Atravel agency did a survey and found that the average local family spends $1900 on a summer vacation. the distribution is normally distributed with standard deviation $390. a. what percent of the families took vacations that cost under $1500. round to the nearest percent.

The percentage is 15%

Step-by-step explanation:

* Lets revise how to find the z-score

- The rule the z-score is z = (x - μ)/σ , where

# x is the score

# μ is the mean

# σ is the standard deviation

* Lets solve the problem

- The average local family spends $1900 on a summer vacation

- The distribution is normally distributed with standard deviation $390

- We need to find what percent of the families took vacations that

 cost under $1500

∵ The mean is $ 1900

∴ μ = 1900

∵ The standard deviation is $390

∴ σ = 390

∵ The vacation cost is under $1500

∴ x = 1500

∵ z-score = (x - μ)/σ

- Substitute the values above in the rule

∴ z-score = (1500 - 1900)/390 = -1.0256

- Lets use the normal distribution table of z

∵ P(z < 1500) = 0.1515

∵ P(x < 1500) = P(z < 1500)

∴ P(x < 1500) = 0.1515

∴ The percentage of the families took vacations that cost under

  $1500 is ⇒ 0.15 × 100% = 15%

∴ The percentage is 15%

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).

the equivalent expression are always the hardest ones but you look at the gcf also

step-by-step explanation: