Answer:
3
Step-by-step explanation:
The factorial of a number n is the product of all the positive integers from 1 to n. In other words, n! = 1 * 2 * 3 * ... * n. For example, the factorial of 5 is 5! = 1 * 2 * 3 * 4 * 5 = 120.
In this case, we are asked to find the value of the expression 10!/(4!7!). To do this, we first need to evaluate the factorials in the numerator and denominator of the expression. Since 10! = 1 * 2 * 3 * ... * 10, we have:
10! = 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 * 10 = 3628800
Similarly, since 4! = 1 * 2 * 3 * 4 and 7! = 1 * 2 * 3 * 4 * 5 * 6 * 7, we have:
4! = 1 * 2 * 3 * 4 = 24
7! = 1 * 2 * 3 * 4 * 5 * 6 * 7 = 5040
Now that we have evaluated the factorials in the expression, we can plug these values into the expression and evaluate it:
10!/(4!7!) = 3628800 / (24 * 5040) = 3628800 / 120960 = 3
Therefore, the value of the expression 10!/(4!7!) is 3.
Note: It is important to remember that the factorial of 0 is defined to be 1, so 0! = 1. This means that any expression involving 0! can be simplified by replacing 0! with 1. For example, the expression 10!/(4!7!0!) can be simplified as follows:
10!/(4!7!0!) = 10!/(4!7!1) = 10!/(4!7) = 10!/(24 * 7) = 10!/168 = 3628800/168 = 3
This is the same result we obtained above using the factorials of 10, 4, and 7.
The value of the given expression is 30.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
The given expression is 10!/(4!7!).
Now, (10×9×8×7!)/(4!7!)
= (10×9×8)/(4×3×2×1)
= 5×3×2
= 30
Therefore, the value of the given expression is 30.
To learn more about an expression visit;
https://brainly.com/question/28170201.
#SPJ2
a fast-food restaurant runs a promotion in which certain food items come with game pieces. according to the restaurant, 1 in 4 game pieces is a winner. if jeff keeps playing until he wins a prize, what is the probability that he has to play the game exactly 5 times?
The probability that Jeff has to play the game exactly 5 times i.e he keeps playing until he wins prize is (0.25)⁵.
We have, a fast-food restaurant runs a promotion which consists some food items with games pieces. 1 in 4 game pieces is a winner. This means, probability of winning game or sucess (p) = 1/4 . Since number of trials is fixed, trials are independent and probability of success is constant in each trial, we can use Binomial distribution. The Binomial distribution probability formula is
P(X= x) = ⁿCₓ(p)ˣ(1-p)⁽ⁿ⁻ˣ⁾
where,n --> number of trials
p --> probability of success
x --> number of times for a specific outcome within n trials
ⁿCₓ --> number of combinations
we have calculate the probability that he has to play the game exactly 5 times, i.e
x = 5 . Jeff keeps playing until he wins and he wins when he play exactly 5 times so,n= 5
Now, plugging all known values in above formula we get,
P(X= 5) = ⁵C₅(0.25)⁵(1-0.25)⁰
=> P(X= 5) = ⁵C₅(0.25)⁵(0.75)⁰
=> P(X= 5) = 1× (0.25)⁵× 1 = (0.25)⁵
Hence, required probability is (0.25)⁵
To learn more about binomial Probability distribution, refer:
https://brainly.com/question/9325204
#SPJ4
the booking limits for four fare classes in a flight are given as . (a) what is the available capacity for these four classes, i.e., what is the booking limit for classes {1, 2, 3, 4}? [ select ] (b) from this available capacity, how many seats are protected for class 1, i.e., what is the protection level for class 1?
The function available capacity for the four classes is 40 seats each. The protection level for class 1 is 40 seats, meaning that 40 seats are protected for class 1. 40 + 40 + 40 + 40 = 160
The booking limits for the four fare classes in a flight are given as 40, 40, 40, and 40, respectively. This means that the available capacity for these four classes is 40 seats each. The protection level for class 1 is 40 seats, meaning that 40 seats are specifically reserved for passengers in class 1. This ensures that passengers in class 1 are guaranteed at least 40 seats on the flight. The protection level for the other classes is also 40 seats each, ensuring that at least 40 seats are available for each class. This allows airlines to ensure that all of their classes have sufficient seating capacity for their passengers. 40 + 40 + 40 + 40 = 160
Learn more about function here
https://brainly.com/question/29633660
#SPJ4
this will be my last question of the day.
Answer:
x = -3
Step-by-step explanation:
See the picture below
A train leaves the station at time t=0. Traveling at a constant speed, the train travels 260 kilometers in 2 hours. Answer parts a and b
The function which can be used to find the relation between distance and time is f(t) = 130t.
As we know the train travels 260 kilometers in 2 hours,
then the distance traveled in one hour will be 130 kilometers.
distance = 130
when time = 0 ,
distance also = 0 , as the train has not started moving yet.
Then , the function which can tell bout the relation will be ,
f(t) = 130t
where d = f(t)
Distance is a scalar quantity which tells us about how far an object is from its starting position. Distance don't have a direction.
The distance unit of measurement in the SI
SI unit of distance is meter in the International System of Units.
Using this as the fundamental unit and a few formulae, a large number of different derived units or quantities are produced, including volume, area, acceleration, and speed.
Distance is measured also using the C.G.S. and M.K.S in metric unit system.
To learn more about distance
brainly.com/question/15172156
#SPJ4
Please help!! Find the equation of variation given that y varies directly with x and y is 25 when x is 5
Answer:
y=5x
Step-by-step explanation:
If y is 25 and x is 5
25 = 5 (5)
25=25
A basketball team has a winning percentage of 62.5% after 8 games. How many games in a row must be won to raise the winning percentage to 75%?
Answer: 11
Step-by-step explanation: To raise the winning percentage to 75%, the team needs to win 3 more games out of 4, for a total of 3/4=75% of the games. Since the team has already won 8 games, they need to win 8+3=11 games in a row to raise the winning percentage to 75%
Tritan purchaed a new car in 2000 for $22,800. The value of the car ha been depreciating exponentially at a contant rate. If the value of the car wa \$10,400$10,400 in the year 2006, then what would be the predicted value of the car in the year 2016, to the nearet dollar?
Tritan purchased a new car in 2000 for $22,800. The value of the car ha been depreciating exponentially at a constant rate then the Cost of the car in year 2016 will be $2811.
Cost price of the car = $22800
Value of the car has been depreciating exponentially, so the formula for value of the car after t years,
Here P(t) = Final value after t years
A = Cost price or initial value
r = rate of depreciation
t = duration in years
r = 100(1 - 0.87737)
r = 12.26%
Now cost of the car in year 2016 (After 16 years)
P(16) = 2810.99
= $2811
Therefore, cost of the car in year 2016 will be $2811.
learn more about of cost here
https://brainly.com/question/16482566
#SPJ4
Identify the angles shown
A. Corresponding angles
B. Alternate interior angles
C. Same side interior angles
D. Alternate exterior angles
Help!!!
HELP PLEASE Note: For questions 22-25, remember to show all of the steps that you use to solve the problem. Be sure to use the text box where the question mark (?) first appears to show your mathematical work. You can use the comments field to explain your work. Your teacher will review each step of your response to ensure you receive proper credit for your answer.
Marietta is selling cheeses for the holiday fundraiser. On Monday, she sold seven-ninths of the boxes of cheeses. On Tuesday she restocked her supply and sold 0.85 of the boxes of cheeses. On which day did Marietta sell more boxes? Explain.
She sold more cheese boxes on Tuesday.
What is comparison?Comparing numbers in maths is defined as a process or method in which one can determine whether a number is smaller, greater, or equal to another number according to their values.
Given that, Marietta is selling cheeses for the holiday fundraiser. On Monday, she sold seven-ninths of the boxes of cheeses. On Tuesday, she restocked her supply and sold 0.85 of the boxes of cheeses.
On Monday = 7/9 = 0.777
On Tuesday = 0.89
Since, 0.89 > 0.777
Hence, she sold more on Tuesday.
For more references on comparison, click;
https://brainly.com/question/14047951
#SPJ1
4) The instantaneous rate of change of f(x)=x³−5 at (2,3) is:
a) 4
b) 12
c) 48
d) 60
The instantaneous rate of change of f(x) = x³ − 5 at (2,3) is (b) 12
How to determine the instantaneous rate of changeFrom the question, we have the following parameters that can be used in our computation:
Function: f(x) = x³ − 5
Point = (2, 3)
Differentiate the function to get the instantaneous rate
This is represented as
f'(x) = 3x²
Substitute 2 for x in the equation
The 2 is coming from the x-coordinate in (2, 3)
So, we have
f'(2) = 3(2)²
Evaluate
f'(2) = 12
Hence, the instantaneous rate of change is 12
Read more about rate of change at
https://brainly.com/question/8728504
#SPJ1
The prices paid for a model of a new car are approximately normally distributed with a mean of $17,000 and a standard deviation of $500.
The price that is 3 standard deviations above the mean is $_
The price that is 2 standard deviations below the mean is $_
The percentage of buyers who paid between $16,500 and $17,500 is %___
The percentage of buyers who paid between $17,000 and $18,000 is %___
The percentage of buyers who paid less than $16,000 is %__
Answer: If the prices paid for a model of a new car are approximately normally distributed with a mean of $17,000 and a standard deviation of $500, it means that the majority of the prices paid for the car will fall within a certain range around the mean. Specifically, approximately 68% of the prices paid will be within one standard deviation of the mean, which in this case would be between $16,500 and $17,500. Approximately 95% of the prices paid will be within two standard deviations of the mean, which would be between $16,000 and $18,000. And approximately 99.7% of the prices paid will be within three standard deviations of the mean, which would be between $15,500 and $18,500. This shows that the prices paid for the car are relatively consistent, with only a small percentage falling outside of the range determined by the mean and standard deviation.
Step-by-step explanation:
If M.P. = Rs 1,530, S.P. = Rs 1,377, find the discount and discount percent.
Answer:
Discount = Rs 153,Discount % = 10%.------------------------------------------------
Given:
Marked price = Rs 1530,Sale price = Rs 1377.Find the discount:
1530 - 1377 = 153Find the discount %:
153/1530 * 100% = 10%Look at this diagram:
The required solutions are as follows,
1. Angle e = Angle a
2. Angle f = Angle c
3. Ange a, b, and c add up to 180°.
The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°
here.
Angle e = Angle and as they are alternate angles,
Angle f = Angle c as they are alternate angles,
Ange a, b, and c add up to 180°. as they lie on a straight line.
Therefore angles e, f, and b also be added to 180°
Thus, the solution of the angles is shown above.
Learn more about triangles here:
https://brainly.com/question/2773823
#SPJ1
Is (1,10) a solution to
y=7x+5
y=x+9
No or yea
Answer:
no
Step-by-step explanation:
we can test it
10=7(1)+5
10=7+5
10=12
not a solution
hopes this helps
find the surface area?
Surface area implies the external surface that bounds a given shape. The surface area of the shape is 384 sq in.
The surface area of a shape is the external side of the shape that can be seen. Sometimes, a given shape may have different shapes that forms its surface area.
From the given question,
i. The area of triangular surface = 1/2 * base* height
= 1/2*12*8
= 48
Area of the triangular surface = 48 sq in.
ii. The area of its rectangular sides = length * width
= 9* 10
= 90
Area of its rectangular sides = 90 sq in.
iii. The area of its base = length * width
= 9 * 12
= 108
Area of its base = 108 sq in.
Therefore,
the surface area of the shape = (2*48) + (2*90) + 108
= 96 + 180 + 108
= 384 sq in.
The surface area of the given shape is 384 square inches.
Learn more about surface area at https://brainly.com/question/28178861
#SPJ1
Solve the word problem below. Enter your answer as a fraction in simplest
terms, using the slash (/) as the fraction bar.
One week a student exercised 3 hours at school and another of an hour at
home. If of the student's total exercise came from playing basketball, how
much time did the student spend playing basketball that week? Enter your
answer in hours; do not include units in your answer.
The number of hours in a week a student played basketball is [tex]11\frac{3}{8}[/tex].
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, One week a student exercised 3 hours at school and another 1/4 of an hour at home.
Also given that 1/4 of the exercise of a student came from playing basketball.
Therefore, Time playing basketball is one-fourth of the total time exercised which is,
= (3 + 1/4)×(1/4).
= (13/4)×(1/4).
= (13/8).
Therefore, In a week the student played (13/8)×7.
= 91/8.
= [tex]11\frac{3}{8}[/tex].
learn more about numerical expressions here :
https://brainly.com/question/29199574
#SPJ1
Please help me with this
Answer:
d = 0
Step-by-step explanation:
7.5d = 2.5d
Divided both sides by factors and we get
d = 0
suppose one individual is randomly chosen. find the probability that this person has an iq greater than 95.
The probability that this person has an IQ greater than 95 =62.93%
What is probability?The area of mathematics known as probability is concerned with the outcomes of random events. Probability refers to a chance or potential for something to happen. It explains the likelihood that a specific event will take place.
We frequently say things like, "It will probably rain today," "He will probably pass the test, "There is very little chance of getting a storm tonight," and "Most likely the price of onions will increase once more." We substitute the word probability for all of the words chance, doubt, maybe, likely, etc. in these sentences.
In essence, probability is the ability to forecast an outcome based on the variety and quantity of potential outcomes or the analysis of historical data.
Let X be the IQ
IQ is normally distributed with a mean of 100 and a standard deviation of 15.
a) the probability that this person has an IQ greater than 95
=62.93%
b) the probability that this person has an IQ less than 125
=4.75%
c) Sample size =500
No of people = 0.2486(500) =124.3
d)
No of persons = 0.0047(500) = 2.35
Learn more about probability
https://brainly.com/question/24756209
#SPJ1
three calculus students entered a pizza parlor. they were quite hungry and ordered an entire pie, but instead of having the pizza maker cut the pie in the usual manner they asked her to slice the pie into three equal areas using only two parallel slices. where should these slices be made in order to accomplish this?
As per the Newton's method, the equal ration of the Pizza is 3: 2: 3
In math, Newton's method states that a technique for solving equations of the form f(x)=0 by successive approximation
Here we have given that three calculus students entered a pizza parlor. they were quite hungry and ordered an entire pie, instead of having the pizza maker cut the pie in the usual manner they asked her to slice the pie into three equal areas using only two parallel slices.
And we need to find these slices be made in order to accomplish this
Here let us assuming that the pizza has unit radius, and the area of the pizza is π and each piece has to have area π/3.
Therefore, the given details is enough to find the height of a circle segment such that its area is one third of the original circle,
As per the Newton's method, we get the value of h as,
=> h ≈ 0.735068 ≈ 4492/6111,
Therefore the three slices have widths approximately proportional to 3:2:3.
To know more about Newton's method here
https://brainly.com/question/29900853
#SPJ4
two of the nine insist on sitting side-by-side. in how many ways can the nine be seated together in a row?
A group of nine people can now be seated in a row in 40320 different ways.
The two people who insist on sitting next to one other can be situated in one of two ways. The remaining seven people can be seated in seven different ways.
As a result, the total number of ways in which the nine persons can be seated in a row is 1 x 7! = 40320.
In this situation, the two people who dislike each other can be seated in
(7-1)! different ways.
The remaining seven people can be seated in seven different ways.
As a result, the total number of possible combinations for seating 9 individuals in a row is (7-1)! x 7! = 40320.
