Suppose that 5% of the general population has a disease and the test for the disease is accurate 80% of the time. what is the probability of testing positive for the disease?

The probability of testing positive for the disease is:

                                23%

The population who have disease = 5%

Hence, the population who do not have disease= 95%

( since 100%-55=95%)

Also, the percent that the test is accurate= 80%

and the percent that the test is not accurate= 100%-80%=20%

Hence, the  probability of testing positive for the disease is :

The person actually has disease×Test is positive+Person do not have disease×test is not accurate

=  0.05×0.80+0.95×0.20

= 0.23

Hence, the probability is: 23%

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)