A and B are two events.
Given that P(A)=0.25 , P(B)=0.2 , and P(A and B)=0.04 .
Drag and drop the answers into the boxes.
Answer:
Not independent.
Step-by-step explanation:
Given that P(A)=0.25 , P(B)=0.2 , and P(A and B)=0.04
To check whether A and B are independent.
Two events are independent if
P(A/B) = P(A) or P(B/A) = P(B) or P(AB) = P(A) P(B)
if any one of the above three is true also, the two events would be independent.
Let us find out first one
P(A/B ) = P(AB)/P(B) (as per conditional probability formula)
= 0.04/0.2=0.2
But P(A) = 0.25 and not equals P(A/B)
Hence we can conclude that A and B are not independent
because P(A/B) not equals P(A)
The original dimensions of the Great Pyramid of Giza in Egypt were 146 meters tall and 229 meters on each side of the square base. What was the original volume of this pyramid?
A. 2,337,655 cubic meters
B. 1,627,121 cubic meters
C. 2,552,129 cubic meters
D. 2,429,586 cubic meters
Answer
C. 2,552,129 cubic meters
Explanation
The volume of a pyramid = (1/3)Ah
Where A ⇒ area of the base
h ⇒ vertical height of the pyramid.
∴ Volume = (1/3) Ah
= 1/3 (229 × 229) × 146
= 1/3 × 52,441 × 146
= 1/3 × 7,656,386
= 2,552,128.667 m³
In whole number = 2,552,129 m³
On Monday, Torrance practiced the violin for 4/10 of an hour. On Tuesday, he practiced for 1 6/8 of an hour. How much time did he practice in all?
Answer: [tex]2\frac{3}{20}[/tex]
Step-by-step explanation:
First, convert mixed numbers into improper fractions and simplify all fractions
[tex]\frac{4}{10}[/tex] ÷ [tex]\frac{2}{2}[/tex] = [tex]\frac{2}{5}[/tex]
[tex]1\frac{6}{8}[/tex] = [tex]\frac{8(1) + 6}{8}[/tex] = [tex]\frac{14}{8}[/tex] ÷ [tex]\frac{2}{2}[/tex] = [tex]\frac{7}{4}[/tex]
Next, find their sum. Remember to find the LCD and convert the fractions so they have like denominators.
Monday + Tuesday = Total
[tex]\frac{2}{5}[/tex] + [tex]\frac{7}{4}[/tex] = Total the LCD of 5 and 4 is 20
[tex](\frac{4}{4})\frac{2}{5}[/tex] + [tex](\frac{5}{5})\frac{7}{4}[/tex] = Total
[tex]\frac{8}{20}[/tex] + [tex]\frac{35}{20}[/tex] = Total
[tex]\frac{43}{20}[/tex] = Total
Then, convert the improper fraction into a mixed number
[tex]\frac{43}{20}[/tex] = [tex]2\frac{3}{20}[/tex]
21 POINTS... Select the correct answer. If g is an odd function, which pair of points could be found on the graph of g? (-1,16) and (1,16) (3,-5) and (-3,-5) (4,28) and (4,-28) (-2,32) and (2,-32
Match the following vocabulary 1. the status of a statement as either true or false contrapositive 2. a logical statement that is broken down into two parts, the hypothesis and the conclusion hypothesis 3. the “if” portion of your conditional statement; what your conditional statement is about inverse 4. the “then” portion of your conditional statement; what your conditional statement is doing conclusion 5. this version of the conditional switches the hypothesis portion with conclusion portion of the statement conditional statement 6. this version of the conditional negates both the hypothesis and the conclusion portions of the statement converse 7. this version of the conditional combines the converse with the inverse and switches the hypothesis and conclusion while negating both portions truth value
1. The status of a statement as either true or false is Truth value.
2. A logical statement that is broken down into two parts, the hypothesis and the conclusion is Conditional statement.
3. The “if” portion of your conditional statement; what your conditional statement is about is Hypothesis.
4. The “then” portion of your conditional statement; what your conditional statement is doing is Conclusion.
5. This version of the conditional switches the hypothesis portion with conclusion portion of the statement is Converse.
6. This version of the conditional negates both the hypothesis and the conclusion portions of the statement is Inverse.
7. This version of the conditional combines the converse with the inverse and switches the hypothesis and conclusion while negating both portions is Contrapositive.
