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3 years ago

30° 8 + 6x 4x + 2 in a triangle

Mathematics

1 answer:

andrey2020 [161]3 years ago

4 0

Answer:

x=12

Step-by-step explanation:

Simplifying

30 + 4x + 2 = 8 + 6x

Reorder the terms:

30 + 2 + 4x = 8 + 6x

Combine like terms: 30 + 2 = 32

32 + 4x = 8 + 6x

Solving

32 + 4x = 8 + 6x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-6x' to each side of the equation.

32 + 4x + -6x = 8 + 6x + -6x

Combine like terms: 4x + -6x = -2x

32 + -2x = 8 + 6x + -6x

Combine like terms: 6x + -6x = 0

32 + -2x = 8 + 0

32 + -2x = 8

Add '-32' to each side of the equation.

32 + -32 + -2x = 8 + -32

Combine like terms: 32 + -32 = 0

0 + -2x = 8 + -32

-2x = 8 + -32

Combine like terms: 8 + -32 = -24

-2x = -24

Divide each side by '-2'.

x = 12

Simplifying

x = 12

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STEP 2: Write the formula for calculating the Standard deviation of a set of numbers

$\begin{gathered} S\tan dard\text{ deviation=}\sqrt[]{\frac{\sum^{}_{}(x_i-\bar{x})^2}{n-1}} \\ where\text{ }x_i\text{ are data points,} \\ \bar{x}\text{ is the mean} \\ \text{n is the number of values in the data set} \end{gathered}$

STEP 3: Calculate the mean

$\begin{gathered} \bar{x}=\frac{\sum ^{}_{}x_i}{n} \\ \bar{x}=\frac{\sum ^{}_{}(321,397,559,454,475,324,482,558,369,513,385,360,459,403,498,477,361,366,372,320)}{20} \\ \bar{x}=\frac{8453}{20}=422.65 \end{gathered}$

STEP 4: Calculate the Standard deviation

$\begin{gathered} S\tan dard\text{ deviation=}\sqrt[]{\frac{\sum^{}_{}(x_i-\bar{x})^2}{n-1}} \\ \sum ^{}_{}(x_i-\bar{x})^2\Rightarrow\text{Sum of squares of differences} \\ \Rightarrow10332.7225+657.9225+18591.3225+982.8225+2740.52251+9731.8225+3522.4225+18319.6225+2878.3225 \\ +8163.1225+1417.5225+3925.0225+1321.3225+386.1225+5677.6225+2953.9225+3800.7225 \\ +3209.2225+2565.4225+10537.0225 \\ \text{Sum}\Rightarrow108974.0275 \\ \\ S\tan dard\text{ deviation}=\sqrt[]{\frac{111714.55}{20-1}}=\sqrt[]{\frac{111714.55}{19}} \\ \Rightarrow\sqrt[]{5879.713158}=76.67928767 \\ \\ S\tan dard\text{ deviation}\approx76.68 \end{gathered}$

Hence, the standard deviation of the given set of numbers is approximately 76.68 to 2 decimal places.

STEP 5: Calculate the First and third quartile

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STEP 6: Find the Interquartile Range

$\begin{gathered} IQR=Q_3-Q_1 \\ \text{IQR}=479.5-363.5 \\ \text{IQR}=116 \end{gathered}$

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