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3 years ago

5

You can tell if the value of a function for a certain interval is positive just by 2 points looking at its graph. If the value i

s positive that part of the graph will:
a: be to the right of the y-axis
b: be above the x-axis
c: intersect the x-axis
d: be below the x-axis

1 answer:

Scilla [17]3 years ago

7 0

It is b. above the x axis

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Thickness measurement ancient prehistoric Native American Pot Shards discovered in Hopi Village are approximately normally distr

beks73 [17]

Answer:

a) $P(X$

And we can find this probability using the normal standard table and we got:

$P(z$

b) $P(X>7)=P(\frac{X-\mu}{\sigma}>\frac{7-\mu}{\sigma})=P(Z>\frac{7-5.1}{0.9})=P(z>2.11)$

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

$P(z>2.11)=1-P(Z$

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 variable of interest of a population, and for this case we know the distribution for X is given by:

$X \sim N(5.1,0.9)$

Where $\mu=5.1$ and $\sigma=0.9$

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 and we got:

$P(z$

Part b

We are interested on this probability

$P(X>7)$

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:

$P(X>7)=P(\frac{X-\mu}{\sigma}>\frac{7-\mu}{\sigma})=P(Z>\frac{7-5.1}{0.9})=P(z>2.11)$

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

$P(z>2.11)=1-P(Z$

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3 years ago

I need answers plz here is the questions 80=-39+c

Maslowich

The answer is c=119...:) hope it helps

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3 years ago

13. Write an equation for the given function given the amplitude, period, phase shift, and vertical shift.

Paul [167]

Answer:

$y=4sin(\frac{2\pi(t+\frac{4}{3}\pi ) }{4\pi } )-2$

Step-by-step explanation:

Let's start with the original function.

$y=a sin\frac{2\pi t}{T}$

We can immediately fill in the amplitude 'a' and period 'T' , as the question defines these for us, and provides values for 'a' and 'T', 4 and 4 $\pi$ respectively.

$y=4sin(\frac{2\pi t}{4\pi } )$

Now we only have phase shift and vertical shift to do. Vertical shift is very easy, you can just add it to the end of the right side of the expression. A positive value will shift the graph up, while a negative value will move shift the graph down. We have '-2' as our value for vertical shift, so we can add that on as so:

$y=4sin(\frac{2\pit }{4\pi } )-2$

Now phase shift the most complicated of the transformations. Basically, it is just movement left or right. A negative phase shift moves the graph right, a positive phase shift moves the graph left (I know, confusing!). Phase shift applies directly to the x variable, or in this case the t variable. To achieve a -4/3 pi phase shift, we need to input +4/3 pi into the function, because of the aforementioned negative positive rule. Here is what the function looks like with the correct phase shift:

$y=4sin(\frac{2\pi(t+\frac{4}{3}\pi ) }{4\pi } )-2$

This function has vertical shift -2, phase shift -4/3 $\pi$ , amplitude 4, and period 4 $\pi$ .

Desmos.com/calculator is a great tool for learning about how various parts of an equation affect the graph of the function, If you want you can input each step of this problem into desmos and watch the graph change to match the criteria.

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