4. The cube root parent function is reflected across the x-axis, vertically stretched by a factor of 3 then
translated 8 units down. Write an equation that could represent this function.
Answers
Using translation concepts, it is found that the equation is given by:
\(y = -3\sqrt[3]{x} - 8\)
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
The parent cube root function is given by:
\(y = \sqrt[3]{x}\)
It was reflected across the x-axis, that is, multiplied by -1, hence:
\(y = -\sqrt[3]{x}\)
It was vertically stretched by a factor of 3, hence:
\(y = -3\sqrt[3]{x}\)
Then, it was translated 8 units down, hence:
\(y = -3\sqrt[3]{x} - 8\)
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Related Questions
the cost of kg of apples is $262.50. find the cost of 25 kg of apples
Answers
Answer:
Step-by-step explanation:
cost of 25 kg =262.50x25
=6562.5
HELP ME ON THIS QUESTION.
Answers
Answer:
8
Step-by-step explanation:
area of parallelogram = b*h
= 27*11
=297 ft^2
1 can = 40 ft^2
? = 297
cans = 8 cans
find the points on the cone z 2 = x 2 y 2 z2=x2 y2 that are closest to the point (5, 3, 0).
Answers
Given the cone z² = x²y² and the point (5, 3, 0), we have to find the points on the cone that are closest to the given point.The equation of the cone z² = x²y² can be written in the form z² = k²(x² + y²), where k is a constant.
Hence, the cone is symmetric about the z-axis. Let's try to obtain the constant k.z² = x²y² ⇒ z = ±k√(x² + y²)The distance between the point (x, y, z) on the cone and the point (5, 3, 0) is given byD² = (x - 5)² + (y - 3)² + z²Since the points on the cone have to be closest to the point (5, 3, 0), we need to minimize the distance D. Therefore, we need to find the values of x, y, and z on the cone that minimize D².
Let's substitute the expression for z in terms of x and y into the expression for D².D² = (x - 5)² + (y - 3)² + [k²(x² + y²)]The values of x and y that minimize D² are the solutions of the system of equations obtained by setting the partial derivatives of D² with respect to x and y equal to zero.∂D²/∂x = 2(x - 5) + 2k²x = 0 ⇒ (1 + k²)x = 5∂D²/∂y = 2(y - 3) + 2k²y = 0 ⇒ (1 + k²)y = 3Dividing these equations gives us x/y = 5/3. Substituting this ratio into the equation (1 + k²)x = 5 gives usk² = 16/9 ⇒ k = ±4/3Now that we know the constant k, we can find the corresponding value of z.z = ±k√(x² + y²) = ±(4/3)√(x² + y²)
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What is the value of the point on the number line?
5/8
3/8
5/7
4/6
Answers
TIME REMAINING
59:54
Fatima evaluated the expression StartFraction 4 m Superscript negative 3 Baseline n Superscript negative 2 Baseline Over m Superscript negative 1 Baseline n EndFraction, when m = negative 2 and n = 4. Her work is shown below.
StartFraction 4 m Superscript negative 3 Baseline n Superscript negative 2 Baseline Over m Superscript negative 1 Baseline n EndFraction = 4 m Superscript negative 2 Baseline n Superscript negative 3 Baseline = 4 (negative 2) Superscript negative 2 Baseline (4) Superscript negative 3 Baseline = StartFraction 1 Over 64 EndFraction times StartFraction 1 Over 64 EndFraction = StartFraction 1 Over 4,096 EndFraction
What was Fatima’s error?
She subtracted the exponents incorrectly when simplifying the expression.
She substituted the wrong values for the variables.
She applied the exponent Negative 2 to 4 (negative 2) instead of applying the exponent to just Negative 2.
She found an incorrect value for (Negative 8) Superscript negative 2 since the value should be negative.
Answers
Answer:
It c
Step-by-step explanation:
She applied the exponent Negative 2 to 4 (negative 2) instead of applying the exponent to just Negative 2.
Find the range, median, first and third quartiles, and interquartile range for each data set OF THE NUMBERS 52 72 96 21 58 40 75
Answers
Answer:
Range: 75 Median: 58 1Q: 40 3Q: 75 Interquartile: 35
A movie begins at 4:30pm and it is 1 hour 50 minutes. What time does it end?
Answers
Answer:
The movie ends at 6:20.
Step-by-step explanation:
4:30
+30
=5:00
+20
=5:20
+1:00
=6:20
Elena notices that when she spends less time on social media the night before a quiz, she gets a higher score. before one quiz, she spent $107$ minutes on social media and earned $37$ points on a quiz. before another quiz, she spent $73$ minutes on social media and earned $41$ points on a quiz. write a function to model a linear relationship between elena's social media usage, in minutes, and her quiz scores, assuming that the total number of points on each quiz remains a constant
Answers
The function to model a linear relationship between elena's social media usage, in minutes, and her quiz scores is - 2x +843
17 17
The function can be write as follows:
37 points after 107 minutes of social media use.
73 minutes and a score of 41 on social media.
You can imagine the two bits of information mentioned above as two points on a line. Given that the quiz's score is a function of the amount of time spent on social media, set the latter to x and the former to y. Two ordered pairs are provided by the available data: (107, 37) and (73, 41).
The equation of a line that passes through these two points must now be written.
The equation of a line in two-point form is:
y -y1 = y2-y1 ( x -x1)
x2-x1
we have x1 = 107, y1 = 37, x2 = 73, and y2 = 41
y-37 = 41 - 37 ( x-107)
73 -107
y-37 = 4 ( x-107)
-34
y-37 = 2 ( x-107)
-17
17y-629 =-2x +214
17 y = -2x +843
y = - 2x +843
17 17
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Does the table contain values that would be considered an arithmetic sequence, a geometric sequence, or neither? *
Term Number 2, 3, 4, 5.
Value 3, 9, 27, 81
Neither
Arithmetic
Geometric
Answers
Answer:
Geometric Sequence
Step-by-step explanation:
As you can see, the terms are of consecutive sequences.
The 3rd term ÷ The 2nd term = 3
The 4th term ÷ The 3rd term = 3
The ratio between the consecutive terms is the same. Therefore, it's a geometric sequence.
y-x=13
x= 11
Simplify your answer as much as possible.
Answers
Answer:
y = 24
Step-by-step explanation:
y - x = 13
x = 11
y - 11 = 13
y = 13 + 11 = 24
suppose that the lifetime income of current graduates of ut is exponentially distributed. of course, the mean of the exponential distribution is different for each student and depends on factors such as major, gpa (very slightly), and many other factors. suppose that the mean of the exponential distribution is uniformly distributed between 1 million dollars and 10.5 million dollars. what is the sum of the mean and standard deviation of the lifetime income of a randomly selected current graduate (in millions of dollars)?
Answers
Answer: 12.5 million dollars.
Step-by-step explanation:
If the mean of the exponential distribution is uniformly distributed between 1 million dollars and 10.5 million dollars, we can find the expected value or mean of this uniform distribution by taking the average of the minimum and maximum values:
E(X) = (1 million dollars + 10.5 million dollars) / 2 = 5.75 million dollars
The standard deviation of a uniform distribution can be calculated using the formula:
SD(X) = (b - a) / sqrt(12)
where a is the minimum value (1 million dollars) and b is the maximum value (10.5 million dollars).
SD(X) = (10.5 million dollars - 1 million dollars) / sqrt(12) = 2.84 million dollars
The mean and standard deviation of an exponential distribution are equal, so the mean of the lifetime income for a randomly selected current graduate is also 5.75 million dollars, and the standard deviation is 2.84 million dollars.
Therefore, the sum of the mean and standard deviation of the lifetime income is:
5.75 million dollars + 2.84 million dollars = 8.59 million dollars
However, the question asks for the answer in millions of dollars, so we need to divide by one million:
8.59 million dollars / 1 million = 8.59
So the final answer is 8.59 + 3 (million dollars) = 11.59 million dollars, which rounds up to 12.5 million dollars.
The sum of the mean and standard deviation of a randomly selected current graduate is 11.5 million dollars.
The mean of the exponential distribution is uniformly distributed between 1 million dollars and 10.5 million dollars. Therefore, the expected value of the mean is the average of the two extremes, which is (1+10.5)/2 = 5.75 million dollars.
Since the exponential distribution has a constant standard deviation (equal to its mean), we can calculate the standard deviation of each student's income as the same value as their mean.
Therefore, the sum of the mean and standard deviation of a randomly selected current graduate is 5.75 million dollars (mean) + 5.75 million dollars (standard deviation) = 11.5 million dollars.
For an exponential distribution, the mean (μ) and standard deviation (σ) are equal to the reciprocal of the rate parameter (λ). Since the mean of the exponential distribution is uniformly distributed between 1 million dollars and 10.5 million dollars, we need to find the average mean (E[μ]).
E[μ] = (1 + 10.5) / 2 = 5.75 million dollars
Since the mean and standard deviation are equal in an exponential distribution, the standard deviation (σ) is also 5.75 million dollars.
The sum of the mean and standard deviation of the lifetime income of a randomly selected current graduate is:
5.75 (mean) + 5.75 (standard deviation) = 11.5 million dollars.
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determine if the function defines an inner product on r3, where u = (u1, u2, u3) and v = (v1, v2, v3). (select all that apply.) u, v = u12v12 u22v22 u32v32a) satisfies (u,v)=(v,u) b) does not satisfy (u, v)=(v,u) c) satisfies (u, v+w) = (u,v)+(u,w) d) does not satisfy (u, v+w) = (u,v)+(u,w) e)satisfies c (u,v) = (cu, v) f) does not satisfies c (u,v) = (cu, v) g) satisfies (v, v) >= 0 and(v,v)=0 if and only if v=0 h) does not satisfies (v, v) >= 0 and(v,v)=0 if and only if v=0
Answers
The function u,v = u1v1 + u2v2 + u3v3 satisfies properties a, c, and e, and g, so it defines an inner product on R3.
To determine if the function defines an inner product on R3, we need to check if the following properties hold:
Commutativity: (u,v) = (v,u)
Non-commutativity: (u,v) ≠ (v,u)
Additivity: (u,v+w) = (u,v)+(u,w)
Non-additivity: (u,v+w) ≠ (u,v)+(u,w)
Homogeneity: (cu,v) = c(u,v)
Non-homogeneity: (cu,v) ≠ c(u,v)
Positive-definiteness: (v,v) ≥ 0 and (v,v) = 0 if and only if v = 0
Non-positive-definiteness: (v,v) < 0 or (v,v) = 0 if and only if v ≠ 0
The function u,v = u1v1 + u2v2 + u3v3 satisfies properties a, c, and e, and g, so it defines an inner product on R3.
satisfies (u,v) = (v,u)
does not satisfy (u, v) = (v,u)
satisfies (u, v+w) = (u,v)+(u,w)
does not satisfy (u, v+w) = (u,v)+(u,w)
satisfies (cu, v) = c(u,v)
does not satisfy (cu, v) = c(u,v)
satisfies (v, v) ≥ 0 and (v,v) = 0 if and only if v=0
does not satisfy (v, v) ≥ 0 and (v,v) = 0 if and only if v=0
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The following functions define an inner product on ℝ³: a) (u, v) = u₁²v₁² + u₂²v₂² + u₃²v₃², b) (u, v) = (v, u), c) (u, v+w) = (u, v) + (u, w), e) c(u, v) = (cu, v), and g) (v, v) ≥ 0 and (v, v) = 0 if and only if v = 0. These properties satisfy the requirements for an inner product on ℝ³.
How did we get the values?To determine if the function defines an inner product on ℝ³, check if the given properties hold:
a) (u, v) = u₁²v₁² + u₂²v₂² + u₃²v₃²
b) (u, v) = (v, u)
c) (u, v+w) = (u, v) + (u, w)
d) (u, v+w) ≠ (u, v) + (u, w)
e) c(u, v) = (cu, v)
f) c(u, v) ≠ (cu, v)
g) (v, v) ≥ 0 and (v, v) = 0 if and only if v = 0
h) (v, v) does not satisfy (v, v) ≥ 0 and (v, v) = 0 if and only if v = 0
Evaluate each property:
a) (u, v) = u₁²v₁² + u₂²v₂² + u₃²v₃²
This property satisfies the requirement for the inner product since it is a sum of squared terms.
b) (u, v) = (v, u)
The given function is symmetric since swapping u and v does not change the result. Therefore, it satisfies (u, v) = (v, u).
c) (u, v+w) = (u, v) + (u, w)
We need to check if the distributive property holds. Let's evaluate both sides:
(u, v+w) = u₁²(v₁+w₁)² + u₂²(v₂+w₂)² + u₃²(v₃+w₃)²
(u, v) + (u, w) = u₁²v₁² + u₂²v₂² + u₃²v₃² + u₁²w₁² + u₂²w₂² + u₃²w₃²
Expanding the squares and comparing the expressions, we can see that (u, v+w) = (u, v) + (u, w). Thus, it satisfies the property.
d) (u, v+w) ≠ (u, v) + (u, w)
Since we have already established that (c) holds, this property cannot hold simultaneously. Therefore, the given function does not satisfy this property.
e) c(u, v) = (cu, v)
We need to check if the given function is linear in the first argument. Let's evaluate both sides:
c(u, v) = c(u₁²v₁² + u₂²v₂² + u₃²v₃²) = cu₁²v₁² + cu₂²v₂² + cu₃²v₃²
(cu, v) = (cu)₁²v₁² + (cu)₂²v₂² + (cu)₃²v₃² = cu₁²v₁² + cu₂²v₂² + cu₃²v₃²
The expressions are equal, so it satisfies this property.
f) c(u, v) ≠ (cu, v)
Since we have already established that (e) holds, this property cannot hold simultaneously. Therefore, the given function does not satisfy this property.
g) (v, v) ≥ 0 and (v, v) = 0 if and only if v = 0
For any vector v = (v₁, v₂, v₃), we can evaluate (v, v) as follows
(v, v) = v₁²v₁² + v₂²v₂² + v₃²v₃² = v₁⁴ + v₂⁴ + v₃⁴
The squared terms are always non-negative, so (v, v) ≥ 0 for any v. Additionally, (v, v) = 0 only when v₁ = v₂ = v₃ = 0. Therefore, this property holds.
h) (v, v) does not satisfy (v, v) ≥ 0 and (v, v) = 0 if and only if v = 0
Since we have already established that (g) holds, this property cannot hold simultaneously. Therefore, the given function does not satisfy this property.
In summary, the given function defines an inner product on ℝ³ for the following properties:
a) (u, v) = u₁²v₁² + u₂²v₂² + u₃²v₃²
b) (u, v) = (v, u)
c) (u, v+w) = (u, v) + (u, w)
e) c(u, v) = (cu, v)
g) (v, v) ≥ 0 and (v, v) = 0 if and only if v = 0
These properties satisfy the requirements for an inner product on ℝ³.
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What difference between the sample and population results regardless of how well the sampling plan has been designed?
Answers
The main difference between sample results and population results is that sample results are less accurate than the population results.
Given nothing and we are required to give the difference between the sample and population results regardless of how well the sampling plan has been designed.
Sample is basically a small part of whole population.
Population is basically includes each unit in the space regarding which the data is to be collected for the research.
The main differences between the sample and population results regardless of how well the sampling plan has been designed are as under:
To collect data of whole population the researcher needs huge money and time whereas in sampling the researcher devotes comparatively less time than data collcection through population.The data collected through population is more accurate than data collected through sample because sample is just a representation of population and there may happen that there are units different from the sample in the population.Hence the main difference between sample results and population results is sample results are less accurate than the population results.
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Find the slope between 2 points.
(16, 12) (40,18)
Answers
Answer:
\(\frac{1}{4}\)
Step-by-step explanation:
In this question, we have to find the slope with the given coordinates.
To find our slope, we would use the slope formula: \(m = \frac{y2-y1}{x2-x1}\)
Plug in your coordinates and solve:
\(m = \frac{18-12}{40-16}\\\\m=\frac{6}{24}\)
Simplify the fraction:
\(m=\frac{1}{4}\)
The slope would be \(\frac{1}{4}\)
Show ABC≈ABD
....,......
.......
Answers
Answer:
Step-by-step explanation:
From the triangles given in the figure,
Given:
AC ≅ AD
m∠ABC = m∠ABD = 90°
To prove:
ΔABC ≅ ΔABD
Solution:
Statements Reasons
1). AC ≅ AD 1). Given
2). AB ≅ AB 2). Reflexive property
3). ΔABC ≅ ΔABD 3). By HL theorem for congruence of the triangles
Which calculation shows the best method for estimating the result of 384 divided by three-sixteenths?
Answers
Answer:
the answer to this is 2048
Step-by-step explanation:
Answer: B
Step-by-step explanation: Just round
find the mean absolute deviation
Answers
Follow these procedures to calculate the mean absolute deviation.
1. Determine the data's mean by adding all of the values and dividing by the number of values in the data set.
2. Subtract the mean from each of the data points.
3. Make each difference a good one.
4. Add up all of the positive differences.
5. Subtract this total from the amount of data values in the collection.
This is the mean absolute deviation.
What is mean absolute deviation?A data set's average absolute deviation is the sum of its absolute departures from a central point. It is a statistical dispersion or variability summary statistic.
The average distance between the values in a data collection and the set's mean is described by mean absolute deviation. A data collection with a mean average deviation of 3.2, for example, has values that are 3.2 units away from the mean on average.
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Which of the following would not be a possible function for f (x) and g(x) such that f of g of x is equal to 6 over the quantity x squared end quantity plus 3
Answers
The equations that could represent f(x) and g(x) are f(x) = 6/x + 3 and g(x) = x
How to determine the possible equations of the functions?From the question, the equation of the function is given as
f of g of x is equal to 6 over the quantity x squared end quantity plus 3
Rewrite properly
So, we have
f(g(x)) = 6/x² + 3
The above equation can be rewitten as
f(g(x)) = 6/g(x)² + 3
This means that
g(x) = x
Remove the occurrence of g(x) from the equation f(g(x)) = 6/g(x)² + 3
So, we have
f(x) = 6/x + 3
Hence, the possible equations are f(x) = 6/x + 3 and g(x) = x
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Which of the sets shown includes the elements of set Z that are both odd numbers and multiples of 7?
Z={-21, -14, -7.0, 7, 14, 21}
A {-21, 21)
B. {-21.-7. 7. 21)
C: {-14, 0.14)
D. {-21, -14, -7)
Answers
Answer:
B. {-21.-7. 7. 21)
Step-by-step explanation:
The set made up of odd numbers and multiples of 7 is given as;
{-21.-7. 7. 21)
Multiples of 7 are usually those numbers where 7 is factor.
Odd numbers are numbers that cannot be divide by 2.
So, the most fitting answer is B.
Shelly and Terrence completed a different number of tasks in a game. Shelly earned 90 points on each task. Terrence's total points were 20 less than Shelly's total. The expression below shows Terrence's total points in the game:
90x − 20
What does the factor x of the first term of the expression represent? (2 points)
Group of answer choices
The total number of tasks Terrence completed
The total number of tasks Shelly completed
The sum of Shelly's and Terrence's total points
The difference between Shelly's and Terrence's total points
Answers
The total number of tasks Terrence completed. By substituting the value of 'x' with the number of tasks Terrence completed
The factor 'x' in the expression '90x - 20' represents the total number of tasks that Terrence completed in the game.