This logic question involves matching terms related to conditional statements such as truth value, hypothesis, conclusion, and forms like converse, inverse, and contrapositive.
Explanation:The question relates to the study of logic, specifically the nature of conditional statements and related logical constructs. Here is the matching list based on the provided definitions:
The status of a statement as either true or false - truth value.A logical statement that is broken down into two parts, the hypothesis and the conclusion - conditional statement.The “if” portion of your conditional statement; what your conditional statement is about - hypothesis.The “then” portion of your conditional statement; what your conditional statement is doing - conclusion.This version of the conditional switches the hypothesis portion with conclusion portion of the statement - converse.This version of the conditional negates both the hypothesis and the conclusion portions of the statement - inverse.This version of the conditional combines the converse with the inverse and switches the hypothesis and conclusion while negating both portions - contrapositive.These logical terms are essential for understanding how to construct and analyze logical arguments, and they are closely tied to the philosophical study of truth
The planets move around the sun in elliptical orbits with the sun at one focus. The point in the orbit at which the planet is closest to the sun is called perihelion, and the point at which it is farthest is called aphelion. These points are the vertices of the orbit. A planet's distance from the sun is 741,000,000 km at perihelion and 817,000,000 km at aphelion. Find an equation for the planet's orbit. (Place the origin at the center of the orbit with the sun on the x-axis. Use the following as necessary: x, y.)
Answer:
The shape of planetary orbits follows from the observed fact that the force of gravity between two objects depends on the square of the distance between them. ... Ellipses are closed so the planets we see in elliptical orbits stick around.
Step-by-step explanation:
We can write the equation for the planet's orbit:[tex]\[ \frac{x^2}{(817,000,000)^2} + \frac{y^2}{(741,000,000)^2} = 1 \][/tex]
How to find an equation for the planet's orbitTo find an equation for the planet's orbit, we can use the properties of an ellipse. The standard form of the equation for an ellipse with its center at the origin and major and minor axes along the x and y-axes is:
[tex]\[ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \][/tex]
In your problem, the distances at perihelion and aphelion are given as 741,000,000 km and 817,000,000 km, respectively. These distances represent the values of \(a\) and \(b\) in our equation.
So, we have:
[tex]\[ a = 817,000,000 \text{ km} \][/tex]
[tex]\[ b = 741,000,000 \text{ km} \][/tex]
Now, we can write the equation for the planet's orbit:
[tex]\[ \frac{x^2}{(817,000,000)^2} + \frac{y^2}{(741,000,000)^2} = 1 \][/tex]
This is the equation for the planet's elliptical orbit with the sun at one of the foci, where the origin is at the center of the orbit.
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what is a counterexample for the following conjecture if a counterexample does not exist choose not possible conjecture all quadrilaterals are rectangles
Counter example:- a trapazoid is a quadrilateral which has only one pair of parallel sides unlike a rectangle which has 2. So the conjecture is false.
Answer:
a trapezoid is a quadrilateral and it is not a rectangle
Step-by-step explanation:
I'd really appreciate it if anyone helped! :)
What type of transformation takes the graph of f(x)=|x| to the graph of g(x)=−3+|x|?
Horizontal translation of 3 units left
Vertical translation of 3 units up
Vertical translation of 3 units down
Horizontal translation of 3 units right
Vertical translation of 3 units down
the graph of g(x) = - 3 + | x| is the graph of f(x) = | x| moved 3 units down ( - 3 ) vertically
The product of two numbers is 240.If their hcf is 12 what is their lcm.
Answer:
20
Step-by-step explanation:
product=240
12*x= 240
12 x =240
x=240/12
x=20
A spinner with two sectors labeled A and B is spun, and a number cube is rolled.
What is the sample space for the experiment?
{A1, A2, A3, A4, A5, A6, B1, B2, B3, B4, B5, B6}
{A, B}
{A, B, 1, 2, 3, 4, 5, 6}
{1, 2, 3, 4, 5, 6}
The sample space for spinning a spinner with two sectors labeled A and B, and rolling a number cube, is {A1, A2, A3, A4, A5, A6, B1, B2, B3, B4, B5, B6}.
Explanation:The sample space for the experiment of spinning a spinner with two sectors labeled A and B, and rolling a number cube, can be determined by listing all the possible outcomes. The outcomes will be the combination of all possible results from spinning the spinner (A or B) and rolling the number cube (1, 2, 3, 4, 5, or 6). Therefore, the sample space is {A1, A2, A3, A4, A5, A6, B1, B2, B3, B4, B5, B6}.
Which of the following numbers are irrational
letter d is one of the irrational numbers
Answer:
The answer is A and B.
Step-by-step explanation:
They cannot be expressed as a ratio of two integers.
Please help its past due!
Quadrilateral ABCD is located at A(−2, 2), B(−2, 4), C(2, 4), and D(2, 2). The quadrilateral is then transformed using the rule (x + 7, y − 1) to form the image A'B'C'D'. What are the new coordinates of A', B', C', and D'? Describe what characteristics you would find if the corresponding vertices were connected with line segments.
A(−2, 2), B(−2, 4), C(2, 4), and D(2, 2).
rule (x + 7, y − 1)
To find new coordinates we add 7 with x and subtract 1 from y
A(−2, 2) -----> A' (5,1)
B(−2, 4) -------> B' (5, 3)
C(2, 4) ---------> C' (9, 3)
D(2, 2) -------->D' (9, 1)
Characteristics
When we connect all the points by line segments, the line A'B' will be parallel to C'D'.
Also, B'C' parallel to A'D'.
All the four lines forms a rectangle .
The new coordinates of the points are A'(5, 1), B'(5, 3), C'(9, 3), and D'(9, 1).
When you connect the vertices, you have a rectangular prism.
Paula is training take part in a fun run fir charity. Paula weighed 65.5 kilogram before she started her training. She has list 3500grams, how much does she weigh now in kilogram
Add using a number line 5/6 plus - 1 1/6
Start at 5/6 on the number line. Move 11/6 spaces to the left (11/6 is negative; if you are adding a negative number, move to the left). You should land on -1.
Name the property of equality that justifies & Name the property of equality that justifies: If x + 3 = 5, then x = 2.
A) In this question two angles are given equal and in next step both sides are multiplied by 5 and the result of both sides is equal to each other. The property used is
"When equal are multiplied by equL number then the result is also equal" the equality property is of multiplication.
B) In this question [tex] x+3=5[/tex] is given
And then [tex] x=2[/tex]
Here number 3 is subtaracted from both the sides to make [tex] x[/tex] equal to 2.
The property of equality used is " If equal are subtracted from equal the result will be equal"
Here the equality property of subtraction is uaed.
What is 99,102 rounded to the nearest hundred thousand
The answer to this question is 100,000 exactly.
Ube had made a banana cream pie. His brother he 1/3 of a pie and his sister had 2/5 of the pie how much less did his brother eat than his sister
An investment firm wants to create a billboard that displays an enlarged $1,000,000 bill. The actual size of the bill is 2.61 inches by 6.14 inches. If the billboard is 48 feet wide, what's the scale of the bill to the billboard?
A. 1′ = 8.71″
B. 1′ = 7.81″
C. 1″ = 8.71′
D. 1″ = 7.81′
We know how wide the billboard will be. Therefore, to know how much the original image should be enlarged, you have to divide the final width of the billboard between the current width of the invoice.
[tex]\frac{48 feet }{6.14 inches} =7.81\frac{feet}{inches}[/tex]
Therefore the correct answer is option D.
In order for the bill to cover the billboard, the bill must be expanded by a factor of 7.81 feet in length by inch in length.
The garden club earned \$15$15dollar sign, 15 per hour by weeding neighborhood gardens for ttt hours. A generous donor has agreed to double their earnings.
how much did the garden club earn in all?
The garden club earned $15 per hour by weeding neighborhood gardens for t hours.
A generous donor has agreed to double their earnings.
Double their earnings means we multiply by 2
So earning 15 per hour becomes 2*15 = 30 per hour
Given the number of hours is t
Earnings = $30 times number of hours
Earnings = 30 * t
Given that earning for 1 hour by weeding neightborhoods garden = $15
Then earning for 2 hours by weeding neightborhoods garden = $15*2= $30
Then earning for 3 hours by weeding neightborhoods garden = $15*3
Using same pattern earning for t hours by weeding neightborhoods garden = $15*t= $15t
Not it says that earning is doubled means you are getting 2*15 or $30 per hour
then new earning will be $30t in place of $15t
Hence final answer is $30t.
4. Calculate the gravity force between the Earth (m = 6*10^24 Kg) and the Moon (m = 7*10^22 Kg) when their distance is 4*10^8 m. (use G = 7*10^-11 Nm2/Kg2)
Fg = 1.8 * 10^52 N
the answer is given, but can someone explain how to get it?? I've tried for an hour to figure it out, but I am not getting it
r = 4*10^8 is the average distance from the earth to the moon (in meters).
m1 = 6*10^24 is the mass of the earth
m2 = 7*10^22 is the mass of the moon
G = 7*10^(-11) is the gravitational constant
Plug those values into the formula shown on the attached image (see below). Then simplify. When doing all that, I get the answer to be 1.8 * 10^20 newtons, so I'm not sure where your teacher is getting 52 as the exponent.
The one-time fling! Have you ever purchased an article of clothing (dress, sports jacket, etc.), worn the item once to a party, and then returned the purchase? This is called a one-time fling. About 20% of all adults deliberately do a one-time fling and feel no guilt about it! In a group of nine adult friends, what is the probability of the following?
Given that about 20% of adults do one time fling.
That is probability of a person doing fling is [tex]\frac{20}{100}=0.2[/tex] . Let it be p.
Then we have to use binomial distribution formula for the given problems.
b(x;n,p)=[tex]n_{C_{x}}p^{x}(1-p)^{n-x}[/tex]
A)Probability of no one has done one time fling means x is 0 here.
Hence [tex]b(0;9,0.2)=9_{C_{0} }(0.2)^{0}(1-0.2)^{9}[/tex]
[tex]=1X1X0.8^{9}=0.1342[/tex]
b) Probability of at least one person has done fling=1-(probability of no one has done)
=1-0.1342=0.8658
c)Probability of no more than two people have done one time fling means we need to add the probabilities for x=1,x=2 along with x=0.
[tex]b(1;9,0.2)=9_{C_{1}}(0.2)^{1}(1-0.2)^{8}[/tex]
[tex]=9X0.2X0.8^{8}=0.302[/tex]
[tex]b(2;9,0.2)=9_{C_{2}}0.2^{2}(1-0.2)^{7}[/tex]
[tex]=36X0.04X0.8^{7}=0.302[/tex]
Hence probability = 0.1342+0.302+0.302 = 0.7382
Jo sold 336 cake at the sale. Bop sold 286 cake.Bop estimate he sold 50 fewer cake than jo.How did he estimate
Bop estimated by subtracting 286 from 336 (equation: 336 - 286). He got the answer 50, so that is how he made his estimation.
What is the next number in the pattern? 4, -12, 36, -108, k
This is a geometric sequence where r = -3.
4 x -3 = -12
-12 x -3 = 36
36 x -3 = -108
-108 x -3 = 324
Answer: 324
What is the measure of the radius of S?
A. 12.2 units
B. 24.4 units
C. 6.1 units
D. 3.05 units
Samaad had $20.He spent $12.50.His mum gave him $10 more.Samaad spent additional $14.50.How much is left?
20-12.50=7.50
7.50+10=17.50
17.50-14.50= 3
$3
Start with the following conditional statement: If it is October 31, then it is Halloween.
a. State the converse of the statement.
b. State the inverse of the statement.
c. State the contrapositive of the statement.
( Answer in your own words, or don't answer at all )
The converse of 'If it is October 31, then it is Halloween' is 'If it is Halloween, then it is October 31.' The contrapositive is 'If it is not Halloween, then it is not October 31.'
Explanation:In logic and mathematics, we often explore the relationships between statements through their converses and contrapositives. Starting with the conditional statement, 'If it is October 31, then it is Halloween,' we can form the converse and contrapositive as follows:
The converse of the statement essentially flips the 'if' and 'then' components. As such, the converse of your statement would be: 'If it is Halloween, then it is October 31.'The contrapositive of a statement switches the 'if' and 'then' components and negates both. Hence, the contrapositive of your statement is: 'If it is not Halloween, then it is not October 31.'Learn more about Conditional Statements here:https://brainly.com/question/36974334
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Use the graph for Parts A and B....
It is a function. It passes the vertical line test, meaning for each x there's at most one y.
When x=2 we see y=-3 as (2,-3) is a point on the graph
The question's subject is about interpreting and representing data using different types of graphs. Each type of graph is chosen based on what we want to show with our data. For instance, line graphs are useful for displaying change over time.
Explanation:The question refers to the use of graphs to illustrate data. These graphs represent the position of a moving object plotted against time. In the presented case, Part A of the graph begins with a nonzero y-intercept with a downward slope that levels off at zero, while Part B begins at zero with an upward slope that decreases in magnitude until the curve levels off.
When creating graphs, it's important to label the axes correctly and, if multiple datasets are shown on one graph, various symbols should be used to differentiate between them. In the example given, three types of graphs can be used: a line graph to show change over time, a bar graph to compare different categories, and a pie chart to represent proportions. The choice of graph depends on the type of data and what you want to show.
As mentioned, a graphing utility allows us to compare trajectories, highlighting the differences and similarities. It is crucial to use that visualization and analysis tool to make effective interpretations.
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2+90000 what is the answer to the question
a play is performed for a crowd of 400 people.adult ticket cost $22 each, student tickets cost $15 each,and tickets for children cost $13.50 each.the revenue for the concert is $7840.there are 40 more children at the concert than students.how many of each type of ticket are sold?
For this case we have the following variables:
A: Represents the number of adults
S: Represents the number of students
C: Represents the number of children
For the income we have:
[tex]22A + 15S + 13.50C = 7840[/tex] -----> (1)
Regarding the number of people at the concert we have:
[tex]A + S + C = 400[/tex] -----> (2)
If there are 40 more children than students, we have:
[tex]C = 40 + S[/tex] -----> (3)
We substitute C in the second equation and it remains:
[tex]A + S + 40 + S = 400[/tex]
[tex]A + 40 + 2S = 400[/tex]
[tex]A + 2S = 400-40[/tex]
[tex]A + 2S = 360[/tex]
[tex]A = 360-2S[/tex] --------> (4)
Substituting (3) and (4) in (1) we have:
[tex]22 (360-2S) + 15S + 13.50 (40 + S) = 7840[/tex]
[tex]7920-44S + 15S + 540 + 13.50S = 7840[/tex]
[tex]7920-7840 + 540 = 44S-15S-13.50S[/tex]
[tex]620 = 15.50S[/tex]
[tex]S = \frac{620}{15.50}[/tex]
[tex]S = 40[/tex]
So, there are 40 children.
Substituting S in (3) and obtaining C:
[tex]C = 40 + S[/tex]
[tex]C = 40 + 40[/tex]
[tex]C = 80[/tex]
Substituting S in (4):
[tex]A = 360-2 (40)\\A = 360-80\\A = 280[/tex]
Thus, 280 tickets of adults, 80 of children and 40 of students were sold.
Answer:
280 tickets for adults, 80 for children and 40 for students
Given right triangle ABC, what is the value of tan (A)?
12/5 is the answer because if you use the help of "SohCahToa" you find that 12 is the opposite side of angle A and 5 is the adjacent angle