Answer:
Step-by-step explanation:
Which number line represents the solutions to –2|x| = –6?
2 answers:
Answer: The fourth number line represents the solutions to –2|x| = –6
Step-by-step explanation:
Given equation:
To solve the given equation, first divide -2 on both the sides, we get
Thus the absolute value of x=3
We know that the absolute value is the distance between a number and zero.
Therefore, the distance between x and zero is 3
Therefore, x=3 and -3
This solution is represented by the fourth number line .
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Answer:
(a) Between 27 and 31 pounds per month = 0.62465
(b) More than 30.2 pounds per month = 0.1357
Step-by-step explanation:
We are given that each month, an American household generates an average of 28 pounds of newspaper for garbage or recycling. Assume the standard deviation is 2 pounds and the variable is approximately normally distributed.
<em>Let X = generation of newspaper for garbage or recycling</em>
The z-score probability distribution for normal distribution is given by;
Z = ~ N(0,1)
where, = population average = 28 pounds
= population standard deviation = 2 pounds
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.
(a) Probability of household generating between 27 and 31 pounds per month is given by = P(27 pounds < X < 31 pounds) = P(X < 31 pounds) - P(X 27 pounds)
P(X < 31 pounds) = P( <
) = P(Z < 1.50) = 0.93319
P(X 27 pounds) = P(
) = P(Z
-0.50) = 1 - P(Z < 0.50)
= 1 - 0.69146 = 0.30854
<em>{Now, in the z table the P(Z </em><em> x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 1.50 and x = 0.50 in the z table which has an area of 0.93319 and 0.30854 respectively.}</em>
Therefore, P(27 pounds < X < 31 pounds) = 0.93319 - 0.30854 = 0.62465
(b) Probability of household generating more than 30.2 pounds per month is given by = P(X > 30.2 pounds)
P(X > 30.2 pounds) = P( >
) = P(Z > 1.10) = 1 - P(Z
<em> </em>1.10)
= 1 - 0.8643 = 0.1357
<em>Now, in the z table the P(Z </em><em> x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 1.10 in the z table which has an area of 0.8643.</em>
Answer:
The equation of the line will be:
Step-by-step explanation:
Given
- slope = m = -1/2
- point (4, -8)
Point slope form:
substituting the values m = -1/2 and the point (4,-8)
subtract 8 from both sides
Therefore, the equation of the line will be: