12w=-8(-4w=10) please help
2 answers:
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<h2>Answer:</h2>
Mean = 24.47
Variance = 108.31
Standard deviation = 10.41
<h2>Step-by-step explanation:</h2>The probability distribution table has been attached to this response.
<em>(1) To calculate the mean (m)</em>
(a) First multiply each of the values of x by their corresponding probability values.
This is shown in the third column of the table.
(b) The sum of the results in the third column gives the mean of the distribution. i.e
m = ∑xP(x) = 11.52 + 9.36 + 3.15 + 0.44
m = 24.47
<em>(2) To calculate the variance </em> <em>(σ²).</em>
(a) First find the square of the difference between the values of x and the mean (m) calculated in (1b) above. i.e
(x - m)²
The result is shown in the fourth column of the table.
(b) Next, multiply each of the results in the fourth column (x - m)², by their corresponding probability values P(X = x). i.e
(x - m)²(P(X = x))
The result is shown in the fifth column of the table.
(c) Now find the variance (σ²) which is the sum of the results in the fifth column. i.e
σ² = ∑(x - m)²(P(X = x)) = 42.5411 + 0.8427 + 18.8330 + 46.0923
σ² = 108.3091
σ² = 108.31 [to 2 decimal places]
<em>(3) To calculate the standard deviation (σ)</em>
The standard deviation is the square root of the variance of the distribution. Calculate this by finding the square root of the result in (2c) above.
σ = √σ²
σ =
σ = 10.4072
σ = 10.41 [to 2 decimal places]
Answer:
First number =26
Second number =49
Step-by-step explanation:
Question:
The sum of two numbers is 75. The second number is 3 less than twice the first. Find the numbers.
Given:
Sum of two numbers = 75
The second number is 3 less than twice the first.
To find the numbers.
Solution:
Let the first number be =
Let second number be =
The sum equation can be given as:
It is given that the second number is 3 less than twice the first.
This can be given as:
Substituting the value of in terms of
in the sum equation.
Combining like terms.
Adding 3 both sides.
Dividing both ides by 3.
Substitution in the second equation to find
.
Thus, first number =26 and second number =49.