a) The value of g(2) = -1/4 and the value of g(-2) = π/2 - 3/2
b) The value of g'(x) = 2 The value of g''(x) =1
c) g has neither a relative maximum nor a relative minimum at x= 1
d) the graph of g has a point of inflection at each of x=-2 , x=0 and x = 1 because g''(x) = f'(x) changes at each of these values.
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).
There are several types of functions in maths. Some important types are:
Injective function or One-to-one function: When there is mapping for a range for each domain between two sets.
Surjective functions or Onto function: When there is more than one element mapped from domain to range.
Polynomial function: The function which consists of polynomials.
Inverse Functions: The function which can invert another function.
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Whats the simplified version of √(√21-2√3)^2
The required simplified solution of the given expression is given as √3(√7 - 2).
Given that,
To determine the simplified solution of the √(√21-2√3)²
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
= √(√21-2√3)²
=√21-2√3 (√a² = a)
= √3(√7 - 2)
Thus, the required simplified solution of the given expression is given as √3(√7 - 2).
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Please can anyone answer this percentage question cor grade 7
well, we know it was 480, then we reduce it by 50.
a)if we take 480 to be the 100%, what's 50 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 480 & 100\\ 50& x \end{array} \implies \cfrac{480}{50}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{ 48 }{ 5 } ~~=~~ \cfrac{ 100 }{ x }\implies 48x=500\implies x=\cfrac{500}{48}\implies x=\cfrac{125}{12}\implies \boxed{x\approx 10.4}[/tex]
now, the TV is only 480 - 50 = 430, then it gets reduced another 50.
if we take 430 to be the 100%, what's 50 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 430 & 100\\ 50& y \end{array} \implies \cfrac{430}{50}~~=~~\cfrac{100}{y} \\\\\\ \cfrac{ 43 }{ 5 } ~~=~~ \cfrac{ 100 }{ y }\implies 43y=500\implies y=\cfrac{500}{43}\implies \boxed{y\approx 11.6}[/tex]
b)hmmm the absolute change of the reductions? that sounds like 480 - 50 - 50 = 380.
c)well, the overall percentage hmmm well, that's the $100 reduction total.
if we take $480 as the 100%, what's $100 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 480 & 100\\ 100& z \end{array} \implies \cfrac{480}{100}~~=~~\cfrac{100}{z} \\\\\\ \cfrac{ 24 }{ 5 } ~~=~~ \cfrac{ 100 }{ z }\implies 24z=500\implies z=\cfrac{500}{24}\implies z=\cfrac{125}{6}\implies \boxed{z\approx 20.8}[/tex]
4.4 times 2.727 km Answer with explanation
Answer:
12 km
Step-by-step explanation:
4.4 * 2.727 km = 11.9988 ( using a calculator)
since the smallest factor (4.4) has only 2 significant digits , your answer should be rounded to only 2 S.D. so = 12 km
What is the domain of the function g(x)=3log2(x-1)+4
Answer: x : x e R and R >
Step-by-step explanation:
Is it ever possible to have a graph of a function that is
symmetric about the y-axis AND the origin? Explain your
thinking.
We know that,
By definition, no function is symmetrical about the x-axis (or any other horizontal line). Because the one flipped with respect to the horizontal violates the vertical line test.
On the other hand, functions can be symmetric about a vertical line or a point. In particular, functions symmetric about the y-axis are also "even" functions, and functions symmetric about the origin are also "odd" functions. Because of this correspondence between graph symmetry and function equality or oddness, "symmetry" in algebra is usually applied to the y-axis and the origin.
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Answer:
yes: f(x) = 0
Step-by-step explanation:
You want to know if a function exists that is symmetrical about the y-axis and the origin.
SymmetryA graph is symmetrical about the y-axis if and only if ...
f(-x) = f(x)
A graph is symmetrical about the origin if and only if ...
f(-x) = -f(x)
For both conditions to be met, we must have ...
f(x) = -f(x)
2f(x) = 0 . . . . . add f(x)
f(x) = 0 . . . . . . . divide by 2
The graph of f(x) = 0 will be symmetrical about the y-axis and the origin. (It is the x-axis.)
Wyatt is deciding between two different movie streaming sites to subscribe to. Plan A costs $ 19 per month plus $0.50 per movie watched. Plan B costs $ 13 per month plus $1.50 per movie watched. Let A represent the monthly cost of Plan A if Wyatt watches x per month, and let B represent the monthly cost of Plan B if Wyatt watches x movies per month. Write an equation for each situation, in terms of x, and determine the number of monthly movies watched, x, that would make the two plans have an equal monthly cost.
A=
B=
Answer=
Equations representing the total costs for plan A and B are A = 19 + 0.50x and B = 13 + 1.5x, respectively, where x is the number of movies watches.
Cost of both the plans will be equal for 6 movies.
What is a linear equation?
A linear function is defined as a function that has either one or two variables without exponents.Given that, Wyatt is deciding between two different film streaming sites to subscribe to, plan A costs $19 per month plus $0.50 per film watched, plan B costs $13 per month plus $1.50 per film watched.
According to question,
A = 19 + 0.50x and
B = 13 + 1.5x
For costs being equal, we have,
A = B
19 + 0.50x = 13 + 1.5x
x = 6
Hence, for 6 films the costs of both the plans will be equal and equation for both the plans are A = 19 + 0.50x and B = 13 + 1.5x
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Can someone help me? I don’t know how to do this
What is the correct to this answer ??? ( answers only)
Answer:
k is greater or equal to -5
Step-by-step explanation:
[tex] - 5 \leqslant k[/tex]
here, -5 is on the left side of the inequality sign which means it is less than or equal to k.
solve each problem below.
A. 5(6x+7)
B. 9(5x+10)
C. 2(14x+23)
D. 12(6x+10)
E. 11(7+5x)
Answer:
A.x=-7/6
B.x=-19/9
C.x=-23/14
D.x=-5/3
E.x=-7/5
Step-by-step explanation:
A. 30x+35, 30x=-35 x = -7/6
B. 45x+90, 45x=-90, x=-19/9
C. 28x+46, 28x=-46, x=-23/14
D. 72x+120, 72x=-120, x=-5/3
E.77+55x, 55x=-77, x=-7/5
Compare the slopes of the lines for y=f(x) and y=g(x) to determine if they are parallel.
x
f(x)
g(x)
0
22
24
1
36
38
2
50
52
3
64
66
Question content area bottom
Part 1
Select the correct choice below and fill in the answer box(es) to complete your choice.
A line's steepness can be determined by looking at its slope. Slope is determined mathematically as increase over run.
How do you find slope of a line?According to the slope equation, the slope of a line may be calculated by dividing the rise of the line between any two places by the run of the same line between the same two sites.
The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation.
Slope of y =f(x)
Slope (m) = ΔY / ΔX = 14 / 1 = 14
y = 14x + 22
When x=0, y = 22
When y=0, x = -1.5714285714286
Slope of y = g(x)
Slope (m) =ΔY / ΔX = 14 / 1 = 14
y = 14x + 24
When x=0, y = 24
When y=0, x = -1.7142857142857
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Match the following terms
Answer:
1.) Feeds on dead organisms – Decomposer
2.)obtain energy nutrients from producers – Consumer
3.)Network of interconnected food chains – Food web
4.)Manufactures food using energy from the sun – Producer
5.)Simple model used for showing how energy passes through an ecosystem – Food chain
6.) Relationship between organisms where both members benefit – Mutualism
Step-by-step explanation:
pls if this answer helped you kindly rate it as brainliest
A local gas station is offering a deal to their customers. If they purchase $8.00 car wash, the cost per gallon of gas is $2.60. Write and solve a linear equation to find how many gallons you can afford if you have $40
The gallons you can afford if you have $40 is 13 gallons.
How to illustrate the equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is a relationship between two expressions that is expressed as an equality on either side of the equal to sign. An equation would be 3x = 18, for instance.
From the information, the local gas station is offering a deal to their customers. If they purchase $8.00 car wash, the cost per gallon of gas is $2.60.
Here, we want to solve a linear equation to find the gallons you can afford if you have $40.
The linear equation to find how many gallons you can afford if you have $40 will be illustrated as x
This would be:
2.60 × (40 / 8) = x
x = 2.60 × 5
x = 13 gallons
The gallons will be 13.
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Dos cuadrados de lado 10 cm se sobreponen formando un rectángulo de 17 cm de largo, como se muestra en la figura. ¿Cuál es el área de la franja amarilla en centímetros cuadrados?
