The dot product of two free vectors is independent of the choice of frames, as it relies only on the inner product of their transposed coordinate vectors.
The dot product of two free vectors, v1 and v2, can be expressed as the inner product of their transposed coordinate vectors, v1t and v2. This inner product is invariant under changes of frames, i.e. the same result will be obtained regardless of the choice of frames in which the coordinates are defined. This is because the transpose of a vector only changes the order of the coordinates, and the inner product of two vectors is unaffected by this reordering. Therefore, the dot product of two free vectors does not depend on the choice of frames in which their coordinates are defined.
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a survey of the larger than life corporation finds that 46 managers have a masters degree. also 60 managers have a b.s. degree and 20 have botha masters and bs degree. they found 10 have neither. how many managers are in this survey?
The number of managers are in this survey = 96
Let us assume that A represents the set of managers with BS degree and B represents the set of managers with masters degree.
46 managers have a masters degree.
⇒ n(A) = 46
60 managers have a B.S. degree
⇒ n(B) = 60
20 have both a masters and bs degree.
⇒ n(A ∩ B) = 20
10 managers have neither degree
⇒ n(A ∪ B)c = 10
We know that the set formula,
n(P U Q) = n(P) + (n(Q) – n (P ⋂ Q)
So, n(A ∪ B) = n(A) + n(B) – n (A ⋂ B)
n(A ∪ B) = 46 + 60 - 20
n(A ∪ B) = 86
Let n(S) be the be the total managers are in this survey.
n(S) = n(A ∪ B) + n(A ∪ B)c
n(S) = 86 + 10
n(S) = 96
Therefore, there are 96 managers in this survey.
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The figure shows two triangles on the coordinate grid:
What set of transformations is performed on triangle ABC to form triangle A′B′C′? (5 points)
A translation 5 units up, followed by a 270-degree counterclockwise rotation about the origin
A 270-degree counterclockwise rotation about the origin, followed by a translation 5 units up
A 180-degree counterclockwise rotation about the origin, followed by a translation 5 units to the right
A translation 5 units to the right, followed by a 180-degree counterclockwise rotation about the origin
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A translation is 5 units to the right, followed by a 180-degree counterclockwise rotation about the origin. Then the correct option is D.
What is a transformation of a shape?A point, line, or mathematical figure can be converted in one of four ways, and each has an effect on the object's structure and/or position.
Rotation does not change the shape and size of the geometry. But changes the orientation of the geometry.
The translation does not change the shape and size of the geometry. But changes the location.
A translation is 5 units to the right, followed by a 180-degree counterclockwise rotation about the origin. Then the correct option is D.
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Mrs. Thakur invested Rs 8000 at an interest rate of 8% per annum. Find the total amount that he will get after 2 years, if the interest is compounded annually.
Mrs. Thakur will receive Rs 9331.2 after 2 years, with an interest rate of 8% compounded annually.
How to determine the amount after tow yearsTo find the total amount Mrs. Thakur will receive after 2 years,
We need to calculate the compound interest.
The formula for compound interest is: A = P * (1 + r/100)^n
Where A is the final amount, P is the principal (Rs 8000),
r is the interest rate (8%), and n is the number of years (2).
So,
A = 8000 * (1 + 8/100)^2
A = 8000 * (1.08)^2
A = 8000 * 1.1664
A = 9331.2
Therefore, Mrs. Thakur will receive Rs 9331.2 after 2 years
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if lim x→1 f(x) − 7 x − 1 = 10 , evaluate lim x→1 f(x).
The value of the given limit (at x =1) f(x)=18.
An output value that a function approaches for the specified input values is referred to as a limit. Calculus and mathematical analysis depend on limits, which are also used to determine integrals, derivatives, and continuity. It is employed in the analysis process and constantly considers how the function will behave at a specific point.
A function may approach two different limits. One where the variable approaches its limit through values larger than the limit and the other where the variable approaches its limit through values smaller than the limit. In such a case, the limit is not defined but the right and left-hand limits exist.
we have given that,
[tex]lim_(x- > 1) f(x)-7x-1=10[/tex]
and find out the limit (x=1)f(x).
[tex]\lim_{x \to \1} f(x)-7x-1=10\\\\f(1)-7-1=10\\\\f(1)=10+8=18\\\\now \ the \ \lim_{x \to 1} f(x)\\f(1)=18.[/tex]
Hence, the value of limit x tends to 1 f(x)= 18.
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On making an horizontal slice through the solid, the
following two-dimensional shape is produced. Select the
solid that will yield this shape.
Answer:
Step-by-step explanation:
C
Seven times the product of three and a number, x
Answer:
7×(3+x)=21+7x or 7x+21
Step-by-step explanation: Simply multiply 7 by 3 and then 7 by x.
b) If 2 tan^2thita. cos^2thita =1 find value of thita
Answer:
The value of θ can be found by solving the equation 2tan2θcos2θ = 1. Using the identities tan2θ = (1 - cos2θ)/(1 + cos2θ) and cos2θ = (1 - tan2θ)/(1 + tan2θ), we get 1 = 2/(1 + cos2θ). Solving for cos2θ gives cos2θ = -1, which implies that tan2θ = 1. Thus, the value of θ is 45°.
A triangle has sides with lengths of 48 inches, 64 inches, and 80 inches. Is it a right triangle?
Right Scalene Triangle.
Sides of the Triangle are,
a = 48 inches
b = 64 inches
c = 80 inches
Area of Triangle = (1/2 × base × height)
= (1/2 × 64 × 80)
= 2560
A triangle is a closed figure made of three lines and three angles, where the sum of all the angles is equal to 180 degree.
In a right scalene triangle all three sides are different in length and one angle is equal to 90 degree. Right scalene triangle contains both the properties of a right triangle and scalene triangle.
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A shop has a sale of 1/5
off all items in stock.
If the original price of a dress is £45, what would be its sale price?
Answer:
36
Step-by-step explanation:
4/5(45) = 36.00
if you are taking 1/5 off, you are leaving 4/5 on.
the top and bottom margins of a poster are 8 cm and the side margins are each 10 cm. if the area of printed material on the poster is fixed at 762 square centimeters, find the dimensions of the poster with the smallest area.
The total area of the poster would actually be 792 square cm, which includes the area of the margins (36 square cm) and the area of the printed material (756 square cm)
To find the smallest area of the poster, we need to determine the size of the poster such that the printed material takes up the maximum amount of space, while still satisfying the margin constraints. Here's the detailed explanation and calculation:
The area of the top and bottom margins is 8 cm × poster width = 8 cm × w.
The area of the side margins is 10 cm × poster height = 10 cm × h.
Total area of the margins = 2 × (8 cm × w) + 2 × (10 cm × h) = 36 cm.
Available space for the printed material = 762 cm - 36 cm = 726 cm.
The optimal dimensions of the printed material would be the closest pair of factors of 726 that add up to 36, which are 18 and 42 cm.
The area of the printed material would be 18 cm × 42 cm = 756 cm.
The total area of the poster = 756 cm + 36 cm = 792 cm.
Therefore, the dimensions of the poster with the smallest area are 756 cm and the total area of the poster is 792 square cm.
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coin $a$ is tossed three times and coin $b$ is tossed two times. what is the probability that more heads are tossed using coin $a$ than using coin $b$? express your answer as a common fraction.
The probability that more heads are tossed using coin A than using coin B is [tex]$\frac{7}{8}$[/tex].
This is because there are 8 possible outcomes when both coins are tossed: (H, H), (H, T), (T, H), (T, T) for both coins A and B.
Out of these 8 possible outcomes, 7 of them have more heads from coin A than from coin B, so the probability is [tex]\frac{7}{8}[/tex].
Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 means that the event is impossible and 1 means that the event is certain to happen. Probability is used to measure the likelihood of uncertain events, such as the outcome of a coin flip or the result of a dice roll.
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Can anyone answer this question?
The required given expression are categorized on perfect cube and square.
What is perfect cube?A number is said to be a perfect cube if it can be multiplied by itself three times. X must equal Y3 if it is a perfect cube of Y. As a result, a natural integer, not a fraction, is obtained when we take the cube root of a perfect cube. Therefore, 3x Equals y. For instance, the number 8 is a perfect cube as 38 = 2.
According to question:1) x³ + 125
= x³ + (5)³
It is perfect cube.
2) 8p³ - 27
= (2p)³ - (3)³
It is difference of perfect cube.
3) 12x³ - 9
We can not make perfect cube of this expression.
4) a² - 100
= a² - 10²
It is a difference of Perfect square.
5) 4m² + 25
= (2m)² + 5²
it is a sum of Perfect square.
6) 16x² - 9
= (4x)² - 3²
It is difference of perfect square.
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simplify the expression
(1-x+4x^2-8x^2)+(2x^3+x^2-6x-3)-(5x^3+8x^2)
Answer: -7x^2 - 6x - 2
Step-by-step explanation:
This expression is equivalent to the sum of three terms:
1 - x + 4x^2, 2x^3 + x^2 - 6x - 3, and -5x^3 - 8x^2.
By combining like terms, the expression can be simplified to -7x^2 - 6x - 2.
If uare pro solve this for 40 points
Show that the line joining the points (0, 2) and (-5,-4) divides the line segment joining the point (6, 3) and (-2, 1) in the ratio 2:1.
The line joining the points (0, 2) and (-5,-4) divides the line segment joining the point (6, 3) and (-2, 1) in the ratio 2:1.
How can we show the intersection?Let the point of intersection of the two lines be (x, y). Using point-slope form, the equation of the line joining the points (0, 2) and (-5,-4) is y-2 = -3/5(x-0), and the equation of the line segment joining the points (6, 3) and (-2, 1) is y-3 = -2/8(x-6).
Solving for x and y, we get x = 8/5 and y = 4/5.
So, the distance from (x, y) to (0, 2) is 2/5 and the distance from (x, y) to (6, 3) is 6/5.
Hence, the ratio of the distances is 2/5 : 6/5 = 2 : 1.
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Describe the translation needed to obtain the graph
Answer:
Shift down 4 units
Step-by-step explanation:
As you can see in the photo, the blue graph, 9^x -4, is 4 units down from the red graph, 9^x.
Curved surface area of a cone is 308 cm2 and its slant height is 14 cm. Find the volume.
The volume of the cone is 615.44 cm³.
What is a cone?It is a shape of a Christmas tree where there is a base of radius r and a top point called the apex.
The volume of a cone is (1/3)πr²h.
We have,
Slant height l = 14 cm.
Curved surface area of a cone = 308 cm².
This means,
πrl = 308
πr x 14 = 308
πr = 308/14
r = 308/(14π)
r = 7 cm
Now,
Volume = (1/3)πr²h.
l² = r² + h²
l² - r² = h²
h = √(l² - r²)
h = √(196 - 49)
h = √(147)
h = 12 cm
Now,
Volume.
= (1/3)πr²h
= (1/3) x π x r² x h
= (1/3) x 3.14 x 49 x 12
= 615.44 cm³
Thus,
615.44 cm³ is the volume of the cone.
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F(x)=1/x+2
Find x and y intercept and the vertical and horizontal asymptotes
For the given asymptotes, y - intercept = not defined and horizontal asymptote at y = 2.
What Are the Asymptote-Finding Rules?[tex]F(x)=1/x+2[/tex] by x and simplify
[tex]F= \frac{1+2x}{x}[/tex]
Apply the limit x or x – to locate the horizontal asymptotes.
Apply the limit y or y – to determine the vertical asymptotes.
Divide the numerator by the denominator to determine the slant asymptote (if any).
Each point on a vertical line has the same x-coordinate. The line equation is x=c if two points share the same x-coordinate. The x-intercept of a vertical line x=c is the point (c,0). Except for the line x=0, vertical lines don't have a y -intercept.
By evaluating the function when the input variable, x, is 0, which is always equal to the constant b, the vertical intercept (y-intercept) can be found. There is a chance.
[tex]F= \frac{1+2x}{x}[/tex]
We can find y - intercept by setting x = 0,
⇒ y - intercept = not defined
horizontal asymptote at y = 2
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A family wants to rent a car to go on vacation. Company A charges $75.50 and 14 cents per mile. Company B charges $45.50 and 8 cents per miles. How much more does Company B charge for x miles than Company A?
Answer:
Company A
Step-by-step explanation:
Company A charges $75.50 + $0.14x per mile.
Company B charges $45.50 + $0.08x per mile.
The difference in charges is:
($75.50 + $0.14x) - ($45.50 + $0.08x) = $30 + $0.06x.
Therefore, for x miles, Company B charges $30 + $0.06x more than Company A.
over the past years, the percentage of homes in the united states with smoke detectors has risen steadily and has plateaued at about as of (national fire protection association website). with this increase in the use of home smoke detectors, what has happened to the death rate from home fires? the file smokedetectors contains years of data on the estimated percentage of homes with smoke detectors and the estimated home fire deaths per million of population. click on the datafile logo to reference the data. a. do you expect a positive or negative relationship between smoke detector use and deaths from house fires? why? we would expect there would be a - select your answer - relationship between smoke detector use and deaths from home fires. that is, as more households have smoke detectors, warning of a fire would help the inhabitants of the home escape and lead to - select your answer - deaths from home fires. b. compute the correlation coefficient (to decimals). if required enter negative value as negative number. is there a positive or negative correlation between smoke detector use and deaths from home fires? comment. there is a - select your answer - correlation between smoke detector use and deaths from home fires. c. select the appropriate scatter plot of the death rate per million of population and the percentage of homes with smoke detectors. 1.
A negative correlation will be expected between smoke detector use and deaths from home fires.
A positive correlation happens when variables that are related(not zero correlation)increase together. In other words, variable an (independent variable) increases and makes variable b(dependent variable) increase too.
There will be a negative correlation if the opposite happens; that is, when related variables go in opposite directions, then one of them will increase while the other decreases.
We observe from what we are told that a negative correlation occurs here since the death rate from fires has likely(assumed) decreased as smoke detectors have increased.
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--The given question is incorrect; the correct question is
"Over the past 40 years, the percentage of homes in the United States with smoke detectors has risen steadily and has plateaued at about 95% (National Fire Protection Association website, January 2015). With this increase in the use of home smoke detectors, what has happened to the death rate from home fires? The DATAfile SmokeDetectors contains 17 years of data on the estimated percentage of homes with smoke detectors and the estimated home fire deaths per million of the population.
Do you expect a positive or negative relationship between smoke detector use and deaths from home fires? Why or why not?"--
(a) how many three-digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, and 6 if each digit can be used only once? (note: 062 is not a legit three-digit number)
There are 720 possible three-digit numbers that can be formed from the digits 0, 1, 2, 3, 4, 5, and 6 if each digit can be used only once. Thus, 6 x 5 x 4 = 120, and 120 x 6 = 720.
There are 720 possible three-digit numbers that can be formed from the digits 0, 1, 2, 3, 4, 5, and 6 if each digit can be used only once. This is because you can have 6 different choices for the first digit, 5 choices for the second digit, and 4 choices for the third digit. This means that for each of the 6 choices for the first digit, you can have 5 choices for the second digit, and for each of those 5 choices, you can have 4 choices for the third digit. This results in 6 x 5 x 4 = 120 possible combinations for each of the 6 choices for the first digit. Since there are 6 choices for the first digit, 120 x 6 = 720 possible three-digit numbers in total.
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what is the eigenvalue for the eigenfunction cosθ of the operator 1sinθddθ(sinθddθ) ?
The eigenvalue for the eigenfunction cosθ of the operator 1sinθddθ(sinθddθ) is -1.
The eigenvalue for the eigenfunction cosθ of the operator 1sinθddθ(sinθddθ) can be calculated by using the formula:
λ = 1/sinθ (d/dθ cosθ)
This formula states that the eigenvalue is equal to the inverse of the sine of θ multiplied by the derivative of the eigenfunction cosθ with respect to θ.
To calculate the eigenvalue, we first take the derivative of the eigenfunction cosθ with respect to θ, which is -sinθ. Then, we multiply this value by the inverse of the sine of θ. This gives us an eigenvalue of -1.
In summary, the eigenvalue for the eigenfunction cosθ of the operator 1sinθddθ(sinθddθ) is -1. This can be calculated by taking the derivative of the eigenfunction and multiplying it by the inverse of the sine of θ.
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Which expression can be used to find the total amount in an account after three years, if the initial deposit is $2,000, and the annual simple interest rate is 2%?
A. 2,000 x 0.02 x 3
B. 2,000 x (2,000 x 0.02 x 3)
C. 2,000 x (2,000 x 2 x 3)
D. 2,000(1 x 0.02)^3
Answer:
Below
Step-by-step explanation:
Actually....NONE of those answers would show the total amount after 3 years
the correct option would be 2000 + (2000*.02 *3) a PLUS sign rather than a multiplication sign ....so the answer MIGHT be B if you transcribed it incorrectly
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Which of the following is an arithmetic sequence with a common difference of +3?
Select the slope-intercept form of the equation of the line.
5x - 4y = -20
x+5
y=
y =
y =
x + 5
y=x+5
y = -x +5
Answer:
5x - 4y = -20
y = x + 5
y = -x + 5
Step-by-step explanation:
The formula for slope-intercept form is y = mx + b, with b being the y-int.
If the equation does not have an x, y, or b, it is not a slope-intercept form.
