Reposting this as a priority question worth 15 points help please ASAP
1 answer:
Answer:
3. f(x) = 5^x
4. f(x) = 3 (8)^x
Step-by-step explanation:
3. Which function represents the data 2=>25, 3=>125, 4 =>625
You just have to plug the values of x in the equations provided and see which one fit, you stop testing for a given equation when it doesn't match the data table.
f(x) = x^4 + 9 - NO
for x = 2, 2^4 + 9 = 16 + 9 = 25 YES
for x = 3, 3^4 + 9 = 81 + 9 = 90 NO, should be 125
f(x) = 4^x + 9 - NO
for x = 2, 4^2 + 9 = 16 + 9 = 25 YES
for x = 3, 4^3 + 9 = 64 + 9 = 73 NO, should be 125
f(x) = x^5 - NO
for x = 2, 2^5 = 32 NO, should be 25
f(x) = 5^x YES
for x = 2, 5^2 = 25 YES
for x = 3, 5^3 = 125 YES
for x = 4, 5^4 = 625 YES
4. Which of the options is equivalent to f(x) = 3(2)^(3x)
By property of the powers you can easily break down the 3x exponent into a much simpler way.
From (2)^(3x) we got to 8^x, so the equation can now be written:
f(x) = 3 (8)^x, which is the first choice.
You could easily verify it with x = 2 in each equation.
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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>