By answering the presented question, we may conclude that Therefore, triangle the length of the base AB is approximately 20.88 centimeters.
What precisely is a triangle?A triangle is a closed, double-symmetrical shape composed of three line segments known as sides that intersect at three places known as vertices. Triangles are distinguished by their sides and angles. Triangles can be equilateral (all factions equal), isosceles, or scalene based on their sides. Triangles are classified as acute (all angles are fewer than 90 degrees), good (one angle is equal to 90 degrees), or orbicular (all angles are higher than 90 degrees) (all angles greater than 90 degrees). The region of a triangle can be calculated using the formula A = (1/2)bh, where an is the neighbourhood, b is the triangle's base, and h is the triangle's height.
the length of the base AB,
Area = (1/2) * base * height
[tex]CB^2 = CD^2 + BD^2\\9^2 = x^2 + (AB - x)^2\\81 = x^2 + (AB^2 - 2ABx + x^2)\\AB^2 - 2ABx + 2x^2 = 81\\[/tex]
We also know that the area of the triangle is:
[tex]46 = (1/2) * AB * CB\\46 = (1/2) * AB * \sqrt(x^2 + 81)\\Now we can solve for AB in terms of x:AB = (2 * 46) / \sqrt(x^2 + 81)\\AB = 92 / \sqrt(x^2 + 81)\\(92 / \sqrt(x^2 + 81))^2 - 2(92 / \sqrt(x^2 + 81))x + 2x^2 = 81\\[/tex]
[tex]8464 / (x^2 + 81) - (184x) /sqrt(x^2 + 81) + 2x^2 = 81\\8464 - 184x(x^2 + 81) + 2x^2(x^2 + 81) * sqrt(x^2 + 81) = 81(x^2 + 81)\\2x^4 - 181x^2 + 7743 = 0\\x^2 = (181 + \sqrt(181^2 - 427743)) / (2*2)\\x^2 = (181 + sqrt(129961)) / 4\\x^2 = (181 + 361) / 4\\x^2 = 90^2 / 4\\x = 45\sqrt(2) / 2\\[/tex]
[tex]AB = 92 / \sqrt(x^2 + 81)\\AB = 92 / \sqrt((45sqrt(2) / 2)^2 + 81)\\AB = 92 / \sqrt(4050)\\AB ≈ 20.88 cm\\[/tex]
Therefore, the length of the base AB is approximately 20.88 centimeters.
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Find the prime factorization of 792. What is the sum of the distinct prime factors?
The sum of the distinct prime factors is 16.
Solution:There are overall 24 factors of 792 among which 792 is the most significant factor and its prime factors are 2, 3, and 11.
Hence sum = 2 + 3 + 11 = 16
Which graph matches the function given:
The graph that matches the piecewise function, f(x) = √(x + 5), if x < -2, f(x) = |x + 1| if -2 ≤ x ≤ 2, and f(x) = (x - 2)² if x > 2 is the graph in the third option.
What is a piecewise function?A piecewise function is a function is a function that consists of two or more subfunctions each of which are applied, based on the specific interval of the input variable.
The intervals of the piecewise function are;
f(x) = √(x + 5) if x < -2
f(x) = |x + 1| -2 ≤ x ≤ 2
f(x) = (x - 2)² if x > 2
The graph of the piecewise function is a three piece graph which consists of the graph of f(x) = √(x + 5), for x values less than -2, f(x) = |x + 1|, for x-values in the interval -2 ≤ x ≤ 2 and the graph of f(x) = (x - 2)²
The <-2, symbol indicates the presence of an open circle in the graph of f(x) = √(x + 5) at x = -2
The interval -2 ≤ x ≤ 2 for the function f(x) = |x + 1| indicates that the graph of f(x) = |x + 1| in the interval -2 ≤ x ≤ 2, consists of closed circles at x = -2 and x = 2.
The interval, x > 2, for the function, f(x) = (x - 2)², indicates that the presence of an open circle in the graph of f(x) = (x - 2)² at x = 2.
The correct option for the graph of the piecewise function is therefore the third option.
Please find the attached the graph of the piecewise function created with MS Excel
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Help would be greatly appreciated.
The description of the ensembles would be: 1. Students who attend both recitals, 2. Students who attend one of the two recitals, 3. students who attend both recitals, 4.The difference between the set P and U, that is, 3 students.
How to graph the information?To graph the information in a Venn diagram we must take into account the information in the statement. In this case we must place 6 students outside the circles because there are 6 who do not attend any activity.
