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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Which of the following sequences is an arithmetic sequence? Why?
1. 3, 7, 11, 15, 19
2. 4, 16, 64, 256
3. 48, 24, 12, 6, 3, ...
4. 1, 4, 9, 16, 25, 36
5. 1, 1/2, 0, -1/2
6. -2, 4, -8, 16, ...
7. 1, 0, -1, -2, -3
8. 1/2, 1/3, 1/4, 1/5, ...
9. 3x, x, x/3, x/9, ...
10. 9.5, 7.5, 5.5, 3.5, ...
From the given sequences following are the arithmetic sequences :
1. 3, 7, 11, 15, 19
5. 1, 1/2, 0, -1/2
7. 1, 0, -1, -2, -3
10. 9.5, 7.5, 5.5, 3.5, ...
As given in the question,
Arithmetic sequences are :-
1) yes, because the difference between the terms is same.
7 - 3 = 11-7 = 15 -11 = 4
5)yes, because the difference between the terms is same.
1/2 -1 = 0 -1/2 = -1/2 -0 = -1/2
7)yes, because the difference between the terms is same.
0 - 1 = -1 -0 = -2 -(-1) = -1
10)yes, because the difference between the terms is same.
7.5 - 9.5 = 5.5 - 7.5 = 3.5 -5.5 = -2
Difference between consecutive terms of these sequences are not equal . so these are not arithmetic sequences :-
2,3,4,6,8, 9
Arithmetic sequence
In an arithmetic sequence, the difference between consecutive terms is always the same. For example, the sequence 3, 5, 7, 9 .. is arithmetic because the difference between consecutive terms is always two.
Therefore, the arithmetic sequences are :
1. 3, 7, 11, 15, 19
5. 1, 1/2, 0, -1/2
7. 1, 0, -1, -2, -3
10. 9.5, 7.5, 5.5, 3.5, ...
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Anything helps. Thank you for the help.
Answer: Attached to the post.
Step-by-step explanation:
First, label points A and B--given as (3, -3) and (3, 1) respectively. Now connect the points to form line segment AB.
We need to reflect this line segment over the line y = x. To visualize this easier, let's draw line y = x. Two coordinates on this line is (1, 1) and (0, 0). Plot these points and connect them to form line y = x.
Finally, we need to reflect line segment AB over y = x. Imagine the line y = x is a mirror and reflect the line segment AB over it. In my diagram, line segment A'B' is the answer.
If AB = BC in traingle ABC, then which of the following must be true?1. m^A < m^C 2. m^A = m^C 3. m^A > m^C 4. m^A > m^B
The condition which is must be true for the given triangle ABC is m∠A = m∠C. Option 2 is correct. If AB = AC, then the triangle is said to be an isosceles triangle.
What is an isosceles triangle?A triangle is said to be an isosceles triangle if it has two equal sides and two equal angles in measurement.
The angles in an isosceles triangle are acute. That means they are less than 90° each. So, their sum results in a total of 180°.
Calculation:Given a triangle, ABC has AB = BC.
So, that means the given triangle is isosceles.
As we know, in an isosceles triangle, two angles are formed between one of the similar sides with the odd side being equal.
I.e., m∠A = m∠C
So, option 2 is correct.
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Let alpha and beta be the roots of the quadratic equation x² - 4x - 6 = 0. Find 1/a² + 1/b²
Answer:
7/9
Step-by-step explanation:
Using vieta's formulas, we know that a + b = 4 and ab = -6.
1/a^2 + 1/b^2 can be written as (a^2 + b^2)/a^2b^2.
(a^2 + b^2)/a^2b^2 can be written as (a+b)^2 - 2ab/(a^2)(b^2)
{4^2 - 2(-6)}/(-6)^2 = 28/36 = 7/9
Which figure has two sets of parallel sides?
Answer: Parallelogram
Step-by-step explanation: [Parallelogram definition]: A parallelogram is a quadrilateral with 2 pairs of parallel sides. In these figures, sides of the same color are parallel to each other. A shape with four sides of equal length.
To see a shape that is a parallelogram, look at the attachment down below:
public accountant financial planner 50.2 48.0 59.8 49.2 57.3 53.1 59.2 55.9 53.2 51.9 56.0 53.6 49.9 49.7 58.5 53.9 56.0 52.8 51.9 48.9
Using the formula of test statistic, the value of the test statistic is 2.6961.
The mean of the public accountant is
Mean x(p) =50.2+59.8+57.3+59.2+53.2+56.0+49.9+58.5+56.0+51.9/10
x(p) = 55.2
Now the standard deviation of public accountant is
SD(p) = √{∑(x-x(p))^2/n-1}
SD(p) = √(50.2-55.2)^2+(59.8-55.2)^2+..................+(51.9-55.2)^2/n-1
After solving;
SD(p) = 3.34
The mean of the financial planner is
Mean x(F) =48.0+49.2+53.1+55.9+51.9+53.6+49.7+53.9+52.8+48.9/10
x(F) = 51.6
Now the standard deviation of financial planner is
SD(F) = √{∑(x-x(p))^2/n-1}
SD(F) = √(48.0-51.6)^2+(49.2-51.6)^2+..................+(48.9-51.6)^2/n-1
After solving;
SD(F) = 2.57
Test Statistic (t) = [tex]\frac{x(P)-x(f)}{\sqrt{\left(\frac{(n(p)-1)s(p)^2+(n(f)-1)s(f)^2}{n(p)+n(f)-2}\left(\frac{1}{n(p)}+\frac{1}{n(f)}\right)\right)}}[/tex]
t = [tex]\frac{55.2-51.61}{\sqrt{\left(\frac{(10-1)(3.34))^2+(10-1)(2.57)^2}{10+10-2}\left(\frac{1}{10}+\frac{1}{10}\right)\right)}}[/tex]
After solving
t = 2.6961
Hence, the value of the test statistic is 2.6961.
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The right question is
public accountant 50.2 59.8 57.3 59.2 53.2 56.0 49.9 58.5 56.0 51.9
financial planner 48.0 49.2 53.1 55.9 51.9 53.6 49.7 53.9 52.8 48.9
Use a 0.05 level of significance and test the hypothesis that there is no difference between the starting annual salaries of public accountants and financial planner
Find the value of the test statistic.
a value of the linear correlation, r, near -1 means the data is tightly bundled around a line, and predictions within the scope of data are very reliable.
The correct statement is,
If the value of the linear correlation coefficient, r, is near −1, then the data viewed as a scatterplot is tightly bundled around some line, and predictions made with the line of best fit within the scope of data are reliable.
What is linear correlation?
When the proportional relationship between two given variables is the same or constant, linear correlation is said to exist. As an illustration, the expenditures increase by 5% each time the income increases by 20%. When the ratio of variations between two given variables changes, there is said to be a non-linear correlation.
Since,
r = - 1 means there is a negative relationship between the two variables
r=+1 means there is a positive relationship between the two variables
r= 0 means that there is no relationship between the two variables so we can not predict the value of dependent variable using the independent variable.
Hence the statement, If the value of the linear correlation coefficient, r, is near −1, then the data viewed as a scatterplot is tightly bundled around some line, and predictions made with the line of best fit within the scope of data are reliable is correct.
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Complete question:
Which of the following statements regarding regression and correlation are true? (There may be more than one correct answer.)
a. If the value of the linear correlation coefficient, r, is near −1, then the data viewed as a scatterplot is tightly bundled around some line, and predictions made with the line of best fit within the scope of data are reliable.
b. When the linear correlation coefficient is positive, then the slope of a linear regression equation must be negative.
c. If the linear correlation coefficient is near –1, then the slope of the related least squares line will also be close to –1.
d. If the linear correlation coefficient is close to 0 in value, then the best prediction model to use for any value of the independent variable is the mean(average) of the dependent variable values.
If a number is added to the numerator of 1/7 and twice the number is subtracted from the denominator, the result is 4. Find the number.
Answer:
2
Step-by-step explanation:
Question 7 of 35
Use the coordinates of the labeled point to find the point-slope equation of
the line.
-5
69
5
(2,-5)
The simplest definition of point-slope form is a line equation expressed using a single line point and the line's slope.
How do you write a point slope equation?When the line to be examined's slope is known, and the provided point also serves as the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b). B stands in for the y value of the y-intercept point in the formula.
An equation for a line stated using a single point on the line and the line's slope is a straightforward definition of point-slope form.
The slope is defined as the rise over run, or the proportion of the change in the y values over the change in the x values, and the point form is denoted by the letters (x,y).
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if the angle between two vectors is represented by , tell if the following angles would mean the vectors are orthogonal, parallel or neither.
If the angle between two vectors is represented by theta and it is equal to zero or 180 degrees then the following angles would mean the vectors are parallel .
Given :
if the angle between two vectors is represented by , tell if the following angles would mean the vectors are orthogonal, parallel or neither.
if two vectors points are given then find the dot product of vectors if the result is equal to zero then the two vectors are orthogonal vectors .
If they were parallel the angle would be 0 or 180 degrees, therefore, the two vectors are not parallel.
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let $abc$ be an acute triangle satisfying the conditions $ab > bc$ and $ac > bc$. denote by $o$ and $h$ the circumcenter and orthocenter, respectively, of the triangle $abc$. suppose that the circumcircle of the triangle $ahc$ intersects the line $ab$ at $m$ different from $a$, and the circumcircle of the triangle $ahb$ intersects the line $ac$ at $n$ different from $a$. prove that the circumcenter of the triangle $mnh$ lies on the line $oh$.
In an acute triangle, the circumcenter of the triangle lies on the line O.
Acute triangle.
In geomentry, acute triangle is the type of triangle in which all the three internal angles of the triangle are acute
Given,
Here we need to prove that in the acute triangle ABC, the circumcenter of the triangle MNH lies on the line OH.
Let us consider T be the intersection of σ1 and σ1 other than W.
Now, the Lemma 1: T is on XY.
Now, the Proof is written as We have ∠XTW} = ∠YTW = 90 degres because they intercept semicircles.
Therefore, ∠XTY = ∠XTW + ∠YTW = 180 degrees,
Then XTY is a straight line.
Here we know that NHLB is cyclic because ∠BNH and ∠BLH, opposite and right angles, sum to 180 degree. Furthermore, we are given that NTWB is cyclic.
Therefore, the triangle MNH lies on the line OH.
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Let C = {n ∈ Z | n = 6r – 5 for some integer r} and D = {m ∈ Z | m = 3s + 1 for some integer s}.
Prove or disprove each of the following statements.
a. C ⊆ D
b. D ⊆ C
Its is true that C ⊆ D means Every element of C is present in D
According to he question,
Let C = {n ∈ Z | n = 6r – 5 for some integer r}
D = {m ∈ Z | m = 3s + 1 for some integer s}
We have to prove : C ⊆ D
Proof : Let n ∈ C
Then there exists an integer r such that:
n = 6r - 5
Since -5 = -6 + 1
=> n = 6r - 6 + 1
Using distributive property,
=> n = 3(2r - 2) +1
Since , 2 and r are the integers , their product 2r is also an integer and the difference 2r - 2 is also an integer then
Let s = 2r - 2
Then, m = 3r + 1 with r some integer and thus m ∈ D
Since , every element of C is also an element of D
Hence , C ⊆ D proved !
Similarly, you have to prove D ⊆ C
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A researcher would like to know the effect of education on income and has hypothesized that the higher one's education, the more income they are likely to get. Here is the data:
years of education
family income level
16
89000
16
16000
8
20000
10
8400
6
11000
16
85000
15
24000
14
56000
13
45000
12
98000
13
23000
10
20000
10
4500
14
13000
12
65000
16
80000
12
55000
13
95000
10
3500
Based on your calculations from previous questions, what is the regression coefficient?
The parameter (the regression coefficient) indicates the degree to which the line slopes upwards or downwards by indicating the amount by which a change in x must be multiplied by the corresponding average change in y, or the amount by which y changes for each unit increase in x.
Understanding Linear Regression Coefficients, A positive coefficient indicates that the mean of the dependent variable tends to rise in tandem with an increase in the independent variable's value. A negative coefficient indicates that the dependent variable tends to decrease as the independent variable rises.
In a regression model, the statistical measure known as R-Squared (also known as R2 or the coefficient of determination) is used to figure out how much of the variance in the dependent variable can be explained by the independent variable. In other words, the goodness of fit, or r-squared, measurement indicates how well the data fit the regression model.
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a chain of sport shops catering to beginning skiers, headquartered in aspen, colorado, plans to conduct a study of how much a beginning skier spends on his or her initial purchase of equipment and supplies. based on these figures, it wants to explore the possibility of offering combinations, such as a pair of boots and a pair of skis, to induce customers to buy more. a sample of 44 cash register receipts revealed these initial purchases: $ 180 $ 186 $ 130 $ 263 $ 258 $ 159 $ 127 $ 84 $ 208 180 104 233 92 223 176 216 219 209 205 150 241 110 239 124 173 174 264 232 182 261 216 193 196 223 239 176 261 150 245 84 232 152 95 233 click here for the excel data file required: a. arrive at a suggested class interval. (round your answer up to the next multiple of 5.) b. organize the data into a frequency distribution using a lower limit of $70.
(a) Class interval of a given data is 36.
(b) Frequency distribution is 44.
We have given that,
total frequency = 44
lower limit = $70
number of class = 5
(a) we have to find class interval,
Class interval = [tex]\frac{Max. number - min. number}{no. of classes}[/tex]
here maximum number is 264 and minimum number is 84
Class interval = [tex]\frac{264 - 84}{5}[/tex]
= [tex]\frac{180}{5}[/tex]
Class interval = 36
we have to round our value to the next multiple of 5
so the class interval will be 40.
(b) A frequency distribution is the pattern of frequencies of a variable. It is the number of times each possible value of a variable occurs in a dataset. There are three types of frequency distribution such as Cumulative frequency distribution, Relative frequency distribution, Relative cumulative frequency distribution.
The frequency distribution is as follows:
Class interval Frequency
70 - 110 6
111 - 151 5
152 - 192 10
193 - 233 14
234 - 274 9
Total 44
This is the organize data into a frequency distribution.
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Which are ways of showing probability select 4?; Can 5 by 4 Be the probability of an event justify your answer?; Can 3 by 5 be the probability of an event?
5/4 cannot be the probability of an event as its value is greater than 1 and probability always lies between 0 and 1. Yes, 3 by 5 can be the probability of an event.
We know that the probability of an event is the chance of occurring of an event. The ways of showing probability could be in ratio or it could be in percentage and the percent may be between 0%-100%
The value of 5/4 = 1.25 which is greater than 1, so it cannot be the probaility of any event.
The value of 3/4 = 0.75, its value is less than 1, so it can be the probability of an event.
The probability of an event always lie between 0 and 1. It is equal to zero if the event will never occur and is equal to 1 if the event is certain to occur.
Therefore, the probability of an event cannot be 5/4 but 3 by 5 can be the probability of an event. as its value of 5/4 is greater than 1 whereas the value of 3/5 is less than 1 and probalilty always lies between 0 and 1.
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Given the speeds of each runner below, determine who runs the fastest.
\text{Adam runs 13 feet per second.}
Adam runs 13 feet per second.
\text{Stephanie runs 199 feet in 17 seconds.}
Stephanie runs 199 feet in 17 seconds.
\text{Noah runs 1 mile in 592 seconds.}
Noah runs 1 mile in 592 seconds.
\text{Katie runs 878 feet in 1 minute.}
Katie runs 878 feet in 1 minute.
Katie runs fastest among all .
What is the units of conversion ?
Unit of Conversion is a multi-step process involving multiplication or division by a numerical factor.
Given:
Speed of Adam = 13 feet per second
Speed of Stephanie = 199 feet in 17 seconds
Speed of Noah = 1 mile in 592 seconds
Speed of Katie = 878 feet in 1 minute
Now on converting all the units to one single unit,we get
1 mile = 5280 feet
1 minute = 60 seconds
Speed of Adam = 13 feet per second
Speed of Stephanie = 199 feet in 17 seconds
= [tex]\frac{199}{17}[/tex] feet per second
= 11.705 feet per second
Speed of Noah = 1 mile in 592 seconds
= 5280 feet in 592 seconds
= [tex]\frac{5280}{592}[/tex] feet per second
= 8.919 feet per second
Speed of Katie = 878 feet in 1 minute
= 878 feet in 60 seconds
= [tex]\frac{878}{60}[/tex] feet per second
= 14.6333 feet per second
Hence ,Katie runs fastest among all sice its speed is the highest .
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a store is selling laptops with six different operating systems. a company would like to buy 35 of those laptops for their employees. in how many ways can this company buy them?. show all your work step by step to get credit. final answers must be provided in decimal form
On solving the provided question, based on the information, we can say that there are 35 X 6 = 210 ways
What are combinations?Combining means selecting all or part of a set of objects, regardless of the order in which the objects are selected. Suppose we have a set of three characters.
[tex]^nC_{r} = \frac{n!}{r!(n - r)!}[/tex]
ways can this company buy them are - 35 X 6 = 210 ways
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What must be true for lines A and B to be parallel lines?; Which lines are parallel justify your answer lines a and b are parallel because their?; Which lines are parallel justify your answer ABEF?; Are parallel lines congruent?
Parallel lines are straight lines that never meet each other no matter how long we extend them
Parallel lines are any two or more lines that all lie in the same plane and never cross one another. They are equally spaced apart and have the same incline.
Numerous pairs of angles are created when a transversal line intersects any two parallel lines. While some angles are additional, others are congruent (equal).
The fundamental characteristics listed below make it simple to recognise parallel lines.
Parallel lines are defined as straight lines that are always the same distance apart.
No matter how far apart they are from one another, parallel lines can never intersect.
I've answered in general as the question is incomplete
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suppose the cost of a car produced in the united states is $20,000. the current exchange rate is us$1= €0.85. What is the cost of the car in euros?
The cost of the car in euros is 17,000 euros
Given that,
Let's say an automobile made in the United States costs $20,000. At this time, one US dollar is worth 0.85 euros. A automobile made in the United States costs $20,000 to construct.
To find : that the car's price in euros ?
The information provided lets us know that,
The car's price in euros= 20,000 * 0.85
= 17,000 euros
Therefore, the car's price in euros is 17,000 euros.
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Show transcribed dataFind the characteristic polynomial of A. Use x for the variable in your polynomial. You do not need to factor your polynomial 12 - 10 0 A = 9 -7 0 0 02 characteristic polynomial of A is: 0
The characteristic polynomial x³ - 7x² + 16x - 12 The characteristic polynomial of a square matrix in linear algebra is a polynomial that is invariant under matrix similarity and has the eigenvalues as roots.
Its coefficients include the determinant and the trace of the matrix.
Characteristic polynomial of a 3×3 matrix A is given by ; x³ - trace(A)x² + (A11 + A22 + A33 )x - determinant(A)
Where Aii is the determinant of the matrix obtained by deleting i th row and i th column.
Here trace(A) = sum of the diagonals = 12 - 7 + 2 = 7
A11 = -7 × 2 = -14
A22 = 2 × 12 = 24
A33 = ( 12×-7) - (-10×9) = 6
Determinant(A) = 12(-7×2 - 0) + 10(2×9 - 0) = 12
Substituting these values in above equation , we obtain;
x³ - 7x² + (-14 + 24 + 6)x - 12 = x³ - 7x² + 16x - 12.
Hence x³ - 7x² + 16x - 12 is the characteristic polynomial of A.
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The consumption function is one of the key relationships in economics, where consumption y depends on disposable income x. Consider the quarterly data for these seasonally adjusted variables, measured in billions of dollars. A portion of the data is shown in the accompanying table. Use Table 2.
DATE Consumption Disposable Income
2006:01 9148.2 9705.2
2006:04 9266.6 9863.8
2006:07 9391.8 9982.5
2006:10 9484.1 10111.2
2007:01 9632.8 10255.5
2007:04 9753.2 10358.6
2007:07 9850.8 10456.9
2007:10 9988.4 10623.4
2008:01 10065.7 10764.6
2008:04 10183.0 11129.3
2008:07 10202.0 11004.7
2008:10 9967.2 10913.3
2009:01 9913.0 10879.8
2009:04 9920.1 11090.9
2009:07 10040.7 11047.0
2009:10 10131.5 11121.7
2010:01 10230.8 11215.6
2010:04 10285.4 11368.0
2010:07 10366.3 11415.1
2010:10 10525.2 11514.7
the consumption function for this data can be expressed as:
y = 0.97x + 11.3
To find the consumption function, we can use a least-squares regression analysis. This process involves finding the line of best fit that minimizes the sum of the squared errors of the data points.
We can use a graphing calculator or a statistical software package to calculate the slope and intercept of the line of best fit. Using a graphing calculator, the slope and intercept of the line of best fit are 0.97 and 11.3, respectively.
