(c) Katrina recorded the average rainfall amount, in inches, for two cities over the course of 6 months. City A: {5, 2. 5, 6, 2008. 5, 5, 3} City B: {7, 6, 5. 5, 6. 5, 5, 6} (a) What is the mean monthly rainfall amount for each city? (b) What is the mean absolute deviation (MAD) for each city? Round to the nearest tenth. (c) What is the median for each city?
Answers
The mean monthly rainfall amount for City A is approximately 338.3 inches, and for City B, it is 6 inches.
The mean absolute deviation for City A is approximately 92.8 inches, and for City B, it is 0.5 inches.
The median for City A is 5.5 inches, and for City B, it is 6 inches.
(a) To find the mean monthly rainfall amount for each city, we sum up the rainfall amounts for each city and divide by the number of months.
For City A:
Mean = (5 + 2.5 + 6 + 2008.5 + 5 + 3) / 6 = 2030 / 6 ≈ 338.3 inches per month
For City B:
Mean = (7 + 6 + 5.5 + 6.5 + 5 + 6) / 6 = 36 / 6 = 6 inches per month
So, the mean monthly rainfall amount for City A is approximately 338.3 inches, and for City B, it is 6 inches.
(b) The mean absolute deviation (MAD) is a measure of the average distance between each data point and the mean. To calculate the MAD, we first find the absolute difference between each data point and the mean, sum them up, and then divide by the number of data points.
For City A:
Absolute differences from the mean: |5 - 338.3|, |2.5 - 338.3|, |6 - 338.3|, |2008.5 - 338.3|, |5 - 338.3|, |3 - 338.3|
MAD = (333.3 + 335.8 + 332.3 + 1670.2 + 333.3 + 335.3) / 6 ≈ 557.0 / 6 ≈ 92.8
For City B:
Absolute differences from the mean: |7 - 6|, |6 - 6|, |5.5 - 6|, |6.5 - 6|, |5 - 6|, |6 - 6|
MAD = (1 + 0 + 0.5 + 0.5 + 1 + 0) / 6 ≈ 3 / 6 = 0.5
So, the mean absolute deviation for City A is approximately 92.8 inches, and for City B, it is 0.5 inches.
(c) To find the median, we arrange the rainfall amounts in ascending order and find the middle value. If there are an even number of data points, we take the average of the two middle values.
For City A: {2.5, 3, 5, 5, 6, 2008.5}
Median = (5 + 6) / 2 = 11 / 2 = 5.5 inches
For City B: {5, 5.5, 6, 6, 6.5, 7}
Median = 6 inches
So, the median for City A is 5.5 inches, and for City B, it is 6 inches.
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Related Questions
An enclosure at a zoo contains giraffes and ostriches. All together the zookeeper counts 70 heads and 200 legs. How many of each animal are there?
Answers
By solving equations we know that there are 30 giraffes and 40 ostriches in the zoo.
A mathematical statement known as an equation is made up of two expressions joined by the equal sign.
A formula would be 3x - 5 = 16, for instance.
When this equation is solved, we discover that the number of the variable x is 7.
So, calculate as follows:
Let g represent giraffes and o represent ostriches.
g + o = 70 ...(1)
4*g + 2*o = 200 ...(2)
g = 70 - o, according to equation 1, therefore we may enter that number in place of g in equation 2 to obtain:
4*g + 2*o = 200
4*(70-o) + 2*o = 200
280 - 4o + 2o = 200
-2o = 200 - 280
2o = 80
o = 80/2
o = 40
Ostriches are 40 then giraffes will be:
70 - 40 = 30
Therefore, by solving equations we know that there are 30 giraffes and 40 ostriches in the zoo.
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While walking in the country, you count 37 heads and 102 feet in a field of horses and geese. Howmany of each animal are there?
Answers
In order to determine the number of horses and geeses, construct a system of equations, as follow:
There are 37 animals. If y is the number of horses and x the number of geeses, then, you can write:
x + y = 37
Now, consider that each geese has two feet and each horse has four feet. Due to you count 102 feet, then you can write:
2x + 4y = 102
Then, the system of equations is:
x+ y = 37
2x+ 4y = 102
Solve the previous system as follow:
Multiply the first equation by -2, then sum the result to the second equation and solve for y:
-2(x+ y = 37)
-2x - 2y = -74
-2x - 2y = -74
2x+ 4y = 102
2y = 28
y = 28/2
y = 14
Replace the previous value of y into any of the equations of the system and solve for x:
x + 14 = 37
x = 34 - 14
x = 20
Hence, there are 14 horses and 20 geeses.
35 of the students in the band play the flute, and another 15 play the clarinet. What fraction of the students in the band plays either the flute or the clarinet? Responses
Answers
As a result, we are unable to further simplify the phrase. The final solution is (35 + 15 - x) / N, where x is the proportion of students who are proficient in both instruments.
We must first ascertain the total number of students in the band in order to calculate the percentage of those who play the flute or clarinet. Let's assume that N kids make up the entire band.
The total number of pupils who play either the clarinet or the flute is then calculated as follows: 35 + 15 - x
The percentage of band students who play either the flute or the clarinet is now (35 + 15 - x) / N, and we need to know what x's value is. Nevertheless, the problem does not provide this information. As a result, we are unable to further simplify the phrase. The final solution is (35 + 15 - x) / N, where x is the proportion of students who are proficient in both instruments.
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What is the equivalent resistance? (in
Ω)(10 Points)
will give brainliest
Answers
Answer:
the answer Is 100........
Can you help me please
Answers
Answer:
D?
Step-by-step explanation:
if i got it wrong im truly sorry
Find the equation of (2,-10) & (6,-4) two points
Answers
Answer:
probably not helpful but a lil guide; first you need to solve for slope. (y2-y1/x2-x1) this will be m. next solve for y, to do this put on of your x values (2 or 6) using y=mx+b. to get b, place x=0.
How many constraints are there in a transshipment problem which has n nodes and m arcs?
a. n
b. m
c. (n + m)
d. (m − n)
Answers
The total number of constraints in a transshipment problem is (2n + m - 2). Therefore, the correct option is (d) (2n + m - 2).
In a transshipment problem, there are three types of variables: supply variables, demand variables, and transshipment variables.
Supply variables represent the amount of supply available at each source node.
Demand variables represent the amount of demand required at each destination node.
Transshipment variables represent the amount of flow that is allowed to transship through each intermediate node.
For each node, there is one supply variable or one demand variable. Therefore, the number of constraints due to supply and demand variables is equal to the number of nodes, which is n.
For each arc, there is a transshipment variable that represents the amount of flow that can be transshipped through that arc. Therefore, the number of constraints due to transshipment variables is equal to the number of arcs, which is m.
In addition, we also have flow conservation constraints at each intermediate node, which require that the total flow into the node must equal the total flow out of the node. There are n-2 intermediate nodes in a transshipment problem. Thus, the number of flow conservation constraints is (n-2).
Therefore, the total number of constraints in a transshipment problem is:
n (for supply and demand) + m (for transshipment) + (n-2) (for flow conservation)
= n + m + n - 2
= 2n + m - 2
Therefore, the correct answer is (d) (2n + m - 2).
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Death Valley National Park, in California and Nevada, is the site of the lowest elevation in the Western Hemisphere. Bad water Basin in the park is about 86 meters below sea level.
Answers
The locus of point equidistant from three vertices of a triangle is……………
Answers
Answer:
circumcenter
Step-by-step explanation:
You want to know the name of the point equidistant from the vertices of a triangle.
CircumcircleThe circle that passes through the vertices of a triangle is called a "circumcircle". It circumscribes the triangle. Its center is equidistant from all points on the circle, so is equidistant from the triangle's vertices.
The point equidistant from the vertices of a triangle is the circumcenter.
__
Additional comment
The circumcenter is at the intersection of the perpendicular bisectors of the sides of the triangle.
FINDING ANGLE MEASURES Find the value of x. Then classify the triangle by its angles.
Answers
Answer:
i hope my answer is right for you
In the given triangle, the value of x is 60°.
What are triangles?A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.Equilateral, right isosceles, obtuse isosceles, acute isosceles, right scalene, obtuse scalene, and acute scalene are the seven different kinds of triangles that can be found in nature.
So, the value of 'x':
We easily know that te given triangle is an equilateral triangle.Where all 3 angles are equal.The Sum of triangles is 180°.Now,
60 + 60 + x = 180120 + x = 180x = 180 - 120x = 60°
Therefore, in the given triangle, the value of x is 60°.
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P= r- s - 9 Solve for R
Answers
Answer:
r=P+s+9
Step-by-step explanation:
Select the correct answer from each drop-down menu.
Two parallel lines AB and CD are intersected by a transversal line EF that intersects AB at a point I and CD at a point K. Another transversal line GH is drawn right to GH and intersects AB at a point J and CD at point L.
In the figure, and ∠EIA ≅ ∠GJB. Complete the following statements to prove that ∠IKL ≅ ∠DLH.
∠EIA ≅ ∠IKC and ∠GJB ≅ ∠JLD because they are corresponding angles of parallel lines cut by a transversal.
So, if ∠EIA ≅ ∠GJB, then ∠IKC ≅ ∠JLD by the ________
A. Subtraction of Property
B. Substitution Property of Congruency
C. Addition Property of Congruency
D. Transitive Property of Congruency
∠IKL and ∠IKC and ∠DLH and ∠JLD are pairs of supplementary angles by the ____
A. Vertical Angles Theorem
B. Congruent Supplements Theorem
C. Linear Pair Theorem
.
m∠IKL + m∠IKC = 180° (1)
∠IKC ≅ ∠JLD, so m∠IKC = m∠JLD (2)
Applying the _____
A. Subtraction Property of Equality
B. Substitution Property of Congruency
C. Addition Property of Congruency
D. Transitive Property of Congruency
to equations (1) and (2), we get m∠IKL + m∠JLD = 180°.
Therefore, ∠IKL and ∠JLD are supplementary angles.
We've already shown that ∠DLH and ∠JLD are supplementary angles. Therefore, ∠IKL ≅ ∠DLH by the ____
A. Vertical Angeles Theorem
B. Definition of Supplementary Angles
C. Congruent Supplements Theorem
D. Linear Pair Theorem
.
Answers
∠IKL and ∠IKC and ∠DLH and ∠JLD are pairs by the Transitive Property of Congruency.
∠IKL and ∠IKC and ∠DLH and ∠JLD are pairs by the Linear Pair Theorem.The angle is Applying the Transitive Property of Congruency and product of m∠IKL + m∠JLD = 180°.Therefore, ∠IKL ≅ ∠DLH by the Congruent Supplements TheoremWhat is the Transitive property of congruence?This states that, if a pair of lines or angles or triangles are said to be congruent to a third line or angle, therefore, the first line or angle or triangle is said to be congruent to the third line or angle.
∠IKL and ∠IKC and ∠DLH and ∠JLD are pairs by the Transitive Property of Congruency. because the two angles and the other side of the angle/triangle are said to be equal to two angles and other side of the other triangle.
∠IKC ≅ ∠JLD, so m∠IKC = m∠JLD and as such angle is Applying the Transitive Property of Congruency because if A =b, and b = c then A = c and therefore, the above is true.
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a poll for a statewide election has a margin of error of percentage points. how many voters should be sampled for a confidence interval? round up to the nearest whole number.
Answers
The number of voters that should be sampled for a confidence interval depends on the desired level of confidence and the margin of error.
A larger sample size generally leads to a smaller margin of error and a higher level of confidence in the accuracy of the results. However, the relationship between sample size and margin of error is not linear, meaning that doubling the sample size will not necessarily halve the margin of error.
To calculate the required sample size, a formula can be used that takes into account the margin of error, level of confidence, and population size.
the number of voters that should be sampled for a confidence interval depends on several factors and cannot be determined without more information.
To determine the required sample size, you can use the following formula:
n = (Z^2 * p * (1-p)) / E^2
Where:
- n is the sample size
- Z is the Z-score (usually 1.96 for a 95% confidence interval)
- p is the estimated proportion of the population (usually 0.5 for the worst-case scenario)
- E is the margin of error (in decimal form)
Hence, without the specific margin of error, we cannot provide the exact sample size needed.
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describe and sketch the surface in r^3 represented by the equation x^2 z^2=9
Answers
The equation given results in a cylinder with radius 3 as shown in the attached sketch.
How to solve three dimensional domains?An equation involving three variables can be represented as a three-dimensional domain. For those involving only two variables, we can use our knowledge of the plane equations to get an idea of what the surface will look like.
Represented by the equation x² + z² = 9
We observe that there is no y term, and as such y can be any value.
x² + z² = 9 is a circle in the xz plane with a radius of 3
We are then "pushing this along the y-axis, resulting in a cylinder with radius 3.
The sketch of the surface is as shown in the attached file.
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2t/t-5 + 1/t-3 = 3 Help..
Answers
Step-by-step explanation:
Given equation is 2t/(t-5) + 1/(t-3) = 3
=> [2t(t-3)+1(t-5)]/(t-5)(t-3) = 3
=> (2t²-6t+t-5)/(t²-5t-3t+15) = 3
=> (2t²-5t-5)/(t²-8t+15) = 3
=> 2t²-5t-5 = 3(t²-8t+15)
=> 2t²-5t-5 = 3t²-24t+45
=>3t²-24t+45-2t²+5t+5 = 0
=> t²-19t+50 = 0
The standard form is t²-19t+50 = 0
Which of the following does not have the same value as the whole number 4?
3 5/5
1/4
4/1
3 4/4
Answers
Answer:
B
Step-by-step explanation:
3 5/5 = 4 because 5/5 is equal to 1, and 3+1 = 4.
1/4 is not equal to 4 because it is equal to 0.25
4/1 = 4 because it is an identity
3 4/4 = 4 because 4/4 is equal to 1, and 3+1 = 4
please help! i have no idea
Answers
Answer:
θ = 51.7
SOH-CAH-TOA
CAH: COS = ADJ/HYP cos(θ) = 19.4/29.3
θ = 48.5
93.2 + 48.5 + x = 180
x = 38.3
90 + 38.3 + θ = 180
θ = 51.7
Step-by-step explanation:
(1 point)
5. Write the polynomial in standard form. Then name the polynomial based on its degree and
number of terms.
5x + 2x4 – 4
O 5x – 4 + 2x4, not a polynomial
O 2x4 + 5x – 4; fourth-degree trinomial
O 5x + 2x4 – 4; quadratic monomial
O 2x4 + 5x – 4; cubic binomial
Answers
Answer:
Option (2)
Step-by-step explanation:
Standard form of the polynomial will be in the form of (ax⁴+ bx³+ cx²+ dx + e).
Which means exponents of each successive term will be in the reducing form and the last term will be a constant term.
Now we can rearrange the terms of the given polynomial (5x + 2x⁴ - 4) for the standard form.
(2x⁴ + 5x - 4)
Since, degree of the leading term = 4
And number of terms = 3
Given polynomial is a fourth degree trinomial.
Option (2) will be the answer.
For a cube whose side length the lexpression
Answers
what is the slope of line AB
Answers
Answer:
2,3
Step-by-step explanation:
you count up 2,then count over three
The soccer team lost three out of seven games so far this season approximately what percent of games has a team one
Answers
Answer:
They won 58% percent of their games
Step-by-step explanation:
3 is about 42% of 7 so just take 100 and subtract 42 to get the percentage of games they won.
Solve for x.
-18x + 21 > -15 OR 20x – 13 >27
Answers
Answer:
C
Step-by-step explanation:
-18x + 21 > -15 /// x = 2
20x – 13 >27 /// x = 2
The solution of inequality -18x + 21 > -15 OR 20x – 13 > 27 is x ∈ (- ∞, ∞), so option E is correct.
What is inequality?An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. It is most frequently used to compare the sizes of two numbers on the number line.
Given:
-18x + 21 > -15 or 20x – 13 >27
Solve the first inequality as shown below,
-18x + 21 > -15
-18x + 21 - 21 > -15 - 21 (Subtract 21 from both sides)
-18x > -36
-18x / -18 > -36 / -18 (Divide by -18 into both sides, the inequality sign changes as the value will become positive)
x < 2
Similarly, solve the second inequality,
20x – 13 > 27
20x > 40
x > 2
Thus, the solution will be x < 2 ∪ x > 2 or x ∈ (- ∞, ∞)
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Let f(x, y) = (4x2 + 2xy + 4y2)/ (x2 + y2), if (x, y) ≠ (0, 0)if (x, y) = (0, 0).(a) If (x, y) ≠ (0, 0); what are fx(x, y) and fy(x, y)?fx =fy =(b) Use the definition of the partial derivatives with respect to x and to y to find, if they exist, fx(0, 0) and fy(0, 0). (If an answer does not exist, enter DNE.)fx(0, 0) =fy(0, 0) =(c) Are both partial derivatives of f continuous at every point in the set {(x, y): (x, y) ≠ (0, 0)}?a. Yes, both the partial derivatives are continuous at every point in that set.b. No, only the partial derivative with respect to y is continuous at every point in that set.c. No, only the partial derivative with respect to x is continuous at every point in that set.d. No, neither partial derivative is continuous at every point in that set.
Answers
(a) To find the partial derivatives, we differentiate the function f(x, y) with respect to x and y while treating the other variable as a constant.
fx(x, y) = d/dx [ (4x^2 + 2xy + 4y^2) / (x^2 + y^2) ]
= [(8x(x^2 + y^2) - (4x^2 + 2xy + 4y^2)(2x)) / (x^2 + y^2)^2]
= [(8x^3 + 8xy^2 - 8x^3 - 4x^2y - 8xy^2) / (x^2 + y^2)^2]
= [-4x^2y / (x^2 + y^2)^2]
fy(x, y) = d/dy [ (4x^2 + 2xy + 4y^2) / (x^2 + y^2) ]
= [(8y(x^2 + y^2) - (4x^2 + 2xy + 4y^2)(2y)) / (x^2 + y^2)^2]
= [(8xy^2 + 8y^3 - 8xy^2 - 4x^2y - 8y^3) / (x^2 + y^2)^2]
= [-4x^2y / (x^2 + y^2)^2]
(b) To find fx(0, 0) and fy(0, 0), we substitute x = 0 and y = 0 into the partial derivative expressions:
fx(0, 0) = -4(0)^2(0) / ((0)^2 + (0)^2)^2 = 0
fy(0, 0) = -4(0)^2(0) / ((0)^2 + (0)^2)^2 = 0
(c) Both partial derivatives, fx(x, y) and fy(x, y), are continuous at every point in the set {(x, y): (x, y) ≠ (0, 0)}.
However, at the point (0, 0), the partial derivatives fx(0, 0) and fy(0, 0) are both 0, indicating that the partial derivatives are continuous at that point as well.
Therefore, the correct answer is (a) Yes, both the partial derivatives are continuous at every point in that set.
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what is the exact value of the expression? tan(π6) sin(5π3)⋅cos(−3π4)
Answers
The exact value of the expression tan(π/6) sin(5π/3)⋅cos(-3π/4) is -√3/2.
We have tan(π/6). The angle π/6 is equivalent to 30 degrees. The tangent of 30 degrees is √3/3.
We have sin(5π/3). The angle 5π/3 is equivalent to 300 degrees. In the unit circle, the sine value at 300 degrees is -√3/2.
Finally, we have cos(-3π/4). The angle -3π/4 is equivalent to -135 degrees. In the unit circle, the cosine value at -135 degrees is -√2/2.
Multiplying these values together, we have (√3/3) * (-√3/2) * (-√2/2). Simplifying, we get (√3 * √3 * √2) / (3 * 2 * 2) = (√3 * √2) / 12.
Taking the negative sign into account, the final value is -√3/2, which is approximately -0.866.
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Sherie bought a beach towel that normally costs $44 but was on sale for half price. She also bought a beach hat that was on sale for $12 off. Before tax, her total cost was $38. What was the regular price of the beach hat?
$22
$28
$48
$56
Answers
Answer:
$28
Step-by-step explanation:
The towel was $44 but at 1/2 off would be $22.
Her total cost was $38 so we subtract $22 from $38 to find how much she paid for the beach hat.
$38-$22 = $16
We add $12 to $16 to find the original price of the hat.
$16+$12 = $28
Answer:
$28
Step-by-step explanation:
i think im gonna buy human flesh off the darkweb today
Answers
Answer:
i- alrighty then
Step-by-step explanation:
You are driving to a city that is 23 miles away. So far, you have driven 10 miles. How many more miles do you have to drive?
Answers
Answer:
13
Step-by-step explanation:
23-10=13 you have 13 miles more to drive.
I NEED HELP ASAP Please and Thank You!
Answers
An exponential decay function that shows the relationship between y and t is y = 16,000 (0.74)^t.
What is an exponential decay function?An exponential decay function is one of the two types of exponential functions, including an exponential growth function.
Exponential functions are depicted as y = abˣ, where "a" is a constant, b is the base and x is the variable exponent.
The purchase value of a car = $16,000
Annual decreasing rate in value = 26%
Decayed value after 1 year = 0.74 (1 - 26%)
Let the number of years after the purchase = t
Let the resale value of the car after t years = y
Exponential Function:Resale value after t years, y = 16,000 x (1.074)^t
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Hi children pls find the area of this shape answer will get brainliest
Answers
Answer.
Answer is 9
Step-by-step explanation:
Multiply height by with.
1,1x8,1
then do whatever that equals times 2,5 and you should get your answer.
At work, you are calculating the cost of insulation for a customer. The customer would like to install his own insulation in an attic that is 12 yards by 18 yards. The insulation will cost $0.89 per square foot. To the nearest dollar, how much will it cost the customer to install the insulation
Answers
Answer:
insulation cost: $1730
Step-by-step explanation:
The area to be covered is 36 ft by 54 ft, so is ...
(36 ft)(54 ft) = 1944 ft^2
At a cost of $0.89 per square foot, the cost of the insulation is ...
(1944 ft^2)($0.89/ft^2) = $1730.16
To the nearest dollar the cost of the insulation will be $1730.
__
The cost of insulation is given. The question asks for the cost of installation. Not enough information is provided to answer that question.