In statistical analysis, the mean absolute deviation (MAD) is a measure of the average distance between each data point and the mean of the data set. For Doctor A's data set on corrective lenses, the MAD is calculated as 0.42, while for Doctor B's data set, it is calculated as 0.38.
This shows that Doctor B's data set has a slightly smaller variation compared to Doctor A's data set.
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F(x, y)=x^2-6xy-2y^3
find the critical points of the
given functions and classify each as a relative
maximum, a relative minimum, or a saddle point
The one critical point at (0, 0).
The critical point (0, 0) is a saddle point, and the critical point (-9, -3) is a relative minimum.
To find the critical points of the given function f(x, y) = x^2 - 6xy - 2y^3, we need to find the points where the partial derivatives with respect to x and y are equal to zero.
Calculate the partial derivative with respect to x (f_x):
f_x = 2x - 6y
Calculate the partial derivative with respect to y (f_y):
f_y = -6x - 6y^2
Set both partial derivatives equal to zero and solve the system of equations:
2x - 6y = 0 ---(1)
-6x - 6y^2 = 0 ---(2)
From equation (1), we can rearrange it to solve for x:
2x = 6y
x = 3y
Substituting x = 3y into equation (2):
-6(3y) - 6y^2 = 0
-18y - 6y^2 = 0
-6y(3 + y) = 0
Now, we have two possible cases:
a) -6y = 0
b) 3 + y = 0
a) -6y = 0
This implies y = 0
Substituting y = 0 into equation (1):
2x - 6(0) = 0
2x = 0
x = 0
So, we have one critical point at (0, 0).
b) 3 + y = 0
This implies y = -3
Substituting y = -3 into equation (1):
2x - 6(-3) = 0
2x + 18 = 0
2x = -18
x = -9
So, we have another critical point at (-9, -3).
Now, to classify each critical point as a relative maximum, relative minimum, or a saddle point, we need to analyze the second-order partial derivatives.
Calculate the second partial derivative with respect to x (f_xx):
f_xx = 2
Calculate the second partial derivative with respect to y (f_yy):
f_yy = -12y
Calculate the mixed partial derivative (f_xy):
f_xy = -6
Now, evaluate the discriminant D = f_xx * f_yy - (f_xy)^2 at each critical point:
For the critical point (0, 0):
D = f_xx * f_yy - (f_xy)^2
= 2 * (-12 * 0) - (-6)^2
= 0 - 36
= -36
For the critical point (-9, -3):
D = f_xx * f_yy - (f_xy)^2
= 2 * (-12 * -3) - (-6)^2
= 72 - 36
= 36
Analyzing the discriminant:
For the critical point (0, 0):
If D < 0, it is a saddle point. In this case, D = -36, so (0, 0) is a saddle point.
For the critical point (-9, -3):
If D > 0 and f_xx > 0, it is a relative minimum. In this case, D = 36 and f_xx = 2, so (-9, -3) is a relative minimum.
Therefore, the critical point (0, 0) is a saddle point, and the critical point (-9, -3) is a relative minimum.
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Pls help me out with this...
Answer:
f(x) = g(x - 9)
Step-by-step explanation:
The transformation from g(x) to f(x) is a translation of 9 units to the right.
A horizontal translation of h units takes place when x is replaced by x - h.
Here, replace x by x - 9.
f(x) = g(x - 9)
N
the accurate scale drawing shows
the positions of port p and a lighthouse l.
n
lindsey sails her boat from port p
on a bearing of 050°
she sails for 12 hours at an average
speed of 5km/h to a port q.
l*
p*
scale: 1 cm represents 3 km.
a) indicate the position of port q on the drawing (use the x tool).
(2)
b) find the distance, in km, of port q from lighthouse l.
(2)
c) find the bearing of port q from lighthouse l.
total marks:
A line segment of length 15 cm at a bearing of 50° from P to locate the position of Q on the drawing. Use the Law of Cosines the distance d between Q and L, which is approximately 71.2 km. Use the Law of Sines the angle x opposite d, which is approximately 29.5°, giving the bearing of Q from L.
Using the given scale of 1 cm represents 3 km, we can draw a line segment of length 15 cm (since 5 km/h x 12 h = 60 km) on a bearing of 50° from P to locate the position of Q. The point Q can be marked on the drawing using the x tool.
We can use the Law of Cosines to find the distance d between Q and L. Let a = 60 km (distance from P to Q), b = 36 km (distance from P to L), and C = 130° (the angle between a and b, which is equal to the sum of the angles at Q and L). Then
d² = a² + b² - 2ab cos(C)
d² = (60)² + (36)² - 2(60)(36)cos(130°)
d ≈ 71.2 km
Therefore, the distance of port Q from lighthouse L is approximately 71.2 km.
We can use the Law of Sines to find the angle x opposite the distance d between Q and L. Let a = 60 km (distance from P to Q), b = 36 km (distance from P to L), and sin(A) = sin(130°)/d. Then
sin(x)/60 = sin(130°)/d
sin(x) = (60/d)sin(130°)
x ≈ 29.5°
Therefore, the bearing of port Q from lighthouse L is approximately 29.5°.
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Which expression should you simplify to find the 90% confidence interval for a sample of 64 people with a mean of 36 and standard deviation of 3?
The 90% confidence interval for the sample is (35.384, 36.616).
How to calculate the interval for a sample of 64 people?We may use the following expression to determine the 90% confidence interval for a sample of 64 participants with a mean of 36 and a standard deviation of 3.
⇄
where: X = sample mean
Z[tex]\alpha[/tex]/2 = critical value for a 90% level from the ordinary normal distribution, which is roughly 1.645
σ = population standard deviation
n = sample size
Inputting the values provided yields:
CI = 36 ± 1.645 * (3 / √64)
When we condense the equation between the brackets, we obtain:
CI = 36 ± 1.645 * (3 / 8)
Further simplification results in:
CI = 36 ± 0.616
Consequently, the sample's 90% confidence interval is as follows:
(36 - 0.616, 36 + 0.616) = (35.384, 36.616)
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Find a formula for the sum of n terms. Use the formula to find the limit as n = [infinity].
lim ∑ ( 6 + i/n) (2/n)
To find a formula for the sum of n terms, we need to first write out the first few terms of the series and look for a pattern:
n=1: (6+1/1) (2/1) = 14
n=2: (6+1/2) (2/2) + (6+2/2) (2/2) = 16
n=3: (6+1/3) (2/3) + (6+2/3) (2/3) + (6+3/3) (2/3) = 17 1/3
n=4: (6+1/4) (2/4) + (6+2/4) (2/4) + (6+3/4) (2/4) + (6+4/4) (2/4) = 18
From this, we can see that the nth term is given by (6+i/n) (2/n). To find the sum of n terms, we simply add up all of the terms from i=1 to i=n:
∑ (6+i/n) (2/n) = (2/n) ∑ (6+i/n)
Using the formula for the sum of an arithmetic series, we get:
∑ (6+i/n) = n/2 (6 + (6+n)/n)
Substituting this back into our expression for the sum of n terms, we get:
∑ (6+i/n) (2/n) = (2/n) * (n/2) * (6 + (6+n)/n) = 6 + (6+n)/n
Taking the limit as n approaches infinity, we get:
lim (6 + (6+n)/n) = 6 + lim ((6+n)/n) = 6 + 1 = 7
Therefore, the limit of the given series as n approaches infinity is 7.
To find the formula for the sum of n terms, we will use the concept of Riemann sums. Given the expression you provided, it appears that you are trying to compute the limit of the Riemann sum as n approaches infinity, which will give you the integral of the function.
Expression: lim (n→∞) ∑ (6 + i/n) (2/n)
First, let's rewrite the Riemann sum in integral form:
∫(6 + x)dx
Now we need to find the integral of the function and evaluate it over a specific interval. However, you haven't provided the interval, so I'll assume it is [a, b].
∫(6 + x)dx evaluated from a to b will give us the formula for the sum of n terms:
F(x) = 6x + (1/2)x^2
Now, evaluate F(x) over the interval [a, b]:
F(b) - F(a) = [6b + (1/2)b^2] - [6a + (1/2)a^2]
This is the formula for the sum of n terms. To find the limit as n approaches infinity, you will need to provide the specific interval [a, b]. Otherwise, the limit cannot be determined without further information.
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Which expression is equivalent to 16 + 2 x 36?
Answer choices:
The correct expression equivalent to 16 + 2 x 36 is 88.
To simplify the expression, we need to follow the order of operations, which is Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). In this case, we have multiplication and addition.
Using the order of operations, we first need to perform the multiplication:
2 x 36 = 72
Then, we add 16 to the product:
16 + 72 = 88
Therefore, 16 + 2 x 36 is equivalent to 88.
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Find the perimeter of the rectangle, in feet.
L: 3 1/4 FT
W: 7/8 FT
Answers:
A. 8 1/4 ft
B: 8 1/5 ft
C: 8 1/2 ft
D: 8 1/3 ft
The perimeter of the rectangle is 8 1/4 feet. the correct answer is A.
Perimeter is the total length of the sides of a two-dimensional shape. In a rectangle, opposite sides are equal in length, so the perimeter can be found by adding the lengths of all four sides. To find the perimeter of a rectangle, we use the formula:
Perimeter = 2(length + width)
In this case, the length is given as 3 1/4 feet and the width is given as 7/8 feet. To find the perimeter, we substitute these values into the formula:
Perimeter = 2(3 1/4 + 7/8)
To simplify, we need to convert the mixed number to an improper fraction and find a common denominator for the fractions:
Perimeter = 2(13/4 + 7/8)
Perimeter = 2(26/8 + 7/8)
Perimeter = 2(33/8)
Now we can simplify the expression by multiplying 2 by the fraction:
Perimeter = 66/8
We can reduce this fraction by dividing both the numerator and denominator by 2:
Perimeter = 33/4
Therefore, the perimeter of the rectangle is 8 1/4 feet, which is answer choice A.
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A woman claims to have the ability to recognize by tasting it, whether tea was poured first and milk added after, or whether tea was added to milk. In order to test her powers, a set of 10 cups is brought to her and she is asked to taste them. She gets 7 out of 10 correct. Assuming each trial is independent, what is the probability that she would have done at least this well if she had no ability to recognize such difference
The probability that the woman would have done at least as well if she had no ability to recognize: the difference between the two methods is 0.117.
Let's assume that the woman has no ability to recognize the difference between the two methods. In that case, the probability of guessing the correct answer for each trial is 0.5 (since there are only two options).
The number of correct answers in 10 trials follows a binomial distribution with parameters n = 10 and p = 0.5. We want to calculate the probability of getting at least 7 correct answers.
Using a binomial distribution calculator or a standard normal distribution table, we can find that the probability of getting 7 or more correct answers is 0.117 (rounded to three decimal places).
Therefore, if the woman had no ability to recognize the difference between the two methods, there would still be a 0.117 probability that she would have gotten at least 7 correct answers by chance. Since 0.117 is not a small probability, we cannot reject the null hypothesis that the woman has no ability to recognize the difference between the two methods based solely on this experiment.
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X-1 if x < 2 Let f(x)=1 if 2sxs6 X+4 if x > 6 a. Find lim f(x). X-+2 b. Find lim f(x). X-6 Select the correct choice and, if necessary, fill in the answer box to complete your choice. O A. lim = X-2 O B. The limit is not - oo or co and does not exist. Select the correct choice and, if necessary, fill in the answer box to complete your choice. O A. lim = X-6 OB. The limit is not - oor oo and does not exist.
a. The limit does not exist.
b. The limit is equal to 4.
a. To find the limit as x approaches 2, we need to evaluate the left-hand and right-hand limits separately and check if they are equal.
Left-hand limit: lim f(x) as x approaches 2 from the left
We have f(x) = x - 1 for x < 2. So, as x approaches 2 from the left, f(x) approaches 1.
