Answer:
y = (-2/3)x + 6
Step-by-step explanation:
To find the equation of the line that passes through the points (-3, 8) and (6, 2), we can use the slope-intercept form of the equation of a line, which is:
y = mx + b
where m is the slope of the line and b is the y-intercept, which is the point where the line crosses the y-axis.
To find the slope of the line, we can use the following formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are two points on the line. Plugging in the coordinates of the two points given in the problem, we get:
m = (2 - 8) / (6 - (-3)) = -6/9 = -2/3
Next, we need to find the y-intercept of the line. This is the point where the line crosses the y-axis, which means that the x-coordinate of this point is 0. Since we know the slope of the line and one of the points that it passes through, we can use the point-slope form of the equation of a line to find the y-intercept:
y - y1 = m(x - x1)
Substituting the values we have calculated above and setting x = 0, we get:
y - 8 = (-2/3)(0 - (-3))
Solving for y, we find that the y-intercept is 8 - (2/3) * 3 = 8 - 2 = 6.
Therefore, the equation of the line that passes through the points (-3, 8) and (6, 2) is:
y = (-2/3)x + 6
Complete this puzzle using each of these numbers only once : 2, 4, 5, 7, 8, 11, 13, 14, 16 Put the even numbers in the squares and the odd nurmbers in the circles. Each row of three numbers must add up to 26.
Here is one solution to the puzzle:
Squares: 2, 8, 16
Circles: 5, 7, 14
Total: 26
You can verify that each row of three numbers adds up to 26: 2 + 8 + 16 = 26, 5 + 7 + 14 = 26.
What are even and odd numbers?An even number is a number that can be divided into two equal groups. An odd number is a number that cannot be divided into two equal groups. Even numbers end in 2, 4, 6, 8 and 0 regardless of how many digits they have. Odd numbers end in 1, 3, 5, 7, 9.
Therefore, the correct answer is as given above
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Sebastian has $600 saved for a trip.
He buys an airline ticket for $120 and reserves a hotel room for $55 each night for 4 nights. He wants to use the same amount of spending money each day. If his trip lasts for 5 days, how much mone can he spend each day?
Answer:
$52
Step-by-step explanation:
Sebastian spent $120 on the airline ticket and $55 * 4 = $<<55*4=220>>220 on the hotel.
So, he spent a total of $120 + $220 = $<<120+220=340>>340 on the airline ticket and hotel.
He has $600 - $340 = $<<600-340=260>>260 left to spend.
He plans to be on the trip for 5 days, so he can spend $260 / 5 = $<<260/5=52>>52 per day.
Use point-slope form to write the equation of a line that passes through the point
(12, 10) with slope 1/3.
Answer:
y - 1/3x - 10 + 4 = 0
Step-by-step explanation:
What we know:
x = 12
y = 10
slope (m) = 1/3
y - y1 = m(x - x1) Point-slope form
Substitute in the values we have
y - 10 = 1/3(x - 12)
Bring all the values to one side
y - 10 - 1/3(x - 12) = 0
y - 1/3x - 10 + 4 = 0
What is the location of Point F, which partitions the directed line segment from D to E into a 5:6 ratio?
Answer:
Step-by-step explanation:
Could someone help me with this trig question?
k= 5.
Step-by-step explanation:1. Write the expression.[tex]ksin^{2} (x)+kcos^{2} (x)=5[/tex]
2. Factorize k.[tex]k(sin^{2} (x)+cos^{2} (x))=5[/tex]
3. Simplify using pythagorean identities.Check attached image 1.
[tex]k(1)=5\\ \\k=5[/tex]
4. Verify.Let's graph the function to see if it's true that it equals 5 for any value of x and k=5.
Check attached image 2.
As we can see in the graph, for any value of x the function returns 5. Hence, the answer is correct.
11 12 13 14 15 16 17 18 19 20 Given: AB = BC Prove: B is the midpoint of AC. A line contains point A, B, C. A flow chart has 3 boxes that go from top to bottom. The first box is labeled given and contains A B = B C. The second box is labeled definition of congruent segments and contains Line segment A B is-congruent-to Line segment B C. The third box is labeled definition of a midpoint and contains B is the midpoint of Line segment A C. What is the format of this proof? two-column proof one-paragraph proof flowchart proof two-paragraph proof Mark this and return
A list of assertions and the justifications for each assertion are included in a two-column geometric proof.
What is The Structure of a Proof?Either two columns or a paragraph can be used to write a geometric proof. A two-column proof stated in sentences is all that a paragraph proof is. But since it's simpler to omit stages when writing a paragraph proof, we'll study the two-column technique.A list of assertions and the justifications for each assertion are included in a two-column geometric proof. The reasons why the claims are true are mentioned in the right column, while the statements themselves are listed in the left column. A row in the two-column proof represents each phase of the proof, or each conclusion reached.Make the illustration of the proof-in-use in a figure. Either the figure will be drawn for you already, or you will need to draw it yourself.List the assertions that are made, and then the assertions that must be proven. At this point, the proof has a start and a finish.Based on what you can infer about the figure from the provided details, mark it accordingly. You actually learn how to make the proof at this stage of the proof process, as well as whether or not you can support the assertion that has been stated.Mark any congruent sides, angles, etc. so you can see for yourself what has to be said in the evidence to persuade the reader that you are correct in your conclusion.Without omitting even the simplest, carefully note down each step. The stated statements are frequently among the initial steps (though not always), and the conclusion you want to prove is the last step.To Learn more About geometric proof refer To:
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A drama club earns $1040 from a production. It sells a total of 64 adult tickets and 132 student tickets. An adult ticket costs twice as much as a student ticket.
a. Write a system of linear equations that represents this situation. Let x represent the cost of an adult ticket and y represent the cost of a student ticket.
System of equations: x=
x+
y=1040
Question 2
b. What is the cost of each ticket?
The cost of an adult ticket is $
.
The cost of a student ticket is $
.
The system of linear equations, that models the problem is represented as x = 2 and 64x + 132y = 1040 while the cost of adult and student tickets is $8 and $4 respectively.
System of Linear EquationThe system of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1.
Let;
x = cost of adult tickety = cost of student ticketa)
x = 2y ...eq(i)
64x + 132y = 1040 ...eq(ii)
b)
From equation (i)
64(2y) + 132y = 1040
y = 4
Put y = 4 into equation (i)
x = 2(4)
x = 8
The cost of adult ticket is $8 and student ticket is $4
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Given the function f(x) = −5x2 + 2x + 9, find f(1) and f(2). Choose the statement that is true concerning these two values
We can solve the question using the concept Polynomial functions. The value of f(1) is 6 and f(2) is -7.
What do you mean by Polynomial function?In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1. A function that can be expressed as a polynomial is referred to as a polynomial function. A polynomial equation's definition can be used to derive the definition. A polynomial is typically denoted by P. (x). The degree of the variable in P(x) is its maximum power. The degree of a polynomial function is crucial because it reveals how the function P(x) will behave when x is very large. Whole real numbers make up a polynomial function's domain (R).
CalculationGiven f(x)=-5x2 + 2x + 9
f(1)=-5(1)2+2(1)+9
∴f(1)=6
f(2)=-5(2)2+2(2)+9
∴f(2)=-7
We can solve the question using the concept Polynomial functions. The value of f(1) is 6 and f(2) is -7.
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Circles P and Q are externally tangent to each other and have radii 18 meters
and 32 meters, respectively. As shown, circles P and Q are externally tangent
to a line segment at points X and Y, respectively. What is XY?
Answer:
48 m
Step-by-step explanation:
You want to know the distance XY between tangent points on a segment tangent to two circles that are externally tangent to each other. The circles have radii 18 m and 32 m.
Pythagorean theoremAs shown in the attachment, a segment parallel to XY joining segments PX and QY can form a right triangle whose hypotenuse is the sum of the radii, and whose short leg is the difference of the two radii. The length of XY is the unknown leg of the right triangle, and can be found using the Pythagorean theorem.
a² +b² = c²
14² +b² = 50²
b² = 50² -14² = 2304
b = √2304 = 48
The length of XY is 48 meters.
__
Additional comment
In this geometry, the length XY is twice the geometric mean of the two radii. XY = 2√(18·32) = 48.
A researcher wishes to test whether two nominal variables with two and three respective categories are statistically independent. She observes a chi square value from Pearson's chi square test of independence of 10.00430. Consider the following propositions: PROPOSITION ONE: At the 5% significance level the appropriate decision could be a Type II Error; PROPOSITION TWO: At the 1% significance level the appropriate decision could be a Type II Error.
A. Proposition I is true and Proposition II is true
B. Proposition I is true and Proposition II is false
C. Proposition I is false and Proposition II is true
D. Proposition I is false and Proposition II is false
E. None of the above
The correct answer is Option A: Proposition I is true and Proposition II is true.
A researcher can use Pearson's chi square test of independence to determine if two nominal variables are independent or not. In this case, the researcher observed a chi-square value of 10.00430.
To determine whether the null hypothesis should be accepted or rejected, the researcher must compare the chi-square value to a critical value associated with the desired level of significance.
At the 5% significance level, the critical value is usually around 7.815, and at the 1% significance level, the critical value is usually around 10.827. Since the observed chi-square value (10.00430) is higher than the critical values for both the 5% and 1% significance levels, the appropriate decision could be a Type II Error for both levels of significance.
In other words, Proposition I (At the 5% significance level the appropriate decision could be a Type II Error) and Proposition II (At the 1% significance level the appropriate decision could be a Type II Error) are both true.
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When 2x^2/y=w+2/4 is solved for w, one equation is w =8x^2/7 -2 Which of the following is an equivalent equation to find w?
w = StartFraction 8 x squared + 2 y Over y EndFraction
w = StartFraction 8 x squared minus 2 y Over y EndFraction
w = 8 x squared minus 3 y
w = 8 x squared minus y
Step-by-step explanation:
To solve an equation for a variable, you can isolate the variable by performing operations that eliminate all other terms.
In this case, the given equation is 2x^2/y = w + 2/4. To solve for w, you can first eliminate the 2/4 term on the right-hand side by multiplying both sides of the equation by 4/2:
4 * (2x^2/y) = 4 * (w + 2/4)
4 * 2x^2/y = 4w + 4 * 2/4
8x^2/y = 4w + 2
Then, you can subtract 2 from both sides to eliminate the 2 on the right-hand side:
8x^2/y - 2 = 4w + 2 - 2
8x^2/y - 2 = 4w
Finally, you can divide both sides of the equation by 4 to eliminate the 4 on the right-hand side:
(8x^2/y - 2) / 4 = (4w) / 4
w = 8x^2/7 - 2
Therefore, the correct answer is w = 8 x squared minus 2 y Over y. This is an equivalent equation to find w, as it gives the same value for w as the original equation when the same values are used for x and y.
The other equations given are not equivalent to the original equation for finding w.
Maribelle uses x yards of material yo make a quilt. A customer requests 5 quilts that are 20% larger than the normal pattern. Write an expression to represent the total yards of material needed for the requested quilts in two different ways.
The expression to represent the total yards of material needed for the requested quilts is 5(1.2x) or 6x.
What is the expression to represent the total yards of material needed for the requested quilts?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
In this situation, Maribelle uses x yards of material to make a quilt and a customer requests 5 quilts that are 20% larger than the normal pattern.
The expression for this will be:
= 5[x + (20% × x)]
= 5[x + 0.2x]
= 5(1.2x]
= 6x
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The table shows the proportional relationship between the number of tickets required per game at a carnival.
Games 3 8 13
Tickets 9 24 39
Determine the constant of proportionality.
18
6
5
3
PLS HELP
Answer:
constant of proportionality = 3Step-by-step explanation:
You want to find the number of tickets required per game, given that the relationship is proportional and 9 tickets are required for 3 games.
ProportionThe equation of a proportional relationship can be written as ...
y = kx
where k is the constant of proportionality.
ConstantSolving for k, we have ...
k = y/x
Using a given ordered pair, we find ...
k = 9/3 = 3
The constant of proportionality is 3 (tickets per game).
__
Additional comment
Since the relationship is given as being proportional, we only need one (x, y) pair to find the constant of proportionality.
During a mathematics test, 18 students answered question 1 correctly, 23 students answered question 2 correctly, 8 students got them both correct and 11 students answered incorrectly on both questions. How many students took the test?(A) 41 (B) 44 (C) 49 (D) 52 (E) 60
Answer:
(D) 52
Step-by-step explanation:
sum up correct answers from questions 1, 2 and both 1 and 2 incorrect this time therefore we have --> 18+23+11=52 students
You could also do a Venn diagram to understand this better with 8 being the intersection of students who goth both 1 and 2 correct and 11 being left out as the number of students who got both questions incorrectly.
A large university with over 40,000 students recently took a survey in which 31% of the students claimed to exercise at least 3 times a week. A simple random sample of 250 students was selected. Let p hat = the proportion of students in the sample who claimed to work out at least 3 times a week. What is the standard deviation of the sampling distribution of p hat ? Enter your answer as a decimal rounded to the hundredths place. The standard deviation of the sampling distribution of p hat is
The shape of the sampling distribution of p hat is approximately Normal, because we would expect at least 10 success and 10 failures
What is meant by sampling distribution ?The probability distribution of a statistic that is acquired by repeated sampling of a particular population is called the sampling distribution. It outlines a variety of potential possibilities for a statistic, such as the mean or mode of a population's mean or mode of some variable.
approximately Normal, because we would expect at least 10 success and 10 failures. because they are dividing three times a week
A typical probability distribution in the natural world is the normal distribution, sometimes known as the bell curve. When the sample size is high enough, scientists often assume that a sequence of measurements obtained from a population would be regularly distributed.
The complete question is : A large university with over 40,000 students recently took a survey in which 31% of the students claimed to exercise at least 3 times a week. A simple random sample of 250 students was selected. Let p hat = the proportion of students in the sample who claimed to work out at least 3 times a week. What is the shape of the sampling distribution of p hat and why?
A. approximately Normal, because all sampling distributions are approximately Normal
B. approximately Normal, because we would expect at least 10 success and 10 failures
C. skewed to the right, because 0.31 is lower than 0.5
D. skewed to the left, because 0.31 is lower than 0.5
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The data below are the temperatures on randomly chosen days during a summer class and the number of absences on those days: Temperature, x | 72 85 91 90 88 98 75 100 80 No. of absences, y | 3 7 10 10 8 15 4 15 5 a) Find the equation of the regression line for the data. b) Assuming that the variables x and y have a significant correlation, what is the predicted number of absences when the temperature is 91? c) Calculate the correlation coefficient. d) Calculate the standard error for the model.
The equation of the regression line is y=-30.27+0.449x and predicted number of absences when the temperature is 910= 10.589
See table for sum of values.
The regression equation is:
y=α+βx
β = [tex]\frac{Sxx}{Syy}[/tex]=6995-97799779[tex]\frac{6995-9\times\frac{779}{9}\times\frac{77}{9}}{68613-9(\frac{779}{9} )2}[/tex]= 0.449
α=y-βx= 779-(0.449)7799 = =-30.27
The equation is y=-30.27+0.449x
Where y = predicted variable; x = independent variable = 0.449; - 30.27 = intercept/ slope
Constructing a 91% prediction interval for y:
x = 910
Inputting x = 91 into the regression equation : y = 0.449(91) - 30.27
y = 40.859 - 30.27 = 10.589
Prediction interval = y pm error margin
To save computing time, error margin (E) can be obtained using the online error margin calculator.
Obtained error margin (E) value = 2.3398
(10.589- 2.3398, 10.589+ 2.3398)
(8.2492, 12.9288)
(8, 13)
The equation of the regression line is y=-30.27+0.449x and predicted number of absences when the temperature is 910= 10.589
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when the admission price for a conference is $400, 1000 people will attend. for each $5 reduction in price, an additional 20 peopel will attend. let x be the number of 5 dollar reductions. determine the number of people that will attend as a function of x.
Let y be the number of people that will attend the conference as a function of x. The given information tells us that when x = 0 (the admission price is $400), y = 1000. Additionally, for each $5 reduction in price, an additional 20 people will attend.
We can express this relationship as a function as follows:
y = 1000 + 20xThis function tells us that the number of people that will attend the conference is equal to 1000, plus an additional 20 people for each $5 reduction in price (represented by the variable x).
For example, if the admission price is reduced by $10 (x = 2), the number of people that will attend the conference is given by:
y = 1000 + 20(2)
y = 1000 + 40
y = 1040
So, if the admission price is reduced by $10, 1040 people will attend the conference.
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The question is in the image. Please go through the image.
The best answer will be marked brainliest.
I hope you will explain nicely and step wise.
Step-by-step explanation:
when defined like this, we remember that when the right-angled triangular is inscribed into a circle, sine of an angle is the length of the opposite side of the angle divided by the radius. while cosine of the same angle is the adjacent side divided by the radius.
so, sin(angle) = 12/13 makes us imagine a circle of radius 13, and the side (or leg) opposite of the angle is 12.
now, Pythagoras tells us
c² = a² + b²
c being the Hypotenuse (which is the radius in our scenario), a and b are the legs.
13² = 12² + second leg²
169 = 144 + second leg²
second leg² = 25
second leg = 5
so,
cos(theta) = 5/13
tan(theta) = sin(theta) / cos(theta) =
= 12/13 / 5/13 = (12×13)/(5×13) = 12/5
sin²(theta) + cos²(theta) = (12/13)² + (5/13)² =
= 144/169 + 25/169 =
= 169/169 = 1
sec²(theta) - tan²(theta) =
= (1/cos(theta))² - (12/5)² =
= (1 / 5/13)² - 144/25 = (13/5)² - 144/25 =
= 169/25 - 144/25 = 25/25 = 1
Jerry flew a total of 4,320 miles over 3 months.
• He flew 6 flights each month.
• He flew the same distance each flight.
How many miles was each of Jerry’s flights?
The number of miles was each of Jerry’s flights travel is 240 miles.
Explain distance in miles.A mile is characterized as the unit of length, which is precisely equivalent to 5280 feet, or 1760 yards, and normalized as precisely 1609.344 meters by the Peaceful accord in 1959. The biggest unit is generally used to quantify the distance between places that are not even close to one another.
According to question:Jerry flew 6 flights each month.
Total flights in 3 months = 3(6) = 18 flights
Let distance traveled in each flight be x
Then,
18x = 4320 miles
x = 4320/18
x = 240 miles
Thus, each flight flow 240 miles.
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how many shapes are drawn based on the code below? def drawshapes(centerx, centery, radius, points, color): star(centerx, centery, radius, points, fill
6 shapes can be drawn by the given code.
Describe shapes.Shapes in mathematics specify an object's boundaries or contour. Depending on their characteristics, the forms can be divided into many types. The shapes are typically enclosed by an outline or boundary that is composed of points, lines, curves, etc. Geometric figures and figures composed of fixed lines or curves are other names for forms. There are two types of shapes: closed shapes and open shapes. Examples of shapes in daily life are the Sun, Earth, Doors, Windows, Watches, Wall Clocks, and so forth.
Given
Codes are def draw shapes( centerx , centery, radius, points, color): star(centerx, centery, radius, points, fill.
6 shapes can be drawn by the given code.
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2. In a school of 160 pupils, 75 have pencils, 87 have pens and 93 have rulers, 25 have both pensils and pens, 30 have both pencils and rulers while 47 have both pens and rulers, each pupil has at least one of the items. a). write the set notation. b) Draw a Venn diagram to illustrate this information c).How many pupils have pencils only
a) The set notation is shown below.
b) 27 pupil have pencils only.
What is Venn Diagram?A Venn diagram depicts the logical relationships between two or more sets of items by using overlapping circles or other shapes. They frequently serve to graphically organise things, demonstrating how similar and dissimilar the pieces are.
