As Jill claims 3 allowances then the amount which is withheld weekly for federal income tax is $11.
Given, Jill earns $264.50 a week.
She is married and claims 3 allowances.
From the table if the wage of a married person is at least $260 but less than $270 and has 3 allowances then weekly income tax is $11.
Individual federal income tax rates in the US are progressive, which means that they rise in proportion to taxable income. Federal income tax rates range from 10% to 37%, and they become effective at a certain level of income. Tax brackets are the ranges of income that the rates apply to. Each tax bracket has a different rate of taxation that applies to certain types of income.
Hence the amount is $11 for federal tax.
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what is the standard form of the equation for part a
Answer:
yea, correct, perfect yes sir
PLS HELP, IN A HURRY. Would Appreciate!!!!!
Answer:
y = w/(h - 5c^3)
Step-by-step explanation:
w = yh - 5yc^3
factorise out y:
w = y(h - 5c^3)
rearrange:
y = w/(h - 5c^3)
I think this is correct.
Estimate √172 to the nearest tenth. Locate the irrational number on a number line.
The irrational number on a number line is 13.1. All real numbers that are not rational are considered irrational numbers. In other words, it is impossible to describe an irrational number as the ratio of two integers.
What is irrational number ?All real numbers that are not rational numbers are referred to be irrational numbers in mathematics. In other words, it is impossible to describe an irrational number as the ratio of two integers.There is no length, no matter how short, that could be used to express the lengths of both of the two supplied segments as integer multiples of itself.
Square Root of 172 to the nearest tenth, means to calculate the square root of 172 where the answer should only have one number after the decimal point.
CalculateWe calculate the square root of 172 to be:
√172 = 13.11487704860400
ReduceReduce the tail of the answer above to two numbers after the decimal point: 13.11
RoundRound 13.11 so you only have one digit after the decimal point to get the answer: 13.1
To check that the answer is correct, use your calculator to confirm that 13.1² is about 172.
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O EQUATIONS AND INEQUALITIESSolving a word problem with two unknowns using a linear...
Given:
Total number of hamburgers and cheeseburgers sold = 439
There were 61 fewer cheeseburgers than hamburgers sold.
Let's determine the number of hamburgers sold.
Let C represent the number of cheeseburgers
Let H represent the number of hamburgers sold.
We have the system of equations:
• H + C = 439
,• C = H - 61
Now, let's solve the equations simultaneously using the substitution method.
Substitute (H - 61) for C in the first equation.
We have:
H + (H - 61) = 439
H + H - 61 = 439
2H - 61 = 439
Add 61 to both sides:
2H - 61 + 61 = 439 + 61
2H = 500
Divide both sides by 2:
[tex]\begin{gathered} \frac{2H}{2}=\frac{500}{2} \\ \\ H=250 \end{gathered}[/tex]Therefore, they sold 250 hamburgers on Friday.
ANSWER:
250 hamburgers
31. a statistics class has 26 students. the instructor would like to select a random sample of 3 students to work together on a group project. a. how many different samples are possible? b. if 13 of the 26 students in class are freshmen, what is the probability that all 3 of the selected students are freshmen?
a. 2600 ways different samples are possible.
b. 0.11 is the probability that all 3 of the selected students are freshmen.
total student = 26
3 students are randomly selected on group project
a. the possible different sample are
[tex]26 C_{3}[/tex] = [tex]\frac{26}{3 (26-3)}[/tex]
= [tex]\frac{26}{3 (23)}[/tex]
= 2600 ways.
b. 13 students are freshmen
Pr ( 3 selected students is freshman)
[tex]\frac{13C_{3} }{26C_{3} }[/tex] = [tex]\frac{286}{2600}[/tex] = 0.11
What is probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.
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Ivy is competing in a Read-A-Thon. Each day , she reads for 25 minutes before school and 45 minutes after school. Find the total number of minutes Ivy spends reading after 5 days. How can you find the total number of minutes Ivy spends reading?
A) Multiply 5 and 25. Then, add 45
B) Multiply 5 and 45. Then, add 25
C) Add 25 and 45. Then, Multiply by 5
D) Add 25 and 45. Then, add 5
Answer: C
Step-by-step explanation:
It the only one that includes both.
In a sale, the normal price of a TV is reduced by 20%.
The sale price of the TV is £660
Work out the normal price of the TV.
A car can be rented for $95 per week plus $0.95 per mile. How many miles can be driven if you have at most $380 to spend for weekly transportation? The car should be driven ....... miles a week?
We have the next inequality
[tex]95+0.95x\le380[/tex]where x is the number of miles.
Then we solve the inequality
[tex]\begin{gathered} 0.95x<380-95 \\ \end{gathered}[/tex][tex]\begin{gathered} 0.95x\le285 \\ x\le\frac{285}{0.95} \\ x\le300 \end{gathered}[/tex]The car should be driven 300 miles a week
Jessica wants to make a spinner that has all of the following characteristicsSketch a possible spinner for Jessica. Be sure to label each section of thespinner with a name and with its theoretical probability.• Blue, red, purple, and green are the only colors on the spinner.• It is half as likely to land on blue as to land on red.• It is three times as likely to land on purple as green.• There is a 50% probability of landing on either blue or red and a 50%probability of landing on either purple or green.
First we have to split the spinner into two equal parts. One half belongs to the blue and red sections, and the other half belongs to the green and purple sections.
Formulating an equation for the first part, we have:
P(b) + P(r) = 0.5 ( P(b): probability of landing on blue section, P (r): probability of landing on red section)
P(r) + 1/2*P(r) = 0.5 ( Since it is half as likely to land on blue as to land on red)
3/2*P(r) = 0.5 (Adding like terms)
P(r)= 0.5 / (3/2) (Dividing on both sides by 3/2)
P(r)= 1/3 (Dividing)
P(b)=1/2*P(r) (Finding the probability of landing on blue section)
P(b)= 1/6
Formulating an equation for the second part, we have:
P(g) + P(p) = 0.5 ( P(g): probability of landing on green section, P (r): probability of landing on purple
section)
P(g) + 3*P(g) = 0.5 ( Since it is three times as likely to land on purple as green)
4*P(g) = 0.5 ( Adding like terms)
P(g) = 0.5/4 (Dividing by 4 on both sides of the equation)
P(g) = 1/8 (Dividing)
P(p) = 3*P(g) (Finding the probability of landing on purple section)
P(p)= 3/8
A shipping box has a volume of 1,000 cubic inches. What is the length of one side of the box?
The length of one side of the box is 10 inches.
How to find the volume of a cube?Suppose that: The side length of the considered cube is L units.
Then, we get the Volume of that cube = L³ cubic units.
The volume of a cube is of the form V = L³, where L is the side length.
Given that the shipping box has a volume of 1,000 cubic inches.
Here, we know the volume V, but not the measure of length. So, we can plug in the value 1000 for V and solve for L:
1000 = L³
Cube root both sides:
L = [tex]\sqrt[3]{1000}[/tex]
Therefore, each side is 10 inches.
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Rewrite one eighth times x cubed times y plus seven eighths times x times y squared using a common factor.
Equation y (1/8 x3 + 7) is rewritten by using a common factor. A literal equation is regarded as having at least two variables.
Given that,
Use a common factor to rewrite one eighth times x cubed times y plus seven eighths times x times y squared.
This is how the equation can be rewritten:
The first equation is written as 1/8 x3y + 7/8 xy2.
It is possible to rewrite the equation 1/8 xy(x2 + y) using the common factor.
Equation two:
1/4x.y.4x2 + 28y
1/4 .4 x³ .y + 28y
x3.y + 28y equation to be solved
Using the formula
y = (x3 + 28).
Third claim:
1/4. x. y. x2 + 7y
Fix the problem.
1/4 . x³ .y + 7y
Write y = (1/4x3 + 7) in a new way.
Fourth assertion:
1/8 x3y2.y + 7 x 1/8 x3y3 + 7 x
After removing the common element x(1/8 x2y3+ 7), rewrite the equation.
Fifth Declaration
1/8 x. y. x² + 7y
1/8 x³. y + 7y
Equation y (1/8 x3 + 7) is rewritten.
Thus, a literal equation is one that contains at least two variables. Solve for one variable in terms of the other variable to rephrase a literal equation.
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Please find the coordinates and also reflect the points on the axis’s, and please demonstrate and plot the points on the graph too reflect it.
A' = (1, 3)
B' = (0, 6)
C' = (-3, 5)
D' = (-2, 2)
15:4y2 – 30:23 + 4554The quotient of517is7. When this quotient is divided bythe result is 3-35-5I3y – 25y2 + 3
We are given the following expression:
[tex]\frac{15x^4y^2-30x^2y^3+45xy}{5xy}[/tex]To determine the quotient of the expression we will factor the numerator. To do that we take the Greatest Common Multiple of the denominator.
The denominator is the following expression:
[tex]15x^4y^2-30x^2y^3+45xy[/tex]To get the greatest common multiple we need to determine the multiples of the coefficients first.
For 15 we have:
[tex]factors\text{ 15= 1, 3, 5, 15}[/tex]For 30 we have:
[tex]\text{factors 30 = }1,2,3,5,6,10,15,30[/tex]For 45 we have:
[tex]\text{factors 45 =}1,3,5,9,15,45[/tex]We notice that the factors that are repeated for each of the numbers are:
[tex]\text{repeated = 1,3,5,15}[/tex]The greatest of the repeated factors is 15, therefore, the greatest common factor is 15.
Now, we take the variables that are repeated in the expression and we take the ones with smaller exponents. The variables repeated are:
[tex]xy[/tex]Of these, the ones with smaller exponents are:
[tex]xy[/tex]Now, combining the two parts we get that the greatest common factor of the denominator is:
[tex]15xy[/tex]We take out that factor and re arrange the expression, like this:
[tex]\frac{15x^4y^2-30x^2y^3+45xy}{5xy}=\frac{15xy(x^3y-2xy^2+3)}{5xy}[/tex]Now, we cancel out the "xy" and simplify 15/5:
[tex]\frac{15xy(x^3y-2xy^2+3)}{5xy}=3(x^3y-2xy^2+3)[/tex]And thus we get the quotient.
We notice that the quotient is multiplied by 3, therefore, if we divide by 3:
[tex]\frac{3(x^3y-2xy^2+3)}{3}[/tex]We can cancel out the 3 and we get:
[tex]\frac{3(x^3y-2xy^2+3)}{3}=x^3y-2xy^2+3[/tex]Therefore, the quotient is divided by 3.
A Ford F-150 truck is considered a half-ton truck because that is how much it can haul. How many pounds can the truck haul?
The truck can haul 1102 pounds.
According to the question,
We have the following information:
A Ford F-150 truck is considered a half-ton truck because that is how much it can haul.
(More to know: ton, pounds and kilograms are the most commonly used units for measuring weight.)
Now, we already have the knowledge that 1 ton is equal to 1000 kilograms.
So, half ton will make 500 kg.
Now, in order to convert this into pounds, we will multiply 500 kg by 2.205 because we know that 1 kg makes 2.205 pounds.
1 kg = 2.205 pounds
500 kg = (500*2.205) pounds
500 kg = 1102.5 pounds
Hence, the truck can haul 1102.5 pounds.
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What is the smallest and greatest number that rounds to 380 when
rounding to the nearest ten?
The smallest and greatest number that rounds to 380 when rounding to the nearest ten are 375 and 384 respectively.
What is rounding a number?Adjusting a number's digits so that it produces an approximation of a result is known as rounding.
The given number is 380.
When rounding a number to the nearest ten, pay attention to the last digit; if it is less than five, round down; if it is five or more, round up.
Therefore, the smallest number that rounds to 380 when rounding to the nearest ten is 375.
Similarly, the greatest number that rounds to 380 when rounding to the nearest ten is 384.
Hence, the smallest and greatest number that rounds to 380 when rounding to the nearest ten are 375 and 384 respectively.
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Olivia purchased two blouses for $12.50 each and a shirt for $11.25.The sales tax rate is *8.5 %. How much will Olivia pay including tax?
Answer:
$39.33
Step-by-step explanation:
11.25 + 12.50 +12.50 = 36.25
36.25 + 8.5% = 39.33
a force of 4 pounds is required to hold a spring stretched 0.2 feet beyond its natural length. how much work (in foot-pounds) is done in stretching the spring from its natural length to 1.1 feet beyond its natural length?
Using the spring's force we know that 48.4 lb-ft work is done in stretching the spring from its natural length to 1.1 feet beyond its natural length.
What does a spring's force mean?When a spring is in its equilibrium position, it applies a force F = -kx in that direction. A spring's force works as a restoring force, bringing the spring back to its equilibrium length.So, F is the 4 lb force required to maintain the spring's stretched position.
The spring has a 0.2-foot stretch, and its spring constant is k.Applying the equation F = k x 4 = k (0.2) k = 80 lb/ft.U is the effort put in to expand the spring, where x' is equal to 1.1 feet.The labor of extending a spring is denoted by the formula:
U = (0.5) k x'2So, calculate:
U = (0.5). (80). (1.1)² U = 48.4 lb-ftTherefore, 48.4 lb-ft work is done in stretching the spring from its natural length to 1.1 feet beyond its natural length.
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math pease help me i need it now asap
1. The mathematical expression for the length is C. 2x + 5.
2. The quadratic equation is A. 2x² + 5x - 18 = 0.
3. The width of the tarpaulin is A. 2 ft.
4. The length of the tarpaulin is D. 9 ft.
5. The perimeter of the tarpaulin is C. 22 feet.
How to calculate the value?From the information, the following can be deduced:
Width = x
Length = (2 × x) + 5 = 2x + 5
Area = 18 ft²
The equation will be:
Length × Width =Area
(2x + 5)x = 18
2x² + 5x = 18
2x² + 5x - 18 = 0
2x² - 4x + 9x - 18 = 0
2x(x - 2) + 9(x - 2)
Therefore, x - 2 = 0
x = 0 + 2 = 2
Width = 2
Length = 2x + 5 = 2(2) + 5 = 9ft
Perimeter = 2( Length + Width)
= 2(2 + 9)
= 22 feet.
This illustrates the concept of addition to calculate the perimeter.
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f (x)=(x-3)^2 + 4 when is f increasing
Answer:
(3,∞)
Explanation:
Given the function:
[tex]f(x)=\mleft(x-3\mright)^2+4[/tex]The graph of f(x) is attached below:
The interval when f(x) is increasing is therefore: (3,∞)
Please help ASAP! Compare and contrast the formulas for P(A and B) for dependent and independent events. What is the relationship between P(B) and P(B|A) and can one equation be used for both independent and dependent events?
Dependent events;
The probability of one event DOES effect the probability of a 2nd event.
Independent events;
The probability of one event DOES NOT effect the probability of a 2nd event
Give the equation for calculating the likelihood that events A and B will occur when A and B are dependent events. The equation P(A and B) = P(A) P(B|A) yields the likelihood that A and B will occur.If the events A and B are not mutually exclusive, the probability is: (A or B) = p(A) + p(B) – p(A and B).We cannot use one equation for both independent and dependent events.Learn more about dependent and independent events here;
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Which statement about the data in the table is true?
O The data represent a proportional relationship, and the constant of proportionality is $10.
The data do not represent a proportional relationship, but the rate of change of the data is $5 per shirt.
There is not a constant rate of change for these data.
The data represent a proportional relationship, and the constant of proportionality is $5.
B) The data does not represent a proportional relation, but it has constant rate of change of $5 per shirt.
A)
Take number of T-shirts up to 3 and calculate their proportions.
2/1 = 15/10 = 1.5 (3/2) = 20/15 = 1.33
Clearly the rate of T- shirts is not proportional.
B)
From option (A) we found the given data is not proportional but from the table given in question the rate of change of T- shirts is indeed $5.
C)
No, there is a constant rate of change of $5 as shown in the table below.
D)
No, the data does not represent a constant proportionality. The rate varies.
2/1 = 15/10 = 1.5 (3/2) = 20/15 = 1.33
What is rate of change ?Rate of change is the rate that describes how one quantity changes relative to another quantity. If x is the independent variable and y is the dependent variable, then
rate of change change=change in y / change x
Rate of change can be positive or negative. This corresponds to an increase or decrease in the y-value between two data points. If a quantity does not change over time, it is called zero rate of change.
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I need help with this geometry question !! Pls help
The values of variable x are x₁ = 16, x₂ = - 4.
The measure of angle R is 60°.
The lengths of side RS are RS₁ = 256 and RS₂ = 16.
The lengths of side RT are RT₁ = 256 and RT₂ = 16.
How to find the variables associated to a given triangle
In this problem we need to find the values of four variables related to a triangle, which is seen in the picture, indicating an equilateral triangle. The solution of this question must be done by using definitions and theorems from Euclidean geometry:
Value of variable x
According to Euclidean geometry, the measures of the three sides in an equilateral triangle are the same. Then, the variable x can be found by solving the following equation:
RT = RS
x² = 12 · x + 64
x² - 12 · x - 64 = 0
(x - 16) · (x + 4) = 0
There are two possible solutions:
x₁ = 16, x₂ = - 4
Measure of the angle R
Equilateral triangles have three internal angles of 60°. Therefore, m ∠ R = 60°.
Length of side RS
There are two options:
RS₁ = 16²
RS₁ = 256
RS₂ = (- 4)²
RS₂ = 16
Length of side RT
There are two options:
RT₁ = 12 · 16 + 64
RT₁ = 256
RT₂ = 12 · (- 4) + 64
RT₂ = 16
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Solve for x. Show each step of the solution.
5(2-x)-10=25-2(3x+40)
Answer:
x = -55
Step-by-step explanation:
Given equation,
→ 5(2 - x) - 10 = 25 - 2(3x + 40)
Now the value of x will be,
→ 5(2 - x) - 10 = 25 - 2(3x + 40)
→ 10 - 5x - 10 = 25 - 6x - 80
→ -5x + 6x = 25 - 80
→ [ x = -55 ]
Hence, the value of x is -55.
Answer:
x = -55
Step-by-step explanation:
Given equation,
→ 5(2 - x) - 10 = 25 - 2(3x + 40)
Now the value of x will be,
→ 5(2 - x) - 10 = 25 - 2(3x + 40)
→ 10 - 5x - 10 = 25 - 6x - 80
→ -5x + 6x = 25 - 80
→ [ x = -55 ]
Hence, the value of x is -55.
Elijah put 2x+3
2
x
+
3
dollars in the bank the first week. The following week he doubled the first week’s savings and put that amount in the bank. The next week, he doubled what was in the bank and put that amount in the bank. He now has $477 in the bank. How much money did he put in the bank the first week?
Elijah put $53 in the Bank in the first week .
In the question ,
it is given that Elijah put (2x+3) in the first week .
In the second week Elijah put double the first week savings
that means second week deposit = 2*(2x+3) = 4x+6
in the third week he doubled the amount that was in the bank ,
which means third week deposit = 2*(first week + second week deposit)
= 2*(2x+3+4x+6)
Also given that total amount in the bank = $477
total amount = first week + second week + third week deposit
substituting the values we get
477 = (2x+3) + (4x+6) + 2*(2x+3+4x+6)
477 = 2x+3+4x+6+4x+6+8x+12
477 = 18x + 27
18x = 477-27
18x = 450
x = 450/18
x = 25
the amount deposited in the first week = 2x+3
= 2(25)+3
= 50+3 = $53
Therefore , Elijah put $53 in the Bank in the first week .
The given question is incomplete , the complete question is
Elijah put 2x+3 dollars in the bank the first week. The following week he doubled the first week’s savings and put that amount in the bank. The next week, he doubled what was in the bank and put that amount in the bank. He now has $477 in the bank. How much money did he put in the bank the first week?
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A rental car company charges $37.50 per day to rent a car and $0.05 for every mile
driven. Alyssa wants to rent a car, knowing that:
. She plans to drive 100 miles.
. She has at most $200 to spend.
Write and solve on
Hello!
Knowing that Alyssa wants to rent a car where the company charges $37.50 per day to rent a car and $0.05 for each mile driven we have to find out how many days she is planning on renting a car for.
Step-by-step explanation:
Using the information we have we can see that it will be an additional $5 based on how many miles she is planning on driving.
If the base cost to rent a car is $37.50 you will have to add an additional $5 for the number of miles she plans to drive making the total $42.50.
Since she has at most $200 to spend on a car rental she can rent a car for a total of 5 days at a total cost of $192.50
[tex]37.50[/tex] × [tex]4=150[/tex] + [tex]42.50[/tex] = [tex]192.50[/tex]
Hope this helps!
The inequality will be 37.5x + (0.05 ×100) ≤ 200, and Alyssa can afford 5.2 days to rent while staying within her budget
How to write and solve an inequality to determine the number of days?Given that the rental car company charges $37.50 per day to rent a car and $0.05 for every mile driven
She plans to drive 100 miles and has at most $200 to spend.
Let x is the number of days, Alyssa can afford to rent while staying within her budget
The inequality can be written as;
37.5x + (0.05 ×100) ≤ 200
Now solve for x:
37.5x + (0.05 ×100) ≤ 200
37.5x + 5 ≤ 200
37.5x ≤ 200 - 5
37.5x ≤ 195
x ≤ 195/37.5
x ≤ 5.2
Therefore, she can afford 5.2 days to rent while staying within her budget.
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Y = 17x - 8, y = 24x +6 Parallel Perpendicular Neither
Two parallel lines in the coordinate system share the same slope, this means that if you have two parallel lines:
[tex]\begin{gathered} y_1=m_1x_1+b_1 \\ y_2=m_2x_2+b_2 \\ \text{Their slopes must be equal:} \\ m_1=m_2 \end{gathered}[/tex]For the given equations, the slopes are:
[tex]\begin{gathered} y=17x-8 \\ m=17 \end{gathered}[/tex][tex]\begin{gathered} y=24x+6 \\ m=24 \end{gathered}[/tex]The slopes are different, so this lines are not parallel.
Two lines are perpendicular, when the slope of one of them is the negative inverse of the first one, this is for the perpendicular lines:
[tex]\begin{gathered} y_1=m_1x_1+b_1 \\ y_2=m_2x_2+b_2 \\ m_2=-\frac{1}{m_1} \end{gathered}[/tex]For the given equations, using y=17x-8 as reference, the slope of a line perpendicular to this one must be:
[tex]m_{}=-\frac{1}{17}[/tex]The slope of a perpendicular line to y=17x-8 is different from the slope of the second given line, so you can conclude that these lines are not perpendicular.
The correct choice is Neither
There are two bags containing only black and green marbles.
Event 4, Event 1, Event 3, Event 2
Explanations:Number of black marbles in bag A = 11
Number of green marbles in bag A = 9
Total number of marbles in bag A = 11 + 9 = 20
Number of black marbles in bag B = 8
Number of green marbles in bag B = 2
Total number of marbles in bag B = 8 + 2 = 10
Event 1:
Likelihood of choosing a black marble from bag A = 11/20 = 0.55
Event 2:
Likelihood of choosing a black or green marble from bag A = 11/20 + 9/20
Likelihood of choosing a black or green marble from bag A = 0.55 + 0.45
Likelihood of choosing a black or green marble from bag A = 1
Event 3:
Likelihood of choosing a balck marble from bag B = 8/10 = 0.8
Event 4:
Likelihood of choosing a purple marble from bag B = 0
Since there is no purple marble in bag B
Arrangement of the events from the least likely to the most likely will be:
Event 4, Event 1, Event 3, Event 2
Find the first five terms of the sequence defined below, where n represents the position of a term in the sequence. Start with n = 1.an = 4n − 5
Okay, here we have this:
Considering the provided sequence, we are going to find the requested first five terms of the sequence, so we obtain the following:
So what we will do is replace n from 1 to 5, we have:
n=1:
an=4n-5
a1=4(1)-5
a1=4-5
a1=-1
n=2:
an=4n-5
a2=4(2)-5
a2=8-5
a2=3
n=3:
an=4n-5
a3=4(3)-5
a3=12-5
a3=7
n=4:
an=4n-5
a4=4(4)-5
a4=16-5
a4=11
n=5:
an=4n-5
a5=4(5)-5
a5=20-5
a5=15
Finally we obtain that the first five terms are: -1, 3, 7, 11, 15
the probability of observing a window given there is no window at its location is 0.2, and the probability of observing a window given there is a window is 0.9. after incorporating the observation of a window, what are the robot's new probabilities for being in
Updated Probabilities are: P(L1/W) = 0.341 & P(L1/w) = 0.949
Let W be the event that the robot's camera observes a window
It is given that the Probability of observing a window there is no window at its location is given 0.2
P(W/ L1) = 0.2 ( L1 which does not have a window)
Also, probability of observing a window is 0.9
P(W/ L2) = 0.9 ( L2 has window)
Now we have to find updated probabilities for the robot being in L1 i.e:- P(L1/W) & P(L1/w)
w means the camera does not observe a window.
By Bayes Rule,
P(L1/W) = P(L1)P(W/L1)/P(L1)P(W/L1)+P(L2)P(W/L2)
= (0.7x 0.2)/ (0.7x0.2) + (0.3x0.9)
= (0.14)/ 0.14+0.27
≈0.341 (rounded to 3. decimal places)
Thus the probability of being in L1 if the camera observes a window is nearly 0.341.
P(L1/w) = P(L1)P(w/L1)/P(L1)P(w/L1)+P(L2)P(w/L2)
As P(W/L1) = 0.2;
P(w/L1) = 1 - P(w/L1) = 1-0.2 = 0.8
Also P(W/L2) = 0.1;
P(w/L2) = 1 - P(w/L2) = 1-0.9 = 0.1
P(L1/w) = (0.7 X 0.8)/ (0.7X0.8) + (0.3X0.1)
=(0.56)/ (0.56+0.03) = (0.56/ 0.59)
≈ 0.949 (rounded to 3 decimal places).
Thus the probability of being in L1 if observe not the window is nearly 0.949.
Updated Probabilities are: P(L1/W) = 0.341 & P(L1/w) = 0.949
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A one way train ticket in the city cost 1.85 a monthly pass cost 65$. For what number of rides should you buy the monthly pass?
Answer: 36 rides
Step-by-step explanation: Because is you divide 65 by 1.85 you get 35.13513513513514 so just round it to the next integer of 36.