We can use the concept of Line Intercept form . She should count up 2 and right 1 . So the correct option is D.
How can we find the intercepts and slope of the equations?When you know the slope of the line to be investigated and the given point is also the y intercept, you can utilize the slope intercept formula, y = mx + b. (0, b). The y value of the y intercept point is denoted by the symbol b in the formula. We set y = 0 and solve the equation for x to determine the x-intercept. This is due to the fact that the line crosses the x-axis at y=0. If an equation is not in the form y = mx + b, we can still solve for the intercepts by substituting 0 where necessary and then solving for the final variable. Set x = 0 and then solve for y to find the y-intercept.
y=mx+b is the slope intercept formula
CalculationThe given equation is y=2x-7.
By comparing to slope intercept formula y=mx+b,
m=2 and b=-7.
So the slope of the given equation is 2 and y-intercept is (0,-7).
we know that,
m=rise/run
so rise=2 and run=1 that means Sam needs to count up 2 and right 1 to graph the equation using the given slope.
We can use the concept of Line Intercept form . She should count up 2 and right 1 . So the correct option is D.
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5/8oz 9/16oz 1/4oz 3/8oz from least to greatest
Please Help will mark Brainly
Answer:
A, B, C
Step-by-step explanation:
You want to know the correct descriptors of the given graph.
SolutionThe solution to a system of equations is the set of points that satisfy all of the equations at once. On a graph, it will be the set of points where the graphs of the equations intersect.
Here the two lines cross at one point, hence there is one solution.
The point where the lines cross is approximately (3, -0.5). That makes (3, -0.5) a reasonable estimate of the solution of the system.
In a normal distribution, a data value located 1.1 standard deviations below the mean has Standard Score: z = In a normal distribution, a data value located 2.5 standard deviations above the mean has Standard Score: z = In a normal distribution, the mean has Standard Score: z =
In a normal distribution, a data value located 1.1 standard deviations below the mean has Standard Score: z = -1.1
What is standard deviation?
In statistics, the quality deviation could be a live of the quantity of variation or dispersion of a group of values. an occasional variance indicates that the values tend to be about to the mean of the set, whereas a high variance indicates that the values area unit opened up over a wider vary
Main body:
The z score tells us the distance, in terms of standard deviation, the raw score is from the mean. Negative z values are below the mean, while positive ones are above the mean.
Something like z = 2.5 indicates we're 2.5 standard deviation units above the mean.
Something like z = -1.1 indicates we're 1.1 standard deviation units below the mean.
The value z = 0 itself is the center of the standard normal distribution (it's the mean mu).
The sigma value for the standard normal Z distribution is sigma = 1
sigma = population standard deviation
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an ellipse has its center at the origin, its foci on the $y$-axis, and its major axis is three times as long as its minor axis. given that the ellipse passes through the point $(-4,0)$, find its equation.
An ellipse's equation has its origin at its center, its foci on the y-axis, and its major axis at x2/16+y2/144, which is three times longer than its minor axis.
What is ellipse's ?In mathematics, an ellipse is a planar curve with two focal points, where the total of the two distances from any point on the curve to the focal points is a constant.
It generalizes the shape of a circle, a unique variety of ellipse in which the two focus points coincide.
The eccentricity of an ellipse, , which ranges from 0 (the limiting case of a circle) to 1 (the length of the ellipse), is used to determine how long it is (the limiting case of infinite elongation, no longer an ellipse but a parabola).
The area of an ellipse has a straightforward algebraic solution, while the perimeter (also known as circumference), for which integration is necessary to arrive at a precise answer, only has approximations.
According to our question-
M(X0|Y) M(0|0)
(X-X0)^2/a^2 +(Y-Y0)^2/b^2=1
x2/a2+x2b2=1
a=4 b=3 .a=12
x2/16+y2/144
Hence, An ellipse's equation has its origin at its center, its foci on the y-axis, and its major axis at x2/16+y2/144, which is three times longer than its minor axis.
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3. A rectangle is 8cm longer than it is wide. If its width is x cm and its area is 84cm², form an equation in x and solve it. Hence find the dimensions of the rectangle.
Answer:
x = 6
Step-by-step explanation:
let x = the width
let x + 8 = the length
Area = w times l
84 = 14 x 6
width = 6
length = 6+8
= 14
Which ordered pair is NOT a solution to the equation y = 2x?
Point A
Point B
Point C
Point D
The ordered pair that is NOT a solution to the equation y = 2x is (3, 8)
How to determine the ordered pairFrom the question, we have the following parameters that can be used in our computation:
y = 2x
From the graph (see attachment), we have the following points:
A = (1, 2)
B = (2, 4)
C = (3, 8)
D = (5, 10)
The equation y = 2x means that
y is twice of x
In C = (3, 8), 8 is not twice of 3
Hence, the ordered pair that is NOT a solution is C = (3, 8)
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What is the result of 6+
3/8?
1/8
1/4
16
48
Answer:
C) 16------------------------------
Simplify:
6 ÷ 3/8 = Given6 × 8/3 = Flip the fraction2 × 8 = Cancel the denominator 16 AnswerAnswer:
[tex] \sf \red{c) \: 16} \: is \: the \: answer.[/tex]
Step-by-step explanation:
Given problem,
[tex] \sf →6 + \frac{3}{8} [/tex]
Changing error in problem,
[tex] \sf →6 \div \frac{3}{8} [/tex]
Let's solve the problem,
[tex] \sf →6 \div \frac{3}{8} [/tex]
[tex] \sf →6 \times \frac{8}{3} [/tex]
[tex] \sf → \frac{(6 \times 8)}{3} [/tex]
[tex] \sf → \frac{48}{3} [/tex]
[tex] \sf \: →16 \:[/tex]
Hence, the answer is 16.
33% of millennials rely on blogs before making a purchase and eight out of 10 millennials never buy anything without reading a review first. In a sample size of 75 Millennials, how many people use blogs to make a purchase? In a sample size of 75 Millennials, how many people never buy anything without reading a review first?
Number of people that use blogs to make a purchase are 24.75= 25 and number of people that never buy anything without reading a review first are 60.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Given, 33% of millennials rely on blogs before making a purchase.
Eight out of 10 millennials never buy anything without reading a review first.
That means,
8 out of 10 is 80%.
In a sample size of 75 millennials:
To find the number of people that never buy anything without reading a review first:
80% of 75
80 x 75 / 100
= 6000/ 100
= 60
To find the number of people that use blogs to make a purchase:
33% of 75
33 x 75 / 100
= 2475/ 100
= 24.75
Therefore, the number of people are 24.75 and 60.
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(Constant of Proportionality, Graphing Proportional Relationships, Real-World Proportional Problems HC)
A restaurant serves pancakes that are made from a powdered pancake mix. There is a proportional relationship between the number of scoops of powdered pancake mix and the amount of water needed to make them. For every 4 scoops of mix, one half quart of water is needed, and for every 12 scoops of mix, one and one half quarts of water are needed.
Part A: Find the constant of proportionality. Show every step of your work. (4 points)
Part B: Write an equation that represents the relationship. Show every step of your work. (2 points)
Part C: Describe how you would graph the relationship. Use complete sentences. (4 points)
Part D: How many quarts of water are needed for 20 scoops of pancake mix? (2 points)
Answer:
See below
Step-by-step explanation:
If I make x the scope of mix and y the quarts of water, my equation would be y = .125x
I can find the constant of Proportionally by y/x
Using points (4,.5) and (12,1.5)
(.5/4) = 0.125
(1.5/12) = 0.125
The equation would then be:
y = 0.125x
C see the graph provided from Desmos (a free graphing calculator). as x Increases by 1, y increases by 0.125
y = 0.125x
y =.0125(20)
y = 2.5
For 20 scoops, I would need 2.5 quarts of water.
You can also see from the graph as 8 scoops, I would need 1 quart of water.
Write the equation in exponential form. Assume that all constants are positive and not equal to 1. logz(w) = p ________
Write the equation in exponential form. Assume that all constants are positive and not equal to 1. log(s) =r ________
Write the equation in logarithmic form. Assume that all constants are positive and not equal to 1. 7m = a ________
To write the equation in exponential form we must follow certain rules:
1. Logarithm product rule - log b ( x ∙ y) = log b ( x) + log b ( y)
2. Logarithm quotient rule - log b ( x / y) = log b ( x) - log b ( y)
3. Logarithm power rule - log b ( x y) = y ∙ log b ( x)
4. Logarithm base switch rule - log b ( c) = 1 / log c ( b)
1. ㏒z(w) = p
Here all constants are taken to be positive and not equal to 1
z = base of the logarithmic function
z^p = w --------> (1)
This z^p = w is the exponential form of ㏒z(w) = p
2. ㏒(s) = r
Here all constants are taken to be positive and not equal to 1
e = base of the logarithmic function
e^r = s --------> (2)
This e^r = s is the exponential form of ㏒(s) = r
3. 7m = a
Here we have to write the equation in logarithmic form
㏒(7m) = log r
log(7m) - log r = 0
We know quotient rule :-
log b ( x / y) = log b ( x) - log b ( y) --------(A)
Applying that same principle to our question by using this equation we have:
log (7m/r)
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Two random number generators each generate a number from 1 to 10. What is the probability that both number generators generated the number 5
Hello,
The probability that both number generators generate the number 5 is (1/10) * (1/10) = 1/100 = 0.01 or 1%.
This is because the probability of an event occurring is the product of the probabilities of each event occurring independently. In this case, the probability of the first generator generating the number 5 is 1/10 and the probability of the second generator generating the number 5 is also 1/10, so the probability of both events occurring is (1/10) * (1/10) = 1/100.
----
Calculate the difference and enter it in the box below.
-7 - 9
Answer:
Step-by-step explanation:
-7-9=-16
When you determine the number of months it will take to pay off a credit card, and you get an answer like 24.35 payments, do you round up or round down? Why?
When you determine the number of months it takes to pay off a credit card and you get 24.35, payments, you have to round up.
How to round up decimals?You should understand that rounding up numbers or decimals involves writing it as a whole number
The question is given in months and we are not asked to state the weekly fractions.
24.35 is 24 months + .35*30=10 weeks
Now 24.35 in months is 24 months 10 weeks and 5 days
Hence payment is in months it should be 24 months only.
In conclusion you should not round it up.
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Determine the nth term formula for the number of square tiles in the nth figure.
Answer:
the nth term is 2n
Step-by-step explanation:
notice how for each number of tiles, 2, 4, 6, 8, 10, they are all multiples of 2, so like ok 2 is definitely in the term, next check how n can fit. Well, since they are multiples, you multiply n by 2, now check to see if you dont need to add any values by the following method:
first number = 2, then 2(1) = 2 if n = 1
second = 4, then (2)(2) = 4 if n = 2
its all the same for the rest. Each new diagram or tile structures represents n, so if n =1, then there are 2 tiles, if n = 4 there are 8 tiles and so on, which explains us why the nth term is 2n
The nth term formula for the number of square tiles in the nth figure is aₙ=2n.
What is an arithmetic sequence?An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same. The general form an arithmetic sequence is aₙ=a+(n-1)d.
The given sequence is 2, 4, 6, 8, 10,.....
Here, a=2 and d=4-2=2
Substitute a=2 and d=2 in aₙ=a+(n-1)d, we get
aₙ=2+(n-1)×2
aₙ=2+2n-2
aₙ=2n
Therefore, the nth term formula for the number of square tiles in the nth figure is aₙ=2n.
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consider the set of students enrolled in a college and the set of faculty members at that college. suppose we define a one to one correspondence between the two sets by saying that a student corresponds to a faculty member if the student is currently enrolled in a course taught by that faculty member. is this correspondence a function? briefly discuss. a simple yes or no needs reasoning so please answer thoughtfully.
We state that a student correlates to a faculty member if somehow the student gets currently enrolled in some kind of a course taught by such faculty member in order to define a one to one relationship between the two sets. The correspondence a function.
Define the term one-to-one relation in function?The symbol for an ordered pair is (INPUT, OUTPUT): The relation denotes the connection between the input and output.
A function, on the other hand, is a relation that yields one Outcome for each input Data.A is a relationship that states that there should only be one outputs for each input. Alternatively, we could say that a function is a special sort of relation (a collection of ordered pairs) that adheres to the rule that every X-value should only be connected with one y-value.A function f: A → B is one-to-one if there is only one instance of a ∈ A with f(a) = b for each instance of b B. It is onto if it has least one a A with f(a) = b for each b B. If it is simultaneously one-to-one and onto, it is a one-to-one correlation or bijection.For the stated question-
We state that a student correlates to a faculty member if somehow the student gets currently enrolled in some kind of a course taught by such faculty member in order to define a one to one relationship between the two sets.
One student is related to one facility.
Thus, correspondence given forms a function.
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When students are admitted to a specific university, they are given a seven (7) digit identification number (NNNNNNN). If the first digit must be either a 0 or 1, how many identification numbers are possible?
Step-by-step explanation:
so, we have 1 position with 2 options (0 or 1).
and 6 positions with 10 options (0 to 9).
so, we have
2×10×10×10×10×10×10 = 2×10⁶ = 2,000,000
different identification numbers possible.
A stock price will rise if:
Supply of stock is greater than demand
The price-earnings ratio is 10 or greater
Stock yield is greater than 8%
Demand for stock is greater than supply
None of these
A stock price will rise if demand for stock is greater than supply. So, the correct answer is option (d).
What is Stock price ?The stock price or share price is the amount of money it costs to buy shares in a company. Stock prices are not fixed and fluctuate based on market conditions. It is likely to go up if the company is viewed as good, and it is likely to go down if the company is not performing as expected. If there are more people who want to buy a demand than sell (supply ) it, the stock price will go up. Conversely, if more people want to sell than buy stocks, there will be more supply than demand and prices will fall. Understanding supply and demand is easy.
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Complete question:
A Stock Price Will Rise If:
a) Supply Of Stock Is Greater Than Demand
b)The Price-Earnings Ratio Is 10 Or Greater
c)Stock Yield Is Greater Than 8%
d) Demand For Stock is Greater Than Supply
e) None Of These.
in triangle abc, lines ad and bd are the angle bisectors of angle a and b and line de is parallel to line ab find the length of line de if perimeter of abde is 30 cm and ab is 12 cm
If the circumference of ABDE is 30 cm, then the length of the line DE is 6 cm.
The answer to the query is
ABDE's perimeter is 30 cm.
AB length is 12 cm.
Let DE ne length be "x"
Since DE and AB are parallel, the alternate interior angles theorem states that
∠ABE = ∠DEB and ∠BAD = ∠ADE.
Since AD is the angle that bisects ∠A,
∠DAB = ∠EAD
BE is the angle bisector of B, therefore
∠EBD = ∠ABE.
∠EAD = ∠ADE and ∠EBD = ∠BED as a result.
If AE = ED and ED = DB, the triangles ADE and EDB are therefore isosceles. AE = DE = DB = x, then.
Given that ABDE's perimeter is 30 cm,
therefore 12 + 3x = 30,
By finding the x,
=> 3x = 30 -12
=> 3x = 18
=> x = 6 cm.
Consequently, DE has a length of 6 cm.
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the temperature in summit green land was -29'F in Fairbanks Alaska the temperature was 23'F in barrels Brazil the temperature was 81'F which two cities had a difference in temperature of 58'F
Answer: Brazil and Alaska
Step-by-step explanation
Take away Brazil's temperature from Alaska's to get your answer
81 - 23 = 58'F
Solve the equation.
