The descending order of the multiplied polynomial is 4x² - 3x + 8xy - 6y
The word polynomial in math refers the algebraic expression in which the exponents of all variables should be a whole number.
Here we have given the polynomial l (x + 2y)(4x - 3).
And we need to do the multiplication operation on it and then write your answer in descending order of x.
AS per the following formula, the multiplication of the polynomial is calculated as,
=> (a + b) ( c + d) = (ac + ad + bc + bd)
Here let us consider a = x and b = 2y, c = 4x and then d = -3
Then the resulting value after the multiplication, it can be written as,
=> (x(4x) + x(-3) + 2y(4x) + 2y(-3))
When we simplify this one then we get
=> 4x² - 3x + 8xy - 6y
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suppose man paints on a she paper 25 in wide by 15 in high. He then places this sheet on a mat so that a uniform wide strip of the mat shows all around the picture. The perimeter of the mat is 96 in How wide is the strip of the mat showing around the picture?
When the mat's perimeter is 96 inches, the strip that shows around the picture is 4 inches broad.
What is perimeter?The perimeter of a shape is the distance around its edge. The perimeter of a form is the length of its contour. To calculate the perimeter of a rectangle or square, sum the lengths of all four sides. The perimeter of a shape is the distance around its exterior. Perimeter is calculated by summing the lengths of all the sides of a form.
Here,
length of paper, l=25 inch
width of paper, w=15 inch
perimeter=96 inch
Let x be the strip of mat,
l=25+2x
w=15+2x
perimeter=2(l+w)
96=2*(25+2x+15+2x)
48=40+2x
2x=8
x=4 inch
The strip of the mat showing around the picture is 4 inch wide when the perimeter of the mat is 96 inch.
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Assume this year's flu vaccine has a 80% chance of being effective. If the vaccine is given to 337 randomly selected people, answer the following.
a) The wording for the random variable is given as follows:
n X = the number of 337 randomly selected people who get the vaccine and do not get the flu;
b) The symbol is: n = 337.
c) The symbol is: p = 0.8.
d) P(X = 265) = 0.0426.
e) P(X < 265) = 0.2451.
f) P(X > 265) = 0.7123.
g) P(X = 268) = 0.0545.
h) P(X < 268) = 0.3859.
i) P(X > 268) = 0.5596.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].The parameters for the binomial distribution in this problem are given as follows:
n = 337, p = 0.8.
Hence the mean and the standard deviation for the approximation are given as follows:
[tex]\mu = 337 \times 0.8 = 269.6[/tex][tex]\sigma = \sqrt{337 \times 0.8 \times 0.2} = 7.34[/tex]Using continuity correction, the probability that exactly 265 people do not get the flu is the p-value of Z when X = 265.5 subtracted by the p-value of Z when X = 264.5.
X = 265.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (265.5 - 269.6)/7.34
Z = -0.56
Z = -0.56 has a p-value of 0.2877.
X = 264.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (264.5 - 269.6)/7.34
Z = -0.69
Z = -0.69 has a p-value of 0.2451.
Hence:
0.2877 - 0.2451 = 0.0426.
Then:
e) P(X < 265) = 0.2451 -> p-value of Z when X = 264.5.
f) P(X > 265) = 1 - 0.2877 = 0.7123 -> one subtracted by the p-value of Z when X = 265.5.
For exactly 268, we have the same logic as follows:
X = 265.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (268.5 - 269.6)/7.34
Z = -0.15
Z = -0.15 has a p-value of 0.4404.
X = 267.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (267.5 - 269.6)/7.34
Z = -0.29
Z = -0.29 has a p-value of 0.3859.
Hence:
0.4404 - 0.3859 = 0.0545.
Then:
h) P(X < 268) = 0.3859 -> p-value of Z when X = 267.5.
i) P(X > 268) = 1 - 0.4404 = 0.5596.
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Classify the polynomial 5x3 + 4x − 2 by degree.
A. cubic
B. constant
C. quartic
D. linear
Classifying the polynomial 5x³ + 4x − 2 by degree gives a degree of
A. cubicHow to determine the degree of the polynomialAn equation made up of variables, exponents, and coefficients along with operations and the equal sign is known as a polynomial equation.
Sums of terms of the form kxⁿ, where k is any number and n is a positive integer, make up polynomials.
