Let A=[1 2 5 4] B=[-1 1 1 10]. Find A^2 B^2. Hint A^2 = A•A
The combination of [tex]A_2[/tex] and [tex]B_2[/tex] results in [tex]A_2[/tex] [tex]B_2[/tex] , where [tex]A_2[/tex] is the product of [tex]A_2[/tex] and [tex]B_2[/tex] , and [tex]B_2[/tex] is the product of [tex]B_2[/tex] and [tex]A_2[/tex] . The dot product of both vectors A and B yields a result of 4738 for the product of [tex]A_2[/tex] and [tex]B_2[/tex] .
What is vector?A vector is a mathematical construct with a length and a direction. It is frequently used to symbolise tangible properties like force, velocity, and acceleration. There are numerous techniques to multiply, add, and manipulate vectors. The characteristics and interactions of vectors in higher dimensions are described using vector calculus.
[tex]A_2B_2=A_2.B_2\\\\A_2=A.A\\\\A.A=[1.1+2.2+5.5+4.4][/tex]
=1+4+25+16
=46
[tex]B_2=B.B\\\\B_2=B.B\\\\B.B=[-1.-1+1.1+1.1+10.10][/tex]
=1+1+1+100
=103
[tex]A_2B_2=46.103\\\\A_2B_2=4738[/tex]
Therefore, [tex]A_2B_2=4738[/tex]
The combination of [tex]A_2[/tex] and [tex]B_2[/tex] results in [tex]A_2[/tex] [tex]B_2[/tex] , where [tex]A_2[/tex] is the product of [tex]A_2[/tex] and [tex]B_2[/tex] , and [tex]B_2[/tex] is the product of [tex]B_2[/tex] and [tex]A_2[/tex] . The dot product of both vectors A and B yields a result of 4738 for the product of [tex]A_2[/tex] and [tex]B_2[/tex] .
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i need help pleaseee!!!
The equation of the function g(x) is g(x) = f(x+3) + 4 and g(x) = log₂(x+3) + 4
State g(x) in terms of f(x)To shift the function 3 units left, we replace x with x+3. To shift it 4 units up, we add 4 to the function.
Therefore, the expression for g(x) in terms of f(x) is:
g(x) = f(x+3) + 4
Determine equation of the function g(x)Substituting f(x) = log₂(x), we get:
g(x) = log₂(x+3) + 4
The equation of the function g(x) is g(x) = log₂(x+3) + 4.
State the domain, range, asymptotes of g(x)The domain of g(x) is all x such that x+3 > 0, since the argument of the logarithm must be positive. This gives x > -3.
The range of g(x) is all real numbers, since the logarithm takes on all real values.
The vertical asymptote is x = -3, since this is where the function becomes undefined (the argument of the logarithm becomes 0).
The horizontal asymptote is y = 4, since as x approaches infinity or negative infinity, the function approaches 4.
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A rare form of malignant tumor occurs in 11 children in a million, so its probability is 0.000011. Four cases of this
tumor occurred in a certain town, which had 17,199 children.
a. Assuming that this tumor occurs as usual, find the mean number of cases in groups of
17,199 children.
b. Using the unrounded mean from part (a), find the probability that the number of tumor cases in a group of
17.199 children is 0 or 1.
c. What is the probability of more than one case?
d. Does the cluster of four cases appear to be attributable to random chance? Why or why not?
a) The mean number of cases in groups of 17,199 children is 0.187.
b) The probability of 0 or 1 case in a group of 17,199 children is 0.832.
c) The probability of more than one case in a group of 17,199 children is 0.168.
d) The expected number of cases is 3.214 and the actual number of cases is 4
What is the probability?Probability is a measure of the likelihood or chance 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.
For example, if you flip a fair coin, the probability of it landing heads up is 0.5, because there are two equally likely outcomes (heads and tails), and one of them is heads. Similarly, if you roll a fair six-sided die, the probability of rolling a 3 is 1/6, because there are six equally likely outcomes (rolling a 1, 2, 3, 4, 5, or 6), and only one of them is a 3.
According to the given informationa. Assuming that the tumor occurs as usual, the mean number of cases in groups of 17,199 children can be calculated as:
mean = (probability of a single case) x (number of children) = 0.000011 x 17,199 = 0.187
So the mean number of cases in groups of 17,199 children is 0.187.
b. The probability of 0 or 1 case can be found using the Poisson distribution, which models the probability of a certain number of events occurring in a fixed interval of time or space, given the mean rate of occurrence. In this case, the Poisson distribution can be used to find the probability of 0 or 1 case in a group of 17,199 children, given the mean of 0.187.
The probability of 0 or 1 case can be calculated as follows:
P(0 or 1 case) = P(0 case) + P(1 case)
= (e⁽⁻⁰°¹⁸⁷⁾ * 0.187⁰) / 0! + (e⁽⁻⁰°¹⁸⁷⁾ * 0.187¹) / 1!
= 0.832
Therefore, the probability of 0 or 1 case in a group of 17,199 children is 0.832.
c. The probability of more than one case can be found as:
P(more than one case) = 1 - P(0 or 1 case)
= 1 - 0.832
= 0.168
Therefore, the probability of more than one case in a group of 17,199 children is 0.168.
d. To determine whether the cluster of four cases is attributable to random chance, we can compare the actual number of cases with the expected number of cases based on the mean rate of occurrence.
The expected number of cases in a group of 17,199 children can be found by multiplying the mean rate of occurrence (0.187) by the number of groups:
expected number of cases = 0.187 x 17199 = 3.214
Since the expected number of cases is 3.214 and the actual number of cases is 4.
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Help plsssssssssssssssssssssssssssss
Answer:
180 square inches
5 x 6 = 32.5
32.5 x 4 = 130
5 x 5 = 25
25 x 2 = 50
130 + 50 = 180
Step-by-step explanation:
first find the area of all the sides (length times width)
width = 5
length = 6.5
5 x 6.5 = 32.5
32.5 is the area for one side. there are 4 others identical to it
32.5 (one side) x 4 (the amount of sides identical) = 130
then you need to find the area for the bottom/top side
5 = length
5= width
5(L) x 5(W) = 25
25 is the area for the bottom. the top is identical to it
25(bottom side) x 2 (the amount of sides identical)
now add all of the sides up
130 + 50 = 180
Simplify
Write your answer with positive exponents only.
The simplified exponential expression for this problem is given as follows:
xy^7/z^(14).
How to simplify the exponential expression?The first step in simplifying the exponential expression is applying the power of power rule at the numerator, as follows:
(y² x z^-5)² = y^4z^(-10).
(for the power of power rule, we keep the bases and add the exponents).
When two terms with the same base and different exponents are divided, we keep the base and subtract the exponents, hence the exponents are given as follows:
x: -1 - (-2) = -1 + 2 = 1.y = 4 - (-3) = 7.z = -10 - 4 = -14.The negative exponent means that the number appears in the denominator, hence the simplified expression is given as follows:
xy^7/z^(14).
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The simplified exponential expression for this problem is given as follows:
xy^7/z^(14).
How to simplify the exponential expression?The first step in simplifying the exponential expression is applying the power of power rule at the numerator, as follows:
(y² x z^-5)² = y^4z^(-10).
(for the power of power rule, we keep the bases and add the exponents).
When two terms with the same base and different exponents are divided, we keep the base and subtract the exponents, hence the exponents are given as follows:
x: -1 - (-2) = -1 + 2 = 1.y = 4 - (-3) = 7.z = -10 - 4 = -14.The negative exponent means that the number appears in the denominator, hence the simplified expression is given as follows:
xy^7/z^(14).
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If the probability that a randomly chosen college student takes statistics is 0.24, then what is the probability that a randomly chosen college student does not take statistics? Give your answer as a decimal.
Answer:
The probability that a randomly chosen college student does not take statistics is 0.76.
Step-by-step explanation:
The probability of an event happening and the probability of its complement (the event not happening) must add up to 1. Therefore, if the probability that a randomly chosen college student takes statistics is 0.24, then the probability that they do not take statistics is:
1 - 0.24 = 0.76
So the probability that a randomly chosen college student does not take statistics is 0.76 or 76%.
Convert 58,080 feet to miles.
Answer: 11 miles
Step-by-step explanation: 1/5280 = x/58,080
Write the equation of the line that passes through the points (0,6) and (-6,6). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
An equation of the line that passes through the points (0, 6) and (-6, 6) is y = 6.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
m represent the slope.x and y represent the points.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (6 - 6)/(-6 - 0)
Slope (m) = 0/-6
Slope (m) = 0.
At data point (0, 6) and a slope of 0, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 6 = 0(x - 0)
y - 6 = 0
y = 6
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Article lll of the constitution gives congress the power to create a system of federal courts , other than the Supreme Court known as
The framers of the Constitution believed that as the country grew, more courts would be needed to meet its needs.
Explanation :
The statement that best explains that Article III of the constitution gives congress the ability to create lower courts inferior to the supreme court from "time to time" is that the framers of the Constitution believed that as the country grew, more courts would be needed to meet its needs.
As there will be more framers of the constitution which gave them as a congress the power to create lower courts as they wanted that the congress should have authority over the courts and to control them.
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complete question:
Which statement best explains why Article lll of the constitution gives Congress the ability to create lower courts inferior to the Supreme Court “from time to time”?
help please I need someone to tutor me with this lol
Answer:
The domain is (-infinity, infinity), or all real numbers.
The range is (-infinity, infinity), or all real numbers.
NEED HELP WILL GIVE BRAINLIEST AND WILL RATE. Show work and I only need #2
Changing the base from 5/7 to 7, the end behavior of the function would be given as follows:
As x -> -∞, f(x) -> 0.As x -> ∞, f(x) -> ∞.How to obtain the end behavior of a function?The end behavior of a function is given by the limit of the function is the input x goes to either negative infinity or positive infinity.
The function for this problem is given as follows:
f(x) = 4(5/7)^x.
Changing the base to 7, it would have an absolute value greater than 1, hence the function would be increasing with the end behavior given as follows:
Approaches the horizontal asymptote y = 0 at the left of the graph -> As x -> -∞, f(x) -> 0.Increases as the input increases, that is, as x -> ∞, f(x) -> ∞.More can be learned about the end behavior of a function at brainly.com/question/1365136
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Help please!!!!
Whoever answers right will fat brainliest!
Answer:
0
Step-by-step explanation:
If we have the function f(x)=sqrt((x-8)/3), where 8 is less than or equal to x which is less than or equal to 16, we can evaluate f(8) as follows:
f(8)=sqrt((8-8)/3)
=sqrt(0/3)
=0
Hope this helps!
HELP PLSZZZZSZZZZZZZZZZ need asap
Answer: [tex]\frac{8}{15}[/tex]
Step-by-step explanation: In total, Patty placed 45 slips of paper in a bag(10+9+8+7+6+5). Out of those 45 slips of paper, only 24 had even numbers on them(10+8+6), resulting in the fraction [tex]\frac{24}{45}[/tex]. If you divide both 24 and 45 by 3, the fraction can be simplified to [tex]\frac{8}{15}[/tex].
In the diagram, m∠1=45° and m∠3=57.5°.
What is m∠4?
Enter your answer as a decimal in the box.
Check the picture below.
HELP PLSZZZZSZZZZZZZZZZ need asap
Answer:
60 (C)
Step-by-step explanation:
65+55=120
180-120=60
Which graph represents the inequality y is greater than or equal to (x+2)^2?
The graph of the inequality y ≥ (x+2)^2 is added as an attachment
How to determine the graph of the inequalityFrom the question, we have the following parameters that can be used in our computation:
y is greater than or equal to (x+2)^2
Express the statement properly
So, we have
y ≥ (x+2)^2
The above expression is a an inequality of a quadratic function
Next, we plot the graph using a graphing tool
To plot the graph, we enter the expression in a graphing tool and attach the display
See attachment for the graph
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Plot the numbers -1 1/4 and 5/2 on the number line below. This is due tonight, pls help ):
PLEASE HELP WILL GIVE BRAINLEST FOR CORRECT ANSWER ONLY !!
Answer:
Option A is the correct choice that shows a function.
Step-by-step explanation:
What is a function?
A function is when there are no repeating "x" values.
For example:
These set of points: {(1,1), (1,2), (1,3), (1,4)} does not show a function because there is repeating "x" values.
Option A shows that the points {(4,5), (5,5), (6,1), (8,2) is a function because there is no repeating "x" values.
Complete the similarity statement
Triangle MTA ~ triangle HTM ~ triangle ___
The similarity statement is completed as below
Triangle MTA ~ triangle HTM ~ triangle HMA
How to complete the similarity statementA similarity statement is a statement in mathematics that expresses the affinity between two or more figures.
These figures are similar, meaning they have corresponding angles that are identical and sides that are equivalent in size ratio. The same shape is shared by them, although their sizes may be different.
The similar triangles are
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work out the some of the interior angles of a pentagon
"Although part of your question is missing, you might be referring to this full question: Work out the sum of the interior angles of a pentagon".
A pentagon is a polygon with five sides. We can use a formula to get the pentagon's interior angle total. According to the formula, (n-2) x 180 degrees can be used to calculate the total of any polygon's internal angles. This formula can be changed to n=5 for a pentagon, giving us (5-2) x 180 degrees = 540 degrees. Consequently, a pentagon's internal angles add up to 540 degrees.
The sum of the interior angles of a pentagon can also be computed by dividing it by the number of sides, and the result can then be subtracted from 180 degrees to determine each inner angle. So, a pentagon's internal angles are each (540/5)-180 degrees, or 108 degrees.
In conclusion, a pentagon's interior angles add up to 540 degrees, and each interior angle is 108 degrees. In order to solve mathematical problems involving polygons, it can be helpful to comprehend the formulas used to calculate these numbers.
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Answer the following questions.
The questions have been answered below based on the concept of apportionment.
Here, we have,
Apportionment is the challenge of distributing a certain number of items among groups of varying sizes. The Mathematics of Apportionment discusses the mathematical concepts and methods used to allocate identical things fairly among parties with differing claims.
In question 1, the quantity that does not vary from state to state when we apportion congress representatives to different states is called the standard quota.
In question 2, the standard quota is found by dividing the state's population by the standard divisor.
In question 3, the modified divisor in Webster's method is found by dividing the state's population by the modified divisor.
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PLEASE HELP WILL GIVE BRAINLEST FOR CORRECT ANSWER ONLY !!
(Enlarge photo)
The length of the diagonal of the cube is x = 3√2 inches
Given data ,
Let the length of the diagonal of the cube be x
Now , the side length of the cube is = 3 inches
From the Pythagoras theorem , we get
x = √s² + s²
On simplifying , we get
x = √ ( 3² + 3² )
x = √18
On simplifying , we get
x = 3√2 inches
Hence , the diagonal is 3√2 inches
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A group of 8 friends went to lunch and spent a total of $76, which included the food bill and a tip of $16. They decided to split the bill and tip evenly among themselves. Which equations and solutions describe the situation? Select two options. The equation StartFraction 1 over 8 EndFraction (x + 16) = StartFraction 76 over 8 EndFraction represents the situation, where x is the food bill. The equation StartFraction 1 over 8 EndFraction (x + 16) = 76 represents the situation, where x is the food bill. The solution x = 60 represents the total food bill. The solution x = 60 represents each friend’s share of the food bill and tip. The equation 8 (x + 16) = 76 represents the situation, where x is the food bill.
An equation and solution that describe the situation is: B. The equation 1/8(x + 16) = 76 represents the situation, where x is the food bill.
How to write an equation to model this situation?In order to write a linear equation to describe this situation, we would a assign variable to the food bill, and then translate the word problem into a linear equation as follows:
Let the variable x represent the total amount of the food bill.
Since this group of 8 friends spent a total of $76, which included the food bill and a tip of $16, and decided to split the bill and tip evenly among themselves, a linear equation that can be used to model this situation is given by;
1/8(x + 16) = 76
(x + 16) = 76(8)
x + 16 = 608
x = 608 - 16
x = $592.
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A function g is defined below. (a) Write g as a set of ordered pairs. (b) Give the domain and range of g. g(-2) = - 5, g(0) = 0, g(2) = 2, g(4) = - 5 write g as a set of ordered pairs
Answer:
(a) To write g as a set of ordered pairs, we can use the given function values as follows:
g = {(-2, -5), (0, 0), (2, 2), (4, -5)}
(b) The domain of g is the set of all input values for which the function is defined. In this case, the domain is {-2, 0, 2, 4}.
The range of g is the set of all output values that the function can produce. In this case, the range is {-5, 0, 2}.
The indirect measurements, round your answer to the nearest meter. (The figure is not drawn to scale)
The similar triangle is solved and the width of the river is R = 33.88 m
Given data ,
Let the base of the larger triangle be = 59 m
Let the base of the smaller triangle be = 35 m
Now , height of smaller triangle = 20.1 m
And , width of the river = height of the larger triangle
From the similar triangles , we get
59 / 35 = R / 20.1
Multiply by 20.1 on both sides , we get
R = 33.88 m
Hence , the width of river is 33.88 m
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Solve the equation 120 + 1814
x = 180 − 134
x for x.
Answer:
Step-by-step explanation:
The equation given is:
120 + 1814x = 180 - 134x
We can simplify this equation by adding 134x to both sides:
120 + 1948x = 180
Next, we can subtract 120 from both sides:
1948x = 60
Finally, we can solve for x by dividing both sides by 1948:
x = 60/1948
Therefore, the solution is:
x = 0.0308 (rounded to four decimal places)
Answer:
To solve the equation, we need to first convert the mixed numbers to improper fractions:
120 + 18 1/4 x = 180 − 1 3/4 x
120 + 73/4 x = 180 - 7/4 x (converting mixed numbers to improper fractions)
Multiplying both sides by 4 to eliminate the fractions, we get:
480 + 73x = 720 - 7x
Combining like terms, we get:
80x = 240
Dividing both sides by 80, we get:
x = 3
Therefore, the solution for x is 3.
Si lanzas una moneda 16 veces, ¿cuál es la mejor predicción posible para el número de veces que caerá cruz?
Add using Scratch Addition. Do your work on paper and upload a screen shot.
45 + 58 + 29 + 59 + 67 + 37 + 55 + 79 + 87
The expressions using scratch addition is 516
Adding the expressions using Scratch AdditionFrom the question, we have the following parameters that can be used in our computation:
45 + 58 + 29 + 59 + 67 + 37 + 55 + 79 + 87
Using the Scratch method of Addition. we add the numbers one after the other
Using the above as a guide, we have the following:
45 + 58 + 29 + 59 + 67 + 37 + 55 + 79 + 87 = 103 + 29 + 59 + 67 + 37 + 55 + 79 + 87
45 + 58 + 29 + 59 + 67 + 37 + 55 + 79 + 87 = 132 + 59 + 67 + 37 + 55 + 79 + 87
45 + 58 + 29 + 59 + 67 + 37 + 55 + 79 + 87 = 191 + 67 + 37 + 55 + 79 + 87
45 + 58 + 29 + 59 + 67 + 37 + 55 + 79 + 87 = 258 + 37 + 55 + 79 + 87
45 + 58 + 29 + 59 + 67 + 37 + 55 + 79 + 87 = 295 + 55 + 79 + 87
45 + 58 + 29 + 59 + 67 + 37 + 55 + 79 + 87 = 350 + 79 + 87
45 + 58 + 29 + 59 + 67 + 37 + 55 + 79 + 87 = 429+ 87
45 + 58 + 29 + 59 + 67 + 37 + 55 + 79 + 87 = 516
HEnce, the solution is 516
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A website is selling barbecue grills for $94, but mentions that they originally cost $200. What
is the discount, as a percentage?
Write your answer using a percent sign (%).
A website is selling barbecue grills for $94, but mentions that they originally cost $200 the discount, as a percentage, is 53%.
The discount is the difference between the original price and the discounted price.
Discount = $200 - $94 = $106
To find the percentage discount, we need to calculate what percentage of the original price the discount represents:
Percentage discount = (Discount/Original price) x 100%
Percentage discount = ($106/$200) x 100%
Percentage discount = 53%
Therefore, the discount, as a percentage, is 53%.
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A sample of 81 items is taken from a population with a standard deviation of 45 kilograms. The sample mean is 112 kilograms. What weights are included in the 99.7% of confidence interval?
The confidence interval of the given data is (117, 107).
Given that:
Sample mean X = 112
Standard deviation σ = 45
Sample size n = 81
Confidence level = 99.7%
Z Score = (x − μ )/σ
Z score = 0.9944
Confidence interval = X±z (σ/√n)
= 112±0.9944(45/√81)
= 112±0.9944(5)
= 112±4.972
= 112+4.972 or 112-4.972
= 116.972 or 107.028
= (117, 107)
Therefore, the confidence interval of the given data is (117, 107).
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