The number of ways to select the banners is given as follows:
a. Matching with the country: 362,880, using the arrangements formula.
b. Not matching with the country: 60,949,324,800, using the permutation formula.
What is the arrangements formula?The number of possible arrangements of n elements is obtained by the factorial of n, that is:
[tex]A_n = n![/tex]
For item a, the arrangements formula is used, as the banner has to match the country, hence only the countries are arranged and then the specific banner is matched with this country.
Considering that there are nine countries, the number of ways of selecting and matching nine banners with a country is calculated as follows:
Total = 9! = 362,880.
What is the permutation formula?The number of possible permutations of x elements from a set of n elements is obtained by the equation as follows:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
For item b, 9 banners are taken from a set of 20, and the permutation formula is used as the order in which the banners are chosen is important, hence the number of ways of selecting nine banners without having to match them with a country is obtained as follows:
N = 20!/(20 - 9)! = 20!/11! = 60,949,324,800.
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5–3 3/5 ÷ (–3– –3 3/4)
Answer:
[tex]0.2[/tex]
Step-by-step explanation:
... .. ... .. .
) 3 1+ − 2 2− + 2 1−
Question 7 of 10
Here is a table of values for y = f(x).
X
-2 -1 0 1 2 3
f(x) 5 6
7
Mark the statements that are true.
4
8 9 10 11
5 6
12 13
A. The range for f(x) is all real numbers.
B. f(5) = -2
C. The domain for f(x) is the set (-2,-1, 0, 1, 2, 3, 4, 5, 6).
D. f(-1) = 6
Option (C) is the correct one and the only true statement is
The domain of the function f(x) is { -2, -1, 0, 1, 2, 3, 4, 5, 6 }.
Given, a table of values for y = f(x)
x -2 -1 0 1 2 3 4 5 6
y 7 8 9 10 11 5 6 12 13
We have to find the correct statements,
as the range of the function f(x) is { 4, 8, 9, 10, 11, 5, 6, 12, 13 }
the image of 5 in the function is 6 i.e. f(5) = 6.
The domain of the function f(x) is { -2, -1, 0, 1, 2, 3, 4, 5, 6 }
the image of -1 in the function is 8 i.e. f(-1) = 8.
Hence, only the option (C) is the correct one and the only true statement is
The domain of the function f(x) is { -2, -1, 0, 1, 2, 3, 4, 5, 6 }.
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The formula A = Pe describes the accumulated value, A, of a sum of money, P, the principal, after t years at annual percentage rate r (in decimal form) compounded continuously. Complete the table for a
savings account subject to continuous compounding.
Amount Invested Annual Interest Rate
$7000
9%
years
Accumulated Amount
Double the amount invested
Time t in Years
?
LIDE
Amount Invested Annual $7000, Interest Rate of 9% Accumulated Amount is Double the amount invested in 7.7 years,
What is an interest rate?
An interest rate tells you how high the cost of borrowing is, or high the rewards are for saving. So, if you're a borrower, the interest rate is the amount you are charged for borrowing money, shown as a percentage of the total amount of the loan.
Here, we have
A = P e^(rt) ......(1)
P = Amount Invested = $7000
Interest Rate = 9%
A = Accumulated Amount Double the amount invested = 2P = $14000
t = time in years
from equation (1) , we get
14000 = 7000×e^(0.09)t
2 = e^(0.09)t
㏑2 = 0.09t
0.6931 = 0.09t
t = 0.6931/0.09
t = 7.7 years
Hence, Amount Invested Annual $7000, Interest Rate of 9% Accumulated Amount is Double the amount invested in 7.7 years.
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The overhead reach distances of adult females are normally distributed with a mean of 202.5 cm and a standard deviation of 8.6 cm.
a. Find the probability that an individual distance is greater than 211.80 cm.
b. Find the probability that the mean for 20 randomly selected distances is greater than 200.30 cm.
c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?
a. The probability is
(Round to four decimal places as needed.)
Answer: I am not sure if you're accustomed to using a z-score and table of probabilities or technology, so I will answer using both!
a) Since you're choosing one person from the population, you will use the mean and standard deviation from the population. z= (210.9-197.5)/8.6 = 1.56 Using a table of normal probabilities,
P(x>210.9)= 1-P(z<1.56)= 1- 0.9406=0.0594
Using technology: normalcdf(210.9, 1E99, 197.5, 8.6)=0.0596
b) Since you're calculating the population for a sample to occur, you need to get a mean of the sampling distribution and standard deviation of the sampling distribution.
