The mass of a penny was measured six times. The following data was reported:
1 answer:
Answer:
a) 8.103 g
b) 9.2948
c) 0
Step-by-step explanation:
Given:
Data reported:
9.314 g, 9.215 g, 9.323 g, 8.103 g, 9.278 g, and 9.344 g
Now,
All the values except the 8.103 are above 9
Here the data 8.103 varies very much with respect to the other values
Hence,
a) the data 8.103 should be excluded
b) average value of the mass of the penny =
= 9.2948 g
c) Deviation = Mean - Data
9.2948 - 9.314 = -0.0192
9.2948 - 9.215 = 0.0798
9.2948 - 9.323 = -0.0282
9.2948 - 9.278 = 0.0168
9.2948 - 9.344 = -0.0492
Thus,
Average deviation from mean = tex]\frac{-0.0192 + 0.0798 -0.0282 + 0.0168 -0.0492 }{5}[/tex]
= 0
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Answer:
1. x = 3, 1/2 (solutions); (x - 3)(2x - 1) (factors)
2. x = -1/3, -2 (solutions); (3x + 1)(x + 2) (factors)
Step-by-step explanation:
<u>1. 2x^2 - 7x + 3</u>
To solve problem 1, you will need to identify your a, b, and c values in this quadratic function.
Since this problem is in standard form, it will be easy to identify these values. The standard form of a quadratic function is ax^2 + bx + c.
The a value is 2, the b value is -7, and the c value is 3 if we use our standard form and see which numbers are plugged into it.
Since we know that
- a = 2
- b = -7
- c = 3
we can use the quadratic formula:
Substitute the a, b, and c values into the quadratic formula:
Now simplify using the laws of pemdas:
Simplify even further:
Now split this equation into two equations to solve for x:
12/4 can be simplified to 3, and 2/4 can be simplified to 1/2.
This means your solutions to problem 1 is 3, 1/2.
There is also another way to solve for the quadratic functions, and this was by factoring.
If you factor 2x^2 - 7x + 3 using the bottoms-up method, you will get (x - 3)(2x - 1).
After factoring, solving for the solutions is simple because all you have to do is set each factor to 0.
- x - 3 = 0
- 2x - 1 = 0
After solving for x by adding 3 to both sides, or by adding 1 to both sides then dividing by 2, you will end up with the same solutions: x = 3 and x = 1/2.
<u>2. 3x^2 + 7x + 2</u>
To save time I'll be using the bottoms-up factoring method, but remember to refer back to problem 1 (quadratic formula) if you prefer that method.
Factor this quadratic function using the bottoms-up method. After factoring you will have (3x + 1)(x + 2). These are your factors.
Now to solve for x and find the solutions of the quadratic function, you will set both factors equal to 0.
- 3x + 1 = 0
- x + 2 = 0
Solve.
<u>First factor:</u> 3x + 1 = 0
Subtract 1 from both sides.
3x = -1
Divide both sides by 3.
x = -1/3
<u>Second factor:</u> x + 2 = 0
Subtract 2 from both sides.
x = -2
Your solutions are x = -1/3 and x = -2.