What’s the number of unique ways that angel can pick and arrange songs for the playlist.
Answers
It is given that 10 out of 12 songs need to be selected first and then arranged in a playlist.
The permutation can be used for the arrangements.
The formula for permutation is:
\(_nP_r=\frac{n!}{(n-r)!}\)Here n is the total number of things and r is the total number of selections.
In this problem n=12, r=10 so the total number of arrangements is given by:
\(\begin{gathered} _{12}P_{10}=\frac{12!}{(12-10)!} \\ =\frac{12!}{2!} \\ =239500800 \end{gathered}\)Hence the total number of arrangements that can be made is 239500800.
Related Questions
a rectangle with a width of 30 centimeters has a perimiter of 100 centimeters to 160 centimeters graph a compound inequality
Answers
Answer:
5 ≤ L ≤ 35
Step-by-step explanation:
Let w represent the width of the rectangle.
The perimeter (P) of the rectangle is given by:
P = 2w + 2L
Where L is the length of the rectangle.
We know that w = 30 cm and that the perimeter is between 100 and 160 cm. We can now set up our compound inequality:
100 ≤ 2(30) + 2L ≤ 160
100 ≤ 90 + 2L ≤ 160
10 ≤ 2L ≤ 70
We can now divide both sides by 2 to solve for L:
5 ≤ L ≤ 35
Therefore, the compound inequality that represents the graph of a rectangle with a width of 30 centimeters and a perimeter of 100 centimeters to 160 centimeters is: 5 ≤ L ≤ 35
In a recent study, 50 males used a new weight-loss supplement, and 37 of them experienced weight loss after two weeks. In the same study, 25 females used the same supplement, and 22 of them experienced weight loss after two weeks.
Fill in the blanks of the statement below to make the statement the most reasonable possible. The new weight-loss supplement was more effective on ? in the study because only % of them failed to lose weight after two weeks, % of the ? whereas failed to lose weight after two weeks. ?
Answers
The new weight-loss supplement was more effective on female in the study because only 12% of them failed to lose weight after two weeks.
Given that, in a recent study, 50 males used a new weight-loss supplement, and 37 of them experienced weight loss after two weeks.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Here, number males did not lost weight
50-37= 13
Number females did not lost weight
25-22= 3
Males proportion who did not lose weight = 13/50
= 0.26×100
= 26%
Females proportion who did not lose weight = 22/25
= 0.12×100
= 12%
Therefore, the new weight-loss supplement was more effective on female in the study because only 12% of them failed to lose weight after two weeks.
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A square pyramid has a volume of 82 cubic meters. The square base has a side length of 7 meters. What is the height?
This is geometry by the way :)
Answers
Check the picture below.
\(\textit{volume of a pyramid}\\\\ V=\cfrac{Bh}{3} ~~ \begin{cases} B=\stackrel{base's}{area}\\ h=height\\[-0.5em] \hrulefill\\ B=\stackrel{7\times 7}{49}\\ V=82 \end{cases}\implies \begin{array}{llll} 82=\cfrac{49h}{3}\implies 246=49h\implies \cfrac{246}{49}=h \\\\\\ 5.02\approx h \end{array}\)
ok y’all help ʜᴇʟᴘᴘᴘᴘᴘ ndjd d dndkdjdjdkdnfn dkcn
Answers
Answer:
C, 108 ft²
Step-by-step explanation:
To solve, we need to find the area of each of the shapes and then add them together.
The top rectangle's area: 8 * 3 = 24
The left triangle: 3 * 4 * 0.5 = 6
The middle rectangle: 8 * 4 = 32
The right triangle: 4 * 3 * 0.5 = 6
The bottom rectangle: 5 * 8 = 40
Add them all together.
24 + 6 + 32 + 6 + 40 = 108 ft²
Thus, the answer is C, 108 ft²
8x3=24
8x4=32
5x8=40
The Triangles
(5x3)/2=7.5
(5x3)/2=7.5
Sunset you have two equal triangles you can think of it as just 5x3=12
Total=108
A local city park rents kayaks for $3.75 per hour. If a customer rents for four or more hours, the cost is only $3.25 per hour, plus a $5 processing fee. If C(x) represents the total cost and x represents the number of rental hours, which of the following functions best models this scenario?
C of x equals 3.75 times x if x is less than 6 and 3.25 plus 5x if x is greater than 6.
C of x equals 3.75 times x if x is less than or equal to 5 and 3.25x minus 5 if x is greater than 6.
C of x equals 3.75 times x if x is less than 6 and 3.25x plus 5 if x is greater than or equal to 6.
C of x equals 3.75 times x if x is less than 5 and 3.25x minus 5 if x is greater than or equal to 6.
Answers
The function that best models this scenario is C of x equals 3.75 times x if x is less than 5 and 3.25x plus 5 if x is greater than 6.
How to calculate the value?Let the number of hours be illustrated as x. In this situation, local city park rents kayaks for $3.75 per hour. This will be:
= 3.75 × x
= 3.75x
Also, customer rents for four or more hours, the cost is only $3.25 per hour, plus a $5 processing fee. This will be illustrated as:
= 5 + (3.25 × x)
= 5 + 3.25x
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100 POINTS HELPPPP What entry on a cash flow statement would indicate that a business had a cash inflow from the sale of equipment?
A. Negative CapEx
C. Negative repayment of debt
B. Inflow from sale of PPE
D. Positive issuance of equity
Answers
Answer:
The cash flow statement paints a picture as to how a company’s operations are running, where its money comes from, and how money is being spent. So i think D is the answer
Which values are equivalent to the fraction below ? Check all that apply 3^4/3^6
Answers
Answer:
You have to apply Indices Law :
\( {a}^{m} \div {a}^{n} ⇒ {a}^{m - n} \)
So for this question :
\( \frac{ {3}^{4} }{ {3}^{6} } \)
\( = {3}^{4} \div {3}^{6} \)
\( = {3}^{4 - 6} \)
\( = {3}^{ - 2} \: or \: \frac{1}{ {3}^{2} } \: or \: \frac{1}{9} \)
A 2-yard roll of waxed paper coats $4.02. What is the price per foot
Answers
Answer: $0.67.
Step-by-step explanation:
To find the price per foot of the waxed paper, we need to convert the price from yards to feet and then divide the total cost by the length in feet.
Given:
Length of waxed paper roll = 2 yards
Cost of waxed paper roll = $4.02
1 yard is equal to 3 feet. Therefore, the length of the waxed paper roll in feet is:
Length in feet = 2 yards * 3 feet/yard = 6 feet
To find the price per foot, we divide the total cost by the length in feet:
Price per foot = Cost / Length in feet
Price per foot = $4.02 / 6 feet
Dividing gives us:
Price per foot = $0.67 per foot
Therefore, the price per foot of the waxed paper is $0.67.
Regs.
Spinner A and Spinner B below are each to be spun once.
0 18
O 12
6
Spinner A
5
2
4
00
D
3
20 of 21
If the pointer cannot land on a line, how many different outcomes of a number and a color are possible?
v
Spinner B
Yellow
Brown
12 13
Red
Answers
Answer:
Step-by-step explanation:
Regs.
Spinner A and Spinner B below are each to be spun once.
0 18
O 12
6
Spinner A
5
2
4
00
29. Assertion :7√5, √2+21 are the irrational number. Reason: every integer is an rational number 30.
Answers
The assertion is true. Both 7√5 and √2 + 21 are irrational numbers because they cannot be expressed as fractions.
The assertion is true. Both 7√5 and √2 + 21 are irrational numbers.
An irrational number is defined as a number that cannot be expressed as a fraction of two integers and has an infinite non-repeating decimal representation.
In the case of 7√5, the square root of 5 is an irrational number because it cannot be expressed as a fraction. Multiplying it by 7 does not change its irrational nature.
Similarly, √2 is also an irrational number because the square root of 2 cannot be expressed as a fraction. Adding 21 to √2 does not alter its irrationality.
The reason provided, that every integer is a rational number, is not relevant to the given assertion. While it is true that every integer is a rational number because it can be expressed as a fraction (e.g., 3 can be written as 3/1), it does not contradict the fact that 7√5 and √2 + 21 are irrational numbers.
