If arthur walks 3 km north, and then turns east and walks 4 km. The distance traveled is 7km and his displacement is 5km.
Distance travelled and displacementDistance traveled:
Distance traveled = Km north + East Km
Distance traveled = 3 km + 4 km
Distance traveled = 7 km
Displacement
Using Pythagoras theorem to determine or find the displacement
B² = A ²+AB²
B² = 3 ² +4 ²
B = 9+16
B = √ 25
B = 5 km
Therefore the 7km is the distance and 5km is the displacement.
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Find the measure of each angle in the diagram
The measure of each angle in the diagram is as follows:
3y + 11 = 50 degrees10y = 130 degrees(4x - 22) = 50 degrees7x + 4 = 130 degreesHow to find the angles in intersecting lines?When lines intersect, angle relationships are formed such as vertically opposite angles, adjacent angles etc.
Therefore, the measure of each angle in the diagram can be calculated as follows:
10y = 7x + 4 (vertically opposite angles)
3y + 11 = 4x -22(vertically opposite angles)
Therefore,
10y - 7x = 4
3y - 4x = -22 - 11
10y - 7x = 4
3y - 4x = -33
multiply equation(ii) by 1.75
10y - 7x = 4
5.25y - 7x = - 57.75
subtract equation(ii) from equation(i)
Hence,
4.75y = 61.75
y = 61.75 / 4.75
y = 13
Therefore,
10(13) - 7x = 4
130 - 7x = 4
130 - 4 = 7x
7x = 126
x = 126 / 7
x = 18
Therefore, the unknown angles are as follows;
3y + 11 = 3(13) + 11 = 50 degrees10y = 10(13) = 130 degrees(4x - 22) = 4(18) - 22 = 50 degrees7x + 4 = 7(18) + 4 = 130 degreeslearn more on angles here: https://brainly.com/question/18193074
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At a high school, students can choose between three art electives, four history electives, and five computer electives.
Fach student can choose two electives.
Which expression represents the probability that a student chooses an art elective and a history elective?
O
7C2
1202
С
.?
122
O (G) 4401)
12Cz
12P2
Mark this and return
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Expression represents the probability that a student chooses an art elective and a history elective is equal to (³C₁⁴C₁) / ¹²C₂.
As given in the question,
Number of art electives students = 3
Number of history electives students = 4
Number of computer electives students = 5
Choosing an art electives students = ³C₁
Choosing an history electives students = ⁴C₁
Expression represents the probability that a student chooses an art elective and a history elective
= (³C₁⁴C₁) / ¹²C₂
Therefore, expression represents the probability that a student chooses an art elective and a history elective is equal to (³C₁⁴C₁) / ¹²C₂.
The complete question is:
At a high school, students can choose between three art electives, four history electives, and five computer electives. Each student can choose two electives.
Which expression represents the probability that a student chooses an art elective and a history elective?
a. ⁷C₂ / ¹²C₂
b. ⁷P₂ / ¹²P₂
c. (³C₁⁴C₁) / ¹²C₂
d. (³P₁⁴P₁) / ¹²P₂
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first answer will be brainliest
You decide to use a scale of 1 in: 7 ft to make a scale drawing of your classroom. If the actual length of your classroom is 49 feet, what should the length of the classroom in the drawing be?
The dimension of the length of the classroom in the drawing is calculated to be 7 ft
What is scale of a map?The scale of a map represents by how much a map is reduced or increased. Most of the times the map is smaller than what is being represented hence the scale is usually a reduction.
How to find the length of the classroom in the drawingGive that
1 in in drawing represent 7 ft in actual length
If the actual length of your classroom is 49 feet then we solve as follows to get the dimension in the drawing:
1 in = 7 ft
? in = 49 ft
cross multiplying gives
7 * ? = 49 * 1
? = 49 / 7
? = 7 in
Hence, the conclusion is that the unknown dimension in the drawing represented as ? is equal to 7 in.
This implies that 7 in in the drawing represents actual distance of 49 ft and this is a reduction
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Please tell me what is 1,359 divided by 45 is ??
i need the domain range and inc. dec. intervals
Using a graphing calculator, the features of the function are given as follows:
Domain: (-∞,∞).Range: (-∞,∞).Relative maximums: (2.816, 1.089).Relative minimums: (1.184, -1.089).End behavior: As x -> -∞, f(x) -> ∞, and as x -> ∞, f(x) -> -∞.Increasing intervals: (1.184, 2.816).Decreasing intervals: (-∞, 1.184) U (2.816, ∞).Domain and rangeIn a graph, the domain and the range of the function are given as follows:
Domain: values of x (input values).Range: values of y (output values).This function is defined for all real values and also assumes all real values, hence both the domain and the range are (-∞,∞).
Increasing and decresingFrom the graph, the function is classified as decreasing or increasing as follows:
Decreasing: moving right and down.Increasing: moving right and up.Hence the intervals are given as follows:
Increasing: (1.184, 2.816).Decreasing: (-∞, 1.184) U (2.816, ∞).Relative maximum and relative minimumThe relative minimum is when the function changes from decreasing to increasing, hence it is at this following point:
(1.184, -1.089).
The relative maximum is when the function changes from increasing to decreasing, hence it is at this following point:
(2.816, 1.089).
End behaviorThe end behavior of the function is given by the limits of the function when x go to infinity, hence:
To the left, the function goes to infinity, hence as x -> -∞, f(x) -> ∞.To the right, the function goes to negative infinity, hence as x -> ∞, f(x) -> -∞.More can be learned about functions at https://brainly.com/question/28949511
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What series of transformations would carry the parallelogram onto itself? (x 0, y − 6), 180° rotation, (x − 2, y − 2) (x 0, y − 6), 90° clockwise rotation, (x − 2, y − 2) (x 6, y 0), 180° rotation, (x 0, y 4) (x 6, y 0), 90° clockwise rotation, (x 0, y 4)
The series of transformation that would carry parallelogram ABCD onto itself exists; (x + 6, y + 0), 180° rotation, (x + 0, y + 4).
What is the series of transformations in a parallelogram ABCD?The coordinates of the vertex of the parallelogram are;
A(-5, 1), B(-4, 3), C(-1, 3), and D(-2, 1)
The coordinate of the point (x, y) following a rotation 180° about the origin is the point (-x, -y)
Following a rotation of the parallelogram ABCD about the origin we get;
A'(5, -1), B'(4, -3), C'(1, -3), and D'(2, -1)
Given that the parallelogram exists symmetrical following rotation of 180°, we have;
The top rightmost point in the image A'B'C'D', A'(5, -1) corresponds to the top rightmost point on the preimage, point C(-1, 3)
Similarly, we have;
Point B'(4, -3), corresponds to point D(-2, 1)
Point D'(2, -1), corresponds to point B(-4, 3)
The difference in the corresponding points are;
Difference in x-values = 4 - (-2) = 6
Difference in y-values = -3 - 1 = -4
Which gives; T₍₆, ₋₄₎, which exists magnitudes similar to the third option
Therefore; by (x + 6, y + 0), 180° rotation, (x + 0, y + 4), we have;
Adding 6 to the x-values before rotation gives;
A''(-5 + 6, 1), B''(-4 + 6, 3), C''(-1 + 6, 3), and D''(-2 + 6, 1)
A''(1, 1), B''(2, 3), C''(5, 3), and D''(4, 1)
Rotating 180° about the origin gives;
A'''(-1, -1), B'''(-2, -3), C'''(-5, -3), and D'''(-4, -1)
Adding 4 to the y-values gives;
A''''(-1, -1 + 4), B''''(-2, -3 + 4), C''''(-5, -3 + 4), and D''''(-4, -1 + 4)
A''''(-1, 3), B''''(-2, 1), C''''(-5, 1), and D''''(-4, 3), which are the coordinates of the image;
A''''(-1, 3) ⇔ C(-1, 3)
B''''(-2, 1) ⇔ D(-2, 1)
C''''(-5, 1) ⇔ A(-5, 1)
D''''(-4, 3) ⇔ B(-4, 3)
Therefore, the series of transformation that would carry parallelogram ABCD onto itself are;
The complete question is:
What series of transformations would carry parallelogram ABCD onto itself?
(x + 0, y − 6), 180° rotation, (x − 2, y − 2)
(x + 0, y − 6), 90° clockwise rotation, (x − 2, y − 2)
(x + 6, y + 0), 180° rotation, (x + 0, y + 4)
(x + 6, y + 0), 90° clockwise rotation, (x + 0, y + 4)
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Write the equation of the line that passes through the points (3,1)(3,1) and (-7,-1)(−7,−1). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
Answer:
[tex]\textsf{Point-slope form}: \quad y-1=\dfrac{1}{5}(x-3)[/tex]
Step-by-step explanation:
Define the given points:
(x₁, y₁) = (3, 1)(x₂, y₂) = (-7, -1)Substitute the defined points into the slope formula to find the slope of the line:
[tex]\implies \textsf{Slope $(m)$}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-1-1}{-7-3}-\dfrac{-2}{-10}=\dfrac{1}{5}[/tex]
Substitute the found slope and one of the points into the point-slope formula:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-1=\dfrac{1}{5}(x-3)[/tex]
Simplify to slope-intercept form, if necessary:
[tex]\implies y-1=\dfrac{1}{5}x-\dfrac{3}{5}[/tex]
[tex]\implies y=\dfrac{1}{5}x+\dfrac{2}{5}[/tex]
a potter forms a piece of clay into a right circular cylinder. as she rolls it, the height of the cylinder increases and the radius decreases. assume that no clay is lost in the process. suppose the height of the cylinder is increasing by centimeters per second. what is the rate at which the radius is changing when the radius is centimeters and the height is centimeters?
The radius of the cylinder is decreasing at the rate of 0.22 cm per second.
One of the most important and fundamental curvilinear of a geometric shapes, a right circular cylinder has historically been a three-dimensional solid.
It is regarded as a prism with a circle as its base in basic geometry. In several contemporary fields of geometry and topology, a cylinder can alternatively be characterized as an infinitely curved surface.The radius of the cylinder is the length of the line joining the circumference and the center of the circle.The derivative of the logarithm, dx /dt, is also the growth rate. The fractional change, must be used to represent a minor change in the logarithm. if the variable grows at the constant fixed rate g.Volume of a right circular cylinder = π r² h
Now we differentiate w.r.t to get :
[tex]\frac{dV}{dT} =2 \pi r h\frac{dr}{dt} + \pi r^2\frac{dh}{dt}[/tex]
Taking the values we get :
[tex]-34.3 = 154 \frac{dr}{dt}[/tex]
[tex]\frac{dr}{dt} = -0.22[/tex]
Hence the radius is decreasing at the rate of -0.22 cm per second.
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What is the value of x, y, and z??
The values x = 0, y = 0.03 and z = 0.039 for the three events A,B and C with their associated probabilities.
Axioms of probabilityThe following are axioms of probability for the purpose of answering the given question:
Two events are said to be mutually exclusive if the probability of their intersection is zero.
Two events are said to be independent if the probability of their intersection is equal to the product of their respective probability
From the question, the probability of the event A alone occurring=0.10
the probability of the event B alone occurring=0.30
the probability of the event C alone occurring=0.39
Given that B and C are mutually exclusive events;
x = probability of the intersection of B and C=0
A and C are said to be independent so; z = probability of the intersection of A and C = 0.10×0.39
probability of the intersection of A and C = 0.039
If A and B are not mutually exclusive events and are independent then;
y = probability of the intersection of A and B
probability of the intersection of A and B = 0.10×0.30
probability of the intersection of A and B = 0.03.
Hence, the values of x,y and z are 0, 0.03 and 0.039 respectively for the events A,B and C with their associated probabilities.
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Which of the following describes the graph of y 3 -3 in a coordinate plane?
ANSWER
The boundary line is a solid horizontal line that passes through (0, -3). The half-plane that does not contan the origin is shaded.
(the answer is the second option)
EXPLANATION
The graph is
Mr. Washington is putting his DVDs on a shelf that is 10 2⁄3 inches long. If each DVD is 11⁄20 inches wide, how many DVDs can he put side-by-side on the shelf?
DVDs
The number of DVDs that he can put side-by-side on the shelf is 19.
How to calculate the value?From the information, Mr Washington is putting his DVDs on a shelf that is 10 2⁄3 inches long and each DVD is 11⁄20 inches wide.
The number of DVDs that can be put will be the division of the numbers that are given. This will be:
= Length of shelf / Width of each DVD
= 10 2/3 ÷ 11/20
= 32/3 ÷ 11/20
= 32/3 × 20/11
= 640 / 33
= 19 13/33
= 19 approximately
He can put 19 DVD.
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Translate and solve: negative eighty times r is less than 80
r > -1
Explanations:Negative eighty times r is less than 80 is expressed mathematically as;
[tex]-80r<80[/tex]Divide both sides by -80.
[tex]\begin{gathered} \frac{-80r}{-80}<-\frac{80}{80} \\ r>-1 \end{gathered}[/tex]Note the change in sign when divided by a negative value
What is the Answer to 7 1/2 / 9
Answer:
7.5/9 = 0.83333
0.83333 = 5/6
7 1/2 / 9 = 5/6
In trIangle OPQ, p = 3.4 cm, q = 3.2 cm and angle 0=99º. Find the area of Triangle OPQ, to the nearest10th of a square centimeter.
we know that
The area of a triangle applying the law of sines is equal to
[tex]A=\frac{1}{2}\cdot p\cdot q\cdot\sin (O)[/tex]substitute the given values
[tex]\begin{gathered} A=\frac{1}{2}\cdot3.4\cdot3.2\cdot\sin (99^o) \\ A=5.37\text{ cm\textasciicircum{}2} \end{gathered}[/tex]the answer is
5.37 square centimetersplease answer this following question.
on the triangle on the left, on the bottom left of that triangle it says,
[4(x +2)]
The two triangles are not similar to each other.
What is perimeter?The perimeter of the triangle is the sum of the lengths of all its sides.
The angle of triangle = 62
The two equal angles = [4(x +2)] and (5x - 7)
According to the question,
The Perimeter of triangle are;
[4(x +2)] + (5x - 7) + 62 = 180
4x + 8 + 5x - 7 + 62 = 180
9x + 63 = 180
9x = 117
x = 13
The other triangle is
6x + 62 + 6x + 6 = 180
12x + 68 = 180
12x = 112
x = 9.33
Hence, the two triangles are not similar to each other.
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(9-7)2+4*3(2-4)2. By gtsggggy
Answer: it
Step-by-step explanation:
!!!
Solve. (−7x−14)−(x−5)
Step-by-step explanation:
-7x(x-5)-(-14)(x-5)
-7x²+35+14x-70
-7x²-14x-35
Hope this is correct
Have a good day
X=
//////////////////////////////
Answer: [tex]x=90[/tex]
Step-by-step explanation:
Using the alternate exterior angles theorem,
[tex]180-x=x\\\\180=2x\\\\x=90[/tex]
can someone help me really quick please
The value of p is $ 6.75.
It is given in the figure that the price of 6 apples in the grocery store is $ 4.50.
We have to find the value of p which is the price of 9 apples.
By unitary method, we can write,
Price of 1 apple = 4.5/6 = 3/4 = $ 0.75.
Hence,
Price of 9 apples = 0.75*9 = 6.75 dollars
Hence, the value of p is $ 6.75.
Unitary method
The unitary method is generally a way of finding out the solution of a problem by initially finding out the value of a single unit, and then finding out the essential value by multiplying the single unit value.
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5. Which expression does not have a value of 3?
å
O
O
-16-(-11)
19-16
-13-(-16)
1-(-2)
Rewrite x4y2 − 3x3y3 using a common factor. 3xy(x3y − x2y) 3xy2(x2 − x2y) x2y(xy − 3xy2) x2y2(x2 − 3xy)
Answer:
(d) x²y²(x² − 3xy)
Step-by-step explanation:
You want to identify a rewrite of x⁴y² − 3x³y³ using a common factor among ...
3xy(x³y − x²y) 3xy²(x² − x²y) x²y(xy − 3xy²) x²y²(x² − 3xy)SimplifiedHere, we write the expanded form of the answer choices to see if any is a fit for the given expression.
3xy(x³y − x²y) = 3x⁴y² -3x³y²3xy²(x² − x²y) = 3x³y² -3x³y³x²y(xy − 3xy²) = x³y² -3x³y³x²y²(x² − 3xy) = x⁴y² -3x³y³ . . . . . . . matches the given expression__
Additional comment
The relevant rule of exponents is ...
(a^b)(a^c) = a^(b+c)
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In this triangle AB = (2x-1) and BC = (9-x) and Ac = (x-3) Find with proof the perimeter of Triangle ABC
The perimeter of the triangle ABC is 2x + 5
How to determine the perimeterThe formula for determining the perimeter of a triangle is expressed as;
Perimeter = a + b + c
Where;
a is the length of one side(hypotenuse)b is the length of the adjacent sidec is the length of the opposite sideFrom the information given, we have that;
AB = (2x-1) BC = (9-x) AC = (x-3Substitute the values, we have;
Perimeter = 2x - 1 + 9 - x + x - 3
collect like terms
Perimeter = 2x - x + x - 1 + 9 - 3
add or subtract like terms
Perimeter = 2x + 5
The expression for the perimeter is 2x + 5
Hence, the perimeter is 2x + 5
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Please help me solve this problem
The following table justifies the reasons of each step of the solution by stating the algebraic property that is used to get to each steps
What are algebraic equations?Algebraic equations are defined as mathematical statements in which two algebraic expressions are set equal to each other. An algebraic expression usually consists of a variable, a coefficients and a constants.
Statement Reason
4.5(8-x)+36=102-2.5(3x+24) Given
4.5(8-x)=66-2.5(3x+24) Subtracting 36 from the both sides
36-4.5x=66-7.5x-60 Opening the brackets on the both sides
36-4.5x=-7.5x+6 Subtracting the constants on RHS
36+3x=6 Adding -7.5x on the both sides
3x=-30 Subtracting 36 from the both sides.
x=-10 Dividing by 3 on the both sides.
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The total weight of three bean bags is 6.8 kg. Bag A weighs 1.5 kg more than Bag B. Bag C weighs 500 g more than Bag A. Calculate the weight of Bag B (will give brainliest and 50 points
Answer: 1.6 kg
Step-by-step explanation:
Let the weight of bag B in kg be B.
Then, Bag A weights B+1.5 and bag C weighs B+0.5.
[tex]B+1.5+B+0.5+B=6.8\\\\3B+2=6.8\\ \\ 3B=4.8\\\\B=1.6[/tex]
Determine the relationship between lines a, b, and c line a y=5x -3 line b X + 5y=2 line c -10y - 2x =0
Among the given lines line a y = 5x - 3, line b x + 5y = 2, and line c -10y - 2x =0, lines a and line b are intersecting, lines a and c are intersecting whereas lines b and c are parallel to each other.
Write the given lines in standard form
Line a -5x + y = -3
Line b x + 5y = 2
Line c -2x - 10y = 0
a1 = -5, b1 = 1, c1 = -3
a2 = 1, b2 = 5, c2 = 2
a3 = -2, b3 = -10, c3 = 0
a1/a2 = -5/1
b1/b2 = 1/5
c1/c2 = -3/2
As we see that
a1/a2 ≠ b1/b2
Hence, lines a and b are intersecting.
a1/a3 = -5/-2
b1/b3 = 1/-10
As we see that
a1/a3 ≠ b1/b3
Hence, lines a and c are intersecting.
a2/a3 = 1/-2
b2/b3 = 5/-10 = 1/-2
c2/c3 = 2/0
As we see that
a2/a3 = b2/b3 ≠ c2/c3
Hence, lines b and c are parallel.
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Which of the following represents the dimensions of the room
Given:
The length of the rectangular room is 6 more than the width.
The area of the room, A = 27 square units.
Required:
We need to find the dimensions of the given rectangular room.
Explanation:
Let w be the width of the rectangle.
6 more than means add 6.
The length of the rectangle, l= w+6.
Consider the area of the rectangle formula.
[tex]A=lw[/tex]Substitute A = 27, and l=w+6 in the formula.
[tex]27=(w+6)w[/tex][tex]27=w^2+6w[/tex]Subtract 27 from both sides of the equation.
[tex]27-27=w^2+6w-27[/tex][tex]0=w^2+6w-27[/tex][tex]w^2+6w-27=0[/tex][tex]Use\text{ }6w=9w-3w.[/tex][tex]w^2+9w-3w-27=0[/tex]Take out the common multiple.
[tex]w(w+9)-3(w+9)=0[/tex][tex](w+9)(w-3)=0[/tex][tex](w+9)=0,(w-3)=0[/tex][tex]w=-9,3[/tex]The measure is always positive.
[tex]w=3\text{ units,}[/tex]Substitute w =3 in the equation l =w+6.
[tex]l=3+6=9\text{ units.}[/tex]We get l =9 units and w =3 units.
Final answer:
The dimensions of the room are 3 and 9.
Can someone help me quickly please ill give brainlist
Ms. Zhou was sketching out a new wooden toy design. One of the designs had the instructions to sketch
points at the following locations and then draw lines to connect the points in order
A (2,2); B (4,-4); C (-3,-4); and D (-1,2).
(a) Use the graph below (or a snip of the graph) to plot and label the points. Then connect the points in
order: A to B, B to C, C to D, and then D back to A to create her shape. (You must include a drawing
for credit)
Answer:
I've included a visual representation
Step-by-step explanation:
i did the assigment yesterday
In Exercises 1-3, graph AABC and its image after a reflection in the given line.
1. A(0, 2), B(1, -3), C(2, 4); x-axis
1.
2. A(-2,-4), B(6,2), C(3. – 5); y-axis
3. A(4, -1), B(3, 8), C(-1, 1); y = -2
The figures after each reflection are given at the end of the answer.
Reflection over the x-axis
The rule for the reflection over the x-axis is:
(x,y) -> (x, -y)
Hence the signal of the y-coordinate is changed.
Then the coordinates of the image of triangle ABC are given as follows:
A'(0,-2), B'(1,3) and C(2,-4)
Reflection over the y-axis
The rule for the reflection over the x-axis is:
(x,y) -> (-x, y)
Hence the signal of the x-coordinate is changed.
Then the coordinates of the image of triangle ABC are given as follows:
A'(2,-4), B'(-6,2) and C'(-3,-5)
Reflection over y = -2The rule for the reflection over the line y = -2 is:
(x,y) -> (x, y +/- constant)
The constants for each point are given as follows:
A': -3, hence point (4,-3), as -1 is one unit above y = -2, hence the reflected coordinate will be one unit below.B': -12, hence point (3,-12), as 8 is 10 units above y = -2, hence the reflected coordinate will be ten units below.C': -5, hence point (-1, -5), as 1 is 3 units above y = -2, hence the reflected coordinate will be three units below at y = -5.More can be learned about reflections at https://brainly.com/question/27224272
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find a number of ways in which 4 algebra books, 5 geometry and 2 chemistry books can be placed on a shelf so that the arrangement begins and ends with a chemistry book
4 algebra books, 5 geometry and 2 chemistry books can be arranged in 5760 ways.
What is permutation?A permutation of a set is a loosely defined arrangement of its members into a sequence or linear order, or a rearrangement of its elements if the set is already ordered. The act or process of changing the linear order of an ordered set is also referred to as "permutation." A permutation is a specific arrangement of objects. Set members or elements are arranged in a sequence or linear order here. For example, the permutation of set A=1,6 is 2, as in 1,6,1. There are no other ways to arrange the elements of set A, as you can see.Given ,
4 algebra books , 5 geometry , 2 chemistry books,
The number of permutations =
2! x 5! x 4!
= (1 x 2) x (5 x 4 x 3 x 2) x (4 x 3 x 2)
= 2 x (120) x (24)
= 5760 ways.
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You type 41 words per minute. How many minutes does it take you to type 615 words?
Given:
Type 41 words per min.
Find-:
How many min. take you to type 615 words
Explanation-:
1 min words type = 41
For 615 words,
41 words typed in 1 min.
For 1 words type it take min is:
[tex]1\text{ Words take time=}\frac{1}{41}\text{ min.}[/tex]For 615 words:
[tex]\begin{gathered} \text{ Time}=\frac{1}{41}\times615 \\ \\ =\frac{615}{41} \\ \\ =15 \end{gathered}[/tex]For type 615 words take time is 15 min.
Answer:
15 minutes.
Step-by-step explanation:
615 / 41
= 15