It is required to find the area of the sector AOB in terms of π.
Notice that the central angle is 120º.
Recall that the Area of a sector is given as:
\(A=\frac{\theta}{360^{\circ}}\times\pi r^2\)Where θ is the central angle and r is the radius.
Substitute θ=120º and r=9 into the formula:
\(\begin{gathered} A=\frac{120^{\circ}}{360^{\circ}}\times\pi(9^2) \\ \end{gathered}\)Evaluate the expression on the right:
\(A=\frac{\cancel{120^{\circ}}1}{\cancel{360^{\circ}}3}\times81\pi=\frac{1}{3}\times81\pi=27\pi\text{ square units}\)Hence, the required area of the sector in terms of π is 27π.
What is the Measure of angle AOE in the figure below?
Answer:
The answer is D: 130
Step-by-step explanation:
(3x-28) +90+(66-x) = 180
2x + 128 = 180
2x = 52
x = 26
Therefore Angle AOE = 90 + (66-26)
= 130
a number has the same digits in its hundreds place and it’s hundrthes place. how many times greater is the value of the digit in the hundreds place than the value of the digit in the hundreds place
In a case whereby a number has the same digits in its hundreds place and it’s hundredths place the number of times that the value is greater in the hundreds place than the value of the digit in the hundreds place is 10,000 times.
How can the value of the digit can be calculated?The question can be interpreted that the particular number has the same digit which is seen in hundreds place hence hundredths place.
we can then represent the digit as '1'.
The value of number's hundreds place can be represented as 100
we can as well represent the number's hundredths place as 0.01
the number of times the value of the hundreds place digit exceeds the value of the hundredths place digit can be expressed as 100/0.01 =(100*100)/1 = 10, 000
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missing options:
A. 100,00
B. 100
C. 1,000
D. 10,000
what is the standard error of mean if o=64 and n=64?
The standard error of mean if o=64 and n=64 will be 8 given the parameters standard deviaion of = 64 and n = 64.
How can the standard error mean be obtained?The formula N provides the standard error mean. We must be aware that the standard error means in the given question is denoted by the letter M.
Applying the formula now, we get the following:
σM = 64/√64
64 divided by its square root gives us the number 8.
The standard error means is thus equal to 64 divided by 8, or 8.
We may then conclude that the standard error means will be 8 given the standard error means of = 64 and n = 64.
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Prove that 5^7 + 5^6 is divisible by 6
5^7 + 5^6 = __ • 6
Answer:
Step-by-step explanation:
\(5^{7}\) + \(5^{6}\) = 5 × \(5^{6}\) + \(5^{6}\) = \(5^{6}\) ( 5 + 1 ) = \(5^{6}\) · 6
Hey there!
\( -› \: {5}^{7} + {5}^{6} \)
\(-› 78,125 + 15,625\)
\(-› \: 93750\)
\(-› \: 93750 \div 6\)
\(-› \: 15625\)
Therefore, It's divisible by 6
Write the polynomial that has factors of -15 and 3.
Answer:
Find the GCF of all the terms in the polynomial.
Express each term as a product of the GCF and another factor.
Use the distributive property to factor out the GCF.
Step-by-step explanation:
In a board game a certain number of points is awarded to a player upon rolling a six sided die labeled 1 to 6 according to the function f(x)=4x+4 whereby is it he value rolled on the die fund and interpret the given functions values and determine an appropriate domain for the function
The function f(x) = 4x + 4 means that for each value of x, the player will receive 4 times that value plus 4 points, and domain for the function is Domain = {1, 2, 3, 4, 5, 6}.
What is the domain?
The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.
The function f(x) = 4x + 4 describes the number of points awarded to a player based on the value rolled on a six-sided die labeled 1 to 6.
To find the function value for a given roll, we simply substitute the roll value for x and evaluate the function. For example, if the roll is 3, then the function value is:
f(3) = 4(3) + 4 = 12 + 4 = 16
This means that the player is awarded 16 points for rolling a 3.
