Answer:
Step-by-step explanation:
given that a deck of cards is shuffled.
we know in a deck there are 52 cards, 13 cards of each variety spade, clubs hearts and dice. Red are 26 and black are 26. kings, will be 4.
(a) the top card is the king of spades and the bottom card is the queen of spades?
(iii) 1/52 × 1/52
Top has 1/52 and bottom has 1/52 and these are independent.
(b) the top card is the king of spades and the bottom card is the king of spades?
(viii) None of the above
Because it is impossible.
(c) the top card is the king of spades or the bottom card is the king of spades?
(iv) 1/52 + 1/52
This is the sum of probabilities because there is no common event for these two.
(d) the top card is the king of spades or the bottom card is the queen of spades?
(ii) 1/52 + 1/51 (once king of spades is there, then probability is 1/51 for bottom card)
(e) of the top and bottom cards, one is the king of spades and the other is the queen of spades?
(vii) 2/52 × 1/51
Because this is twice of probability d.
The sum of the first 20 terms of an arithmetic sequence with the 18th term of 8.1 and a common difference of 0.25 is 124.5
Given,
18th term of an arithmetic sequence = 8.1
Common difference = d = 0.25.
<h3>What is an arithmetic sequence?</h3>
The sequence in which the difference between the consecutive term is constant.
The nth term is denoted by:
a_n = a + ( n - 1 ) d
The sum of an arithmetic sequence:
S_n = n/2 [ 2a + ( n - 1 ) d ]
Find the 18th term of the sequence.
18th term = 8.1
d = 0.25
8.1 = a + ( 18 - 1 ) 0.25
8.1 = a + 17 x 0.25
8.1 = a + 4.25
a = 8.1 - 4.25
a = 3.85
Find the sum of 20 terms.
S_20 = 20 / 2 [ 2 x 3.85 + ( 20 - 1 ) 0.25 ]
= 10 [ 7.7 + 19 x 0.25 ]
= 10 [ 7.7 + 4.75 ]
= 10 x 12.45
= 124.5
Thus the sum of the first 20 terms of an arithmetic sequence with the 18th term of 8.1 and a common difference of 0.25 is 124.5
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Weird question xD
You have to use the Pythagorean theorem on this one.
a^2 + b^2 = c^2
11^2 + h^2 = 12^2
121 + h^2 = 144
h^2 = 23
h = 4.79583
Rounded to the nearest tenth
The height of the kite is 4.8 ft.
The longest possible altitude of the third altitude (if it is a positive integer) is 83.
According to statement
Let h is the length of third altitude
Let a, b, and c be the sides corresponding to the altitudes of length 12, 14, and h.
From Area of triangle
A = 1/2*B*H
Substitute the values in it
A = 1/2*a*12
a = 2A / 12 -(1)
Then
A = 1/2*b*14
b = 2A / 14 -(2)
Then
A = 1/2*c*h
c = 2A / h -(3)
Now, we will use the triangle inequalities:
2A/12 < 2A/14 + 2A/h
Solve it and get
h<84
2A/14 < 2A/12 + 2A/h
Solve it and get
h > -84
2A/h < 2A/12 + 2A/14
Solve it and get
h > 6.46
From all the three inequalities we get:
6.46<h<84
So, the longest possible altitude of the third altitude (if it is a positive integer) is 83.
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