Answers
The first and second equations satisfy standard form of the linear equation, hence they are linear. While, third, fourth, and fifth are non linear equations.
What is system of linear equation?A group of two or more simultaneous solutions to linear equations is referred to as a system of linear equations. A collection of values that satisfy every equation in a system of linear equations is the solution. There might not be a unique solution if the number of equations in the system is less than or equal to the number of variables in the system. Systems of linear equations can be solved using various methods, such as substitution, elimination, or matrix algebra.
The standard form of linear equation is given as:
y = mx + b
The first and second equations satisfy, or represent the standard form of the linear equation, hence they are linear.
While, third, fourth, and fifth do not represent the standard form and hence are non linear equations.
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1. linear function 2. non linear function 3. linear function 4. non linear function 5. non linear function.
What is linear function?
In mathematics, a linear function is a type of function that can be represented by a straight line on a graph.
1.The equation m = 5.45p represents a linear function. It has the form y = mx + b, where m is the slope and b is the y-intercept. In this case, m = 5.45, which is a constant rate of change, and there is no other term involving p, so the equation is linear. When p increases or decreases by 1 unit, m increases or decreases by 5.45 units, respectively.
2.The equation 1=56.01+5 is not a function. It is a simple linear equation in one variable, but it has no independent variable to define a function. It is just an equation that states a relationship between two constants, 56.01 and 5, which sum up to 61.01.
3.The function d = (g-28)7/11 is a linear function because it can be written in the form y = mx + b, where m and b are constants and y and x are variables.
In this case, if we let d = y and g = x, we get:
y = (x-28)7/11
This can be simplified as:
y = 7/11 * x - 196/11
So we can see that the function has a constant slope of 7/11, and a constant intercept of -196/11. Therefore, it is a linear function.
4. This is a non-linear function since it includes a variable raised to a power (r³).
5.The function e=124² is a non-linear function as it involves squaring the value of 124, which produces a curved graph instead of a straight line.
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Related Questions
You went out to dinner and your meal $22.00. If you want to leave a 20% tip, how much will you pay total?
Answers
You will pay a total of $26.40 including the 20% tip.
To calculate the total amount including the 20% tip, you need to add 20% of the meal cost to the original meal cost:
A gratuity or a small amount of money given to someone for their service, such as a waiter or a hairdresser.
A piece of advice or a suggestion given to someone to help them do something better or more efficiently.
A pointed or tapered end of an object, such as the tip of a pen or a needle.
Tip amount = 20% of $22.00 = 0.2 x $22.00 = $4.40
Total amount including tip = $22.00 + $4.40 = $26.40
Therefore, you will pay a total of $26.40 including the 20% tip.
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Set of natural numbers is denoted by letter
Answers
Answer: N
Step-by-step explanation: The set of natural numbers is represented by the letter “N”. A natural number is a number that occurs commonly and obviously in nature. As such, it is a whole, non-negative number. The set of natural numbers, denoted N, can be defined in either of two ways: N = {0, 1, 2, 3, ...}
Let's say you took a sample of 445 voice-activated smart TVs. The mean rate at which these TVs need to be serviced or replaced is every 3.5 years, with a standard deviation of 0.8 years. Given a confidence level of 95%, what is the maximum error of estimate?
Answers
The maximum errοr οf estimate is 0.092 years οr apprοximateIy 1 mοnth.
What is Standard Deviatiοn?The standard deviatiοn is a measure οf the amοunt οf variatiοn οr dispersiοn οf a set οf vaIues frοm their mean οr average. It is caIcuIated as the square rοοt οf the variance.
Tο find the maximum errοr οf estimate, we need tο use the fοrmuIa:
Maximum errοr οf estimate = z * (standard deviatiοn / √(sampIe size))
where z is the z-scοre assοciated with the given cοnfidence IeveI, standard deviatiοn is the pοpuIatiοn standard deviatiοn (0.8 years), and sampIe size is the number οf TVs sampIed (445).
At a cοnfidence IeveI οf 95%, the z-scοre is 1.96.
Substituting the vaIues in the fοrmuIa, we get:
Maximum errοr οf estimate = 1.96 * (0.8 / √(445))
= 0.092 years (rοunded tο 3 decimaI pIaces)
Therefοre, the maximum errοr οf estimate is 0.092 years οr apprοximateIy 1 mοnth. This means that we can be 95% cοnfident that the true mean rate at which the TVs need tο be serviced οr repIaced is within 1 mοnth οf the sampIe mean οf 3.5 years.
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A diner has 645 napkins. 325 napkins are used at lunch. 113 napkins are used at dinner.Melanie says that 325−113=n325-113= napkins are used in all, and that 645−212=r645-212= napkins are left.Is her answer reasonable? Explain why or why not.
Answers
Melanie's answer that 212 napkins were used in all and 433 napkins were left is reasonable and can be verified by using simple algebraic equations.
Yes, Melanie's answer is reasonable. She correctly determined that the total number of napkins used in lunch and dinner was 325-113 = 212. From this, we can also confirm that the total number of napkins left was 645 - 212 = 433. We can verify these answers by using simple algebraic equations to solve the problem. Using the equation 645 = 325 + x, where x is the number of napkins used at dinner, we can solve for x by subtracting 325 from both sides to get x = 320. Similarly, using the equation 645 = 433 + y, where y is the number of napkins used in all, we can solve for y by subtracting 433 from both sides to get y = 212. This confirms Melanie's answer that 212 napkins were used in all and 433 napkins were left.
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A study found that the mean amount of time cars spent in drive-throughs of a certain fast-food restaurant was 137.5 seconds. Assuming drive-through times are normally distributed with a standard deviation of 27 seconds, complete parts below:
Answers
To solve this problem, we need to standardize the drive-through time using the formula z = (x - μ) / σ, where x is the drive-through time, μ is the mean, and σ is the standard deviation. Then we can look up the area under the standard normal curve corresponding to a z-score of z using a standard normal distribution table or a calculator.
In this case, we want to find the probability that a randomly selected car spends more than 2 minutes in the drive-through, which corresponds to a drive-through time of x > 120 seconds. To standardize this value, we use:
z = (x - μ) / σ = (120 - 137.5) / 27 = -0.648
Looking up the area under the standard normal curve corresponding to a z-score of -0.648, we find:
P(z > -0.648) = 0.7406
Therefore, the probability that a randomly selected car spends more than 2 minutes in the drive-through is approximately 0.7406 or 74.06%.
b) What is the probability that a randomly selected car spends between 90 and 150 seconds in the drive-through?
To find the probability that a randomly selected car spends between 90 and 150 seconds in the drive-through, we need to standardize these values using the formula z = (x - μ) / σ, where x is the drive-through time, μ is the mean, and σ is the standard deviation. Then we can find the area under the standard normal curve between the corresponding z-scores using a standard normal distribution table or a calculator.
To standardize 90 seconds and 150 seconds, we use:
z1 = (90 - 137.5) / 27 = -1.7593
z2 = (150 - 137.5) / 27 = 0.4629
Using a standard normal distribution table or a calculator to find the area under the standard normal curve between z1 = -1.7593 and z2 = 0.4629, we get:
P(-1.7593
(I hope that helps you)
Write a quadratic function in standard form to represent the data in the table.
Answers
Therefore, the quadratic function in standard form that represents the data in the table is: y = 1/2 x² - 5/2 x + 5.
What is function?A function is a mathematical concept that describes the relationship between two sets of numbers. It is a rule that assigns to each input (or element in the domain) exactly one output (or element in the range). In simpler terms, a function is like a machine that takes in a number and produces another number as output, according to some specific rules. The input is usually denoted by x, and the output by f(x), which is read as "f of x". Functions can take many forms, such as linear, quadratic, trigonometric, exponential, logarithmic, and more. They are widely used in mathematics, science, engineering, and many other fields to model and analyze various phenomena.
Here,
To write a quadratic function in standard form, we need to use the general form of the quadratic equation:
y = ax²+ bx + c
where a, b, and c are constants. We can use the values in the table to find these constants.
When x = 2, y = 3
When x = 4, y = 1
When x = 6, y = 3
When x = 8, y = 9
When x = 10, y = 19
Substituting these values into the quadratic equation, we get:
3 = 4a + 2b + c
1 = 16a + 4b + c
3 = 36a + 6b + c
9 = 64a + 8b + c
19 = 100a + 10b + c
We can now use these equations to solve for a, b, and c. One way to do this is to use a matrix equation:
|16 4 1| |a| |1|
|36 6 1| |b| = |3|
|64 8 1| |c| |9|
Using a calculator or matrix software, we can solve for a, b, and c:
a = 1/2
b = -5/2
c = 5
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Point GG is located at (-3,6)(-3,6) on the coordinate plane. Point GG is reflected over the xx-axis to create point G'G ′ . Point G'G ′ is then reflected over the yy-axis to create point G''G ′′ . What ordered pair describes the location of G''?G ′′ ?
Answers
For given coordinates, the ordered pair describing the location of G'' is (3,-6).
What are coordinates?
Coordinates are a set of numbers that specify the position or location of a point or object in space, relative to a reference point or system. In two-dimensional space, coordinates are usually represented by a pair of numbers (x, y), where the first number represents the horizontal position of the point along the x-axis, and the second number represents the vertical position of the point along the y-axis. In three-dimensional space, coordinates are usually represented by a triple of numbers (x, y, z), where the first number represents the horizontal position of the point along the x-axis, the second number represents the vertical position of the point along the y-axis, and the third number represents the position of the point along the z-axis, which is perpendicular to the x-y plane.
Now,
When a point is reflected over the x-axis, the y-coordinate is negated. So the image of G(-3,6) over the x-axis is G'(-3,-6).
When a point is reflected over the y-axis, the x-coordinate is negated. So the image of G'(-3,-6) over the y-axis is G''(3,-6).
Therefore, the ordered pair describing the location of G'' is (3,-6).
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Un camino recto que continua para siempre en ambas direcciones es un
Answers
Answer: una linea
Step-by-step explanation:
A cabinet was ordered from a carpenter with a volume of 1.08 m³. He wrote down the following measurements: 1.2 m wide and 1.8 m high, but forgot to write down the depth. Therefore, the depth measurement is
Answers
The depth of this cabinet is equal to 0.5 m³.
VolumeVolume is a three-dimensional measure that indicates the space occupied by an object. It is a physical quantity that expresses the amount of space an object occupies in three dimensions - length, width and height.
Note that this cabinet has the shape of a parallelepiped, and its volume is found by multiplying its dimensions. Calculating the depth measurement, we have:
1,08 m³ = 1,2 m * 1,8 m * p
p = 1,08 m³/(1,2 m * 1,8 m)
p = 1,08 m³ / 2,16 m³
p = 0,5 m
A company makes 140 bags. 47 of the bags have buttons but no zips. 48 of the bags have zips but no buttons. 22 of the bags have neither zips nor buttons. How many bags have zips on them?
Answers
Required number of bags which have zips on them are 71.
Here given, A company makes 140 bags.
So, total number of bags = 140
It is also given, 47 of the bags have buttons but no zips 48 of the bags have zips but no buttons.
So, number bags which have buttons but no zips = 47 and number bags which have zips but no buttons = 48
and numbers of bags which have neither zips nor buttons = 22.
If we subtract number of bags which have no zips from total number of bags then we will get total number of bags which have zips
So, number of bags have zips on them
[tex] = 140 - 47 - 22 = 71[/tex]
Therefore, 71 bags have zips on them.
This is a problem of Subtraction.
