<h3>Answer: 1981</h3>
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Work Shown:
Recall that P is in thousands, so P = 95 means 95,000.
Plug in P(x) = 95. Solve for x. Use logarithms to get this done.
P(x)=230(0.881)^x
95=230(0.881)^x
95/230 = (0.881)^x
0.41304347826087 = (0.881)^x
(0.881)^x = 0.41304347826087
Log( (0.881)^x )= Log( 0.41304347826087 )
x*Log( 0.881 )= Log( 0.41304347826087 )
x= Log( 0.41304347826087 )/Log( 0.881 )
x= 6.97883817154785
x= 7
Approximately 7 years after 1974 is when the population will be around 95,000.
7 years after 1974 = 1974+7 = 1981
Answer:
x = 77.8 ft
General Formulas and Concepts:
<u>Pre-Algebra</u>
- Order of Operations: BPEMDAS
<u>Trigonometry</u>
- sin∅ = opposite over hypotenuse
Step-by-step explanation:
<u>Step 1: Define</u>
∅ = 40°
opposite leg of angle = 50 ft
hypotenuse = x ft
<u>Step 2: Solve for </u><em><u>x</u></em>
- Substitute: sin40° = 50/x
- Multiply <em>x </em>on both sides: xsin40° = 50
- Divide sin40° on both sides: x = 50/sin40°
- Evaluate: x = 77.7862
- Round: x = 77.8 ft
Answer:
57.93% probability that a trip will take at least 35 minutes.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean 
and standard deviation 
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value 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. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
What is the probability that a trip will take at least 35 minutes
This probability is 1 subtracted by the pvalue of Z when X = 35. So
has a pvalue of 0.4207
1 - 0.4207 = 0.5793
57.93% probability that a trip will take at least 35 minutes.
