Solution :
a).
Given :
R = 0.636, [tex]$S_x = 99$[/tex], [tex]$S_y=113, M_x=108, M_y=129$[/tex]
Here R = correlation between the two variables
[tex]$S_x , S_y$[/tex] = sample standard deviations of the distance and travel time between the two train stops, respectively.
[tex]$M_x, M_y$[/tex] = means of the distance and travel between two train stops respectively.
The slope of the regression line is given by :
Regression line, [tex]b_1[/tex] [tex]$=R \times \left(\frac{S_y}{S_x}\right)$[/tex]
[tex]$=0.636 \times \left(\frac{113}{99}\right)$[/tex]
= 0.726
Therefore, the slope of the regression line [tex]b_1[/tex] is 0.726
The equation of the regression line is given by :
[tex]$\overline {y} = b_0+b_1 \overline x$[/tex]
The regression line also has to pass through the two means. That is, it has to pass through points (108, 129). Substituting these values in the equation of the regression line, we can get the value of the line y-intercept.
The y-intercept of the regression line [tex]$b_0$[/tex] is given by :
[tex]$b_0=M_y-(b_1 \times M_x)$[/tex]
= 129 - (0.726 x 108)
= 50.592
Therefore, the equation of the line is :
Travel time = 20.592 + 0.726 x distance
b).[tex]\text{ The slope of the line predicts that it will require 0.726 minutes}[/tex] for each additional mile travelled.
The intercept of the line, [tex]$b_0$[/tex] = 0.529 can be seen as the time when the distance travelled is zero. It does not make much sense in this context because it seems we have travelled zero distance in 50.529 minutes, but we could interpret it as that the wait time after which we start travelling and calculating the distance travelled and the additional time required per mile. Or we could view the intercept value as the time it takes to walk to the train station before we board the train. So this is a fixed quantity that will be added to travel time. It all depends on the interpretation.
c). [tex]$R^2=0.404$[/tex]
This means that the model accounts for around 40.4% variation in the travel time.
16. Using divisibility tests, check whether the number 240720 is divisible by
2, 3, 4, 5, 6, 8, 9, 10 and 11. (Give reason)
find the quotient of 8 divided by one-third, multiply 8 by
A:1/8
B:1/3
C:3
D:8
are the possible answers
Answer:
find the quotient of 8 divided by one-third, multiply 8 by
A:1/8
B:1/3( true
C:3
D:8
are the possible answers
Which one is this please help thank u
Answer:
isosceles
Step-by-step explanation:
Two sides are the same length as indicated by the lines on the sides.
This tells use that the triangle is isosceles
Answer:
Hi, this an isoceles triangle
Step-by-step explanation:
An isoceles triangle has 2 equal sides
A right angled one has a right angle (90 degrees)
An equilateral traingle has all of his sides equal
A scalene has all of his sides different.
So this must be an isoceles triangle because there is basically a proof of the two equal sides (the bars).
Hope its clear!
pls help asap!!
For the following geometric sequence, find the recursive formula.
(-80,20,-5...)
Answer:
For the geometric sequence, it has two forms of formula
We are interested in the recursive formula now
{-80, 20, -5, ...}
The common ratio is (20/-80)=(-5/20)=-1/4=-0.25
So our recursive formula would bea_n=a_{n-1}*(-0.25)=a_{n-1}*(- \frac{1}{4} )an=an−1∗(−0.25)=an−1∗(−41)
Step-by-step explanation:
For the geometric sequence, it has two forms of formula
{-80, 20, -5, ...}
The common ratio is (20/-80)=(-5/20)=-1/4=-0.25
So our recursive formula would be a n=a {n-1}*(-0.25)=a_{n-1}*(- \frac{1}{4} )an=an−1∗(−0.25)=an−1∗(−41)
3.) If y varies directly as x and y = 24 when x = 6, find the variation constant and the equation of variation.
3.) If y varies directly as x and y = 24 when x = 6, find the variation constant and the equation of variation.
Solution:-A. Express the statement “y varies directly as x”, as y = kx .
B. Solve for k by substituting the given values in the equation.
[tex]\sf\rightarrow{y = kx}[/tex]
[tex]\sf\rightarrow{24 = 6k}[/tex]
[tex]\sf\rightarrow{K = \frac{24}{6} }[/tex]
[tex]\sf\rightarrow{K={\color{magenta}{4}}}[/tex]
Answer:-Therefore, the constant of variation is 4.C. Form the equation of the variation by substituting 4 in the statement y = kx. Thus , y = 4 x.
[tex]{\large{—————————————————————}}[/tex]
#CarryOnMath⸙
1)
Ay
X
1
A)
Nin
B) -2
2
C)
D) 2.
2
Answer:
A) -1/2
Step-by-step explanation:
the slope is defined by the ratio of y/x.
that means that for a change of a certain number of units in x, y changes this number of units.
e.g. a slope of 5/3 means, if x changes by 3 units, y changes by 5.
the graphic shows a line that goes "down" with increasing x.
that means the slope is negative.
that eliminates C and D.
and we see that when x increases by 2 units, y decreases by 1 unit.
that means the slope is -1/2.
An industrial process produces batches of a chemical whose impurity levels follwo a normal distribution with standard deviation 1.6 grams of chemical. A random sample of 100 batches is selected in order to estimate the population mean impurity level. The probability is 0,0367 that the sample mean impurity level exceeds the population mean by how much?
Answer:
The probability is 0,0367 that the sample mean impurity level exceeds the population mean by 0.2864 grams of chemical.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Standard deviation 1.6 grams of chemical. Random sample of 100.
This means that [tex]n = 100, s = \frac{1.6}{\sqrt{100}} = 0.16[/tex]
The probability is 0,0367 that the sample mean impurity level exceeds the population mean by how much?
Z multiplied by s, in which Z has a p-value of 1 - 0.0367 = 0.9633, so Z = 1.79.
1.79*0.16 = 0.2864.
The probability is 0,0367 that the sample mean impurity level exceeds the population mean by 0.2864 grams of chemical.
Solve each question (a, b, c) and show your work. Thank you <3
Answer:
a) 112 ft.
b) 256 ft. and 3 seconds
c) 7 seconds
Step-by-step explanation:
a) The model rocket is lauched from a platform. To find the height of the platform, we need to find h when t = 0, because the rocket starts from the platform when no time has elapsed:
[tex]h=-16t^2+96t+112[/tex]
[tex]h=-16*0+96+0+112\\\\h=112[/tex]
Therefore, the height of the platform is [tex]\fbox{112}[/tex] ft.
b) If you learned calculus before, we can find the maximum height easily. We take the derivative of h and set it equal to 0. Remember, the derivative of a function is simply the slope of it at an instantaneous point. At the maximum point of a function, it's slope equals to 0.
[tex]h=-16t^2+96t+112\\h'=-32t+96+0\\h'=-32t+96[/tex]
Ok! Let's set the derivative of h to 0!
[tex]0=-32t+96\\-96=-32t\\t=3[/tex]
We now know how long it takes for the rocket to reach maximum point (t represents seconds), but we also need to find the maximum height. We can simply plug our t=3 into the function of h, because t=3 is the point where the rocket reaches maximum height:
[tex]h(3)=-16(3)^2+96*3+112\\h(3)=-144+288+112\\h(3)=256[/tex]
The maximum height of the rocket is [tex]\fbox{256}[/tex] ft and the rocket takes [tex]\fbox{3}[/tex] seconds to reach the height.
c) The rocket reaches the ground when h equals 0. We can set up the equation to solve for it:
[tex]h=-16t^2+96t+112\\0=-16t^2+96t+112\\0=-16(t+1)(t-7)\\0=(t+1)(t-7)\\t=-1, t=7[/tex]
However, time can never be negative.
Therefore, it takes the rocket [tex]\fbox{7}[/tex] seconds to reach the ground.
I hope this helps! Let me know if you have any questions :)
Bob's Gift Shop sold 650 cards for Mother's Day. One salesman, Scarlett, sold 10% of
the cards sold for Mother's Day. How many cards did Scarlett sell?
Answer:
65
Step-by-step explanation:
To find the amount of something given a percentage, we first must translate the percentage into a fraction or decimal. One way to do this is to divide the percentage by 100. In this case, we can divide 10% by 100 to get 0.1
We can then multiply the percent by the total, or 100%. In this case, we have 0.1 of 650, so we multiply the two to get 0.1 * 650 = 65 as 10% of 650, or how many cards Scarlett sold
Answer:
65
Step-by-step explanation:
650 x .10 (or 10%)=65
What is a demand schedule?
А.
a chart that shows the demand for a type of product at various prices
B.
a graph that shows the demand for a product at a single price point
C.
a chart that shows the demand for a product at various prices
Answer:
Answer is C
Step-by-step explanation:
In demand when the price goes up the quantity goes up and when the price goes down the quantity also goes down
In Supply when the price goes up the quantity goes down and when the price goes down the quantity goes up
Demand Schedule is a Chart
Demand Curve is a graph
Supply Schedule is a Chart
Supply Curve is a graph
Hope this helps
Step-by-step explanation:
[tex]hope \: it \: helps[/tex]
The name of the circle pictured is circle C
A. True
B. False
Answer:
TRUE IS THE ANSWER
Step-by-step explanation:
The name of the circle pictured is circle C is True statement.
What is Circle?A circle is a collection of points in a plane that are all equally spaced apart from one another. The radius is the distance from the centre, while the centre is the location of the point. The diameter is defined as twice the radius. A complete angle, which is equal to or radians, is the angle that a circle subtends from its centre.
we have a graph for a circle.
We know a circle many parts such as Center, Radius, Diameter, Chord, etc.
A circle usually know from its Center.
Also, the center of circle shows the point of circle.
Thus, the given statement is True.
Learn more about Circle here:
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pls I have limited time left pls help
Answer:
2B+5C
Step-by-step explanation:
Multiply them out....
2B=2*(4i-j) = 8i-2j
5C=5*(2i+3j) = 10i+15j
2B+5C= 8i-2j+10i+15j =18i+13j = A
9514 1404 393
Answer:
a) 2B +5C
Step-by-step explanation:
It is probably easiest to simply try the answer choices. You find the first one works, which means it is the one you want.
2B +5C = 2(4i -j) +5(2i +3j) . . . . choice (a)
= 8i -2j +10i +15j
= 18i +13j = A
__
In general, you can solve for the coefficients p and q that make ...
pB +qC = A
p(4i -j) +q(2i +3j) = 18i +13j
(4p+2q)i +(-p +3q)j = 18i +13j
Equating the coefficients of i and j gives us 2 equations in p and q.
4p +2q = 18
-p +3q = 13
Adding 2 times the second equation to 1/2 the first, we get ...
1/2(4p +2q) +2(-p +3q) = 1/2(18) +2(13)
7q = 35
q = 5
Using the second equation to find p, we get ...
p = 3q -13 = 3(5) -13 = 2
These coefficients tell us ...
A = 2B +5C . . . . . . . matches choice (a)
help me find the perimeter of this square. if you can do it step by step please!
Answer:
396
Step-by-step explanation:
It's a square.
That means that all four sides are equal.
So the two expressions you have been given are equal.
2.5x + 76.5 = 12x - 9 Subtract 2.5x from both sides.
-2.5x -2.5x
76.5 = 9.5x - 9 Add 9 to both sides
9 9
85.5 = 9.5x Divide by 9.5
85.5/9.5 = x
x = 9
That is just the value for x. It is not the answer
Side = 12x - 9
Side = 12*9 - 9
Side = 108 - 9
Side = 99
The perimeter = 4 * Side
The perimeter = 4 * 99
Perimeter = 396
emma can read 4 pages of a book in 8 minutes how many pages can she read per minute if she still had it 24 pages how many pages are there in the book
Answer:
Emma can read 30 pages per minute
Number of book pages 28
Step-by-step explanation:
If f(x)=2x²-x find f(-3)
Answer:
21
Step-by-step explanation:
f(x) = 2x^2 - x
f(-3) = 2*(-3)^2 - (-3)
=2*9 +3
=18 +3
=21
Answer: 21
Step-by-step explanation: To find f(-3) or the value of the function when x = -3, we plug in a -3 for the x in our function and we have 2(-3)² - (-3).
Start by simplifying the exponent to get 9.
So we have 2(9) - (-3) or 18 + 3 which is 21.
using the digits 0-9 at most one time each fill in the boxes so that the fraction equals the decimal
Step-by-step explanation:
Z 00m
336"083"2553
(wZE2XQ) are
Rewrite the equation by completing the square.
x^2 + 7x + 12 = 0
Answer:
x^2 + 7x + 12 = 0
x^2 + 7x = -12
(+3)(+4)=0
=−3
=−4
I also love r o blox
Hope This Helps!!!
Answer:
(x + [tex]\frac{7}{2}[/tex] )² - [tex]\frac{1}{4}[/tex] = 0
Step-by-step explanation:
Given
x² + 7x + 12 = 0
To complete the square
add/subtract ( half the coefficient of the x- term)² to x² + 7x
x² + 2([tex]\frac{7}{2}[/tex] )x + [tex]\frac{49}{4}[/tex] - [tex]\frac{49}{4}[/tex] + 12 = 0
(x + [tex]\frac{7}{2}[/tex] )² - [tex]\frac{49}{4}[/tex] + [tex]\frac{48}{4}[/tex] = 0 , that is
(x + [tex]\frac{7}{2}[/tex] )² - [tex]\frac{1}{4}[/tex] = 0
5.
An object has a constant acceleration of 40 ft/sec2, an initial velocity of -20 ft/sec, and an initial position of 10 ft. Find the position function, s(t), describing the motion of the object. (10 points)
You can solve for the velocity and position functions by integrating using the fundamental theorem of calculus:
a(t) = 40 ft/s²
v(t) = v (0) + ∫₀ᵗ a(u) du
v(t) = -20 ft/s + ∫₀ᵗ (40 ft/s²) du
v(t) = -20 ft/s + (40 ft/s²) t
s(t) = s (0) + ∫₀ᵗ v(u) du
s(t) = 10 ft + ∫₀ᵗ (-20 ft/s + (40 ft/s²) u ) du
s(t) = 10 ft + (-20 ft/s) t + 1/2 (40 ft/s²) t ²
s(t) = 10 ft - (20 ft/s) t + (20 ft/s²) t ²
A trinomial is a perfect square when two terms are
a. Positive
b.negative
c. Neither positve
d. Either negative
Answer:
a trinomial is a perfect square trinomial if it can be factorized into a binomial multiplies to itself. In a perfect square trinomial, two of your terms will be perfect squares.
The sum of three numbers is fourteen. The first number minus three times the third number is the second number. The second number is six more than the first number. Find the three numbers.
Answer:
1st number (x) = 5
2nd number (y) = 11
3rd number (z) = -2
Step-by-step explanation:
Let the generic solution for this problem be x + y + z = 14.
The first number minus three times the third number equals the second number, so x - 3z = y. The second number is 6 more than the first number, so y = 6 + x.
x - 3z = y, we know that y = 6 + x, so the equation becomes x - 3z = 6 + x.
After some arithmetic, we find that z = -2.
Plugging our knowns back into the generic solution becomes:
x + x - 3z + z = 14
2x - 3(-2) - 2 = 14
2x + 6 - 2 = 14
2x + 4 = 14
2x = 10
x = 5
So we know that z = -2, and x = 5, it's just simple substitution from there.
5 + y + (-2) = 14
5 + y = 16
y = 11
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YO LISTEN UP I GIVE SOMEONE 50 POINTS IF THEY ANSWER THIS QUESTION. answer it correctly
Emma and Zeke own an on-line business, EZ Coasters, that sells cork beverage coasters, which can be bought plain or with logos. The price for both types of coasters is $3.00 each. There is also a one-time set-up charge of $25 for coasters with a logo.
1) Write an equation describing the relationship between:
a) The number of plain coasters bought and the cost of the coasters.
b) The number of coasters with a logo bought and the price of the coasters.
c) Is either coaster relationship proportional? Explain in writing how you know.
d) Explain what the unit rate of the line described by each equation means in the context of the coasters.
2) EZ Sales also sells plain natural sandstone coasters for $4.00 each.
a) Write the equation describing this relationship.
b) Indicate whether or not it is a proportional relationship and explain why?
c) Will the graph of this equation ever intersect the graph of the equations for either of the other two EZ Coasters? Explain in typing how you made your decision.
Answer:
.
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
Factor completely, then place the factors in the proper location on the grid. 25a2 +9b2 + 30ab
Answer:
(5a+3b)(5a+3b) or SQ(5a+3b)
Step-by-step explanation:
Now you can plot by referring to the above factors
consider the figure below
Answer:
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What is the probability of spinning a natural number and a number less than 5?
Answer:
The probability of spinning a 5 or less is 1/8 or, you can say ⅛
Really Hope I helped! ♡♡♤♤♧♧
The probability of spinning a natural number and a number less than 5 would be 2/3.
What is probability?The probability exists the branch of mathematics involving numerical descriptions of how likely an event is to happen, or how likely it exists that a proposition is true. The probability of an event exists in a number between 0 and 1, where, roughly speaking, 0 demonstrates the impossibility of the event and 1 demonstrates certainty.
No of total outcomes =6
No of favorable outcomes=4 {1,2,3,4}
Therefore, Probability of getting a number less than 5 is= 4/6 = 2/3.
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What is the effect on the graph of the function f(x) = 2* when f(x) is replaced with f(-x)?
A)
vertical stretching
B)
vertical compression
horizontal compression
D)
horizontal stretching
Simplify the expression
Answer:
6
Step-by-step explanation:
3 sqrt(20) / sqrt(5)
We know that sqrt(a) /sqrt(b) = sqrt(a/b)
3 sqrt(20/5)
3 sqrt(4)
3 *2
6
Answer fast please and thanks!
Answer:
tan 30 = x / 15
General Formulas and Concepts:
Trigonometry
[Right Triangles Only] SOHCAHTOA[Right Triangles Only] tanθ = opposite over adjacentStep-by-step explanation:
Step 1: Define
Identify variables
Angle θ = 30°
Opposite Leg = x
Adjacent Leg = 15
Step 2: Solve for x
Substitute in variables [tangent]: tan 30 = x / 15Answer:
3rd one
Step-by-step explanation:
Recall that
Sin = opposite over hypotenuse
Cos = adjacent over hypotenuse
Tan = opposite over adjacent
For the angle with a measure of 30 degrees we are given it's adjacent side length and need to find it's opposite side length
When dealing with opposite and adjacent we use tangent
If tan = opposite over adjacent
Then tan30 = x / 15 and the correct answer choice is the third one
The following data represent the maximum wind speed (in knots) and atmospheric pressure (in millibars) for a random sample of hurricanes that originated in the Atlantic Ocean.
Atmospheric Pressure (mb) Wind Speed (knots) Atmospheric Pressure (mb) Wind Speed (knots)
993 50 1006 40
995 60 942 120
994 60 1002 40
Required:
a. Find the y-intercept of the least-squares regression line, treating atmospheric pressure as the explanatory variable (round to four decimal places.)
b. Find the slope of the least-squares regression line, treating atmospheric pressure as the explanatory variable (round to four decimal places.)
c. Is it reasonable to interpret the y-intercept of the least-squares regression line, treating atmospheric pressure as the explanatory variable? Why or why not?
Answer:
Step-by-step explanation:
X Y X² Y² XY
993 50 986049 2500 49650
995 60 990025 3600 59700
994 60 988036 3600 59640
1006 40 1012036 1600 40240
942 120 887364 14400 113040
1002 40 1004004 1600 40080
[tex]\sum X: 5932[/tex] [tex]\sum Y : 370[/tex] [tex]\sum X^2 : 5867514[/tex] [tex]\sum Y^2 = 27300[/tex] [tex]\sum XY : 362350[/tex]
To determine the regression:
[tex]Mean \ (X) = \dfrac{\sum X }{n} \\ \\ = \dfrac{5932}{6} \\ \\ = 988.67[/tex]
[tex]Mean \ (Y) = \dfrac{\sum Y}{n} \\ \\ = \dfrac{370}{6} \\ \\ = 61.67[/tex]
Intercept [tex]b_o = \dfrac{\sum YX *\sum X^2 - \sum X \sum Y}{n(\sum X^2) - (\sum X)^2}[/tex]
[tex]=\dfrac{370(5867514) -(5932)(370)}{6(5867514) - (5932)^2}[/tex]
= 131760.9563
Slope [tex]b_1 = \dfrac{n(\sum XY) -(\sum X *\sum Y) }{n(\sum X^2)-(\sum X)^2}[/tex]
[tex]b_1 = \dfrac{6(362350) -(5932*370) }{6(5867514)-(5932)^2}[/tex]
[tex]b_1 = -1.2600[/tex]
The regression line equation [tex]Y = b_o +b_1X[/tex]
[tex]Y = 131760.96 -1.2600 X[/tex]
We then make a comparison of the slope of the equation to y = mx+c
slope of the equation = -1.2600
the y-intercept corresponds to when X = 0, thus:
y-intercept = 131760.9563
Yes, it is reasonable to interpret the y-intercept of the regression line, Using atmospheric pressure as an explanatory variable due to the fact that:
X is the independent variable and Y exists as the dependent variable.
Can someone please help me?
Answer:
A is the correct answer
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
Remember X intercept is when y is equal to zero
So basically f(x-4) is literally equal to y=radical (x-4)
When graphing them you will notice that the x intercept is 4 units lower
