To check which of the quotients is correct, multiply 43 times 20 and add the remainder. The result must be equal to 876.
First, notice that 20 times 43 equals 860.
A)
The remainder is 17. 860 + 17 = 877, which is not equal to 876.
B)
The remainder is 16. 860 + 16 = 876, which is equal to 876.
C)
The remander is 7. 860 + 7 = 867, which is not equal to 876.
D)
The remainder is 6. 860 + 6 = 866, which is not equal to 876.
Since 20*43 + 16 = 876, then the correct quotient is shown in option B:
876 ÷ 43 = 20 r 16
Explanation:
first find the slope m of the line passing through the
the 2 given points
to calculate the slope m use the
gradient formula
∙
x
m
=
y
2
−
y
1
x
2
−
x
1
let
(
x
1
,
y
1
)
=
(
1
,
3
)
and
(
x
2
,
y
2
)
=
(
−
5
,
6
)
m
=
6
−
3
−
5
−
1
=
3
−
6
=
−
1
2
given a line with slope m then the slope of a line
perpendicular to it is
∙
x
m
perpendicular
=
−
1
m
hence
m
perpendicular
=
−
1
−
1
2
=
2
the equation of a line in
slope-intercept form
is.
∙
x
y
=
m
x
+
b
where m is the slope and b the y-intercept
here
m
=
2
y
=
2
x
+
b
←
is the partial equation
to find b substitute
(
−
2
,
7
)
into the partial equation
7
=
−
4
+
b
⇒
b
=
7
+
4
=
11
y
=
2
x
+
11
←
is the required equation
Assuming these are two six-sided dice, you'll have 36 total combinations to test out. To get the 36, I just multiplied the 6 sides on both dice (6x6=36). First you have to test out all the possible combinations. Making it easier for you, I'll just list the ones that work. The combinations that work are 3+6, 4+5, 5+4, and 6+3. This means there are 4 combinations that work out of 36. This gives us the fraction 4/36. Now, this needs to be simplified. Both numbers are divisible by four, so we'll divide by four. The new fraction is 1/9, which is your answer. This means that, statistically speaking, if you rolled those two dice nine times, the sum of the numbers would be 9 only once. You have an 11% chance of having two numbers on the dice that have a sum of 9.
9 and then 4 for every 9 goldfish, there are 4 gallons of water