The area of the rectangular yellow region is of:
30 cm².
How to obtain the area of a rectangle?The area of a rectangle of base b and height h is obtained as the multiplication of these dimensions, as follows:
Area = base x height.
From the image given at the end of the answer, these dimensions are given as follows:
Height = 10 cm, which is the side length of the square.Base = 3 cm, as the two squares would combine for a side length of 20 cm, but they combine for 17 cm, hence 20 - 17 = 3 cm.Then the area of the yellow region is calculated as follows:
Area = 10 x 3 = 30 cm².
TranslationThe problem asks to obtain the area of the rectangular region, considering that:
The squares have side length of 10.The combined squared combine for a side length of 17.Missing InformationThe region is given by the image shown at the end of the answer.
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In a food cocktail,the ratio of orange juice to apple juice to coconut milk is 3:2:4, respectively. How much of each do I need to take if I have 5 more oz of orange juice than apple juice
By ratios ,orange = 15 , apple = 10 , coconut = 20 are needed to make 45 liters of this cocktail.
What does the math ratio mean?
When b does not equal 0, an ordered pair of numbers a and b, represented as a / b, is said to be a ratio. A proportion is an equation that sets two ratios at the same value.
As an illustration, you could express the ratio as 1: 3 if there is 1 guy and 3 girls (for every one boy there are 3 girls)
orange = 3
apple = 2
coconut = 4
total = 9
orange = 3/9 * 45 = 15
apple = 2/9 * 45 = 10
coconut = 4/9 * 45 = 20
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The complete question is -
In a fruit cocktail, the ratio of orange juice to apple juice to coconut milk is 3:2:4, respectively. How much of each type is needed to make 45 liters of this cocktail?
Help i need help with this question.
Based on the SAS, SSS, and the transitive property of congruence, the reason why ΔABC ≅ ΔGHJ is because of option B.
What is SAS and SSS?The SAS is a triangle theorem that states that two triangles are congruent if they both have two pairs of congruent sides and a pair of included congruent angles.
On the other hand, the SSS states that two triangles that have three pairs of congruent sides are equal.
What is the Transitive Property of Congruence?The transitive property of congruence states that if two triangles are congruent to a third triangle, then all three triangles are congruent to each other.
Based on the SSS, triangle ABC is congruent to triangle DEF.
Based on the SAS, triangle DEF is congruent to GHJ.
Therefore, based on the transitive property of congruence, triangle ABC is congruent to triangle GHJ.
Therefore, the reason why ΔABC ≅ ΔGHJ is because of the reason given in option B.
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Write equations for the horizontal and vertical lines passing through the point (4,-3)
The equations for the horizontal line and the vertical line are y = - 3 and x = 4, respectively.
How to determine the equation of a horizontal line and a vertical line
Herein we find the case of a point (x, y) = (a, b), from which we must derive the equations for the horizontal line and the vertical line, whose forms are described below:
Horizontal line
y = b
Vertical line
x = a
If we know that (x, y) = (4, - 3), then the equations for the horizontal and vertical lines are, respectivelly:
Horizontal line
y = - 3
Vertical line
x = 4
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Give the equation of each quadratic in the form, picture of formula and graphs attached.
The equation of each quadratic in the picture of formula and graphs attached is y=-1(x+8)^2 +9 and y=1/4*(x-6)^2 +3
What is Graph Transformation?
When a graph is transformed, the graph's curve either "moves to the left/right/up/down," "expands or compresses," or "reflects." For instance, by simply pushing the graph of the function g(x) = x2 up by 3 units, the graph of the function f(x) = x2 + 3 is generated. graph transformations are highly useful for graphing functions without having to start from scratch since they allow you to move, extend, compress, or reflect the curve. The graph of the parent function is either "moved," "resized," or "reflected" by a graph transformation. The three primary categories of graph transformations are as follows:
Translation DilationReflectionA)
first of all we need to find which type of parabolic graph is it
from the picture give we can clearly see it is a x^2=-4ay type of graph
and using graph transformation formula
i.e. y= a(x-h)^2 + k
where h = -8
k=9
we get y=a(x+8)^2+9
as we know (-5,0) lie on this graph
so,
0=a(-5+8)^2+9
a=-1
so the equation is y=-1(x+8)^2 +9
B)
first of all we need to find which type of parabolic graph is it
from the picture give we can clearly see it is a x^2=-4ay type of graph
and using graph transformation formula
i.e. y= a(x-h)^2 + k
where h = 6
k=3
we get y=a(x-6)^2+3
as we know (0,12) lie on this graph
so,
12=a(0-6)^2+3
a=1/4
so the equation is y=1/4*(x-6)^2 +3
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The local deli serves pasta salad every 5 days and pretzel salad every 3 days. If pasta salad and pretzel salad are both on today's menu, how many days before they are both on the menu again?
Answer: 15 days
Step-by-step explanation:
Pasta salad; 5 10 15
Pretzel salad; 3 6 9 12 15
An Amazon driver makes 35 deliveries in 3.5 hours. How many deliveries has he
made in 2 hours and 30 minutes?
*
Answer:25
Step-by-step explanation:
We have the rate: 35 deliveries in 3.5 hours. or 35/3.5
Find the unit rate -> 35/3.5/
/3.5/3.5
10/1
10
10 deliveries per hour
in 2.5 hours
10*2.5
25
*Assuming the rate of deliveries is constant*
Solve the system below by substitution
6x-y=-23
2x+5y=-13
Answer:
x= -4 y= -1
6x - y = - 23
-y=-23-6x
y=6x+23, use this to plug in for y in the second equation.
2x + 5y = -13
2x + 5(6x+23) = -13
2x+30x+115=-13
x= -4, use this to plug in for x in the first equation.
6x - y = - 23
6(-4)-y=-23
-24-y=-23
-y=-23+24
-y=1
y= -1
Step-by-step explanation: not doing this to steal points
Answer:
here is your solution.
Step-by-step explanation:
x=4 & y=1
How many degrees do the angles of a triangle contain?
Answer: 180
Step-by-step explanation:
all 3 angles equal 180 degrees if you divide by 3 each angle will be 60 degrees
How do I find the test statistic and the critical value???
We can find the test statistic and the critical value by the distributed the test statistic under the assumption that the null hypothesis hold.
What is Statics?It is the study of external and the internal force.
When the first data will be pretext and the 2nd the joe will be the first test, the d will be mu joule -1. The alternative hypothesis to em d is the smaller than the 0. The first time we need to find the rest that sticks by the tree is when we were given the question n equal to the 15 and the d p equal to -15.1. The formula with the werther to the end has a big square root of 15 points.
times square 15 equal to the 1.399 point, and the next time we need to find a p value for this, we will use by left hand test.To The 14 degree freedom will be smaller than the minus 1.399 point if the value of the d n -1 degree, freedom and equal to the 15 minus 1 is equal. Energy use the t distribution when it is = 14 degree- freedom is smaller = 1.399 point. I going to compare to 918 point.
We're gong to regent the noon because the alpha is smaller than the 11.
Thus,
We can defined The mean difference is less than 0 points.
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Using the methods provided in the text for computing confidence intervals for population proportions, a marketing analyst takes a survey of 1000 randomly selected consumers. She asks if they prefer low-sodium soup products. Using the results, she provides a 95% confidence interval for the population proportion of consumers who prefer low-sodium soup products. The interval has a margin of error of 03. Which of the following is an appropriate interpretation of these results? (a) The sample proportion from the survey differs from the population proportion by at most 03. (b) 95% of all possible values of the population proportion are contained in the interval provided. (c) The analyst is 95% confident that all possible values for the sample proportion from a sample of 1000 consumers are in the interval provided. (d) Using these methods, 95% of all possible confidence intervals from a sample of 1000 consumers will contain the population proportion. (e) The reported confidence interval will contain the population proportion 95% of the time.
The reported confidence interval will contain the population proportion of consumers 95% of the time.
In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts. Therefore, it can be concluded that there is a 95% probability that the true value falls within that range if a point estimate of 10.00 is produced using a statistical model with a 95% confidence interval of 9.50 - 10.50.
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3 ( 2 x + 7 ) = 8 ( 4 − x )
Answer:x=11/14
Step-by-step explanation:
3(2x+7)=8(4-x)
Multiply the first part of the equation
6x+21=
multiply the 2nd half of the equation
32-8x
6x+21=32-8x
Move the -8x to the left side of the equation making it a positive 8x
8x+6x+21=32
Move the 21 to the right side of the equation
8x+6x=32-21
Add the x’s on the left and subtract the 21 from 32 on the right
14x=11
Divide the 14 into the 11
x=11/14
JK is a midsegment of FGH. Find the values of x and y.
JK is a midsegment of triangle FGH. Hence, the values of x and y are 18 and 14 respectively.
What is a midsegment of a triangle?A triangle's midsegment is a line segment that connects the midpoints or centers of two of its opposite or adjacent sides.
Given that, JK is a midsegment of triangle FGH.
Also the values of:
FG = 28
FJ = x
JH = 10
JK = y
As, JK is midsegment of FG, we have:
JK = FG / 2
y = 28 / 2
y = 14
So, the value of y could be 14.
Also, FG = 28
FJ + JH = FG
10+x = 28
x = 28 - 10
x = 18
So, the value of x could be 18.
Hence, the values of x and y are 18 and 14 respectively.
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Answer:
x=10
Y=14
Step-by-step explanation:
big ideas
The sum of two mixed fractions is 12 3/35
If one mixed fractions is 5 31/35 find the other mixed fraction.
let's convert the mixed fractions to improper fractions and then let's proceed.
[tex]\stackrel{mixed}{12\frac{3}{35}}\implies \cfrac{12\cdot 35+3}{35}\implies \stackrel{improper}{\cfrac{423}{35}} ~\hfill \stackrel{mixed}{5\frac{31}{35}}\implies \cfrac{5\cdot 35+31}{35}\implies \stackrel{improper}{\cfrac{206}{35}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]12\frac{3}{35}~~ + ~~x~~ = ~~5\frac{31}{35}\implies \cfrac{423}{35}+x=\cfrac{206}{35}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{35}}{35\left( \cfrac{423}{35}+x \right)=35\left( \cfrac{206}{35} \right)} \\\\\\ 423+35x=206\implies 35x=-217 \\\\\\ x=\cfrac{-217}{35}\implies x=\cfrac{-31}{5}\implies {\Large \begin{array}{llll} x=- 6\frac{1}{5} \end{array}}[/tex]
to convert an improper fraction like -31/5 to a mixed fraction, well, first off, we nevermind the sign, so we only use 31/5 and then we divide 31 ÷ 5.
hmm 31 ÷ 5 gives us a quotient of 6, and a remainder of 1, we put the quotient upfront and the remainder as the numerator, with the old denominator and sign back in.
There are 4.6 grams of
protein in 1 serving of a brand
of yogurt. You eat 3 servings
of the yogurt. How many
grams of protein did you
consume?
The serving size of a certain brand of yoghurt has 4.6 grams of protein. The yoghurt is consumed in three portions. They eat 13.8 grams of protein daily.
Explain about the mathematical operations?A field of mathematics known as arithmetic operations deals with the study of numbers and the operations on those numbers that are relevant to all other branches of mathematics. The basic operations included in it are addition, subtraction, multiplication, and division.
Calculations involving numbers are done using arithmetic operators. The numerical results that are produced by arithmetic operators are associated from left to right.
The following are the three properties you should consider: Commutative addition applies to full numbers. Associative math is the addition of whole integers. When adding whole numbers, the number 0 serves as an identity.
In several contexts, including multiplication (repeated addition), division, and other operations, the fundamental operations of addition and subtraction are applied (repeated subtraction). These operations are used to transform the word problems into mathematical expressions.
= 4.6 x 1 = 4.6
= 4.6 x 3 =13.8
Hence the total grams of protein consumed is 13.8
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Answer: 13.8 grams of protein
Step-by-step explanation:
If there are 4.6 grams of protein in 1 serving, then to find the number of grams in 3 servings we can use multiplication to solve this question.
4.6 grams of protein * 3 servings = 13.8 grams of protein
100 points. Which is the graph of f (x) x - 1/ x2 - x 6
Answer:
A – see below
Step-by-step explanation:
You want to identify the graph of f(x) = (x -1)/(x² -x -6).
Factored formThe function can be factored as ...
[tex]f(x) = \dfrac{x-1}{(x-3)(x+2)}[/tex]
The numerator is zero when x=1, so that is where the x-intercept lies.
The denominator is zero for x=-2 and x=3, so those are the locations of the vertical asymptotes.
The graph that has vertical asymptotes at x=-2 and x=3, and an x-intercept of x=1 is Graph A.
<95141404393>
Simplify by reducing. Begin by determining the domain restrictions. Show all work.
x2 + 6x + 9 over x2 - 9
x2+6x+9/x2-9
3x2 - 9x over x2 - x - 6
3x2-9x/x2-x-6
Using simplification by factorisation and division
(x² + 6x + 9)/(x² - 9) = (x + 3)/(x - 3) and (3x² - 9)/(x² - x - 6) = 3x/(x + 2)
How to simplify the equations by factorizationTo simplify the equations, we shall factorize both the numerator and the denominator, and divide through by a common factor.
for the equation (x² + 6x + 9)/(x² - 9);
the numerator:
x² + 6x + 9 = x² + 3x + 3x + 9
x² + 6x + 9 = x(x + 3) +3(x + 3)
x² + 6x + 9 = (x + 3)(x + 3)
the denominator:
x² - 9 = x² - 3²
x² - 9 = (x + 3)(x - 3) {difference of two squares}
(x² + 6x + 9)/(x² - 9) = (x + 3)(x + 3)/(x + 3)(x - 3)
divide through by the common factor (x + 3)
(x² + 6x + 9)/(x² - 9) = (x + 3)/(x - 3)
For the equation; (3x² - 9)/(x² - x - 6)
the numerator:
3x² - 9 = 3x(x -3)
the denominator:
x² - x - 6 = x² -3x + 2x - 6
x² - x - 6 = x(x - 3) + 2(x - 3)
x² - x - 6 = (x + 2)(x - 3)
divide through by the common factor (x - 3)
(3x² - 9)/(x² - x - 6) = 3x/(x + 2)
Thus, (x + 3)/(x - 3) and 3x/(x + 2) are the results for simplifying (x² + 6x + 9)/(x² - 9) and (3x² - 9)/(x² - x - 6) respectively using factorization.
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A data set includes data from student evaluations of courses. The summary statistics are n=85, x=3.42, s=0.56. Use a 0.05 significance level to test the claim that the population of student course evaluations has a mean equal to 3.50. Assume that a simple random sample has been selected. Identify the null and alternativehypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim.
What are the null and alternative hypotheses? A.) H0: μ=3.50 H1: μ>3.50 B.) H0: μ≠3.50 H1: μ=3.50 C.) H0: μ=3.50 H1: μ≠3.50 D.) H0: μ=3.50 H1: μ<3.50
Determine the test statistic= ____ (Round to two decimal places as needed.)
Determine the P-value = ____ (Round to three decimal places as needed.)
State the final conclusion that addresses the original claim. ▼ Fail to reject OR Reject H0. There is ▼ sufficient OR not sufficient evidence to conclude that the mean of the population of student course evaluations is equal to 3.50 ▼ is OR not is correct.
- The null hypothesis Is: [tex]$H_0: \mu=4.5$[/tex]
- The alternative hypothesis Is: [tex]$H_1: \mu \neq 4.50$[/tex]
- The test statistic is: t=-0.43
- The p-value of the test is of 0.6684.
What is p-value?
The p-value Is of 0.6684>0.05, which means that we can conclude that the population of student course evaluations has a mean equal to [tex]\mathbf{4 . 5 0}$.[/tex]
We are going to test If the mean Is equals to 4.50, thus, the null hypothesis Is:
[tex]H_0: \mu=4.5[/tex]
At the alternative hypothesis, we test If the mean Is different to 4.50, that is:
[tex]H_1: \mu \neq 4.50[/tex]
Since we have the standard devlation for the sample, the t-distribution is used. The value of the test statistic Is:
[tex]t=\frac{\pi-\mu}{\frac{\sqrt{n}}{\sqrt{n}}}$$[/tex]
For this problem:
[tex]$$\begin{aligned}& t=\frac{4.30-1.5}{\frac{2.21}{\sqrt[3]{80}}} \\& t=-0.43\end{aligned}$$[/tex]
We are testing If the mean is dlfferent from a value, thus, the p-value of test is found using a two-talled test, wlth t=-0.43 and [tex]$80-1=79 \mathrm{df}$[/tex].
Using a t-distribution calculator, the [tex]$\mathrm{p}$[/tex]-value is of [tex]$\mathbf{0 . 6 6 8 4}$[/tex].
The p-value is of 0.6684 > 0.05, which means that we can conclude that the population of student course evaluations has a mean equal to 4.50.
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