Solve for length of segment d.
= 4 cm
b = 12 cm
c = 6 cm
4. ? =
].d
Enter the segment length tha
belongs in the green box.
If two segments intersect inside
or outside a circle: ab = cd
Answer: Using the given information and the formula ab = cd, we can write:
d = (ab) / c
We are given b = 12 cm and c = 6 cm. To find ab, we can use the Pythagorean theorem:
a^2 + b^2 = c^2
where a is the unknown length we want to find. Substituting the given values, we get:
a^2 + 12^2 = 6^2
a^2 + 144 = 36
a^2 = -108 (which is not a possible solution)
This means that the given values do not form a valid triangle. Therefore, we cannot find the length of segment d using the given information.
Step-by-step explanation:
A mathematics teacher wanted to see the correlation between test scores and homework. The homework grade (x) and test grade (y) are given in the accompanying table. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest tenth . Using this equation, find the projected test grade, to the nearest integer, for a student with a homework grade of 45.
The sampling distribution in this case is positively skewed. This is due to the fact that the mean is greater than the median, and the data is spread out further to the right than to the left, resulting in a long right tail on the histogram.
What is data?Data is information that has been collected, organized, and presented in a meaningful way. It can include facts, figures, observations, and other information, such as survey responses, images, and videos. Data is used to inform decision-making, inform research and analysis, and generate insights. Data can be qualitative or quantitative, and it is often gathered from multiple sources. Data can be collected through surveys, experiments, observational studies, or other methods. When combined with analytical tools, data can be used to identify patterns and trends, generate insights, and develop strategies.
The best description of the shape of the sampling distribution in this case would be positively skewed. Positively skewed distributions occur when the mean is greater than the median, and the data is spread out further to the right than to the left. This results in a long tail on the right side of the histogram that skews the data in a positive direction. To determine if this is the case, we can calculate the mean and median of the data.
To calculate the mean, we will use the formula for the population mean: $$\mu = \frac {\sum_{i=1}^n x_i} n$$
where $\mu$ is the population mean, $\sum_{i=1}^n$ represents the sum of all the data points, and $n$ is the sample size.
For the median, we can use the formula for the population median: $$Median = \frac{n+1}{2}th \ \ term$$
where $n$ is the sample size.
In this case, the sample size is 36, so the median would be the 18.5th term.
Now that we have the formulas, we can calculate the mean and median of the data.
The mean of the data is $46,408.89$.
The median of the data is $25,000.
Since the mean is greater than the median, it indicates that the data is positively skewed. This is further confirmed by examining the histogram of the data, which shows a long right tail on the right side of the histogram.
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An artist melts one-half of a crayon per minute. Another artist takes x minutes to melt a crayon of the same size. Write an expression for the number of crayons the two artists melt in twenty minutes when they both work for the full twenty minutes.
WILL GIVE BRAINLIEST!!
The two artists will melt:
10 + 20/x crayons
in 20 minutes.
Write an expression for the number of crayons the two artists melt in twenty minutes when they both work for the full twenty minutes.The first artist melts one-half of a crayon per minute, so in 20 minutes, they will melt:
(1/2) x 20 = 10 crayons
The second artist takes x minutes to melt a crayon, so in one minute, they will melt:
1/x crayons
Therefore, in 20 minutes, the second artist will melt:
(1/x) x 20 = 20/x crayons
Together, the two artists will melt:
10 + 20/x crayons
in 20 minutes.
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2. There are 80 girls in the sophomore class of 200 students. Find the ratio of girls to non-girls.
Answer: 2 girls to 3 non-girls
Step-by-step explanation:
80 are girls
120 are boys (200-80)
80:120
simplify
2:3
Write the coordinates of the vertices after a reflection over the line x = 1.
The coordinates of the vertices B, D and C after a reflection over the line x = 1 are B'(1,7), D'(1,6) and C'(-8, 7).
Explain about reflection about x axis:The picture M', whose coordinates are in the fourth quadrant and created when point M is mirrored in the x-axis, is (h, -k). As a result, we deduce that when a point is reflected along the x-axis, the x-coordinate stays constant while the y-coordinate changes to the negative.
As a result, M'(h, -k). is the image for point M (h, k)
Given data:
coordinates of the vertices before reflection:
B(1,7), D(1,6) and C(10, 7).
Reflection about x = 1.
As Point B and D lies on the line x = 1, their coordinates will not change.
C is 9 units to the right of the line x = 1 at (10, 7)
Thus, after reflection C will be 9 units to the left of the line x = 1 at (-8, 7).
Therefore, the coordinates of the vertices B, D and C after a reflection over the line x = 1 are B'(1,7), D'(1,6) and C'(-8, 7).
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Solve x^2 + 6x + 9 = 0 by graphing. Please enter the number part of your answer only.
If your answer has two numbers, enter them like this: x = 6 and -1 should be entered as "6, -1" (no quotes).
Answer:
-3
Step-by-step explanation:
You want the graphical solution to x² +6x +9 = 0.
GraphThe graph of the expression on the left shows it has a value of 0 when x = -3.
The solution is x = -3.
__
Additional comment
A graphing calculator is very helpful when you want a graphical solution.
If you want to graph this by hand, you can rewrite it as ...
(x +3)² = 0
The graph of (x +3)² is a graph of the parent function y = x² after it has been shifted left 3 units. The graph will go through points (-5, 4), (-4, 1), (-3, 0), (-2, 1), (-1, 4). Of course the point at (-3, 0) indicates the solution is x=-3.
g fit the logistic regression model to predict diabetic status based on age and glucose levels. what is the odds of ratio of being diabetic for older adults compared to adults while controlling for glucose levels? round your answer to 0.01.
To calculate the odds ratio of being diabetic for older adults compared to adults while controlling for glucose levels in a logistic regression model, we exponentiate the coefficient estimate for Age. For example, if the estimate is 0.05, the odds ratio is 1.65.
To obtain the odds ratio for older adults compared to adults while controlling for glucose levels in a logistic regression model predicting diabetic status based on age and glucose levels, we would need to look at the coefficient estimate for the age variable. Let's say the logistic regression model is
logit(P(Diabetic)) = β_0 + β_1Age + β_2Glucose
where P(Diabetic) is the probability of being diabetic, Age is the age in years, and Glucose is the glucose level in mg/dL. β_1 represents the coefficient estimate for Age.
To calculate the odds ratio for older adults (e.g., those who are 10 years older than the average age in the sample) compared to adults while controlling for glucose levels, we can exponentiate the coefficient estimate for Age and round to 0.01. That is
OR = exp(β_1*10)
For example, if the coefficient estimate for Age is 0.05, then:
OR = exp(0.05*10) = 1.65
This means that for every 10-year increase in age, the odds of being diabetic compared to non-diabetic increase by a factor of 1.65 while holding glucose levels constant.
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which expressions are equivalent to 8 13 ?
The next four equivalent fractions of 8/13 are:
16/2624/3932/5240/65What are some equivalent fractions of 8/13?Equivalent fractions are fractions that represent the same value but have different numerator and denominator. To find equivalent fractions of 8/13, we can multiply both the numerator and the denominator by the same non-zero integer.
In this case, we multiplied the numerator and denominator by 2, 3, 4, and 5, respectively, to obtain the next four equivalent fractions: 16/26, 24/39, 32/52, and 40/65. These fractions have different numerators and denominators, but they are equivalent to 8/13 as they represent the same value or amount.
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Jessica wants to add a border around the edge of the solar panels to help protect them from weather events. Write the standard form expression that represents the amount of border material Jessica will need. Enter the correct answer in the box.
answer : 8c^2 + 24c - 6
The standard form expression that represents the amount of border material Jessica will need is 2L + 2W - 2x - 2y = -2B
To create this expression, we need to consider a few things. Firstly, we need to know the length and width of the solar panels. Let's say the length of the solar panel is L and the width is W. We also need to know the width of the border that Jessica wants to add. Let's call this value B.