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A line has a slope of 5/6
and passes through the point (7,6). Write its equation in slope-intercept form.
Answers
Answer:
y = 5/6x + 1/6
Step-by-step explanation:
m = 5/6, x = 7, y = 6
y = mx + b
6 = 5/6(7) + b
b = 6 - 35/6
b = 36/6 - 35/6 = 1/6
y = 5/6x + 1/6
Answer:
Below
Step-by-step explanation:
Here is another way:
Start with point ( 7,6) slope ( m= 5/6) form :
(y-6) = 5/6 ( x-7) expand
y-6 = 5/6 x - 35/6 add 6 to both sides
y = 5/6 x + 1/6 Done.
what is required for a current to flow?
A. Electrons, protons, and an energy source
B. An insulator, battery, and recipient
C. A recipient, a connection, and something made out of rubber
D. An Energy source, a recipient, and a connection
Answers
Answer:
D. An Energy source, a recipient, and a connection
-5 + x-2 = 3x + 10 - x Which of the following statements correctly describe the solution(s) of the equation above? Select all that apply. • The equation has only one solution. • The equation has no solutions. F The equation has infinitely many solutions. ) The equation's only solution is x = - 17. • The equation is solved by all numbers less than 17.
Answers
The equation's only solution is x = -17.
Simplifying the left-hand side of the equation:
-5 + x - 2 = -7 + x
Simplifying the right-hand side of the equation:
3x + 10 - x = 2x + 10
Substituting into the original equation, we get:
-7 + x = 2x + 10
Subtracting x from both sides, we get:
-7 = x + 10
Subtracting 10 from both sides, we get:
-17 = x
So the only solution to the equation is x = -17. Therefore, the correct statement about the solution(s) of the equation is:
• The equation's only solution is x = -17.
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Find the value of x and y. Not drawn to scale
Answers
Using the definitions for the types of triangles in the image, we can see that the interior angles are:
x = 37°
y = 14°
How to find the value of x and y?First, on the right side we can see an equilateral triangle, then all its interior angles are of 60°.
Amd the triangle in the left side is isoceles, then the angle in the right side has the same measure than x, and now with that we can write the equation:
x + 83° + 60° = 180°
Solving for x, we will get:
x = 180° - 83° - 60°
x = 37°
Now let's find the value of y, we cansee that the triangle in the middle is also isoceles, and remember that for any triangle the sum of the interior angles must be 180°, so here we can write:
83° + 83° + y = 180°
y = 180° - 2*83°
y = 14°
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PLEASE HELP! URGENT AND WORTH 50 POINTS!!!
Answers
Answer: 3.5
Step-by-step explanation: sry if im wrong ):
?how do i do this pleas help
Answers
The angles 5 and 6 which are given in the diagram above are typical example of an adjacent angle.
What is an adjacent angle?An adjacent angle is defined as the type of angle that has a common sides which is shared by the two angles that are being compared.
A vertical angle is the type of angle that is usually opposite and they constructed by the intersection of two lines.
Therefore since a common sides exists between angle 5 and 6.
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Martha made 2 2/3 pounds of pasta. she divided the pasta into fourths. how much pasta is in each portion?
Answers
Step-by-step explanation:
2 2/3 = 8/3
8/3 * 1/4 = 8/12 = 2/3 pound in each portion
Nicole bought
6
CDs that were each the same price. Including sales tax, she paid a total of
$
69.60
. Of that total,
$
4.20
was tax. What was the price of each CD before tax?
Answers
Answer: $11.60
Step-by-step explanation: Since ur finding the cost of one cd and she bought 6 and since is before tax you do 36.90/(divided by) 6 and boom #!
129. (1+x)y' = (x + 2)(y − 1)
Calculus vol 2 need help solving this!!!!
Answers
By answering the question using the information provided, we can conclude that in order to arrive at the general solution, we must take into account the scenario in which [tex]y-1\neq 0 , y \neq 1[/tex], by constructing equations.
