There are 279,072,000 different ways the DJ can arrange the first 6 songs on the playlist.
The number of ways to arrange the first 6 songs on the playlist is a permutation of 6 objects taken from a set of 19 objects. The order matters because the first 6 songs will be played in a specific sequence.
We can calculate the number of permutations using the formula:
P(19, 6) = 19! / (19 - 6)!
where "!" denotes the factorial function.
Using this formula, we get:
P(19, 6) = 19! / 13!
= 19 × 18 × 17 × 16 × 15 × 14
= 279,072,000
Therefore, there are 279,072,000 different ways the DJ can arrange the first 6 songs on the playlist.
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Which of the following is the MOST accurate definition of standard deviation
The average of a set of scores
The typical amount by which scores differ from the mean of a set of scores
The average of the sum of squared deviations from the mean
The mean absolute deviation of the sum of the squared deviation from the average
The MOST accurate definition of standard deviation is the mean absolute deviation of the sum of the squared deviation from the average. Option 4
Definition of standard deviation
Standard deviation can be defined as a statistic tool that measures the dispersion of a dataset in relation to its mean and is calculated as the square root of the available variance of the set.
It is calculated as the square root of the given variance.
Thus, the MOST accurate definition of standard deviation is the mean absolute deviation of the sum of the squared deviation from the average.
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verbal scale uses a representative fraction to describe the ratio between the map and the real world
Verbal scale uses a representative fraction to describe the ratio between the map and the real world is a "true" statement.
What is verbal scale/expression?A verbal scale is also known as a "word statement" or a "scale expression," and it is one of the possibilities for entering "scale text" in the ArcGIS software.
It is presented as a relationship between map distance and ground distance that is stated in common units that both parties can agree upon.
Uses of the verbal scale:
Verbal scales are widely employed on large-scale maps and planning documents, most frequently by civil engineers, just like representative fractions. On some smaller-scale maps, you can discover them, although not as frequently as you can with representative fractions. The verbal scales have already been calculated in some common map scales, so you might utilize those. The best treatment of verbal scales and the other scale indications may be found in Map Use by Kimerling, Muehrcke, and Muehrcke.To know more about the verbal expression(scale), here
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The complete question is-
Verbal scale uses a representative fraction to describe the ratio between the map and the real world.(True/False).
Suppose you drop a ball from a height of 10 feet. after the ball hits the floor, it rebounds to a height defined by the recursive formula an = 0.85an – 1. what is a1? feet what is the height the ball rebounds to after its third bounce? round your answer to three decimal places. feet
The maximum height of the ball after its third bounce is equal to 3.568 feet.
What is the maximum height of a ball at the third bounce?
In this question we are aware that the maximum height reached by the ball decreases linearly after each bounce. To determine that height, we must take advantage of the recursive formula described in statement:
n = 0
a₀ = 10 ft
n = 1
a₁ = 0.85 · 10 - 1
a₁ = 8.5 - 1
a₁ = 7.5 ft
n = 2
a₂ = 0.85 · 7.5 - 1
a₂ = 5.375 ft
n = 3
a₃ = 0.85 · 5.375 - 1
a₃ = 3.568 ft
The maximum height of the ball after its third bounce is equal to 3.568 feet.
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The first one is 10 feet.
The second one is 6.141 feet.
Step-by-step explanation: Edge 2023
i’m a bit confused here
To solve this system of equations using substitution, what could be substituted in place of y in the first equation? 4x = 5 − 2y y − 2x = 7
Answer:
y = [tex]-\frac{4x-5}{2}[/tex]
Step-by-step explanation:
Step 1: Switch sides
5 - 2y = 4x
Step 2: Subtract 5 from both sides
5 - 2y - 5 = 4x - 5
Step 3: Simplify
-2y = 4x - 5
Step 4: Divide both sides by -2
[tex]\frac{-2y}{-2} = \frac{4x}{-2} - \frac{5}{-2}[/tex]
Step 5: Simplify
y = [tex]-\frac{4x-5}{2}[/tex]
a cube with volume 343 cubic inches is inscribed in a sphere so that each vertex of the cub touches the sphere. what is the lenght of the radius in inches of the sphere
The length of the radius of the sphere is 9.26 inches.
What is a sphere?A sphere is a geometrical object that resembles a two-dimensional circle in three dimensions. In three-dimensional space, a sphere is a collection of points that are all located at the same r-distance from a single point. The radius of the sphere is denoted by the letter r, and the specified point represents its center.
Volume of cube=343 cubic inches
Side of cube=[tex]\sqrt[3]{343}[/tex] = 7 inches
The radius of the sphere is equal to half the diagonal length of the cube since the cube is inscribed inside the sphere, whose diameter is the cube's diagonal length. Utilizing the distance formula, we can determine the cube's diagonal length.
[tex]d=\sqrt{7^{2}+7^{2}+7^{2} } \\=\sqrt{7*7^{2} } \\=7\sqrt{7}[/tex]
To determine the radius of the sphere, divide the value by two.
Radius of sphere=[tex]\frac{7\sqrt{7} }{2}[/tex] = 9.26 inches
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determine the slope of the line!!!!!
Answer: -3/2
Step-by-step explanation:
we could use the two points (2,3) and (0,4) from the graph
y2-y1/x2-x1
= 0-3/4-2
= -3/2
Kevin was asked to determine the length of side XZ. His work is shown.
Triangle X Y Z is shown. Angle Y Z X is 90 degrees and angle Y X Z is 34 degrees. The length of hypotenuse X Y is 18.
cos(34°) =
(XZ)cos(34°) = 18
XZ =21.7
Which error did Kevin make?
He has the side lengths in the wrong place in the cosine ratio.
He multiplied both sides by the length of XZ instead of dividing by XZ.
He should have used the sine ratio.
He should have used the tangent ratio.
Answer:
The answer is A) He has the side lengths in the wrong place in the cosine ratio.
Answer:
A. He has the side lengths in the wrong place in the cosine ratio.
Step-by-step explanation:
got it right on edge23
A comet is estimated to be about 960,000,000 km from Earth. Write this distance in scientific notation. [?] × 10 km Enter 13
Answer:
[tex](9*10^{9})( 6*10^{8})[/tex] or 9.6×10^8
Step-by-step explanation:
The answer is written above.
Hope this helps!
Answer:
9.6 * 10^8 km.
Step-by-step explanation:
960,000,000
= 9.6 * 10^8 km.
The value of the exponent = number of digits after the 9, which = 8.
What is the simplified form of tan (pi÷4-x)
Answer:
π/4 − x
Step-by-step explanation:
I hope its correct
I enter the mall with dollars. I spend dollars at American Eagle, which is more than the amount I spent at Banana Republic. I also spent less at American Eagle than I spent at Cole Haan. How much money do I have left after shopping at these three stores
The correct answer is 64 - 3 a.
What is a linear equation in math?
A linear equation only has one or two variables. No variable in a linear equation is raised to a power greater than 1 or used as the denominator of a fraction. When you find pairs of values that make a linear equation true and plot those pairs on a coordinate grid, all of the points lie on the same line.I spent a dollars at American Eagle, which is 4 more than the amount I spent at Banana Republic ( b ).
a = b + 4. Therefore: b = a - 4
Also I spent 15 less at American Eagle than I spent in Cole Haan ( c ).
a = c - 15, or: c = a + 15.
75 - a - ( a - 4 ) - ( a + 15 ) = 75 - a - a + 4 - a - 15 =
= 64 - 3 a
Therefore, I have 64 - 3a dollars left after shopping at these three stores. Now we just have to know how much dollars I spent at American Eagle and we will have the amount in dollars.
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The complete question is -
I enter the mall with $75 dollars. I spend a dollars at American Eagle, which is 4 more than the amount I spent at Banana Republic. I also spent 15 less at American Eagle than I spent at Cole Haan. How much money do I have left after shopping at these three stores?
A quadrilateral has congruent side lengths. 2 opposite angles have measures of 100 degrees. The other 2 opposite angles have measures of 70 degrees and (5 x) degrees. What is the value of x
Answer: 18
Step-by-step explanation:
Angles of a quadrilateral add to 360 degrees, so
[tex]100+100+70+5x=360\\\\270+5x=360\\\\5x=90\\\\x=18[/tex]
Select the correct answer. A linear function on a coordinate plane passes through (minus 5, minus 3), (0, minus 4), and (5, minus 5) Which equation describes the line graphed above? A. y = − 4 x − 5 B. y = − 1 5 x − 4 C. y = − 5 x − 4 D. y = − 4 x − 1 5
The linear function on a coordinate plane passes through (-5, -3) and (0, -4) is y = -1/5x-4
Linear functionLinear function are functions that has a leading degree of 1. The equation of a linear function is expressed as y = mx + b
where
m is the slope
b is the intercept
Given the coordinates (-5, -3) and (0, -4)
Slope = -4+3/0+5
Slope = -1/5
The y-intercept of the line will be -4
Determine the equation
y = -1/5x-4
Hence the linear function on a coordinate plane passes through (-5, -3) and (0, -4) is y = -1/5x-4
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Express sin S as a fraction in simplest terms. R S
Answer:
[tex]\sf Sin \ S = \dfrac{2}{9}[/tex]
Step-by-step explanation:
Trigonometry ratios:[tex]\sf \boxed{\bf Sin \ S = \dfrac{opposite \ side \ of \ \angle S}{hypotenuse}}[/tex]
[tex]\sf = \dfrac{RQ}{SQ}\\\\= \dfrac{2}{9}[/tex]
Christopher decides that another road to be named Saturn Avenue is needed that will go past
the cleaners and be perpendicular to Sunshine Avenue. Determine the slope of the equation
of the line that represents Saturn Avenue. [Show your work. Draw and label Saturn Avenue
on the coordinate plane. (Optional)
Slope of the equation of the line that represents Saturn Avenue: slope =
y = 4 is the equation of the line that represents Saturn Avenue given that Christopher decides that another road to be named Saturn Avenue is needed that will go past the cleaners and be perpendicular to Planet Drive. This can be obtained by using the formula for finding the equation of the line.
Find the equation of the line:
Equation of a line can be determined using the formula,
y = mx + c
where m is the slope of the line and c is the y - intercept.
m = rise/run = Δy/Δx = (y₂ - y₁)/(x₂ - x₁)
Here in this question draw the line passing through cleaners and perpendicular to Planet Drive.
The point where x = 0 is (0, 4)
This means that y - intercept is 4
By considering two points on the line we can find the slope of the equation,
Consider the points (8, 4) and (16, 4)
m = rise/run = Δy/Δx = (y₂ - y₁)/(x₂ - x₁)
m = (4 - 4)/(16 - 8) = 0/8 = 0
So we got that,
y - intercept of the line = 4 slope of the line = 0Putting in the equation of line we get,
y = mx + c
⇒ y = (0)x + 4 ⇒ y = 4
Hence y = 4 is the equation of the line that represents Saturn Avenue given that Christopher decides that another road to be named Saturn Avenue is needed that will go past the cleaners and be perpendicular to Planet Drive.
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Disclaimer: The question was given incomplete on the portal. Here is the complete question.
Question: Christopher decides that another road to be named Saturn Avenue is needed that will go past the cleaners and be perpendicular to Planet Drive. Determine the equation of the line that represents Saturn Avenue. Show your work. Draw and label Saturn Avenue on the coordinate plane.
Dalvin took a taxi from his house to the airport. The taxi company charged a pick-up fee of $4.80 plus $2 per mile. The total fare was $30.80, not including the tip. Which tape diagram could be used to represent the context if mm represents the number of miles in the taxi ride?
Answer:
The equation should be 2.5x+1.8=59.3
Step-by-step explanation:
The number of miles in the taxi ride is 10
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Given;
Dalvin took a taxi from his house to the house. The taxi company charged a pick-up fee of $4.80;
The fare per mile is $2
The total fare was $30.80, not including the tip;
Let the number of mile is x
Total fare = pick up fee + fee per mile
30.80 = 4.80 + 2x
2x = 26
x = 13
Therefore, the number of miles by algebra Dalvin took a taxi will be 13
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If 0° < θ < 90° or 180° < θ < 270°, explain why sin 2θ is always positive.
Using a trigonometric identity, since in the first quadrant and in the third quadrant the sine and the cosine have the same sign, [tex]\sin{2\theta}[/tex] is always positive.
What is the trigonometric identity for sin 2θ?It is given by:
[tex]\sin{2\theta} = 2\sin{\theta}\cos{\theta}[/tex]
In the first quadrant(0° < θ < 90°) and in the third(180° < θ < 270°), the sine and the cosine have the same sign, hence the multiplication is positive and [tex]\sin{2\theta}[/tex] is always positive.
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Solve the system of equations 4x+5y=-1 and -5x-8y=10 by combining the equations.
Evaluate the following expression by applying the appropriate properties (24) 3 (31.7)/ 172
−3/7×14/15×7/12×(−30/35)
=(−3/7×14/15)×(7/12×−30/35)
On further calculation, we get
=−2/5×−1/2
We get,
=1/5.
Property 1:
If a/b is a rational number and m is a non-zero integer then a/b =(a*m)/(b*m). In other words, we can say that the rational number remains unaltered if we multiply both the numerator and denominator with the same integer. Ex: 2/3 = 2*2/3*2 = 4/6, 2*3/3*3 = 6/9, 2*4/3*4 = 8/12.
Math Properties
Commutative Property.
Associative Property.
Distributive Property.
Identity Property.
Inverse Property.
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PLEASE HELP WILL GIVE BRAINLIEST
Arrange the tiles on both boards to find the value of x.
Board sum: 3x + (-5) = 1
What x value solves the equation?
3x - 5 = 1
X =
Answer: x = 2
Step-by-step explanation:
3x - 5 = 1
add 5 to both sides
3x - 5 (+5) = 1 (+5)
3x = 6
divide by 3 on both sides
3x/3 = 6/3
x = 2
Loc can mow his entire lawn in 20 minutes; Loc's roommate Reza needs 30 minutes to mow the entire lawn. If Loc starts mowing at 1:00, mows for five minutes and then Reza starts to help with his own mower, at what time will they finish mowing the lawn
Loc and Reza together will finish the entire mowing process on the lawn at 1:14 p.m.
Calculation of total mowing time takenLoc mow the total area in 20 mins.
So, his pace is 1 lawn / 20 minutes or 1/20th of a lawn each minute.
Reza's pace is 1 lawn / 30 minutes, or 1/30th of a lawn each minute because he can mow the grass in that amount of time.
Reza joins Loc after he has been mowing for 5 minutes. He can mow 1/20th of the grass in these 5 minutes, which is 5/20th of the lawn =1/4th lawn
There is currently just
1-1/4=3/4 of the lawn left to complete.
We may construct the following equation by assuming that they mow together for x mins:
1/20x + 1/30x = 3/4 [amount done by Loc + Reza = total amount]
⇒(3x+2x)/60x = 3/4
⇒5x/60 = 3/4
⇒x/12= 3/4
⇒4x=36
⇒x= 9 mins
So, when they collaborate, they can complete the lawn in 9 minutes.
Hence, Loc mows alone for 9+5 mins = 14 mins
Therefore, it is concluded that starting at 1 p.m they finish the mowing at 1:14 p.m.
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WILL MAKE BRAINLIEST!! Solve for x
Answer:
5
Step-by-step explanation:
6x+4=34
6x=30
x=5
hope this helps <3
Suppose a normal distribution has a mean of 50 and a standard deviation of
3. What is P(x≤44)?
Answer:
.0228
Step-by-step explanation:
44 is two standard deviations below the mean z-score = -2
look up z-score = -2 in z-score table
= .0228 or 2.28 %
Answer:
0.025
Step-by-step explanation:
a rotation is a transformation where an object
Rotation is a transformation where an object is rotated about a fixed point.
What is a transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.
Translation, reflection and rotation are rigid transformations because they preserve the shape and size of the figure.
Rotation is a transformation where an object is rotated about a fixed point.
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Sumaya's smoothie store is planning to sell an extra-large size. the extra-large size will have three times the volume of the small size (the small size is (8,4) ). it will cost twice as much as the small size.
which coordinate pair represents the volume and cost of the extra-large size?
The coordinate pair that represents the volume and cost of the extra-large size is (24, 8).
A coordinate plane is a plane that can be used to represent the position of a point. The plane consists of x-axes and y-axes. The position of a point is referenced from the origin.
The small size of a pizza is represented by the coordinate pair (8, 4) ⇒ (volume, cost)
Since the volume of the extra-large size will have three times the volume of the small size, hence:
Volume of extra-large size = 8 * 3 = 24
The cost of an extra large is twice as much as the small size, hence:
Cost of extra large = 4 * 2 = 8
A coordinate plane is a graphing and outline machine for factors and lines. A vertical (y) axis and a horizontal (x) axis make up the coordinate plane. There are four quadrants inside the coordinate plane. The point at which these strains join is known as the starting place (0, zero).
Coordinates are written as (x, y) meaning the point on the x-axis is written first, followed by the point on the y-axis. a few children can be taught to keep in mind this with the phrase 'along the hall, up the stairs, that means that they must observe the x-axis first after which the y.
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Need help understanding how to find the answer to problem
Answer:
3.Tan(45)=n/2
1=n/2
n=2
Cos(45)=2/m
1/√2=2/m
m=2√2
5.Sin(60)=x/14
√3/2=x/14
14√3/2=x
x=7√3
Cos(60)=y/14
1/2=y/14
y=7
Solve the system of equations 2x-2y=-14 and 3x-y=-1 by combining the equations.
The solution to the system of equations is x = 3 and y = 10
How to solve the equations?The system is given as:
2x-2y=-14
3x-y=-1
Multiply (1) by 1 and (2) by 2
So, we have:
1(2x-2y=-14)
2(3x-y=-1 )
This gives
2x - 2y=-14
6x - 2y=-2
Subtract the equations
-4x = -12
Divide by -4
x = 3
Substitute x = 3 in 3x-y=-1
3(3)-y=-1
Evaluate
9 - y = -1
Solve for y
y = 10
Hence, the solution to the system of equations is x = 3 and y = 10
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A train leaves the station at 11 a.m. traveling at the rate of 40 miles per hour. A faster train leaves the same station at 1 p.m. that afternoon and travels in the same direction on a parallel track at a rate of 60 miles per hour. At what time will the faster train overtake the slower one
The faster train overtake the slower on 5 p.m.
How to solve such time related questions?
The key concept for solving such questions is the relationship between speed, distance and time.
The relationship between them is Distance = Speed x Time.
Let the number of hours after 1pm at which faster train will overtake slower train be x.
At overtaking point,
Distance travelled by slower train = Distance travelled by faster train
Given :
Speed of slower train = 40 miles per hourSpeed of faster train = 60 miles per hourTime taken by faster train = xTime taken by slower train = x + 2.On equating distances we get
40 x ( x + 20) = 60 x (x)
40x + 80 = 60x
20x = 80
x = 4.
∴The faster train overtake the slower on 1 + 4 = 5 p.m.
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9. Two hexagons are similar in shape. The larger hexagon has an area of
7350 mm². Find the area of the smaller hexagon.
22,509.3 mm²
12,862.5 mm²
4,214.3 mm²
2,400 mm²
Answer:
2400 mm^2.
Step-by-step explanation:
The ratio of their areas = ratio of the squares of their sides.
So x / 7350 = 40^2 / 70^2 where x is area of smaller hexagon.
x = 7350 * 40^2 / 70^2
= 2400 mm^2.
The area of the smaller hexagon is found to be 2,400 mm², given the two hexagons are similar. Hence, 4th option is the right choice.
The areas of two similar figures are in the ratio which is equal to the square of the ratio of their corresponding sides.
If we have two figures A and B, and they are similar, then we can say that:
(Area of A)/(Area of B) = {(Side of A)/(Side of B)}².
In the question, we are informed that the two hexagons are similar in shape.
We are asked to find the area of the smaller hexagon, given the larger hexagon has an area of 7350 mm².
As the two hexagons are similar, we can show that:
(Area of the smaller hexagon)/(Area of the larger hexagon) = {(Side of the smaller hexagon)/(Side of the larger hexagon)}².
The side of the smaller hexagon is given to be 40mm, whereas the corresponding side of the larger hexagon is given to be 70 mm.
Thus, we can show that:
(Area of the smaller hexagon)/7350 = {40/70}²,
or, Area of the smaller hexagon = (16/49)*7350 = 16*150 mm² = 2400 mm².
Thus, the area of the smaller hexagon is found to be 2,400 mm², given the two hexagons are similar. Hence, 4th option is the right choice.
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An owner of a large car lot believes that fuel prices are going to rise significantly and wonders how this rise might affect demand for the high performance vehicles. Specifically, the owner is investigating a link between how fast a car can go from 0 to 60 miles per hour (measured in seconds) and the car's economy as measured in miles traveled per gallon used (mpg). If fast cars, which are normally high in demand, are associated with higher mpg then there will be much less demand if gas prices rise as predicted. The owner gathers data on 20 vehicles. The data is provided below. Use Excel to calculate the correlation coefficient r between the two data sets. Round your answer to two decimal places. "mpg" 0 to 60 time (seconds) 28 7.7 25 8.2 25 8.6 22 7.4 22 8 21 6.9 21 7.5 21 7.4 21 7.8 21 8.8 20 6.1 20 6.9 20 7.2 20 7.5 20 7.5 20 7.5 20 7.7 19 6.7 19 7.9 19 8.5
The correlation coefficient r between the two data sets is 0.33
How to determine the correlation coefficient r?From the table of values, we make use of the following representations:
Represent the mpg on the x axisRepresent the time on the y axisUsing the above representations, we can now plot our data values in the Excel software
From the Excel application, we have the following summary:
X Values
∑ = 424
Mean = 21.2
∑(X - Mx)2 = SSx = 101.2
Y Values
∑ = 151.8
Mean = 7.59
∑(Y - My)2 = SSy = 8.238
X and Y Combined
N = 20
∑(X - Mx)(Y - My) = 9.54
R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))
This gives
r = 9.54 / √((101.2)(8.238))
Evaluate
r = 0.3304
Approximate
r = 0.33
Hence, the correlation coefficient r between the two data sets is 0.33
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