With 95% of confidence interval for the time it takes salesperson to talk to a potential customer is (12.42 , 5.38).
A Random sample is a randomly selected subset of a population. In this sampling method, each member of the population has an exactly equal chance of being selected, minimizing the risk of selection bias.
In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its population mean or sample mean. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers is spread out from their average value. Variance is an important tool in the sciences, where statistical analysis of data is common. The variance is the square of the standard deviation, the second central moment of a distribution, and the covariance of the random variable with itself, and it is often represented by σ ² ,s² ,Var(X) , or V(X).
A confidence interval (CI) is a range of estimates for an unknown parameter. A confidence interval is computed at a designated confidence level; the 95% confidence level is most common, but other levels, such as 90% or 99%, are sometimes used. The confidence level represents the long-run proportion of corresponding CIs that contain the true value of the parameter. For example, out of all intervals computed at the 95% level, 95% of them should contain the parameter's true value.
Given in the question:
n = 46
x = 8.90
σ = 6
α = 0.95
As we know that:
[tex]X[/tex] ±[tex]Z_{\alpha /2} * \frac{\beta }{\sqrt{n} }[/tex]
putting the values we get,
8.90 ± Z (0.95/2) ×6/√46
Now, considering the positive sign, we get,
= 8.90 + 3.52
= 12.42
Now considering the negative sign,
8.90 ± Z (0.95/2) ×6/√46
= 8.90 - 3.52
= 5.38
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can someone please help me solve the systems by graphing?
The graphs for the given systems of linear equations are shown below.
From the graph, the solution to the first system is (8, -5)
From the graph, the solution to the second system is (-7, -6)
Graphing system of linear equationsFrom the question, we are to graph the given system of equations
The given system of equations is
y = 1/4x - 7
y = -1/2x - 1
First, we will plot the graph by using the x-intercepts and the y-intercepts of the lines
y = 1/4x - 7
Set y = 0 to determine the x-intercept
0 = 1/4x - 7
7 = 1/4x
x = 28
The x-intercept of the equation is 28
Set x = 0 to determine the y-intercept
y = 1/4(0) - 7
y = 0 - 7
y = -7
The y-intercept of the equation is -7
For y = -1/2x - 1
Set y = 0 to determine the x-intercept
0 = -1/2x - 1
1 = -1/2x
-x = 2
x = -2
The x-intercept of the equation is -2
Set x = 0 to determine the y-intercept
y = -1/2(0) - 1
y = 0 - 1
y = -1
The y-intercept of the equation is -1
Using the x-intercepts and y-intercepts, the graph of the system is shown below
For the second system of equations
y = 1/7x - 5
y = 8/7x + 2
For y = 1/7x - 5
Set y = 0 to determine the x-intercept
0 = 1/7x - 5
5 = 1/7x
x = 35
The x-intercept of the equation is 35
Set x = 0 to determine the y-intercept
y = 1/7(0) - 5
y = 0 - 5
y = -5
The y-intercept of the equation is -5
For y = 8/7x + 2
Set y = 0 to determine the x-intercept
0 = 8/7x + 2
-2 = 8/7x
8x = -14
x = -14/8
x = -7/4
The x-intercept of the equation is -7/4
Set x = 0 to determine the y-intercept
y = 8/7(0) + 2
y = 0 + 2
y = 2
The y-intercept of the equation is 2
Using the x-intercepts and y-intercepts, the graph of the system is shown below
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Avery is signing up for a gym membership with a one-time fee to join and then a monthly fee to remain a member. The total cost of the gym membership over tt months is given by the equation C=40t+150.C=40t+150. What is the slope of the equation and what is its interpretation in the context of the problem?
The slope of line C = 40t+150 will be 40.
What is equation straight line?
Y = mx + c is the general equation for a straight line, where m denotes the line's slope and c the y-intercept. It is the version of the equation for a straight line that is used most frequently in geometry. There are numerous ways to express the equation of a straight line, including point-slope form, slope-intercept form, general form, standard form, etc. A straight line is a geometric object with two dimensions and infinite lengths at both ends. The formulas for the equation of a straight line that are most frequently employed are y = mx + c and axe + by = c. Other versions include point-slope, slope-intercept, standard, general, and others.
The total cost of the gym membership over tt months is given by the equation C=40t+150
The slope of the given equation will be the append of t which is 40.
Hence, the question indicates that the starting value is 150 already without eve before the time stated.
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how long will it take for the population of a small town with 500 people to double in size if the population increases at a rate of 15% per year
The small town would take up 5 years to double the population from 500 people.
What is percentage ?As its sign is "%," the word "percent" implies "for every hundred". Since it is read as a percentage, "x%" should be read as "x percent." So, a percent is a fraction with a denominator of 100. 30%, for instance, equals 30/100 (i.e. 30 parts from 100). You can also write this as 0.30.
Population of small town = 500
Population Growth rate = 15 %
To find :
Time when the population is doubled.
We will use successive change
500 People after 1 year = 575
575 People after 1 year = 661.25
661.25 People after 1 year = 760.4375
760.4375 People after 1 year = 874.503125
874.503125 People after 1 year = 1005.67859
Hence it will total take the time of 5 years to double the population.
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kal and kara solve this problem in two different ways. the perimeter of a rectangle is 4646 centimeters. its length is 88 centimeters. what is its width? use the drop-down menus to complete the sentences below.
If the perimeter of the rectangle is 4646 centimeters and its length is 88 centimeters then its width would be 2235 centimeters
What is meant by the term Perimeter?The perimeter of a form in geometry is defined as the entire length of its border. A shape's circumference is calculated by summing the lengths of all of its sides and edges. Its dimensions are expressed in linear units like centimeters, meters, inches, and feet.
In daily life, people constantly employ the idea of perimeter. For instance, we measure the perimeter of the area to be fenced in or decorated for Christmas to determine how much wire you will need.
We are aware that a regular polygon has equal-length sides.
A regular polygon's perimeter is equal to the product of all of its sides, which is equal to the quantity o sides times the length of a side.
How to solve?
width = 4646 - 2*88 =4470
width of one side = 4470/2 = 2235 centimeters
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A decision maker has five potential independent variables with which to build a regression model to explain the variation in the dependent variable. At step 1, variable x3 enters the regression model. Which of the following indicates which of the four remaining independent variables will be next to enter the model?A) The variable with the highest coefficient of partial determinationB) The variable that has the next highest correlation with the dependent variableC) The variable that will provide the next largest value for the slope coefficientD) Can't be determined without seeing the correlation matrix.
When building a regression model provided the given information from the four remaining independent variables the variable to be entered next (second) would be variable with the highest coefficient of partial determination. (Option A)
A regression model refers to a function that illustrates the relationship between one or more independent variables and a response, target, dependent variable. The primary uses of regression analysis are forecasting, time series modeling and identifying the cause-and-effect relationship between variables. When building a regression model with five potential independent variables to explain the variation in the dependent variable, at step 1, variable x3 enters the regression model. Of the four remaining independent variables, the variable entered next into the model would be the variable with the highest coefficient of partial determination. A coefficient of partial determination refers to the measurement of marginal (extra) contribution of X variable or percentage of variation in the response variable that can be explained by the explanatory variables and can be used to measure how strongly two variables are related to one another.
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Distribute to create an equivalent expression with the fewest symbols possible. 6(5x−3)=
Answer:
30x-18
Step-by-step explanation:
Keilantra runs a farm stand that sells strawberries and blueberries. Each pound of strawberries sells for $2. 25 and each pound of blueberries sells for $4. Keilantra made $204. 50 from selling a total of 73 pounds of strawberries and blueberries. Determine the number of pounds of strawberries sold and the number of pounds of blueberries sold.
There were 50 pounds of strawberries and 23 pounds of blueberries sold by Keilantra.
Given,
The cost of 1 pound of strawberry = 2.25
The cost of 1 pound of blueberry = 4
Total cost made by Keilantra = 204.50
The quantity of strawberry sold = x
The quantity of blueberry sold = y
Total quantity of berries sold = 73 pounds
We have to find the quantity of strawberries and blueberries sold:
Here,
2.25x + 4y = 204.50 and x + y = 73
Then,
x + y = 73
x = 73 - y
Substitute this in; 2.25x + 4y = 204.50
That is,
2.25 × (73 - y) + 4y = 204.50
(2.25 x 73) - 2.25y + 4y = 204.50
164.25 + 1.75y = 204.50
1.75y = 204.50 - 164.25
y = 40.25/1.75
y = 23
Then,
x + 23 = 73
x = 73 - 23 = 50
Therefore The quantity of strawberries and blueberries sold by Keilantra is 50 pounds and 23 pounds.
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Joan's nursery specializes in custom-designed landscaping for residential areas. The estimated labor cost associated with a particular landscaping proposal is based on the number of plantings of trees, shrubs, and so on to be used for the project. For cost-estimating purposes, managers use two hours of labor time for the planting of a medium-sized tree. Actual times from a sample of 10 plantings during the past month follow (times in hours).
The average sample of 10 plantings tree-planting time is two hours- P-value = 0.251453
The estimated labor cost associated with a particular landscaping proposal is based on the number of plantings of trees, shrubs, and so on to be used for the project-P-value = 0.251453
We are unable to reject the null hypothesis and accept it because the p value is higher than the significance level.
As a result, we draw the conclusion that the average tree-planting time is two hours.
Hypothesis:
In statistics, hypothesis testing is used to identify the variance in the group of data that results from genuine variation. Based on the presumptions, the sample data are taken from the population parameter. The hypothesis can be divided into many categories. A hypothesis is described in statistics as a formal statement that explains the relationship between two or more variables belonging to the specified population. It aids the researcher in converting the stated issue into an understandable justification for the study's findings. It provides examples of various experimental designs and guides the investigation of the research procedure.
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consider any two numbers a, b with a < b. if x is the uniform distribution on the interval [a, b], what is the variance of x?
The variance over an interval for a uniform distribution is
V(X) = ( b - a )²/ 12
Here,
a and b are intervals .
By the definition of the variance, V(X) = E[X2] − (EX)2.
On solving ,
V(X)
=(a²+ab+b²)/3−(a²+2ab+b²)/4
=(a²−2ab+b²)/12
=( b - a )²/ 12
A continuous probability distribution is a Uniform distribution and is related to the events which are equally likely to occur. It is defined by two parameters, x and y, where x = minimum value and y = maximum value. It is generally denoted by u(x, y).
A two-parameter family of curves known as the uniform distribution (sometimes known as the rectangle distribution) is famous for having a constant probability distribution function (pdf) between its two bounding parameters.
For values tabulated to a specific number of decimal places, this distribution is suitable for illustrating the distribution of round-off mistakes. Techniques for generating random numbers , like the inversion method, use the uniform distribution.
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alice walks from the top to the bottom of an escalator that is moving up and counts 150 steps. her friend, bob, walks from the bottom to the top of the escalator and counts 75 steps. if alice's walking speed (in steps per unit of time) is three times bob's walking speed, how many steps are visible on the escalator at a given time? (assume that this value is constant.)
Based on the information provided, it can be determined that there are 120 steps visible on the escalator at any given time.
Assume that there are x total steps, e for the escalator speed, and b for Bob's pace.
Bob noticed 75 stairs and climbed the entire escalator in the time it took him to ascend it. As a result, the escalator must have added an extra x + 75 steps.
Let e and b be the speeds of the escalator and Bob, respectively.
Alice took 150 steps at a speed of (3b-e) step rate as she descended the stairs.
Bob took 75 steps at a speed of (b+e) each step as he ascended.
Since, Al and Bob were walking the same distance at a time , we have,
150(3b-e) = 75(b+e)
Solving these two equation we get , e/b = 3/5
Thus while Bob took 75 steps to go up, the escalator contributed an extra
3/5 * 75 = 45 steps
Finally, there is a total of 75+45=120 steps in the length of the escalator.
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I need help pls!!!!!!!!!!!!!!!!!!
Answer:
First line: First box:1 Second box: 5
Second line: First box: 20 Second box: 15 Third box: 5
Step-by-step explanation:
This is two ways to do the same problem.
5(4-3) The first problem. We are subtracting the numbers in the parentheses and then multiplying that by 5
5(1) = 5
The second way to solve this is by using the distributive property. We are multiplying 5 by both numbers in the parentheses and then subtracting those two numbers
5(4-3)
5(4) - 5(3)
20 - 15
5
2.66 as a fraction in simplest form
Answer:
133/50
Step-by-step explanation:
2.66 as a fraction in simplest form
(2.66 × 100)/100 =
266/100 =
133/50
-----------------
check
133 : 50 = 2.66
the answer is good
What’s the difference between factoring x4+9x2+8 and factoring x2+9x+8?
Answer:
The difference between factoring x4+9x2+8 and factoring x2+9x+8 is that the first equation is a fourth degree polynomial, while the second equation is a second degree polynomial. The first equation can be factored into (x2 + 3)(x2 + 8), while the second equation can be factored into (x + 8)(x + 1).
Linda kept track of her times in the 50-meter freestyle at her team's swim meets.
Distance = 50 meters
Slowest means, longest time =58 seconds
Speed is equal to distance divided by time:
Speed = 50/58
=25/29 m/s
=0.86m/s which is the answer.