-1/6x-5=2/3x
A. x= - 6.
B. x = -5.
C. x = 3.
D. x = 6.
Answer:
A. x = -6
Step-by-step explanation:
-1/6x - 5 = 2/3x
add 1/6x to both sides:
-1/6x - 5 + 1/6x = 2/3x + 1/6x
-5 = 2/3x + 1/6x
common denominator on right side:
-5 = 4/6x + 1/6x
combine right side:
-5 = 5/6x
multiply both sides by 6/5:
(-5)(6/5) = (5/6x)(6/5)
-30/5 = x
reduce left side:
-6 = x
x = -6 (option a)
Answer: A) x=-6
Step by step explanation:
[tex]\boldsymbol{\sf{\dfrac{-1}{6}x-5=\dfrac{2}{3}x }}[/tex]
We calculate the multiplication expression.
[tex]\boldsymbol{\sf{\dfrac{-1}{6}x-5=\dfrac{2}{3}x \iff \ -\dfrac{x}{6}-5=\dfrac{2}{3} x \iff -\dfrac{x}{6}-5=\dfrac{2x}{3} }}[/tex]
Eliminate the fractions by multiplying by the least common multiple of the denominators of both sides.
[tex]\boldsymbol{\sf{ -\dfrac{x}{6}-5=\dfrac{2x}{3} \iff \ -x-30=4x}}[/tex]
The variable is moved to the left and the symbol is changed.
[tex]\boldsymbol{\sf{-x-30=4x \iff -x-30-4x=0}}[/tex]
We move the constant to the right side and change the sign.
[tex]\boldsymbol{\sf{-x-30-4x=0 \iff -x-4x=30}}[/tex]
[tex]\boldsymbol{\sf{-x-4x=30 \ < == We \ organize \ the \ equation== > \ -5x=30 }}[/tex]
[tex]\bf{\underline{Change \ the \ sign \ on \ both \ sides \ of \ the \ equation.}}[/tex]
[tex]\boldsymbol{\sf{-5x=30 \iff \ 5x=-30 \ < ==Split== > \ x=-\dfrac{30}{5}=\boxed{\boxed{\boldsymbol{\sf{-6}}}} }}[/tex]
Write 28 as a product of its prime factors, write factors in order from smallest to largest
Answer:
2 × 2 × 7
Step-by-step explanation:
start dividing by the lowest prime and work up until 1 is reached
28 ÷ 2 = 14
14 ÷ 2 = 7
7 ÷ 7 = 1
then
28 = 2 × 2 × 7 = 2² × 7
g. find polar coordinates of the following points given in cartesian coordinates (x, y): (2,5), (3,-6), (-4,9), (-8,-1
The polar coordinates of the points are: A(√29,68.1°),B(√45,-63.4°),C(√97,66.0°),D(√65,7.12°)
consider A=(2,5)
To find the polar coordinates we have the formula:
[tex]r=\sqrt{x^2+y^2} and tan^{-1} (\frac{y}{x} )----------(1)[/tex]
Assume that x=2,y=5 and substitute in equation(1)
r=√2^2+5^2 and tan^-1(5/2)
r=√4+25 and tan^-1(2.5)
r=(√29,68.1°)
For point B =(3,-6)
Assume that x=3,y=-6 and substitute in equation(1)
r=√3^3+(-6)^2 and tan^-1(-6/2)
r=√9+36 and tan^-1(-2)
r=(√45,-63.9°)
For point C=(-4,9)
Assume that x=-4,y=9 and substitute in equation(1)
r=√(-4)^2+9^2 and tan^-1(9/-4)
r=√16+81 and tan^-1(2.25)
r=(√97,66.0°)
For the point D=(-8,-1)
Assume that x=-8,y=-1 and substitute in equation(1)
r=√(-8)^2+(-1)^2 and tan^-1(-1/-8)
r=√64+1 ,7.12°
r=(√65,7.12°)
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missing angle of 28 and 21 trigonometry
Letss try using Pythagoras Theorem with
[tex]a+b+c=180\\21+28+c=180\\c=180-21-28\\c=131[/tex]
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factor this expression completely, then place the factors in the proper location on the grid. 5x 3 40y 6
The factorized expression of 5x³ + 40y⁶ is 5 ((x + 2y²) (x² - 2xy² + 4y⁴))
Factorisation of an algebraic expression means writing the given expression as a product of its factors. These factors can be numbers, variables, or an algebraic expression.
