Answer:
65º
Step-by-step explanation:
- The angle of a straight line is 180º, so ∠ABD=180º and ∠ABC=(180-6x)º
- The sum of the interior angles of a triangle is 180, so (x+40)º+(3x+10)º+(180-6x)º=180
- We can solve from there, x+40+3x+10+180-6x=180
- Combine like terms, -2x+230=180
- Subtract 230, -2x=-50
- Divide by -2, x=25
- m∠CAB=(x+40)º=(25+40)º=65º
- m∠ABC=(180-6x)º=(180-150)º=30º
- m∠BCA=(3x+10)º=(75+10)º=85º
Answer:
![\[\frac{1}{24}\]](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7B1%7D%7B24%7D%5C%5D)
Step-by-step explanation:
Let the total number of batteries produced daily be represented by x.
7/8 of the batteries are packaged immediately.
So the total number of packaged batteries = ![\[\frac{7x}{8}\]](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7B7x%7D%7B8%7D%5C%5D)
Remaining batteries = ![\[x-\frac{7x}{8}\]](https://tex.z-dn.net/?f=%5C%5Bx-%5Cfrac%7B7x%7D%7B8%7D%5C%5D)
= ![\[\frac{x}{8}\]](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7Bx%7D%7B8%7D%5C%5D)
Two third of the remaining batteries are sent to charity.
So the total number of batteries sent to charity= ![\[\frac{2}{3} * \frac{x}{8}\]](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7B2%7D%7B3%7D%20%2A%20%5Cfrac%7Bx%7D%7B8%7D%5C%5D)
= ![\[\frac{x}{12}\]](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7Bx%7D%7B12%7D%5C%5D)
Remaining batteries are faulty.
So the total number of faulty batteries = ![\[\frac{x}{8} - \frac{x}{12}\]](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7Bx%7D%7B8%7D%20-%20%5Cfrac%7Bx%7D%7B12%7D%5C%5D)
= ![\[\frac{3x - 2x}{24}\]](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7B3x%20-%202x%7D%7B24%7D%5C%5D)
= ![\[\frac{x}{24}\]](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7Bx%7D%7B24%7D%5C%5D)
So the faction of batteries which are faulty =
= ![\[\frac{x}{24} \div x\]](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7Bx%7D%7B24%7D%20%5Cdiv%20x%5C%5D)
= ![\[\frac{1}{24}\]](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7B1%7D%7B24%7D%5C%5D)
In order of blank boxes going from left to right then down will be 1, 9, 5, 75, 35.
The missing table is given below.
<h3>What are ratio and proportion?</h3>
A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.
Shawn is collecting money from students at his school for a charity.
The table gives the ratios of the number of students who have donated and the amount of money he has collected from them.
Since 30 is 1/3 of 90, we know the ratio is 1:3.
In order of blank boxes going from left to right then down
1, 9, 5, 75, 35
The complete table is attached below.
More about the ratio and the proportion link is given below.
brainly.com/question/14335762
#SPJ1
Answer: $2203.74
Step-by-step explanation: