Answers
The questions are all illustrations of conditional probabilities, and they can be solved using the general conditional probability formula; P(A|B) = P(A and B)/P(B)
How to determine the conditional probabilities?The conditional probability P(A|B) is calculated using:
P(A|B) = P(A and B)/P(B)
Using the above formula, we have:
P(has at least 4 sides| not a hexagon) = 38/50
P(has at least 4 sides| not a hexagon) = 0.76
P(not a square | has less than 7 sides) = 30/45
P(not a square | has less than 7 sides) = 0.67
P(not an octagon | not a triangle) = 39/51
P(not an octagon | not a triangle) = 0.76
P(octagon | sum of interior angle measures is at least 600) = 9/25
P(octagon | sum of interior angle measures is at least 600) = 0.36
Students in Wayland high schoolThe conditional probability is calculated using:
P = P(perfect attendance and honor roll)/P(Honor roll)
So, we have:
P = 25%/38%
Evaluate
P = 0.66
Hence, the probability that a student has a perfect attendance, given that he made the honor roll is 0.66
Homes on the marketThe conditional probability is calculated using:
P = P(Home has a pool and at least 3 bedrooms)/P(at least 3 bedrooms)
So, we have:
P = 25%/70%
Evaluate
P = 0.36
Hence, the probability that a home has a pool, given that it has at least 3 bedrooms is 0.36
Conditional probability using Venn diagramUsing the conditional probability formula in (a), we have:
P(uses Ins tag ram| does not use Sna pch at) = 45/(20 + 45)
P(uses Ins tag ram| does not use Sna pch at) = 0.69
P(does not use Ins tag ram| uses Sna pch at) = 25/(30 + 25)
P(uses Instag ram| does not use Sna pch at) = 0.45
Sports and Part-time jobUsing the conditional probability formula in (a), we have:
P(plays sport| has a part-time job) = 22/68
P(plays sport| has a part-time job) = 0.32
P(has a part-time job| plays sport) = 22/40
P(has a part-time job| plays sport) = 0.55
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Related Questions
The mean of this data set is 9. What number is missing?
11,20,_,3,1
Answers
Mean is the total sum of data over the number of data therefore,
(11+20+x+3+1) / 5 = 9
Then simplify
(35 + x) / 5 = 9
Then multiply 5 to both sides
35 + x = 45
Then subtract 35 to both sides to find x
X= 10
Hope this helps!
10 is the mean of the number that is missing.
What is mean?A property of an assortment of data that represents an average is called the mean. Depending on the nature of the information as well as the kind of average you require, one can compute the mean theoretically employing any of the several ways. Scheming the data distribution constantly allows one to visually determine the mean as well.
Let the missing number be x.
The sum of all the numbers will be
= 11 + 20 + 3 + 1 + x
= 35 + x
The total number is 5.
The mean is given to be 9.
The mean will be
9 = (35 + x) / 5
9 * 5 = 35 + x
45 = 35 + x
10 = x
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Which expression represents the volume of the cone that is startfraction pi over 4 endfraction times the volume of the pyramid that it fits inside? startfraction pi over 4 endfraction(2r2h) startfraction pi over 4 endfraction(4r2h) startfraction pi over 4 endfraction(startfraction r squared h over 3 endfraction) startfraction pi over 4 endfraction(startfraction 4 r squared h over 3 endfraction)
Answers
The expression of the volume of the cone that is π/4 of the volume of the pyramid, is expressed as: [tex]\mathbf{\frac{\pi}{4} (\frac{4r^2h}{3} )}[/tex].
What is the Volume of a Pyramid?Volume of a pyramid = 1/3(length)(width)(height)
Find the volume of the pyramid in the image given:
Volume of the pyramid = 1/3(2r)(2r)(h)
Volume of the pyramid = 4r²h/3
We are given that the volume of the cone is π/4 of the volume of the pyramid.
Therefore, the expression that represents the volume of the cone would be: [tex]\mathbf{\frac{\pi}{4} (\frac{4r^2h}{3} )}[/tex]
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Answer:
D:
Step-by-step explanation
Tried to do this one on my own but still dont get how to do it.
Answers
Answer:
238
Step-by-step explanation:
First, you must find the ratio between the one measurement of the larger octagon and the smaller octagon. Just divide 28 by 4 to get 7. This is what you have to multiply the perimeter by to get the larger octagon's perimeter. 34 times 7 equals 238. There are multiple ways to do this problem but this way is the simplest. If this helped you, please click the "Thanks" button!
The sides of a triangle are 5.2 cm, 6.3 cm and 9.4 cm, each correct to the nearest millimetre.
Calculate the lower bound of the perimeter of the triangle.
Answers
Answer:
20.75
Step-by-step explanation:
5.2 lower bound = 5.15
6.3 lower bound = 6.25
9.4 lower bound = 9.35
5.15 + 6.25 + 9.35 = 20.75
Y-intercept of x- 2y = -10
Please help
Answers
Answer:
y = [tex]\frac{1}{2} x\\[/tex]+5
Step-by-step explanation:
Y-intercept 5
Answer:
y- intercept = 5
Step-by-step explanation:
to find the y- intercept let x = 0 in the equation and solve for y
this relies on the fact that when the line crosses the y- axis the x- coordinate is zero, then
0 - 2y = - 10 , that is
- 2y = - 10 ( divide both sides by - 2 )
y = 5
then y- intercept = 5
Find the surface area of the pyramid. The side lengths of the base are equal.
Answers
the radius of a sphere is r=17
what is the volume
Answers
Answer:20579.53
Step-by-step explanation:round it to its hundreth or tenth based on the question or full
For a science experiment, maria threw an egg 88.2 meters in 3 seconds. what was the average rate of speed of the egg? a. 88.2 m/sec. b. 44.1 m/sec. c. 29.4 m/sec. d. 9.8 m/sec.
Answers
Answer: its not A its b c or d sorry i could not help more
Answer:
The answer is C. 29.4 m/sec.
Step-by-step explanation:
I got it right ^w^
Calculus - need work shown
Answers
Easy evaluation!
[tex]5( ln( |4x - 15| ) + c[/tex]
Step-by-step explanation:
Feel free to ask if you're left with any doubts.
Answer:
[tex]\large \text{$ 5 \ln|4x-15|+C $}[/tex]
Step-by-step explanation:
[tex]\large \displaystyle\begin{aligned}\textsf{let }\:u & =4x-15\\\implies \dfrac{du}{dx} & =4\\\implies dx & =\dfrac{1}{4}\: du\\\end{aligned}[/tex]
[tex]\large\displaystyle\begin{aligned}\int \dfrac{20}{4x-5}\:dx &=\int \dfrac{20}{u}\cdot \dfrac{1}{4}\:du\\\\&=\int \dfrac{20}{4u}\:du\\\\&=\int \dfrac{5}{u}\:du\\\\&=5 \ln |u| +C\\\\&=5 \ln |4x-15| + C\end{aligned}[/tex]
HELP PLSSSSS!!!! ASAP!!! Insert operation signs (+,-,*,/) and parentheses as needed to make the equation true.
4 3/4 _ 7 1/2 _ 1 1/6 _ 1 1/3 = 1
Or in other words:
4.75 _ 7.5 _ 1.16666... _ 1.33333... = 1
TY PLSS HURRY!!!!
Answers
Answer:
This cannot be explained properly by me, but the answer is 4 3/4*1 1/3 divided by (7 1/2-1 1/6). I just did a lot of trial and error
Step-by-step explanation:
The mathematical operations used [tex](4.75/7.50) * 1.17 * 1.34[/tex].
What are mathematical operations?
An operation exists as a mathematical action. Addition, subtraction, multiplication, division, and calculating the root exist all instances of a mathematical operation.
Given: 4 3/4 _ 7 1/2 _ 1 1/6 _ 1 1/3 = 1 or
4 3/4 _ 7 1/2 _ 1 1/6 _ 1 1/3 = 1
Convert mixed fraction into a proper fraction we have
[tex](19/4) * (15/2) * (7/6) * (4/3) = 1[/tex]
Now convert the proper form of the fraction into a decimal
[tex]$4.75 * 7.50 * 1.16 * 1.34[/tex]
Inserting operation signs, then we get
[tex]= (4.75/7.50) * 1.17 * 1.34[/tex]
= 0.99294
= 1 (approximately)
Therefore, the correct answer is [tex](4.75/7.50) * 1.17 * 1.34[/tex].
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What is the distance between points a(-3,2) and b(-6,-2)
Answers
Work Shown:
[tex]A = (x_1,y_1) = (-3,2) \text{ and } B = (x_2, y_2) = (-6,-2)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-3-(-6))^2 + (2-(-2))^2}\\\\d = \sqrt{(-3+6)^2 + (2+2)^2}\\\\d = \sqrt{(3)^2 + (4)^2}\\\\d = \sqrt{9 + 16}\\\\d = \sqrt{25}\\\\d = 5\\\\[/tex]
I used the distance formula. Alternatively, you can plot the two points and form a right triangle. Then use the pythagorean theorem. The distance formula is effectively a modified version of the pythagorean theorem.
A line passes through the two points (-4,6) and (2,-5). Calculate the following parts:
Answers
A line passes through the two points (-4,6) and (2,-5). 11x +6y - 80 = 0 is the given line equation.
What is the slope of a line which passes through points ( p,q) and (x,y)?Its slope would be:
[tex]m = \dfrac{y-q}{x-p}[/tex]
The slope of parallel lines are same. Slopes of perpendicular lines are negative reciprocal of each other.
The slope m of the line is given as
[tex]m = \dfrac{y-q}{x-p}\\\\ m = \dfrac{-5-6}{2+4}\\\\ m = \dfrac{-11}{6}[/tex]
The equation of a line is
[tex]( y -y_0) = m (x - x_0)\\\\( y -6) = \dfrac{-11}{6} (x+4)\\\\6( y -6) = (-11) (x+4)\\\\6y -36 = (-11x +44)\\\\11x +6y - 80 = 0[/tex]
Hence, the equation is 11x +6y - 80 = 0
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7. Use the compound-interest formula to find the account balance A with the given conditions, where P=principal, r=interest rate, n=number of compounding periods per year, t=time, in years, and A=account balance.
Answers
Answer:
$173,954.01
Step-by-step explanation:
Finding compound interest :
A = (150,000)(1 + 0.025)⁶A = (150,000)(1.025)⁶A = (150,000)(1.15969342)A = $173,954.01A 60 foot by 20 foot garden is enclosed by a fence. To increase the area of the garden, while still using the same fence, its shape is changed to a square. By how many square feet does this enlarge the garden
Answers
The increase in square feet when the garden is enlarged is 400 square feet.
What is the increase in square feet?The first step is to determine the perimeter of the fence:
Perimeter = 2( length + width)
2 (60 + 20)
= 160 feet
When the shape of the garden is changed to a square, the perimeter of the square and the rectangle has to be the same.
Length of side of the square = 160 / 4 = 40 feet
Area of the square = 40 x 40 = 1600 square feet
Area of the garden = 60 x 20 - 1200 square feet
Difference = 1600 - 1200 = 400 square feet
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Half of a circular cake is left after a party. A piece of cake with a 44˚ angle is eaten.
What is the angle in the piece that is left?
Answers
Answer:
136°
Step-by-step explanation:
The whole of the cake angle = 360°
Half of it = 180°
Therefore; if 44° angle is eaten out of the half i.e 180°
Then what's left = 180° - 44° = 136°
It's seventh grade social studies the question is written "how did the issue of slavery cause the Civil War?"
Answers
Answer:
The civil war started because the south wanted to keep the country enslaved while the north wanted a free slave country. This divison between the north and the south created the civil war
Answer:
It divided the nation.
Step-by-step explanation:
North wanted to banned slavery, while the south didn't. At that time states from the north and the south were in the union. The south succeeded from the union, because of some slavery issues which lead to the Civil War.
Given: ∠ABC and ∠CBD are complementary angles and m∠ABC=35°
Prove:m∠CBD=55°
Answers
Answer:
we know that sum of two complementary angles always equals to 90°
now ∠ABC and ∠CBD are complementary which means ∠ABC + ∠CBD = 90
∠ABC = 35° given
so ∠CBD = 90° - ∠ABC = 90° - 35° = 55°
therefore hence proved ∠CBD = 55°
What is the measure of
Answers
Answer:
can i have life orientation project memo for term 2
can anybody help me...
Answers
Answer: The 3 angles shown need to equal 180 degrees
x = 180 - 75 - 65
x = 40 degrees
Step-by-step explanation:
I had someone help out with this one...hope this helps u out have a good rest of ur day!!!!!
50 POINTS AND BRAINLIEST!!!!!!!
This table represents a proportional relationship between x and y.
x 1.3 1.6 1.9 2.2
y 1.82 2.24 2.66 3.08
What is the constant of proportionality?
Enter your answer as a decimal in the box.
Answers
Reason:
Pick any column and divide y over x
column one: y/x = (1.82)/(1.3) = 1.4column two: y/x = (2.24)/(1.6) = 1.4column three: y/x = (2.66)/(1.9) = 1.4column four: y/x = (3.08)/(2.2) = 1.4You only need to pick one column when it comes to showing your work.
The constant of proportionality is 1.4
This leads to the equation being y = 1.4x
HELP ILL GIVE BRAINLIEST
Answers
Answer:
B) 8/9
Step-by-step explanation:
0.3 + 0.5 = 0.8Change to repeating decimal (0.888888...)The decimal converts to 8/9Answer:
B
Step-by-step explanation:
0.3333 + 0.5555 = 0.8888
as a fraction it's 8/9
A plane convex lens is made of glass ( n = 1. 5) with one flat surface and the other having a radius of 20 cm. What is the focal length (in cm) of the lens?
Answers
The focal length of the lens is 40cm.
What is the focal length?The distance between the center of a lens or curved mirror and its focus.
A plane convex lens is made of glass ( n = 1. 5) with one flat surface and the other having a radius of 20 cm.
The focal length of the lens is given by the following formula;
[tex]\rm \dfrac{1}{f}=(n-1) \left ( \dfrac{1}{r_1}-\dfrac{1}{r_2} \right)\\\\Where; \ r_1 =\infty , \ r_2=20, \ and \ n = 1.5[/tex]
Substitute all the values in the formula;
[tex]\rm \dfrac{1}{f}=(n-1) \left ( \dfrac{1}{r_1}-\dfrac{1}{r_2} \right)\\\\\rm \dfrac{1}{f}=(1.5-1) \left ( \dfrac{1}{\infty}-\dfrac{1}{20} \right)\\\\ \rm \dfrac{1}{f}=(0.5) \left ( 0-\dfrac{1}{20} \right)\\\\ \dfrac{1}{f} = \dfrac{-0.5}{20}\\\\\dfrac{1}{f}=-0.025\\\\f = \dfrac{-1}{0.025}\\\\f=-40[/tex]
Hence, the focal length of the lens is 40cm.
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Find the value of X round to the nearest degree
Answers
Answer:
50
Step-by-step explanation:
to find the value of x use "sinerule"
sinx/13= Sin90/17
sinx = sin90×13/17
sinx= 14/17
sinx= 0.764705882
X= SIN^-1(0.764705882)
X = 49.888
X= 50
5
Find the missing angle.
94
23°
?
Answer:
degrees
Answers
Answer:
63 degrees as 94 +23 =117
180-117=63
is this the right answer
Answers
Answer: A
Step-by-step explanation:
Origin is at 0,0, and the arrow is pointing towards the center which is 0,0.
PLEASE HELP I NEED THE CORRECT ANSWER AS I ONLY HAVE ONE TRY AND I NEED TO SUBMIT IT IN 10 MINUTES
Answers
Answer:
A, B, D
Step-by-step explanation:
A 6x3 =18
B 9x2=18
D 9x2=18
The area of a
triangle is 21 in
The base is 7cm.
What is the
height?
Answers
Answer:
7 inches
Step-by-step explanation:
1. Covert 7cm into inches: approximatly 3 inches.
2. 21/3: 7
3. 7 inches
Zane took Jessica to dinner. The check was $31.23. They left a tip of 25% the total check. How much was the total cost of the dinner (including tip)?
Answers
Step-by-Step Explanation:
Amount for Dinner = $31.23
Tip Rate = 25%
Total Amount = ?
Therefore,
= (25/100 * 31.23) + 31.23
= (780.75/100) + 31.23
= 7.8075 + 31.23
=> 39.0375
Total Amount = $39.0375 or $39.04
Use the product rule to simplify a ^7 x a ^11
Answers
Answer:
The answer to the question a∧18
Answer:
[tex]a^{18}[/tex]
Step-by-step explanation:
Use the product rule to simplify a ^7 x a ^11
[tex]a^{7}[/tex] × [tex]a^{11}[/tex] =
(add the exponents)
7 + 11 = 18
[tex]a^{18}[/tex]
[3 - (6 ÷ 3)3] x 11 + 11?
Answers
Answer:
The answer is -11(3x-1)
Step-by-step explanation:
Thats what the calculator said
Hope this helps!!!