Answer: In the beginning he was given 27 sweets.
Step-by-step explanation: The most logical thing to do is to solve it backwards, that is, from what he had at the end of the third day up till the beginning of the first day.
On the third day he ate one-third and had 8 sweets left over. To determine how many he started with on the third day, let the total on day three be called a. If one-third of a is eaten, then the left over which is two-thirds is 8. That is;
8/a = 2/3
By cross multiplication we now have
8 x 3 = 2a
24/2 = a
a = 12
Let the number of sweets he had on day two be called b. If he ate one-third of b and he had 12 left over, then the two-thirds left over is 12 and we now have;
12/b = 2/3
By cross multiplication we now have
12 x 3 = 2b
36 = 2b
36/2 = b
b = 18
Let the number of sweets he had on day one be called x. If he ate one-third of x and he had 18 left over, then the two-thirds left over is 18, and we now have;
18/x = 2/3
By cross multiplication we now have
18 x 3 = 2x
54 = 2x
x = 27
Therefore Tim was given 27 sweets at the beginning.
Answer:
Her expenses are $25 per week.
Step-by-step explanation:
Given :Jessica earns a commission on each sale but has to pay for her own expenses.
She writes the equation of the function like this:
, where x is the number of doors she knocks on during the week and E(x) is her earnings for the week in dollars.
To Find: Which of the following are reasonable interpretations of the y-intercept of Jessica's function?
Solution:

x is the number of doors she knocks on during the week
E(x) is her earnings for the week in dollars.
Calculate y intercept
Substitute x = 0

Since E(x) is her total earning after clearing the payment of all her expenses.
So, 25 is her expenses per week.
Since we are given that she need to pay her expenses .
So, if there is no sale , still she need to pay expenses.
Thus the reasonable interpretations of the y-intercept of Jessica's function is Her expenses are $25 per week.
Answer:
Year in which the entrepreneur break even is 4
Step-by-step explanation:
We are given:
p(x) = x^3-4x^2+5x-20
We would find the value of x
Solving:
x^3-4x^2+5x-20 = 0
(x^3-4x^2)+(5x-20) = 0
x^2(x-4)+5(x-4) = 0
(x-4)(x^2+5)=0
=> x-4 = 0 and x^2+5 =0
x = 4 and x^2 = -5
x = 4 and x = ±√-5 or ±√5 i (not real solutions)
So, x = 4
So, year in which the entrepreneur break even is 4
Let the price of 1 shirt be represented by = s
A pair of pants costs twice as much as a shirt, then the cost of pants is = 2s
The total cost of 1 pair of pants and 1 shirt is $18 , means : 
Solving this we get,


So, the price of 1 shirt is $6 and price of 1 pair of pants is = 2s = 2*6 = $12.
Answer: 
Step-by-step explanation:
Using Pythagoras theorem , since it is a right angled triangle ,
side 1 = 10cm
side 2 = x cm
side 3 = x cm
Pythagoras theorem states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides. That is

100 = 
divide through by 2 , we have
50 = 
find the square root of both sides

