A. the 1500 randomly selected voters receiving the questionnaire.
What is survey?
A survey is a technique for acquiring data from a sample of individuals by asking pertinent questions with the goal of comprehending populations as a whole. Everyone involved in the information economy, from corporations to the media to the government and academia, relies on surveys as a vital source of information and insights.
A political party sends a mail survey to 1500 randomly selected registered voters in a community. The survey asks respondents to give an opinion about the job performance of the current President. Of the 1500 surveys sent out, 480 are returned, and of these, only 120 say they're satisfied with the President's job performance.
The sample remains the total people to whom the survey is sent
The sample is the 1500 randomly selected voters receiving the questionnaire.
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The distance between P and T on the coordinate grid is
units. (Input whole numbers only.)
Image of a coordinate grid with point P located at negative 10, 15 and point T located at 15, 15.
Answer:
25
Step-by-step explanation:
The telephone company offers two billing plans for local calls. Plan 1 charges $25 per month for unlimited calls and Plan 2 charges $18 per month plus $0.05
per call.
a. Use an inequality to find the number of monthly calls for which Plan 1 is more economical than Plan 2.
b. Explain the meaning of the answer to part
a.
For the number of calls greater than 140, the plan [1] is more economical than plan [2].
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 a telephone company offers two billing plans for local calls. Plan 1 charges $25 per month for unlimited calls and Plan 2 charges $18 per month plus $0.05 per call.
For the part [1] -
25 < 18 + 0.05x
25 < 18 + 0.05x
25 - 18 < 0.05x
7 < 0.05x
x > (7/0.05)
x > 140
For part [2] -
For the number of calls greater than 140, the plan [1] is more economical than plan [2].
Therefore, for the number of calls greater than 140, the plan [1] is more economical than plan [2].
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A random sample of 65 high school seniors was selected from all high school seniors at a certain high school. The following scatterplot shows the height, in centimeters (cm) , and the foot length, in cm , for each high school senior from the sample. The least-squares regression line is shown. The computer output from the least-squares regression analysis is also shown.
The figure presents a scatterplot in a coordinate plane. The horizontal axis is labeled Foot Length, in centimeters, and the numbers 18 through 34, in increments of 2, are indicated. The vertical axis is labeled Height, in centimeters, and the numbers 150 through 190, in increments of 10, are indicated. There are 65 data points in the scatterplot, and a trend line is given as follows. Note that all values are approximate. The data points begin in the lower left part of the plane at the point with coordinates 19 comma 160. The data points trend upward and to the right and end with the coordinates 33 comma 190. The least-squares regression line begins at the point 18 comma 153, and slants upward and to the right at a constant rate to end at the point 35 comma 197.
Term Coef (SE) Coef T -Value P -Value
Constant 105.08 6.00 17.51 0.000
Foot length 2.599 0.238 10.92 0.000
S=5.90181 R–sq=65.42%
(a) Calculate and interpret the residual for the high school senior with a foot length of 20cm and a height of 160cm .
(b) The standard deviation of the residuals is s=5.9 . Interpret the value in context.
Unit 2 Progress Check: FRQ
Aubree Flores
As per the least-squares regression,
a) The residual for the high school senior with a foot length of 20cm and a height of 160cm is 2.94
b) As per the given standard deviation, the value of the context 5.9
The term standard deviation in math is defined as a measure of how dispersed the data is in relation to the mean.
Here we have given that the random sample of 65 high school seniors was selected from all high school seniors at a certain high school.
And we need to find following.
While we looking into the given question, as per the least-squares regression line, here the estimated height for a high school senior with a foot length of 20 cm is calculated as,
=> y = 2.599x + 105.08
Now, we have to apply the value of x as 20, then we get,
=> y = 2.599(20) + 105.08
=> y = 157.06
Therefore, the residual is calculated as,
=> 160 − 157.06 = 2.94
b) As per the given standard deviation, here the differences between each data point and its corresponding estimate varies with a standard deviation of 5.9 cm.
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At any given time there are N people on an elevator, N being a discrete random variable with mean E(N)=n. The weight of the i th person in the elevator Is a continuous random variable Y, with mean E(Yi)=w. The random variable N and the random variables Yi are independent. Let W be the total weight of all people in the elevator at a given time. Prove that E(w)=w. (Hint: This is very simple to prove if you use properties of conditional expectation).
At any given time there are N people on an elevator, N being a discrete random variable with mean E(N)=n, then E(Y1) = w
Let W be the total weight of all people in the elevator at a given time and N be the number of people in the elevator at a given time.
E(W) = E[E(W|N)]
Since N and Y are independent, we can also write with mean:
E(W|N) = E[E(W|N,Y)]
Since the weight of each person is independent of the others, we can write:
E(W|N,Y) = E[E(W|N,Y1)]
Since Y is a continuous random variable and the weights of each person are independent, we can further write:
E(W|N,Y1) = E(Y1) = w
Therefore, we can conclude that:
E(W) = E[E(W|N)] = E[E(W|N,Y)] = E[E(W|N,Y1)] = E(Y1) = w
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a die is rolled until the first time t that a six turns up, what is the probability distribution for t
The probability of rolling a six on any given roll is constant, so the probability distribution is a geometric distribution.
What is a probability distribution?
A probability distribution is a function that describes the probabilities of different outcomes in a random event or experiment. It is used to represent the likelihood of different outcomes occurring in a given situation.
In the case of rolling a die until the first time that a six turns up, the probability distribution for t (the number of rolls it takes to get a six) would describe the probability of getting a six on each roll.
The probability of getting a six on the first roll is 1/6, since there is a 1 in 6 chance of rolling a six on any given roll. The probability of getting a six on the second roll is 1/6, since there is still a 1 in 6 chance of rolling a six on any given roll. The probability of getting a six on the third roll is also 1/6, and so on.
The probability distribution for t in this case can be represented by the following table:
t Probability
1 1/6
2 1/6
3 1/6
4 1/6
5 1/6
... ...
This probability distribution indicates that the probability of getting a six on the first roll is 1/6, the probability of getting a six on the second roll is 1/6, and so on.
Hence, the probability of rolling a six on any given roll is constant, so the probability distribution is a geometric distribution.
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Pentagons ABCDE and FGHIl are similar. The ratio of each side of pentagon ABCDE to its corresponding side of pentagon FGHIJ is 4:1. If AB and FG are corresponding sides, and the length of AB is 4x + 4, what is the length of FG?
Pentagons ABCDE and FGHIl are similar. The ratio of each side of pentagon ABCDE to its corresponding side of pentagon FGHIJ is 4:1. the length of FG is x + 1.
What is the length of FG?Generally, A distance may be measured in terms of its length. A quantity that has the dimension distance in the International System of Units is referred to as length. In the vast majority of measuring systems, a length base unit is selected, and it is from this unit that all other units are derived.
The meter serves as the fundamental measuring device for length in accordance with the International System of Units.
Since the ratio of the sides of the two pentagons is 4:1, the length of FG is 1/4 of the length of AB.
Therefore, the length of FG is
(1/4)(4x + 4) = x + 1.
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Complete Question not found
Image not found
Answer:
its 1/4
Step-by-step explanation:
Step 1: Calculate the ratio of the side lengths for the original image to the corresponding side lengths of the transformed image using side FG and its corresponding side in
is it possible to use the law of cosines to solve for one angle in a triangle?
Yes, it is possible to use the law of cosines to solve for one angle in a triangle.
The law of cosines states that in any triangle, the square of the length of any side (c) is equal to the sum of the squares of the lengths of the other two sides (a and b) minus twice the product of those sides and the cosine of the angle between them (C):
c^2 = a^2 + b^2 - 2ab * cos(C)
If you know the lengths of all three sides of a triangle (a, b, and c), you can use the law of cosines to solve for the cosine of one of the angles (C). Once you have the cosine of the angle, you can use the inverse cosine function (also known as the arccosine) to find the measure of the angle in degrees.
For example, if you know the lengths of sides a and b and the measure of angle C in a triangle, you can use the law of cosines to find the length of side c:
c = sqrt(a^2 + b^2 - 2ab * cos(C))
Alternatively, if you know the lengths of sides a and c and the measure of angle B in a triangle, you can use the law of cosines to find the length of side b:
b = sqrt(c^2 - a^2 - 2ac * cos(B))
In both cases, once you have found the value of one of the sides, you can use the law of sines to find the measure of the remaining angle in the triangle.
