Using the radians we know that the length of the arc in terms of π is s = 1.53 * π * 12 ft or s = 57.60 ft.
What is a circle?
All points in a plane that are at a specific distance from a specific point, the center, form a circle.
In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.
So, the central angle of degrees must first be converted to radians.
θ(rad) = 275/180 * π = 1.53 rad
Then, by multiplying the Central angle (in rad units) by the circle radius r, the arc length may be determined:
s = θ * r
Changing the θ and r values:
s = 1.53 * π * 12 ft
s = 57.60 ft
Therefore, using the radians we know that the length of the arc in terms of π is s = 1.53 * π * 12 ft or s = 57.60 ft.
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Correct question:
Find the length of the arc, s, on a circle of radius r intercepted by a central angle θ. Express arc length in terms of π. Then round your answer to two decimal places.
Radius, r = 12 feet; Central angle, θ = 275
The point (4, -12) is on a circle with center (-2,-4). Write the standard equation of the circle.
(x ?)² + (y ?)² =
the standard equation of the circle is (x + 2)² + (y + 4)²= 100 . we can use The standard equation of a circle with center (h,k) and radius r is:
(x - h)² + (y - k)² = r²
what is standard equation of circle ?
The standard equation of a circle with center (h,k) and radius r where (x,y) are the coordinates of any point on the circle. This equation represents all the points in the plane that are a fixed distance (the radius r) from the center of the circle (h,k).
In the given question,
The standard equation of a circle with center (h,k) and radius r is:
(x - h)² + (y - k)² = r²
In this case, we know that the point (4, -12) is on a circle with center (-2, -4). We also know that the radius of the circle is the distance between the center and the point on the circle, which we can find using the distance formula:
r = √((4 - (-2))² + (-12 - (-4))²)
r = √(6² + (-8)²)
r = √(100)
r = 10
So the equation of the circle is:
(x - (-2))² + (y - (-4))² = 10²
(x + 2)² + (y + 4)² = 100
Therefore, the standard equation of the circle is:
(x + 2)² + (y + 4)²= 100
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EREGENT PLEASE HURRY DONT LIE
7 students divided by 8 sandwiches. How many pieces of the sandwiches does each student get?
If 7 students divided by 8 sandwiches each student gets 8 pieces of sandwich.
If 7 students are divided by 8 sandwiches, we can start by calculating the total number of pieces of sandwich available:
Total number of pieces of sandwich = 7 * 8 = 56
So there are 56 pieces of sandwich available for 7 students.
To find out how many pieces of sandwich each student gets, we divide the total number of pieces of sandwich by the number of students:
Each student gets 56 / 7 = 8 pieces of sandwich.
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i need to find the product
Answer:
c ik this because I took the same question as you
The product of the given algebraic expression is [tex]\frac{4}{(x-1)}[/tex].
The given expression is [tex]\frac{8x+8}{x^2-2x+1} .\frac{x-1}{2x+2}[/tex].
Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.
Here, [tex]\frac{4(2x+2)}{x^2-1x-1x+1} \times \frac{x-1}{2x+2}[/tex]
= [tex]\frac{4(2x+2)}{x(x-1)-1(x-1)} \times \frac{x-1}{2x+2}[/tex]
= [tex]\frac{4(2x+2)}{(x-1)(x-1)} \times \frac{x-1}{2x+2}[/tex]
Cancel the same factors, that is
= [tex]\frac{4}{(x-1)} \times \frac{1}{1}[/tex]
= [tex]\frac{4}{(x-1)}[/tex]
Therefore, the product of the given algebraic expression is [tex]\frac{4}{(x-1)}[/tex].
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PLEASE HELP I NEED HELP
Question 1
(Comparing Data LC)
The histograms display the frequency of temperatures in two different locations in a 30-day period.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. A shaded bar stops at 10 above 60 to 69, at 9 above 70 to 79, at 5 above 80 to 89, at 4 above 90 to 99, and at 2 above 100 to 109. There is no shaded bar above 110 to 119. The graph is titled Temps in Sunny Town.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 16. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 12 above 80 to 89, at 6 above 90 to 99, at 4 above 100 to 109, and at 2 above 110 to 119. The graph is titled Temps in Desert Landing.
When comparing the data, which measure of variability should be used for both sets of data to determine the location with the most consistent temperature?
IQR, because Sunny Town is skewed
IQR, because Desert Landing is symmetric
Range, because Sunny Town is skewed
Range, because Desert Landing is symmetric
Question 2
(Comparing Data MC)
The data given represents the number of gallons of coffee sold per hour at two different coffee shops.
Coffee Ground
1.5 20 3.5
12 2 5
11 7 2.5
9.5 3 5
Wide Awake
2.5 10 4
18 4 3
3 6.5 15
6 5 2.5
Compare the data and use the correct measure of center to determine which shop typically sells the most amount of coffee per hour. Explain.
Wide Awake, with a median value of 4.5 gallons
Wide Awake, with a mean value of about 4.5 gallons
Coffee Ground, with a mean value of about 5 gallons
Coffee Ground, with a median value of 5 gallons
Question 3
The box plots display measures from data collected when 20 people were asked about their wait time at a drive-thru restaurant window.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 8.5 to 15.5 on the number line. A line in the box is at 12. The lines outside the box end at 3 and 27. The graph is titled Super Fast Food.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 9.5 to 24 on the number line. A line in the box is at 15.5. The lines outside the box end at 2 and 30. The graph is titled Burger Quick.
Which drive-thru is able to estimate their wait time more consistently and why?
Burger Quick, because it has a smaller IQR
Burger Quick, because it has a smaller range
Super Fast Food, because it has a smaller IQR
Super Fast Food, because it has a smaller range
Question 4
The line plots represent data collected on the travel times to school from two groups of 15 students.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 4,6,14, and 28. There are two dots above 10, 12, 18, and 22. There are three dots above 16. The graph is titled Bus 47 Travel Times.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 10,16,20, and 28. There are two dots above 8 and 14. There are three dots above18. There are four dots above 12. The graph is titled Bus 14 Travel Times.
Compare the data and use the correct measure of variability to determine which bus is the most consistent. Explain your answer.
Bus 47, with an IQR of 8
Bus 14, with an IQR of 6
Bus 47, with a range of 8
Bus 14, with a range of 6
Question 5
The data given represents the height of basketball players, in inches, on two different girls' teams.
Allstars
73 62 60
63 72 65
69 68 71
66 70 67
60 70 71
Champs
62 69 65
68 60 70
70 58 67
66 75 70
69 67 60
Compare the data and use the correct measure of center to determine which team typically has the tallest players. Explain your answer.
The Allstars, with a mean of about 67.1 inches
The Champs, with a mean of about 66.4 inches
The Allstars, with a median of about 68 inches
The Champs, with a median of about 67 inches
Question 6
The stem-and-leaf plot displays data collected on the size of 15 classes at two different schools.
Bay Side School Seaside School
8, 6, 5 0 5, 8
8, 6, 5, 4, 2, 0 1 0, 1, 2, 5, 6, 8
5, 3, 2, 0, 0 2 5, 5, 7, 7, 8
3 0, 6
2 4
Key: 2 | 1 | 0 means 12 for Bay Side and 10 for Seaside
Part A: Calculate the measures of center. Show all work. (2 points)
Part B: Calculate the measures of variability. Show all work. (1 point)
Part C: If you are interested in a smaller class size, which school is a better choice for you? Explain your reasoning. (1 point)
1. IQR, because Sunny Town is skewed 2. Both coffee shops typically sell the same amount of coffee per hour. 3. Burger Quick is able to estimate their wait time more consistently than Super Fast Food, since it has a smaller IQR.
What is IQR?The middle 50% of a dataset are represented by the interquartile range (IQR), a measure of variability. It is computed as IQR = Q3 - Q1, where IQR is the difference between the first and third quartiles (Q1 and Q3). The dataset is divided into four equal portions by quartiles, with Q1 standing for the 25th percentile and Q3 for the 75th percentile. The IQR is an effective tool for comparing the spread of datasets since it is a robust measure of variability that is unaffected by extreme values or skewness.
To determine the location with the most consistent temperature use IQR, since it is the best way to compare the consistency of temperature readings between the two sites.
2. The mean is:
(1.5 + 20 + 3.5 + 12 + 2 + 5 + 11 + 7 + 2.5 + 9.5 + 3 + 5) / 12 = 6.25
Arrange the values in order: 1.5, 2, 3, 3.5, 5, 7, 9.5, 11, 12, 20
The middle two values are 7 and 9.5.
The median is (7 + 9.5) / 2 = 8.25
Thus, we can conclude that both coffee shops typically sell the same amount of coffee per hour.
3. Super Fast Food:
IQR of 7.5 (15.5 - 8.5) and a range of 24 (27 - 3)
Burger Quick:
IQR of 15 (24 - 9.5) and a range of 28 (30 - 2).
Burger Quick is able to estimate their wait time more consistently
than Super Fast Food, since it has a smaller IQR.
4. Bus 47 :
IQR of 8 (16 - 8) and a range of 24 (28 - 4)
Bus 14:
IQR of 6 (18 - 12) and a range of 18 (28 - 10).
Hence, Bus 14 is the most consistent, since it has a smaller IQR.
5. For the Allstars, the mean is:
(73 + 62 + 60 + 63 + 72 + 65 + 69 + 68 + 71 + 66 + 70 + 67 + 60 + 70 + 71) / 15 = 67.
The Champs, with a median of about 67 inches
6. For the given data:
Median = (5 + 5) / 2 = 5
The measures of center for Bay Side School and Seaside School are both 5.
B: Range = 8 - 0 = 8.
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Determine the surface area of a right circular cone that has a slant height of 5.8 ft and a diameter of 6.4 ft? Round your answer to the nearest whole.
After answering the presented question, we can conclude that Rounding this to the nearest whole number, we get a surface area of 91 sq. ft.
What is diameter?In geometry, the diameter of a circle is any straight line segment that has an endpoint on the circle and travels through its centre. Another way to put it is the longest chord of a circle. Either idea can be used to define the diameter of a sphere. The diameter is the length of the line that runs tangent to the two points at either end of the circle. If you take length to be the distance between two points, diameter equals length. The diameter of a circle is the distance between its two furthest points.
First, we need to find the radius of the cone:
[tex]radius = diameter/2 = 6.4/2 = 3.2 ft[/tex]
Now we can use the Pythagorean theorem to find the height of the cone:
[tex]height^2 = slant height^2 - radius^2[/tex]
[tex]height^2 = 5.8^2 - 3.2^2[/tex]
[tex]height^2 = 20.84[/tex]
height ≈ 4.56 ft
Next, we can find the surface area of the cone by adding the area of the base to the lateral surface area. The base is a circle with radius 3.2 ft, so its area is:
base area =[tex]\pi (radius)^2[/tex]
base area =[tex]\pi (3.2)^2[/tex]
base area ≈ 32.17 sq. ft.
The lateral surface area is the curved surface area of the cone, which can be found using the slant height and the radius:
lateral surface area = [tex]\pi (radius)(slant height)[/tex]
lateral surface area = [tex]\pi (3.2)(5.8)[/tex]
lateral surface area ≈ 58.92 sq. ft.
Therefore, the total surface area is:
total surface area ≈ base area + lateral surface area
total surface area ≈ [tex]32.17 + 58.92[/tex]
total surface area ≈ 91.09 sq. ft
Rounding this to the nearest whole number, we get a surface area of 91 sq. ft.
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My sister is 11 years old. My brother says that his age minus nineteen is equal to my sister's age. How old is my brother? Enter an equation, using b as your variable, to find how old my brother is. The equation is My brother is years old.
Answer:
He would be 28
Step-by-step explanation:
You would add the 11 plus the 17 and you should get 28.To check your answer, you would now subtract the 17 from the 28.Your answer should be 11.you run a one-sample z test (z.test) in excel and get the following result: 0.7326 what does the output of 0.7326 represent? group of answer choices the sample value the critical value the one-tailed probability value the significance level
The output of 0.7326 represents the test statistic (Z-score) computed from the 1-sample Z-test in Excel.
It tells you how many standard deviations the sample mean is from the population mean under the null hypothesis.
A test statistic (Z-score) is a numerical value used in statistical hypothesis testing to assess the evidence against the null hypothesis.
A test statistic measures the difference between a sample statistic (eg sample mean) and the corresponding population parameter (eg population mean) assuming the null hypothesis is true.
For the Z-test, the test statistic is computed as
z = (x - μ) / (σ / √n)
where x = sample mean,
μ = population mean,
σ= population standard deviation,
and n = sample size.
The resulting Z-score indicates how many standard deviations the sample mean is from the population mean, assuming the null hypothesis is true.
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-8(2x-4) i need help help
Answer:
Therefore, -8(2x-4) simplifies to -16x + 32.
Step-by-step explanation:
-8 * 2x - (-8 * 4)
Simplifying this expression further gives:
-16x + 32
Therefore, -8(2x-4) simplifies to -16x + 32.
Answer:
Step-by-step explanation:
8. true or false: the population parameter will always be between the lower and upper bounds of the confidence interval. 9. true or false: the sample statistic will always be between the lower and upper bounds of the confidence interval.
The population parameter will always be between lower and upper bounds of the confidence interval. - True, whereas sample statistic will always be between lower and upper bounds of the confidence interval - False
With a certain degree of certainty, the population parameter is anticipated to lie between the lower and higher limits of the confidence interval. The confidence interval, which gives an interval estimate of the unidentified population parameter, is created based on the sample data. The interval's level of confidence shows the amount of ambiguity we are prepared to accept when determining the actual population parameter.
The confidence interval's lower and upper limits may or may not be met by the sample statistic used to compute them. A single point estimate, the sample figure is susceptible to sampling error. On the other hand, based on the observed sample data and the selected degree of confidence, the confidence interval is a range of values that we can be fairly confident includes the true population parameter.
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Mr. Foster is a librarian at Eastside Library. In examining a random sample of the library's book collection, he found the following.
722 books had no damage,
75 books had minor damage, and
29 books had maior damage.
Based on this sample, how many of the 70,500 books in the collection should Mr. Foster expect to have no damage or minor damage? Round your answer to the nearest whole number. Do not round any intermediate calculations.
The number of books that had no damage or minor damage in the sample is:
722 + 75 = 797
To estimate the number of books in the entire collection that would have no damage or minor damage, we can assume that the proportion of books with no or minor damage in the sample is approximately equal to the proportion of books with no or minor damage in the entire collection.
The proportion of books with no or minor damage in the sample is:
797 / (722 + 75 + 29) = 0.9064
So we can estimate the number of books with no damage or minor damage in the entire collection as:
0.9064 x 70,500 = 63,912.6
Rounding to the nearest whole number, we get:
63,913
The citizens of a city were asked to choose their favorite pet. The circle graph shows how the citizens answered. If 95,000 citizens answered the question, how many chose
Snakes or Dogs?
fish 13%
dogs 26%
birds 21%
cats 23%
snakes 10%
hamsters 7%
First, we need to calculate the percentage of citizens who chose either Snakes or Dogs.
The percentage of citizens who chose Dogs is 26%, which is equivalent to 0.26 as a decimal.
The percentage of citizens who chose Snakes is 10%, which is equivalent to 0.10 as a decimal.
To find the number of citizens who chose either Snakes or Dogs, we need to multiply the total number of citizens by the combined percentage of Snakes and Dogs:
0.26 + 0.10 = 0.36
So the combined percentage of Snakes and Dogs is 36%.
To find the number of citizens who chose Snakes or Dogs, we can multiply the total number of citizens by this percentage:
0.36 x 95,000 = 34,200
The ratio of girls to boys on team 6-5 is 4:5. If there are 99 students, how many boys are there
Answer:
There are 55 boys.
Step-by-step explanation:
The ratio of
girls: boys:total
4 5 4+5
4 5 9
The total is 99
To get from 9 to 99, we multiply by 11.
girls: boys:total
4*11 5*11 9*11
44 55 99
There are 55 boys.
The original price of a jar of paint is $1.20.The store manager gets a 10% discount for 50 jars of paint. How much does the store manager pay for 50 jars of paint?
Step-by-step explanation:
10 % off means you pay 90 %
the price of 50 jars times 90 % is:
50 * 1.20 * .90 = $ 54.00
Find the value of x, y and z
The values of x, y, and z in the given rhombus are: x = -31, y = 20, z = -87.
What do you mean by Equation ?An equation is a mathematical statement saying that two amounts or values are the same, for example 6 x4=12x
We know that the side of a rhombus are equal in length.therefore we can solve the given equation
4y + 8 = -3x - 5 = -z + 1 = 88
Solving each equation for the variables, we get:
4y + 8 = 88
4y = 80
y = 20
-3x - 5 = 88
-3x = 93
x = -31
-z + 1 = 88
-z = 87
z = -87
Heance , the values of x, y, and z in the given rhombus are:
x = -31, y = 20, z = -87.
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There are many cones with a radius of 7 units the equation v= 6pi h relates the height of the cone in units and the volume of the cone in cubic units complete the table using 3.14 for pi
Completed table is shown below. With this h number, we can calculate the cone's volume as V = (1/3)(72)h[tex]\pi[/tex] = 49/3h[tex]\pi[/tex] = 6[tex]\pi[/tex]h = 131.88.
To complete the table relating the height and volume of cones with a radius of 7 units using the equation[tex]v = 6\pi h[/tex], we need to substitute the radius value of 7 units into the formula for volume and then solve for height.
Height (h) Volume (V)
1 131.88
2 263.76
3 395.64
4 527.52
5 659.4
To obtain volume for each height, we plug in radius value of 7 units into the formula for the volume of a cone, which is given by [tex]V = (1/3)\pi r^{2} h[/tex]. This gives us [tex]V = (1/3)\pi (7^{2} )h = 49/3\pi h[/tex],
which simplifies to V = 16.33h. Then we substitute this expression for V into given equation [tex]v = 6\pi h[/tex] to obtain [tex]16.33h = 6\pi h[/tex], and solve for h to obtain h = 6.56.
Using this value of h, we can obtain the volume of the cone as [tex]V = (1/3)\pi (7x^{2} )h = \\49/3\pi h = \\6\pi h = \\131.88[/tex]
After that, by multiplying the value of h by 16.33 and rounding to two decimal places, we can determine the volumes for the other heights in the table.
Therefore, the completed table is as shown above.
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The rectangular
base of a
20ft tall storage unit is shown
below. Which statement is
FALSE?
a)
b)
c)
The area of the
base is 30ft²
The area is 26ft²
The perimeter is
26ft
d) The perimeter is
(3+3)+(10+10)
MD
Th
3ft
Oft
Answer:
The statement that is FALSE is b) "The area is 26ft²".
Mia buys 50 coats at $28 each.
She sells 38 of these coats at $49 each.
She sells the rest of the coats at $40 each.
