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Alex787 [66]
3 years ago
7

You and two friends are playing basketball. You make 7 out of 15 shots. Your first friend makes 6 out of 10 shots and your secon

d friend makes 5 out of 12 shots. Who is the better shooter? How would you solve this problem using what you know about rational numbers?
Mathematics
1 answer:
Nina [5.8K]3 years ago
4 0
First, you will need to find the percentage of shots made for each person, or you can find the least common denominator. This is because it makes it easier to see how the numbers compare to each other in size. You can find the percentage of shots made by looking at how many shots a person made and dividing it by the total shots that person made, which us the denominator. Then, you would take the decimal and move it two places to the right. Once you find the percentages of all three people, you can then compare the percentages to each other. In this case, the higher the percentage, the better the shooter that person is.
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Find an equation for the perpendicular bisector of the line segment whose endpoints
TEA [102]

Answer:

y= -2x -8

Step-by-step explanation:

I will be writing the equation of the perpendicular bisector in the slope-intercept form which is y=mx +c, where m is the gradient and c is the y-intercept.

A perpendicular bisector is a line that cuts through the other line perpendicularly (at 90°) and into 2 equal parts (and thus passes through the midpoint of the line).

Let's find the gradient of the given line.

\boxed{gradient =  \frac{y1 -y 2}{x1 - x2} }

Gradient of given line

=  \frac{1 - ( - 5)}{3 - ( - 9)}

=  \frac{1 + 5}{3 + 9}

=  \frac{6}{12}

=   \frac{1}{2}

The product of the gradients of 2 perpendicular lines is -1.

(½)(gradient of perpendicular bisector)= -1

Gradient of perpendicular bisector

= -1 ÷(½)

= -1(2)

= -2

Substitute m= -2 into the equation:

y= -2x +c

To find the value of c, we need to substitute a pair of coordinates that the line passes through into the equation. Since the perpendicular bisector passes through the midpoint of the given line, let's find the coordinates of the midpoint.

\boxed{midpoint = ( \frac{x1 + x2}{2} , \frac{y1 + y2}{2})  }

Midpoint of given line

= ( \frac{3  -  9}{2} , \frac{1 - 5}{2} )

= ( \frac{ - 6}{2}  , \frac{ - 4}{2} )

= ( - 3 , - 2)

Substituting (-3, -2) into the equation:

-2= -2(-3) +c

-2= 6 +c

c= -2 -6 <em>(</em><em>-</em><em>6</em><em> </em><em>on both</em><em> </em><em>sides</em><em>)</em>

c= -8

Thus, the equation of the perpendicular bisector is y= -2x -8.

5 0
3 years ago
What is the speed of a horse that runs a distance of 2,592 meters in 144 seconds? ____meters
horsena [70]

Answer: 18 meters/s

Step-by-step explanation: Divide meters by seconds to find out how many meters the horse traveled per second.

4 0
2 years ago
A piece of art is in the shape of an equilateral triangle with sides of 25in. Find the area of the piece of art. Round your answ
mojhsa [17]
A=\sqrt{3}/4 * side length^2
A=270.663
The answer is B.
6 0
3 years ago
Read 2 more answers
Can someone help with this question?
elixir [45]
When you subtract flip the signs of the second set.
2x^2+5-4x+3

Now combine like terms
2x^2-4x+8

Final answer: B
5 0
3 years ago
Read 2 more answers
Fewer young people are driving. In 1983, 87% of 19-year-olds had a driver’s license. Twenty-five years later (in 2008) that perc
Dima020 [189]

Answer:

a) ME=1.96\sqrt{\frac{0.87 (1-0.87)}{1200}}=0.019  

b) ME=1.96\sqrt{\frac{0.75 (1-0.75)}{1200}}=0.0245  

c) On this case it's not the same since the proportion estimated for 1983 it's different from the proportion estimated for 2008. So since the margin of error depends of \hat p the margin of error change for part a and b.

Step-by-step explanation:

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

The population proportion have the following distribution

p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})

The margin of error for the proportion interval is given by this formula:  

ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}    (a)  

If solve n from equation (a) we got:  

n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}   (b)  

Part a

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by \alpha=1-0.95=0.05 and \alpha/2 =0.025. And the critical value would be given by:

z_{\alpha/2}=\pm 1.96

If we replace the values into equation (a) for 1983 we got:

ME=1.96\sqrt{\frac{0.87 (1-0.87)}{1200}}=0.019  

Part b

Since is the same confidence level the z value it's the same.  

If we replace the values into equation (a) for 2008 we got:

ME=1.96\sqrt{\frac{0.75 (1-0.75)}{1200}}=0.0245  

Is the margin of error the same in parts (a) and (b)? Why or why not?

On this case it's not the same since the proportion estimated for 1983 it's different from the proportion estimated for 2008. So since the margin of error depends of \hat p the margin of error change for part a and b.

3 0
3 years ago
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