A pianist plans to play 5 pieces at a recital from her repertoire of 27 pieces. How many different recital programs are possible?
The different recital programs that are possible is 80,730 ways
Combination and permutationPermutation has to do with arrangement while combination has to do with the selection.
According to the question, a pianist plans to play 5 pieces at a recital from her repertoire of 27 pieces, this shows that he can select the 5 pieces in any form.
The number of ways this can be done is given as:
[tex]27C_5=\frac{27!}{(27-5)!5!}\\ 27C_5=80,730[/tex]
Hence the different recital programs that are possible is 80,730 ways
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How can you use
probability to draw conclusions about the
likelihood that something will occur?
(Probability)
The closer the probability is to 1, the more likely it is to occur and the closer the probability is to 0, the less likely it is to occur.
ProbabilityThis is the likelihood that an event will occur.
Probability of an event occuring is calculated thus P(event) = event space/sample space.The event space is the set of desired outcomes in which the event can occur while the sample space is the set of all possible outcomes.Now, the probability P(x) of an event x is in the range 0 ≤ P(x) ≤ 1 where P(x) = 0 implies that the event cannot occur and P(x) = 1 implies that the event will definitely occur.To draw conclusions about the likelihood that something will occurFor an event will occur, it value must be close to 1. For example, a probability P(x) = 0.38 is less likely to occur than a probability P(x) = 0.78.So, the closer the probability is to 1, the more likely it is to occur and the closer the probability is to 0, the less likely it is to occur.
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What is the volume of the sphere below?
Answer:
D
Step-by-step explanation:
4/3 (3.14) r^3 is the equation, so since the radius is 4
It's 4/3x(pi)64
256/3x(pi)
Find the area and perimeter of the figure below.
Answer:
x to the 3rd power
Step-by-step explanation:
x+x to the 2nd power = x to the 3rd power
Step-by-step explanation:
The area is the sum of three figures
A = 1*1 + 1*x + x²
= x² + x + 1
The perimeter is the sum of border segments
P = x*4 + 1*4
= 4x + 4
Find the simple Intrest for
$ 2000 at 4% for 3 months
Answer:
Simple interest: 240, Final amount: 2240
hope im right
Step-by-step explanation:
Find The Zeroes:
Answers:
x = 1 and -2
x = 2 and -1
x = -0.5 and -2.25
Answer:
x = -2 & x= 1
Step-by-step explanation:
Zeroes are the x-axis value where the function crosses the x-axis!
Solve the system of equations.
2x−9y=14
x=−6y+7
Step-by-step explanation:
[tex]put \: x \: into \: equation \: 1[/tex]
[tex]2( - 6y + 7) - 9y = 14[/tex]
[tex] - 12y + 14 - 9y = 14[/tex]
[tex] - 21y + 14 = 14[/tex]
[tex] - 21y = 14 - 14[/tex]
[tex] - 21y = 0[/tex]
[tex] \frac{ - 21y}{12} = \frac{0}{21} [/tex]
[tex]y = 0[/tex]
[tex]put \: y = 0 \: into \: equation \: 2[/tex]
[tex]x = 6y + 7[/tex]
[tex]x = 6(0) + 7[/tex]
[tex]x = 0 + 7[/tex]
[tex]x = 7[/tex]
Answer:
y = 0
x = 7
Step-by-step explanation:
2x − 9y = 14 ⇒ ( 1 )
x = − 6y +7 ⇒ ( 2 )
First, let us find the value of y.
For that, replace x with ( - 6y + 7 ).
Let us take equation 1 for that.
2x − 9y = 14
2 ( - 6y + 7 ) - 9y = 14
-12y + 14 - 9y = 14
21y = 14 - 14
21y = 0
Divide both sides by 21.
y = 0
And now let us take equation 2 to find the value of x by replacing y with 0.
2x − 9y = 14
2x - 9 × 0 = 14
2x - 0 = 14
2x = 14
Divide both sides by 2.
x = 7
Transform the table below given that g(x) = 2 f(6x).+ 8. Enter your answers as reduced fractions if necessary. Make sure your answers line up vertically with the corresponding x and f(x) values. As a hint, you can consider y f(x) to be the base graph of g(x).
