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Natasha2012 [34]
3 years ago
6

A small auditorium has 10 rows of seats. There are 12 seats in the row and 16 seats in the second row the number of seats in a r

ow continues to increase by 4 with each additional row. What is the total number of seats in the auditorium?
Mathematics
1 answer:
guapka [62]3 years ago
4 0

This problem can be solved through simple arithmetic progression

Let

a1 = the first term of the sequence

a(n) = the nth term of the sequence

n = number of terms

d = common difference

Sn = sum of all terms

 

given

a1 = 12

a2 = 16

n = 10

 

d = 16 -12 = 4

@n = 10

a(n) = a1 + (n-1)d

a(10) = 12 + (9)4

a(10) = 48 seats

 

Sn = (n/2) * (a1 + a(10))

Sn = 5* (12 + 48)

Sn = 300 seats

 

Therefore the total number of seats is 300.

 

 

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Step-by-step explanation:

To find the area of a triangle you do base x height/2

9x4.5/2

40.5/2= 20.25

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Henry's baseball practice starts at 2:00 pm. It lasts 1 hour and 45 minutes. What time does he get out of baseball practice? Wri
tresset_1 [31]

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Henry's baseball practice starts at 2:00, will last an hour and forty-five minutes, and will end at 3:45.

Step-by-step explanation:

2 + 1 = 3

3  + 45 minutes = 3 : 45

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2 years ago
A research study uses 800 men under the age of 55. Suppose that 30% carry a marker on the male chromosome that indicates an incr
ss7ja [257]

Answer:

a) There is a 12.11% probability that exactly 1 man has the marker.

b) There is a 85.07% probability that more than 1 has the marker.

Step-by-step explanation:

There are only two possible outcomes: Either the men has the chromosome, or he hasn't. So we use the binomial probability distribution.

Binomial probability

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}

In which C_{n,x} is the number of different combinatios of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And \pi is the probability of X happening.

In this problem, we have that:

30% carry a marker on the male chromosome that indicates an increased risk for high blood pressure, so \pi = 0.30

(a) If 10 men are selected randomly and tested for the marker, what is the probability that exactly 1 man has the marker?

10 men, so n = 10

We want to find P(X = 1). So:

P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}

P(X = 1) = C_{10,1}.(0.30)^{1}.(0.7)^{9} = 0.1211

There is a 12.11% probability that exactly 1 man has the marker.

(b) If 10 men are selected randomly and tested for the marker, what is the probability that more than 1 has the marker?

That is P(X > 1)

We have that:

P(X \leq 1) + P(X > 1) = 1

P(X > 1) = 1 - P(X \leq 1)

We also have that:

P(X \leq 1) = P(X = 0) + P(X = 1)

P(X = 0) = C_{10,0}.(0.30)^{0}.(0.7)^{10} = 0.0282

So

P(X \leq 1) = P(X = 0) + P(X = 1) = 0.0282 + 0.1211 = 0.1493

Finally

P(X > 1) = 1 - P(X \leq 1) = 1 - 0.1493 = 0.8507

There is a 85.07% probability that more than 1 has the marker.

3 0
3 years ago
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kkurt [141]

Answer:

i think 16

Step-by-step explanation:

this is what makes sense to be boo<3

4 0
3 years ago
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