ms. mckee wants to give each student in her class some candy. She wants everyone to recieve an equal number of jelly beans. She has less than 100 jellybeans. If she makes groups of 2,3, or 4 she will have 1 jelly bean left over. If she makes groups of 5, she will have no jellybeans left over, How many jellybeans could she have?
Answers
means that it ends with 5 or 0
possible ones are
5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90,95
groups of 2, will have 1 jelly bean left over
it is not divisble by 2, means it doesn't end with 0 (ending with 0 means it is divisible by 10, and 10 is divisible by 2)
5,15,25,35,45,55,65,75,85,95
groups of 3
not divisble by 3 (a hack to test, is that you add the digits and if the sum is divisble by 3, then the number is divisble), the list below is eliminated numbers divisble by 3
5,25,35,55,65,85,95
if makes group of 2 will have exactly 1 left over
5/3 has remainder of 2, eliminate
25 works so far (2*12=24,3*8=24,4*6=24)
35/4 has remainder of 3, eliminate
55/4 has remainder of 3, eliminate
65/3 has remainder of 2, eliminate
85 works
95/3 has remainder of 2,eliminate
the ones that work are 25 aand 85
she could have 25 or 85 jelly beans
12, 24, 36, 48, 60, 72, 84, 96 (we stop listing here because the number of jelly beans is less than 100)
this also means the possible number of jelly beans she can have is the numbers in the previous list plus 1 (remember it is x-1 NOT x that is the common multiple of 2, 3, 4):
13, 25, 37, 49, 61, 73, 85, 97
now we use our last clue which is if the teacher groups her jelly beans in groups of 5 there will be none left over. this is equivalent to saying that the number of jelly beans is a multiple of 5. we look through our 2nd list and find that only 25, and 85 is a multiple of 5. therefore the number of jelly beans the teacher can have is 25 and 85.
note that we took the problem in steps and used process of elimination to determine which of the natural numbers less than 100 can be the answer to the question. this is a very very good strategy in problem solving, but it can be challenging to know what order to take the "steps" but that can be mastered with patient practice.
let me know if you have any questions!!!!
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Answers
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Answers
The right answer is 10√5..
please see the attached picture for full solution
Hope it helps
Good luck on your assignment
Answer:
2nd one
Step-by-step explanation:
If you look at all the factors the highest pair with a square root is 5•100
The square root of 100 is 10
And then the square root of 5 is left
What is the midpoint of the segment shown below?
(-1,2)
(73)
O A. (6,3)
O B. (3,3)
O C. (3.)
O D. (6,5)
10
Answers
The midpoint of the segment is approximately (3, 2.5).
What is a midpoint of a line segment?
The midpoint of a line segment is given as,
x = (a + c)/2
y = (b + d) / 2
Where (x, y) is the midpoint and (a, b) and (c, d) are the two endpoints.
We have,
To find the midpoint of the segment between two points, we take the average of their x-coordinates and the average of their y-coordinates.
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
where (x1, y1) = (-1, 2) and (x2, y2) = (7, 3)
Midpoint
= ((-1 + 7)/2, (2 + 3)/2)
= (6/2, 5/2)
= (3, 2.5)
Therefore,
The midpoint of the segment is approximately (3, 2.5).
Learn more about midpointsoflinesegments here:
#SPJ7
Answer:
Step-by-step explanation:
First, these are points in a plane, hence should be (-1,2) and (7,3)
Then we'll have
-1+7=6/2=3
2+3=5/2=2.5
Then midpoint is (3,2.5)
Answers
The rate of change of f is twice the rate of change of g.
B.
The rate of change of g is twice the rate of change of f.
C.
The rate of change of f is 3 times the rate of change of g.
D.
The rate of change of f is the same as the rate of change of g.
Answers
Answer:
A. The rate of change of f is twice the rate of change of g.
Step-by-step explanation:
The first function is
The slope of this function is the coefficient of x. It is the same as the rate of change of f(x)
From the graph, g(x) passes through(-2,-4) and (0,2)
We use the slope formula: to find the slope of g(x).
Since 6=2(3), we conclude that, the rate of change of f is twice the rate of change of g.
Answer:
A
Step-by-step explanation:
Answers
Answer:
V = 4500 m³
Step-by-step explanation:
The cross section of the swimming pool is a trapezium with parallel sides 1m and 8m (depth of both ends) and 50m (length of pool) as the perpendicular distance between the parallel sides.
The width of pool 1m can be the length of cross section.
Length of swimming pool = 50m
Breadth of the pool = 20m
Depth of the pool=1m and 8m
Let's assume it slopes uniformly, thus;
Volume of water when full;
V = ½[(1 + 8) × 50] × 20 = 25 × 9 × 20
V = 4500 m³
Answer:
4500 m³
Step-by-step explanation:
The surface of a swimming pool is 50-meter long and 20-meter wide rectangle. The pool is 1 meter deep at the shallow end and 8 meters deep at the other end.
The pool can be divided into two sections, the first section (top) is a rectangular prism which sits on top of the bottom section. The second section (bottom) is a triangular prism sits below the top section.
The rectangular prism has a length of 50 m, width of 20 m and a height of 1 m.
The volume of a rectangular prism = length × width × height = 50 × 20 × 1 = 1000 m³
The triangular prism has a base of 50 m, length of 20 m and a height of 8 m - 1 m = 7 m.
The volume of a triangular prism = 1/2 × base × length × height = 1/2 × 50 × 20 × 7 = 3500 m³
The volume of water in the pool = volume of a rectangular prism + volume of a triangular prism = 1000 m³ + 3500 m³ = 4500 m³