Police chases a driver. Originally, the police is 1 mile behind the driver. The speed of the police car is 90 mph, and the speed
1 answer:
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Answer:
a)
b) 69.764
Step-by-step explanation:
1) Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
2) Part a
Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:
Where and
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability on this way:
And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.
3) Part b
For this part we want to find a value a, such that we satisfy this condition:
(a)
(b)
Both conditions are equivalent on this case. We can use the z score again in order to find the value a.
As we can see on the figure attached the z value that satisfy the condition with 0.95 of the area on the left and 0.05 of the area on the right it's z=1.64. On this case P(Z<1.64)=0.95 and P(z>1.64)=0.05
If we use condition (b) from previous we have this:
But we know which value of z satisfy the previous equation so then we can do this:
And if we solve for a we got
So the value of height that separates the bottom 95% of data from the top 5% is 69.764.
Answer:
-22
Step-by-step explanation:
According to the question you need to find a number that gives the result of 22 when multiplied with -1
So,
The point slope form of the line which passes through the points and
is
i.e.,
.
Further explanation:
It is given that line passes through the points and
.
The objective is to determine the point slope form of the line which passes through the points and
.
The options given are as follows:
Option A: 2x-5y=-15
Option B: 2x-5y=-17
Option C: 2x+5y=-15
Option D: 2x+5y=-17
Consider the point as
and
as
.
Slope of a curve is defined as the change in the value of with respect to change in value of
.
The slope of the line is calculated as follows:
To obtain the value of slope substitute the value of in the above equation.
Therefore, the slope of the line is
The general way to express the equation of a line in its point slope form is as follows:
To obtain the point slope form of the equation of the line substitute the value of ,
and
in the above equation.
From the above calculation it is concluded that the point slope form the equation of a line is
Figure 1 (attached in the end) represents the graph of the function .
This implies that the correct option for the point slope form of the line is option C.
Therefore, the point slope form of the line which passes through the points and
is
i.e., option C.
Learn more:
1. A problem to complete the square of quadratic function brainly.com/question/12992613
2. A problem to determine the slope intercept form of a line brainly.com/question/1473992
3. Inverse function brainly.com/question/1632445.
Answer details
Grade: High school
Subject: Mathematics
Chapter: Linear equation
Keywords: Equation, linear equation, slope, intercept, x-intercept, y-intercept, intersect, graph, curve, slope intercept form, line, y=3x/2-3, standard form, point slope form.
