The statement which is true about the two equilateral triangles is b)The two triangles are the same shape but not the same size. So, correct option is b.
In calculation, a symmetrical triangle is a triangle where every one of the three sides have a similar length. In the natural Euclidean calculation, a symmetrical triangle is likewise equiangular; that is, every one of the three inward points are additionally compatible to one another and are each 60°. It is likewise an ordinary polygon, so it is additionally alluded to as a normal triangle.
Some of hypotheses which are made sense of utilizing symmetrical triangle:
Morley's trisector hypothesis expresses that, in any triangle, the three marks of convergence of the contiguous point trisectors structure a symmetrical triangle.Napoleon's hypothesis expresses that, in the event that symmetrical triangles are built on the sides of any triangle, either all outward, or all internal, the focuses of those symmetrical triangles themselves structure a symmetrical triangle.The side length of the primary symmetrical triangle is 3 inches.The side-length of the second symmetrical triangle is 4 inches.Since both the triangles are symmetrical triangles, in this way they have same shape.
Be that as it may, the two triangles have different side lengths in this way they have different size.
Hence, option b is correct.
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(Complete question) is:
on a piece of paper, use a protractor and a ruler to construct two equilateral triangles: one with a side length of 3 inches and one with a side length of 4 inches. which statement is true about the two triangles?
a. The two triangles are the same size but not the same shape.
b. The two triangles are the same shape but not the same size.
c. The two triangles are the same size and same shape.
d. It is impossible to construct equilateral triangles with these side lengths.
A bucket can hold a total of 5 gallons of water. If the bucket is 9/20 full, how much water is in the bucket?
Answer:2.25 gallons
Step-by-step explanation:
select the first correct reason why the given series converges. a. convergent geometric series b. convergent p series c. comparison (or limit comparison) with a geometric or p series d. alternating series test e. ratio test
Because it diverges using a comparison test, the correct answer is an option (E).
What is a comparison test?The comparison test, also known as the direct comparison test to distinguish it from other closely related tests, offers a method for determining whether an infinite series or an improper integral will converge or diverge.
The test is effective in both situations by contrasting the given series or integral with one whose convergence characteristics are known.
So, refer to the image attached below.
According to the image which has the reason for convergence and divergence, we know that the correct answer would be option (E).
The reason is the comparison test.
Therefore, because it diverges using a comparison test, the correct answer is an option (E).
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Suppose that a monopolistically competitive firm must build a production facility in order to produce a product. The fixed cost of this facility is FC = $24. Also, the firm has constant marginal cost, MC = $3. Demand for the product that the firm produces is given by P = 27- 3Q.
Fill in the entire table below. All of the numbers you fill in will be integers (no decimals), some have been added.
Quantity of Output Price Total Cost Average Total Cost Total Revenue Profits
1 2 3 4 5 7.8 6 7 6.4 8 9 5.7 B. How many units of output will the firm produce if it maximizes its profit?
C. What price should this firm charge if it wants to maximize its profit?
The output firm will get maximum profits when the quantity is 4 units and the company will charge a price of $15 for maximum profit.
The fixed cost of this facility is FC = $24. Also, the firm has constant marginal cost, MC = $3
Demand for the product that the firm produces is given by P = 27- 3Q.
The total cost is calculated by adding fixed cost and variable cost.
TC = FC + VC
Average total cost = total cost / quantity
Quantity price (37 - 3Q) fixed cost variable cost total cost average cost
1 27 - 3(1) = 24 24 3 (1) 27 27
2 27 - 3(2) = 21 24 3(2) = 6 30 15
3 27 - 3(3) = 18 24 3(3) = 9 33 11
4 27 - 3(4) = 15 24 3(4) = 12 36 9
5 27 - 3(5) = 12 24 3(5) = 15 39 7.8
Upon analysing the table we can say that
B) the number of output units is 4
C) Maximum profit is when price is $15
Therefore, the maximum profit is when the output units is 4 and the company will charge a price of $15 for maximum profit.
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Assume that the probability a child is a boy is 0.51 and that the sexes of children born into family are independent. What is the probability that a family of five children hasa. exactly three boys?b. all girls?c. at least one girl?
a) Probability of exactly three boys is 0.3185
b) Probability of at least one boy is 0.9717
c) Probability of at least one girl is 0.9655
d) Probability of all of same sex is 0.06275
What is probability?
Probability refers to potential. A random event's occurrence or the outcome is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means.The potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.a) Probability of exactly three boys
Choose 3 out of 5 in C(5,3)=10 ways
So probability is:10*0.51^3*0.49^2
~0.3185
(b) Probability of at least one boy
p(at least one boy)=1-p( all girls)
=1-0.49^5
=0.9717
c) Probability of at least one girl
p(at least one girl)=1-p( all boys)
=1-0.51^5
=0.9655
d) Probability of all of same sex
p(all of same sex)=p(all boys)+p(all girls)=
0.51^5+0.49^5
=0.06275
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(a) what was the average newspaper circulation from 1986 through 2000. (round your answer to three decimal places.) 557.680 incorrect: your answer is incorrect. million newspapers (b) in what year was the newspaper circulation closest to the average circulation from 1986 through 2000? (round your answer up to the nearest integer.)
The year becomes 1993, when the newspaper circulation is closest to the average circulation.
Part a:
The function is n(x)=0.00792x^3−0.37x^2+3.557x+51.588
The formula for the average of the function is 1b−a∫baf(x)dx
The year 1986 corresponds to 6 and 2000 corresponds to 20 as x is the number of years since 1980.
Obtain the average:
1b−a∫baf(x)dx==≈1/20−6∫20-6[0.00792x^3−0.37x^2+3.557x+51.588]dx
1/14[0.00792x^4/4−0.37x^3/3+3.557x^2/2+51.588x]20-6
51.70094
Therefore, the average newspaper circulation from 1986 to 2000 was 51.70094.
Part b:
Now, the equation is obtained as
0.00792x^3−0.37x^2+3.557x+51.588=51.70094
0.00792x^3−0.37x^2+3.557x−0.11294=0
Obtain the value of x using an online graphing calculator as follows:
Thus, the value of x becomes 13.481
Hence, 1993 is the year of the closest average circulation
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If there are 39 students and 4 have blue eyes what is the fraction?
Answer:
4/39
Step-by-step explanation:
You want to know the fraction of 39 students represented by the 4 that have blue eyes.
FractionThe fraction is the ratio of the part of interest to the whole.
(students with blue eyes)/(total number of students) = 4/39
The question is below! Will mark brainliest! Best answer!
Answer: 315 children and 15 adults
Step-by-step explanation:
15 x 21 = 315
315 + 15 = 330
c = 315
a = 15
(7, 5) and (8, 7). What is its equation in slope-intercept form?
Answer:
y = 2x - 9
Step-by-step explanation:
The slope is the change in y over the change in x. From the 2 points, the y's are 7 and 5. The x's are 8 and 7.
[tex]\frac{7-5}{8-7}[/tex] = [tex]\frac{2}{1}[/tex] = 2
2 is the slope.
Now we need to find the y intercept (b). Use one of the points on the line. It does not matter which one. I am going to use (8,7)
slope (m) = 2
x = 8
y = 7
y=mx + b
7 = 2(8) + b Plug in what we know and solve for b
7 = 16 + b Subtract 16 from both sides
-9 = b
The y intercept (b) is -9
y = mx + b
y = 2x -9
Evaluate the expression for n = 2 and p = –6.
np + n =
Answer: -10
Step-by-step explanation:
Substitute the numbers in for the variables.
np + n = (2)(-6) + 2
-12 + 2
-10
a number, y, is equal to twice the sum of a smaller number and 3. the larger number is also equal to 5 more than 3 times the smaller number. which equations represent the situation? 2 x minus y
The equations represent the given situation is:
2x - y = -6
3x - y = -5
where, x is the smaller number and y is the larger number.
Let the smaller number be x.
We have been given a number, y, is equal to twice the sum of a smaller number and 3
So, we get an equation,
y = 2(x + 3)
y = 2x + 6
2x - y = -6
The larger number is also equal to 5 more than 3 times the smaller number.
So, we get an equation,
y = 5 + 3x
3x - y = -5
Therefore, the equations represent the situation:
2x - y = -6
3x - y = -5
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y is five times X +15
a rectangle has a length of 1 inches and a width of 6 inches whose sides are changing. the length is increasing by 4 in/sec and the width is shrinking at 2 in/sec. what is the rate of change of the perimeter?
The rate of change of the perimeter is 4 in/sec .
In the question ,
it is given that ,
the length of the rectangle is [tex]=[/tex] 1 inch
the width of the rectangle is = 6 inch
the rate of increasing length is (dL/dt) = 4 in/sec
rate of shrinking width is (dW/dt) = -22 in/sec ,
We know that the perimeter of the rectangle is = 2(L + W) ,
that is , P = 2L + 2W ,
Differentiating perimeter with respect to time "t" ,
we get ,
dP/dt = 2 × ( dL/dt) + 2 × (dW/dt )
Substituting the values from above ,
we get ,
= 2 × (4) + 2 × (-2)
= 8 - 4
= 4
Therefore , the required rate of change is = 4 in/sec .
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rosie is driving from knoxvile, tennesse orlando, florida. she drives 317.88 miles before she stops for lunch and then another 203 4/5 miles before taking a break. rosie has driven 4/5 of the entire trip. how many total miles is her trip?
The total miles of the trip are 521.68 miles.
What is addition?Addition in maths, a process of combining two or more numbers.
Given that, Rosie drives 317.88 miles before lunch and then [tex]203\frac{4}{5}[/tex] miles before break,
Total miles = 317.88 + [tex]203\frac{4}{5}[/tex] miles = 521.68 miles
Hence, The total miles of the trip are 521.68 miles.
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A store manager would like to set the three-digit code of the store's new safety vault. How many possible 3-digit code choices does he have if he can pick digits from 0 to 9 with repetition allowed?.
Answer: 270 I think
Step-by-step explanation:
try it you can get this right
PROBLEM SOLVING A train travels from Orlando to Miami, and then back to Orlando. The table shows the numbers of tickets purchased for each leg of the trip. The cost per ticket is the same for each leg of the trip. Is there enough information to determine the cost of one coach ticket?
Answer:
Step-by-step explanation: 10.75
6 3/ 4 divide by 4 1/2
The value of the equation A = ( 6 3/4 ) / ( 4 1/2 ) is 3/2 or 1 1/2
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the first number be A = 6 3/4
A = 27/4
Let the second number be B = 4 1/2
B = 9/2
Now , the equation is C = A/B
The value of C = A / B
Substituting the values of A and B in the equation , we get
Value of C = ( 6 3/4 ) / ( 4 1/2 )
Value of C = ( 27/4 ) / ( 9/2 )
Value of C = ( 27 / 9 ) / 2
Value of C = 3 / 2
Therefore , the value of C is 3/2 or 1 1/2
Hence , The value of the equation A = ( 6 3/4 ) / ( 4 1/2 ) is 3/2 or 1 1/2
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The city council voted on a new tax. 63 council members voted in favor of the tax. The
council has 90 members. What percentage of the council members voted in favor of the tax?
Write your answer using a percent sign (%).
Answer: 70%
Step-by-step explanation:
A CBS News/New York Times poll found that 329 out of 763 randomly selected adults said they would travel to outer space in their lifetime, given the chance. Estimate the true proportion of adults who would like to travel to outer space with 88% accuracy. Round your answers to at least three decimal places.
The true proportion of adults is in the interval 0.4026< P< 0.4594.
Here we have to estimate the true population of adults who would like to travel to outer space with 88% accuracy.
Data provided:
selected (x) = 329
Total(n) = 763
Sample proportion (p') = x/n
= 329/ 763
= 0.431
Critical z-value = 1.59
margin of error(E) = z[tex]\sqrt{p'( 1-p')/n}[/tex]
= 1.59 [tex]\sqrt{0.431(1-0.431) / 763}[/tex]
= 1.59 × 0.0179
= 0.0284
88% confidence interval is:
(p' ± E) = ( 0.431 ± 0.0284)
= 0.4594 and 0.4026
Therefore the estimate is 0.4026< P< 0.4594.
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Given the algebraic expression (125x^7/3) ^-1/3 create an equivalent expression
The resulting value of the given indices expression is: [tex]\frac{1}{5x^{7/3}}[/tex]
What is indices and exponents?A term's multiplicative history can be determined by an index, which is a discrete number. Indexes is the plural of index.
The exponentiation operator is the caret (). It is important to distinguish the exponent operator from the base-10 exponent sign. In a numeric literal, a base-10 exponent sign (scientific notation) can be represented by either an uppercase "E" or a lowercase "e."
[tex](125x^{7/3})^{-1/3}[/tex]
Using the indices law that states;
[tex](a^n)^m = a^{mn}[/tex]
Given,
[tex](125x^{7/3})^{-1/3}[/tex]
Since, [tex](125x^{7/3})^{-1/3}[/tex]= [tex][((5x)^3)^{7/3}]^{-1/3}[/tex]
= [tex][(5x)^7]^{-1/3}[/tex]
= [tex]5x^{-7/3}[/tex]
= [tex]\frac{1}{5x^{7/3}}[/tex]
Hence the resulting value of the given indices expression is: [tex]\frac{1}{5x^{7/3}}[/tex]
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nine tiles are numbered 1, 2, 3, . . . , 9, respectively. each of three players randomly selects and keeps three of the tiles, and sums those three values. the probability that all three players obtain an odd sum is m/n, where m and n are relatively prime positive integers. find m n.
The value of m and n from the obtained probability is equal to 3 and 14 respectively.
As given in the question,
Nine tiles numbered 1, 2, .....9
Number of odd numbered tiles are 1,3,5,7,9 = 5
Number of even numbered tiles are 2,4,6,8 = 4
Number of players =3
Possibility to choose 3 tiles by first player out of 9 tiles = ⁹C₃
= 84 ways
Possibility to choose 3 tiles by second player out of 6 tiles = ⁶C₃
=20 ways
Possibility to choose 3 tiles by third player out of 3 tiles = ³C₃
= 1 way
Total number of ways = 84× 20 ×1
= 1680
To have a sum of 3 tiles is odd number at least one tile should be odd.
Chances of first player all the 3 tiles are 0dd out of 5 = ⁵C₃
Next two players must 2 even tiles and 1 odd tile.= ²C₁
One player can be selected in ³C₁ way
Remaining 4 even tiles distributed equally = (4!)(2!)/ (2!)² ( 2!)
Number of favourable outcomes = ⁵C₃ × ²C₁ ׳C₁ × (4!)(2!)/ (2!)² ( 2!)
= 10 × 2 × 3 × 6
= 360
Probability (m/n) = 360 /1680
= 3/14
m = 3 and n = 14.
Therefore, from the probability that all three players obtain an odd sum is m/n , the value m = 3 and n = 14.
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Answer please! I couldn’t figure it out.
By solving a system of equations we will see that she sold 80 phones and 240 accessories.
How many phones and accessories were sold?
Let's define the variables:
x = number of phones.
y = number of accessories.
We know that she makes $160 on commissions, and that she sold 3 times as many accessories as phones, so we can write the system of equations:
y = 3x
x*$8 + y*$4 = $160
To solve the system, we can replace the first equation into the second one.
x*$8 + (3x)*$4 = $160
x*$8 + x*$12 = $160
x*$20 = $160
x = $160/$20 = 80
She sold 80 phones, and the number of accessories is:
y = 3x
y = 3*80 = 240
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A function is represented by the graph.
Complete the statement by selecting from the drop-down menu.
The y-intercept of the function y = 3x + 2 is
Choose...
the y-intercept of the function represented in the graph.
A graph with a line through point (0, 2) and point (2, 6)
We want to finish each statement by analyzing the graph provided.
The function's y-intercept is y =2.
y = 3x+2 is the equation.
The line connects (0, 2) and (2, 6).
What is meant by a function?The earliest known attempt to the concept of function may be traced back to the works of Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. Functions were initially the idealization of how a variable quantity depended on another quantity. The position of a planet, for example, is a function of time.
So, first, we need to find the y-intercept. We know that the y-intercept is the y-value at which the function intersects the y-axis, and we can see from the graph that the y-intercept is y = 2.
Then we'd like to see the line's equation.
Remember that y = ax + b is a generic line.
Where a denotes the slope and b the y-intercept, we may deduce:
y = ax + 2
We know that if a line passes through two points (x₁, y₁) and (x₂, y₂), then the slope is:
a=(y₂-y₁)/(x₂-x₁)
Given that the line passes through (0, 2) and (-2/3, 0), the slope is as follows:
a=(-2/3)/(-2)
a=1/3
The equation of the line is:
y =3x+2
And using that equation, we can show that the line does indeed pass through the points (0, 2) and (2, 6)
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a study of 1000 randomly selected flights of a major airline showed that 798 of the flights arrived on time.what is the probability of a flight arriving on time?
By using the concept of probability, it can be calculated that
Probability that the flight arrives on time = [tex]\frac{399}{500}[/tex]
What is probability?
Probability gives us the information about how likely an event is going to occur
Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.
Probability of any event is greater than or equal to zero and less than or equal to 1.
Probability of sure event is 1 and probability of unsure event is 0.
Total number of flights = 1000
Number of flights arriving on time = 798
Probability that the flight arrives on time = [tex]\frac{798}{1000}[/tex]
= [tex]\frac{399}{500}[/tex]
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would it be unusual for a random sample of 500 adult americans to result in 210 or more who believe marriage is obsolete?
Yes, it would be unusual for a 500 adult Americans to result in 210 or more who believe marriage is obsolete. The probability value is 0.39 for adult Americans.
We know very well that probability is defined as the ratio of number of favorable outcomes to the total number of outcomes.
We have given that 39% american adults women believes that marriage is now obsolete.
So,39% of 500 adult American women is =[(39/100)×500]
=39×5=195
So,probability of adult women who believes marriage is obsolete is =(195/500)=0.39
Now, we need to check that whether 210 women believes marriage is obsolete or not.
So, number of favorable outcome is 210 and total number of outcomes=500.
Therefore, probability of adult women who believes marriage is obsolete is=(210/500)=0.42
Now,we can see that 195 women probability is lower than 210 women probability. It means that more number of women considered marriage is obsolete.
Hence, yes it is unusual and the probability value of adult Americans is 0.39
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(Complete question) is:
would it be unusual for a random sample of 500 adult americans to result in 210 or more who believe marriage is obsolete?If so determine the probability, otherwise type 0 for this result NOT to be unusual
If a cyclist rides at an average speed of 18 miles per hour, how many miles does she ride in seven hours?.
If a cyclist rides at an average speed of 18 miles per hour then she ride 126 miles in seven hours.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
A cyclist rides at an average speed of 18 miles per hour.
We have to find the number of miles she ride in seven hours
Assume x be the number of miles she ride
Let us form a proportional equation
18/1 = x/7
Apply cross multiplication
18×7=x
126=x
Hence, if a cyclist rides at an average speed of 18 miles per hour then she ride 126 miles in seven hours.
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Select the price per unit in blanks a. And b, and choose which is the best buy. A. Tomato juice, 46 oz. Can for $2. 53 would = b. Tomato juice, 6-pack of 10 oz. Cans for $4. 50 would = c. The best buy would be.
The first deal in which 1 can costs $0.055, is the best buy as it costs $0.020 less than the second deal in which 1 can costs $0.075.
Given, A Tomato juice 46 oz. Cans cost $2. 53
B Tomato juice 6-pack of 10 oz. Cans costs $4. 50
we have to find the best buy between the given two.
In first case,
46 cans cost $2.53
46 cans = $2.53
1 can = 2.53/46
1 can costs $0.055
In second case,
60 cans cost $4.50
60 cans = $4.50
1 can = 4.50/60
1 can costs $0.075
So, it is clear that first deal in which 1 can costs $0.055, is the best buy as it costs $0.020 less than the second deal in which 1 can costs $0.075.
Hence, the first deal in which 1 can costs $0.055, is the best buy as it costs $0.020 less than the second deal in which 1 can costs $0.075.
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The weight (in pounds) and height (in inches) for a child were measured every few months over a two-year period. The results are given in the table.
A 2-column table with 9 rows. Column 1 is labeled Weight (x) with entries 8, 12, 18, 24, 30, 32, 35, 37, 40. Column 2 is labeled Height (y) with entries 22, 23, 26, 30, 32, 33, 35, 36, 38.
Using technology, what is the correlation coefficient?
–0.997
–0.503
0.503
0.997
Using technology, the correlation coefficient is 0.997
How to calculate correlation coefficient?We should know that correlation coefficient is a statistical model which is used to determine or measure the relationship between two variables.
The table is
x y x² y² xy
8 22 64 484 176
12 23 144 529 276
18 26 324 676 468
24 30 567 900 720
30 32 900 1024 960
32 33 1024 1089 1056
35 35 1225 1225 1225
37 36 1369 1369 1332
40 38 1600 1444 1520
Total 236 275 7226 8740 7733
[tex]r= \frac{nExy)-(Ex)(Ey)}{\sqrt{[n(EX^{2}][nEy^{2}(Ey)^{2} } }[/tex]
applying the figures from the table we have
r=[tex]\frac{9*7733-(236)(275)}{\sqrt{[9*7226-55696][9*8740-75625]} }[/tex]
Simplifying the expression we have
r=[tex]\frac{4697}{\sqrt{28340830} }[/tex]
r=0.88
r=0.9 approximately
Therefore the correct answer is 0.997 which is the correlation coefficient.
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E. Realiza las divisiones de polinomio
a) (15a²-a-28)÷(3a + 4) =
Given that the dividend is 15a²-a-28 and the divisor is 3a+4, the quotient will be 5a-7 and the remainder will be 0.
What is polynomial?A multi-term algebraic statement is referred to as a polynomial. It contains exponents, coefficients, variables, constants, and arithmetic operators. It uses a polynomial long division algorithm to divide the polynomials. It is the long division technique in a more generalized form. In this method, a polynomial is divided by other polynomials of the same degree or lower. Synthetic division method is a simple and quick technique that is occasionally employed as well.
Here,
dividend=15a²-a-28
divisor=3a+4
remainder=0
15a²-a-28=(3a+4)(5a-7)
quotient=5a-7
The quotient will be 5a-7 and remainder will be 0 as dividend is 15a²-a-28 and divisor is 3a+4.
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Which expression is equal to (3x − 4)(2x − 5)?
-
O 3x²
-
23x - 20
O 6x² - 7x+20
O 6x²-23x+20
O 6x² - 23x - 20
what fraction of seven number combinations formed used the numbers of the patter 3795523 will have the 2 3's always together
By using the concept of permutation, it can be calculated that
Fraction of seven number combinations formed used the numbers of the pattern 3795523 will have the two 3's always together = [tex]\frac{360}{1260}[/tex]
= [tex]\frac{2}{7}[/tex]
What is permutation?
Permutation is the arrangement technique that determines how many possible arrangement that can be made in a set where the order of arrangement matters.
Here, concept of permutation is used
Number of 7 number combinations that can be formed using the number 3795523 = [tex]\frac{7!}{2! \times 2!}[/tex] = 1260
The two 3's are always together
Number of 7 digit numbers formed = [tex]\frac{6!}{2!}[/tex] = 360
Fraction of seven number combinations formed used the numbers of the pattern 3795523 will have the two 3's always together = [tex]\frac{360}{1260}[/tex]
= [tex]\frac{2}{7}[/tex]
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