The force exerted by the brick on the window is equal in magnitude but
opposite in direction to the force exerted by the window on the brick.
When a brick hits a window and smashes it, there are two forces
involved: the force exerted by the brick on the window and the force
exerted by the window on the brick.
According to Newton's third law of motion, for every action, there is an
equal and opposite reaction.
The magnitude of the forces involved depends on several factors,
including the mass of the brick, its velocity, the angle of incidence, and
the strength of the window. The force exerted by the brick on the
window will be the impact force, which is the force applied over a short
period of time during the collision.
The impact force will depend on the momentum of the brick, which is
the product of its mass and velocity.
It's not possible to say which force is larger because the two forces are
equal in magnitude but opposite in direction, according to Newton's third
law of motion.
The strength of the window will also play a role, as a stronger window
will be able to resist a higher impact force before breaking.
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Make a table of ordered pairs for the equation
Y= - 1/3x + 1
In this equation, the ordered pairings are (0, 1), (3, 0), (6, -1), and (9, -2).
What are equations used for?A mathematical equation is a statement that two amounts and values are equal, such as 6 x 4 = 12 x 2. 2. A noun that counts. When two or more components must be taken into account simultaneously in order to comprehend or describe the overall situation, this is known as an equation.
We may select several values of x and enter them into the equation to get the associated values of y to create a table of tuple for the solution y = (-1/3)x + 1:
x y = (-1/3)x + 1
0 1
3 0
6 -1
9 -2
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In this equatiοn, the οrdered pairings are (0, 1), (3, 0), (6, -1), and (9, -2).
What are equatiοns used fοr?A mathematical equatiοn, like 6 + 4 = 12, states that twο amοunts and values are equal. An equatiοn is when twο οr mοre cοmpοnents must be cοnsidered simultaneοusly in οrder tο cοmprehend οr describe the οverall situatiοn.
We may select several values οf x and enter them intο the equatiοn tο get the assοciated values οf y tο create a table οf tuple fοr the sοlutiοn y = (-1/3)x + 1:
x y = (-1/3)x + 1
0 1
3 0
6 -1
9 -2
Therefοre, In this equatiοn, the οrdered pairings are (0, 1), (3, 0), (6, -1), and (9, -2).
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I really need some help please
The solution of the absolute inequality is as follows:
x < 22 / 5 or x > 6 / 5
How to solve absolute inequalities?The absolute inequalities can be solved as follows:
An absolute value inequality is an inequality that has an absolute value sign with a variable inside, modulus of a complex number.
Therefore,
|14 - 5x| > 8
let's find x as follows:
|14 - 5x| > 8
14 - 5x > 8 or 14 - 5x < - 8
-5x > 8 - 14 or - 5x < - 8 - 14
-5x > -6 or - 5x < - 22
Therefore,
x > 6 / 5 or x < 22 / 5
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Becky wants to buy some fish for her aquarium. she has $20 to spend and the fish cost $2.50 each. write an inequality that can be used to determine how many fish, x, becky can afford to buy.
To solve this inequality, the left side can be divided by $2.50 and the value of x can be determined. The solution to this inequality is that Becky can afford to buy a maximum of 8 fish.$2.50x ≤ $20
$2.50x ≤ $20
The given situation is that Becky wants to buy some fish for her aquarium and she has $20 to spend and the cost of the fish is $2.50 each. To determine how many fish, x, Becky can afford to buy, an inequality can be written. Since the cost of each fish is $2.50, the total cost for buying x number of fish is $2.50x. To find out how many fish Becky can afford to buy, the inequality $2.50x ≤ $20 can be written. To solve this inequality, the left side can be divided by $2.50 and the value of x can be determined. The solution to this inequality is that Becky can afford to buy a maximum of 8 fish.
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what is 30.7% of 520
Answer:
159.64
Step-by-step explanation:
30.7% / 100 = 0.307 then you would do
0.307 x 520 = 159.64
An object being pushed with 5 pounds of course in the θ=45˚ direction and also with 7 pounds of force in the θ =-60˚ direction. Find the total force on the object
Force on the object is 7.04 pounds in the x-direction
Force on the object is -2.52 pounds in the y-direction
The total force on an object being pushed with 5 pounds of course in the θ=45˚ direction and also with 7 pounds of force in the θ =-60˚ direction can be found by resolving each force into its x- and y-components, and then adding them to obtain the net force acting on the object.An object being pushed with 5 pounds of course in the θ=45˚ direction and also with 7 pounds of force in the θ =-60˚ direction is shown below:An object being pushed with 5 pounds of force in the θ=45˚ direction and also with 7 pounds of force in the θ=-60˚ direction.To resolve the forces, we use the following identities:Fx = Fcosθ, andFy = Fsinθ.The x- and y-components of the 5-pound force in the θ=45˚ direction are:Fx = Fcosθ = 5 cos 45˚ = 3.54 pounds,andFy = Fsinθ = 5 sin 45˚ = 3.54 pounds.The x- and y-components of the 7-pound force in the θ=-60˚ direction are:Fx = Fcosθ = 7 cos (-60˚) = 3.5 pounds,andFy = Fsinθ = 7 sin (-60˚) = -6.06 pounds.The total force acting on the object is the sum of the x- and y-components of the forces acting on it, or:Fx = 3.54 pounds + 3.5 pounds = 7.04 pounds,Fy = 3.54 pounds - 6.06 pounds = -2.52 pounds.Therefore, the total force on the object is 7.04 pounds in the x-direction and -2.52 pounds in the y-direction.
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NEED HELP WITH ALL QUESTIONS! Find x for all of them.
The value of x for all the figures are given below respectively.
What is trigonometry?The branch of mathematics that studies the relationships between the sides and angles of triangles is known as Trigonometry.
1. In given figure base = 5 and hypotenuse = 10 .
to find x i.e height we will use trigonometry-
tan 60° = x/5
√3 = x/5
5√3=x
Therefore, the value of x is 5√3.
2. In given figure base = 1 and height = √3 and angle given is 60°.
to find x i.e hypotenuse we will use trigonometry-
sin 60° = √3/x
√3/2 = √3/x
x = √3×2/ √3
x = 2
Therefore ,value of x is 2.
3. In given figure base = 3 and hypotenuse = 6 .
to find x i.e height we will use trigonometry-
tan 60° = x/3
√3 = x/3
3√3 = x
Therefore,value of x is 3√3.
4. In given figure base = 1 and height = 1 and angle given is 45°.
to find x i.e hypotenuse we will use trigonometry-
sin 45° = 1/x
1/√2 = 1/x
x = √2
Therefore ,value of x is √2.
5. In given figure height = 4√2 and angle given is 45°.
to find x i.e hypotenuse we will use trigonometry-
sin 45° = 4√2/x
1/√2 = 4√2/x
x = 4√2 × √2
x = 8
Therefore,value of x is 6.
6. In given figure hypotenuse = 10 and angle given is 45°.
to find x i.e base we will use trigonometry-
cos 45° = x/10
1/√2 = x/10
10/√2 = x
Therefore,value of x is 10/√2.
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someone help me simplify pls
Answer:
10^0
Step-by-step explanation:
Anything that has a exponent of 0 will always equal 1 therefore if 10^-3/10^-3 it will equal 1 so they both are 1
Answer: A 10^0
10^-3 is 0.001. 0.001 divided into 0.001 is 1.
A- 10^0 is 1 so this correct.
B- 10^-6 is 1.0e-6, so this is incorrect.
C-10^1 is 10, so this is incorrect.
D.10^6 is 1000000, so this is incorrect.
After solving our equation 10^-3/ 10^-3, we have concluded that that answer is 1, meaning that answer choice A, 10^0 is our correct answer.
Notes- ^ means to the power of, which is an exponent.
I hope this helped & Good Luck <3!!!!
Look at the imagien BUT QUICKLY help
Find the measure of each angle a positive angle measure, a negative angle measure, and an angle measure that is greater 360 degrees.
Help with the 3 problems attached, please. :)
This is an Angles and Coordinate Systems problem.
6)
7)
Positive angle measure: 410°Negative angle measure: -310°Angle measure greater than 360°: 770°.8)
Positive angle measure: 660°Negative angle measure: -660°Angle measure greater than 360 degrees: 1020°.What is Positive Angle Measure and Negative angle measure?Positive angle measure is measured counterclockwise and negative angle measure is measured clockwise. These concepts are used in navigation, engineering, and physics.
6)
An angle of 40 degrees measured out in the upper left quadrant will have its initial side along the positive x-axis and its terminal side in the upper left quadrant, making it a counter-clockwise angle.
-(360° - 40°) = -320°
So the angle of 40 degrees is equivalent to a negative angle measure of -320 degrees.
320° + 360° = 680°
So the angle of 40 degrees is equivalent to an angle measure of 680 degrees.
7)
To convert the angle measure of 50 degrees in the lower right quadrant to a positive angle measure, we add 360 degrees to it since one full revolution around the coordinate system is equal to 360 degrees.
To convert the angle measure to a negative angle measure, we subtract it from 360 degrees, since a negative angle is measured in the clockwise direction.
Negative angle measure: 360 degrees - 50 degrees = -310 degreesTo find an angle measure that is greater than 360 degrees, we simply add 360 degrees to the positive angle measure.
Angle measure greater than 360 degrees: 410 degrees + 360 degrees = 770 degrees.8)
The angle 60 degrees measured in the lower right quadrant in a counter-clockwise direction is equivalent to the angle 360 degrees - 60 degrees = 300 degrees measured in the upper right quadrant in a counter-clockwise direction.
To convert the angle measure of 300 degrees to a positive angle measure, we add 360 degrees to it since one full revolution around the coordinate system is equal to 360 degrees.
Positive angle measure: 300 degrees + 360 degrees = 660 degreesTo convert the angle measure to a negative angle measure, we simply add a negative sign to the positive angle measure.
Negative angle measure: -660 degreesTo find an angle measure that is greater than 360 degrees, we simply add 360 degrees to the positive angle measure.
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A workman has two pieces of wire, each of length 26 m. One is a piece to be bent into a square. The other piece is to be bent into a rectangle whose width is 3 m shorter than its length
a)Hence the side of the square = 15.5 m
b)Hence the length of the rectangle is 8m and the width is 5m.
c)Hence the rectangle is greater than the square.
a)
The length of each wire =26m
To bend it into a square it has to be bent into four parts = [tex]\frac{26}{4}[/tex] = 5.15m
Hence the side of the square = 15.5 m
b)
A rectangle whose width is 3 m shorter than its length,
let the length of the rectangle = l
And the width of the rectangle h= l-3,
now,
2(l+l-3)=26
4l-6=26
4l=32
l=8m
h=8-3=5
Hence the length of the rectangle is 8m and the width is 5m.
c)
The area of the square= 5.15²=26.52 sq cm
The area of the rectangle = 8*5=40 sq cm
Hence the rectangle is greater than the square.
The complete question is-
A workman has two pieces of wire, each of
length 26 m. One piece is to be bent into a
square. The other piece is to be bent into a
rectangle whose width is 3 m shorter than its
length.
(a) What is the length of a side of the square?
(b) What are the dimensions of the rectangle?
(c) Which shape has the greater area?
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Find the missing side. Round answers to the nearest tenth! Show or explain your work. Pleases
Answer:
Proofs attached to answer
Step-by-step explanation:
Proofs attached to answer
A likelihood of 1 is also known as...
Answer:
A likelihood of 1 is also known as the Discrete probability distribution
An arc subtends an angle of 86 at the cir- cumference of a circle whose radius is 8 cm. Find the length of the are to the near- est whole number. (Take = 3.14) (Hint: an angle at the centre = 2x the angle at the circumference).
Answer:
We can use the formula for the length of an arc of a circle, which is:
length of arc = (angle/360) × 2πr
where angle is the angle subtended by the arc at the center of the circle, r is the radius of the circle, and π is approximately 3.14.
In this problem, the angle subtended by the arc at the circumference of the circle is 86 degrees. Since the radius of the circle is 8 cm, the diameter is 2 × 8 = 16 cm, and the circumference is 2πr = 2π(8) = 16π cm.
Using the hint given in the problem, we can find the angle subtended by the arc at the center of the circle:
angle at center = 2 × angle at circumference
= 2 × 86
= 172 degrees
Substituting into the formula, we have:
length of arc = (172/360) × 2π(8)
≈ 7.5 cm
Rounding to the nearest whole number, the length of the arc is 8 cm.
Complete the table for the quadratic function below. Type the value of y that
corresponds with each value of x.
y=2(x-3)²-2
xy=2(x-3)²-2
1
2
3
4
5
Values of y that corresponds with the value of x as per quadratic functions are as follows:
6
0
-2
0
6
What are quadratic functions?A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree. A quadratic function must have at least one second-degree term. It performs algebraic operations.
The parent quadratic function connects the locations whose coordinates have the type f(x) = x2 and is of the kind (number, number2).
Just need to evaluate the function for each value of X.
for x=1 y=2(1-3)²-2= 6
for x=2 y=2(2-3)²-2= 0
for x=3 y=2(3-3)²-2= - 2
for x=4 y=2(4-3)²-2= 0
for x=5 y=2(5-3)²-2= 6
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I dont know how to do this
the answer isnt 4
pls answer if u know with simple working
Answer:25 sticks
Step-by-step explanation:
each time you will add 4 sticks
Answer: 37
Step-by-step explanation:
Add 4
which of the following experiments is likely to produce a uniform discrete distribution? multiple select question. the values that occur from repeated spins of a roulette wheel at a casino. the answer selected on a multiple choice question that has four choices by a student who did not study. the number of patrons arriving every 3 minutes at a sandwich shop. test scores on a college entrance exam, such as the act or sat.
The experiment that is most likely to produce a uniform discrete distribution is the number of patrons arriving every 3 minutes at a sandwich shop.
Test scores on a college entrance exam, such as the ACT or SAT, is an example of continuous distribution.
What is a uniform discrete distribution?A uniform distribution is a kind of probability distribution in which all of the potential outcomes have an equal likelihood of occurring. A uniform distribution with a limited set of potential outcomes is referred to as a discrete uniform distribution. In a discrete uniform distribution, there is a finite number of potential outcomes that are all equally probable.
It is important to note that the sum of the probabilities of all possible outcomes in a uniform distribution is always equal to 1 since the outcomes are equally likely to happen. The following experiments are less likely to generate a uniform discrete distribution:
Values obtained from repeated spins of a roulette wheel at a casino: Because the roulette wheel is designed to produce a non-uniform distribution, the values that result from the spins of the roulette wheel are not uniformly distributed. The answer is selected on a multiple choice question that has four choices by a student who did not study: Since the student did not study, their answers will be arbitrary and unpredictable, making a uniform distribution unlikely.Test scores on a college entrance exam, such as the ACT or SAT: Because test scores are continuous data, a uniform distribution is unlikely to occur.
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Given that the measurement is in centimeters, find the circumference of the circle to the nearest tenth. (use 3.14 for π)
The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle and π (pi) is a constant approximately equal to 3.14.
To find the circumference of the circle, we need to know the radius. If we are not given the radius directly, we may be given another measurement that we can use to calculate it. For example, we may be given the diameter, which is the distance across the circle passing through its center. The radius is half the diameter.
Assuming we have been given the diameter of the circle, we can calculate the circumference as follows:
Write down the formula for the circumference of a circle: C = 2πr
Identify the diameter of the circle. Let's say it is 10 cm.
Calculate the radius by dividing the diameter by 2: r = 10/2 = 5 cm.
Plug in the value of the radius into the formula: C = 2π(5) = 10π.
Use the approximation of π as 3.14: C = 10(3.14) = 31.4 cm.
Therefore, the circumference of the circle is approximately 31.4 cm, to the nearest tenth of a centimeter.
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Complete question:
A circle of radius 3 cm is drawn .Given that the measurement is in centimeters, find the circumference of the circle to the nearest tenth. (Use 3.14 for π)
A) 9.4 cm
B) 18.8 cm
C) 37.7 cm
D) 56.6 cm
The first three questions refer to the following information:The random variable X, representing the number of accidents in a certain intersection in a week, has the following probability distribution:x 0 1 2 3 4 5P(X=x) 0.20 0.30 0.20 0.15 0.10 0.05Question 1Select one answer.10 pointsWhat is the probability that in a given week there will be at most 3 accidents?0.700.850.350.151.00
The probability that in a given week there will be at most 3 accidents is 0.85. These event would be mutually exclusive as they do not influence the other results, Therefore the correct answer is 0.850.
The probability that in a given week there will be at most 3 accidents can be found by adding the probabilities of having 0, 1, 2, or 3 accidents. This is because the events are mutually exclusive, meaning that they cannot occur at the same time.
[tex]P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
From the given probability distribution, we can find the probabilities of each of these events:
[tex]P(X = 0) = 0.20P(X = 1) = 0.30P(X = 2) = 0.20P(X = 3) = 0.15[/tex]
Plugging these values into the equation, we get:
[tex]P(X ≤ 3) = 0.20 + 0.30 + 0.20 + 0.15P(X ≤ 3) = 0.85[/tex]
Therefore, the probability that in a given week there will be at most 3 accidents is 0.85. The correct answer is 0.850.
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If it take me 5 hours to drive to grandmas house and I drive at a constant speed of 65 mph.
How far away is her house to mine?
Answer:
325 miles
Step-by-step explanation:
speed = distance/time
=> distance = speed x time = 65 x 5 = 325 miles
Step-by-step explanation:
If you drive at a constant speed of 65 miles per hour for 5 hours, you would cover a distance of:
Distance = Speed x Time
Distance = 65 mph x 5 hours
Distance = 325 miles
Therefore, your grandmother's house is 325 miles away from yours.
There are three colors of marbles in the
bag: red, green, and purple. There are
4 green marbles in the bag. What is the
probability of Carol picking a purple
marble and, without replacing this marble,
then picking a green marble?
The expression for the probability of picking a purple marble and then a green marble without replacement is: P(P and G') = (p / (4 + p + r)) * (3 / (3 + r))
Let's denote the event of picking a purple marble by P and the event of picking a green marble after a purple marble has been picked by G'. Since we do not replace the marble after the first pick, the probability of picking a purple marble is the proportion of purple marbles in the bag. Let's assume that there are r red marbles, g green marbles (including the 4 already picked), and p purple marbles. Then the total number of marbles in the bag is r + g + p.
Since we know that there are 4 green marbles already in the bag, the total number of marbles in the bag is g + p + r = 4 + p + r. We can use this equation to eliminate g from the probability calculation.
The probability of picking a purple marble is:
P(P) = p / (4 + p + r)
After a purple marble is picked, the total number of marbles in the bag is 4 + r. The probability of picking a green marble from this reduced bag is:
P(G' | P) = (4 - 1) / (4 + r - 1) = 3 / (3 + r)
The probability of both events occurring is the product of their probabilities:
P(P and G') = P(P) * P(G' | P) = (p / (4 + p + r)) * (3 / (3 + r))
We don't have enough information to determine the values of p and r, so we cannot calculate the exact probability. However, we can give an expression for the probability in terms of p and r.
As a final step, we can check that our expression for the probability satisfies some common-sense constraints. The probability should be between 0 and 1, and it should increase as the number of purple marbles increases (since this makes it more likely to pick a purple marble) and decrease as the number of red marbles increases (since this makes it less likely to pick a green marble after a purple one has been picked).
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Perform the operation and simplify such that
The value οf a, b, and c are 3, 5, and 25 respectively.
What is an equatiοn?There are many different ways tο define an equatiοn. The definitiοn οf an equatiοn in algebra is a mathematical declaratiοn that illustrates the equality οf twο mathematical expressiοns.
The given equatiοn is
1/(x + 5) + 2/(x -5) = (ax + b)/ (x² - c)
Sοlve the left-hand side οf the equatiοn:
L.H.S = 1/(x + 5) + 2/(x -5)
= [x-5 + 2(x+5)]/(x + 5)(x -5)
= [x-5 + 2x+ 10]/(x + 5)(x -5)
Cοmbine like terms:
= [3x + 5]/(x + 5)(x -5)
Nοw apply fοrmula (a-b)(a+b) =a² - b²:
= [3x + 5]/(x² - 5²)
= [3x + 5]/(x² - 25)
Put 1/(x + 5) + 2/(x -5) = [3x + 5]/(x² - 25) in the given equatiοn:
[3x + 5]/(x² - 25) = (ax + b)/ (x² - c)
Nοw cοmpare bοth sides:
a = 3
b = 5
c= 25
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AB is the diameter of a circle C. What is the measure of arc DB?
Answer:
arc DB = 45°
Step-by-step explanation:
the measure of an arc is the same as the central angle that intercepts it.
∠ DCB = 180° - 135° = 45°
∠ DCB is the central angle intercepted by arc DB , then
arc DB = 45°
What is the positive solution to 2x^2−9x−5
2x²-9x-5
2x²-x-10x-5
(x-5)(2x+1)
Suppose that X1, X2,. . . Xn are random sample of
P(X=x│θ)= θ^x/x! E^- θ
(a) Find the MSE of X bar
(b) Find the limit of MSE when n tends to infinity
(a) To find the mean squared error (MSE) of X bar, we need to first find its expected value and variance.
The expected value of X bar is:
E(X bar) = E((X1 + X2 + ... + Xn) / n) = (n * E(X)) / n = E(X) = θ
The variance of X bar is:
Var(X bar) = Var((X1 + X2 + ... + Xn) / n) = (1/n^2) * Var(X1 + X2 + ... + Xn) = (1/n^2) * n * Var(X) = θ/n
Therefore, the MSE of X bar is:
MSE(X bar) = Var(X bar) + [E(X bar) - θ]²= θ/n + [θ - θ]² = θ/n
(b) To find the limit of MSE when n tends to infinity, we can take the limit of the MSE formula as n approaches infinity:
lim(n → ∞) MSE(X bar) = lim(n → ∞) θ/n = 0
Therefore, as the sample size becomes larger, the MSE of X bar approaches zero. This means that X bar becomes a better and better estimator of the true parameter θ as the sample size increases.
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What is the equation of the line that passes through the point (-6, -4) and has a slope of 1/3
Answer:
y = 1/3x - 2
Step-by-step explanation:
The equation is y = mx + b
m = the slope
b = y-intercept
We know
m = 1/3
Y-intercept is located at (0, -2)
So, the equation is y = 1/3x - 2
What coefficient of term xy² in expression 2xy² + x³ – x⁵ + xy² is?
Answer:
The coefficient is 3.
Answer:
3
Step-by-step explanation:
Here 2xy² + x³ – x⁵ + xy², there are two like terms
2xy² and xy², so the coefficient of xy² = 2 + 1
Coefficient of xy² in the given expression is 3.
An instructor has given a short quiz consisting of two parts. For a randomly selected student, let X = the number of points earned on the first part and Y = the number of points earned on the second part. Suppose that the joint pmf of X and Y is given in the accompanying table.
y
p(x, y)
0 5 10 15
x 0 0. 03 0. 06 0. 02 0. 10
5 0. 04 0. 15 0. 20 0. 10
10 0. 01 0. 15 0. 13 0. 01
(a) Compute the covariance for X and Y. (Round your answer to two decimal places. )
Cov(X, Y) =
(b) Compute rho for X and Y. (Round your answer to two decimal places. )
rho =
(a) The covariance for X and Y Cov(X, Y) = -1.05
(b) The correlation number (rho) is rho = Cov(X, Y)/(X, Y) = -1.05/(5).
The expected values of X and Y must first be determined in order to find the covariance and correlation coefficient for X and Y.
The amount of X is anticipated to be:
(a) E(X) = xP(X=x) = (0.03) + (5) (0.04 + 0.15 + 0.01) + (10) (0.06 + 0.20 + 0.15 + 0.13) + (15) (0.02 + 0.10 + 0.01) = 8.4
E(Y) = yP(Y=y) = (0.05) + (5) (0.04 + 0.01) + (10) (0.06 + 0.15 + 0.15) + (15) (0.02 + 0.20 + 0.13 + 0.01) = 10.5
X and Y's correlation is:
Cov(X, Y) = XY - XE (Y)
Each number of X and Y must be multiplied by their combined probability before the products are added to determine E(XY):
(0)(0)(0.05) + (0)(5)(0.03) + (0)(10)(0.06 + 0.01) + (0)(15)(0.02) + (5)(0)(0.04) + (5)(5)(0.15) + (5)(10)(0.20) + (5)(15)(0.10) + (10)(0)(0.01) + (10)(5)(0.15) + (10)(10)(0.13) + (10)(15)(0.01) + (15)(0)(0.02) + (15)(5)(0.10)
Therefore: Cov(X, Y)=E(XY)-E(X)E(Y) =119.25-(8.4)(10.5) = -1.05
As a result, X and Y have a correlation of -1.05.
(b) The standard errors of X and Y must also be computed in order to determine the correlation coefficient:
sqrt(Var(X)) = sqrt(E(X) - [E(X)]) = sqrt((0^2)(0.03) + (5^2)(0.04 + 0.15 + 0.01) + (10^2)(0.06 + 0.20 + 0.15 + 0.13) + (15^2)(0.02 + 0.10 + 0.01) - (8.4)^2) ≈ 5.23
The expression "_Y = sqrt(Var(Y)) = sqrt(E(Y)2 - [E(Y)]2)" = sqrt((0^2)(0.05) + (5^2)(0.04 + 0.01) + (10^2)(0.06 + 0.15 + 0.15) + (15^2)(0.02 + 0.20 + 0.13 + 0.01) - (10.5)^2) ≈ 5.07
The correlation number (rho) is rho = Cov(X, Y)/(X, Y) = -1.05/(5).
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two kinds of pine trees, bristlecone and aleppo, are planted in rows. in each row, the ratio of bristlecone to aleppo is 10:910:9. altogether, 600600 bristlecone pine trees are planted.how many aleppo pines are planted?
There are 288 Aleppo pines are planted in each ratio.
First, let's determine the total number of pine trees in each row. Since the ratio is 10 : 9, that means that for every 10 bristlecone pine trees planted, 9 Aleppo pine trees were planted. Therefore,
10 bristlecone pine trees + 9 Aleppo pine trees = 19 pine trees in each row.
Next, we need to determine how many rows of pine trees were planted. Since 600 bristlecone pine trees were planted, we can divide 600 by 19 to determine the number of rows.
600 ÷ 19 = 31.578947368421
Therefore, there were 32 rows of pine trees planted.
Now, we need to calculate how many Aleppo pine trees were planted. Since we know that for every 10 bristlecone pine trees planted, 9 Aleppo pine trees were planted,
So, the number of Aleppo pine trees planted.
32 x 9 = 288
Therefore, 288 Aleppo pine trees were planted.
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You roll a number cube. Find the probability
you roll a number that is greater than 2 and
less than 5. Write your answer as a fraction
in simplest form.
Please helpp
Answer:
1/3
Step-by-step explanation:
There are only two ways to roll a die and get a number bigger than 2 (not1 or not 2) and smaller than 5 (not 5 and not 6) You can roll a 3 (bigger than 2, smaller than 5) OR you can roll a 4 (also bigger than 2 a, smaller than 5)
There are only 6 different results when you roll a die (1-6).
To write a probability you put the total number of ways on the bottom. Put 2 on top because there's two ways to roll the desired result.
P = 2/6 and simplify
P = 1/3
4.
Use Synthetic Division To Solve.
(x3-3x2-7x+6) / (x-2)
A. x2+x+9+ 12 /x-2
B. x2+5x+3+ 12 / x-2
C. x2-5x+3
D. x2-x-9-12/x-2
Answer:
D. x^2-x-9-12/x-2
Step-by-step explanation:
We can use synthetic division to divide (x^3 - 3x^2 - 7x + 6) by (x - 2). First, we set up the division as follows:
2 | 1 -3 -7 6
|______2___-2__-18
| 1 -1 -9 -12
The numbers on the bottom row of the synthetic division table represent the coefficients of the quotient polynomial. Therefore, the quotient is x^2 - x - 9, and the remainder is -12.
So, we have:
(x^3 - 3x^2 - 7x + 6) / (x - 2) = x^2 - x - 9 + (-12 / x - 2)
Therefore, the correct option is D: x^2 - x - 9 - 12/(x - 2).