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4 years ago

When does the value of f(x) = (1/2)x equal the value of g(x) =2x+8 ?

Mathematics

1 answer:

Zanzabum4 years ago

8 0

Answer:

$\huge\boxed{f=g(x)\ \text{for}\ x=-\dfrac{16}{3}=-5\dfrac{1}{3}}$

Step-by-step explanation:

When does the value of f(x) = (1/2)x equal the value of g(x) =2x+8?

$f(x)=g(x)\iff\dfrac{1}{2}x=2x+8\qquad|\text{subtract}\ 2x\ \text{from bpoth sides}\\\\\dfrac{1}{2}x-2x=2x-2x+8\\\\-1\dfrac{1}{2}x=8\qquad|\text{convert the mixed number to the improper fraction}\\\\-\dfrac{2\cdot1+1}{2}x=8\\\\-\dfrac{3}{2}x=8\qquad\text{multiply both sides by}\ -\dfrac{2}{3}\\\\\left(-\dfrac{2\!\!\!\!\diagup}{3\!\!\!\!\diagup}\right)\left(-\dfrac{3\!\!\!\!\diagup}{2\!\!\!\!\diagup}x\right)=\left(-\dfrac{2}{3}\right)\cdot8\\\\x=-\dfrac{2\cdot8}{3}\\\\x=-\dfrac{16}{3}$

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Step-by-step explanation:

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Answer:

1. Sample Mean = 2.50

2. Sample Variance = 1.35

3. Standard Deviation = 1.16

Step-by-step explanation:

Note: As this question is not complete, similar can be found on internet where following are asked to calculate and here I will calculate these as well.

1. Sample Mean.

2. Sample Variance.

3. Sample Standard Deviation.

So, for sample mean to calculate from the given data points. We need to apply to following formula to calculate sample mean.

Sample Mean = (X1 + X2 + .... + XN) divided by Total number of data points.

Sample Mean = (0.17 + 1.94 + 2.62 + 2.35 + 3.05 + 3.15 + 2.53 + 4.81 + 1.92) divided by (9).

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Likewise, from the answer of sample mean we can calculate sample variance by following steps.

Solution:

1. Subtract the obtained mean from each of the data point given.

(0.17 - 2.50) = -2.33

(1.94 - 2.50) = -0.56