A postman delivers mail daily starting on Day 1. The conditional probability that he is bitten by a dog onDay n, given that he has not been bitten on any of the preceding days, equals qn. Let X be the number ofdays until the postman sustains his first bite (i.e., the first bite occurs on Day X).(a) Write an expression for P(X > n) in terms of qi’s.(b) Write an expression for P(X = n) in terms of qi’s.For the remainder of the problem, let qn = α for all n, where 0 < α < 1.(c) What is the probability that the postman is never bitten by a dog? Justify your answer.
The probability that the postman is never bitten by a dog is equal to the product of all qi's from i=1 to infinity, which is equal to (1-α)^∞. This is equal to 0 since α is a positive number.
The probability that the postman is never bitten by a dog is given by P(X > n), where X is the number of days until the postman sustains his first bite. This probability can be expressed as the product of all of the qi's from i=1 to n, which is equal to (1-α)^n, where qn = α for all n, and 0 < α < 1. The probability that the postman is never bitten by a dog is equal to the product of all qi's from i=1 to infinity, which is equal to (1-α)^∞. Since 0 < α < 1, (1-α)^∞ is equal to 0, meaning that the probability that the postman is never bitten by a dog is 0. This is because as n increases, the probability that the postman is not bitten by a dog on Day n decreases, and as n approaches infinity, it approaches 0.
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The graph of the function g(x) = a |x| includes the point (1, 16). What is another point on the graph of the function? What is the value of a?
The graph of the function g(x) = a |x| includes the point (1, 16). (-1, 16) is another point on the graph of the function.
What is function?Exactly one element of Y is assigned to each element of X in a mathematical function from a set X to a set Y. Both the set X and the set Y are referred to as the function's domain and co-domain, respectively. The basic conception of functions was the relationship between fluctuating quantities and other variables.
Given that,
g(x) = a |x|
In a absolute value graph the value of y is the same in -x and x.
Then if the coordinates (x,y) one point is (1, 16), the graph have another point in (- 1, 16).
To find the value of a you use one of the points (x,y) in the general form of absolute value:
( 1 , 16) x = 1 f(x) = y = 16
16 = a | 1 |
As, |±a| = a
we get:
16 = a . 1
then, a = 16
The equation for the graph with points (1 , 16) and ( -1, 16) is:
g(x) = 16 |x|
a = 16
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The ratio of boys to girls in a class is 3:1. There are 36 students in the class. How
many more boys than girls are there?
Answer:
There are 18 more boys than girls.
Step-by-step explanation:
Let's think of the ratio 3 : 1 as 3x : x
If 3 : 1 added up is the total students in the class (36) then 4x = 36
Now we just divide 36 by 4
36/4 = 9
so x = 9
The number of boys is 3 * 9 = 27
The number of girls is 9
27 - 9 = 18.
There are 18 more boys than girls.
Answer:
There are 18 more bots than girls.
Step-by-step explanation:
total units=3+1
=4
4 units=36
1 unit=36÷4
=9
difference in units=3-1
=2
2 units=2×9
=18
2.
A new pipeline is being constructed to re-route its oil flow around the exterior of a
national wildlife preserve. The plan showing the old pipeline and the new route is
shown below.
PIPELINE
60 miles
NEW
OLD PIPELINE
32 miles
About how many extra miles will the oil flow once the
new route is established?
101 101
The new route will require the oil to travel 28 extra miles, for a total of 60 miles.
What is miles?Miles is unit of distance that is commonly used in mega the distance between 2.1 map of the link of that is divided for the letting word measurements. It is sometimes also referred to as as statute mile.
This is because the old route was 32 miles long and the new route is 60 miles long. This means that the extra distance traveled is 28 miles. The extra distance is necessary to ensure that the pipeline does not interfere with the wildlife preserve.
How do you compute miles?One can determine distance in miles assuming that you already understand the speed and the time it takes to travel a specific distance. Easily calculate the time by the speed. For example - A automobile travelling at 64 miles per hour for two hours will have driven 130 miles.
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Select all the true equations
B, C, E
--5 + 0 does not equal zero
--any value tomes zero equals zero
--1.4 + 2.7 => 1.0 + 2.0 + 1.1 => 4.1
--2/3(5/9) = 10/27 not 7/12
--4(2/3) = 4.66666 and 5 - 1/3 = 4.66666
Answer:
B, C, and E
Step-by-step explanation:
A is incorrect because any number plus zero results in that number, not 0.