Therefore, the consumption function for this data can be expressed as:
y = 0.97x + 11.3
The consumption function is a mathematical expression of the relationship between consumption (y) and disposable income (x). The consumption function for this data can be expressed as:
y = 0.97x + 11.3
This equation states that for every one dollar increase in disposable income, consumption is expected to increase by 0.97 dollars. The 11.3 in the equation represents the intercept, which is the expected consumption level when disposable income is zero.
This equation can be used to estimate the expected consumption level for any given level of disposable income. For example, if disposable income is $10,000, then the expected consumption level is $9,703 (10,000 x 0.97 + 11.3).
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Use the distributive property to write an equivalent expression.
4 (w - 2r + 4)
The distributive equivalent expression of 4(w -2r + 4) is 4w -4(2r) + 4(4)
How to write the Distributive law?distributive law, also called distributive property, in mathematics, the law relating the operations of multiplication and addition, stated symbolically as a(b + c) = ab + ac; that is, the monomial factor a is distributed, or separately applied, to each term of the binomial factor b + c, resulting in the product ab + ac. From this law it is easy to show that the result of first adding several numbers and then multiplying the sum by some number is the same as first multiplying each separately by the number and then adding the products.
a(b + c) = ab + ac
using the above distributive law and comparing the expression below
4 (w - 2r + 4)
we can write it as 4w -4(2r) + 4(4)
In conclusion the equivalent expression is 4w -4(2r) + 4(4)
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write the polynomial in standard form. then classify the polynomial by degree and by number of terms x + 2x^2
The equation is therefore in Standard Form: 2 Degree :Quadratic number of terms :Binomial
What is equation?There are numerous ways to define an equation in mathematics .In algebra, a statement that mathematically establishes the equality of two mathematical expressions is known as an equation. Take into consideration the equation 3x + 5 = 14, in which 3x + 5 and 14 are two variables that are separated by the word "equal." Even the most elementary and simple algebraic equations use mathematical variables.
To construct a polynomial in standard form in this instance, you begin writing with the term having the highest degree, or exponent (in this example, the
2[tex]x^{2}[/tex] +x
word), and after that, in descending order. due to the two
[tex]x^{2}[/tex] is used to the greatest degree:
You look at the highest exponent, or degree, to categorize a polynomial. Considering that 2 is the highest exponent,
That is a quadratic equation. First few are as follows:
1- linear
2- quadratic
3- cubic
4- quartic
5- quintic
Count the terms in the polynomial to categorize it according to its term count: There are two terms in this polynomial,
2[tex]x^{2}[/tex]and x
. This is therefore a binomial.
Monomial is one term.
binary two terms
trinomial, 3 terms
4-plus terms; polynomial
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Variability of a statistic from sample to sample due to chance. Same thing as "variability due to chance." Error refers to how samples vary from one to another. Good sampling techniques control for this.
Random error is the variation in a statistic from sample to sample due to chance. It is the difference between a sample statistic and the true population parameter that it is estimating.
Good sampling techniques help to reduce the amount of random error in a sample by reducing the variability of the sample results.
Random error is the variability of a statistic from sample to sample due to chance. It occurs when a statistic from a sample does not accurately reflect the true population parameter it is attempting to estimate. Random error can be minimized through the use of good sampling techniques, such as randomization and stratification, as these help to reduce the variability of results from sample to sample. Good sampling techniques also help to ensure that the sample is representative of the population, thus reducing the amount of random error.
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Which of the following describes a function?
A. 1,2,1,3,2,2,2,3
C. -1,6, 7,-1,-1,3 – 4,3
B. 2,3, 2,-3, 2,6 , 2.0
D. 1,2,2,3,3,4,4,5
Among the following relations, the Function is option D,{1,2,2,3,3,4,4,5}.
In simple words, a function is a relationship between inputs where each input is related to exactly one output. Functions are often defined by a formula that describes a combination of arithmetic operations
A function is uniquely represented by the set of all pairs (x, f (x)), called the graph of the function, a popular means of illustrating the function. To identify a function from a relation, we just have to see if any 'x' values are being repeated, if not, it is a function. If x values are repeated, and y values are different, then we have a relationship and not a function.
In the question, we can see that values 2,3, and 4 are repeating. This specifies that they are a function.
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which statement is true about the graphed function? F(x) < 0 over the intervals (–[infinity], –2.5) and (–0.75, 0.75).
F(x) > 0 over the intervals (–[infinity], –2.5) and (–0.75, 0.75).
F(x) < 0 over the intervals ( –2.5, –0.75) and (–0.75, [infinity]).
F(x) > 0 over the intervals ( –2.5, –0.75) and (0.75, [infinity]).
F(x) > 0 over the intervals (–∞, –2.5) and (–0.75, 0.75).
Lets explain the graph to answer the problem
- When we ask about f(x) we means the values of y
- f(x) > 0 means the graph is over the x-axis because over the x-axis
y is positive
- f(x) < 0 means the graph is under the x-axis because under the x-axis
y is negative.
* Lets describe each part of the graph
- The graph intersect the x-axis at :
x = -2.5 , x = -0.75 , x = 0 , x = 0.75
- The graph is over the x-axis between -∞ and -2.5 and between
-0.75 and 0.75
At x = -2.5 f(x) = 0 , at x = -0.75 f(x) = 0 , at x = 0.75 f(x) = 0
∴ x = (-∞ , -2.5) and (-0.75 , 0.75)
∴ f(x) > 0 over the intervals (-∞ , -2.5) and (-0.75 , 0.75)
- The graph is under the x-axis between -2.5 and -0.75 and between
0.75 and ∞
At x = -2.5 f(x) = 0 , at x = -0.75 f(x) = 0 , at x = 0.75 f(x) = 0
∴ x = (-2.5 , -0.75) and (0.75 , ∞)
∴ f(x) < 0 over the intervals (-2.5 , -0.75) and (0.75 , ∞)
* The true statement in the answer is;
F(x) > 0 over the intervals (–∞, –2.5) and (–0.75, 0.75).
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Can a triangle have sides with the given lengths? 11, 12, 15
Use synthetic division to completely factor this polynomial.
3x4 - 14x³ 3x²+54x -40
Which expressions are factors of the polynomial?
-
(3x - 5)
(x + 4)
(x - 4)
(x 2)
(x + 2)
0 (x + 1)
(x - 1)
(3x + 5)
The expressions are factors of the polynomial 3x4 - 14x³ 3x²+54x -40 are
(x + 4)(x + 2)(x + 1)(x - 1)What are polynomials?Generally, To factor a polynomial using synthetic division, we need to find a factor of the polynomial that can be divided into the leading coefficient and the constant term of the polynomial.
In this case, the leading coefficient is 3 and the constant term is -40. One factor of 3 and -40 is (-4)(10).
The complete factorization of the polynomial is 3x⁴ - 14x³ + 3x² + 54x - 40 gives The remainder is 0, so the other factor is (x - 4)(x + 2)(x - 1)(x + 1).
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You wish to conduct your own study to estimate the miles per gallon on a 2007 Ford Taurus. How large a sample would you need to estimate the mean per gallon within 0.5 miles per gallon with 95% confidence if you read in a previous study that the standard deviation of miles per gallon for a 2007 Taurus is 3.21.
The sample required to estimate the mean per gallon within 0.5 miles per gallon with 95% confidence is 158.
Given:
You wish to conduct your own study to estimate the miles per gallon on a 2007 Ford Taurus.
How large a sample would you need to estimate the mean per gallon within 0.5 miles per gallon with 95% confidence = ?
if you read in a previous study that the standard deviation of miles per gallon for a 2007 Taurus is 3.21.
we know that :
z value of 95% is 1.96
Margin of error = E = z × sd/√n
we have:
n = (z×sd/E)²
= 158.33
= 158
Hence we get the sample as 158
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**Classified DataWhich of the following is a good practice to protect classified information?
The good practice to protect the classified information is labelling them with markings.
In the question ,
we have been asked about the good practice that can help in protecting the classified information .
we know that ,
the term Classified means when something is arranged in classes. and
the term Labeling means that when something is assign to a category.
So , the best practice is to Ensure the proper labeling by appropriately marking all the classified material and when required, sensitive material.
Therefore , the best practice is Ensure proper labeling by appropriately marking all classified material .
The given question is incomplete , the complete question is
What is a good practice to protect classified information ?
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