Sporting Goods Company could ship 6 footballs in each carton how many cartons are needed to ship 75 football
1 answer:
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Answer:
OC=48
RK=100
Step-by-step explanation:
We can use proportions to find both OC and RK.
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.
Answer:
Yes, he made a reasonable inference by saying about 25 percent of students choose the science.
Step-by-step explanation:
Given that
Number of students for survey = 50
Number of students who choose science = 12
Now
Percentage of student who choose science =
Percentage of student who choose science =
Percentage of student who choose science = 24 %
Now as Mr. Yule said "about 25" percent of students choose the science it can be treated as reasonable approximation.
Now if the number of students in survey become 200, then we can expect 12 out of every 50 students would choose the science. So, in total 48 students would choose the science.
Now lets calculate the percentage of students who choose science.
Percentage of student who choose science =
Percentage of student who choose science =
Percentage of student who choose science = 24 %