Find the overall percentage profit Mia has made on these coats.
Answer: 1264.2857%
Step-by-step explanation:
Answer:
She earned 67.29% profit
Step-by-step explanation:
First let's find how much she spent on the coats.
50 x $28
$1400
So, her expense was $1400
Now, let's find how much she earned selling these coats.
We know she sold 38 of these coats at $49 each. Let's find how much she earned for these 38 coats.
38 x $49
$1862
She earned $1862 on these 38 coats.
Now, let's find how much she earned on the rest of the coats (50-38 which is 12). We know she sold the remaining for $40 each.
12 x $40
$480
She earned $480 on the rest of the coats.
The total she earned $2342
To find the profit:
Profit= $ Earned - Expenses
Profit= 2342-1400
Profit=$942
The question is asking for the percentage.
To find the percentage, we can use the percentage formula:
[tex]\frac{Profit}{Expense}[/tex] x 100
We know that the profit is $942 and the expense is $1400
(We want to find how much profit she made out of the expense)
[tex]\frac{942}{1400}[/tex] x [tex]\frac{100}{1}[/tex]
If you round your answer, you will get 67.29
Answer: She earned 67.29% profit
Match the term on the left with the equivalent term on the right.
(x)(2)
x/2
5+x
(1/5)x
↑
(x)/5
2x
(1/2)x
5/x
By answering the presented question, we may conclude that the value of the equation is 5/x --> x/5 or (1/5)x
What is equation?In mathematics, an equation is a statement that states the equivalence of two expressions. An equation is made up of two sides separated by an algebraic equation (=).
For example, the argument contends that the phrase "2x Plus 3" equals the number "9." The purpose of equation solving is to identify the value or values of the variable(s) that will make the equation true.
Simple or complicated equations, regular or nonlinear, with one or more components are all possible. For example, in the equation [tex]"x2 + 2x - 3 = 0,"[/tex] the variable x is raised to the second power. Lines are utilized in many areas of mathematics, including algebra, calculus, and geometry.
[tex](x)(2) -- > 2x[/tex]
[tex]x/2 -- > 0.5x or (1/2)x[/tex]
[tex]5+x -- > x+5[/tex]
[tex](1/5)x -- > x/5 or (x \times 0.2)[/tex]
[tex](x)/5 -- > 0.2x or (1/5)x[/tex]
2x --> same as (x)(2)
[tex](1/2)x -- > 0.5x or x/2[/tex]
Therefore, [tex]5/x -- > x/5 or (1/5)x[/tex]
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In a circle dance, everyone is evenly spaced around a circle and has
a number in the order 1, 2, 3, 4, 5, ... , and so on. The dancer with
number 15 is directly opposite dancer number 3. How many dancers
are in the circle?
In a circle dance, there are 17 dancers in the circle.
What is circle dance?Circle dance is a type of folk dance that involves people holding hands and dancing in a circular formation. The dancers move around in a circle, following a set of steps or patterns, and the dance may include turns, hops, and other movements.
According to question:In a circle dance, the total number of dancers is equal to the sum of the dancers on opposite sides of the circle.
Let's assume there are "x" dancers in the circle.
Since dancer 15 is directly opposite dancer 3, there are (x - 1) dancers between them.
Therefore, the sum of the dancers on opposite sides of the circle is (15 + 3) + (x - 1) = (x + 17).
Since the dancers are evenly spaced around the circle, the sum of the dancers on opposite sides of the circle is equal to the total number of dancers in the circle.
So we can write:
x + 17 = x
Solving for x, we get:
x = 17
Therefore, there are 17 dancers in the circle.
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give the percentage of measurements in a data set that are above and below each of the following percentiles. a. th percentile b. th percentile c. th percentile d. th percentile
The percentage of measurements in a data set that are above and below each of the following percentiles are 68%, 95% and 99.7%.
We need to calculate the percentage of the measurements contained in each of the following intervals:
According to the empirical rule, approximately 68% of the measurements in a normally distributed data set will fall within one standard deviation of the mean. Therefore, approximately 68% of the measurements will fall within the interval (mean - s, mean + s).
Similarly, approximately 95% of the measurements in a normally distributed data set will fall within two standard deviations of the mean. Therefore, approximately 95% of the measurements will fall within the interval (mean - 2s, mean + 2s).
Likewise, approximately 99.7% of the measurements in a normally distributed data set will fall within three standard deviations of the mean. Therefore, approximately 99.7% of the measurements will fall within the interval (mean - 3s, mean + 3s).
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(3x²y³ + x² - 7x³y²) - (4x³y² - 6y³ + 2x²)
The simplified expression for the given variables is -7x³y² + 3x²y³ + 6y³.
What is order of operation?A set of principles called the algebraic order of operations specifies the order in which mathematical operations should be carried out in order to simplify equations. The following is the order of events:
Operation inside parentheses should come first. Simplify exponential formulas by using exponents.
Division and multiplication should be done from left to right.
Operationally, add and subtract should be done from left to right.
The given expression can be simplifies as follows:
(3x²y³ + x² - 7x³y²) - (4x³y² - 6y³ + 2x²)
= 3x²y³ + x² - 7x³y² - 4x³y² + 6y³ - 2x²
= -7x³y² + 3x²y³ + 6y³
Hence, the simplified expression is -7x³y² + 3x²y³ + 6y³.
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O A. (x, y) - (x - 2, y+ 6)
O B. (x, y) - (x+ 2, y - 6)
O C. (x, y) - (x - 6, y + 2)
O D. (x, y) - (x+ 6, y - 2)
The answer is C. (x,y) - (x - 6, y + 2)
Note that A, B, C, and D are single decimal digits (from 0 through 9), although they don't have to be
unique (e.g., B and D could be equal). AB is then a two-digit decimal integer, BA is its reverse, and
CDC is a three-digit decimal number
A and B can have values that would give a sum of 11 when they are added together, such as (2,9), (3,8), (4,7), and (5,6).
Here, it is evident that since
AB+ BA= CDC
the hundreds and ones digit of the answer are equal and since we are talking about 2 digit numbers, hundreds place C can only be 1 since it is obtained from carry of the tens place (B+A) and the maximum carry that a 2 digit number can give is 1 (99+99 gives carry 1).
Also, D must be equal to C+1 since it is obtained by B+A and carry of ones place.
C=A+B= 1
D=C+1= 2
The possible values of A and B can be the ones that result in 11 when added, i.e. (2,9),(3,8),(4,7) and (5,6).
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Complete question is attached below
1/2(x-3)(x+5) Find the vertex and write it as an ordered pair
The vertex of the parabola is (-2, -3/2).
First, let's expand the given expression:
[tex]1/2(x-3)(x+5) = 1/2(x^2 + 2x - 15)[/tex]
Now, we can see that the coefficient of[tex]x^2[/tex] is positive, which means the parabola opens upwards.
To find the vertex, we can use the formula:
Vertex = (-b/2a, f(-b/2a))
where a = 1/2, b = 2, and f(x) =[tex]1/2(x^2 + 2x - 15).[/tex]
Substituting the values, we get:
Vertex = (-2/(21/2), f(-2/(21/2))) = (-2, f(-2))
To find f(-2), we can substitute x = -2 in the expression for f(x):
f(x) = [tex]1/2(x^2 + 2x - 15)[/tex]
f(-2) = [tex]1/2((-2)^2 + 2(-2) - 15)[/tex]
= 1/2(-3)
= -3/2
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SEE PHOTO SOLVE ONLY d NOT OTHERS
What is limit of the function f(x) at x = 1 ?
Answer:
Step-by-step explanation:
[tex]f(x)=\frac{(x-1)(x+1)}{x-1}[/tex]
[tex]=x+1[/tex]
Limit is found by substitution: Limit = 1+1 = 2
jordan's mom bought 7 77 packs of juice boxes for the team to drink after practice. each pack had 8 88 boxes of juice. after the team drank as much juice as they wanted, there were 29 2929 boxes of juice remaining. the team only opened each pack after they drank all the boxes from the pack before. how many packs of juice did the team open? packs
The team opened 4 packs of juice.
How to find opened packs?To find out how many packs of juice the team opened, follow these steps:
1. First, find the total number of juice boxes bought by multiplying the number of packs by the number of boxes in each pack: 7 packs × 8 boxes = 56 boxes.
2. Next, subtract the remaining boxes of juice to find out how many boxes the team drank: 56 boxes - 29 boxes = 27 boxes.
3. Finally, divide the number of boxes the team drank by the number of boxes in each pack to find the number of packs they opened: 27 boxes ÷ 8 boxes = 3.375 packs.
Since they only opened each pack after they drank all the boxes from the pack before, the team opened 4 packs of juice.
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a company employs eight people and plans to select a group of five of these employees to receive advanced training. how many ways can the group of five employees be selected?
There are 56 ways to select a group of five employees from the eight employees in the company for advanced training.
To select a group of five employees from a company that employs eight people, you can use the concept of combinations.
A combination is the selection of items from a larger set, where the order of items does not matter.
In this case, we want to choose 5 employees from a group of 8.
The formula for calculating combinations is:
C(n, k) = n! / (k!(n-k)!)
Where n is the total number of items, k is the number of items you want to select, and ! denotes the factorial.
So, for this problem:
n = 8 (total employees)
k = 5 (employees to be selected)
Now, we can plug these values into the formula:
C(8, 5) = 8! / (5!(8-5)!)
C(8, 5) = 8! / (5!3!)
C(8, 5) = (8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) / ((5 × 4 × 3 × 2 × 1)(3 × 2 × 1))
C(8, 5) = (8 × 7 × 6) / (3 × 2 × 1)
C(8, 5) = (336) / (6)
C(8, 5) = 56
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true or false. determine if the following statements are true or false, and explain your reasoning. if false, state how it could be corrected. a. if a given value (for example, the null hypothesized value of a parameter) is within a 95% confidence interval, it will also be within a 99% confidence interval. b. decreasing the significance level ($\alpha$) will increase the probability of making a type 1 error. c. suppose the null hypothesis is p
Answer:
True
Step-by-step explanation:
The following parts can be answered by the concept of confidence interval.
a. True
b. False
c. Incomplete statement, please provide complete statement.
a. True. A 95% confidence interval includes the range of values that are consistent with the observed data at the 95% level of confidence. Since a 99% confidence interval is wider than a 95% confidence interval, it must also include the null hypothesized value within it.
b. False. Decreasing the significance level ($\alpha$) reduces the probability of making a type 1 error, as it sets a higher threshold for rejecting the null hypothesis.
c. The statement is incomplete, and therefore cannot be evaluated.
Therefore, if a given value is within a 95% confidence interval, it will also be within a 99% confidence interval. However, decreasing the significance level ($\alpha$) reduces the probability of making a type 1 error. It is important to provide a complete statement for proper evaluation
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the billy bob landed on the coordinate plane at (-3,3 ), bertha landed at ( 1,0 ). how far did billy bob land from bertha
Answer:
5 units
Step-by-step explanation:
The distance from -3 to 1 is 4 and the distance from 3 to 0 is 3. Use the Pythagorean Theorem.
[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]
[tex]4^{2}[/tex] + [tex]3^{2}[/tex] = [tex]c^{2}[/tex]
16 + 9 = [tex]c^{2}[/tex]
25 = [tex]c^{2}[/tex]
[tex]\sqrt{25}[/tex] = [tex]\sqrt{c^{2} }[/tex]
5 = c
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