The length of a rectangle is twice the width. The area of the rectangle is 96 square units. Notice that you can divide the rec
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Answer:
The variance is
Step-by-step explanation:
From the question we are told that
The sample size is n = 21
The sum of squares is
Generally the variance is mathematically represented as
substituting values
<h3><em><u>Question:</u></em></h3>
Lyla is shopping for school supplies. She has $20.00 to spend. She
plans to buy a package of pens for $4.98. She also wants to buy a
calculator. All calculators are being sold for 30 percent less than the
original price. write an inequality that can be used to find the original price, x, of a calculator lyla can buy.
<h3><em><u>Answer:</u></em></h3> inequality that can be used to find the original price, x, of a calculator lyla can buy
Given that,
Lyla has $ 20 to spend
So she can spend entire $ 20 or less than $ 20
Total amount she has = $ 20
She plans to buy a package of pens for $4.98
Cost of package of pens = $ 4.98
She also wants to buy a calculator
Let "x" be the original price of calculator
All calculators are being sold for 30 percent less than the original price
Selling price of calculator = original price - 30 % of original price
Selling price of calculator = x - 30 % of x = x - 0.3x = 0.7x
Selling price of calculator = 0.7x
<em><u>Thus a inequality can be framed as:</u></em>
Cost of package of pens + Selling price of calculator 20
This means that, combined cost of package of pen and selling price of calculator must be less than or equal to the amount with Lyla ( 20 $ )
Thus the inequality is found
Answer:
31.5 kilograms of a 5% salt solution and 13.5 kilograms of a 15% salt solution must be mixed together to make 45kg of an 8% salt solution .
Step-by-step explanation:
Let us assume that the number of kilograms of a 5% salt solution used be x .
Let us assume that the number of kilograms of a 15% salt solution used be y .
As given
A 5% salt solution and 15% salt solution must be mixed together to make 45kg of an 8% salt solution .
Equation becomes
x + y = 45
5% is written in the decimal form .
= 0.05
15% is written in the decimal form .
= 0.15
8% is written in the decimal form .
= 0.08
Thus
Concentration of 5% salt solution × Number of kilograms of 5% salt solution used + Concentration of 15% salt solution × Number of kilograms of 15% solution used = Concentration of 8% salt solution × Number of kilograms of 8% salt solution
Thus
0.05x + 0.15y = 0.08 × 45
Simplify the above
5x + 15y = 360
Thus two equations becomes
x + y = 45
5x + 15y = 360
Multiply x + y = 45 by 5 and subtracted from 5x + 15y = 360 .
5x - 5x + 15y - 5y = 360 - 225
10y = 135
y = 13.5 kilograms
Put value of y in the equation
x + 13.5 = 45
x = 45 - 13.5
x = 31.5 kilograms
Therefore the 31.5 kilograms of a 5% salt solution and 13.5 kilograms of a 15% salt solution must be mixed together to make 45kg of an 8% salt solution .