The total amount of material needed for the border will be the sum of the material needed for the four sides of the solar panel. Each side will need a length of B, so the total length of the material needed will be 2B + 2L + 2W.
However, we can simplify this expression by putting it into standard form. Standard form expressions are written in a specific way that makes them easier to read and work with. In standard form, the expression is written as Ax + By = C, where A, B, and C are constants and x and y are variables.
To put the expression 2B + 2L + 2W into standard form, we need to group the variables together and move the constants to the other side of the equation. This gives us the expression 2L + 2W - Ax - By = -2B, where A and B are both equal to -2, and C is equal to -2B.
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Answer:
8c^2 + 24c - 6
Step-by-step explanation:
I got it right on edmentum
Choose the correct statement about best-fit lines. a. A best-fit line is close to most of the data points. b. A best-fit line describes the exact coordinates of each point in the data set. c. A best-fit line always has a positive slope. d. A best-fit line must go through at least two of the data points. Please select the best answer from the choices provided A B C D Mark this and return
a. A best-fit line is close to most of the data points.
Step-by-step explanation:Best-fit lines help show trends or correlations in data
Best-fit Lines
Best-fit lines attempt to create a line that is close to most data points. This line is a function that can be used to estimate data points that are not a part of the original data set. Additionally, best-fit lines will show the trend of the data. For example, if the slope of the best-fit line is constant, then the data points are directly proportional.
Common Misconceptions
Although best-fit lines can be extremely accurate and helpful, they are not perfect. A best-fit line will attempt to minimize the distance between the line and data points, but it will rarely be perfect. In most cases, there is no way to write a line that will perfectly describe the exact coordinates of each data point.
Additionally, data sets can have any type of correlation. It does not need to be proportional or positive. This means that the slope of a best-fit line can be anything.
Finally, as aforementioned, best-fit lines try to fit the data as much as possible. However, this does not mean that the line has to go through any data points. It is possible for best-fit lines to not go through any data points at all.
Lin plans to swim 12 laps in the pool. She has swum 9.75 laps so far.
How many laps does she have left to swim? Use y
for the number of laps that Lin has left to swim.
Lin plans to swim 12 laps and has already swum 9.75 laps, so the number of laps she has left to swim can be found by subtracting 9.75 from 12:
y = 12 - 9.75
Simplifying the right side:
y = 2.25
Therefore, Lin has 2.25 laps left to swim.
Louise and girl lol repaired a computer and we're paid 1165.50 if Carla work for 12 hours and Louis work for nine hours how much was their pay per hour?
The amount of their pay per hour is $55.5
How to determine the amount?The given parameters that will help us to get the amount are.
Louise repaired a computer for each hour she works and we're paid 1165.50
The question reads that if Carla work for 12 hours and Louise work for nine hours
this implies that 12x + 9x = 1165.50
This implies that 21x = 1165.50
Dividing both sides of the equation by 2 to get
21x/21 = 1165.50/21
x = 55.5
So, their their pay per hour is $55.5
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I will be given brainliest!!!!
Answer:2/3
Step-by-step explanation:
its the only possible answer because it needs to have a scale factor below one as A'B'C'D' is smaller than ABCD
Answer: 2/3
Step-by-step explanation:
The corresponding side of AD is A'D'.
AD = 30
A'D' = 20
Scale factor = 2/3 because AD * 2/3 = A'D'
If I'm wrong, please tell me.
Find the number of possibilities in each scenario
Find the number of ways 4 members from a family’s of 5 can line up for a photo shoot
There are [tex]5[/tex] ways to choose 4 members from a family of 5 to line up for a photo shoot.
What is the number of possibilities?The problem you are describing is a classic example of a combination problem, specifically choosing a certain number of items from a larger set without regard to the order in which they are arranged.
The formula to calculate the number of ways to choose "r" items from a set of "n" items without replacement is given by the combination formula, also known as "n choose r" or denoted as C(n, r). The formula is:
[tex]C(n, r) = n! / (r! \times (n - r)!)[/tex]
where "!" denotes the factorial of a number, which is the product of all positive integers up to that number.
In your case, you are choosing 4 members from a family of 5 for a photo shoot, and the order in which they line up does not matter. So you need to find C(5, 4).
Plugging the values into the formula:
[tex]C(5, 4) = 5! / (4! \times (5 - 4)!) = 5! / (4! \times 1!) = (5 \times 4 \times 3 \times 2 \times 1) / ((4 \times 3 \times 2 \times 1) \times 1) = 5[/tex]
Therefore, there are [tex]5[/tex] ways to choose 4 members from a family of 5 to line up for a photo shoot.
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plsss answer i'll give 50
Step-by-step explanation:
I know it not all but this is what I have
Write a quadratic function in intercept (factored) form that passes through (-4,0), (4,0), and (−2,12).
The equation of the quadratic function is y = -x² + 16 in intercept (factored) form.
How to Write a Quadratic Function in Intercept Form?To write a quadratic function in intercept (factored) form that passes through (-4,0), (4,0), and (−2,12), we need to use the factored form of the quadratic equation:
y = a(x - r)(x - s)
where a is the leading coefficient, and r and s are the x-intercepts.
From the given points, we can see that the x-intercepts are -4 and 4, so we have:
y = a(x + 4)(x - 4)
To find the value of a, we can use the point (-2, 12) which lies on the curve. Substituting these values, we get:
12 = a(-2 + 4)(-2 - 4)
12 = a(2)(-6)
a = -1
Thus, the quadratic function in intercept (factored) form that passes through (-4,0), (4,0), and (−2,12) is:
y = -1(x + 4)(x - 4)
y = -(x²- 16)
y = -x² + 16
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This is for the unit 4 lesson 7 Triangles Unit Test please help. Identify the combination of angle measures that could form a triangle
The combination of angle measures that could form a triangle are (a) 22, 140, 18 degrees and (c) 55, 67, 58 degrees.
In a triangle, the sum of the three interior angles is always equal to 180 degrees. Therefore, if the sum of the given angle measures is equal to 180 degrees, they could form a triangle.
For option a) 22 + 140 + 18 = 180, so the given angles could form a triangle.
For option b) 72 + 92 + 46 = 210, which is greater than 180, so the given angles could not form a triangle.
For option c) 55 + 67 + 58 = 180, so the given angles could form a triangle.
Therefore, the correct options are (a) 22,140,18 degrees and (c) 55,67,58 degrees
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The given question is incomplete, the complete question is:
Identify the combination of angle measures that could form a triangle
a) 22,140,18 degrees
b) 72,92,46 degrees
c) 55,67,58 degrees
we wish to estimate the proportion of all college students who are working while going to school to within 4% at the 90% confidence level. we believe the true proportion is around 40%. how large a sample should we take to get the desired accuracy?
To estimate the sample size required for estimating the proportion of college students who are working while going to school with a desired accuracy of 4% at a 90% confidence level, we can use the following formula:
n = (Z^2 * p * (1-p)) / (E^2)
where:
n is the sample size
Z is the Z-score corresponding to the desired confidence level (90% confidence level corresponds to a Z-score of 1.645)
p is the estimated proportion (or expected proportion) of the population
E is the desired margin of error
Given:
Desired accuracy (E): 4% or 0.04
Confidence level (Z-score): 1.645 (corresponding to 90% confidence level)
Estimated proportion (p): 0.40 (or 40%)
Plugging the values into the formula, we get:
n = (1.645^2 * 0.40 * (1-0.40)) / (0.04^2)
n = 0.1239 / 0.0016
n ≈ 77.4375
Rounding up to the nearest whole number, the estimated sample size required to achieve the desired accuracy is 78.
So, a sample size of at least 78 college students would be needed to estimate the proportion of college students who are working while going to school with a margin of error of 4% at a 90% confidence level, assuming an estimated proportion of 40%.
