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Ad libitum [116K]
3 years ago
10

Which expression represents the number of sides in the polygon for the nth member of the pattern?

Mathematics
1 answer:
Ira Lisetskai [31]3 years ago
5 0
Given a triangle (3 sides), a hexagon (6 sides) and a nonagon (9 sides).

The sides increases by 3 and the equation that represents the pattern is 3n.

Therefore, the <span>expression that represents the number of sides in the polygon for the nth member of the pattern is 3n.</span>
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Charles is going to buy 3 computer tables for 390$. If he pays the same rate, how much would it cost for 8 computer tables?
Dafna1 [17]
390 divided by 3= $130.
So 130 x 8 = $1040
7 0
3 years ago
New York City is the most expensive city in the United States for lodging. The mean hotel room rate is $204 per night (USA Today
Ierofanga [76]

Answer:

a) We can find the z score for the value of 225 and we got:

z = \frac{225-204}{55}=0.382

And we can find this probability with the complement rule:

P(z>0.382)=1-P(z

b) z = \frac{140-204}{55}=-1.164

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

P(z

c) P(200

And we can find this probability with this difference:

P(-0.072

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.  

P(-0.072

d) For this part we want to find a value a, such that we satisfy this condition:

P(X>a)=0.2   (a)

P(X   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.8 of the area on the left and 0.2 of the area on the right it's z=0.842. On this case P(Z<0.842)=0.8 and P(z>0.842)=0.2

If we use condition (b) from previous we have this:

P(X  

P(z

But we know which value of z satisfy the previous equation so then we can do this:

z=0.842

And if we solve for a we got

a=204 +0.842*55=250.31

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

X \sim N(204,55)  

Where \mu=204 and \sigma=55

We are interested on this probability

P(X>225)

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}

We can find the z score for the value of 225 and we got:

z = \frac{225-204}{55}=0.382

And we can find this probability with the complement rule:

P(z>0.382)=1-P(z

Part b

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:

z = \frac{140-204}{55}=-1.164

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

P(z

Part c

P(200

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(200

And we can find this probability with this difference:

P(-0.072

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.  

P(-0.072

Part d

For this part we want to find a value a, such that we satisfy this condition:

P(X>a)=0.2   (a)

P(X   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.8 of the area on the left and 0.2 of the area on the right it's z=0.842. On this case P(Z<0.842)=0.8 and P(z>0.842)=0.2

If we use condition (b) from previous we have this:

P(X  

P(z

But we know which value of z satisfy the previous equation so then we can do this:

z=0.842

And if we solve for a we got

a=204 +0.842*55=250.31

5 0
3 years ago
After which value of x does function g exceed function f
nalin [4]
We have that

for x=1
f(x)=1.5  and g(x)=-1
so
g(x) < f(x)

for x=2
f(x)=5  and g(x)=5
so
g(x)= f(x)

for x=3
f(x)=9.5  and g(x)=23
so
g(x) > f(x)

therefore

the answer is
<span>After x=2 function g exceeds function f</span>


5 0
3 years ago
What is the length of the line
love history [14]

Answer:

any idea about the length of the box

8 0
3 years ago
Read 2 more answers
Please help me with this
Furkat [3]

Answer:

$1224

Step-by-step explanation:

72 adults in the theater, and 17$ per adult ticket.

72 x 17 is 1224.

6 0
3 years ago
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