The number of possible combinations for this scenario is 35
A combination is a way of selecting items from a set, where the order of the items does not matter.
Let's assume that each adventurous citizen has a demand for visiting three flags. This means that each citizen wants to visit three flags out of the seven available flags. To find the number of possible combinations, we can use the formula for combinations, which is:
C(n, r) = n! / (r! * (n - r)!)
Where n is the total number of flags available (7), and r is the number of flags that each citizen wants to visit (3). So, the number of possible combinations is:
C(7, 3) = 7! / (3! * (7 - 3)!) = 35
This means that there are 35 different combinations of flags that an adventurous citizen can choose from at 7 flags amusement park.
Complete Question:
Initially, suppose that only adventurous citizens buy tickets at 7 flags. each adventurous citizen has an individual demand given by those 3 flags. Find the number of possible combinations for this one.
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If the public debt in 2006 was 6,783,231,062,743.62 and the budget for 2007 was in deficit by 595,821,633,586.70 what was the public debt in 2007?
Answer: The public debt in 2007 would be 6,783,231,062,743.62 + 595,821,633,586.70 = 7,379,052,696,330.32
Step-by-step explanation:
Solve, for 0 ≤ x < 360°, the equation
5 sinx - 5 cosx = 2
In response to the query, x is equal to 60°, 120°, 240°, and 300°. These four options are the answer to the equation.
What does equation mean in its entirety?A mathematical equation is a statement that two amount or values are equal, such as 6 x 4 = 12 x 2. 2. A noun that counts. An equation is applied when several or more factors must be considered jointly in order to understand or explain the whole situation.
This equation can be solved using the trigonometric identity:
[tex]sinx = \sqrt{ (1 - cos^2x)}[/tex]
This identity can be used as a substitution in the equation:
5 sinx - 5 cosx = 2
5 [tex]\sqrt{(1 - cos^2x) }[/tex] - 5 cosx = 2
5 sqrt[tex](1 - cos^2x)[/tex]) = 7 + 5 cosx
Squaring both sides:
25([tex]1 - cos^2x[/tex]) = 49 + 70 cosx + 25 [tex]cos^2x[/tex]
25 - 25 [tex]cos^2x[/tex] = 49 + 70 cosx + 25 [tex]cos^2x[/tex]
0 = 74 + 45 cosx
45 cosx = -74
cosx = -74/45 = -2/3
The inverted cosine function can be used to determine that x = cos-1(-2/3). x must be within the range of 0° to 360°, hence x must be 300°.
5 sin - 5 cos - 5(-1/2) = 5 sqrt(3)/2 + 5/2 = 2 + 2.5 = 2.5
Since the left side of the equation is not equal to 2, x = 300° is not a solution to the equation.
We can repeat this process for the other solutions to the equation:
x = 60°, x = 120°, x = 240°, and x = 300°
These are the four solutions to the equation for 0° <= x < 360°.
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Find the values of a and b that make the following piecewise defined function both continuous and differentiable everywhere. - 6 x <5 f(x) = { -27 *"ax + b, 125
The values of a = 17 and b = - 56
that make the following piece wise defined function both continuous and differentiable everywhere.
What is continuous function?A continuous function in mathematics is one that doesn't change value unexpectedly due to discontinuities, or breaks in the function's continuity. A continuous function in mathematics is a function that causes the value of the function to continuously vary as a result of a continuous variation of the argument, or a change without a leap. Thus, there aren't any discontinuities—rapid changes in value.
conditions are:
1.
f(x) is continuous if,
[tex]\lim_{x \to \ 5^{-}}f(x)[/tex] = [tex]\lim_{x \to \ 5^{+}}f(x)[/tex] = f(5)
2.
differentiable if,
[tex]\lim_{x \to \ 5^{-}}f^'(x)[/tex] = [tex]\lim_{x \to \ 5^{+}}f^'(x)[/tex]
for 1st condition:
⇒ [tex]\lim_{x \to \ 5^{-}}f(x) = \lim_{x \to \ 5^{+}}f(x)[/tex]
⇒ [tex]\lim_{x \to \ 5^{-}}(-3x -6) = \lim_{x \to \ 5^{+}}(-2x^2+ax+b)[/tex]
⇒ (-3 × (-5) - 6) = - 2(5)² + a(5) + b
⇒ - 21 = - 50 + 5a + b
⇒ 5a + b = 29 ................... (1)
For 2nd condition:
⇒ [tex]\lim_{x \to \ 5^{-}}f^'(x) = \lim_{x \to \ 5^{+}}f^'(x)[/tex]
⇒ [tex]\lim_{x \to \ 5^{-}} \frac{d}{dx} (-3x - 6) = \lim_{x \to \ 5^{+}} \frac{d}{dx}(-2x^2 + ax + b)[/tex]
⇒ - 3 = - 4x + a
⇒ - 3 = - 4 (5) + a
⇒ a = 17
Substitute a = 17 in equation (1) we get:
5(17) + b = 29
or, b = - 56
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The complete question is as follows:
An emergency plumber charges $65 as a call out few plus an additional $75 per hour. He arrives at the house at 9:30 and works to repair a water tank. The total repair bill is $196.25. Use the variable t for the number of hours.
Answer:
Step-by-step explanation:
Answer:
Around 11:15 am
Step-by-step explanation:
Let h represents the number of hours the plumber works
Since the plumber charges $65 fee plus $75 per hour, the bill can be calculated by:
→ bill = 65 + 75h
Since the bill is $195.25
→ 195.25 = 65 + 75h
→ 75h = 130.25
→ h = 1.74
1.74 implies that the plumber worked almost 1 hour and 45 minutes. Since the plumber started at 9:30, the repair was completed around 11:15 am.
what is the smallest number that you can add to 17,438 that will make the sum divisible by 25?
Check the picture below.
Solve the equation for the specified variable.
M = F/a
a=
Answer:
A=F/M
Step-by-step explanation:
m=f/a ......,,, cross product
f= ma......,..., both sides divided by m
then the answer is a=f/m
Let P(x) = 3x³ - 7x² + 3x-4 and Q(x) = 2x³ - 6x² - 15. Add the polynomials functions, as indicated below.
(P+Q)(x)
(P+Q)(x) = (Simplify your answer. Do not factor.)
K
The addition of the polynomial P(x) and Q(x) is 5x³ - 13 x² + 3x - 19.
What is Polynomial?A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminates in mathematics.
Given:
P(x) = 3x³ - 7x² + 3x-4 and Q(x) = 2x³ - 6x² - 15.
Now, adding the both Polynomials
P(x) + Q(x)
= 3x³ - 7x² + 3x-4 + 2x³ - 6x² - 15.
Now, solving the like terms
= 3x³ + 2x³ - 7x² - 6x² +3x -4 -15
= (3+ 2) x³ + (-7-6) x² +3x -4 - 15
= 5x³ - 13 x² + 3x - 19
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A teacher randomly chooses a two-person leadership team from a group of four qualified students. Three of the students, Sandra, Marta, and Jane, are girls. The fourth student, Franklin, is a boy.
Using the sample space of possible outcomes listed below, where each student is represented by the first letter of his or her name, answer each of the following questions.
What is P(A)P, left parenthesis, A, right parenthesis, the probability that the first student is a boy?
Answer: The sample space of possible outcomes is:
{SM, SJ, MJ, MS, JS, JM}.
There are 6 possible outcomes in the sample space, and 1 of these outcomes results in the first student being a boy (Franklin, represented by "F").
Therefore, the probability of the first student being a boy is P(A) = 1/6.
Step-by-step explanation:
what are some services offered by the banks and credit unions
Step-by-step explanation:
mortgages, lines of credit, checking and savings accounts, auto loans and the convenience of electronic banking and Automated Teller Machines (ATMs)
Step-by-step explanation:
Banks and credit unions offer a variety of financial services, including:
Checking and savings accounts
Personal loans
Mortgages
Credit cards
Investment products (e.g. mutual funds, individual retirement accounts (IRAs))
Foreign currency exchange
Online and mobile banking
Wire transfers
Automated teller machines (ATMs)
Insurance products (e.g. life, auto, homeowners)
Wealth management services
Small business banking services.
Note that the exact services offered may vary depending on the institution.
PLS HELP me I am in need of help will mark brainiest
Answer:
Fourth option: √65/4
Step-by-step explanation:
Since the angles are similar, each of the angles of ΔEFG must be equal to each of the corresponding angles of ΔHIJ
Specifically, m ∠J in ΔHIJ = m∠G in Δ EFG
Let's first find ∠G
Since EFG is a right triangle,
tan(G) = EF/FG = √65/4
tan J must be the same as tan G = √65/4
This is the fourth option
The value of tanJ is in the right angled triangle HIJ√65 / 4
What is an equation?An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either be linear, quadratic, cubic, depending of the degree of the variable.
Two triangles are similar if their corresponding angles are equal to each other.
Given that triangle EFG and triangle HIJ are similar, hence:
Angle G = Angle J
tanJ = tanG = √65 / 4
The value of tanJ is √65 / 4
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suppose that x is a discrete random variable that takes integer values from 1 to 100 (both inclusive), and has cumulative distribution function (cdf)
The probability that the discrete random variable x takes a value less than or equal to 50 is 0.50, since F(50) = 50/100 = 0.50.
F(x) = x/100
Then, the probability that x takes a value less than or equal to 50 is 0.50, since
F(50) = 50/100 = 0.50
The cumulative distribution function (CDF) of a random variable is a function that gives the probability that the random variable is less than or equal to a certain value. In this case, the CDF of the random variable x is given by F(x) = x/100.
Therefore, to find the probability that x takes a value less than or equal to 50, we simply need to evaluate the CDF at x = 50. This is done by substituting 50 into the CDF, which gives us F(50) = 50/100 = 0.50. This means that the probability that x takes a value less than or equal to 50 is 0.50.
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hey thank for helping me
Answer: -1
Step-by-step explanation:
When the graph g hits g=2, the y is -1
I really need help with these questions pls?
Answer:
Top one is 3/8
Middle is 4/7
Bottom is 1/3
Step-by-step explanation:
Given a simplified rate of (2), determine the percent change.
The percent change of an object is the ratio of its final value to its initial value.
What is meant by percent change?The percentage of an item's final value versus its starting value is its percent change. By dividing the difference in data by the starting value, you can get the percent change.
"Rate" simply refers to the quantity divided by another number, typically 100, 1,000, or another multiple of 10. A rate per 100 is known as a percentage.
Percentage Change is the difference that results from deducting the old value from the new value, dividing by the old value, and multiplying the result by 100 to represent it as a percentage. In most cases, multiplying a fraction by 100 results in a percent conversion.
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There are 80 people at the movie theater today 2/5 of the people are eating popcorn one for eating chocolate candy and the rest are eating record twist how many people are eating record toys
The people that are eating record toys are 48
How many people are eating record toysFrom the question, we have the following parameters that can be used in our computation:
People at the movies = 80
People are eating popcorn = 2/5
Using the above as a guide, we have the following:
Record toys = (1 - People are eating popcorn) * People at the movies
Substitute the known values in the above equation, so, we have the following representation
Record toys = (1 - 2/5) * 80
Evaluate
Record toys = 48
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Solve with the box method
The polynomial n² + 6n - 1 can be factored as,
(n + 3 + √10)(n - 3 + √10)(3n - 2).
What is a factor of a polynomial?We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.
To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.
Given, A product of two polynomials (n² + 6n - 1)(3n - 2).
Now, The quadratic expression n² + 6n - 1 can be factored as,
n² + 6n - 1.
[- 6 ± √(36 + 4)]/2.
= [- 6 ± √40]/2.
= [- 6 ± 2√10]/2.
= - 3 ± √10.
Therefore, (n² + 6n - 1)(3n - 2)
= (n + 3 + √10)(n - 3 + √10)(3n - 2).
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rewrite the expression $6j^2 - 4j 12$ in the form $c(j p)^2 q$, where $c$, $p$, and $q$ are constants. what is $\frac{q}{p}$?
The expression 6j^2 - 4j 12 can be rewritten as [tex]$-24(j\frac{1}{2})^2 -12$[/tex]where , and [tex]$q=-12$[/tex]. Thus,[tex]$\frac{q}{p}=-24$[/tex].
The expression[tex]$6j^2 - 4j 12$[/tex] can be rewritten in the form [tex]$c(j p)^2 q$[/tex], where c, p, and q are constants. To do this, we can factor out a common factor from the expression. In this case, the common factor is j. Then, we can rewrite the expression as [tex]$j(6j - 12)$[/tex] which simplifies to [tex]$-24j^2 -12$[/tex]. Dividing both sides by j, we can rewrite the expression as [tex]$-24(j\frac{1}{2})^2 -12$[/tex] where [tex]$c=-24$[/tex], [tex]$p=\frac{1}{2}$[/tex] and [tex]$q=-12$[/tex]. Thus, [tex]$\frac{q}{p}=-24$[/tex]. To summarize, the expression [tex]$6j^2 - 4j 12$[/tex] can be rewritten in the form [tex]$c(j p)^2 q$[/tex] where c, p, and q are constants, and [tex]$\frac{q}{p}=-24$[/tex].
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Two houses are 1.5 inches apart on a map. The actual distance between the houses is 10.8 miles. What is the scale of the map?
Answer:
I inch = 7.2 miles
Step-by-step explanation:
Proportion method is applied:
1.5 inches on a map = 10.8 miles of actual distance
∴ 1 inches on the map = x miles of the actual distance
Cross-multiplication is applied:
(1.5 inches)(x miles) = (1 inch)(10.8 miles)
x needs to be isolated and made the subject of the equation:
x miles = [tex]\frac{(1 inch)(10.8 miles)}{1,5 inches}[/tex]
Inches in the numerator and denominator will cancel eachother out:
x miles = [tex]\frac{10.8 miles}{1.5}[/tex]
x miles = 7.2 miles
∴ Scale on the map:
1 inch = 7.2 miles
given the parallelagram below, micheal writes triangle abc
Michael writes, "Triangle ABC is congruent to triangle CDA'',
if the segment AC ≅ AC.
What is congruent?In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.
Given the parallelogram below,
Michael writes, "Triangle ABC is congruent to triangle CDA''.
By the parallelogram property:
AB ≅ CD
BC ≅ AD.
If triangle ABC is congruent to triangle CDA,
then the segment AC ≅ AC.
Therefore, the segment AC ≅ AC.
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please help with finsing the lemgth of x
Answer:
x = 5
Step-by-step explanation:
You want the length of x in the figure showing similar triangles.
ProportionThe bottom edge of the triangle is 2/3 of the left edge.
The similar triangles have the same ratio of side lengths. That means x is 2/3 of (3+4.5):
(2/3)(7.5) = 5
The length x is 5 units.
Suppose that Y1 and Y2 are independent, standard normal random variables. Find the density function of U = Y1^2 +Y2^2.
The cumulative distribution function (CDF) of U is also well known and is given by:
F(u) = 1 - [tex]e^{(-u/2)}[/tex] × γ(1/2, u/2)
where γ is the lower incomplete gamma function.
What is the chi-squared distribution?
The chi-squared distribution is a continuous probability distribution that is widely used in statistics and other fields.
The random variable U = Y1^2 + Y2^2 has a well-known distribution called the chi-squared distribution with two degrees of freedom. The density function of U is given by:
[tex]f(u) = (1 / (2 \times \pi)) \times e^{(-u/2)} \times (u/2)^{(1/2 - 1)}[/tex]
where e is the base of the natural logarithm and π is the mathematical constant pi. This distribution has a positive support on the interval [0, +∞).
The cumulative distribution function (CDF) of U is also well known and is given by:
F(u) = 1 - [tex]e^{(-u/2)}[/tex] × γ(1/2, u/2)
where γ is the lower incomplete gamma function.
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Math 5th grade
Roshaun walks around the city park. The square park measures 61 1/4 yards on each side. How far does Roshaun walk?
Answer: 245 yds
Step-by-step explanation:
61 1/4 times 4 = 245
Angel read for 1/2 hour. Margo read 1/6 hour. Who read for the greater amount of time.
Cavalleria Pizza sells only pizza. They offer five types of crust, two types of cheese, four meat toppings and
four vegetable toppings. If you must order exactly one type of cheese, one meat topping and one vegetable
topping on your pizza, how many different pizzas can you order at Cavalleria Pizza?
Answer:
3?
Step-by-step explanation:
im not sure sorry
What is the answer to x in this equation 4x+4=12?
Answer:
x=2
Step-by-step explanation:
4x+4=12
-4 -4
_______
4x=8
_____
4 4
x=2
In a group of 21 students, 8 students take Art courses, 7 students take Music courses. Two students take both courses. A student is chosen randomly from this group.
What is the probability that the student takes either Art or Music courses?
Three classes ordered lunch from a restaurant. In one class 5/6 of the children ordered hamburger, In the other class 2/4 ordered hot days. 1/2 of the other class ordered chicken wings. what is the total number of children that ordered Sandwiches ?
The total number of children that ordered Sandwiches is 1 5/6
What is the total number of children that ordered SandwichesFrom the question, we have the following parameters that can be used in our computation:
Class 1 = 5/6 Hamburger
Class 2 = 2/4 Hot days
Class 3 = 1/2 Chicken wings
So, the total number of children that ordered Sandwiches is
Total = 5/6 + 2/4 + 1/2
Evaluate
Total = 1 5/6
Hence, 1 5/6 of the three classes ordered sandwiches
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What number should go in the space?
Multiplying by 1.15 is the same as increasing by _____%.
Answer: 115%
Step-by-step explanation:
100% = 1
10%=0.1
5%=0.05
100%+10%+5%=115%
1+0.1+0.05=1.15
Answer: 15
Step-by-step explanation:
x+x*15/100
x(1+.15)
1.15x
Simplify expression[5-6+1]
Answer: 0
Step-by-step explanation:
Using GEMDAS
- Grouping
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
[5-6+1]
= [-1+1] because you add/subtract from left to right
= [0] because -1+1=0.
Answer is 0
An automobile manufacturer can produce up to 300 cars per day. The profit made from the sale of these vehicles can be modelled by the function p(x) = -x²+ 350x-6600 where p(x) is the profit in thousand Rupees and x is the number of automobiles made and sold. Answer the following questions based on this
model:
(i) When no cars are produce what is a profit/loss?
(ii) What is the break even point? (Zero profit point is called break even)?
(iii) What is the profit/loss if 400 cars are produced?
i) The profit/loss when no cars are produced is a loss of 6600 Rupees.
II) The break even point is at 20 cars
III) The profit/loss if 400 cars are produced is; a loss of 13400Rupees.
How to solve Profit functions?(i) When no cars are produced, x = 0.
Thus, plugging this value into the function p(x) = -x² + 350x - 6600, we have;
p(0) = -0² + 350(0) - 6600 = -6600.
Therefore, the profit/loss when no cars are produced is a loss of 6600 thousand Rupees.
(ii) The break-even point is the point at which the profit is zero, i.e., p(x) = 0. Setting p(x) = 0 and solving for x, we find that;
-x² + 350x - 6600 = 0
x = 20
Therefore, the break-even point is x = 20 cars. T
(iii) If 400 cars are produced, the profit can be found by plugging this value into the function p(x) = -x² + 350x - 6600.
We find that p(400) = -400² + 350(400) - 6600
= -160000 + 140000 + 6600 = -13400. Therefore, the profit/loss if 400 cars are produced is a loss of 13400 Rupees.
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