Determine whether the given set S is a subspace of the vector space V. Note: Pn(R) is the vector space of all real polynomials of degree at most n and Mn(R) is the vector space of all real n x n matrices = OA. V is the vector space of all real-valued functions defined on the interval [a, b], and S is the subset of V consisting of those functions satisfying f(a) = f(b). B. V = P5(R), and S is the subset of V P5(R) consisting of those polynomials satisfying p(1) > p(0). C. V = C3(1), and S is the subset of V consisting of those functions satisfying the differential equation y'" + 2y = x2. D. V = Mn(R), and S is the subset of all skew-symmetric matrices. VE. V = C2(I), and S is the subset of V consisting of those functions satisfying the differential equation y" – 4y' + 3y = 0. F. V = R", and S is the set of solutions to the homogeneous linear system Ax = 0 where A is a fixed m X n matrix. OG. V = R", and S is the set of vectors (x1 , X2, X3 ) in V satisfying x1 – 4x2 + x3 = 3
S is a subspace of the vector space V.
For four conditions are satisfied,
The set S is a subspace of C3(1)
The set S is a subspace of Mn(R)
The set S is a subspace of C2(I)
The set S is a subspace of [tex]R^n[/tex]
The set S is not a subspace of P5(R) because it is not closed under scalar multiplication.
If p(x) is a polynomial in S, then 2p(x) may not satisfy the condition. [tex]p(1) > p(0).[/tex]
The set S is a subspace of C3(1).
The differential equation [tex]y\prime\prime\prime + 2y = x^2[/tex] is linear and homogeneous, so the sum of two solutions is also a solution, and a constant multiple of a solution is also a solution.
S is closed under linear combinations.
The set S is a subspace of Mn(R) because it is closed under addition and scalar multiplication.
If A and B are skew-symmetric matrices, then[tex](A + B)^T = A^T + B^T = -A - B = -(A + B), so A + B[/tex]is skew-symmetric. Similarly, if c is a scalar, then [tex](cA)^T = cA^T = -cA, so c A[/tex] is skew-symmetric.
S is a subspace of C2(I) because it is closed under addition and scalar multiplication.
If y1 and y2 are solutions to[tex]y\prime\prime - 4y\prime+ 3y = 0, then y1\prime\prime - 4y\prime + 3y1 = 0[/tex] and [tex]y2\prime\prime - 4y2\prime + 3y2 = 0[/tex].
Adding these equations gives [tex](y1 + y2)\prime\prime - 4(y1 + y2)\prime + 3(y1 + y2) = 0,[/tex] so [tex]y1 + y2[/tex]is also a solution.
Similarly, if c is a scalar, then [tex](cy)\prime\prime - 4(cy)\prime + 3(cy) = c(y\prime\prime - 4y\prime+ 3y) = 0[/tex], so cy is also a solution.
The set S is a subspace of [tex]R^n[/tex]because it is the null space of a fixed matrix A.
The null space of a matrix is always closed under addition and scalar multiplication.
The set S is not a subspace of [tex]R^n[/tex]because it is not closed under addition. If (1, 1, 0) and (0, 2, 1) are in S, then their sum (1, 3, 1) is not in S because. [tex]1 - 4(3) + 1 \neq 3.[/tex]
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find the measurement of angle A and round the answer to the nearest tenth.
(Show work if you can plsss).
Answer:
40.8°
Step-by-step explanation:
SohCahToa
use tan
tan^-1(19/22)
=40.81508387
=40.8
Answer:
Step-by-step explanation:
Here,
Opposite side is 19
Adjacent side is 22
To find : The value of Angle A, that is X°.
Formula
Tan X° = Opposite side/Adjacent side
Tan X° = 19/22 = 0.863 ( approximately )
X° = Tan inverse (0.863)
X° = 40.79° ~ 40.8°
Rounding off this to nearest tenth is 41°.
Hence,
X° = 41°
That is,
Angle A is 45°.
The function y =30+5x represents the cost y (in dollars) of having your dog groomed and buying x for extra services. Sorry my mind is numb I have had a butt ton of work cut out for me.
Yes, the situation is a linear function as y = 30 + 5x is representing the standard form of a linear equation y = mx + b where m is the slope and b is the y-intercept.
Function is equal to ,
y = 30 + 5x
General form of the linear function is written as
y = mx + b
Here, the slope of the equation is 5,
This implies that for every additional service bought the cost increases by $5.
The y-intercept of the equation is 30.
This represents the initial cost of getting the dog groomed without any additional services.
The graph of this function will be a straight line.
And the relationship between the cost and the number of extra services bought will be linear.
When the number of extra services bought increases the cost of grooming the dog will increase by a constant amount .
Here the constant amount is equals to $5 per service.
Therefore, the function y = 30 + 5x is representing a linear function with slope 5 and y-intercept 30.
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The above question is incomplete, the complete question is:
The function y =30+5x represents the cost y (in dollars) of having your dog groomed and buying x extra services. Does this situation represent a linear function? Explain
A bookstore had 90 copies of a magazine. Yesterday, it sold 1/6 of them. Today, it sold 2/5 of the remaining copies. How many copies does the bookstore still have
Therefore , the solution of the given problem of unitary method comes out to be 45 copies of the magazine are still available at the bookstore.
Definition of a unitary method.Use the tried-and-true core approach, the real variables, nor any useful information you learn from the general and detailed questions to finish the project expression. Customers may be given another chance to taste the products in response. If these improvements don't happen, we'll miss out on significant advancements in programming comprehension.
Here,
Let's figure out how many issues of the magazine are still available in the store.
Given: There were 90 copies in all when the bookstore opened.
1/6 of the total copies were sold at the bookstore yesterday.
=> 15 copies were sold yesterday = (1/6) * 90.
=> Total copies - Copies sold yesterday = 90 - 15 = 75 Remaining copies after yesterday's sale
=> 2/5 of the remaining copies were sold in the bookstore today.
30 copies were sold today, which
=> (2/5) * 75.
The quantity of copies left after today's sale equals the quantity left after yesterday's sale. - Today's sales of copies:
=> 75 - 30 = 45
45 copies of the magazine are still available at the bookstore.
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answer please!!!!!! i need this so i can pass my classes
The area of the shaded region is given as follows:
1.25 units squared.
How to obtain the area of a rectangle?To obtain the area of a rectangle, you need to multiply its length by its width. The formula for the area of a rectangle is:
Area = Length x Width
The parameters for the shaded region in this problem are given as follows:
Length of 5 units.Width of 1/4 units.Hence the area is given as follows:
Area = 5 x 1/4
Area = 1.25 units squared.
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Please help Thank you
The values of trigonometric-ratios in the given triangle whose legs are 4 and [tex]4\sqrt{3}[/tex] are:
a)sinθ=0.5
b)cosθ=0.866
c)tanθ=0.577
What is trigonometric-ratios ?
A right angle triangle has six trigonometric ratios: Sin, Cos, Tan, Cosec, Sec, and Cot. Sine, Cosine, Tangent, Cosecant, Secant, and Cotangent are their respective acronyms. These ratios show the ratio of various sides depending on the angle selected.
Given sides of triangle: 4 and [tex]4\sqrt{3}[/tex]
hypotenuse=[tex]\sqrt{perpendicular^{2}+base^{2} }[/tex]
=[tex]\sqrt{4^{2}+\((4\sqrt{3}) ^{2} }[/tex]
=[tex]\sqrt{16+48}[/tex]
=8
a)Sin θ=[tex]\frac{side opposite to the given angle}{hypotenuse}[/tex]
Sin θ=[tex]\frac{4 }{8}[/tex]
Sin θ=[tex]\frac{1}{2}[/tex]
Sin θ=0.5
b)Cos θ=[tex]\frac{side adjacent to the given angle}{hypotenuse}[/tex]
=[tex]\frac{4\sqrt{3} }{8}[/tex]
=[tex]\frac{\sqrt{3} }{2}[/tex]
=[tex]\frac{1.732}{2}[/tex]
Cos θ=0.866
c)tan θ=[tex]\frac{side opposite to the given angle}{side adjacent to the given angle}[/tex]
=[tex]\frac{4}{4\sqrt{3} }[/tex]
=[tex]\frac{1}{\sqrt{3} }[/tex]
tan θ=0.577
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find the volume of a cylinder with a diameter of 16 mi and a height of 5 mi
Answer: 320π or approximately 1005.31 mi
Step-by-step explanation:
The formula for the volume of a cylinder is
π r² h
we need to find the radius which is 16/2 = 8
plug in and solve
π 8² *5
π 64 *5
320π or approximately 1005.31 mi
for which data frequency is seasonality not a problem? group of answer choices monthly. weekly. annual. daily. quarterly.
Seasonality may be less of a problem for annual data frequency as there may be less variation due to the longer time interval.
What is annual data frequency?Annual data frequency refers to data that is collected and reported on an annual basis. This means that the data points in the dataset represent a full year's worth of data, with one data point for each year. Annual data is often used in economic indicators, such as gross domestic product (GDP) or unemployment rates, and can provide insights into long-term trends and changes over time.
What is GDP?GDP stands for Gross Domestic Product, which is a measure of the total value of goods and services produced within a country's borders during a specific time period, typically a year. It is used as an indicator of a country's economic health and growth. GDP is calculated by adding up the total spending on consumption, investment, government spending, and net exports (exports minus imports) during the period.
According to the given informationSeasonality may still be a problem for data frequencies of monthly, weekly, daily, and quarterly as certain patterns or fluctuations may occur within each of these time intervals. Seasonality may be less of a problem for annual data frequency as there may be less variation due to the longer time interval.
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please help it’s a review question but i don’t get it
Possible translations such that the graph passes through the point (1,2) are given as follows:
Translate the graph one unit right and one unit up.Translate the graph three units right and two units down.What is a translation?A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.
The four translation rules for functions are defined as follows:
Translation left a units: f(x + a).Translation right a units: f(x - a).Translation up a units: f(x) + a.Translation down a units: f(x) - a.Two possible translations for the function to pass through the point (1,2) are given as follows:
Translate the graph one unit right and one unit up, considering that the function passes through the point (0, 1), hence x + 1, y + 1.Translate the graph three units right and two units down, considering that the function passes through the point (-2, 4).More can be learned about translations at brainly.com/question/28174785
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The arrival times of vehicles at the ticket gate of a sports stadium may be assumed to be poisson with a mean of 25 veh/hr. It takes an average of 1. 5 min for the necessary tickets to be bought for occupants of each car. (a)what is the expected length of queue at the ticket gate, not including the vehicle being served? (b)what is the probability that there are no more than 5 cars at the gate, including the vehicle being served? (c)what will be the average waiting time of a vehicle?
(a) The expected length of the queue, not including the vehicle being served, is 0.625 vehicles.
(b) The probability that there are no more than 5 cars at the gate, including the vehicle being served, is approximately 0.0176.
(c) The average waiting time of a vehicle at the ticket gate is 1.5 minutes or 0.025 hours.
(a) To find the expected length of the queue at the ticket gate, we need to calculate the expected number of vehicles waiting in the queue at any given time. This can be found by using the Little's Law, which states that the expected number of customers in a stable system is equal to the arrival rate multiplied by the average time spent in the system.
In this case, the arrival rate is 25 vehicles per hour, and the average time spent in the system is the time it takes to buy the tickets, which is 1.5 minutes or 0.025 hours. Therefore, the expected number of vehicles waiting in the queue is
E[N] = λW = 25 x 0.025 = 0.625 vehicles
So the expected length of the queue, not including the vehicle being served, is 0.625 vehicles.
(b) To find the probability that there are no more than 5 cars at the gate, including the vehicle being served, we need to use the Poisson distribution with a mean of 25 vehicles per hour. Let X be the number of vehicles arriving in an hour, then X Poisson(25).
P(X ≤ 5) = ∑ P(X = k) for k = 0 to 5
= ∑ (e^(-λ) × λ^k / k!) for k = 0 to 5
= e^(-25) × (25^0 / 0!) + e^(-25) × (25^1 / 1!) + ... + e^(-25) × (25^5 / 5!)
Using a calculator or software, this probability is found to be approximately 0.0176.
(c) The average waiting time of a vehicle can be found by dividing the expected number of vehicles waiting in the queue by the arrival rate. From part (a), we know that the expected number of vehicles waiting in the queue is 0.625 vehicles. The arrival rate is 25 vehicles per hour. Therefore, the average waiting time of a vehicle is
W = E[N] / λ = 0.625 / 25 = 0.025 hours or 1.5 minutes
So the average waiting time for a vehicle at the ticket gate is 1.5 minutes.
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Sky attempted to score a goal five times. For each attempt, she was equally likely to make a goal or miss. What is the probability that Sky scored at least two goals? Express your answer as a common fraction.
To solve this problem, we can use the binomial probability distribution. Let's define a "success" as scoring a goal and a "failure" as missing a goal.
Then, each attempt by Sky can be considered a Bernoulli trial with probability of success p = 1/2.
Let X be the number of goals that Sky scores in five attempts. Then, X follows a binomial distribution with parameters n = 5 and p = 1/2.
To find the probability that Sky scores at least two goals, we need to calculate the probability of the following events:
P(X ≥ 2) = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)
We can use the binomial probability formula to calculate these probabilities:
P(X = k) = (n choose k) * [tex]p^k[/tex] *[tex](1-p)^(n-k)[/tex]
where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n distinct items.
Using this formula, we get:
P(X = 2) = (5 choose 2) * [tex](1/2)^2[/tex] * [tex](1/2)^3[/tex] = 10/32
P(X = 3) = (5 choose 3) * [tex](1/2)^3[/tex] * [tex](1/2)^2[/tex] = 10/32
P(X = 4) = (5 choose 4) * [tex](1/2)^4[/tex] *[tex](1/2)^1[/tex] = 5/32
P(X = 5) = (5 choose 5) * [tex](1/2)^5[/tex] * [tex](1/2)^0[/tex] = 1/32
Therefore, the probability that Sky scores at least two goals is:
P(X ≥ 2) = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = (10 + 10 + 5 + 1)/32 = 26/32 = 13/16
So the probability that Sky scored at least two goals is 13/16.
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The total probability of scoring 1 goal is 5 * (1/32) = 5/32.Now we find the complementary probability:1 - (Probability of 0 goals + Probability of 1 goal) = 1 - (1/32 + 5/32) = 1 - 6/32 = 26/32.
Sky attempted to score a goal five times. For each attempt, she was equally likely to make a goal or miss. So the probability that Sky scored at least two goals is 13/16.
To find the probability that Sky scored at least two goals, we can use complementary probability, which means finding the probability that she scored fewer than two goals (either 0 or 1 goal) and subtracting that from 1.1.
Probability of scoring 0 goals: Since there are 5 attempts and she is equally likely to make a goal or miss (1/2 chance for each), the probability of missing all 5 is (1/2)^5 = 1/32.2.
Probability of scoring 1 goal: Sky could score in any of the 5 attempts, so we need to consider all possible ways of scoring one goal.
There are 5 ways (score in the 1st, 2nd, 3rd, 4th, or 5th attempt). The probability for each of these scenarios is (1/2)^5 = 1/32.
Therefore, the total probability of scoring 1 goal is 5 * (1/32) = 5/32.Now we find the complementary probability:1 - (Probability of 0 goals + Probability of 1 goal) = 1 - (1/32 + 5/32) = 1 - 6/32 = 26/32.
To express this as a common fraction, we can simplify it by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 2:26/32 = (26/2) / (32/2) = 13/16So the probability that Sky scored at least two goals is 13/16.
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One computer can process a payroll in 6 hours a new computer can do it in 4 hour how long would it take both computers together
Both computers working together can process the payroll in 2.4 hours.
Let's denote the time it takes for both computers working together to process the payroll as "t".
We can use the formula:
work done = rate x time
where "work done" is the same in both cases, as they are processing the same payroll. Therefore, we can set up an equation using the rates :
1/6 + 1/4 = 1/t
We can simplify the left-hand side of the equation:
2/12 + 3/12 = 1/t
5/12 = 1/t
Multiplying both sides by 12t:
5t = 12
t = 12/5
t = 2.4
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