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3 years ago

In a set of integers from 140 to 200 inclusive, how many integers are divisible by 4 and 6?

Mathematics

1 answer:

Ronch [10]3 years ago

3 0

The answer to the question asked is 5.

The least common multiple of 4 and 6 is 12. In the range 140 to 200, there are

... floor(200/12) - ceiling(140/12) + 1 = 16 - 12 + 1 = 5

integers divisible by 12.

_____

The list of answer choices suggests that the question is intended to be, "how many integers are divisible by 4 or 6?"

The number divisible by 4 is

... floor(200/4) - ceiling(140/4) + 1 = 50 - 35 + 1 = 16

The number divisible by 6 is

... floor(200/6) - ceiling(140/6) + 1 = 33 - 24 + 1 = 10

We know from the above that there are 5 values that are divisible by both 4 and 6, so will be counted twice if we simply add the above numbers. Hence the number of values divisible by 4 or 6 is

... 16 + 10 - 5 = 21 . . . . . corresponds to selection C)

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From a pool of 12 candidates, the offices of president, vice-president, secretary, and treasurer will be filled. In how many dif

Romashka [77]

Answer:

11,880 different ways.

Step-by-step explanation:

We have been given that from a pool of 12 candidates, the offices of president, vice-president, secretary, and treasurer will be filled. We are asked to find the number of ways in which the offices can be filled.

We will use permutations for solve our given problem.

$^nP_r=\frac{n!}{(n-r)!}$ , where,

n = Number of total items,

r = Items being chosen at a time.

For our given scenario $n=12$ and $r=4$ .

$^{12}P_4=\frac{12!}{(12-4)!}$

$^{12}P_4=\frac{12!}{8!}$

$^{12}P_4=\frac{12*11*10*9*8!}{8!}$

$^{12}P_4=12*11*10*9$

$^{12}P_4=11,880$

Therefore, offices can be filled in 11,880 different ways.

3 0

3 years ago

Professional plumbers suggest that a sewer pipe should be sloped 0.25 inch for every foot. find the recommended slope for a sewe

erik [133]

We have been given that professional plumbers suggest that a sewer pipe should be sloped 0.25 inch for every foot.

Therefore, we can find the slope as:

$\text{Slope}=\frac{0.25\text{ inch}}{\text{1 foot}}=\frac{0.25\text{ inch}}{\text{12 inch}}$

$\text{Slope}=\frac{0.25}{12}=\frac{25}{1200}=\frac{1}{48}$

Therefore, the recommended slope for a sewer pipe is $\frac{1}{48}$

5 0

2 years ago

use the explicit formula an = a1 + (n - 1) * d to find the 500th term of the sequence below. 24,30,36,42,48,... A. 3018 B. 3042

marishachu [46]

Answer:

Option A.

Step-by-step explanation:

The given sequence is

24, 30, 36, 42, 48, ...

It is an AP. Here,

First term = 24

Common difference = 30-24 = 6

The given explicit formula for nth term is

$a_n=a_1+(n-1)d$

where, $a_1$ is first term, d is common difference.

Substitute $a_1=24, d=6 \text{ and }n=500$ in the above formula.

$a_{500}=24+(500-1)(6)$

$a_{500}=24+(499)(6)$

$a_{500}=24+2994$

$a_{500}=3018$

The 500th term of the sequence is 3018.

Therefore, the correct option is A.

3 0

2 years ago

What is the probability of rolling a dice at most 3 times until a 6 occurs

IRISSAK [1]

Answer:

Probablity of getting six in at most three roll= 0.199.

Step-by-step explanation:

Given: Dice rolled at most 3 times untill a 6 occurs.

First, finding the probablity of getting 6 in a dice if rolled once.

Probablity= $\frac{chances\ of\ occurance}{Total\ number\ of\ event}$

We know, dice have six side, therefore, total number of event will be 6.

∴ Probablity of getting six in one roll= $\frac{1}{6}$

As given, Dice is rolled at most 3 times.

Now, finding the probablity of getting 6 in a dice if rolled 3 times.

∴ Probablity of getting six in three roll= $\frac{1}{6}+(\frac{1}{6})^{2} +(\frac{1}{6})^{3}$

⇒ Probablity of getting six in three roll= $\frac{1}{6}+\frac{1}{36} +\frac{1}{216}$

Taking LCD 216

⇒Probablity of getting six in three roll= $\frac{1\times 36+ 6\times 1+1}{216}$

⇒Probablity of getting six in three roll= $\frac{43}{216}$

∴Probablity of getting six in three roll=0.199

3 0

3 years ago

1. Which two points fail the VLT here in this graph?<br><br><br> PLEASE HELP!!!!

ivolga24 [154]

Kiki and Rose's points

They are on the same vertical line so they fail

4 0

2 years ago