Answer:
34 feet
Step-by-step explanation:
418 - 384 = 34 feet above sea level
Answer:
![\frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D)
Step-by-step explanation:
Given:
A gear bag with 3 bungee cords, 5 socket wrenches, and 2 hammers.
Total number of instruments = 3 + 5 + 2 = 10
<u>Question asked:</u>
What is the probability a person will randomly draw a socket wrench from the bag?
Solution:
As we know:
![Probability =\frac{Favourable \ outcome}{Total\ outcome}](https://tex.z-dn.net/?f=Probability%20%3D%5Cfrac%7BFavourable%20%5C%20outcome%7D%7BTotal%5C%20outcome%7D)
First of all we will find favorable outcome for drawing 1 socket wrench from the bag randomly:
Favorable outcome for drawing 1 socket wrench out of cookies 3 bungee cords =![^{3} C_{0}](https://tex.z-dn.net/?f=%5E%7B3%7D%20C_%7B0%7D)
Favorable outcome for drawing 1 socket wrench out of 5 socket wrenches = ![^{5} C_{1}](https://tex.z-dn.net/?f=%5E%7B5%7D%20C_%7B1%7D)
Favorable outcome for drawing 1 socket wrench out of 2 hammers = ![^{2} C_{0}](https://tex.z-dn.net/?f=%5E%7B2%7D%20C_%7B0%7D)
Thus, total Favorable outcome for drawing 1 socket wrench from the bag randomly: <u>By using</u>:
![^{n} C_{r}=\frac{n!}{(n-r)!\ r!}](https://tex.z-dn.net/?f=%5E%7Bn%7D%20C_%7Br%7D%3D%5Cfrac%7Bn%21%7D%7B%28n-r%29%21%5C%20r%21%7D)
![\times](https://tex.z-dn.net/?f=%5Ctimes)
![^{5} C_{1}](https://tex.z-dn.net/?f=%5E%7B5%7D%20C_%7B1%7D)
![\frac{3!}{(3-0)!\ 0!} \times\frac{5!}{(5-1)!\ 1!}\times\frac{2!}{(2-0)!\ 0!}](https://tex.z-dn.net/?f=%5Cfrac%7B3%21%7D%7B%283-0%29%21%5C%200%21%7D%20%5Ctimes%5Cfrac%7B5%21%7D%7B%285-1%29%21%5C%201%21%7D%5Ctimes%5Cfrac%7B2%21%7D%7B%282-0%29%21%5C%200%21%7D)
![\frac{3!}{3!\times1} \times\frac{5!}{4!\times1} \times\frac{2!}{2!\times1} \\\\ 1\times\frac{5\times4!}{4!} \times\frac{2!}{2!} \\\\ 1\times5\times1=5](https://tex.z-dn.net/?f=%5Cfrac%7B3%21%7D%7B3%21%5Ctimes1%7D%20%5Ctimes%5Cfrac%7B5%21%7D%7B4%21%5Ctimes1%7D%20%5Ctimes%5Cfrac%7B2%21%7D%7B2%21%5Ctimes1%7D%20%5C%5C%5C%5C%201%5Ctimes%5Cfrac%7B5%5Ctimes4%21%7D%7B4%21%7D%20%5Ctimes%5Cfrac%7B2%21%7D%7B2%21%7D%20%5C%5C%5C%5C%201%5Ctimes5%5Ctimes1%3D5)
Total outcome for drawing 1 socket wrench out of 10 pieces of instruments:
![^{10} C_{1} =\frac{10!}{(10-1)!\times1!} =\frac{10\times9!}{9!} =10](https://tex.z-dn.net/?f=%5E%7B10%7D%20C_%7B1%7D%20%3D%5Cfrac%7B10%21%7D%7B%2810-1%29%21%5Ctimes1%21%7D%20%3D%5Cfrac%7B10%5Ctimes9%21%7D%7B9%21%7D%20%3D10)
Now,
![Probability =\frac{Favourable \ outcome}{Total\ outcome}](https://tex.z-dn.net/?f=Probability%20%3D%5Cfrac%7BFavourable%20%5C%20outcome%7D%7BTotal%5C%20outcome%7D)
![=\frac{5}{10} =\frac{1}{2}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B5%7D%7B10%7D%20%3D%5Cfrac%7B1%7D%7B2%7D)
Thus, the probability that a person will randomly draw a socket wrench from the bag is ![\frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D)
Answer:
There are 25 males and 21 females in the class
Step-by-step explanation:
Let us use the equation to solve the question
∵ A Spanish class has a total of 46 students
∵ The number of males is 4 more than the number of females
→ Assume that the number of females is x
∵ The number of females = x
∴ The number of males = x + 4
→ Add the numbers of males and females and equate the sum by 46
∴ x + x + 4 = 46
→ Add the like terms in the left side
∴ 2x + 4 = 46
→ Subtract 4 from both sides
∴ 2x + 4 - 4 = 46 - 4
∴ 2x = 42
→ Divide both sides by 2
∴ ![\frac{2x}{2}=\frac{42}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B2x%7D%7B2%7D%3D%5Cfrac%7B42%7D%7B2%7D)
∴ x = 21
∵ x represents the number of females
∴ There are 21 females
∵ x + 4 represents the number of males
∴ The number of males = 21 + 4 = 25
∴ There are 25 males
You just need to multiply 14 miles by 14 days so the answer is 196
Answer:
100
Step-by-step explanation:
The population is changing linearly. This means that the population is increasing by a particular value n every year.
From 2009 to 2017, there are 8 increases and so, the population increases by 8n.
The population increased from 1700 to 2500. Therefore, the population increase is:
2500 - 1700 = 800
This implies that:
8n = 800
=> n = 800/8 = 100
The average population growth per year is 100.