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oee [108]
3 years ago
8

Find the sum of the first one hundred positive integers. see fig 6.26

Mathematics
1 answer:
nignag [31]3 years ago
8 0
Here's a pattern to consider:
1+100=101
2+99=101
3+98=101
4+97=101
5+96=101
.....
This question relates to the discovery of Gauss, a mathematician. He found out that if you split 100 from 1-50 and 51-100, you could add them from each end to get a sum of 101. As there are 50 sets of addition, then the total is 50×101=5050
So, the sum of the first 100 positive integers is 5050.

Quick note
We can use a formula to find out the sum of an arithmetic series:
s =  \frac{n(n + 1)}{2}
Where s is the sum of the series and n is the number of terms in the series. It works for the above problem.
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What is the probability that a randomly number from 20 to 30 is divisible by 3 and then divisible by 12 after replacing first
tester [92]
Probability of divisibility by3=4/11
probability of divisibility by 12 =1/11
probability of divisibility by 12 and 3=4/11×1/11
answer is 4/121

7 0
3 years ago
Hãy chỉ cho tôi học thực hiện phép tính lớp 9
butalik [34]

Answer:

thật ngu ngốc

Stethật ngu ngốcp-by-step explanation

4 0
3 years ago
Assume that a sample is used to estimate a population proportion p. find the margin of error e that corresponds to the given sta
Leno4ka [110]

Let p be the proportion. Let c be the given confidence level , n be the sample size.

Given: p=0.3, n=1180, c=0.99

The formula to find the Margin of error is

ME = z _{\alpha/2}  \sqrt{\frac{p*(1-p)}{n}}

Where z (α/2) is critical value of z.

P(Z < z) = α/2

where α/2 = (1- 0.99) /2 = 0.005

P(Z < z) = 0.005

So in z score table look for probability exactly or close to 0.005 . There is no exact 0.005 probability value in z score table. However there two close values 0.0051 and 0.0049 . It means our required 0.005 value lies between these two probability values.

The z score corresponding to 0.0051 is -2.57 and 0.0049 is -2.58. So the required z score will be average of -2.57 and -2.58

(-2.57) + (-2.58) = -5.15

-5.15/2 = -2.575

For computing margin of error consider positive z score value which is 2.575

The margin of error will be

ME = z _{\alpha/2}  \sqrt{\frac{p*(1-p)}{n}}

= 2.575  \sqrt{\frac{0.30*(1-0.3)}{1180}}

= 2.575 * 0.0133

ME = 0.0342

The margin of error is 0.0342

7 0
3 years ago
Please help me......​
Scilla [17]

Answer:

-1/4

Step-by-step explanation:

I'm not sure what exactly you needed. But this is the slope of the line. Hope this helps! Have a great day! :)

3 0
3 years ago
Find the total surface area of the following pyramids: A regular square pyramid has a height of 4 and a base with area 36.
Artemon [7]

Answer:

2623.6144m²

Step-by-step explanation:

Total Surface Area of a Square Pyramid

a * (a + √(a² + 4h²))

where,

a = area of base

h = height

Using the formula above

a * (a + √(a² + 4h²))

data given :

a = 36

h = 4

a * (a + √(a² + 4h²))

T.S.A. = a * (a + √(a² + 4h²))

Inputting values

T.S.A. = 36 * (36 + √(36² + 4 * 4²))

T.S.A. = 36 * (36 + √(36² + 4 * 16))

T.S.A. = 36 * (36 + √(36² + 64))

T.S.A. = 36 * (36 + √(1296 + 64))

T.S.A. = 36 * (36 + √(1360))

T.S.A. = 36 * (36 + 36.87817782917154)

T.S.A. = 36 * (72.87817782917154)

T.S.A. = 36 * 72.8782

T.S.A. = 2623.614401850175

Therefore Total Surface Area (T.S.A.) is 2623.6144m²

6 0
3 years ago
Read 2 more answers
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