If we want to choose 6 objects, without replacement, from 8 distinct objects then total number of ways are 20160 (8x7x6x5x4x3).We can use the concept of permutation to find number of ways.
The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation. Simply put, a permutation is a term that refers to the variety of possible arrangements or orders. The arrangement's order is important when using permutations.
Combination and permutation are part of the accounting discipline's mathematical branch. Combinations are used in business decision-making to choose from among the available objects. In contrast, the arrangement of such objects that are chosen through combinations uses permutations.
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Hi! Can someone please explain?I will give brainliest :)
Answer:
$8.20
Step-by-step explanation:
2.35+2.35=4.7
4.7+1.5=6.2
6.2+2=8.2
Joel digs a hole at a rate of 3/5 feet every 10 minutes. After digging for 30 minutes, Joel places a bush in the hole that fills exactly 1/2 feet of the hole. Relative to ground level, what is the elevation of the hole after placing the bush in the hole? Enter your answer as a simplified mixed number in the box.
After excavating and inserting bushes, the hole's elevation in feet is 1 1/10 feet.
3/5 feet per 10 minutes are dug up on average.
After 30 minutes, the elevation or depth of the hole:
3/5 × (30/10) = (3/5 × 3) = 9/5 feets
Consequently, after 30 minutes, the hole's height will be 9 1/2 feet.
Elevation after planting bushes in half of the hole:
After 30 / 2 minutes, the hole's elevation was 2/ (9/5)
=2/(9 /5 )
= (9 /5 ) × 1/2
= 9/10 feet.
Consequently, the hole is elevated by 1 1/10 of a foot above the surrounding ground.
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Show that the set {-1, 0, 1} is closed under multiplication
The statement that the set {-1, 0, 1} is closed under multiplication, is true and can be proven.
As per the question statement, we are provided with a set {-1, 0, 1}.
We are required to determine if the above mentioned set is closed under multiplication or not.
To solve this question, we simply need to verify if the products of every distinct combination of 2 elements from the concerned set, belongs to the set itself or not, i.e., if we take any two elements "x" and "y", say, from the set "Z", then, [(x*y) ∈ Z].
Here, [tex][(-1)*0]=0[/tex], i.e., belongs to set {-1, 0, 1}.
[tex][(-1)*1]=(-1)[/tex] i.e., also belongs to set {-1, 0, 1}.
Finally, [tex](0*1)=0[/tex] i.e., also belongs to set {-1, 0, 1}.
Since, the products of every distinct combination of 2 elements from the concerned set, belongs to the set itself, the statement that the set
{-1, 0, 1} is closed under multiplication, is true and proven.
Set closed under multiplication: This means that, for any set say "Z", the product of distinct combinations of it's elements, say (x*y) belongs to Z, such that [(x, y) ∈ Z].To learn more about Sets closed under multiplication, click on the link below.
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Which of the following represents
this graph?
-1
a. |2x - 3|< 4
b.x - 3|< 12
c. |2y - 7 > 9
d. 5x + 2 <3
8
Answer:
c
Step-by-step explanation:
The average of -1 and 8 is 7/2, so the absolute value should equal 0 at 7/2.
The only option that satisfies this is c.
Multiply 6 1/4 x 3 3/5
In a day care center each child takes three classes and either passes or fails each class. The grades are shown in the table below. P represents a passed class, and F represents a failed class. Let X represent the number of classes failed by a child. Construct a probability distribution for X. Arrange x in increasing order and write the probabilities P(x) as simplified fractions. Child Grades Child 1 PFP Child 2 PPF Child 3 FFP Child 4 PPP Child 5 PFP Child 6 PPF Child 7 FPF Child 8 PPP Provide your answer below:
The probability distribution for X in a day care center where each child takes three classes and either passes or fails each class will be:
0 = 1/4
1 = 1/4
2 = 1/4
How to illustrate the information?It should be noted that from the information, the grades are shown in the table below.
P represents a passed class.
F represents a failed class.
X represent the number of classes failed by a child.
The probability that the number of classes failed by a child is 0 will be:
= 2/8
= 1/4.
The probability that the number of classes failed by a child is 1 will be:
= 4/8
= 1/2
The probability that the number of classes failed by a child is 2 will be:
= 2/8
= 1/4.
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42
== (3)
b= (10)
Write a + b- c as a column vector
The column vector is discussed below.
What is column vector?In order to write a vector as a column vector: Work out the horizontal component ( x component). Work out the vertical component ( y component). Write the column vector.
Given:
a + b- c
So, If the number is positive, the direction is to the right.
If the number is negative, the direction is to the left.
Also, If the number is positive, the direction is upwards.
If the number is negative, the direction is downwards.
So, according to that 'a' will be in right ( upward) direction and 'b' also be in right ( upward) direction.
Then, 'c' is negative in left ( downward ) direction.
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4x^2 - 25 < 0 inequality
Answer:
x∈(−25,25)
SOLUTION STEPS4x2−25<0
Add 425 to both sides.
x2<425
Calculate the square root of 425 and get 25. Rewrite 425 as (25)2.
x2<(25)2
Inequality holds for ∣x∣<25.
∣x∣<25
Rewrite ∣x∣<25 as x∈(−25,25).
x∈(−25,25)
Answer: x > 5/4
First, add 25 to both sides
4x² < 25
Then take the square root
4x < 5
Finally, isolate the variable by dividing by 4
x < 5/4
Because you divided, the sign gets flipped
x > 5/4
Hope this helps!
Find the slope of the line graphed below.
Answer:
m=4/3
Step-by-step explanation:
slope=rise/run or y=mx+b
rise/run=8/6=4/3
In a given bag of M & M's, 16 were yellow, 15 were green, 21 were brown, and 11 were red.
How many M&M's were in the bag?
What fraction were yellow?
What fraction were green?
What fraction were brown?
What fraction were red?
Answer:
There are 63 M&M's in the bag when all of them are added together.
16 out of 63 (16/63) were yellow.
5 out of 21 (5/21) were green. This answer is simplified. The original is 15/63.
1 out of 3 (1/3) were brown. This answer is simplified. The original is 21/63.
11 out of 63 (11/63) were red.
Tip:
To find the fraction of something, put the total on the bottom and the wanted portion on the top.
Example: 5 yellow and 10 red birds were in a cage. Which fraction were yellow?
We put the total of birds (5+10 = 15) on the bottom and the portion wanted ("5 yellow") on the top. The fraction is 5 out of 15 (5/15). This fraction can be simplified because 5 goes into 15 three times (5 x 3 = 15), so divide the fraction 5/15 by 3 to get 1/3. (5 goes into 5 one time.)
If 3sinθ + 4cosθ = 5, Prove that tanθ= 3/4.
I'll use x in place of θ
Let's isolate the sine term and then square both sides
3sin(x) + 4cos(x) = 5
3sin(x) = 5-4cos(x)
(3sin(x))^2 = ( 5-4cos(x) )^2
9sin^2(x) = 25-40cos(x)+16cos^2(x)
9sin^2(x) = 25-40cos(x)+16(1-sin^2(x))
9sin^2(x) = 25-40cos(x)+16-16sin^2(x)
9sin^2(x)+16sin^2(x) = 25-40cos(x)+16
25sin^2(x) = 41-40cos(x)
25(1-cos^2(x)) = 41-40cos(x)
25-25cos^2(x) = 41-40cos(x)
Now let w = cos(x), so we now have the following
25-25w^2 = 41-40w
25w^2-40w+41-25 = 0
25w^2-40w+16 = 0
(5w - 4)^2 = 0
5w-4 = 0
w = 4/5
Therefore cos(x) = 4/5
Use the pythagorean theorem or unit circle to find that if cos(x) = 4/5, then it leads to sin(x) = 3/5. This is exactly because of the 3-4-5 right triangle.
Then lastly,
tan(x) = sin(x)/cos(x)
tan(x) = sin(x) ÷ cos(x)
tan(x) = (3/5) ÷ (4/5)
tan(x) = (3/5) * (5/4)
tan(x) = (3*5)/(5*4)
tan(x) = 3/4
x−5≥−8 Solve the inequality for x. Graph the solution.
HELP! ALgebra 2 Honors
How do you find the x-intercept and y-intercept of
f(x)-2|x+4|-3
Teri tau KO tailai Mubarak ha bak
2)
Which set is of whole numbers but not natural numbers?
Of 1 1 11
2'4'8
0 {1/1/2
;}}
O {-2,-3,-4}
O{0, 1, 2, 3}
O {√-1,√-4,√-5}
O {√2, T, √3}
The set which represents whole numbers but are not natural numbers is:{0,1,2,3 }
Given, we have the following sets:
{₋2,₋3,₋4} = Integers
Negative numbers and all entire numbers are both considered integers. A number without a decimal or fractional element is known as an integer, which encompasses both positive and negative numbers, including zero.
{0,1,2,3} = whole numbers
Whole numbers refer to all natural numbers, including zero (0). We are aware that the term "natural numbers" refers to a group of counting numbers beginning with 1, 2, 3, and so forth. Simply said, a collection of numbers that are whole numbers are those that do not contain any fractions, decimals, or even negative integers. There are zeroes and a group of positive integers in it. whereas all positive integers from 1 to infinity are included in the number system, which also contains natural numbers, which are also used for counting. There is no zero included.
{√₋1 , √₋4 , √₋5 }= Irrational numbers
We are aware that the only numbers that cannot be stated in the form of p/q, where p and q are integers and q 0, are real numbers. For instance, the numbers √5, √3, and so on are irrational.
hence we get the set which represents whole numbers but not natural numbers is {0,1,2,,3,4}
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How much interest would 2000 earn, with simple interest, in two years at the rate of 1.2%?
The simple interest, in two years at the rate of 1.2% is 880
In this case, we must calculate how much interest 2000 would earn compounded yearly over two years at a rate of 1.2.
I = 880 in interest earned
Annually, the system may be evaluated in terms of simple interest.
A = P(rt) for the first year, where r = 1.2 and t = 1.
Therefore;
A = 2000(1.2×1).
A = 2400.
As a result, the revised Principal amount for the second year is 2400.
As a result, A' = 2400 (1.21).
A' = 2880.
As a result, the sum owing after two years is 2880.
However, because the initial principal is $2,000,
The interest is defined as I = A' - P, or I = 2880 - 2000.
I = 880 as a result of interest.
Simple interest is computed as S.I. = P R T, where P = Principal, R = Annual Rate of Interest in %, and T = Time, commonly expressed as the number of years. The interest rate is expressed as a percentage r% and is written as r/100.
The principle is the money borrowed from the bank or invested at the outset. P represents the principal.
Rate: The rate of interest at which the principle amount is handed to someone for a specific period of time; the rate of interest can be 5%, 10%, or 13%, for example. R represents the interest rate.
Time is the length of time for which the primary amount is supplied to someone. T represents time.
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a kind of sampling strategy least likely to produce statistics that are good estimates of population perameters is a
A kind of sampling strategy least likely to produce statistics that are good estimates of population parameters is a haphazard sample.
What is haphazard sampling ?A haphazard sampling is method of sampling in which the performer does not intend to use a systematic approach for choosing a sample rather they do the random selection without using anu conscious bias.
Haphazard sampling assumes that all population units are alike but unless they are really similar there is always a chance of selection falling prey to biases. Therefore, haphazard sample is least likely to produce statistics that are good estimates of population parameters.
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if a + b = 23 and a= 47 what would B be?
Answer:
B = -24
Step-by-step explanation:
a + b = 23
Since a = 47
47 + b = 23
Subtract 47 from each side
47 - 47 + b = 23 - 47
Therefore:
B = -24
Answer:
b = -24
Step-by-step explanation:
a + b = 23
Substitute 47 for a.
47 + b = 23
Rearrange the equation.
23 - 47 = b
-24 = b
Check your answer by substituting the value you found for b into the equation.
47 + (-24) = 23
Need help with my homework. Do not really get how I am supposed to do it.
PLEASE HELP 50 POINTS!!
In the triangle below, which of the following equations could be used to find z?
The equation that can be used to find z in the right triangle is sin 28° = 20 / z
How to find the side of a right triangle?A right angle triangle is a triangle that has one of its angles as 90 degrees.
The side and angles of a right angle triangle can be found using trigonometric ratios.
The triangle XMI is a right angle triangle.
where
∠M = 90 degrees
∠X = 28 degrees
∠I = ?
Therefore, the side z can be found as follows;
sin ∅ = opposite / hypotenuse
where
opposite side = 20
∅ = 28°
Hence,
sin 28° = 20 / z
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Answer: a
Step-by-step explanation:
a
What is the value of x?
Enter your answer in the box.
The value of x in the given object is 12.
What is the value of x?The given shape is an equilateral triangle. A triangle is a three-sided polygon with three edges and vertices. The sum of angles in a triangle is equal to 180 degrees.
An equilateral triangle is a triangle in which the three angles are equal. This means that each angle in an equilateral triangle measures 60 degrees. Also, in an equilateral triangle the three sides are equal.
Since, all the three sides of an equilateral triangle is equal, the expressions for their sides can be equated to each other to determine the value of x
4x - 10 = 5x - 22
Combine similar terms: 22 - 10 = 5x - 4x
Add similar terms: 12 = x
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Find the mode for the following distribution. Number Frequency 36 3 40 5 44 9 48 7 52 7 56 5 60 3 What is the mode? 48 44 52 40
The mode for the following distribution is-
Number Frequency 36, 3, 40, 5 ,44, 9, 48, 7 ,52 7, 56, 5, 60, 3
is 56.
Mode is most occurring number is 56.
One of the values of the measurements of central tendency is the mode. This figure offers us an approximate notion of which elements in a data collection appear the most frequently.
For example, you may be aware that a college offers ten distinct courses to students. Now, out of them, the course with the most student registrations will be counted as the mode of our supplied data (number of students taking each course). Overall, mode notifies us about the item with the highest frequency in the data set.
The mode is one of the values of the central tendency measurements. This number offers us a sense of which elements in a data collection appear the most frequently.
For example, you may be aware that a college offers ten distinct courses to students. Out of these, the course with the most student registrations will be counted as the mode of our supplied data (number of students taking each course). Overall, mode informs us about the most frequent item in the data collection.
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Answer:
The answer is 44, as it occurs most frequently. The easiest way to remember this is "mode" equals "most".
Zoe and Claire are sisters. They are giving clues about their heights. Write an equation and solve to determine the height of both Zoe and Claire. Claire is twice as tall as Zoe. Together, Claire and Zoe are 108 inches tall.
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The explanation is below. Enjoy!
- - - - - - - - - - - - - - - - - - - - - - - -
First off- I'll divide the total by two. This ensures they both have a basic height.
108 / 2 = 54
Say Claire is double Zoe's height, divide 54 (Zoe's height) by 2 and give the quotient to Claire.
54 / 2 = 27
(Claire's height)
54 + 27 = 81 inches
(Zoe's height)
27 inches
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Have a great day/night!
(Consider leaving a Brainly, it'd help me quite a bit!)
~pinetree
Yossi used to have a square garage with ft of floor space. recently built an addition to it. The garage is still a square, but now it has 50% more floor space. What was the length of one side of the garage originally? What is the length of one side of the garage now? What was the percent increase in the length of one side?
The length of one side of the garage originally is 18.17 feet.
The length of one side of the garage now is 22.25 feet.
The percent increase is 22.4%.
What is the increase in the length of the garage?A square is a quadrilateral with four sides of equal length. A square has two diagonals of equal length that intersect at right angles.
Given the area of a square, the length of one side can be determined by calculating the square root of the area.
Area of the square = length²
Length of one side of the square = √area
√330 = 18.17 ft
Area of the garage after it was increased : (1 + percentage increase) x initial area
(1 + 0.5) x 330
1.5 x 330 = 495 feet²
Length of the side of the garage after it is increased = √495 = 22.25 feet
The percentage increase = (22.25 / 18.17) - 1 = 0.224 = 22.4%
Here is the complete question:
Yossi used to have a square garage with 330ft of floor space. recently built an addition to it. The garage is still a square, but now it has 50% more floor space. What was the length of one side of the garage originally? What is the length of one side of the garage now? What was the percent increase in the length of one side?
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Suppose that you invest $5800 in an account that earns interest at an APR of 4.4%, compounded monthly. Determine the accumulated balance after 7 years.
After 7 years, the total amount accumulated is $13,691.43.
What is described as annual percentage rate (APR)?An annual percentage rate (APR) is the annual interest rate charged on a loan or earned on an investment.Even before agreement is signed, financial firms must disclose the APR of a financial instrument.To protect customers from misleading advertising, the APR offers a consistent foundation for introducing annual interest rate information.For the given question;
The formula for compound interest is;
CI = P(1 + r/n)∧nt
The rate rate of interest is according to APR; r = 4.4% = 0.044
P = principal amount ($5800).
t = time in years (7 years)
n = number of times interest given per time period
n = 7×12 = 84 (as compounded monthly)
CI = 5800( 1 + 0.044/84)∧(84×7)
CI = 5800×(1.36)
CI = 7891.43
Thus, the total interest formed after 7 years.
Total amount in bank = principal amount + CI
= 5800 + 7891.43
= 13,691.43
Therefore, the total amount accumulated after 7 years is $13,691.43.
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I’m confused pls help
Answer: answer is 3
Step-by-step explanation: it is 3 because you do 1 d.p. plus a and b and you get 3
PLS HELP THIS IS DUE FIRST THING TMR
Answer:
m<a=45
m<b=90
m<c=45
m<d=45
m<e=90
m<g=130
m<h=50
m<i=130
m<k=85
m<l=95
m<n=95
an amusement park sells child and adult tickets at a ratio of 7 child tickets for every 1 adult ticket. on saturday, they sold 147 child tickets. how many total tickets did the amusement park sell on saturday?
Answer:
189 tickets
Step-by-step explanation:
The ratio 8 : 1 has a difference of 7 ratio units. The difference in tickets is 147, so each ratio unit must represent ...
(147 tickets)/(7 ratio units) = 21 tickets/ratio unit
The total sales was 8+1 = 9 ratio units, so was ...
(9 ratio units)(21 tickets/ratio unit) = 189 tickets
brainy please
Pls help me as fast as possible
What is 4389+342 equal to
Answer:
4731
Step-by-step explanation:
4389+342=4731
pls don't forget to mark as brainliest
Two parallel lines cut by a transversal. The transversal makes 4 angles with the top line. Angles 1 and 2 are above the line and angles 3 and 4 are between the lines. The transversal also makes 4 angles with the bottom line. Angles 5 and 6 are between the lines and angles 7 and 8 are below the bottom line. Between the lines, angles 3 and 6 are on opposite sides of the transversal and angles 4 and 5 are on opposite sides of the transversal. A. ∠3 ≅ ∠2 because they are alternate interior angles. B. m∠1 + m∠3 = 180 because they form a straight angle. C. ∠3 ≅ ∠6 because they are alternate interior angles. D. ∠1 and ∠6 are supplementary because ∠3 ≅ ∠6 and m∠1 + m∠3 = 180. E. ∠1 ≅ ∠3 because they are vertical angles.
Based on this parallel lines cut by a transversal, the true statements include the following:
B. m∠1 + m∠3 = 180 because they form a straight angle.
C. ∠3 ≅ ∠6 because they are alternate interior angles.
D. ∠1 and ∠6 are supplementary because ∠3 ≅ ∠6 and m∠1 + m∠3 = 180.
What are parallel lines?Parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.
What is the Alternate Interior Angles Theorem?The Alternate Interior Angles Theorem states that when two (2) parallel lines are cut through by a transversal, the alternate interior angles that are formed are congruent.
What is a supplementary angle?A supplementary angle can be defined as two (2) angles or arc whose sum is equal to 180 degrees (180°).
In conclusion, ∠1 and ∠6 are supplementary angles because ∠3 is congruent to ∠6 and m∠1 + m∠3 = 180 degrees as shown in the image attached below.
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Complete Question:
Select all the true statements. Two parallel lines cut by a transversal. The transversal makes 4 angles with the top line. Angles 1 and 2 are above the line and angles 3 and 4 are between the lines. The transversal also makes 4 angles with the bottom line. Angles 5 and 6 are between the lines and angles 7 and 8 are below the bottom line. Between the lines, angles 3 and 6 are on opposite sides of the transversal and angles 4 and 5 are on opposite sides of the transversal.
A. ∠3 ≅ ∠2 because they are alternate interior angles.
B. m∠1 + m∠3 = 180 because they form a straight angle.
C. ∠3 ≅ ∠6 because they are alternate interior angles.
D. ∠1 and ∠6 are supplementary because ∠3 ≅ ∠6 and m∠1 + m∠3 = 180.
E. ∠1 ≅ ∠3 because they are vertical angles.