Answer:
<em>The fraction of the beads that are red is</em>
Step-by-step explanation:
<u>Algebraic Expressions</u>
A bag contains red (r), yellow (y), and blue (b) beads. We are given the following ratios:
r:y = 2:3
y:b = 5:4
We are required to find r:s, where s is the total of beads in the bag, or
s = r + y + b
Thus, we need to calculate:
![\displaystyle \frac{r}{r+y+b} \qquad\qquad [1]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Br%7D%7Br%2By%2Bb%7D%20%20%20%20%20%20%20%5Cqquad%5Cqquad%20%20%20%20%5B1%5D)
Knowing that:
![\displaystyle \frac{r}{y}=\frac{2}{3} \qquad\qquad [2]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Br%7D%7By%7D%3D%5Cfrac%7B2%7D%7B3%7D%20%20%20%20%20%20%5Cqquad%5Cqquad%20%20%20%20%5B2%5D)

Multiplying the equations above:

Simplifying:
![\displaystyle \frac{r}{b}=\frac{5}{6} \qquad\qquad [3]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Br%7D%7Bb%7D%3D%5Cfrac%7B5%7D%7B6%7D%20%20%20%20%20%20%20%5Cqquad%5Cqquad%20%20%20%20%5B3%5D)
Dividing [1] by r:

Substituting from [2] and [3]:

Operating:



The fraction of the beads that are red is 
Given :
An expression D = 401 km 101 m – 34 km 153 m.
To Find :
Value of D.
Solution :
We know, 1 km = 1000 m.
So, 401 km 101 m =( 401000 + 101 ) m = 401101 m.
Also, 34 km 153 m = ( 34000 + 153 ) m = 34153 m.
Now, D is given by :
D = 401101 - 34153 m
D = 366948 m
Now, D = 366948 m = 366 km 948 m.
Therefore, the difference is 366 km 948 m.
Hence, this is the required solution.
The algebraic expression for the statement Cindy's age, x, is 3 times her age 6 years ago is 3(x-6).
The given statement is Cindy's age, x, is 3 times her age 6 years ago.
We need to represent the given statement as the algebraic expression.
<h3>What is an algebraic expression?</h3>
In mathematics, an algebraic expression is an expression built up from integer constants, variables, and algebraic operations.
6 years ago Cindy's age(x) is x-6.
3 times Cindy's age=3(x-6)
Therefore, the algebraic expression for the statement Cindy's age, x, is 3 times her age 6 years ago is 3(x-6).
To learn more about the algebraic expression visit:
brainly.com/question/953809.
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