In equation form: [tex]x + 0 = x[/tex]
B is correct because any number multiplied by zero results in 0.
In equation form: [tex]0(x) = 0[/tex]
C is correct. We can split the added numbers into their decimal place values and add the values separately to get 4.1.
[tex]1.4 + 2.7 = (1 + 2) + (0.4 + 0.7) = 3 + 1.1 = 4.1[/tex]
D is incorrect because when multiplying fractions, you simply multiply the numerator and denominator; however, this is not done here.
E is correct because 4 2/3 is one third less than 5; we can show this using improper fractions:
[tex]4 \dfrac{2}{3} = \dfrac{(4 \times 3) + 2}{3} = \dfrac{14}{3}[/tex] [tex]5 = \dfrac{5 \times 3}{3} = \dfrac{15}{3}[/tex]
[tex]\dfrac{15}{3} - \dfrac{14}{3} = \dfrac{1}{3}[/tex]
consider a sample with a mean of 500 and a standard deviation of 100. what are the z-scores for the following data values: 550, 660, 500, 440, and 270?
z-score for value 550 = 0.5
z-score for value 660 = 1.6
z-score for value 500 = 0
z-score for value 440 = -0.6
z-score for value 270 = -2.3
What is the standard deviation?
A standard deviation is a measurement of the data's dispersion from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.
We are given a sample with a mean of 500 and a standard deviation of 100.
i.e., µ= 500 and s= 100
The z score distribution is given by;
Z = (X-µ)/s ~ N(0,1)
where X represents the data values;
So, z score for value 550 is;
z score =(550-500)/100 = 0.5
So, z score for value 660 is;
z score = (660-500)/100 = 1.6
So, z score for value 500 is;
z score = (550-500)/100 = 0
So, z score for value 440 is;
z score = (440-500)/100 = -0.6
So, z score for value 270 is;
z score = (270-500)/100 = -2.3
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z-score for value 550 = 0.5
z-score for value 660 = 1.6
z-score for value 500 = 0
z-score for value 440 = -0.6
z-score for value 270 = -2.3
What is the standard deviation?
A standard deviation is a measurement of the data's dispersion from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.
We are given a sample with a mean of 500 and a standard deviation of 100.
i.e., µ= 500 and s= 100
The z score distribution is given by;
Z = (X-µ)/s ~ N(0,1)
where X represents the data values;
So, z score for value 550 is;
z score =(550-500)/100 = 0.5
So, z score for value 660 is;
z score = (660-500)/100 = 1.6
So, z score for value 500 is;
z score = (550-500)/100 = 0
So, z score for value 440 is;
z score = (440-500)/100 = -0.6
So, z score for value 270 is;
z score = (270-500)/100 = -2.3
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please answer the screenshot question
Answer:
sin(H) = 4/5cos(H) = 3/5tan(H) = 4/3Step-by-step explanation:
You want the primary trig functions of angle H in right triangle FGH with sides FG=12, GH=9, FH=15.
Trig ratiosThe mnemonic SOH CAH TOA is intended to help you with problems like this. Its purpose is to remind you that ...
Sin = Opposite/HypotenuseCos = Adjacent/HypotenuseTan = Opposite/AdjacentWith respect to angle H, the sides are ...
Opposite = 12Adjacent = 9Hypotenuse = 15Then the values you want are ...
sin(H) = 12/15 = 4/5
cos(H) = 9/15 = 3/5
tan(H) = 12/9 = 4/3
A batch of 150 containers for frozen orange juice contains 3 that are defective. Two are selected, at random, without replacement, from the batch. Let A and B denote the event that the first and second container selected is defected, respectively.
(a) Are A and B independent events
(b) If the sampling were done with replacement, would A and B be independent.
A) The events are not independent.
B) The events are independent.
Are A and B independent events?There are 150 containers (the probabilities depend on that number), and we draw two of them.
In event A we draw one, then the number of containers after that will be 149.
Then the probabilities for event B (the second draw) are different, which means that the events are not independent.
B) If the containers are replaced, then the events are independent.
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9
She wants to find the distance from barn B to the north end of pipe 2. The distance from the barn
to the south end of pipe 1 is 111 ft, the distance from there to the south end of pipe 2 is 23 ft, and
the distance from the barn to the north end of pipe 1 is 127 ft. How far is barn B from the north
end of pipe 27 Round your answer to the nearest foot. The map is not drawn to scale. M
The distance of barn B from the north end of pipe 27 is 258 ft to the nearest foot.
