Yes, knowing the value of b, the slope of the regression line, allows us to predict the correlation coefficient value with accuracy.
Regression and correlation techniques can be used to establish links between variables.
Every day, we refer to any form of association as a "correlation," using that word.
To determine whether or if there is a relationship between the variables under investigation, correlation analysis is used.
Although regression illustrates how the variables are related,
Correlation and regression analysis can be shown graphically using scatter plots.
According to the question,
If we know the value of the slopes of the regression line say byx and bxy
We can Calculate the value of Correlation coefficient by using the relation
=> r = √(byx × bxy)
Hence , Yes We can accurately guess the value of correlation when slope of regression line is given
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9. (5.NBT.B.7} Adrian ran 8.547 km in 1.5 hours. How many kilometers did Adrian *
run in one hour?
O 5.689 km
O5.869 km
5.698 km
Adrian run in one hour is 5.698 km.
How to calculate speed, Distance and Time ?
To work out speed, divide the distance of the journey by the time it took to travel, so speed = distance divided by time. To calculate time, divide the distance by speed. To get the distance, multiply the speed by time. You may see these equations simplified as s=d/t, where s is speed, d is distance, and t is time.Given,
Adrian ran in 1.5 hours = 8.547 km
We know, in 1.5 hours there is 90 minutes
so, in 1 min adrian ran = 8.547 / 90
= 0.09496 km
We need to find the km in one hour means in 60 minutes
So, Adrian ran in 60 min = 60 * 0.09496
= 5.6979 km or 5.698 km per hour
Hence, Adrian run in one hour is 5.698 km.
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a circle of radius 935.62 ft, centered at point a, intersects another circle of radius 959.630 ft, centered at point b. the x and y coordinates (in feet) of a are 553.70 and 1147.86, respectively, and those of b are 1162.93 and 269.83, respectively.
The point of interaction of two circles:
(x-a)²+(y-b)² = ro²
(x-c)²+(y-d)² = r1²
The e point of interaction of the two circles is given by the formulas given below:
D = √(c-a)²+(d-b)²
б = √(D+r0+r2)(D+r0-r2)(D-r0+r2)(-D+r0+r2)
X1,2 = a + c/2 + (c-a)(r0² - r1²)/2D² ± 2 b-d/D²
X1,2 = b + d/2 + (d-b)(r0² - r1²)/2D² ± 2 a-c/D²
r0 = 935.62 ft
r1 = 959.630 ft
a = 553.7
b = 1147.86
c = 1162.93
d = 269.83
First we calculate,
D = √(c-a)²+(d-b)²
= 1980.95 ft
Lets check whether these circles intersect or not:
D<r0+r1 and D> r0-r1
r0+r1 = 2166.57 ft and D = 1980.95 ft -192.51 = 192.51 which is less than D
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Part A: Given the function g(x) = |× + 31, describe the graph of the function, including the vertex, domain, and range. (5 points) Part B: If the parent function f(x) - |×] is transformed to h(x) = |× - 2, what transformation occurs from f(x) to h(x)? How are the vertex and range of h(x) affected?
A. The graph of the absolute value function is V-shaped, with the features given as follows:
Vertex: (-3,0).Domain: All real values.Range: [0, ∞).B. The transformation is that the function was shifted right two units, hence the features are given as follows:
Vertex: (2,0).Domain: All real values.Range: [0, ∞).What is the absolute value function?The absolute value function, with vertex (h,k), is defined as follows:
y = |x - h| + k.
The features of the function are given as follows:
Vertex: (h,k).Domain: All real values.Range: [k, ∞).For the first item, the function is |x + 3|, hence we just have to identify the features.
For the second function, the definition if h(x) = |x - 2|, with vertex at (2,0), meaning that the function was shifted two units right from the parent absolute value function y = |x|. The shift just changes the turning point of the graph, not altering domain and range.
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Using the 22n rule, determine the number of classes needed for the following data set sizes.
a) n = 50
b) n = 250
c) n = 1000
d) n = 3000
a) The number of classes needed when n = !
= 50 is
...
we have a room full of n people. any given pair of people are either friends or strangers. in this room, alex is considered the most popular because he has k friends, and no other person in the room has more than k friends. prove that we can find a group with at least n k 1 people such that no two members of the group are friends.
a group with at least n k 1 people such that no two members of the group are friends,We will prove this statement by inductive hypothesis.
Base Case: If n=k+1, then we can easily find a group with nk1 people such that no two members of the group are friends. We simply select the k+1 people in the room, excluding Alex. Since Alex has k friends, and no other person in the room has more than k friends, it follows that none of these k+1 people are friends.
Inductive Step: Assume that the statement is true for n=k+1. Now we must show that it is true for n=k+2.
We can select a group of k+1 people from the room, again excluding Alex. By the inductive hypothesis, we know that no two members of this group are friends. Now, we select the remaining person in the room, and add them to the group. This person cannot be friends with any of the members of the group, since Alex has k friends and no other person in the room has more than k friends. Therefore, the group we have formed has at least nk1 people, and no two members of the group are friends.
Therefore, by induction, we have proved that we can find a group with at least nk1 people such that no two members of the group are friends.
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se the alternating series estimation theorem to estimate the range of values of x for which the given approximation is accurate to within the stated error. check your answer graphically. (round your answers to three decimal places.) |error| < 0.05
The percent of error for the given measured value and the absolute error is equal to 0.392%
As given in the question,
Measurement value is equal to 12.8 inches
Absolute error in the measurement is equal to 0.05
True value is equal to ( Measurement value - absolute error )
= ( 12.8 + 0.05 )
= 12.75
Percent of error is given by
= |True value - Measured value |/ (true value) × 100
= [ | 12.75 - 12.8 |/ 12.75 ] × 100
= 0.392%
Therefore, the percent of error for the given measured value and the absolute error is equal to 0.392%
The given question is incomplete, I answer the question in general according to my knowledge:
A measurement is taken to be 12.8 in. and the absolute error is 0.05 in. What is the percent of error? Round off your answer to 3 decimal places.
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A line passes through the point (-4,8) and has a slope of -6 .
Write an equation in slope-intercept form for this line.
Answer:
y = (-6)*x - 16
Step-by-step explanation:
The slope-intercept form of a line is given by the equation:
y = mx + b
where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).
In this case, the line passes through the point (-4,8) and has a slope of -6, so we can plug these values into the equation to find the y-intercept:
y = (-6)*x + b
We know that the line passes through the point (-4,8), so we can substitute these values into the equation to solve for b:
8 = (-6)*(-4) + b
8 = 24 + b
b = -16
Therefore, the equation of the line in slope-intercept form is:
y = (-6)*x - 16
the limit of a function exists at a cluster point c if and only if the left- and right-handed limits both exist at c and are equal.
By using ε - δ definition of limit, the proof of
The limit of a function exists at a cluster point c if and only if the left- and right-handed limits both exist at c and are equal
has been shown below.
What is ε - δ definition of limit?
Let the function be f(x), cluster point be c and the limit be l. Then
the limit of a function exists at a cluster point c if
For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that |x − c |< δ ⟹ |f(x) − l| < ε
Let the limit exist at a cluster point c. Let the limit be l
For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that |x − c |< δ ⟹ |f(x) − l| < ε
For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that 0 < c - x < δ ⟹ |f(x) − l| < ε or
0 < x - c < δ ⟹ |f(x) − l| < ε
For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that c - δ < x < c ⟹ |f(x) − l| < ε or
c < x < c + δ ⟹ |f(x) − l| < ε
For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that c - δ < x < c ⟹ |f(x) − l| < ε and
For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that c < x < c + δ ⟹ |f(x) − l| < ε
So the left hand and right hand limit exist and are equal.
Let the left hand and right hand limit exist and are equal.
For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that c - δ < x < c ⟹ |f(x) − l| < ε and
For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that c < x < c + δ ⟹ |f(x) − l| < ε
Let [tex]\delta_3 = min\{\delta_1, \delta_2\}[/tex]
For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that c - [tex]\delta_1[/tex] < x < c ⟹ |f(x) − l| < ε and
For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that c < x < c + [tex]\delta_2[/tex] ⟹ |f(x) − l| < ε
For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that c - [tex]\delta_1[/tex] < x < c or c < x < c + [tex]\delta_2[/tex]⟹ |f(x) − l| < ε
For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that |x - c| < [tex]\delta_3[/tex] ⟹ |f(x) − l| < ε
The limit of a function exists at a cluster point c and the limit is l
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Complete each of the following statements with the letter that represents the expression.
Answer:
B
Step-by-step explanation:
[tex]3x {}^{2} - 7x + 14 + 5 {x }^{2} + 4x - 6 = 8 {x}^{2} - 3x + 8[/tex]
In testing for correlation the relationship between two variables, the best fitting line is often call the regression equation and denoted as ^y=b1x+b0. What formula is used to compute the slope of this line and its y intercept?
For the regression equation, ŷ = b₀ + b₁x where b₁ is slope of this line and it is equals to (n∑xy - ∑x∑y)/(n∑x² - (∑x)²) and b₀ is y-intercept which is equals to (∑y - b₁ ∑x)/n .
What is Regression line in simple linear regression model?A regression line indicates the linear relationship between the dependent variables on the y-axis and the independent variables on the x-axis. Correlation is determined by analyzing the data pattern formed by the variables.
The regression line is plotted closest to the data points in the regression plot. We use the ordinary least squares estimation method (O.L.S.E), to find the formulas to calculate the slope and intercept of the regression line, which minimizes the sum of squares due to the error. A simple linear regression model is given by y = b₀ + b₁x --(*)
where y : dependent variable
x: independent variable
b₁ --> slope of regression line
b₀ --> y-intercept
We have , regression line is ,
ŷ = (slope )x+ (y intercept)
ŷ represet the predicted value.
The formulas to compute slope(b₁) value and y-intercept (bo) value of regression line are following:
b₁ = (n∑xy - ∑x∑y)/(n∑x² - (∑x)²) and
b₀ = ŷ - b₁x = (∑y - b₁ ∑x)/n
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Find a power series representation for the function; find the interval of convergence. (Give your power series representation centered at x = 0.)
f(x)= 1/(1-9x)
sum from n=0 to infinity [?] provided |x| < [?]
The power series representation for the given function is:
1+ 9x + (9x)² + (9x)³ + .... (9x)ⁿ (where 0 ≤ n ≤ ∞).
What is the power series?
Power series is a sum of terms of the general form aₙ(x-a)ⁿ. Whether the series converges or diverges, and the value it converges to, depends on the chosen x-value, which makes power series a function.
Let u = 9x.
Return to the series above and replace each u with a 9x directly:
Where 0 n , 1 + 9x + (9x) 2 + (9x) 3 +.... (9x) n
Here, the interval of convergence is easily found. It follows that
|9x| 1 -1/9 x 1/9 because we know that geometric series must have | u | = 1
Finally, we may leverage the fact that geometric series have a sum to get the sum: S = a / (1 - u).
Here, u = 9x and a = 1
Therefore, the total is simply S = 1 /(1 - 9x).
Any sum can be calculated provided x is between -1/9 and x and less than 1/9.
Hence, The power series representation for the given function is:
1+ 9x + (9x)² + (9x)³ + .... (9x)ⁿ (where 0 ≤ n ≤ ∞).
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of the five points $(3, 10),$ $(6, 20),$ $(12, 35),$ $(18, 40)$ and $(20, 50),$ what is the sum of the $x$-coordinates of the points that lie in the region above the line $y
The sum of the x-coordinates of the points that lie in the region above the straight line y = 2x + 7 in coordinate plane is thirty-eight.
A point lies above the straight line , y = 2x + 7 in co-ordinate plane . If its y -coordinate is greater than two times its x-coordinate plus 7. Now, we are checking the each ordered pair one by one ,
(i) plug x = 3 and y = 10
2x + 7 = 3×2 + 7 = 13 > 10
(ii) plug x = 6 in 2x+7
=> 2× 6 + 7 = 19 < 20
(iii) x = 12
=> 2x + 7 = 2× 12 + 7 = 31 < 35
(Iv) x = 18
=> 2x + 7 = 2× 18 + 7 = 43 > 40
(v) x = 20
2x + 7 = 2×20 + 7 = 47 < 50
We see (6, 20) , ( 12,35) and (20,50) satisfy this condition. Now, we determine the sum of x-coordinates . The sum of the x-coordinates of these points is 6 + 12 + 20 = 38 . So, required sum of x-coordinates is 38.
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Complete question:
Of the five points (3, 10), (6, 20),(12, 35), (18, 40)and (20, 50), what is the sum of the x-coordinates of the points that lie in the region above the line
y = 2x + 7 in coordinate plane.
what is the equation of the line that passes through (6,2) and (8,0)
Answer:
y = -x + 8
Step-by-step explanation:
First find the slope (m):
m = (0-2) / (8-6) = -1
Next put one of the points (I pick (8,0)) into the point-slope formula:
y-y1 = m(x-x1)
y-0 = -1(x-8)
Now write it in slope-intercept form:
y = -x + 8
PLEASE HELP 40 POINTS PLEASE HELP PLEASE HELP 40 POINTS ASAP
What major change took place in the U.S. economy during the mid-1800s?
A.
Workers began moving to cities to work in factories.
B.
The government began managing the economy.
C.
Americans began buying most products from overseas.
D.
Farming became the most important sector of the economy.
Answer:
A
Step-by-step explanation:
A. This is true and occurred during the industrial revolution
B. The government had not started managing the economy (yet)
C. This was happening even in the 1700s
D. This was also more apparent in the 1700s with the 13 colonies, especially with cash crops such as tobacco.
If x + y = x – y, then x – 2y is:
The value of the expression is x
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
x + y = x - y
x - 2y = ?
Recall that. we have
x + y = x - y
Add y to both sides of the equation
So, we have the following representation
x + 2y = x
Add -2y to both sides of the equation
So, we have the following representation
x = x - 2y
Rewrite as
x - 2y = x
Hence, the solution of x - 2y is x
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1.
Mateo brought in donuts for his class. Each box had 3 rows of donuts with 5
donuts in each row. He bought 8 boxes. How many donuts did he buy?
2.
At Benny's Café, a mixed-greens salad costs $5.75.
Additional toppings can be added for $0.75 each.
Which function could be used to determine the
cost, c(s), in dollars, of a salad with s additional
toppings?
A.
C.
c(s) = 0.75s +5.75
D.
D. c(s) = 0.75s +5.00
c(s) = 5.75s +0.75 B.
B.
c(s) = 5.00s +0.75
Determine the area of the shaded region in the following figure.\
y=x
y=x^2-2
The area of the shaded region is 425 cm².
Determine the area of the shaded region ?Let us find the area of the entire figure first and subtract the unshaded region area to find the area of the shaded region.
The given figure is of a square of side 25 cm.
Total area = 25²
=> 625 cm²
The shaded figure inserted is a rhombus.
Apart from this , we can observe four unshaded triangles of equal area.
Area of each individual triangle :
=> ½ × 5 × 20
=> 50 cm²
Area of 4 triangles ;
=> 200 cm²
Remaining area of the shaded figure :
=> 625 - 200
=> 425 cm² .
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12, 18, 10, 20, 8, pattern
Answer:
The pattern is in the order of even number being added or subtracting (takes turns)
Step-by-step explanation:
12,18,10,20,8
12 to 18 is plus 6
18 to 10 is minus 8
10 to 20 is plus 10
20 to 8 is minus 12
[tex]12 + 6 = 18 \\ 18 - 8 = 10 \\ 10 + 10 = 20 \\ 20 - 12 = 8 \\ 8 + 14 = 22 \\ 22 - 16 = 6 \\ = 24 \\ = 4 \\ = 26 \\ = 2 \\ ..[/tex]
Question 14 of 25
Which of the following functions is graphed below?
The function of the line and parabola shown in the graph is x + 6 ≤ 1 and x² + 3 > 1 respectively, so, option A is correct.
What is function?Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and co-domain, respectively.
Given:
The graph of the function,
Calculate the equation of the line which is passing through (-6, 0) and (0, 5) as shown below,
y - 5 = 5 - 0 / 0 - (-6) (x - 0)
y - 5 = 5 / 6 x
6y - 30 = 5x
And the equation of the parabola can be written as,
x² + 3 = 0
From the graph, it can be seen that the solution of the line is where the line graph and parabola graph can meet,
Thus, the line will be x + 6 ≤ 1 and x² + 3 > 1.
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answer.
3) Samantha baked 16 chocolate cupcakes for her children. If the cupcakes are shared
equally among four of her children, how many cupcakes will each child get?
cupcakes are shared
equally among four of her children, 4 Cupcakes will each child get
what do you mean by share?
An equity ownership stake in a corporation is represented by a share. Dividends from any earnings the company makes are owed to the shareholders. They also bear the brunt of any losses the business may sustain.
Ordinary shares.
Non-voting shares.
Preference shares.
Redeemable shares.
There are a number of different types of shares including equity shares, preference shares, right shares, bonus shares, sweat equity shares (where companies issue shares at a discount or for consideration) and employees stock options plans.
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A typical tip in a restaurant is 15% of the total bill. If the bill is $110, what would the typical tip be?
Answer:
$16.50
Step-by-step explanation:
$110 * 15% =
$110 * 15/100 = ==> percent value is 100 times greater than the fraction
$1650/100 = ==> multiply 110 and 15
$16.50
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Answer:
Tip=[tex]16.50[/tex]
Step-by-step explanation:
Tip%=15
Bill=$110
Tip=[tex]\frac{15}{100}[/tex]x[tex]110[/tex]
Tip=[tex]16.50[/tex]
Hope this helps u
Question 4 of 10
Which situation best illustrates the concept of absolute advantage?
A. A German factory can build more sports cars than foreign factories.
B. Most of the world's largest companies have operations in many different countries.
C. The total value of Japanese imports is greater than the total value of the country's exports.
D. A French restaurant buys food from nearby farms to support the local economy.
Situation which illustrates best the concept of absolute advantage is: Option A - A German factory can build more sports cars than foreign factories.
Absolute advantage is the potential of an individual, a company, or a country to produce a higher quantity of output than its competitors while using the same inputs. It means an institution with absolute advantage has more efficiency in producing a particular commodity than its rivals. It utilizes lower marginal cost (materials and labor), making its output much cheaper than others.
A factory in German has an absolute advantage because it can produce more sports car than foreign countries. Absolute advantage makes the factory more competitive in the market than its rivals.
Therefore, the correct answer is option A.
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please help me with this
Hamadi and Aisha solve this problem in two different ways.
Carlos paid a total of $64 to rent a car.
The rental company charges a one-time fee of $20, with an additional charge of $0.50
per mile driven.
How many miles did Carlos drive the rental car?
Use the drop-down menus to complete the sentences below.
The number of miles Carlos drove the rental car is 88 miles.
How to find the number of miles Carlos drove?Carlos paid a total of $64 to rent a car. The rental company charges a one-time fee of $20, with an additional charge of $0.50 per mile driven.
Therefore, the number of miles Carlos drive the rental car can be calculated as follows:
Using equation,
let
x = number of miles driven
64 = 20 + 0.50x
subtract 20 from both sides of the equation'
64 - 20 = 20 - 20 + 0.50x
44 = 0.50x
divide both sides by 0.50
Therefore,
44 / 0.50 = 0.50x / 0.50
x = 88
Therefore, the number of miles is 88 miles.
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diane will donate up to to charity. the money will be divided between two charities: the city youth fund and the educational growth foundation. diane would like the amount donated to the educational growth foundation to be at least three times the amount donated to the city youth fund. let denote the amount of money (in dollars) donated to the city youth fund. let denote the amount of money (in dollars) donated to the educational growth foundation. shade the region corresponding to all values of and that satisfy these requirements.
The value of x is $53.34 but cannot exceed $115, while the value of y can be as low as $160 but cannot exceed $345.
What is an inequality?Relationships that compare two numbers or other mathematical expressions in an unequal manner are known in mathematics as inequalities. The most common use is to compare the magnitude of two numbers on a number line.
The answer to the query is
Diane will make a charitable donation "up to $460," which indicates it can be less than or equal to 460 but not more. Then,
$460 donated to charity (max)
plus $160 for educational (160 being the minimum)
Education is also stated to be three times (or greater) than City.
If x represents the city and y represents education, then
x + y = 460 . And we are aware that y 3x.
x + 3x = 4x = 460
x = 115.
This implies that she will contribute $345 to Educational when she donates 3 times (or $115) to City. The maximum value is these.
She won't provide more than $460.
Earlier, Educational had a minimal need.
When y = 160,
x equals y/3,
=> x = 160/3 = $53.34. She so gave 213.34 dollars, which is still less than $460.
As a result, x (which is City) might be anywhere between $53.34 and $115.
x, which stands for educational, might be as little as $160 or as high as $345.
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The concept of best-, worst-, and average-case analyses extends beyond algorithms to other counting problems in mathematics. Recall that the height of a binary tree is the number of edges in the longest path from the root to a leaf. Find the best-case height of a binary tree with seven nodes.
[-12 Points) DETAILS SCALCET8 12.3.011. If u is a unit vector, find u v and u. w. (Assume v and w are also unit vectors.) u u v = Uw= 5. [-12 Points] DETAILS SCALCET8 12.3.015. Find the angle between the vectors. (First find an exact expression and then approximate to the nearest degree.) a = (7,2), b = (3,-1) exact approximate 6. [-/2 points) DETAILS SCALCET8 12.3.019. Find the angle between the vectors. (First find an exact expression and then approximate to the nearest degree.) a = 71 - 2j + k, b = 3i - k exact approximate
Details scalcets,
a) If u is unit vector , then, ⃗u.⃗v = 1/2 and ⃗u.⃗w = - 1/2 where v and w also unit vectors.
b) Exact value of angle between the vectors is 34.3803442 and Approximation value, 34.4..
c) Exact value of the angle between the vectors, a = 71 - 2j + k, b = 3i - k is 30.60889766 ~ 30.61 (approximation value).
What is Unit vector ?In mathematics, a unit vector is defined as a normed vector space is a vector of length one.
a) If u is a unit vector , we have to calculate ⃗u.⃗v and ⃗u.⃗w where v and w are also unit vectors.
We know that, Angle between two vectors θ is
Cosθ = u⃗ .⃗v/|u| |v|
=> cos 60° |u| |v| = ⃗u.⃗v
=> ⃗u.⃗v = 1/2(1)(1) = 1/2
Also, Cosθ = ⃗u.⃗v/|u| |w|
=> Cosθ |u| |w| = ⃗u.⃗w
=> ⃗u.⃗w = cos 120° (1)(1)
=> ⃗u.⃗w = -1/2
So, ⃗u.⃗v = 1/2 and ⃗u.⃗w = - 1/2
b) We have, a = (7,2), b = (3,-1)
Cosθ = a.b/|a| |b|
|a| = √(7)²+ (2)² = √49+4 = √53
|b| = √(3)²+ (-1)²= √9+1 = √10
a.b = 7×3 - 2×1 = 21 - 2 = 19
so, Cos θ = 19/√10 (√53) = 19/√530
=> θ = Cos⁻¹( 19/√530)
=> θ = 34.3803442 ~ 34.4
c) We have, a = 7i - 2j + k, b = 3i - k
Cos θ = a.b/|a| |b|
|a| = √(7)² + (-2)² +(1)² = √49+4+1 = √54
|b| = √(3)²+ 0 +(-1)² = √9+1 = √10
a.b = (7i - 2j + k).(3i - k) = 21 -0 - 1 = 20
Cosθ = 20/√10√54 = 20/√540
θ = cos⁻¹(20/√540) = 30.60889766 ~ 30.61
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Two buses are driving along parallel freeways that are 12 mi apart, one heading east and the other heading west. Assuming that each bus drives a constant 58 mph, find the rate at which the distance between the buses is changing when they are 13 mi apart and heading toward each other. (Round to 2 decimal places) a. -44.62 mph b. 44.62 mph c. 22.31 mph d. -22.31 mph
The rate at which the distance between the buses is changing when they are 13 miles apart is -85.25 mph.
Given, two buses are driving along parallel freeways that are 12 miles apart, one heading east and the other heading west.
Assuming that each bus drives a constant 58 mph.
Now, we have to find the rate at which the distance between the buses is changing when they are 13 miles apart and heading towards each other.
Considering distance as a function of time,
D = f(t) = √((12)² + (13 - 116t)²)
f'(t) = (13 - 116t)(-116)/√((12)² + (13 - 116t)²)
f'(0) = (13 - 116(0))(-116)/√((12)² + (13 - 116(0))²)
f'(0) = -1508/√(144 + 169)
f'(0) = -1508/√313
f'(0) = -85.25
So, the rate of distance is decreasing at the rate of 85.25
Hence, the rate of distance is decreasing at the rate of 85.25
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Assume the random variable X is normally distributed with mean μ = 50 and standard deviation σ= 7, Compute the probability. Be sure to draw a normal curve with the area corresponding to the probability shaded. P(X> 37) Click the icon to view a table of areas under the normal curve. Which of the following normal curves corresponds to P(X> 37)? OA. OC. 37 50 37 50 37 50 PX-37)-□ (Round to four decimal places as needed.)
The normal curve that corresponds to P (X > 37) is C, as the shaded area corresponds to the probability of 0.4207.
The normal curve is a bell-shaped curve which is used to represent a continuous probability distribution. It is used to represent the probability of a random variable X, which is normally distributed with mean μ and standard deviation σ. In this case, we have X with mean μ = 50 and standard deviation σ = 7. To compute the probability P(X > 37), we first draw a normal curve with the area corresponding to the probability shaded. Then, we can look up the area from the table of areas under the normal curve. The area corresponds to 0.4207, and the normal curve that corresponds to this probability is C, as the shaded area corresponds to the probability of 0.4207. This normal curve has the mean of 50 and the standard deviation of 7, with the area beyond 37 shaded.
P(X > 37)
= 1 - P(X ≤ 37)
= 1 - 0.4207
= 0.5793
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