Answer:
12/ 100 ,0.12
Step-by-step explanation:
12 percent is equivalent to 12/100 and 0.12 because if you simplify 12/100 you get 0.12. If you turn 0.12 into a percent you get 12 percent
By the polynomial remainder theorem,
will be a factor of
if the remainder upon division is 0, and this remainder is given by
:
Since
, it follows that
. But notice that if
, then we have
and since
, the equation above requires that either
or
, which is impossible. So
.
So we have 8 cases to check:
(1) Notice that if
, we have
. This is only possible for
.
(2) If
, then
, and so we can have
.
(3) If
, then
, and so
.
(4) If
, then
.
(5) If
, then
.
(6) If
, then
.
(7) If
, then
.
(8) If
, then
.
At the same time, we have 8 cases to consider to find how many options there are for
.
(1)
. We have only one choice of
.
(2)
. This is the same as when
, which we found to be 2 choices.
(3) Same as
; 3 choices.
(4) Same as
; 4 choices.
(5) 5.
(6) 4.
(7) 3.
(8) 2.
In total, there are
ways to choose
such that
is a factor of
, so the answer is B.
Note the symmetry of the sum above. You can easily give a slightly briefer combinatorial argument for this answer, but I figured a more brute-force approach would be easier to follow.
There are so many parts to this question that I would normally skip it ...
I mean, even though there are only 4 letters, it needs 7 answers.
But I was so overcome with shock and awe at the sight of the bountiful
5 points at the end of the rainbow that I just couldn't pass it by.
Tim can paint a house in 6 days.
Tara can paint a house in 3 days.
a). Tim paints 1/6 of a house in one day.
Tara paints 1/3 of a house in one day.
b). In 'd' days, Time can paint d/6 of a house.
In 'd' days, Tara can paint d/3 of a house.
c). In one day, Tim and Tara together can paint (1/6 + 1/3) = 1/2 of a house.
In 'd' days, Tim and Tara together can paint (d/6 + d/3) = d/2 of a house.
d). The number of days it will take Tim and Tara together to paint
a whole house is
N = 1 / (1/6 + 1/3)
N = 1 / (1/2)
N = 2 .
Answer:
h = -16t^2+60t+5
Step-by-step explanation:
We have given that:
Rachel’s ball is modeled by the equation h = –16t2 + 30t + 5.
Dominique throws his tennis ball with the same acceleration, a, from the same initial height, h = -16t2 + 30t - 5, but with an initial velocity, v, double that of Rachel’s.
We have to find:
Which equation best models the height of Dominique’s tennis ball?
<u>Solution:</u>
The equation we have been given is:
h = –16t2 + 30t + 5.
where -16 is the acceleration
30 is the initial velocity
5 is the initial height
So when the initial velocity is doubled then the final equation we get is:
h = -16t^2+60t+5
Thus the equation that models the height of Dominique's tennis ball is
h = -16t^2+60t+5
680,000 is the answer. Hope this helps!