The sum of integers is: S = n(a + l)/2
Integer numbers are those without fractional or decimal parts. When there are fewer numbers to add, it is possible to determine the sum of integers using basic mathematics. However, we employ the sum of integers formula if we need to add multiple consecutive integers at once. Our computations are made easier, and the amount of time we spend adding is reduced.
The sum of an arithmetic sequence's n terms is what is meant by the sum of integers formula. The formula for the sum of integers is:
S = n(a + l)/2
where,
S = sum of the consecutive integers
n= number of integers
a= first term
l = last term
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Write in the space provided the property or properties that each relation possesses (reflexive, symmetric, transitive). For example, write r,s if the relation is reflexive and symmetric.1.) R is a relation on the set of all people. (a,b) is in R if a is taller than b.2.) R is a relation on the set of integers > 0. (a,b) is in R if a divides b. (eg. 3 divides 3 and 3 divides 15 etc.)3.) R is a relation on the set of all people. (a,b) is in R if a is married to b.4.) R is a relation on the set of all nonnegative integers. (a,b) is in R if a and b have the same remainder when divided by 5. (eg. (7,12) is in R)
The relation in option (a) is Transitive , in option (b) is Reflexive and Transitive and option (c) is Symmetric .
In the question ,
it is given that ,
Option(a) ,
R is a relation on set of all people where (a,b) is in R if a is taller than b .
Reflexive : NO , because "a" cannot be taller than "a" itself .
Symmetric : NO , because if "a" is taller than "b" , then "b" will be shorter than "a" .
Transitive : YES , because if "a" is taller than "b" and "b" is taller than "c" , then "a" is taller than "c" .
Option(b)
R is a relation on set of integers > 0 where (a,b) is in R if a divides b .
Reflexive : YES , because every number divides itself .
Symmetric : NO , because if "a" divided "b" , then "b" may not divide "a" .
Transitive : YES , because if "a" divided "b" and "b" divides "c" , then "a" must divide "c" .
Option(c)
R is a relation on set of all people where (a,b) is in R if a is married to b .
Reflexive : NO , because marriage is between two people , and "a" cannot marry "a" .
Symmetric : YES , because if "a" is married to "b" , then "b" is married to "a" .
Transitive : NO , because if "a" is married to "b" and "b" is married to "c" , then "a" is not married to "c" .
Therefore , The relation in option (a) is Transitive , in option (b) is Reflexive and Transitive and option (c) is Symmetric .
The given question is incomplete , the complete question is
Write in the space provided the property or properties that each relation possesses (reflexive, symmetric, transitive).
(a) R is a relation on the set of all people, (a,b) is in R if a is taller than b .
(b) R is a relation on the set of integers > 0 , (a,b) is in R if a divides b .
(c) R is a relation on the set of all people , (a,b) is in R if a is married to b .
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Identify the simplest polynomial function having integer coefficients with the given zeros.
The polynomial for the given zeros is p(x) = x⁴ + 4x³ - 3x² - 12x. The correct answer is option (B).
What is factor theorem?The factor theorem for a polynomial p(x) states that for some real number a if p(a) = 0, then (x - a) is one of the factors of p(x).
Given that,
The zeros for a polynomial are 0, -4 and√3.
As per the factor theorem the polynomial for zeros a, b, c and d can be written as,
p(x) = (x - a)(x - b)(x - c)(x - d)
Thus the polynomial for the given zeros is,
(x - 0)(x - (-4))(x - √3)(x + √3)
= x(x + 4)( x² - 3)
= x(x³ + 4x² - 3x - 12)
= x⁴ + 4x³ - 3x² - 12x
Hence, the required polynomial is p(x) = x⁴ + 4x³ - 3x² - 12x.
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1. A polynomial equation of the 5th degree has ___________ 5 roots.
2. A depressed equation is a/an ____________, when equated to zero.
3. A root of multiplicity 5 means that _______.associate the mechanisms of plate boundaries?
The Fundamental Theorem of Algebra states that a polynomial of fifth degree will have five roots, which is the case with this particular polynomial.
What are the principles governing plate boundaries?The theory that underlies plate boundaries. The primary characteristics of plate tectonics are: The ocean floors are constantly shifting, extending outward from the center, settling outward at the edges, and regenerating. The crustal plates are moved in various directions by convection currents beneath the plates.The Fundamental Theorem of Algebra states that a polynomial of fifth degree will have five roots, which is the case with this particular polynomial.5 roots are required for a polynomial of fifth degree. Since all Complex roots are paired, if 5i is a root, then -5i must also be a root. 1-3i must be a root in order for 1+3i to also be a root.A depressed equation is quadratic when equated to zero.To learn more about Fundamental Theorem of Algebra refer to:
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PLEASE HELP!!!!!!!!!!!!!!
Which graph represents the solution to the inequality −0.96 is greater than or equal to the product of a number and 0.3?
number line with closed circle on point negative 9.3 and arrow shaded to the right number line with open circle on point negative 9.9 and arrow shaded to the left number line with closed circle on point negative 3.2 and arrow shaded to the left number line with closed circle on point negative 3.2 and arrow shaded to the right
The graph of the solution set of the given inequality can be seen in the image at the end.
Which graph represents the solution of the inequality?
Here we have the following inequality:
-0.96 ≥ x*0.3
To solve this, we need to isolate the variable x in one of the sides of the inequality.
To do that, we need to divide both sides by 0.3
-0.96/0.3 ≥ x*0.3/0.3
-3.2 ≥ x
So our variable x is smaller than or equal to -3.2
Then the graph will be a closed circle at x = -3.2 and a line that extends to the left side.
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Find the flux of f = x3 i y3 j z3 k out of the closed surface z = x2 y2 , 0 ≤ z ≤ 5 oriented outward. g
The flux of the given function f = x³i + y³j + z³k is given by f',
f' = 3(x²i + y²j + z²k)
Given, f = x³i + y³j + z³k
we have to find the flux of the given function f = x³i + y³j + z³k
On partial differentiating the function, we get
f' = 3x²i + 3y²j + 3z²k
f' = 3(x²i + y²j + z²k)
So, the flux of the given function f = x³i + y³j + z³k is given by f',
f' = 3(x²i + y²j + z²k)
Hence, the flux of the given function f = x³i + y³j + z³k is given by f',
f' = 3(x²i + y²j + z²k)
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name the property shown m + 0 = m
Answer:
Additive identity
Step-by-step explanation:
When a number that when added to any number it results in itself as the sum
please answer asap (25 points)
only write down what I gotta put in the box and explanation
Answer:
12
Step-by-step explanation:
Use 5 for m
Use -3 for x
Use 7 for y
y =mx + b
7 = (5)(-3) + b
7 = -5 +b
12 = b
determine the equation of the parabola graphed below. note: when responding if the number is negative you can't change the plus sign to a negative sign. just type the negative in the box (ie -4 would read -4).
The equation of the graphed parabola is y=a (x + 3) ^2 -4.
Given that parabola is plotted, concave upwards, with vertex located at coordinates (-3, -4).
According to the question, we need to find the equation of the graphed parabola.
The equation of a quadratic function of vertex (h, k) is given by y=a + k
In the above equation the leading coefficient is "a"
We are given point (-3, -4).
We need to put the value of h=-3 and k=-4 and the required equation, and we will get the equation as: -
y=a (x + 3) ^2 -4
Therefore, the equation of the parabola that is plotted, concave up, with vertex located at coordinates (-3, -4) is y=a (x + 3) ^2 -4.
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constant of proportionality of y=5x-1/3
The equation given is linear, not proportional, and thus, there is no constant of proportionality.
What is the constant of proportionality?
Here we have the following linear equation:
y = 5*x - 1/3
The general linear equation is:
y = m*X + b
Where m is the slope and b is the y-intercept, so in this case we have:
slope = 5
y-intercept = -1/3
Partocularly, when the y-intercept is 0 we have a proportional relation:
y = m*x
And then m is called the "constant of proportionality"
In this case the y-intercept is not zero, thus, there is no constant of proportionality, just a slope.