Given:
In a school of 160 pupils, 75 have pencils, 87 have pens and 93 have rulers.
25 have both pencils and pens,
30 have both pencils and rulers while 47 have both pens and rulers.
a) The set notation is
n(p)= 75
n(Pens)= 87
n(R)= 93.
n (p∩ pens) = 25
n (p∩ R) = 30
n (pens ∩ R) = 47
n (p∩ R ∩ pens) = x
c) Number of Pupil that have only pencils
= 75- [(30-7) + 25-7 +7]
=75-(23+18+7)
= 75-48
=27
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How did the Three-Fifths Compromise affect the 1790 census results? *
Use the following information to answer the questions.
A. Citizens in each state were counted as three-fifths of a person.
B. Enslaved persons in each state were counted as three-fifths of a person.
C. Only three-fifths of the citizens in each state were eligible to vote in elections.
D. Only three-fifths of enslaved peoples in each state were eligible to vote in elections.
The way that the Three-Fifths Compromise affected the 1790 census results was B. Enslaved persons in each state were counted as three-fifths of a person.
What was the Three - Fifths Compromise ?A settlement known as the "three-fifths compromise" was reached at the 1787 Constitutional Convention and permitted Southern states to count some of their enslaved population as three-fifths of a person for taxes and representational purposes. This first happened in the 1790 census results.
Many of the Founding Fathers recognized that slavery went against the ideal of liberty that was at the heart of the American Revolution, but they were unable to act decisively to end it because they were dedicated to the sanctity of private property rights, the ideas of limited government, and the pursuit of intersectional harmony.
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Russell is going to hire a makeup artist for a fashion show and is comparing prices. Martha charges $10 as a booking fee and an additional $40 per hour. Jackie charges $35 per hour, plus a booking fee of $20. Depending on the length of the show, the cost could end up being the same for either artist. Write the system of equations for this scenario and define the variables.
After solving the equation, the number of hours obtained is that after 2 hours, the cost ends up being the same for either artist.
What is an equation?Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.
This relationship is illustrated by the left and right expressions being equal. The left-hand side equals the right-hand side is a basic, straightforward equation.
As per the given information in the question,
Booking fee of Martha = $10
Additional hourly charge of Martha = $40
Then, the equation will be,
y = $10 + $40x (i)
Here, y is the total cost and x is the number of hours.
Booking fee of Jackie = $20
Additional hourly charge of Jackie = $35
Then, the equation for this will be,
y = $20 + $35x (ii)
Here, y is the total cost and x is the number of hours.
Then, depending on the length of the show, the cost could end up being the same for either artist.
So,
From equations (i) and (ii)
$20 + $35x = $10 + $40x
20 - 10 = 40x - 35x
5x = 10
x = 2 hours
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HELP ASAP!! READ CAREFULLY
Answer:
not true:
3. AD = DC
4. YZ = XW
explanation:
lower base is only congruent to upper base.
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-Is there a transformation that maps shape I onto shape IV? Explain your answer.
Yes, there is a transformation that maps shape I onto shape IV. If the figure I is reflected over the x-axis, we get figure IV.
What is a transformation in math?In mathematics, a transformation is a function or a mapping that takes a set of inputs and produces a new set of outputs.
Transformations can be applied to geometric shapes, functions, and other mathematical objects to change their properties or positions.
There are various types of transformations that can be performed in mathematics, including translation, rotation, reflection, dilation, and more. Each type of transformation has its own specific rules and properties that dictate how it affects the original object.
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Full Question:
See the attached Image
The edge of a cube has length 10 inches with a possible error of 1%. The possible error, in cubic inches, in the volume of the cube is: a) 3 b) 1 c) 10 d) 30 e) all of these
Answer:
d) 30
Step-by-step explanation:
1% of 10 inch is 0.1 inch
10 inch + 0.1 inch = 10.1 inch
10 inch - 0.1 inch = 9.9 inch
V = s³
For s = 9.9 in., V = (9.9 in.)³ = 970.299 in.³
For s = 10.1 in., V = (10.1 in.)³ = 1030.301 in.³
For 10 in., V = (10 in.)³ = 1000 in.³
|1000 in.³ - 970.299 in.³| = 29.701 in.³
|1000 in.³ - 1030.301 in.³| = 30.301 in.³
The error is 30 in.³.
