The transformation of the function g ( x ) = | x + 4 | - 2 is
Horizontal shift : Left by 4 units
Vertical shift : Down by 2 units
How does the transformation of a function happen?
The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs)
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units: y=f(x+c) (same output, but c units earlier)
Right shift by c units: y=f(x-c)(same output, but c units late)
Vertical shift:
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
Stretching shift:
Vertical stretch by a factor k: y = k × f(x)
Horizontal stretch by a factor k: y = f(x/k)
Given data ,
Let the parent function be f ( x )
The value of f ( x ) = | x |
Now , the transformation from the first function f ( x ) to g ( x ) is of the form
g ( x ) = | x + 4 | - 2
And , transformation is
y = a | x - h | + k
where the values of y , a , x , h and k are
The value of a = 1
The value of h = -4
The value of k = -2
Now , The Horizontal shift is given by
Left shift by c units: y=f(x+c) (same output, but c units earlier)
Right shift by c units: y=f(x-c)(same output, but c units late)
So , h = -4 means left shift by 4 units
And , The Vertical shift is given by
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
So , k = -2 means down shift by 2 units
Hence , The transformation of the function g ( x ) = | x + 4 | - 2 is
Horizontal shift : Left by 4 units
Vertical shift : Down by 2 units
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What value does each equation need to be multiplied by in order to eliminate the y-terms?
Equation 1: 6x − 5y = -4
Equation 2: 4x + 2y = 28
Please Help, I don't get it
Equation 1 needs to be multiplied with + 2
Equation 2 needs to be multiplied with + 5.
Step-by-step explanation:
Here, the given system of equation is given as:
Equation 1 : 6 x − 5 y = -4
Equation 2: 4 x + 2 y = 28
Here, in equation 1, the coefficient of y = - 5
Also, in the equation 2, the coefficient of y = + 2
Now, in order to eliminate the y coefficients,
Coefficient of y in 1 = - Coefficient of y in 2
Now, to make -5 and + 2 to eliminate each other,
Multiply -5 with 2, we get -5 x 2 = -10
And Multiply the coefficient + 2 with 5, we get +2 x 5 = + 10
The new coefficient of y is equation 1 = - 10 y
The new coefficient of y in equation 2 = + 10 y
They will cancel out each other, when both equations are ADDED.
Hence, equation 1 needs to be multiplied with + 2
and the equation 2 needs to be multiplied with + 5.
does the sequence { y k } converge? recall that there are four notions of convergence of random variables viz., almost sure, mean square, in probability and in distribu- tion. you should answer this question for each of these four modes of convergence. whenever you have convergence, also indicate what the limiting random variable is
Consider a sequence of random variables X1, X2, X3, ⋯ that is defined on an underlying sample space S. For simplicity, let us assume that S is a finite set, so we can write
S = {s₁, s₂,⋯,sₙ }.
Remember that each Xₙ is a function from S to the set of real numbers. Thus, we may write
Xₙ (sₐ) = xₙₐ, for a=1,2,⋯,k.
After this random experiment is performed, one of the sₐ' s will be the outcome of the experiment, and the values of the Xₙ's are known. If sₐ is the outcome of the experiment, we observe the following sequence:
x₁ₐ ,x₂ₐ,x₃ₐ,⋯.
Mean Square Convergence:Let [Xₙ] be a sequence of square integral random variables defined on a sample space Omega. We say that [Xₙ] is mean-square convergent (or convergent in mean-square) if and only if there exists a square integral random variable X such that
[tex]\lim_{n \to \infty} E[ X_{n} - X^{2} ][/tex]
Distribution Convergence:Convergence in distribution is in some sense the weakest type of convergence. All it says is that the CDF of Xₙ's converges to the CDF of X as n goes to infinity. It does not require any dependence between the Xₙ's and X. We saw this type of convergence before when we discussed the central limit theorem. To say that Xₙ converges in distribution to X, we write:
Xₙ →d X.
Probability Convergence:Convergence in probability is stronger than convergence in distribution. In particular, for a sequence X₁, X₂, X₃, ⋯ to converge to a random variable X, we must have that P(|Xₙ−X|≥ϵ) goes to 0 as n→∞, for any ϵ>0. To say that Xₙ converges in probability to X, we write:
Xₙ →p X.
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11. BC
5/4y-1
B
A
7/3y-2
C
Answer:
[tex]\frac{2}{13}[/tex]
Step-by-step explanation:
All the sides have equal lengths. Set the two sides equal to each other and solve for y
[tex]\frac{5}{4}[/tex]y + 1 = [tex]\frac{7}{3}[/tex]y -2 I am going to clear the fractions by multiplying through by 12
[tex](\frac{12}{1})[/tex][tex]\frac{5}{4}[/tex] y + (12)(-1) = [tex](\frac{12}{1})[/tex][tex]\frac{7}{3}[/tex] y - (12)2
15y - 12 = 28y - 24 Subtract 15y from both sides
-12 = 13y - 24 Add 24 to both sides
12 = 13y Divide both sides by 13
[tex]\frac{12}{13}[/tex] = y
Plug 12/13 into the expression for either side to find the length of BC. All the sides have the same length
[tex]\frac{7}{3}[/tex][tex](\frac{12}{13})[/tex] - 2
[tex]\frac{28}{13}[/tex] - [tex]\frac{26}{13}[/tex] = [tex]\frac{2}{13}[/tex]
Match each item with the correct unit price.
1. 78 cents each 20 for $1.56
2. 40 cents each 2 for one dollar
3. $1.05 each 5 at $3.90
4. 7.8 cents each $3.78 for 6
5. 63 cents each 1 for $1.58
The correct unit prices are,
1. 20 for $1.56 = A. 7.8 cents each
2. $3.78 for 6 = B. 63 cents each
3. 2 1/2 for one dollar = C. 40 cents each
4. 5 at $3.90 = D. 78 cents each
5. 1 1/2 for $1.58 = E. $1.05 each
From the given cases;
1. Given that 20 things cost $1.56,
So, the price of one item is = $1.56/20
= $0.078.
Cents for every dollar,
So, $0.078 equals $0.078 * 100
= 7.8 cents.
2. Since the cost of six products is $3.78,
The cost of one item is 3.78/6
= $0.63.
Cents for every dollar,
Thus, $0.63 equals $0.63 * 100
= 63 cents.
3. 2 1/2 = 5/2 = 1 as a price
So, the price of one item is equal to 2/5 of a dollar, or 100 cents.
$2/5 equals 2/5 * 100, or 40 cents.
4. Given that the price of 5 things is $3.90
The price of 1 item is 3.90/5, or $0.78.
Cents for every dollar
So, $0.78 = $0.78 * 100 = 78 cents.
5. Cost of 1 1/2 = 3/2 = $1.58
So, cost of 1 item = 1.58/(3/2)
= 1.05
Hence, these are the solutions for the given cases.
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can someone help me with this problem please…? ;))
Answer:
B.
Process of elimination.
A is incorrect because 6 out of 10 people is 60 percent.
C is wrong because if you consider just half (50 percent) of 65, you'll get 32.5 . In order to get 65 percent, C would have to be over 32.5, and 10 is not.
D is wrong because once again, half (50 percent) of 13 is 6.5 and in order to get 65 percent, D would have to be over 6.5, and 5 is not.
if the set s consists of five consecutive positive integers, what is the sum of these five integers? the integer 11 is in s, but 10 is not in s. the sum of the even integers in s is 26.
Answer:
sum = 65
Step-by-step explanation:
You want the sum of the set of 5 consecutive positive integers such that the sum of the even integers in the set is 26.
SolutionThe sum of even integers will be a multiple of 3 if the middle integer of the set is even. Here, that sum is 26, not a multiple of 3. Hence the middle integer of the set is 26/2 = 13, and the sum of the set is 13·5 = 65.
The sum of the five integers is 65.
__
Additional comment
When working "consecutive integer" problems, it is often useful to think in terms of the average of the integers, the middle one of an odd-length set, or the number halfway between the two middle ones of an even-length set.
A set of 5 integers will have either 3 odds and 2 evens, or 3 evens and 2 odds. The set here obviously does not have 3 even integers (whose sum would be 3 times the middle one).
The set is s = {11, 12, 13, 14, 15}. 10 is not in the set, but 11 is. The sum of evens is 12+14=26.
Find the equation of a line that passes through the points (1,-5) and (3,-6). Leave your answer in the form y = m x + c.
what is the remainder when the positive integer n is divided by the positive integer k, where k > 1 ? (1) n
The remainder will be less than k, when the positive integer n is divided by the positive integer k, where k > 1.
What are integers?Positive, negative, and zero are all examples of integers. The Latin word "integer" signifies "whole" or "intact." As a result, fractions and decimals are not included in integers. In this essay, we will learn more about integers, their definition, and their characteristics.
All whole numbers and negative numbers are considered integers. This means that if we combine negative numbers with whole numbers, a collection of integers results.
An integer, which can comprise both positive and negative integers, including zero, is a number without a decimal or fractional portion. Integers include things like -5, 0, 1, 5, 8, 97, and 3,043. Z is a set of integers.
Hence, The remainder will be less than k, when the positive integer n is divided by the positive integer k, where k > 1.
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The map of Texas shows several major cities in Texas. On the map 1 inch (in) represents
75 miles (mi). Use the map to answer questions 1-3.
Answer:
1. 150mi
2. 2&1/2
3. He needs to know how many miles is each city.
Step-by-step explanation:
you are the manager of a restaurant for a fast-food franchise. last month, the mean waiting time at the drive-through window for branches in your geographical region, as measured from the time a customer places an order until the time the customer receives the order, was 3.6 minutes. you select a random sample of 81 orders. the sample mean waiting time is 3.45 minutes, with a sample standard deviation of 0.9 minute. complete parts (a) and (b) below. question content area bottom part 1 a. at the 0.05 level of significance, is there evidence that the population mean waiting time is different from 3.6 minutes? state the null and alternative hypotheses.
There is not evidence that the population mean waiting time is different from 3.6 minutes.
What is the p-value?
A statistical measurement known as a p-value is employed to check a hypothesis' validity against actual data. A p-value calculates the likelihood of getting the outcomes that were observed, presuming that the null hypothesis is correct. The statistical significance of the difference that was found increases with decreasing p-value.
From the question, we know that the size (n), the mean (x), and the standard deviation (s) of the sample are 81, 3.45 minutes and 0.9 minutes. Additionally, we are going to decide if the waiting time is different or not from 3.6 minutes, so the null and alternative hypotheses are:
H0: m=3.6
H1: m≠3.6
Where m is the mean of the population.
Then, we don't need to be concerned about the shape of the population distribution because the value of the n is bigger than 30 and we can use the statistic z as:
[tex]z = \frac{x-m}{\frac{a}{\sqrt{n} } }[/tex]
So, replacing the values, the test statistic is:
[tex]z = \frac{3.45 - 3.6}{\frac{0.9}{\sqrt{81} } }[/tex]
= 2.50
On the other hand, the p-value for this test is calculated as:
p-value = 2P(z >2.50) = 2(0.0668) = 0.134
Taking into account that the p-value is bigger than the level of significance 0.01, the null hypothesis is not rejected, and there is not evidence that the population mean waiting time is different from 3.6 minutes.
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Please help i really need it only number 4
Answer:
(2) 11
Step-by-step explanation:
You want the area of the triangle with vertices (1, 3), (3, -1), and (-2, -2).
Pick's theoremPick's theorem says the area of a figure drawn on a grid can be found by counting the grid points on the boundary (b) and the interior grid points (i). Then the area is ...
A = (b/2) +i -1
This figure has a boundary grid point at (2, 1) in addition to the three vertices. So, b = 4.