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please answer asapp (25 points)
Answer:
b = -2
Step-by-step explanation:
y = mx + b
use -2 for m
use 1 for x
use -4 for y
-4 = (-2)(1) = B
-4 = -2 + b Add two to each side
-2 = b
[tex]\huge \boxed{\sf -2}\\\\\\\displaystyle \sf Line\ equation\ y=mx+b \\\\Substituting \ m=-2 \ and\ (1,-4) \\\\-4=-2(1)+b\\\\-4=-2+b\\\\Adding\ 2\ to\ each\ side \\\\-4+2=-2+b+2\\\\-2=b[/tex]
now suppose the price of good x increases to $12 while the price of good y remains $4. utility will be maximized on which indifference curve?
The correct option is option (d). The utility will be maximum on indifference curve below I.
Indifference curve:
An indifference curve is a graph that shows the combination of two products that provide consumers with equal satisfaction and utility. Each point on the indifference curve indicates that the consumer is indifferent to his two points, all delivering equal utility.
The equation of a typical indifference curve is, U(x,y)=c
where the constant c stands for the utility level achieved on the curve
Since consumer has an income of $48 which means consumer budget line initially was,. 4x+4y=48 ---(1)
And final budget line after price change is 12x+4y=48 ---(2)
With the above budget line it is impossible to have any of the indifference curve. Because for equilibrium Budget line should be tangent to Indifference curve and thus equilibrium will be below point D.
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Complete question :
Refer to the following indifference map for a consumer who has a income of $48 to spend on goods x and y and the market price of x and y are both $4.now suppose the price of good x increases to $12 while the price of good y remains $4. utility will be maximized on which indifference curve?
a) I
b) II
c) III
d) on an indifference curve below I
a rocket is launched straight up from the earth's surface at a speed of 15000 m/s.for help with math skills, you may want to review: mathematical expressions involving squares
The speed of rocket when it is very far away from the the rocket is 9990 m/s.
In the given question, a rocket is launched straight up from the earth's surface at a speed of 15000 m/s.
v = 15000m/s = 1.5×10^{4} m/s
We have to find the speed of rocket when it is very far away from the the rocket.
As we know,
Mass of Earth(M) = 5.972×10^{24} kg
Radius of Earth(R) = 6.371×10^{6} m
The value of G = 6.67×10^{-11}
Applying law of conservation of energy,
-GMm/R + 1/2 mv^2 = 0+1/2 mV^2
Taking common m on both side, we get
-GM/R + v^2/2 = V^2/2
Substituting the value
-(6.67×10^{-11})(5.972×10^{24})/ 6.371×10^{6} + (1.5×10^{4})^2/2 = V^2/2
V^2/2 = -6.67×5.972×10^{-11+24}/ 6.371×10^{6} + 2.25×10^{8}/2
V^2/2 = -6.252×10^{13-6} + 1.125×10^{8}
V^2/2 = -6.252×10^{7} + 11.25×10^{7}
V^2/2 = 4.998×10^{7}
Multiply by 2 on both side we get
V^2 = 9.996×10^{7}
V^2 = 99.96×10^{6}
Taking square root on both side, we get
V = 9.99×10^{3}
V = 9990 m/s
Hence, the speed of rocket when it is very far away from the the rocket is 9990 m/s.
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Salma ha et up a lemonade tand outide her houe and ell mall cup and large cup of lemonade. Each mall cup hold 12 ounce of lemonade and each large cup hold 16 ounce of lemonade. Salma old 60 cup of lemonade totaling 920 ounce. Determine the number of mall cup old and the number of large cup old
The number of small cups is 10, and the number of large cups is 50.
What is a linear equation?
A linear equation is an equation in which each term has at max one degree. Linear equations in variables x and y can be written in the form y=mx+c.