What is equivalent to 1:9
Answer:
2 : 18
Step-by-step explanation:
to find equivalent ratios , multiply or divide each part of the ratio by the same numeric value.
1 : 9 ( multiply both parts by 2 )
= 2 : 18
or
1 : 9 ( multiply both parts by 3 )
= 3 : 27
and so on...
What fraction is equal to 75% of 1/2
Answer:
3/8
Step-by-step explanation:
75% of 1/2
3/4 of 1/2
3/4x1/2
3/8
The diagram below shows a cylinder with diameter 6 cm and height 20 cm. The
Volume, in cm³, of the cylinder is
-6 cm
20 cm
The volume of the cylinder is 180π cm³.
What is volume ?
Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.
Volume is a measurement of three-dimensional space that is occupied. Numerous imperial or US customary units, as well as SI-derived units (such the cubic meter and liter), are frequently used to quantify it numerically (such as the gallon, quart, cubic inch). Volume and length (cubed) have a symbiotic relationship.
As diameter = 6cm
We know that radius is half of diameter
∴ radius = 3 cm
height = 20 cm
Volume = π r² h
= π (3)²×20
= π × 9 × 20
= 180 π cm³
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People at an airport can pass through security on one of two levels: level A or level B. Suppose that, on average, it takes people
22
2222 minutes to pass through security on level A with a standard deviation of
7
77 minutes. On level B, the mean and standard deviation are
20
2020 and
6
66 minutes, respectively.
Every day, the airport looks at an SRS of
100
100100 people who use level A, and an independent SRS of
150
150150 people who use level B. They calculate the mean time for each sample, then look at the difference
(
A
−
B
)
(A−B)left parenthesis, start text, A, end text, minus, start text, B, end text, right parenthesis between the sample means.
What are the mean and standard deviation (in minutes) of the sampling distribution of the difference in sample means?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
μ
x
ˉ
A
−
x
ˉ
B
=
2
σ
x
ˉ
A
−
x
ˉ
B
=
7
2
+
6
2
250
μ
x
ˉ
A
−
x
ˉ
B
σ
x
ˉ
A
−
x
ˉ
B
=2
=
250
7
2
+6
2
(Choice B)
B
μ
x
ˉ
A
−
x
ˉ
B
=
2
σ
x
ˉ
A
−
x
ˉ
B
=
7
2
100
+
6
2
150
μ
x
ˉ
A
−
x
ˉ
B
σ
x
ˉ
A
−
x
ˉ
B
=2
=
100
7
2
+
150
6
2
(Choice C)
C
μ
x
ˉ
A
−
x
ˉ
B
=
21
σ
x
ˉ
A
−
x
ˉ
B
=
7
2
+
6
2
250
μ
x
ˉ
A
−
x
ˉ
B
σ
x
ˉ
A
−
x
ˉ
B
=21
=
250
7
2
+6
2
(Choice D)
D
μ
x
ˉ
A
−
x
ˉ
B
=
21
σ
x
ˉ
A
−
x
ˉ
B
=
7
2
100
+
6
2
150
μ
x
ˉ
A
−
x
ˉ
B
σ
x
ˉ
A
−
x
ˉ
B
=21
=
100
7
2
+
150
6
2
The mean and standard deviation (in ) of the sampling distribution of the difference in sample means [tex]\sigma_1[/tex] - [tex]\sigma_2[/tex] = (7)² ÷100+ 6² /150.
What is standard deviation?A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
Given:
Level A:
S.D. = 7
Level B: Mean = 20
S.D. = 6
So, [tex]\nu_1[/tex] = 22
[tex]\nu_2[/tex] = 20
Then, [tex]\nu_1[/tex] - [tex]\nu_2[/tex] = 22-20=2
and, [tex]\sigma_1[/tex] - [tex]\sigma_2[/tex]
= (7)² ÷100+ 6² /150
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