To the factor, a number means to break it up into numbers that can be multiplied to get the original number
According to the question,
We have to factorize the expression
5x³ + 40y⁶
Taking a Common factor 5 out ,
5 (x³ + 8y⁶)
Factoring the expression within the parenthesis we have:
5 ((x + 2y²) (x² - 2xy² + 4y⁴))
Now, we cant do further factor
Hence , The factored expression is given by: 5 ((x + 2y²) (x² - 2xy² + 4y⁴))
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Attending Class The following data represent the number of days absent, x, and the final grade, y, for a sample of college students in a general education course at a large state University
No. of Absensense, x 0 1 2 3 4 5 6 7 8 9
Final grade, y 89.2 86.4 83.5 81.1 78.2 73.9 64.3 71.8 65.5 66.2
A) Find the least-sqaures regresssion line treating number of absenses as the explanatory variable and final grade as a response variable.
B) Interpret the slope and y-intercept , if appropriate.
C) Predict the final grade for a student who misses five class periods and compute the residual. Is the final grade abover or below average for this number of absenses.
D) Draw a least-sqaures regression line on the scatter diagram of the data.
E) Would it be reasonable to to use the least-sqaures regression line to predict the final grade for a student who has missed 15 class periods? why or why not?
We get the following answers:
A) The least square regression line is:
yi = 88.73 - 2.827(xi)
B) The slope is β₁ = -2.827 and The intercept is β₀ = 88.73.
C) e*₆ = -0.6964, final grade is below average grade.
E) It would not be reasonable since no of absence increases the score decreases, it works well for small no of absences but will not work for large number of absences since it may give absurd final grade.
we have Xi = No of absences
Yi = Final grade
The regression model is
Yi = β₀ + β₁Xi + i
β₀ = y - β₁x
we have n = 10, x bar = 4.5 , y bar = 76.01
cov(x,y) = -23.325 and var(x) = 9.1667
therefore, β₀ = 88.73 and β₁ = -2.827
A) Least square regression line is given by:
yi = β₀+ β₁Xi
yi = 88.73 - 2.827(xi)
B) The slope β₁ = -2.827 which means when no of absence is increased by 1 duty then the final grade will decrease by 2.827
The intercept β₀ = 88.73 when there are 0 days absence the average grade is 88.73
C) Predicted graph for student who misses five class periods is
x = 5
y*5 = 88.73 - 2.827(5) = 74.5964
Hence for corresponding residual is:
e*₆ = 73.9 - 74.5964
e*₆ = -0.6964, final grade is below average grade.
D) please see graph
E) when student miss 15 class periods the final grade will be
X = 5
y* = 88.73 - 2.827(15)
= 46
It would not be reasonable since no of absence increases the score decreases, it works well for small no of absences but will not work for large number of absences since it may give absurd final grade.
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Find the function represented by the following series and find the interval of convergence of the series. Sigma Infinity k=0[x^2+3/4]^k. The function represented by the series Sigma Infinity k=0[x^2+3/4]^k is f(x)= The interval of convergence is (Simplify your answer. Type your answer in interval notation. Type an exact answer, using radicals as needed.)