In conclusion, the assertion is valid, and both 7√5 and √2 + 21 are irrational numbers.
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A ball is thrown into the air. Its height (in feet) t seconds later is given by h ( t ) = 64 t − 16 t 2 Based on the two equivalent forms of the function h ( t ) = 64 t − 16 t 2 = t ( 64 − 16 t ) , answer the following questions: a) What is the height of the ball 1 second after it has been thrown? (Include units) b) After how many seconds does the ball hit the ground? (Include units) c) At what time(s) is the ball 50 feet above the ground?
Answers
After 1 second, the height of the ball will be 48 feet above the ground, and if the ball lands after 4 seconds of being thrown into the air the ball is 50 feet above the ground after 4.66 seconds.
So we have the function:
h(t)=64t-16t²
height h(t) is measured as the ball after t seconds.
A) To find the height of the ball after 1 second if it has been thrown, then substitute 1 for t. Thus:
h(1)=64(1)-16(1)²
Simplify:
h(1)=64-16
Subtract:
h(1)=48
Thus, after 1 second, the height of the ball is 48 feet above the ground.
B) To know how many seconds after being thrown the ball hit the ground, we have to set h(t) to 0. 0 can be defined as that it will be 0 feet above ground level: in another word, on the ground. So:
0=64t-16t²
Solve for t. Factor out a 16t
0=16t(4-t)
Zero Product Property:
16t=0, 4-t=0
Solve for t:
t=0 or t=4.
We have to ignore the first zero. So, the value of t is 4 and the ball lands after 4 seconds of being thrown into the air.
C) To calculate at what time(s) the ball is 50 feet above the ground, set h(t) to 50 and solve for t:
50=64t-16t²
First, we have to divide everything in 2 to simplify things:
25=32t-8t²
Subtract 15 from both sides:
-8t²+32t-10=0
Now, to find the zeros, we can use the quadratic formula. a=-8, b=32, and c=-10. Thus:
\(x=\frac{-b+\sqrt{b^{2}-4ac } }{2a}\)
Substitute:
\(x=\frac{-32+\sqrt{(32)^2-4(-8)(-10)} }{2(-10)}\)
Simplify:
\(x=\frac{32+\sqrt{704} }{20}\)
Use a calculator. Approximate:
x=4.6647
Therefore, the ball is 50 feet above the ground after 4.66 seconds.
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Prove that:
1 - cos 2Θ is identical to: tanΘsinA
where A is an expression to be found.
what is the value for A
Answers
Answer:
Step-by-step explanation:
I don't know this one, sorry
All six digits in the number are even one digit is used twice all other digits are used once the ones digit is 4 times the hundreds digit the tens digit id the difference of the ones digit and hundreds digit the same digit is in the tens place and hundreds thousands place the thousands digit is not zero
Answers
Answer:
rffrefr
Step-by-step explanation:
Please find the area of the figure.
Could someone explain how to count the little bits?
Answers
Answer:
√250 + 2 = 5√10 + 2
Step-by-step explanation:
1. refer to image attached
2. split the area into a rectangle and triangle (see red line)
3. find the area of the triangle
a. find the base (2)
b. find the height (2)
area = base * height / 2 = 2 * 2 / 2 = 2
4. find the area of the rectangle
a. find the width
the width can be found from the right triangle at the top right. the height is 2 and the bottom leg is 1, so using the pythagorean theorem, the hypotenuse, which is the width of the triangle, equals
√(2²+1²) = √5 as our width
b. find the length
given the top right triangle, we have a height of 5 and another leg length of 5, so the length = √(5²+5²) = √50
the area of the rectangle is thus √50 * √5 = √250
4. the area is thus the two areas added up, or √250 + 2
5. What is the different forms of 5.39?
Answers
5 39/100-mixed number
539/100-fraction
539%-percent
in the coordinate plane, the vertices of triangle PAT are P(-1,-6), A(-4,5), and T(5,-2). Prove that PAT is an isosceles triangle.
Answers
In the coordinate plane, the vertices of triangle PAT are P(-1,-6), A(-4,5), and T(5,-2) forms an isosceles triangle.
To prove that triangle PAT is an isosceles triangle, we need to show that at least two sides of the triangle are congruent.
Let's calculate the distances between the vertices:
Distance between P and A:
PA = √[(x₂ - x₁)² + (y₂ - y₁)²]
= √[(-4 - (-1))² + (5 - (-6))²]
= √[9 + 121]
= √130
Distance between P and T:
PT = √[(5 - (-1))² + (-2 - (-6))²]
= √[(5 + 1)² + (-2 + 6)²]
= √[36 + 16]
= √52
= 2√13
Distance between A and T:
AT = √[(5 - (-4))² + (-2 - 5)²]
= √[(5 + 4)² + (-2 - 5)²]
= √130
We can see that PA = AT = √130, and PT = 2√13.
Since PA = AT, we have shown that two sides of the triangle are congruent.
Therefore, triangle PAT is an isosceles triangle.
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Assign a variable to each quantity and write each statement as an inequality. Then give an example
of an actual value that would match each description. [3 points each)
a. We can fit at most 12 people on the boat.
Variable:
Inequality:
Value that matches:
b. A heater turns on whenever the temperature of a room drops below 66°.
Variable:
Inequality:
Value that matches:
Answers
Answer:
1.
Variable: x
Inequality: x ≤ 12
Value that matches: 12
2.
Variable: y
Inequality: y < 66
Value that matches: 60
Step-by-step explanation:
Solving (1):
Let x be the variable
Reading through the question, we have the inequality to be represented by "at most".
At most is used for less than or equal to.
Hence, the expression can be represented by:
x ≤ 12
The range of this inequality is limited to all natural number that do not exceed 12.
Examples are 8, 2, 11, 12
Solving (2):
Let the variable be y
Reading through the question, we have the inequality to be represented by "below".
Below means less than
Hence, the expression can be represented by:
y < 66
The range of this inequality is limited to all number less than 66.
Examples are 65, 1 , 60......
Michael wants to plant a circular flower garden in his backyard. If the radius of his garden is 12.5 feet, what is the circumference of the
garden in terms of pi?
Answers
Answer: 78.54
Step-by-step explanation: :D
Find the area of the figure below
Answers
Answer:
216 yds^2
Step-by-step explanation:
12*16=192
3*8=24
192+24=216
Lana owns an office supply shop. At the beginning of each school year, she chooses two or three products to donate to the local middle school.
The table shows the school supplies that Lana has in her shop and how many of each kind she has in stock. Lana is considering different options of supplies to donate. For each option, determine the greatest number of identical boxes she could pack and the number of each supply item she could put in the boxes.
school supplies stock:
pencils-78
markers-110
notebooks-195
erasers-143
folders-330
A option 1: pencils and erasers: ____boxes with ____ pencils and ____ erasers
B option 2: notebooks and folders: ____ boxes with ____notebooks and ____ folders in each box.
C option 3: erasers, markers, and folders: ____ boxes with ____ erasers ____ markers and ____ folders in each box.
Answers
Option-1: 221 boxes with 78 pencils and 143 erasers.
Option-2: 525 boxes with 195 notebooks and 330 folders in each box.
Option-3: 583 boxes with 143 erasers 110 markers and 330 folders in each box.
Given that,
Owning an office supplies store is Lana. Each school year, she selects two or three items to give to the neighborhood middle school.
We have to find the correct answer for the given options.
The table is
school supplies stock:
pencils-78
markers-110
notebooks-195
erasers-143
folders-330
Option1:
Pencils and erases:
78+143=221
221 boxes with 78 pencils and 143 erasers.
Option 2:
Notebooks and folders:
195+330=525
525 boxes with 195 notebooks and 330 folders in each box.
Option 3:
Erasers, markers, and folders:
143+110+330= 583
583 boxes with 143 erasers 110 markers and 330 folders in each box.
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YZ is tangent to circle V. What is the length of YZ? 5 23.8
Answers
65 points!!!!!!!!!
Malaya is standing directly between a 90 foot tall courthouse and a 54 foot tall bank. If the angle of elevation from the point where Malaya is standing to the top of the courthouse is 72 degrees, while the angle of elevation to the top of the bank is 35 degrees. What is the distance between the courthouse and the bank? Show all your work to get credit!
