I am reviewing for my final exam on December 11. I'm working on a practice sheet and I want to know if my answers are correct.
1) Find the equation of the line passing through the points (1,3) and (5,2). Put into slope-intercept if possible?
2-3/5-1= -1/4
y-3=-1/4(x-1)
y=-1/4x+13/4
2) Determine the simple interest rate at which $1000 grows to $1,300 in 300 days?
A= 1,300 P=1,000 T=1 (1 year right? Since the unit is by years I'm guessing)
1300=1000 (1+r)
=.3=r
3) How much money should be deposited in a bank earning interest at 3.0% per year compounded monthly such that at the end of 5 years, the amount will be $30,000?
m= 12 (since it's monthly) t= 5 (5 years) r=0.03 A=$30,000
30,000=p(1+0.03/12)^12*5
= 3.14
4) 50% of the fruit on a farm is pick your own. 25% of all the fruit that is picking your own and apples. What is the percentage of fruit that is apples given that it is pick-your own?
p(A) = Pick your own p(B) = apples
Find P(B l A) I'm guessing:
p(B l A) = P(BintersectA)/p (A) = .25/.50 = .5
Thats what the calculator gave me and the question was actually written like that. It was on a review sheet.
But are 3 and 4 set up right? That's all I'll ask and I'll shut up.
I think I used the wrong formula for 3.
Actually, the formula for #3 is correct. I have no idea how you ended up with 3.14 ... I got 25826.10
1) To find the equation of a line passing through two points, you can use the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
To find the slope (m), you can use the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.
Using the given points (1,3) and (5,2), we can calculate the slope:
m = (2 - 3) / (5 - 1) = -1 / 4
So the slope (m) of the line is -1/4.
To find the y-intercept (b), you can substitute one of the points into the equation and solve for b.
Using (1,3):
3 = (-1/4)(1) + b
3 = -1/4 + b
b = 13/4
So the y-intercept (b) is 13/4.
Therefore, the equation of the line passing through the points (1,3) and (5,2) in slope-intercept form is:
y = (-1/4)x + 13/4
2) To determine the simple interest rate, you can use the formula: A = P(1 + rt), where A is the final amount, P is the principal amount, r is the interest rate, and t is the time in years.
Given that A = 1300, P = 1000, and t = 1, we can solve for r:
1300 = 1000(1 + r)
Dividing both sides by 1000:
1.3 = 1 + r
Subtracting 1 from both sides:
0.3 = r
So the interest rate is 0.3, which is equivalent to 30%.
3) To calculate the amount of money that should be deposited, you can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the interest rate per period, n is the number of compounding periods per year, and t is the number of years.
Given that A = 30000, r = 0.03, n = 12, and t = 5, we can solve for P:
30000 = P(1 + 0.03/12)^(12*5)
Dividing both sides by (1 + 0.03/12)^(12*5):
P = 30000 / (1 + 0.03/12)^(12*5)
Calculating this expression will give you the value of P, which is the amount of money that should be deposited.
4) To find the percentage of fruit that is apples given that it is pick-your-own, you can use conditional probability.
Let p(A) represent the probability of pick-your-own and p(B) represent the probability of apples.
We want to find p(B|A), which represents the probability of apples given that it is pick-your-own.
The formula for conditional probability is p(B|A) = p(B ∩ A) / p(A), where p(B ∩ A) represents the probability of both apples and pick-your-own.
Given that p(B ∩ A) = 0.25 and p(A) = 0.5, we can calculate p(B|A):
p(B|A) = p(B ∩ A) / p(A) = 0.25 / 0.5 = 0.5
So the percentage of fruit that is apples, given that it is pick-your-own, is 50%.
#1 ok
#2 is correctly calculated, but the interest rate is 30%
#3 seriously? Did you ask yourself whether $3.14 could grow to #30,000 in 5 years?
#4 Can't tell. Your whole question is impossible to parse. That can't be the way it was written.