So, there would be 34 remaining students, of which 20 go to the piano recital and 23 to the voice recital. So, we can establish that 20 go to both recitals, 3 go to the voice recital, and 1 go to the piano recital.
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please help with with this math
The slope of this linear function is equal to: B. -2/9.
The volume of a cylinder with a height of 10 m and a radius of 5 m is equal to 785 m³.
The value of each expression is: C. a) 2, b) 1/2, c) 2/9.
How to calculate the slope of a line?In Mathematics, the slope of any straight line can be determined by using the following mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (8 - 10)/(6 - (-3))
Slope (m) = (8 - 10)/(6 + 3)
Slope (m) =
Slope (m) = -2/9.
How to calculate the volume of a cylinder?In Mathematics, the volume of a cylinder can be calculated by using this formula:
Volume of a cylinder, V = πr²h
Where:
V represents the volume of a cylinder.h represents the height of a cylinder.r represents the radius of a cylinder.By substituting the given parameters, we have:
Volume of cylinder, V = 3.14 × 5² × 10
Volume of cylinder, V = 785 m³
(√2)² = 2
(1/√2)² = 1/2
(√2/3)² = 2/9
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The data represent the results for a test for a certain disease. Assume one individual from the group is randomly selected. Find the probability of getting someone who tested positive given that he or she had the disease.
Answer:
To find the probability of getting someone who tested positive given that he or she had the disease, we need to use the formula for conditional probability:
P(positive|disease) = P(positive and disease) / P(disease)
From the given data, we can see that there are 136 individuals who tested positive and actually had the disease. Therefore, P(positive and disease) = 136.
We can also see that there are a total of 136 + 8 = 144 individuals who actually had the disease. Therefore, P(disease) = 144.
Substituting these values into the formula, we get:
P(positive|disease) = 136 / 144
Simplifying, we get:
P(positive|disease) = 0.944
Rounding to three decimal places, we get:
P(positive|disease) ≈ 0.944
Therefore, the probability of getting someone who tested positive given that he or she had the disease is approximately 0.944.
Pls help me right now
Which of the following tables represents a linear relationship that is also proportional?
x 2 3 4
y −3 0 3
x 4 2 0
y −2 −1 0
x −2 1 4
y 0 1 2
x 0 1 2
y −4 0 4
Answer:
This table represents a linear relationship that is also proportional:
x 0 1 2
y −4 0 4
Answer:
The second table represents a linear relationship that is also proportional.
To check if a relationship is proportional, we need to see if the ratio of y to x is constant for all values of x and y. In other words, if we divide any y value by its corresponding x value, we should get the same number for all values.
Let's check the ratio for each table:
Ratio for the first table:
-3/2 = -1.5
0/3 = 0
3/4 = 0.75
The ratio is not constant, so this relationship is not proportional.
Ratio for the second table:
-2/4 = -0.5
-1/2 = -0.5
0/0 = undefined
The ratio is constant (-0.5), so this relationship is proportional.
Ratio for the third table:
0/(-2) = 0
1/1 = 1
2/4 = 0.5
The ratio is not constant, so this relationship is not proportional.
Ratio for the fourth table:
-4/0 = undefined
0/1 = 0
4/2 = 2
The ratio is not constant, so this relationship is not proportional.
Therefore, the second table is the only one that represents a linear relationship that is also proportional.
The result of adding 15 to x and dividing the answer by 4 is the same as taking x from 80. a Express this statement as an algebraic equation. b Hence find the value of x.
Answer:
(15+x)÷4 = 80-x
by criss cross we'll get:
15+x = 4(80-x)
15+x = 320-4x
x+4x=320-15
5x = 305
x = 61
help ASAP PLSSSS
The table of values represents a linear function.
Enter the rate of change of this function.
The rate of change (or slope) of this linear function is -1/2.
Describe Linear Function?A linear function is a mathematical function that has a constant rate of change, meaning that the output (y-value) changes at a constant rate for every unit increase in the input (x-value). In other words, the graph of a linear function is a straight line.
The general form of a linear function is y = mx + b, where m is the slope of the line (the rate of change) and b is the y-intercept (the point where the line crosses the y-axis). The slope represents how much the y-value changes for every one-unit increase in the x-value.
Linear functions can be used to model many real-world situations, such as distance vs. time or cost vs. quantity. They are also commonly used in economics, physics, and engineering.
The rate of change of a linear function represents the slope of the line. We can calculate the slope using the formula:
slope = (change in y) / (change in x)
Let's use the points (0, -3) and (2, -4) to calculate the slope:
slope = (-4 - (-3)) / (2 - 0)
slope = -1 / 2
Therefore, the rate of change (or slope) of this linear function is -1/2.
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A photography student took portrait photos of people from his hometown. He wants to
develop 21 of the photos, 9 of which were photos of babies.
If he randomly chooses to make 4 of the photos black and white, what is the probability that
all of them are of babies?
Answer: The total number of ways the photography student can choose 4 photos out of 21 is given by the combination formula:
Step-by-step explanation: C(21, 4) = (21!)/((4!)(21-4)!) = 5985
Out of the 21 photos, 9 were photos of babies. The number of ways the student can choose 4 baby photos out of 9 is given by:
C(9, 4) = (9!)/((4!)(9-4)!) = 126
Therefore, the probability that all 4 photos chosen are of babies is:
P = (number of ways to choose 4 baby photos)/(total number of ways to choose 4 photos)
P = C(9, 4)/C(21, 4)
P = 126/5985
P ≈ 0.021
So, the probability that all 4 photos chosen are of babies is approximately 0.021 or 2.1%.
given :√9+25 : π-4 : ³√-27 : 2÷3 : 18÷2 : √-27
√9+25 = 28
π-4 = -0.8571
³√-27 = -3
2 / 3 = 0.6667
18÷2 = 9
√-27 = 5.196
What is surdsIn mathematics, a surd is a term used to describe an irrational number that is expressed as the root of an integer. Specifically, a surd is a number that cannot be expressed exactly as a fraction of two integers, and is usually written in the form of a radical (e.g. √2, √3, √5, etc.).
We have √9+25 = 28
find the square root of 9 = 3
3 + 25 = 28
π-4 = 3.14 - 4
= -0.8571
³√-27 = ³√3³
= 3
2÷3 = 0.6667
18÷2 = 9
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question:
given :√9+25 : π-4 : ³√-27 : 2÷3 : 18÷2 : √-27
find the value of the terms
For numbers 3, 4, and 5, find the value of the indicated length(s) in ⨀C. A and B are points of tangency. Simplify all radicals.
I just need help with these three problems!
As a result, AB = 52 and AC = BC = 5 as AC and BC are both the circle's radii since A and B are points of tangency .
what is circle ?A circle is a closed object made up of all points in a plane that are separated from the center by a predetermined distance, known as the radius. The diameter is the distance across the circle that passes through its center, while the circumference is the distance around the circle. The ratio of a circle's circumference to its diameter is always pi (), or roughly 3.14. Pi is also known as the proportionality constant. Circles are significant geometric forms that are used frequently in mathematics, science, and daily life.
given
AC and BC are both the circle's radii since A and B are points of tangency. Hence, AC = BC = 5.
We can apply the Pythagorean theorem to segment AB as follows:
[tex]AB^2 = 52 + 52 \\AB^2 = AC^2 + BC^2[/tex]
AB² = 50
AB = √50 = 5√2
As a result, AB = 52 and AC = BC = 5 as AC and BC are both the circle's radii since A and B are points of tangency .
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Help me please.
Whoever answers right gets brainliest
Answer:y=x-5
Step-by-step explanation:this is the answer for sure
Answer:
[tex]y=x-5[/tex]
Step-by-step explanation:
Notice for every X you do increase your Y by 1, this is the slope must be 1, to check you can use the slope equation with any two points
[tex]m= \frac{-4-(-3)}{1-(2)} =-1[/tex]
The lets use one point and the line equation:
[tex]y-yo=m(x-xo)[/tex]
[tex]y+4=-1(x-1)[/tex]
Solving for Y you can obtain
[tex]y=x-5[/tex]
You can input any X value and check the Y value to be sure, for example, for X=3 you can check Y=3-5=-2. In the table for X=3 the Y value is -2, so this checks.
An inlet pipe on a swimming pool can be used to fill the pool in 16
hours. The drain pipe can be used to empty the pool in 24
hours. If the pool is 13
filled and then the inlet pipe and drain pipe are opened, how long from that time will it take to fill the pool?
Answer:
Step-by-step explanation:
I give brainliest for the answer
The intersection of two parallel lines; x = 10 metres.
Describe another angle using an example.Alternate angles are created when two parallel lines are intersected by a transversal. Have a look at the given illustration; the two parallel lines are EF and GH. When a transversal splits two parallel lines, the alternate angles are equal.
The alternate interior angles are equal because of the parallel lines characteristic.
Angle STQ (denoted as 2x+10) and angle RQS are hence equal. Angle QRP (shown as x+20) and angle RQS are likewise equal.
Setting these two angles equal to each other, we can get:
x+20 = 2x+10
Simplifying this equation, we get:
x = 10.
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Best describes , whats the best possible answer
Answer:
D?
Step-by-step explanation:
I'm not completely sure, but there are 2 different 180 degree lines that y falls on. On one line (y+70=180) it is for sure 110 degrees
When measured on the other line it is (y+70+x=180) I'm not too familiar with this??
Can you help me, please!?
Answer:
The correct answer is (b+2)
Step-by-step explanation:
(3b-7) + (-2b+9)
3b-7-2b+9
3b-2b+9-7
b+2 Ans
Answer:
b+2 is the answer of this expression.
Step-by-step explanation:
(3b-7) and (-2b+9)
3b+(-2b) + (-7+9)
(3b-2b) + 2
b+2
Find the exact value of the expression: tan270 degrees
Answer:
What is the Value of Tan 270 Degrees? The value of tan 270 degrees is undefined. Tan 270 degrees can also be expressed using the equivalent of the given angle (270 degrees) in radians (4.71238 . . .) ⇒ 270 degrees = 270° × (π/180°) rad = 3π/2 or 4.7123 . . .
please marke a a brainalist pls
Suppose that an individual has a body fat percentage of 16.3% and weighs 163 pounds. How many pounds of his weight is made up of fat? Round your answer
to the nearest tenth.
pounds
X
Consequently, the person's weight is roughly 26.5 pounds of fat (rounded to the nearest tenth).
what is unitary method ?By determining the value of a single unit or quantity and then scaling that value up or down to determine the value of another quantity, the unitary method is a mathematical strategy used to solve problems. According to the unitary method's guiding concept, if one quantity or unit has a certain value, then a predetermined number of those same quantities or units will have a proportionate value. For instance, 5 apples would cost $5 if 1 fruit cost $1.
given
We can use the person's weight and body fat proportion to determine how many pounds of body fat they have. We can commence by calculating the decimal weight of the body fat:
weight of body fat Equals body fat percentage * weight
= 0.163% * 163 lbs.
= 26.509 lbs.
Consequently, the person's weight is roughly 26.5 pounds of fat (rounded to the nearest tenth).
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sams rectangular swimming pool has a volume of 600 cubic feet, the neighbors pools the same length and height but the width is three times larger. what is the volume of the neighbors pool?
Answer: Let's denote the length, width, and height of Sam's pool as l, w, and h, respectively. Then, we have:
lwh = 600
For the neighbor's pool, we know that it has the same length and height as Sam's pool, but the width is three times larger. Let's denote the width of the neighbor's pool as 3w. Then, the volume of the neighbor's pool is:
l(3w)h = 3lwh = 3(600) = 1800 cubic feet
Therefore, the volume of the neighbor's pool is 1800 cubic feet.
Step-by-step explanation:
I’m not sure what the limit would be if it’s discontinued but defined
The graph's function limit at x=4 is 6.
Define limitIn mathematics, the limit of a function is the value that the function approaches as the input approaches a certain value or as the input approaches infinity or negative infinity. A function may or may not have a limit at a given point or as the input goes to infinity or negative infinity.
The formal definition of the limit of a function f(x) as x approaches a value a is as follows:
For every positive number ε (epsilon), there exists a corresponding positive number δ (delta) such that if 0 < |x-a| < δ, then |f(x)-L| < ε.
Limit f(x) at x tend to 4⁺ =6.
Limit f(x) at x tend to 4⁻ =6
Hence, the graph's function limit at x=4 is 6.
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explain integral calculus
Answer:
Integral
Step-by-step explanation:
explain integral calculus
Between which two consecutive integers does [tex]\sqrt138[/tex]lie?
The square root of 138 lies between 11 and 12, as 11²=121 and 12²=144.
What is number?Number is a mathematical object used to count, measure, and label. Numbers are used in almost every field of mathematics and science, including algebra, calculus, geometry, physics, and computer science. Numbers can also be used to represent data, such as population, income, temperature, or time. In addition, numbers are used to represent abstract concepts, such as love, truth, beauty, and justice.
This is because the square root of a number is the number that, when multiplied by itself, produces the original number. Therefore, to find the square root of 138, we need to identify two consecutive integers such that one of them squared is smaller than 138 and the other squared is larger than 138.
To do this, we can work our way up from the integer closer to 0, in this case 11. 11 squared is 121, which is smaller than 138, so we know that the square root of 138 must be between 11 and a larger integer. Then, if we square 12, we get 144, which is larger than 138. Therefore, we can definitively say that the square root of 138 lies between 11 and 12.
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The square root of 138 lies between 11 and 12, as 11² is 121 and 12² is 144.
What is number?Number is a mathematical object used to count, measure, and label. Numbers are used in almost every field of mathematics and science, including algebra, calculus, geometry, physics, and computer science. Numbers can also be used to represent data, such as population, income, temperature, or time. In addition, numbers are used to represent abstract concepts, such as love, truth, beauty, and justice.
To calculate this, we can divide 138 by 11 and 12, and see which integer is closer to the answer.
138 divided by 11 is 12.545454545454545454545454545455.
138 divided by 12 is 11.5.
Since 11.5 is closer to the answer, the square root of 138 lies between 11 and 12.
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First-year students at a university must take history or philosophy during their first semester. 400 are enrolled in both out of a total of 1200 first-year students. If 600 are enrolled in philosophy, how many are taking history?
Answer: I really don't know I'm just trying to get a quest done sorry
Bria is a customer who would like to display her collection of soap carvings on top of her bookcase. The collection needs an area of 300 square inches. What should b equal for the top of the bookcase to have the correct area? Round your answer to the nearest tenth of an inch.
I need help D: Please !!!!
The width of the top of the bookcase should be approximately 12.2 inches to give Bria's soap carving collection an area of 300 square inches.
How do you compute the area of a square inch?Simply multiply the length and width measurements to get the area of your square or rectangular area in square inches.
Assume the bookcase's top is rectangular, with length "L" and width "b". Because the area of a rectangle is the product of its length and width, we get:
L * b = 300
To find "b," we can rearrange the equation as follows:
b = 300 / L
We don't have enough information to directly solve for "L," but we can make an educated guess based on the figure provided. Based on the illustration, the bookcase appears to be roughly twice as long as it is wide. So let us suppose:
L ≈ 2b
When we plug this into the equation above, we get:
b = 300 / (2b) (2b)
To simplify, we have:
b^2 = 150
When we take the square root of both sides, we get:
b ≈ 12.2
We have, rounded to the nearest tenth of an inch:
b ≈ 12.2 inches
As a result, the width of the top of the bookcase should be approximately 12.2 inches in order to give Bria's soap carving collection a 300-square-inch area.
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Graph the system of linear equations.
4x + 3y = 24
-2x + 6y = 18
Use the Line tool to graph the lines.
Replace the loading system by an equivalent resultant force and couple moment acting at point o. Assume F1 = {-300i + 170j + 190k}N (Figure 1) Part A Determine the resultant force. Enter the 2, y and a components of the resultant force separated by commas. A vec O ? FR = Submit Request Answer Part B Determine the couple moment acting at point 0. Enter the x, y and 2 components of the couple moment separated by commas. Figure O AQ O vec O ? < 1 of 1 > (Mon= N.mn Submit Request Answer 1 m OS Provide Feedback F = (-450k) N
The resultant force is equal to F1, which is {-300i + 170j + 190k}N, and the couple moment acting at point 0 is (-0.19i - 0.34j + 0.15k) N.m.
To determine the resultant force acting at point O, we can add all the forces acting at point O. In this case, we have only one force F1 = {-300i + 170j + 190k}N. Therefore, the resultant force acting at point O is F1 itself.
To determine the couple moment acting at point O, we can use the formula:
M = r x F
where r is the position vector from point O to any point on the line of action of force F.
Since we don’t know the position vector r, we can choose any arbitrary point on the line of action of force F. Let’s say we choose point A which lies on the line of action of force F and is perpendicular to it.
Therefore, r = OA where OA is the position vector from point O to point A. We can find OA by subtracting position vectors of points O and A i.e., OA = A - O.
Now, let’s calculate M using M = r x F.
M = (OA) x F1
M = (A - O) x {-300i + 170j + 190k}N M
= (-0.19i - 0.34j + 0.15k) N.m
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Complete question is:
Replace the loading system by an equivalent resultant force and couple moment acting at point o. Assume F1 = {-300i + 170j + 190k}N
Part A Determine the resultant force. Enter the 2, y and a components of the resultant force separated by commas.
Part B Determine the couple moment acting at point 0. Enter the x, y and 2 components of the couple moment separated by commas.
Find the standard normal area for each of the following(round your answers to 4 decimal places)
The standard normal area is the region under the standard normal distribution curve, which has a mean of 0 and a standard deviation of 1. One is equal to the entire area under the normal distribution curve.
What is the standard normal area?To determine the probability for the above intervals using a typical normal distribution table or a calculator with a normal distribution function:
[tex]P(1.22 < Z < 2.15) = 0.1143[/tex]
[tex]P(2.00 < Z < 3.00) = 0.0228[/tex]
[tex]P(-2.00 < Z < 2.00) = P(Z < 2.00) - P(Z < -2.00) = 0.9772 - 0.0228 = 0.9544[/tex]
The number of standard deviations the variable is from the mean is shown by the ensuing Z-score. The chance of detecting a certain value of the variable in a given interval can then be determined using the standard normal area.
Therefore, The symmetry of the normal distribution allows us to use the third interval's coverage of 4 standard deviations to simplify the calculation, as illustrated above.
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Estimate the product. Then find each product 3/4 8 1/2
PLEASE HELP
The product of the number 3/4 and 8 1/2 is 51/8.
What is mixed fraction and improper fraction?A mixed number is one that has a fraction and a whole number, separated by a space. An example of a mixed number is 8 1/2. Contrarily, an improper fraction is one in which the numerator exceeds or is equal to the denominator. For instance, 17/2 is a bad fraction. An improper fraction is a fraction in which the numerator is more than or equal to the denominator, as opposed to a mixed number, which combines a whole number with a proper fraction.
The given numbers are 3/4 and 8 1/2.
Convert the mixed number to an improper fraction:
8 1/2 = (8 x 2 + 1) / 2 = 17/2
Then, we can multiply the fractions:
3/4 x 17/2 = (3 x 17) / (4 x 2) = 51/8
Hence, the product of 3/4 and 8 1/2 is 51/8.
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Standard Error of the Mean =
Confidence Interval Estimate for the Mean
Margin of Error E= Z
= Z. V
±Z
You want to rent a one-bedroom apartment near BCIT for next term. The mean
monthly rent for a random sample of 36 apartments advertised for rent on Craigslist is $1,235. Assume that the population standard deviation is $150.
(a) Give the point estimate of the true mean monthly rent for one-bedroom
apartments available for rent near BCIT.
Answer=$
(b) At the 95% confidence level, what is the margin of error on your estimate of
the true mean monthly rent for one-bedroom apartments available for rent near
BCIT.
Answer=$
(c) Construct a 95% confidence interval for the true mean monthly rent for one-
bedroom apartments.
Lower value=$
Upper value=$
Choose the correct statement to interpret the confidence interval.
1) I am totally confident that the population mean belongs to this confidence interval.
2) Clam 95% confident that the true population mean belongs to this confidence
interval.
(d) A friend claims the average monthly rent for a one-bedroom apartment available for rent near BCIT is at least $1,300. Based on your confidence interval do you agree?
• Yes
• No
(e) What is the z-score used to construct a 92% confidence interval?
Answer= (Enter a positive value in 2 decimal places)
The answers are a)the sample mean, which is $1,235. b) margin of error = $58.50. c)95% .d)the average monthly rent is at least $1,300.e)The z-score for a 92% confidence interval is 1.75.
How to calculate the sample mean and z-score ?a) The sample mean is the point estimate of the true mean monthly rent for one-bedroom apartments available for rent near BCIT, which is $1,235.
(b) At a 95% confidence level, the margin of error on the true mean monthly rent estimate is calculated as follows:
Margin of error = Z * (standard deviation / square root of sample size), where Z is the desired confidence level's z-score, which is 1.96 for a 95% confidence level.
Thus, the margin of error is equal to 1.96 * (150 / sqrt(36)) = $58.50.
(c) The 95% confidence interval for the true mean monthly rent is calculated as follows:
Lower value = point estimate minus margin of error = $1,235 minus $58.50 equals $1,176.50
Upper estimate + margin of error = $1,235 + $58.50 = $1,293.50.
(d) To see if the confidence interval supports the friend's claim that the average monthly rent for a one-bedroom apartment available for rent near BCIT is at least $1,300, we need to see if the lower limit of the confidence interval is greater than or equal to $1,300.
Given that the confidence interval is $1,176.50 $1,300, we can conclude that the confidence interval does not support the friend's claim that the
average monthly rent is at least $1,300. As a result, the answer is "No."
(e) A standard normal distribution table or calculator can be used to calculate the z-score corresponding to a 92% confidence interval.
A 92% confidence interval has a z-score of 1.75. (to two decimal places).
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