Select ALL solutions
Answer:
in the picture
Step-by-step explanation:
in the picture
PLS HELP I’m struggling with this question and could use some help to answer it.
The required inverse function of the given function is given as f⁻¹(x) = [9 - 8y] / [1 + y], the domain of the inverse function is all real numbers except -1, and the range of the inverse function is all real numbers.
What are functions?Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
here,
f(x) = -x + 9 / [8 + 9x]
Now,
y = f(x)
y = -x + 9 / [8 + 9x]
x = 9 - 8y / [1 + y]
Now,
x ⇄ y
y = 9 - 8x / 1 + x
Now y = f⁻¹[x]
f⁻¹(x) = [9 - 8y] / [1 + y],
Thus, the required inverse function is f⁻¹(x) = [9 - 8y] / [1 + y], the domain of the inverse function is all real numbers except -1, and its range is all real numbers.
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Is it true n ⊥ p? Your response should be at least 3 complete sentences. Be sure to include any relevant measurements and calculations.
No, the lines are not perpendicular because Line m has a slope of 2/3 and line n has a slope of 3/5.
What is the slope of a line which passes through points ( p,q) and (x,y)?Its slope would be:
[tex]m = \dfrac{y-q}{x-p}[/tex]
Slope of parallel lines are same. Slopes of perpendicular lines are negative reciprocal of each other.
For two lines to be perpendicular if the slopes are reciprocal of each other.
line m: 2/3
line n: 3/5
Therefore,
n ⊥ p is False.
The slopes are not negative reciprocal of each other. so the lines are not perpendicular.
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Sharon wants to make keychains with different colored beads as shown below.
Each key-chain will look the same Sharon will use a total of 20 green beads to make all her keychains. What is the number of red Beads and the number of blue Beads she will need to make all of the keychains
The numbers of each beads that Sharon will need to make all of the key chains is given as follows:
Red beads: 15.Blue beads: 30.How to obtain the amounts needed of each bead?The amounts for each bead are obtained applying the proportions built from the image given at the end of the answer.
From the images, for a single key chain, the amounts needed are given as follows:
4 green beads.3 red beads. 6 blue beads.Hence, for each 4 green beads, 3 red beads are needed. For 20 green beads, the number of red beads needed is given as follows:
3/4 x 20 = 60/4 = 15 red beads.
For each 4 green beads, 6 blue bears are needed. For 20 green beads, the number of blue beads needed is given as follows:
6/4 x 20 = 120/4 = 30 blue beads.
Missing InformationThe image is given at the end of the answer.
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The integer 5 makes which of the following equation false
Answer:
(a) 3m +4 = 6m
Step-by-step explanation:
You want to know which of the equations is false when the value of the variable is 5.
3m +4 = 6m3(5) +4 = 19 ≠ 6(5) . . . . . the given equation is false for m=5
-5(t -7) = 10-5(5 -7) = -5(-2) = 10 . . . . true
17 = 4x -317 = 4(5) -3 = 20 -3 . . . . true
t +9 = 145 +9 = 14 . . . . true
for an closed cylinder with radius r cm and height h cm, find the dimensions giving the minimum surface area, given that the volume is 6 cm3
The dimensions giving the minimum surface area are r = 0.98 cm approx. and h = 1.998 cm .
What is surface area?
The surface area of a solid object could be a live of the full area that the surface of the article occupies.
Main body:
The surface area of the closed cylinder is given by,
S = 2πr²+2πrh
And volume is given by,
V = πr²h
Where, R is radius and h is height of cylinder.
Volume is given to be 6 cm³.
V = πr²h = 6
h = 6/πr²
Inserting this value of h in Surface area equation, we get,
S = 2πr²+ 2πr ( 6/πr²)
S = 2πr² + 12 /r
Now differentiating wrt x to find minimum, inserting ds/dr = 0 , we get,
4πr = 12/r²
r = (3/π)¹/³
r = 0.98 cm approx.
h = 6/π *(0.98)²
h = 6/3.017
h = 1.998 cm
Hence ,the dimensions giving the minimum surface area are r = 0.98 cm approx. and h = 1.998 cm .
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Help please fast!! What is the measure of angle C? I’m confused please help!
Answer:
[tex]61.8^{\circ}[/tex]
Step-by-step explanation:
Vertical angles are congruent
Answer:
61.8
Step-by-step explanation:
The measure of angle C is 61.8 degrees.
Vertical angles are a pair of nonadjacent angles formed by two intersecting lines. They are called "vertical" because they are opposite each other and share the same vertex (the point at which the two lines intersect). Because vertical angles share the same vertex, they are always congruent, which means that they have the same measure.
In this case, angles C and E are a pair of vertical angles, so they are congruent. Since the measure of angle E is 61.8 degrees, the measure of angle C must also be 61.8 degrees. Therefore, the answer is 61.8 degrees.
Ajay and deepak can do an allocated work in 15 days and 10days respectively. They stated the work together but Deepak left after sometimes and ajay finished the remaining work in 5 days. After how many days (from the start)did Deepak leave
Answer:
Deepak have taken 5 days leave from the start of the work.
ryland is creating an article about commonly used compression algorithms for an online educational site. he's debating whether to express each algorithm in natural language, flow charts, pseudocode, or c , a general-purpose programming language. which of these is a good argument for expressing the algorithm in pseudocode? choose 1 answer:
Pseudocode doesn't depend on the syntax and subtitles of a particular programming language, so his readers will be able to understand it as long as they know at least one language.
In computer science, pseudocode is a undeniable language description of the stairs in an set of rules or any other system. Pseudocode frequently makes use of structural conventions of a regular programming language, however is supposed for human studying as opposed to gadget studying. Pseudocode is known via way of means of the programmers of all types. it allows the programmer to pay attention most effective at the set of rules a part of the code development. It can't be compiled into an executable program.
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Complete question:
Ryland is creating an article about commonly used compression algorithms for an online educational site.
He's debating whether to express each algorithm in natural language, flow charts, pseudocode, or C++, a general-purpose programming language.
Which of these is a good argument for expressing the algorithm in pseudocode?
Judy purchased a home in 1956. The
function represents y, the value of the home
x years since 1956.
f(x) = 11,500(1.09)^x
A. Judy purchased the home for
$109,000.
B. The value of the home increases by 9%
each year.
C. In 1986, Judy's home had a value over
$150,000.
After 26 years Judy purchased the home for $109,000.
What is function?
A function from a set X to a set Y in mathematics assigns each element of X exactly one element of Y. The set X is known as the function's domain, and the set Y is known as the function's codomain.
A function is a relationship between a set of inputs and a set of potential outputs, where each input is related to exactly one output.
Given:
Judy purchased a home in 1956.
The function represents y, the value of the home x years since 1956.
f(x) = 11,500(1.09)^x
Let Judy purchased the home for $109,000.
We have to find the the number of years when Judy purchased the home for $109,000.
Plug f(x) = 109,000 in the above equation.
109,000 = 11,500(1.09)^x
218/23 = (1.09)^x
Taking log on both sides,
ln(218/23) = ln(1.09)^x
ln(218/23) = x ln(1.09)
x = ln(218/23)/ln(1.09)
x = 26.097
⇒ x ≈ 26
Hence, after 26 years Judy purchased the home for $109,000.
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Write an equation for a parabola with x-intercepts (-4,0) and (3,0) which passes through the point (2,-24).
Answer:
good job
Step-by-step explanation:
which measures do not represent the length of 3 sides of a triangel
Answer: correct answer is A
Step-by-step explanation:The numbers of sets which cannot represent the lengths of the sides of a triangle are 8, 9, 11.We have to determineWhich set of numbers cannot represent the lengths of the sides of a triangle?According to the questionThe length of sides which can not form a triangle is determined in the following steps given below.
Answer:
The correct answer is A.
Step-by-step explanation:
You have to look at the triangle inequality theorem where a + b ≥ c. Any two sides of a triangle must be greater than or equal to the third, in this case, 1 ft + 3 ft only = 4. Therefore A does not represent the length of 3 sides of a triangle.
Hope this helps, Have an amazing day!
Graph line segment BC with endpoints B(8 and
C(-4,5) and label the points.
Steps for solving:
Draw and label an x and y axis (make sure you include arrows).
Plot the given points.
Label the given points.
The graph of the Line Segment BC with the endpoints B(8,9) and C(-4,5) is shown below.
In the question ,
it is given that ,
the end points of the line segment is B(8,9) and C(-4,5) .
we have to graph the line segment BC.
first we mark the point on the coordinate plane , with point B and point C .
after that we join the points .
and the equation of the line segment is
(y - 5) = (9-5/8+4)*(x + 4)
(y - 5) = (1/3)*(x + 4)
3y - 15 = x + 4
x - 3y + 19 = 0
Therefore, the graph of the line segment BC is shown below.
The given question is incomplete , the complete question is
Graph line segment BC with endpoints B(8,9) and C(-4,5) and label the points.
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the positive integers are arranged in the patterm illustrated below: if this pattern continues indifinetely, what is the number immediately above 39863
Answer:
Step-by-step explanation:
986
Help as soon as possible
The value of /BD/ in the quadrilateral is 16.9m
How to determine length in a triangle?A quadrilateral is polygon with four sides, four angles, four vertices, two diagonals whose sum of angles is 360 degrees
The diagonal of the quadrilateral forms a triangle.
From the triangle ΔABD, two sides are given with an included angle.
/AB/=16m
/AD/=19m
/BD/=?
To find the length /BD/
let it be a.
Using cosine rule, we have
a²=b²+d²-2bdcosA
a²=19²+16²-2*19*16*cos57⁰
Simplifying the formula
a²=361+256-608*0.5446
a²=617-311.1168
a²=285.8832
taking the square of both sides we have
a=√285.8832
a=16.9m
Therefore the length of the side /BD/ = 16.9m
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34. selecting from urns an urn contains four red marbles and three green marbles. one marble is removed, its color noted, and the marble is not replaced. a second marble is removed and its color noted.
The probability states that- (r+w+b+g)min =21,
What is probability ?Probability refers to possibility.
A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.
Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.
According to our question-
r−3=4w,r−2=3b,r−1=2g
r=4w+3,r=3b+2,r=2g+1
rmin=11⇒w min=2⇒bmin=3⇒g min =5
Hence, (r+w+b+g)min =21,
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θ =120°
θ =240°
θ =270°
θ =0°
θ =210°
θ =180°
θ =90°
02410.0 points
The charge on an electron is 1.60218 x 10⁻¹⁹C and its mass is 9.10939 x 10⁻³¹ kg.
What is the kinetic energy of an electron that passes undeviated through perpendicular electric and magnetic fields if E=0.18 kV m and B=1.1mT ?
Answer in units of eV.
The kinetic energy of an electron that passes undeviated through perpendicular electric and magnetic fields if E=0.18 kV m and B=1.1 mT is 0.07623125 eV.
In the given question, the charge on an electron is 1.60218 x 10^(-19) C and its mass is 9.10939 x 10^(-31) kg.
We have to find the kinetic energy of an electron that passes undeviated through perpendicular electric and magnetic fields if E=0.18 kV m and B=1.1 mT.
E = 0.18 kV/m
B = 1.1 mT
mass m = 9.10939*10^(-31) kg
Then force on a moving charge in electric and magnetic field = Lorentz force
F = qE+ q*VB
So,
F = qE+ q*VB = 0
E = V*B
Find V , so
V = E/B
V = 0.18*10^3 /( 1.1*10^-3)
V =163637 m/s
so KE = 1/2*m*v^2
Then put values..
KE = 0.5*9.11*10^(-31)*163637^(2)
KE = 1.2197*10^(-20) J
in eV = 1.2197*10^-20 / ( 1.6*10^-19 )
eV = 0.07623125 eV
Hence, the kinetic energy of an electron that passes undeviated through perpendicular electric and magnetic fields if E=0.18 kV m and B=1.1 mT is 0.07623125 eV.
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96% of Americans report eating a diet that includes meat, 3.5% of Americans claim to be exclusively vegetarian, and 0.5% claim to be strictly vegan. Of a random sample of undergraduates in the University of Virginia dining hall (n = 175), 156 students report eating a diet that includes meat, 11 report being exclusively vegetarian, and 8 are strictly vegan.
5. State the test you would use to determine if the observed and expected frequencies of diets are consistent. List the conditions required for this test and verify that they are satisfied.
