A young boy dropped his deck of baseball cards. Unwilling to count them again he remembered that when he put them in piles of two, there was one card left over. When he put them in stacks of three, there was one card left over. The same thing happened for stacks of 4, 5, 6, but when he put them in stacks of 7, there were no cards left over!How many cards did the boy have? Is there only one possibility? Can you generalize a solution?

Answers

Answer 1

Answer: so if he put them in 2 stacks and there was 1 card left over, he has an odd number of cards

when he put them in 3 stacks there was 1 card left over
we can tell that if he took away one of his card and divided
the stack of cards by two or three the number would be the
same

so he divides it by 4 5 and 6 so the number of cards is not divisible by 2,3,4,5,6
but it is divisable by 7
so we must find a number that when you subtract one you can divide it by 2,3,4,5,6
so i just guessed a term from 7^n
so 49 doesn't work because 48 doesn't divide into 5
343 doesn't work because 342 doesn's divide by 6
but 2401 (7^4) works because 2400 divides evenly by 2,3,4,5, and 6

Just a note, this number is not very logical that he would have time to count them all but hey, it's math

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A square has sides 10x. write and simplify an expression for the perimeter of that square

Answers

One side = 10x and a square has 4 equal sides.
10x * 4=40x

1+4=5 2+5=12. 3+6=21. 8+11=?

Answers

Hi there this is a puzzle question. So lets get to the answer. If 1+4=5 then we take 1+(4*1)=5. 2+5=12 so lets take 2+(5*2)=12. 3+6=21 so lets take 3+(6*3)=21. After all of this you should probably know now that I multiplied the first number with the second number then added both of the numbers. So, 8+11=8+(11*8)=8+88=96. Therefore, the answer is 96.

Find the unit rate. Round your answer to the nearest hundredth.3500 calories for 6 servings of pie

Answers

3500cals/6 servings

583 1/3 cals per serving.

583 calories per serving.

Can someone help me and explain step by step?

Answers

I'm not a master of probabilities, but I reckon the answer is 3/16.

The probability that the first spin lands on blue is $(6)/(8)$ (6 blue sections of all possible 8)
The probability that the second spin lands on grey is $(2)/(8)$ (2 gray sections of all possible 8)

So, the probability that the first spin lands on blue and the second spin lands on grey is $(6)/(8)\cdot(2)/(8)=(3)/(4)\cdot(1)/(4)=\boxed{(3)/(16)}$

The population of bacteria in a petri dish doubles every 24 h. The population of the bacteria is initially 500 organisms.How long will it take for the population of the bacteria to reach 800?

Round your answer to the nearest tenth of an hour.

Answers

Answer:

16.3h

Step-by-step explanation:

population 2x in 24 h

going from 500 to 800 is less than double so ans is <24h

solving t: 2^(t/24)=800/500

t/24=ln(8/5)/ln2

t=24*ln(8/5)/ln2

=16.3

Find the solutions to sin2(x) + cos(x) = 1, keeping 0 ≤ x < 2π

Answers

sin2(x) +cos(x)=1
from the relation: (sin2(x) +cos2(x) =1 )
so , sin2(x)=1-cos2(x)
by subs. in the main eqn.
1-cos2(x) + cos(x) =1
by simplify the eqn.
cos(x) -cos2(x)=0
take cos(x) as a common factor
cos(x)* (1-cos(x))=0
then cos(x)=0 && cos(x)=1
cos(x)=0 if x= pi/2
& cos(x) = 1 if x = 0 , 2*pi
so the solution is x= {0,pi/2 , 2*pi}

Answer:

Which statements did you include in your answer?

Isolate sin(x) by adding 4 and taking the square root of both sides.

State that sin(x) = 2 or sin(x) = –2.

State that –2 and 2 are undefined values of the inverse sine function.

There are no solutions because –2 and 2 are not in the domain of the function.

Step-by-step explanation:

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