To understand why, let's break down the given information. It states that Shelly and Terrence completed a different number of tasks. Shelly earned 90 points on each task, so the total number of tasks she completed is not represented by 'x'.
On the other hand, Terrence's total points were 20 less than Shelly's total. This means that Terrence's total points can be calculated by subtracting 20 from Shelly's total points. Since Shelly earned 90 points on each task, her total points would be 90 multiplied by the number of tasks she completed.
So, the expression '90x - 20' represents Terrence's total points in the game, where 'x' represents the total number of tasks that Terrence completed. By substituting the value of 'x' with the number of tasks Terrence completed, we can calculate his total points.
Therefore, the correct answer is: The total number of tasks Terrence completed.
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Solve for y:
4x-8y=32
Answers
Answer: y = -4 + x/2
Step-by-step explanation:
Use math vocabulary to explain why you think this number does not belong in the group. Be sure to write in complete sentences.
Answers
Answer:
because like for example the given number are 01 12
23 34
or 12233445566778 and etc.
your situation are 4556 and 3224 because are not ordered pair
when will the height be 37 feet?
Answers
As the tree grows 1& 3/4 feet per year, it will take 9 years to reach a height of 37 feet.
What is division?Division is a basic procedure in which an integer is divided. It's best to imagine of it as a number of things being distributed among a particular number of persons, such as in the previous example. In mathematics, division is the process of dividing a number into equal parts and determining how many equal parts can be made. For instance, dividing 15 by 3 implies dividing 15 into three equal groups of five. Dividend Divisor = Quotient + Remainder is the formula for dividing two numbers. The dividend is the number that is being divided in this case. The divisor is the number, which divides the number (dividend) into equal parts.
Here,
37 - 21 and 1/4 = 36 and 4/4 - 21 and 1/4 = 15 and 3/4 = 63/4
63/4 divided by 1 and 3/4 = 63/4 divided by 7/4 = 63/4 * 4/7 = 9 years
It will take 9 years to reach at the height of 37 feet as the tree grow 1& 3/4 feet per year.
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Complete question:
A tree grow 1& 3/4 feet per year. How long will it take the tree to grow from a height of 21 & 1/4 feet to a height of 37 feet?
2 How and why would lighting and ventilation needs
differ between the dining area and the kitchen used to prepare food
in a university dining center?
Divide into groups of two to three people. Visit t
Answers
Regular maintenance and inspections are essential to ensure the systems are functioning effectively and meeting the required standards.
The dining area and the kitchen used to prepare food in a university dining center have different lighting and ventilation needs due to their distinct purposes and requirements. Here's how and why their needs may differ:
1. Lighting:
- Dining Area: The dining area is primarily a space for eating and socializing. It requires comfortable and pleasant lighting to create a welcoming and inviting atmosphere.
The lighting should be evenly distributed to ensure visibility and allow people to see their food and interact with others. Warm and soft lighting can enhance the ambiance and promote a relaxed dining experience.
- Kitchen: The kitchen is a functional area where food is prepared, cooked, and plated. It requires bright and focused lighting to ensure proper visibility and facilitate safe and efficient food handling.
Bright task lighting is necessary for food preparation areas, cooking stations, and cutting surfaces to ensure accuracy, cleanliness, and food safety. Additionally, proper lighting helps staff identify food quality, monitor cooking processes, and prevent accidents.
2. Ventilation:
- Dining Area: The dining area typically requires adequate ventilation to maintain a comfortable and pleasant environment for diners. Ventilation systems in the dining area primarily focus on maintaining air circulation, controlling temperature, and removing odors.
- Kitchen: The kitchen, on the other hand, has more stringent ventilation requirements due to the nature of food preparation. A commercial kitchen generates heat, steam, smoke, and food odors, which can affect air quality and pose health risks if not properly managed.
The kitchen requires specialized ventilation systems, such as exhaust hoods, fans, and ductwork, to remove heat, steam, and grease-laden air. This helps maintain a clean and safe working environment, minimize odors, control humidity, and prevent the buildup of harmful contaminants.
It's important to note that specific regulations and guidelines may vary depending on local health and safety standards. Therefore, it's crucial for dining centers in universities to comply with applicable codes and regulations regarding lighting and ventilation in both the dining area and the kitchen.
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HELP is it a, b, c , or d?
Answers
Answer:
B
when you input the first value of y which is -2
-2+2=(4/5)(x+9)
0=(4x+36)/5
multiply both sides by 5
0=4x +36
4x =-36
divide both sides by 4
x=-9
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State the range of the relation.
{(3,-2),(4, -3), (5, -4), (6, 0) }
Answers
Explain: the y variables are always the range, if they repeat only list one of them ☺️
help me plsssssssss
Answers
Answer: 13. 30
Step-by-step explanation:
13. Area = 18x * 10y = 180xy
Length = 6th
With ?
180xy = 6xy x width
180 x/6xy
Width = 30
14. 3^(9-5)= 3^4 = 81 the truck weighs 81 times as the driver
3^5
The following table specifies the joint distribution of Age group (3 levels) and Education level (4
levels) for U.S. adults.
Education Level
Age group Not HS grad HS only Some college College grad
25–44 77 101 99 123
45–64 123 171 46 60
65+ 101 59 20 20
(a) Summarize the association between these variables by reporting the 2 ×3 table of local odds
ratios
θij = πij πi+1,j+1
πi,j+1πi+1,j
for i = 1,2 and j = 1,2,3 .
Identify the odds ratio corresponding to the strongest of these pairwise associations, and
carefully interpret that odds ratio.
(b) Summarize the association between these variables by reporting the 2×3 table of odds ratios
θij = πij π14
πi4π1j
for i = 2,3 and j = 1,2,3 ;
that is, treating the youngest age group and highest education level as baseline categories
for comparison. Identify the odds ratio corresponding to the strongest of these pairwise
associations, and carefully interpret that odds ratio.
Answers
(a) 25-44
(b) 45-64
(a) The 2×3 table of local odds ratios for the association between age group and education level is as follows:
The odds ratio corresponding to the strongest of these pairwise associations is 1.78, which indicates that adults aged 45-64 are 78% more likely to have a high school diploma than adults who are 25-44.
(b) The 2×3 table of odds ratios for the association between age group and education level when treating the youngest age group and highest education level as the baseline categories for comparison is as follows:
The odds ratio corresponding to the strongest of these pairwise associations is 1.48, which indicates that adults aged 25-44 are 48% more likely to have a high school diploma than adults aged 45-64.
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exponential equations
Answers
The solutions of the logarithmic equations are:
i) Ln(5x) = 7 if x = 219.32
ii) Logₓ(25) = 2 if x = 5
How to solve the logarithmic equation?Here we want to solve the logarithmic equation:
Ln(5x) = 7
If we apply the exponential function in both sides, we will get:
exp(ln5x)) = exp(7)
5x = exp(7)
x = exp(7)/5 = 219.32
The second equation is:
Logₓ(25) = 2
Remember that logₐ(x) = ln(x)/ln(a)
Then we can rewrite:
Logₓ(25) = 2
ln(25)/ln(x) = 2
ln(25)/2 = ln(x)
exp(ln(25)/2) = x
5 = x
These are the solutions.
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Find the value of the variable.
20
12
A. 10
В. 13
C. 16
D.18
Answers
Answer:
option c.
by Pythagoras theorem.
hypotenuse²=height ²+base²
20²=x²+12²
400=x²+144
400-144=x²
256=x²
256½=x
16=x