When a set of given numbers or items is to be arranged in a definite way or pattern, permutation can be used to determine the number of ways in which this can be done. Thus the required answer to the question is 990.
When a set of given numbers or items is to be arranged in a definite way or pattern, permutation can be used to determine the number of ways in which this can be done. The applicable formula is:
[tex]_{n} P_{r}[/tex] = [tex]\frac{n!}{(n - r)!}[/tex]
where: n is the total number of items given, and r is the number of items selected.
Thus the given question can be solved as :
[tex]_{11} P_{3}[/tex] = [tex]\frac{11!}{(11-3)!}[/tex]
= [tex]\frac{11!}{8!}[/tex]
= [tex]\frac{11 * 10 * 9 * 8!}{8!}[/tex]
= 11 x 10 x 9
= 990
[tex]_{11} P_{3}[/tex] = 990
Therefore, the required answer is 990.
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(20x2 – 12x) + (25x– 15)
4x(5x – 3) + 5(5x – 3)
(5x – 3)(
x +
)
Answer:
(4x+5)
Step-by-step explanation:
4x(5x-3)+5(5x-3)
collecting like terms, first part is (5x-3) hence second part of the equation is (4x+5) from the equation above.
Answer:
Step-by-step explanation:
(20x2 – 12x) + (25x– 15)
4x(5x – 3) + 5(5x – 3)
(( (5x – 3)(4x +5) ))
Is the answer true or false?
When we use statistical software to compare the means with a significance test, we obtain the following printout: Variance T DF Prob>|T| Unequal 2.9146 41.9 0.006 1.3.1 Interpret the P-value, in context, based on its definition. (Note: You are not being asked to make a decision at some α-level.
The interpretation of the p-value is that there is a 0.006 = 0.6% probability of the sample means differing by the amount that they differed on the sample.
What are the hypothesis tested?At the null hypothesis, it is tested if the means are equal, that is:
[tex]H_0: \mu_1 = \mu_2[/tex]
At the alternative hypothesis, it is tested if the means are different, that is:
[tex]H_1: \mu_1 \neq \mu_2[/tex]
Since we are testing if the means are different, we have a two-tailed test, which means that the p-value is the probability of the means differing by the amount they different on the sample, or a greater amount.
Hence, the interpretation is that there is a 0.006 = 0.6% probability of the sample means differing by the amount that they differed on the sample.
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A clothing store can make 4 dress shirts out of 14 yards of cotton cloth. At that rate, how many dress shirts can be made out of 63 yards of cotton cloth?
What is the mean of 13, 7, 8 and 4
Answer:
16
Step-by-step explanation:
Mean is same as average. To find the average, add all items and divide the sum by the number of items in the list.
Avg = (13 + 7 + 8 + 4) / 2 = 32 / 2 = 16
Hi there,
please see below for solution steps :
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To find the mean you first need to add all numbers and divide by how many there are :
[tex]\sf{\dfrac{13+7+8+4}{4}}[/tex]
⨠ simplify
[tex]\sf{\dfrac{32}{4}}[/tex]
[tex]\boxed{\sf 8}[/tex] [tex]\tiny\pmb{\sf{Frozen \ melody}}[/tex]
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Solve b + 3∕8 = 4∕9 for b.
A. 32/27
B. 59/72
C. 5/72
D. 1/6
Answer:
The value of b equals to
[tex] \frac{5}{72} [/tex]
Step-by-step explanation:
Hello!steps given below
given expression
[tex]b + \frac{3}{8} = \frac{4}{9} \\ [/tex]
subtract
[tex] \frac{3}{8} [/tex]
from both sides
[tex]b + \frac{3}{8} - \frac{3}{8} = \frac{4}{9} - \frac{3}{8} \\ b = \frac{4}{9} - \frac{3}{8} [/tex]
To, continue find the L.C.M of 9 and 8 thus, it's 72
So, plug 72 and solve the expression as follows
[tex]let \: \frac{a}{c} - \frac{b}{c} = \frac{a - b}{c} \\ b = \frac{32 - 27}{72} = \frac{5}{72} [/tex]
Hope it helps!
Which shapes have less than 3 lines of symmetry?
A) B and C
B) A and D
C) B and D
D) A and C
The shapes that have less than 3 lines of symmetry are Isosceles trapezoid and Isosceles triangle
How to determine the shapes that have less than 3 lines of symmetry?The shapes are given as:
Isosceles trapezoidSquareIsosceles triangleRegular PentagonThe lines of symmetry are the lines that, when the shape is rotated through this line, the shape remains the same
As a general rule:
An Isosceles trapezoid and an Isosceles triangle have two lines of symmetry
Hence, the shapes that have less than 3 lines of symmetry are Isosceles trapezoid and Isosceles triangle
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I roll two dice and observe two numbers X and Y . If Z = X − Y , find the range and PMF of Z.
[tex]X[/tex] and [tex]Y[/tex] are independent and identically distributed with PMF
[tex]\mathrm{Pr}(X = x) = \begin{cases}1/6 & \text{if } x \in\{1,2,3,4,5,6\} \\ 0 & \text{otherwise}\end{cases}[/tex]
If [tex]Z=X-Y[/tex], then [tex]Z[/tex] has range/support
{-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}
where we can get
-5 = 1 - 6 in 1 way, hence with probability 1/36-4 = 1 - 5 = 2 - 6 in 2 ways, with probability 2/36 = 1/18-3 = 1 - 4 = 2 - 5 = 3 - 6 in 3 ways, with probability 3/36 = 1/12and so on, so that the PMF of [tex]Z[/tex] is
[tex]\mathrm{Pr}(Z=z) = \begin{cases}1/36 & \text{if } z\in\{-5,5\} \\ 2/36 & \text{if } z\in\{-4,4\} \\ 3/36 & \text{if }z\in\{-3,3\} \\ 4/36 & \text{if } z\in\{-2,2\} \\ 5/36 & \text{if } z\in\{-1,1\} \\ 6/36 & \text{if } z =0 \\ 0 & \text{otherwise}\end{cases}[/tex]
One hundred dollars less
than twice last year's
income?
Answer:
2y - 100
Step-by-step explanation:
Last year's income = y
2y-100
Evaluate The quantity of x cubed plus 3x squared minus 2x plus 7 divided by the quantity of x minus 2 end quantity period.
1. x squared minus 5x plus 2 plus 23 divided by the quantity of x minus 2
2.x cubed plus 5x plus 8 plus 11 divided by the quantity of x minus 2 end quantity
3.x squared minus 5x plus 6 plus 3 divided by the quantity of x minus 2 end quantity 4. x squared plus 5x plus 8 plus 23 divided by the quantity of x minus 2 end quantity
The value of x^3 + 3x^2 - 2x + 7 divided by x- 2 is (x^2 + 5x + 8) + 23/(x - 2)
What is a quotient?Quotients involve the result of dividing a dividend by a divisor.
In other words, quotient means division or the result of a division operation
How to solve the quotient?The quotient expression is given as:
(x^3 + 3x^2 - 2x + 7)/x- 2
Expand the numerator in the above expression
(x^3 + 5x^2 - 2x^2 + 8x - 10x - 16 + 23)/(x - 2)
Rearrange the terms of the numerator in the above expression
(x^3 + 5x^2 + 8x - 2x^2 - 10x - 16 + 23)/(x- 2)
Factorize the numerator in the above expression
[x(x^2 + 5x + 8) - 2(x^2 + 5x + 8) + 23]/(x - 2)
Factor out x^2 + 5x + 8
[(x -2)(x^2 + 5x + 8) + 23]/(x - 2)
Split the fractions
(x -2)(x^2 + 5x + 8)/(x - 2) + 23/(x - 2)
Divide the common factors
(x^2 + 5x + 8) + 23/(x - 2)
Hence, the value of x^3 + 3x^2 - 2x + 7 divided by x- 2 is (x^2 + 5x + 8) + 23/(x - 2)
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Complete question
Evaluate (x^3 + 3x^2 - 2x + 7)/x- 2
Answer:
4 / D | x^2 + 5x + 8 + 23/x - 2Step-by-step explanation:
The correct answer is D because when you divide & simplify the original question's equation, you get the results that are equivalent to answer D.
Find the point at which the line with parametric equations x = 2 3t, y =-4t, z =5 t intersects the plane 4x 5y -2z=18
It looks like you have
[tex]\begin{cases}x=2+3t\\y=-4t\\z=5+t\end{cases}[/tex]
Substituting these in to the plane equation, we have
[tex]4x+5y-2z = 4(2+3t) + 5(-4t) - 2(5+t) = -2-10t = 18 \\\\ \implies-10t = 20 \implies t = -2[/tex]
When [tex]t=-2[/tex], we get the point
[tex]\begin{cases}x=2+3(-2)\\y=-4(-2)\\z=5+(-2)\end{cases} \implies (x,y,z) = \boxed{(-4,8,3)}[/tex]
If the scale factor between two circles is 2x/5y, what is the ratio of their areas?
Given that the length ratio between the radii of the two circles is (2 · x) / (5 · y). The ratio of the areas of the two circles is (4 · x²) / (25 · y²).
What is the area ratio of two circles?According to the statement we know that the radius ratio between two circles. Given that the area of the circle is directly proportional to the square of its radius, then the area ratio is shown below:
A ∝ r²
A = k · r²
A' · r² = A · r'²
A' / A = r'² / r²
A' / A = (r' / r)²
A' / A = [(2 · x) / (5 · y)]²
A' / A = (4 · x²) / (25 · y²)
Given that the length ratio between the radii of the two circles is (2 · x) / (5 · y). The ratio of the areas of the two circles is (4 · x²) / (25 · y²).
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For a segment of a radio show, a disc jockey can play 7 records. If there are 13 records to select from, in how many ways can the program for this segment be arranged?
The number of ways the program can be arranged for this segment is 8, 648, 640 ways
What is permutation?It is important to note that the formula for finding the permutation or arrangement of a set of dats is given as;
Permutation = [tex]\frac{n!}{(n-r)!}[/tex]
where
n = number to select from = 13r = number of objects selected = 7Let's substitute the values into the formula for permutation, we have
Permutation = [tex]\frac{13!}{13 - 7!}[/tex]
Find the difference of the denominator
Permutation = [tex]\frac{13!}{6!}[/tex]
Find the factorial of the values
Permutation = [tex]\frac{6,227,020,800}{720}[/tex]
Divide the numerator by the denominator
Permutation = 8, 648, 640 ways
Thus, the number of ways the program can be arranged for this segment is 8, 648, 640 ways
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A community college employs 88 full-time faculty members. To gain the faculty's opinions about an upcoming building project, the college president wishes to obtain a simple random sample that will consist of 9 faculty members. He numbers the faculty from 1 to 88. Complete parts (a)
-Using the provided random number table, the president closes his eyes and drops his ink pen on the table. It points to the digit in row 3, column 6. Using this position as the starting point and proceeding downward, determine the numbers for the 9 faculty members who will be included in the sample.
The numbers that would be included in the sample are 4, 1, 1, 4, 7, 9, 2, 6, 4, 7, 4, 4, 1, 0, 3, 0, 5, 0, 7, 1, 1, 6, 5, 4, 9
How to determine the number that will be included in the sample?The complete question is added as an attachment
The given parameters are:
Row = 3
Column = 6
From the attached figure, the entries in row 3 are:
4, 1, 1, 4, 7, 9, 2, 6, 4, 7, 4, 4, 1, 0, 3, 0, 5, 0, 7 1
From the attached figure, the entries in column 6 are:
1, 6, 9, 5, 4, 9
Hence, the numbers that would be included in the sample are 4, 1, 1, 4, 7, 9, 2, 6, 4, 7, 4, 4, 1, 0, 3, 0, 5, 0, 7, 1, 1, 6, 5, 4, 9
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Which of the following tables represents a proportional relationship?
Input
Input Output
7
21
35
49
1357
Input Output
5
42
10
75
15
110
20
145
Input Output
18
46
74
102
26
10
14
Input Output
30
4567
37
44
51
Answer:
The top left answer is correct.
Step-by-step explanation:
If you take each ordered pair and put them in the form y/x. The top left corner is the only one where all of the equations are equivalent.
7/1 = 21/3 = 35/5 = 49/7
A $8,000 principal is invested in two accounts, one earning 1% interest and another earning 6% interest. If the total interest for the year is $405, then how much is invested in each account?
The amount invested in the first account is $1,500 and $6,500 was invested in the second account.
What is simple interest?
Simple interest is determined as the principal multiplied by the interest rate ,then multiplied by the duration of the investment.
The formula for simple interest on an investment is as shown below:
I=PRT
P=principal=$8,000
R=interest rates= 1% and 6%
T=duration of investment=1 year
Let assume that X was invested at 1% and that the remaining of $8000-X is invested at 6%.
Interest on the first account=X*1%*1
Interest on the first account=0.01X
Interest on second account=($8000-X)*6%*1
Interest on second account=480-0.06X
Total interest=0.01X+480-0.06X
Total interest=480-0.05X
Total interest=$405
405=480-0.05X
0.05X=480-405
0.05X=75
X=75/0.05
X=amount invested in the first account=$1,500
Amount invested in the second account=$8000-X
Amount invested in the second account=$8,000-$1,500
Amount invested in the second account=$6,500
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QUESTION IS DOW BELOW 5 POINTS EACH PLEASE HELP PLEASE HELP PLEASE HELP
a. Central angle in the circle is: Angle BAC
b. A major arc is: Arc BEC
c. A minor arc is: Arc BC
d. m(arc BEC) = 260°.
e. m(arc BC) = 100°.
What is the Central Angle Theorem?The central angle theorem states that: the central angle measure of a circle equals the measure of the intercepted arc.
What is a Central Angle?A central angle is formed by two radii of a circle, and the vertex of the angle is at the center of the circle.
What is a Major Arc?Any arc that is more than half a circle (semicircle) or has a measure that is greater than 180 degrees, is referred to as a major arc of that circle. The measure of the major arc > 180 degrees.
What is a Minor Arc?Any arc that is not more than half a circle (semicircle) or has a measure that is less than 180 degrees, is referred to as a minor arc of that circle. The measure of the minor arc < 180 degrees.
a. One central angle that can be identified in circle A is: Angle BAC
b. A major arc that can be identified in circle A is: Arc BEC
c. A minor arc that can be identified in circle A is: Arc BC.
d. According to the central angle theorem, we have:
m(arc BEC) = 360 - 100
m(arc BEC) = 260°
e. We are given that m(angle BAC) = 100°, therefore, according to the central angle theorem, we have:
m(arc BC) = m(angle BAC )
m(arc BC) = 100°
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In quadrilateral ABCD, the sides BC and AD are congruent. The diagonal AC is the bisector of the angle BAD=160 degrees, thats is 8 times greater than angle ACB. Find the measure of angle ADC
pls help
Answer: [tex]50^{\circ}[/tex]
Step-by-step explanation:
[tex]m\angle CAB=m\angle CAD=80^{\circ}[/tex] (angle bisector)
[tex]m\angle ACB=20^{\circ}[/tex] (one-eighth of [tex]\angle BAD[/tex])
[tex]m\angle ABC=80^{\circ}[/tex] (sum of angles in a triangle)
[tex]\overline{AC} \cong \overline{BC}[/tex] (converse of base angles theorem)
[tex]m\angle ADC=50^{\circ}[/tex] (base angles theorem)
m∠1 =
✔ 131
degrees
m∠2 =
✔ 49
degrees
m∠3 =
✔ 112
degrees
Answer:
what is the question show the pic
When an integer is subtracted from 2 times the next consecutive odd integer, the difference is 1. Find the value of the greater integer.
The value of the greater integer which is the next consecutive odd integer is; -1.
What is the value of the greater integer as described by the task content?By observation, it follows that the first integer can be represented by 2x+1 while the next consecutive odd integer can be represented as 2x+3.
Hence, it follows that we have;
2(2x+3) - 2x - 1 = 1
4x +6 -2x - 1 = 1
2x = -4
x = -2.
Consequently, the value of the next consecutive greater integer is; 2(-2) + 3= -1.
It consequently follows from the computations above that the value of the greater odd integer is; -1.
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Residents in a city are charged for water usage every three months. The water bill is computed from a common fee, along with the amount of water the customers use. The last water bills for 40 residents from two different neighborhoods are displayed in the histograms. 2 histograms. A histogram titled Pine Road Neighbors has monthly water bill (dollars) on the x-axis and frequency on the y-axis. 100 to 125, 1; 125 to 150, 2; 150 to 175, 5; 175 to 200, 10; 200 to 225, 13; 225 to 250, 8. A histogram titled Front Street Neighbors has monthly water bill (dollars) on the x-axis and frequency on the y-axis. 100 to 125, 5; 125 to 150, 7; 150 to 175, 8; 175 to 200, 5; 200 to 225, 8; 225 to 250, 7. Which statement correctly compares the water bills for the two neighborhoods? Overall, water bills on Pine Road are less than those on Front Street. Overall, water bills on Pine Road are higher than those on Front Street. The range of water bills on Pine Road is lower than the range of water bills on Front Street. The range of water bills on Pine Road is higher than the range of water bills on Front Street.
The statement that correctly compares the water bills for the two neighborhoods based on the histogram given is that the range of water bills on Pine Road is higher than the range of water bills on Front Street.
What is a histogram?It should be noted that a histogram means a graph that shows the frequency of the numerical data using rectangles.
In this case, the statement that correctly compares the water bills for the two neighborhoods based on the histogram given is that the range of water bills on Pine Road is higher than the range of water bills on Front Street. This was the difference between the highest and lowest number.
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Answer: More homes on Pine Road had water bills above $200 than on Front Street.
Step-by-step explanation: edge 2023
What is the length of each leg of the triangle below?
Answer:
C
Step-by-step explanation:
32/sqrt(2) = 32sqrt(2)/2 = 16sqrt2
Answer:
C.
Step-by-step explanation:
It is a right triangle with hypotenuse c = 12, also for having two equal angles is an isosceles triangle, the missing sides (catethus) are equal (a and b)
a = b = the legs
Apply the Pythagorean theorem
[tex]c^{2}=a^{2} +b^{2} \\c^{2} =2a^{2}[/tex]
[tex]a^{2} =\frac{c^{2} }{2}=\frac{(32)^{2} }{2} =512[/tex]
[tex]a=\sqrt{512} =\sqrt{256(2)} =16\sqrt{2}[/tex]
Hope this helps
Please help it would be much appreciated
Answer:
calcium =1x40=40
chlorine=2x35=70
40+70=110
ca=40/110×100=36.36
when we approximate it become 36.4
thanks
Using the standard form of the equation in question 1, what are the length of the radius and the coordinates of the center for this particular circle? Watch your signs for the variables h and k. 12pt
The coordinates of the center is at (1, 0) and the length of the radius is 4 units.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The standard form of a circle is:
(x - h)² + (y - k)² = r²
Where (h, k) is the center of the circle and r is the radius.
The coordinates of the center is at (1, 0) and the length of the radius is 4 units.
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Each outcome or a collections of outcomes in a experiment is called as?
Answer:
event
What is an event?
An event can be described as an individual or set of outcomes of an experiment.
Events are a subset of the experiment's sample space.
What is sample space?The sample space of an experiment is the complete set of possible outcomes of that experiment.
Poormina spends all of her money on comic books and mandarins. in 2013, she earn $12 per hour, the price of a comic book was six dollars, and the price of a mansion was one dollar
The price of a mansion is $1.00 in 2013.
What is difference between a nominal and real variable?
Nominal variables are expressed in money or dollar terms, whereas the real variable compares the wage earned per hour to the basket of goods or services that it can purchase.
In comparing the wage earned per hour to 2 comic books, since the two would cost $12,that explains real variable, which is not required in this case.
However, comparing the the wage of $12 per hour to the price of mansion, which is $1 per one, indicates nominal variable.
In essence, the correct option in this case is that price of a mansion is $1.00 in the year 2013.
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IF A BASEBALL TEAM CONSISTS OF 18 PLAYERS, HOW MANY POSSIBLE GROUPS
OF 9 MAN TEAMS ARE POSSIBLE?
The number of ways men can be selected from the team of 18 is 48,620ways
Combination and PermutationPermutation has to do with arrangement while combination has to do with selection.
If a baseball team consists of 18 players and 9 man are possible in the team, the number of ways the men can be chosen is calculated using the combination formula below;
nCr = n!/(n-r)!r!
Given the following
n =18
r = 9
Substitute
18C9 = 18!/(18-9)!9!
18C9 = 18!/9!9!
18C9 = 48,620
Hence the number of ways men can be selected from the team of 18 is 48,620ways
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What form is 950,000 in
Answer:
standard form
hope this helps! <3
what is 4,928 will rounded to the nearest hundred
Answer:
4900
That is your answer..........
Really not sure what is meant by this when I'm only given one number, would appreciate help very much!!!!
Using continuous compounding, it is found that the value of r is of r = 7.7%.
What is continuous compounding?The amount of money after t years in continuous compounding is:
[tex]P(t) = P(0)e^{rt}[/tex]
In which:
P(0) is the initial amount.r is the exponential growth rate.The doubling time of 9 years means that P(9) = 2P(0), which is used to find r, hence:
[tex]P(t) = P(0)e^{rt}[/tex]
[tex]2P(0) = P(0)e^{9r}[/tex]
[tex]e^{9r} = 2[/tex]
[tex]\ln{e^{9r}} = \ln{2}[/tex]
[tex]9r = \ln{2}[/tex]
[tex]r = \frac{\ln{2}}{9}[/tex]
r = 0.077.
r = 7.7%.
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