Linda kept track of her times in the 50-meter freestyle at her team's swim meets. Swim times (sec.) H 40 44 48 52 56 60 What was Linda's slowest time in the 50-meter freestyle? 60 seconds 52 seconds 56 seconds 58 seconds
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create a class to calculate the areas of differents geometrical shapes, the shapes are square, rectangal, triangle. class should methods name area,
Creation of class to calculate the areas of different geometrical shapes requires to use certain rules which are mentioned in detail here.
How to name a Class?Developers frequently encounter naming issues. I lost count of the number of hours I've spent considering what to name things and the amount of time it took me to decipher code that had inappropriate names. Whether it was an object, methods, class, or something else is irrelevant. Given that we spend more time reading code than developing it, effective naming is usually beneficial in the long run.
Your code becomes better and cleaner when you use excellent names. It aids in helping you recognize the functions of each piece of code intuitively. It makes your application easier to read in the future by other developers as well as yourself.
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If you earn $0. 25 per quart of berries picked, how much will you earn if you pick 900 quarts?.
Answer: $225
Step-by-step explanation: .25 x 900 = 225
Answer: $225
Step-by-step explanation:
You earn $.25 for every quart picked. You pick 900 quarts. take 900 and times it by .25. You get 225 so you earn $225
Write the slope-intercept form of the line
y=2x/3-2 is the required slope-intercept form of the line
The coordinate of points where the line intersects at the x-axis is (-3,0) and at the y-axis is (0,-2) now from there two points we can find slope if line that is
slope=y₂-y₁/x₂-x₁=(-2-0)/(0-(-3))
slope =-2/3
with one point (0,-2) and slope we can find the slope-intercept form that is y=mx+c
where m is slope and c is intercept on the y-axis
y=2x/3-2 this is the slope-intercept form and by simplifying it we get
3y=2x-6
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The population of a bee hive is growing with a monthly percentage rate compounded continuously. the population doubles in 3 months. find the monthly percentage rate according to the exponential growth function. leave your answer in terms of ln. note: when entering natural log in your answer, enter lowercase ln as "ln". there is no "natural log" button on the alta keyboard.
The exponential growth function's estimate of the monthly percentage rate is; log 3/ 3.
Explain the term exponential growth function?A function called exponential growth depicts an expansion within a population than happens at the same pace across time. If a population doubles or triples in size, you can assume that the data grows exponentially. Exponential decay is the inverse of exponential growth, in which data contracts rather than expands.We will employ the exponential function, as indicated, to determine the monthly percentage rate;
P(t) = P(0)e∧(rt)
The initial population is P0 for the bee hive.The end population will be 3P0 if the beginning population doubles in three months.Enter the following parameters into the calculation to obtain the rate "r".
P(t) = P(0)e∧(rt)
3P(0) = P(0)e∧(rt)
3 = e∧(rt)
Taking log both sides.
log 3 = (rt)
r = log 3 / 3
r = 0.366
r = 36.6%
Consequently, the exponential growth function's estimate of the monthly percentage rate compounded continuously is; log 3/ 3.
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Answer: the answer is ln(2)/3
Step-by-step explanation:
A round shaped wall clock frame is made of a steel rod with length of 1.57m. calculate the radius,in m, of the frame.
Check the picture below.
[tex]\textit{Circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=1.57 \end{cases}\implies 1.57=2\pi r\implies \cfrac{1.57}{2\pi }=r\implies {\Large \begin{array}{llll} \stackrel{meters}{0.25}\approx r \end{array}}[/tex]
(14+ 8²︎) ÷ 2 - 10
Help on this please
Answer:
29
Step-by-step explanation:
(14+8²︎) ÷ 2 - 10
(14+64) ÷ 2 - 10
(78) ÷ 2 - 10
39 - 10
29
Could you please mark me brainliest for this? Thank you!
a 2.2 GB game is being downloaded onto your laptop. When you have downloaded half a gigabyte, you notice that your computer has been downloading at a rate of .01GB/min. Write an inequality that represents at least how many minutes it will take to download the whole game.
The inequality that represents at least how many minutes it will take to download the whole game
is x ≥ (2.2 - 0.5)/0.01
What is an inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
In this scenario, 2.2 GB game is being downloaded onto your laptop and when you have downloaded half a gigabyte, you notice that your computer has been downloading at a rate of .01GB/min.
The inequality will be illustrated. Let the number of minutes be x.
x ≥ (2.2 - 0.5)/0.01
This illustrates the inequality.
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a measurement of how well a child can do certain tasks at a certain time in comparison to other children is a(n) test.
A(n) IQ test evaluates a child's performance in relation to other kids in terms of how well they can perform specific activities at a specific time.
Each individual IQ exam is made up of a number of smaller questions, and no reading nor writing are required. Some verbal subtests consist of spoken questions with no set time restriction. Other subtests are frequently timed and typically have a visual or spatial focus. It takes one to two hours to give the exam.
115 to 129: Superior or intelligent. 130 through 144: Fairly talented. From 145 through 159: Very talented. Exceptionally talented from 160 to 179.
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in 2019 i sold 105 276 tickets. this is 7% less than the number of tickets i sold in 2018."" (a) how many tickets did airon sell in 2018
The total number of tickets sold in the year 2018 was 113,200.
Explain the term percentage decrease?The difference among starting and final numbers is the percentage drop. It displays a percentage loss of value compared to the original regardless of the units. The difference between the initial and final amounts is the amount of decline.For the stated question-
Total tickets sold in 2019 = 105,276
Let the tickets sole in 2018 be 'x'.
Then, percentage decrease in the year 2019 be-
x - 7% of x = 105,276
x - 7x/100 = 105,276
93x/100 = 105,276
x = 105,276 x 100 / 93
x = 113,200
Thus, the total number of tickets sold in the year 2018 was 113,200.
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4.
Raquel scored an
80% on her science
test. If she got 20
questions correct,
how many
questions were on
the test?
5.
Answer:
25
Step-by-step explanation:
knowing that 80 is 4/5 of 100, we need to find the number that is 5/4 of 20. That number is 25. This can be proven by calculating that 20/25 and 80/100 both can be simplified to 4/5.
A, B, and C are three landmarks in a national park. Landmarks A and B are 650 meters apart. Landmarks B and C are 822 meters apart. Carla takes 4 minutes to run from Landmark A Landmark B, and another 6 muinutes to run from Landmark B to Landmark C. What is Carla's average speed in meters per minute for the run from Landmark A to Landmark C?
Please help on this question
Answer:yes
Step-by-step explanation: 2/8=4
4/1=4 since both of them equal 4 they are equivalent
an open-top box is to be made by cutting small congruent squares from the corners of a 12- in.-by-12-in. sheet of tin and bending up the sides. how large should the squares cut from the corners be to make the box hold as much as possible? what are the dimensions of the box with the largest volume?
The squares cut from the corners should be large in width and length 6 to hold the box as much as possible. The dimensions of the box with the largest volume are 6 x 6.
If the squares cut from the corners are h × h inches
The open-top box will have
A height of h
A width of 12 - 2h
and a length of 12 - 2h
So its volume will be
V(h) = h × (12 - 2h) × (12 - 2h)
= 4h³ - 48h² + 144h (square inches)
dV/dh= 12h² - 96h + 144
Critical points occur when the derivative (dV/dh) is zero.
12h² - 96h + 144 = 0
h² - 8h + 12 = 0
(h − 2)(h − 6) = 0
It is clear that h = 6 is not the crucial point for the maximum as it would produce widths and lengths of zero (and so a volume of zero).
In order to cut out squares measuring 6 × 6 inches from the corners of the bigger sheet, the most volume may be obtained.
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please help!
factor 2x^2-7x-9
Answer:
(x + 1 ) (2x-9)
Step-by-step explanation:
Break The expression into groups
= ([tex]2x^{2} +2x)+(-9x-9)[/tex]
Factor out 2x from [tex]2x^{2}[/tex] + 2x: 2x (x + 1)
and then you want to factor out the -9x - 9 -9( x + 1 )
and that equals 2x( x + 1 ) [tex]-9(x+1)[/tex]
And now do it again Factor out common term x + 1
and now it " Equals" [tex](x + 1)(2x-9)[/tex]
help me solve this one! please.
thank u.
The required are of shaded region for the given question is 20.7 cm^2.
Explain sector of circle.A circle is partitioned into two areas, specifically the significant area, and the minor area. A bigger piece of the circle involved by the radii and the significant circular segment is supposed to be a significant area. A more modest part involved by two radii and a minor circular segment is known as the minor area.
According to question:We have,
∠BOC = 2π/5, radius = 6 cm, OA = 2 cm, DC = 2 cm
OD = 6 - 2 = 4 cm,
We know that
Area of triangle = OA×OD×sin(2π/5)/2
A = 2×4×0.475/2 = 1.9 sq. cm
And
Area of sector = (π/5)/2π ×πr^2
Area of sector = π(6)^2/5
Area of sector = 22.6 sq. cm
Area of shaded region = 22.6 - 1.9 = 20.7 sq. cm
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why is it inportant to use the order of operations to evaluate algebracic expressions
Answer:
To get the correct answer.If it isnt followed you will get a number/answer but that is incorrect