Answer:
a 1053
b 250
multiply 650 by 1.62 for part a.
for part b divide by 1.62 since pound is less than dollar
hope this helps :)
if x is a matrix of centered data with a column for each field in the data and a row for each sample, how can we use matrix operations to compute the covariance matrix of the variables in the data, up to a scalar multiple?
To compute the covariance matrix of the variables in the data, the "matrix-operation" which should be used is ([tex]X^{t}[/tex] × X)/n.
The "Covariance" matrix is defined as a symmetric and positive semi-definite, with the entries representing the covariance between pairs of variables in the data.
The "diagonal-entries" represent the variances of individual variables, and the off-diagonal entries represent the covariances between pairs of variables.
Step(1) : Compute the transpose of the centered data matrix X, denoted as [tex]X^{t}[/tex]. The "transpose" of a matrix is found by inter-changing its rows and columns.
Step(2) : Compute the "dot-product" of [tex]X^{t}[/tex] with itself, denoted as [tex]X^{t}[/tex] × X.
The dot product of two matrices is computed by multiplying corresponding entries of the matrices and summing them up.
Step(3) : Divide the result obtained in step(2) by the number of samples in the data, denoted as "n", to get the covariance matrix.
This step scales the sum of the products by 1/n, which is equivalent to taking the average.
So, the covariance matrix "C" of variables in "centered-data" matrix X can be expressed as: C = ([tex]X^{t}[/tex] × X)/n.
Learn more about Covariance Matrix here
https://brainly.com/question/30481066
#SPJ4
The given question is incomplete, the complete question is
Let X be a matrix of centered data with a column for each field in the data and a row for each sample. Then, not including a scalar multiple, how can we use matrix operations to compute the covariance matrix of the variables in the data?
A circle with center O and radius 5 has central angle XOY. X and Y are points on the circle. If the measure of arc XY is 90 degrees, what is the length of chord XY?
The length of chord XY is 5√2.
What is the length of the chord?
It is described as the line segment that connects any two points on the circle's circumference without going through the circle's center. As a result, the diameter is the chord of a particular circle that is the longest and goes through its center. In mathematics, determining the chord's length can be crucial at times.
Here, we have
Given: A circle with center O and radius 5 has a central angle XOY. X and Y are points on the circle. If the measure of arc XY is 90 degrees.
We have to find the length of chord XY.
∠XOY = 90°
OX = OY = 5
We draw a perpendicular from the center to chord XY bisect XY at D.
Now, since OD bisects ∠XOY
∠XOD = ∠YOD = 90°/2 = 45°
Now, in ΔXOD
sin45° = XD/OX
1/√2 = XD/5
5/√2 = XD...(1)
In ΔYOD
sin45° = YD/OY
5/√2 = YD...(2)
Adding (1) and (2), we get
XD + YD = 5/√2 + 5/√2
XY = 5√2
Hence, the length of chord XY is 5√2.
To learn more about the length of the chord from the given link
https://brainly.com/question/26094865
#SPJ1
The box plots display measures from data collected when 20 people were asked about their wait time at a drive-thru restaurant window.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 10 to 14.5 on the number line. A line in the box is at 12.5. The lines outside the box end at 5 and 20. The graph is titled Fast Chicken.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 8.5 to 15.5 on the number line. A line in the box is at 12. The lines outside the box end at 3 and 27. The graph is titled Super Fast Food.
Which drive-thru typically has less wait time, and why?
Fast Chicken, because it has a smaller median
Fast Chicken, because it has a smaller mean
Super Fast Food, because it has a smaller median
Super Fast Food, because it has a smaller mean
The correct answer is: Fast Chicken, because it has a smaller median.
What is median?
Median is a measure of central tendency that represents the middle value in a dataset when the values are arranged in order of magnitude. To find the median, you need to arrange the values in order from smallest to largest and then find the middle value.
Based on the information provided, the drive-thru restaurant with less wait time is Fast Chicken, as it has a smaller median wait time of 12.5 minutes compared to the median wait time of 12 minutes for Super Fast Food. The mean wait time is not given, and even if it were, the median is a better measure of central tendency to compare in this scenario, as the box plots suggest some potential outliers.
Therefore, the correct answer is: Fast Chicken, because it has a smaller median.
To learn more about median from the given link:
brainly.com/question/28060453
#SPJ1
Quilt squares are cut on the diagonal to form triangular quilt pieces. The hypotenuse of the resulting triangles is 20 inches long. What is the side length of each piece?
1. 10√2
2. 20√2
3. 10√3
4. 20√3
Answer:
The correct answer is:
10√2
Explanation:
In a right triangle, the hypotenuse is the side opposite the right angle and is also the longest side. The other two sides are called the legs.
In this problem, the hypotenuse of the resulting triangles is given as 20 inches. Since the quilt squares are cut on the diagonal to form triangular quilt pieces, the hypotenuse of each triangle is formed by the diagonal cut of a square.
Let's denote the side length of each square as "s" inches.
According to the Pythagorean Theorem, which relates the sides of a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two legs.
In this case, the hypotenuse is 20 inches, so we have:
20^2 = s^2 + s^2 (since the two legs of the right triangle are the sides of the square)
400 = 2s^2
Dividing both sides by 2, we get:
200 = s^2
Taking the square root of both sides, we get:
s = √200
Since we are looking for the side length of each piece in simplified radical form, we can further simplify √200 as follows:
√200 = √(100 x 2) = 10√2
So, the side length of each quilt piece is 10√
The side length of each piece of the triangular pieces of quilt cut from squares will be 10√2 inches.
This is a simple mathematics problem that can be solved using the Pythagoras theorem. This theorem states that in a right-angled triangle, the square root of the sum of the two perpendicular sides (p,b) is equal to the longest side, called the hypotenuse (h).
[tex]h = \sqrt{p^2 + b^2}[/tex]
Since the triangle pieces have been cut from a square, they will be right-angled triangles, and the two perpendicular sides will be equal, i.e., p = b.
20 = √2p² (since p and b are equal, b can be taken as p)
On squaring both sides,
400 = 2p²
p² = 400/2
p² = 200
p = √200
p = 10√2 = b
To know more about Pythagoras theorem,
https://brainly.com/question/28981380
brainlist
show all steps nd i will make u brainlist
Step-by-step explanation:
Again, using similar triangle ratios
7.2 m is to 2.4 m
as AB is to 12.0 m
7.2 / 2.4 = AB/12.0 Multiply both sides of the equation by 12
12 * 7.2 / 2.4 = AB = 36.0 meters
A tram moved downward 12 meters in 4 seconds at a constant rate. What was the change in the tram's elevation each second?
Therefore , the solution of the given problem of unitary method comes out to be during the 4-second period, the tram's elevation changed by 3 metres every second.
What is an unitary method?To complete the assignment, use the iii . -and-true basic technique, the real variables, and any pertinent details gathered from basic and specialised questions. In response, customers might be given another opportunity to sample expression the products. If these changes don't take place, we will miss out on important gains in our knowledge of programmes.
Here,
By dividing the overall elevation change (12 metres) by the total time required (4 seconds),
it is possible to determine the change in the tram's elevation every second. We would then have the average rate of elevation change per second.
=> Elevation change equals 12 metres
=> Total duration: 4 seconds
=> 12 meters / 4 seconds
=> 3 meters/second
As a result, during the 4-second period, the tram's elevation changed by 3 metres every second.
To know more about unitary method visit:
https://brainly.com/question/28276953
#SPJ1
# 15) A boat is heading towards a lighthouse, where Jeriel is watching from a vertical distance of
113 feet above the water. Jeriel measures an angle of depression to the boat at point A to be
8°. At some later time, Jeriel takes another measurement and finds the angle of depression to
the boat (now at point B) to be 52°. Find the distance from point A to point B. Round your
answer to the nearest tenth of a foot if necessary.
the distance between point A and point B is approximately 777.9 feet.
what is distance ?
Distance is a numerical measurement of how far apart two objects or points are from each other. It is a fundamental concept in mathematics and physics, and it can be defined in different ways depending on the context.
In the given question,
Let's denote the distance between Jeriel and point A as x, and the distance between Jeriel and point B as y. We want to find the distance between point A and point B, which we can call d.
From the first measurement, we can draw a right triangle with one leg of length x, another leg of length 113, and an acute angle of 8 degrees. The angle opposite the leg of length 113 is 90 degrees minus 8 degrees, or 82 degrees. We can use tangent to find x:
tan(8) = 113/x
x = 113/tan(8)
x =802.5
From the second measurement, we can draw another right triangle with one leg of length y, another leg of length 113, and an acute angle of 52 degrees. The angle opposite the leg of length 113 is 90 degrees minus 52 degrees, or 38 degrees. We can use tangent to find y:
tan(52) = 113/y
y = 113/tan(52)
y =72.4
Now we can use the Law of Cosines to find d:
d² = x² + y² - 2xy cos(130)
where 130 degrees is the angle between the sides of length x and y. We can simplify this equation and substitute the values we found for x and y:
d² = (802.5)² + (72.4)² - 2(802.5)(72.4) cos(130)
d =777.9
Therefore, the distance between point A and point B is approximately 777.9 feet.
To know more about distance , visit:
https://brainly.com/question/15172156
#SPJ1
PLEASE HELP ME
I’LL GIVE YOU BRAINLIEST
The profit function of the company is given by P(x)=-4x^3 + 32x^2 - 64, where x is the number of toys sold in hundreds, and P(x) is the profit in thousands of dollars.
How to explain the graphThe key features of the graph of the profit function are the following:
The degree of the polynomial function is 3, which means that the graph is a cubic curve.
The coefficient of the leading term is negative (-4), which means that the graph opens downwards.
The coefficient of the quadratic term is positive (32), which means that the graph is concave up.
The y-intercept of the graph is -64, which means that the company will incur a loss of $64,000 if it does not sell any toys.
It should be noted that to find the maximum profit, we need to evaluate the profit function at x = 5.33:
P(5.33) = -4(5.33)^3 + 32(5.33)^2 - 64 = 23.78
Therefore, the maximum profit that the company can make is $23,780.
In summary, the graph of the profit function reveals that the company will incur a loss if it does not sell any toys, but it can make a profit if it sells at least some toys. The profit function has a cubic shape that opens downwards, indicating that the profit decreases as the number of toys sold increases beyond a certain point. The maximum profit occurs at x = 5.33, where the profit is $23,780.
Learn more about graph on;
https://brainly.com/question/19040584
#SPJ1
WILL MARK AS BRAINLEIST!!
Question in picture!!
Note: The graph above represents both functions “f” and “g” but is intentionally left unlabeled
Answer:
f(x) is the blue graph, g(x) is the red graph.
x^2 - 3x + 17 - (2x^2 - 3x + 1) = 16 - x^2
16 - x^2 = 0 when x = -4, 4
So the area between these two graphs is (using the TI-83 graphing calculator):
fnInt (16 - x^2, x, -4, 4) = 85 1/3
2. when conducting a hypothesis test, the hypothesis that illustrates what we really think is going on in the population is called the hypothesis. an. analytical b. hypothetical c. null d. theoretical e. alternative
Consider a sequence whose first five terms are:-1.75, -0.5, 0.75, 2, 3.25
Which explicit function (with domain all integers n ≥ 1) could be used to define and continue this sequence?
Step-by-step explanation:
+ 1.25
every new term is the previous term + 1.25.
with starting value -1.75
f(n) = 1.25n - 1.75
cuantos números
primos son a la vez la suma y la diferencia
Answer: there is only one number
Answer:
Solo hay un número primo que se puede escribir como suma de dos números primos y también como diferencia de dos números primos.
Espero haber ayudado :D
Please only do 9,11, and 13! And please help!! 40 points!!!
9. The volume of the triangular pyramid is given by:
V = (1/3)Bh
Here, B is the base area.
The base is shaped as a right triangle thus, using the Pythagoras Theorem we have:
h = sqrt(26.7² - 11.7²) = 23.274 km
The area if the base is:
B = (1/2)bh = (1/2)(11.7 km)(23.4 km) = 136.89 sq. km
Now, the volume is:
V = (1/3)(136.89)(15) = 2053.35 cubic km
Hence, the volume of the triangular pyramid is 2053.35 cubic km.
9. The volume of the triangular pyramid is 2053.35 cubic km. 11. The area of the shaded portion is 348.19 cubic in 13. The slant height of the cone is 8.53 meters.
What is Pythagoras Theorem?A fundamental conclusion in geometry relating to the lengths of a right triangle's sides is known as Pythagoras' theorem. According to the theorem, the square of the length of the hypotenuse, the side that faces the right angle, in any right triangle, equals the sum of the squares of the lengths of the other two sides, known as the legs.
9. The volume of the triangular pyramid is given by:
V = (1/3)Bh
Here, B is the base area.
The base is shaped as a right triangle thus, using the Pythagoras Theorem we have:
h = √(26.7² - 11.7²) = 23.274 km
The area if the base is:
B = (1/2)bh = (1/2)(11.7 km)(23.4 km) = 136.89 sq. km
Now, the volume is:
V = (1/3)(136.89)(15) = 2053.35 cubic km
Hence, the volume of the triangular pyramid is 2053.35 cubic km.
11. The volume of a cone is given by:
V = (1/3)πr²h
The dimension of the bigger cone is radius is 9 in, and height 15 in:
V1 = (1/3)π(9 in)²(15 in) = 381.7 cubic in
The dimension of the smaller cone is radius is 4 in, and height 10 in:
V2 = (1/3)π(4 in)²(10 in) = 33.51 cubic in
Now, the area of the shaded portion is:
V1 - V2 = 381.7 - 33.51 = 348.19
13. The volume of a cone is given by:
V = (1/3)πr²h
Substituting the values we have:
542.87 = (1/3)π(6 m)²h
h = 542.87 / [(1/3)π(6 m)²] = 6.05 m
Now, using the Pythagoras Theorem for the slant height we have:
s² = r² + h²
s² = (6 m)² + (6.05 m)²
s² = 72.9
s = √(72.9) = 8.53 m
The slant height of the cone is 8.53 meters.
Learn more about Pythagoras Theorem here:
https://brainly.com/question/21926466
#SPJ1
of the cartons produced by a company, 3% have a puncture, 6% have a smashed corner, and 1.4% have both a puncture and a smashed corner. find the probability that a randomly selected carton has a puncture or a smashed corner.
The probability that a randomly selected carton has a puncture or a smashed corner is 0.076, or 7.6%.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
To find the probability that a randomly selected carton has a puncture or a smashed corner, we can use the formula:
P(puncture or smashed corner) = P(puncture) + P(smashed corner) - P(puncture and smashed corner)
where P(puncture) is the probability of a carton having a puncture, P(smashed corner) is the probability of a carton having a smashed corner, and P(puncture and smashed corner) is the probability of a carton having both a puncture and a smashed corner.
Substituting the given probabilities into the formula, we get:
P(puncture or smashed corner) = 0.03 + 0.06 - 0.014
P(puncture or smashed corner) = 0.076
Therefore, the probability that a randomly selected carton has a puncture or a smashed corner is 0.076, or 7.6%.
To learn more about probability from the given link:
https://brainly.com/question/30034780
#SPJ1
PLEASE HELP DUE TODAY!!!!!!!
Consider the functions g(x) = 2x + 1 and h(x) = 2x + 2 for the domain 0 < x < 5
a. Without evaluating or graphing the functions, how do the ranges compare?
b. graph the 2 functions and describe each range over the given interval
Answer:
see the images and explanation
Step-by-step explanation:
for the graph:
the domain 0 < x < 5
the range for each functions:
g(x) = 2x + 1
g(x) = y , 1 < y < 11
h(x) = 2x + 2 , 2 < y < 12
2. Which sequence of transformations takes the graph of y = k(x) to the graph of
y=-k(x + 1)?
A. Translate 1 to the right, reflect over the x-axis, then scale vertically by a factor of 1/2
B. Translate 1 to the left, scale vertically by 1/2 , then reflect over the y-axis.
C. Translate left by 1/2, then translate up 1.
D. Scale vertically by 1/2, reflect over the x-axis, then translate up 1.
The correct answer is option B. Translate 1 to the left, scale vertically by 1/2, then reflect over the y-axis.
What does term "transformation of a graph" means?The process of modifying the shape, location, or features of a graph is often referred to as graph transformation. Graphs are visual representations of mathematical functions or data point connections, often represented on a coordinate plane.
Translations, reflections, rotations, dilations, and other changes to the look of a graph are examples of graph transformations.
For the given problem, Transformation to get the desired result can be carried out as:
Translate '1' to the left: The transformation "x + 1" in "-k(x + 1)" shifts the graph horizontally to the left by 1 unit.Scale vertically by '1/2' : The 1/2 factor in "-k(x + 1)" vertically scales the graph, compressing it vertically.Reflect over the y-axis: The minus sign before "k" in "-k(x + 1)" reflects the graph over the y-axis, flipping it horizontally.Hence, to convert the graph of "y = k(x)" to the graph of "y = -k(x + 1)," the correct sequence of transformations is to translate 1 unit to the left, scale vertically by 1/2, and then reflect across the y-axis, which is option B.
Learn more about Graph Transformation here:
https://brainly.com/question/10059147
#SPJ1
what is the 4th term/number of (a+b)^9, pascal’s triangle?
Step-by-step explanation:
hope this will help you Thanks
the profit p (in dollars) generated by selling x units of a certain commodity is given by the function p ( x ) = - 1500 + 12 x - 0.004 x ^ 2 What is the maximum profit, and how many units must be sold to generate it?
The profit (p) is $7500 generated by selling 1500 units of a certain commodity is given by the function p ( x ) = - 1500 + 12 x - 0.004 x²
To maximize our profit, we must locate the vertex of the parabola represented by this function. The x-value of the vertex indicates the number of units that must be sold to maximize profit.
We may use the formula for the x-coordinate of a parabola's vertex:
x = -b/2a
where a and b represent the coefficients of the quadratic function ax² + bx + c. In this situation, a = -0.004 and b = 12, resulting in:
x = -12 / 2(-0.004) = 1500
This indicates that when 1,500 units are sold, the profit is maximized.
To calculate the greatest profit, enter x = 1500 into the profit function:
P(1500) = -1500 + 12(1500) - 0.004(1500)^2
P(1500) = -1500 + 18000 - 9000
P(1500) = $7500
Therefore, the maximum possible profit is $7,500 and it is generated when 1,500 units are sold.
Learn more about Profit maximization:
https://brainly.com/question/30436087
#SPJ4
To achieve this maximum profit, exactly 1500 units must be sold.
To find the maximum profit and the number of units needed to generate it, we can use the given profit function p(x) = -1500 + 12x - 0.004x^2. We need to find the vertex of the parabola represented by this quadratic function, as the vertex will give us the maximum profit and the corresponding number of units.
Step 1: Identify the coefficients a, b, and c in the quadratic function.
In p(x) = -1500 + 12x - 0.004x^2, the coefficients are:
a = -0.004
b = 12
c = -1500
Step 2: Find the x-coordinate of the vertex using the formula x = -b / (2a).
x = -12 / (2 * -0.004) = -12 / -0.008 = 1500
Step 3: Find the maximum profit by substituting the x-coordinate into the profit function p(x).
p(1500) = -1500 + 12 * 1500 - 0.004 * 1500^2
p(1500) = -1500 + 18000 - 0.004 * 2250000
p(1500) = -1500 + 18000 - 9000
p(1500) = 7500
So, the maximum profit is $7,500, and 1,500 units must be sold to generate it.
To learn more about parabola: brainly.com/question/8227487
#SPJ11
A tile is selected from seven tiles, each labeled with a different letter from the first seven letters of the alphabet. The letter selected will be recorded as the outcome. Consider the following events. Event X: The letter selected comes before "D". Event Y: The letter selected is found in the word "CAGE". Give the outcomes for each of the following events. If there is more than one element in the set, separate them with commas.
(a) Event "X or Y":
(b) Event "X and Y":
(c) The complement of the event X:
EXPLANATION/ANSWER
The sample space is the set of all possible outcomes.
In this case, the sample space is , A, B, C, D, E, F, G.
The event X is "The letter selected is found in the word "BEAD". "
The outcomes in this event are A, B, D, and E.
The event Y is "The letter selected comes after "D". "
The outcomes in this event are E, F, and G.
(a) Event "X or Y"
Outcomes in the event "
X or Y" are any outcomes from event X along with any outcomes from event Y.
So the outcomes in the event "X or Y " are A, B, D, E, F, and G. Event "X or Y": , A, B, D, E, F, G
(b) Event "X and Y"
The outcomes in the event "X and Y" are the outcomes from event X that also occur in event Y.
So the outcome in the event "X and Y" is E. Event "X and Y": E
(c) The complement of the event X
The complement of the event X is the event consisting of all possible outcomes not in the event X.
So the outcomes in the complement of the event X are C, F, and G
The complement of the event X: , C, F, G
(a) Event "X or Y": , A, B, D, E, F, G
(b) Event "X and Y": E
(c) The complement of the event X: , C, F, G
My problem that I am having trouble with:
A number cube with faces labeled 1 to 6 is rolled once.
The number rolled will be recorded as the outcome.
Consider the following events.
Event A: The number rolled is odd.
Event B: The number rolled is less than 4
Give the outcomes for each of the following events.
If there is more than one element in the set, separate them with commas.
(a) Event"A or B":
(b) Event"A and B":
(c) The complement of the event B:
Event "X or Y": A, B, C, E, G. Event "X and Y": C. The complement of event X: D, E, F, G.
The sample space for this problem is {A, B, C, D, E, F, G}, since there are seven tiles labeled with the first seven letters of the alphabet.
Event X: The letter selected comes before "D". Outcomes in this event are A, B, and C.
Event Y: The letter selected is found in the word "CAGE". Outcomes in this event are A, C, E, and G.
Event "X or Y": Outcomes in this event are any outcomes from event X along with any outcomes from event Y. So the outcomes in the event "X or Y" are A, B, C, E, and G.
Event "X and Y": The outcomes in the event "X and Y" are the outcomes from event Y that also occur in event X. So the only outcome in the event "X and Y" is C.
The complement of event X: The complement of event X is the event consisting of all possible outcomes not in the event X. So the outcomes in the complement of event X are D, E, F, and G.
To know more about complement of event:
https://brainly.com/question/30212841
#SPJ4
--The given question is incomplete, the complete question is given
" A tile is selected from seven tiles, each labeled with a different letter from the first seven letters of the alphabet. The letter selected will be recorded as the outcome. Consider the following events. Event X: The letter selected comes before "D". Event Y: The letter selected is found in the word "CAGE". Give the outcomes for each of the following events. If there is more than one element in the set, separate them with commas.
(a) Event "X or Y":
(b) Event "X and Y":
(c) The complement of the event X: "--
how many intervals (or 'bins' or 'classes') should be chosen when creating a histogram? question 1 options: most often, about 8-10. eleven. it can vary - it really depends on the distribution of the variable. a minimum of 5.
"It can vary - it really depends on the distribution of the variable."
The number of intervals, or bins, to choose when creating a histogram can vary depending on the distribution of the variable.
Most often, about 8-10 intervals are used, but there is no set rule. It is generally recommended to have at least 5 intervals, but if the data is highly skewed or has outliers, more intervals may be needed to accurately represent the distribution.
Ultimately, the goal is to choose a number of intervals that provides a clear visual representation of the data without oversimplifying or overcomplicating the histogram.
The number of intervals or bins to be chosen when creating a histogram can vary and it really depends on the distribution of the variable.
While most often, about 8-10 bins are used, there is no hard and fast rule for the number of bins to be used in a histogram.
In general, the number of bins should be large enough to display the shape of the distribution clearly, but not so large that it obscures important features of the distribution or leads to overfitting.
A minimum of 5 bins is recommended to display the basic shape of the distribution, but more bins may be necessary for complex or multi-modal distributions.
Depending on the distribution of the variable, a histogram's number of intervals or bins can be altered.
There is no established guideline, however 8–10 intervals are typically utilized.
A minimum of five intervals are often advised, however if the data is extremely skewed or contains outliers, more intervals could be required to correctly depict the distribution.
For similar questions on variable.
https://brainly.com/question/27894163
#SPJ11