All categories

3 years ago

give 12 consecutive integers, in how many ways can three of these integers be selected to give a sum which divides by 4?

Mathematics

1 answer:

BaLLatris [955]3 years ago

7 0

Answer:

55 ways

Step-by-step explanation:

Out of 12 consecutive integers:

3 - divide by 4, so the remainder is 0
3- give remainder of 1
3- give remainder of 2
3 - give remainder of 3

Sum of 3 integers will be divisible by 4 if the remainders are:

0 - 0 - 0 ⇒ 1 combination
0 - 1 - 3 ⇒ 3*3 = 9 combinations
0 - 3 - 1 ⇒ 3*3 = 9 combinations
1 - 1 - 2 ⇒ 2*3 = 6 combinations
1 - 2 - 1 ⇒ 2*3 = 6 combinations
2 - 1 - 1 ⇒ 2*3 = 6 combinations
3 - 0 - 1 ⇒ 3*3 = 9 combinations
3 - 1 - 0 ⇒ 3*3 = 9 combinations

So total number of combinations is:

1 + 4*9 + 3*6 = 55

You might be interested in

A committee at the College Board has been asked to study the SAT math scores for students in Pennsylvania and Ohio. A sample of

ozzi

Answer:

Step-by-step explanation:

From the given information:

The null hypothesis and the alternative hypothesis can be computed as:

$H_0 :\mu_1 -\mu_2 = 0$ (i.e. there is no difference between the SAT score for students in both locations)

$H_1 :\mu_1 -\mu_2 \geq0$ (i.e. there is a difference between the SAT score for students in both locations)

The test statistics using the students' t-test for the two-samples; we have:

$t = \dfrac{\overline x_1 -\overline x_2}{\sqrt{\dfrac{s_1^2}{n_1}+\dfrac{s_2^2}{n_2} } }$

$t = \dfrac{580 -530}{\sqrt{\dfrac{105^2}{45}+\dfrac{114^2}{38} } }$

$t = \dfrac{50}{\sqrt{\dfrac{11025}{45}+\dfrac{12996}{38} } }$

$t = \dfrac{50}{\sqrt{245+342 } }$

$t = \dfrac{50}{\sqrt{587} }$

$t = \dfrac{50}{24.228}$

t = 2.06

degree of freedom = ( $n_1 + n_2$ ) -2

degree of freedom = (45+38) -2

degree of freedom = 81

Using the level of significance of 0.05

Since the test is two-tailed at the degree of freedom 81 and t = 2.06

The p-value = 0.0426

Decision rule: To reject $H_o$ if the p-value is less than the significance level

Conclusion: We reject the $H_o$ , thus, there is no sufficient evidence to conclude that there is a significant difference between the SAT math score for students in Pennsylvania and Ohio.

5 0

3 years ago

5 1/4 written in radical form

emmainna [20.7K]

Answer:Exact Form:

4 √ 5

Step-by-step explanation:

5 0

3 years ago

What are the coefficients in the expression -8y^ + 12x + 5y + 7

schepotkina [342]

Answer:

-8 12 5

Step-by-step explanation:

they are the numbers attached to the variables

8 0

3 years ago

Find out the cylinders volume whose height is 3 cm and radius 5cm

Studentka2010 [4]

Volume = πr²h

Volume = π(5)²(3)

Volume = 75π = 235.62 cm³ (nearest hundredth)

----------------------------------------------
Answer: Volume = 235.62 cm³.
----------------------------------------------

8 0

3 years ago

Read 2 more answers

Please help with this

Blizzard [7]

The probability is 4:20

It is correct because there are 20 students and there could be 4 guesses

5 0

3 years ago