Answer:
19. -3
20. 4
21. 6/7
Step-by-step explanation:
Since the variables are proportional, you can multiply the given x value by the new/old ratio of y-values.
19. x = 6/4(-2) = -3
20. x = (12/6)(2) = 4
21. x = (3/7)(2) = 6/7
To reduce the average cost per item to less than $500, it is necessary to produce more than 20 items according to the function C(x)=300x+6000.
The function C(x)=300x+6,000 represents the cost to produce x items. The average cost per item is given by C(x)/x. We need to find when this average cost is less than $500.
Setting up the inequality, we get C(x)/x < 500. Substituting the value of C(x) into the inequality, we get (300x + 6000)/x < 500. Simplifying this inequality, we end up with: x > 20.
Therefore, more than 20 items need to be produced for the average cost to be less than $500.
#SPJ3
Answer:
More than 30 items
Step-by-step explanation:
C(x)=300x+6,000
First, find c(x), the average cost function.
c(x)c(x)=C(x)x=300x+6,000x
The average cost function is shown below.
c(x)=300x+6,000x
We want the function c(x) to be less than 500.
c(x)<500
Substitute the rational expression for c(x).
300x+6,000x<500x≠0
Subtract 500 to get 0 on the right.
300x+,6000x−500<0
Find the LCD, and rewrite the left side as one quotient.
300x+6,000x−500xx−200x+6,000x<0<0
Factor the numerator to show all factors.
−200(x−30)x<0
Find the critical points when the numerator or denominator are equal to 0.
−200(x−30)−200≠0x−30x=0x=0=0=30
More than 30 items must be produced to keep the average cost below $500 per item.
Answer:
20.4 years
Step-by-step explanation:
The future value formula is ...
FV = P(1 +r/n)^(nt)
where P is the principal invested (6000), n is the number of times per year compounding occurs (12), r is the interest rate (.045), and t is the number of years.
Perhaps you're interested in a future value of $15,000 (not 1500). Then we can find t from ...
15000 = 6000(1 +.045/12)^(12t)
2.5 = 1.00375^(12t) . . . . . divide by 6000
log(2.5) = 12t·log(1.00375) . . . . . take logarithms
log(2.5)/(12log(1.00375)) = t ≈ 20.4
It will take 20.4 years for the investment to reach $15,000.
Sorry it took a long time.
Answer:
Thor is the best deal.
Step-by-step explanation:
Thor is $10.35, Lemon is $11.73, Patrick is $14.66, and Sarah is $16.63.
For Thor, multiply $1.15(2)=$2.30. Then multiply $1.15(7)=$8.05. Add these together to get $10.35.
For Lemon, multiply 17($1.15)=$19.55. Then subtract by $7.82 to get $11.73.
For Patrick, use the equation we already did 17($1.15) and subtract $4.89 from it to get $14.66.
Last, For Sarah multiply our $19.55 (.15) to find 15% and get 2.934. Then subtract $19.56 - 2.934 to get $16.626. Round to $16.63.
Hope this helped!
Answer:
Sarah's Store
Step-by-step explanation:
1001-1400 1
1401-1800 11
1801-2200 14
2201-2600 38
2601 3000 36.
Answer:
The mean monthly salary of these 100 graduates is $2388.5
Step-by-step explanation:
First, lets make all of the salaries a set, so:
S = {S1,S2,S3,S4,S5}
where
S1 = {1001-1400}
S2 = {1401-1800}
S3 = {1801-2200}
S4 = {2201-2600}
S5 = {2601-3000}
Each element S1,S2,..,S5 will have it's own mean, that will be the upper range + lower range divided by 2.
So
M(S1) = (1400+1001)/2 = 2401/2 = 1200.5
M(S2) = (1401+1800)/2 = 3201/2 = 1600.5
M(S3) = (1801+2200)/2 = 4001/2 = 2000.5
M(S4) = (2201+2600)/2 = 4801/2 = 2400.5
M(S5) = (2601+3000)/2 = 5601/2 = 2800.5
To find the approximate mean, now we calculate a weigthed mean between M(S1),M(S2),...,M(S5)
So the mean will be
M = (M(S1)+11*M(S2)+14*M(S3)+38*M(S4)+36*M(S5))/100
M = 238850/100
M = 2388.5
So the mean monthly salary of these 100 graduates is $2388.5
2. 245.00
3. 246.08
Answer:
246.000
Step-by-step explanation:
Well If you take it and Line it up like this,
(A)Amy; 58.75
(J)Jeremy; A+23.25
(O)Oscar; A+23.25= ?x3
This is an easy way to find out what it is you need to do, So A+23.25 is 58.75+23.2 which should give you the value of 82, which brings you to the next step of A+23.25= ?x3 which in this you only wanna focus on the ?x3, we now know ?= 82 so this brings it to 82 times 3 which gives you a value of 246. Thus giving you your answer.
Hope this helps.