X = 1 hr lessons and y = 1/2 hr lessons
x + y = 35......y = 35 - x
40x + 25y = 1115
40x + 25(35 - x) = 1115
40x + 875 - 25x = 1115
40x - 25x = 1115 - 875
15x = 240
x = 240/15
x = 16 <=== there are 16 one-hr lessons
and 19 half-hr lessons
Answer:
Height of each triangle: 14cm
Area of each triangle: 168cm²
Step-by-step explanation:
So we know that the base of the area is 24. Lets find the height.
336 ÷ 24 = 14
If he makes two triangles out of the rectangle that just means he cuts it in half.
To find the area of one triangle lets do:
336 ÷ 2 = 168
Let's double check our answer:
(14 × 24) ÷ 2 = 168
Seems great!
Answer:
For first lamp ; The resultant probability is 0.703
For both lamps; The resultant probability is 0.3614
Step-by-step explanation:
Let X be the lifetime hours of two bulbs
X∼exp(1/1400)
f(x)=1/1400e−1/1400x
P(X<x)=1−e−1/1400x
X∼exp(1/1400)
f(x)=1/1400 e−1/1400x
P(X<x)=1−e−1/1400x
The probability that both of the lamp bulbs fail within 1700 hours is calculated below,
P(X≤1700)=1−e−1/1400×1700
=1−e−1.21=0.703
The resultant probability is 0.703
Let Y be a lifetime of another lamp two bulbs
Then the Z = X + Y will follow gamma distribution that is,
X+Y=Z∼gamma(2,1/1400)
2λZ∼
X+Y=Z∼gamma(2,1/1400)
2λZ∼χ2α2
The probability that both of the lamp bulbs fail within a total of 1700 hours is calculated below,
P(Z≤1700)=P(1/700Z≤1.67)=
P(χ24≤1.67)=0.3614
The resultant probability is 0.3614
Answer:
Step-by-step explanation:
Sales tax 25000(0.07) = $1,750.00
Property tax (25000 / 1000)(14.62) <u>= + $ 365.50</u>
Total tax $ 2115.50
44 - 9 = 35
If we have 44 apples and we take away 9, we have 35 left.