6. How many students would you expect to eat meat, be exclusively vegetarian, and be a strict vegan?
7. Calculate the chi-square statistic, the degrees of freedom associated with it, and the p-value.
8. Based on the p-value calculated in Question 7, what is the conclusion of the hypothesis test at α = 0.05? Interpret your conclusion in context of the question.
A study about the diet of undergraduate students,
5) Chi-square statistic test , would use to determine if the observed and expected frequencies of diets are consistent. With null hypothesis as the observed and expected frequencies of diets are consistent.
6) The excepted students to eat
meat = 165
exclusively vegetarian= 6
strict vegetarian= 1
7) Chi-square statistic value is 62.755 and degree of freedom are 2 . The critical value for Chi-square statistic is 0.00001
8) P-value< 0.05, so reject the null hypothesis.
Therefore there is no sufficient evidence to support that the observed and expected frequencies of diets are consistent.
A random sample of undergraduates in the University of Virginia dining hall.
Sample size , n = 175
Three categories are given as shown in above table with percentage of report eating a diet.
Report also consists observed values about the number of students diet including the three different categories
5) The Chi-square test would use to determine the required result. Consider Null and alternative hypothesis as :
H₀ : the observed and expected frequencies of diets are consistent
Hₐ : the observed and expected frequencies of diets are not consistent
χ² =∑(Oᵢ - Eᵢ)²/Eᵢ
where, χ² --> chi-square cofficient or value
Oᵢ --> observed values which are provided
Eᵢ --> excepted values
Excepted values , Eᵢ = n× p
here we assume that,
These categories are independentindividuals are selected randomly6) The number of students would you expect to eat meat = 168
The number of students would you expect to eat exclusively vegetarian
= 6.125 ~ 6
The number of students would you expect to eat strict vegetarian = 0.875 ~ 1
7) Degree of freedom,df = k - 1 = 2, where k denotes total number of categories here
Chi-square statistic, χ² = ∑(Oᵢ - Eᵢ)²/E
χ² = 62.755
Using chi-square table, the critical chi-square value for χ² = 62.755 and degree of freedom 2 is 0.00001 ..
8) Significance level, alpha = 0.05
As we see that p-value = 0.00001< alpha = 0.05
So, we reject the null hypothesis.
Thus, there is no sufficient evidence to support null hypothesis.
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Identify the slope and y-intercept of each linear function's equation.
x-3=y
-x + 3 = y
y=1-3x
y=3x-1
Intro
slope = 3, y-intercept at -1
slope =-3, y-intercept at 1
slope = 1 y-intercept at -3
slope-1-y-intercept at 3
Done
A. y = 3x-1; slope is 3 and y-intercept is -1
B. -x+3 = y; slope is -1 and y-intercept is 3
C. x-3 = y; slope is 1 and y-intercept is -3
D. y = 1-3x; slope is -3 and y-intercept is 1
What is slope-intercept form?In math, slope interceptor form is the method of writing an equation for a line in the form y = mx + b.
Slope-Intercept form
The slope - intercept form equation with slope m and y intercept c is given by, y = mx+c
Option A:
y = 3x-1
slope m = 3
y-intercept c = -1
Option B:
-x+3 = y
slope m = -1
y-intercept c = 3
Option C:
x-3 = y
slope m = 1
y-intercept c = -3
Option D:
y = 1-3x
slope m = -3
y-intercept c = 1
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Given the function:
f(x) = (3x+7)
What is the output of the function when the input is x = 9?
A 9
B 15
C 17
D 21
Answer isn't one of your options, it is 34.
Step-by-step explanation:1. Write the function.[tex]f(9) = (3(9)+7)[/tex]
3. Calculate.[tex]f(9) = (27+7)\\ \\f(9) = 34[/tex]
4. Conclude.[tex]f(9) = 34[/tex].
in a recent poll of 1,000 homeowners in the united states, one in eight homeowners reports having a home equity loan that he or she is currently paying off. using a confidence coefficient of 0.99, construct the confidence interval for the proportion of all homeowners in the united states that hold a home equity loan.
Use Table 1. (Round intermediate calculations to 4 decimal places. Round "z-value" and final answers to 3 decimal places.)
Confidence interval to
For the proportion of all hometowners in the united states that hold a home equity loan, confidence interval is (0.0992, 0.1508).
