The transformation [tex]$\mathrm{T}^{-1}$[/tex] exists described as
[tex]$T^{-1}:(x, y) \rightarrow(x-4, y-3)$$[/tex]
The value of a exists -4 and value of b exists -3.
How to determine the value of [tex]$\mathrm{T}^{-1}$[/tex]?
The transformation T exists given as
[tex]$T:(x, y) \rightarrow(x+4, y+3)[/tex]
Let the transformation [tex]$\mathrm{T}^{-1}$[/tex] exists described as
[tex]$T^{-1}:(x, y) \rightarrow(x+a, y+b)$$[/tex]
If T and [tex]$T^{-1}$[/tex] exists inverses each other, then
[tex]$&T\left(T^{-1}(x)\right)=x \\[/tex]
[tex]$&T(x+a)=x \\[/tex]
[tex]$&x+a+4=x \\[/tex]
[tex]$&a=-4[/tex]
The value of a exists -4.
If T and [tex]$\mathrm{T}^{-1}$[/tex] exists inverses each other, then
[tex]$&T\left(T^{-1}(y)\right)=y \\[/tex]
[tex]$&T(y+b)=y \\[/tex]
[tex]$&y+b+3=y \\[/tex]
b = -3
The value of b exists -3.
The transformation [tex]$\mathrm{T}^{-1}$[/tex] exists described as
[tex]$T^{-1}:(x, y) \rightarrow(x-4, y-3)$$[/tex].
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What is the value of x?
90 degrees
170 degrees
X
Z
Answer:
x = 45 degrees.
Step-by-step explanation:
The arc of 90 degrees an angle of 1/2 its value on the circumference.
1/2 * 90
= 45 degrees.
13% of a sample of 200 students do not like ice cream. what is the 95% confidence interval to describe the total percentage of students who do not like ice cream?
Using the z-distribution, the 95% confidence interval to describe the total percentage of students who do not like ice cream is:
(8.34%, 17.66%).
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
For this problem, the estimate and the sample size are given, respectively, by:
[tex]\pi = 0.13, n = 200[/tex]
Hence the bounds of the interval are:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.13 - 1.96\sqrt{\frac{0.13(0.87)}{200}} = 0.0834[/tex][tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.13 + 1.96\sqrt{\frac{0.13(0.87)}{200}} = 0.1766[/tex]As a percentage, the interval is:
(8.34%, 17.66%).
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Find the area of the shaded region if the dimensions of the unshaded region are 20ft x 35ft . use 3.14 for π as necessary.
Area of the shaded region is 1397.46 square feet.
what is area of shaded region?The area of the shaded region is the difference between the area of the entire polygon and the area of the unshaded part inside the polygon. The area of the shaded part can occur in two ways in polygons. The shaded region can be located at the center of a polygon or the sides of the polygon.
We are to find the area of the shaded region. For that, we will divide the figure into smaller shapes, find their areas separately and then add them up.
From the given figure, we can see that there are two semi circles or say one whole circle if we combine them at the ends while 2 rectangles at the top and bottom.
Radius of circle = [tex]\frac{20+7+7}{2}[/tex] = 17
Area of circle = [tex]\pi r^{2}[/tex]
= [tex]\pi( 17)^{2}[/tex]
= 907.92 square ft.
Area of rectangles =2×(l×b)
= 2×20×35
= 490 square ft
Then,
Area of the shaded region = 907.92 +490
= 1397.46 square ft
Hence,Area of the shaded region is 1397.46 square ft.
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A gardener uses 1/3 of a liter of water to water 2/7 of a garden.
the gardener would need (1 + 1/6) liters of water to water the whole garden.
How much water would the gardener need to water the whole garden?Here we know that the gardener needs 1/3 of a liter of water to water 2/7 of a garden.
Then we have the relation:
1/3 L = 2/7 of a garden.