The degree refers to the highest exponents which is a positive integer
examining the function the degree is 3 and referred to as cubic
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The table to the right shows binned data for the percentages of high school graduates who took a national ___ in 2016 among the 50 states and the District of Columbia. Make a histogram of the data.Test Takers by State Percentage of high school graduates Number of states s 20% 2 21-40% 13 41-60% 4 61-80% 7 81-100% 25 O A. 0 B. O C. D. 30- a Number of states Number of states 0 0 100 Percentage of students 100 Percentage of students 0 100 Percentage of students 0- 0 100 Percentage of students
Number of states , 100 Percentage of students 0- 0 100 Percentage of students 20 21- 40 41- 60 61- 80 81- 100
1. Draw a horizontal axis with percentages of students (0 - 100%) marked along the axis.
2. Draw a vertical axis with number of states (0 - 25) marked along the axis.
3. Divide the horizontal axis into sections, with each section corresponding to one of the percentage ranges in the table (20%, 21-40%, 41-60%, 61-80%, 81-100%).
4. For each section, draw a rectangle with a height that corresponds to the number of states in that range. For example, for the 81-100% section, the rectangle should have a height of 25.
5. Label each rectangle with the corresponding percentage range.
The final result should be a histogram that shows the percentage of high school graduates who took a national test in 2016 among the 50 states and the District of Columbia.
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the graph below shows two different types of plans published by a cell phone company. ryan claims that the cost of plan a and plan b differ a lot. which statement best explains why ryan was misled by the graph? a.) the scale of intervals on the horizontal axis is inconsistent. b.) the graph of plan a shows a gradual increase in price. c.) the graph of plan b shows a rapid increase in price. d.) the scale of intervals on the vertical axis is inconsistent.
Answer:
d.) the scale of intervals on the vertical axis is inconsistent.
Step-by-step explanation:
A university dean is interested in determining the proportion of students who receive some sort of financial aid: Rather than examine the records for all students the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. Use 95% confidence interval to estimate the true proportion of students on financial aid: (Type your answers in using PARENTHESES in the CORRECT ORDER and use comma to separate your answers as necessary_ Round to the nearest thousandth)
The 95% confidence interval to estimate the proportion of students on financial aid = (0.522, 0.658)
In this question we have been given a university dean is interested in determining the proportion of students who receive some sort of financial aid.
Let p be the population proportion of students who receive some financial aid.
The dean randomly selects 200 students and finds that 118 of them are receiving financial aid.
i.e. n= 200
p{hat} = 118/200 = 0.59
We know that the critical value for 95% confidence interval : z = 1.96
The standard deviation would be,
σ = √[p{hat}(1 - p{hat})/N]
σ = √0.59(1 - 0.59)/200
σ = √(0.0012095)
σ = 0.0348
The 95% confidence interval for population proportion would be,
(0.59 ± (1.96 * 0.0348))
= (0.59 - (1.96 * 0.0348), 0.59 + (1.96 * 0.0348))
= (0.5218, 0.6582)
Therefore, the 95% confidence interval : (0.522, 0.658)
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(a) Write 130% as a decimal.
(a) 130% =
Answer: 1.3
Step-by-step explanation:
We know that in order to convert from percentages to decimals, we divide by 100. Therefore, 130 percent is the same as 1.3.
Answer: 1.3
Step-by-step explanation:
100% is equal to 1. Now we just have to find the value of 30%. Divide 1 by 10 and multiply by 3 to get 0.3. Since 0.3 is 30% and 1 is 100%, 130% = 1 + 0.3 = 1.3.
An easier way of converting is dividing the percentage by 100.
write a single statement that declares and initializes an array named a that has 10 elements of type int. the array should be initialized with the following values: 10, 20, 30, 40, 50, 60, 70, 80, 90, and 100
A single statement that declares and initializes an array named a that has 10 elements of type int. is as:
int [] denominations = {10,20,30,40,50,60,70,80,90,100};
We know that there are two ways you can declare and initialize as array in Java.
The first with the new keyword, where you have to initialize the values one by one.
The second is by putting he values in curly brackets.
An Array is a collection of data of the same type. Arrays are an important part of the fundamental data structures in Java.
An Array is usually declared so you can have multiple values in the same memory.
The syntax for declaring an array is: datatype[] arrayName;
Datatype means the type of objects that will be stored in the array ed. int, char,etc.
You can declare an array of arrays by following the array declarator with a list of bracketed constant expressions.
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Its Kumon So It Is Very Easy.
Answer: It's kumon?
Step-by-step explanation:
I can’t find the answer
Answer:
C. 225m^2
Step-by-step explanation:
Let's find the area of the shaded region. There are 5 whole squares shaded. There are 8 half squares shaded. (Each pair of triangles makes a whole square.) We have 4 more whole squares.
There are a total of 9 whole squares shaded.
The length of the side of the entire shape is 25m. The entire shape is divided into 25 squares. 25/5 = 5.
Each small square has an area:
A_smallsquare
= 5×5
= 25m^2
A_shaded
= 25 × 9
= 225m^2
a group of researchers wants to study the effect of listening to music at different volumes on driving reaction times. they recruit 100100100 volunteers. half of the subjects with fewer than 101010 years of driving experience are randomly assigned to take the test with one music volume, and the other half are assigned to take the test at the other music volume. the same method is used to randomly assign half of the drivers with at least 101010 years of driving experience to each testing condition.
Due to the comparison of the responses of drivers at two distinct volume levels, the experiment reported provides an illustration of matched pairs.
What does the experiment using matched pairings involve?For the purpose of comparing the outcomes and coming to a conclusion about this reaction, matched pairs are a sort of experiment that places one or more people in two distinct scenarios.
According to the aforementioned, the scenario described is an example of matched pairs because it calls for the driver to react to obstacles while listening to music at two different volume levels. In this regard, their results are compared to see if the volume affects their performance and reaction time.
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Write down all the factors of:
1. 12p
2. 16ax^{2}
Answer:
1. 2,2,3,p
2. 2,2,2,2,a,x,x
Use the Alternating Series Estimation Theorem to estimate the range of values of x for which the given approximation is accurate to within the stated error.sin x = x − x 36 ( | error | < 0.01)
The Alternating Series Estimation Theorem to estimate the range of values of x for which the given approximation is ( -0.0654 , 0.0654 ) .
Given :
Use the Alternating Series Estimation Theorem to estimate the range of values of x for which the given approximation is accurate to within the stated error.sin x = x − x^3 / 6 ( | error | < 0.01 )
The next nonzero term in the Taylor series for sine is x^5 / 120 .
x^5 / 120 < .00000001
-0.00000001 < x^5 / 120 < .00000001
-0.0000012 < x^5 < .0000012
( -0.0000012 )^1/5 < x < ( .0000012 )^1/5
we have ( .0000012 )^1/5 ≈ .0654
= ( -0.0654 , 0.0654 )
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6) Pamela wants to buy a new Mercedes. The Mercedes wheel has a radius of
15", what is the area of the Mercedes wheel? (State answer to nearest tenth.)
Answer:
706.5 inches^2.
Step-by-step explanation:
The area of a circle is given by the formula A = πr^2, where A is the area of the circle, r is the radius of the circle, and π is a mathematical constant approximately equal to 3.14.
To find the area of a Mercedes wheel with a radius of 15 inches, we can substitute these values into the formula:
A = πr^2 = π(15 inches)^2 = 706.5 inches^2
Rounding to the nearest tenth, the area of the Mercedes wheel is approximately 706.5 inches^2.
Match the equation with its graph
Y=2/5x-1
Answer:
the second one
Step-by-step explanation:
When Mara started at her current job, her employer gave her 3 days of paid vacation with a promise of 4 additional paid vacation days for each year she remains with the company to a maximum of 5 workweeks of paid vacation time.
If Mara's annual vacation time is viewed as an arithmetic sequence, give the first term and common difference?
When will she reach the maximum number of paid vacation days allowed?
linear equation
An equation with a maximum power of 1 for a variable is called a linear equation.
How to form a linear equation based on a given situation?
The total number of paid holidays is y.
Also, let x be the number of years Mara worked for the company.
4 days of fixed paid vacation. The additional number of years of paid leave is 3 days.
So, the linear equation that forms is
y = 3x + 4... (1)
Five years from now, how many days of paid vacation will she take?
Substitute the value of x = 5 into equation (i).
y = 3(5) + 4
y = 15 + 4
y = 19
Mara therefore has 19 days of paid leave after her five years of service.
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Tiana is toid to carry out the following polynomial division:
(2x³+4x² - 9x -18) + (x + 5)
quotient (answer without remainder
remainder(written as a fraction)
When the polynomial (2x³+4x² - 9x -18) is divided by x+5, the quotient is 2x²-6+21 and the remainder is -123/(x+5).
What is polynomial?Polynomials are sums of k-x^n terms, where k can be any number and n can be any positive integer. 3x+2x-5, for example, is a polynomial. Polynomials are introduced. This video defines words such as degree, standard form, monomial, binomial, and trinomial. A polynomial is an equation made up of variables, constants, and exponents that are mixed using mathematical operations including addition, subtraction, multiplication, and division (No division operation by a variable).
Here,
Dividend=(2x³+4x² - 9x -18)
Divisor=(x+5)
On dividing them using long division,
quotient=2x²-6+21
remainder=-123/(x+5)
The quotient is 2x²-6+21 and remainder is -123/(x+5) for the polynomial (2x³+4x² - 9x -18) when divided by x+5.
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Find the sixth number in this sequence. (a.) The fourth number is equal to 3x10. (b.) The second number is equal to 10+6. (c.) The Third number is halfway between the second and fourth numbers. (d.) The fifth number is 7 more than the fourth number.
The sixth number of the arithmetic progression is 44
What is arithmetic progression?Arithmetic Progression (AP) is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value.
For example 3, 8 , 13, 18, 23 is an arithmetic progression with common difference of 5
The nth term of a sequence is given as a1+(n-1)d
where a1 is the first number
Therefore
a5= 37
a4= 30
a2= 16
a3 = (30+16)÷2 = 46÷2= 23
therefore common difference = 23-16 = 7
a1 = 16-7= 9
therefore a6 = fifth number + common difference
a6= 37+7= 44
therefore the sixth number is 44
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3. The point (−5,3) is on the terminal arm of an angle θ in the standard position.
(a) Find θ
Answer:
Step-by-step explanation:
T/F alma corp. issues 1,000 shares of $10 par common stock at $14 per share. when the transaction is journalized, credit(s) are made to
Cash is debited for increasing assets and credited for increasing stockholder equity by crediting common stock and paid-in capital.
Given,
Alma corp. issues 1,000 shares of $10 par common stock at $14 per share.
We have to find the credits made to when the transaction is journalized;
The journal entry is displayed below;
Cash; 1,000 shares at $14 = 1000 × 14 = $14,000
To Common Stock ; 1,000 shares at $10 = 1000 × 10 = 10,000
To Paid in capital in excess of par value; 3,000 shares at $4 = 14,000 - 10,000 = 4,000
Being documented as the common stock's issue
Here, cash is debited because it increased assets and credited because it increased stockholder equity by purchasing common shares and paying for capital.
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Four students were given paint supplies for an art project. The table shows the amount of paint used by each student.
Student 1 Student 2 Student 3 Student 4
seventeen twentieths 1 and one fourth 65% 0.20
Which student used the least amount of paint for their art project?
Student 1
Student 2
Student 3
Student 4
Student 4 used the least amount of paint for the art project
How to determine which student used the least amount of paint?Given:
Student 1 used seventeen twentieths => 17/20
Student 2 used 1 and one-fourth => 1 1/4 = 5/4
Student 3 used 65% = 65/100
Student 4 used 0.20 = 20/100
Since the amount of paint used for the art project has been expressed in fractions. Find the LCM:
17/20, 5/4, 65/100, 20/100
The LCM of 20, 4 and 100 is 100
Student 1: 17/20 = 85/100
Student 2: 5/4 = 125/100
Student 3: 65/100
Student 4: 20/100
Thus, student 4 used the least amount of paint
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Answer: Student 4 (d)
Step-by-step explanation:
Brainliest?
At a large conference of teachers from a variety of subjects, a random sample of 50 mathematics teachers attending the conference was selected. Among the selected mathematics teachers, 28% had taken 1 or more courses in statistics. For which of the following populations is 28% a reasonable estimate of the percentage of those who have taken 1 or more courses in statistics?
(B) All mathematic teachers who attended the conference
(B) All mathematic teachers who attended the conference.
Option B is the correct option.
By statistics, what do you mean?The study and development of techniques for gathering, processing, interpreting, and presenting empirical data are the focus of the science of statistics.
What types of statistics are there?A statistic is a numerical representation of a sample property. One example of a statistic is the average number of points students in one math class got at the conclusion of the term if we assume that class to be representative of the population of all math classrooms.
The significance of statisticsDue to their role in assisting decision-making, statistics are crucial. To track progress, evaluate performance, identify issues, and set priorities, governments, organizations, and corporations all gather statistics.
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2.
Possible choices for correct answer:
a.
Using linear first order method, solve the following IVP:
(x(xy'-1) In(x) = 2y,
y(e) = 0.
b.
C.
d. None of the above
y=(ln(x)-1)²-In(x)
y=(In(x)-1)²
y=(In(x))²-In(x)
The IVP has only one solution with the initial condition y(0)=1 which corresponds to C=2
How to use linear first order method?You should understand that the square root of a number y is a non-negative number.
To this effect, take C = -2 - 1/2In(1+x) + c/2 and this is a negative value in the neighborhood of x=0
On the other hand, the square root of y(x) = -1/2In(1+x)-2)²
⇒√y(x) = -1/2In(1+x) -2.
This is also non-negative in the neighborhood
Note that √y(x) = 1/2In(1+x) +2
And y(x) is not a solution of the original IVP
In conclusion, The IVP has only one solution with the initial condition y(0)=1 which corresponds to C=2
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Enter the ordered pair for the vertices for (Ry-axis o T(2,0))(QRST).
On solving the provided question, we got to know the vertices those are - Q' = (-3, 3), R' = (-5, -3), S' = (-2, -2), T' = (0, 1)
what is vertices?As kids learn about the characteristics of 3D forms, vertices, faces, and edges start to appear often in geometry. Here's what it means and how to figure out how many vertices, faces, and edges each form has. The most popular forms' edge, face, and vertex counts are also included.
[tex]The coordinates of the vertices of the quadrilateral are;[/tex]
[tex]T(-2, 1), Q(1, 3), S(0, -2), R(3, -3)[/tex]
T
The coordinates of the vertices of the quadrilateral are;
[tex]T(2, 0)QRST, gives;\\ T(2, 0)QRST→ T(-2 + 2, 1), Q(1 + 2, 3), S(0 + 2, -2), R(3 + 2, -3)\\ T(2, 0)QRST→ T(0, 1), Q(3, 3), S(2, -2), R(5, -3)\\[/tex]
For the next process R y-axis which is the reflection about the y-axis, the preimage (x, y) becomes the image (-x, y)
Therefore, we have;
[tex]R y-axis(T(0, 1), Q(3, 3), S(2, -2), R(5, -3)) = T'(0, 1), Q'(-3, 3), S'(-2, -2), R'(-5, -3)\\ From which we get (Ry-axis T(2, 0))(QRST = T'(0, 1), Q'(-3, 3), S'(-2, -2), R'(-5, -3).[/tex]
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FILL IN THE BLANK. the___prompts the user to select a model, allowing the user to access the database and select data for the decision process or to set criteria for selecting such data.
The Dialog module prompts the user to select a model, allowing the user to access the database and select data for the decision process or to set criteria for selecting such data .
Given :
prompts the user to select a model, allowing the user to access the database and select data for the decision process or to set criteria for selecting such data.
Dialog module :
The dialog module provides dialog awareness for the Kamailio proxy. It's functionality is to keep track of the current dialog , to offer information about them .
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A piñata is a container filled with toys and candy and is broken open by hitting it with a stick. Sophia is trying to break the piñata. The probability that she will break the piñata on the first hit is 0.7. She will continue to hit the piñata until it breaks. If she does not break the piñata on a particular hit, the piñata is weakened and the probability that she will break it on the next hit is 0.1 greater than the probability on the previous hit. For example, if the piñata does not break on the first hit, the probability that it will break on the second hit is 0.8.
(a) Calculate the probability that Sophia docs.not break the piñata on the first hit and does break the piñata on the second hit. Let the random variable X represent the number of hits required for Sophia to break the piñata.
(b) Complete the probability distribution of X in the table below Probability of x 0.7
The probability that Sophia does not break the piñata on the first hit and does break the piñata on the second hit is of:
0.24 = 24%.
How to calculate the probability?In the context of a problem, a probability is calculated as the division of the number of desired outcomes divided by the number of total outcomes.
In the context of this problem, these probabilities are given by the percentages/proportions stated in the problem.
