\hat p$ represent the estimated proportion for the sample

n is the sample size required (variable of interest)

$z$ represent the critical value for the margin of error

The population proportion have the following distribution

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

Part 1

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by $\alpha=1-0.90=0.10$ and $\alpha/2 =0.05$ . And the critical value would be given by:

$z_{\alpha/2}=-1.64, z_{1-\alpha/2}=1.64$

The margin of error for the proportion interval is given by this formula:

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

And on this case we have that $ME =\pm 0.1$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

We can assume that the estimated proportion is 0.23 for the 25 to 30 group. And replacing into equation (b) the values from part a we got:

$n=\frac{0.23(1-0.23)}{(\frac{0.1}{1.64})^2}=47.63$

And rounded up we have that n=48

Part 2

The margin of error on this case changes to 0.04 so if we use the same formula but changing the value for ME we got:

$n=\frac{0.23(1-0.23)}{(\frac{0.04}{1.64})^2}=297.7$

And rounded up we have that n=298

Part 3

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by: