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Answer:</h3>
3) likely
4) 1/2; equally likely
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Step-by-step explanation:</h3>
3) You are being asked to translate a numerical value to a subjective statement. There are no hard-and-fast rules for this. Generally, the meanings of the terms you're asked to choose from are ...
- impossible: probability is zero. The outcome cannot occur.
- unlikely: chances are less than even; often, "unlikely" means a probability of 10%, 5%, 1% or lower, depending on the context.
- equally likely: probability is near 50%
- likely: more likely than not. Again, this depends on the context.
- certain: probability is 1. There is no chance the outcome will not occur.
An 80% probability is greater than 50%, so might reasonably be called "likely."
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4) a. Four of the eight numbers are even, so the probability of obtaining an even number at random is 4/8 = 1/2.
b. A probability of 50% might reasonably be called "equally likely", as the probability the event will occur is equal to the probability it won't.
I believe you should try to plug in the ordered pair to see if the solutions work.
The ordered pair is (x,y) because x is on the x-axis and y is on the y-axis, therefore in (16,-3) the x=16 and y=-3.
Now substitute, meaning plug in those numbers into the equation.
For x+2y=10 would be 16+2(-3)=10
Now you just need to solve one side and see if it equals the other side.
16+2(-3)
First you use order of operations to solve this. PEMDAS. So you multiply 2(-3) first because of the parenthesis and it being multiplication.
16+(-6) and when you have a positive number adding a negative number it’s going backwards of the number line, basically meaning subtraction in a way. Sorry if this confuses you, if you already know how to do negatives and such nevermind this part.
But 16+(-6)=10
So now you look at both side of the equation, does the left side equal to the right? 10=10, so yes. It is a solution for that equation.
Now for the next equation, 7y=-21
Again, plug in the ordered pair (16,-3) into the equation. Remember that it’s (x,y).
There is no x in this equation so no need to worry about that; you only plug in y for this one.
7(-3) Now you multiply. Whenever you multiply a positive number and a negative number, the answer will always be negative. So 7(-3) is -21.
Now look if the left side is equivalent to the right. Does -21=-21? Yes. The ordered pair is a solution.
(16,-3) is a solution to both equations.
Hope this helps!
Answer:
x = 3 + i, x = 3 - i , x = 5 , and x = -1
Step-by-step explanation:
We know that given the polynomial with real coefficients, if x = 3 + i is a root, then x = 3 - i must be another root. These two roots can combine multiplicative factors as shown:
(x - 3 - i) * (x - 3 + i) = (x-3)^2 + 1 = x^2 - 6 x + 9 + 1 = x^2 - 6 x + 10
Then we divide the given polynomial: x^4 - 10x^3 + 29x^2 - 10x - 50 by the quadratic one we just found, and get a perfect division:
{x^4 - 10x^3 + 29x^2 - 10x - 50} / {x^2 - 6 x + 10} = x^2 - 4 x - 5
which can be factored out by grouping as shown below:
x^2 - 4 x - 5 = x^2 - 5 x + x - 5 = x (x - 5) + x - 5 = (x - 5 ) * (x + 1)
then the full factor form of the quartic polynomial given is:
(x - 3 - i) * (x - 3 + i) * (x - 5 ) * (x + 1)
and therefore the associated roots are:
x = 3 + i, x = 3 - i , x = 5 , and x = -1
Answer:
Step-by-step explanation:
Initial value ( y - value) for Function A is 12.
For B its 3(-1) + 2 = -1 so the answer is Function A.
Circumference of circular track, C = 0.5 miles = 0.5×5280 feet = 2640 feet.
We know, circumference in circle is given by :
( Here, r is radius i.e distance of centre from track )
Putting values in above equation :
2 × 3.14 × r = 2640
6.28 × r = 2640
r = 420.38 feet
Therefore, distance between centre and track is 420.38 feet .
Hence, this is the required solution.
