The number of distinguishable ways the letters of the following word can be arranged 'KNICKKNACK' is 37800.
When the order of the arrangements counts, a permutation is a mathematical technique that establishes the total number of alternative arrangements in a collection. Choosing only a few items from a collection of options in a specific sequence is a common task in arithmetic problems.
The number of different permutations of n objects with m₁ repeated items, m₂ repeated items,...,mₙ repeated items can be computed as
m!/(m₁!)(m₂!)...(mₙ!)
Here, the letter 'KNICKKNACK' is a total of 10 letters with 4 K's, 2 N's, 1 I, 2 C's, and 1 A.
So, the number of possible arrangements is
(10!)/(4!*2!*1!*2!*1!) = (10*9*8*7*6*5*4!)/(4!*2*2) = 10*9*7*6*5*2 = 37800
Therefore the number of distinguishable ways the letters of the following word can be arranged 'KNICKKNACK' is 37800.
Learn more about permutations here -
https://brainly.com/question/4301655
#SPJ10
Addison and Kelsey are running on a path modeled by x2 + y2 – 14x – 16y – 287 = 0, where the distance is in meters. What is the maximum distance between the runners at any given time?
20 meters
32 meters
40 meters
140 meters
Answer:
40 meters
Step-by-step explanation:
The maximum distance between the runners at any given time 40 meters. Therefore, option C is the correct answer.
Given that, Addison and Kelsey are running on a path modeled by x² + y² - 14x - 16y - 287 = 0.
What is a circle equation?The equation of circle provides an algebraic way to describe a circle, given the center and the length of the radius of a circle. The equation of a circle is different from the formulas that are used to calculate the area or the circumference of a circle.
The standard equation of a circle with center at (x1,y1) and radius r is (x-x1)²+(y-y1)²=r²
Here, the circular path is modeled by x² + y² - 14x - 16y - 287 = 0
We complete the squares to place it in the standard format, thus:
x² - 14x + 49 + y² - 16y +64 = 287+49+64
⇒ (x-7)² + (y-8)² = 400
⇒ (x-7)² + (y-8)² = 20²
So, r² = 20²
⇒ r = 20 meters
Maximum distance = d = 2r
= 40 meters
The maximum distance between the runners at any given time 40 meters. Therefore, option C is the correct answer.
To learn more about an equation of a circle visit:
https://brainly.com/question/23799314.
#SPJ2
Fill in the blanks below.
Find the slope of the line passing through the points (8,5) and (8,-4).
Step-by-step explanation:
please mark me as brainlest
On a coordinate plane, a dashed solid line has an equation of y less-than five-thirds x + 1. It has a positive slope and goes through (negative 3, negative 4) and (0, 1). Everything to the right of the line is shaded.
Which linear inequality will not have a shared solution set with the graphed linear inequality?
y < Five-thirdsx – 2
y < Negative five-thirdsx + 1
y > Five-thirdsx + 2
y > Negative five-thirdsx + 2
The inequality is represented by y < 5/3(x+1)
Use the information about the straight line and find the equation of the line.
Given coordinates (-3,-4) and (0,1), we can find the slope
Slope,
Change in y = y2 – y1 = 1-(-4) = 5
Change in x = x2 – x1 = 0-(-3) = 3
Therefore, Slope (m) = Change in y / Change in x = 5/3
Equation of line using m = 5/3 and points (0,1) and (x, y) in form of y = mx + c
Y – 1/ X – 0 =5/3
3(Y-1) = 5(X)
3Y -3 = 5X
3Y = 5X + 3
Y = 5X + 3/3
Y = 5/3(X + 1)
To find the inequality take a point in the shaded region and check it in the above equation.
Given Options
a. y < Five-thirds x – 2
b. y < Negative five-thirds x + 1
c. y > Five-thirds x + 2
d. y > Negative five-thirds x + 2
Let’s take points (-3,-4) for verification
Option a: y < 5/3 (x-2)
-4 < 5/3(-3-2)
--4 < -3.33
-4 is less than -3.33
Thus option a is in the shaded region
Option b: y < -5/3 (x+1)
-4 < -5/3(-3+1)
--4 < 3.33
-4 is less than 3.33
Thus option a is in the shaded region
Option c: y > 5/3 (x+2)
-4 > 5/3(-3+2)
--4 > -1.67
-4 is NOT GREATER than -1.67
Thus option c is NOT in the shaded region
Option d: y > -5/3 (x+2)
-4 > - 5/3(-3+2)
--4 > 1.67
-4 is NOT GREATER than 1.67
Thus option d is NOT in the shaded region
Learn more about Inequalities at
https://brainly.com/question/13447558
#SPJ10
Answer:
y > Five-thirdsx + 2
Step-by-step explanation:
Question 7 of 10
Classify the following triangle. Check all that apply.
Answer:
A,C,E
(if you find a better answer choose that.)
Step-by-step explanation:
This one has two acute angles and one obtuse.
This one is a scalene.
So, tick A,C,E
Figure ABCD is transformed to obtain figure A′B′C′D′:
DIAGRAM INCLUDED! 100 Points!
Part A: Write the sequence of transformations that changes figure ABCD to figure A′B′C′D′. Explain your answer and write the coordinates of the figure obtained after each transformation. (6 points)
Part B: Are the two figures congruent? Explain your answer. (4 points)
Answer:
Part A
Reflect over the y-axis: (x, y) → (-x, y)Part B
Two figures are congruent if they have the same shape and size. (They are allowed to be rotated, reflected and translated, but not resized).
Therefore, ABCD and A'B'C'D' are congruent. They are the same shape and size as they have only be reflected and translated.
Find the equation of a line containing the points (−2,−4) and (1,−3).
1. What is pi?
2. And why is it important?
Answer:
pi [π] is the ratio of a circle's circumference to its diameter, and it is constant [meaning it is always the case] for all circles.
{this is a long number, 3.141592653589793238... is not even the full length, but 3.14 [or 3.14159] is typically used for estimation}
The significance of pi is typically centered in math--it can be used to find values that we don't know of circles. There are other areas of math that have been related back to the value of pi--which is incredible, and genuinely relevant.
We can find pi in the shape of rivers, physics--including waves--DNA
[+ anywhere there is a circle]
hope this helps!! :)
Answer:
ratio of circle's circumference to diameter
it is constant
At 50 minutes how far is the winning runner use ur equations
Answer:
3.5 km
Step-by-step explanation:
1
2
3
at
4
927
5
6
Which graph represents g(x)?
7
8
The graph of f(x) = x² is translated to form g(x) = (x - 5)² + 1. What does the graph look like?
6
10
Please help, will give the brainliest!
(J) 80 • 125
(K) (80+65) • 125
(L) (65 • 80) + (80 • 60)
M (65•80)+(80•60)
N (65•80)+ 1/2 (125 • 100)
Answer:
option N is the correct option, apply Formula of area of rectangle and triangle by splitting figure into 2 parts
Which of the following best describes the expression below when i = √-1?
3+4i
A. Complex number
B. Real number
C. Irrational number
D. Rational number
The answer is A. Complex number
41% of adults say cashews are their favorite kind of nut. You randomly select 12 adults and ask each to name his or her favorite nut. Find the probability that the number who say cashews are their favorite nut is (a) exactly three, (b) at least four, and (c) at most two. If convenient, use technology to find the probabilities.
The probability for part (a) is 0.131, for part (b) is 0.795, for part (c) is 0.0733.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
We have:
41% of adults say cashews are their favorite kind of nut.
P = 41% = 0.41
Q = 1 - P = 1 - 0.41 = 0.59
n = 2
From the binomial distribution:
[tex]\rm P(X = r) = C(n, r) P^r(1-P)^{n-r}[/tex]
a) Exactly three
[tex]P(X=3) = C(12, 3) (0.41)^3(0.59)^9[/tex]
P(X = 3) = 0.131
b) At least four:
P(X≥4) = P(X=4)+ P(X=5)+ P(X=6)+..............+ P(X=13)
[tex]\rm P(X\geq 4)=C(12, 4) (0.41)^4(0.59)^9+C(12, 5) (0.41)^5(0.59)^8+...............+C(12, 3)(0.41)^3(0.59)^9[/tex]
P(X ≥ 4) = 0.795
c) At most two:
P(X≤2) =P(X=0)+ P(X=1)+ P(X=2)
[tex]\rm =C(12, 0) (0.41)^0(0.59)^12+C(12, 1) (0.41)^1(0.59)^1^1+C(12, 2)(0.41)^2(0.59)^1^0[/tex]
P(X ≤ 2) = 0.0733
Thus, the probability for part (a) is 0.131, for part (b) is 0.795, for part (c) is 0.0733.
Learn more about the probability here:
brainly.com/question/11234923
#SPJ1
There are nine baseball players in the cafeteria The number of baseball players is one less than twice the number of golfers find the number of golfers
Using a system of equations, it is found that the number of golfers in the cafeteria is of 5.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable x: Number of baseball players.Variable y: Number of golf players.The number of baseball players is one less than twice the number of golfers, hence:
x = 2y - 1.
Since x = 9:
9 = 2y - 1
2y = 10
y = 5.
There are 5 golfers in the cafeteria.
More can be learned about a system of equations at https://brainly.com/question/24342899
#SPJ1
The earnings for a cashier at the local grocery store varies directly with how many hours she works. If the cashier is paid $524 for a 40 hour work week, how many hours would it take for him to make 720.50? Enter the number only.
Using proportions, it is found that it would take 55 hours for him to make $720.50.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
He is paid $524 for a 40 hour work week, hence per hour he earns?
r = 524/40 = $13.1.
The amount of hours he would need to make $720.50 is given by:
h = 720.50/13.1 = 55.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
\Triangle X Y Z is shown. Angle X Z Y is 63 degrees. The length of X Z is 2.7 and the length of X Y is 2.8.
Law of sines: StartFraction sine (uppercase A) Over a EndFraction = StartFraction sine (uppercase B) Over b EndFraction = StartFraction sine (uppercase C) Over c EndFraction
Which is the approximate measure of angle Y? Use the law of sines to find the answer.
52°
59°
64°
67°
Two trains leave station 416 miles apart. One train is traveling 90 miles per hour while the other is traveling 70 miles per hour. How long will it take the two trains to meet
Answer:
2.6 hours
Step-by-step explanation:
Let t be the time that the trains meet.
[tex]90t = 416 - 70t[/tex]
[tex]160t = 416[/tex]
[tex]t = 2.6[/tex]
If AABC= ADEF, which congruences are true by CPCTC? Check all that
apply.
∠A ≅ ∠D , BC≅ EF , AC ≅ DF , option B , C , F are the correct answer.
What is CPCTC ?CPCTC stands for corresponding parts of congruent triangles are congruent .
This means when two triangles are congruent then the corresponding sides are also congruent.
In the given triangles , Δ ABC ≅ ΔDEF
∠A ≅ ∠D
BC≅ EF
AC ≅ DF
Therefore option B , C , F are the correct options
To know more about CPCTC
https://brainly.com/question/14361320
#SPJ1
The mean of 6 numbers is 17. Four of the numbers are 15, 17, 20, and 22. The remaining two numbers are each equal to x. Calculate the sum of the 06 numbers and the value of x.
Answer:
Sum of 6 no. = 102X = 14
Let the unknown no. be X
mean= sum of all no. / no. of terms
17 = 15 + 17 + 20 + 22 + X+ X / 6
17 * 6 = 74 + 2X
102 - 74 = 2X
28 = 2X
28/2 = X
14= X
On a unit circle, Ø = 60°. Identify the terminal point and Tan Ø
The terminal points when the value of r is 1 will be 0.5 and 0.86 and the value of tan 60 will be 1.732.
What is angle measurement?An angle measure is the measurement of the angle created by two rays or arms at a shared vertex in geometry. A protractor is used to measure angles in degrees (°).
Given;
Ø = 60°
Let's assume the value of r = 1 units
The terminal points are;
x= rcosΘ
x=1 × cos 60°
x=0.5
y=rsinΘ
y=rsin60°
y = 0.86
The terminal points when the value of r is 1 will be 0.5 and 0.86.
The value of the tan for the given value of the angle;
Tan 60° = 1.732
Hence, the terminal points when the value of r is 1 will be 0.5 and 0.86 and the value of tan 60 will be 1.732.
To learn more about the angle measurement, refer to the link;
https://brainly.com/question/14684647
#SPJ1
In the following answer, why does 830 convert to 83000?
Answer:
Money borrowed from insurance company = $1000
Step-by-step explanation:
Let the money borrowed by her friend at 8% interest = x
Then the money borrowed by bank at 9% interest = 2x
Total money borrowed = $10,000
So, the money borrowed from insurance company = 10,000-(2x+x)
= 10,000-3x
Total interest for the first year = $830
We have the equation,
8%(x) + 9%(2x) +5% (10,000-3x) = 830
8x+18x+50,000-15x = 83,000
11x = 83000-50000
11x = 33,000
x = $3000
Then the money borrowed insurance company = 10,000-3x
= $1,000
Then the money borrowed insurance company is $1,000.
Money borrowed from insurance company = $1000
Let the money borrowed by her friend at 8% interest = x
Then the money borrowed by the bank at 9% interest = 2x
What is the total money?Total money borrowed = $10,000
So, the money borrowed from the insurance company = 10,000-(2x+x)
= 10,000-3x
Total interest for the first year = $830
We have the equation,
8%(x) + 9%(2x) +5% (10,000-3x) = 830
8x+18x+50,000-15x = 83,000
11x = 83000-50000
11x = 33,000
x = $3000
Then the money borrowed insurance company = 10,000-3x
Then the money borrowed insurance company is $1,000.
To learn more about the insurance visit:
https://brainly.com/question/25855858
#SPJ1
What is the square root of -1? Complex numbers
Answer:
The square root of -1 is i
Step-by-step explanation:
"i" is the imaginary unit and represents the value of sqrt -1
in the game of roulette, a player can place a $ 7 bet on the number 28 and have a 1/38 probability of winning. if the metal ball lands on 28, the player gets to keep the $7 paid to play the game and the player is awarded $245. otherwise, the player is awarded nothing and the casino takes the player's $7. what is the expected value of the game to the player? if you played the game 1000 times, how much would you expect to lose?
Answer: The player expects to lose 184.21 dollars.
=========================================================
Explanation:
X = net winnings in dollars
Ignore the "28" because it's really not that relevant here. All we care about is the probability 1/38 which is the probability of winning money. The probability of losing money is 1 - (1/38) = 37/38. Put another way: there's 1 way to win, and 37 ways to lose.
If the player wins, then they walk away with 7+245 = 252 dollars
If the player loses, then their "winnings" is -7
So either X = 252 or X = -7 are the only two options.
Let's form a table showing those options with their corresponding probabilities.
[tex]\begin{array}{|c|c|} \cline{1-2}X & P(X)\\\cline{1-2}252 & 1/38\\\cline{1-2}-7 & 37/38\\\cline{1-2}\end{array}[/tex]
Now multiply each X value and P(X) value across the rows.
252*(1/38) = 6.631579
-7*(37/38) = -6.815789
These values are approximate.
[tex]\begin{array}{|c|c|c|} \cline{1-3}X & P(X) & X*P(X)\\\cline{1-3}252 & 1/38 & 6.631579\\\cline{1-3}-7 & 37/38 & -6.815789\\\cline{1-3}\end{array}[/tex]
Add up the results of the third column
6.631579 + (-6.815789) = -0.18421
This represents the net winnings for any average spin of the wheel. The player unfortunately expects to lose, on average, about $0.18421 or 18.421 cents per spin.
Do this 1000 times and the player should expect to lose about
1000*(0.18421) = 184.21 dollars
Keep in mind that due to the random nature of roulette wheel, the player may get lucky or their luck may be worse than what is described. The idea is that over the long run, the average should be somewhat close to losing 184.21 dollars.
Another way to think of it could be to have 1000 players doing the same game (rather than have 1 person play the same game 1000 times). Some players may get lucky, while others may not get so lucky. But their collective average should be losing that $184.21
Based on the circle graph,how many pounds of milk and eggs does the average American consume each year?PLEASE EXPLAIN IMAGE IS PROVIDED
E.300
F.368
G.460
H.552
About 492 pounds of milk and egg were consumed each year
Pie charts and percentagesGiven the following parameters from the chart
Total consumption = 1640 pounds per person
The percentage of milk and egg = 100 -(38 + 10 + 10 +8 + 4)
The percentage of milk and egg = 30%
Determine the amount consumed each year
Amount of milk and egg consumed = 30% of 1640
Amount of milk and egg consumed = 492 pounds
Hence about 492 pounds of milk and egg were consumed each year
Learn more on pie chart here; https://brainly.com/question/26851221
#SPJ
The pH can be calculated using the equation pH = –log(H+), where H+ is the hydronium ion concentration. Find the hydronium ion concentration of a particular soda if the pH level is 2.3.
Answer:
Step-by-step explanationp :
ph =lo 4
A Cepheid star is a type of variable star, which means that its brightness is not constant.
The relationship between the brightness of a Cepheid star and its period, or length of its pulse, is given by
M = − 2.78 (log P) − 1.35,
where M is the absolute magnitude, or brightness, of the star, and P is the number of days required for the star to complete one cycle.
Use a calculator to solve each problem. Round your answers to the nearest hundredth.
What is the absolute magnitude of a star that has a period of 62 days?
A function assigns the values. The absolute magnitude of a star that has a period of 62 days is -6.3328.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The relationship between the brightness of a Cepheid star and its period, or length of its pulse, is given by
M = − 2.78 (log P) − 1.35,
Given the absolute magnitude of a star that has a period of 62 days is,
M = − 2.78 (log 62) − 1.35
M = -6.3328
Hence, the absolute magnitude of a star that has a period of 62 days is -6.3328.
Learn more about Function:
https://brainly.com/question/5245372
#SPJ1
Solve the compound inequality .
2w-2<-8 and 4w+3<11
Write the solution in interval notation. If there is no solution, enter 0
Answer: [tex](-\infty, -3)[/tex]
Step-by-step explanation:
[tex]2w-2 < -8\\\\2w < -6\\\\w < -3[/tex]
[tex]4w+3 < 11\\\\4w < 8\\\\w < 2[/tex]
So, the solution is [tex](-\infty, -3)[/tex]
Which expression is equivalent?
Answer:
Last one/D 9^9/5/5^9/10
Step-by-step explanation:
in a study of birth orders and intelligence, IQ test were given to 18 and 19 years old men to estimate the size of difference, if any, between the main IQs of firstborn sons and second born sons. The following data for 10 firstborn sons and 10 second born sons are consistent with the means and standard deviation's reported in the article. It is reasonable to assume that the samples come from populations that are approximately normal. First born numbers are 107, 113, 84, 126, 99, 95, 98, 109, 91, 90. Second born numbers are 112, 92, 102, 86, 97, 106, 105, 116, 109, 95. construct a 95% confidence interval for the difference in mean IQ between first born and second born sons. Let them one denote the main IQ of firstborn sons.
In a study of birth orders and intelligence, IQ tests were given to 18 and 19 years old men to estimate the size of the difference, we have that [tex]|t|=0.618\leq t_c =2.101[/tex] and for this reason, we cannot reject the null hypothesis.
What are the Test Statistics?Null and Alternative Hypotheses
[tex]H_o: \mu_{1} = \mu_{2}\\\\Ha: \mu_1 \neq \mu_2 .[/tex]
Since the population standard deviations are unknown, we will apply a t-test on the means of the two populations, using two independent samples.
The degrees of freedom are df = 18, and the significance threshold is set at alpha = 0.05, based on the data presented. If we assume that the population variances are the same, we can calculate the degrees of freedom in this way:
The rejection region for this two-tailed test is R = \{t : |f| > 2.101}
Therefore the Test Statistics is
[tex]t= \frac{X 1 -X 2 }{\frac{\sqrt{ (n_1 -1)s_1 ^ 2 +(n_2 -1)s_2 ^2}} {n_1 +n_2 -2} (( 1/n_1 + 1 n_2 )}}[/tex]
[tex]t= \frac{X 1 -X 2 }{\frac{\sqrt{ (n_1 -1)s_1 ^ 2 +(n_2 -1)s_2 ^2}} {n_1 +n_2 -2} (( 1/n_1 + 1 n_2 )}}[/tex]
t=0.618
In conclusion. we have that [tex]|t|=0.618\leq t_c =2.101[/tex]
For this reason, we cannot reject the null hypothesis.
Read more about probability
https://brainly.com/question/795909
#SPJ1
i give brainliest to first person who gets it correct
Answer:
(-4,-3)
Step-by-step explanation:
The point where those 2 equations intersect is (-4,-3)
there are 48 tables at a school.
3/8 of the tables are in the dining hall.
the rest are shaded equally between 5 classrooms.
how many tables are in the main hall
Total: 48
DIning Hall: 48(3/8)=18
so theres 30 left for the classes
30/5(#of classes)=6 per class