We have given that in a recent poll of 1000 homeowners in the United states, one in eight homeowners reports havinf a home equity loan that he or she is curently paying off.
If one in eight reports having a home equity loan then for 1000 hometowners = 1000/8 = 125.
Sample proportion p = 125/1000 = 0.125
given that confidence coefficient = 0.99
α = 1 - confidence coefficient = 1 - 0.99
α = 0.01
z₀.₀₁ / 2 = 2.58
Therefore the interval estimate for the proportion of all homeowners in the United states that hold a home equity
= p ± z₀.₀₁/2 √p(1-p)/n
= 0.125 ± 2.58 √0.125(0.875)/1000
= 0.125 ± 2.58 √0.0001
= 0.125 ± 0.0258
= (0.125 - 0.0258,0.125 + 0.0258)
= (0.0992, 0.1508)
Hence (0.0992, 0.1508) is the confidence interval.
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HELP ME PLEASE ASAP!!!
Maya has 360 meters of fencing and wishes to form three sides of a rectangular field. The fourth side borders a river and will not need fencing. As shown below, one of the sides has length x (in meters).
Answer:
a) [tex]A(x)=360x-2x^2[/tex]
b) [tex]90m[/tex]
c) [tex]16200m^2[/tex]
Step-by-step explanation:
This is related to a differential topic called optimisation.
We here have two sides of the field that are equal to [tex]x[/tex], and another unknown (that we will call [tex]y[/tex]). Maya has 360m of fencing, so we will say that [tex]2x+y=360[/tex], and this means that [tex]y=360-2x[/tex].
Our first task is to find a function for the area of the field. We know that the area of a field is length × width. We know we have a length of [tex]y[/tex] which is [tex]360-2x[/tex] and a width of [tex]x[/tex], therefore:
[tex]A(x)=x(360-2x)=360x-2x^2[/tex]
To find the maximum value of [tex]x[/tex], we must first differentiate the function:
[tex]A'(x)=360-4x[/tex]
We must then set the equation equal to 0 and solve for [tex]x[/tex], where the line/curve would be stationary.
[tex]360-4x=0[/tex]
[tex]4x=360[/tex]
[tex]x=90[/tex]
Finally, to find the maximum area, we would substitute this value of [tex]x[/tex] back into the original equation:
[tex]A(x)=360x-2x^2\\\\A(90)=360(90)-2(90)^2\\\\A(90)=16200[/tex]
For the following:
(a) The area is A(x) = x × (180 - x)(b) The side length x that gives the maximum area is 90 meters.(c) Maximum area that the field can have is 8100 square meters.How to find area and length?(a) To find a function A(x) that gives the area of the field in terms of x, use the information given about the fencing and the shape of the field.
Let the length of the other two sides (perpendicular to the side with length x) be y (in meters).
The perimeter of the rectangle is given by the sum of all four sides:
Perimeter = 2x + 2y
According to the problem, the perimeter is 360 meters, set up an equation:
2x + 2y = 360
Now, solve this equation for y in terms of x:
2y = 360 - 2x
y = (360 - 2x) / 2
y = 180 - x
The area A(x) of the rectangle is given by the product of its length (x) and width (y):
A(x) = x × y
A(x) = x × (180 - x)
(b) To find the side length x that gives the maximum area for the field, maximize the function A(x) from part (a). To do that, take the derivative of A(x) with respect to x, set it equal to zero, and solve for x:
A(x) = x × (180 - x)
dA/dx = (180 - x) - x
dA/dx = 180 - 2x
Now, set dA/dx = 0 and solve for x:
180 - 2x = 0
2x = 180
x = 90
So, the side length x that gives the maximum area is 90 meters.
(c) Now there is the value of x, find the maximum area by substituting x = 90 into the area function A(x) from part (a):
A(x) = x × (180 - x)
A(90) = 90 × (180 - 90)
A(90) = 90 × 90
A(90) = 8100
The maximum area that the field can have is 8100 square meters.
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Sam wanted to graph the equation
y = 2x -7. She plotted her y-intercept
point and started to count the slope.
Which of the following should she do?
A. count up 2, and left 1
B. count down 2, over 0
C. count down 2, and right 1
D. count up 2, and right 1
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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