Answer:
Step-by-step explanation:
In this question, one is asked to multiply a fraction by a whole number, first model the question.
In a situation like this, one multiplies the whole number by the numerator (number) over the fraction.
Simplify,
A common error that people make is that they will multiply both the numerator and denominator by the whole number, this is the same as multiplying the answer by (1), thus it is incorrect.
1/2+1/2=2/2=1 so 1/2 was eaten and the other half was leftovers.
Answer:
B
Step-by-step explanation:
x² - 12x + 11 = 0 ( subtract 11 from both sides )
x² - 12x = - 11
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 6)x + 36 = - 11 + 36
(x - 6)² = 25 ( take square root of both sides )
x - 6 = ± 
= ± 5 ( add 6 to both sides )
x = 6 ± 5
Then
x = 6 - 5 = 1 ⇒ (1, 0 )
x = 6 + 5 = 11 ⇒ (11, 0 )
Team A) 45 people
Team B) 55 people
A)There are two ways to solve this problem, finding the number of combinations possible for Team B, or the number of combinations possible for Team A.
Team A
It's a given that 20 mathematicians are on team A, which leavs the other 25 people for team A to be chosen from a pool of 80 (100- 20 mathletes)
80-C-25 = 80! / (25!/(80-25)!) =<span>363,413,731,121,503,794,368
</span>or 3.63 x 10^20
Solving using Team B
Same concept, but choosing 55 from a pool of 80 (mathletes excluded)
80-C-25 = 80! / (55!(80-55!) = 363,413,731,121,503,794,368
or 3.63 x 10^20
As you can, we get the same answer for both.
B)
If none of the mathematicians are on team A, then we exclude the 20 and choose 45:
80-C-45 = 80! / (45!(80-45)!) = <span>5,790,061,984,745,3606,481,440
or 5.79 x 10^22
Note that, if you solve from the perspective of Team B (80-C-35), you get the same answer</span>
Answer:
<em>mDBC = 341 °</em>
Step-by-step explanation:
Arc DBC is almost the whole circle, if you were to exclude the degree measure of minor arc DC; which is, in other words m∠ DPC
Now by Vertical Angles Theorem:
m ∠ DPC = m∠ APB, ⇒ provided BD, and AC are diameters
m∠ DPC = 19°
This would mean ⇒
mDBC = 360 - m∠ DPC,
mDBC = 360 - 19,
mDBC = 341 degrees ( ° )