The probability that Sophia does not break the piñata on the first hit and does break the piñata on the second hit is calculated considering these two outcomes given as follows:
First outcome -> does not break -> 0.3 probability.Second outcome -> breaks -> 0.8 probability.The probability is calculated as the multiplication of these outcomes, as follows:
p = 0.3 x 0.8 = 0.24 = 24%.
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Question is attached
Answer:
56°
Step-by-step explanation:
the measurement of angle O is less than 90°, but not 62°, and angle O is larger than angle R, so angle O is not 28°, so the only other option less than 90° is 56°
YodelAir operates a charter jet service out of an airport in a secluded mountain ski resort. The chief safety officer for YodelAir uses a normal distribution with a
mean of 629 m and a standard deviation of 120 m to model the takeoff distance of the company's X15 jets in wintry weather.
Use this table or the ALEKS calculator to find the percentage of takeoff distances between 467 m and 611 m according to the model. For your intermediate
computations, use four or more decimal places. Give your final answer to two decimal places (for example 98.23%).
By "standard deviation", 30.62% the percentage of takeoff distances .
How to interpret a standard deviation?
The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean.
Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.
X ~ N ( µ = 628 , σ = 80 )
P ( 464 < X < 592 ) = ?
Standardizing the value
Z = ( X - µ ) / σ
Z = ( 464 - 628 ) / 80
Z = -2.05
Z = ( 592 - 628 ) / 80
Z = -0.45
P ( -2.05 < Z < -0.45 )
P ( 464 < X < 592 ) = P ( Z < -0.45 ) - P ( Z < -2.05 )
P ( 464 < X < 592 ) = 0.3264 - 0.0202
P ( 464 < X < 592 ) = 0.3062
= 30.62%
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please I need help, only complete answers please, if you can do it in that photo the answers would help me a lot please
The z-scores of the monthly utility bills for the value of x as $60, $71 and $9 are -1.25, 0.125, and 2.25 respectively.
What is Z-score?
A Z-score helps us to understand how far is the data from the mean. It is a measure of how many times the data is above or below the mean. It is given by the formula,
Z = (X - μ)/σ
Where Z is the Z-score,
X is the data point,
μ is the mean and σ is the standard variable.
As it is given that the standard deviation of the monthly utility bills is $8, while the mean is $70. Therefore, the z-score can be written as,
A.) X= 60
z= (60- 70 )/8 = -1.25
B.) X = 71
z = ( 71 -70)/8 = 0.125
C.) X = 92
z= (92 - 70)/8 = 2.25
Hence, the z-scores of the monthly utility bills for the value of x as $60, $71 and $9 are -1.25, 0.125, and 2.25 respectively.
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in which section of the graph does the actual solution to the system lie? 1 2 3 4; consider this system of inequalities. x + y โค โ3 y < which graph shows the solution for this system?; modeling with systems of linear inequalities ; consider the system of inequalities and its graph; consider the system of inequalities and its graph y x/4; a school is planning for an addition; which graph represents the system of inequalities y 34x 2y โ 1 โฅ 2x; which graph represents the solution set of the system of inequalities? (x+y 12y โฅxโ4)
The graph of the system of inequalities y ≤ –0.75x , y ≤ 3x – 2 is attached.
Actual solution of the inequalities in the graph is shown by common shaded region of both the inequalities below A(-0.533 , 0.4 ).
As shown in the question,
Given system of inequalities are :
y ≤ –0.75x
y ≤ 3x – 2
Graph of the inequalities is attached.
For first inequality :
y ≤ –0.75x
When x = 0
y ≤ 0
when y =0 ⇒ x ≤ 0
For second inequality :
y ≤ 3x – 2
x = 0⇒ y ≤ -2
when y =0 ⇒x ≥ 2/3
Actual solution by converting into equalities
y = -0.75x
Substitute in second equation
-0.75x = 3x -2
⇒ 3.75x =2
⇒ x= 0.5333
⇒ y= -0.4
Graph below ( 0.533 , -0.4 ) represents the actual solution.
Therefore, the actual solution of the attached graph of the inequalities is region below ( 0.533 , -0.4 ) common shaded region.
The complete question is :
Consider the system of inequalities and its graph. y ≤ –0.75x , y ≤ 3x – 2 In which section of the graph does the actual solution to the system lie? 1 2 3 4.
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