a)
There are 3268760 different ways for the company to place the lunch order for the 10 lunches
b)
There are 11861676288000 ways for the company to place the lunch order if the 10 lunches purchased are all different
What is permutation and combination?
The process of placing all the components of a set into a certain sequence or order is known as permutation in mathematics. In other terms, the process of permuting is the reordering of the components of a set if the set is already ordered. Nearly all areas of mathematics include permutations in some form or another. They frequently appear when various orderings on certain finite sets are taken into account.
Contrary to permutations, the order of selection is irrelevant when choosing elements from a collection using the combination method. The number of combinations may be counted in simpler situatiThe combinationation is the taking together of n items, k at a time, without repetition. The terms k-selection or k-combination with repetition are frequently used to describe combinations where repetition is permitted.
a) total different ways are [tex]C^{25} _{10}[/tex]
= 25!/(25-10)!10!
= 25!/15! * 10!
= 3268760
b) total different ways are [tex]P^{25} _{10}[/tex]
= 25!/(25-10)!
= 25!/15!
= 11861676288000
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professional tennis players may constitute a(n) group for an amateur tennis player who identifies with certain players by imitating their behavior whenever possible despite the fact that the amateur tennis player does not qualify for membership as a professional tennis player because he/she has neither the skills nor the opportunity to compete professionally.
Professional tennis players may constitute a(n) symbolic group for an amateur tennis player
A symbolic group is one in which a person is unlikely to be accepted even if they act like a member by emulating their beliefs, attitudes, and behaviors. For young people, cricket players like Sachin Tendulkar, Sourav Ganguly, etc., may serve as a representative group. By concentrating on the small scale, symbolic interactionism examines the individual within a community and their relationships with others.
Similar to this, professional tennis players may serve as a symbolic group for an amateur tennis player who identifies with certain players by mimicking their behavior whenever possible, even though the amateur tennis player does not meet the criteria for membership in the category of professional tennis players because he or she does not have the necessary skills or access to the professional circuit.
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For each relation, indicate whether the relation is a partial order, a strict order, or neither. If the relation is a partial or strict order, indicate whether the relation is also a total order. Justify your answers.
(a)
The domain is the set of all words in the English language (as defined by, say, Webster's dictionary). Word x is related to word y if x appears before y in alphabetical order. Assume that each word appears exactly once in the dictionary.
The domain is the set of all words in the English language that has a partial order relation and not a total order relation.
Given:
The domain is the set of all words in the English language (as defined by, say, Webster's dictionary.
Assume,
The domain is the set of all words in the English language (as defined by, say, Webster's dictionary). Word x is related to word y if x appears as a substring of y. x is a substring of y if all the letters in x appear in consecutive order somewhere in y. For example, "logical" is a substring of "topological" because the letters l-o-g-i-c-a-l appear consecutively in the order of the word "topological". However, "local" is not a substring of "topological" because the letters l-o are separated from c-a-l by the letters g and i.
Now, x is related to y if x is a substring of y.
Considering the following points through the example:
(A) Clearly, x is a substring of itself. Therefore, x is related to x and hence it is called reflexive.
(B) If x is related to y or y is related to x then x =y and it is called antisymmetric.
(C) If x is related to y and y is related to û then we can say that x is related to û (i.e. if x is a substring of y and y is a substring of û then x is also inscribed in û. Hence, we called it transitive.
Hence, the order is not the total order relation. It is a partial order relation.
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For the circle centered at the origin with radius 4 and equation x^2+y^2=16 find dx/dt.
dx/dt = 4+3√3 in the case of the circle with radius 4 and the equation x²+y²=16.
What is implicit differentiation?The method of finding an implicit function's dependent variable's derivative by differentiating each term individually, symbolizing the derivative, and then solving the resulting expression for the symbol.
Without having to solve the provided equation for y, you may use the implicit differentiation technique to determine the derivative of y with respect to x.
Because we assume that y may be written as a function of x, the chain rule must always be applied when differentiating the function y.
So, the dx/dt will be:
The circle's equation is: x² + y² = 16
Assuming that x = 2, then:
2² + y² = 16
y² = 12
y = ±√12
Hence, the first quadrant is positive:
y = √12
y = 2√3
When implicit differentiation is used, we get that:
2x dx/dt + 2y dy/dt = 16
If fracdydt = -3, as is the case, then
2(2) dx/dt - 12√3 = 16
4 dx/dt = 16 + 12√3
dx/dt = 16+12√3/4
dx/dt = 4+3√3
Therefore, dx/dt = 4+3√3 in the case of the circle with radius 4 and the equation x² + y² = 16.
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(t/f) true or false. with sample size greater than 30, the standard error of sample means is the same as sample standard deviation.
The standard error for sample means is equal to the sample standard deviation when the sample size is more than 30 is a "false" statement.
Define the term standard error?When comparing a population mean to a sample mean, the standard error of mean, called simply standard error, shows how dissimilar the two are likely to be.It reveals how much doing the sample mean could change if a study were to be repeated with fresh samples drawn from a single population.For the stated question-
Let's assume that our sample size is 30 and that the population standard deviation is 10.
standard error = 10/√30 = 1.83
Now let me use a sample size of 100 while keeping overall population standard deviation constant.
=10/10 = 1
It is obvious that with this sample size, the standard error will alter.
Therefore, when our sample size grows, the standard error will drop rather than stay the same.
Thus, the standard error for sample means is equal to the sample standard deviation when the sample size is more than 30 is a "false" statement.
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At a company meeting, there were 75 people in attendance. 68% of them were managers.
How many managers were in the meeting?
Answer:
There were 51 managers.
Step-by-step explanation:
First, turn the percentage into a decimal by moving the decimal point over twice to get 0.68. Then, set up this equation:
0.68 x 75 = 51 managers.
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a waiter earned $300 in tips during his shift on friday. on saturday, he earned $335 in tips. what is the percent increase of his tips from friday to saturday?
The percent increase of his tips from Friday to Saturday is 35/3%.
T is equal to 112/3% as a mixed percentage fraction or 35/3% as an uncommon percentage fraction (decimal fraction: 0.116667)
PREMISES
T is the proportion of a waiter's tips that increased from $300 on Friday to $335 on Saturday.
CALCULATIONS
T=($335-$300)/$300
T=[($35/$300)100]%
T=[(7/60)100]%
T=[(7×100)/60]%
T=70/6%
A mixed percentage fraction of 112/3% or a percentage fraction of 35/3% (decimal fraction: 0.116667)
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geometric sequence with a ratio of 2 and a first term of 1/3.
Answer:
1/3, 2/3, 4/3, 8/3, 16/3, 32/3
or
1/3, 2/3, 1 1/3, 2 2/3, 5 1/3, 10 2/3
Step-by-step explanation:
what must be true for any direction if the instantaneous rate of change from (1,3,2) is equal to 0? what shape is formed by the collection of these vectors? (be as specific as you can.)
The instantaneous rate of change is the change in the rate at a particular instant and it is same as the change in derivative value at a specific point.
From the above given data, the following solution is given below:
Given:
Let f(x,y,z) = x³z - yz²
To find the partial derivatives of f
Here the directional derivative of a function f(x,y,z) is given by:
(df/dx , df/dy, df/dz)
df/dx = 3x²
df/dy = -z²
df/dz = x³ - 2yz
at points(1,3,2)
(df/dx)₍₁,₃,₂₎ = 3(1)² = 3
| (df/dx)₍₁,₃,₂₎ | = 3
(df/dy)₍₁,₃,₂₎ = -2² = 4
| (df/dy)₍₁,₃,₂₎ | = 4
(df/dz)₍₁,₃,₂₎ = 1³ - 2*3*2 = 1-12 = -11
| (df/dz)₍₁,₃,₂₎ | = 11
As we got the maximum modulus of derivative in direction of x. Since, therefore we should move into z direction to maximize the directional derivative.
(df/dz)₍₁,₃,₂₎ = -11
Hence, the instantaneous rate of change is the change in the rate at a particular instant and it is same as the change in derivative value at a specific point.
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The instantaneous rate of change is the change in the rate at a particular instant and it is same as the change in derivative value at a specific point | (∂f/∂z)₍₁,₃,₂₎ | = 11.
What is instantaneous rate of change?
The derivative value change at a particular point is the same as the instantaneous rate of change, which is the change in rate at a specific instant. The tangent line slope and the instantaneous rate of change at a given point on a graph are the same. That is, the slope is curved.
From the given data, the solution is given below:
Given:
Let f(x, y, z) = x³z - yz²
To find the partial derivatives of f
Here the directional derivative of a function f(x, y, z) is given by:
(∂f/∂x , ∂f/∂y, ∂f/∂z)
∂f/∂x = 3x²
∂f/∂y = -z²
∂f/∂z = x³ - 2yz
at points(1,3,2)
(∂f/∂x)₍₁,₃,₂₎ = 3(1)² = 3
| (∂f/∂x)₍₁,₃,₂₎ | = 3
(∂f/∂y)₍₁,₃,₂₎ = -2² = 4
| (∂f/∂y)₍₁,₃,₂₎ | = 4
(∂f/∂z)₍₁,₃,₂₎ = 1³ - 2*3*2 = 1-12 = -11
| (∂f/∂z)₍₁,₃,₂₎ | = 11
As we got the maximum modulus of derivative in direction of z. Since, therefore we should move into z direction to maximize the directional derivative.
(∂f/∂z)₍₁,₃,₂₎ = -11
Hence, The instantaneous rate of change is the change in the rate at a particular instant and it is same as the change in derivative value at a specific point.
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Complete question:
Complete question is attached below.
-4/7+2/7x-14x+4/7
please answer the question with work :))
Answer: -13.7142x ≈ -13.72x
Step-by-step explanation:
Combine like terms. (-4/7) and (4/7) cancel each other out because you are subtracting the exact number you are starting with. So you are left with 2/7x - 14x. 2/7-14 = -13.7142 so the answer is -13.7142x. Depending on how you round, the number will be slightly different. You may want to round to the nearest hundredth or tenth place.
(I left out the x in the answer in the picture but it is supposed to be after the -13.7142)
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Prove that a line that divides two sides of a triangle proportionally is parallel to the third side. Be sure to create and name the appropriate geometric figures. (10 points)
Answer:
Use the Triangle Proportionality Converse. If the ratios are equal, then the lines are parallel.
Ginny and Bob are both locksmiths.
Ginny uses the function f(x) = 60z+80 to determine the charge to her customers, where x represents the number of hours of
labor.
The table shows what Bobcharges a customer for x hours of labor.
x (hours)
cost ($)
0
60
140
Which locksmith charges less for an initial fee for a service call?
Drag a value or name to the boxes to correctly complete the statements
Ginny initial charge = $80, Bob initial charge =$60 For the initial fee, Bob charges less than Ginny.
What is unit rate?
A unit rate is the cost for only one of anything. This is expressed as a ratio with a denominator of 1. For instance, if you covered 70 yards in 10 seconds, you did so at an average speed of 7 yards per second. Although both of the ratios—70 yards in 10 seconds and 7 yards in one second—are rates, only the latter is a unit rate.
Given that Ginny charges by uses the function f(x)=60x+80 where x represents the number of hours of labour.
Ginny initial charge = $80
Bob initial charge =$60
Hence, For the initial fee, Bob charges less than Ginny.
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to obtain a 99.7% (virtually all-encompassing) confidence interval for the true population proportion, you would add and subtract about how many standard deviations to/from the sample proportion?
We would add and subtract about three standard deviations from the sample proportion to get a 99.7% (nearly full) confidence interval for the real population proportion.
What is a confidence interval?A confidence interval is a range of estimates for an unknown quantity in frequentist statistics.
The most frequent confidence level is 95%, but other levels, such as 90% or 99%, are infrequently used for generating confidence intervals.
To obtain a 99.7% (almost complete) confidence range for the real population proportion, you would add and deduct around three standard deviations from the sample proportion.
A confidence interval is a range of values that are bound by the statistic's mean and that is likely to include an unidentified population parameter.
The proportion of probability, or certainty, that the confidence interval would include the real population parameter when a random sample is drawn numerous times is referred to as the confidence level.
Therefore we would add and subtract about three standard deviations from the sample proportion to get a 99.7% (nearly full) confidence interval for the real population proportion.
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Correct question:
To obtain a 99.7% (virtually all-encompassing) confidence interval for the true population proportion, you would add and subtract about __________ standard deviations to/from the sample proportion.
5. Identify each of the following as convex or concave polygons:
Answer:
A) convex B) convex C) concave D) concave
Step-by-step explanation:
concave means going in on itself and convex is going outwards.
The ratio of the number of students in the Chess Club to the number of students on the Math Team is 3:7.
There are 12 students in the chess club.
How many students are on the math team?
Answer:
28
Step-by-step explanation:
first, find out 12 / 3, which is 4
next multiply 4 by 7, which is 28
3:7 = 12:28
Help me please with my homework Find the b and r
rhambus has four equal sides
so r+l=2r-4
r=5
b-3=r+l=6
b=9
Diamond adjacent angle complementation
So (x+2x+6)=180*
3x=174
x=58
All in all r=5 b=9 x=58 4b-6r=21-4=r+l=b-3=6
2x+6=122
this is the answer thank you when you have th problem you can tell me
In a city in Ohio, the sales tax rate is 7.25% . Complete the table.
if the sales tax is 1.16 what is the price before tax and the price including the tax
Answer: $17.16
Step-by-step explanation:
To find the cost of the untaxed money, you have to divide your sales tax amount by the tax rate.
1.16÷.0725=16
Once you have your untaxed amount, you then add your sales tax to your untaxed amount,
16+1.16=17.16
A particle accelerates from rest with an acceleration of 3 ms2 to a speed V. It continues at
this speed for time T and then decelerates to rest at 1.5 ms. The total time for the motion
is 1 minute, and the total distance travelled is 1 km. Find a value for V.
The value for speed V is 188.15 m/s
How to find a value for V?It was given that a particle accelerates from rest with an acceleration of 3 m/s² to a speed V
It continues at this speed for time T and then decelerates to rest at 1.5m/s². The total time for the motion is 1 minute, and the total distance traveled is 1 km
During acceleration:
a = 3 m/s², at rest u = 0, t = T
V = u + at
V = 0 + 3T
V = 3T
During deceleration:
a = 1.5 m/s², t = 1 minute = 60 s, distance(s) = 1 km = 1000 m
V² = u² +2as
V² = (3t)² +2(1.5×1000)
V² = (3×60)² + 3000
V² = 32400 + 3000
V² = 35400
V = √35400
V = 188.15 m/s
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using the significance levels reported by forecast xtm, at what level can we reject a one-sided null relating to a slope coefficient's statistical significance such that we are 95% confident?
If the value of test statistic does not lie between -1.96 and +1.96 then, the difference would be significant and the null hypothesis will be rejected.
Using the significance levels as reported by forecast Xtm, we would check the difference of means between the two items.
The critical value of Z at 95% confidence level is 1.96.
Then we would calculate the Test statistic, viz, difference of means/ standard deviation.
Decision Rule:
If we find that the value of test statistic is more than the value of Z, i.e., the test statistic does not lie between -1.96 to +1.96, then, the difference would be significant and the null hypothesis must be rejected.
But, the other way round, if the difference between the two means is not significant at the 95% confidence level, then the null hypothesis should not be rejected.
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An 8-ounce container of yogurt is on sale for $1.12. What is the cost of 1 ounce of yogurt?
Answer: $0.14
Step-by-step explanation: All we have to do is divide $1.12 by 8 to get our answer, that being $0.14.
Unit 3 Parallel & Perpendicular Lines: Homework 3
Answer:
check the attached file
Step-by-step explanation:
i nee help please and thankyou
Question 7
Using the secant-secant theorem,
[tex]4(x+4)=3(8) \\ \\ x+4=6 \\ \\ \boxed{x=2}[/tex]
Question 8
Using the intersecting chords theorem,
[tex]8(4x+2)=9(4x) \\ \\ 32x+16=36x \\ \\ 16=4x \\ \\ \boxed{x=4}[/tex]
2x-y=1 , if x=-1 , then y=?
Answer: y=-3
Step-by-step explanation: In order to figure out what y would be in this problem, you would subtitute -1 in for x . and ask your self " What is 2* a -1? , The answer to that question would be -2 , ok. then the next step is to take the -2 and subtract by y which in case is 1 or -1 which will get you the answer of y=-3.
Hoped that helped!
Colin loves to eat tuna salad for lunch. His mom is always looking for a bargain on 12-ounce cans of tuna. Today, his local grocery store is offering 4 cans of Sea Star tuna for $3.28 and 2 cans of Ocean's Best tuna for $1.88. Which brand is the better deal?
Answer:
Sea star tuna
Step-by-step explanation:
Solve: -5/6 + m = -3 1/6
m= -4
m= -2
m= -2 1/6
m= -2 1/3
Answer: -2 1/3
Step-by-step explanation:
Okay
A survey conducted asked 110 people what type of pets they owned. The results showed that 72 owned a dog, 58 owned a cat, and 37 owned both a dog and a cat. What is the probability of choosing a person who owns a dog or a cat? Enter your answer as a simplified fraction
The probability of choosing a person who owns a dog or a cat will be;
⇒ 0.845
What is mean by Probability?
The term probability refers to the likelihood of an event occurring.
Given that;
Number of peoples in survey = 110
And, The results showed that 72 owned a dog, 58 owned a cat, and 37 owned both a dog and a cat.
Now,
Since, Number of peoples in survey = 110
And, Number of peoples owns a dog or a cat = 72 + 58 - 37
= 93
Thus, The probability of choosing a person who owns a dog or a cat is,
Probability = 93 / 110
= 0.845
Therefore, The probability of choosing a person who owns a dog or a cat will be;
⇒ 0.845
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Identify the terms and like terms in the expression. 1/2s−4+3/4s+1/8−s3
HELP ME PLEASE TvT
1/2s, -4, 3/4s, 1/8 and -s³ are the terms and 1/2s and 3/4s are the like terms of the expression. 1/2s−4+3/4s+1/8−s³
What is Expression?An expression is combination of variables, numbers and operators.
Given expression is 1/2s−4+3/4s+1/8−s³
One by two times of s minus four plus three by four times of s plus one by eight minus s cube.
In the given expression minus, plus are the operators, s is the variable,
The expression has five terms
1/2s, -4, 3/4s, 1/8 and -s³ are the terms
Like terms contain the same variable which is raised to the same power.
In the given expression 1/2s and 3/4s are the like terms
Hence, 1/2s, -4, 3/4s, 1/8 and -s³ are the terms and 1/2s and 3/4s are the like terms of the expression. 1/2s−4+3/4s+1/8−s³
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Kim had 4 chocolate chip cookies and 3 sugar cookies. Kim’s sister ate two of her chocolate chip cookies. Kim shared her remaining cookies with her brothers. How many cookies does one brother get?
Answer:
Your answer would be 1 chocolate chip cookie and 1.5 sugar cookie each.
Step-by-step explanation:
We know that Kim's sister ate two Chocolate Chip cookies, so: [tex]4-2 =2[/tex] and we also know that the rest of the cookies were shared by two people, so:
[tex]3[/tex] ÷ [tex]2 = 1.5[/tex] and [tex]2[/tex] ÷ [tex]2=1[/tex]
HELP SOLVE!
name the property if 3x= 4 and 4=z then 3 =z
The name of the property is transitive property if 3x= 4 and 4=z then 3 =z.
What is a transitive property?According to the transitive property, "if two quantities are equal to the third quantity, then we can claim that all quantities are equal to each other." The term transitive refers to the act of transferring something. If a, b, and c are three quantities and an is connected to b by some rule and b is related to c by the same rule, then a and c are related to each other by the same rule; this is known as the transitive property of equality.
The transitive property of equality states that if a = b and b = c for any values of a, b, and c, then a = c. In other words, because a and c are both equal to the same item (in this case, b), they must be equal as well.
Given,
3x=4 and 4=z then 3=z
Here a=3, b=4, c=z
The name of the property is transitive property
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The mean of a set of normally distributed data is 600 with a standard deviation of 20. What percent of the data is between 580 and 620?.
We know that 68.26% of data is between 580 and 620 using a normal distribution table.
What is a normal distribution?A data set must (when graphed) follow a bell-shaped, symmetrical curve that is centered around the mean in order to be regarded as having a normal distribution.
Additionally, it must follow the empirical rule that shows the proportion of the data set that lies within (plus or minus) 1, 2, and 3 standard deviations of the mean.
So, we know that:
μ = 600
σ = 20
Use the equation:
z - score = x-μ/σ
580 in the data's Z-score:
= 580-600/20
= -20/20
= -1
While the data's z-score in 620:
= 620-600/20
= 20/20
= 1
Using a table of the normal distribution:
P(580 < z) = 0.1587
Also, P(620 > z) = 0.8413
As a result, the percent of the data that falls between 580 and 620 is given by: P(620 > z) - P(580 z).
= 0.8413 - 0.1587
= 0.6826
= 68.26 %
Therefore, we know that 68.26% of the data is between 580 and 620 using a normal distribution table.
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Answer the picture in 5 minutes, please
Answer:
area of the isosceles triangle is [tex]60cm^{2}[/tex]
Step-by-step explanation:
three sides are a=10, b=13, c=13
Area of Triangle:
[tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]
where,
[tex]s=\frac{a+b+c}{2}[/tex]
[tex]s=\frac{10+13+13}{2}[/tex]
s = 18
now,
[tex]A = \sqrt{18(18-10)(18-13)(18-13)}[/tex]
[tex]A =\sqrt{9(16)(5)(5)}[/tex]
A = 3x4x5
[tex]A =60cm^{2}[/tex]