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xeze [42]
3 years ago
14

Judson collected information about the name length and the population of a random sample of 296 American cities. Here are the re

sults:
Name length Less than Between 150,000 More than Total
150,000 and 250,000 250,000
Less than 8
characters 30 29 41 100
8 to 10
characters 43 41 33 117
More than 10
characters 26 28 25 79
Total 99 98 99 296
Judson wants to perform a X2 test of independence between name length and population. What is the expected count for the cell corresponding to cities with more than 250,000 residents whose name has less than 8 characters?
Mathematics
1 answer:
Natasha2012 [34]3 years ago
6 0
It would be 90 - 10
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On the last day of school, Mrs. Awesome gave jelly beans to her class. She gave each boy as many jelly beans as there were boys
professor190 [17]

Answer:

28 students

Step-by-step explanation:

Let x be the number of girls in the class. There were two more boys than girls in her class, then the number of boys is x + 2.

Mrs. Awesome gave each boy as many jelly beans as there were boys in the class, so each of x + 2 boys got x + 2 jelly beans, so

Number of boys = x + 2

Number of jelly beans each boy got = x + 2

Total number of jelly beans all boys got = (x + 2)(x + 2)

Mrs. Awesome gave each girl as many jelly beans as there were girls in the class, so each of x girls got x jelly beans, so

Number of girls = x

Number of jelly beans each girl got = x

Total number of jelly beans all girls got = (x)(x)

Hence,

Total number of jelly beans class got = (x + 2)(x + 2) + (x)(x)

Mrs. Awesome brought 400 jelly beans, and when she finished, she had six jelly beans left, so she gave 400 - 6 = 394 jelly beans to the calss.

So,

(x+2)(x+2)+(x)(x)=394\\ \\x^2+2x+2x+4+x^2=394\\ \\2x^2+4x+4-394=0\\ \\2x^2+4x-390=0\\ \\x^2+2x-195=0\\ \\D=2^2-4\cdot (-195)=4+780=784\\ \\\sqrt{D}=28\\ \\x_{1,2}=\dfrac{-2\pm 28}{2\cdot 1}=-15,\ 13

Number of girls cannot be negative, so x = 13, x + 2 = 15 and total number of students is 13 + 15 = 28

3 0
3 years ago
Suppose a and b are both non zero real numbers. Find real numbers c and d such that 1/a+ib= c+id
Thepotemich [5.8K]

\begin{gathered} c=\frac{a}{a^2+b^2} \\ d=\frac{-b}{a^2+b^2} \end{gathered}

Explanation

\frac{1}{a+bi}=c+di

Step 1

multiplicate by the conjugate

\begin{gathered} \frac{1}{a+bi}\cdot\frac{a-bi}{a+bi}=\frac{a-bi}{(a+bi)(a-bi)}=\frac{a-bi}{a^2-(bi)^2} \\ \frac{1}{a+bi}\cdot\frac{a-bi}{a+bi}=\frac{a-bi}{(a+bi)(a-bi)}=\frac{a-bi}{a^2-(-b^2)}=\frac{a-bi}{a^2+b^2} \end{gathered}

notice that

\begin{gathered} \frac{1}{a+bi}=\frac{a-bi}{a^2+b^2}=\frac{a}{a^2+b^2}-\frac{b}{a^2+b^2}i \\ \frac{a}{a^2+b^2}-\frac{b}{a^2+b^2}i=c+di \\ so \\  \end{gathered}\begin{gathered} c=\frac{a}{a^2+b^2} \\ d=\frac{-b}{a^2+b^2} \end{gathered}

I hope this helsp you

6 0
1 year ago
In a class there are two girls for every three boys. The ratio 2 : 3 compares the
alekssr [168]

Answer:

a. I'm not sure if there's more to the question but I can't answer without knowing how many is the whole class

B. 12 boys

4 0
2 years ago
27? Thanks and please have step to step
Studentka2010 [4]
I hope this helps you

5 0
3 years ago
Have no idea helppppppppppp
mario62 [17]
Answer: choice A) 7017

==========================================================

Work Shown:

The first term is a_1 = 24 and we go up by 7 each time.
The common difference is d = 7

The nth term formula we'll use is
a_n = a_1 + (n-1)*d
a_n = 24 + (n-1)*7

----------

The 1000th term corresponds to n = 1000

Replace every n with 1000
Then use the order of operations (PEMDAS) to simplify

a_n = 24 + (n-1)*7
a_1000 = 24 + (1000-1)*7
a_1000 = 24 + (999)*7
a_1000 = 24 + 6993
a_1000 = 7017
3 0
3 years ago
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