Answer:
There are 685464 ways of selecting the 5-card hand
Step-by-step explanation:
Since the hand has 5 cards and there should be at least 1 card for each suit, then there should be 3 suits that appear once in the hand, and one suit that apperas twice.
In order to create a possible hand, first we select the suit that will appear twice. There are 4 possibilities for this. For that suit, we select the 2 cards that appear with the respective suit. Since there are 13 cards for each suit, then we have 
possibilities. Then we pick one card of all remaining 3 suits. We have 13 ways to pick a card in each case.
This gives us a total of 4*78*13³ = 685464 possibilities to select the hand.
Answer:
<u>Given expression:</u>
<u>The first root is valid when:</u>
- 2x + 2 ≥ 0 ⇒ 2x ≥ - 2 ⇒ x ≥ - 1
<u>The second root is valid when:</u>
- 6 - 4x ≥ 0 ⇒ 4x ≤ 6 ⇒ x ≤ 1.5
<u>So the variable x can get values within interval:</u>
- -1 ≤ x ≤ 1.5 or
- x = [-1, 1.5]
A) Angle A has to be congruent to Angle D
Answer:
k = 0.25
Step-by-step explanation:
The standard equation of a proportional relationship is
y = kx ← k is the constant of proportion
y = 0.25x ← is in this form
with k = 0.25
Missing information
Take local speed ad 30 mph and express your answer in miles
Answer:
7.5 miles
Step-by-step explanation:
Time for lunch is 1 hour but once will wait for 30 minutes before served and eat.
Out of 1 hour, 30 mins is for service and eating to mean time to get from work to restaurant, to and fro is the other 30 mins
Since 30 mins is for to and fro, then one way direction takes 15 mins.
Speed, s=d/t and distance d=speed*time
Given local speed of 30 mph and time as 15 mins,
To convert minutes to hours, we divide it by 60 hence the distance is
30*15/60=7.5 miles
Therefore, the student can go to a restaurant that is 7.5 miles from the office.