Meanpop=Meansampling dist.=197.5
St. Devsampling dist.= Stdpopulation/√n = 8.6/√15 = 2.22
Using technology, P(X>196.20)= normalcdf( 196.20, 1E99, 197.5, 2.22) = 0.7209
c) You only have to worry about the sample size in a sampling distribution if you either do not know the shape of the distribution of the population or if the distribution of the population is not normally distributed. Since this population is normally distributed (as stated in the given information), then your sample size does not have to be greater than 30.
Hope this helps! I can solve part b using a z-score if you need me to.
Step-by-step explanation:
can you help meeeeeeeeeeeeeeeeeeee pleaseeeeeeee!!!
Answer:
[tex]f(x) = 2(x-9)^{2} + 3[/tex]
Step-by-step explanation:
In vertex form, (h, k) represents the vertex.
With the given vertex of (9, 3), h = 9 and k = 3. You can substitute those values into the equation.
In vertex form, a represents vertical stretch or compression.
In this case, since the parent function, x^2 is multiplied by 2, a = 2. You can substitute this into the equation.
You end up with [tex]f(x) = 2(x-9)^{2} + 3[/tex]
help me please I am in need of this answer too
When corresponding angles are congruent, the lines are parallel
Congruent AnglesCongruent angles are two or more angles that are identical to each other. Thus, the measure of these angles is equal to each other. The type of angles does not make any difference in the congruence of angles, which means they can be acute, obtuse, exterior, or interior angles. The angles which occupy the same relative position at each intersection where a straight line crosses two others. If the two lines are parallel, the corresponding angles are equal.
Examples of the corresponding angle are any angles which are formed on the opposite side of the transversal. Now, it should be noted that the transversal can intersect either two parallel line or two non-parallel lines. Thus, corresponding angles can be of two types:
Corresponding angles formed by parallel lines and transversals
Corresponding angles formed by non-parallel lines and transversals
Looking at the image, angle I is congruent to each other. Angle II is congruent with each other as well as angle III.
When corresponding angles are congruent, the lines connecting them must be parallel. This is the only valid or correct options in the task.
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Write an equation for the quadratic graphed below:
x-intercepts: (-3,0) and (1,0); y-intercept: (0,-3)
Answer:
y = (x + 3)(x - 1) or y = x² + 2x - 3Step-by-step explanation:
Quadratic equation:
y = a(x - p)(x - q), where a - constant, p and q - x-intercepts.Substitute p and q:
y = a(x - (-3))(x - 1)y = a(x + 3)(x - 1)Find the value of a, using the y-intercept:
- 3 = a(0 + 3)(0 - 1)- 3 = a*3*(-1)-3 = - 3aa = 1The equation is:
y = (x + 3)(x - 1)or
y = x² + 2x - 3Please help with the following question.
The probabilities, using the Poisson distribution, are given as follows:
a) Two earthquakes in a year: 0.0446 = 4.46%.
b) No earthquakes in two consecutive months: 0.3679 = 36.79%.
c) No earthquakes in two consecutive months, given that there were no earthquakes in the previous month: 0.3679 = 36.79%.
What is the Poisson distribution?The Poisson distribution is used when we only have the mean in a given interval and the mass function is given as follows:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
The parameters are listed as follows:
x is the number of successes.e = 2.71828 is the Euler number.[tex]\mu[/tex] is the mean in the given interval or range of values of the input parameter.For one year, the mean number of earthquakes is given as follows:
[tex]\mu = 6[/tex]
The probability of exactly two earthquakes in a year is obtained as follows:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 2) = \frac{e^{-6}6^{2}}{(2)!} = 0.0446[/tex]
For two months, the mean is given as follows:
[tex]\mu = 2 \times 6 \times \frac{1}{12} = 1[/tex]
For items b and c, the probabilities are the same, P(X = 0), as the events are independent, hence:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-1}1^{0}}{(0)!} = 0.3679[/tex]
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This is what I need help with
Answer:no picture
Step-by-step explanation:
0.721x10 to the second power
Answer:
72.1
Step-by-step explanation:
It is 10 to the power of 2 because the exponent is 2. The result is a number bigger than the origin or base number because the exponent is positive. We move the decimal two times to the right to arrive at our conclusion:
0.721--> 72.1
therefore, your answer will be 72.1
The sum of twelve times a number and eleven is 251. Find the number.
Answer:
x = 20
Step-by-step explanation:
12x + 11 = 251
12x + 11 - 11 = 251 - 11
12x = 240
12x /12 = 240/12
x=20
Solve for x in the equation. The equation is added as an image below.
Answer:
x = 10
Step-by-step explanation:
You want the value of x that satisfies x -(x-1)/3 -(2x-5)/5 +(x+8)/6 = 7.
SolutionThe least common denominator is 5·6 = 30, so we can eliminate the fractions by multiplying by 30:
30x -10(x -1) -6(2x -5) +5(x +8) = 7·30
30x -10x +10 -12x +30 +5x +40 = 210 . . . . . eliminate parentheses
13x +80 = 210 . . . . . . . . . collect terms
13x = 130 . . . . . . . . . . subtract 80
x = 10 . . . . . . . . . . divide by 13
__
Additional comment
Often an equation can be nicely solved by a graphing calculator. We like to write the equation in the form f(x) = 0, and look for the x-intercepts. Those are usually labeled by the calculator. Here that rewrite is accomplished by subtracting 7 from both sides.
Determine the perimeter of the right triangle shown.
Answer:
27
Step-by-step explanation:
I looked at the graph and added 6+6=12 so the bottom is 12 and for the height i added 1+8=9 and then i added another 12 because the bottom is also 12 and divided that by 2 which is 6 so i got 27.
this may not be right but i am hoping that is it!
Have A Great Day!!!
What are numbers that have 2,3,4,5,6 as their factors? (under 200)
Answer:
120, 60, 180
Step-by-step explanation:
Which transformation always preserves distance and angle measures?
Step-by-step explanation:
Rigid motion
Rigid motion – A transformation that preserves distance and angle measure (the shapes are congruent, angles are congruent).
two buses leave a station at the same time and travel in opposite directions. One bus travels 15 km/h faster than the other. If the two buses are 1004 kilometers apart after 4 hours, what is the rate of each bus?
The speed of slower bus is 118 km/hr and speed of faster bus is 133 km/hr
What is speed?Speed is a scalar quantity that refers to "how fast an object is moving".
Given that, two buses leave a station at the same time and travel in opposite directions, one bus travels 15 km/h faster than the other, the two buses are 1004 kilometres apart after 4 hours,
Speed = distance/ time
Let the speed of the slower bus be v and the faster bus be (v+15)
According to the question,
vt + (v+15)t = 1004
vt + vt + 15t = 1004
t = 4
4v + 4v + 60 = 1004
8v = 944
v = 118
Hence, The speed of slower bus is 118 km/hr and speed of faster bus is 133 km/hr
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400 passengers go on a coach trip.
Each coach takes 50 passengers.
Each passenger pays £23
The table shows the costs for the
coach company.
Each coach travels 200 miles.
Work out the total profit the company makes from this trip.
The total profit that the company would make on the trip can be found to be £7,320
How to find the total profit made?The revenue that the company makes would be:
= Number of passengers x Amount that each passenger pays
= 400 x 23
= £9, 200
Each coach takes 50 passengers so the number of coaches needed are:
= 400 passengers / 50 passengers per coach
= 8 coaches
The total cost to the company for the trip is:
= (Number of coaches x Driver cost per coach) + (Number of coaches x Fuel per mile x Distance traveled for each coach)
= ( 8 x 95) + ( 8 x 70p x 200)
= 760 + 112, 000 p
= 760 + 112, 000/ 100 pence per pound
= £ 1,880
The total profit is:
= Revenue - total cost
= 9, 200 - 1, 880
= £7,320
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Solve for a.
a+45=112
Enter your answer as a fraction in simplest form in the box.
a =
Answer:
67
Step-by-step explanation:
a+45=112
-45. -45
a=67
Hopes this helps please mark brainliest
Answer:
a = 67
Step-by-step explanation:
Given equation,
→ a + 45 = 112
Now the value of a will be,
→ a + 45 = 112
→ a = 112 - 45
→ [ a = 67 ]
Hence, the value of a is 67.
2 Which of the following statements is true?
A.Every irrational number can be represented as a fraction.
B.Every irrational number can be represented with the help of decimals.
C.Every rational number can be represented as a terminating decimal.
D.Every rational number can be represented as an integer.
The true statement is 'Every irrational number can be represented with the help of decimals.'
The correct answer is an option (B)
We know that the rational numbers are of the form p/q (i.e., simple fraction) where p, q are integers with q ≠ 0
And an irrational numbers are real numbers that cannot be represented as simple fractions.
An irrational numbers can be written in decimals.
√3 = 1.7321
We know that every terminating decimal is a rational number (for example, 2.5 = 5/2) but every rational number may not be a terminating decimal (for example, 2/3 = 0.666...)
So, a statement 'Every irrational number can be represented as a fraction.' is false.
A statement 'Every irrational number can be represented with the help of decimals.' is True
A statement 'Every rational number can be represented as a terminating decimal.' is False.
and a statement 'Every rational number can be represented as an integer.' is False.
Therefore, the true statement is 'Every irrational number can be represented with the help of decimals.'
The correct answer is an option (B)
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A coach can take 40 passengers.how many passenger can be carried by 18 coaches
What is the image of (3,3)(3,3) after a dilation by a scale factor of 1/3
centered at the origin?
