As per the regression equation, the value of intercept coefficient is 1.5707
Regression is a statistical technique used to determine the relationship between an independent variable and a dependent variable.
In this case, the regression statistics provided in table 6 show the results of estimating the model
=> Δln (Sales t) = b0 + b1Δln (Sales t −1) + εt,
where Δln (Sales t) is the change in the natural log of sales for Cisco Systems quarterly observations from 3Q:1991 to 4Q:2000.
The R-squared value of 0.0661 indicates that only about 6.61% of the variation in the change in the log of sales can be explained by the change in the log of sales from the previous quarter.
The standard error of 0.4698 indicates the average deviation between the actual and predicted change in the log of sales.
If the results show that the specification is correct, then the long-run change in the log of sales toward which the series will tend to converge can be determined by the intercept coefficient, which in this case is 1.5707.
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a rectangle is 8 km longer than it is wide. find the dimensions of the rectangle if its area is 345 sq-km.
The length of the rectangle is 23 km and the width of the rectangle is 15 km.
A rectangle is 8 km longer than it is wide.
Its area is 345 sq-km.
Let the width of the rectangle is x.
The length is 8 km longer than the width.
So the width of the rectangle is x + 8 km.
The formula of the area of rectangle is:
A = length × width
We know A = 345 sq-km.
Now putting the value
x × (x + 8) = 345
Now simplifying
x^2 + 8x = 345
Subtract 345 on both side, we get
x^2 + 8x - 345 = 0
Now factor the equation
x^2 + (23 - 15)x - 345 = 0
x^2 + 23x - 15x - 345 = 0
x(x + 23) - 15(x + 23) = 0
(x - 15)(x + 23) = 0
Now equation the factor equal to zero.
x - 15 = 0 or x + 23 = 0
x = 15 or x = -23
Since the dimension of the rectangle can't be negative. So
The width of the rectangle is 15 km.
Now we determine the value of length
x + 8 = 15 + 8 = 23
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Fill in the missing values in the formula. What is the variance?
0
3.217
3.522
12.405
148.86
Answer:12.405 would be correct
Step-by-step explanation:
What is variance?In probability theory and statistics, variance is the squared deviation from the mean of a random variable. The variance is also often defined as the square of the standard deviation. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers is spread out from their average value
The variance is a measure of variability
Therefore c is your answer!
There is a proportional relationship between hours, x, and number of miles, y, of water in a tank. The point (2, 80) is on a graph of this relationship. Part A: Explain what the point (2, 80) represents. Part B: Write an equation for the relationship in the form of y = mx.
(A) The point (2, 80) represents that at 2 hours there are 80 miles of water in a tank.
(B) Writing an equation for the relationship in the form of y = mx, we get y = 40x.
What is Proportionate Relationship?
Relationships between two variables where their ratios are equal are known as proportional relationships.Two quantities that directly vary from one another are said to be in a proportionate relationship. If y = mx, for some constant m referred to as the constant of proportionality, then we say the variable y fluctuates directly as x.Accordingly, the ratio between x and y always remains the same and as x rises, y rises, and as x falls, y falls.The proportional relationship equation has a straight line across the origin as its graph.It is given that there is a proportional relationship between hours, x, and number of miles, y, of water in a tank.
Also, the point (2, 80) is on a graph of this relationship.
(A) The point (2, 80) represents that at 2 hours there are 80 miles of water in a tank.
(B) We have the given point, (2, 80)
Writing the relationship in the form of equation, y = mx using the point (2, 80), we get
80 = m × 2
⇒ m = 80/2
⇒ m = 40
Thus, writing an equation for the relationship in the form of y = mx when m = 40, we get y = 40x.
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[PLS HELP WILL GIVE BRAINLIEST!!]
Given that sin θ = – 4/9 and 3π/2 ≤ θ ≤ 2π, find cot θ.
Answer:
Step-by-step explanation:
Given that sin θ = -4/9 and 3π/2 ≤ θ ≤ 2π, we can use the trigonometric identities to find cot θ.
cot θ = 1/tan θ = 1/ (sin θ / cos θ) = cos θ / sin θ
As we know the sin θ = -4/9, we can find cos θ = √(1 - sin^2 θ) = √(1 - (-4/9)^2) = √(1 - 16/81) = √(65/81)
So cot θ = (√(65/81)) / (-4/9) = -9/4 * √(65/81) = -(9/2) √(65/81)
Note that, since 3π/2 ≤ θ ≤ 2π, the value of cot θ will be negative
how to write an expression for csc[arccos(x -1)]
An algebraic expression which is equivalent to the expression
csc[arccos(x -1)] is equal to 1 / √2x - x² .
Let us consider the expression arccos(x - 1 ) = y .
arccos(x - 1 ) = y
⇒ cos y = (x - 1 ) ___( 1 )
Now the required algebraic expression is equivalent to :
csc[arccos(x -1)]
= csc y
= ( 1 / sin y )
= 1 / √ 1 - cos²y __(2)
Substitute the value of cosy from (1 ) in the expression ( 2 ) we get,
= 1 / √ 1 - ( x - 1 )²
= 1 / √ 1 - ( x² -2x + 1 )
= 1 / √ 1 - x² + 2x - 1
= 1 / √ 2x - x²
Therefore, the expression csc[arccos(x -1)] is equivalent to an algebraic expression is 1 / √ 2x - x².
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someone help please. i need to turn this in tomorrow. Question is in the picture!
Answer: A=4.5m²
Step-by-step explanation: length: 1.5 Width: 300
Unit Conversion:l=1.5mw
A=wl=3·1.5=4.5m²
Form an equation of line given these coordinates (2,4) and (-2,-8)
The equation of a line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept.
To find the slope of the line, we can use the following formula:
m = (y2 - y1) / (x2 - x1)
Plugging in the coordinates (2,4) and (-2,-8) into the formula:
m = (-8 - 4) / (-2 - 2) = -12/ -4 = 3
We can use one of the coordinates to find the y-intercept.
Plugging in the point (2,4) and the slope 3 into the equation y = mx + b, we get:
4 = 3*2 + b
so b = -2
Therefore, the equation of the line is y = 3x - 2.
approximate the integral using the trapezoidal rule with ten equal subintervals, compute the error as follows. find the exact value of the integral (it must be a fraction): 4x 1
The approximate value of the integral using the trapezoidal rule with ten equal subintervals is [tex]2 + |E_T| = 2 - 1/300 = 599/300[/tex].
To find the exact value of the definite integral of 4x over the interval [0,1] we can found using the antiderivative:
[tex]\int_0^1 4x dx = 2x^2 |_0^1 = 2(1)^2 - 2(0)^2 = 2.[/tex]
To approximate the value of the integral using the trapezoidal rule with ten equal subintervals, we can break the interval into ten equal subintervals of length 1/10 and approximate each subinterval using a trapezoid.
The error of the trapezoidal rule is given by:
[tex]|E_T| = -(b-a)^3/(12n^2) * f''(c)[/tex]
where a and b are the limits of the integration, n is the number of subintervals, and f''(c) is the second derivative of the integrand evaluated at some value c in the interval.
The error of this approximation will depend on the value of f''(c) for some value c in the interval [0,1]. The second derivative of 4x is constant and equal to 4, so the error will be a constant value:
[tex]|E_T| = -(1-0)^3/(12*10^2) * 4 = -1/300.[/tex]
Thus, the approximate value of the integral using the trapezoidal rule with ten equal subintervals is [tex]2 + |E_T| = 2 - 1/300 = 599/300[/tex].
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the population, p, of grasshoppers after t weeks where 0 < t < 12 is estimated
The population of grasshoppers can be estimated by using a formula that takes into account the number of weeks that have passed since the start of the experiment (0 < t < 12).
The population of grasshoppers can be estimated with a formula that takes into account the amount of weeks that have passed since the start of the experiment (0 < t < 12). The first step in this process is to define the variables that will be used. The variable p will represent the population of grasshoppers after t weeks and t will represent the number of weeks that have passed. The next step is to use a formula to estimate the population of grasshoppers. This formula will take into account the amount of weeks that have passed and will likely result in an exponential increase in the population of grasshoppers as the weeks pass. After the formula is applied, the result will be the estimated population of grasshoppers after t weeks.
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Can anyone help me please
In the line of symetry for this parabola is x = -1.
The maxima or minima of the parabola is [tex]-\frac{21}{4}[/tex]
Estimate the gradient of the curve at x = 4 is 5.
The equation of the tangent of the point (4, 1) is 5x² - y² - 40x + 2y + 89 = 0.
The gradient of the curve at the point (-1, 1) is -1.
The steps are as follows:
The function of parabola y = x² - 3x - 3
(i) In the line of symetry for this parabola.
Symetry of the parabola:
x = [tex]-\frac{b}{2a}[/tex] → for y = ax² + bx + c
x = [tex]-\frac{-3}{-3}[/tex]
x = -1
(ii) The maxima or minima of the parabola.
The maximum or minimum parabola can be found when the derivative is 0
y = x² - 3x - 3
y' = 2x - 3
0 = 2x - 3
2x = 3
x = [tex]\frac{3}{2}[/tex]
The maxima or minima of the parabola
y = x² - 3x - 3
= ( [tex]\frac{3}{2}[/tex] )² - 3 ( [tex]\frac{3}{2}[/tex] ) - 3
= [tex]\frac{9}{4}[/tex] - [tex]\frac{9}{2}[/tex] - 3
= [tex]\frac{9}{4}[/tex] - [tex]\frac{18}{4}[/tex] - [tex]\frac{12}{4}[/tex]
= [tex]-\frac{21}{4}[/tex]
(iii) Estimate the gradient of the curve at x = 4
y = x² - 3x - 3
y' = 2x - 3
y' = m = 2(4) - 3
= 8 - 3
= 5
y = x² - 3x - 3
y = 4² - 3(4) - 3
= 16 - 12 - 3
= 1
(iv) The equation of the tangent of the point (4, 1)
(y - b)² = m (x - a)²
(y - 1)² = 5 (x - 4)²
y² - 2y + 1 = 5 (x² - 8x + 16)
y² - 2y + 1 = 5x² - 40x + 90
5x² - y² - 40x + 2y + 90 - 1 = 0
5x² - y² - 40x + 2y + 89 = 0
(v) The gradient of the curve at the point (-1, 1)
y = x² - 3x - 3
y' = 2x - 3
y' = m = 2(1) - 3
= 2 - 3
= -1
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what is the missing number ? : 7 = 45 : 63
Answer:
5
Step-by-step explanation:
Graph a line that contains the point ( 6 , − 5 ) and has a slope of -2/3
Answer: this is the answer it is a screenshot of the graph
I think its kinda easy but the I couldn't answer for positive
|x^3-1|-7=0
The solution to the equation is x = 2
How to determine the solution to the equationFrom the question, we have the following parameters that can be used in our computation:
|x^3-1|-7=0
Add 7 to both sides
So, we have
|x^3-1| = 7
Remove the absolute bracket
x^3 - 1 = 7
So, we have
x^3 = 8
Take tge cube roots of both sides
x = 2
Hence, the solution is 2
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A tour guide needs one vehicle to transport 14 tourists.calulate how many vehicles like this are needed to transport 34 tourists
Answer:
Step-by-step explanation:
As stated in the question that One vehicle transports 14 tourists and there are 34 tourists
Number of vehicles required = 34/14 = 2 vehicles + 6 people left
So, the remaining 6 people will be transported through 3rd vehicle.
So, there are 3 vehicles needed to transport 34 tourists.
Find the y-intercept of the line 5x+2y= – 5
Answer:-2.5
Step-by-step explanation:
1. Set up your problem it would be 5x+2y=-5
2. Then you would set your x to be 0 so you can solve for y
5(0)+2y=-5 aka 2y=-5
3. Divide each side by 2
2y (divided by 2) = -5 (divided by 2)
y=-2.5
I hope this helps!
how tofind probabilities, expected values and net expected values for a decision tree
The probability of all outcomes must add up to 1. The Expected Value (EV) shows the weighted average of a given choice.
A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100% and can be denoted as the possible outcomes upon the total number of outcomes.
To calculate this expected values multiply the probability of each given outcome by its expected value and add them together. And the net expected values can be found out by summing up all the possible expected values.
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three cards are randomly selected from an ordinary playing deck. what is the probability that one of the cards is an ace and another one is either a ten or a jack, and the other one is either a queen or a king?
The probability that one of the cards is an ace and another one is either a ten or a jack, and the other one is either a queen or a king is [tex]$\frac{4}{2197}[/tex] (or) 0.00182
Let:
A: Drawing one ace card
B: Drawing either a ten or a jack card
C: Drawing either a queen or a king card
Probability of drawing one ace card
P(A) = [tex]$\frac{4}{52} \\[/tex]
Probability of drawing one ten-numbered card.
A number of ten cards 4.
= [tex]$\frac{4}{52}[/tex]
Probability of drawing one jack card.
A number of jack cards 4.
= [tex]$\frac{4}{52}[/tex]
[tex]$ P(B)=\frac{4}{52}+\frac{4}{52}=\frac{8}{52}[/tex]
Probability of drawing one queen card.
A number of queen cards 4.
= [tex]$\frac{4}{52}[/tex]
Probability of drawing one king card.
A number of king cards 4.
= [tex]$\frac{4}{52}[/tex]
[tex]$P(C)=\frac{4}{52}+\frac{4}{52}=\frac{8}{52}[/tex]
Now Probability (one of the cards is an ace and another one is either a ten or a jack and the other one is either a queen or a king
[tex]P(A \cap B \cap C)[/tex] = P(A) P(B) P(C)
[tex]$=\frac{4}{52} \times \frac{8}{52} \times \frac{8}{52}[/tex]
[tex]$=\frac{4}{2197}[/tex] (or)
= 0.00182
Therefore the probability is [tex]$\frac{4}{2197}[/tex] (or) 0.00182
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Please help me answer this question on equations of lines. 10 POINTS AND BRAINLIEST available.
Answer:
y=x+3
Step-by-step explanation:
Use the Binomial Theorem to expand (a+b)^15. You can use your calculator to determine the coefficient. Show the step.
In the figure below F is between E and G,and G is between F and H if EG=11 EH=17 and FH=9 find FG
Answer:
Since you are finding FG, FG=3
Step-by-step explanation:
picture above
The data in this table is going to be plotted on a dual bar chart. If the grid is 16 rows tall, what number should replace A to give the best scale for the vertical axis of this data?
The number should replace A to give the best scale for the vertical axis of this data is 15.75
How to find the number?From the given parameters and graphs, we notice that we should find the mean of the set of data.
The scale should be chose in a way that the center shows the the mean of the frequencies
Recall that mean is the average of all the frequencies, then we have to find the mean of the means of the two frequencies.
(30+12+10)/2 52/3 = 17.3
Also, (27+6+13)/3 = 14.2
Then we find the average of the two averages to have
(17.3+14.2)/2 = 31.5/215.75
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The caniter contained 6 1/8 cup of flour when Karina tarted making cookie. She ued 2 1/2 cup. How many cup were left in the caniter? Subtract. (Enter a an improper fraction
If Canister contained [tex]6\frac{1}{8}[/tex] cup of flour when Karina started making cookie and used [tex]2\frac{1}{2}[/tex] cup then number of cup left in Canister is 29/8 cups .
the number of cups of floor in the canister initially is = [tex]6\frac{1}{8}[/tex] = 49/8 ;
the amount of floor that she used is = [tex]2\frac{1}{2}[/tex] = 5/2 cups ,
To find out how much flour is left in the canister, we need to subtract the amount used from the total amount.
We can start by converting the mixed fractional cups to improper form ,
we get ;
number of cups left in the canister is = 49/8 - 5/2 = 49/8 - 20/8 = 29/8 .
Therefore , 29/8 cups were left in the canister .
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Suppose that a and b are nonzero vectors.
a) Under what circumstances is compa b=compb a
b) Under what circumstances is proja b=proj b a
a) The vectors a and b are collinear when compa b=compb a. This means that they have the same direction, so that they're pointing in the same direction or opposite directions. In other words, if the angle between them is 0° or 180°, then they are collinear.
b) The vectors a and b are orthogonal when proja b=proj b a. This means that they are perpendicular to each other, so that the angle between them is 90°. Furthermore, it means that the projection of one vector onto the other is equal to zero.
This is because the projection of a vector onto itself is equal to the magnitude of the vector, while the projection of a vector onto a vector orthogonal to it is equal to zero.
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find the velocity and acceleration vectors and the equation of the tangent line for the curve ()=3cos() sin(6)r(t)=3cos(t)i sin(6t)j at =0.
The velocity and acceleration vectors and the equation of the tangent line for the curve = 3i+4tj
What is Velocity?
When an item is moving, its velocity is the rate at which it is changing position as seen from a certain point of view and as measured by a specific unit of time.
What is Acceleartion?
Acceleration is the rate at which an object's velocity with respect to time changes. They are vector quantities, accelerations. The direction of the net force acting on an object determines the direction of its acceleration.
r(t) = 3cos(t)+sin4(t)j
velocity,V(t) = dr(t)/dt
=3sin(t)i + 4cos4(t)j
and acceleration a(t) = dv(t)/dt
= [tex]d^{2}r(t)/dt^{2}[/tex]
i.e a(t) = -3cos(t)i - 16sin(4t)j
v(0) = 0.i + 4j =4j
and a(0) = -3i -0j
=-3i
now we find the equation of the tangent line for the curve (t) at t=0
r(0) = 3i
r(t) = -3sin(t)i +4 cos 4(t)j
r (0) = 4j
equation target to the curve r(t) at t=0 is
1(t) = r (0) + (t)r(0)
= -3i+(t).4j
= -3i+4tj
The curve's tangent line equation, velocity and acceleration vectors, is -3i+4tj
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What is the value of x?
X =
33°+19x=90°
Answer:
3°
Step-by-step explanation:
33 +19x = 90 subtract 33 from both sides of the equation
19x = 57 divide both sides by 19
x = 3°
Find the sum of the first 20th term of a linear sequence 1,5,9,13
Answer:
Step-by-step explanation:
The sum of the first 20 terms of a linear sequence can be found using the formula for the sum of an arithmetic series:
S = n/2 * (a1 + a20)
where n = number of terms = 20, a1 = first term = 1, and a20 = 20th term = 1 + 4 * (20 - 1) = 77
Substituting these values, we have:
S = 20/2 * (1 + 77) = 20/2 * 78 = 20 * 39 = 780
So, the sum of the first 20 terms of the sequence 1, 5, 9, 13 is 780.
Find the measure of two complementary 8. angles if one angle is four times the measure
of the other angle.
Answer:
Below
Step-by-step explanation:
Complementary angles sum to 90 °
x = angle 1
4x = other angle they sum to 90°
x + 4x = 90 °
5x = 90°
x = 18° then 4x = 72°
how many {0, 1, 2, . . . , 9}-strings of length eight are there containing exactly six distinct characters (e.g. 00154943, which has length of eight and contains only the six distinct digits 0, 1, 3, 4, 5, and 9)?
Total 13,608,000 has length of eight are there containing exactly six distinct characters.
Total number of string = 10
The length of the string should be = 8
The distinct characters = 6
So the same character should be = 2
There are total 10 numbers in which 6 are distinct, so
[tex]^{10}P_{6}=\frac{10!}{(10-6)!}[/tex]
[tex]^{10}P_{6}=\frac{10!}{4!}[/tex]
[tex]^{10}P_{6}[/tex] = 3,628,800/24
[tex]^{10}P_{6}[/tex] = 151,200
Hence, strings of length eight are there containing exactly six distinct characters = 151,200 × 10 × 9
Strings of length eight are there containing exactly six distinct characters = 13,608,000
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Need help answering these
The Simplified values are
1. 7∛3 + 2∛192 = 15∛3.
2. 10√7 - √28- 6√180 = 8√7 - 36√5
3. 8[tex]\sqrt[4]{48}[/tex] - 5√90 + 9[tex]\sqrt[4]{3}[/tex] = 25[tex]\sqrt[4]{3}[/tex] - 15√10
4. 5∛32x³[tex]y^4[/tex] - 3xy∛4y = 7xy ∛4y
What are Exponents and power?Exponents and powers are ways used to represent very large numbers or very small numbers in a simplified manner.
For example, if we have to show 3 x 3 x 3 x 3 in a simple way, then we can write it as [tex]3^4[/tex], where 4 is the exponent and 3 is the base. The whole expression 34 is said to be power.
Given:
1. 7∛3 + 2∛192
= 7∛3 + 2 ∛ 2 x 2 x 2 x 2 x 2 x 2 x 3
= 7∛3 + 2 x 2 x 2 ∛3
= 7∛3 + 8∛3
= 15∛3.
2. 10√7 - √28- 6√180
= 10√7 - √2 x 2 x 7 - 6√2 x 2 x 3 x 3 x 5
= 10√7 - 2√7 - 36√5
= 8√7 - 36√5
3. 8[tex]\sqrt[4]{48}[/tex] - 5√90 + 9[tex]\sqrt[4]{3}[/tex]
= 8 x 2 [tex]\sqrt[4]{3}[/tex] - 5 x 3 √10 + 9[tex]\sqrt[4]{3}[/tex]
= 25[tex]\sqrt[4]{3}[/tex] - 15√10
4. 5∛32x³[tex]y^4[/tex] - 3xy∛4y
= 10xy ∛4y - 3xy∛4y
= 7xy ∛4y
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the temperature outside was 88 degrees fahrenheit. what would be the temperature is it is increased by %25
Answer:
110.0%
Step-by-step explanation:
25% of 88 is 22. 88+22=110 Fahrenheit
to get this you divide 88 by 100 which is 0.88, then multiply by 25 which gets you 22.
