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Karolina [17]
2 years ago
11

Lisa is 10 centimeters taller than her friend Ian. Ian is 14 centimeters taller than Jim. Every month, their heights increase by

2 centimeters. In 7
months the sum of Ian's and Jim's heights will be 170 centimeters more than Lisa's height. How tall is Ian now?
Mathematics
1 answer:
bekas [8.4K]2 years ago
5 0
Let Lisa's height be x, Ian's be y and Jim's be z
x = 10 + y . . . (1)
y = 14 + z . . . (2)
y + 14 + z + 14 = 170 + x + 14
y + z - x = 170 + 14 - 28 = 156 . . . (3)
From (2), z = y - 14 . . . (4)
Putting (1) and (4) into (3) gives,
y + y - 14 - 10 - y = 156
y = 156 + 24 = 180

Therefore, Ian's height is 180 centimeters
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Answer:

\frac{8}{25}

Step-by-step explanation:

probability of selecting a girl from students is \frac{4}{5}

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hence, probability of selecting a girl wearing a sneaker will be,

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⇒ probability = \frac{8}{25}

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1 year ago
62% of U.S. adults have very little confidence in newspapers. You randomly select 10 U.S. adults. Find the probability that the
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Answer:

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b) 0.6823

c) 0.0413

Step-by-step explanation:

We are given the following information:

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Then the number of adults follows a binomial distribution, where

P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}

where n is the total number of observations, x is the number of success, p is the probability of success.

Now, we are given n = 10

a) exactly 5

P(x =5)\\\\=\binom{10}{5}(0.62)^5(1-0.62)^5\\\\=0.1829

0.1829 is the probability that exactly 5 out of 10 U.S.adults have very little confidence in newspapers.

b) atleast six

P(x \geq 6)\\\\ = P(x = 6) + P(x = 7)+P(x = 8)+P(x = 9)+P(x=10)\\\\= \displaystyle\sum \binom{10}{n}(0.62)^n(1-0.62)^{10-n}, n =6,7,8,9,10\\\\= 0.6823

0.6823 is the probability that atleast 6 out of 10 U.S. adults have very little confidence in newspapers.

c) less than four

P(x

0.0413 is the probability that less than 4 out of 10 U.S. adults have very little confidence in newspapers.

8 0
1 year ago
James is the manager at an entertainment arena that draws an average 7,000 patrons per event. Each ticket taker can process 350
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Answer:

No. James didn't have enough ticket takers to process the average number of patrons hat usually attend the events.

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Step-by-step explanation:

Given:

Average amount of patron per event= 7000

Each ticket taker can process = 350

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We need to find the whether he hire enough to process the average number of patrons that usually attend the events.

Solution:

We will find the Average amount of patron ticket takers can process.

Now we can say that

Average amount of patron ticket takers can process is equal to Each ticket taker can process multiplied by Number of ticket takers hired.

framing in equation form we get;

Average amount of patron ticket takers can process = 350 \times 18 = 6300\ patrons

Hence With the required hires James cannot fully process the patrons usually attending the event.

To find how many ticket takers required we will divide average number of patrons with  Each ticket taker can process.

framing in equation form we get;

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Answer:

For First Solution: y_1(t)=e^t

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Step-by-step explanation:

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In order to prove whether it is a solution or not we have to put it into the equation and check. For this we have to take derivatives.

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For 2nd Solution:

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In order to prove whether it is a solution or not we have to put it into the equation and check. For this we have to take derivatives.

y_2(t)=cosht

First order derivative:

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y''_2(t)=cosht

Put Them in equation y''-y=0

cosht-cosht=0

0=0

Hence y_2(t)=cosht  is the solution of equation y''-y=0.

3 0
2 years ago
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