Furnace repair bills are normally distributed with a mean of 263 dollars and a standard deviation of 25 dollars. If 100 of these repair bills are randomly selected, find the probability that they have a mean cost between 263 dollars and 265 dollars.

0.28814

Step-by-step explanation:

Given that (m) = 263

Standard deviation (s) = 25

Sample size (n) = 100

find the probability that they have a mean cost between 263 dollars and 265 dollars

Using the z formula :

Zscore = (x - m) / (s/√n)

For x = 263

Zscore = (263 - 263) / (25/√100) = 0

P(z < 0) = 0.5 ( Z probability calculator)

For x = 265

Zscore = (265 - 263) / (25/√100) = 0

Zscore = 2 / (25/10)

Zscore = 2 / 2.5

Zscore = 0.8

P(z < 0.8) = 0.78814 ( Z probability calculator)

(0.78814 - 0.5) = 0.28814

20%

step-by-step explanation:

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)