Answers
The answers to the questions are:
a) P(A|B) = 1/3
b) P(B|A) = 1.15
c) A. A student given a $1 bill is more likely to have kept the money.
What is the probability?
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.
Because the probability of 0.659 is almost two times greater than 0.341
Assuming the following table:
Purchased Gum Kept the Money Total
Students Given 4 Quarters 25 19 44
Students Given $1 Bill 13 26 39
Total 38 45 83
a. find the probability of randomly selecting a student who spent the money, given that the student was given a $1 bill.
For this case let's define the following events
B= "student was given $1 Bill"
A="The student spent the money"
For this case we want this conditional probability:
P(A|B) = P(A And B) / P(B)
We have that
P(A) = 38/83, P(B) = 39/83
P(A And B) = 13/83
And if we replace we got:
P(A|B) = (13/83)/(45/83) = 13/39 = 1/3
b. find the probability of randomly selecting a student who kept the money, given that the student was given a $1 bill.
For this case let's define the following events
B= "student was given a $1 Bill"
A="The student kept the money"
P(A|B) = P(A And B) / P(B)
We have that
P(A) = 45/83, P(B) = 39/83
P(A And B) = 26/83
And if we replace we got:
P(B|A) = (45/83)/(39/83) = 45/39 = 1.15
c. what do the preceding results suggest?
For this case the best solution is:
A. A student given a $1 bill is more likely to have kept the money.
Because the probability of 0.659 is almost two times greater than 0.341
Hence, The answers to the questions are:
a) P(A|B) = 1/3
b) P(B|A) = 1.15
c) A. A student given a $1 bill is more likely to have kept the money.
To learn more about the probability visit,
https://brainly.com/question/25839839
#SPJ1
Related Questions
Over a 24-hour period, the tide in a harbor can be modeled by one period of a sinusoidal function. The tide measures 5 ft at midnight, rises to a high of 9.5 ft, falls to a low of 0.5 ft, and then rises to 5 ft by the next midnight.
Give the value of each given that x represents time in hours since the beginning of the 24 hour period that models the situation.
Answers
Answer:
Step-by-step explanation:
The tide over a 24-hour period can be modeled by a sinusoidal function of the form:
f(x) = A * sin(Bx) + C
where A is the amplitude, B is the frequency, and C is the vertical shift.
To determine the values of A, B, and C, we need three points. Let's use the following points:
(0, 5): This is the value of the tide at midnight, 5 ft.
(12, 9.5): This is the value of the tide at its high, 9.5 ft.
(6, 0.5): This is the value of the tide at its low, 0.5 ft.
Using the first point (0, 5), we can calculate the vertical shift, C:
C = 5
Using the second point (12, 9.5), we can calculate the amplitude, A:
A = (9.5 - 5) / 2 = 2.25
Using the third point (6, 0.5), we can calculate the frequency, B:
0.5 = 2.25 * sin(B * 6) + 5
4.5 = 2.25 * sin(B * 6)
2 = sin(B * 6)
B * 6 = sin^-1(2)
B * 6 = pi / 2
B = pi / (2 * 6) = pi / 12
So, the final equation is:
f(x) = 2.25 * sin(pi * x / 12) + 5
This represents one period of the sinusoidal function that models the tide over a 24-hour period, with time x measured in hours since midnight.
Solve the system by substitution.
y = 5x
y = 4x + 9
Answers
attached is the explanation!
Nicholas works at the car dealership, if he gets a 4% commission, and 10 pants
sells the two cars ($33,500/car) to Mr. Sherman, how much commission
will he earn?
A $2,917.85
B. $3,040
C $3,309 80
D $2,680
Answers
Nicholas will earn a commission of
D $2,680How to find the commissionNicholas will earn a commission of 4% on the total price of the two cars sold to Mr. Sherman.
The total price of the two cars is $33,500 per car, so for two cars, the total price would be
= $33,500 * 2
= $67,000.
Therefore, Nicholas will earn a commission of 4% of $67,000
= $67,000 * 0.04
= $2,680.
hence, Nicholas will earn $2,680 in commission for selling the two cars to Mr. Sherman.
Learn more about commission at:
https://brainly.com/question/26283663
#SPJ1
Help me with this question
Answers
Answer:
D.666 cubic centimeters
Step-by-step explanation:
Volume of cylinder is 3 time the volume of cone of the same radius.
