Let us assume that the given speed is in miles per hour.
A race car is driven by a professional driver at 99 mph.
We have to find the speed in kilometer per hour and kilometer per minutes
As 1 mile = 1.61 km
So, 99 miles = kmph
1 km per hour = 0.0166 km per minute
So, 159.39 kmph = km per minute
Hence, The speed is equivalent to 159.39 kilometers /hour, or 2.645 kilometers/minutes .
Answer:
There is an 8.38% probability that the anchor will be fired.
Step-by-step explanation:
For each resident, there is only two possible outcomes. Either they can name the news anchor on the evening news at their station, or they cannot.
This means that the binomial probability distribution will be used in our solution.
However, we are working with samples that are considerably big. So i am going to aaproximate this binomial distribution to the normal.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
The standard deviation of the binomial distribution is:
Normal probability distribution
Problems of normally distributed samples can be 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.
When we are approximating a binomial distribution to a normal one, we have that .
In this problem, we have that:
400 city residents are going to be asked. So .
Suppose that in fact 12% of city residents could name the anchor if asked. This means that .
So,
.
They plan to fire the news anchor if fewer than 10% of the residents in the sample can do so.
What is the approximate probability that the anchor will be fired?
10% of the residents is 0.10*400 = 40 residents.
Fewer than 10% is 39 residents. So the probability that the anchor will be fired is the pvalue of Z when .
So:
has a pvalue of 0.0838. This means that there is an 8.38% probability that the anchor will be fired.
The area of the composite figure is 264 square centimeters, if a composite figure comprised of a square, trapezoid and a rectangle.
Step-by-step explanation:
The given is,
Dimensions of square has length of 10 cm
Trapezoid has base lengths of 8 cm and 14 cm
The length of the trapezoid is 4 cm
Rectangle has side length of 20 cm and 6 cm
Step:1
Area of composite figure = Area of square + Area of Trapezoid
+ Area of rectangle.......................(1)
Step:2
Formula for area of square,
where, a - side of length = 10 cm
Area of square, = 100 Square centimeter
Step:3
Formula for area of Trapezoid,
=
.......................................(2)
Where, a - 8 cm
b - 14 cm
h - 4 cm
From equation (2)
=
=
= 44
Area of Trapezoid, = 44 square centimeters
Step:4
Formula for area of rectangle,
......................................(3)
Where, l = 20 cm
b = 6 cm
Equation (3) becomes,
= 120
Area of rectangle, = 120 square centimeters
Step:5
From Equation (1),
= 100 + 44 + 120
= 264 square centimeters
Result:
The area of the composite figure is 264 square centimeters, if a composite figure comprised of a square, trapezoid and a rectangle.