Step-by-step explanation:
The volume = 15 × 4.2 × 9.9 = 623.7
please give me a brainliest answer
A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund that yields a rate of 3. 0%. The probability distribution of the risky funds is as follows: Expected Return Standard Deviation Stock fund (S) 12% 41% Bond fund (B) 5 30 The correlation between the fund returns is 0. 18. Solve numerically for the proportions of each asset and for the expected return and standard deviation of the optimal risky portfolio. (Do not round intermediate calculations and round your final answers to 2 decimal places. Omit the "%" sign in your response. )
We can respond to that by addressing the problem at hand by equation Intended outcome: E(Rp) = 10.36%; Typical deviation: 28.79% and 0.29% Sharpe ratio
What is equation?A math equation is a procedure that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions
x + y + z = 1 (the proportions must sum up to 1) (the proportions must add up to 1) Portfolio return anticipated: E(Rp) is defined as x * E(Rs) + y * E(Rb) + z * Rf. Deviation from the portfolio's mean: p = sqrt(x2 * s2, y2 * b2, z2 * 0 + 2xy * sb, s, and b)
We must do a problem to determine the values that maximise the Sharpe ratio in order to determine the ideal ratios of x, y, and z:
Sharpe ratio is equal to (E(Rp) - Rf) / p.
To calculate the ideal ratios and portfolio statistics, we can use a spreadsheet or a solver. The answer is:
In other words, invest 74% in the stock fund and 26% in the bond fund, with the ratios being x = 0.74, y = 0.26, and z = 0.
Intended outcome: E(Rp) = 10.36%
Typical deviation: 28.79%
0.29% Sharpe ratio
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3. Which list shows the lengths of three segments that could be the sides of a right triangle? A. 6 cm, 8 cm. 10 cm B. 5 cm. 7 cm. 9 cm C.2 cm. 4 cm. 6 cm D. 1 cm. 2 cm. 3 cm ОА B OD
Answer:
7c,m
Step-by-step explanation:
you bad at math im smart your not sike you are smart haha
Gracie and Mark are having a
contest to see who can sell the most
cupcakes. For every 3 that Mark
sold, Gracie sold 4. If Gracie sold 4
more than Mark, how many total
cupcakes were sold?
Answer:
Mark sold 12 cupcakes, meaning Gracie sold 16.
4 threes, and 4 fours.
Mark Gracie
O O O O O O O
O O O O O O O
O O O O O O O
O O O O O O O
Answer:
Step-by-step explanation:
m/g=3/4
m=3g/4, now we can express m in terms of g
g=4+m, using m found above in this equation gives you
g=4+(3g)/4
4g=16+3g
g=16, since m=3g/4
m=3(16)/4
m=48/4
m=12
So total cupcakes sold is 12+16=38.
38 cupcakes were sold.
In a certain city with a working population of 10,500 , 8925 people and less than $75,000 per year what is a percentile rank of someone who earns $75,000 per year
Answer:
The percentile rank of someone who earns $75,000 per year is the 85th percentile.
Step-by-step explanation:
Meaning of percentile:
When a value V is said to be in the xth percentile of a set, x% of the values in the set are lower than V and (100-x)% of the values in the set are higher than V.
In this question:
Working population of 10,500
8,925 people earn less than $75,000 per year.
8925/10500 = 0.85
0.85*100 = 85
The percentile rank of someone who earns $75,000 per year is the 85th percentile.
an ambulance is traveling north at 46.1 m/s, approaching a car that is also traveling north at 36.2 m/s. the ambulance driver hears his siren at a freq
The frequency of the sound heard by the ambulance driver is approximately 1.05 times the frequency of the sound emitted by the siren.
We can use the Doppler effect equation to find the frequency of the sound heard by the ambulance driver.
The Doppler effect describes the change in frequency of a wave (such as sound or light) due to the relative motion of the source and the observer.
The equation for the Doppler effect for sound is:
f' = f (v + vo) / (v + vs)
where f is the frequency of the sound emitted by the siren (in Hz), f' is the frequency of the sound heard by the observer (in Hz), v is the speed of sound in air (approximately 343 m/s at room temperature), vo is the velocity of the observer (in m/s), and vs is the velocity of the source (in m/s).
In this case, the ambulance is the observer and the car is the source. Both are traveling north, so we can take their velocities as positive. Plugging in the given values, we get:
f' = f (v + vo) / (v + vs)
= f (v + 46.1) / (v + 36.2)
= f (343 + 46.1) / (343 + 36.2)
≈ 1.05 f.
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As the ambulance and car are approaching each other. The frequency heard by the driver is approximately 1.05 times the frequency of the siren.
To calculate the frequency of the sound heard by the ambulance driver, we can use the Doppler effect equation. The Doppler effect describes the change in frequency of a wave, such as sound or light, due to the relative motion of the source and the observer.
In this case, the ambulance is the observer, and the car is the source. Both are travelling north, so we can take their velocities as positive. We are given that the ambulance is travelling at a speed of 46.1 m/s, and the car is travelling at a speed of 36.2 m/s.
We also need to know the speed of sound in air, which is approximately 343 m/s at room temperature. With this information, we can use the Doppler effect equation for sound:
f' = f (v + vo) / (v + vs)
where f is the frequency of the sound emitted by the siren, f' is the frequency of the sound heard by the observer (in this case, the ambulance driver), v is the speed of sound in air, vo is the velocity of the observer (in this case, the ambulance), and vs is the velocity of the source (in this case, the car).
Plugging in the given values, we get:
f' = f (v + vo) / (v + vs)
= f (v + 46.1) / (v + 36.2)
= f (343 + 46.1) / (343 + 36.2)
≈ 1.05 f
Therefore, the frequency of the sound heard by the ambulance driver is approximately 1.05 times the frequency of the sound emitted by the siren.
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100 points!!!
Determine the solution to the system of equations graphed below and explain your reasoning in complete sentences.
The solution to the system of equations graphed below is,
⇒ (0, 1)
Since, We have to given that;
Two system of equations are,
⇒ g (x) = 3x + 2
⇒ f (x) = |x - 1| + 1
Here, The graph of both system of equation are shown in graph.
We know that;
In a graph, the solution of system of equation are represented by a intersection point of both graph.
Here, In the graph of system of equation,
Intersection point is,
⇒ (0, 1)
Hence, The solution to the system of equations graphed below is,
⇒ (0, 1)
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in order to calculate the pearson correlation between x and y please provide the numerator and demonenator of the correlation formula
The denominator of the formula, sqrt(Σ((x -x )²) * Σ((y - y)²)), is the product of the standard deviations of x and y.
The numerator of the Pearson correlation formula is the sum of the products of the deviations of x and y from their respective means. The denominator is the product of the standard deviations of x and y.
The Pearson correlation coefficient measures the strength and direction of the linear relationship between two variables, x and y. It is computed using the following formula:
r = (Σ((x - x)(y - y))) / sqrt(Σ((x - x)²) * Σ((y -y)²))
In the formula, Σ represents the sum, x and y are the individual data points, x and y are the means of x and y respectively.
The numerator of the formula, Σ((x - x)(y - y)), represents the sum of the products of the deviations of x and y from their means. It measures how the values of x and y vary together.
The denominator of the formula, sqrt(Σ((x - x)²) * Σ((y - y)²)), is the product of the standard deviations of x and y. It scales the numerator to ensure that the correlation coefficient is between -1 and +1.
By calculating the numerator and denominator and performing the division, we obtain the Pearson correlation coefficient, which indicates the strength and direction of the linear relationship between x and y.
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Calculate the area of this triangle
Answer:
99cm^2
Step-by-step explanation:
The formula for area of a triangle is 1/2bh=a with b being the base and h being the height. Base and height here are 18cm and 11cm so multiplying them gets 198, multiply by 1/2 and get 99cm^2.
f(x) = - X2 + 6x - 11.
Answer:
×=11/4
Step-by-step explanation:
0=-2x+6x-11
0=4x-11
-4x=-11
x=11/4
6) a) you roll a die, and are given an amount in dollar equal to the number on the die. what would you pay to play this game if you played it a lot of times? b) now say that when you roll the die, you're allowed to either take the money that you'd get with the roll, or roll a second time; if you roll a second time, you're obligated to take the number of dollars that you get with the second roll. now what is the worth of the game?
The worth of the game remains at 3.5 dollars. The second roll is the only one that matters, the expected value is now equal to the average value of a single roll,
a) In the first scenario, where you roll a die and are given an amount in dollars equal to the number on the die, the expected value of the game can be calculated by taking the average of all possible outcomes.
Since the die has six sides and each side is equally likely to come up, the expected value is calculated as (1/6 * 1) + (1/6 * 2) + (1/6 * 3) + (1/6 * 4) + (1/6 * 5) + (1/6 * 6) = 3.5 dollars.
Therefore, if you played this game a lot of times, you would expect to pay an average of 3.5 dollars per game.
b) In the second scenario, where you have the option to roll a second time and are obligated to take the number of dollars from the second roll, the expected value changes. Let's analyze the possible outcomes:
- If you decide to take the money from the first roll, the expected value is the same as in the previous scenario, which is 3.5 dollars.
- If you decide to roll a second time, the expected value is again calculated by taking the average of all possible outcomes.
However, since the second roll is the only one that matters, the expected value is now equal to the average value of a single roll, which is (1/6 * 1) + (1/6 * 2) + (1/6 * 3) + (1/6 * 4) + (1/6 * 5) + (1/6 * 6) = 3.5 dollars.
The worth of the game in the second scenario is the maximum value between the expected value of taking the money from the first roll (3.5 dollars) and the expected value of rolling a second time (3.5 dollars).
Therefore, the worth of the game remains at 3.5 dollars.
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The worth of the game depends on the scenario. In the first scenario, where you only roll once, the worth is around 3.5 dollars. In the second scenario, where you have the option to roll a second time, the worth is less than 2 dollars.
a) If you roll a die and are given an amount in dollars equal to the number on the die, the expected value of this game can be calculated by taking the average of the possible outcomes. Since there are six possible outcomes (numbers 1 to 6), the expected value is the sum of these outcomes divided by 6.
The expected value is (1+2+3+4+5+6) / 6 = 3.5 dollars.
To find what you would pay to play this game, you would ideally want to pay an amount less than the expected value to make it a profitable game. However, if you played this game a lot of times, the law of large numbers suggests that your average outcome will approach the expected value. Therefore, it would be reasonable to pay around 3.5 dollars to play this game.
b) In the second scenario, if you roll the die and have the option to either take the money from the first roll or roll a second time and take the second roll's amount, the expected value changes. Now, you have a 1/6 chance of getting each number from the first roll and a 1/6 chance of getting each number from the second roll.
To calculate the expected value, you need to consider both possibilities. You would calculate the average of the outcomes from the first roll and the outcomes from the second roll, and then take the maximum of these two values.
For example, if you roll a 1 on the first roll, the expected value from the first roll would be 1. If you roll a 2 on the second roll, the expected value from the second roll would be 2. The maximum of these two values is 2. Therefore, the expected value for this game is 2 dollars.
When deciding what this game is worth, you would want to pay an amount less than the expected value to make it profitable. So, in this scenario, you would ideally want to pay less than 2 dollars to play this game.
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Kate just bought a tv that measures 42 inches diagonally, and is 18 inches tall. She wants to place the tv into a 40 inch wide cabinet. Will the tv fit and if so, how much room will be left (width) in the cabinet after the tv is placed?
9514 1404 393
Answer:
yes, about 2.05 inches
Step-by-step explanation:
The Pythagorean theorem can be used to find the width of the TV.
w^2 +h^2 = d^2
w = √(d^2 -h^2)
w = √(42^2 -18^2) = √1440 = 12√10
w ≈ 37.95 . . . inches
This dimension is less than 40 inches by a margin of ...
40 -37.95 = 2.05 . . . inches
The TV will fit, with 2.05 inches of space remaining.
What is m∠G to the nearest tenth? A right angle triangle EFG. The length of EF is 28. 2 and GF is 45. 8. Angle GFE is given as 90 degrees
Answer:
Step-by-step explanation:
ion even kno fr big dawg but imma go with 30.9
I will give brainliest
The a-value for the quadratic equation x² - 7x - 18.5 = 0 is 1.
The b-value for the quadratic equation x² - 7x - 18.5 = 0 is -7.
The c-value for the quadratic equation x² - 7x - 18.5 = 0 is -18.5.
The a-value for the quadratic equation 2x² + 15x + 12 = 0 is 2.
The b-value for the quadratic equation 2x² + 15x + 12 = 0 is 15.
The c-value for the quadratic equation 2x² + 15x + 12 = 0 is 12.
What is a quadratic equation?In Mathematics, a quadratic equation can be defined as a mathematical expression that can be used to define and represent the relationship that exists between two or more variable on a graph.
In Mathematics, the standard form of a quadratic equation is given by;
ax² + bx + c = 0
Mathematically, the quadratic formula is modeled or represented by this mathematical expression:
\(x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}\)
For the quadratic equation x² - 7x - 18.5 = 0, we have:
\(x = \frac{-(-7)\; \pm \;\sqrt{(-7)^2 - 4(1)(-18.5)}}{2(1)}\)
For the quadratic equation 2x² + 15x + 12 = 0, we have:
\(x = \frac{-(5)\; \pm \;\sqrt{(5)^2 - 4(2)(12)}}{2(2)}\)
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Amy has 14 more swimming records than Charles. Together they have 46 records. How many records does each person have?
Amy would 30 swimming records and Charles would have 16 swimming records.
What is an Equation?
An equation is a mathematical statement that shows the equality between two quantities.
Let the records of Amy and Charles be x and y respectively.
If Amy has 14 more records than Charles,
Then, X = y + 14----------1
Their combined record is 46
X + y = 46 -----------2
substituting for x in equation 2
y + 14 + y = 46
2y + 14 = 46
2y = 46 - 14
2y = 32
y = 32/2 = 16
x = 14 + y = 14 + 16 = 30
In conclusion, The number of swimming records of Amy and Charles is 30 and 16 respectively
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for the region rr below, write ∬rfda∬rfda as an iterated integral in polar coordinates.
No function f(r,θ) is given, we cannot evaluate the integral further.
To write ∬rfda as an iterated integral in polar coordinates for the given region rr, we need to determine the limits of integration for r and θ.
Let's first look at the region rr. From the given graph, we can see that the region is bounded by the circle with radius 3 centered at the origin. Therefore, we can express the region as:
r ≤ 3
To determine the limits for θ, we need to examine the region rr more closely. We can see that the region is symmetric about the x-axis, which means that the limits for θ are:
0 ≤ θ ≤ π
Now, we can write the iterated integral as:
∬rfda = ∫₀³ ∫₀ᴨ f(r,θ) r dθ dr
where f(r,θ) is the integrand function and r and θ are the limits of integration. Note that r is integrated first, followed by θ.
In this case, since no function f(r,θ) is given, we cannot evaluate the integral further.
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Scenario A. The manager at Dunder-Mifflin Paper Company interested in understanding how a company's employee benefits influence employee satisfaction. In 2020 the company implemented a new benefits package that included optional benefits such as childcare, eldercare, and retirement packages. The manager compares the employee satisfaction ratings from before and after the new benefits package was implemented.
1. What is the independent variable for Scenario A?
a. The employee benefits package
b. The work from home policy
c. Employee productivity
d. The employees at the company
e. The office layout (floorplan)
The independent variable for Scenario A is given as follows:
a. The employee benefits package.
What are dependent and independent variables?In the case of a relation, we have that the independent and dependent variables are defined by the standard presented as follows:
The independent variable is the input of the relation.The dependent variable is the output of the relation.In the context of this problem, we have that the input and the output of the relation are given as follows:
Input: Employee benefits package.Output: Employee satisfaction.Hence the independent variable for Scenario A is given as follows:
a. The employee benefits package.
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If the cube is divided into two equal parts by a plane parallel to the face defined by vertices 2, 3, 6, and 7, what will be the area of the cross-section?
A.
48 sq cm
B.
256 sq cm
C.
16 sq cm
The area of the cross-section is 16 sq. cm. Thus, option C is the correct answer.
Vertices sides = 2, 3, 6, and 7
Divide part face = parallel to the face of vertices
It is given that a square face is present in the middle of the cube. The area of the cross-section of the cube results from the plane and cube intersection.
To find the distance between the square face of the cube and the length of the side:
distance = \(\sqrt{[(x^{2} - x1)^2 + (y^{2} - y1)^2 + (z^{2} - z1)^2]}\)
we can use the coordinates of any two adjacent sides to find the distance.
distance = \(\sqrt{[(3-2)^2 + (3-2)^2 + (3-1)^2] }\)
distance = \(\sqrt{11}\)
To calculate the area of the face of the cube:
area = \(side^{2}\)
area = \(\sqrt{(11)^2}\)
area = 11
The area of the cross-section can be estimated as:
area = (1/2) x 11 x 4) + 5 vertices of plane
area = 16 sq. cm
Therefore we can infer that the area of the cross-section is 16 sq. cm
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what is 1/4 divided by 5.
Answer: 1/20 or 20
Step-by-step explanation:
solving a system of two linear equations means??
98 points if you answer
Mrs. Jenkins gave her class the function f(x)=(x-5)(x+1). Four students made a claim about the function. Each student's claim is below.
• Annie: The x-intercepts are (5,0) and (1,0)
•Jacob: The y-intercept is at (-5,0)
• Neil: The vertex is at (2, -9)
•Zoey: The midpoint between the x-intercepts is at (-2,0)
Which student's claim about the function is correct?
The only student with the correct claim about the given quadratic equation is; Neil: The vertex is at (2, -9)
How to identify the features of a quadratic function?We are given the quadratic function;
f(x) = (x - 5)(x + 1)
1) The x-intercepts of the quadratic function are simply the roots of the quadratic function. Now, the roots are at; (5, 0) and (-1, 0). Thus, Annie's claim is not correct.
2) The y-intercept is the point at which x = 0. Thus;
f(0) = (0 - 5)(0 + 1)
f(0) = -5
y-intercept is at; (0, -5)
Thus, Jacob is wrong.
3) The x-coordinate of the vertex is;
x = -b/2a
The equation is; x² - 4x - 5
Vertex = -(-4)/(2 * 1) = 2
y-coordinate is;
y = 2² - 4(2) - 5
y = -9
Thus, Jacob is correct
4) Zoey is incorrect because she didn't properly find the midpoint of the x-intercepts.
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If two parallel lines are cut by non-perpendicular transversal, which type of angles are NOT congruent?
Worth 60 points for a rapid reply- find the area of each regular polygon. Answers are rounded to the nearest whole number.
The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.
How to calculate for the area of the polygonArea of regular polygon = 1/2 × apothem × perimeter
perimeter = (s)side length of octagon × (n)number of side.
apothem = s/[2tan(180/n)].
11 = s/[2tan(180/12)]
s = 11 × 2tan15
s = 5.8949
perimeter = 5.8949 × 12 = 70.7388
Area of dodecagon = 1/2 × 11 × 70.7388
Area of dodecagon = 389.0634 in²
Area of pentagon = 1/2 × 5.23 × 7.6
Area of pentagon = 19.874 in²
Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.
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1. Use an antiderivative to show that for every contour C extending from a point z
1
to a point z
2
, ∫
C
z
n
dz=
n+1
1
(z
2
n+1
−z
1
n+1
)(n=0,1,2,…)
The formula ∫Cz^n dz = (z^(n+1))/(n+1) holds true for every contour C extending from z1 to z2, using antiderivative F(z) of z^n as F(z) = (z^(n+1))/(n+1) + C.
Let's consider the contour integral of z^n with respect to z over a contour C extending from z1 to z2. We can use the Fundamental Theorem of Calculus to evaluate this integral by finding an antiderivative of z^n.
We have the antiderivative F(z) of z^n as F(z) = (z^(n+1))/(n+1) + C, where C is a constant of integration.
Now, applying the Fundamental Theorem of Calculus, we can evaluate the integral ∫Cz^n dz by subtracting the value of F(z) at the endpoints:
∫Cz^n dz = F(z2) - F(z1) = [(z2)^(n+1)/(n+1) + C] - [(z1)^(n+1)/(n+1) + C]
= (z2^(n+1) - z1^(n+1))/(n+1)
Therefore, we have shown that for every contour C extending from z1 to z2, the integral of z^n with respect to z is given by (z2^(n+1) - z1^(n+1))/(n+1). This formula holds true for any nonnegative integer n.
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task 1 Find the surface area of the Onion. pls help
The surface area of the onion is 133π cm^2 or approximately 417.94 cm^2.
To find the surface area of the onion, we can use the given formulas and values to compute each section's area and then add them together. Let's express the calculations using correct mathematical expressions:
Given:
Diameter of the onion = 7 cm
Radius of the onion (r) = 3.5 cm
Surface area of the body of the onion (S_body) = 2πrh + 2πr^2
S_body = 2π(3.5 cm)(12 cm) + 2π(3.5 cm)^2
S_body = 2π(3.5 cm)(12 cm) + 2π(3.5 cm)^2
S_body = 2π(3.5 cm)(12 cm) + 2π(3.5 cm)^2
S_body = 2π(42 cm^2) + 2π(12.25 cm^2)
S_body = 84π cm^2 + 24.5π cm^2
S_body = (84 + 24.5)π cm^2
S_body = 108.5π cm^2
Surface area of each end of the onion (S_end) = πr^2
S_end = π(3.5 cm)^2
S_end = π(12.25 cm^2)
S_end = 12.25π cm^2
Total surface area of the onion (S) = S_body + 2S_end
S = 108.5π cm^2 + 2(12.25π cm^2)
S = 108.5π cm^2 + 24.5π cm^2
S = 133π cm^2
Therefore, the surface area of the onion is 133π cm^2 or approximately 417.94 cm^2.
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Identify bias based on a survey of 2718 people the national opinion research center concluded that 30% 32% of americans always make a special effort to sort and recycle glass cans plastic or papers 24% americans often make such an effort
Based on a survey of 2718 people, a research center concluded that 32% of Americans "always" make a special effort to sort and recycle glass, cans, plastic, or papers. Participation bias is there in this case.
The bias would have no effect on a reader's perception of the assertion because no group of persons is much more likely to respond to the poll than any other.
When comparisons are performed between groups of patients who differ in outcome determinants and the differences are connected to the result, participation bias emerges.
1. Participation bias is inherent in studies that involve participant enrollment.
2 Because selective participation might jeopardize study external validity, determining the magnitude of participation bias is critical for optimizing inference from these investigations.
Few community studies have looked into the impact of participation bias. Nonparticipants in one population-based study of myocardial infarction (MI) were older, had more comorbidity, and had a lower survival rate than participants.
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Solve the systent of equations algebraically . 5x - 3y = 6; 6x - 5y = 10
Step-by-step explanation:
x will be 0
y will be -2
thats the answer babe
the product of two numbers is 8933. If each of the two numbers is doubled the product of these larger numbers is?
The product of two numbers when doubled, the product of these larger numbers is 35,732
Productlet
The two unknown number = x and yproduct of x and y = 8933
x × y = 8933
If each of the two numbers is doubled2x × 2y = 8933
4xy = 4(8933)
4xy = 35,732
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The Durbin-Watson statistic for a regression model of weekly commodity prices for heating oil (cents) against time was found to be 0.244822. This value indicates that the test is inconclusive. residuals are positively autocorrelated. residuals are not autocorrelated. none of these; the Durbin Watson cannot be used for this model. I don't want to answer this question
The correct answer is "residuals are positively autocorrelated."
The Durbin-Watson statistic is used to test for autocorrelation in the residuals of a regression model. The statistic has a value between 0 and 4, with a value of 2 indicating no autocorrelation.
A Durbin-Watson statistic value less than 2 indicates positive autocorrelation, while a value greater than 2 indicates negative autocorrelation. A value of 2 indicates no autocorrelation, and a value of 0 or 4 indicates perfect positive or negative autocorrelation, respectively.
In this case, the Durbin-Watson statistic value of 0.244822 is less than 2, indicating positive autocorrelation in the residuals. Therefore, the correct answer is "residuals are positively autocorrelated."
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Find the average rate of change of the following line WITHOUT CALCULATING. y=18 on [1000,10000]
Answer
The average rate of change of the function y = 18 on the interval [1000, 10,000] is ZERO
SOLUTION
Problem Statement
The question wants us to find the average rate of change of the function y = 18 on the interval [1000, 10,000].
Method
- The function given is a constant function. This means that for every value of x from -∞ to +∞, the value of the function will always be y = 18.
- Since y is a function of x (albeit a constant function of x), it can be written as y = f(x).
- With these in mind, we can find the average rate of change of the function using the formula given below:
\(\begin{gathered} \bar{\Delta}=\frac{f(b)-f(a)}{b-a} \\ \text{where} \\ \lbrack a,b\rbrack\text{ is the interval for which we want to know the rate of change of the function }f(x) \end{gathered}\)- Note that since the function is a constant function, we should expect that its rate of change should be ZERO since the function is constant throughout despite the value of x.
Let us apply the formula above to find the average rate of change of the given function.
Implementation
The average rate of change of the function y = 18 is gotten below:
\(\begin{gathered} b=10,000,a=1000 \\ f(b)=f(10,000)=18\text{ (Since the function does not change)} \\ f(a)=f(1000)=18\text{ (Since the function is constant)} \\ \\ \therefore\bar{\Delta}=\frac{18-18}{10,000-1000}=\frac{0}{9,000} \\ \\ \therefore\bar{\Delta}=0 \end{gathered}\)Final Answer
The average rate of change of the function y = 18 on the interval [1000, 10,000] is ZERO
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