Answer:
a = 6 units
Step-by-step explanation:
Given:
Let Labelled the diagram first
Δ ABC right angle at ∠ C = 90°
∠ B = 45 °
AB = c
BC = a
AC = 6
To Find:
a =?
c =?
Solution:
In Δ ABC
∠ A + ∠ B + ∠ C = 180°.....{Angle Sum Property of a Triangle}
∴ ∠ A + 45 + 90 = 180°
∴ ∠ A = 180 - 135
∴ ∠ A = 45°
Now ∠ A = ∠ B = 45° in Δ ABC
∴ Δ ABC is an Isosceles Triangle.
∴ Two sides are equal of an Isosceles Triangle.
∴ AC = BC = a = 6 units
Now for c we use Pythagoras theorem
Substituting the given values we get
c² = a² + 6²
c² = 6² + 6²
c² = 36 + 36
c² = 72
∴ c = ±√72
as c cannot be negative
∴ 
a = 6 units
Answer:
Step-by-step explanation:
<u>Probabilities</u>
The question describes an event where two counters are taken out of a bag that originally contains 11 counters, 5 of which are white.
Let's call W to the event of picking a white counter in any of the two extractions, and N when the counter is not white. The sample space of the random experience is
We are required to compute the probability that only one of the counters is white. It means that the favorable options are
Let's calculate both probabilities separately. At first, there are 11 counters, and 5 of them are white. Thus the probability of picking a white counter is
Once a white counter is out, there are only 4 of them and 10 counters in total. The probability to pick a non-white counter is now
Thus the option WN has the probability
Now for the second option NW. The initial probability to pick a non-white counter is
The probability to pick a white counter is
Thus the option NW has the probability
The total probability of event A is the sum of both
Answer:
There is no unique solution to this problem.
There are infinitely many solutions to this problem.
Step-by-step explanation:
Let B denotes broccoli crop
Let S denotes spinach crop
Last year, he grew 6 tons of broccoli per acre and 9 tons of spinach per acre, for a total of 93 tons of vegetables.
Mathematically,
6B + 9S = 93 eq. 1
This year, he grew 2 tons of broccoli per acre and 3 tons of spinach per acre, for a total of 31 tons of vegetables.
Mathematically,
2B + 3S = 31
2B = 31 - 3S
B = (31 - 3S)/2 eq. 2
Substitute eq. 2 into eq. 1
6B + 9S = 93
6[(31 - 3S)/2] + 9S = 93
3(31 - 3S) + 9S = 93
93 - 9S + 9S = 93
- 9S + 9S = 93 - 93
0 = 0
Therefore, there is no unique solution to this problem.
Which means that there are infinitely many solutions to this problem.
9514 1404 393
Answer:
$0.50/lb
Step-by-step explanation:
The increase in cost is $40-25 = $15 for an increase in weight of 50-20 = 30 lb. That makes the cost per pound be ...
cost/pounds = $15/(30 lb) = $0.50/lb