The function represented by the series is [tex]$\quad f(x)=\frac{4}{1-x^2}$[/tex]
The interval of convergence of the series is ( - 1, 1 )
As per the question the given function is:
[tex]$$\sum_{k=0}^{\infty}\left(\frac{x^2+3}{4}\right)^k$$[/tex]
[tex]$$\sum_{n=0}^{\infty} a r^n=\frac{1}{1-r}$$[/tex]
[tex]$$\sum_{n=0}^{\infty} x^n=\frac{1}{1-x}$$[/tex]
[tex]$$\begin{aligned}\sum_{k=0}^{\infty}\left(\frac{x^2+3}{4}\right)^k & =\frac{1}{1-\frac{x^2+3}{4}} \\& =\frac{1}{\frac{4-x^2-3}{4}} \\& =\frac{4}{1-x^2}\end{aligned}$$[/tex]
Thus, [tex]$\quad f(x)=\frac{4}{1-x^2}$[/tex]
[tex]$$\sum_{k=0}^{\infty}\left(\frac{x^2+3}{4}\right)^k=\sum_{k=0}^{\infty} \frac{\left(x^2+3\right)^k}{4^k}$$[/tex]
[tex]$$\begin{aligned}L & =\lim _{k \rightarrow \infty}\left|\frac{\left(x^2+3\right)^{k+1}}{4^{k+1}} \frac{4^k}{\left(x^2+3\right)^k}\right| \\& =\lim _{k \rightarrow \infty}\left|\frac{\left(x^2+3\right)}{4}\right| \\& =\left|\frac{\left(x^2+3\right)}{4}\right|\end{aligned}$$[/tex]
The series will converge, if L<1
[tex]$$\begin{array}{ll} & \left|\frac{\left(x^2+3\right)}{4}\right| < 1 \\ & \frac{\left(x^2+3\right)}{4} < 1 \\ & x^2+3 < 4 \\\end{array}[/tex]
[tex]& x^2 < 1 \\[/tex]
|x| < 1
-1 < x < 1
Substitute the values of 'x' in the given function
At, x = - 1
[tex]\begin{aligned} \\\qquad \begin{aligned}\sum_{k=0}^{\infty}\left(\frac{x^2+3}{4}\right)^k & =\sum_{k=0}^{\infty}\left(\frac{(-1)^2+3}{4}\right)^k \\& =\sum_{k=0}^{\infty}\left(\frac{4}{4}\right)^k \\& =\sum_{k=0}^{\infty} 1^k\end{aligned}\end{aligned}$$[/tex]
Also, at x = 1
[tex]$$\begin{aligned}\sum_{k=0}^{\infty}\left(\frac{x^2+3}{4}\right)^k & =\sum_{k=0}^{\infty}\left(\frac{(1)^2+3}{4}\right)^k \\& =\sum_{k=0}^{\infty}\left(\frac{4}{4}\right)^k \\& =\sum_{k=0}^{\infty} 1^k\end{aligned}$$[/tex]
Thus, the interval of convergence is ( - 1, 1 )
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Enter the ordered pair for the vertices for (Ry-axis T(2, 0))(QRST).
I need help with this please help me
The ordered pair for the vertices after the transformation will be:
Q' = (3, 5)
R' = (5, -1)
S'= (2, 0)
T' = (0, 3)
How to find the ordered pair for the vertices for (Ry-axis T(2, 0))(QRST)?
A geometric transformation is a function that maps points in a plane or space to other points in the same plane or space. Geometric transformations can be used to change the size, shape, orientation, or position of an object or image.
Given: (Ry-axis T(2, 0))(QRST). That means we have a translation T(2, 0). This implies (x,y) → (x + 2, y + 0). Thus, the ordered pair for the vertices will be:
Q (x = 1, y = 5)
Q' = Q(x+2, y + 0) = (1+2, 5+0) = (3, 5)
R (x = 3, y = -1)
R' = R(x+2, y + 0) = (3+2, -1+0) = (5, -1)
S (x = 0, y = 0)
S' = S(x+2, y + 0) = (0+2, 0+0) = (2, 0)
T (x = -2, y = 3)
T' = T(x+2, y + 0) = (-2+2, 3+0) = (0, 3)
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In each case below find an equation for the line with the given information about the linear equation and
give the slope of each line.
a) Vertical line through point (2, -65)
b) Horizontal line through point (-2, 4)
a) The equation of a vertical line is x = k, where k is the x-coordinate of the point where the line intersects the y-axis. In this case, the point where the line intersects the y-axis is (2, -65), so the equation of the line is x = 2. The slope of a vertical line is undefined, since it has no slope.
b) The equation of a horizontal line is y = k, where k is the y-coordinate of the point where the line intersects the x-axis. In this case, the point where the line intersects the x-axis is (-2, 4), so the equation of the line is y = 4. The slope of a horizontal line is 0, since it has no slope.
