47 = 50 - 3 or:
47 = Mean - 1 Standard deviation
For normal distribution it means that 4 bags represent 16 % of all samples.
4 bags ------ 16%
x bags ------ 100 %
---------------------------
4 * 100 = x * 16
16 x = 400
x = 400 : 16
x = 25
Answer: 25 bags were probably taken as samples.
Answer:
y = x²/4 + x/2 + 21/4 ⇒ -9 ≤ x ≤ 7
Step-by-step explanation:
∵ x = 2t - 1
∴ 2t = x + 1 ⇒ t = (x + 1)/2
∵ y = t² + 5
∴ y = [(x + 1)/2]² + 5 = (x² + 2x + 1)/4 + 5
y = x²/4 + x/2 + 1/4 + 5 = x²/4 + x/2 + 21/4
∵ -4 ≤ t ≤ 4
∴ -9 ≤ x ≤ 7
The price of one hat is $2 and price of one pair of mittens is $5.
Step-by-step explanation:
Let,
Price of one hat = x
Price of one pair of mittens = y
According to given statement;
5x+4y=30 Eqn 1
2x+3y=19 Eqn 2
Multiplying Eqn 1 by 2
![2(5x+4y=30)\\10x+8y=60\ \ \ \ Eqn\ 3](https://tex.z-dn.net/?f=2%285x%2B4y%3D30%29%5C%5C10x%2B8y%3D60%5C%20%5C%20%5C%20%5C%20Eqn%5C%203)
Multiplying Eqn 2 by 5
![5(2x+3y=19)\\10x+15y=95\ \ \ \ Eqn\ 4](https://tex.z-dn.net/?f=5%282x%2B3y%3D19%29%5C%5C10x%2B15y%3D95%5C%20%5C%20%5C%20%5C%20Eqn%5C%204)
Subtracting Eqn 3 from Eqn 4
![(10x+15y)-(10x+8y)=95-60\\10x+15y-10x-8y=35\\7y=35\\](https://tex.z-dn.net/?f=%2810x%2B15y%29-%2810x%2B8y%29%3D95-60%5C%5C10x%2B15y-10x-8y%3D35%5C%5C7y%3D35%5C%5C)
Dividing both sides by 7
![\frac{7y}{7}=\frac{35}{7}\\y=5](https://tex.z-dn.net/?f=%5Cfrac%7B7y%7D%7B7%7D%3D%5Cfrac%7B35%7D%7B7%7D%5C%5Cy%3D5)
Putting y=5 in Eqn 1
![5x+4(5)=30\\5x+20=30\\5x=30-20\\5x=10](https://tex.z-dn.net/?f=5x%2B4%285%29%3D30%5C%5C5x%2B20%3D30%5C%5C5x%3D30-20%5C%5C5x%3D10)
Dividing both sides by 5
![\frac{5x}{5}=\frac{10}{2}\\x=2](https://tex.z-dn.net/?f=%5Cfrac%7B5x%7D%7B5%7D%3D%5Cfrac%7B10%7D%7B2%7D%5C%5Cx%3D2)
The price of one hat is $2 and price of one pair of mittens is $5.
Keywords: linear equation, subtraction
Learn more about linear equations at:
#LearnwithBrainly
Answer: Since the equation works out, then the ordered pair (2,-1) is a solution of the linear system 5x-2y=12. Just plug in the value 2 for x and -1 for y. If you end up with 12 = 12 then the ordered pair is a solution; otherwise it isn't.
Step-by-step explanation: