A. The Utilization rate is 0.5714 or 57.14%, B. The average number of students in line is 0.9 students and C. The average time of waiting in line was 4.57 minutes.
The utilization rate refers to the proportion of time Judy Gumshoes spends processing student requests.
To calculate this rate, divide the average service time by the average time between arrivals. In this case, the average service time is 8 minutes, and students arrive every 14 minutes on average.
a) Utilization rate: 8 minutes / 14 minutes = 0.5714 or 57.14%
b) To determine the average number of students in line,
we can use the formula L = λW, where L represents the average number of students in the system, λ is the arrival rate (1 student per 14 minutes), and W is the average time a student spends in the system (waiting and being served). Since we know the utilization rate,
we can calculate the average waiting time (Wq) using the formula,
Wq = (U^2) / (1 - U), where U is the utilization rate.
In this case, Wq = (0.5714^2) / (1 - 0.5714) = 0.3265 or 32.65% of 14 minutes = 4.57 minutes.
W = Wq + service time
= 4.57 minutes + 8 minutes
= 12.57 minutes.
Finally, L = λW = (1 student / 14 minutes) * 12.57 minutes
= 0.9 students.
c) The average time of waiting in line is the same as the average waiting time in the system (Wq), which we calculated as 4.57 minutes.
In summary, the utilization rate of the service counter is 57.14%, the average number of students in line is 0.9, and the average waiting time in line is 4.57 minutes.
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Which expression is equivalent to x-4?.
Answer:
x⁻²· x⁻²
Step-by-step explanation:
x⁻⁴ = x⁻²· x⁻² = x⁽⁻² ⁺ ⁻²⁾ = x⁻⁴
Create a real life example that includes function composition in it and solve it?
how can you multiply binomial with a trinomial? Give an example about it and solve it.
Function composition is a mathematical concept that involves combining two or more functions to create a new function. A real-life example of function composition might involve a company that uses a software program to calculate payroll. The program might use one function to calculate an employee's hourly rate based on their salary, and another function to calculate their total hours worked based on their timecard data. These two functions could be combined using function composition to create a new function that calculates the employee's total pay.
As for multiplying a binomial with a trinomial, here's an example:
(2x + 3)(4x² + 5x - 6)
To solve this, we use the distributive property of multiplication, which involves multiplying each term in one set of parentheses by each term in the other set of parentheses. We can break this down into three separate multiplications:
2x (4x² + 5x - 6) = 8x³ + 10x² - 12x
3 (4x^2 + 5x - 6) = 12x² + 15x - 18
Adding these two results together, we get:
(2x + 3)(4x² + 5x - 6) = 8x³ + 22x² + 3x - 18
Therefore, the product of the binomial (2x + 3) and the trinomial (4x² + 5x - 6) is 8x³ + 22x² + 3x - 18.
[tex] \: [/tex]
a professional basketball player makes 80% of the free throws he tries. assuming this percentage holds true for future attempts, use the binomial formula to find the probability that in the next eight tries, the number of free throws he will make is: a. exactly 8 b. exactly 5 c. 3 or 4
a) The probability that in the next eight tries, the number of free throws he will make exactly 8 is equals to the 0.27249.
b) The probability that in the next eight tries, the number of free throws he will make exactly 5 is equals to the 0.08386.
We have a professional basketball player makes 80% of the free throws he tries.
let X be the number of free throws he will make in the next 8 tries. He makes 80% of the free thwors he tries. So, for binomial distribution, X~Bin(8,0.80)
so the probability mass function of X is P[X =x] = ⁸Cₓ 0.85ˣ (1-0.85)⁽⁸⁻ˣ⁾, x = 0,1, 2,..8
P[ X = x] = 0 otherwise.
a) So, the probability that he makes exactly 8 throws isP,(X=8)
= ⁸C₈(0.85)⁸ (1- 0.85)⁰
=0.27249
b) the probability that he makes exactly 5 throws is, P[X=5]
=⁸C₅0.855(1-0.85)⁽⁸⁻³⁾=56×0.855×0.153
=0.08386
Hence required probability is 0.083.
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Given two polygons, you perform the following transformations:
1) Translate (x+1, y-7)
2) Rotation 180°
3) Dilate by a scale factor of ½
The final image will be...
a
Congruent to the original image
b
Similar to the original image
c
Not congruent and Not similar
Recall the definitions for congruence and similarity.
similar - the shapes are the same shape but are different sizes
congruent - the shapes are identical
Now if you have two polygons, assuming that they are identical to start out with (If not you won't be able to solve the problem. Do you see why?) and you perform the operations to one of them, the translation and the rotation will not change anything. But the dilation will make one shape 1/2 as big as the other. So in this case the two polygons are similar but not congruent.
Please please help i'm trying to get an A
The area of the triangle is: 24 unit²
What is an area ?
Area is a measurement of the amount of space inside a two-dimensional figure or shape. It is typically measured in square units, such as square meters or square feet. The area of a shape is calculated by multiplying its length by its width, or by using a specific formula for the shape.
We can find the area of the triangle by using the formula:
Area = 1/2 * base * height
where the base is the distance between points A and B, and the height is the distance from point C to the line containing AB.
The distance between points A and B is 4 units (since they have the same x-coordinate). To find the height, we can use the equation of the line containing AB, which is:
y = 4x - 3
Substituting x = 4 (the x-coordinate of point C) gives us:
y = 4(4) - 3 = 13
So the height is 13 - 1 = 12 units.
Therefore, the area of the triangle is:
Area = 1/2 * base * height
= 1/2 * 4 * 12
= 24
So the answer is not one of the given choices. The correct answer is 24.
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2x - 7y=-3
4x - 5y = 12
If (x, y) is the solution to the system of equations above, what is the
value of y²?
First, we multiply the first equation by 5 and the second equation by 7, then subtract the first equation from the second equation to eliminate y. Next, we substitute x = 11/2 into one of the original equations to solve for y. The solution is (x, y) = (11/2, 2). To find the value of y2, we square the value of y.
What is an equation?A mathematical statement known as an equation utilizes the equal symbol (=) to demonstrate the equality of two expressions. A mathematical equation normally consists of constants, variables, and operations such addition, subtraction, multiplication, and division.
To solve this system of equations, we can use the method of elimination.
First, we will multiply the first equation by 5 and the second equation by 7 to get:
10x - 35y = -15
28x - 35y = 84
Now, we can subtract the first equation from the second equation to eliminate y:
28x - 10x - 35y + 35y = 84 - (-15)
18x = 99
x = 99/18 = 11/2
Next, we can substitute x = 11/2 into one of the original equations to solve for y. We'll use the first equation:
2x - 7y = -3
2(11/2) - 7y = -3
11 - 7y = -3
-7y = -14
y = 2
Therefore, the solution to the system of equations is (x, y) = (11/2, 2).
To find the value of y², we simply square the value of y:
y² = 2² = 4
So the value of y² is 4.
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one bar of candy a and two bars of candy b have 779 calories. two bars of candy a and one bar of candy b contain 793 calories. find the caloric content of each candy bar.
The caloric content in candy A is 269 and that of candy B is 255.
The caloric content is the quantity of energy required to increase the temperature of one liter of water by one degree. A calorimeter was initially used to determine a food's calorie count.
Let us consider:
Caloric content of Candy A = x
Caloric content of Candy B = y
We can thereby make two equations:
Eqn 1: 1x + 2y = 779
Eqn 2: 2x + 1y = 793
By elimination method, we have
2x + 4y = 1558
Solving for x by subtracting with Eqn 2, we have,
3y = 765
y = 765 ÷ 3
y = 255.
Now substituting the value of y in Eqn 2, we have:
2x + 1y = 793
2x + 1 × 255 = 793
2x + 255 = 793
2x = 793 - 255
2x = 538
x = 538 ÷ 2
x = 269.
Hence caloric content in candy A is 269 and that of candy B is 255.
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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
Answer please mark as brainliest:
Allstars typically have the tallest players.
Step-by-step explanation:
To determine which team typically has the tallest players, we can compare the measures of center for each team. The measures of center we can use are the mean and median.
Using a calculator or a spreadsheet, we can calculate the mean and median for each team:
Allstars mean: (73+62+60+63+72+65+69+68+71+66+70+67+60+70+71)/15 = 67.1 inches
Allstars median: arrange the heights in order from smallest to largest: 60, 60, 62, 63, 65, 66, 67, 68, 69, 70, 70, 71, 71, 72, 73. The median is the middle value, which is 68 inches.
Champs mean: (62+69+65+68+60+70+70+58+67+66+75+70+69+67+60)/15 = 66.4 inches
Champs median: arrange the heights in order from smallest to largest: 58, 60, 60, 62, 65, 67, 67, 68, 69, 69, 70, 70, 70, 75. The median is the middle value, which is 67 inches.
Based on the measures of center, we can see that the Allstars have a higher mean and median height than the Champs. Therefore, we can conclude that the Allstars typically have the tallest players.
x^2+x factorised in full answer
This is the original expression x(x + 1) = [tex]x^{2}[/tex] + x that we started with, so we can be confident that our factorization is correct.
What is Algebraic expression ?
An algebraic expression is a mathematical phrase that can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. Algebraic expressions are used to represent and solve problems in many areas of mathematics, science, engineering, and finance.
To factorize an expression means to write it as a product of factors. In this case, we want to write [tex]x^{2}[/tex] + x as a product of factors. One way to do this is to look for common factors that we can take out of both terms in the expression.
In this case, the only common factor in both [tex]x^{2}[/tex] and x is x itself. Therefore, we can take out an x from both terms to get:
x(x + 1)
This is the fully factorized form of the expression [tex]x^{2}[/tex] + x. It shows that [tex]x^{2}[/tex] + x can be written as a product of two factors: x and (x + 1).
We can verify that this is correct by multiplying out the two factors:
x(x + 1) = [tex]x^{2}[/tex] + x
Therefore, This is the original expression x(x + 1) = [tex]x^{2}[/tex] + x that we started with, so we can be confident that our factorization is correct.
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In the diagram below, fg is parallel to CD, if CE = 32, FE = 20 and CD = 16 find the length of FG . Figures are not necessarily drawn to scale.
The length of FG is 40 units.
What are parallel lines?
Two or more lines that are consistently parallel to one another and that are located on the same plane are referred to as parallel lines. No matter how far apart parallel lines are, they never cross. The relationship between parallel and intersecting lines is the reverse. The lines that never meet or have any possibility of meeting are known as parallel lines.
Since FG is parallel to CD, triangles CDE and FGE are similar. Thus, we can set up the following proportion:
CE/CD = FG/FE
Substituting the given values, we get:
32/16 = FG/20
Simplifying the left side, we get:
2 = FG/20
Multiplying both sides by 20, we get:
FG = 40
Therefore, the length of FG is 40 units.
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Jordan compared 10 books at the school library. The following table shows the number of chapters and the total number of pages for each book.
Number of Chapters 3 4 5 8 10 12 13 14 16 20
Total Pages 18 38 45 85 76 145 138 160 180 220
Which of the following representations is most appropriate to show the relationship between the number of chapters and the total pages of a book?
scatter plot titled school library, with the x axis labeled number of chapters ranging from 0 to 20 and the y axis labeled total pages ranging from 0 to 275 with points at 3 comma 18, 4 comma 38, 5 comma 45, 8 comma 85, 10 comma 76, 12 comma 145, 13 comma 138, 14 comma 160, 16 comma 180, and 20 comma 220
line graph titled school library, with the x axis labeled number of chapters ranging from 0 to 20 and the y axis labeled total pages ranging from 0 to 275 with points at 3 comma 18, 4 comma 38, 5 comma 45, 8 comma 85, 10 comma 76, 12 comma 145, 13 comma 138, 14 comma 160, 16 comma 180, and 20 comma 220
scatter plot titled school library, with the x axis labeled number of chapters ranging from 0 to 38 and the y axis labeled total pages ranging from 0 to 450 with points at 3 comma 18, 4 comma 38, 5 comma 45, 8 comma 85, 10 comma 76, 12 comma 145, 13 comma 138, 14 comma 160, 16 comma 180, and 20 comma 220
line graph titled school library, with the x axis labeled number of chapters ranging from 0 to 38 and the y axis labeled total pages ranging from 0 to 450 with points at 3 comma 18, 4 comma 38, 5 comma 45, 8 comma 85, 10 comma 76, 12 comma 145, 13 comma 138, 14 comma 160, 16 comma 180, and 20 comma 220
The most appropriate representation to show the relationship between the number of chapters and the total pages of a book would be a scatter plot titled "School Library".
with the x-axis labeled "Number of Chapters" ranging from 0 to 20 and the y-axis labeled "Total Pages" ranging from 0 to 275 with points at (3, 18), (4, 38), (5, 45), (8, 85), (10, 76), (12, 145), (13, 138), (14, 160), (16, 180), and (20, 220).
A scatter plot is a graph used to display the relationship between two variables. In this case, the two variables are the number of chapters and the total number of pages in a book. The plot consists of dots, each representing a single data point. The x-axis represents the independent variable, which in this case is the number of chapters. The y-axis represents the dependent variable, which is the total number of pages. By plotting each data point on the graph, it is easier to visualize the relationship between the two variables.
A line graph is not appropriate for this situation because it suggests a continuous relationship between the two variables, which is not the case here. The number of chapters and total pages are discrete variables, and there is no natural order to the data points that would justify connecting them with a line.
The first scatter plot option is not appropriate because it shows the y-axis ranging up to 450, which is much higher than the maximum value of 275 for the total pages in this data set. This exaggerates the differences between the data points and can be misleading.
The chosen scatter plot is appropriate because it clearly shows the relationship between the number of chapters and the total pages of a book. It is easy to see that as the number of chapters increases, the total pages also tend to increase. The scatter plot also helps to identify any outliers or patterns in the data that may not be apparent from just looking at the numbers. It is a visual tool that helps to quickly understand the data and draw conclusions from it.
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Mr. Kelly Is a librarlan at Central Library. In examining a random sample of the library's book collection, he found the following.
936 books had no damage,
63 books had minor damage, and
41 books had major damage.
Based on this sample, how many of the 24,000 books in the collection should Mr. Kelly expect to have no damage? Round your answer to the nearest whole number. Do not round any intermediate calculations.
5-|p+6|=-8 pls wut is answer
Answer:
+ or - (7)
Step-by-step explanation:
5-|p+6|= -8
-|p+6|=-8-5
|p+6|= 13
p+6 = + or - (13)
so case 1
p+6 = 13
p = 7
case 2
p+6 = -13
p+ -7
Find the 27th term. -21, -14, −7, 0, 7, ... 27th term = [ ? ]
Answer: the term 27 ; a27=a1+(n-1)d. a27=38+(27-1)(-7)
Step-by-step explanation:
Given a1=38,a17=-74. a17=a1+(n-1)d. =38+(17-1)d. -74=38+16d. -74-38=16d. -112=16d. d= -7. the term 27 ; a27=a1+(n-1)d. a27=38+(27-1)(-7).
Answer: 7
Step-by-step explanation: number adds up by 7
Look at the picture and help me pass math it would be very nice
Answer:
[tex] \frac{1}{3} [/tex]
The answer is B
Step-by-step explanation:
There are six outcomes in total (numbers: 1; 2; 3; 4; 5 and 6)
The number she had spinned must be greater than 4 (that means there are two favorable outcomes: 5 and 6)
n = 6
m = 2
[tex]p = \frac{m}{n} = \frac{2}{6} = \frac{1}{3} [/tex]
helpp asapp will give brainliest!!!
Answer:
10.14 inches square
What is the percent of change from 8,000 to 6,000?
Answer:
here you go
Step-by-step explanation:
The percent of change from 8,000 to 6,000 can be calculated using the formula:
�������;�ℎ����=���;�����−���;��������;�����×100Percent;change=Old;ValueNew;Value−Old;Value×100
Substituting the given values, we get:
�������;�ℎ����=6,000−8,0008,000×100Percent;change=8,0006,000−8,000×100
Therefore, there is a decrease of 20% from 8,000 to 6,000.
Answer: decreases 6000 to 8000 = 33.33
x-
6000−50005000×100 = 20%
Step-by-step explanation:hope that helps have a great day and stay safe (;
PLS HELP WILl MARK BRAiNLIEST
Step-by-step explanation:
draw a triangle then label corners a and b. spread them 120 degrees apart and there you have it.
Evaluate each expression for the given value.
a. a2 when a= 3/4
b. b3 when b = 1.1
Answer:
a. 9/16 or 0.5625
b. 1.331 or 1331/1000
Step-by-step explanation:
I’m assuming you meant a^2 and b^3
11. FINANCIAL LITERACY Jerome is buying paint for a mural. The cost of the paints can be
modeled by f(p) = 6.99p, where p is the number of paints he buys. He has a coupon for
15% off his purchase at the paint store.
a. Write a function n(p) that represents the costs of the paints with the 15% discount.
b. Find the cost of purchasing 5 paints before and after the discount.
a. The function n(p) that represents the cost of the paints with the 15% discount is n(p) = 6.99p - 0.15(6.99p).
b. The 15% discount reduces the cost of the paints from 34.95 to 29.70.
What is discount?Discount is term used for reduction in the original price of a good or service. It is a common practice used by retailers and businesses to attract customers.
a. The function n(p) that represents the cost of the paints with the 15% discount is given by:
n(p) = 6.99p - 0.15(6.99p)
= 5.94p
b. The cost of purchasing 5 paints before the discount is 6.99 x 5 = 34.95.
The cost of purchasing 5 paints after the discount is 5.94 x 5 = 29.70.
Therefore, the 15% discount reduces the cost of the paints from 34.95 to 29.70.
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A garter snake is 22 inches long.if a python is 9 times as long as the garter snake,how much longer is the python?write and solve equaions
By answering the presented question, we may conclude that So, the equation python is 176 inches longer than the garter snake.
What is equation?In mathematics, an equation is a claim that two expressions are equivalent. Two sides that are separated by the algebraic symbol (=) make form an equation. As an illustration, the claim "2x + 3 = 9" makes the statement "2x plus 3 equals the quantity "9." Finding the value or values of the variable(s) necessary for the equation to be true is the goal of equation solving. Equations can include one or more parts and be straightforward or complex, regular or nonlinear. The formula "x2 + 2x - 3 = 0" raises the variable x to the second power. In many different branches of mathematics, including algebra, calculus, and geometry, lines are used.
Let's use "P" to represent the length of the python in inches.
P = 9(22):
P = 198
Therefore, the python is 198 inches long.
198 - 22 = 176
So, the python is 176 inches longer than the garter snake.
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Find the angle measure indicated. Assume that lines which appear tangent are tangent.
A. 110 degrees B. 175 degrees C. 155 degrees D. 120 degrees
The value of the angle QSR in the given circle containing lines and tangents is 120 degrees.
What is a circle?A circle is a two-dimensional geometric object made up of all points on a plane that are equally spaced from a central fixed point. The radius of a circle is the distance from the centre to any point on the circle. One of the most fundamental and significant geometric forms, the circle has many uses in mathematics, science, and engineering, including the study of trigonometry, coordinate geometry, and calculus. Moreover, circles are utilised in numerous practical contexts, including the creation of wheels, gears, and lenses as well as the simulation of physical phenomena like the motion of planets and electrons.
The measure of angle QSR is determined using the formula:
angle QSR = arc a + arc b / 2
Here, arc a = 150 and arc b = 90 thus:
angle QSR = 150 + 90 / 2
angle QSR = 240 / 2 = 120 degrees.
Hence, the value of the angle QSR in the given circle containing lines and tangents is 120 degrees.
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What would a monthly payment be on a purchase of a $10,000 car at 5.9% for
4 years?
A. $212.50
OB. $250.00
OC. $234.39
OD.
-$234.39
SUBMIT
The monthly payment on a purchase of a $10,000 car at 5.9% for 4 years is: C. $234.39.
How to find the monthly payment?To calculate the monthly payment for a car loan, we can use the formula:
M = P [ i(1 + i)^n / ((1 + i)^n – 1) ]
Where:
M = Monthly payment
P = Principal (he amount of the loan)
i = Monthly interest rate (annual interest rate divided by 12)
n = Number of months in the loan term
Using this formula with the given information, we get:
P = $10,000
i = 5.9% / 12 = 0.004917
n = 4 years x 12 months/year = 48 months
M = $10,000 [ 0.004917(1 + 0.004917)^48 / ((1 + 0.004917)^48 – 1) ]
M = $234.39 (rounded to the nearest cent)
Therefore, the answer is option C.
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WXYZ is a trapezium . If WY//XY and M is the mid point of YZ then prove that:
Area of triangle WXM = 1/2 AREA OF TRAPEZIUM WXYZ
Therefore , the solution of the given problem of triangle comes out to be the desired outcome is demonstrated.
What precisely is a triangle?If a polygon has at least one additional segment, it is a hexagon. Its structure is a simple rectangle. Something like this can only be distinguished from a regular triangular form by edges A and B. Euclidean geometry only creates a portion of the cube, despite the precise collinearity of the borders. A triangular has three sides and three angles.
Here,
Area is equal to (sum of parallel edges) / 2 * (distance between them)
=> WXYZ area equals (WZ plus XY) / 2 * hS
=> (XM / XY)2 equals Area of WXM / Area of WXY
=> XM / XY = 1/2
=> WXM area divided by WXY area equals (1/2)2 = 1/4.
=> WXY plus WXM together make up the area of WXYZ.
=> WXY / 2 + WXM / 4 equals (WZ + XY) / 2 * h
=> WZ * h equals WXY * h plus 2 * WXM:
=> (WZ - WXY) / 2 * h equals WXM
=> WXYZ area equals (WZ plus XY) / 2 * h
=> (WZ+WXY+(WZ-WXY)) / 2 * h
=> (2WZ) / 2 * h
=> WZ * h
=> WXYZ Area equals 2 * WXM Area
Thus, the desired outcome is demonstrated.
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The measure of an angle is 121.9°. What is the measure of its supplementary angle?
If a function is increasing throughout its domain the y-value are greater and greater as x approaches infinity. Libby claims that any function that has all real number as a domain and is increasing everywhere must have all real numbers as it's range as well. Is Libby correct? Explain why or why
Not
Libby is correct in claiming that a function with a domain of all real numbers and is increasing everywhere must have all real numbers as its range.
Libby is correct. If a function is increasing throughout its domain, the y-values become greater as x approaches infinity.
This is because the function can take any y-value without restriction as x approaches positive or negative infinity.
The domain of the function is all real numbers, it means that the function is increasing for every x-value, and there are no limits to how large or small x can be.
The given function has a domain of all real numbers, which means it is defined for any value of x.
The function is increasing throughout its domain, which means that as x increases, the y-value of the function also increases.
Conversely, as x decreases, the y-value of the function decreases.
Since there is no restriction on the x-values in the domain, we can let x approach positive infinity to find the largest possible y-value, and negative infinity to find the smallest possible y-value.
As x approaches positive infinity, the y-value of the function keeps increasing without any upper limit, meaning that the function can take any arbitrarily large positive y-value.
Similarly, as x approaches negative infinity, the y-value of the function keeps decreasing without any lower limit, meaning that the function can take any arbitrarily large negative y-value.
Therefore, the range of the function must include all real numbers since the function is able to take any positive or negative y-value without restriction.
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Vector u has initial point at (4, 4) and terminal point at (–12, 8). Which are the magnitude and direction of u?
||u|| = 14.422; θ = 33.690°
||u|| = 14.422; θ = 146.310°
||u|| = 16.492; θ = 14.036°
||u|| = 16.492; θ = 165.964°
||u|| = 16.492; θ = 165.964° are the vector magnitude and direction of u.
What is a straightforward definition of a vector?
A quantity or phenomena with both size and direction being independent of one another is called a vector. Also, the phrase specifies how such a quantity is represented mathematically or geometrically. Examples of vectors in nature include weight, force, electromagnetic fields, momentum, and velocity.
Let's find the magnitude of each component:
Let
(x₁,y₁ ) = (4,4)
(x₂ , y₂ ) = (-12 , 8 )
u = ax + by
ll u ll = √a² + b²
So, let's find a and b:
a = l x₂ - x₁ l =l -12 - 4 l = l -16 l = 16
b = l y₂ - y₁ l = l 8 - 4 l = l4l = 4
so,
ll u ll = √16² + 4²
= √272
≈ 16.492
And the direction is:
θ = 180 - tan⁻¹ (b/a )
= 180 - tan⁻¹(4/16)
θ ≈ 180 - tan⁻¹ (4/16)
≈ 165.953.
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1 /4 of the schoolyard is used by the fifth graders for recess, as shown by the shaded part of the diagram. Teachers have 3 different activities planned for recess that will take up the same amount of space.
The shaded part of the figure in choice B is divided into three equal parts
There are 12 equal parts in total so each activity takes up 1/12.
What is the fraction?
A fraction is a part of a whole or a ratio of two numbers expressed with a horizontal line between them.
Part A: The shaded part of the figure in choice B
is divided into three equal parts
there are three kinds of activities
Part B: According to the choice B of part A. there are 12 equal parts in total so each activity takes up 1/12.
figure in all the parts of the choice up to B of part A, get 12 equal parts
Hence, The shaded part of the figure in choice B is divided into three equal parts
There are 12 equal parts in total so each activity takes up 1/12.
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please help with this geometry hmw
5x² - 25x - 30 has a common factor with 4x² - 25x + 6, which is (x - 6).
option C.
Which polynomial shares a common factor with 4x² - 25x + 6?
To find the common factor of two polynomials, we can use the method of polynomial factorization.
First, let's factor the polynomial 4x² - 25x + 6:
4x² - 25x + 6 = (4x - 1)(x - 6)
Now, let's factor each of the answer choices:
A. 3x² - 15x + 18 = 3(x² - 5x + 6) = 3(x - 2)(x - 3)B. 4x² + 20x + 24 = 4(x² + 5x + 6) = 4(x + 2)(x + 3)C. 5x² - 25x - 30 = 5(x² - 5x - 6) = 5(x - 6)(x + 1)D. 2x² + 8x - 24 = 2(x² + 4x - 12) = 2(x + 6)(x - 2)We can see that only choice C has a common factor with 4x² - 25x + 6, which is (x - 6). Therefore, the answer is C.
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Parallel lines r and s are cut by two transversals, parallel lines t and u
10 points
Angles corresponding with ∠8 are ∠4 and ∠12.
Define corresponding angleIn geometry, corresponding angles are angles that are in the same relative position at the intersection of two lines when a third line crosses them. When two lines are intersected by a third line, they form pairs of corresponding angles that are congruent, meaning they have the same measure.
In the given figure;
Lines r,s,t and u are parallel lines.
Angles ∠8 and ∠12 are in corresponding angle ( line t and u are parallel ands line intersect it)
Angle ∠4 and ∠8 are corresponding angle (line r and s are parallel and t line intersect it)
Hence, Angles corresponding with ∠8 are ∠4 and ∠12.
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