Linear equation with two variables, when graphed on the cartesian plane with axes of those variables, give a straight line.
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p = the number of small cups sold,
q = the number of large cups sold,
Salma sold 60 cups then the equation becomes:
p + q = 60 ---------------(1)
Salma sold 60 cups of lemonade total of 920 ounces then the equation becomes:
12p + 16q = 920 ---------------(2)
Multiplying the equation 1 by 12 then substracted from equation 2, we get:
12p + 16q = 920
12p + 12q = 720
4q = 200
q = 50
Substituting q = 50 into equation (1) we get,
p + 50 = 60
p = 10
Hence, the number of small cups is 10, and the number of large cups is 50.
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How many people have the sprinter gene?.
According to reserch about 18 percent people worldwide having sprinter gene.
In the given question, we have to find how many people have the sprinter gene.
As we know that;
The ACTN3 gene is the recently identified "sprinters gene."
A gene, as we already stated, codes for a protein. Alpha-actinin-3 is designated by ACTN3. This protein, which can only be found in fast twitch muscle fibres, gives muscles their explosive ability.
In order to summarise the genetic component, an individual has the ACTN3 gene if alpha-actinin-3 is present in muscle cells. They are therefore better suited for quick movements.
According to reserch about 18 percent people worldwide having sprinter gene.
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In a poll of 200 randomly selected U.S. adults, 104 said they favored a new proposition. Based on this poll, compute a 90% confidence interval for the proportion of all U.S. adults in favor of the proposition (at the time of the poll). Then complete the table below. Carry your intermediate computations to at least three decimal places. Round your answers to two decimal places. lower limit of 90%? upper limit of 90%
The lower limit of the 90% confidence interval is 0.429 when in a survey of 200 randomly chosen American adults, 104 responded in favor of the proposed proposal.
Given that
In a survey of 200 randomly chosen American adults, 104 responded in favor of the proposed proposal. Calculate a 90% confidence interval for the percentage of all U.S. adults who support the proposal based on the results of this poll (at the time of the poll). Complete the table below after that. Carry your calculations to a minimum of three decimal places.
We have to find the lower limit of 90%.
We know that
In a poll of 200 randomly selected U.S. Among adults, 104 expressed support for the novel idea.
p-hat = 104/200 = 0.52
ME = z×√[pq/n] = 2.5758×√[0.52*0.48/200] = 0.091
Now, the lower limit of the 90% confidence interval well be
p-hat-ME = 0.52-0.091 = 0.429
Therefore, The lower limit of the 90% confidence interval is 0.429 when in a survey of 200 randomly chosen American adults, 104 responded in favor of the proposed proposal.
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What are the 4 parent functions?.
The four parent functions are Linear Functions, Parabolas and Quadratic Functions, Polynomial Functions - Cubic Functions and Absolute Value Functions.
In the given question we have to write the four parent function.
As we know that;
The simplest function in a family of functions, a parent function maintains the definition of the entire family.
There are several basic functions that we run with frequently in math. These fundamental functions include the square root function, basic polynomials, absolute values, and rational and exponential functions.
The 4 parent functions are;
Linear Functions: y=xParabolas and Quadratic Functions: y=x^2Polynomial Functions - Cubic Functions: y=x^3Absolute Value FunctionsTo learn more about parent functions link is here
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One fluid ounce i approximately 30 mm a water bottle holding 20 fluid ounce would have how many millimeter
A water bottle would have 600 milimeters.
What is multiplication?
In mathematics, multiplying means adding equal groups. The number of things in the group grows as we multiply. A multiplication problem includes the two factors and the product. In the multiplication problem, 6 9 = 54, the numbers 6 and 9 are factors, and 54 is the product.
If one fluid ounce has approximately 30mm.
then 20 fluid ounce will have = 30 * 20
= 600 millimeters.
Hence, a water bottle would have 600 milimeters.
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HELP ME PLEASEEEE TY
Answer:
414.69
Step-by-step explanation:
2*pi*r
How do you graph a line that passes through the given points and y-intercept?.
The graph of a straight line can be drawn as described in the solution.
How to represent a straight line on a graph?To represent a straight line on a graph consider two points namely x and y-intercepts of the line. To find x-intercept put y = 0 and for y-intercept put x = 0. Then draw a line passing through these two points.
The graph for a straight line for given points and y-intercept can be drawn as follows,
The point-slope equation of the straight line is,
y = mx + c
Where m is the slope and c is the y-intercept of the straight line.
Suppose there are two points (x₁, y₁) and (x₂, y₂).
Then the slope of the straight line passing through them is given as,
Slope = (y₂ - y₁)/(x₂ - x₁)
Substituting the slope in the point-slope equation of the straight line the equation is obtained as,
y = ((y₂ - y₁)/(x₂ - x₁))x + c
Hence, the equation of the straight line passing through points (x₁, y₁) and (x₂, y₂) and having y-intercept c can be given as y = ((y₂ - y₁)/(x₂ - x₁))x + c.
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the point given below is on the terminal side of an angle in standard position. find the exact value of each of the six trigonometric functions of . of θ. (-4,5)
The exact value of all six trigonometric functions from the given below point (-4,5) on the terminal side of an angle θ in standard position are as follow:
sinθ = (-4/√41) , cosecθ = ( -√41/4)
cosθ =(5/√41) , secθ = ( √41 /5)
tanθ =(-4/5) , cotθ = ( -5/4)
As given in the question,
Given point ( x, y) = (-4,5) which is below on the terminal side of an angle θ in standard form.
Coordinate y represents the perpendicular side
Coordinate x represents the base
Using Pythagoras theorem ,
Let 'r' represents the hypotenuse .
r = √x² + y²
= √(-4)² + 5²
= √16 + 25
= √41
Exact value of all the trigonometric functions are as follow:
sinθ = (x/r)
= (-4 /√41)
cosθ = ( y /r)
= ( 5/ √41 )
tanθ = ( x/y)
= ( -4 /5)
cosecθ = ( r / x)
= ( -√41 /4)
secθ = ( r/y)
= ( √41/ 5)
cotθ = ( y/x)
=( -5/4)
Therefore, the exact value of all six trigonometric functions from the given below point (-4,5) on the terminal side of an angle θ in standard position are as follow:
sinθ = (-4/√41) , cosecθ = ( -√41/4)
cosθ =(5/√41) , secθ = ( √41 /5)
tanθ =(-4/5) , cotθ = ( -5/4)
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Suppose a jar contains r red balls and b blue balls, each with a unique identifier on it. How many ways are there to choose a set of two balls of the same color? Of different colors? Show that the sum of these two numbers is the number of ways of choosing two balls from the total, ignoring color.
Answer:
Ways to choose a set two balls of the same color:
[0.5 * (b) * (b - 1)] + [0.5* (r) * (r - 1)]
Different colors:
0.5 * [(b) * (r) + (r) * (b)] = 0.5 * (2 * b * r)
= b * r
Any two balls
0.5 * (b + r) * (b + r - 1)
= 0.5 * [b * (b + r - 1) + r * (b + r - 1)]
= 0.5 * [b^2 + b * r - b + b * r + r^2 - r]
= 0.5 * [b^2 - b + r^2 - r + b * r + b * r]
= 0.5 * [b * (b - 1) + r * (r - 1) + 2 * b * r]
= 0.5 * (b * (b - 1)) + 0.5 * (r * (r - 1)) + 0.5 * (2 * b * r)
= [0.5 * (b * (b - 1)) + 0.5 * (r * (r - 1))] + [b * r]
= Number of ways of choosing two balls of the same color + number of ways of choosing two balls with different colors
Step-by-step explanation:
TRUE/FALSE. we use anova to test for differences between population means by examining the amount of variability between the samples relative to the amount of variability within the samples.
We use ANOVA to test for differences between population means by examining the amount of variability between the samples relative to the amount of variability within the samples. Hence, it is TRUE
What is ANOVA ?The statistical analysis tool known as analysis of variance (ANOVA) divides the observed aggregate variability present in a data set into two categories: systematic variables and random components. The random factors have no statistical impact on the presented data set, whereas the systematic factors do. The ANOVA test is used by analysts to ascertain how independent factors in a regression analysis affect the dependent variable.
ANOVA basically stands for analysis of the variance.
Analysis of variance, or ANOVA, is a statistical method that separates observed variance data into different components to use for additional tests.A one-way ANOVA is used for three or more groups of data, to gain information about the relationship between the dependent and independent variables.If no true variance exists between the groups, the ANOVA's F-ratio should equal close to 1Hence, according to above statements, given fact is true.
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How do you know which function is linear?.
The function whose graph is a straight line ; slope is constant and highest degree is one then that function is known as linear function.
Linear function:-
A linear function may be produced by only one type of equation, which has the form [tex]y=mx+c[/tex] where m and c are constants.When the x and y coordinates of a function are plotted on the cartesian plane, it produces a straight line.Because the slope of a straight line is always constant, the slope of a linear function is always constant.The greatest degree of linearity of the function should always be 1.Thus, an function whose graph is a straight line ; slope is constant and highest degree is one then that function is known as linear function.
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What is the range of f/x )=( 3/4 x 4?.
The range of f(x) = 3/4ˣ - 4 is all real numbers greater than -4. I.e. (-4, ∞).
Given,
The function, f(x) = 3/4ˣ - 4
We have to find the range of the function;
Function;-
A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics and the sciences, functions are fundamental for constructing physical relationships.
Domain and Range of a Function;-
It is the collection of all potential function inputs. For instance: F(x) = x2 in the illustration below. The domain is the set of all the inputs, and the range is the set of all the outputs.
Here,
The function, f(x) = 3/4ˣ - 4
That is,
The range of f(x) = 3/4ˣ - 4 is all real numbers greater than -4. I.e. (-4, ∞).
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explain what the p-value means for this problem. if h0 is true, then there is a chance equal to the p-value that the average number of hours women work each week is 83 hours or more. if h0 is false, then there is a chance equal to the p-value that the average number of hours women work each week is 83 hours. or more
P-values means in this problem is that to reject a null hypothesis it should be smaller . If p-value is large , means the alternate hypothesis is weak, so you do not reject the null.
In statistics, the p-value is the probability of obtaining results at least as extreme as the observed results of a statistical hypothesis test, assuming that the null hypothesis is correct.
The p-value serves as an alternative to rejection points to provide the smallest level of significance at which the null hypothesis would be rejected.
A smaller p-value means that there is stronger evidence in favor of the alternative hypothesis .The p-value approach to hypothesis testing uses the calculated probability to determine whether there is evidence to reject the null hypothesis.
According to the question,
If h₀ ( null hypothesis ) is true then there is a chance equal to the p-value that the average number of hours women work each week is 83 hours
It means if our p-value is bigger that it couldn't get any evidence to reject null hypothesis But if h₁ (alternative hypothesis ) is true then there is chance to the p-value that the average number of hours women work is not more 83 hours or more means the to p-value is smaller and stronger to reject null hypothesis.
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A commuter airline flies small planes between San Luis Obispo and San Francisco. For small planes, the baggage weight is a concern especially on foggy mornings, because randomly selected passenger is normally distributed has a mean of 38 pounds and a standard deviation of 10 pounds. a.) First, if there are only two passengers on the plane, what are the mean and standard deviation of the total passenger baggage weight? Mean: Standard deviation: b.) What is the probability that the total passenger baggage weight from only two passengers exceeds90lbs? With only 2 passengers, we can't use the CLT.0.14460.16110.1515c.) Now suppose the plane has ten passengers. What are the mean and standard deviation of the total passenger baggage weight in this case? Mean: Standard deviation: c.) In the current weather conditions, the pilot will not take off if the total passenger baggage weight from these ten passengers is greater than 480 pounds. What is the probability the pilot will not take off?
The values of mean and standard deviation of the total passenger baggage weight in respected cases of commuter airline is given below:
How do you calculate probability?The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas. Odds are the probability that something happens divided by the probability that it doesn't happen.
What are the 2 types of probability?Relative Frequency Definition.
Subjective Probability.
a.) If there are only two passengers on the plane, the mean of the total passenger baggage weight would be 76 pounds and their standard deviation would be10 pounds.
b.) The probability would be 0.1611 that the total passenger baggage weight from two passengers exceeds 90 pounds.
c.) If the plane has ten passengers, the mean of the total passenger baggage weight would be 380 pounds and their standard deviation would be 30 pounds.
d.) The probability would be 0.1515 that the pilot will not take off.
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Formulating Hypotheses. In exercises 2-5, formulate the null and alternative hypotheses fora hypothesis test. For each exercise, write both hypotheses both in statistical symbols and in everyday language. [1 point] 2) The federal government has established 15 micrograms per liter as the maximum safe level of lead in drinking water. The Iinois state department of health samples water from a large sample of residents' homes because it suspects that the water in the city of Steel is unsafe.
The both hypotheses in statistical symbols and in everyday language is:
Null Hypothesis: H₀:μ=15 micrograms
Alternative Hypothesis: H₁:μ>15 micrograms.
What is meant by null hypothesis?The null hypothesis in inferential statistics is that two possibilities are the same. The null hypothesis states that the observed difference is attributable solely to chance. The likelihood of the null hypothesis being true can be calculated using statistical testing.
Given,
The federal government has established 15 micrograms per liter as the maximum safe level of lead in drinking water. The Linois state department of health samples water from a large sample of residents' homes because it suspects that the water in the city of Steel is unsafe.
Null Hypothesis:
The federal government has established that the maximum safe level of lead in drinking water is 15 micrograms.
H₀:μ=15 micrograms
Alternative Hypothesis:
The federal government has established that the maximum safe level of lead in drinking water is more than 15 micrograms.
H₁:μ>15 micrograms.
Null Hypothesis: H₀:μ=15 micrograms
Alternative Hypothesis: H₁:μ>15 micrograms
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the degrees of freedom for an unequal variance test of means is calculated as 16.67. what should you do with the calculated number to get the degrees of freedom for the t-distribution?
We shall round it down to 16 in the circumstance when we need to determine the degrees of freedom for the t-distribution.
What is t-distribution?Any member of the family of continuous probability distributions known as the Student's t-distribution (or simply the t-distribution) in probability and statistics is used to estimate the mean of a normally distributed population when the sample size is small and the population's standard deviation is unknown.
Under the alias "Student," English statistician William Sealy Gosset created it.
The Student's t-test for determining the statistical significance of the difference between two sample means, the construction of confidence intervals for the difference between two population means, and linear regression analysis are just a few commonly used statistical analyses that make use of the t-distribution.
So, in the given situation where we need to get the degrees of freedom for the t-distribution, we will round it down to 16.
Therefore, we shall round it down to 16 in the circumstance when we need to determine the degrees of freedom for the t-distribution.
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What is a linear function table?.
A linear function table is a table having a constant rate of change between its datapoints
A linear equation is is an equation that consists of each variable raised with a maximum of one degree. the linear equation in terms of variables x and y can be written in the form of y = mx + c, where m is the slope and x is the independent variable, and y is the dependent variable when the data points of the given table are potted in a graph, we get a straight line for a linear function table, a such function must have a constant slope in between its points
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How do you solve a system of inequalities using substitution?.
Substitution is one method for solving linear equation systems.
First, arrange the equations so that the variables are vertically arranged.
Step 2: Pick the variable that is most straightforward to take out, and multiply it by a different value in each equation so that its coefficients are the same.
Subtract the two equations in step three.
Solve the one variable system in step four.
Step 5: To find the other equation, re-enter that number into either equation.
Step 6: Reread the question and re-enter your responses to double-check.
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