A county in Oklahoma has a current population of 5847 people. This number has decreased over the last 5 years. On average, it ha
2 answers:
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Answer:
The values are:
Step-by-step explanation:
Given:
- P = (x₁, y₁, z₁) = (1, 2, b)
- Q = (x₂, y₂, z₂) = (c, -7, 4)
- m = R = (x, y, z) = (-3, a, -1)
To Determine:
a = ?
b = ?
c = ?
Determining the values of a, b, and c
Using the mid-point formula
- As the point R(-3, a, -1) is the midpoint of the line segment jointing the points P(1,2,b) and Q(c,-7,4), so
- m = R = (x, y, z) = (-3, a, -1)
Using the mid-point formula
given
(x₁, y₁, z₁) = (1, 2, b) = P
(x₂, y₂, z₂) = (c, -7, 4) = Q
m = (x, y, z) = (-3, a, -1) = R
substituting the value of (x₁, y₁, z₁) = (1, 2, b) = P, (x₂, y₂, z₂) = (c, -7, 4) = Q, and m = (x, y, z) = (-3, a, -1) = R in the mid-point formula
as (x, y, z) = (-3, a, -1), so
<u>Determining 'c'</u>
-3 = (1+c) / (2)
-3 × 2 = 1+c
<u>Determining 'a'</u>
a = (2+(-7)) / 2
<u>Determining 'b'</u>
-1 = (b+4) / 2
Therefore, the values are:
Answer:
The probability that the card will be a heart or a face card is P=0.4231.
Step-by-step explanation:
We have a standard deck of 52 cards.
In this deck, we have 13 cards that are a heart.
We also have a total of 12 face cards (4 per each suit). So there are 3 face cards that are also a heart.
To calculate the probability that a card be a heart or a face card, we sum the probability of a card being a heart and the probability of it being a face card, and substract the probability of being a heart AND a face card.
We can express that as: