1.13 UNIT TEST GRAPH OF SINUSOIDAL FUNCTION PART 1

The seventh grade class is putting on a variety show to raise money. It cost $700 to rent the

Nataly_w [17]

Well, you would need to compensate for the cost of the banquet hall adding an addition $700 to the goal of $1000.

If you need to raise at least $1700 you can write this inequality.

Let x represent the number of tickets sold.

15x≥1700

x≥ 114 (rounded to the nearest whole number because you can't sell half a ticket)

So, at least 114 tickets need to be sold.

6 0

3 years ago

A vending machine automatically pours soft drinks into cups. The amount of soft drink dispensed into a cup is normally distribut

labwork [276]

Answer:

a) $P(X>8)=P(\frac{X-\mu}{\sigma}>\frac{8-\mu}{\sigma})=P(Z>\frac{8-7.6}{0.4})=P(Z>1)$

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

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

b) $P(X$

And we can find this probability using the standard normal table or excel:

$P(Z$

c) For this case we have a total of 868 cups and we know that the fraction of cups that will be overflow is 0.159, so then the expected number of cups overflow would be:

$N = 868*0.159= 138.012 \approx 138$

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".

Part a

Let X the random variable that represent the amount of soft frink of a population, and for this case we know the distribution for X is given by:

$X \sim N(7.6,0.4)$

Where $\mu=7.6$ and $\sigma=0.4$

We are interested on this probability

$P(X>8)$

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:

$P(X>8)=P(\frac{X-\mu}{\sigma}>\frac{8-\mu}{\sigma})=P(Z>\frac{8-7.6}{0.4})=P(Z>1)$

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

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

Part b

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 standard normal table or excel:

$P(Z$

Part c

For this case we have a total of 868 cups and we know that the fraction of cups that will be overflow is 0.159, so then the expected number of cups overflow would be:

$N = 868*0.159= 138.012 \approx 138$

6 0

4 years ago

Help me asap! A parka that sold for $50 is marked up to $60. What is the percent of markup?

nirvana33 [79]

Answer:

the markup is 20 percent

7 0

3 years ago

If T={x:X is an integer between 1 and 4} (A) List down the elements of set T in set notation. B write down the number of element

GarryVolchara [31]

Answer:

The answer is given below

Step-by-step explanation:

A) Integers are whole numbers (without fraction) that are either positive or negative. If T={x:X is an integer between 1 and 4}, therefore the elements in set T = {2, 3}

B) Since the elements in set T = {2, 3}, then the number of elements in set T = 2

C) The subsets of set T are {}, {2}, {3} and {2,3}

D) Proper subset of set T are subsets of T that is not equal to T. The proper subsets of T are {2} and {3}

An improper subset of set T contains all the element of set T and a null element. The improper subset of set T are {2,3} and {}

6 0

3 years ago

What is the missing side length in the triangle?<br><br> plsss someone help!!

UkoKoshka [18]

Answer:

The measure of the missing side length = 45

Step-by-step explanation:

Pythagorean Theorem states: A² + B² = C²

28² + B² = 53²

784 + B² = 2809

B² = 2809 - 784

B² = 2025

B = $\sqrt{2025}$

B = 45

Therefore the measure of the missing side length = 45

Hope this helps!

6 0

3 years ago

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