The ratio of the area of the inscribed circle to the area of the square ABFE is π:2.
Define the term diameter of a semicircle?If AB is divided into four congruent segments, each of which is the diameter of a semicircle, then we can draw four semicircles such that each one has its diameter on AB and they all have the same radius. Let the radius of each semicircle is r.
Let's assume the radius of each semicircle to be "r" and AB to be equal to "4r" because AB is divided into four congruent segments. Let the center of the inscribed circle be "O". Draw radii from the center of the inscribed circle to the tangent points, and let the tangent points on the semicircles be "C" and "D", and the midpoint of AB be "M".
Since CM and DM are radii of semicircles, they each have a length of "2r". So, MC = MD = 2r. Additionally, since CMDO is a square (as opposite sides are parallel and equal in length), we have CM = MD = CO = DO = 2r.
By the Pythagorean theorem, we have MC² = MO² - OC². Substituting the values we have, we get:
(2r)² = MO² - (2r)²
4r² = MO² - 4r²
MO² = 8r²
The area of the inscribed circle can be calculated as πr², so substituting MO² = 8r², we get the area of the inscribed circle as 8πr².
The area of the square ABFE is (4r)² = 16r².
So, the ratio of the area of the inscribed circle to the area of the square ABFE is:
(8πr²) : (16r²) = π : 2
Therefore, the ratio of the area of the inscribed circle to the area of the square ABFE is π : 2.
To know more about semicircle, visit:
brainly.com/question/15822332
#SPJ1
The complete question: AB is divided into four congruent segments, each of which is the diameter of a semicircle. If a circle is inscribed in the quadrilateral formed by connecting the endpoints of the semicircles, what is the ratio of the area of the inscribed circle to the area of the square ABFE?
A cylinder is full at 471 cubic centimeters and has a radius of 5 centimeters. What is the height of the cylinder?
Answer:
the height is 6 meters
Step-by-step explanation:
v = [tex]\pi r^{2} h[/tex]
471 = 3.14(25)h
471 = 78.5h Divide both sides by 78.5
[tex]\frac{471}{78.5}[/tex] = [tex]\frac{78.5h}{78.5}[/tex]
6 = h
Helping in the name of Jesus.
The function F is defined by F(x) = 12/x+1/2. Find each value of the function.
F(k) =
Each values of the function are;
[tex]F(3) = \frac{9}{2} , F(-12) = -\frac{1}{2} , F(\frac{1}{3}) = \frac{73}{2} , F(\frac{3}{4}) =\frac{33}{2}[/tex]
Define the term function?A function is a relationship between two sets of numbers, called the domain and the range, such that each input value from the domain corresponds to exactly one output value from the range. A function can be thought of as a rule that assigns to each input value a unique output value. The most common way to represent a function is by using an equation or formula that defines the relationship between the input values and the output values. The variable in a function represents the input values from the domain.
Given function;
[tex]F(x) = \frac{12}{x} + \frac{1}{2}[/tex]
We need to find the values of function [tex]F(3) , F(-12) , F(\frac{1}{3}) , F(\frac{3}{4})[/tex]
Put the values of x = 3, -12, 1/3, 3/4 one by one in the given function of [tex]F(x) = \frac{12}{x} + \frac{1}{2}[/tex]
1. If x= 3; [tex]F(3) = \frac{12}{3} + \frac{1}{2} = \frac{9}{2}[/tex]
2. If x= -12; [tex]F(-12) = \frac{12}{(-12)} + \frac{1}{2} = -1 + \frac{1}{2}[/tex] [tex]= -\frac{1}{2}[/tex]
3. If [tex]x=\frac{1}{3}[/tex]; [tex]F(\frac{1}{3} ) = \frac{12}{(\frac{1}{3}) } + \frac{1}{2} = 36+\frac{1}{2}[/tex] [tex]= \frac{73}{2}[/tex]
4. If [tex]x=\frac{3}{4}[/tex]; [tex]F(\frac{3}{4} ) = \frac{12}{(\frac{3}{4}) } + \frac{1}{2} = 16 +\frac{1}{2}[/tex] [tex]= \frac{33}{2}[/tex]
Therefore the values are; [tex]F(3) = \frac{9}{2} , F(-12) = -\frac{1}{2} , F(\frac{1}{3}) = \frac{73}{2} , F(\frac{3}{4}) =\frac{33}{2}[/tex]
To know more about function, visit:
https://brainly.com/question/11624077
#SPJ1
Complete question-
a jury has 12 jurors. a vote of at least 10 of 12 for guilty is necessary for a defendant to be convicted of a crime. assume that each juror acts independently of the others and that the probability that anyone juror makes the correct decision on a defendant is .80. if the defendant is guilty, what is the probability that the jury makes the correct decision? round your answer to 4 decimal places.If the defendant is guilty, the probability that the jury makes the correct decision is ____
The probability that the jury makes the correct decision is 0.9999
This is a binomial distribution problem where the event of interest is a juror making a correct decision (voting guilty) and the number of trials is 12 (the number of jurors).
The probability of a single juror making the correct decision is 0.80. Therefore, the probability of a single juror making the incorrect decision (voting not guilty) is 1 - 0.80 = 0.20.
To calculate the probability that at least 10 out of 12 jurors make the correct decision (voting guilty) if the defendant is guilty, we can use the binomial distribution formula:
P(X ≥ 10) = 1 - P(X < 10)
where X is the number of jurors who make the correct decision.
Since the probability of a single juror making the correct decision is 0.80, we can use the binomial probability formula to calculate the probability of X jurors making the correct decision
P(X = x) = (12 choose x) * 0.80^x * 0.20^(12-x)
where (12 choose x) is the number of ways to choose x jurors out of 12.
Using this formula, we can calculate the probability of fewer than 10 jurors making the correct decision:
P(X < 10) = P(X = 0) + P(X = 1) + ... + P(X = 9)
We can use a calculator or software to calculate this probability:
P(X < 10) = 0.00000436
Therefore, the probability of at least 10 out of 12 jurors making the correct decision if the defendant is guilty is:
P(X ≥ 10) = 1 - P(X < 10) = 1 - 0.00000436 = 0.99999564
Rounding to four decimal places, the probability is 0.9999.
Learn more about probability here
brainly.com/question/29350029
#SPJ4
The larger leg of a right triangle is 3 cm longer than its smaller leg. The hypotenuse is 6 cm longer than the? smaller leg. How many centimeters long is the smaller leg
Answer:
3cm or 1.5
Step-by-step explanation:
Long leg = radical of 3
Short leg = 1
Hypotenuse= 2
Which of the following is closest to the circumference of a circle that has a diameter of 8 inches?
Answer: The formula for the circumference of a circle is C = πd, where d is the diameter of the circle.
If the diameter of the circle is 8 inches, then:
C = πd
C = π(8)
C = 8π
Using an approximation of π as 3.14, we can estimate the circumference:
C ≈ 8 × 3.14
C ≈ 25.12
Therefore, the answer closest to the circumference of the circle is 25.12 inches.
Step-by-step explanation:
6. Which of the following is the turning point of the function y = (x-8)²-2?
(1) (8,-2)
(2) (-8, 2)
(3) (-8,-2)
(4) (8, 2)
Answer:2
Step-by-step explanation:bc
a newsletter publisher believes that 71% 71 % of their readers own a rolls royce. a testing firm believes this is inaccurate and performs a test to dispute the publisher's claim. after performing a test at the 0.02 0.02 level of significance, the testing firm fails to reject the null hypothesis. what is the conclusion regarding the publisher's claim?
We cannot claim that the newsletter publisher's statement is incorrect. Hence, the conclusion is uncertain.
The newsletter publisher's claim is uncertain after performing a test at the 0.02 level of significance as the testing firm fails to reject the null hypothesis.
In this case, we cannot claim that the publisher's statement is incorrect without additional tests and proof. Here is an explanation of the above statement.
A hypothesis test is conducted to find out whether or not there is sufficient evidence to contradict a hypothesis. In this case, the hypothesis test's null hypothesis claims that the newsletter publisher's statement is correct.
The alternate hypothesis claims that the newsletter publisher's claim is incorrect. As a result, the null hypothesis is represented by [tex]H_0[/tex]:
p = 0.71 (71%) and
the alternate hypothesis is represented by [tex]H_a[/tex]:
p ≠ 0.71 (71%).
Where 'p' denotes the percentage of newsletter readers who own a Rolls Royce.
The test statistic for a sample proportion can be calculated by
z = (p - P) / √(P(1 - P) / n)
Where 'p' denotes the sample proportion,
P denotes the population proportion, and
n denotes the sample size.
A two-tailed test is used because the alternate hypothesis is written as [tex]H_a[/tex]:
p ≠ 0.71 (71%).
At a 0.02 significance level, the test statistic's critical value is ±2.58 (round off) Because the test statistic does not fall in the rejection region, we fail to reject the null hypothesis.
For similar question on hypothesis test
https://brainly.com/question/15980493
#SPJ11
7.3.AP-5
Question content area top
Part 1
Find the area of the shape.
10 ft
7 ft
11 ft
10 ft
Question content area bottom
Part 1
The area is
enter your response here
▼
ft cubed .
ft.
ft squared .
(Type a whole number or a decimal.)
The area of the given shape is 73.5 ft squared
The question content area indicates that we need to find the area of a shape with dimensions of 10 ft, 7 ft, and 11 ft. However, the units are not specified, so it is assumed that we are dealing with a two-dimensional shape and the units are in feet.
To find the area of this shape, we need to use the appropriate formula for the shape.
Since the question does not provide any further information about the shape, we cannot determine the formula for certain. However, based on the dimensions given, we can assume that this is a trapezoid.
The shape can be divided into a rectangle and a triangle.
Calculate the area of the rectangle.
The dimensions of the rectangle are 7 ft by 10 ft.
To find the area, multiply the length by the width:
Area of rectangle = length × width = 7 ft × 10 ft = 70 ft²
Calculate the area of the triangle.
The base of the triangle is 10 ft, and its height is the difference between the 11 ft and 7 ft sides of the shape, which is 4 ft.
Multiply the base by the height and then divide by 2:
Area of triangle = (base × height) / 2 = (10 ft × 4 ft) / 2 = 20 ft²
Total area = area of rectangle + area of triangle = 70 ft² + 20 ft² = 90 ft²
The formula for the area of a trapezoid is:
Area = ((b1 + b2) / 2) * h
where b1 and b2 are the lengths of the two parallel sides, and h is the height (or perpendicular distance between the parallel sides).
Using the given dimensions, we can plug them into the formula:
Area = ((10 + 11) / 2) * 7
Area = (21 / 2) * 7
Area = 147 / 2
Area = 73.5 ft squared
For similar question on area :
https://brainly.com/question/27683633
#SPJ11
I need help with one of my math problems. I need to simplify, not answer it
20 divided by(4-(10-8)
Answer:
Step-by-step explanation:
20 ➗ (4 * (10 - 8)
10 - 8 = 2 * 4 = 8
Then, 20 ➗ 8 = 2.5
A rectangular poster has an area of 35 square feet. It is 5 ft. at its base. What is the
height of the poster?
The rectangular poster is 7 feet tall.
which has the form of a rectangle?The rectangular shape in two dimensions has four sides, four corners, and four right angles (90°). Equal and parallel opposing sides make form a rectangle. Being a two-dimensional form, a rectangle has length and breadth as its two dimensions.
The procedure for calculating a rectangle's area may be used to get the rectangular poster's height:
Area = length * width
In this case, we know that the area is 35 square feet and the width (or base) is 5 feet. So we can rearrange the formula to solve for the length (or height):
length = Area / width
Substituting the values we get:
length = 35 sq ft / 5 ft = 7 ft
To know more about rectangular visit:-
https://brainly.com/question/21308574
#SPJ1
A tangent segment is a line segment that has a point on the tangent line and on the center of the circle.
It is a true statement that tangent segment is a line segment that has a point on the tangent line and on the center of the circle.
What does tangent segment means on a Circle?In geometry, a tangent segment is a line segment that intersects a circle at exactly one point, known as the point of tangency. This line segment is called a tangent because it touches the circle at a single point and does not cross through the circle.
The tangent segment's length is determined by the distance between the point of tangency and a point on the line that is outside the circle, known as the external point. This distance is equal to the radius of the circle, as the radius is the distance between the center of the circle and any point on the circle's circumference.
Read more about tangent segment
brainly.com/question/4470346
#SPJ1
Evaluate the expression: |8| - 2 x |-3| + 4
22
10
42
6
Answer:
6
Step-by-step explanation:
What is the equivalent?
Drag the answer into the box to match the fragative.
The equivalent decimal of a fraction of 6/11 is given as follows:
0.5454.
How to obtain the equivalent decimal of a fraction?To obtain the equivalent decimal of a fraction, divide the numerator (the top number) by the denominator (the bottom number) using a calculator or long division.
The fraction for this problem is given as follows:
6/11.
The numerator and the denominator of the fraction are given as follows:
Numerator of 6.Denominator of 11.The division of 6 by 11 has a result of 0.5454, hence the equivalent decimal of the fraction is given as follows:
0.5454.
More can be learned about the equivalent decimal of a fraction at https://brainly.com/question/24807791
#SPJ1
Adam, Ben and Carly work out the mean of their ages.
Adam is 4 years older than the mean. Ben is 1 year younger than the mean.
Is Carly older or younger than the mean?
By how many years?
Answer:
messageAdam, Ben and Carly work out the mean of their ages.Adam is 4 years older than the mean. Ben is 1 year younger than the mean.Is Carly older or younger than the mean?By how many years?Let's start by finding the mean of their ages. We can do this by adding their ages and dividing by the number of people: Mean = (Adam's age + Ben's age + Carly's age) / 3 Let's call the mean "M" for now. We can use this to create two equations based on the information given: Adam = M + 4 Ben = M - 1 We can substitute these equations into the mean equation to get: M = (M + 4 + M - 1 + Carly's age) / 3 Simplifying this equation gives us: 3M = 2M + 3 + Carly's age Carly's age = M - 3 So Carly's age is younger than the mean by 3 years
help me please! thanks bud
Answer:
Steps:
1. Draw a 3 x 3 table
2. Place the titles on the left and top of the table (play sports and don't play sports on left for example and instruments on top)
3. Place the numbers inside accordingly
Hope this helped! Please mark brainliest!
Determine whether the function is a polynomial function. Check by setting in standard from, identifying leading coefficient, constant, Highest degree, and type of function
The function is not a polynomial function,
Leading coefficient, Constant, Highest degree, is not possible with a rational function, Type of function: Rational function
What is an expression?An expression is a mathematical equation that combines variables, numbers, and other mathematical operations to represent a value or a set of values. It can be simple or complex, and it is often used in algebra to solve problems and represent mathematical relationships.
We have the given function is, [tex]f(x)= 5x - 12 + x^3 + 9x^{-4} + x^2[/tex]
The standard form, means arranging the terms in descending order of degree; So,
[tex]f'(x) = x^3 + x^2 + 5x - 12 + 9x^{-4}[/tex]
No, the function f'(x) is not a polynomial function because it contains a term with a negative exponent, which makes it a rational function rather than a polynomial function.
To find the leading coefficient, constant, highest degree, and type of function of a polynomial function, we would put it in standard form, but this is not possible with a rational function.
Instead, we can identify that the term 9[tex]x^{-4}[/tex] is a rational term, which means it contains a variable raised to a negative exponent. Polynomial functions, by definition, cannot have terms with negative exponents, so f(x) is not a polynomial function.
In summary, the function [tex]f'(x) = x^3 + x^2 + 5x - 12 + 9x^{-4}[/tex] is a rational function, not a polynomial function, because it contains a term with a negative exponent.
To know more about expression, visit:
https://brainly.com/question/1859113
#SPJ1
Britney is mapping out a new running path around her local park. She is going to run west for 2.1 km, before turning 105" to the night and running another 3.3 km From there, she will run in a straight line back to her starting position. How far will Britney run in total? Give your answer correct to the nearest meter.
Answer:
Britney will run approximately 9,090 meters in total.
Step-by-step explanation:
To solve the problem, we can use the Law of Cosines to find the distance of the final straight line back to her starting position.
Let A be the starting position, B be the end of the first leg, and C be the end of the second leg. Then, we have:
AB = 2.1 km BC = 3.3 km ∠ABC = 180° - 105° = 75°
Using the Law of Cosines, we have:
AC² = AB² + BC² - 2(AB)(BC)cos(∠ABC)
AC² = (2.1)² + (3.3)² - 2(2.1)(3.3)cos(75°) AC ≈ 3.69 km
Therefore, Britney will run a total distance of approximately:
2.1 km + 3.3 km + 3.69 km ≈ 9.09 km
So, Britney will run approximately 9,090 meters in total.
What is the measure of the indicated (?) angle?
a
68 degrees
b
112 degrees
c
136 degrees
d
144 degrees
Answer:
c 136 degrees
Step-by-step explanation:
a surgical procedure requires choosing among four alternative methodologies. the first can result in five possible outcomes, the second can result in two possible outcomes, and the remaining methodologies can each result in three possible outcomes. what is the total number of outcomes possible?
A surgical procedure requires choosing among four alternative methodologies. the first can result in five possible outcomes, the second can result in two possible outcomes, and the remaining methodologies can each result in three possible outcomes. The total number of outcomes possible is 90.
The first one can result in five possible outcomes, the second one can result in two possible outcomes, and the remaining methodologies can each result in three possible outcomes. The total number of outcomes possible is a question the student needs an answer to.
To calculate the total number of outcomes, we have to multiply the number of results from the first methodology by the number of results from the second, third, and fourth methodologies. There are four alternative methodologies, and so we multiply the number of results from each methodology to calculate the total number of outcomes.However, we should use a calculator to solve this problem.
The first methodology can result in five possible outcomes, the second methodology can result in two possible outcomes, and the remaining methodologies can each result in three possible outcomes. We can use the following expression to determine the total number of outcomes:
5 × 2 × 3 × 3 = 90
for such more question on total number
https://brainly.com/question/9879870
#SPJ11
The graph of h(x) = -log(x + 5).
-6
d
h(x)
9
7
6
5
4
3
2
1
3 -2 -1 0
-2
دی
-4
-5
-6
1
2
3 4 5 6
What are the intercepts and asymptote of h(x)? Explain how to find these using the graph. Please help
Answer:
The function h(x) = -log(x + 5) has a vertical asymptote at x = -5, since the logarithm of a non-positive number is undefined. To find the intercepts of this function, we can set h(x) equal to zero and solve for x:
h(x) = 0
-log(x + 5) = 0
x + 5 = 1
x = -4
So the function has an x-intercept at (-4, 0). To find the y-intercept, we can set x equal to zero and evaluate h(x):
h(0) = -log(0 + 5) = -log(5)
So the function has a y-intercept at (0, -log(5)).
To verify these intercepts using the graph, we can look for the points where the graph intersects the x and y axes. The x intercept is where the graph crosses the x-axis, which in this case is at x = -4. The y-intercept is where the graph crosses the y-axis, which is at y = -log(5) or approximately -1.609. The vertical asymptote is the vertical line where the graph approaches but never touches. From the graph, we can see that this occurs at x = -5.
It is important to note that when graphing logarithmic functions, it is recommended to plot a few points, including the intercepts and vertical asymptote, to help visualize the graph accurately.
AUGH WHAT EVEN IS!!PLEASE HELP
The length of the base of the given parallelogram is 2 feet.
The area of a parallelogram is all the square units that fit inside, measured in square units (cm2, m2, in2, etc.). It is the area surrounded or enclosed by parallelograms in two places. The elements of a parallelogram. Since a rectangle and a parallelogram have the same properties, the area of the rectangle is the same as that of the parallelogram.
Given us the area in sq. feet but height in yards, So let's convert the height in feet instead.
We know, 1 yard = 3 feet
∴ Height = 5 feet.
Now, We know
⇒ Area = Base × Height
⇒ 10 = Base × 5
⇒ Base = 2 feet
Hence, The length of the base of the given parallelogram is 2 feet.
Learn more about Parallelogram:
https://brainly.com/question/555469
#SPJ1
please help i have until saturday
After answering the provided question, we can state that As a result, the equation shortcut is approximately 72.1 metres long. The length is 72.1 metres, rounded to the nearest tenth.
To calculate the length of the shortcut, we must apply the Pythagorean theorem, which states that the square of the hypotenuse (the longest side) in a right triangle is equal to the sum of the squares of the other two sides. The hypotenuse in this case is the shortcut PQ, and the other two sides are the distances from P to the park's corner (which we'll call A) and from Q to A.
shortcut length2 = 402 + 602
shortcut length2 = 1600 + 3600
shortcut length2 = 5200 = 72.1 metres
As a result, the shortcut is approximately 72.1 metres long. The length is 72.1 metres, rounded to the nearest tenth.
To know more about equation visit:
brainly.com/question/649785
#SPJ1
Find the perimeter of the shaded region. Round your answer to the nearest hundredth.
The perimeter is about _ units
The perimeter of the shaded region is 22.58 units.
What is perimeter of rectangle?
Perimeter of a rectangle is 2×(Length+Breadth).
Here in this figure we have three part. They are a rectangle and two semicircles.
Length of the rectangle is 13 unit and breadth is 6 unit
So, perimeter of the rectangle part = 2×(length+breadth) = 2×(13+6) = 38 unit
Again, diameter of two semicircles is 6 unit
So, radius of two semicircles will be [tex] \frac{6}{2} = 3 \: unit[/tex]
So, perimeter of one semicircle
[tex] = \pi \: r + 2r \\ = \pi \times 3 + 2 \times 3 \\ = 3\pi + 6[/tex]
Now, perimeter of two semicircles will be
[tex]2 \times (3\pi + 6) = 3(\pi + 2) \: unit[/tex]
If we subtract perimeter of two semicircles from the perimeter of rectangle then we will get perimeter of the shaded portion.
So, required perimeter of shaded region
[tex] = 38 - 3(\pi + 2) = (32 - 3\pi) = 22.58 \: unit[/tex]
Learn more about perimeter here,
https://brainly.com/question/25092270
#SPJ1
suppose the cpa practice advisor reports that the mean preparation fee for 2017 federal income tax returns was $273. use this price as the population mean and assume the population standard deviation of preparation fees is $100. (a) what is the probability that the mean price for a sample of 40 federal income tax returns is within $16 of the population mean? (round your answer to four decimal places.) (b) what is the probability that the mean price for a sample of 60 federal income tax returns is within $16 of the population mean? (round your answer to four decimal places.) (c) what is the probability that the mean price for a sample of 81 federal income tax returns is within $16 of the population mean?(round your answer to four decimal places.) (d) which, if any, of the sample sizes in parts (a), (b), and (c) would you recommend to ensure at least a 0.95 probability that the sample mean is within $16 of the population mean? (select all that apply.)
(a)The probability that the mean price for a sample of 40 federal income tax returns is within $16 of the population mean is 0.6884, (b)The probability that the mean price for a sample of 60 federal income tax returns is within $16 of the population mean is 0.7805. (c) The probability that the mean price for a sample of 81 federal income tax returns is within $16 of the population mean is 0.8502. (d) The best sample sizes are 153, and 154 so that at least a 0.95 probability that the sample mean is within $16 of the population mean
The solution to the given problem is as follows:A) For sample size of 40 Sample size, n=40Sample Mean, x = $273 Standard deviation of the population, σ= $100. Sampling Error = Standard error of mean = σ/√n = 100/√40 = $15.8114 therefore, the required probability is P(273-16 < x < 273+16) = P(256.99 < x < 289.0 1)Using the Central Limit Theorem, the standard normal distribution can be used for solving the problem.The required probability is given by;P(Z < (289.01 - 273)/15.81) - P(Z < (256.99 - 273)/15.81)P(Z < 1.012) - P(Z > -1.012) = 0.8453 - 0.1569 = 0.6884. (B) For sample size of 60, sample size, n=60 sample Mean, x = $273 standard deviation of the population, σ= $100 sampling Error = Standard error of mean = σ/√n = 100/√60 = $12.9155. therefore, the required probability is P(273-16 < x < 273+16) = P(256.99 < x < 289.01). Using the Central Limit Theorem, the standard normal distribution can be used for solving the problem.The required probability is given by;P(Z < (289.01 - 273)/12.92) - P(Z < (256.99 - 273)/12.92)P(Z < 1.2389) - P(Z > -1.2389) = 0.8907 - 0.1102 = 0.7805.
C) For sample size of 81Sample size, n=81, sample Mean, x = $273 standard deviation of the population, σ= $100 sampling Error = Standard error of mean = σ/√n = 100/√81 = $11.111. Therefore, the required probability is P(273-16 < x < 273+16) = P(256.99 < x < 289.01)Using the Central Limit Theorem, the standard normal distribution can be used for solving the problem.The required probability is given by;P(Z < (289.01 - 273)/11.11) - P(Z < (256.99 - 273)/11.11)P(Z < 1.4403) - P(Z > -1.4403) = 0.9251 - 0.0749 = 0.8502.D) To ensure that the sample mean is within $16 of the population mean with 95% confidence, we need to find out the sample size that has a probability of 0.95.Probability is given by;P(-1.96 < Z < 1.96) = 0.95The Z-scores are obtained from the standard normal distribution table or calculator. Here, the probability of Z being less than -1.96 is equal to the probability of Z being greater than 1.96. The Z-score for a 95% confidence interval is 1.96. Therefore,1.96 = (289.01 - 273)/σnFor n = 152.94For n = 153, 1.96 = (289.01 - 273)/σ√153The best sample sizes are 153, and 154 so that at least a 0.95 probability that the sample mean is within $16 of the population mean.
To know more about probability click here
https://brainly.com/question/15696262
#SPJ11
weight loss x runs a number of weight reduction centers within a large city. from the historical data it was found that the weight of the participants is normally distributed with a mean of 175 lbs and a standard deviation of 35 lbs. calculate the standard error of the average sample weight when 15 participants are randomly selected for the sample? enter your answer rounded to two decimal places. for example, if your answer is 12.345 then enter as 12.35 in the answer box.
The standard error of the average sample weight when 15 participants are randomly selected for the sample is 9.05 (rounded to two decimal places).
The standard error of the average sample weight when 15 participants are randomly selected for the sample can be calculated using the formula given below:SE = σ/√nWhere,σ = standard deviation of the populationn = sample sizeSE = standard error of the meansubstituting the given values,SE = 35/√15 = 9.05
Note:When using the given formula, it is important to note that it assumes a normal distribution of sample means. The standard error is used to estimate the true value of the mean from the sample data. The larger the sample size, the smaller the standard error. The smaller the standard error, the more precise the estimate of the true value of the mean.
Learn more about Standard error
brainly.com/question/13179711
#SPJ11
The Hcf and Lcm of two numbers are 4 and 288. What are the two numbers?
Step-by-step explanation:
Let the two numbers be x and y.
We know that:
HCF(x,y) × LCM(x,y) = x × y
Substituting the given values:
4 × 288 = x × y
Simplifying:
x × y = 1152
Now we need to find two numbers whose product is 1152 and HCF is 4. One way to do this is to list all the factors of 1152 and find a pair of factors whose HCF is 4. However, we can also solve this problem by prime factorization.
Prime factorization of 1152:
1152 = 2^7 × 3^2
To find the two numbers, we need to divide these factors into two groups, one group for x and the other group for y. We can choose any combination of factors, as long as their product is 1152. However, we also need to ensure that the HCF of x and y is 4.
One possible way to do this is to choose one factor of 2 from the prime factorization of 1152 for x and the remaining factors for y:
x = 2^1 × 3^a
y = 2^6 × 3^b
where a and b are non-negative integers.
Multiplying x and y and equating to 1152, we get:
2^1 × 3^a × 2^6 × 3^b = 1152
Simplifying:
2^7 × 3^(a+b) = 1152
Since 1152 = 2^7 × 3^2, we have:
2^7 × 3^(a+b) = 2^7 × 3^2
Equating the exponents of 2, we get:
7 + 0 = 7
a + b = 2
Since the HCF of x and y is 4, we need to ensure that both x and y have a factor of 2^2 = 4. Thus, we choose a = 2 and b = 0:
x = 2^1 × 3^2 = 12
y = 2^6 × 3^0 = 64
Therefore, the two numbers are 12 and 64.
R(55, -75) W(-15,-40)
Find the slope
Answer:
- 1/2
Step-by-step explanation:
We can use the slope formula to find the slope.
m = ( y2-y1)/(x2-x1)
= ( -40 - -75)/(-15 - 55)
= (-40+75)/( -15-55)
=35/-70
=- 1/2
Answer:
m = -0.5
Step-by-step explanation:
Given that, ( Coordinates of a line )
( 55, - 75 ) ⇒ ( x₁ , y₁ )
( - 15 , - 40 ) ⇒ ( x₂ , y₂ )
The formula to find the slope of a line is:
[tex]\sf m =\frac{y_1-y_2}{x_1-x_2}[/tex]
Let us find it now.
[tex]\sf m =\frac{y_1-y_2}{x_1-x_2} \\\\\sf m =\frac{-75-(-40)}{55-(-15)} \\\\\sf m =\frac{-75+40}{55+15} \\\\\sf m =\frac{-35}{70} \\\\m = -0.5[/tex]
21.
Ada Mae bought a pen for $1.50 and 3 DVDs that each cost the same amount. She spent $22.50
in all. Which equation models the situation?
A, 1.5+3d=22.5
B. 3(1.5) +d=22.5
C. 3d-1.5=22.5
D. 1.5=22.5+3d
Items: 1 Pen: 1.50
3 DVDS: ???
Total : 22.50
It is A, 1.5+3d=22.5.
Hope this helps!!!
It is not B because you are not multiplying the number and cost of 3 DVDS by the cost of one pen.
It is not C because you are not subtracting to find the total cost. You are adding.
It is not D because 3d is part of the total cost so that option just doesn't make sense.
A bird travels 71. 2 kilometers after 2 hours of flying. Complete the equation to represent the number of hours, t, the bird will take to fly d kilometers at this rate
the equation to represent the number of hours, t, the bird will take to fly d kilometers at this rate is t = 2d / 71.2
We can use the formula for distance, rate, and time:
distance = rate x time
We can rearrange this formula to solve for time:
time = distance / rate
If we substitute the given distance of 71.2 km and rate of (71.2 km / 2 hours) into this formula, we can find the time it took the bird to fly 71.2 km:
time = 71.2 km / (71.2 km / 2 hours) = 2 hours
Now, we can use the same formula to find the time it will take the bird to fly d kilometers:
time = d km / (71.2 km / 2 hours) = 2d / 71.2 hours
Therefore, the equation to represent the number of hours, t, the bird will take to fly d kilometers at this rate is t = 2d / 71.2
To know more about equation, visit: brainly.com/question/29538993
#SPJ4
What is the axis of symmetry?
x=