Answer:
a) 0.00031
b) 0.0017
c) 0.31
d) 0.00018
Step-by-step explanation:
attached below is the detailed solution
Total number of 7-poker cards are 52P7 = 133784560
A) Determine the probabilities of Seven-card straight
probability of seven-card straight = 0.00031
B) Determine the probability of four cards of one rank and three of a different rank
P( four cards of one rank and three of different rank ) = 0.0017
C) Determine probability of three cards of one rank and two cards of each two different ranks
P( three cards one rank and two cards of two different ranks ) = 0.31
D) Determine probability of two cards of each of three different ranks and a card of a fourth rank
P ( two cards of each of three different ranks and a card of fourth rank ) = 0.00018
Let the number of hours = X
Multiply the speed of each train by the number of hours (x) and add them together to equal the total miles:
75x + 95x = 238
Simplify:
170x = 238
Divide both sides by 170:
x = 238/170
x = 1.4 hours.
Check:
75 x 1.4 = 105 miles
95 x 1.4 = 133 miles
105 + 133 = 238 miles
It will take 1.4 hours ( 1 hour and 24 minutes).
Answer:
Step-by-step explanation:
#22
<h3>Given </h3>
- Equation x² -4x + 1 = k(x - 4) with equal roots
<h3>To find</h3>
<h3>Solution</h3>
<u>The equation in standard form is:</u>
- x² -4x + 1 = k(x - 4)
- x² - 4x - kx + 1 + 4 = 0
- x² - (k + 4)x + 5 = 0
<u>When the quadratic equation has equal roots its discriminant is zero</u>
- D = 0
- b² - 4ac = 0
- (k + 4)² - 4*5 = 0
- (k + 4)² = 20
- k + 4 = ± √20
- k = - 4 ± √20
- or
- k = -4 ± 2√5
Answer:
=1.5
Step-by-step explanation: