There are 840 permutations of the set a, taken 4 at a time.
What is integer ?
An integer is the number zero, a positive natural number or a negative integer with a minus sign. The negative numbers are the additive inverses of the corresponding positive numbers.
A permutation of a set is an arrangement of its elements in a specific order. To find the number of permutations of a set with n elements, taken r at a time, the formula is given by n! / (n - r)!, where n! is the factorial of n.
Given the set a = {x | x is an integer and x^2 < 16}, we can find the elements of the set:
x^2 < 16
x = ±1, ±2, ±3, ±4
So the set a has 8 elements: {-4, -3, -2, -1, 1, 2, 3, 4}.
The number of permutations of a set with 8 elements, taken 4 at a time, is given by 8! / (8 - 4)! = 8! / 4! = 40320 / 24 = 840.
Therefore, there are 840 permutations of the set a, taken 4 at a time.
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When is minimal deception considered ethical in research? Select one
A. When you need to put limits on the study
B. Only when you have a control group
C. When there is no other way to achieve a specific research goal
D. Deception of any kind is never allowed
Option C is correct. When there is no other way to achieve a specific research goal minimal deception considered ethical in research.
When there is no other way to achieve a specific research goal. Minimal deception is considered ethical in research only when it is necessary to achieve a specific research goal, and there is no other way to achieve that goal without using deception. In these cases, the use of deception should be justified and minimized as much as possible.
Researchers should consider the potential harm to participants, and carefully weigh the potential benefits of the research against any potential harm.
Additionally, the use of deception should be disclosed to participants as soon as possible after the completion of the study, so that they can understand what has occurred and why. Overall, researchers should strive to be transparent and to minimize the use of deception whenever possible, and to use it only when it is necessary to achieve a specific research goal that cannot be accomplished through other means.
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Triangle ABC is an isosceles triangle. Select a possible ratio for the lengths of the sides of triangle ABC if its perimeter is 42 inches and the length of each side is a whole number. A) 7:4:4 B) 5:4:4 C) 4:3:3 D) 3:2:2
Answer:
D
Step-by-step explanation:
isosceles triangle = 2 sides equal
multiply each by 6 you'll get D 18:12:12 sum of all three is 42
blitzen, the reindeer, walks seven times faster thank nikolas. nikolas walked 15 hours and rode blitzen for 3 hours to travel 144 miles. how fast does nikolas walk and how fast does blitzen walk.
ps. i need more than just the answer, gotta show my work
The respective speeds of Blitzen and Nikolas are 28 miles per hour and 4 miles per hour.
What is the speed of an object?Speed is the rate at which an object's position changes, measured in meters per second. For example, if an object starts at the origin, and then moves three meters in three seconds, its speed is one meter per second. The equation for speed is simple: distance divided by time
Given here: Blitzen walks 7 times faster than nikolas and nikolas walked 15 hours and rode blitzen for 3 hours to travel 144 miles.
Let the speed of nikolas be x then we have
speed of Blitzen as = 7x
x×15+3×7x=144
15x+21x=144
36x=144
x=4
∴ Speed of Blitzen = 28 miles per hour and Speed of Nikolas=4 miles per hour
Hence, The respective speeds of Blitzen and Nikolas are 28 miles per hour and 4 miles per hour.
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Blake got a summer job delivering newspapers. He decided to keep a chart of how money he earns. Which equation could be used to show how money (m) Blake earns after h hours of working?
The equation could be used to show how money (m) Blake earns after h hours of working is m = 12 h
What is linear equation ?
Linear equation can be defined as equation in which the highest degree is one.
Given ,
Blake got a summer job delivering newspapers. He decided to keep a chart of how money he earns.
So, we have to find equation could be used to show how money (m) Blake earns after h hours of working
m = kh + b
(2,24 ) , (4,48 )
So substitute the given points in the equation ,
24 = 2k + b
48 = 4k+ b
So,
subtract the two equations,
2k = 24
k = 24 / 2
k = 12
substitute k=12 in 24 = 2k+b
we get,
24 = 2*12 + b
b = 24-24
b = 0
So, substitute k = 12 , b = 0
we get,
m = 12h + 0
m = 12 h .
Therefore, The equation could be used to show how money (m) Blake earns after h hours of working is m = 12 h
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The sum of the least and greatest of 3 consecutive even numbers is 84. Find the numbers.
When the total of the least and greatest digits of three consecutive even numbers is 84, the correct responses are 26, 28, and 30.
what is arithmetic progression ?An arithmetic progression is defined as a constant difference between terms that follow one another in a series. For instance, the number sequence 5, 7, 9, 11, 13, and 15 is an example of an exponential function with a tolerance of two. A progression with a set tolerance either between two consecutive numbers is referred to as a "arithmetic progression" (A.P.). Two types of mathematical progression are possible: series in mathematics with a finite length A finite geometric evolution is a line with a finite number of terms. The early, tardy, tolerance, the number of terms may all be calculated using the terms in the series.
given
Suppose three consecutive numbers are
X, X+2, X+4.
Considering the query,
X+X+2+X+4= 84,
3X+6=84
3X=84–6
3X=78
X=26.
When the total of the least and greatest digits of three consecutive even numbers is 84, the correct responses are 26, 28, and 30.
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car a leaves santa barbara at noon traveling south toward los angeles at mph. at 1pm car b leaves los angeles traveling north toward santa barbara at mph. the distance between the cars at noon was miles. if car b does not get pulled over, how many minutes after car b leaves will they pass each other?
The 11.25 minutes required after car b leaves will they pass each other and A meets B at 01:11:15 PM.
Car A leaves Santa Barbara at noon traveling south toward Los Angeles at 70 mph.
At 1pm car B leaves Los Angeles traveling north toward Santa Barbara at 90 mph.
The distance between the cars at noon was 100 miles.
If car B does not get pulled over, how many minutes after car B leaves will they pass each other?
:
Let t = travel time of Car B
then
(t+1) = travel time of Car A
:
Write a distance equation:
Speed tells us how fast something or someone is travelling. You can find the average speed of an object if you know the distance travelled and the time it took.
The formula for speed is speed = distance ÷ time. To work out what the units are for speed, you need to know the units for distance and time. In this example, distance is in meters (m) and time is in seconds (s), so the units will be in meters per second (m/s).
The formula speed = distance ÷ time can be rearranged, just like any other equation.
⇒90t + 70(t+1) = 100
⇒90t + 70t + 70 = 100
⇒160t = 100 - 70
⇒160t = 30
⇒t = 30/160
⇒t =0 .1875 hrs, 0.1875(60) = 11.25 minutes
⇒A meets B, at 01:11:15 PM
Therefore, the 11.25 minutes after car b leaves will they pass each other.
and A meets B at 01:11:15 PM.
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Car A leaves Santa Barbara at noon traveling south toward Los Angeles at 70 mph. At 1pm car B leaves Los Angeles traveling north toward Santa Barbara at 90 mph. The distance between the cars at noon was 100 miles. If car B does not get pulled over, how many minutes after car B leaves will they pass each other?
A mathematics teacher wanted to see the correlation between test scores and
homework. The homework grade (x) and test grade (y) are given in the accompanying
table. Write the linear regression equation that represents this set of data, rounding
all coefficients to the nearest tenth. Using this equation, find the projected test grade,
to the nearest integer, for a student with a homework grade of 35
Homework Grade (x) Test Grade (y)
78
87
85
78
74
76
41
55
90
88
88
83
81
81
52
62
The projected test grade for a student with a homework grade of 35 is 47.74.
What is slope intercept form of line?The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
Homework Grade (x) Test Grade (y)
78 90
87 88
85 88
78 83
74 81
76 81
41 52
55 62
Let us find the slope m=62-52/55-41
=10/14=0.714
62=0.714(55)+b
b=22.75
Now let us find the projected test grade, to the nearest integer, for a student with a homework grade of 35 is 47.74
So y=0.714(35)+22.75
y=47.74
Hence, the projected test grade for a student with a homework grade of 35 is 47.74.
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what verbal expressions are represented by the algebraic expression?
2x + 5
The verbal expression for the algebraic expression can be written as: "two times a number plus five" or "five more than two times a number."
What is an Algebraic Expression?An algebraic expression is a mathematical phrase that can contain numbers, variables, and operations. It can be simplified or evaluated for a specific value of the variable to find its numerical value.
The algebraic expression "2x + 5" represents the verbal expression "two times a number plus five" or can be written as "five more than two times a number."
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Two times a number plus ten times a second number is twenty. Thirty times the second number plus three times the first number is 45.
Calculating a binomial probability PROBLEM: When rolling two fair six-sided dice, getting a pair of ls is called "snake eyes." The probability of getting "snake eyes" on any roll is 1/36. Suppose that a game player rolls the two dice 80 times. Let X = the number of rolls that result in "snake cyes." Find P(X = 2). Interpret this value in context If two dice are rolled 80 times, then there is a 27.089% chance that we get a pair of snake eyes. Question 3 (25 points) Calculating a binomial probability PROBLEM: See the preceding alternate example. Should the player be surprised if fewer than 2 of the rolls result in snake eyes? Calculate an appropriate probability to support your answer.
No, if less than two of the rolls produce snake eyes, the player shouldn't be startled. Out of 80 rolls, there is a 97.78% probability of receiving fewer than two snake eyes, making this scenario highly probable.
P(X < 2) = 1 - P(X = 2) = 1 - 0.27089 = 0.97711
No, if less than two of the rolls produce snake eyes, the player shouldn't be startled. There is a 1/36 chance of receiving "snake eyes" on any roll. Accordingly, the likelihood of receiving two snake eyes out of 80 rolls is only 0.27089, or roughly 27%. The likelihood of receiving fewer than two snake eyes, on the other hand, is 0.97711, or roughly 97.78%, out of 80 rolls. As a result, statistically speaking, it is more likely that less than 2 of the rolls will produce snake eyes. The player shouldn't be shocked if less than two of the dice produce snake eyes.
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The cost of a stereo cable has risen to $21 today. Yesterday's cost was $16 . Find the percentage increase. Round your answer to the nearest tenth of a percent.
PLSSSSSSSSS HELPPPPPPPP!!!!!!!!!!!
Answer:
23.81%
Step-by-step explanation:
because 21-16 is 5 so 5/12 into a percentage is 23.81 percent.
1. (cards) assume we have a well-shuffled, standard deck of playing cards (a) how many poker hands (sets of 5 cards) consist of exactly 2 aces and 3 kings? (b) assume we deal the entire deck. what is the probability that the first king is dealt out on the 13th card ?
The number of poker hands consisting of 2 aces and 3 kings is 41,472.
The probability that the first king is dealt out on the 13th card is 1/52.
(a) There are 4 aces and 4 kings in a standard deck of playing cards, so there are C(4,2) = 6 ways to choose 2 aces out of 4, and C(4,3) = 4 ways to choose 3 kings out of 4. Then, there are C(48,3) = 17, 296 ways to choose the remaining 3 cards from the remaining 48 cards in the deck. The number of poker hands consisting of 2 aces and 3 kings is 6 * 4 * 17, 296 = 41,472.
(b) The probability that the first king is dealt out on the 13th card is 1/52, since there are 52 cards in a standard deck and the first king can be any of them. The probability that the first king is dealt out on the 13th card is independent of the order in which the other cards are dealt, so this is the final answer.
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At a gla vae factory 2 out of the lat 20 vae produced were chipped. Conidering thi data, how many of the next 10 vae would you expect to be chipped
Based on the data you provided, the proportion of chipped vae in the last 20 produced was 2/20 = 0.1.
Therefore, we would expect the number of chipped vae in the next 10 to be approximately 0.1 * 10 = 1.
Estimating Chipped Vae CountThe estimate of the number of chipped vae in the next 10 was determined by multiplying the proportion of chipped vae in the last 20 produced (0.1) by the number of vae to be produced in the next 10.
0.1 * 10 = 1
This estimate assumes that the proportion of chipped vae in the next production batch is the same as the proportion in the last 20. This is known as a point estimate and it's based on the information we have available.
Keep in mind that this is just a rough estimate and actual results may vary. Other factors such as changes in production processes or quality control measures may affect the proportion of chipped vae in the next batch.
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J.D. opened a savings account with $425. After 4 years, the total interest he earned was $10.20. What was the interest rate?
Answer: 1.2%
Step-by-step explanation:
Find the length of side to the nearest tenth.
Special right triangles
Answer:
see the attachment of the answer!
A company's profit (P) is related to its worker's average pay (x) y a linear equation. If the company's profit drops by $1500 per month for every increase $450 per year in the worker's average pay, what is the slope of the graph of the equation?
The slope of the graph of the equation is 40.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that a company's profit (P) is related to its worker's average pay (x) a linear equation.
We can write the linear equation as -
P = Kx
Now, the total profit drop in single year -
P = 1500 x 12
P = 18000
Now, we can write the slope as -
{m} = 18000/450
{m} = 1800/45
{m} = 40
Therefore, the slope of the graph of the equation is 40.
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Is this a function? Explain.
(-4, 8) , (-1, 2) , (2, -4), (5, -10)
Answer:
Yes, it is a function.
Step-by-step explanation:
Function is a mapping between two sets meaning we are creating a set of pairs where the first element of a pair comes from the first set and the second one from the second set. The first set is called function domain and the second one is called the set of function values.
There are two conditions that must be satisfied:
every element of the domain must be paired with an element from the set of valueseach element of the domain can be paired with only one element from the set of values.In our case the set: {-4, -1, 2, 5} would be our domain and the set: {8, 2, -4, 10} would be the set of values. We see that all elements of the domain have a pair and each of its element is paired with only one value (There are no pairs where for example -4 would be repeated as a first element).
Use table to find each product
According to the problem the product of (X —6)(3X + 4) is 3X² - 18X - 24.
What is product?Product is any item or service that is offered to the public for sale. It can be a physical product such as a car, a piece of clothing, or a computer, or it can be a service such as a haircut, a massage, or a restaurant meal. Products are typically developed to meet a customer's need or to solve a problem, and they are usually sold in exchange for money.
The product of (X —6)(3X + 4) can be found by using the distributive property and multiplying each term of the first binomial (X —6) by each term of the second binomial (3X + 4). This can be done by creating a table with the two binomials written out in two columns.
| X | -6 |
| 3X | 4 |
Then, multiply each term in the first column by each term in the second column and add the products together.
X*3X = 3X²
X*4 = 4X
-6*3X = -18X
-6*4 = -24
Therefore, the product of (X —6)(3X + 4) is 3X² - 18X - 24.
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A fair coin is tossed four times. A Is the evmt that at least one of the first three tosses was a head and B is the event that at least one of the last three tosses was a tail. Are A and B indepednent?
i said no because the outcome of the first three tosses affects the outcome of the last three tosses. if at least one of the first three tosses was a head, it increases the chance that at least one of the last three tosses will also be a tail. conversely, if at least one of the last three tosses was a tail, it increases the chance that at least one of the first three tosses was a head. so, the outcome of one event affects the outcome of the other event, thus, A and B are not independent events.
The solution is, A and C are not independent.
B and C are not independent either.
What is probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
here, we have,
By the multiplication rule, the sampling space has possible outcomes.
Let's compute P(A), P(B), P(C), P(A∩C), P(B∩C), P(A|C) and P(B|C).
As there are only two outcomes that does not have at least on tail in the first three tosses (H,H,H,H) and (H,H,H,T) then
P(A) = 14/16 = 7/8
Similarly, as there are only two outcomes that does not have at least on head in the last three tosses (H,T,T,T) and (T,T,T,T) then
P(A) = 14/16 = 7/8
A∩C and B∩C have 4 possible outcomes (T,H,T,T), (T,H,T,H), (H,H,T,T) and (H,H,T,H), so
P(A∩C) = P(B∩C) = 4/16 = ¼
P(A) given C and P(B) given C have the following probabilities:
P(A|C) = P(A∩C)/P(C) = 1
P(B|C) = P(B∩C)/P(C) = 1
Since P(A|C)≠P(A), A and C are not independent
Since P(B|C)≠P(B), B and C are not independent
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since u = 4 − 4x, then converting back to an expression in x we get the following. (remember to use absolute values where appropriate.) − 1/4 ln(|u|)+ c =
The value of expression of the equation in terms of u is x = (4 - u)/4.
the given expression is u = 4 - 4x
u +4x = 4
4x = 4 - u
x = (4 - u)/4
The value of expression of the equation in terms of u= (4 - u)/4.
given equation is converted in terms of u .
Equation
Equation in mathematics is an expression or a statement that comprises two algebraic expressions with the same value and are separated by an equal symbol in between them. It is a mathematically quantified form of a statement written otherwise.
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the complete question is ,
value of u convert the equation in terms of u.
u= 4 - 4x
Question below. Please leave a step-by-step! I am having issues finding this out without another bottom.
The length of side qs in triangle qrs is 6 units.
What is the length of side of a similar triangle?Two objects are similar in Euclidean geometry if they have the same shape or one has the same shape as the mirror image of the other. One can be obtained from the other by uniformly scaling (enlarging or contracting), possibly with additional translation, rotation, and reflection.When all three sides of a triangle are proportional to the three sides of another triangle, the two triangles are said to be similar.Given:
On the abc triangle,
ab = 5, ac = 3
And the qrs triangle,
qr = 10, qs = x(we have to find)
Because both triangles are similar, the ratio of their sides must also be congruent.
ac / qs = ab / rq
3/ x = 5/10
3/x = 1/2
x = 3(2)
x = 6
Therefore the length of side qs is 6 units.
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given that set q {1,2,3,4,5}
write down four proper subsets of set q,each with three elements
Answer:
a = {1,2,3}
b = {3,4,5}
c = {1,3,5}
d = {2,4,3}
Step-by-step explanation:
Answer:
Step-by-step explanation:
jvlvhj;vh i need the points sorry
ms. lee is shopping for a new electric warer heater. brand A cost $575 and uses 442 kiliwatt- hours per month. brand B cost $651 and uses 397 kiliwatt-hours per month. if electricity costs $0.17 per kilowatt-hour, how much would ms. lee save on electricity per month by buying brand B
Answer:
7.65
Step-by-step explanation:
Brand A:
442(times)0.17=75.14 each month
Brand B:
397(times)0.17=67.49 each month
75.14-67.49=7.65
Ms.Lee would save 7.65 each month with brand B
How Do You Find a Scale Factor in Similar Figures?
To find the scale factor of similar figures ratio the equivalent sides of the original figure to the generated one.
What is a scale Factor ?The scale factor is the ratio obtained by dividing the equivalent side lengths of like figures. The ratios in the previous example were all reduced to 3/4, so we can conclude that the scale factor of the triangles LMN and QRS is 3/4. A scale factor can also be thought of as a multiplier.
When both the original dimensions and the new dimensions are known, the scale factor may be determined. The following is a basic formula to determine a figure's scale factor: Dimension of the new shape divided by Dimension of the previous shape is the scale factor.
The ratio that establishes the proportionality between the sides of like figures is known as the scale factor. The scale factor of the pairs of sides must match for them to be proportionate to one another. In other words, comparable figures have the same scale factor and congruent angles and sides.
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What is a formula for the nth term of the given sequence? 32 8 2
Formula for finding the nth term of an arithmetic sequence:
[tex]an=a+(n-1)d[/tex]
an(nth term) = a(first term) + (n(term you are looking for) - 1) * d(common difference)
Function gcan be thought of as a translated (shifted) version of f(x)=x^2f(x)=x
Write the equation for g(x).
After translations function of g becomes g(x)=x²-1.
What is the translation?A translation in math moves a shape left or right and/or up or down. The translated shapes look exactly the same size as the original shape, and hence the shapes are congruent to each other. They just have been shifted in one or more directions.
The given function is f(x)=x².
When the shape is moved up by k units, then replace y with y + k.
When the shape is moved towards the left by k units, then replace x with x - k.
From the graph, we can see graph of function g is shifted 1 unit up and 2 units left.
Now, g(x)= f(x)+1-2
g(x)=x²-1
Therefore, after translations function of g becomes g(x)=x²-1.
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Rates
9
Jethro is planting flowers in his garden. He wants the ratio of tulips to roses to be 4 to 1. Jethro wants to plant a total of 45 flowers.
How many tulips should he plant?
OA. 34
OB. 36
OC. 11
OD.
9
) use truth tables to determine if the statements are logically equivalent and explain how you reached your conclusion. p →q ∨r , and p∧~q→r
p → q ∨ r and p ∧ ~q → r are not logically equivalent based on our truth table analysis.
To determine if two statements are logically equivalent, we can use truth tables. A truth table is a table that lists all possible combinations of truth values for the propositions in a logical formula and the resulting truth value for the formula.
The first statement is: p → q ∨ r
The second statement is: p ∧ ~q → r
We can construct the truth tables for each statement and compare the resulting truth values.
Here's the truth table for the first statement:
p | q | r | q ∨ r | p → (q ∨ r)
T | T | T | T | T
T | T | F | T | T
T | F | T | T | T
T | F | F | F | T
F | T | T | T | T
F | T | F | T | T
F | F | T | T | T
F | F | F | F | T
Here's the truth table for the second statement:
p | q | ~q | p ∧ ~q | p ∧ ~q → r
T | T | F | F | T
T | F | T | T | T
F | T | F | F | T
F | F | T | F | T
Comparing the truth tables, we can see that the truth values for the two statements are not the same for all combinations of truth values for p, q, and r. Hence, the given two statements are not logically equivalent.
In conclusion, p → q ∨ r and p ∧ ~q → r are not logically equivalent based on our truth table analysis.
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A picture of a parallelogram with width 38in. and side 44in. A perpendicular line with a height of 35in. is shown inside the parallelogram and forms a right triangle.
Find the area of the parallelogram. The figure is not drawn to scale.
The area of the parallelogram is 1710 square inches
How to find the area of the parallelogram.From the question, we have the following parameters that can be used in our computation:
Base = 38 inches
Side = 44 inches
Height = 35 inches
We can find the area of the parallelogram by multiplying the base (width) by the height
Using the above as a guide, we have the following:
Area = 38 * 45
Evaluate
Area = 1710
Hence, the area is 1710 square inches
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Answer:
Area of a parallelogram (base x height)
Given:-Base = 38 in.Height = 35 in.Area of the parallelogram = 38 x 35
Area of the parallelogram = 1,330 in.²
Can someone please answer this?
Answer:
149 [tex]ft^{2}[/tex]
Step-by-step explanation:
The total area is
20 x 9.25 = 185
The two triangles together would be
6 x 6 = 36 subtract this from 185
185 - 36 = 149
