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4 years ago

Solving Equations with Variables on both sides

Mathematics

2 answers:

Rzqust [24]4 years ago

7 0

You do not need to know the variable to solve the equation

Kamila [148]4 years ago

6 0

If the variables on each side are the same, then you simply ignore them
For example

n3*3 = n81/9
You do not need to know n to solve the equation

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In a survey of 100 students of Surkhet, 65 like to play football, 55 like

Katyanochek1 [597]

Answer:

15 students do not like either sport

Step-by-step explanation:

See the attached image.

Step 1: put 35 in the "like to play both" (intersection) area.

Step 2: subtract those 35 from the 65 football players. 65 - 35 = 30 players like football but not cricket. Put 35 in the football but not cricket area.

Step 3: subtract 35 from the 55 cricket players. 55 - 35 = 20 players like cricket but not football. Put 20 in the cricket but not football area.

Step 4: Add the 30 + 35 + 20 = 85 together. So 85 players are accounted for as players of one or more sports.

Step 5: 100 - 85 = 15 must be the number of students who did not like either sport. Put 15 in the area outside both circles.

6 0

3 years ago

What is the distance between (2,-5) and (2,5)

tresset_1 [31]

Answer:

5 Units

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Circle E has a radius of 40 inches with = 324°. Find the exact length of

Anni [7]

Let the arc is ABC with angle 324 degree, to find the length of that arc follow the steps;
The circumference of the circle E is :C = 2 r π
C = 2 * 40 π = 80 π cm.
Also 324° / 360° = 0.9m Arc (ABC ) = 0.9 * 80 π = 72 π cm
There is also formula for calculating the measure of an arc:
m Arc = r π α / 180°
m Arc = 40 π * 324 / 180
= 40π * 1.8 = 72 π
Now we have to find the exact length ( π ≈ 3.14 )
m Arc ( ABC ) = 72 * 3.14 = 226.08 cm

8 0

3 years ago

Read 2 more answers

Find the eqation of the line perpendicular to y=3x-6 that runs through the point (-1, -3)

alexgriva [62]

The coefficient of x in the equation of the given line, 3, is its slope. The slope of the perpendicular line is the negatve reciprocal of that, -1/3. You now have the slope and a point on the perpendicular line, so you can write its equation using the point-slope form:
y = m(x -x₁) +y₁
where m is the slope and (x₁, y₁) is the point.

An equation for your perpendicular line is
y = (-1/3)(x -(-1)) -3
y = (-1/3)x -10/3

The slope-intercept form of the equation of the perpendicular line is ...
y = (-1/3)x -10/3

3 0

3 years ago

The following data are the joint temperatures of the O-rings (oF) for each test firing or actual launch of the space shuttle roc

12345 [234]

Answer:

The sample mean is $\bar{x}=\frac{1183}{18}\approx 65.722$ .

The sample standard deviation is $s=\frac{\sqrt{1666105}}{105}\approx 12.293$ .

The lower quartile is 59.

The upper quartile is 75.

The median is $\frac{135}{2}=67.5$ .

Step-by-step explanation:

We have the following data:

83, 45, 61, 40, 83, 67, 45, 66, 70, 69, 80, 58, 68, 60, 67, 72, 73, 70, 57, 63, 70, 78, 52, 67, 53, 67, 75, 61, 70, 81, 76, 79, 75, 76, 58, 31.

(a)

The sample mean of data is given by the formula

$\large{{\overline{{{x}}}}=\frac{{1}}{{n}}{\sum_{{{i}={1}}}^{{n}}}{x}_{{i}}}$ ,

where n is the number of values and $\large{{x}_{{i}},{i}={\overline{{{1}..{n}}}}}$ are the values themselves.

Since we have 36 points, then n = 36.

The sum of the points is $\sum_{i=1}^{n} x_i=2366$ .

Therefore, the sample mean is $\bar{x}=\frac{1}{36}\cdot2366=\frac{1183}{18}$ .

The sample standard deviation of data is given by the formula

$\large{{s}=\sqrt{{\frac{{1}}{{{n}-{1}}}{\sum_{{{i}={1}}}^{{n}}}{{\left({x}_{{i}}-{\overline{{{x}}}}\right)}}^{{2}}}}}$ ,

where n is the number of values, $\large{{x}_{{i}},{i}={\overline{{{1}..{n}}}}}$ are the values themselves, and ${\overline{{{x}}}$ is the mean of the values.

The mean of the data is $\bar{x}=\frac{1183}{18}$ .

n = 36.

Sum of ${{\left({x}_{{i}}-{\overline{{{x}}}}\right)}}^{{2}}$ is $\sum_{i=1}^{n} (x_i-\bar{x})^2=\frac{47603}{9}$ .

Now,

$\frac{1}{n-1} \sum_{i=1}^{n} (x_i-\bar{x})^2=\frac{1}{36-1}\cdot\frac{47603}{9}=\frac{1}{35}\cdot\frac{47603}{9}=\frac{47603}{315}$

Finally,

$s=\sqrt{\frac{47603}{315}}=\frac{\sqrt{1666105}}{105}\approx 12.2931133127713$

(b)

The $p^{th}$ percentile is a value such that at least $p$ percent of the observations is less than or equal to this value and at least ( $100-p$ ) percent of the observations is greater than or equal to this value.

The first step is to sort the values.

The sorted values are 31, 40, 45, 45, 52, 53, 57, 58, 58, 60, 61, 61, 63, 66, 67, 67, 67, 67, 68, 69, 70, 70, 70, 70, 72, 73, 75, 75, 76, 76, 78, 79, 80, 81, 83, 83.

The lower quartile or 25th percentile is the median of the lower half of the data set.

Now, calculate the index $i=\frac{p}{100}\cdot n=\frac{25}{100}\cdot 36=9$

Since the index $i$ is an integer, the 25th percentile is the average of the values at the positions $i$ and $i+1$ .

The value at the position $i=9$ is 58 and at the position $i+1=10$ is 60.

Their average is: $\frac{58+60}{2}=59$ .

The lower quartile is 59.

The upper quartile or 75th percentile is the median of the upper half of the data set.

Now, calculate the index $i=\frac{p}{100}\cdot n=\frac{75}{100}\cdot 36=27$

Since the index $i$ is an integer, the 75th percentile is the average of the values at the positions $i$ and $i+1$ .

The value at the position $i=27$ is 75 and at the position $i+1=28$ is 75.

Their average is: $\frac{75+75}{2}=75$ .

The upper quartile is 75.

(c) The median is the middle value of the data set. The median value depends on the number of values. If the number of values is odd, then the median is the "central" value among the sorted values. If the number of values is even, then the median is the average of the two "central values".

The first step is to sort the values.

We have 36 values, so their number is even.

Since the number is even, the median is the average of the "central values":

31, 40, 45, 45, 52, 53, 57, 58, 58, 60, 61, 61, 63, 66, 67, 67, 67, 67, 68, 69, 70, 70, 70, 70, 72, 73, 75, 75, 76, 76, 78, 79, 80, 81, 83, 83.

Calculate the median: $m=\frac{67+68}{2}=\frac{135}{2}$ .

The median is $\frac{135}{2}=67.5$ .

4 0

3 years ago