King Tut has a castle with one hundred rooms that all have doors labeled 1 to 100 that are shut. His crazy son Calvin runs around the castle and opens all the doors. Then he runs around the castle and closes every other door (2, 4, 6, 8, … 100). Then he runs around the castle and when he comes to every third door (3,6,9,12,…99) if it is open he closes it and if it is closed he opens it. He then does the same for every 4th door, then every 5th door and then every 6th door, and so on until then does it for every 100th door. At the end of this exhausting run clearly door 1 is open, but what other door are also open? (hint: Grappling would suggest you try using a smaller number like 20 doors and see if there is a pattern)

answer: ♡♡♡♡♡♡♡♡♡♡

step-by-step explanation:

the speed is   miles per hour > is false

step-by-step explanation:

we know that  

a relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form or

in a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

the graph shown in the figure represent a direct variation

the slope of the line represent the speed

for the point

substitute the values of x and y

the linear equation is equal to

statements

case a) it takes hours to go miles

the statement is true

because

substitute

for

find the value of y in the linear equation

> is correct

case b) the speed is   miles per hour

the statement is false

because the speed is

case c) the unit rate for the trip is

the statement is true

because the speed is equal to the slope of the linear equation

case d) it took minutes to go the first miles

the statement is true

because

substitute

for

find the value of y in the linear equation

> is correct

0 and 5 minutes

step-by-step explanation:

given that one morning eight buses arrive late by the number of minutes given below:

0 8 2 6 9 2 0 7 8

write these in ascending order

0   0 2 6 7 8 8 9

in the afternoon two more buses arrive at the bus stop say by x and y minutes late.

total number of buses = 10

median = average of 4th and 5th after arranging in ascending order

since 4th entry is 6, the values of x and y should be below 6

also given 0 is the mode so either x or y or both should be 0 because then only 0 gets the maximum frequency and hence mode

thus we have

0 0 0 2 6 7 8 8 9 and another unknown entry which is below 6.

since median is 3.5, we have the unknown entry to be 5 only because then only median =( 2+5)/2

thus the after noon buses were late by 0 and 5 minutes.