Answer: No, the events are not mutually exclusive
Work Shown:
P(A and B) = P(A) + P(B) - P(A or B)
P(A and B) = 0.51 + 0.79 - 0.66
P(A and B) = 0.64
Since the result is not zero, this means the events are not mutually exclusive.
Mutually exclusive events are ones that cannot happen at the same time. Example: getting a "2" and a "3" on the same roll of a number cube.
Answer:
i don't know how to answer
Step-by-step explanation:
Answer:
D
21√2/2
C
C
C
Step-by-step explanation:
For all problems, the ratios of the lengths of the sides are:
30-60-90 triangle 1 : √3 : 2
45-45-90 triangle 1 : √2 : √2
Problem 3:
30-60-90 triangle at left
Hypotenuse = 11
Short leg = 11/2
Long leg = 11/2 × √3
45-45-90 triangle at right
x = 11/2 × √3 × √2 = 11√6/2
Answer: D
Problem 4:
30-60-90 triangle at top
Hypotenuse = 7√3
Short leg = 7√3/2
Long leg = 7√3/2 × √3 = 7 × 3/2 = 21/2
45-45-90 triangle at right
x = 21/2 × √2 = 21√2/2
Answer: 21√2/2
Problem 7:
30-60-90 triangle
Long leg = 4√3
Short leg = y = 4√2/2 = 2√2
Answer: C.
Problem 6:
30-60-90 triangle at left
Hypotenuse = 12√6
Short leg = 12√6/2 = 6√6
Long leg = 6√6 × √3 = 6√2√3√3 = 18√2
45-45-90 triangle at right
x = 18√2/√2 = 18
Answer: C.
Problem 8:
45-45-90 triangle
Hypotenuse = 2
Leg = y = 2/√2 = 2√2/(√2√2) = √2
Answer: C.
Ten-thousands place value
Answer: (2, 5)
Step-by-step explanation:
y = 2x + 1 y = 4x − 3
Eliminate the equal sides of each equation and combine.
2x + 1 = 4x − 3
Solve 2x + 1 = 4x − 3 for x.
Move all terms containing x to the left side of the equation.
Subtract 4x from both sides of the equation.
2x + 1 − 4x = −3
Subtract 4x from 2x.
−2x + 1 = −3
Move all terms not containing x to the right side of the equation.
Subtract 1 from both sides of the equation.
−2x = −3 − 1
Subtract 1 from −3.
−2x = −4
Divide each term by −2 and simplify.
x = 2
Evaluate y when x = 2.
Substitute 2 for x. y = 4 (2) − 3
Simplify 4 (2) − 3.
Multiply 4 by 2.
y = 8 − 3
Subtract 3 from 8.
y = 5
The solution to the system is the complete set of ordered pairs that are valid solutions.
(2, 5)
The result can be shown in multiple forms.
Point Form:
(2, 5)
Equation Form:
x = 2, y = 5