The image of (3, 3) after dilation by a scale factor of 1/3 centered at the origin will have coordinate (1, 1)
What is dilation?Dilation refers to the transformation that increases or reduces the image formed after the transformation
When the scale factor is greater that 1 the transformation will lead to magnification when the scale factor is less than 1 the image formed is compressed.
The transformation rule fir dilation is (x, y) → (kx, ky)
where k is the scale factor = 1/3
(3, 3) → (1/3 * 3, 1/3 * 3) → (1, 1)
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Make the subject of
X
16
=
р
Answer: x= p16
Step-by-step explanation:
Bike Cost $800 $600 $400 $200 $0 Bike City Comparing Costs Fast BMX Bike World Bike Store Awesome Bikes How much more is the cost at Fast BMX than Bike World?
Using the mathematical operation of subtraction, the cost at Fast BMX is $200 more than the cost at Bike World.
How is the difference computed?The difference in the cost of bikes can be computed using the mathematical operation of subtraction.
Subtraction operations involve deducting the subtrahend from the minuend to get the result known as the difference.
Bike Stores Prices
Bike City $300
Fast BMX $500
Bike World $300
Awesome Bikes $400
Difference between Fast BMX and Bike World
= $200 ($500 - $300)
Thus, the cost of bikes is higher at Fast BMX than at Bike World by $200.
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6. A garbage truck collects trash from
68 trash cans. Another truck collects
trash from 39 fewer trash cans. How
many trash cans do the trucks collect
trash from in all?
trash cans
A car travels 210 kilometres in 3 hours 30 minutes
Calculate the average speed, in km/h, of the car.
Answer:
70 km/hr
Step-by-step explanation:
Complete the square to make a perfect square trinomial. Then, write the result as a binomial squared.
d²-3d
The trinomial and binomial form of the incomplete algebraic expression is [tex]d^{2}[/tex] -3d + 9/4 and [tex](d-\frac{3}{2}) ^{2}[/tex]
What is a perfect square expression?A perfect square is a quadratic expression that factors into two identical binomials.
For example, if you multiply these two identical binomials factors:
(x + 2)(x + 2)
to complete the square in the expression [tex]d^{2}[/tex] -3d, we square the half of the coefficient of d which is -3/2
so the expression becomes,
[tex]d^{2}[/tex] -3d + [tex](\frac{-3}{2}) ^{2}[/tex] = [tex]d^{2}[/tex] -3d +[tex]\frac{9}{4}[/tex]
The Binomial form of the expression [tex]d^{2}[/tex] -3d + [tex](\frac{-3}{2}) ^{2}[/tex]
can be written by take [tex]d^{2}[/tex] term and the constant and putting them in a bracket and squaring
which becomes
[tex](d - \frac{3}{2} )^{2}[/tex]
In conclusion, the trinomial form of the expression is [tex]d^{2}[/tex] -3d +[tex]\frac{9}{4}[/tex] while the Binomial form of the expression is [tex](d - \frac{3}{2} )^{2}[/tex]
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The siding of a house is 2250 square feet. The siding needs two coats of paint.
1 quart costs 18 dollars and covers 80 square feet;
1 gallon, costs 29 dollars, covers 320 square feet.
A. What is the minimum cost of the paint needed to complete the job?
B. How much paint is left over when you spend the minimum amount?
Answer: Minimum cost = $264
Paint left over = 7/8 qt
Step-by-step explanation:
6 gal covers 1920 sf (6 gal x 320 sf/gal)
6 gal x $29/gal = $174
2250 sf - 1920 sf = 330 sf
Need 4.125 qt to cover 330 sf, but you can't buy a partial quart
5 qt x $18/qt = $90
Total cost = $174 + $90 = $264
You have 7/8 qt left over
. √-100 rewrite each expression using I
Answer:
?????
Step-by-step explanation:
Dwayne wants to redecorate his bedroom and decides to purchase new furniture. The following graph could be used to represent the value of the new bedroom furniture, f(x), after x years.
A graph of an exponential function which decreases through the points 0 comma 1200 and 2 comma 675.
Which of the following statements is/are true based on the graph and the context of the problem?
The y-intercept (0, 1200) represents the initial cost of the bedroom furniture.
The function is negative on its entire domain.
The domain is x ≥ 0 to represent the number of years after the bedroom furniture was purchased.
The y-intercept (0, 1200) represents the initial cost of the bedroom furniture option (A) is correct.
What is an exponential function?It is defined as a function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = a×
where a is a constant and a>1
The exponential function is of the form:
y = ab×
Plug x = 0 and y = 1200
1200 = a
Plug x = 2, y = 675, and a = 1200
675 = 1200(b)²
b = 0.75
y = 1200(0.75)×
y = 1200
Thus, the y-intercept (0, 1200) represents the initial cost of the bedroom furniture option (A) is correct.
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