How can the complete transformation be described to a person who cannot see the transformations to the right?
Select the correct choice below and fill in the answer box(es) to complete your choice.
OA. The complete transformation is T
B. The complete transformation is R, where k is the line with equation
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Answers
Answer:
T〈-7,0〉
Step-by-step explanation:
You want a description of the transformation of triangle ABC to triangle A"B"C".
Transformation∆A"B"C" has the same orientation as ∆ABC, so no reflection is involved (eliminates choice B).
Point A" is 7 units to the left of point A, so the translation is 7 units left (and no units up or down).
The transformation is ...
[tex]\boxed{T_{\langle-7,0\rangle}}[/tex]
Related Questions
Solve Z = 5x+2y-7/ 3w
for x.
Answers
Answer:
see the attachment photo!
a random number generator that draws digits at random with replacement from {0,1,2,3,4,5,6,7,8,9} is run three times. find the chance that the digits drawn can form the number 510, by rearrangement if necessary.
Answers
The required chance that the digits can form the number 510 is 6/1000, or approximately 0.006, or 0.6%.
What is permutation?The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation. Simply said, a permutation is a term that refers to the variety of possible arrangements or orders. The arrangement's order is important when using permutations.
According to question:The chance that the digits drawn can form the number 510 is given by the probability of drawing the digits 5, 1, and 0 in that order or in some rearrangement of the order.
There are 3! = 6 ways to arrange the digits 5, 1, and 0, and there are 10^3 = 1000 total possible outcomes when the random number generator is run three times.
So, the chance that the digits can form the number 510 is 6/1000, or approximately 0.006, or 0.6%.
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4.44 is what percent of $37
Answers
Answer:
12%
4.44 / 37
Step-by-step explanation:
Answer: 12%
Step-by-step explanation: 4.44 is 12% of 37.
To solve, use this example:
[tex]\frac{x}{100} = \frac{4.44}{37}[/tex]
First, divide the part percent by the whole percent. That'd be 4.44 / 37 which is 0.12. Now, we need to multiply 100 by 0.12 is 12. So, 4.44 is 12% of 37. I hope this helped!
An art teacher pours of 2/3 gallon of paint into a jug and the jug is 1/4 of the way full. If the art teacher pours an additional 1 gallon of paint into this jug, what fraction of the jug will be filled?
Answers
The fraction of the jug filled is given by the equation A = 5/8 of the jug
What is a Fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
Given data ,
Let the fraction of the jug filled be represented as A
Now , the equation will be
The amount of paint poured initially = ( 2/3 ) gallons
The amount of jug filled initially = ( 1/4 ) of the jug
Now ,
The amount of jug filled for 1 gallon = ( 1/4 ) / ( 2/3 ) of the jug
On simplifying the equation , we get
The amount of jug filled for 1 gallon = ( 3/8 ) of the jug
And , an additional 1 gallon of paint is added
So , the new amount of paint = [ ( 2/3 ) + 1 ] = ( 5/3 ) gallons
And , the amount of jug filled for ( 5/3 ) gallons = ( 5/3 ) x amount of jug filled for 1 gallon
Substituting the values in the equation , we get
The amount of jug filled for ( 5/3 ) gallons A = ( 5/3 ) x ( 3/8 )
On simplifying the equation , we get
The amount of jug filled for ( 5/3 ) gallons A = ( 5/8 ) of the jug
The amount of jug filled for ( 5/3 ) gallons A = 0.625 of the jug = 62.5 %
Hence , the fraction is ( 5/8 ) of the jug
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Question To solve 6÷1/4, James thinks about how the distance from his home to the store is 1/4 mile and he wonders how many times he would have to walk that distance to walk 6 miles. What is the quotient of 6 and 1/4?
Answers
Answer:
Step-by-step explanation:
James is thinking of 6 miles as the total distance and 1/4 mile as one part of that distance. To find out how many parts of 1/4 mile he would have to walk to cover 6 miles, he needs to divide 6 by 1/4.
To perform this division, we need to remember that dividing by a fraction is the same as multiplying by its reciprocal.
The reciprocal of 1/4 is 4, so to divide 6 by 1/4, we multiply 6 by 4:
6 * 4 = 24
So, the quotient of 6 and 1/4 is 24.
Find where
tan^-1 (xy^2/x+y) is continuous
Answers
Answer:
The inverse tangent function, tan^-1, is continuous over its domain, which is the range of values from -π/2 to π/2. However, the function tan^-1 (xy^2/(x+y)) may not be continuous at all points in this domain, as the denominator (x + y) can be zero for some values of x and y.
Step-by-step explanation:
A machine can label 4,000 cans in 10 minutes. At this rate, which answer choices best represent the machine labeling y cans in x minutes?
Answers
The proportional relationship that best represent the machine labeling y cans in x minutes is given as follows:
y = 400x.
What is a proportional relationship?A proportional relationship is defined as follows:
y = kx.
In which k is the constant of proportionality.
A machine can label 4,000 cans in 10 minutes, hence the constant is given as follows:
k = 4000/10
k = 400.
Hence the proportional relationship that best represent the machine labeling y cans in x minutes is given as follows:
y = 400x.
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an entomologist expects an insect population to increase by about 20% each month from may 1 to spetember 1
Answers
The insects population expected after 4 months is 414.
What is an equation?An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either be linear, quadratic, cubic, depending of the degree of the variable.
The standard form of an exponential function is:
y = abˣ
where a is the initial value and b is the multiplication factor.
An entomologist expects an insect population to increase by about 20% each month from may 1 to September 1.
Let us assume that the population of insect on May first was 200. If y represent the population of insects x months after May 1, hence:
y = 200(1.2)ˣ
At September 1; after 4 months:
y = 200(1.2)⁴ = 414
The insects population after 4 months is 414.
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An old medical textbook states that the mean sodium level for healthy adults is 141 mEq per liter of blood. A medical researcher believes that, because of modern dietary habits, the mean sodium level for healthy adults, μ, now differs from that given in the textbook. A random sample of 21 healthy adults is evaluated. The mean sodium level for the sample is 149 mEq per liter of blood. It is known that the population standard deviation of adult sodium levels is 13 mEq. Assume that the population is normally distributed. Can we conclude, at the 0.01 level of significance, that the population mean adult sodium level differs from that given in the textbook?
Perform a two-tailed test. Then complete the parts below.
Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.)
(a) State the null hypothesis H0 and the alternative hypothesis H1.
H0:
H1:
(b) Determine the type of test statistic to use.
▼(Choose one)
(c) Find the value of the test statistic. (Round to three or more decimal places.)
(d) Find the p-value. (Round to three or more decimal places.)
(e) Can we conclude that the population mean adult sodium level differs from that given in the textbook?
Yes No
Answers
Therefore , the solution of the given problem of test statistics comes out to be the p-value is 0.00052.
What is the test statistic?The Z-statistic, which demonstrates that the ordinary normal balanced hypothesis is true, has been used as the statistic for anything resembling a Z-test. Let's say you run two separate X-y tests with a 0.05 level of significance, and the results show that you got a 2.5 R t. (also referred as a Z-value). The p-value for this Z-value is 0.0124.
Here,
(a) State the null hypothesis [tex]H_{0}[/tex] and the alternative hypothesis H1.
The null hypothesis (H0) is that the population mean sodium level for healthy adults is equal to the textbook value of 141 Eq per liter of blood.
[tex]H_{0}[/tex] : μ = 141
The alternative hypothesis (H1) is that the population mean sodium level for healthy adults differs from the textbook value.
H1: μ ≠ 141
(b) Determine the type of test statistic to use.
Since the sample size is greater than 30 and the population standard deviation is known, we can use a z-test to test the hypothesis.
(c) Find the value of the test statistic. (Round to three or more decimal places.)
The test statistic is calculated as:
z = (x'- μ) / (σ / √n)
Where x' is the sample mean, μ is the population mean under the null hypothesis, σ is the population standard deviation, and n is the sample size.
Substituting the given values, we get:
z = (149 - 141) / (13 / √21) = 3.464
Therefore, the value of the test statistic is 3.464.
(d) Find the p-value. (Round to three or more decimal places.)
Since this is a two-tailed test, we need to find the area under the normal curve beyond 3.464 in both directions. Using a standard normal table or calculator, we find that the area beyond 3.464 is 0.00026 in one direction. So, the p-value is:
p-value = 2 * 0.00026 = 0.00052
Therefore, the p-value is 0.00052.
(e) Can we conclude that the population mean adult sodium level differs from that given in the textbook?
Since the p-value (0.00052) is less than the level of significance (0.01), we can reject the null hypothesis and conclude that the population mean adult sodium level differs from that given in the textbook at the 0.01 level of significance.
Answer: Yes, we can conclude that the population mean adult sodium level
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Select ALL the statements about the number 2⁻³ that are true.
2⁻³ raised to the third power equals 1.
2⁻³ is less than 1.
2⁻³ is greater than 3⁻².
2⁻³ multiplied by -1 equals 2³.
2⁻³ is equal to -8.
Answers
Answer:
B and C
------------------------
Verify each statement.
A) 2⁻³ raised to the third power equals 1.
(2⁻³)³ = 2⁻³°³ = 2⁻⁹ ≠ 1, this is incorrectB) 2⁻³ is less than 1.
2⁻³ = 1/2³ = 1/8 < 1, this is correctC) 2⁻³ is greater than 3⁻².
2⁻³ = 1/8 and 3⁻² = 1/3²= 1/9, therefore 1/8 > 1/9, this is correctD) 2⁻³ multiplied by -1 equals 2³.
2⁻³*(-1) = 1/2³*(-1) = - 1/2³ ≠ 2³, this is incorrectE) 2⁻³ is equal to -8.
2⁻³ = 1/8 ≠ - 8, this is incorrectFind the area of the shaded figure below.
Answers
Answer:
x(y/2 + z)
Step-by-step explanation:
There are two triangles here.
The small triangle which is bound by dotted lines has base = y and height = x
The height of the larger triangle is 2x and its base is y + z
Area of larger triangle = 1/2 · 2x · (y + z)
= x(y + z) = xy + xz
Area of smaller triangle = 1/2 · x · y = xy/2
Shaded region area = Area of larger triangle - area of smaller triangle
= xy + xz - xy/2
= xy/2 + xz
= x(y/2 + z)
Find common denominator for 4/5 and 2/3
Answers
Answer:
15
Step-by-step explanation:
5*3 = 15
Solve the equation for x. 3x^2-bx=0
Answers
Answer:
The equation 3x^2 - bx = 0 can be factored into two linear factors as follows:
x (3x - b) = 0
So either x = 0 or 3x - b = 0, which gives x = b/3.
Therefore, the solutions to the equation 3x^2 - bx = 0 are x = 0 or x = b/3.
it is stated in a question form it poses an expected relationship between variables it reflects a theory it is testable
Answers
The correlational hypothesis is a type of research hypothesis that proposes a relation between two variables.
Hypothesis proposes that there is a relationship or association between two variables, known as the independent and dependent variables.
The relation between the two variables can be positive or negative. A positive relation means that as the independent variable increases, the dependent variable also increases.
On the other hand, a negative relation means that as the independent variable increases, the dependent variable decreases.
The strength of the relation can be determined by calculating the correlation coefficient, which is a numerical representation of the strength of the relation between two variables.
In the mathematical representation of a correlational hypothesis, the equation
=> Y = mX + b
is used, where m represents the slope of the line and b represents the intercept. The slope of the line reflects the strength of the relation between the independent and dependent variables, while the intercept reflects the starting point of the relation.
Complete Question:
What is meant by the thing that it is stated in a question form it poses an expected relationship between variables it reflects a theory it is testable?
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a productive approach to identifying a research topic, and subsequent research question, is to utilize which of the following sources?
Answers
Answer:
Step-by-step explanation:
A productive approach to identifying a research topic and subsequent research question can involve utilizing multiple sources, including:
Literature review: Reviewing existing research in the field can help identify gaps in knowledge and areas that need further investigation.
Personal interests and experiences: Consider your own experiences, interests, and expertise to identify a topic that you are passionate about and can contribute to.
News articles and current events: Stay up-to-date on current events and identify topics that are relevant and pressing in your field.
Professional associations and organizations: These organizations often have conferences and publications that highlight current research trends and topics.
Government reports and data sources: These sources can provide data and information on a wide range of topics and can serve as a starting point for identifying a research question.
Ultimately, a combination of these sources can be useful in identifying a research topic and subsequent research question. It's important to consider the feasibility, importance, and originality of the research topic, and to choose a topic that you can research thoroughly and effectively.
a carpenter worked on a job for 10 weeks. the carpenter worked 9 hours each weekday and 4 hours each saturday. the carpenter was paid $30 per hour for regular time and $45 per hour for overtime. if there are 8 hours in a regular work day, how much money did the carpenter earn on the job
Answers
Answer:
$16,050.00
Step-by-step explanation:
10[(40 x 30) + (9 x 45)]
In one week, he works 40 hours (8 x 5) for $30 and 9 hours of overtime each week (one extra hour 5 days during a week week plus 4 hours on Sat.)
10(1200 +405)
10(1605)
$16,050.00
To calculate the carpenter's earnings, separate the regular work hours from the overtime hours. Compute earnings for both from their respective rates and add them together. Multiply by the number of days worked and finally, by the total number of weeks.
Explanation:In order to calculate the earnings of a carpenter during a 10-week period, we must consider how many hours were worked at regular and overtime rates. During the weekdays, the carpenter worked 9 hours per day. The first 8 hours were paid at the regular rate, and the remaining 1 hour was considered overtime. On Saturdays, the carpenter worked 4 hours at the regular rate as it didn't supersede the 8-hour workday.
So, on weekdays, he earned: 8 hours * $30 + 1 hour * $45. On Saturdays, his earnings were 4 hours * $30. To find the weekly earnings we add weekday and Saturday earnings, then multiply by 5 (for weekdays) and add 1 Saturday, then multiply the total earnings by 10 weeks. Using these computations, we are able to find the total amount earned by the carpenter.
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100 POINTS HELPWhich column on an accounting worksheet may not balance at the end of an accounting period?
A. The Adjusted Trial Balance
B. The Trial Balance
D. The Adjustments
C. The Income Statement
Answers
Graph 3/2x-2
(PLEASE SHOW A PICTURE OF THE GRAPH)
Answers
First we put the equation in slope intercept form y = mx + b.
y = 3/2x -2 is our equation
3/2 is our slope (y/x or rise over run)
-2 is our y intercept
Start by graphing y intercept (0, -2)
Which is a -2 on the y axis.
From there, rise 3 (up) and run 2 (right) and plot your point. Draw your line.
Your solution is where the line crosses the x and y axis. ( 1 1/3, -2 )
What is the measure of angle a?
Answers
So an equation we could make to solve is 4x + 6x + 2x = 180
12x = 180
x = 180/12
x= 15
Since we want angle A, you would do 4 • 15 which gives you the answer: 60°
An urn initially contains a single red ball and a single green ball. A ball is drawn at random, removed, and replaced by a ball of the opposite color, and this process repeats so that there are always exactly two balls in the urn. Let Xn be the number of red balls in the urn after n draws, with X0 = 1. Specify the transition probabilities for the Markov chain {Xn}.
Answers
The state space for the Markov chain {Xn} is {0, 1, 2}. At any time, Xn can only be 0, 1, or 2, depending on how many red balls are in the urn.
The transition probabilities for the Markov chain are as follows:
If Xn = 0, the next state Xn+1 can only be 1, with a probability of 1.0.
If Xn = 1, the next state Xn+1 can either be 0 or 2, with a probability of 0.5 each.
If Xn = 2, the next state Xn+1 can only be 1, with a probability of 1.0.
So, the transition probabilities can be represented in a transition matrix as follows:
P = [ [0, 1, 0],
[0.5, 0, 0.5],
[0, 1, 0]
]
This transition matrix represents the probabilities that the Markov chain will transition from one state to another in one step.
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PLEASE HELP!
Your good friend, Harold, was just offered the choice between two jobs, and now he needs to decide which job offer he should take. There are three major factors that he will consider: salary, gas expenses, and vacation days. You want to help your friend decide on which job to take; at which job he will earn more money?
What is the salary of each job? - A.$51,000 & B.$53,000
How far away is the job? A. 9 miles from home & B. 22 miles from home
How many vacation days does he get? A. 12% of weekdays & B. 8% of weekdays
Gas prices in the area ? $5.25 per gallon
Mileage on his car? 24 miles per gallon
Answers
The more money will be earned for job B.
What is Subtraction?Subtraction can be done for any numbers or algebraic expressions. It is the process of taking out certain value from a given amount of number.
For Job A :
Salary = $51,000
Distance = 9 miles from home
Total distance needed to travel to and back from job in a day = 18 miles
Number of working days in a year = 260
Number of working days in a year after vacation = 260 - (12% × 260) = 228.8 days
Total distance for working days in a year = 228.8 × 18 = 4118.4 miles
Mileage on his car = 24 miles per gallon
Amount of gas for 24 miles = 1 gallon
Amount of gas for 4118.4 miles = 171.6 gallon
Gas price for 1 gallon = $5.25
Gas price for 171.6 gallon = 171.6 × $5.25 = $900.9
Net salary after gas price = $51,000 - $900.9 = $50,099.1
For Job B :
Salary = $53,000
Distance = 22 miles from home
Total distance needed to travel to and back from job in a day = 44 miles
Number of working days in a year after vacation = 260 - (8% × 260) = $239.2 days
Total distance for working days in a year = 239.2 × 44 = 10,524.8 miles
Mileage on his car = 24 miles per gallon
Amount of gas for 24 miles = 1 gallon
Amount of gas for 10,524.8 miles = 438.533 gallon
Gas price for 1 gallon = $5.25
Gas price for 171.6 gallon = 438.533 × $5.25 = $2302.3
Net salary after gas price = $53,000 - $2302.3 = $50,697.7
The net salary after gas price is higher for job B.
Hence Net salary after gas price is higher for job B.
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Find the volume of the figure. Express the answer in terms of pi
and then round to the nearest whole number.
Answers
Answer expressed in terms of pi: [tex]V=2304 \pi (m^{3})\\[/tex].
Answer rounded to the nearest whole number: [tex]V=7238(m^{3})[/tex].
Step-by-step explanation:1. Annotate the given data.Given figure: Sphere.
Given dimension: diameter (d)= 24m.
2. Recall the formula.
We're trying to calculate the volume of a sphere, here's the formula for that:
[tex]V=\frac{4}{3} \pi r^{3}[/tex]
3. Use the given data (step 1) to substitute variables in the formula.There's something worth paying a bit extra ttention in this problem, and that is the fact that we were not given a value of radius (r) to use in the formula. Instead, we were given the diameter (d), which happens to be double of the radius, by definition. Hence, to find the radius we do the following:
[tex]d=2r\\\\ r=\frac{d}{2} =\frac{24m}{2} =12m[/tex]
Use the data in the volume formula:
[tex]V=\frac{4}{3} \pi (12m)^{3}[/tex]
[tex]V= \pi(\frac{4}{3} (12m)^{3})\\ \\V= \pi(2304m^{3} )\\ \\V=2304 \pi (m^{3})\\[/tex]
4. Express the answers.We were asked to express our answer in terms of pi. Therefore, let's isolate pi from the calculations for now:
[tex]V= \pi(\frac{4}{3} (12m)^{3})\\ \\V= \pi(2304m^{3} )\\ \\V=2304 \pi (m^{3})\\[/tex]
Answer expressed in terms of pi: [tex]V=2304 \pi (m^{3})\\[/tex].
The problem also asks to round to the nearest whole number. So, let's go ahead and calculate an approximate value and round it to the nearest whole number:
[tex]V=7238.229474 (m^{3})[/tex]
Since the first number after the dot (.) isn't 5 or greater, we may leave the whole part of the number as it is and delete the remaining decimal numbers.
Answer rounded to the nearest whole number: [tex]V=7238(m^{3})[/tex].
suppose x is a continuous random variable that is uniformly distributed between 3 and 8. which one of the following functions can be used to find p(x
Answers
The Cumulative Distribution Function (CDF) can be used to find the probability of a continuous random variable that is uniformly distributed between 3 and 8.
The formula for the CDF is F(x) = (x-a)/(b-a) where a is the lower bound of the distribution and b is the upper bound of the distribution. In this case, a = 3 and b = 8. Therefore, the CDF equation is F(x) = (x-3)/(8-3). The Cumulative Distribution Function (CDF) can be used to find the probability of a continuous random variable that is uniformly distributed between 3 and 8.As an example, let's find the probability of x being less than or equal to 5. The CDF equation would be F(5) = (5-3)/(8-3) = 2/5. Therefore, the probability of x being less than or equal to 5 is 2/5.
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Please help!
Find the area of FGH with coordinates F (-4,6) G(-2,1) H (2,6)
Step by Step explanation please
Answers
The area of triangle FGH is given as follows:
15.05 units².
How to obtain the area of the triangle?The area of a triangle is given by half the multiplication of the base length by the height.
The base length is given by the distance between points F and G, hence:
b = sqrt((-2 - (-4))² + (6 - 1)²)
b = 5.385.
The coordinates of the midpoint of segment FG are given as follows:
x = (-4 - 2)/2 = -3.y = (6 + 1)/2 = 3.5.The distance between the midpoint and vertex H is the height, given as follows:
h = sqrt((-3 - 2)² + (3.5 - 6)²)
h = 5.59.
Hence the area of the triangle is given as follows:
A = 0.5 x 5.385 x 5.59
A = 15.05 units².
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Find a value of the constant k such that the indicated limit exists. 3* _ 4 lim X-0 ekx +1 k = (If any value of k will work; enter any; if none will work, enter none ) Are there any other values of k that will work?
Answers
Any value of k greater than 0 will work, since the limit will be 1 as x approaches 0, regardless of the value of k. Other values of k can also work.
The limit in question is 3*_4limX-0 ekx+1. For any limit to exist, the expression must approach a finite number as x approaches 0. In this case, that number is 1. As long as the exponent k is greater than 0, the exponential expression will approach 0 as x approaches 0, and the limit will be 1. Therefore, any value of k greater than 0 will work. It is worth noting, however, that other values of k can also work. For example, if k is equal to 0, then the expression reduces to 3/4 as x approaches 0, and the limit still exists and is equal to 1. Similarly, if k is less than 0, then the expression will approach infinity as x approaches 0, and the limit will still exist and be equal to 1.
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Suppose there is an electric field Ē = -3.67 +-4.359 in N/C. What is the + change in the electric potential in volts if you move from coordinate (-8.03, -4.24) to coordinate (7.02, 2.60)?The coordinates are given in meters
Answers
The change in electric potential is approximately 135.19 volts if you move from coordinate (-8.03, -4.24) to coordinate (7.02, 2.60)
What is a coordinate point?
Coordinates are a pair of numbers that are used to determine the position of a point or a shape in a 2-dimensional plane. We define the position of a point on a 2D plane using two numbers, called the x-coordinate and the y-coordinate.
The change in electric potential (ΔV) can be calculated using the equation:
ΔV = -∫ E dl
where E is the electric field and dl is an infinitesimal displacement along the path. We need to find the path integral of the electric field between the two coordinates.
Since the electric field is in the x-y plane, we can use the two-dimensional version of the equation:
ΔV = -∫ E * dx - ∫ E * dy
where dx and dy are the changes in x and y, respectively.
We can calculate the change in x and y as follows:
dx = 7.02 m - (-8.03 m) = 7.02 m + 8.03 m = 15.05 m
dy = 2.60 m - (-4.24 m) = 2.60 m + 4.24 m = 6.84 m
Next, we'll use the electric field equation to find the components of the electric field in the x and y directions:
Ex = -3.67 N/C
Ey = -4.359 N/C
Finally, we can use these values to calculate the change in electric potential:
ΔV = -∫ E * dx - ∫ E * dy = -Ex * dx - Ey * dy = -(-3.67 N/C) * (15.05 m) - (-4.359 N/C) * (6.84 m)
Converting from joules to volts:
ΔV = ΔV / (1.602 * 10^-19 C)
ΔV = (3.67 N/C * 15.05 m + 4.359 N/C * 6.84 m) / (1.602 * 10^-19 C) = 135.19 Volts
Hence, the change in electric potential is approximately 135.19 volts.
