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Serga [27]
3 years ago
14

What is the largest three-digit number divisible by 24 and 54?

Mathematics
1 answer:
tensa zangetsu [6.8K]3 years ago
4 0

Answer:

The largest three-digit number divisible by 24 and 54 is:

  • <u>864</u>

Step-by-step explanation:

To identify the largest number what I did was dividing 999 (the largest whole three-digit number of all) in the first number given (24):

  • \frac{999}{24}=41.625

With this number, you know that you must multiply 24 by a number like 41 or less until you find a number that can be divisible by 54 and obtain a whole number, so:

  • 24*41= 984/54= 18.22 (how the number obtained is not a whole number, this is not the correct).
  • 24*40= 960/54= 17.77 (this is not).
  • 24*39= 936/54= 17.33 (this is not).
  • 24*38= 912/54= 16.88 (this is not).
  • 24*37=888/54= 16.44 (this is not).
  • <u>24*36= 864/54= 16 (This is the correct</u>).

Now, you have identified that the number 864, you can prove it by dividing this in 24 and 54:

  • \frac{864}{24}=36
  • \frac{864}{54}= 16

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162 short sleeve shirts; if you add 9 and 4, you get 13. Then, divide 234 by 13, which equals 18. 18 multiplied by 9 is 162.
3 0
3 years ago
4. A random variable X has a mean of 10 and a standard deviation of 3. If 2 is added to each value of X, what will the new mean
Ede4ka [16]

Adding 2 to each value of the random variable X makes a new random variable X+2. Its mean would be

E[X+2]=E[X]+E[2]=E[X]+2

since expectation is linear, and the expected value of a constant is that constant. E[X] is the mean of X, so the new mean would be

E[X+2]=10+2=12

The variance of a random variable X is

V[X]=E[X^2]-E[X]^2

so the variance of X+2 would be

V[X+2]=E[(X+2)^2]-E[X+2]^2

We already know E[X+2]=12, so simplifying above, we get

V[X+2]=E[X^2+4X+4]-12^2

V[X+2]=E[X^2]+4E[X]+4-12^2

V[X+2]=(V[X]+E[X]^2)+4E[X]-140

Standard deviation is the square root of variance, so V[X]=3^2=9.

\implies V[X+2]=(9+10^2)+4(10)-140=9

so the standard deviation remains unchanged at 3.

NB: More generally, the variance of aX+b for a,b\in\mathbb R is

V[aX+b]=a^2V[X]+b^2V[1]

but the variance of a constant is 0. In this case, a=1, so we're left with V[X+2]=V[X], as expected.

5 0
3 years ago
Use the equation t^2p=3vb^3−t^2pnr to answer the question. How can you rearrange the equation to isolate b?
lukranit [14]

Answer:

its b

Step-by-step explanation:

4 0
3 years ago
A rectangular library has a length os 36 feet and a perimeter of 116 feet what is the width in feet of the library
Vera_Pavlovna [14]
Answer: The width of the library is 22feet.

Perimeter = length+ length+ width+ width

The problem is telling us that the perimeter is 116 and the length is 36. So let’s plug it in and solve for width which equal w
w= width
Step 1: 116= 36+ 36+ w+w

Step 2: 116=72+ 2w

Step 3: 116= 72+2w
-72 -72

Step 4: 44=2w

Step 5: divide 2w on both sides ( 44 divided by 2)

Step 6: w= 22
5 0
3 years ago
PLS HELP WILL MARK BRAINLEST!!
GenaCL600 [577]

Answer:

x=147

(x-24) = 123

Step-by-step explanation:

x + (x-24)=360

since all paralelograms equal up to 360

simplify 2x - 24 = 260

add 24 on both sides to isolate

2x = 294

divide both sides by 2

x = 147

(x-24) = 123

3 0
3 years ago
Read 2 more answers
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