5x - 4y = -20 (can be rearranged to y = 5/4x + 5)
y = 1, x = 5/4, b = 5
y = x + 5y
x = 1, y = 1, b = 5
y = -x + 5
x = -1, y = 1, b = 5.
Other answer choices does not have all three variables.
sam takes out a loan of R 1 2000 for a year .if the rate is 12% per annum ,how much interest will he pay
Answer:
R 1440
Step-by-step explanation:
Given:-
Principal Amount = R 12000
Time = 1 year
Rate = 12% pa
The Interest can be calculated using the following formula:-
Interest = (Principal Amount * Rate * Time) / 100
Substituting the respective values:-
Interest = (12000 * 12 * 1) / 100
Interest = 144000 / 100
Interest = R 1440
So, Sam will pay an interest of R 1440
2x+5x 2nd power +7x+10+6+4+-2x
x=-.7+1.8734994i and x=-.7-1.8734994i
Step-by-step explanation:
2x+5x² +7x+10+6+4+-2x=(5x²)+(2x+7x-2x)+(10+6+4)=5x²+7x+20
quadratic equation
x=(-b±√(b²-4ac))/2a
where a=5, b=7, c=20
x=(-7±√(7²-4(5)(20)))/(2(5))
x=(-7±√((49-400))/10
x=(-7±√(-351))/10
x=(-7±18.734994i)/10
x=-.7+1.8734994i and x=-.7-1.8734994i
a statistics professor asked students in a class their ages. based on this information, the professor states that the average age of all the students in the university is 24 years. this is an example of a. an experiment. b. an observational study. c. statistical inference. d. descriptive statistics.\
The correct option is statistical inference (b).
The professor uses sample data from the population to determine the average age. Anytime inferential statistics or statistical inference is used to make inferences from samples.
Instead of gathering data from the entire institution, the professor took age samples from a class and used those data to draw conclusions about the entire university.
Descriptive statistics in statistics help you describe the facts, whereas inferential statistics assist you in drawing conclusions from the data.
Data from the sample are used in inferential statistics, which allows you to generalise about the population.
Inference generally refers to "guessing," which involves drawing conclusions about something.
So, drawing conclusions about the population is what is meant by statistical inference. It makes use of a number of statistical analytic tools to draw a conclusion about the population.
Therefore, the correct option is statistical inference.
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What type of angle is x?
Answer:
reflex angle since it's greater than 180 degrees
Step-by-step explanation:
There are right angles (exactly 90 degrees), acute angles (less than 90 degrees), obtuse angles (more than 90 degrees), and reflex angles (more than 180 degrees).
If we know that there is 360 total degrees, we can figure out what number degree is x by using this equation:
360 - 50 = 310
Therefore, because 310 is more than 180 degrees, it is considered a reflex angle.
Write five linear equations based on the directed graph below.
Given x5 = 15, determine the values of x1, x2, x3 and x4.
The solution is,
x1 = 5
x2 = -1
x3 = 3
x4 = 2
x5 = 1
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
x1 + x2 − 2x3 + 3x4 + 2x5 = 6
3x1 + 3x2 − x3 + x4 + x5 = 12
2x1 + 2x2 − x3 + x4 − 2x5 = 5
4x1 + 4x2 + x3 +0x4 − 3x5 = 16
8x1 + 5x2 − 2x3 − x4 + 2x5 = 29;
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Jaime Reparte su fortuna de la siguiente manera a Rosa le da el 28% de la fortuna,a Maria el 32% y a Fidel los 160 soles restantes ¿ de cuanto fue la Fortuna?
Jaime's total fortune was 4. Rosa received 28% of the fortune which is 4 x 28% = 1.12, Maria received 32% of the fortune which is 4 x 32% = 1.28 and Fidel received the remaining 160 soles.
The fortune of Jaime can be calculated with the following formula:
F = 28% x F + 32% x F + 160
Where F is the total fortune.
Therefore, to find the total fortune we need to solve the equation and we do this by multiplying both sides of the equation by F:
F = 28% x F + 32% x F + 160
F x 100% = 28% x F x 100% + 32% x F x 100% + 160
F x 100% = 28F + 32F + 160
100F = 28F + 32F + 160
100F - 60F = 160
40F = 160
F = 160 ÷ 40
F = 4
Therefore, Jaime's total fortune was 4. Rosa received 28% of the fortune which is 4 x 28% = 1.12, Maria received 32% of the fortune which is 4 x 32% = 1.28 and Fidel received the remaining 160 soles.
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