Answers
Answer:
106.36 ftStep-by-step explanation:
Let the distance from the point Malaya is standing to the courthouse be x and the distance to the bank is y
x + y is the distance between the courthouse and the bankThen we have:
x/90 = cot 72° ⇒ x = 90 cot 72° = 90*0.3249196962 = 29.24 ft (rounded)y/54 = cot 35° ⇒ y = 54 cot 35° = 54*1.4281480067 = 77.12 ft (rounded)x + y = 29.24 + 77.12 = 106.36 ftAnswer:
106.3ft
Step-by-step explanation:
x= tan72=90/x
x= 90/tan 72
x= 29.2
y= tan35=54/y
y= 54/tan35
y= 77.1
x+y= answer
29.2 + 77.1 = 106.3
. Where is the vertex of the graph that represents y=(x−2)2−8 ? Type the answers in the boxes below. ( , ) b. Where is the y -intercept? Type the answers in the boxes below.
Answers
The vertex of the given equation is (0,12) and (1, -10). The value of y-intercept will be -12.
Given equation :
y=(x−2)2−8
y = 2x - 4 - 8
= 2x - 12
The final equation is y = 2x - 12.
Compare this equation with slope and y-intercept formula :
y = mx+c
So that c = -12
The value of y-intercept according to the solution is -12.
To find the vertex. Let's assume x=0; Substitute in the equation
y = 2(0) -12
y = -12
The first vertex will be (0, -12)
If x = 1; y = 2(1) -12
y = -10
Then the second vertex will be (1, -10).
Hence, the vertex of the given equation is (0,12) and (1, -10). The value of y-intercept will be -12.
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what is the solution and steps to the system of equations
y = 2x - 9
y = -x + 3
Answers
Answer:
( 4 , - 1 )
Step-by-step explanation:
Explain what this student is doing to go from x^2−6x−3= 0 to (x−3)^2 =12
Answers
The student is solving the quadratic equation by completing the square.
In parallelogram ABCD shown, point E and F are located on diagonal BD and point G is located on side AB such that GE and CF are perpendicular to BD. Prove: trainge BEG is similar to traingle DFC
Answers
Answer:
Match the Statement number with the Reason number.
Step-by-step explanation:
Statements:
1.GE is perpendicular to BD
CF is perpendicular to BD
2. Angle GED equal 90
Angle DFC equal 90
3. Angle GED is congruent to Angle DFC
4. Angle GBE is congruent to Angle FDC
5. Triangle BEG is similar to DFC
Reasons:
1.Given
2. Definition of perpendicular lines
3. Transitive property
4. Alternate Interior Angles
5. AA Similarity
By satisfying essential conditions for two triangles to be similar, we can say that triangle BEG is similar to triangle DFC.
What is a parallelogram?A quadrilateral in which opposites sides are equal and parallel. Also, opposite angles are equal to each other.
As we know that AB║ DC
so,∠GBE = ∠CDF (alternate angles)
∠GEB= ∠DFC = 90°
so triangle BEG≈DFC
Therefore, we can say that triangle BEG is similar to triangle DFC
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justine answered 68 questions correctly on an 80- question test. Express this amount as a fraction , percent, and decimal
Answers
Answer:
percent- 85%
fraction- 17/20 (simplified) or written like this: \(\frac{17}{20}\)
decimal- 0.85
Step-by-step explanation:
I hope this helps you! Good luck and have a great day. ❤️✨
Which algebraic expression represents “Nicholas tripled his workout time”?
3 + w
3 w
3 minus w
/ w Over 3 /
Answers
Answer:
3 w
Step-by-step explanation:
because if you think about it nick was doing a lot and then he needs to triple so the equation would be 3 w
Answer. w over 3
Step-by-step explanation:
Which function is an even function?
Answers
f is an even function if f(-x) = f(x)
f is an odd function, if f(-x) = -f(x)
\( \csc( \frac{ - 3\pi \: x}{2} ) = - \csc( \frac{3\pi x}{2} ) \)
Option B is an odd function
i dont understand how this question works so therefeore i dont know how to do it, can anyone help?
Answers
is simply changing from percentage form to a decimal form usually, but the fractional form works the same. Check the picture below.
