Answer:
The equation of the line in standard form is
Step-by-step explanation:
The equation of the line in point slope form is
we have
so
step 2
Find the equation of the line in standard form
The equation of the line in standard form is
where
A is positive integer
B and C are integers
we have
Multiply by 4 both sides to remove the fraction
Answer: 14,000 i think
Step-by-step explanation:
We have the following equation:
x2 + y2 + 42x + 38y - 47 = 0
We rewrite the equation:
x2 + 42x + y2 + 38y - 47 = 0
x2 + 42x + y2 + 38y = 47
Rewriting we have:
x2 + 42x + (42/2) ^ 2 + y2 + 38y + (38/2) ^ 2 = 47 + (42/2) ^ 2 + (38/2) ^ 2
x2 + 42x + 441 + y2 + 38y + 361 = 47 + 441 + 361
Rewriting we have:
(x + 21) ^ 2 + (y + 19) ^ 2 = 849
The center of the circle is:
(x, y) = (-21, -19)
The radio is:
r = root (849)
r = (849) ^ 2
A circle of the same radius is given by:
x ^ 2 + y ^ 2 - 50x - 30y + 1 = 0
Let's check:
x ^ 2 - 50x + y ^ 2 - 30y + 1 = 0
x ^ 2 - 50x + y ^ 2 - 30y = - 1
x ^ 2 - 50x + (-50/2) ^ 2 + y ^ 2 - 30y + (-30/2) ^ 2 = - 1 + (-30/2) ^ 2 + (-50/2) ^ 2
x ^ 2 - 50x + (-50/2) ^ 2 + y ^ 2 - 30y + (-30/2) ^ 2 = - 1 + 225 + 625
(x-25) ^ 2 + (y-15) ^ 2 = 849
Answer:
(x + 21) ^ 2 + (y + 19) ^ 2 = 849
(x, y) = (-21, -19)
r = (849) ^ 2
x ^ 2 + y ^ 2 - 50x - 30y + 1 = 0
Given :
For the school's sports day, a group of students prepared 12 1/2 litres of lemonade. At the end of the day they had 2 5/8 litres left over.
To Find :
How many litres of lemonade were sold.
Solution :
Initial amount of lemonade, I = 12 1/2 = 25/2 litres.
Final amount of lemonade, F = 2 5/8 = 21/8 litres.
Amount of lemonade sold, A = I - F
A = 25/2 - 21/8 litres
A = 9.875 litres
Therefore, 9.875 litres of lemonade were sold.
Hence, this is the required solution.
Answer:
a) 0.9644 or 96.44%
b) 0.5429 or 54.29%
Step-by-step explanation:
a) The probability that at least 1 defective card is in the sample P(A) = 1 - probability that no defective card is in the sample P(N)
P(A) = 1 - P(N) .....1
Given;
Total number of cards = 140
Number selected = 20
Total number of defective cards = 20
Total number of non defective cards = 140-20 = 120
P(N) = Number of possible selections of 20 non defective cards ÷ Number of possible selections of 20 cards from all the cards.
P(N) = 120C20/140C20 = 0.0356
From equation 1
P(A) = 1 - 0.0356
P(A) = 0.9644 or 96.44%
b) Using the same method as a) above
P(A) = 1 - P(N) .....1
Given;
Total number of cards = 140
Number selected = 20
Total number of defective cards = 5
Total number of non defective cards = 140-5 = 135
P(N) = 135C20/140C20 = 0.457
From equation 1
P(A) = 1 - 0.4571
P(A) = 0.5429 or 54.29%