The function g(x) = 2f(6x) + 8 is a function transformation of the function f(x)
How to transform the table?The function g(x) is given as:
g(x) = 2f(6x) + 8
The table is not given.
So, I will provide a general explanation
Using the following values of x:
x = 0, 1, 2, 3......
We have:
g(0) = 2f(6 *0) + 8
g(0) = 2f(0) + 8
g(1) = 2f(6 *1) + 8
g(1) = 2f(6) + 8
g(2) = 2f(6 *2) + 8
g(2) = 2f(12) + 8
g(3) = 2f(6 *3) + 8
g(3) = 2f(18) + 8
Next, we assume the following values
f(0) = 4, f(6) = 5; f(12) = 6 and f(18) = 7
The values become:
g(0) = 2f(0) + 8 = 2 * 4 + 8 = 16
g(1) = 2f(6) + 8 = 2 * 5 + 8 = 18
g(2) = 2f(12) + 8 = 2 * 6 + 8 = 20
g(3) = 2f(18) + 8 = 2 * 7 + 8 = 22
So, the table of values would be:
x g(x)
0 16
1 18
2 20
3 22
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Please Helpp!!!! Pythagorean theorem
Answer:
12.6 = c
Step-by-step explanation:
The Pythagorean therom is a^2 + b^2 = c^2
We already know 2 varibles (12 and 4) so we can just plug them in.
12^2 + 4^2 = c^2
144 + 16 = c^2
160 = c^2
[tex]\sqrt{160}[/tex] = [tex]\sqrt{c^2}[/tex]
12.6 = c
Hope this helps :)
Find two positive numbers whose product is 192 and their sum is a minimum.
Answer:
8√3
Step-by-step explanation:
Let a, b = the positive numbers, and the sum = s,
(1)---- ab = 192
(2)--- a + b = s
Since we want to find the minimum sum, we'll have to substitute one of the variables (either a or b) from (1) to (2), I'll choose b,
From (1), b = 192/a
Substitute b = 192/a into (2),
s = a + 192/a
Now, we are able to use a concept of calculus (maximum & minimum) to solve it, just remember 2 steps in finding the values of x in maxima minima question:
1) find dy/dx
2) Find x from dy/dx = 0
ds/da = 1 - 192/a²
When ds/da = 0,
1 - 192/a² = 0
a² = 192
a = ±√192
a = 8√3 , -8√3
Since a is positive, a = 8√3
Substitute a into (1),
b = 192/(8√3)
b = 8√3
Therefore, the two positive numbers are 8√3... and 8√3
help pls quick i need the answer pls
Answer:
multicultural
Step-by-step explanation:
Answer:
A. Multicultural
Step-by-step explanation:
It shows later in the sentence that they ate Thai noodles and Egyptian falafel those come from different cultures so it must be multicultural
What is the smallest number which is reversed when 2 is added to its double?
Answer:
25
Step-by-step explanation:
Let the number be 10x+y.
So we have 2(10x+y)+2 = 10y+x, or
20x + 2y + 2 = 10y+x, or
19x=8y-2 …(1)
Try different values of x which satisfy (1) giving an integer value of y. Moreover x should be less than y. The only value of x is 2 which gives us y = 5.
So y = 5 and x = 2.
And the answer is 25.
We can prove this by simply doing the question's equation:
50(since it's the double of 25) + 2 =
50+2= 52
Hope this helps
What is the solution to x^3 + 4x^2 > x + 4?
Answer:
-4 < x < -1 or x > 1 (the third option)
Step-by-step explanation:
hope this helps
i need this with the steps
Jayne stopped to get gas before going on a road trip. The tank already had 4 gallons of gas in it. Which equation relates the total amount of gasoline in the tank, y, to the number of gallons that she put in the tank, x?
y=4+x
y = x − 4
y = 4 · x
y = x ÷ 4
Answer:y=4+x
Step-by-step explanation:
You are adding gallons not *,/,-,. So it's y=4+x.
The required equation is y = 4 + x. The correct answer would be an option (A).
What is an equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Jayne stopped for gas before embarking on a road trip. There were already 4 gallons of gas in the tank.
As per the question, the required equation would be as:
y = 4 + x
This equation relates the total amount of gasoline in the tank, y, to the number of gallons that she put in the tank, x. The total amount of gasoline in the tank, y, is equal to the number of gallons that she put in the tank, x, plus the 4 gallons that were already in the tank.