Volume of cylinder= πr²h
Volume of cone = 1/3 x πr²h
is 5.2481 a ratinal number
Answers
Answer:
Step-by-step explanation:
Rational numbers are numbers that can be written in the form pq, where p and q are integers and q≠0. The difference between rational numbers and fractions lies in the fact that fractions cannot have negative numerator or denominator.
so, yes.
PLEASE HELP
Draw a pie chart for the given data:
Rugby Team
England
France
Ireland
Scotland
Wales
Frequency
20
5
15
25
25
Answers
Step-by-step explanation:
you draw a circle ⭕ then you do lines inside the circle the you write the numbers aside
For his birthday, Tyler's parents gave him $7,000.00 which they put into a savings account that earns 15% interest compounded quarterly. When Tyler started college, he withdrew the entire balance of $26,725.00 and used it to pay for tuition. How long was the money in the account?
Answers
The number of years the interest was compounded quarterly is given by the equation b = 9.098 years
What is Compound Interest?Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.
The formula for calculating Compound Interest is
A = P ( 1 + r/n )ⁿᵇ
where A = Final Amount
P = Principal
r = rate of interest
n = number of times interest is applied
b = number of time periods elapsed
Given data ,
Let the amount after b years be A = $ 26,725.00
The number of years be = b
The number of times the interest is applies n = 4 ( quarterly )
Let the principal amount be P = $ 7,000
A = P ( 1 + r/n )ⁿᵇ
Substituting the values in the equation , we get
t = ln ( A/P ) / n [ ln ( 1 + r/n ) ]
t = b = n ( 26,725.00 / 7,000.00 ) / ( 4 × [ ln ( 1 + 0.15/4 ) ] )
On simplifying the equation , we get
b = ln ( 26,725.00 / 7,000.00 ) / ( 4 × [ ln ( 1 + 0.0375 ) ] )
b = ln ( 3.81785714 ) / 4 [ ln ( 1.0375 ) ]
On further simplification , we get
b = 9.098 years
Hence , the number of years the interest was applied is 9 years 1 months
To learn more about compound interest click :
https://brainly.com/question/21270833
#SPJ1
The table represents an exponential function. What is the multiplicative rate of change of the function? 2 5.
Answers
From the table which represents the exponential function , the multiplicative rate of change of function is (a) 1/5 .
The exponential function is expressed mathematically as : y = a(b)ˣ ;
where "a" is = initial value of function , and "b" is = multiplicative rate of change ;
We first substitute , the first two values from the exponential table ;
we get ;
⇒ 2 = a(b)¹
⇒ 2 = ab ,...,,....equation(1) ;
Now substituting the second value ,
we get ;
⇒ 2/5 = a(b)² ,....equation(2) ;
On dividing equation(2) by equation(1) ,
we get;
⇒ 2/(2/5) = ab/ab² ;
⇒ 5 = 1/b ;
⇒ b = 1/5 .
Therefore , the multiplicative rate of change is b = 1/5 .
Learn more about Exponential Function here
https://brainly.com/question/14355665
#SPJ4
The given question is incomplete , the complete question is
The table represents an exponential function.
What is the multiplicative rate of change of the function ?
(a) 1/5
(b) 2/5
(c) 2
(d) 5
Based on the records for the past several seasons a sports fan believes the probability the red team wins is 0.55. The fan also believes the probability the blue team will wins is 0.60. In a season with 160 games, how many fewer games should the fan expect the red team to win?
Answers
The fan should expect the red team to win 8 fewer games than the blue team in a season of 160 games
What is probability?Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
If the probability that the red team wins is 0.55, then the probability that they lose is 1-0.55 = 0.45.
Similarly, if the probability that the blue team wins is 0.60, then the probability that they lose is 1-0.60 = 0.40.
If we assume that the outcomes of each game are independent of each other and that there are no ties, then the expected number of games that the red team will win in a season of 160 games is:
Expected number of wins for the red team = (probability of winning) x (number of games)
= 0.55 x 160
= 88
Similarly, the expected number of wins for the blue team is:
Expected number of wins for the blue team = (probability of winning) x (number of games)
= 0.60 x 160
= 96
Therefore, the fan should expect the red team to win 8 fewer games than the blue team in a season of 160 games (96 - 88 = 8).
Learn more about probability here:
brainly.com/question/11234923
#SPJ9
find two numbers if their sum is 91 and their ratio is 6:7
Answers
Answer:
Step-by-step explanation:
The two numbers are 42 and 49.
Let us suppose the numbers are x and y.