A combination is a mathematical technique for determining the number of potential arrangements in a set of objects where the order of the selection is irrelevant. You can choose the components in any order in combinations. Permutations and combinations are often mistaken.
To learn more about combination visit:
https://brainly.com/question/28720645
#SPJ4
Write a linear function f(x) = mx + b for the table.
The linear function is f(x) = 3x -5.
What is a function?A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.
Given linear function expression,
f(x) = mx + b
From the table,
x = -2
then, 1 = -2m +b ......equation 1
Put x = 0
then, b = -5
Substitute the value of b to the equation 1, we get
m = 3
Finally, the function is f(x) = 3x -5
Therefore, the linear function is f(x) = 3x -5
To learn more about the function;
brainly.com/question/28303908
#SPJ1
Given f (x) = 3x + 15, find a when f (x) = 51.
Answer: 168
Step-by-step explanation: f(51)= 3(51)+15, 3(51)=153. 153+15=168
Answer:
x = 12
Step-by-step explanation:
given
f(x) = 51
f(x) = 3x + 15
51 = 3x + 15
3x = 51 - 15
3x = 36
x = 12
Question 1-8
Cameron goes to the grocery store every 15 days. Brooks goes to the grocery store every 12 days. If both Cameron and Brooks go to the grocery
store today, how many days until they go to the grocery store on the same day again? Enter the answer in the box.
days
Answer:
60
Step-by-step explanation:
To find the least common multiple of 15 and 12, we can list the multiples of 15 and 12 and find the smallest number that appears in both lists:
Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, ...
Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, ...
The least common multiple of 15 and 12 is 60, so Cameron and Brooks will go to the grocery store on the same day every 60 days.
mince pies and 2 jars of cranberry sauce costs £4.80 10 mince pies and 3 jars of cranberry sauce costs £7.60 How much does a mince pie and a jar of cranberry sauce cost each?
Answer:
£2.53 just divide£7.60by 3
Given m\parallel nm∥n, find the value of x and y. (3x-19)° (2x+1)° (5y+19
Answer:
Step-by-step explanation:
3x - 19 = 2x + 1
x - 19 = 1
x = 20
2(20) + 1 + 5y + 19 = 180
40 + 1 + 5y + 19 = 180
41 + 5y + 19 = 180
5y + 19 + 41 = 180
5y + 60 = 180
5y = 120
y = 24
Which division problem is represented in this model?
Answer:
try 5/15 or 1/15
Step-by-step explanation:
this is because it shows one shaded box we know it's a third out of just that one column
so you multiple a third by 5 and you get 15 what ever you do to the denominators you do to the numerator
y is directly proportional to x. When x = 2, y = 64. Find x when y = 80
Answer:
64 divided by 2= 32 80 divided by 32= 2.5
a deck of playing cards contains 52 cards, four of which are aces. what is the probability that the deal of a five-card hand provides a pair of aces?
The probability that the deal of a five-card hand provides a pair of aces is 0.0399
In this question, we have been given a deck of playing cards contains 52 cards, four of which are aces.
We need to find the probability that the deal of a five-card hand provides a pair of aces.
The sample space for given experiment is: choosing 52 cars choosing 5.
n(S) = 52C_5
We need to find the chance of getting a pair of aces, there are 4 aces in the pack on 2 of them.
So, n(A) = 4C_2
So that means there are 48 cards left which are not aces in the pack and want 2 of those.
So, the required probability is:
P(A) = (4C_2 * 48C_3) / 52C_5
P(A) = (6 * 17296) /2598960
P(A) = 103776 / 2598960
P(A) = 0.0399
Therefore, the required probability is 0.0399
Learn more about the probability here:
https://brainly.com/question/11234923
#SPJ4
Plllssssss help In which function has f(x) been shifted up 2 units and to the right 7 units?
O f(x - 7) + 2
O f(x- 2) + 7
O. f(x + 2) + 7
O. f f(x + 7) - 2
Which statement is true?
Answer:
Correct Statement : The y- intercept of Function A is greater than the y- intercept of Function B