Response:
Detailed explanation:
The timing data for each lap will form an arithmetic progression (AP) with a first term of 25 s and a common difference of 1.6 s.
a )
first term a = 25
common difference d = 1.6.
The 10th term of the sequence can be found using the formula
a₁₀ = 25 + (10-1) x 1.6
= 25 + 1.6 x 9
= 39.4 s
b )
Let n be the final lap
a(n) = a + (n-1) x d
55.4 = 25 + (n-1) x 1.6
n - 1 = 19
n = 20.
c )
The total for all terms in the AP
=(first term + last term) x number of terms / 2
= (25 + 55.4) x 20 / 2
= 804 s.
= 804 / 60 min
= 13.4 min.
We will require the table mentioned above to respond to this inquiry.
Answer:
4 nickels
12 dimes
Step-by-step explanation:
Dimes have a value of $0.10 each, while nickels are worth $0.05 each.
There are 8 more dimes than nickels. Let d represent the count of dimes and n represent nickels, so d equals n plus 8.
The total value of nickels and dimes is $1.40, giving the equation 0.10d + 0.05n = 1.40.
Combining equations:
d = n + 8
0.10d + 0.05n = 1.40
— Substitute the first into the second:
0.10(n + 8) + 0.05n = 1.40
Distribute terms:
0.8 + 0.10n + 0.05n = 1.40
Combine like terms:
0.8 + 0.15n = 1.40
Subtract 0.8 from both sides:
0.15n = 0.6
Divide both sides by 0.15:
n = 0.6 / 0.15 = 4
Since there are 8 more dimes, d = 4 + 8 = 12.
Let x represent the desired warranty duration, thus
P(X < x) = P(z < (x - 12)/(8/12)) = 1 - 0.067 = 0.933
P(z < 12(x - 12)/8) = P(z < 1.498)
12(x - 12)/8 = 1.498
x - 12 = 8(1.498) / 12 = 0.9987
x = 12 - 0.9987 = 11
Thus, they ought to warranty for 11 years to ensure that fewer than 6.7% encounter failures during that timeframe.
production cost = %13
Let p be the price, then
revenue minus the cost of failed units = p - 0.067(13) = p - 0.871
Profit = p - 0.871 - 13 = 5
p - 13.871 = 5
p = 5 + 13.871 = 18.871
Consequently, they need to price each waffle iron at $18.87.