From the above question,
=> x + y = 91 ------(1)
Also,
=> x:y = 6:7
If we express y in terms of x,
Then, x/y = 6/7
It can also be written as,
=> y = 7x/6 ------(2)
On substitution of value from (2) into (1),
We get,
=> x + 7x/6 = 91
=> 13x/6 = 91
=> x = 6*7
=> x = 42
Now, Substituting the value of x in (1),
We get,
=> 42 + y = 91
=> y = 91 - 42
=> y = 49
Therefore, The values of the two numbers are 42 and 49.
To learn more about finding numbers,
https://brainly.com/question/26398661
Neeed help!!!!!!!!!!!!!!
Answers
An area of a rectangle is 32x¹²y⁹ square inches and the length is 8x⁴y³ therefore the expression which represents the width of the rectangle in inches is 4x⁸y⁶.
What is a Rectangle?
This is referred to as a quadrilateral with four right angles.
Area of rectangle = Length × width
Width = Area/ Length
= 32x¹²y⁹ / 8x⁴y³
= 4x⁸y⁶
Read more about Rectangle here https://brainly.com/question/25292087
#SPJ1
the company bought $15000 worth of equipment beginnning of year 2018 the equipment is est. to increase in value at a rate of 15.9% per year how many yers, t , after which the value of the company's new equipment will be less than 7500
Answers
The number of years, t , after which the value of the company's new equipment will be less than 7500 is 2.64 years
How to determine the valueTo solve this problem, we can use the formula for exponential growth:
V(t) = V₀ * (1 + r)^t
Given that the parameters are;
V(t) is the value of the equipment at a time tV₀ is the initial value of the equipment ($15,000)r is the growth rate (15.9% or 0.159)t is the time in yearsTo determine time t when the value of the equipment will be less than $7500.
Let's set up an inequality;
V(t) < 7500
Substituting the formula for V(t), we get:
V₀ * (1 + r)^t < 7500
Substitute the values
(1 + 0.159)^t < 0.5
t * log(1 + 0.159) < log(0.5)
t > log(0.5) / log(1 + 0.159)
Using a calculator, we get:
t > 2.64
Hence, the value is 2.64 years.
Learn about exponential growth at: https://brainly.com/question/27161222
#SPJ1
division resultado
de residuo sea 400
Answers
A division problem that would lead to a division remainder of 400 is 2, 400 ÷ 500.
How to find the division problem ?You need to find a division problem where the quotient would be such that there would be a remainder of 400.
In that case, the first thing to do is to ensure that the divisor is greater than 400. If it is less, then the remainder cannot be 400.
We can the pick the next hundred after 400 which would be 500. Then, we need to find a number that when divided by 500, would result in 400 as a remainder.
This can be 900, 1, 400, 1, 900, 2, 400 etcetera.
The trick is to ensure that the number is 400 more than a multiple of 500.
Picking 2, 400, the division is therefore:
= 2, 400 ÷ 500
Find out more on division at https://brainly.com/question/29194557
#SPJ1
3ab2 +1
3a²b-1
(a = 2 ; b = -2)
EVALUATE THE EXPRESSION
Answers
Answer:
3ab2+1 = -23
3a^2b-1 =-25
Step-by-step explanation:
Luis compro un refrigerador de 7827.40 si va a pagar el 15%IVA ¿cuánto le cobraron en total?
Answers
Luego de el 15% de iva, el precio será 9001.51
¿Cuánto le cobraron en total?Si le aplicamos un incremento de un porcentaje x a un precio P, entonces el nuevo precio será:
P' = P*(1 + x)
Donde x es el porcentaje en forma decimal.
En este caso tenemos un 15% de IVA, entonces x = 0.15
Y el precio original es 7827.40
Entonces el nuevo precio será:
P' = 7827.40*(1 + 0.15) = 9001.51
Esa es la cantidad que Luis pago.
Aprende más sobre porcentajes:
https://brainly.com/question/843074
#SPJ1
Why we use Permutation to find the number of ways of something can be arranged when order matters. While use Combination when order does not matter.
Answers
The permutation formula is used when the order matters as it does not remove the combinations with the same elements and different order from the equation.
For the combination formula, the term x! is removed, as it removes all the combinations with the same elements but different order.
What is the combination formula?The number of different combinations of x objects from a set of n elements is obtained with the formula presented as follows, using factorials.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
What is the permutation formula?The number of possible permutations of x elements from a set of n elements is given by:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
More can be learned about combination and permutation at https://brainly.com/question/11732255
#SPJ1
please help I really really need it.
Answers
Answer:3/a-6
Step-by-step explanation:
n the blanks below.
Find the slope of the line passing through the points (8, -4) and (8, -7).
slope:
Find the slope of the line passing through the points (-3, -9) and (-3, 9).
slope:
Answers
The slope of the line passing through the points (8, -4) and (8, -7) is undefined.
The slope of the line passing through the points (-3, -9) and (-3, 9) is undefined.
How to calculate the slope of a line?In Mathematics, the slope of any straight line can be determined by using this mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Substituting the given data points into the slope formula, we have the following;
Slope, m = (-7 - (-4))/(8 - 8)
Slope, m = (-7 + 4)/0
Slope, m = -3/0
Slope, m = undefined.
Since the change in the x-axis equals to zero, the slope of the two lines are undefined:
Slope, m = (9 - (-9))/(-3 - (-3))
Slope, m = 18/0
Slope, m = undefined.
Read more on slope here: brainly.com/question/3493733
#SPJ1
In country A, there were 131,000 foreign students from country B. This number is 23% more than the number from country C. How many foreign students were from country C
Answers
There were a total of 95,082 students from country C.
What is percentage?A percentage in mathematics is a figure or ratiο that is stated as a fractiοn of 100. The abbreviatiοns "pct.," "pct," and "pc" are alsο occasionally used. It is frequently denοted using the percent symbol "%," though. The amοunt of percentages has no dimensions. With a denominatοr of 100, percentages are basically fractiοns.
To shοw that a number is a percentage, place a percent symbol (%) next to it. Fοr instance, if you correctly answer 75 out of 100 questiοns on a test (75/100), you receive a 75%. Tο compute percentages, divide the amount by the tοtal and multiply the result by 100. The percentage is calculated using the fοrmula (value/total) x 100%.
x represents the number οf students from cοuntry C.
then 122percent of x = 116,000
122/100 * x = 116000
x = 116000 * 100/122 = 95,082 students
To know more about percentage visit:
brainly.com/question/28269290
#SPJ1
Is 2/9 = 10/45 a true proportion?
Answers
Answer:
Yes
Step-by-step explanation:
To find this out. If you divide the denominators by each other, they would need to be the same value as if you divide the numerators by each other
[tex]45 \div 9 = 5[/tex]
^ 45 and 9 were the denominators, we divide and get 5
Now for the numerators
[tex]10 \div 2 = 5[/tex]
^ 10 and 2 we're the numerators, dividing also gave 5
Answer:
yes.
Step-by-step explanation:
let us check. to be a proportion they must be equivalent
however, what do we multiply to get there? let us check..
[tex]\frac{2x}{9x} =\frac{10}{45}[/tex]
cross multiply...
2x * 45 = 9x * 10
90x = 90x
yes, they will be proportional!
you can even do it without the X, i just put x in to make it clearer.
Find the value of sin D rounded to the nearest hundredth, if necessary.
Answers
The value of the trigonometric equation sin D = 0.923
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the triangle be represented as ΔBCD
Now , the measure of BC = 24
The measure of side CD = 10
So , the measure of hypotenuse BD = √ ( BC )² + ( CD )²
Substituting the values in the equation , we get
The measure of BD = √ ( 576 ) + 100
The measure of BD = √ ( 676 )
The measure of BD = 26
Now , from the trigonometric relations ,
sin θ = opposite / hypotenuse
Substituting the values in the equation , we get
sin D = 24 / 26
On simplifying the equation , we get
sin D = 0.923
Hence , the equation is sin D = 0.923
To learn more about trigonometric relations click :
https://brainly.com/question/14746686
#SPJ1
Can someone please me with this
Answers
Answer:
It would be C.
Step-by-step explanation:
It would be C.
JKP, the smaller triangle, needs to be turned into J'K'P' to show proof the the triangles are similar. So the first thing you would have to do, because J'K'P' is exactly 2 times bigger than JKP, is multiply the x and the y by 2. However, this shifts the triangle, and we need the triangles to overlap to prove they are also the same size. So comparing the x and y values after we increase the sides of JKP, we would see we need to subtract the x value by 3, and the y value by 2.
Complete the inequality to represent the following: 13 times a number x
is less than or equal to 200.
Answers
The value for the Inequality 13x ≤ 200 is x ≤ 15.384.
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
13 times a number x is less than or equal to 200.
Now, Writing the Inequality Mathematically
13x ≤ 200
x ≤ 200 / 13
x ≤ 15.384
Learn more about Inequality here:
https://brainly.com/question/2675848
#SPJ1
Homer places a toy rocket on the ground of his backyard, When Homer turns it on, he moves 8 meters away from it. Five seconds after the rocket is launches, Homer can see the rocket from a 75° angle of elevation while he is standing up. If Homer is 1.8 meters tall, how high is the rocket?
Answers
Answer:
Step-by-step explanation:
To find the height of the rocket, we can use the tangent function. We know the angle of elevation (75°), the height of Homer's eyes (1.8 meters), and the distance from Homer to the rocket (8 meters), so we can use the formula:
tan(angle) = height / distance
We'll solve for the height:
height = distance * tan(angle)
height = 8 * tan(75°)
However, we need to convert the angle from degrees to radians first, as the tangent function operates in radians. We can use the formula:
radians = degrees * (π / 180)
radians = 75° * (π / 180) = 1.309 radians
Now, we can substitute the value for the angle in radians back into the original equation:
height = 8 * tan(1.309)
Using a calculator, we can find that the height is approximately 15.57 meters.
So, the height of the rocket is approximately 15.57 meters.
Need Help Asap Today
Answers
The area of the wall is 275 ft square
The number of gallon to cover the wall approximately is 3
the price of the paint is $73.5
How to solve for the area of the wall1. The area of the wall is given as l * w
this is the value that is used to solve for the area of a rectangle
the length is given as 10 ft
the width is given as 22 ft
the area would be 10 * 22
= 220 ft square
find the area of the triangle = rectangular part is given as height = 15 ft - 10 ft = 5 ft
base = 22 ft
area = 1/2 b h
= 0.5 * 22 * 5
= 55
total area = 220 + 55 = 275 ft square
2. If 1 gallon of paint covers 105 ft
the amount that would cover 275 ft would be gotten when we cross multiply
1 = 105 ft
x = 275 ft
275 ft = 105 x
x = 275 / 105
x = 2.619
x ~ 3 gallons of paint
3. If one gallon is 24.5 dollars, the total amount that you would purchase is 3 * 24.5
= $73.5
Read more on area here:https://brainly.com/question/25292087
#SPJ1
what is the solution set to the inequality -4x - 2 ≤ - 14
Answers
Answer:
x[tex]\geq[/tex] 3
Step-by-step explanation:
-4x -2 ≤ -14
-4x ≤ -12
x ≥ 3
Move the constant to the right-hand side and change its sign: -4x<_ -14+2
Calculate the sum: -4x<_-12
Divide both sides of the inequality by and flip the inequality sign: x>_3
Please help me. I'll give brainliest.
Answers
Answer: The final balance is $11,015.84.
The total compound interest is $3,845.84.
If x = -2, what is y = ?
Answers
Answer:
y = 2
Step-by-step explanation:
If x = -2, what is y = ?
When x = -2 the line crosses the y axis at 2, so y = 2
Rick was given 2 new gaming consoles for his birthday, one from each set of grandparents. He wants to return one of the consoles and use the store credit to buy new video games. He will receive $299 in store credit, and each video game costs $60. You can use a function to describe the amount of store credit he will have left after purchasing x video games. Write an equation for the function. If it is linear, write it in the form f(x)=mx+b. If it is exponential, write it in the form f(x)=a(b)x. f(x)=
Answers
The solution is, the required cost of the used game X= 19.
What is equation?An equation which can be expressed as a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
here, we have,
So he bought the $120 game with $82
and 2 equally priced game.
This can be changed to an equation: 120= 82+2X.
The X represents the cost of the used game.
120= 82+2X
-82 -82
——————-
38= 2X
38= 2X
Divide by 2 on both sides
X= 19
To learn more on equation click:
brainly.com/question/24169758
#SPJ9
A ball bounces to a height of 5.2 feet on the first bounce. Each subsequent bounce reaches a height that is 83% of the previous bounce. What is the height, in feet, of the fifth bounce? Round your answer to thousandths place.
1.680 ft
2.048 ft
2.468 ft
4.316 ft
Answers
Answer:
Below
Step-by-step explanation:
5.2 * .83 second
(5.2 * .83) * .83 = 5.3 * .83^2 third
.
= 5.2 ( .83)^4 Fifth = 2.468 ft
