You work at a pioneer historical site. On this site you have handcarts. One cart has a handle that connects to the center of the wheel. We have to maintain the handle of the cart at an angle of no more than 20° with the ground so the contents do not spill out. The distance from where the handle rests on the ground to the point where the wheel is sitting on the ground is 45 inches. The distance of the center of the wheel to the end of the handle is approximately 48 inches.
a. Identify the parts of the handcart wheel that would represent congruent chords and congruent central angles. Explain why.
b. Find the radius of the wheel.
c. If the measure of the arc from to around the outside of the wheel were changed to 72°, what is the new angle the handle makes with the ground? Will the contents remain in the handcart at that angle? Will the handle rest on the ground?
d. If a pioneer pulling the handcart held the handle at a height of 48 inches off the ground, would the contents of the cart spill out the back? How high can the pioneer lift the handle off the ground before the contents started spilling out?
Answers
Answer:
a) see below
b) radius = 16.4 in (1 d.p.)
c) 18°. Yes contents will remain. No, handle will not rest on the ground.
d) Yes contents would spill. Max height of handle = 32.8 in (1 d.p.)
Step-by-step explanation:
Part a
A chord is a line segment with endpoints on the circumference of the circle.
The diameter is a chord that passes through the center of a circle.
Therefore, the spokes passing through the center of the wheel are congruent chords.
The spokes on the wheel represent the radii of the circle. Spokes on a wheel are usually evenly spaced, therefore the congruent central angles are the angles formed when two spokes meet at the center of the wheel.
Part b
The tangent of a circle is always perpendicular to the radius.
The tangent to the wheel touches the wheel at point B on the diagram. The radius is at a right angle to this tangent. Therefore, we can model this as a right triangle and use the tan trigonometric ratio to calculate the radius of the wheel (see attached diagram 1).
[tex]\sf \tan(\theta)=\dfrac{O}{A}[/tex]
where:
[tex]\theta[/tex] is the angleO is the side opposite the angleA is the side adjacent the angleGiven:
[tex]\theta[/tex] = 20°O = radius (r)A = 45 inSubstituting the given values into the tan trig ratio:
[tex]\implies \sf \tan(20^{\circ})=\dfrac{r}{45}[/tex]
[tex]\implies \sf r=45\tan(20^{\circ})[/tex]
[tex]\implies \sf r=16.37866054...[/tex]
Therefore, the radius is 16.4 in (1 d.p.).
Part c
The measure of an angle formed by a secant and a tangent from a point outside the circle is half the difference of the measures of the intercepted arcs.
If the measure of the arc AB was changed to 72°, then the other intercepted arc would be 180° - 72° = 108° (since AC is the diameter).
[tex]\implies \sf new\: angle=\dfrac{108^{\circ}-72^{\circ}}{2}=18^{\circ}[/tex]
As the handle of the cart needs to be no more than 20° with the ground for the contents not to spill out, the contents will remain in the handcart at an angle of 18°.
The handle will not rest of the ground (see attached diagram 2).
Part d
This can be modeled as a right triangle (see diagram 3), with:
height = (48 - r) inhypotenuse ≈ 48 inUse the sin trig ratio to find the angle the handle makes with the horizontal:
[tex]\implies \sf \sin (\theta)=\dfrac{O}{H}[/tex]
[tex]\implies \sf \sin (\theta)=\dfrac{48-r}{48}[/tex]
[tex]\implies \sf \sin (\theta)=\dfrac{48-45\tan(20^{\circ})}{48}[/tex]
[tex]\implies \theta = 41.2^{\circ}\:\sf(1\:d.p.)[/tex]
As 41.2° > 20° the contents will spill out the back.
To find the maximum height of the handle from the ground before the contents start spilling out, find the height from center of the wheel (setting the angle to its maximum of 20°):
[tex]\implies \sin(20^{\circ})=\dfrac{h}{48}[/tex]
[tex]\implies h=48\sin(20^{\circ})[/tex]
Then add it to the radius:
[tex]\implies \sf max\:height=48\sin(20^{\circ})+45\tan(20^{\circ})=32.8\:in\:(1\:d.p.)[/tex]
(see diagram 4)
------------------------------------------------------------------------------------------
Circle Theorem vocabulary
Secant: a straight line that intersects a circle at two points.
Arc: the curve between two points on the circumference of a circle
Intercepted arc: the curve between the two points where two chords or line segments (that meet at one point on the other side of the circle) intercept the circumference of a circle.
Tangent: a straight line that touches a circle at only one point.
Related Questions
PLEASE HELP IM STUCK
Answers
It’s relation
The last time troy checked, his dog weighed 60 kilograms. troy just measured his dog again and found out that it weighs 5% less now. how much does the dog weigh now?
Answers
Answer:
57 kg
Step-by-step explanation:
5% less means it weighs 95% of what it used to weigh
95% is .95 in decimal
.95 * 60 = 57 kg
The graph of the piecewise function f(x) is shown.
On a coordinate plane, a piecewise function has 2 connecting lines. The first line has a closed circle at (negative 2, negative 5) and goes up to a closed circle at (2, negative 1). The second line has a closed circle at (2, negative 1) and goes down to an open circle at (4, negative 2).
What is the range of f(x)?
{x | −2 ≤ x < 4}
{x | −2 < x ≤ 4}
{y | −5 < y < −1}
{y | −5 ≤ y ≤ −1}
Answers
Answer: {y | −5 ≤ y ≤ −1}
Step-by-step explanation:
The extreme values are -5 and -1.
There is a closed circle at (-2, -5), so -5 is in the range.There is a closed circle at (2, -1), so -1 is in the range.So, the answer is {y | −5 ≤ y ≤ −1}.
volume of a cone = r²h,
where r is the radius and h is the height.
A frustum is formed by removing a small cone from a similar, larger cone, as
shown below.
a) Calculate the radius of the original large cone.
b) Calculate the volume of the frustum to the nearest integer.
50 m height
10 m height of frustum
6m radius of frustum
Answers
Answer:
7.5 m 457.5[tex]\pi[/tex] [tex]m^{2}[/tex]
Step-by-step explanation:
First, visualize the original cone and the smaller cone as overlapping similar triangles. The scale factor of the original cone to the smaller cone is 50:40, so if the smaller cone has a radius of 6 m, then the radius of the original cone would be 7.5 m.
The volume of the frustum is the volume of the original cone minus the volume of the smaller cone. The formula for the volume of a cone is V = [tex]\frac{1}{3} \pi r^{2}h[/tex].
Original Cone = [tex]\frac{1}{3} \pi r^{2}h[/tex] = [tex]\frac{1}{3} \pi *7.5^{2}*50[/tex] = 937.5[tex]\pi[/tex]
Smaller Cone = [tex]\frac{1}{3} \pi r^{2}h[/tex] = [tex]\frac{1}{3} \pi *6^{2}*40[/tex] = 480[tex]\pi[/tex]
Frustum = 937.5[tex]\pi[/tex] - 480[tex]\pi[/tex] = 457.5[tex]\pi[/tex]
Using the quadratic formula, solve the
equation below to find the two possible
values of t.
6x^2-35=-11x
Give each value as a fraction in its
simplest form.
Answers
Answer:
x= 19/12, -41/12
Step-by-step explanation:
I'm guessing x is "t".
The quadratic formula is x=(-b+-sqrtb^2-4ac)/2a I know that this is hard to read sorry!
Plug in a, b, and c.
Oh yeah, first convert it to the form Ax^2+bx+c
so 6x^2-35=-11x
6x^2+11x-35=0
(-11+-sqrt11^2-(-4*6*35))/2*6
Simply: (-11+-sqrt 121+840)/12
(-11+-sqrt961)/12
(-11+-31)/12
-11+30=19
-11-30=-41
x= 19/12, -41/12
what's y=1/4x-4 on a graph? please helppppppp!!!!
Answers
Answer:
Please see attachment.
Step-by-step explanation:
Remember, the 1/4x is the slope, and the -4 is the y-intercept.
Please see attachment for the graph.
Hope this helps!
Jessica and her best friend found some money under the couch. they split the money evenly, each getting $16.32. how much money did they find?
Answers
Based on the fact that Jessica and her best friend split the money and were able to get $16.32, the total amount that they found was $32.64
How much did Jessica and her friend find?The fact that they split the money evenly means that they split it in half which each person getting the same amount.
This means that the total amount they found was twice the amount that Jessica and her best friend got.
The total amount found is therefore:
= Jessica's share + Best friend's share
= 16.32 + 16.32
= $32.64
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The 90% confidence interval for the mean one week amusing time in new york city is 5.22 less than mean less than 5.98 minutes construct a 95% confidence interval based on the same data which interval provides more information
Answers
The 95% confidence interval based on the same data is 5.15 < μ < 6.05
Because it has a longer interval, the 95 percent confidence interval offers more details.
What is a confidence interval?The likelihood that a parameter will fall between two values near the mean is shown by a confidence interval.
Confidence intervals quantify how certain or uncertain a sampling technique is.
Confidence intervals are used by statisticians to gauge the degree of uncertainty in a sample variable.
The 90% confidence interval is given by:
Mean - 1.645(S.D./[tex]\sqrt{n}[/tex]) < μ < Mean + 1.645(S.D./[tex]\sqrt{n}[/tex])
2μ = 5.22 + 5.98 = 11.2
μ = 11.2 / 2 = 5.6
Thus,
5.6 - 5.22 = 1.645(S.D./[tex]\sqrt{n}[/tex]) = 0.38
S.D./[tex]\sqrt{n}[/tex] = 0.38 / 1.645 = 0.231
The 95% confidence interval is given by:
Mean - 1.96(S.D./[tex]\sqrt{n}[/tex]) < μ < Mean + 1.96(S.D./[tex]\sqrt{n}[/tex])
=5.6 - 1.96(0.231) < μ < 5.6 + 1.96(0.231)
= 5.6 - 0.4528 < μ < 5.6 + 0.4528
= 5.15 < μ < 6.05
The 95% confidence interval provides more information because it has a larger interval.
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A cross section is made by the intersection of a plane and a square pyramid at an angle either parallel or perpendicular to the base. the cross section can be which of these shapes? select three options.
Answers
A cross-section is made by the intersection of a plane and a square pyramid at an angle either parallel or perpendicular to the base square, triangle, and, trapezoid.
What is an area of cross-section?A cross-section parallel to the base will be a square.
One perpendicular to the base will be a trapezoid, or if it passes through the vertex of the pyramid, a triangle.
The cross-section of the pyramid is perpendicular to the base and through the vertex will be a triangle.The cross-section has the same shape but it has a smaller base.The cross-section perpendicular to the triangular bottom then it will be a trapezoid.Hence, a cross-section is made by the intersection of a plane and a square pyramid at an angle either parallel or perpendicular to the base square, triangle, and, trapezoid.
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HELPPPPPPPPPPPP (-12)^3:8^3
Answers
Answer:
-1728:512
Step-by-step explanation:
(-12)³ = -1728
8³ = 512
ratio is -1728:512
Simplify
32x^8 ÷ 8x^32
Answers
Hello,
[tex] \frac{32 {x}^{8} }{8x {}^{32} } = \frac{4 \times 8 \times x {}^{8} }{8x {}^{32} } = \frac{4x {}^{8} }{x {}^{32} } = 4x { }^{8 - 32} = 4x {}^{ - 24} [/tex]
Answer:
[tex] \red{4 {x}^{ - 24} }[/tex]
Step-by-step explanation:
We know that,
[tex] {a}^{m} \times {a}^{m} = {a}^{m + n} \\ \\ \frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n} \: \: \: \: \: \: \: \: \: \: \: \\ \\ ({a}^{m})^{n} = {a}^{mn} \: \: \: \: \: \: \: \: \: \: [/tex]
Now using the above knowledge let us solve the sum.
[tex] \frac{32 {x}^{8} }{8 {x}^{32} } \\ ( \frac{32}{8} ) \times ( \frac{ {x}^{8} }{ {x}^{32} } ) \\ 4 \times {x}^{8 - 32} \\ 4 \times {x}^{ - 24} \\ = 4 {x}^{ - 24} [/tex]
Under his cell phone plan, Liam pays a flat cost of $69.50 per month and $5 per gigabyte. He wants to keep his bill under $90 per month. Write and solve an inequality which can be used to determine x, the number of gigabytes Liam can use while staying within his budget.
Answers
Using a linear function, the inequality is given by: 69.5 + 5x < 90.
The solution is: x < 4.1.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.In this problem, we have that:
The y-intercept is the flat cost of $69.50.The slope is the cost per gigabyte of $5.Hence the cost of using x gigabytes is:
C(x) = 69.5 + 5x.
The cost has to be under 90, hence the inequality is:
C(x) < 90
69.5 + 5x < 90.
Then the solution is:
5x < 90 - 69.5.
x < 20.5/5
x < 4.1.