What do you mean by equations?Two equations are said to be equivalent when their bases and solutions line up. To create an equivalent equation, the same quantity, symbol, or expression must be added to or removed from both of the equation's two sides.
We can also create an analogous equation by multiplying or dividing both sides of an equation by a nonzero integer.
Solving differntial calculus
[tex](1+x)y'=( x+2) (y-1)[/tex]
We will first employ varying separation. The variables y and x will be placed on the opposite sides of the equation, and both sides will be integrated.
[tex](1+x)y'/(y-1) = (x+2)dx[/tex]
We will integrate both sides using the substitution[tex]u= y-1,\frac{du}{dy} =y'[/tex]
∫[tex](x+2)dx[/tex] =∫[tex](1+x)\frac{du}{u}[/tex]
㏑l[tex]u[/tex]l +[tex]x[/tex]㏑l[tex]u[/tex]l= [tex]\frac{1}{2} x^{2}+2x+c[/tex]
Substituting [tex]u= y-1[/tex]
㏑l[tex]y-1[/tex]l+ [tex]x[/tex]㏑l[tex]y-1[/tex]l= [tex]\frac{1}{2x^{2} } +2x+c[/tex]
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The complete question is: Find the general solution to the differential equation (1+x)y' = (x + 2)(y − 1).
Please help quick!! Given m || n, find the value of x.
Answers
In the given angles the required value of x is 17° respectively.
What are angles?An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively.
Angles created by two rays are in the plane where the rays are located.
The meeting of two planes also creates angles. We refer to these as dihedral angles.
Based on the measurement, there are many kinds of angles in geometry.
The names of fundamental angles include acute, obtuse, right, straight, reflex, and full rotation.
So, we know that:
2x+5 + 8x+5 = Straight angle
2x+5 + 8x+5 = 180
Now, solve for x as follows:
2x+5 + 8x+5 = 180
10x+10 = 180
10x = 170
x = 17
Therefore, in the given angles the required value of x is 17° respectively.
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Determine the order of the following matrix:
[9 6 -4 8]
Answers
The order of the matrix is 2 x 2.
What is a matrix and what is meant by its order?
In the field of mathematics, matrices are rectangular arrangements of numerical values, symbols, or algebraic expressions, organized in rows and columns. Matrices are used in many areas of mathematics and science, as well as in engineering, physics, and computer graphics.
The term 'order' in the context of matrices refers to the dimensions of the matrix, which are determined by the number of rows and columns it contains. It is denoted by m x n, where m is the number of rows and n is the number of columns. To find the order of a matrix, we simply count the number of rows and columns. The order is usually written as a pair of numbers in the form m x n.
Determine the order of the given matrix:
In the given problem, we are asked to find the order of the matrix:
[tex]\begin{pmatrix}9 &6 \\-4 & 8\end{pmatrix}[/tex]
we count the number of rows and columns.
This matrix has 2 rows and 2 columns, so its order is 2 x 2.
Therefore, the order of the matrix is 2 x 2.
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Lee watches TV for 4 hours per day. During that time, the TV consumes 200 watts per hour. Electricity costs (12 cents)/(1 kilowatt-hour). How much does Lee’s TV cost to operate for a month of 30 days?
Answers
The cost to operate Lee's Tv is 2.88 dollars.
How to find the cost to operate for a month?Lee watches TV for 4 hours per day. During that time, the TV consumes 200 watts per hour. Electricity costs (12 cents)/(1 kilowatt-hour).
Therefore, the cost for Lee to operate in 30 days can be calculated as follows:
200 watt = 0.2 kilowatt
Therefore,
1 day = 4 hours
30 days = ?
cross multiply
number of hours = 120 hours.
Therefore, in 30 days he watches television for 120 hours.
Let's find the cost
0.12 dollars = 12 cent
1 hour = 0.2 kilowatt
120 hours =
kilowatt use in 30 days = 0.2 × 120 = 24 kilowatts
Therefore,
1 kilowatts = 0.12 dollars
24 kilowatts = ?
cost of Tv for a month of 30 days = 24 × 0.12
cost of Tv for a month of 30 days = 2.88 dollars
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Write a paragraph proof of the Quadrilateral Sum Theorem.
Given: Quadrilateral ABCD
Prove: m
Answers
Step-by-step explanation:
Quadrilateral Sum Theorem. The total sum of the interior angles of a quadrilateral is 360°. A quadrilateral is formed by joining four non-collinear points. A quadrilateral has four sides, four vertices and four angles. Therefore, that is the Quadrilateral Sum Theorem.
Weathering and erosion are two processes that shape Earth’s surface. Which of the
following sets of factors cause both weathering and erosion?
a) acid rain, tree roots, waves
b) glaciers, waves, wind
c) moving water, plants, wind
d) acid rain, plants, ice
Answers
Majesty Video Production Inc. wants the mean length of its advertisements to be 35 seconds. Assume the distribution of ad length follows the normal distribution with a population standard deviation of 2 seconds. Suppose we select a sample of 14 ads produced by Majesty.
a. What percent of the sample means will be greater than 36.50 seconds? (Round your z-value and final answer to 2 decimal places.)
b. What percent of the sample means will be greater than 34.45 seconds. (Round your z-value and final answer to 2 decimal places.)
c. What percent of the sample means will be greater than 34.45 but less than 36.50 seconds? (Round your z-value and final answer to 2 decimal places.)
d. What is the probability that the sampling error would be less than or more than 1.5 seconds? (Round your z-value and final answer to 2 decimal places.)
Answers
The shape of the distribution of the sample mean time is normal.
The standard error of the mean time is 0.5.
The percentage of the sample means that would be greater than 31.25 seconds is 0.621%.
The percentage of the sample means that would be greater than 28.25 seconds is 99.977%.
The percentage of the sample means that would be greater than 28.25 but less than 31.25 seconds is 99.357%.
Given the following data:
Mean = 30.
Standard deviation = 2.
Sample = 16 ads.
What is a normal distribution?
A normal distribution is also referred to as the Gaussian distribution and it can be defined as a probability distribution that is continuous and symmetrical on both sides of the mean, which shows that all data near the mean have a higher frequency than data far from the mean.
a. The shape of the distribution of the sample mean time is normal.
b. To calculate the standard error of the mean time, we would apply this formula:
Standard error = 0.5.
c. To calculate the percentage of the sample means that would be greater than 31.25 seconds:
P(Z>2.5) = 0.621%.
d. To calculate the percentage of the sample means that would be greater than 28.25 seconds:
P(Z>2.5) = 99.977%.
e. To calculate the percentage of the sample means that would be greater than 28.25 but less than 31.25 seconds:
P(-3.5<Z<2.5) = 99.357%.
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Find the value of X
Answers
The measure or value of x = 55°. This is solved using the Tangent, Secant and Arc theorems.
What is the explanation for the above response?Note that the Measure of and x (m∠x) = (Far Arc - Near Arc)/2
Where
Far Arc = 360 - 65 - 120 = 175°
Near Arc = 65°
thus, m∠x = (175-65)/2
m∠x = 55°
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what is required for a current to flow?
A. Electrons, protons, and an energy source
B. An insulator, battery, and recipient
C. A recipient, a connection, and something made out of rubber
D. An Energy source, a recipient, and a connection
Answers
Therefore , the solution of the given problem of unitary method comes out to be enable the current to travel, a connection, such as a wire or conductor, is required.
What is a unitary method?Utilizing previously well-known variables, this uniform convenience, or all crucial elements from a prior flexible study that followed a particular methodology event can all be used to achieve the goal. It will be possible to contact the entity again if the anticipated assertion outcome actually happens; if it doesn't, both important systems will surely miss the statement.
Here,
D. In order for a current to move, there must be an energy source, a recipient, and a connection.
Current is the movement of charged ions through a conductor, most frequently electrons.
The energy required to transport the charged particles is provided by an energy source, such as a battery or generator.
The current has a route through a recipient, which can be a machine or a circuit.
In order to finish the circuit and enable the current to travel, a connection, such as a wire or conductor, is required.
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Points D, B, and E are collinear. Find
the value of a so that points A, B, and
C are collinear.
A
(4x)
O
E
B
148°
D
C
Answers
Using the supplementary angle theorem, the value for x so that points A, B, and C are collinear is 8.
What is a supplementary angle?
The definition of "supplementary" in mathematics relates to angles that combine to form a straight angle. It indicates that when two angles sum up to 180 degrees, they are said to be supplementary angles.
A line segment AC is drawn.
Point B is in between A and C.
A transversal DE is drawn passing through point B.
Points D, B, and E are collinear.
The measure of angle CBE is 148° and the measure of angle EBA is 4x°.
The angles ∠CBE and ∠EBA forms a pair of supplementary angles.
Their sum result in value of 180°.
Mathematically, this can be represented as -
∠CBE + ∠EBA = 180°
Substituting the values into the equation -
148° + 4x° = 180°
Solving for x, we get -
4x° = 180° - 148°
4x° = 32°
x = 32 / 4
x = 8
Therefore, the value for x is obtained as 8.
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The physical fitness score for a population of police officers at a local police station is 73, with an SD of 8 on a 100-point physical endurance scale. Suppose the police chief selects a sample of 64 local police officers from this population and records a mean physical fitness rating on this scale equal to 75. He conducts a single-sample z test to determine whether physical endurance increased for this group. Based on your outcome, what is the proper format for writing out the results for this problem?
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The p-value, under the assumption that the null hypothesis is correct, is the likelihood of receiving a test statistic that is as extreme as the one that was observed.
what is null hypothesis ?A declaration or assumption that there is no significant difference or association between two or more variables or populations being studied is known as the null hypothesis in statistics. The default hypothesis that is evaluated against an alternative hypothesis is known as the null hypothesis and is frequently represented as "H0." Typically, the null hypothesis is formulated in light of prior research, theoretical predictions, or accepted wisdom. It posits that any observed differences or correlations between groups or variables are the result of chance or random variation and serves as the foundation for evaluating a hypothesis.
given
We can use a standard format that includes the following details to present the z test results:
This is a claim regarding the population parameter being tested, or the null hypothesis.
In this instance, the null hypothesis is that the population of police officers' mean physical fitness score is equal to 73.
This assertion defies the null hypothesis, according to the alternative. The alternative hypothesis in this situation is that the sample of police officers' mean physical fitness score is higher than 73.
The p-value, under the assumption that the null hypothesis is correct, is the likelihood of receiving a test statistic that is as extreme as the one that was observed.
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If the graph of a polynomial function P(x) has x-intercepts at x = -4, x = 0, x = 5, the following must be true for P(x): D. The degree of the polynomial is greater than or equal to three.
Based on the graph of the polynomial f(x), the following is not a factor: B. (x - 1).
What is a polynomial graph?In Mathematics and Geometry, a polynomial graph simply refers to a type of graph that touches the x-axis at zeros, roots, solutions, x-intercepts, and factors with even multiplicities.
Generally speaking, the zero of a polynomial function simply refers to a point where it crosses or cuts the x-axis of a graph. Since the polynomial function with x-intercepts at x = -4, x = 0, and x = 5 cuts the x-axis at three (3) points. Therefore, the degree of this polynomial is either greater than or equal to three (3).
By critically observing the graph of the polynomial function shown above, we can logically deduce that its x-intercepts include the following;
x = -1 ⇒ x + 1 = 0.
x = -2 ⇒ x + 2 = 0.
x = 2 ⇒ x - 2 = 0.
x = 3 ⇒ x - 3 = 0.
Therefore, (x - 1) is not a factor.
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