Thus, the number of ways in which to choose 4 letters, without replacement, from 17 distinct letters is 57,120.
Define the term permutation?The term permutation applies to a mathematical computation of a number of possible arrangements of a given collection. Simply said, a permutation is a term that defines the amount of different ways something can be organized or arranged.Total distinct letters are 17.
There are 17 alternatives for the initial letter if there are 17 letters.
There are just 16 alternatives left once you remove the letter.
Each time you remove a letter, the bag contains one fewer letter.
Number of ways = 17 x 16 x 15 x 14
Number of ways = 57,120
Thus, if the sequence of the alternatives is irrelevant, there are 57,120 options.
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suppose the counts recorded by a geiger counter follow a poisson process with an average of 2 counts per minute. what is the probability that there are no counts in a 30 second interval? round your answer to 3 decimal places. suppose the counts recorded by a geiger counter follow a poisson process with an average of 2 counts per minute. what is the probability that there are no counts in a 30 second interval? round your answer to 3 decimal places.
The probability that there are no counts in a 30 second interval is 0.284
What is probability ?
Probability refers to potential.This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Before we can determine the probability that a particular event will occur, we must first know the total number of outcomes.
Given that,
Assume that a Geiger counter records counts using a poisson process, with an average rate of 2 counts per minute.
0.284
P(X < 10 Seconds) = P(X<1/6 minutes) = F(1/6) = 1-e-2*1/6 = 1-e-1/3 = 0.284
Therefore, the probability that there will be no counts in a 30-second period is 0.284.
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what is ( 7 5/6 - 5 1/3 ) +1 1/9?
Answer:
i don't know
Step-by-step explanation:
Mathematical induction
Yes this question can be proven by mathematical induction
What do you mean by induction in mathematics?
For each and every natural number n, a statement, theorem, or formula can be proved using the mathematical induction technique. By generalizing this into the "Principle of Mathematical Induction," which we would utilize to demonstrate any mathematical assertion.
Here, n ≥ 1
1/1.2 + 1/2.3 + 1/3.4 + .............. + 1/n(n +1)
We employ the idea of Sigma here.
S/1/r(r + 1) { r = 1 to n }
Sigma [1/(r + 1) - 1/(1/r)] { r = 1 to n }
put r = 1 \s1/1 - 1/(1 + 1) = 1 - 1/2
put r = 2 \s1/2 - 1/(2 +1) = 1/2 - 1/3
put r = 3 \s1/3 - 1/(3 +1) = 1/3 - 1/4
........................................................... put r = n 1/n - 1/(n + 1)
after adding
Sigma = [1/(r+1) - 1/(1/r)] {r = 1 to n } = 1 -1/2 + 1/2 -1/3 + 1/3 - 1/4 + ............1/n - 1/(n +1)
= 1 - 1/( n +1) = n/( n +1)
Consequently, 1/1.2 + 1/2.3 + 1/3.4 +... 1/n(n + 1) = n/(n + 1).
so it proved
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Find the asymptotes and intercept of the following rational function
Show your work for the intercepts!
Answer:
VA: x = 1, x = -1
HA: y = 0
x-int: (4, 0)
y-int: (0, 4)
Step-by-step explanation:
x-int:
0 = (x-4)/((x-1)(x+1))
0 = (x-4) because the (x-1)(x+1) are multiplied by 0
4 = x
x = 4
(4, 0)
y-int:
y = (0 - 4)/((0 - 1)(0 + 1))
y = (-4)/((-1)(1))
y = (-4)/(-1)
y = 4/1 = 4
(0, 4)
the coordinates of point are (-3,5). what are the coordinates of point B, which is a reflection of point A across the x-axis?
Answer:
Step-by-step explanation:
3 as the x axis and -5 for the y axis
Help me please image is attached I really appreciate it
An inequality to find the number of batches of rolls Liz can make is 13n/4 ≤ 26 and she cannot make more than 8 batches of rolls.
How to write and solve this inequality?In order to solve this word problem, we would assign a variable to the number of batches, and then translate the word problem into an algebraic inequality as follows:
Let the variable n represent the number of batches.
Since Liz has 26 tablespoons of yeast left in the jar and each batch of biscuits takes 3 1/4 -tablespoons, we have:
3 1/4 (n) ≤ 26
13n/4 ≤ 26
Cross-multiplying, we have:
13n ≤ 26 × 4
13n ≤ 104
n ≤ 104/13
n ≤ 8.
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Complete Question:
Liz wants to make several batches of biscuits. She has 26 tablespoons of yeast left in the jar and each batch of biscuits takes 3 1/4 -tablespoons. Write and solve an inequality to find the number of batches of rolls Liz can make.
Which lists of terms are ordered from least to greatest?
Select TWO correct answers.
√6 2.5 8/3
√8 11/4 2.9
9/5 1.9 √5
13/5 2.8 √7
1.8 7/4 √3
The terms ordered from least to greatest are √6, 2.5, 8/3, and 9/5, 1.9, √5. Then the correct options are A and C.
What is ascending order?It is the order of the numbers in which a smaller number comes first and then followed by the next number and then the last number will be the biggest one.
Let's check all the options. Then we have
a) √6, 2.5, 8/3, convert the numbers into a decimal form. Then we have
⇒ 2.449, 2.5, 2.667, order is in ascending form.
b) √8, 11/4, 2.9, convert the numbers into a decimal form. Then we have
⇒ 2.828, 2.75, 2.667, order is not in ascending form.
c) 9/5, 1.9, √5, convert the numbers into a decimal form. Then we have
⇒ 1.8, 1.9, 2.236, order is in ascending form.
d) 13/5, 2.8, √7, convert the numbers into a decimal form. Then we have
⇒ 2.6, 2.8, 2.645, order is not in ascending form.
e) 1.8, 7/4, √3, convert the numbers into a decimal form. Then we have
⇒ 1.8, 1.75, 1.732, order is not in ascending form.
The terms ordered from least to greatest are √6, 2.5, 8/3, and 9/5, 1.9, √5. Then the correct options are A and C.
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One out of every ten students in a school takes lunch to school. If there are two hundred students in the school, how many of them do not take lunch to school?
180 students do not take lunch to school.
From the question, we have
Number of students do not take lunch to school= 200-20
=180 students
Subtraction:
Subtraction represents the operation of removing objects from a collection. The minus sign signifies subtraction −. For example, there are nine oranges arranged as a stack (as shown in the above figure), out of which four oranges are transferred to a basket, then there will be 9 – 4 oranges left in the stack, i.e. five oranges. Therefore, the difference between 9 and 4 is 5, i.e., 9 − 4 = 5. Subtraction is not only applied to natural numbers but also can be incorporated for different types of numbers.
The letter "-" stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.
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each face of a cube is painted either red or blue, each with probability 1/21/2. the color of each face is determined independently. what is the probability that the painted cube can be placed on a horizontal surface so that the four vertical faces are all the same color?
The probability that the vertical faces have the same color painted is 0.6875
There are 6 faces on a cube.
Each face of the cube will either be red or blue.
The probability that one face will have red color = probability that the face will have blue color = 1/2
It is given that the cube is placed on a horizontal surface and the 4 vertical faces have the same color.
The painting of the faces of the cube clearly follows a binomial distribution.
Therefore the probability to color the faces of a cube
= P(4 faces are red, 2 faces blue) + P(4 faces are blue, 2 faces red) + P(5 faces blue) + P(5 faces red) + P(All faces blue) + P(all faces red)
For any binomial distribution
ⁿCₓ X pˣ (1 - p)ⁿ⁻ˣ
where
n = no. of sample
x = random variable
p = probability of success
Hence we get
⁶C₄ X 0.5⁴ 0.5² + ⁶C₄ X 0.5⁴ 0.5² + ⁶C₅ X 0.5⁵ 0.5 + ⁶C₅ X 0.5⁵ 0.5
⁶C₆ X 0.5⁶ + ⁶C₆ X 0.5⁶
= 15 X 0.015625 + 15 X 0.015625 + 6 X 0.015625 + 6 X 0.015625 + 0.015625
= 0.6875
Therefore we get the probability of having the four vertical faces of the same color to be 0.6875.
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dave is making a rectangular garden bed. after assembling it, he finds that the bed has a width of three-fourths of a foot and a length of nine and one-third feet. what is the area of the garden in square feet
The area of the garden is 7 square feet.
Define area.The area a rectangle occupies is the space it takes up inside the limitations of its four sides. The dimensions of a rectangle determine its area. In essence, the area of a rectangle is equal to the sum of its length and breadth. An example of a quadrilateral with equal and parallel opposite sides is a rectangle. It is a polygon with four sides and four angles that are each 90 degrees. A rectangle is a shape with only two dimensions. A rectangle's area (A) is calculated by multiplying its length ('a') by its breadth ('b'). Area of Rectangle is therefore equal to (a× b) square units.
Given,
Width = 3/4
Length = 9 + 1/3
Length = 28/3
Area:
Length × Width
3/4 × 28/3
84/12
7
The area of the garden is 7 square feet.
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I NEEEDD HELP ASAPP PLEASE
Solve negative three minus one and two fifths.
three fifths
one and two fifths
negative four and two fifths
four and two fifths
Answer:
Step-by-step explanation:
1. Put Words into Math.
Negative three minus one and two fifths= -3- 1 2/5
2. Solve the math problem
-3-1 2/5= -4 2/5 or -22/5 in improper fraction
Answer: -4 2/5 or -22/5
What is the equation of the line in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
See below
Step-by-step explanation:
Find slope using two convenient integer coordinates
(-1,4) and (1, -8) are convenient
slope = (y1-y2) / (x1-x2) = (4 - -8) / ( -1 -1) = 12/-2 = -6
the y-axis intercept is -2 ( by looking at the graph)
y = -6x -2 Done.
In the first week of July, a record 1,040 people went to the local swimming pool. In the second week, 110 fewer people went to the pool than in the first week. In the third week, 145 more people went to the pool than in the second week. In the fourth week, 139 fewer people went to the pool than in the third week. What is the percent decrease in the number of people who went to the pool over these four weeks?
Answer:
62%
Step-by-step explanation:
1040-110-145-139=646
646/1040=62%
How to solve: n-4= 5n + 1/2
4-9×2^x+2+1=0. Please help me to solve the question please
Answer:
x=[tex]log_{2} 7/9[/tex]
Step-by-step explanation:
4-9×2^x+2+1=0
4-9×2^x+3=0
4+3-9×2^x=0
7-9×2^x=0
7-7-9×2^x=0-7
-9×2^x=-7
9×2^x=7
9×2^x/9=7/9
2^x=7/9
[tex]log_{2} 2^x[/tex]=[tex]log_{2} 7/9[/tex]
x=[tex]log_{2} 7/9[/tex]
the line passes through (6,6) and (-2,2)
Answer:
Step-by-step explanation:
slope=change in y over change in x
6-2=4
6--2=6+2=8
-4/-8=1/2
. Identify the key features of g(x) = x², including the domain, range, x and y intercepts, and
intervals of increase and decrease.
The required key features of [tex]g(x) = x^{2}[/tex] including domain is (-∞, ∞) (i.e. all real values), range = [0,∞), x-intercept = (0,0), y-intercept = (0,0), interval of increasing = (0,∞) and interval of decreasing = (-∞, 0)
What is a quadratic function?
A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function.
The graphs of quadratic functions are frequently curved or nonlinear. A parabola, a kind of U-shaped curve, is the particular type of curve that makes up the graph of a quadratic function.
Given, [tex]g(x) = x^{2}[/tex]
The graph of the given function is given below:
From the graph,
Domain = (-∞, ∞) (i.e. all real values)
Range = [0,∞)
x-intercept = (0,0)
y-intercept = (0,0)
Interval of increasing = (0,∞)
Interval of decreasing = (-∞, 0)
Hence, these are the required key features of [tex]g(x) = x^{2}[/tex].
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observation refers to the . a. mean of all variable values associated with one particular entity b. estimated continuous outcome variable c. set of recorded values of variables associated with a single entity d. goal of predicting a categorical outcome based on a set of variables
The correct option is c. that is observation is set of recorded values of variables associated with a single entity.
What is observation?
An observation is a case of the data being collected.
For example, if we were collecting data on students in the class, the observations would be each individual student in the class. It could be the student's height, weight, marks scored, etc.
A variable is an attribute or characteristic of the observation we record in our data.
Also an observation in statistics is a value of something of interest measured or counted during a study or experiment: a person’s height, a bank account value at a certain point in time, or number of animals.
Therefore from the given option c is correct.
Observation is set of recorded values of variables associated with a single entity.
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Rodrigo is taking an SAT prep class at the Westminster Community Center. The community center is 3.1 miles away from Rodrigo's house. How far apart are Rodrigo's house and the community center on a map with a scale of 3 inches : 9.3 miles?
1 inch is the distance between Rodrigo's house and the community center on a map with a scale of 3 inches : 9.3 miles
What is Unit of Measurement?A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.
Given,
The community center is 3.1 miles away from Rodrigo's house.
We need to find how far apart are Rodrigo's house and the community center on a map with a scale of 3 inches : 9.3 miles
As given, 3 inches : 9.3 miles
1 mile = 3/9.3 inches
1 mile = 0.323 inches.
So let us multiply 3.1 with 0.323
3.1×0.323
1.0013 inches
Hence 1 inch is the distance between Rodrigo's house and the community center on a map with a scale of 3 inches : 9.3 miles
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Fill in the blanks below in order to justify whether or not the mapping shown
represents a function.
Set A
Submit Answer
+
2
Ń
9.
The mapping diagram above
where there
Set B
5
C
a function since
C
in
attempt 1 out of 2
0.00147 In standard form
Answer:
It can be written as 1.47x10-³.Answer:
This is in Standard form. Did you mean scientific form?
1.47 x [tex]10^{-4}[/tex]
Step-by-step explanation:
You move the decimal so that the number is between 1 and 10. Then since in standard form the number is much less than 1.47, you determine how muhc less my how many places you need to move the decimal to put it back in standard form. Since you would need to move the decimal 4 places to the left, the exponent would be -4
Which of the following is equivalent to 60 Superscript one-half?
Answer
[tex]60\sqrt{x} 2[/tex]
Step-by-step explanation:
Answer:
StartRoot 60 EndRoot
Step-by-step explanation:
Edge
a solid triangular prism has a height of 12 inches. the triangular base of this prism is shown below. what is the surface area, in square inches, of this prism?
The surface area of the triangular prsim is 290.4 in² and the right option is B. 290.4 in².
What is surface area?Surface area is the space occupied by a two-dimensional flat surface is called the area. It is measured in square units.
To calculate the surface area of the triangular prism, we use the formula below.
Fromula:
S.A = (a+b+c)L+bh.................... Equation 1Where:
S.A = Surface area of the prisma , b, c = Three sides of the base triangle respectively.h = Height of the triangular baseL = Lenght of the prismFrom the question,
Given:
L = 12 ina = 5 inb = 9 inc = 7.2 inh = 4 inSubstitute these values into equation 1
S.A = (5+9+7.2)12+(4×9)S.A = 254.4+36S.A = 290.4 in²Hence, the right option is B. 290.4 in².
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a company makes a bracelet containing magnets that they claim improves balance and overall athletic performance. researchers recruit volunteers for an experiment. the subjects will test the effectiveness of the bracelet by performing a variety of athletic challenges with and without the bracelet. each subject will do each challenge 333 times: wearing the actual bracelet, wearing a placebo bracelet, and wearing no bracelet at all. the order will be randomized for each activity, subjects won't know which bracelet is which. why did the researchers include the scenario where subjects wear no bracelet at all?
The researchers include the scenario where subjects wear no bracelet at all are when it comes to mosquitoes, volunteers in each block should live in similar conditions.
Define experiment.An experiment might involve giving a novel drug to rats to see how they respond to learning about it. When you visit a new coffee shop but are unsure of how the coffee will taste, that is an example of an experiment. the act of carrying out a test like that; experimenting. An experiment is a procedure used as part of the scientific method to test a hypothesis. The independent and dependent variables are the two most important variables in every experiment. To investigate the impact of the independent variable on the dependent variable, it is either controlled or altered.
Given,
A company makes a bracelet containing magnets that they claim improves balance and overall athletic performance. researchers recruit volunteers for an experiment.
The researchers include the scenario where subjects wear no bracelet at all are:
When it comes to mosquitoes, volunteers in each block should live in similar conditions.
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the mean selling price of senior condominium in green valley over a year was $215,000. the population standard deviation was $25,000. a random sample of 100 new unit sales was obtained. a. what is the probability that the sample mean selling price was more than $210,000?
The probability that the sample mean selling price was more than $210,000 is 0.9772.
The given values are:
The mean selling price(μ) = $215000
Standard deviation(σ) = $25000
The random sample (n) = 100
We have to find the probability that the sample mean selling price was more than $210000.
z-score with z-bar= 210000
z = (x-bar - μ) / (σ/ √n)
= ( 210000 - 215000) / (25000/ √100)
= -5000/ 2500
=-2
Using z-tables, the probability is:
Probability = P[z> -2]
= 1 - 0.0228
= 0.9772
Therefore the probability is 0.9772.
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can someone help me really quick
Answer:
18$
Step-by-step explanation:
this is so i can reach twenty characters.
In triangle ABC, side AB is one-third of the length of side AC. Side BC is 5 more than the length of side AC. The perimeter is 19. What is the length of side AC?
Answer:
AC = 6 units===========
GivenAB = AC/3BC = AC + 5P = 19AC = ?SolutionP = AB + AC + BCSubstitute and solve for ACAC/3 + AC + AC + 5 = 192 1/3 AC = 147/3 AC = 14AC = 14*3/7AC = 6Note:
Other sides are 2 and 11. This is not a correct question as sum of two smaller sides (2 + 6) is less than the longest one (11), hence there is no such possible triangle.
1/7a + 1/7 = ?
YALL HELP I LOST MY NOTES
Step-by-step:
1)Combine multiplied terms into a single fraction
1/7a+ 1/7
1a/7+1/7
2)Multiply by 1
3)Combine fractions with a common denominator
Solution
a+1/7
Hope That helps!
A rectangular blacktop with a length of 5x and a width of 3x has been erected inside a rectangular !eld that has a length of 12x and a width of 7x.a. What is the area of the part of the !eld that is not blacktop?b. "ere is a circular fountain in the rectangular !eld that has a radius of 3x. What is the area of the part of the !eld that does not include the blacktop or the fountain? Factor your answer. Pls help
Answer:
Step-by-step explanation:
to find area of a rectangle we use (L)(W) so we do that here for both of these rectangles first find the area of the black top
5x(3x)
15x^2 is the area of the blacktop
The “!ield” area is next
12x(7x)
84x^2 is the area now we just subtract the two numbers by subtracting coefficients but keeping the rest the same
84x^2-15x^2
69x^2 is the area of the rectangle that is not black top
B- the foundtain we find with the area of circle formula r squared times pi
3x(3x)pi
9x^2pi
Now we just subtract this from the area of the rectangle
69x^2 -9x^2pi is the area
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What is the equation of the line in slope-intercept form?
pls help me!
Answer:
y = [tex]\frac{4}{3}[/tex] x + 4
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 3, 0) and (x₂, y₂ ) = (0, 4) ← 2 points on the line
m = [tex]\frac{4-0}{0-(-3)}[/tex] = [tex]\frac{4}{0+3}[/tex] = [tex]\frac{4}{3}[/tex]
the line crosses the y- axis at (0, 4 ) ⇒ c = 4
y = [tex]\frac{4}{3}[/tex] x + 4 ← equation of line