Answer:
We know that for a standard dice the probability of obtain a 6 is:
[tex] P=\frac{1}{6}[/tex]
And for this case our value of x=3 and replacing we got:
[tex] f(x=3) = (1- \frac{1}{6})^{3-1} \frac{1}{6}[/tex]
[tex]f(x=3)=\frac{25}{36} \frac{1}{6}= \frac{25}{216}= 0.116[/tex]
Step-by-step explanation:
For this case we have the following function:
[tex] f(x) = (1-P)^{x-1} P[/tex]
We want to find the approximate probability of rolling a standard die and getting the first 6 on the 3rd try
We know that for a standard dice the probability of obtain a 6 is:
[tex] P=\frac{1}{6}[/tex]
And for this case our value of x=3 and replacing we got:
[tex] f(x=3) = (1- \frac{1}{6})^{3-1} \frac{1}{6}[/tex]
[tex]f(x=3)=\frac{25}{36} \frac{1}{6}= \frac{25}{216}= 0.116[/tex]
Which of the following best describes so ?
A.
Center
B.
Radius
C.
Diameter
D.
Chord
Step-by-step explanation:
D.
chord
hope you like this
stay at home stay safe
Answer: d
Step-by-step explanation:
Using the quadratic formula y=4x ²-81
Answer:
[tex]\huge\boxed{x=\pm4.5}[/tex]
Step-by-step explanation:
The quadratic formula of
[tex]ax^2+bx+c=0\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
We have:
[tex]y=4x^2-81\to 4x^2-81=0\\\\a=4;\ b=0;\ c=-81[/tex]
substitute
[tex]x=\dfrac{-0\pm\sqrt{0^2-4(4)(-81)}}{2(4)}=\dfrac{\pm\sqrt{1296}}{8}=\dfrac{\pm36}{8}=\pm4.5[/tex]
what is the slope of the line described by the equation below? Y=-x+8
Answer:
The slope of line is -1.
Step-by-step explanation:
This equation is in the form Y=mx+b form, where m is the slope of the line. in this equation, -1 is m.
100 POINTS!!!! Answer to the picture below.
Answer:
A 23 of people who prefer plan 1 are from the 35-45 age group and 42% of people from the 46-55 age group prefer plan 2.
Step-by-step explanation:
add everyone who prefers plan 1 = 60
age 36-45 / total of plan 1 = 14/60 = .23 or 23%
add everyone in age group 46-55 = 50
in age group 46-55 and prefers plan 2 = 21 / 50 = 0.42 or 42%
Answer:
[tex]\boxed{\mathrm{Option \ B}}[/tex]
Step-by-step explanation:
Total people in 36 - 45 age group = 50
Who prefer plan I = 14
%age of people preferring plan 1 among 36-45 age group:
=> [tex]\frac{14}{50} * 100[/tex]
=> 0.28 * 100%
=> 28%
Now,
Total People in 46-55 age group = 50
Those who prefer plan II = 21
%age of people preferring plan II among 46-55 age group:
=> [tex]\frac{21}{50} * 100[/tex]
=> 0.42 * 100%
=> 42%
Imagine you have a data set with 9,987 names. The data set is sorted alphabetically. You want to find out if the name "David Joyner" is in the data set. Using a linear search, what is the minimum number of names we might have to check?
Answer:
1
Step-by-step explanation:
David Joyner might be the first name, so you may only have to check 1 name.
a political candidate has asked you to conduct a poll to determine what percentage of people support her. if the candidate only wants a 8% margin of error at a 95% cnofidence level, what size of sample is needed
Answer:
The sample needed is [tex]n =150[/tex]
Step-by-step explanation:
From the question we are told that
The margin of error is [tex]E = 0.08[/tex]
The confidence level is [tex]C = 95 \% = 0.95[/tex]
Given that the confidence level is 95% the level of significance is mathematically represented as
[tex]\alpha = 1 - 0.95[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the z-table , the value is [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
The reason we are obtaining critical value of [tex]\frac{\alpha }{2}[/tex] instead of [tex]\alpha[/tex] is because
[tex]\alpha[/tex] represents the area under the normal curve where the confidence level interval ( [tex]1-\alpha[/tex] ) did not cover which include both the left and right tail while
[tex]\frac{\alpha }{2}[/tex] is just the area of one tail which what we required to calculate the margin of error
The sample size is mathematically represented as
[tex]n = [\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \r p[1-\r p][/tex]
Here [tex]\r p[/tex] is sample proportion of people that supported her and we will assume this to be 50% = 0.5
So
[tex]n = [\frac{1.96}{ 0.08} ]^2 * [0.5 (1- 0.5)][/tex]
[tex]n =150[/tex]
50 POINTS!!!! I ALSO GIVE BRAINLIEST, BUT YOU HAVE TO ANSWER QUICK Choose the correct graph of the given system of equations. A pair of linear equations is shown: y = −x + 1 y = 2x + 4 Which of the following statements best explains the steps to solve the pair of equations graphically? On a graph, plot the line y = −x + 1, which has y-intercept = −1 and slope = 1, and y = 2x + 4, which has y-intercept = 2 and slope = 4, and write the coordinates of the point of intersection of the two lines as the solution. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = 1, and y = 2x + 4, which has y-intercept = 1 and slope = 4, and write the coordinates of the point of intersection of the two lines as the solution. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = −1, and y = 2x + 4, which has y-intercept = −2 and slope = 2, and write the coordinates of the point of intersection of the two lines as the solution. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = −1, and y = 2x + 4, which has y-intercept = 4 and slope = 2, and write the coordinates of the point of intersection of the two lines as the solution.
Answer:
D. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = −1, and y = 2x + 4, which has y-intercept = 4 and slope = 2, and write the coordinates of the point of intersection of the two lines as the solution.
Step-by-step explanation:
Correct answer is in bold. Incorrect answer have the mistakes put between stars *** ***.
50 POINTS!!!! I ALSO GIVE BRAINLIEST, BUT YOU HAVE TO ANSWER QUICK Choose the correct graph of the given system of equations. A pair of linear equations is shown: y = −x + 1 y = 2x + 4 Which of the following statements best explains the steps to solve the pair of equations graphically?
A. On a graph, plot the line y = −x + 1, which has y-intercept = ***−1*** and slope = 1, and y = 2x + 4, which has y-intercept = 2 and slope = 4, and write the coordinates of the point of intersection of the two lines as the solution.
B. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = ***1***, and y = 2x + 4, which has y-intercept = 1 and slope = 4, and write the coordinates of the point of intersection of the two lines as the solution.
C. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = −1, and y = 2x + 4, which has y-intercept = ***−2*** and slope = 2, and write the coordinates of the point of intersection of the two lines as the solution.
D. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = −1, and y = 2x + 4, which has y-intercept = 4 and slope = 2, and write the coordinates of the point of intersection of the two lines as the solution.
Ava wants to figure out the average speed she is driving. She starts checking her car’s clock at mile marker 0. It takes her 4 minutes to reach mile marker 3. When she reaches mile marker 6, she notes that 8 minutes total have passed since mile marker 0. What is the average speed of the car in miles per minute? What is an equation of the line that represents n, the number of mile marker passed, as a function of t, time in minutes? PLEASE HELP
Answer:
Below
Step-by-step explanation:
The average speed is given by the following formula:
● V = d/t
● d is the distance covered
● t is the time spent to cover the distance d
■■■■■■■■■■■■■■■■■■■■■■■
Ava takes 8 minutes to go from mile marker 0 to mile marker6.
● the distance Ava traveled is 6 miles
● the time Ava spent to reach mile marker 6 is 8 minutes
So the average speed of Ava is:
● V = 6/ 8 = 3/4 = 0.75 mile per min
●●●●●●●●●●●●●●●●●●●●●●●●
Let's The equation of the line that links the number of milemarkers (n) and the time (t).
Ava went from mile marker 0 to mile marker 6.
At t=0 Ava just started travelling from mile marker 0 to 1.
Afrer 8 minutes,she was at mile marker 6.
So 8 min => 6 mile markers (igonring mile marker 0 since the distance there was 0 mile)
6/8= 0.75
Then n/t = 0.75
● n = 0.75 * t
Let's check
● n= 0.75*4 = 3
That's true since after 4 minutes Ava was at mile marker 3.
Multiply. Write your answer using the smallest numbers possible. 2 teaspoons times 21 = ____tablespoons ____teaspoons
Answer: 12 Tbsp
Step-by-step explanation:
Note: 1 Tbsp = 3 tsp
2 tsp x 21 = 42 tsp
42 tsp ÷ 3 = 12 Tbsp
What is the y-value in the solution to this system of linear equations?
4x + 5y = -12
-2x + 3y = -16
-4.
-2
оооо
2
5
Answer:
y = -4
Step-by-step explanation:
4x + 5y = -12 ....eq1
-2x + 3y = -16 ...eq2
From eq1, solve for x:
4x + 5y = -12
4x = -12 - 5y
x = -12 - 5y/4
From eq2, substitute value of x:
-2(-12-5y/4) + 3y = -16
3y - 2 (-5y-12/4) = -16
3y - 2(-5y-12)/4 = -16
12y - 2(-5y - 12) = -16
4*3y - 4*2(-5y-12)/4 = 4*(-16)
12y - 2(-5y-12) = -64
12y + 10y + 24 = -64 (divide both sides by common factor 2)
6y + 5y + 12 = -32
11y = -32 - 12
11y = -44
Divide both sides by 11
11y/11 = -44/11
y = -4
find the standard deviation for the binomial distribution which has the stated values of n and p n=47 p= 0.4 round you answer to the nearest hundredth
Answer:
Option (3)
Step-by-step explanation:
Standard deviation for the binomial distribution is given by,
σ = [tex]\sqrt{n\times P(1-P)}[/tex]
where n = Number of trials
P = probability of success of an individual trail
If n = 47 and P = 0.4
σ = [tex]\sqrt{47\times 0.4(1-0.4)}[/tex]
= [tex]\sqrt{47\times 0.24}[/tex]
= [tex]\sqrt{11.28}[/tex]
= 3.3586
≈ 3.36
Therefore, standard deviation for the binomial distribution will be 3.36.
Option (3) will be the answer.
Which of the following is the minor arc for the circle shown below?
A. AWR
B. AW
C. RAW
D. RA
Answer:
RA
Step-by-step explanation:
A box contains 100 marbles, some of which are red and the rest blue. A sample of 10 marbles is taken randomly (with replacement) from the box and the statistic: number of red marbles in the sample is calculated. The probability model for this statistic is shown below. (Note: the probabilities should add to 1 - any difference from 1 is due to round-off errors.)
values probability
(%)
0 0.6047
1 4.0311
2 12.0932
3 21.4991
4 25.0823
5 20.0658
6 11.1477
7 4.2467
8 1.0617
9 0.1573
10 0.0105
a. Roughly, what is the shape of the probability model? Write the shape in a complete sentence
b. Calculate the center (mean) of the probability model. Use R as a calculator to calculate the mean. Write the mean in a complete sentence
c. Argue that 1.5 is a good guess for the standard deviation of the probability model. Write a brief answer
d. Suppose you repeat the experiment of sampling 10 randomly with replacement n times. Each time, you calculate the number of red marbles in your sample. Suppose you were to make a plot of the running means of the results, what would happen as n increases?
Step-by-step explanation:
a) The Roughly shape of the probability model is bell shaped or symmetric
( normal )
(b) Roughly, guess the center (mean) of the probability model
The mean is 5/10 =0.5
Because the symmetric distribution mean is middle bar and here we see using histogram 5/10 is mean .
(c) Argue that 1.5 is a good guess for the standard deviation of the probability model.
Yes 1.5 is very good guess because then it follow normal distribution it is exactly correct .
Find x.................
Answer:
90°
Step-by-step explanation:
Theres a right angke beside x
And Angles on a straight line = 180 so 180-90°= 90°
Answer:
90
Step-by-step explanation:
I looked it up on the internet
What is the product of the polynomials below? (4x^2-2x-4)(2x+4)
Answer: 8x³ + 12x² - 16x - 16
Step-by-step explanation:
(4x² - 2x - 4)(2x + 4)
= (2x + 4)(4x² - 2x - 4)
= 2x(4x² - 2x - 4) + 4(4x² - 2x - 4)
= 8x³ - 4x² - 8x + 16x² - 8x - 16
= 8x³ + (-4x² + 16x²) + (-8x - 8x) - 16
= 8x³ + 12x² - 16x - 16
Every year the United States Department of Transportation publishes reports on the number of alcohol related and non-alcohol related highway vehicle fatalities. Below is a summary of the number of alcohol related highway vehicle fatalities from 2001 to 2010.
Line graph about Alcohol related fatalities
Determine the average number of alcohol-related fatalities from 2001 to 2006. Round to the nearest whole number.
Complete question:
The line graph relating to the question was not attached. However, the line graph has can be found in the attachment below.
Answer:
17,209
Step-by-step explanation:
The line graph provides information about alcohol-related highway fatalities between year 2001 to 2010.
Determine the average number of alcohol-related fatalities from 2001 to 2006. Round to the nearest whole number.
The average number of alcohol related fatalities between 2001 - 2006 can be calculated thus :
From the graph:
Year - - - - - - - - - - Number of fatalities
2001 - - - - - - - - - - 17401
2002 - - - - - - - - - 17525
2003 - - - - - - - - - 17013
2004 - - - - - - - - - 16694
2005 - - - - - - - - - 16885
2006 - - - - - - - - - 17738
To get the average :
Sum of fatalities / number of years
(17401 + 17525 + 17013 + 16694 + 16885 + 17738) / 6
= 103256 / 6
= 17209.333
Average number of alcohol related fatalities is 17,209 (to the nearest whole number)
The data found below measure the amounts of greenhouse gas emissions from three types of vehicles. The measurements are in tons per year, expressed as CO2 equivalents. Use a 0.05 significance level to test the claim that the different types of vehicle have the same mean amount of greenhouse gas emissions. Based on the results, does the type of vehicle appear to affect the amount of greenhouse gasemissions?
Type A Type B Type C
7.6 6.2 6.4
6.1 7.6 7.5
6.1 6.7 7.4
6.7 7.5 6.6
7.4 7.7 6.1
7.4 7.5 7.5
5.9 5.8 6.6
5.9 6.8 6.3
6.2 7.3
7.4
What are the hypotheses for this test?
A. H0: μ1 = μ2 = μ3
H1: μ1 ≠ 2μ ≠ μ3
B. H0: μ1 = μ2 = μ3
H1: At least one of the means is different from the others.
C. H0: μ1 ≠ μ2 ≠ μ3
H1: μ1 = μ2 = μ3
D. H0: At least one of the means is different from the others.
H1: μ1 = μ2 = u3
Determine the test statistic.
F = ________
What is the critical F value?
F = _________
Identify the P-value.
P-value = __________
What is the conclusion of the test?
_________ the null hypothesis. Conclude that the type of vehicle ______________ appear to affect the amount of greenhouse gas emissions for these three types.
Answer:
1.
A. H0 : μ1 = μ2 = μ3
Ha : μ1 ≠ 2μ ≠ μ3
2. Test Statistics = 95%
3. Critical F-Value = 3.76
4. P-Value = 2.32
5. Conclusion : Reject the null hypothesis
6. Type of vehicle does effect the amount of green house gas emissions.
Step-by-step explanation:
The correct order of the steps of a hypothesis test is given following
1. Determine the null and alternative hypothesis.
2. Select a sample and compute the critical value F-test for the sample mean.
3. Determine the probability at which you will conclude that the sample outcome is very unlikely.
4. Make a decision about the unknown population.
These steps are performed in the given sequence to test a hypothesis.
The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. It is not necessary that all null hypothesis will be rejected at 95% level of significance. To determine the criteria for accepting or rejecting a null hypothesis we should also consider p-value.
A. H 0 μ1 = μ2 = μ3
Ha μ1 ≠ 2μ ≠ μ3
2. Test Statistics is 95%
3. Critical F-Value is 3.76.
4. P-Value is 2.32.
5. Conclusion Reject the null hypothesis.
6. Type of vehicle does effect the amount of green house gas emissions.
The correct order of the steps of a hypothesis test is given below.
1. Determine the null and alternative hypothesis.
2. Select a sample and compute the critical value F-test for the sample mean.
3. Determine the probability at which you will conclude that the sample outcome is very unlikely.
4. Make a decision about the unknown population.
All steps are performed in the given sequence to test a hypothesis.
The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. It is not necessary that all null hypothesis will be rejected at 95% level of significance. To determine the criteria for accepting or rejecting a null hypothesis we should also consider p-value.
For more details on hypothesis test follow the link:
https://brainly.com/question/10758924
29% of workers got their job through networking. A researcher feels this percentage has changed. Express the null and alternative hypotheses in symbolic form for this claim (enter as a percentage).
Answer: [tex]H_0:p=0.29[/tex]
[tex]H_a: p \neq0.29[/tex]
Step-by-step explanation:
A null hypothesis[tex](H_0)[/tex] is a type of statement used in statistics that proposes that there is no difference between particular characteristics of a population whereas the alternative hypothesis[tex](H_a)[/tex] proposes that there is a difference.
Let p be the population proportion of workers got their job through networking.
Given: 29% of workers got their job through networking.
i.e. [tex]H_0:p=0.29[/tex]
A researcher feels this percentage has changed.
i.e. [tex]H_a: p \neq0.29[/tex]
Hence, the required null and alternative hypotheses in symbolic form for this claim:
[tex]H_0:p=0.29[/tex]
[tex]H_a: p \neq0.29[/tex]
When using the Distance Formula, the solution is the perimeter of a polygon.
true or false?
Answer:
false
Step-by-step explanation:
When solving the distance formula it is the distance from one point to another. If you had a rectangle and used the distance formula from each point then you would have a perimeter
Each of the following linear equations defines y as a function of x for all integers x from 1 to 100. For which of the following equations is the standard deviation of the y-values corresponding to all the x-values the greatest?
a) y = x/3
b) y = x/2+40
c) y = x
d) y = 2x + 50
e) y = 3x − 20
Answer:
Option E
Step-by-step explanation:
y = x /3
let x = 1, 2, 3
y = 0.333, 0.667, 1
y = x/2 + 40
let x = 1, 2, 3
y = 40.5, 41, 41.5
y = x
let x = 1, 2, 3
y = 1, 2, 3
y = 2x + 50
let x = 1, 2, 3
y = 52, 54, 56
y = 3x - 20
let x = 1, 2, 3
y = -17, -14, -11
The standard deviation is the spread of data, the data that is most spread is option E.
Rotation
The triangle DEF with vertices D (-4, 4), E (-1, 2), F (-3, 1). Graph the figure and its image after a 90 ° clockwise rotation about its origin.
Answer:
Step-by-step explanation:
The vertices of the already rotated triangle are:
D '(4, 4)
E '(1, 3)
F '(2, 1)
Answer:
D '(4, 4)
E '(1, 3)
F '(2, 1)
Step-by-step explanation:
6th-grade math, fill out the table! :)
Answer:
21 wins, table is attached.
