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Rudiy27
2 years ago
5

What is the least amount of integers you must pick in order to be sure that at least two of them have the same remainder when di

vided by 15
Mathematics
1 answer:
LiRa [457]2 years ago
4 0

There are exactly 15 remainders modulo 15 and they are 0,1,2,…,14.

It is given that at least two of them should have the same remainder when divided by 15.

Division algorithm.

Let aa be an integer and d a positive integer. Then there are unique integers q and r with 0\leq r < d such that a=dq+r

q is called the quotient and r is called the remainder

q=a div d

r=a mod d

Pigeonhole principle If k is a positive integer and k+1or more objects are placed into k boxes, then there is at least one box containing two or more objects.

Hence, there are exactly 15 remainders modulo 15 and they are 0,1,2,…,14.

Learn more about integers here: brainly.com/question/20521181

#SPJ4

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Help help help help helpe​
andrew-mc [135]

Answer:

H = 58, I = 71, J = 51

Step-by-step explanation:

Set all angles equal to 180

3x - 2 + 4x - 9 + 3x - 9 = 180

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2 years ago
The U.S. Energy Information Administration claimed that U.S. residential customers used an average of 10,608 kilowatt hours (kWh
Marat540 [252]

Answer:

The calculated value Z = 1.4460 < 1.96 at 0.05 level of significance.

The null hypothesis is accepted

A local power company believes that residents in their area use more electricity on average than EIA's reported average

Step-by-step explanation:

<u><em>Step(i):-</em></u>

Given that the mean of the Population = 10,608 kWh of electricity this year.

Given that the size of the sample n = 187

Given that mean of sample x⁻ = 10737 kWh

The Standard deviation of the Population = 1220kWh

Level of significance = 0.05

The critical value (Z₀.₀₅)= 1.96

<u><em>Step(ii):-</em></u>

Null Hypothesis: H₀:μ > 10608 kWh

Alternative Hypothesis: H₁: μ < 10608kWh

Test statistic

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                Z = \frac{10737- 10608 }{\frac{1220}{\sqrt{187} } }

                Z = 1.4460

<u>Final answer:-</u>

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The null hypothesis is accepted

A local power company believes that residents in their area use more electricity on average than EIA's reported average.

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3 years ago
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