A hip joint replacement part is being stress-tested in a laboratory. The probability of successfully completing the test is 0.830. 7 randomly and independently chosen parts are tested. What is the probability that exactly two of the 7 parts successfully complete the test

0.00205

Step-by-step explanation:

This is binomial distribution problem.

Binomial distribution function is represented by

P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

n = total number of sample spaces = 7

x = Number of successes required = 2

p = probability of success = 0.830

q = probability of failure = 1 - 0.83 = 0.17

P(X =2) = ⁷C₂ 0.83² 0.17⁷⁻²

P(X =2) = ⁷C₂ 0.83² 0.17⁵ = 0.00205

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions