How will you differentiate linear inequalities in two variables from systems of linear inequalities in two variables?.
Answers
Linear equation and Linear inequality are differentiatable on the sybolically. The symbol used in linear equation is "=" equality sign and the symbols used in linear inequality are ">","<","
"≤", " ≥".
We need to distinguish between linear inequalities in two variables and systems of linear equations in two variables.
We will first discuss linear equations and then linear inequalities.
Linear Equations:
If a equation is written in the form ax + by + c=0, the equation is said to be a linear equation in two variables. where a, b & c are real numbers and coefficients of x and y. , that is, a and b are not equal to zero.
Characterstic :
Variables in a linear equation are not raised to powers or used as denominators of fractionsFind pairs of values that make the linear equation true, and plot those pairs on a coordinate grid so that all points are Lying on the same line. The graph of a linear equation is a straight line.A linear equation in two variables can be written as a linear relationship between x and y.For example, 10x+4y = 3 and -x+5y = 2 are linear equations in two variables.
methods for solving linear equations in two variables:
graphical methodsreplacement methodscross-multiplication methodselimination methodsLinear inequality:
Linear inequalities in two variables use the greater than (>), less than (<), greater than or equal to (≥), and less than or equal to (≤) symbols instead of the equal (=) symbol. Use the.
Features:
You can add, subtract, multiply and divide with the same number to solve inequalitiesMultiply and divide with negative numbers reverse the inequalityOrder outside shaded area Pairs are inequalities that cannot be solved graphically.Example: 8x + 3y ≥ 5 and 2x + 3y < 10 are linear inequalities in two variables.
Method: Graphical
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Related Questions
The population of a town i 3808000. What i the value of the digit 3 in 3808000?
(a) 3 million (b) 3 hundred thouand
(c) 3 thouand (d) 3 hundred
Answers
The value of the digit 3 in 3808000 is 3 million.
What are population digits?
A population is a distinct group of individuals, animals, or objects that can be distinguished from one another for the purposes of data collection and analysis in statistics and other branches of mathematics. Data is typically collected from a sample in order to learn more about a large population.
Here, we have
The population of the town is 3808000.
We have to find the value of the digit 3 in 3808000.
We concluded from the given statement is the value of the digit 3 in 3808000 is 3 million.
Hence, the value of the digit 3 in 3808000 is 3 million.
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A card is drawn from an ordinary deck and we are told that it is red. What is the probability that the card is greater than 2 but less than 92
Answers
The probability that the card is greater than 2 but less than 9 is 6 / 13.
Probability is the branch of discrete mathematics. It is used for calculating how likely an event is to occur or happen.
P ( E ) = Number of favourable outcomes / Total number of outcomes → 1
In an ordinary deck of cards,
Total number of cards = 52Number of suites = 4 ( Hearts, Clubs, Diamonds and spades )Each suite has 13 cards = Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack,Queen, King
Number of black suites = 13( Clubs ) + 13( Spades ) = 26Number of red suites = 13( Hearts ) + 13( Diamonds ) = 26As per the question,
A card is drawn from an ordinary deck and that is red.
⇒ Total number of red cards in an ordinary deck = 26 cards
∴ Total number of outcomes = 26
The card that is greater than 2 but less than 9,
⇒ Number of cards that are greater than 2 but less than 9 in red suite = 12
∴ Number of favourable outcomes = 12
Substitute the values in 1,
P ( E ) = Number of favourable outcomes / Total number of outcomes
= 12 /26
P ( E ) = 6 / 13
Therefore, 6 / 13 is the probability that the card is drawn in a red suite greater than 2 but less than 9.
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The complete question is
A card is drawn from an ordinary deck and we are told that it is red. What is the probability that the card is greater than 2 but less than 9?
mother spent Php 134.25 for a box of chocolate php 385.75 for a pair of slippers and php 235.50 for a shirt as her Christmas present to her family the money she had left was 269.50 how much money did she have at first?
Answers
Before buying Christmas presents for her family, Mother had Php 1,025 initially.
How to calculate total money before spending?
To calculate the initial amount before spending add the amount spent and left after spending.
According to the given question:
Mother spent 134.25 on chocolate box, 385.75 on pair of slippers and 235.50 for a shirt.
Therefore total money spent = 134.25 + 385.75 + 235.50 = 755.50
Money left after spending = 269.50
So, the total money mother had initially = 755.50 + 269.50 = 1025
The actual amount mother had was Php 1,025
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the birth weight of newborns, measured in grams, is an example of . a. quantitative data b. either categorical or quantitative data c. neither categorical nor quantitative data d. categorical data
Answers
The birth weight of newborns, measured in grams, is an example of quantitative data. So the option a is correct.
In the given question,
The birth weight of newborns, measured in grams, is an example of .
a. quantitative data
b. either categorical or quantitative data
c. neither categorical nor quantitative data
d. categorical data
The quantitative data means data that is explain in the subjective ways. It is also explain quantity, amount and range.
Categorical data is a body of knowledge that is organised into categories. For instance, the data obtained when an organisation or agency tries to collect the biodata of its employees is referred to as categorical data.
The birth weight of newborns measured in grams, is an example of quantitative data.
Birth weight is quantitative because it can take on multiple numerical values. So the option a is correct.
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A random sample of 50 suspension helmets used by motorcycle riders and automobile race-car drivers was subjected to an impact test, and on 18 of these helmets some damage was observed. (a) Test the hypotheses H_0: p = 0.3H 0:p=0.3 versus H_{1} : p \neq 0.3H 1 :p
=0.3 with \alpha = 0.05.α=0.05. (b) Find the P-value for this test. (c) Find a 95% two-sided traditional CI on the true proportion of helmets of this type that would show damage from this test. Explain how this confidence interval can be used to test the hypothesis in part (a). (d) Using the point estimate of p obtained from the preliminary sample of 50 helmets, how many helmets must be tested to be 95% confident that the error in estimating the true value of p is less than 0.02? (e) How large must the sample be if we wish to be at least 95% confident that the error in estimating p is less than 0.02, regardless of the true value of p?
Answers
On testing the hypothesis , We fail to reject the null hypothesis at 5% level of significance.
In the question ,
it is given that ,
sample size (n) is = 50 ,
sample proportion(â) = 18/50 = 0.36
The null hypothesis is given as H₀ : p = 0.3
and the alternate hypothesis is [tex]H_{\alpha }[/tex] : p ≠ 0.3
The z - test statistics can be calculated using the formula
z = (â - p) / √(p(1-p)/n)
Substituting the value â = 0.36 , p = 0.3 and n = 50 ,
we get ,
z = (0.36 - 0.3) / √(0.3(1-0.3)/50)
On simplifying ,
we get ,
z = 0.93
the excel function for the critical value ,
=NORMINV(0.05/2,0,1)
we get , the critical value as 1.96
we can see that the critical value is greater than test statistic value ,
So , we fail to reject null hypothesis at 5% level of significance .
Therefore , On testing given hypothesis , We fail to reject the null hypothesis at 5% level of significance.
The given question is incomplete , the complete question is
A random sample of 50 suspension helmets used by motorcycle riders and automobile race-car drivers was subjected to an impact test, and on 18 of these helmets some damage was observed.
Test the hypotheses H₀ : p = 0.3 versus H₁ : p ≠ 0.3 with α = 0.05 .
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Determine the number that will complete the square to solve each equation after the constant term has been written on the right side. Do not actually solve. 3 w^{2}-w-24=03w 2 −w−24=0
Answers
The number that will complete the square to solve equation is 1/36.
What is completing the square?
For some values of h and k, completing the square is an elementary algebraic method for changing a quadratic polynomial of the form
ax^2 + bx + c to the form a^2 + k. In other words, the quadratic expression is completed by inserting a perfect square trinomial.
Consider, the given polynomial
3w^2 - w - 24 = 0
Rewrite the polynomial in the form ax^2 + bx = c
Add 24 on both sides,
3w^2 - w - 24 + 24 = 24
⇒ 3w^2 - w = 24
Divide both sides by 3,
[tex]w^2-\frac{1}{3}w = 8[/tex]
To complete the square x^2 + bx, we add [tex](\frac{b}{2} )^2[/tex]
Here, b = -1/3
So, [tex](\frac{b}{2})^2 = (\frac{-1/3}{2})^2 = (-\frac{1}{6})^2 = \frac{1}{36}[/tex]
Adding to both sides of the equation, we have
[tex]w^2-\frac{1}{3}w+\frac{1}{36} = 8+\frac{1}{36}[/tex]
Hence, the number that will complete the square to solve an equation is 1/36.
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In a recent year, an author wrote 177 checks. Use the Poisson distribution to find the probability that, on a randomly selected day, he wrote at least one check.
Answers
The probability that on a randomly selected day, he wrote at least one check is 0.3843
How to solve for the Poisson distributionA year is made up of 365 days
The number of checks written = 177
λ = 177 / 365
= 0.4849
P(x ≥ 1) = 1 - p(x < 1)
p(x < 1) is going to be 0
so we would have 1 - p(x = 0)
the Poisson distribution is given as
P = e^-λ (λκ) / κ!
This is written as
1 - e^-0.485 x 0.485⁰ / 0!
1 - 0.6157
= 0.3843
The probability that on a randomly selected day, he wrote at least one check is 0.3843
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Airlines typically accept more reservations for flight than the number of seats on the plane. Suppose that for certain route an airline accepts 40 reservations on plane that carries 38 passengers Based on experience the probability distribution of Y = the number of passengers who actually show up for randomly selected flight is given in the following table You can check that Hlr 37.4 and "- 1.24 Number of passengers Yi 35 36 37 38 39 40 Probability pi 0.10 0.10 0.30 0.35 0.10 0.05 There is also crew of two flight attendants and two pilots on each flight Let X = the total number of people (passengers plus crew) on randomly selected flight
Answers
The probability that there are not enough seats left is given by:
0.15 = 15%.
How to obtain the probability?The probabilities in this problem are given from the discrete probability table, as follows:
P(X = 35) = 0.1 -> exactly 0.1 = 10% probability that exactly 35 passengers show up.P(X = 36) = 0.1 -> exactly 0.1 = 10% probability that exactly 36 passengers show up.P(X = 37) = 0.3 -> exactly 0.3 = 30% probability that exactly 37 passengers show up.P(X = 38) = 0.35 -> exactly 0.35 = 35% probability that exactly 38 passengers show up.P(X = 39) = 0.1 -> exactly 0.1 = 10% probability that exactly 39 passengers show up.P(X = 40) = 0.05 -> exactly 0.05 = 5% probability that exactly 40 passengers show up.There will not be enough seats if:
Exactly 39 or 40 passengers show up.
Hence the probability is given as follows:
p = P(X = 39) + P(X = 40) = 0.1 + 0.05 = 0.15.
Missing InformationThe problem asks for the probability that there are not enough sets left.
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Genevieve is cutting a 60-inch piece of ribbon into a ratio of 2:3. since 2 inches are frayed at one end of the ribbon, she will need to start 2 inches in. this is indicated as 2 on the number line. 25.2 in. 29.4 in. 35.1 in. 40.7 in.
Answers
If she will need to start 2 inches in then total length of ribbon is 25.2 needs.
In the given question, Genevieve is cutting a 60-inch piece of ribbon into a ratio of 2:3.
2 inches are frayed at one end of the ribbon, she will need to start 2 inches.
Total length of ribbon is 60-inches.
Ratio of pieces = 2:3
Let the one piece length is 2x and other piece is 3x.
So 2x+3x=60
5x=60
Divide by 5, we get
x = 12
Now the length of one piece = 2*12 = 24
Other piece length = 3*12 = 36
Since, 2 inches are frayed at one end of the ribbon, she will need to start 2 inches.
So
=2* (3/2+3)
=2* 3/5
=1.2 inches
So the total length = 24+1.2 = 25.2
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Answer: A (25.2 in)
Step-by-step explanation:
:3
suppose that an accounting firm does a study to determine the time needed to complete one person's tax forms. it randomly surveys 175 people. the sample mean is 23.1 hours. there is a known population standard deviation of 6.0 hours. the population distribution is assumed to be normal. note: if you are using a student's t-distribution, you may assume that the underlying population is normally distributed. (in general, you must first prove that assumption, though.)
Answers
(i) The lower end of the confidence interval is
22.8 - 0.80 = 22
and, The upper end of the confidence interval is
22.8 + 0.80 = 23.6
ii) Error bound is the same as the margin of error
Error bound = 0.8
This is incomplete question:
Complete question is :
Suppose that an accounting firm does a study to determine the time needed to complete one person's tax forms. it randomly surveys 175 people. the sample mean is 23.1 hours. there is a known population standard deviation of 6.0 hours. the population distribution is assumed to be normal. note: if you are using a student's t-distribution, you may assume that the underlying population is normally distributed. (in general, you must first prove that assumption, though.)
Construct a 90% confidence interval for the population mean time to complete the tax forms.
i. State the confidence interval. (Round your answers to two decimal places.)
ii. Calculate the error bound. (Round your answer to two decimal places.
Now, According to the question:
Considering the central limit theorem, the distribution is normal since the number of samples is large. Also, the population standard
deviation is known. We would determine the z score.
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.90 = 0.1
α/2 = 0.1/2 = 0.05
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.05 = 0.95
The z score corresponding to the area on the z table is 2.05. Thus, confidence level of 90% is 1.645
Confidence interval is written in the form,
(Sample mean - margin of error, sample mean + margin of error)
The sample mean, x is the point estimate for the population mean.
Confidence interval = mean ± z × σ/√n
Where
σ = population standard Deviation
Confidence interval = x ± z × σ/√n
x = 22.8 hours
σ = 6.4 hours
n = 175
i) Confidence interval = 22.8 ± 1.645 × 6.4/√175
= 22.8 ± 0.80
The lower end of the confidence interval is
22.8 - 0.80 = 22
The upper end of the confidence interval is
22.8 + 0.80 = 23.6
ii) Error bound is the same as the margin of error
Error bound = 0.8
Hence,(i) The lower end of the confidence interval is
22.8 - 0.80 = 22
and, The upper end of the confidence interval is
22.8 + 0.80 = 23.6
ii) Error bound is the same as the margin of error
Error bound = 0.8
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if a bacterial culture starts with 8000 bacteria and doubles every 20 minutes, how many minutes will it take the population to reach 33000?
Answers
A bacterial culture that starts with 8000 bacteria of population and doubles every 20 minutes will reach 33000 bacteria in 40.887 minutes.
Calculate t in 33,000
33,000 = 8000 (2)^t/20
33,000/8000 = 2^t/20
log(33,000/8000) = (t/20) log2
t = 20 log(33,000/8000) / log 2 = 40.887 minutes.
Hence the time taken to reach 33000 population is 40.877mins.
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The population of a city has increased by 26% since it was last measured. If the current population is 18900 , what was the previous population?
Answers
Answer:
15,000
Step-by-step explanation:
The population of a city has increased by 26% since it was last measured. If the current population is 18,900 , what was the previous population?
increase of 26% means the current population is 126% of the previous.
126% = 1.26
18,900 = 1.26x
divide both sides by 1.26:
18,900/1.26 = 1.26x/1.26
x = 15,000
previous population was 15,000
Twenty out of 150 call received by each cutomer ervice repreentative from Company X are complaint. What i the percentage of complaint from the total call received by each cutomer ervice repreentative?
Answers
A customer service representative receives about 20% calls expressed as percentage which are complaints.
Total calls received = 150
Total number of complaint calls = 30
percentage of complaint calls = 30 /150 × 100% = 20%
Hence the total number of complaint calls is 20%.
Gains and losses in percentage terms are derived by computing the difference between two numbers and comparing that difference to the initial value.
One can calculate how much the initial value has changed mathematically by dividing the result by the starting value and using the absolute value of the difference between the two values.
By dividing the absolute difference between two numbers by their average, one can determine the percentage difference between two values. You will receive the answer in % rather than decimal multiplied by 100.
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A test of writing ability is given to a random sample of students before and after they completed a formal writing course. The results are given below. Construct a 99% confidence interval for the mean difference between the before and after scores. Round the limits to the nearest tenth. Before 70 80 92 99 93 97 76 63 68 71 74 After 69 79 90 96 91 95 75 64 62 64 76
Answers
-0.5 < µd< 4.5 are the limits of the given data.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
Given,
The results are given below. Construct a 99% confidence interval for the mean difference between the before and after scores
Before 70 80 92 99 93 97 76 63 68 71 74
After 69 79 90 96 91 95 75 64 62 64 76
Mean SD SEM N
80.27 12.76 3.85 11
78.27 12.92 3.89 11
df = 10
standard error of difference = 0.798
The mean of Before minus After equals 2.00
Given a=0.01, |t(0.005, df=10)|=3.17 (check student t table)
So 99% confidence interval is 2±ts
2±3.17(0.798)
-0.5 < µd< 4.5
Hence, -0.5 < µd< 4.5 are the limits of the given data.
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The sides of a triangle with positive area have lengths 4, 6 and x . The sides of a second triangle with positive area have length 4, 6 and y. The smallest positive number that is not the positive number that is not the possible value of | x - y | is ( x and y are integer ) a. 2 b. 4 c. 6 d. 8
Answers
The value of |x - y| which is not possible is 8.
Here we have to find the value of | x - y| which is not possible.
Given data:
The sides of a triangle are 4,6 and x and the other sides of a triangle are 4, 6, and y.
We know the fact that the sum of the lengths of two sides of a triangle is always greater than the third side.
Let us take the minimum and maximum values of the third side as x and y.
Minimum value is ≥ 6 - 4 that is ≥ 2
Maximum value is ≤ 6 + 4 that is ≤ 10
So, | x - y | ≤ | 10 - 2| that is ≤ 8.
The smallest positive number that is not the possible value of | x - y| is 8.
Therefore the value of | x-y| which is not possible is 8.
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How do you make a function table?.
Answers
These are the following steps you should follow to create a function table:
Function - A function is a mathematical concept that describes the relationship between an input and an output. A function can be expressed in four different ways. They can be communicated in a variety of methods, including spoken language, math, pictures, and function tables. Function table - A visual griddled table with input and output cells arranged in rows and columns is referred to as a function table. When students first learn function tables, they are sometimes referred to as function machines. The input value is subjected to the special rule of the table to produce the result.Rules of function tableThe rules of the function table can be used to comprehend the relationship between the input and the output. The rule of the table must be followed for all inputs and outputs. Function tables are helpful in this application. The rule must work if it is applied to one input/output and then verified with other sets to make sure it holds true.Another question that the rules subtly raises is the relationship between the input and the result. The question varies based on the table variable. What input value would result in the desired outcome when exposed to the known rule?, What outcome will result from using the known rule with the known input?, What mathematical technique—also referred to as a rule—can be used to generate the desired output from a known input?, Writing the input, output, and rule as a single line equation, solving it, and then figuring out the variable is commonly preferred.The third important item to note about the rule governing the relationship between the input and the output is that the mathematical operation will be constrained dependent on the input and output values. If the input is less than the result, the rule will be an operation that raises values, such as addition, multiplication, or exponents. If the input is more than the output, an operation such as subtraction, division, or square roots reduces the values. Example: If a cell contained the number 10 and another contained the number 12, what would be the logical conclusion? In plain English, what could be done to the 10 to get 12? The function's rule is to add two because adding two to ten results in seven. In a function table, there would have been more inputs and outputs than just 10 and 12, but the function would still have been the same. As a result, if the next input cell contained the number 16, the output would be 18 because the rule is add 2, which adds twoBy rule since [tex]X^{2} = Y[/tex] or square of input = output
By output since [tex]\frac{x}{5}[/tex] = output
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A company famous for its nacho-flavored corn chips has developed two new formulas, A and B, which they hope their customers will like even more than the original formula. To determine whether customers prefer one of the new formulas over the current nacho flavoring, a sample of 50 customers is obtained. Each customer tastes both formula A and formula B in a randomly assigned order and indicates which one they prefer more. Which of the following best describes this study?
This study is not well designed because formulas A and B are not compared with the original formula.
Answers
This study is not well designed because formulas A and B are not compared with the original formula.
Given:
A company famous for its nacho-flavored corn chips has developed two new formulas, A and B, which they hope their customers will like even more than the original formula. To determine whether customers prefer one of the new formulas over the current nacho flavoring, a sample of 50 customers is obtained. Each customer tastes both formula A and formula B in a randomly assigned order and indicates which one they prefer more.
sample customers = 50
But here there is not given a relation or comparing between A and B so we cannot predict which one is prefer more.
Therefore This study is not well designed because formulas A and B are not compared with the original formula.
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When the scale factor is greater than 1 the size of the image?.
Answers
If the scale factor is greater than 1, the image is larger than the preimage
What do dilations entail?Increasing the size of a figure without changing its shape is a process known as dilatation. Dilation can result in a figure growing or shrinking. Preimage is the name for the earliest figure in dilatation. A figure has been magnified Figures are warped from the center of dilatation, which is a fixed point.
What are shrinkage and growth?By enlarging or contracting a figure, the scale factor indicates how much the image will change in size.
1) If the scaling factor is between 0 and 1, the picture is smaller than the preimage. With a scale factor of between 0 and 1, reductions are known as dilations.
2) If the scale factor is more than 1, the picture will be bigger than the preimage. When a dilatation has a scale factor higher than 1, it is said to be an enlargement. Each new point in a dilated figure may be located using the prime symbol, ". The dilated version of point, which stands for "prime," would be point'.
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a square with a side length of 2 units is drawn on the coordinate plane with a vertex at the origin. Which shows a dilation of the square by a scale factor of 2
Answers
the dilation factor will change the square of the side 2 units.
What is square?
Having four equal sides, a square is a quadrilateral. There are numerous square-shaped objects in our immediate environment. Each square form may be recognised by its equal sides and 90° inner angles. A square is a closed form with four equal sides and interior angles that are both 90 degrees. Numerous different qualities can be found in a square.
A square with a side length of 2 units is drawn on the coordinate plane with a vertex at the origin.
If a scale factor of 2 is applied to the given square, with point D serving as the centre of dilation
A point is enlarged by a scale factor k according to the following rule:
(x, y) → (kx, ky)
According to this rule, k =2
A(-2, 0) → A'(-4, 0)
B(-2, 2) → B'(-4, 4)
C(0, 2) → C'(0, 4)
D(0, 0) → D'(0, 0)
Hence the dilation factor will change the square of the side 2 units.
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Helen draws a random circle.
She then measures its diameter and circumference.
She gets a circumference, C, of 405 mm correct to 3 significant figures.
She gets a diameter, d, of 130 mm correct to 2 significant figures.
Helen wants to find the value of r using the formula n = C
Calculate the lower bound and upper bound for Helen's value of r.
Give your answers correct to 3 decimal places.
Answers
The lower bound and upper bound for Helen's value would be; 3.165, and 3.065.
What is circumference?The circumference is the perimeter of the circle.
Given that the circumference of circle C, at 405 mm to three significant numbers.
Helen correctly estimates the diameter of circle, d, to be 130 mm to two significant numbers.
She wants to find the value of Pi using the formula π=C/D
We have, the circumference of the circle, C = 405 mm
The diameter of the circle, d = 130 mm
π=C/D
π= 405 mm / 130 mm
= 405 / 130
π= 3.115 measured to the nearest 0.1.
The degree of accuracy is nearest 0.1.
Then;
0.1/2 = 0.05
Therefore, Upper bound = 3.115 + 0.05 = 3.165
Lower bound = 3.115 - 0.05 = 3.065
Therefore, the lower bound and upper bound for Helen's value would be; 3.165, and 3.065.
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Efficiency ratio: deutsche bearings has total sales of $9,745,923, inventories of $2,237,435, cash and equivalents of $755,071, and days' sales outstanding of 49 days. if the firm's management wanted its dso to be 35 days, by how much will the accounts receivable have to change?
Answers
The change in the accounts receivable is -$373,816.23 if the firm's management wanted its to be done in 35 days.
Here we have to find the change in the accounts receivable.
The given data:
Sales = $ 9,745,923
inventory = $ 2,237,435
cash = $ 755,071
day's sales outstanding(DSO) = 49 days
Formula to find DSO:
DSO = 365/ accounts receivable turnover
= 365/ ( net sales/ accounts receivable)
= 365 × accounts receivable/ net sales
Account receivables = DSO × net sales / 365
= 49 × 9,745,923 / 365
= $1,308,356.70
Target DSO = 35 days
Net accounts received = DSO × net sales / 365
= 35 × 9,745,923 / 365
= $934,540.56
ΔAccounts received = $1,308,356.79 - $ 934,540.56
= - $373,816.23
Therefore change in accounts received is -$373,816.23.
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What is the median of the following numbers? 8, 10, 8, 5, 4, 7, 5, 10, 88,10,8,5,4,7,5,10,8.
Answers
The median of the following numbers
8, 10, 8, 5, 4, 7, 5, 10, 88, 10, 8, 5, 4, 7, 5, 10, 8 is 8.
Given numbers is
8, 10, 8, 5, 4, 7, 5, 10, 88,10, 8, 5, 4, 7, 5, 10, 8
First you have to organize them in least to greatest order,
4, 5, 5, 7, 8, 8, 8, 10, 10
Second now take these numbers and climate one from each side until you have 1 or 2 numbers left.
that is the
4 5 5 7 8 8 8 10 10
x x x x ! x x x x
So, the middle number will be the median of the given numbers.
Hence the answer is the median of the following numbers
8, 10, 8, 5, 4, 7, 5, 10, 88, 10, 8, 5, 4, 7, 5, 10, 8 is 8.
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write an equivalent expression for -2x + 7 1/5
Answers
Answer: -2x + 7.20
Step-by-step explanation: This equation is in simplified form, given the fraction is already a mixed number. Since 7 1/5 is a mixed number, we can find the equivalent expression by identifying 1/5 of 100.
1/5 × 100 = 100/5 ⇒ 20
Finally, we substitute 20 in for 1/5 to find the equivalent expression:
-2x + 7 1/5 ⇒ -2x + 7.20
How is a treaty defined?.
Answers
A treaty is defined as a peaceful accord closed between States written down and represented by worldwide regulation, whether typified in a solitary instrument or in at least two related instruments and whatever its specific assignment.
Treaty is an exceptionally misconstrued term, so we really want a meaning of deal that is exact and definitive. The definition that makes reference is the one tracked down in the Vienna Show on the Law of Deals of 1969.
Presently, there is likewise a Vienna Show of 1986 which manages understanding among States and worldwide associations, however for the essential definition manages arrangement between States. The necessities are:
the understanding should be in writing the arrangement should be represented by global regulation, and that implies that it makes regulations and commitments under worldwide lawthe name (assignment) of the understanding isn't significant (an "Trade of Notes" likely could be a treaty) the structure might be that of at least one related reports, for instance a trade of letters (two records) can frame a solitary deal.To know more about treaty, visit here:
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20. Every day Isabel swims 10 to 20 laps in a 50-meter pool. She tracks the numbers of laps she swims and how long it takes her to complete the lap, in
minutes.
Answers
All integers higher than or equal to 10 and less than or equal to 20 are included in the domain.
What is meant by domain?The domain of a function is the set of all possible inputs. The set of all potential values that can be used as inputs, or alternatively, the entire range of possible values for independent variables, constitutes the domain of a function.
As, The domain of a function is the set of all values that can be put into it while assuring that it exists and accepts a real number as a value.
The domain of a function is understood to be the set of values that we are permitted to enter into our function.
This set consists of the x values for a function like f(x).
Hence, the correct answer is the domain consists of all integers greater than or equal to 10 and less than or equal to 20.
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The Complete Question is:
Every day Isabel swims 10 to 20 laps in a 50-meter pool. She tracks the numbers of laps she swims and how long it takes her to complete the laps, in
minutes
Choose the correct answer below.
O A. The domain consists of all integers greater than or equal to 0.
OB. The domain consists of all integers greater than 0 and less than or equal to 20.
OC. The domain consists of all integers greater than or equal to 0 and less than or equal to 20
D. The domain consists of all integers greater than or equal to 10 and less than or equal to 20.
E. The domain consists of all integers less than or equal to 20.
If x is the interval (pi/2,pi) and y is in the interval (pi,3pi/2) and the sin x= 3/4 and cot y=5/6, evaluate each of the following.
a) sin (x+y) b) cos(x-y) c) tan(x-y)
Answers
The given trigonometric identities can be evaluated as (a) sin(x + y) = (-15 + 6√7)/4√61, (b) cos(x - y) =(5√7 - 18)/4√61 and (c) tan(x - y) = (-15 - 6√7)/(5√7 - 18).
What are trigonometric ratios?The trigonometric ratios are defined for a right angled triangle.
The example of these ratios are sin, cos, tan, cosec, sec and cot.
The trigonometric ratios are useful in determining the heights and distances of the large objects.
Given that,
The value sin(x) = 3/ 4 for π/2 < x < π.
And, cot(y) = 5/6 for π < y < 3π/2.
Since x is given in the second quadrant cos(x) is negative such that,
cos(x) = -√ (1 - sin²(x) )
= - √(1 - (3/4)²
= -√7/4
Since, y is in third quadrant sin(y) and cos(y) is negative.
sin(y) = -1/√(1 + cot²(y))
= -1/√(1 + (5/6)²)
= -6/√61
Cos(y) = -√ (1 - sin²(y))
= - √(1 - (-6/√61)²
= -5/√61
tan(x) = sin(x)/cos(x)
= -3/√7
tan(y) = sin(y)/cos(y)
= 6/5
Now, the following trigonometric identities can be evaluated as follows,
(a)
sin(x + y) = sin(x)cos(y) + cos(x)sin(y)
Substitute the respective values to get,
sin(x + y) = 3/4 × -5/√61 + -√7/4 × -6/√61
= (-15 + 6√7)/4√61
(b) cos(x - y) = cos(x)cos(y) + sin(x)sin(y)
= -√7/4 × -5/√61 + 3/4 × -6/√61
= (5√7 - 18)/4√61
(c) tan(x - y) = (tan(x) - tan(y))/(1 +tan(x)tan(y))
= (-3/√7- 6/5)/(1 +-3/√7 × 6/5)
= (-15 - 6√7)/(5√7 - 18)
Hence, the required values are sin(x + y) = (-15 + 6√7)/4√61, cos(x - y) =(5√7 - 18)/4√61 and tan(x - y) = (-15 - 6√7)/(5√7 - 18).
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What is the equation of the line written in general form? -3x - y 2 = 0 3x - y - 2 = 0 3x y - 2 = 0
Answers
The equation of the line is -3x - y + 2 = 0.
Here, we are given a graph of a line as shown in the image below.
From the graph we can see that the line cuts the y axis at -2. This means that when x = 0, y = -2.
Thus, we get one point, that is, (0, -2)
Similarly, the line cuts x axis at 2/3.
Thus, we get another point, that is, (2/3, 0)
Thus, the slope of the line will be-
(0 + 2)/ (2/3 - 0)
= 2*3/2
= 6/2
= 3
The equation of a line is given as y = mx + c, where m is the slope and c is the y intercept.
Here, m = 3 and c = -2
Thus, equation of the line will be-
y = 3(x) - 2
y = 3x - 2
-3x - y + 2 = 0
Thus, the equation of the line is -3x - y + 2 = 0.
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Your question was incomplete. Check for the missing figure below.
Which of factors has a product of 96?.
Answers
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
1 x 96 = 96 (1, 96)
2 x 48 = 96 (2, 48)
3 x 32 = 96 (3, 32)
4 x 24 = 96 (4, 24)
6 x 16 = 96 (6, 16)
8 x 12= 96 (8, 18)
T/F there was a spike of competitive authoritarian regimes in the years immediately following world war 2, but the last decade has seen a sharp decline in competitive authoritarian regimes.
Answers
It is true that the last decade has seen a sharp decline in competing authoritarian regimes.
Competing authoritarian – dictators submit to meaningful multiparty elections but engage in serious democratic abuses – proliferated in the post-Cold War era. Africa, Asia, Latin America, post-communism Based on an in-depth study of 35 cases in Eurasia, this book examines the fate of competing authoritarian regimes from 1990 to 2008. , in places such as Eastern Europe and the United States, the external costs of abuses have led incumbents to relinquish power rather than crack down, leading to democratization. political pressure has been weaker and the country has democratized less frequently.
Competitive authoritarianism is a type of hybrid government, or political regime that combines elements of democracy and authoritarianism. Highly competitive dictatorships regularly hold intense multi-party elections. However, the “playing field” is not the same. Media control, abuse of state resources, coercion and/or limited fraud give incumbents an unfair advantage over the opposition. These governments are not democratic because elections are not free and fair. But they aren't entirely authoritarian either. Unfair, but not completely pointless. In competitive authoritarian regimes, there is real competition and some uncertainty about the outcome of elections.
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What are the types of outlier?.
Answers
The Three Kinds of Outliers
All outliers fit into one of three well recognized groups in statistics and data science:
1 Global outliers, type 1 (aka Point Anomalies)
2 Contextual outliers, type 2 (aka Conditional Anomalies)
3 Collective outliers, type 3
Global outliers, type 1
In the same way that "global variables" in a computer program can be accessed by any function in the program, a data point is considered to be a global outlier if its value is significantly outside the bounds of the data set in which it is found.
Contextual (Conditional) Outliers, Type 2
Data points that dramatically differ from other data within the same context are known as contextual outliers. When it comes to time-series data, such as records of a certain number across time, the "context" is nearly always temporal.
Collective outliers, type 3
If a subset of data points inside a data set exhibits values that considerably differ from the overall data set, but the values of the individual data points do not exhibit abnormal behavior either globally or contextually, then the subset is said to be anomalous.
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