The number of ways in which the name 'ESTABROK' can be made with no restrictions is 40, 320 ways.
<h3>How to determine the number of ways</h3>
Given the word:
ESTABROK
Then n = 8
p = 6
The formula for permutation without restrictions
P = n! ( n - p + 1)!
P = 8! ( 8 - 6 + 1) !
P = 8! (8 - 7)!
P = 8! (1)!
P = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 × 1
P = 40, 320 ways
Thus, the number of ways in which the name 'ESTABROK' can be made with no restrictions is 40, 320 ways.
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First, we define variables:
x: small hat
y: medium hat
z: large hat
We now write the system of equations:
x + y + z = 47
5.50x + 6y + 7z = 302
-3x + y = 0
We can write the system in matrix form as:
Ax = b
Where,
A = [1 1 1; 5.50 6 7; -3 1 0]
b = [47; 302; 0]
x = [x; y ; z]
Solving the system we have:
x = 6
y = 18
z = 23
Answer:
the coach did purchase 23 large hats
d. 23
4/3 • 5/3 = 20/9 divided by 2 = 10/9
Answer:
90
Step-by-step explanation:
Start with changing 35% and 30% to a decimal.
35% = .35%
30% = .30%
Then multiply 105 by .30%. ( but don't put the percent sign in the calculator when multiplying)
105 x .30% = 31.5
Then you want to divide 31.5 by .35%
31.5 / .35% = 90
Answer:
Step-by-step explanation:
The universal set, U is a set of all vehicles produced by the manufacturer.
U = red, blue and green vehicles(both cars and trucks)
B = all red vehicles produced by the manufacturer(both cars and trucks)
C = red, blue and green trucks
C ' = all elements that are not in C but are in the universal set
C ' = red, blue and green cars
B intersection C ' = all elements that are common to set B and set C '. Therefore,
B intersection C ' = red cars