Give f(x) = 2x2 + 1 and g (x) = 3x -5 , find the following f(g)(2))
The function f{ g(2) } is equivalent to for the functions f(x) = 2x² + 1 and g(x) = 3x - 5 is 3.
What is a mathematical function, equation and expression?function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is that f(x) = 2x² + 1 and g(x) = 3x - 5.
We have to find -
f{g(2)}
Now -
g(2) = g(2) = 3 x 2 - 5 = 6 - 5 = 1
g(2) = 1
f{g(2)} = 2x² + 1 = 2 x 1 x 1 + 1
f{ g(2) } = 3
Therefore, the function f{ g(2) } is equivalent to for the functions f(x) = 2x² + 1 and g(x) = 3x - 5 is 3.
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A city has 4 voting districts. Records from previous years show what proportion of residents live in each district. A political analyst wondered if those proportions still held true, so they took a random sample of 120 residents. Here are their results along with a chi-square goodness-of-fit test:District A B C DHypothesized 0.39 0.27 0.15 0.19 Observed 58 22 12 28 Expected 46.80 32.40 18.00 22.80 Components 2.68 3.34 2.001.19 x² = 9.20, DF = 3 P-value = 0.027 Which voting district contributed the most to the test statistic?
Answer: The voting district that contributed the most to the test statistic is District B.
Step-by-step explanation:
How do you calculate the contribution of each voting district to the test statistic?
The contribution of each voting district to the test statistic is calculated by taking the difference between the observed and expected values for that district, squaring it, and then dividing it by the expected value. In this case, the contribution for District A is (58-46.80)^2/46.80 = 2.68, the contribution for District B is (22-32.40)^2/32.40 = 3.34, the contribution for District C is (12-18)^2/18 = 2.00, and the contribution for District D is (28-22.80)^2/22.80 = 1.19. Therefore, District B contributed the most to the test statistic.
The chi-square goodness-of-fit test compares observed and expected values to determine if they are significantly different from each other. The test statistic is calculated by summing the squared differences between the observed and expected values, divided by the expected values. The larger the difference between the observed and expected values, the larger the contribution to the test statistic. In this case, District B had the largest difference between the observed and expected values, therefore it had the greatest impact on the overall test statistic.
District B contributed the most to the test statistic because it had the highest value in the "Components" column. The formula for the chi-square goodness-of-fit test is (Observed - Expected)^2 / Expected, and the resulting value for District B is 3.34, which is the highest of the four districts. Therefore, District B had the biggest deviation from the hypothesized proportions.
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Answer: Voting district B contributed the most to the test statistic.
Step-by-step explanation:
How do you determine each voting district's contribution to the test statistic?
By subtracting the observed value from the predicted value for each voting district, square rooting the result, and then dividing the result by the expected value, the contribution of each voting district to the test statistic is determined. In this instance, the contributions for Districts A, B, C, and D are as follows:
District A's contribution is (58-46.80)²/46.80 = 2.68; District B's contribution is (22-32.40)²/32.40 = 3.34; District C's contribution is (12-18)²/18 = 2.00; and District D's contribution is (28-22.80)²/22.80 = 1.19. As a result, District B was most responsible for the test statistic.
In order to assess if actual and expected values differ significantly from one another, the chi-square goodness-of-fit test compares observed and expected values. The test statistic is determined by multiplying the expected values by the total of the squared discrepancies between the actual and predicted values. The contribution to the test statistic increases as the gap between observed and predicted values widens. In this instance, District B's largest disparity between actual and predicted values had the biggest effect on the test statistic as a whole.
Due to having the highest value in the "Components" column, District B had the greatest impact on the test statistic. (Observed - Expected)² / Expected is the formula for the chi-square goodness-of-fit test, and the result for District B, which is the highest of the four districts, is 3.34.
District B therefore, showed the greatest departure from the predicted proportions.
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