Let the first integer be x. Then the next consecutive integer is x+1.
Translating the word problem into symbols, x(x+1)-20(x+1) = 442.
Then x^2 + x - 20x - 20 = 442
or x^2 - 19x - 462 = 0
Solve by completing the square:
x^2 - 19x + 90.25 - 90.25 - 462 = 0
(x-9.5)^2 - 552.25 = 0
Taking the positive square root of both sides, we get x-9.5 = 23.5, or
x = 33
The two consecutive integers are 33 and 34.
Check: (33)(34)-20(34) = 442 (as expected).
Answer:
(a) The probability of more than one death in a corps in a year is 0.1252.
(b) The probability of no deaths in a corps over 7 years is 0.0130.
Step-by-step explanation:
Let <em>X</em> = number of soldiers killed by horse kicks in 1 year.
The random variable 
.
The probability function of a Poisson distribution is:
(a)
Compute the probability of more than one death in a corps in a year as follows:
P (X > 1) = 1 - P (X ≤ 1)
= 1 - P (X = 0) - P (X = 1)
Thus, the probability of more than one death in a corps in a year is 0.1252.
(b)
The average deaths over 7 year period is: 
Compute the probability of no deaths in a corps over 7 years as follows:
Thus, the probability of no deaths in a corps over 7 years is 0.0130.
Answer:
The amount the school pays is £32.40
Step-by-step explanation:
The cost of each pen = 15 pence
The cost of each ruler = 20 pence
The number of pens bought by the school = 150
The number of rulers bought by the school = 90
The cost reduction (discount) on the items bought = 1/5
Therefore, we have;
The total cost of the pens bought by the school = 150 × 15 = 2250 = £22.50
The total cost of the rulers bought by the school = 90 × 20 = 1800 = £18.00
The total cost of the writing materials (rulers and pens) bought by the school = £22.50 + £18.00 = £40.50
The discount = 1/5 total cost reduction = 1/5×£40.50 = $8.10
The amount the school pays = The total cost of the writing materials - The discount
The amount the school pays = £40.50 - $8.10 = £32.40
The amount the school pays = £32.40.
Answer:
Step-by-step explanation:
(a) H0: μ_D=0
Ha: μ_D ≠ 0
b) Find attached the solution
(c) By technology,
p - value = 0.4437
Hence,
the p-value is 0.4437
Answer:
Step-by-step explanation:
- 13t - 3t = (13 - 3)t = 10t
- 3t - 13t = (3 - 13)t = -10t
- 10t ≠ -10t
They are not equivalent
<u>When t = 2</u>
- 13t - 3t = 13*2 - 3*2 = 26 - 6 = 20
- 3t - 13t = 3*2 - 13*2 = 6 - 26 = -20