How to calculate distance?Let's call the distance from Barn B to the north end of pipe 2 as "d".
The distance from the barn to the south end of pipe 1 is 111 ft, the distance from there to the south end of pipe 2 is 23 ft, and the distance from the barn to the north end of pipe 1 is 127 ft.
So the total distance from barn B to the south end of pipe 2 is 111 + 23 = 134 ft.
Since the distance from barn B to the north end of pipe 1 is 127 ft, then the distance from the north end of pipe 1 to the north end of pipe 2 is d - 127 ft.
Since the distance from barn B to the south end of pipe 2 is 134 ft, then the distance from the south end of pipe 2 to the south end of pipe 1 is 134 - d ft.
Now, two right triangles with legs (d - 127) ft and (134 - d) ft.
By the Pythagorean Theorem, we have: (d - 127)² + (134 - d)² = 25²
Expanding and simplifying the equation gives us:
d² - 260d + 17296 = 625
d² - 260d + 16671 = 0
Using the quadratic formula:
d = (260 ± √(260² - 4 x 16671)) / 2
d = (260 ± √(677600 - 66768)) / 2
d = (260 ± √(61032)) / 2
d = (260 ± 246.9) / 2
d = 258 ± 123.5
So, the distance from barn B to the north end of pipe 2 is 258 ft or 381 ft.
Since the question asks to round the answer to the nearest foot, we can conclude that the answer is 258 ft.
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Zachary purchased a computer for $1,800 on a payment plan. Three months after he purchased the computer, his balance was $1,440. Six months after he purchased the computer, his balance was $1,080. What is an equation that models the balance y after × months?
The equation __________ models the balance y after x months.
(Type your answer in slope-intercept form. Use integers or fractions for any numbers in the equation. Do not include the $ symbol in your answer.)
Answer:
Equation: y = 1800 - 120x
Step-by-step explanation:
y = 1800 - mx Where x = months after purchase of computer
y = balance remaining
1800 = y-intercept because this is your initial balance remaining as it is the actual price of the computer.
The coefficient of ‘m’ will be negative for this equation because the value of y decreases as x increases. (NOTE: y is NOT indirectly proportional to x as the line of the equation does not pass through the origin)
Next step is to determine 'm’:
m = slope of equation
Two sets of x and y values have been provided:
[tex](x_{2}, y_{2}) = (3, 1440)[/tex]
[tex](x_{3} ,y_{3})= (6, 1080)[/tex]
Use any set and substitute in the slope-intercept equation to determine the value of m:
1080 = 1800 - 6m
All the like terms are brought together and m needs to be isolated:
6m = 1800 - 1080
6m = 720
m = [tex]\frac{720}{6}[/tex]
m = 120
Therefore:
y = 1800 - 120x
kevin and sam are having a competition on their bikes to see who can ride at a faster rate. kevin rides 600 meters in 45 seconds while same rides 800 meters in 55 seconds which choice best describes who is the faster rider?
A. kevin he rides 10 second faster than sam
B.kevin he rides 13.33 meters per second
C.Sam he rides 800 meters total which is 200 more than Kevin
D.Sam he rides 14.5 meters per second which is over a meter per second faster than kevin
Answer:
D.Sam he rides 14.5 meters per second which is over a meter per second faster than kevin
Step-by-step explanation:
Kevin:
Distance = 600m
Time = 45s
Speed = Distance/time = 600/45 = 13.33m/s
Sam:
Distance = 800m
Time = 55s
Speed = 800/55 = 14.54m/s
Therefore option D will be the answer
Mary draws the number line below to represent the solution set of the inequality 50-8f<90. What mistake did Mary make? Use the drop-down menus to explain your answer.
-8 -6 -4 -2
Mary divided both sides of the inequality by a
Choose...
value, so she needed to Choose...
inequality symbol.
The solution to the inequality 50 - 8f < 90 is f > -5
What is an equation?An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either be linear, quadratic, cubic, depending of the degree of the variable.
Inequality is an expression that is used to show the non equal comparison of numbers and variables
Given the equation:
50 - 8f < 90
subtract 50 from both sides:
50 - 8f - 50 < 90 - 50
-8f < 40
Divide both sides by -8:
-8f / -8 < 40 / -8
f > -5
The solution to the inequality is f > -5
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From a sample with n=12, the mean number of television per household is 3 with a standard deviation of 1 television. Using Chebychev Theorem,determine at least how many of the households have between 1 and 5 televisons
Answer:
9
Step-by-step explanation:
Chebyshev's Theorem states that for any given sample, at least 1 - 1/k^2 of the data falls within k standard deviations from the mean.
Let's use k = 2. Then, at least 1 - 1/2^2 = 1 - 1/4 = 3/4 of the households should have between 3 - 2 = 1 and 3 + 2 = 5 televisions.
So, at least 12 * 3/4 = 9 of the households in the sample have between 1 and 5 televisions.
Jackie and Ken shared a bag of popcorn on a field trip. If Ken ate 2/3 of the bag of popcorn and Jackie ate 1/3 of the bag of popcorn, what fraction of the popcorn is left?
Answer:
4/9
Step-by-step explanation:
If Jackie at 1/3, that means that 2/3 was left
2/3 x 2/3 = 4/9
y=4 over x + square x + 0.2 - 5x
Answer: The expression Y = 4 / (x + sqrt(x) + 0.2) - 5x represents a mathematical function that maps values of x to values of Y. The input x represents the independent variable and Y represents the dependent variable. For any given value of x, the expression calculates the value of Y.
Step-by-step explanation:
A two-digit number is formed using the digits 1, 2 and 3. Repetition of digits is allowed. (a) List the sample space. (b) Find the probability that the two-digit number formed is (i) divisible by 3, (ii) a perfect square, (iii) a prime number, (iv) a composite number.
Answer:
two plus two equals five
Step-by-step explanation:
covert the given amount go the given unit
3 qt ; liters
Answer:
Below
Step-by-step explanation:
1 qt = .9463529 L
3 Qt * .9463529 L/Qt = 2.84 Liters
man bought a second hand car for $8 500, spent $1 500 on repairs and then sold it for $12 000. what was his percentage profit?
Answer:
20%
Step-by-step explanation:
He spent (8500+ 1500) = 10 000 then sold it for 2000 MORE
Profit = 2000 / 10 000 * 100% = 20%
The movement of the progress bar may be uneven because questions can be worth more or less (including zero) depe
Determine whether 318 is divisible by 2, 3, 4, or 6.
O2, 3, 4, and 6
O3 and 6 only
O2, 3, and 6 only
O2 and 3 only
Submit
Pass
At a particular restaurant, each onion ring has 40 calories and each pizza roll has 80
calories. A combination meal with pizza rolls and onion rings is shown to have 800
total calories and 4 more pizza rolls than onion rings. Graphically solve a system of
equations in order to determine the number of onion rings in the combination meal,
x, and the number of pizza rolls in the combination meal, y.
As a result, the combo meal includes 4 onion rings and 8 pizza buns.
What is equation?An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equals symbol =. In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign.
Here,
Let x be the number of onion rings in the combination meal and y be the number of pizza rolls. We can write the following system of equations to represent the given information:
40x + 80y = 800 (the total calories of the meal)
y = x + 4 (the number of pizza rolls is 4 more than the number of onion rings)
We can substitute the second equation into the first equation to solve for x:
40x + 80(x + 4) = 800
40x + 80x + 320 = 800
120x = 480
x = 4
We can use this value to find y:
y = x + 4 = 4 + 4 = 8
So, the combination meal contains 4 onion rings and 8 pizza rolls.
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which represents the solution for the inequality 2x-5>7
a.x>2
b.x>4
c.x>6
d.>10
Answer: C. x>6
Step-by-step explanation:
2x-5 >7 (Move the constant to the right)
2x >7+5 (Calculate)
2x >12 (Divide both sides by 2)
x> 6 Answer
Learning aids, listed along the bottom of the window, are available for most problems on homework assignments and study plan practice but are not available on tests and quizzes. Identify the learning aid described in each part below.
One learning aid that provides an interactive walk-through for solving the particular problem you are working on is "view an example"
What does learning aid offer student?It is also known as teaching aids, which are an essential part of any classroom. Teaching aids can help students improve their reading comprehension skills, illustrate or reinforce a skill or concept, differentiate instruction, and relieve anxiety or boredom by presenting information in a new and exciting way.
Teaching aids also engage students' other senses because there are no restrictions on what aids can be used to supplement a lesson. As technology advances, so do teaching aids, which are now classified as audio aids, visual aids, mechanical teaching aids, audio-visual aids, and more.
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The arrow on the spinner below is spun once
What is the probability the arrow on the spinner does not stop on a number DIVISIBLE by 3? pls help ty
A. 1/8
B. 1/4
C. 3/4
D. 1/8
If the arrow on spinner is spun once, then the probability that the arrow do not stop on number which is divisible by 3 is (c) 3/4.
We know that the spinner contains 8 numbers and each number is equally likely to be selected. Out of the 8 numbers, the numbers which are divisible by 3 are {3, 6}.
So, the numbers which are not-divisible by 3 are {1, 2, 4, 5, 7, 8},
We select one of the 6 numbers that are not divisible by 3 out of the total 8 numbers. so, the probability is :
⇒ Probability = (Number of favorable outcomes)/(Total number of outcomes),
⇒ Probability = 6/8,
⇒ Probability = 3/4,
Therefore, the correct option is (c).
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Find the volume of the figure.
Answer:
see below
Step-by-step explanation:
memorize the following formula:
V = 1/3 * lenght * width * height = 1/3 * 3*6*4 =24
Use these graphics to answer the question.
A lobbyist for road safety collects data about accident trends for men and women. Assuming both graphics represent data in the same country, about how many women were involved in accidents while riding in a two wheeler in 2010?
about 50
about 250
about 1,000
about 5,000
Therefore , the solution of the given problem of graph comes out to be about 5,000 .
What is a graph?To rationally chart or graphically portray events or quantities, academics use graphs. A chart point is a typical tool for showing how various variables interact. Nodes, also known as vertices and lines, make up the non-linear storage arrangement known as a graph. The borders, also referred to as nodes, should be joined together using glue. (4.5) Visualizations, such as flowcharts, graphs, and bar graphs, that graphically depict explosive development within data.
Here,
Based on the graph,
it appears that in 2010, about 5,000 women were involved in accidents while riding in a two-wheeler.
Therefore , the solution of the given problem of graph comes out to be about 5,000 .
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Write an expression for the product (√6)(‾‾‾√15)without a perfect square factor in the radicand.
A. 3‾√5
B. 3‾‾√10
C. 9‾√5
D. 9‾‾‾√10
pls answer quick
An expression for the product (√6)(‾‾‾√15)without a perfect square factor in the radicand is -3√10. Option A
How to determine the expressionIt is important to note that surds are expressions that includes a square root, cube root or any other root symbol.
They are used to write irrational numbers because the decimals of irrational numbers do not recur, they cannot be written in decimal form.
From the information given, we have the surds;
(√6)(‾‾‾√15)
expand the bracket, we get;
-√90
Find the square root of the value and allow others in radical forms, we get;
- √9 × √10
Find the perfect square, we get;
-3√10
Hence, the value is -3√10
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HELP ME PLEASE I WILL GIVE BRAINLIEST QUICK
Answer:
27 and 13
Step-by-step explanation:
let the second number be x then the first number is x - 14
sum the 2 numbers and equate to 40
x - 14 + x = 40
2x - 14 = 40 ( add 14 to both sides )
2x = 54 ( divide both sides by 2 )
x = 27
x - 14 = 27 - 14 = 13
the first number is 27 and the second number is 13
Suppose 2.5 liters of water come out of a faucet each minute. For how many minutes was the faucet on if 38.5 liters of water came out?
Answer:
15.4 min
Step-by-step explanation:
rate = liters/min = 2.5 l/min
time = liters/rate = 38.5 l / (2.5 l/min) = 15.4 min
Calculate the Social Security and Medicare deductions for the following employee (assume a tax rate of 6.2% on $128,400 for Social
Security and 1.45% for Medicare): (Round your answers to the nearest cent.)
Employee
Rouche
$
Cumulative earnings
before this pay period
Pay amount this
period
122,300 $
Social
Security
Medicare
Answer:
Social Security: $7582.60Medicare: $1773.35Step-by-step explanation:
You want to know the Social Security and Medicare taxes on an annual income of $122,300, given the respective tax rates are 6.2% and 1.45%.
TaxThe income is less than the Social Security maximum of 128,400, so the 6.2% tax applies to the full amount. Each tax amount is found by multiplying the income by the tax rate:
SS: $122,300 × 0.062 = $7582.60 . . . . Social Security tax
Med: $122,300 × 0.0145 = $1773.35 . . .Medicare tax
find the area of a radius of 5 feet use 3.14 for pi
Answer: A=78. 5 [tex]feet^{2}[/tex]
Step-by-step explanation: