In this case, there are 8 letters, so the total number of 4-letter words possible is 8^4 = 4096.
(b) In this case, each letter can be used only once, so we must choose 4 different letters out of 8 letters. This can be done using the combination formula C(8,4) = 70.
(c) Since each word must begin with the letter A, the remaining 3 letters must be chosen from the remaining 7 letters. This can be done using the combination formula C(7,3) = 35.
(d) The letter C must be at the end, so the first 3 letters must be chosen from the remaining 7 letters. This can be done using the combination formula C(7,3) = 35.
(e) The second letter must be a vowel, so the first letter can be chosen out of 4 letters (A, E, I, O). The remaining 3 letters can be chosen out of 7 letters. This can be done using the combination formula C(4,1) x C(7,3) = 140.
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An aquarium tank can hold 6300 liters of water. There are two pipes that can be used to fill the tank. The first pipe alone can fill the tank in 84 minutes. The second pipe can fill the tank in 42 minutes by itself. When both pipes are working together, how long does it take them to fill the tank?
It will take 28 minutes for them to fill the tank.
What is work done?Work done is defined as the amount of force needed to move and object a certain distance. In essence, it is a measure of an energy transferred to or from an object which allows it to be moved.
Given that, an aquarium tank can hold 6300 liters of water. There are two pipes that can be used to fill the tank. The first pipe alone can fill the tank in 84 minutes. The second pipe can fill the tank in 42 minutes by itself.
Work done by first pipe in 1 minute = 1/84
Work done by second pipe in 1 minute = 1/42
The time taken by both the pipes together =
1 / 84 + 1 / 42 = 3 / 84
= 1/28
Therefore, time taken by both the pipe = 28 minutes.
Hence, it will take 28 minutes for them to fill the tank.
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You plan to drive north from city A to town B and then continue North to city C. The distance between City A and town B is 39mi and the distance between town B and city C is 99mi.
A. Assuming that you follow a straight driving path, after how many miles of driving will you reach the midpoint between city A and city C?
B. If you drive an average of 46/mi/h how long will it take you to drive from city A to city C?
Here we are given that the distance between city A and B is 39miles and that between city B and C is 99miles . in order to find after how many miles we would reach the midpoint of city A and C , divide the total distance between A and C by 2 as ,
Total distance between A and C =[tex] d_{AB}+d_{BC}[/tex] = 39mi. + 99mi. = 138 miles
Divide this distance by 2 ,
138/2 = 69miles [ answer to Part A ]
_______________
Now the speed is 46miles/hr . In order to find time , use relation,
Speed * time = distance
So that,
time = distance/speed
time = 138/46
time = 3hrs [ answer to Part B ]
and we are done!
Erick and Mia live the same distance from the park and decide to meet at the park one afternoon. The graphs show
their distances from home over the same 30-minute period as they walked to the park. Each section of each graph
represents 10 minutes.
Distance from Home
Erick
Time
Distance from Home
Mia
Time
Which of the following statements is true?
It took Mia 10 minutes to walk to the park
Mia left home immediately to head to the park
Erick and Mia arrived at the park at different times
It took Frick only 10 minutes to walk to the park
Erick and Mia both live the same distance from the park and decided to meet there one afternoon.
Which of the following statements is true?The graphs show their distances from home over a 30-minute period as they both walked to the park. Each section of each graph represents 10 minutes. From the graphs, it appears that Mia left home immediately to head to the park, while Erick took a few minutes before leaving.This is evidenced by the fact that Mia's graph shows that she was already walking for 10 minutes, while Erick's graph shows that his distance from home had not changed after 10 minutes.Additionally, since Mia's graph is further along than Erick's, this suggests that Mia arrived at the park before Erick. Therefore, it is true that Mia left home immediately to head to the park, and it took her 10 minutes to walk there.However, it took Erick more than 10 minutes to walk to the park, and the two arrived at the park at different times.That it took Mia 10 minutes to walk to the park. Although Erick and Mia left home at the same time, they may have chosen different routes, or one of them may have stopped along the way, so they arrived at the park at different times. It is not stated that it took Erick only 10 minutes to walk to the park.To learn more about The distance refer to:
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Assume that the duration of human pregnancies can be described by a Normal model with mean 265 days and standard deviation 17 days.
a) What percentage of pregnancies should last between 269 and 282 days?
b) At least how many days should the longest 10% of all pregnancies last?
c) Suppose a certain obstetrician is currently providing prenatal care to 67 pregnant patients. Let y represent the mean length of their pregnancies. According to the
Central Limit Theorem, what is the distribution of this sample mean, y? Specify the model, mean, and standard deviation.
d) What's the probability that the mean duration of these patients' pregnancies will be less than 258 days?
a) The percentage of pregnancies should last between 269 and 282 days is 18%
b) The days should the longest 10% of all pregnancies last is 291 days.
c) According to the Central Limit Theorem, the distribution of this sample mean is 265. The model is a Normal model, and standard deviation is 17/(√(67)).
d) The probability that the mean duration of these patients' pregnancies will be less than 258 days is 0.03 or 3%
How do we determine the values?a) To find the percentage of pregnancies that should last between 269 and 282 days, we need to find the proportion of the area under the normal distribution curve that falls between those two values. This can be done using a standard normal table or calculator. Using a calculator, we find that the proportion of the area under the curve between 269 and 282 days is approximately 0.18 (or 18%).
b) To find the longest 10% of all pregnancies, we need to find the duration that corresponds to the 90th percentile. We can use the standard normal table or calculator to find that the duration that corresponds to the 90th percentile is approximately 291 days.
c) According to the Central Limit Theorem, the distribution of the sample mean, y, is a normal distribution with a mean of 265 days (the population mean) and a standard deviation of 17/(√(67)) days. So the model is a Normal model with mean 265 and standard deviation 17/(√(67))
d) To find the probability that the mean duration of these patients' pregnancies will be less than 258 days, we need to find the proportion of the area under the normal distribution curve that falls to the left of 258 days. Using a calculator, we can find that the proportion of the area under the curve to the left of 258 days is approximately 0.03 (or 3%).
Therefore, the correct answers are as given above
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PLEASE HELP...PLEASE
Answer:
(4,8) (0,2) (-6,-7)
Step-by-step explanation:
Perpendicular means it sort of makes a cross with 90º angle from the already existing line. Imagine it starts at (4,8) coordinate and comes falling to the left, passing through p(-4,-4) coordinate, the points it will go through will be (4,8) (0,2) and (-6,-7) respectively.
A sure way to do this is to mark every point that's on the table below and see which ones form a perpendicular line with the original.
peter's international barbershop is a popular haircutting and styling saloon near the campus of the brooklyn college. one barber is available to work full time and spend an average of 4 minutes on each customer. customers arrive all day long at an average rate of 5 minutes arrivals tend to follow the poisson distribution, and service times are exponentially distributed. explain your results. [5 points]
If we assume that the average rate of arrivals is 5 minutes, then this means that the Poisson distribution will have a mean of 5 customers/minutesThis means that the probability that a customer arrives in the next minute is 0.2 (1/5).
The exponential distribution will have a mean of 4 minutes, meaning that the probability that the customer is served in the next minute is 0.25 (1/4).
Therefore, the expected number of customers that the barber can serve in an hour is 15 (5*4). The expected number of customers served in a given minute is 0.2 (1/5) * 0.25 (1/4) = 0.05. This means that the barber can expect to serve an average of 3 customers per hour.
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Note: Please make sure to properly format your answers. All dollar figures in the answers need to include the dollar sign and any amount over 1,000 should include the comma
($2,354.67). All percentage values in the answers need to include a percentage sign (96). For all items without specific rounding instructions, round your answers to two decimal places,
show both decimal places (5.06).
Use the graph of a piecewise function with three equations.
25,000
20,000
$21,197-
15,000
10,000
$5,448-5,000
$1,045-
0
20,000 40.000 60,000 80,000
$39,800
$10,450
Taxable Income
a. A taxpayer has a taxable income of $39,800. What is her tax?
b.
A taxpayer will owe $21,197. What is his taxable income?
100,000
$102,800
a. Taxpayer having a taxable income of $39,800 has $5,448 as the income tax.
b. The taxable income of taxpayer owing $21,197 is $102,800.
What is Income Tax?
Income tax is the tax which is levied on all individuals and businesses. The individual income taxes are calculated on the basis of the income received by the individual. Typically, it is categorized as a direct tax because the burden is thought to fall on the people who pay it. Net profits, calculated as the excess of receipts over permitted costs, are subject to corporate income tax.
We are given graph of a piecewise function with three equations which is attached below.
From the graph, it can be observed that the taxpayer who has the taxable income of $39,800 has to pay income tax of $5,448.
Also, a taxpayer owing $21,197 means that he has to pay income tax of $21,197.
His taxable income is $102,800 as shown in the graph below.
Hence, taxpayer having a taxable income of $39,800 has $5,448 as the income tax and the taxable income of taxpayer owing $21,197 is $102,800.
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Drag the files to the correct boxes to complete the pairs make each system of linear equations with the correct number of solutions 
The number of solutions for given three system of linear equations.
We can simply solve this numerical problem by using the following process.
3x - y = 4 ==> a₁/a₂ = b₁/b₂ = c₁/c₂ = 1/2
What is meant by numerical?
The phrase "numerical" refers to something that involves numbers.Numerical expression is made up of the two words numerical, which refers to numbers, and expression, which refers to a statement. Consequently, it is a statement that uses numbers.A numerical solution entails speculating about the answer and determining if the issue is sufficiently resolved to end.This formula has numerous complicated terms, making it difficult to recall. Additionally, finding a solution takes time. There are instances when a system has access to a lot of data, and the data can also be analyzed to find a solution. But because there is so much data, finding a solution to these issues takes time.Based on the formula is:
Let the system of equations be a₁x + b₁y = c₁ and a₂x + b₂y = c₂ then
Condition for One solution: a₁/a₂ ≠ b₁/b₂ ≠ c₁/c₂
Condition for No Solution: a₁/a₂ = b₁/b₂ ≠ c₁/c₂
Condition for infinitely many solutions: a₁/a₂ = b₁/b₂ = c₁/c₂
Now in the given question:
a.) 3x - y = 4
6x - 2y = 8
⇒ a₁/a₂=3/6 = 1/2 ; b₁/b₂ = -1/-2 = 1/2 ; c₁/c₂ = 4/8 = 1/2
⇒ a₁/a₂ = b₁/b₂ = c₁/c₂ = 1/2
The given system of equations is coincident lines, hence has infinitely many solutions.
b.) -3x + y = 7
2x - 4y = -8
⇒ a₁/a₂= -3/2 ; b₁/b₂ = 1/-4 ; c₁/c₂ = 7/-8
⇒ a₁/a₂ ≠ b₁/b₂ ≠ c₁/c₂
The given system of equations is intersecting lines, hence having a single solution.
c.) y = -4x - 5
y = -4x +1
⇒ a₁/a₂= -4/-4 = 1 ; b₁/b₂ = 1/1 = 1 ; c₁/c₂ = -5/1 = -5
⇒ a₁/a₂ = b₁/b₂ ≠ c₁/c₂
The given system of equations is parallel lines, hence having no solution.
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a car dealer is deciding what kinds of vehicles he should order from the factory. he looks at his sales report for the preceding period. construct a pareto chart to help him decide. choose the vertical scale so that the relative frequencies are represented.
The vertical scales for each type of vehicle are:
Economy, 0.2Sports, 0.5Family, 0.35Luxury, 0.1Truck, 0.3The rationale is to choose a vertical scale that represents the relative frequencies, or the proportion of each type of vehicle sold compared to the total number of vehicles sold. The calculation for each type of vehicle is as follows:
Economy: 30 / 150 = 0.2 Sports: 7.5 / 150 = 0.05Family: 52.5 / 150 = 0.35 Luxury: 15 / 150 = 0.1 Truck: 45 / 150 = 0.3Here, the total number of vehicles sold (150) is calculated by adding up the sales for each type of vehicle. The relative frequency for each type of vehicle is then calculated by dividing the sales for that type of vehicle by the total number of vehicles sold.
This question should be provided as:
A car dealer is deciding what kind of vehicles he should order from the factory. he looks at his sales report for the preceding period. choose the vertical scale so that the relative frequencies are represented:
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non-decreasing function over r is continuous at any point except on a countable set using g delta set
A discontinuity the left and right limits still need to exist but are different.
Since bounded, growing sequences of numbers have limits, a non-decreasing function can only have leap discontinuities, which means that at
Every leap indicates that one interval is missing from the function's range, and these intervals are all disconnected (since the function is non-decreasing, the skipped intervals march up the y-axis).
Since there are only a finite number of discontinuous intervals, there can only be a finite number of discontinuity sites (to see this last bit, just pick a rational number in each interval).
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29. Candice and Leila arrived at a birthday party at 5:20 p.m. The party lasted for 3 hours. They then took 20 minutes to arrive home. What time did they arrive home?
write a function void print int vector(int *ptr, int length) that prints the values in the vector of integers indicated by ptr of length length to the standard output. a vector is a 1-dimensional array. for example, the following c statement declares an integer vector of 10 elements: int avector[10]; each integer should be printed as a decimal number, one entry per line.
The function void print int vector(int *ptr, int length) prints the values in the vector of integers indicated by ptr of length length to the standard output.
The vector is a 1-dimensional array. The formula for this function is:
For i = 0 to length-1
Print ( ptr[i] )
End
The calculation for this function is as follows:
The function starts with a for loop, where the initial value of i is set to 0, and the condition for the for loop is i < length, and the increment value of i is 1. The body of the for loop prints the value of ptr[i], which is the value at the i-th position in the vector. This loop is repeated until the condition i < length is false, at which point the function terminates.
In summary, the function void print int vector(int *ptr, int length) prints the values in the vector of integers indicated by ptr of length length to the standard output. The formula for this function is a for loop, where the initial value of i is set to 0 and the condition for the for loop is i < length. The body of the for loop prints the value of ptr[i], and the loop is repeated until the condition i < length is false.
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in a survey of 260 college students, the following data were obtained: 64 had taken a mathematics course, 94 had taken a computer science course, 58 had taken a business course, 28 had taken both a mathematics and a business course, 26 had taken both a mathematics and a computer science course, 22 had taken both a computer science and a business course, and 14 had taken all three types of courses.
There were 64 students who had taken a mathematics course. Of those 64, 28 had also taken a business course, and 26 had also taken a computer science course. This leaves 10 students who had taken only a mathematics course.
To calculate this, we start by subtracting the number of students who had taken all three courses (14) from the total number of students who had taken a mathematics course (64).
Then we subtract the number of students who had taken both a mathematics and a business course (28) and the number of students who had taken both a mathematics and a computer science course (26) from the result. This gives us 10 students who had taken only a mathematics course.
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Which unit rate corresponds to the proportional relationship shown in the graph?
Drag and drop the answer into the box to match the graph with its unit rate.
A graph with a line running through coordinates left parenthesis 0 comma 0 right parenthesis and coordinates left parenthesis 12 comma 16 right parenthesis.
1.33 cm/s
Step-by-step explanation:
The line is going from point (0;0) to point (12;16), the proportional relationship between these points refer to the slope of the line, which can be found with this expression:
Replacing all values we have:
Therefore the relation shown in the graph is represented by 1.33 cm/s, which refers to the constant speed developed by the object.
Is this what your looking for if not let me know
Answer:
1.33 cm/s
Step-by-step explanation:
What is the distributive property of 32+44?
Answer:
66
Step-by-step explanation:
32+44=66
32
+42
____
66
Help me pls!!!!!!!! I NEED HELPPP
Noah had 151 stamps. He had has 42 more stamps than Jonas. How many stamps did Jonas have? How many stamps must Noah give to Jonas so that they each have the same number of stamps?
=109
No. of stamps that Noah should give to Jona to get equal no. of stamps = 151 -31=130 and 109+31=130 So now they get an equal share.Select the correct answer.
Simplify the following expression.
A.
B.
C.
D.
Find domain and range of the relation: (-2,7), (-2,6), (-2,5), (-2,4).
Then determine whether the relation of a function (yes or no).
The domain and range of the relation are { -2 } and { 4, 5, 6, 7 } respectively. The relation is not a function.
Is the relation a function? What are the domain and range?A function is simply a relationship that maps one input to one output, that is, each x-value can only have one y-value.
Given the relation in the question;
(-2,7), (-2,6), (-2,5), (-2,4)
For a relation to be a function, every x-value must have only one y-value mapped to it.
-2 appeared twice and its corresponding y-values are different.
Hence, the relation is Not a Function.
The Domains are the x-values and the Range are the y-values,
Domain: { -2 }
Range: { 4, 5, 6, 7 }
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multiply 101 base two by 11 base two
Answer:
1 1 1 1 to base two
Step-by-step explanation:
1 0 1 base two
× 1 1 base two
+ 1 0 1
1 0 1
=1 1 1 1 base two
in four football games, antoine carried the ball for 98, 146, 84, and 105 yards. how many total yards did antoine have for the four games?
Answer: she had 433 yards
Step-by-step explanation:
solve the equation: x2+7x=0
Answer: X=
Write your answers as a list of integers or reduced fractions, with your answers separated by (a) comma(s). For example, if you get
and
as your answers, then enter 4,-2/3 in the box.
The solution to the given equation x² + 7x = 0 is x = 0, -7.
What is a quadratic equation?The quadratic equation is defined as a function containing the highest power of a variable is two.
The quadratic equation is given in the question, as follows:
x² + 7x = 0
We have to determine the solution to the given equation.
As per the question, we have
x² + 7x = 0
x(x + 7) = 0
Equating factors to zero, we get
x = 0 and (x + 7) = 0
x = 0 and x = -7
Thus, the solution to the given equation is x = 0, -7.
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How do you solve these step by step (circled problems)
To create a dot plot, we have to first choose an appropriate scale for the given number line, and then mark a dot over the given numbers.
What is a dot plot?Data points are represented as dots on a graph with an x- and y-axis in a dot plot, sometimes referred to as a strip plot or dot chart, which is a straightforward type of data visualization. These kinds of graphs are employed to visually represent particular data patterns or groups.
To create a dot plot, we have to first choose an appropriate scale for the given number line, and then mark a dot over the given numbers.
For the first question:
Scale on the number line from the first tick, 310 to 335.
For the second question:
Scale on the number line from the first tick, 18 to 31.
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what is the slope of the line which passes through the origin (-3,5)
Answer:
Step-by-step explanation:
Cuales son los primeros 10 múltiplos de 18 y 27?
Answer:0, 18, 36, 54, 72, 90, 108, 126, 144, 162
Step-by-step explanation:0 es múltiplo de 18, pues 18 x 0 = 0
18 es múltiplo de 18, pues 18 x 1 = 18
36 es múltiplo de 18, pues 18 x 2 = 36
54 es múltiplo de 18, pues 18 x 3 = 54
72 es múltiplo de 18, pues 18 x 4 = 72
90 es múltiplo de 18, pues 18 x 5 = 90
108 es múltiplo de 18, pues 18 x 6 = 108
126 es múltiplo de 18, pues 18 x 7 = 126
Answer:
Step-by-step explanation:
18: 0, 18, 36, 54, 72, 90, 108, 126, 144, 162
27: 27, 54, 81, 108, 135, 162, 189, 216, 243, 270
For the following exercises, use a calculator to find the length of each side to four decimal places.
In the given right-angled triangle, the sides are 21.3617 and 22.8815.
The given figure is a right-angled triangle. Hence, sides can be determined by using trigonometric function and/or the Pythagorean theorem. It is known that angle A = 69 and side b = 8.2. The side b is an adjacent side to angle A. Using the trigonometric function of tangent
tan Ɵ = opposite side/adjacent side
tan A = a/b
a = b tan A = 8.2 tan 69 ≈ 21.3617
As the two sides a and b are known, the remaining side c can be determined by using Pythagorean theorem,
Hypotenuse^2 = Opposite^2 + Adjacent^2
c^2 = a^2 + b^2
c^2 = (21.3617)^2 + (8.2)^2
c^2 = 523.3635
c =√523.3635
c ≈ 22.8815
Note: The question is incomplete. The complete question probably is: Use a calculator to find the length of each side to four decimal places. (Assume triangle ABC where side a is opposite angle A, side b is opposite angle B, and side c is the hypotenuse.) side length b = 8.2 and angle A = 69 degrees.
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Consider a function f defined as follows: f(x)=(x-3)^2, x belongs to [1,2]. Is f invertible in the domain [1,2]? If yes, find the inverse of the function.
(Need a detailed explanation showing the function is invertible, then determining the inverse.)
The function f(x) = (x - 3)² is invertible on the interval [1,2], as each output is related only with a single input.
The inverse of the function is given as follows:
[tex]f^{-1}(x) = -\sqrt{x} - 3[/tex]
How to obtain the inverse function?The function for this problem is defined as follows:
f(x) = (x - 3)²
The x-coordinate of the vertex of the quadratic function is given as follows:
x = 3.
Hence the function is invertible on the domain [1,2], which is entirely on one side of the vertex, and thus each output is related only with a single input.
The inverse function is obtained exchanging the variables x and y, and then isolating y, thus:
x = (y - 3)²
[tex]y - 3 = -\sqrt{x}[/tex]
[tex]y = -\sqrt{x} - 3[/tex]
[tex]f^{-1}(x) = -\sqrt{x} - 3[/tex]
The negative symbol is because the function is on the left side of the vertex.
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The figure below is a square find the length of size x in simplest radical form with a rational denominator
x² + x² = 4
2x² = 4
x² = 2
x=√2
hope it helps
10) A boat travels 30 km up a river in the same time it takes to travel 50 km down the same river. If the current of water is 5km/h. What is the speed of the boat in still water? Be sure to show your work to earn full credit. Here's a chart to get you started: Travel Rate Time Distance
As a result, when a boat goes 30 km up a river in the same amount of time, its speed in still water is 20 km/h.
what is equation ?The numeral is said to be in this simplest form when divided into its smallest equivalent fraction. How to do to find the most basic form. Find common factors in the denominator and numerators. Verify a fractional integer to verify if it passes as a prime number. A statement having two collinear and an equally sign in the middle is called an equation in mathematics. The general form of any equation contains the degrees of all the variables in descending order. The normal form of a linear function is an x + b = 0. The general form of a linear equation with two variables is an x + b y + c = 0. (or something similar). Equations can be categorised as identities or conditional equations. An identity holds true regardless of the value given to the variables.
given
Let the boat's speed in calm water be x km/h.
Boat speed downstream is equal to x plus 5.
Upstream boat speed is equal to x - 5
Distance x time speed
Time is therefore determined by speed and distance.
Boat travel time is equal to 30/km upstream (x – 5)
50/(x + 5) is the time it takes a boat to travel 50 kilometres downstream.
Since the boat takes the same amount of time in both scenarios, 30 (x + 5) = 50 (x -5), 30 x +150 = 50 (x -250), 20 (x = 400), and 20 (x = 20).
As a result, when a boat goes 30 km up a river in the same amount of time, its speed in still water is 20 km/h.
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7.) +9 – +16 = N
8.) +85 – +12 = N
9.) –6 –2 = N
10.) +13 – +12 = N Someone please need it right now
Arithmetic operations on the directed numbers gives;
7) -7
8) +73
9) - 8
10) + 1
What are directed numbers?Any given number which has either a positive or negative sign is a directed number. Thus all numbers are directed in one way or the other. Some examples are: 8, +2, - 8.35, 10, 520 etc.
Performing an arithmetic operations on the given question, we have;
7) +9 - + 16 = +9 -(+16)
applying the rule of signs
+9 - (+16) = + 9 - 16
= -7
8) +85 - + 12 = +85 - (+12)
applying the rule of signs
+85 - (+12) = +85 - 12
= +73
9) -6 - 2
applying the rule of signs
-6 -2 = -8
10) +13 - + 12 = +13 - (+12)
applying the rule of signs
+13 - (+12) = +13 - 12
= +1
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