The domain of the function is the set of possible input values, which in this case are the numbers 1, 2, 3, 4, 5, and 6. This is because the die is labeled with these numbers and only these numbers, so it is not possible to roll any other value. Therefore, we can write the domain as:
Domain = {1, 2, 3, 4, 5, 6}
Interpretation: The function f(x) = 4x + 4 means that for each value of x, the player will receive 4 times that value plus 4 points.
The function provides a linear relationship between the roll value on the die and the points awarded to the player.
The function has a positive slope, which means that higher roll values result in more points awarded.
Hence, The function f(x) = 4x + 4 means that for each value of x, the player will receive 4 times that value plus 4 points, and the domain for the function is Domain = {1, 2, 3, 4, 5, 6}.
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A scale drawing of a lake has a scale of 1 cm to 75 m. If the actual width of the lake is 1,000 m, what is
the width of the lake on the scale drawing? Explain or show your reasoning.
After calculating the value of 1 cm to 75 m, we have come to find that the width of the lake on the scale drawing is 13.3cm
What is scale drawing?A drawing of a real object with accurate sizes that have been reduced or enlarged by a certain amount (called the scale).
A floor plan is a scale drawing of the relationships between rooms, spaces, and other physical features at one level of a structure in architecture and building engineering.
In the most basic sense, floor plans (scaled drawings) are a set of instructions used to construct the space (object).
We have given that 1cm is equal to 75 m in a scale drawing of a lake
If 75 m is 1cm
then 1000m is 13.3cm
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2x-1=y
3x-1=y
Consider the system of equations above. Which of the following statements about this system is true?
Answer:
B; There is only one (x,y) solution and y is negative
Step-by-step explanation:
First, I graphed the two equations. Attached is an image of the equations graphed. Next, I looked for overlapping points. Wherever the two points overlap, there is a solution. When looking at the graph, we can see the lines overlap at only one point, (0,-1). Since y is negative, the answer must be B; there is only one (x,y) solution and y is negative.
If this answer helped you, please leave a thanks!
Have a GREAT day!!!
URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
The point (2, 5) is a solution to the system of equations:
y = -x/2 + 6
y = 3x - 1
To determine which system of equations the point (2, 5) is a solution to, we can substitute the values of x and y into each equation and check if they satisfy the equations.
Let's substitute (2, 5) into each system of equations:
1. y = x - 8:
Substituting x = 2 and y = 5:
5 = 2 - 8
This equation is not satisfied.
2x + y = 7:
Substituting x = 2 and y = 5:
2(2) + 5 = 7
4 + 5 = 7
This equation is not satisfied.
2. y = x + 2:
Substituting x = 2 and y = 5:
5 = 2 + 2
5 = 4
This equation is not satisfied.
y = x + 5:
Substituting x = 2 and y = 5:
5 = 2 + 5
5 = 7
This equation is not satisfied.
3. y = -x/2 + 6:
Substituting x = 2 and y = 5:
5 = -(2)/2 + 6
5 = -1 + 6
5 = 5
This equation is satisfied.
y = 3x - 1:
Substituting x = 2 and y = 5:
5 = 3(2) - 1
5 = 6 - 1
5 = 5
This equation is satisfied.
4. y = 2x/3 + 6:
Substituting x = 2 and y = 5:
5 = 2(2)/3 + 6
5 = 4/3 + 6
This equation is not satisfied.
3y + 6x - 18 = 0:
Substituting x = 2 and y = 5:
3(5) + 6(2) - 18 = 0
15 + 12 - 18 = 0
27 - 18 = 0
9 = 0
This equation is not satisfied.
From the above calculations, we can see that the point (2, 5) is a solution to the system of equations:
y = -x/2 + 6
y = 3x - 1
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Consider a function f(x) = |x|. A second function g(x) is the result of translating f(x) by 5 units in
the negative y-direction (downward), and 3 units in the positive x-direction (to the right). Write the equation of g(x)
Please Help!!!
The translated function g(x) = | x - 3 | - 5 shifted 3 units along the positive x-axis and 5 units along the negative y-axis.
What are some transformations of functions?Suppose we have a function f(x).
f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).
f(x ± c) = Horizontal left/right shift by c units (x - + c, y).
(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).
f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).
f(-x) = Reflection over y axis, (-x, y).
-f(x) = Reflection over x-axis, (x, -y).
Given, A parent function f(x) = | x |.
Now the result of translating f(x) by 5 units in the negative y-direction and 3 units in the positive x-direction g(x) = | x - 3 | - 5.
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Which ordered pair is a solution to the system of inequalities
Answer:
A
Step-by-step explanation:
i took the test
Jaime earned some money mowing the neighbor's lawn. He spent one-fourth of his money to take his friends to see a movie. Then he spent $7.00 on popcorn and drinks. When he went home, he had $71.00 left. How much did Jaime earn mowing the neighbor's lawn?
A. $13
B. $64
C. $78
D. $104
The surface area of given figure is 200cm². i. Find height of triangle. ii. Find value of y. 80⁰ 5cm 5cm
Answer:
the answer is 16 . the explanation is that because if you have. 200 cm y axis it overcomes the x of other 80
What is the answer -13.62-(27.9)
Answer:
− 1049
Step-by-step explanation:
-13.62-(27.9)
primero haremos los paréntesis y después las demás multiplicaciones de izquierda a derecha.
-13.62-243
-806-243
Finalmente tenemos − 1049
Espero te ayude :)
Answer:
-41.52
Step-by-step explanation:
-13.62 - (27.9) = -13.62 - 27.9When you subtract from a negative, the answer will be smaller than the starting number:
-13.62 - 27.9 = -41.52Therefore, the answer is -41.52.
Which values are possible rational roots of 9x3+14x2−x+18=0 according to the rational root theorem? Select each correct answer.
The possible roots of the cubic polynomial 9x³ + 14x² - x + 18 are 1, 2, and 3.
What is the rational root theorem?The rational root theorem explains how a polynomial's roots and coefficients are related. It explains the kind of rational roots that the polynomial might have in particular.
According to the rational root theorem, the possible roots of a polynomial of degree three and above are,
± (coefficient of the last term)/(coefficient of the first terms).
Given, A polynomial 9x³ + 14x² - x + 18 it is a cubic polynomial so it should have three roots they could be,
The factors of the constant term divided by the factors of the first terms,
So, 18 has factors ± (1, 2, 3, 6, 9, 18) and 9 has factors ± (1, 3, 9).
So, The possible roots are ± (1, 2, 3) and so on.
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Find the equation of the line that satisfies the conditions given in each of the following: 1. Through (3, 2) and (5, 7) 2. Through (-3, 4), m = 2 3. m = -3, b = 5 4. x-intercept = 3, y-intercept
The equation of each line that satisfies the given conditions are:
1. y - 2 = 5/2(x - 3)
2. y - 4 = m(x + 3)
3. y = -3x + 5
What is the Equation of a Line?If we know the slope (m) and the y-intercept (b) of a line, we can write the equation of the line as y = mx + b in slope-intercept form.If we know the point (a, b) and the slope (m) of the line, we can write the equation of the line in point-slope form as y - b = m(x - a).1. Given the points, (3, 2) and (5, 7), find the slope (m):
Slope (m) = change in y / change in x = (7 - 2)/(5 - 3)
m = 5/2
Write the equation in point-slope form by substituting m = 5/2 and (a, b) = (3, 2) into y - b = m(x - a):
y - 2 = 5/2(x - 3)
2. Given:
A point = (-3, 4)
Slope (m) = 2
Substitute (a, b) (-3, 4), and m = 2 into y - b = m(x - a):
y - 4 = m(x + 3) [equation of the line]
3. Given:
Slope (m) = -3
Y-intercept (b) = 5
Substitute m = -3 and b = 5 into the equation y = mx + b:
y = -3x + 5
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Which of the following is the surface area of the right cylinder below?
Write and solve an equation for the following.
Four more than one-half a number is three. What is the number?
Answer:
4+ \(\frac{1}{2}\)x = 3
Step-by-step explanation:
4 + \(\frac{1}{2}\)x = 3 (subtract 4 from both sides)
\(\frac{1}{2}\)x = -1 (multiply both sides by 2)
x = -2
Answer:
4+ 1/2 x = 3
Step-by-step explanation:
X =-2
What is the measure of angle jnk?
The hourly wage, the number of hours and the number of days Jaxon works indicates that the amount Jaxon gets paid is $192
What is the formula for calculating hourly wage?The formula for hourly wage can be presented as follows;
Hourly wage = Total earnings/Total hours worked
The question in the link is presented as follows;
Jaxon gets paid $6 an hour. He works for 8 hours each day for four days. How much will Jaxon get paid
The amount Jaxon gets paid per hour (his hourly wage) = $6
The number of hours he works each day = 8 hours
The number of days Jaxon works = Four days
The amount Jaxin gets paid = Hourly wage × Hours per day × Number of days
Therefore we get;
Amount he gets paid = $6 per hour × 8 hours/day × 4 days = $192
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A fast-food worker works Monday through Friday, 8 hours per day. Daily, the worker receives a -hour break in the morning, a -hour break for lunch, and a -hour break in the afternoon. How many hours of break time does the worker receive per day?
The worker recieves 3 hours of break time per day.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that a a fast-food worker works Monday through Friday, 8 hours per day. Daily, the worker receives a hour break in the morning, a hour break for lunch, and a hour break in the afternoon.
The worker recieves three breaks, meaning it recieves 3 hours of break time per day.
Therefore, the worker recieves 3 hours of break time per day.
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Can someone please answer and provide an explanation for these problems?
Step-by-step explanation:
The way you can think about volume is that we have some cross sectional area times the height of the solid.
27.
The volume of a square based pyramid is
\(v = {s}^{2} ( \frac{h}{3} )\)
where h is the height of the pyramid
s is the side length of the square base.
S=7
h=12
\(v = {7}^{2} ( \frac{12}{3} ) = 49 \times 4 = 196\)
28. The volume of a rectangular prism
\(v = l \times w \times h\)
where l is length
w is width
h is height
\(v = 11 \times 11 \times 8 = 968\)
29.
Use the same formula in 27
\(v = 100(3) = 300\)
30.
Volume of a Cylinder is
\(v = \pi {r}^{2} h\)
where r is the radius of the circle
where h is the height
r is half of the diameter
The diameter is 22, thus the radius is 11.
\(v = {11}^{2} (8)(\pi)\)
\(v = 968\pi\)
pi is approximately 3.14
\(v = 3041.06\)
31. Volume of A Sphere
\( \frac{4}{3} \pi {r}^{3} = v\)
The radius is half of diamter, thus r=7
\( \frac{4}{3} \pi( {7}^{3} ) = 1436.76\)
Please i need the answer fast k12
(A) The range and IQR for boxplot 1 is 10 and 6 respectively.
(B) The range and IQR for boxplot 2 is 12 and 7 respectively.
What is the IQR?The interquartile range defines the difference between the third and the first quartile.
The formula for the interquartile range is given below.
Interquartile range = Upper Quartile – Lower Quartile = Q3 – Q1
What is the range?The range is the difference between the lowest and highest values.
The formula for the interquartile range is given below.
Range = Maximum – Minimum
(A) For boxplot 1, we need to find the range and IQR from the given data set.
So, let 34 be the maximum and 24 be the minimum.
\(\text{Range}=\sf 34-24\)
\(\text{Range}=\sf10\)
Therefore, the range is 10.
Now time to find the IQR.
So, let 33 be Q3 and 27 be Q1.
\(\text{IQR}=\sf 33-27\)
\(\text{IQR}=\sf 6\)
Therefore, the IQR is 6.
(B) Now for boxplot 2, we will do the same thing as from part A.
Let's find the range.
So, let 24 be the maximum and 12 be the minimum.
\(\text{Range}=\sf 24-12\)
\(\text{Range}=\sf12\)
Hence, the range is 12.
Now for the IQR.
So, let 22 be Q3 and 15 be Q1.
\(\text{IQR}=\sf 22-15\)
\(\text{IQR}=\sf 7\)
Hence, the IQR is 7.
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8x+7.5=3.5 What's the value of x? Please show your work. :)
Answer:
x = 0.5
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Exact Form: x = -1/2
A satellite orbits the Earth with an elliptical orbit modeled by x squared over 47 million four hundred seventy two thousand one hundred plus y squared over forty four million two hundred twenty two thousand five hundred equals 1 comma where the distances are measured in km. The Earth shares the same center as the orbit. If the radius of the Earth is 6,370 km, what is the maximum distance between the satellite and the Earth?
The maximum distance between the earth and the satellite orbit with an elliptical orbit is 520 km.
In the question, we are given that a satellite orbits the Earth with an elliptical orbit modeled by x squared over 47 million four hundred seventy two thousand one hundred plus y squared over forty four million two hundred twenty two thousand five hundred equals 1, where the distances are measured in km. The Earth shares the same center as the orbit.
We are asked to find the maximum distance between the satellite and the Earth if the radius of the Earth is 6,370 km.
Given elliptical form is:
x²/47,472,100 + y²/44,222,500 = 1,
or, x²/6,890² + y²/6,650² = 1.
The radius of the Earth, R = 6,370 km.
We know that the standard elliptical form is:
(x - h)²/a² + (y - k)²/b² = 1, Where, in a horizontal ellipse;
a = The major axis (the longer axis), which gives the maximum distance between the satellite and Earth.
b = The minor axis (the shorter axis).
On comparing the given elliptical form to the standard elliptical form, we get a = 6,890.
The distance between the satellite and the surface of the Earth, d, is given as follows:
d = a - R
Which gives;
d = 6,890 km - 6,370 km = 520 km.
Thus, the maximum distance between the earth and the satellite orbit with an elliptical orbit is 520 km.
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1 + 1 = ?
just so you can get some points ;)
Answer:
2
Step-by-step explanation:
no explanation lol hahahahha
Answer:
tyyyy
Step-by-step explanation:
Can someone help me with this? I want to understand each step.
Thank you
The first 5 terms of the sequence is given by A = { -4.8 , 1.92 , -0.768 , 0.3072 , -0.12288 }
Given data ,
Let the geometric sequence be represented as A
Now , the value of A is
A = 12 ( -2/5 )ⁿ
On simplifying , we get
when n = 1
A₁ = 12 ( -2/5 ) = -4.8
A₂ = 12 ( -2/5 )²
A₂ = 12 ( 4/25 ) = 1.92
A₃ = 12 ( -2/5 )³
A₃ = -12 ( 8/125 ) = -0.768
A₄ = 12 ( -2/5 )⁴
A₄ = 12 ( 16 / 625 ) = 0.3072
A₅ = 12 ( -2/5 )⁵
A₅ = -12 ( 32 / 3,125 ) = -0.12288
Hence , the geometric sequence is solved
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given f(x) = x - 2 and g(x) = x^2 + 2, find (fog)(x)
Answer:
(f ○ g)(x) = x²
Step-by-step explanation:
to find (f ○ g)(x) , substitute x = g(x) into f(x)
(f ○ g)(x)
= f(g(x) )
= f(x² + 2)
= x² + 2 - 2
= x²
Please check all that apply
The symbols which correctly relates the two numbers are :
>≥≠We could relate the two given numbers 100 and 20 on the basis of magnitude and equality.
100 is greater than 20, 100> 20
100 is greater than or equal to 20 , 100 ≥ 20
100 is not equal to 20 , 100≠20
Therefore, the symbols which relates the numbers are :
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please help thanks I will follow if you answer correctly
One truck from Lakeland Trucking, Inc. can carry a load of 3880.8 lb. Records show that the weights of boxes that it carries have a mean of 75 lb and a standard deviation of 14 lb. For samples of size 49, find the mean and standard deviation of overbar(x).
Question 10 options:
A)
μoverbar(x)= 2; σoverbar(x)= 75
B)
μoverbar(x)= 14; σoverbar(x)= 75
C)
μoverbar(x)= 75; σoverbar(x)= 2
D)
μoverbar(x)= 75; σoverbar(x)= 14
Answer:
A
Step-by-step explanation:
The correct option is A) μoverbar(x)= 2; σoverbar(x)= 75.