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jeka94
3 years ago
15

In class A, John got 85 for his first test John's class mean was 75 and standard deviation was 5. In class B, Kathy got 80 in he

r first test. Kathy's class mean was 50and standard deviatoin was 10. In a fair comparison of the two studens in two different classes who did better in his or her test. a. John b. Kathyc. same d. none of the above
Mathematics
1 answer:
ivanzaharov [21]3 years ago
6 0

Answer:

b. Kathy

Step-by-step explanation:

We compare each of their score by how far away from the mean when in term of the standard deviation. Using the following formula

\frac{x - \mu}{\sigma}

For John he is (85 - 75)/5 = 2.

For Kathy she is (80 - 50)/10 = 3.

Since Kathy is 3 standard deviation better than her class' average, while John is only 2's. We conclude that Kathy did better.

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Answer:

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Step-by-step explanation:

Tinatamad akong mag explain basta tama 'yan

7 0
3 years ago
Prove the following by induction. In each case, n is apositive integer.<br> 2^n ≤ 2^n+1 - 2^n-1 -1.
frutty [35]
<h2>Answer with explanation:</h2>

We are asked to prove by the method of mathematical induction that:

2^n\leq 2^{n+1}-2^{n-1}-1

where n is a positive integer.

  • Let us take n=1

then we have:

2^1\leq 2^{1+1}-2^{1-1}-1\\\\i.e.\\\\2\leq 2^2-2^{0}-1\\\\i.e.\\2\leq 4-1-1\\\\i.e.\\\\2\leq 4-2\\\\i.e.\\\\2\leq 2

Hence, the result is true for n=1.

  • Let us assume that the result is true for n=k

i.e.

2^k\leq 2^{k+1}-2^{k-1}-1

  • Now, we have to prove the result for n=k+1

i.e.

<u>To prove:</u>  2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-1

Let us take n=k+1

Hence, we have:

2^{k+1}=2^k\cdot 2\\\\i.e.\\\\2^{k+1}\leq 2\cdot (2^{k+1}-2^{k-1}-1)

( Since, the result was true for n=k )

Hence, we have:

2^{k+1}\leq 2^{k+1}\cdot 2-2^{k-1}\cdot 2-2\cdot 1\\\\i.e.\\\\2^{k+1}\leq 2^{(k+1)+1}-2^{k-1+1}-2\\\\i.e.\\\\2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-2

Also, we know that:

-2

(

Since, for n=k+1 being a positive integer we have:

2^{(k+1)+1}-2^{(k+1)-1}>0  )

Hence, we have finally,

2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-1

Hence, the result holds true for n=k+1

Hence, we may infer that the result is true for all n belonging to positive integer.

i.e.

2^n\leq 2^{n+1}-2^{n-1}-1  where n is a positive integer.

6 0
3 years ago
13. Danny is in science class and is given a square block of metal with
jenyasd209 [6]

Answer: 336g.

Step-by-step explanation:

the formula for density is mass divided by volume (m/v). In this problem, you mus first find the volume of the square block. The formula for volume is length multiplied by width multiplied by height (LxWxH). To solve for volume you plug in the values to the equation: 6x4x2 = 48.

Now, you have the volume, and you have the density. Now you need to solve for mass. Plug in the values you have into the density equation (d=m/v):

7=m/48

to isolate M, multiply each side by 48. this leaves you with 7x48 = m. now all thats left is to solve. 7x48 = 336g. You can double check by plugging the values back into the equation. 336/48 = 7.

5 0
3 years ago
A class of 25 students took a math test. Ten students had an average of 88. The other students had an average of 76. What is the
VLD [36.1K]

The answer is B. 80.8

8 0
3 years ago
Read 2 more answers
glenn bought a $5 coffee and four magazines. If he spent a total of $25 how much did each magazine cost?
ladessa [460]

Answer:

5 each

Step-by-step explanation:

we will minus the coffee from the total

25 - 5 = 20

there's was 4 magazines so we do...

20 ÷ 4 = 5

5 0
3 years ago
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