Now, we want to get a "1 garden" in the right side of the equation, then we can multiply both sides by (7/2), so we get:
(7/2)*(1/3) L = (7/2)*(2/7) of a garden
(7/6)L = 1 garden.
(1 + 1/6) L = 1 garden
This means that the gardener would need (1 + 1/6) liters of water to water the whole garden.
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What is the value of x to the nearest tenth? The figure is not drawn to scale
Answer:
(b) x = 10.5
Step-by-step explanation:
The angle bisector divides the triangle line segments proportionally.
ProportionThe proportion between corresponding line segments can be written several ways. One of them is ...
long side/long side = short side/short side
x/19.3 = 3.9/7.2
Multiplying by 19.3, we get ...
x = 19.3×3.9/7.2 ≈ 10.5 . . . units
__
Additional comment
You can eliminate the incorrect answer choices simply by looking at the possible side lengths of x.
19.3 -(3.9+7.2) < x < 19.3 +(3.9+7.2) . . . . . from triangle inequality
8.2 < x < 30.4 . . . . . . . simplify
There is only one answer choice in this range: the correct one.
In accordance with the marshaling of assets provision of the uniform partnership act, the correct ranking of the following liabilities of a partnership in order of payment is: $20,000 loan from a partner. $30,000 of profits from the last year of operations. $3,000 payable to a supplier. $100,000 in capital balances of the partners.
The correct order is 3,1,4,2.
(3) $3,000 payable to a supplier. (1) $20,000 loan from a partner. (4) $100,000 in capital balances of the partners.(2) $30,000 of profits from the last year of operations. What is the uniform partnership act?The Uniform Partnership Act (UPA) governs corporate partnerships in various states in the United States. When a partner dissociates, the UPA provides regulations for the dissolution of the partnership. Several revisions to the Uniform Partnership Act have been made over the years (UPA). The Revised Uniform Partnership Act refers to the revised act and changes (RUPA).The Uniform Partnership Act also governs partnership formation, liabilities, assets, and fiduciary obligations.Marshaling of assets:
The process of organizing the balance sheet elements (assets and liabilities) in a specified sequence is referred to as the marshaling of assets and liabilities. In other words, it is the process of organizing the various assets and liabilities on a balance sheet in a particular order.The order is the amount owed to a supplier, the amount of a loan from a partner, the amount of the partners' capital balances, and the number of profits from the previous year of operations.Therefore, the correct order is 3,1,4,2.
(3) $3,000 payable to a supplier. (1) $20,000 loan from a partner. (4) $100,000 in capital balances of the partners.(2) $30,000 of profits from the last year of operations.Know more about the uniform partnership act here:
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The correct question is given below:
In accordance with the marshaling of assets provision of the uniform partnership act, the correct ranking of the following liabilities of a partnership in order of payment is:
(1) $20,000 loan from a partner.
(2) $30,000 of profits from the last year of operations.
(3) $3,000 payable to a supplier.
(4) $100,000 in capital balances of the partners.
An equation is shown below:
6(2x – 11) + 15 = 3x + 12
Part A: Write the steps you will use to solve the equation, and explain each step. (6 points)
Part B: What value of x makes the equation true? (4 points)
Source
StylesFormatFontSize
Answer:
x = 7
Step-by-step explanation:
Distribute -
12x − 66 + 15 = 3x + 12
Combine Numbers and Variables -
12x - 51 = 3x +12
Get x on one side (isolate x) -
9x - 51 = 12
9x = 63
Divide 9 -
x =7
If you were solving a system of equations and you came to a statement like 1 = 3, what do you know about the solution to the system? (1 point) Group of answer choices The solution is (1, 3) The solution is x = 1 and y = 3 There is no solution There are infinitely many solutions
Solving the Question
When both sides of the equal sign are equal, there are infinite solutions.
When you are able to isolate the variable, there is only one solution.
When the equation states an untrue expression, there is no solution.
1=3 is an untrue fact. Therefore, there would be no solutions to the system.
AnswerThere is no solution
A pyramid has the same volume as a cube of side 10.0 cm
The height of the pyramid is the same as the side of the square base
Calculate the height of the pyramid
Textbook says the answer is 14.4 cm but i don't understand how
Please explain with step by step explanation
The height of the pyramid is 14.4 cm.
How to find the height of the pyramid?volume of a pyramid = 1 / 3 Bh
where
B = base areah = height of the pyramidTherefore,
volume of the cube = L³
where
L = side length of the cubeHence,
volume of the cube = 10³
volume of the cube = 1000 cm³
The volume of the pyramid is the same with the volume of the cube.
Hence,
1000 = 1 / 3 Bh
The height of the pyramid is the same as the square base.
Therefore,
1000 = 1 / 3 (h²)h
1000 = 1 / 3 h³
cross multiply
3000 = h³
h = ∛3000
h = 14.4224957031
Hence, the height of the pyramid is 14.4 cm.
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In the driest part of an Outback ranch, each cow needs about 40 acres for grazing. Write and solve an equation to find how many cows can graze on 720 acres of land.
Answer: 18 cows
Step-by-step explanation: C = how many cows can graze on 720 acres of land. 40(C) = 720. 720/40 = 18 C = 18.
Answer:
40x = 720
x = 18
Step-by-step explanation:
x = number of cows
Prove that 1 + cos theta - sin^2 theta
divided by sin theta [ 1 + cos theta]
is equal to cot theta
Answer:
CotO
Step-by-step explanation:
The process is int the picture
what is the equivalent expression (3*5)^6=?
Answer:
15^6
Step-by-step explanation:
According to BODMAS
where;
B - Bracket ()
O - Off (*)
D - Division (/)
M - Multiplication (*)
A - Addition (-)
S - Subtraction (+)
Bracket should be solved first
therefore;
(3*5)^6
15^6 = 11390625
Which can be approximately in standard form written as 1.1*10^7
What is the solution to the inequality 3x - 12| ≥ 6?
0-6
02
Ox<-6 or x> 18
Ox≤2 or x ≥6
========================================
Work Shown:
|3x-12| ≥ 6
3x-12 ≥ 6 or 3x-12 ≤ -6 ..... see note below
3x ≥ 6+12 or 3x ≤ -6+12
3x ≥ 18 or 3x ≤ -6+12
3x ≥ 18 or 3x ≤ 6
x ≥ 18/3 or x ≤ 6/3
x ≥ 6 or x ≤ 2
x ≤ 2 or x ≥ 6
----
Note: if |A| ≥ B, then A ≥ B or A ≤ -B where B is some positive number.
Example: |x| ≥ 5 means either x ≥ 5 or x ≤ - 5
The function f(x) = x2 6x 3 is transformed such that g(x) = f(x − 2). find the vertex of g(x).
the vertex of the function g(x) = f(x 2) .
A quadratic equation's vertex form is defined.If a quadratic equation is expressed as the following
[tex]y=a(x-h)^{2}+k[/tex]
It is then said to be in vertex form. Because the vertex point (peak point) occurs on the graph of this equation, it is so named (h,k)
The parabola that the quadratic equation depicts has this point (h,k) as its vertex.
How may the given equation be changed to be in vertex form?We first remove the x squared coefficient, and then inside the bracket, we strive to create a condition that resembles a perfect square.
So, this is what we have:
[tex]$f(x)=x^{2}+6 x+3$\\$g(x)=f(x-2)$[/tex]
Thus, we obtain:
[tex]\begin{aligned}&g(x)=f(x-2) \\&g(x)=(x-2)^{2}+6(x-2)+3 \\&g(x)=x^{2}-4 x+4+6 x-12+3 \\&g(x)=x^{2}+2 x-5\end{aligned}[/tex]
Vertex form transformation of g(x):
[tex]\begin{aligned}&g(x)=x^{2}+2 x-5 \\&g(x)=x^{2}+2 x+1-1-5 \\&g(x)=(x+1)^{2}-9 \\&g(x)=(x-(-1))^{2}-6 \\&g(x)=(x-(-1))^{2}+(-6)\end{aligned}[/tex]
By comparing this[tex]a(x-h)^{2}+k[/tex] to, we obtain the coordinates of the vertex of the graph of g(x) as (h,k) = (-1,-6), as shown below.
As a result, the vertex of the function g(x) = f(x 2) .
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How long does it take the wave to travel 6.0 m in the x-direction? 0.13 seconds 0.67 seconds 2.0 seconds 8.0 seconds
It takes the time for the wave to travel 6.0 m in the x-direction of 8s.
What is the wavelength?A wave's wavelength is measured in meters since it is the separation between its two peaks (or troughs). Since waves can be any size or shape, the prefix for meters can vary significantly, from km for radio waves to micrometers for visible light (although it is sometimes stated in nanometers) to picometers for gamma rays..
According to the information:the wavelength is 1.5 m.
λ/2 = 1 s
1.5/2 =1 s
0.75 m in 1 s is travelled by the wave.
To travel 6m , the time required is
= 6/0.75
=8s
Thus,
it takes the time for the wave to travel 6.0 m in the x-direction is 8s.
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100 POINTS HELP EXPERTS PLEAASE!
The graph shows the functions f(x), p(x), and g(x):
Graph of function g of x is y is equal to 2 multiplied by 0.85 to the power of x. The straight line f of x joins ordered pairs minus 7, 3 and minus 3, minus 2 and is extended on both sides. The straight line p of x joins the ordered pairs 4, 1 and minus 3, minus 2 and is extended on both sides.
Part A: What is the solution to the pair of equations represented by p(x) and f(x)? (4 points)
Part B: Write any two solutions for f(x). (4 points)
Part C: What is the solution to the equation p(x) = g(x)? Justify your answer. (6 points)
Answer:
A) (-3, -2)
B) (-7, 3) and (-3, -2)
C) (4.074, 1.032)
Step-by-step explanation:
An ordered pair is a solution to an equation if it satisfies the equation — makes it true. The given points are solutions to the functions whose graphs pass through those points.
Part A.The function p(x) is defined to pass through points (4, 1) and (-3, -2).
The function f(x) is defined to pass through points (-7, 3) and (-3, -2).
These function definitions have point (-3, -2) in common.
(-3, -2) is the solution to the equation p(x) = f(x).
Part B.The function f(x) is defined to pass through points (-7, 3) and (-3, -2).
Two solutions to f(x) are (-7, 3) and (-3, -2).
We could identify other solutions, (1, -7) for example, but there is no need since the problem statement already gives us two solutions.
Part C.The solution to the equation p(x) = g(x) can be read from the graph as approximately (4.074, 1.032). This is close to the point (4, 1) that is used to define p(x). With some refinement (iteration), we can show the irrational solution is closer to ...
(4.07369423957, 1.03158324553)
Answer:
A) (-3, -2)
B) (1, -7) and (5, -12)
C) (4, 1) to the nearest whole number
Step-by-step explanation:
Function g(x):
[tex]g(x)=2(0.85)^x[/tex]
Function f(x) (straight line):
Given ordered pairs:
Let (x₁, y₁) = (-7, 3)Let (x₂, y₂) = (-3, -2)Calculate the slope of the straight line:
[tex]\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-2-3}{-3-(-7)}=-\dfrac{5}{4}[/tex]
Using the Point-slope form of linear equation:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-3=-\dfrac{5}{4}(x-(-7))[/tex]
[tex]\implies y=-\dfrac{5}{4}x-\dfrac{23}{4}[/tex]
[tex]\implies f(x)=-\dfrac{5}{4}x-\dfrac{23}{4}[/tex]
Function p(x) (straight line):
Given ordered pairs:
Let (x₁, y₁) = (4, 1)Let (x₂, y₂) = (-3, -2)Calculate the slope of the straight line:
[tex]\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-2-1}{-3-4}=\dfrac{3}{7}[/tex]
Using the Point-slope form of linear equation:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-1=\dfrac{3}{7}(x-4)[/tex]
[tex]\implies y=\dfrac{3}{7}x-\dfrac{5}{7}[/tex]
[tex]\implies p(x)=\dfrac{3}{7}x-\dfrac{5}{7}[/tex]
Part AWe have been given two ordered pairs for function f(x) and function p(x).
One of those ordered pairs is the same for both functions.
The solution to a pair of equations is their point(s) of intersection.
Therefore, as both functions pass through (-3, -2), this is their point of intersection and therefore the solution.
Part BThe solutions for f(x) are any points on the line of the function f(x).
To find any two points, substitute values of x into the found equation for f(x):
[tex]\implies f(1)=-\dfrac{5}{4}(1)-\dfrac{23}{4}=-7[/tex]
[tex]\implies f(5)=-\dfrac{5}{4}(5)-\dfrac{23}{4}=-12[/tex]
Therefore, two solutions are (1, -7) and (5, -12).
Part C
The solution to p(x) = g(x) is where the two graphs intersect. From inspection of the graphs, p(x) intersects g(x) at approximately (4, 1).
Therefore, the approximate solution to p(x) = g(x) is (4, 1).
To prove this, substitute x = 4 into the equations for p(x) and g(x):
[tex]\implies p(4)=\dfrac{3}{7}(4)-\dfrac{5}{7}=1[/tex]
[tex]\implies g(4)=2(0.85)^4=1.0440125=1.0\:(\sf nearest\:tenth)[/tex]
The actual solution to p(x) = g(x) is (4.074, 1.032) to three decimal places, which can be found by equating the functions and solving for x using a numerical method such as iteration.
un tablero de plastico)
Answer:
A plastic board
all common factors of 24
Answer:
The all common Factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24
The picture below illustrates a special type of conic section called a circle.
Which of the following offers the best description of how a circle is formed?
W
A. The plane passes through the vertex of a right circular cone.
B. The plane passes through only one nappe of a right circular cone
and is perpendicular to its base.
C. The plane passes through both nappes of a right circular cone and
is perpendicular to its base.
D. The plane passes through only one nappe of a right circular cone
and is parallel to its base.
Answer:
D
Step-by-step explanation:
circles are parallel to the base and therefore only pass through 1 nappe
if the plane weren't parallel, we would make an ellipse
AB=
BC=
Help me please!! Asap thanks so much
Answer:
5 and 5
Step-by-step explanation:
[tex]AB = BC =\sqrt{(4-0)^2+(3-0)^2}=5[/tex]
Answer:
AB = 5
BC = 5
Step-by-step explanation:
The formula to find the distance between two points is: [tex]\sqrt{(x_2-x_1)^2 +(y_2-y_1)^2}[/tex]
AB: 5
The two points are A(-4,0) and B(0,3).
In the formula, it will be expressed as:
[tex]\sqrt{(0-(-4))^2+(3-0)^2}[/tex]
--> [tex]\sqrt{4^2+3^2}[/tex] .
--> [tex]\sqrt{16+9}[/tex]
--> [tex]\sqrt{25}[/tex]
--> 5
BC: 5
The two points are: B(0,3) and C(4,0)
In the formula, it will be expressed as:
[tex]\sqrt{(4-0)^2+(0-3)^2}[/tex]
--> [tex]\sqrt{(4)^2 + (-3)^2}[/tex]
--> [tex]\sqrt{16 + 9}[/tex]
--> [tex]\sqrt{25}[/tex]
--> 5
So both AB and BC is 5.
Find the maximum and minimum values attained by f(x, y, z) = 2xyz on the unit ball x2 y2 z2 ≤ 1
The maximum and minimum values of f(x,y,z) = 2xyz are [tex]\frac{2}{\sqrt{3} } and \frac{-2}{\sqrt{3} }[/tex]
The value of the function at a maximum point is called the maximum value of the function and the value of the function at a minimum point is called the minimum value of the function. Differentiate the given function.
f(x,y,z)=2xyz
Computation:
Differentiating the given equation up to second order
[tex]\begin{gathered}f_x=2yz\Rightarrow 2yz=0 either y=0 or z=0\\f_y=0\Rightarrow 2xz=0 either x=0 or z=0\\f_z=0\Rightarrow 2xy=0 either x=0 or y=0\end{gathered}[/tex]
So, the critical point is (0,0,0)
Now, using the Lagrange's on the boundary,
[tex]\begin{gathered}g(x,y,z)=x^2+y^2+z^2-1=0\\g_x=2x\\g_y=2y\\g_z=2z\end{gathered}[/tex]
[tex]So, \bigtriangledown f=\lambda \bigtriangledown g\left < 5yz,5xz,5xy \right > =\lambda \left < 2x,2y,2z )[/tex]
By solving we get,
[tex]x^2=y^2=z^2[/tex] then,
[tex]\begin{gathered}x^2+y^2+z^2=1\\3z^2=1\\z=\pm \frac{1}{\sqrt{3} } \\y=\pm \frac{1}{\sqrt{3} } \\\\x=\pm \frac{1}{\sqrt{3} } \\\end{gathered} x 2+y 2+z 2=13z 2=1z=± 31[/tex]
[tex]So, the critical points are (0,0,0),(\frac{1}{\sqrt{3} } ,\frac{1}{\sqrt{3} } ,\frac{1}{\sqrt{3} } )and (\frac{-1}{\sqrt{3} }, \frac{-1}{\sqrt{3} },\frac{-1}{\sqrt{3} })[/tex]
So, by substituting the critical points we get,
[tex]\begin{gathered}f(0,0,0)=0\\f(\frac{1}{\sqrt{3} }, \frac{1}{\sqrt{3} },\frac{1}{\sqrt{3} })=2(\frac{1}{\sqrt{3} })(\frac{1}{\sqrt{3} })(\frac{1}{\sqrt{3} })\\=\frac{2}{3\sqrt{3} } \\f(-\frac{1}{\sqrt{3} },-\frac{1}{\sqrt{3} },-\frac{1}{\sqrt{3} })=2(-\frac{1}{\sqrt{3} })(-\frac{1}{\sqrt{3} })(-\frac{1}{\sqrt{3} })\\=-\frac{2}{3\sqrt{3} }\end{gathered}[/tex]
Hence the maximum and minimum values of f(x,y,z) are [tex]\frac{2}{\sqrt{3} } and \frac{-2}{\sqrt{3} }[/tex]
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The SkyWheel has a diameter of 183 feet. What is the radius? (don't round and just write the numerical answer, no units)
Answer:
The answer is
→ 91.5 feet
Step-by-step explanation:
Given:
183 feet
What were supposed to find:
The radius of the SkyWheel
Solve:183 / 2 = 91.5
How to find the radius:
To find the radius, you must divide 183 with 2, giving 91.5
Hence, the answer you are looking for is 91.5
- ✨7272033Alt✨Izzo's Pizza sells four types of pizza crust. Last week, the owner tracked the number sold of each type, and this is what he found. Type of Crust Number Sold
Thin crust 307
Thick crust 224
Stuffed crust 161
Pan style 191
Based on this information, of the next 2000 pizzas he sells, how many should he expect to be stuffed crust or pan style? Round your answer to the nearest whole number. Do not round any intermediate calculations.
Answer:
797
Step-by-step explanation:
First, we need to find the number of pizzas sold last week by finding the sum of the pizzas sold:
307 + 224 + 161 + 191 = 883
Next, we need to find the proportion of stuffed crust and pan style pizzas sold last week by adding the number of both sold and dividing by the total number of pizzas sold:
(191+161) / 883 = 352 / 883
Now we need to multiply this proportion by 2000 to find the expected number of stuffed crust or pan style pizzas:
(352 / 883) * 2000 = 797.28 = 797
Sandy used a virtual coin toss app to show the results of flipping a coin 80 times, 800 times, and 3,000 times. Explain what most likely happened in Sandy's experiment.
Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 80 flips.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 800 flips.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 3,000 flips.
Question 2(Multiple Choice Worth 2 points)
(Experimental Probability MC)
A spinner with 4 equal sections is spun 20 times. The frequency of spinning each color is recorded in the table below.
Outcome Frequency
Pink 6
White 3
Blue 7
Orange 4
What statement best compares the theoretical and experimental probability of landing on orange?
The theoretical probability of landing on orange is one fifth, and the experimental probability is 20%.
The theoretical probability of landing on orange is one fourth, and the experimental probability is 20%.
The theoretical probability of landing on orange is one fifth, and the experimental probability is 30%.
The theoretical probability of landing on orange is one fourth, and the experimental probability is 50%.
Question 3(Multiple Choice Worth 2 points)
(Experimental Probability MC)
Michael has a bag of marbles. The frequency of selecting each color is recorded in the table below.
Outcome Frequency
Green 4
Black 6
Orange 5
Based on the given frequency, determine the experimental probability of selecting an orange marble.
0.27
0.33
0.40
0.67
Question 4(Multiple Choice Worth 2 points)
(Experimental Probability LC)
A number cube is tossed 60 times.
Outcome Frequency
1 12
2 13
3 11
4 6
5 10
6 8
Determine the experimental probability of landing on a number less than 2.
35 over 60
25 over 60
13 over 60
12 over 60
Question 5(Multiple Choice Worth 2 points)
(Experimental Probability MC)
A coin is flipped 200 times. The table shows the frequency of each event.
Outcome Frequency
Heads 98
Tails 102
Determine the experimental probability of landing on heads.
102%
98%
50%
49%
Question 6 (Essay Worth 4 points)
(Experimental Probability HC)
A coin is flipped at the start of every game to determine if Team A (heads) or Team B (tails) will get the ball first.
Part A: Find the theoretical probability of a fair coin landing on heads. (1 point)
Part B: Flip a coin 14 times and record the frequency of each outcome. Be sure to include the frequency of each outcome in your answer. Then, determine the experimental probability of landing on heads and compare it to the theoretical probability. (3 points)
Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.
The theoretical probability of landing on orange is one fourth, and the experimental probability is 20%.
The experimental probability of selecting an orange marble is 0.33.
The experimental probability of landing on a number less than 2 is 12 over 60.
The experimental probability of landing on heads is 49%.
The theoretical probability of a fair coin landing on heads is 0.5.
How to calculate the probability?It should be noted that a coin has a head and tail. Therefore, the probability of getting either will be:
= 1/2 = 0.5
Therefore, Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.
The statement that compares the theoretical and experimental probability of landing on orange is that the theoretical probability of landing on orange is one fourth, and the experimental probability is 20%.
The experimental probability will be:
= 4/(6+3+7+4)
= 4/20 = 1/5
Based on the given frequency, the experimental probability of selecting an orange marble will be:
= 5/(4+6+5)
= 5/15
= 0.33
The experimental probability of landing on a number less than 2 is 12 over 60.
The experimental probability of landing on heads will be:
= 98/(98 + 102)
= 98/200
= 49%
The theoretical probability of a fair coin landing on heads will be:
= 1/2 = 0.5
Flip a coin 14 times and record the frequency of each outcome gives:
Head, Tail, Head, Head, Head, Tail, Tail, Head, Tail, Tail, Tail, Tail, Head, Head. The theoretical and experimental probability are 0.5.
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f(x)=x^2-6. find the inverse
Answer:
f-1(x) = +- sqrt(x + 6)
Step-by-step explanation:
f(x) = x^2 - 6
y = x^2 - 6
x = y^2 - 6
x + 6 = y^2
y = +- sqrt(x + 6)
f-1(x) = +- sqrt(x + 6)
Hi :)
Let's find the inverse of the function
——————————Remember, inverse functions do the opposite things in the opposite order.
To find the inverse,
replace [tex]\boldsymbol{f(x)}[/tex] with [tex]\boldsymbol{y}[/tex]swap x's and y'ssolve for yReplace f(x) with y. (one step)
Then
[tex]\boldsymbol{y=x^2+6}[/tex]
Swap x's and y's (one step)
Then
[tex]\boldsymbol{x=y^2+6}[/tex]
Solve for y (several steps)
[tex]\boldsymbol{x-6=y^2}[/tex] > square root both sides
[tex]\boldsymbol{\sqrt{x-6}=y}[/tex] > swap y and √x-6
[tex]\boldsymbol{y=\sqrt{x-6}}[/tex]
[tex]\tt{Learn~More;Work~Harder}[/tex]
:)
Find the sum of the arithmetic series given a=2, a=35, and n=12.
The sum of an arithmetic progression with first term of 2 and the common difference of 35 is 2340
Sum of arithmetic sequenceSeries are defined as the sum of sequence. The formula for calculating the nth term of an arithmetic sequence is expressed as:
S = n/2[2a+(n-1)d]
where;
n is the number of terms
d is the common difference
a is the first term
Given the following parameters from the question
a -2
d = 35
n = 12
Substitute
S = 12/2[2(2)+(12-1)(35)]
S = 6(4+11(35))
S = 6(5+385)
S = 6(390)
S = 2340
Hence the sum of an arithmetic progression with first term of 2 and the common difference of 35 is 2340
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Compare and contrast dot plots and histograms. Make a list of the benefits and downsides of each.
A dot plot displays the individual data values and a histogram displays data ranges along the x-axis and uses rectangular bars to show the frequencies of values that fall into each range.
How to illustrate the information?It should be noted that dot plots, histograms, and box plots are all common graphical ways to represent data sets.
The dot plot represents data by placing a dot for each data point. Also, the histogram groups the data into ranges and then plots the frequency that data occurs in each range.
The similarities is that the dot plot and the histogram can more easily tell us the mode of our data set. A dot plot gives you a visual idea of your data, but histogram gives you additional information.
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How many numbers from 100 to 999 have exactly one zero digit
Answer:
180.
Step-by-step explanation:
100 contains 2 zero digits.
101 - 109 have 9 numbers, 110 to 200 have 11 numbers
so for 101 to 200 its 20 numbers
Its also 20 for 201 to 300 and for all sets of 100 up to 900.
- that is 7 * 20 = 140 numbers
Finally from 901 to 999 we have 18.
Total = 20 + 140 + 18
= 2 + 20 + 140 + 18
= 180.
Which of the following terms is best described as the point halfway between
the endpoints of a line segment?
O
O
A. Ordered pair
B. Vertex
OC. Coordinate
O
D. Midpoint
SUBMIT
Answer:
D. Midpoint...
Step-by-step explanation:
I hope it helps You:)
Need help. i dont understand this!!!
By the quadratic formula, the solution set of the quadratic equation is formed by two real roots: x₁ = 0 and x₂ = - 12.
How to find the solution of quadratic equation
Herein we have a quadratic equation of the form a · m² + b · m + c = 0, whose solution set can be determined by the quadratic formula:
x = - [b / (2 · a)] ± [1 / (2 · a)] · √(b² - 4 · a · c) (1)
If we know that a = - 1, b = 12 and c = 0, then the solution set of the quadratic equation is:
x = - [12 / [2 · (- 1)]] ± [1 / [2 · (- 1)]] · √[12² - 4 · (- 1) · 0]
x = - 6 ± (1 / 2) · 12
x = - 6 ± 6
Then, by the quadratic formula, the solution set of the quadratic equation is formed by two real roots: x₁ = 0 and x₂ = - 12.
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