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Answer:
Inequality: 5x+35<50
Answer: x<3
Step-by-step explanation:
On a monday a friend says he will meet you again in 34 days. What day of the week will that be?
Answers
Answer:
On a Sunday?
Step-by-step explanation:
C
The graph of f(x) is shown.
O-4,0,2
For what values of x does f(x) = 0?
O-2.0.4
O-5.0.17
45
O-17.0.5
40 bcpp
Answers
Answer: -4, 0, 2
Step-by-step explanation:
The graph intersects the x-axis at [tex]x=-4, x=0, x=2[/tex].
Which statement correctly describes the expression 19×4?
A. Both factors are negative, so the product will be positive.
B. One factor is positive and one factor is negative, so the product will be positive.
C. Both factors are positive, so the product will be negative.
D. Both factors are positive, so the product will be positive.
Answers
Answer:
D. Both factors are positive, so the product will be positive.
The denominator of a fraction exceeds numerator by 3. If the numerator is doubled and the denominator is increased by 14, then fraction becomes 2/3rd of the original fraction.
Answers
Answer:
The original fraction is 4/7Step-by-step explanation:
Let the fraction be x/y.
According to question we have the following equations.
The denominator of a fraction exceeds numerator by 3:
y = x + 3If the numerator is doubled and the denominator is increased by 14, then fraction becomes 2/3rd of the original fraction:
2x/(y + 14) = (2/3)*(x/y)Change the fraction as below and solve for y:
2x /(y + 14) = 2x/(3y) Nominators are samey + 14 = 3y Compare denominators2y = 14y = 7Find the value of x using the first equation:
7 = x + 3x = 7 - 3x = 4The fraction is:
x/y = 4/7Answer:
Original fraction = ⁴/₇
Step-by-step explanation:
Numerator: top of the fraction
Denominator: bottom of a fraction
Let x be the original numerator.
If the denominator of a fraction exceeds the numerator by 3:
[tex]\implies \dfrac{x}{x+3}[/tex]
If the numerator is doubled and the denominator is increased by 14, then fraction becomes 2/3rd of the original fraction:
[tex]\implies \dfrac{2x}{x+3+14}=\dfrac{2}{3}\left(\dfrac{x}{x+3}\right)[/tex]
[tex]\implies \dfrac{2x}{x+17}=\dfrac{2x}{3(x+3)}[/tex]
[tex]\implies \dfrac{2x}{x+17}=\dfrac{2x}{3x+9}[/tex]
Cross multiply:
[tex]\implies 2x(3x+9)=2x(x+17)[/tex]
Divide both sides by 2x:
[tex]\implies 3x+9=x+17[/tex]
Subtract x from both sides:
[tex]\implies 2x+9=17[/tex]
Subtract 9 from both sides:
[tex]\implies 2x=8[/tex]
Divide both sides by 2:
[tex]\implies x=4[/tex]
Substitute the found value of x into the original fraction:
[tex]\implies \dfrac{4}{4+3}=\dfrac{4}{7}[/tex]
Therefore, the original fraction is ⁴/₇.
What is the GCF of:
9a^4b^4 - 27a^3b^3
Answers
Answer:
9a^3b^3
Step-by-step explanation:
The greatest common factor is the greatest factor that divides both numbers. To find the greatest common factor, first list the prime factors of each number
Find the prime factors of each term in order to find the greatest common factor (GCF).
The length of a rectangle is 6 more than twice the width. if the area is 40 cm^2, find the length and breadth of the rectangle
Answers
Answer: 3.217 & 12.434
Step-by-step explanation:
If we use w to represent the width, the length will be 6 more than 2 times w.
Hence, the length is [tex]2w+6[/tex].
The area of a rectangle would be its length times its width, so let's make an equation to represent it's area.
[tex]A=w(2w+6)[/tex]
We can also substitute 40 in for A as it's given in the question.
[tex]40 = w(2w+6)[/tex]
Distributing w by multiplying it by both terms in the parentheses, we get
[tex]40 = 2w^2+6w[/tex]
We can make the equation simpler by dividing both sides by 2.
[tex]20 = w^2+3w[/tex]
Subtracting both sides by 20 will make the left-hand side 0.
[tex]0=w^2+3w-20[/tex]
Now that we have put this quadratic equation into standard form (ax²+bx+c), we can find its solutions using the quadratic formula.
For reference, the quadratic formula is
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
In this case, a is 1, b is 3, and c is -20.
Substituting, we get
[tex]w=\frac{-3\pm\sqrt{3^2-4(1)(-20)}}{2(1)}[/tex]
[tex]w= \frac{-3\pm\sqrt{9+80}}{2}[/tex]
[tex]w=\frac{-3+\sqrt{89}}{2}\hspace{0.1cm}or\hspace{0.1cm}\frac{-3-\sqrt{89}}{2}[/tex]
Since the second solution results in a negative number, it cannot be the length of w.
[tex]w=\frac{-3+\sqrt{89}}{2}\approx3.217[/tex]
The width/breadth of the rectangle is 3.217 cm.
To calculate the length, let's substitute the width into the expression for the length:
[tex]l=2(3.217)+6[/tex]
[tex]l=12.434[/tex]
The length of this rectangle is 12.434 cm.
In how many ways can max select 3 toppings from 10 available toppings for his
12. pizza?
Answers
Max can select 3 toppings from 10 available toppings for his pizza in 120 ways.
A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter. In combinations, you can select the items in any order. Combinations can be confused with permutations.
Thus number of ways in which Max can select 3 toppings from 10 available toppings for his pizza is 10C3
=[tex]\frac{10!}{7!3!}[/tex]
= [tex]\frac{8.9.10}{3!}[/tex]
= 120
Thus Max can select 3 toppings from 10 available toppings for his pizza in 120 ways.
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You are performing an experiment in your lab. to compare with other experiments your results must be in moles. during your final step you burn a strip of magnesium (mg), which results in 187 grams of magnesium oxide (mgo). how should you enter your results?
Answers
4.6 moles in 187 grams of magnesium oxide (mgo).
What is mole explain with example?One mole is defined as the amount of substance containing as many elementary entities (atoms, molecules, ions, electrons, radicals, etc.) as there are atoms in 12 grams of carbon - 12(6. 023×1023). The mass of one mole of a substance equals to its relative molecular mass expressed in grams.The relative formula mass of a compound is calculated by adding together the relative atomic mass values for all the atoms in its formula. Moles are units used to measure substance amount. Chemistry (Single Science) Atomic structure.
To solve ,
number of moles is equals to the mass in grams divided by RFM
RFM=16+24.3=40.3
=187/40.3
=4.6 moles of MgO
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Explaining the Error in a Propo
A student uses the ratio of 4 oranges to 6 fuld ounces
find the number of oranges needed to make 24 fluid
ounces of juice. The student writes this proportion:
24
4
=
6 16
Explain the error in the student's work.
Answers
Answer:
16
Step-by-step explanation:
The student uses the ratio of 4 oranges to 6 fluid ounces.
When there are 24 fluid ounces, the number of oranges will be:
= 4/6 × 24
= 16 oranges
Triangle ABC Is shown on the coordinate plane.
What is the area of AABC?
OA 22.63 square units
OB. 24 square units
OC 48 square units
OD.
m. All rights reserved
16.97 square units
4
A(4.4)
-6
8-3,-3
6
42
A
42
4
-6-
C(3,3)
Answers
Answer: B
Step-by-step explanation:
Using the distance formula, we get the height is [tex]4\sqrt{2}[/tex].
Similarly, we get the base is [tex]6\sqrt{2}[/tex].
So, the area is [tex]\frac{1}{2}(4\sqrt{2})(6\sqrt{2})=24[/tex]
PLEASE HELP DUE TONIGHT
Answers
1. The time taken for the water to fall that much is 0.2 s
2. The initial speed of the water is 4 m/s
1. How to determine the time Height (h) = 20 cm = 20 / 100 = 0.2 mAcceleration due to gravity (g) = 9.8 m/s²Time (t) =?h = ½gt²
0.2 = ½ × 9.8 × t²
0.2 = 4.9 × t²
Divide both side by 4.9
t² = 0.2 / 4.9
Take the square root of both side
t = √(0.2 / 4.9)
t = 0.2 s
2. How to determine the initial speedHorizontal distance (s) = 80 cm = 80 / 100 = 0.8 mTime (t) = 0.2 sInitial speed (u) =?s = ut
Divide both sides by t
u = s / t
u = 0.8 / 0.2
u = 4 m/s
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Solve the system of equations 4x+5y=-1 and -5x-8y=10 by combining the equations.
Answers
The solution of the equation are as follows:
x = 6 and y = -5
How to solve the system of equation?4x + 5y = -1
-5x - 8y = 10
Therefore,
20x + 25y = -5
-20x - 32y = 40
-7y = 35
y = -5
Hence,
4x + 5(-5) = -1
4x - 25 = -1
4x = -1 + 25
4x = 24
x = 24 / 4
x = 6
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Polynomial Question
Find the roots if one of the roots is the product of the other two
Answers
Step-by-step explanation:
x³ - x² - 24x - 36
factors of -36 are 1, 2, 3, 4, 6, 9, 12, 18, 36 and negative equivalents.
1 - 1 - 24 - 36 != 0
8 - 4 - 48 - 36 != 0
27 - 9 - 72 - 36 != 0
64 - 16 - 96 - 36 != 0
216 - 36 - 144 - 36 = 0
So one factor is 6
x = 6
(x - 6) = 0
x²(x - 6) = x³ - 6x²
5x(x - 6) = 5x² - 30x
6(x - 6) = 6x - 36
x³ - 6x² + 5x² - 30x + 6x - 36
(x - 6)(x² + 5x + 6)
(x - 6)(x² + 3x + 2x + 6)
(x - 6)(x(x + 3) + 2(x + 3))
(x - 6)(x + 3)(x + 2)
x - 6 = 0
x = 6
x + 3 = 0
x = -3
x + 2 = 0
x = -2
x = -2, -3, 6.
One is the product of the other 2 as -2 x -3 = 6.
Graphic proof is shown above or below in the image
Subtract.
3 x - z + 9
3 x - 16 y - z + 9
3 x + z + 9
Answers
Answer:
1)3×-8
-24
Step-by-step explanation:
2)bshejejnenenejejkejehrh
Suppose the variable x is represented by a standard normal distribution. What value of x is at the 40th percentile of the distribution
Answers
The value value of x is at the 40th percentile of the distribution is 0.65.
The standard normal distribution is a normal distribution with a mean of zero and standard deviation of 1. The standard normal distribution is centered at zero and the degree to which a given measurement deviates from the mean is given by the standard deviation
Given:- μ[tex]_X[/tex]=0,σ[tex]_X[/tex]=1
We can standardize the random variable: Z=(X−μx)/σx,
Then the equation is P(X≤ x )=Φ(x−μx/σx)=Φ(x−0/1)=0.4
Inverse function
Ф[tex]\\^{-1}[/tex](0.4) = [tex]\frac{x-0}{1}[/tex]
From the table we get,
Ф[tex]^{-1}[/tex] = 0.65
Thus
[tex]\frac{x-40}{10}[/tex] = 0.65
x -0 = 0.65
x = 6.5
Thus the value value of x is at the 40th percentile of the distribution is 0.65
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1. Which fraction is equivalent to 2/3.¸?
(A) 4
9
B
C
(D)
0100
24
Answers
Answer:
The answer options appear garbled. If A is 4/9, then this is equal to 2/3. The others I can't see/understand.
Step-by-step explanation:
A die is rolled twice. What is the probability of getting either a multiple of 2 on the first roll or a total of 6 for both rolls
Answers
The correct answer is 7/12.
What is probability?
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e. how likely they are to happen, using it.Let A = Getting multiple of on the first one
B = A total of for both roll
P (A U B) = P(A) + P(B) - P(A ∩ B)
[tex]\frac{18}{36} + \frac{5}{36} - \frac{2}{36} \\\\ = \frac{21}{36} \\[/tex]
[tex]\frac{7}{12}[/tex]
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In Bayes Theorem, you have some starting information, then you collect some new information so that you can _______ the original probabilities so you now have better information.
Answers
In Bayes Theorem, apart from the already starting information, some new information so that you can update or transform the original probabilities so you now have better information.
What is Bayes Theorem?
The Bayes' theorem was named after Thomas Bayes and it is used in probability theory and statistics as one of the fundamental theorems. It estimates the likelihood of an event based on knowledge of circumstances that might be connected to it in the past.
The Formula for Bayes' Theorem
The Bayes' theorem is given as,
P(A|B) = P(A).P(B|A) / P(B)
Here, for two events A and B,
P(A|B) is the probability for likelihood of A when B is true
P(B|A) is probability for likelihood of B when A is true
P(A) is the independent probability of event A
P(B) is the independent probability of event B
Learn more about Bayes' theorem here:
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