There are 10 interior grid points, a number that can be arrived at by counting them. The numbers in each row, starting from the bottom, are 4, 3, 2, 1.
Then the area is ...
A = (4/2) +10 -1 = 11
The area of the triangle is 11 square units.
From CoordinatesThe area can be computed from the coordinates by the formula ...
A = 1/2|x1(y2 -y3) +x2(y3 -y1) +x3(y1 -y2)|
A = 1/2|1(-1 -(-2)) +3(-2 -3) +(-2)(3 -(-1))| = 1/2|1 -15 -8| = 11
The area is 11 square units.
Using geometryThe triangle can be bounded by a square 5 units on a side. The triangle area is smaller than the square area by the sum of the three triangles cut from the corners of the square. Clockwise from left, those triangle areas are ...
1/2(5·3) +1/2(4·2) +1/2(1·5) = 1/2(15 +8 +5) = 14
Then the area of the triangle of interest is ...
5² -14 = 11
The area of the triangle is 11 square units.
Using trigonometryThe angle the bottom edge makes with the horizontal is ...
arctan(1/5) ≈ 11.3099°
and the length of that edge is ...
5/cos(11.3099°) ≈ 5.099
The angle the left side makes with the horizontal is ...
arctan(5/3) ≈ 59.0362°
and the length of that edge is ...
3/cos(59.0362°) ≈ 5.831
The area of the triangle with sides 'a' and 'b' and angle C between them is ...
Area = 1/2(ab·sin(C)) = 1/2(5.099·5.831·sin(59.0362° -11.3099°)) = 11
The area of the triangle is 11 square units.
__
Additional comment
Side lengths could also be determined using the Pythagorean theorem, and the angle between any two of them could be found using the Law of Cosines.
Heron's formula could be used to find the area from the three side lengths.
The Central Limit Theorem states that The distribution of the population mean p will be about normal provided that the sample size n is sufficiently large If the sample size n is large, then z follows a standard normal distribution, provided that the population is normally distributed The sample mean X will always equal the population mean / when the sample size n is large enough_ As the sample size n gets larger and larger, the sampling distribution of the sample mean X is less concentrated around the central value The sampling distribution of the sample proportion p will be approximately normal provided that the population is normally distributed The sampling distribution of the sample mean x will be about normal provided that the sample size n is sufficiently large
the standard deviation of the sample means:
σ(x) = σ/[tex]\sqrt{n}[/tex]
The central limit theorem states that if you have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement text annotation indicator, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large (usually n > 30). If the population is normal, then the theorem holds true even for samples smaller than 30. In fact, this also holds true even if the population is binomial, provided that min(np, n(1-p))> 5, where n is the sample size and p is the probability of success in the population. This means that we can use the normal probability model to quantify uncertainty when making inferences about a population mean based on the sample mean.
For the random samples we take from the population, we can compute the mean of the sample means:
μ (x) = μ
and the standard deviation of the sample means:
σ(x) = σ/[tex]\sqrt{n}[/tex]
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Product filling weights are normally distributed with a mean of 350 grams and a standard deviation of 10 grams. a. Develop the control limits for the $\oveline x$ chart for samples of size 10, 20, and 30. b. What happens to the control limits as the sample size is increased? c. What happens when a Type I error is made? d. What happens when a Type II error is made? e. What is the probability of a Type I error for samples of size 10, 20, and 30? f. What is the advantage of increasing the sample size for control chart purposes? What error probability is reduced as the sample size is increased?
The control limits for the x chart for a sample of size 10,
a-Develop the control limits for the $\oveline x$ chart for samples of size 10, 20, and 30
UCL = 359.48
LCL = 340.51
b. What happens to the control limits as the sample size is increased
The control limits for the x chart for a sample of size 20,
UCL = 356.71
LCL = 343.29
c-What happens when a Type I error is made
The control limits for the x chart for a sample of size 30,
UCL = 355.47
d- What happens when a Type II error is made? e. What is the probability of a Type I error for samples of size 10, 20, and 30
LCL = 344.52
Possibility is referred to as probability. This branch of mathematics deals with the occurrence of a random event.
