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const2013 [10]
3 years ago
11

Find the value of each variable ​

Mathematics
2 answers:
aalyn [17]3 years ago
7 0

Answer:

x = 12\sqrt{2}

y = 12

z = 12\sqrt{3}

Step-by-step explanation:

The triangle with z as one of it's sides is a 30, 60, 90 triangle where the longest side of the triangle is 2x, the shortest side as x, and the middle side as x*sqrt of 3.

The shared line between the two triangle is 12 and z is 12*sqrt of 3

The left triangle is a 45, 45, 90 triangle where the 2 sides that look the same are the same and the hypotenuse is x sqrt of 2 so y is 12 and x is 12 sqrt of 2

PSYCHO15rus [73]3 years ago
3 0

Answer:

x = 12\sqrt{2} units

y = 12 units

z = 12\sqrt{3} units

Step-by-step explanation:

Notice that the biggest triangle is broken up into a 45-45-90 isosceles triangle with hypotenuse x and leg y, as well as a 30-60-90 triangle with hypotenuse 24 and long leg z.

Let's focus on finding z first. Remember that in a 30-60-90 triangle, the ratio of the short leg to the long leg to the hypotenuse is: 1:\sqrt{3} :2. Here, the hypotenuse is 24 and z is the longest leg, so we have the proportion:

\frac{\sqrt{3} }{2} =\frac{z}{24}

Cross-multiply:

24\sqrt{3} =2z

z = 12\sqrt{3} units

Now, let's find the smallest leg of the 30-60-90 triangle; it is simply 24/2 = 12 units. Let's move onto x and y.

Remember that in a 45-45-90 triangle, the ratio of one leg to the second leg to the hypotenuse is: 1:1:\sqrt{2}. So, since y is a leg of this triangle and the smallest leg of the 30-60-90 triangle coincides with the second leg of the 45-45-90 triangle, y = 12 units.

Finally, x is found by multiplying 12 by \sqrt{2}: 12 * \sqrt{2} = 12\sqrt{2} units

Hope this helps!

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Given:

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10, 10, 11, 12, 13, 13, 13, 14, 14, 15, 15, 15, 16, 17, 17, 17, 35

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Effect on mean, median, range after removing the outlier, 35.

Solution:

We have, the data set

10, 10, 11, 12, 13, 13, 13, 14, 14, 15, 15, 15, 16, 17, 17, 17, 35

\text{Mean}=\dfrac{\text{Sum of observations}}{\text{Number of observations}}

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Mean of the data set is 15.12.

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Median=\dfrac{17+1}{2}\text{th term}

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Median=9\text{th term}

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Range is 25.

After removing the outlier, 35, the data set is

10, 10, 11, 12, 13, 13, 13, 14, 14, 15, 15, 15, 16, 17, 17, 17

\text{Mean}=\dfrac{10+10+11+12+13+13+13+14+14+15+15+15+16+17+17+17}{16}

\text{Mean}=\dfrac{222}{16}

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Mean of the new data set is 13.875, which is less than 15.12.

Median=\dfrac{\dfrac{n}{2}\text{th term}+(\dfrac{n}{2}+1)\text{th term}}{2} because n=16, which is even.

Median=\dfrac{\dfrac{16}{2}\text{th term}+(\dfrac{16}{2}+1)\text{th term}}{2}

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Median=\dfrac{14+14}{2}

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Range=17-10

Range=7

So, the new range is 7 which is less than 25.

Therefore, the mean of the data set will decrease, the median of the data set will not change, the Range of the data set will decrease.

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