Step-by-step explanation:
The ratio of 7 wins to 2 losses is 7:2. A ratio is just saying that every time one value is increased by 7, the other is increased by 2.
So we can fill out the table, in every iteration wins increases by 7 and losses increases by 2.
When we fill this out, we find that when losses is 6, wins is 21, so when you have 2 losses you have 21 wins.
Hope this helped!
Brainliest for the correct awnser!!! In general, when solving a radical equation with square roots, you should first isolate the radical and then _____ both sides.A.addB.squareC.multiplyD.subtract
Answer:
B
Step-by-step explanation:
Answer:
The answer for this Question is Elementary
It is B.
Find the value of x, rounded to the nearest tenth.
Answer:
x = 8.9 units
Step-by-step explanation:
We will use the theorem of intersecting tangent and secant segments.
"If secant and tangent are drawn to a circle from an external point, the product of lengths of the secant and its external segment will equal the square of the length of tangent."
8(8 + 2) = x²
x² = 80
x = √80
x = 8.944
x ≈ 8.9 units
Therefore, length of the tangent = 8.9 units
Find the graph of the inequality y>-(1/6)x+1.
Answer:
y > -x/6 + 1
Step-by-step explanation:
Hope this can help
The graph of the inequality [tex]y > -(\frac{1}{6} )x+1[/tex] is option "A" .
What is graph of inequality?The graph of an inequality in two variables is the set of points that represents all solutions to the inequality. A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality. The boundary line is dashed for > and < and solid for ≤ and ≥.If the symbol ≥ or > is used, shade above the line. If the symbol ≤ or < is used shade below the line.
According to the question
The inequality : [tex]y > -(\frac{1}{6} )x+1.[/tex]
now first we take out points to plot graph for that we will assume inequality to equation
i.e
[tex]y = -(\frac{1}{6} )x+1[/tex]
x y
0 1
6 0
Now , as inequality have > sign
i.e according to the graph of inequality rules:
The boundary line is dashed for > and < and If the symbol ≥ or > is used, shade above the line.
Therefore,
Graph will be option "A" only .
Hence, the graph of the inequality [tex]y > -(\frac{1}{6} )x+1[/tex] is option "A" .
To know more about graph of inequality here:
https://brainly.com/question/21857626
#SPJ3
he data represents the daily rainfall (in inches) for one month. Construct a frequency distribution beginning with a lower class limit of 0.000.00 and use a class width of 0.200.20. Does the frequency distribution appear to be roughly a normal distribution? 0.310.31 0 0 0 0.190.19 0 0.150.15 0 0.010.01 0.190.19 0.530.53 0 0
Answer:
It is not normally distributed as it has it main concentration in only one side.
Step-by-step explanation:
So, we are given that the class width is equal to 0.2. Thus we will have that the first class is 0.00 - 0.20, second class is 0.20 - 0.40 and so on(that is 0.2 difference).
So, let us begin the groupings into their different classes, shall we?
Data given:
0.31 0.31 0 0 0 0.19 0.19 0 0.150.15 0 0.01 0.01 0.19 0.19 0.53 0.53 0 0.
(1). 0.00 - 0.20: there are 15 values that falls into this category. That is 0 0 0 0.19 0.19 0 0.15 0.15 0 0.01 0.01 0.19 0.19 0 0.
(2). 0.20 - 0.40: there are 2 values that falls into this category. That is 0.31 0.31
(3). 0.4 - 0.6 : there are 2 values that falls into this category.
(4). 0.6 - 0.8: there 0 values that falls into this category. That is 0.53 0.53.
Class interval frequency.
0.00 - 0.20. 15.
0.20 - 0.40. 2.
0.4 - 0.6. 2.
The doubling time of a cityʹs population is 8 years. How long does it take for the population to quadruple.
Answer:
16 Years
Step-by-step explanation:
Find all of the angle measures in the image.
Answer:
Angle 2= 45
Angle 3= 45
Angle 4= 135
Angle 5= 135
Angle 6= 45
Angle 7= 45
Angle 8= 135
What is 0.09% written as a decimal?
A. 0.9
B. 0.009
C. 0.0009
D. 0.09
Answer:
C. 0.0009
Step-by-step explanation:
0.09/100
= 0.0009
Answer:A
Step-by-step explanation:0.09=0.9
A motorcycle stunt rider jumped across the Snake River. The path of his motorcycle was given
approximately by the function H(1) 0.0004.x2 + 2.582 + 700, where H is measured in
feet above the river and is the horizontal distance from his launch ramp.
How high above the river was the launch ramp?
What was the rider's maximum height above the river, and how far was the ramp when he reached maximum height?
Correct question:
A motorcycle stunt rider jumped across the Snake River. The path of his motorcycle was given
approximately by the function H(t) = - 0.0004.x2 + 2.582 + 700, where H is measured in
feet above the river and is the horizontal distance from his launch ramp.
How high above the river was the launch ramp?
What was the rider's maximum height above the river, and how far was the ramp when he reached maximum height?
Answer:
A) 700 feet ; 4866.7025 feet above the river
3227.5 Feets from the ramp
Step-by-step explanation:
Given the Height function:
H(t) = 0.0004x^2 + 2.582x + 700
H = height in feet above the river
x = horizontal distance from launch ramp.
How high above the river was the launch ramp?
H(t) = - 0.0004x^2 + 2.582x + 700
To find height of launch ramp above the river, we set the horizontal distance to 0, because at this point, the motorcycle stunt rider is on the launch ramp and thus the value of H when x = 0 should give the height of the launch ramp above the river.
At x = 0
Height (H) =
- 0.0004(0)^2 + 2.582(0)+ 700
0 + 0 + 700 = 700 Feets
B) Maximum height abive the river and how far the rider is from the ramp when maximum height is reached :
Taking the derivative of H with respect to x
dH'/dx = 2*-(0.0004)x^(2-1) + 2.582x^(1-1) + 0
dH'/dx = 2*-(0.0004)x^(1) + 2.582x^(0) + 0
dH'/dx = - 0.0008x + 2.582
Set dH'/dx = 0 and find x:
0 = - 0.0008x + 2.582
-2.582 = - 0.0008x
x = 2.582 / 0.0008
x = 3227.5 feets
To get vertical position at x = 0
Height (H) =
- 0.0004(3227.5)^2 + 2.582(3227.5)+ 700
- 4166.7025 + 8333.405 + 700
= 4866.7025 feet
4866.7025 feet above the river
3227.5 Feets from the ramp
Using quadratic function concepts, it is found that:
The launch ramp was 700 feet above the river.The maximum height is of 4866.7 feet.The ramp was 3227.5 feet along when he reached maximum height.The height after x seconds is given by the following equation:
[tex]H(x) = -0.0004x^2 + 2.582x + 700[/tex]
Which is a quadratic equation with coefficients [tex]a = -0.0004, b = 2.582, c = 700[/tex]
The height of the ramp is the initial height, which is:
[tex]H(0) = -0.0004(0)^2 + 2.582(0) + 700 = 700[/tex]
Thus, the launch ramp was 700 feet above the river.
The maximum height is the h-value of the vertex, given by:
[tex]h_{MAX} = -\frac{\Delta}{4a} = -\frac{b^2 - 4ac}{4a}[/tex]
Then, substituting the coefficients:
[tex]h_{MAX} = -\frac{(2.582)^2 - 4(-0.0004)(700)}{4(-0.0004)} = 4866.7[/tex]
The maximum height is of 4866.7 feet.
The horizontal distance is the x-value of the vertex, given by:
[tex]x_V = -\frac{b}{2a} = -\frac{2.582}{2(-0.0004)} = 3227.5[/tex]
The ramp was 3227.5 feet along when he reached maximum height.
A similar problem is given at https://brainly.com/question/24705734