Answer:
Two systems of equations are equivalent if they have the same solution(s).
Answer:
Function 2 has a greater initial valueStep-by-step explanation:An initial value of a function, aka y-intercept, is obtained by using x=0 and evaluating the function at that point. Evaluating the two functions given:Function1: Function2 has value 3 for x=0So, Function 2 has a greater initial valueFunction 2 has a greater initial valueStep-by-step explanation:An initial value of a function, aka y-intercept, is obtained by using x=0 and evaluating the function at that point. Evaluating the two functions given:Function1: Function2 has value 3 for x=0So, Function 2 has a greater initial value
Step-by-step explanation:
Answer:
- Library 2 charges more for each book loaned.
- Library 1 has a cheaper subscription fee.
Step-by-step explanation:
Based on the table, we can write the equation for the cost of borrowing from Library 2 using the two-point form of the equation of a line:
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
for (x1, y1) = (2, 15.50) and (x2, y2) = (8, 26) this equation becomes ...
y = (26 -15.50)/(8 -2)(x -2) +15.50 . . . . . fill in the values
y = (10.50/6)(x -2) +15.50 . . . . . . . . . . . . simplify a bit
y = 1.75x -3.50 +15.50 . . . . . . simplify more
In the above, we have x = number of books; y = cost. We can use "n" and "C" for those, respectively, as in the equation for Library 1. Then the monthly cost for Library 2 is ...
C = 12 + 1.75n . . . . . . . arranged to the same form as for Library 1
_____
Now, we can answer the questions.
Library 2 charges more for each book loaned. (1.75 vs 1.50 for Library 1)
Library 1 has a cheaper subscription fee. (10 vs 12 for Library 2)
_____
The numbers in the cost equations are ...
C = (subscription fee) + (cost per book loaned)·n
Answer:
P(2U5) = 7/21 = 1/3
the probability of getting either a 5 or a 2 in one throw is 1/3
Step-by-step explanation:
Given that; the probability of each face turning up is proportional to the number of dots on that face
P(1) = 1×P(1)
P(2) = 2×P(1)
P(3) = 3×P(1)
P(4) = 4×P(1)
P(5) = 5×P(1)
P(6) = 6×P(1)
P(T) = 21×P(1)
Where;
P(x) is the probability of getting number x on the dice.
P(T) is the total probability of obtaining any number
N(x) is the number of possible number x in terms of the distribution function.
P(x) = N(x)/N(T) ....1
And since P(T) is constant, and P(T) is proportional to N(T) then,
P(x) is directly proportional to N(x)
So, equation 1 becomes;
P(x) = N(x)/N(T) = P(x)/P(T) ....2
The probability of getting either a 5 or a 2 in one throw
P(2U5) = (P(2) + P(5))/P(T)
Substituting the values of each probability;
P(2U5) = (2P(1) + 5P(1))/21P(1)
P(2U5) = 7P(1)/21P(1)
P(1) cancel out, to give;
P(2U5) = 7/21 = 1/3
the probability of getting either a 5 or a 2 in one throw is 1/3
48 - 896.00 = 884
884-800=84
so the interest rate was 84