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Brendan is building a dog house, and the
dimensions of the roof are shown below. What is
the lateral surface area of the roof?
2.7f
5 ft
3 f+
A. 24.84 f+2
B. 46 f+2
C. 54.1 f+2
D. 43.2 f+2
Answer:
B. 46 ft²
Step-by-step explanation:
Two sides are rectangles 3.1 ft by 5 ft.
One side is a rectangle 5 ft by 3 ft.
area = 2(3.1 ft × 5 ft) + (5 ft × 3 ft)
area = 46 ft²
I really need help now. 100 points plus brainly if correct. I GOT THINGS TO DO!!! Answer the question in the picture
Answer: 4,000
Step-by-step explanation:
The only logical choice there because of the rate of others
Answer: c is the answer
Step-by-step explanation:
Please help ASAP I need an answer now!
Answer:
Final answer -
Area of paperboard = [tex]565.92 \: inches {}^{2} [/tex]
hope helpful :D
10.A water tank has strps inside it. A monkeyis sitting on topmost floor(i.e.,the first step).The water level is at ninth step. (ii)After drinking water,he wants to go back 2 steps down in every move.In how many jumps will he reach back the tops step?
Answer:
11 id.k i think
Step-by-step explanation:
i think that it
• Identifică, în fiecare plan al clasei, obiectul care nu este reprezentat. Scrie în caiet numele acestuia.
Answer:
a
Step-by-step explanation:
An asteroid is a minor planet of the inner Solar System. Historically, these terms have been applied to any astronomical object orbiting the Sun that did not resolve into a disc in a telescope and was not observed to have characteristics of an active comet such as a tail.
A biologist is studying the exponential growth of a colony of bacterial cells. The table gives the
number of cells, y, in the colony over time, x, in hours.
Time, x (hours)
0
Number of Cells, y
100
1
200
N
400
h
6,400
Replace the values of A, b, x, and y to write an exponential equation that represents the number of
cells present at h hours.
The exponential function that represents the number of cells present at x hours is y = 100(2)ˣ
What is an exponential function?An exponential function is in the form:
y = abˣ
Where a is the initial value and b is the multiplication factor.
Let y represent the number of cells after x hours.
From the table, at point (0, 100):
100 = ab⁰
a = 100
At point (1, 200):
200 = 100b
b = 2
The exponential function is y = 100(2)ˣ
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Answer:
100(2)^h=6,400
Step-by-step explanation:
Explanation:
For an equation in the form A(b)^x=y, A represents the initial amount, and b represents the growth rate. At 0 hours, there were 100 cells, so A=100.
Between 0 hours and 1 hour, the number of cells doubled from 100 to 200, or 100(2). Between 1 and 2 hours, the number of cells again doubled from 200 to 400, or 100(2)^2. So the growth rate, or b, is 2.
The table shows that at h hours, there were 6,400 cells. Therefore, the equation that represents the number of cells at h hours is .100(2)^h=6,400
sin160°cos110°+sin290°cos340°+tg110°tg160°
Answer:
-0.0092
Step-by-step explanation:
sin160°cos110° + sin290°cos340° + tan110°tan160°
(0.34)(-0.34) + (-0.94)(0.94) + (-2.75)(-0.36)
- 0.1156 - 0.8836 + 0.99
-0.0092
I hope this helps!
[tex]\sin 160^{\circ} \cos 110^{\circ} + \sin 290^{\circ} \cos 340^{\circ} + \tan 110^{\circ} \tan 160^{\circ}\\\\=\sin\left(2 \times 90^{\circ} - 20^{\circ} \right) \cos \left(90^{\circ} + 20^{\circ} \right) + \sin \left(3 \times 90^{\circ}+20^{\circ}\right) \cos\left(4 \times 90^{\circ}-20^{\circ \right) + 20^{\circ} \right) + \tan \left( 90^{\circ} +20^{\circ}\right) \tan\left( 2 \times 90^{\circ} - 20^{\circ} \right)\\\\[/tex]
[tex]=-\sin 20^{\circ} \sin 20^{\circ} -\cos 20^{\circ} \cos 20^{\circ}+\cot 20^{\circ} \tan 20^{\circ}\\\\=-\left(\sin^2 20^{\circ} + \cos^2 20^{\circ} \right) + \tan 20^{\circ} \cdot \dfrac 1{\tan 20^{\circ}}\\\\=-1 + 1\\\\=0[/tex]
These diagrams show the dimensions of two different windows. Which of the following statements are true? Choose all that apply.
Window A
3 ft
8 ft
Window
B
4 ft
6 ft
O A. The windows have the same area.
B. The perimeter of Window A is less than the perimeter of Window B.
C. The perimeter of Window B is 20 feet.
OD. The area of Window A is 22 square feet.
Tammy took a total of 14 quizzes over the course of 7 weeks. How many weeks of school will Tammy have to attend this quarter before she will have taken a total of 18 quizzes? Solve using unit rates. Answer: weeks.
Answer:
9 weeks
Step-by-step explanation:
So he basically took 14 quizzes in 7 weeks.
14/7 = 2/quizzes per week
18/2 = 9 weeks
I don't know what you mean by unit rates but this is what I got.
guy is half as old as Gerald, who is three times older than gill. If the sum of their ages is 99, what are their ages?
Answer:
Step-by-step explanation:
gerald=2x
guy=x
gill= aproximately 0.3x
2x+x+0.3x=99
2.3x=99
x=43.04
The age of the guy is 29.72 years, the age Gerald is 59.44 years and the age of gill is 9.8 years.
What is an arithmetic operation?The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.
As per the given data in the question,
The equation according to the given statement will be,
The age of Gerald is 2x,
The age of the guy is x and the age of the gill is 0.33x.
So, the equation will be,
x + 2x + 0.33x = 99
3.33x = 99
x = 99/3.33
x = 29.72
Age of Gerald, 2x = 2(29.72) = 59.44 years.
Age of guy, x = 29.72 years and,
Age of gill, 0.33x = 0.33(29.72) = 9.8 years.
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A stone is projected vertically upward from a platform that is 18ft high at a rate of 114ft/sec. Use h=−16t^2+v0t+h0.
Using the vertex of the quadratic equation, it is found that the stone reaches a maximum height of 221.0625 ft after 3.5625 s.
What is the vertex of a quadratic equation?A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
The vertex is given by:
[tex](x_v, y_v)[/tex]
In which:
[tex]x_v = -\frac{b}{2a}[/tex]
[tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]
Considering the coefficient a, we have that:
If a < 0, the vertex is a maximum point.If a > 0, the vertex is a minimum point.In this problem, considering initial velocity of v(0) = 114 and an initial height of h(0) = 18, the equation is:
h(t) = -16t² + 114t + 18.
Which is a quadratic equation with coefficients a = -16, b = 114, c = 18.
Hence:
[tex]x_v = -\frac{114}{2(-16)} = 3.5625[/tex]
[tex]y_v = -\frac{114^2 - 4(-16)(18)}{4(-16)} = 221.0625[/tex]
Hence, the stone reaches a maximum height of 221.0625 ft after 3.5625 s.
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Based on the pattern, which power of 10 would have a value of StartFraction 1 Over 1,000,000 EndFraction?
Answer:
powers of 10
Step-by-step explanation:
Simone examined the pattern in the table
If you deposit `\$300` in an account and it grows by `6\%` each year, how much money will be in your account after `1` year?
Answer:
$318
Step-by-step explanation:
6% x 300 = 18
300 + 18 = 318
Good people please help me!!!!
Answer:
P=90°
R=45°
Step-by-step explanation:
PQR=180°
180°-45°=135°
R=45°(iscoles triangle)
P=90°
Madelyn has 4 pairs of red socks, 6 times as many pairs of blue socks 1 as white pairs of socks, and I as many white pairs as red pairs. How many pairs of socks does she have in all? How many socks does Madelyn have?
The Total Number of socks is 10 in all, bear in mind that there is no blue socks hence it will not add to the total amount of socks
Addition of NumbersNote : 1 pais = 2 socks
Given Data
Red Socks = 4 pairs = 4*2 = 8 socks 6 times as many pairs of blue socks = 0 1 as many pairs of white socks = 2 socksThe statement " 6 times as many pairs of blue socks" is equivalent to no socks, since we have no blue socks, hence 6*0 = 0
Let us find the total socks
= 8+0+2
= 10 socks
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