Answers:
1. 1/4
2. 12:10
3. 3/23 in fraction form, or 0.13 in decimal form (though please note that the decimal form has been rounded to the nearest hundredth).
Explanations:
1. In order to simplify a fraction, you need to find a number that both the numerator and denominator can be divided by evenly. Once you cannot find any number that fits that description, you have found the simplest form. Both numbers 10 and 40 can be divided by the number 10 - so let's divide 10 by 10 and 40 by 10. After doing that, your answer should be 1/4.
2. In order to find an equivalent ratio of an existing ratio, you can just multiply or divide the numbers of that ratio by a same number. Knowing this, this question can have many correct answers, but in this case, I used the number 2, and multiplied both 6 and 5 by it. This left me with an equivalent ratio of 12:10.
3. In order to calculate probability, you need to divide the number of "winners" (or the outcome we want to have) by the number of all possible outcomes you could have. For this problem, that "winner" is the number of green shirts, which is 3. The number of outcomes would be the number of all the shirts in total, which adds up to 23. Thus, using that method explained earlier, the probability would be 3/23 in fraction form or 0.13 in decimal form (note that this is rounded to the nearest hundredth since dividing 3 by 23 would result in a long answer).
<span>Plan 1: $50 for a monthly pass and a $3 fee for each gym visit
So, the monthly pass is 50 plus 3 for each visit. You know 50 stays constant no matter how much Hayley goes to the gym so you can already put that into the form as 'b' also known as the y-intercept.
y=mx+50
Now, you need to find the slope which is the amount it increases or decreases by every time. Since Hayley gets charged $3 every visit, that would be the slope (m).
Plan 1: y=3x+50
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</span><span>
Plan 2: $10 for each gym visit
</span>
There is only a slope (m) for this. Technically there is a y-intercept (b), but since that is 0 it is not needed. Plug in the values.
y=mx+b
y=10x
The <em><u>correct answer</u></em> is:
A line of reflection would need to be drawn as a line that bisects a vertex angle of the pentagon.
Explanation:
A line that bisects a vertex angle of a pentagon will be a line of symmetry within the pentagon. The pentagon can be "folded" through this line into two equal halves.
This imaginary line represents the center of the pentagon. A reflection through this line will carry the pentagon onto itself. This is due to the definition of line symmetry:
"A set of points has line symmetry if and only if there is a line, l, such that the reflection through l of each point in the set is also a point in the set."
Additionally, for any regular polygon, the number of lines of symmetry equals the number of sides.
This means that this line can be through any vertex angle of the polygon.
Answer:
It would be 18 to the nearest hundredth percent