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Find the lateral area of a cylinder whose radius is 6 cm and height is 20 cm.
240 π cm 2
312 π cm 2
120 π cm 2
Answers
Answer:
[tex]240\pi cm^{2}[/tex]
Step-by-step explanation:
Lateral area of a cylinder is the curved surface area, (which connects the top with the base)
Curved Surface Area= [tex]2\pi rh[/tex]
where r = radius of base
h = height of cylinder
Substituting the provided values:
Lateral area of cylinder = [tex]2\pi (6 cm)(20 cm)[/tex]
= [tex]240\pi cm^{2}[/tex]
The demand function for a certain product is known to be linear.
When the price of the product is $12, the number of units sold is 5000.
But if the price of the product is $9, the number of units sold is 10000.
a) Find the demand function, expressed as price p
in terms of quantity q
p=
b) Find the price at which the demand will reach 20000 units.
Answers
The answers for demand function are a) p(x) = -0.0006q + 15 and b) the price at which the demand will reach 20000 units put q = 20000, is $3
What is demand function?A demand function is a mathematical equation which expresses the demand for a product or service as a function of its price.
Given that, the demand function for a certain product is known to be linear.
When the price of the product is $12, the number of units sold is 5000.
But if the price of the product is $9, the number of units sold is 10000.
We need to find the demand function, expressed as price p in terms of quantity q and the price at which the demand will reach 20000 units.
a) P(x) can be calculated using point slope equation given:
Price is $12 for 5000 units sold. A decrease in price to $9 increases units sold to 10000.
Slope = Δ price / Δ units = 9-12 / 10000 - 5000
= -3 / 5000 = -0.0006
p(q) = m(q - x₁) + p₁
= -0.0006(q-5000) + 12
= -0.0006q + 3 + 12
= -0.0006q + 15
Therefore, the demand function is p(x) = -0.0006q + 15
b) To find the price at which the demand will reach 20000 units put q = 20000, put q = 20000
p(x) = -0.0006 × 20000 + 15
= -12 + 15
= 3
Therefore, the price at which the demand will reach 20000 units put q = 20000, is $3
Hence, the answers for demand function are a) p(x) = -0.0006q + 15 and b) the price at which the demand will reach 20000 units put q = 20000, is $3
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Generally which one of the following the least appropriate measure of central tendency for data set that contains outliets? A) mean B) median C) 2nd quantile D) 50th percentile
Answers
The (A) mean is the least acceptable metric of central tendency for data collection with outliers.
What is mean?There are various mean types in mathematics, particularly in statistics.
Each mean helps to summarize a certain set of data, frequently to help determine the overall significance of a specific data set.
In mathematics, the mean is the average of a set of data, which is calculated by adding all the numbers together and then dividing the result by the total number of numbers.
For instance, the mean for the collection of values 8, 9, 5, 6, and 7 is 7, since 8 + 9 + 5 + 6 + 7 = 35, and 35/5 = 7.
For data collection with outliers, the mean is the least acceptable measure of central tendency.
Therefore, the (A) mean is the least acceptable metric of central tendency for data collection with outliers.
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You are given an Isosceles Trapezoid,
If one of the base angles equals 45 then what is the measure of it's opposite angle?
180
135
45
90
Answers
The measure of it's opposite angle is 135
How to determine the measure of it's opposite angleFrom the question, we have the following parameters that can be used in our computation:
The base angles equals 45
Using the above as a guide, we have the following:
Base angle + Opposite angle = 180
Substitute the known values in the above equation, so, we have the following representation
45 + Opposite angle = 180
Evaluate the like terms
Opposite angle = 135
Hence, the angle is 135 degrees
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