Right-hand limit: lim f(x) as x approaches 2 from the right
We have f(x) = 1 for 2 ≤ x ≤ 6 and f(x) = x + 4 for x > 6. So, as x approaches 2 from the right, f(x) approaches 6.
Since the left-hand and right-hand limits are not equal, the limit as x approaches 2 does not exist.
b. To find the limit as x approaches 6, we need to evaluate the left-hand and right-hand limits separately and check if they are equal.
Left-hand limit: lim f(x) as x approaches 6 from the left
We have f(x) = 1 for 2 ≤ x ≤ 6 and f(x) = x + 4 for x > 6. So, as x approaches 6 from the left, f(x) approaches 1.
Right-hand limit: lim f(x) as x approaches 6 from the right
We have f(x) = x + 4 for x > 6. So, as x approaches 6 from the right, f(x) approaches 10.
Since the left-hand and right-hand limits are not equal, the limit as x approaches 6 does not exist.
Therefore, the correct choices are:
a. The limit is not -oo or co and does not exist.
b. lim = 4.
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Which conic section is formed when a plane intersects the central axis of a double-napped cone at a 90° angle?
circle
ellipse
hyperbola
parabola
Answer: A
The conic section formed when a plane intersects the central axis of a double-napped cone at a 90° angle is circle.
The conic curve refers to the intersection of right circular cone via the plane. The shape of conic sections are determined by the location of the plane that intersects or divides the angle of intersection and cones.
These can be of four types, parabola, circle, ellipse and hyperbola. The conic curves find application in daily life such as mirrors, satellites, telescopes and other similar devices.
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Answer:circle A.
Step-by-step explanation:
What's the volume of a rectangular prism with a base area of 52 square inches and a height of 14 inches?
The volume of the rectangular prism is 728 cubic inches.
How to find the volume of a rectangular prism?A rectangular prism is a three-dimensional object that has six faces, all of which are rectangles. It is also known as a rectangular parallelepiped. To find the volume of a rectangular prism, we need to know the area of the base and the height of the prism.
The base of a rectangular prism is a rectangle, and its area is given by the formula A = lw, where l is the length and w is the width of the rectangle. Once we know the area of the base, we can find the volume of the prism by multiplying the base area by the height of the prism. The formula for the volume of a rectangular prism is:
V = Bh
where B is the area of the base and h is the height of the prism.
In the given problem, we are given the base area of the rectangular prism as 52 square inches and the height as 14 inches. Therefore, we can substitute these values into the formula to find the volume of the rectangular prism:
V = Bh = 52 sq in * 14 in = 728 cubic inches
So the volume of the rectangular prism is 728 cubic inches.
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Given: PA tangent to circle k(O) at A and PB tangent to circle k(O) at B.
Prove: m∠P=2·m∠OAB
PA is tangent to circle k(O), ∠OAP is a right angle. Similarly, ∠OBP is a right angle.
How to prove that m∠P=2·m∠OAB?To prove that m∠P=2·m∠OAB, we need to use the properties of tangents to a circle and the angle relationships between tangent lines and chords in a circle.
First, let's draw a diagram of the situation:
P
/ \
/ \
/ \
/ \
/ \
A-----------B
/ \
/ \
/ \
O \
| \
| \
| \
----------------------------
We are given that PA and PB are tangents to circle k(O) at A and B, respectively. This means that PA and PB are perpendicular to OA and OB, respectively, at the points of tangency A and B. We can also infer that OA and OB are radii of the circle k(O).
Let ∠OAB = x. Then, ∠OBA = x (since OA = OB), and ∠APB = 180° - ∠OAB - ∠OBA = 180° - 2x.
Since PA is tangent to circle k(O), ∠OAP is a right angle. Similarly, ∠OBP is a right angle. Therefore, ∠OAP + ∠OBP = 180°.
Let ∠P = y. Then, we have:
∠OAB + ∠OBA + ∠APB + ∠P = 180°
x + x + (180° - 2x) + y = 180°
y = 2x
Therefore, we have shown that m∠P = 2·m∠OAB, as required.
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Pythagorean theorem help quickly please
Answer:
In an isosceles right triangle, the length of the diagonal is √2 times the length of a leg.
c = 6√2 in. = 8.5 in.
the box-and-whisker plot shows the number of pigeons spotted by visitors at the park during the last weekend. the horizontal axis ranges from 0 to 20 in increments of 1. a horizontal line segment, or whisker, begins at 1 and ends on the left vertical side of the rectangle at 8. a vertical line segment passes through the rectangle at 10. the right vertical side of the rectangle is at 11. a second horizontal line segment, or whisker, begins on the right vertical side of the rectangle and ends at 13. what is the range of the data?
The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1) of the data. From the box-and-whisker plot given, the IQR is 12.
The box-and-whisker plot provides us with the following information:
The minimum value is 1 (the left end of the left whisker)The first quartile (Q1) is 8 (the end of the left whisker)The median (Q2) is 10 (the middle of the box)The third quartile (Q3) is 11 (the end of the right whisker)The maximum value is 13 (the right end of the right whisker)Therefore, the range of the data is the difference between the maximum and minimum values:
Range = maximum value - minimum value = 13 - 1 = 12
So, the range of the data is 12.
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Full Question: The box-and-whisker plot shows the number of pigeons spotted by visitors at the park during the last weekend. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 What is the interquartile range of the data? Provide your answer below:
Image attached
The data in socioeconomic. Jmp consists of five socioeconomic variables/features for 12 census tracts in the LA Metropolitan area. (a) Use the Multivariate platform to produce a scatterplot matrix of all five Features. (b) Conduct a principal component analysis (on the correlations) of all five features. Considering the eigenvectors, which are the most useful features
To produce (a) a scatterplot matrix of all five Features: we can use the Multivariate platform in JMP. (b) To conduct a principal component analysis (PCA) on the correlations select "Principal Components" from the red triangle menu. In the resulting dialog box, we can select the five features and check the "Correlations" option.
(a)You would utilise the Multivariate platform in JMP software to generate a scatterplot matrix of each of the five features. This allows you to visualize the relationships between each pair of features and identify any correlations or trends that may exist.
(b) You would use the PCA function in JMP or another statistical programme to perform a principal component analysis (PCA) on the correlations of all five features.
PCA is a technique used to reduce the dimensionality of data by identifying the most important features (principal components) that account for the largest variance in the data. Eigenvectors are used to determine the importance of each feature, with higher values indicating more significant features.
Considering the eigenvectors, the most useful features are those with the highest values, as they contribute the most to explaining the variation in the data. These high-value eigenvectors will help you identify the key socioeconomic factors driving differences between the census tracts in the LA Metropolitan area.
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A fair 6-sides die is rolled 550 times. What is a reasonable prediction for the number of times the event of landing on an even number?
The prediction for the number of times the event of landing on an even number in 550 rolls is 275
Estimating the reasonable predictionFrom the question, we have the following parameters that can be used in our computation:
The number of times = 550
The sample space of a fair 6-sided die is
S = {1, 2, 3, 4, 5, 6}
And as such the even numbers are
Even = {2, 4, 6}
This means that in a fair 6-sided die, we have
P(Even) = 3/6
When evaluated, we have
P(Even) = 1/2
So, when the die is rolled 550 times, we have
Expected value = 1/2 * 550
Evaluate
Expected value = 275
Hence, the number of times is 275
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What is the volume of the composite figure if both the height and the diameter of the cylinder are 3. 5 feet? Give the exact answer and approximate to two decimal places
The exact volume of the composite figure with a cylinder of height and diameter 3.5 feet and a hemisphere on top is 49.92 cubic feet.
How to find the volume?To find the volume of the composite figure, we need to add the volumes of the cylinder and the hemisphere on top of it.
The formula for the volume of a cylinder is:
V_cylinder = π[tex]r^2[/tex]h
where r is the radius of the cylinder and h is its height.
The formula for the volume of a hemisphere is:
V_hemisphere = (2/3)π[tex]r^3[/tex]
where r is the radius of the hemisphere.
In this case, the diameter of the cylinder is given as 3.5 feet, so the radius is half of that, or 1.75 feet. The height of the cylinder is also given as 3.5 feet. Therefore, the volume of the cylinder is:
V_cylinder = π(1.75[tex])^2[/tex](3.5) ≈ 32.67 cubic feet
To find the volume of the hemisphere, we need to first find its radius. Since the diameter of the cylinder is also the diameter of the hemisphere, the radius of the hemisphere is also 1.75 feet. Therefore, the volume of the hemisphere is:
V_hemisphere = (2/3)π(1.75[tex])^3[/tex] ≈ 17.25 cubic feet
Finally, we add the volumes of the cylinder and hemisphere to get the total volume of the composite figure:
V_total = V_cylinder + V_hemisphere
≈ 32.67 + 17.25
= 49.92 cubic feet
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Melanie knows she needs 5kg of grass seed to make a square lawn 8m by 8m. Grass seed is sold in 3kg boxes. Melanie wants to make a rectangular lawn by 12m by 14m. She has 4 boxes of grass seed. Has Melanie got enough grass seed to make a lawn by 12m by 14. Show your working out
Melanie does not have enough grass seed to make a lawn.
To find out if Melanie has enough grass seed to make a lawn by 12m by 14m, we need to calculate the area of the lawn and compare it to the amount of grass seed she has.
The area of the square lawn is 8m x 8m = 64 square meters. To cover this area with 5kg of grass seed, we can calculate the amount of grass seed needed per square meter: 5kg / 64 square meters = 0.078125 kg/square meter.
The area of the rectangular lawn is 12m x 14m = 168 square meters. To cover this area with the same amount of grass seed per square meter, we can calculate the total amount of grass seed needed: 168 square meters x 0.078125 kg/square meter = 13.125 kg.
Since Melanie only has 4 boxes of grass seed, which is a total of 12kg, she does not have enough to cover the rectangular lawn. She would need at least 1.125 kg more grass seed to cover the area.
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5. Vanessa and Nancy plan to make a birthday cake. Working together, Vanessa and Nancy can complete the
birthday cake in 2 hours. If Nancy works alone, it will take her 3 times as long as it would take Vanessa to
complete the birthday cake. The equation below represents this situation.
2 2
-+-=1
3x
How many hours would it take Nancy to complete the birthday cake if she worked alone?
X
Using an equation, if Nancy worked alone, the number of hours it would take her to complete the birthday cake is 1 hour 30 minutes.
What is an equation?An equation is a mathematical statement that proves the equality or equivalence of two or more mathematical expressions.
Equations use the equal symbol (=) unlike algebraic expressions, which combine variables with numbers, constants, and values using mathematical operands.
The number of hours for Vanessa and Nancy working together to make a birthday cake = 2 hours
The number of hours it takes Vanessa to complete the cake working alone = x
The number of hours it takes Nancy to complete the cake alone = 3x
Equation:3x + x = 2
4x = 2
x = 0.5 = 30 minutes
The total time for Nancy to complete the cake = 3x = 1.5 (3 x 0.5)
= 1 hour 30 minutes
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Q. 1: Expand and simplify each of the following expression:
6m- 2(4n+5m+1)-2n + 4
12x + 5(-5y-2z+2) – 2(8x+z) + 7
Q. 2: Factorize the following:
8pq + 20qr – 16s
4a2 + 7a + 3
a2-5a + 2ab – 10b
Q. 3: Express each of the following as a fraction in its simplest form:
3m4 + 5m8 – m2
2p3 -3p +p2
Answer:
Step-by-step explanation:
Q.1:
6m - 8n - 10m - 2 - 2n + 4 = -6n - 4m + 2
12x - 25y - 10z + 10 - 16x - 2z + 7 = -4x - 25y - 12z + 17
Q.2:
8pq + 20qr - 16s = 4(2pq + 5qr - 4s)
4a2 + 7a + 3 = (4a + 3)(a + 1)
a2 - 5a + 2ab - 10b = (a - 2)(a + 2b - 5)
Q.3:
3m4 + 5m8 - m2 = m2(3m2 + 5m6 - 1)/(m2) = 3m2 + 5m6 - 1
2p3 - 3p + p2 = p2(2p - 3)/(p2) = 2p - 3
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Find the necessary sample size.
A population is normal with a variance of 99. Suppose you wish to estimate the population mean μ. Find the sample size needed to assure with 68. 26 percent confidence that the sample mean will not differ from the population mean by more than 4 units.
A. 9
B. 7
C. 613
D. 25
If a population is normal with a variance of 99, the necessary sample size is 7 (Option B).
To find the necessary sample size for a given confidence level and margin of error, we can use the formula:
n = (Z² * σ²) / E²
where n is the sample size, Z is the Z-score corresponding to the desired confidence level, σ² is the population variance, and E is the margin of error.
In this case, the population variance (σ²) is 99, the desired confidence level is 68.26%, and the margin of error (E) is 4 units. The Z-score corresponding to a 68.26% confidence level is approximately 1, as it is close to one standard deviation from the mean in a normal distribution.
Now, we can plug the values into the formula:
n = (1² * 99) / 4²
n = (1 * 99) / 16
n = 99 / 16
n ≈ 6.19
Since we cannot have a fraction of a sample, we round up to the nearest whole number, which is 7. So, the necessary sample size is 7 (Option B).
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if y varies directly with x and y =20 when x=-2 find y when x=-1
Answer:
y = 10
Step-by-step explanation:
If y varies directly with x, and y=20 when x=-2, the best way to find y when x=-1 is to divide 20/-2, which equals -10.
Now cancel out -1 by dividing it by 1, and do the same with -10 by dividing it by 1 also. This equals 10, and that's your answer. Check the table I made below representing the problem. It should make it easier understand.
Find all the points that are described by the following statement.
the first number of my ordered pair is 50. fo 20 points hurry!!!!!
The statement "the first number of my ordered pair is 50" implies that all the points are of the form (50, y), where y can be any real number.
Therefore, the set of points that satisfy this statement is infinite, and it is not possible to list all of them.
However, if you need 20 specific points, you can choose any 20 values for y and pair them with 50 to obtain 20 points that satisfy the given condition.
For example, some of the points that satisfy this statement are (50, 0), (50, 1), (50, -2), (50, π), and (50, 10^6).
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Which relationship does not represent a direct proportion?
A. y = −
3
8
x
B.
Pounds Cost
3 $3.87
5 $6.45
8 $10.32
C. A dog groomer charges $15 per hour.
D.
The correct relationship which does not represent a direct proportion is,
⇒ A dog groomer charges $15 per hour.
Given that;
The graph is shown relation between number of minutes and Distance.
Take two points on the line are,
(2, 100) and (4, 150)
Hence, From graph we get;
The equation of line is,
⇒ y - 100 = (150 - 100)/ (4 - 2) (x - 2)
⇒ y - 100 = 25 (x - 2)
⇒ y - 100 = 25x - 50
⇒ y = 25x - 50 + 100
⇒ y = 25x + 50
Thus, The correct relationship which does not represent a direct proportion is,
⇒ A dog groomer charges $15 per hour.
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Find the missing point of the following parallelogram. (2,4) (6,5) (7,5) (5,3)
Answer:
The missing point of this parallelogram is (6, 5).
In the equation
In the equation
T = -mv²,
T = = my², find the value of T when m = 50 and v= 2
hon simplify.
When m = 50 and v = 2, the value of T is -200 according to Equation 1 and 200 according to Equation 2.
In the given equations, T represents a variable and m and v are constants.
We need to find the value of T when m = 50 and v = 2.
Let's evaluate each equation separately.
Equation 1: T = -mv²
Substituting the given values, we have:
T = -(50)(2)²
T = -(50)(4)
T = -200
Equation 2: T = my²
Substituting the given values, we have:
T = (50)(2)²
T = (50)(4)
T = 200
Thus, when m = 50 and v = 2, Equation 1 gives T = -200 and Equation 2 gives T = 200.
These equations represent two different relationships between the variables.
Equation 1 has a negative sign in front of the result, indicating that T will have a negative value.
On the other hand, Equation 2 does not have a negative sign, resulting in a positive value for T.
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A home buyer is financing a house for $135,950. The buyer has to pay $450 plus 1.15% for a brokerage fee. How much are the mortgage brokerage fees?
$2,489.25
$2,013.43
$2,018.60
$2,031.43
Answer: $2,013.43
Step-by-step explanation:
$135,950 x 1.15% = 1,563.425
Round to $1,563.43
Add in $450
$1,563.43 + $450 = $2,013.43
An object accelerates from rest to a speed of 10 m/s over a distance 25 m. What acceleration did it experience?
The acceleration is 2 m/s²
How to calculate the acceleration?The first step is to write out the parameters given in the question
Initial velocity which is denoted u= 0final velocity which is denoted with v= 10 m/sdistance which is denoted with s = 25 mAcceleration is the rate at which an object changes its velocity over time.
The formula to calculate the acceleration is v²= u² + 2as10²= 0² + 2(a)(25)100= 2a(25)100= 50a
Divide both sides by the coefficient of a which is 50
100/50 = 50a/50
a= 2
Hence the acceleration of the object is 2 m/s²
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What is the area that has 160ft tall 100 feet wide and another area that has 60ft long and 40ft wide , add both shapes together
The area for the first shape is 16,000 square feet, the area for the second shape is 2,400 square feet. The total area of both shapes added together is 18,400 square feet.
To find the area of the first shape, which is a rectangle that is 160 feet tall and 100 feet wide, we can use the formula:
Area = length x width
So, for the first shape, the area is:
Area = 160 ft x 100 ft
Area = 16,000 square feet
To find the area of the second shape, which is a rectangle that is 60 feet long and 40 feet wide, we can use the same formula:
Area = length x width
So, for the second shape, the area is:
Area = 60 ft x 40 ft
Area = 2,400 square feet
To find the total area of both shapes added together, we simply add the two areas:
Total Area = 16,000 square feet + 2,400 square feet
Total Area = 18,400 square feet
Therefore, the total area of both shapes added together is 18,400 square feet.
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Find the standard matrix for the linear transformation T:R2 + R2 that shears horizontally, with T "((A)) = (-1,67)
The standard matrix for the linear transformation T that shears horizontally is T = [(1 1) (0 1)] [(1 0) (-6 1)] [(1 1) (0 1)]^(-1) = [(1 -6) (0 1)].
To find the standard matrix for the linear transformation T that shears horizontally, we need to determine the matrix that transforms the standard basis vectors e1 and e2 into the shear vectors s1 and s2. The shear vectors are obtained by applying the linear transformation T to the standard basis vectors e1 and e2, respectively.
The shear vector s1 is obtained by shearing the point (1,0) horizontally by -1 unit, and then vertically by 6 units. This gives us s1 = (-1,6). Similarly, the shear vector s2 is obtained by shearing the point (0,1) horizontally by -1 unit and leaving it vertically unchanged. This gives us s2 = (-1,1).
To obtain the standard matrix for the linear transformation T, we need to find the matrix A that transforms the standard basis vectors e1 and e2 into the shear vectors s1 and s2, respectively. We can express A as [s1 s2] [e1 e2]^(-1), where [s1 s2] is a 2x2 matrix whose columns are the shear vectors, and [e1 e2]^(-1) is the inverse of the 2x2 matrix whose columns are the standard basis vectors.
Substituting the values of s1, s2, e1, and e2, we get:
A = [(1 -1) (6 1)] [(1 0) (0 1)]^(-1) = [(1 -1) (6 1)] [(1 0) (0 1)] = [(1 -1) (6 1)]
Therefore, the standard matrix for the linear transformation T that shears horizontally is T = [(1 1) (0 1)] [(1 -1) (6 1)] [(1 1) (0 1)]^(-1) = [(1 -6) (0 1)].
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