The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events.
Probability generally refers to the degree to which something is likely to occur.
This fundamental theory of probability, which also applies to the probability distribution, can help you comprehend the possible outcomes for a random experiment. Gonna determine how likely something is to occur, use probability. Many things are hard to predict with 100% certainty. We can only anticipate the possibility of an event occurring using it, or how likely it is.
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Determine the distance between the points (−1, −4) and (−9, −8).
square root of 208 units
square root of 166 units
square root of 124 units
square root of 80 units
The required distance between the points (−1, −4) and (−9, −8). is the square root of 80 units. Option D is correct.
Given that,
The distance between points (−1, −4) and (−9, −8) is to be determined.
Distance is defined as the object traveling at a particular speed in time from one point to another.
here,
D = √[[x₂ - x₁]² + [y₂+ - y₁]²]
Substitute the value in the above equation,
D = √[[-9 + 1]² + [-8 + 4]²]
D = √[[-8]² + [ 4]²]
D = √[64 + 16]
D = √80
Thus, the required distance between the points (−1, −4) and (−9, −8). is the square root of 80 units. Option D is correct.
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Answer:
the person above is correct, the answer is D "[tex]\sqrt{80[/tex] units"
Step-by-step explanation:
I took this exam and got this answer right, hope this helps :))
central limit theorem: nationally, the composite score of students taking the act (american college testing) college entrance examination has a normal distribution with a mean of 18.0 and a standard deviation of 6.0. at kent roosevelt high school, 36 seniors take the test. assume the act scores at this school have the same distribution as national scores and the students who take the act test are considered as a simple random sample.a. Then the average ACT score of the sample of Kent Roosevelt students who took the test has a distribution function b. with mean c. and standard deviation (standard error)
The standard deviation of the sampling distribution of the average (sample mean) score for the 36 students = 1
What is standard deviation?
The standard deviation of the sampling distribution of mean is given by :- σₓ = σ/√n, where = population standard deviation and n= sample size.
According to the given question:
The scores of individual students on the American college testing program composite college entrance examination have a normal distribution with mean 18.0 and standard deviation 6.0. at kent roosevelt high.
i.e. μ = 18.0, σ = 6.0
Sample size : n= 36
Then, the standard deviation of the sampling distribution of the average (sample mean) score for the 36 students will be :-
σₓ = 6/√36 = 1
Hence, The standard deviation of the sampling distribution of the average (sample mean) score for the 36 students = 1
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Solve the equation for v.
0.5v + 0.06 < 3.46
v > 1.8
v < 1.8
v > 6.8
v < 6.8
Answer:
[tex]\boxed{\tt v < 6.8}[/tex]
Step-by-step explanation:
[tex]\tt 0.5v+0.06 < 3.46[/tex]
Multiply both sides by 100:-
[tex]\tt 0.5v\times\:100+0.06\times\:100 < 3.46\times\:100[/tex]
[tex]\tt 50v+6 < 346[/tex]
Subtract 6 from both sides:-
[tex]\tt 50v < 340[/tex]
Divide both sides by 50:-
[tex]\tt \cfrac{50v}{50} < \cfrac{340}{50}[/tex]
[tex]\tt v < \cfrac{34}{5}[/tex]
Or
[tex]\tt v < 6.8[/tex]
Therefore, your answer is v < 6.8!!! :)
______________________
Hope this helps!
Have a great day!
You are separating 16 tomatoes equally among 3 baskets.
Drag tomatoes to show how many tomatoes will be in each basket and how many tomatoes will be left over.
If the bond angle between two adjacent hybrid orbitals is 180°, which is the hybridization?.
If the bond angle between two adjacent hybrid orbitals is 180 degree then the hybridization is sp hybridization , it forms linear molecules with an angle of 180°.
Hybridization is a theory that is used to explain certain molecular geometries that would have not been possible otherwise.
In sp hybridization, the s orbital of the excited state carbon is mixed with only one out of the three 2p orbitals. It is called sp hybridization because two orbitals (one s and one p) are mixed.
The resulting two sp hybrid orbitals are then positioned at 90 degree and 180 degree, respectively, with the two 2p unhybridized orbitals:
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A type of green paint us made by mixing 2 cups of yellow with 3.5 cups of blue. a. Find a mixture that will make the same shade of green but larger amount.
Step-by-step explanation:
easiest example : multiply both (it is important to do it to both) by 2 :
2×2 = 4 cups of yellow
3.5×2 = 7 cups of blue
will make the same shade of green, as the mixing ratio is the same.
just, instead of 5.5 cups, it gives us 11 cups of green paint (surprise, surprise, this is also twice as much) .
What number is 0.44 more than 0.25?
Answer: 0.69
Step-by-step explanation:
0.44 + 0.25 = 0.69
The correct answer is [tex]\boxed{0.69}[/tex]
How did figure out this?For this question we will be adding the numbers given.
Given:
[tex]0.44\\0.25[/tex]
Therefore, the equation is:
[tex]\boxed{0.44 +0.25}[/tex]
Adding the given numbers 0.44 and 0.250.44 + 0.25 = 0.69Therefore, the correct answer is [tex]\boxed{0.69}[/tex]
You purchase 5 pounds of apples and 2 pounds of oranges for $9. Your
friend purchases 5 pounds of apples and 6 pounds of oranges for $17.
a. Write a system of linear equations that represents this situation.
b. What is the price per pound for apples?
c. What is the price per pound for oranges?
Answer:
8 pounds of oranges for $12.
Step-by-step explanation:
What is fractions for this pls help
Answer:
Step-by-step explanation:
1 1.5/2
an architect is making a floor plan for a rectangular gymnasium. if the gymnasium is 80 feet long and 60 feet wide, what will the distance be between opposite corners?
In the gym, there are 100 feet between the opposing corners.
Given,
The length of the rectangular gymnasium = 80 feet
The width of the rectangular gymnasium = 60 feet
We have to find the distance between opposite corners of the gymnasium;
Here,
The distance between opposite corners of the gymnasium is the diagonal of the rectangle;
Diagonal of rectangle = [tex]\sqrt{width^{2} + length^{2} }[/tex]
Then,
Diagonal = [tex]\sqrt{80^{2} +60^{2} }[/tex]
Diagonal = [tex]\sqrt{6400+3600}[/tex]
Diagonal = √10000
Diagonal = 100 feet
That is,
The distance between the opposite corners if the gymnasium is 100 feet.
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Jessica reduced the size of a rectangle to a height of 2 inches. What is the new width if it
was originally 4 inches tall and 8 inches wide?
The new width is 4 inches.
Step-by-step explanation:The Property of Equality:Since Jessica reduced one side (the length), that means that she also reduced the other side (the width) by the same number:
Original length:
4
New length:
2
4 ÷ 2 = 2
Original Width:
8
New Width:
4
8 ÷ 2 = 4
Solution:4 inchesI hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!
Answer:
2/12 = 1/6
24 * 1/6 = 4
or
12/24 = 2/x
12 x = 48
x = 4
or the original width was twice the length
twice 2 is 4
maybe
help guys i don’t understand
Answer:
Step-by-step explanation:
You need to set the problem up like this:
VX=VW+WX. 4x=3x+5subtract 3 from both sides. x=5because 'x' equals 5, plug that 4(5)=3(5)+5back in for all the 'x's
simplify the equation 20=20The length of the line segmentshould be 20
A computer store buys a computer system at a cost of $456.60. The selling price was first at 776 , but then the store advertised a 10% markdown on the system.Members of the store's loyalty club get an additional 10% off their computer purchases. How much do club members pay for the computer with their discount?
Answer: The selling price was at first $776 but then the store advertised a 30% markdown on the system. Find the current sale price.
Step-by-step explanation:
$776 - (30% of $776) = $ x :: current sale price
776 - 776 * 0.3 = x
776 * (1 - 0.3) = x
776 * 0.7 = 543.20
Current sale price for the computer system is $543.20.
Place the figures in order from least volume to greatest volume.
At a real estate agency, an agent sold a house for $348000. The commission rate is 7.5% for the real estate agency and the commission rate for the agent is 25%
of the amount the real estate agency gets. How much did the agency make on the house? How much did the agent earn in commission?
The amount which the agency makes on the house as described is; $26,100.
The amount earned in commission by the agent is; $6,525.
What is the amount made by the agency on the house?It follows from the task content that the house in discuss was sold for $348,000.
Also, since the commission rate for the real estate agency is; 7.5%.
It therefore follows that the commission earned by the real estate agency is;
7.5% of 348,000 = 0.075 × 348,000
= $26,100.
Also, since the commission rate for the agent is 25% of the agency's commission.
Therefore, the amount earned by the agent is;
25% of 26,100 = 0.25 × 26,100
= $6,525.
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a city hosted a music festival that included three concerts. according to the sales database, 28% of the audience attended the first concert, 42% attended the second one, 30% attended the third one, 80% attended at least one of the three concerts, 10% attended the first and second ones, 8% attended the first and third ones, and 7% attended the second and third ones. find the probability that a randomly selected audient attended all the concerts? assume event a: an audient attended the first concert; event b: an audient attended the second one; event c: an audient attended the third one.
Probability that randomly selected audient attend all the concerts is 0.05.
What is probability?
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.P(A) = 28/100 = 0.28
P(B) = 42/100 = 0.42
P(C) = 30/100 = 0.30
P(A∩B) = 10/100 = 0.10
P(A∩C) = 8/100 = 0.08
P(B∩C) = 7/100 = 0.07
P(A∪B∪C) = 80/100 = 0.80
P(A∩B∩C) = ?
P(A∪B∪C) = P(A) + P(B) + P(C) - P(A∩B) - P(A∩C) - P(B∩C) + P(A∩B∩C)
P(A∩B∩C) = - 0.28 - 0.42 - 0.30 + 0.10 + 0.08 + 0.07 + 0.80
= 0.05
Probability that randomly selected audient attend all the concerts is 0.05.
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1. this question concerns the group z26 under addition modulo 26. a) list the elements of this group. b) is this group cyclic? c) is 16 a generator of this group? what about 5?
The element of this group is {0, 1, 2, 3, ...., 25}, this group is a cyclic group, and 16 is not a generator for this group but 5 is a generator for this group.
How to find element of group under addition modulo?
[tex]Z_{26}[/tex] ≡ Group of integers under addition modulo 26
addition modulo is all addition of integer in ordinary way than remove integral multiple. For example, addition modulo a+mb is a+b than remove all integral multiple m and the result is lower than m (residue).
a) The elements of this group is all the integers remainder after mod 26. So,
x = k (mod 26) where 0 ≤ k < 26
or we can write each of them as {0, 1, 2, ..., 23, 24, 25}
b) Cyclic group is a group that is generated by 1 element. Since, the group is integers under addition modulo with all integers can be generated by adding 1 repeatedly, so the group [tex]Z_{26}[/tex] is cyclic group.
c) As 1 ∈ [tex]Z_{26}[/tex] but there is no m ∈ N such that [tex]16^m[/tex] = 1, but for [tex]5^m[/tex] is
{0, 5, 10, 15, 20, 25, 4, 9, 14, 19, 24, 3, 8, 13, 18, 23, 2, 7, 12, 17, 22, 1, 6, 11, 16, 21}
or in simply way, we can say there is m ∈ N for [tex]5^m[/tex] = 1. So, 16 is not generator of this group, but 5 is generator of this group.
Thus, the number of {0, 1, 2, 3, ...., 25} is the element for this group, cyclic group is a type of this group, and 5 is a generator for this group but 16 is not a generator for this group.
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