The area of the sector is approximately 1954.77 square yards.
A circular sector, also known as a circle sector or a disc sector (symbol:), is a piece of a disc (a closed region bordered by a circle) encompassed by two radii and an arc. The smaller area is known as the minor sector, and the bigger is known as the major sector.
Any point on the circle outside of the sector can be connected to the arc's endpoints to produce half of the central angle.
We know that the area of a circle is πr² and the area of the sector of a circle with angle θ is given by θ/360 πr² .
Area of the sector
= 140°/360° × π × 40²
= 1954.7687... square yards.
≈ 1954.77 square yards.
Therefore the area of the sector is approximately 1452.113 square yards.
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If f(x) = 4x + 12 is graphed on a coordinate plane, what is the y-intercept of the graph?
4
8
12
16
Answer: y-intercept is 12
Step-by-step explanation:
y = mx +b
m = slope
b = y-intercept
y | = | x | + | b
f(x) | = | 4x | + | 12
b = y-intercept
A $300 fax machine is on sale for 45% off. Find the amount of the discount and the sale price.
The amount of discount is $
The sale price is $
Use the following information to prepare a classified balance sheet for Alpha Co. at the end of Year 1. Accounts receivable $ 26,500 Accounts payable 12,200 Cash 20,500 Common stock 30,000 Land 10,000 Long-term notes payable 17,500 Merchandise inventory 26,300 Retained earnings 23,600
The classified balance sheet for Alpha Co. at the end of Year 1 is illustrated below.
What is a classified balance sheet?A financial statement incorporating classifications as current assets and liabilities, long-term liabilities, and other things is called a classified balance sheet. It may be simpler to read and extract the information you need by categorizing the information than if it were just listed in a lot of line items.
It is a financial report that includes totals for all of the different revenue and expense classifications and displays revenues, expenses, and profits.
The balance sheet is illustrated below:
Current Assets
Accounts Receivable 26500
Cash 20500
Merchandise Inventory 26300
Total Current Assets 73300
Property, Plant and Equipment
Land 10000
Total Property, Plant and Equipment 10000
Total Assets 83300
Current Liabilities
Accounts Payable 12200
Long Term Liabilities
Long-Term Notes Payable 17500
Stockholders' Equity
Common Stock 30000
Retained Earnings 23600
Total 53600
Total Liabilties 83300
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87 billion 295 million written out
Answer: 87, 295,000,000 or eighty-seven two hundred ninety-five Billion
Im pretty sure
When your spel of dice, there are several homes, showWhen rolling the dice, the outcome is expressed as a sum of the two dice. Forcrample, il after you rolled the dice, and one die was 33 and the other was 34 youwill have rolled aSelect all of the TRUE statements below There may be more than oneThe probabiliny troling the same digit with cach die is 1/4The odds in favour of roliga 10 is 1:13.The odds against rolling a nurther leathan 7 is 7:5.1$
The total possible outcome for the experiment is 36.
The ossible outcomes for same number on each dice is 6.
So probability for the same number on dice is,
[tex]\frac{6}{36}=\frac{1}{6}[/tex]So probability for the same number on dice is 1/6. So first statement "The probability of rolling the same digit with each die is 1/4" is false.
Consider the system of equations x+2y=8 -3x-2y=12 How do you solve the system of equations with Cramer's rule? Drag a value or determinant expression into each box to correctly solve the system using Cramer'
The solution to the system of equations are, x + 2y = 8 and -3x-2y = 12 is: X = -10 , Y = 9
The given system of equations:
x + 2y = 8 (Equation - 1)
-3x - 2y = 12 (Equation - 2)
This can be written in matrix form as shown:
[tex]\left[\begin{array}{ccc}1&2&\\-3&-2&\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right][/tex] [tex]= \left[\begin{array}{ccc}8\\12\\\end{array}\right][/tex]
Let us assume, D = [tex]\left[\begin{array}{ccc}1&2\\-3&-2\\\end{array}\right][/tex]
We can use cross multiplication,
= (-2)(1) - (-3)(2)
= -2 + 6
= 4 ≠ 0
So the system has a unique solution,
Then,
[tex]D_{1} = \left[\begin{array}{ccc}8&2\\12&-2\\\end{array}\right][/tex]
We can use cross multiplication,
[tex]D_{1} = (8)(-2)-(12)(2)\\D_{1} = -16-24\\D_{1} = -40[/tex]
[tex]D_{2} =\left[\begin{array}{ccc}1&8\\-3&12\\\end{array}\right][/tex]
We can use cross multiplication,
[tex]D_{2} = (12)(1)-(-3)(8)\\D_{2} = 12+24\\D_{2} = 36[/tex]
So, they can solve the X and Y values,
X = D1 / D
X = -40/4
X = -10
Y = D2 / D
Y = 36/4
Y = 9
Therefore,
The solution to the system of equations are, x + 2y = 8 and -3x-2y = 12 is: X = -10 , Y = 9
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Find the value of each variable.
7
(4x + 8)
x=
Answer:
x=-1/4 or -.25
Step-by-step explanation:
I took the test and double checked it
find the surface area of the figure in square yards.
Answer:
578.0 yd^2
Explanation:
The formula for finding the surface area of a cylinder is given as;
[tex]A=2\pi r(h+r)[/tex]where A = surface area
pi = 3.14
r = radius of the base of the circle = diameter/2 = 8/2 = 4 yd
h = height = 19yd
Let's go ahead and substitute these values into our formula and solve for A;
[tex]\begin{gathered} A=2\ast3.14\ast4(19+4) \\ =25.12(23) \\ =577.76 \\ \therefore A=578.0yd^2 \end{gathered}[/tex]Find the perimeter of hexagon ABCDEF plotted below.
The mass, m kilograms, of a horse is 429 kg, correct to the nearest kilogram.
Complete this statement about the value of m.
Answer:
400 < m< 430 kg
Step-by-step explanation:
the mass of horse is 429 kg
estimated to the nearest hundred is 400 kg
estimated to the nearest tens is 430 kg
thus the value of m mass lies between 400 to 430
therefore
400 < m< 430 kg
The answer is 400 < m< 430 kg
Similarities and differences between AAS and ASA Congruence Postulates
Answer:
Similarity: Both are geometry terms, used in proofs.
Difference: When to use, in the ASA we have two angles and one included side, while the AAS we have two angles, but we want to find a relation involving the non-involved size.
Step-by-step explanation:
ASA: Angle, Side, Angle
AAS: Angle, Angle, Side
Similarity: Both are geometry terms, used in proofs.
Difference: When to use, in the ASA we have two angles and one included side, while the AAS we have two angles, but we want to find a relation involving the non-involved size.
I am going to use the drawer to show the differences:
Karen the trainer has two solo workout plans that she offers her clients: Plan A and Plan B. Each client does either one or the other (not both). On Monday therewere 3 clients who did Plan A and 5 who did Plan B. On Tuesday there were 6 clients who did Plan A and 2 who did Plan B. Karen trained her Monday clients fora total of 10 hours and her Tuesday clients for a total of 10 hours. How long does each of the workout plans last?
ive n
lan A
Plan B
Monday: 3 clients - Plan A
5 clients - Plan B
Total 10 hours
Tuesday
6 clients - Plan A
2 clients - Plan B
Total 10 hours
rocedure
Let's define a system of linear equations that represents the above problem.
A: Number of hours of workout in plan A
B: Number of hours of workout in plan B
[tex]\begin{gathered} 3A+5B=10 \\ 6A+2B=10 \end{gathered}[/tex]The goal here is to solve
3A+5B=10 and
6A+2B=10 for the variables A and B.
The solutions to your equations are:
A = 5/4 hour
B = 5/4 hour
If m angle ABD=100^ , what is the relationship between AD and CD? OAD AD + DC < AC; CD = AD; CD > AD; CD < AD
Answer: CD<AD
Step-by-step explanation:
Just got it right on the test.
Answer: CD<AD
Step-by-step explanation:
Took the test!
Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1. If P(aza)0.4314, find a. Round to two decimal places.
The z-score of the given expression P(-a < z < a) = 0.4314 is; 0.55
How to Interpret Normal Distribution?We are told that P(-a < z < a) = 0.4314. Thus;
P(-a < z < a) = 0.4314 is represented by the area about mean. This means that; 0.4314/2 = 0.2157 is the area each on the left side and right side of mean.
Now, from online z-score calculator, we see that the z value corresponding to 0.2157 is 0.55.
Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1, if P(-a < z < a) = 0.4314, then it means that the z score is 0.55.
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Complete question is;
Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1. If P(−a < z < a) = 0.4314, find d a. Round to two decimal places
8. There were a total of 117 football games in
the season, and 33 were played at night. The
season was nine months long. How many
games were played each month, if each month.
had the same number of games?
So, 13 games were played each month, if each month had the same number of games.
What is division?Compared to multiplication, division is the opposite. If three groups of four add up to 12, then division of 12 into three groups of equal size yields four in each group. Creating equal groups or determining how many people are in each group after a fair distribution is the basic objective of division. It is referred to as a method of division to divide anything. According to the degree of difficulty, there are three different sorts of division procedures. These include the bus stop approach, the chunking method, and the long division method. The chunking method is also known as division by repeated subtraction.
Given Data
A total of 117 football games in the season, and 33 were played at night.
The season was nine months long.
Each month same numbers of game were played.
So,
117 ÷ 9
13
So, 13 games were played each month, if each month had the same number of games.
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Need help with the bottom ones.. which is part b please.
EXPLANATION:
Solution first(a) exercise part b:
All the internal angles of a right triangle must add up to 180, so to order the internal angles from least to greatest we must find the missing angle;
The exercise is as follows:
[tex]\begin{gathered} D=61\text{ degr}ees \\ E=48\text{ degre}es \\ F=X \\ D+E+F=180 \\ 61+48+F=180 \\ 61+48-180=F \\ 71=F \\ The\text{ thre}e\text{ angles }added\text{ }must\text{ give 180;} \\ (D+E+F)=180 \\ (61+48+71)=180 \\ \\ \end{gathered}[/tex]Now we must order them from lowest to highest, the order is as follows:
[tex]ANSWER\colon E=48;\text{ D=61, F=71}[/tex]Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.Lauren had brochures printed for her new business venture. She originally ordered 4 boxes of black-and-white brochures and 4 boxes of color brochures, which cost a total of $148. After those ran out, she spent $125 on 4 boxes of black-and-white brochures and 3 boxes of color brochures. Given that the prices didn't change, what was the price of each type of brochure?
Let the price of black and white brouchers be x
The price of color brochures be y.
A/q,
4x+4y=148.....(1)
4x+3y=125 .....(2)
The equation (1) becomes,
x+y=37
y=37-x.......(3)
Putting (3) in (2) we have,
4x+3(37-x)=125
4x+111-3x=125
x=14
Putting the value of x in (3) we have,
y=37-14=23
The price of black and white brouches is $14
The price of color brouchers is $23.
Which relation is a function?
im stuck on this question
a) g(3) = -182
b) g(0) = 7
c) g(-1) = 70
Explanation:[tex]\begin{gathered} \text{Given:} \\ g(x)\text{ = }7\text{ - 63x} \end{gathered}[/tex]a) g(3): To get this, we will substitute 3 for x in the function g(x)
[tex]\begin{gathered} \text{x = 3} \\ g(3)=\text{ 7 - 63(3) = 7 - 189} \\ g(3)\text{ = }-182 \end{gathered}[/tex]b) g(0): To get this, we will substitute 0 for x in function g(x)
[tex]\begin{gathered} x\text{ = 0} \\ g(0)\text{ = 7 - 63(0) = 7 - 0} \\ g(0)\text{ = 7} \end{gathered}[/tex]c) g(-1): To get this, we will substitute -1 for x in function g(x)
[tex]\begin{gathered} x\text{ = -1} \\ g(-1)\text{ = 7 - 63(-1)} \\ mu\text{ltiplication of same signs give positive sign} \\ g(-1)\text{ = 7 + 63} \\ g(-1)\text{ = 70} \end{gathered}[/tex]The right angled triangle has an area of 22.5 cm² X+1 X-3 help quick with no calcalator way or quadratic formula
Answer:
x = 8
Step-by-step explanation:
You want the value of x for a right triangle with side lengths (x+1) and (x-3) and an area of 22.5 cm².
Triangle areaThe area of a triangle is given by the formula ...
A = 1/2bh
Then the area of this triangle is ...
22.5 = 1/2(x -3)(x +1)
45 = x² -2x -3
48 = x(x -2) . . . . . . . add 3 and factor out x
We know that 48 can be factored as (8)(6). Comparing this to x(x-2), we see that x=8.
__
Additional comment
x could also be -6, but that would make the side lengths be negative. The only applicable solution for this geometry is x=8.
Suppose there are 17 jelly beans in a box-2 red, 6 blue, 4 white, and 5 green.
What part of the jelly beans is blue? Express your answer in each of the forms requested.
I need help with this question
Probability that first three price winners are omar, kira and elsa is [tex]\frac{1}{84}[/tex]
Probability that omar is first prize winner and kira is second prize winner and elsa is third price winner is [tex]\frac{1}{504}[/tex]
What is permutation and combination ?When things are of diverse kinds, the term "permutation" is used to describe the various arrangements that could be made. Combination, meanwhile, is the quantity of smaller groups or sets that can be created from the components of a bigger set.
(i)First 3 prizes must be given to 3 persons regardless of order
Hence they can also be arranged in 3! ways.
est 6 can be arranged in 6! ways.
positions ___ ___ ___ ___ ___ ___ ___ ___ ___
number of ways 3 2 1 6 5 4 3 2 1
total number of ways to arrange 9 people = 9!
[tex]P(A)= \frac{(3)(2)(1)(6)(5)(4)(3)(2)}{(9).(8).(7).(6).(5).(4).(3).(2))}[/tex][tex]P(A)=\frac{6}{9.8.7}[/tex][tex]P(A)= \frac{1}{84}[/tex]
(ii)Event A
In event A three positions are fixed .
Omar -1 Kira -2 Elsa -3
Therefore there is only 1 way to fill the 1st,2nd and 3rd position
Permutations can only be made among the other positions.
Positions - ___ ___ ___ ___ ___ ___ ___ ___ ___
Number of ways- 1 1 1 6 5 4 3 2 1
Total number of ways of arranging 9 people =9×8×7×6×5×4×3×2×1
Number of ways to satisfy event A =1×1×1×6×5×4×3×2×1
P(A)= [tex]\frac{(6)(5)(4)(3)(2)(1)}{(9)(8)(7)(6)(5)(4)(3)(2)(1)}[/tex]
P(A)= [tex]\frac{1}{504}[/tex]
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Two friends, Grayson and Santiago, had just bought their first cars. The equation y=31.9xy=31.9x represents the number of miles, yy, that Santiago can drive his car for every xx gallons of gas. Grayson uses 8 gallons of gas to drive 328.8 miles in his car.
How many miles less does Santiago's car travel on one gallon of gas than Grayson's car?
Step-by-step explanation:
Two friends, Grayson and Santiago, had just bought their first cars. The equation y=31.9xy=31.9x represents the number of miles, yy, that Santiago can drive his car for every xx gallons of gas. Grayson uses 8 gallons of gas to drive 328.8 miles in his car.
How many miles less does Santiago's car travel on one gallon of gas than Grayson's car?
..
please post full questions
please followThe city of St. Louis is creating a welcome sign on a billboard for visitors to see as they enter the city. The following picture needs to be enlarged so that 1/2 inch represents 7 feet on the actual billboard. Will it fit on a billboard that measures 14 feet in height if the height of the figure is 1 in?
The scale is 1/2 to 7 feet. That means that for each half of an inch of the original picture, the scaled figure will have 7 feet.
Now,
[tex]1\text{ in = }\frac{1}{2}in\text{ +}\frac{1}{2}in.[/tex]That means that 1 inch corresponds to 7ft +7ft= 14ft.
Therefore, if my original figure is 1 inch in height the scaled picture will be 14 ft in height.
Answer: The scaled figure will fit in the billboard.
2a + 3b = 8 and 4x + 10y = 50
(i) What is the value of 6a + 9b?
(ii) What is the value of 2x + 5y?
a. It should be noted that the equation illustrates that the value of 6a + 9b is 24.
b. The value of 2x + 5y is 25.
How to illustrate the information?a. From the information, 2a + 3b = 8. The value of 6a + 9b will be:
6a + 9b = 3(2a + 3b)
This implies that the value will be multiplied by 3. Therefore, 8 × 3 = 24
(ii) What is the value of 2x + 5y?
4x + 10y = 50
It should be noted that this can be divided through by 2. This will be;
(4x + 10y = 50) / 2
2x + 5y = 25
The value is 25.
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Simplify: (7r³ + 10r²s) + (−3rs² − 8s³) − (−r²s + 6rs²).
7r³ + 11r²s -9rs² - 8s³ is the simplification of the expression (7r³ + 10r²s) + (−3rs² − 8s³) − (−r²s + 6rs²).
How to simplify equation?The process of writing an expression in the most effective and compact way possible without affecting the original expression's value is known as simplification of an algebraic expression.
Collecting similar terms is the process, which entails expanding or contracting the terms in an expression.
Let's review some of the crucial words used during expression simplification:
In an algebraic expression, a variable is a letter with an undetermined value.
A coefficient is a number that is used with a variable.A term with a fixed value is called a constant.Variables with the same letter and power are known as like terms. Sometimes, similar terms will have different coefficients.We have been asked to simplify the expression
(7r³ + 10r²s) + (−3rs² − 8s³) − (−r²s + 6rs²)
Let's simplify
⇒ (7r³ + 10r²s) + (−3rs² − 8s³) − (−r²s + 6rs²)
⇒ 7r³ + 10r²s −3rs² − 8s + r²s -6rs²
⇒ 7r³ + 11r²s -9rs² - 8s³
Thus, 7r³ + 11r²s -9rs² - 8s³ is the simplified form of the expression (7r³ + 10r²s) + (−3rs² − 8s³) − (−r²s + 6rs²).
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Use the Polygon tool to draw an image of the given polygon under a dilation with a scale factor of and center of dilation (0,0)
The dilated polygon image is attached below under a dilation with a scale factor of 3 and center of dilation (0,0)
What exactly is a polygon?In geometry, a polygon is a two-dimensional closed shape with straight sides that is flat or plane. It doesn't have any curved edges. A polygon's sides are also known as its edges. The vertices (or corners) of a polygon are the points where two sides meet.
What is transformation and dilation?Transformation is the movement of a point from one location to another. Transformations include rotation, reflection, translation, and dilation.
Dilation is the process of increasing or decreasing the size of a figure by a factor k. If a point A(x, y) is dilated about the origin by a factor k, the new point is A' (kx, ky).
Assume the polygon has vertices at A(0, 0), B(3, 3) and C. (-3, 3). If the polygon is dilated by a factor of three with the center of dilation at (0, 0), the new vertices are as follows:
A'(0,0), B'(1, 1) and C'(-1, 1)
Therefore, the polygon graph is attached in which the polygon is dilated by a factor of three with the center of dilation at (0, 0),
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g(x) = 5x – 3g(-2) =?
Can you help me solve this question?
SOLUTION
Step1:
hence from the diagram above, the dimension of the rug is
[tex]\begin{gathered} 34-2x\text{ and } \\ 24-2x \end{gathered}[/tex]Since we have area of the rug,
then we have
[tex](34-2x)(24-2x)=704[/tex]We now solve the equation above quadratically
[tex]\begin{gathered} (34-2x)(24-2x)=704 \\ \text{expand the parenthesis } \\ 16-116x+4x^2=704 \\ \text{subtract 704 from both sides } \\ 816-116x+4x^2-704=704-704 \end{gathered}[/tex]Then we have
[tex]4x^2-116x+112=0[/tex]Solve using factor method we obtain
[tex]\begin{gathered} \text{Divide through by 4} \\ x^2-29x+28=0 \\ x^2-28x-x+28=0 \\ x(x-28)-1(x-28)=0 \\ (x-28)(x-1)=0 \end{gathered}[/tex]Equating each factor to zero we have
[tex]\begin{gathered} x-28=0,x-1=0 \\ x=28,1 \end{gathered}[/tex]Since x can not be 28, the value of x is 1
The Dimension of the rug becomes
[tex]\begin{gathered} 34-2x=34-2(1)=32 \\ \text{and } \\ 24-2x=24-2(1)=22 \end{gathered}[/tex]Hence the dimension of the rug is 32 ft by 22ft (22,32)
[tex]\rm \int_{-\infty}^0\sqrt{1+2^2}e^{2\theta}d\theta=\phi-\frac12\\[/tex]
Nothing tricky here:
[tex]\displaystyle \int_{-\infty}^0 \sqrt{1+2^2} \, e^{2\theta} \, d\theta = \sqrt5 \int_{-\infty}^0 e^{2\theta} \, d \theta \\\\ ~~~~~~~~ = \frac{\sqrt5}2 \left(e^0 - \lim_{\theta\to-\infty} e^{2\theta}\right) \\\\ ~~~~~~~~ = \frac{\sqrt5}2[/tex]
Recall that
[tex]\phi = \dfrac{1+\sqrt5}2[/tex]
and this is exactly 1/2 more than the value of the integral.