Given that In 3 years, Dianna will be 4 times as old as she was 33 years ago, her present age is 45.
How old is Dianna now?
Given that, in 3 years, Dianna will be 4 times as old as she was 33 years ago.
Let x represent the age of Dianna presently.
Dianna's age in 3 years time will be: x + 3
Dianna's age 33 years ago is: x - 33
Since in 3 years, she will be 4 times as old as she was 33 years ago.
x + 3 = 4( x - 33 )
We solve for x
x + 3 = 4x - 132
3 + 132 = 4x - x
135 = 3x
x = 135/3
x = 45
Given that In 3 years, Dianna will be 4 times as old as she was 33 years ago, her present age is 45.
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Solve the following equation for X, if Y = 3 and Z = -1. 3XY- 5XZ^2+Y=19
sketch the graph of f(x)=((x^(3)-1)/(x^(2)-1))
It's easier to sketch if you simplify [tex]f(x)[/tex]. Factorize the numerator and denominator - simple to do with a difference of cubes or squares.
[tex]\dfrac{x^3 - 1}{x^2 - 1} = \dfrac{(x - 1)(x^2 + x + 1)}{(x - 1) (x + 1)}[/tex]
If [tex]x\neq1[/tex], we can cancel the factors of [tex]x-1[/tex]. Note that [tex]f(1)[/tex] itself is undefined. For all intents and purposes, aside from the singularity at [tex]x=1[/tex], the graph of [tex]f(x)[/tex] will look exactly like the graph of
[tex]\dfrac{x^2 + x + 1}{x + 1}[/tex]
Now, rewrite this as
[tex]\dfrac{x(x + 1) + 1}{x + 1}[/tex]
Then when [tex]x\neq-1[/tex] (note that [tex]f(-1)[/tex] is also undefined), we can cancel [tex]x+1[/tex] to reduce this to
[tex]x + \dfrac1{x+1}[/tex]
On its own, the graph of [tex]x[/tex] is a line through the origin. When [tex]x[/tex] is a large number [tex]\frac1{x+1}[/tex] is small. But as [tex]x[/tex] gets closer to -1, the rational term blows up. Effectively, this means the graph of [tex]f(x)[/tex] looks like [tex]\frac1{x+1}[/tex] around [tex]x=-1[/tex], and far enough away it looks like [tex]x[/tex].
See the attached plot for a sketch of these details.
what number could t represent to make the inequality true? 2t+4<-8
2t + 4 < -8
2t < -12
t < -6
For the inequality to be true, t must be a number that is less than -6.
Hope this helps!
Miles is starting a tree farm. His plot of land is triangular with one side 36 feet and the other two sides 30 feet each. The height of this triangle-shaped plot is 24 feet. If each tree needs 8 square feet of space to grow, how many trees can Miles plant?
a. 35 b. 42 c. 54 d. 76
Answer:
54
Step-by-step explanation:
the plot of land is an isosceles triangle, meaning two sides and angles are the same in value.
height (h)= 24
base (b)= 36
length (l)= 30
solution
find the area of triangle using area=half the product of the base and height.
A=1/2(36×24)
A= 216 square feet.
each tree needs 8 square feet
therefore using ratio and proportion,
1 tree= 8 square feet
x trees= 216 square feet
cross multiply and it'll be
216/8=x
therefore x= 54 trees
CIRCLE question is in the picture
Answer:
27π cm² or 84.8 cm²
Explanation:
[tex]\sf Formula \ for \ area \ of \ sector = \dfrac{\theta}{360 } \ x \ \pi (radius)^2[/tex]
Shaded region angle: 360° - 90° = 270°
Given radius: 6 cm
Applying formula:
[tex]\rightarrow \sf \dfrac{270}{360} \ x \ \pi (6)^2[/tex]
[tex]\rightarrow \sf 27\pi[/tex]
[tex]\rightarrow \sf 84.823 \ cm^2[/tex]
[tex]\rightarrow \sf 84.8 \ cm^2 \quad (rounded \ to \ nearest \ tenth)[/tex]
Volume and surface area
Answer:
The volume of the suitcase will be 199.5 [tex]ft^{3}[/tex]
Step-by-step explanation:
To find the volume of a 3D shape (in question, the suitcase) we use the formula length x width x height. With this in mind, we multiply 19 x 7 = 133. Multiply 133 by 1.5, which equals 199.5. With a final answer of 199.5, the volume of the suitcase will be 199.5 [tex]ft^{3}[/tex].
Please help! I will give you lots of points!!!
Directions: construct the bisector of the following figures.
Note: please draw them out each on a piece of paper or laptop. Thank you!
A bisector is a line that divides either a given line or an angle into two equal parts. The answer to the given question is in the attachments to this answer.
The process of bisection implies dividing a given angle or line into two equal parts. Thus a bisector should be constructed.
The construction required is as given below:
For figure 1:
With center S and any radius, draw an arc to intersect S and T.Using the end of the arc on SR and a greater radius, draw two arcs.Using the end of the arc on ST and the same radius, draw another arc to intersect the previous arc.Join S to the point of intersection of the arcs by a straight line. Thus this line is the required bisector of <RST.For figure 2:
With center u and any radius, draw an arc to intersect T and V.Using the end of the arc on uT and a greater radius, draw two arcs.Using the end of the arc on uV and the same radius, draw another arc to intersect the previous arc.Join u to the point of intersection of the arcs by a straight line. Thus this line is the required bisector of <TuV.For figure 3:
With center B and any radius, draw an arc to intersect A and C.Using the end of the arc on AB and a greater radius, draw two arcs.Using the end of the arc on BC and the same radius, draw another arc to intersect the previous arc.Join B to the point of intersection of the arcs by a straight line. Thus this line is the required bisector of <ABC.The required construction is as shown in the attachments to this answer.
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If y is inversely proportional to the square root of x and y=−70 when x=49, find y if x=2401.
The value of y when x= 2401 is -10
How to determine the value of x?An inverse variation is represented as:
[tex]y = \frac{k}{\sqrt x}[/tex]
Where k is the proportionality constant
When y = -70, x = 49
So, we have:
[tex]-70 = \frac{k}{\sqrt {49}}[/tex]
Take the square root of 49
[tex]-70 = \frac{k}{7}[/tex]
Multiply through by 7
k = -490
Substitute k = -490 in [tex]y = \frac{k}{\sqrt x}[/tex]
[tex]y = -\frac{490}{\sqrt x}[/tex]
When x =2401, we have
[tex]y = -\frac{490}{\sqrt {2401}}[/tex]
Evaluate the square root
[tex]y = -\frac{490}{49}[/tex]
Divide
y = -10
Hence, the value of y when x= 2401 is -10
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A driveway 18 ft wide and 36 ft. long is to be paved with concrete 3 in. thick. How many cubic yards of concrete are required?
Answer:
6 yds^3
Step-by-step explanation:
I find these easiest if you put all of the dimensions into yards and then multiply
18 ft = 6 yds
36 ft = 12 yds
3 in = 3/36 yds = 1/12 yds now multiply them together
6 x 12 x 1/12 = 6 yds^3
A single die is rolled twice. Find the probability of rolling a 1 the first time and a 4 the second time.
Answer:
1/36
Step-by-step explanation:
There is an 1/6 chance of rolling 1 the first time and 1/6 chance of rolling a 4 the second time. 1/6 * 1/6 = 1/36 chance of rolling a 1 then 4.
Simplify (38)-2(13⋅38)3(13)4.
The value of (38)-2(13⋅38)3(13)4. is -154090
How to simplify the expression?The expression is given as:
(38)-2(13⋅38)3(13)4.
Rewrite properly as:
(38) - 2 * (13 * 38) * 3 * (13) * 4.
Evaluate the products in the bracket
(38) - 2 * (494) * 3 * 52
Further, expand
38 - 154128
Evaluate the difference
-154090
Hence, the value of (38)-2(13⋅38)3(13)4. is -154090
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A job order cost sheet for Ryan Company is shown below.
Job No. 92
For 2,000 Units
Date
Direct
Materials
Direct
Labor
Manufacturing
Overhead
Beg. bal. Jan. 1 6,300 7,000 4,900
8 7,000
12 8,000 6,400
25 2,600
27 4,000 3,200
15,900 19,000 14,500
The balance in the Work in Process Inventory on January 1, if this was the only unfinished job for Ryan Company, is $18,200.
What makes up the work in process inventory?The work-in-process inventory is made up of the costs of direct materials, direct labor, and manufacturing overhead at the beginning or end of the period.
Data and Calculations:Work in Process Balance on January 1:
Direct materials $6,300
Direct labor $7,000
Manufacturing overhead $4,900
Total = $18,200
Question Completion?What was the balance in the Work in Process Inventory on January 1 if this was the only unfinished job?
Thus, the balance in the Work in Process Inventory on January 1, if this was the only unfinished job for Ryan Company, is $18,200.
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What method of matrixes would be used for this question? ( Inverse Matrices, Cramer's Rule, Gaussian Elimination, and Gauss-Jordan Elimination)
May’s restaurant ordered 200 flowers for Mother’s Day. They ordered carnations at $1.50/each, roses at $5.75 each, and daisies at $2.60 each. They ordered mostly carnations, and 20 less roses than daisies. The total order came to $589.50. How many of each type of flower was ordered?
Answer:
(d) Gauss-Jordan Elimination
80 carnations; 50 roses; 70 daisies
Step-by-step explanation:
The given relations can be written as equations, which can be expressed as one matrix equation. Any of the methods listed can be used to solve the matrix equation.
EquationsIf we let c, r, d represent numbers of carnations, roses, and daisies ordered, respectively, then the given relations can be written as ...
c + r + d = 200 . . . . . . 200 flowers were ordered
0c -r +d = 20 . . . . . . . . . . . . . 20 more daisies than roses were ordered
1.50c +5.75r +2.60d = 589.50 . . . . . the total value of the order
Matrix EquationWritten as a matrix equation, it will be of the form ...
AX = B
where A is the square matrix of variable coefficients, X is the column vector of variables, and B is the column vector of equation right-side constants. This is the matrix equation:
[tex]\left[\begin{array}{ccc}1&1&1\\0&-1&1\\1.50&5.75&2.60\end{array}\right] \left[\begin{array}{c}c\\r\\d\end{array}\right] =\left[\begin{array}{c}200\\20\\589.50\end{array}\right][/tex]
Solution MethodsThe mathematical operations required to find the equation solution can be briefly described as ...
Inverse Matrices
The coefficient matrix is inverted and multiplied by the constant column vector:
[tex]X=A^{-1}B[/tex]
The inversion operation requires computation of 10 determinants, of which 9 are of 2×2 matrices. That's a total of about 39 multiplications, 9 divisions, and 20 additions.
Cramer's Rule
Using Cramer's rule requires computation of 4 determinants of 3×3 matrices. The total number of operations comes to about 48 multiplications, 3 divisions, and 20 additions.
Gaussian Elimination
To obtain the upper triangular matrix that results from Gaussian Elimination requires about 11 multiplications, 11 additions, and 2 divisions. This finds the value of one variable, but the others must be found by substitution into the remaining two equations, requiring an additional 3 multiplications and 3 additions.
Gauss-Jordan Elimination
This method starts with an augmented matrix that appends column vector B to the square matrix A. The result of this is shown in the attachment. It is a diagonal matrix with the variable values a direct result of the matrix operations. The calculator's RREF( ) function performs matrix row operations to transform the augmented matrix to this Reduced Row-Echelon Form. About 6 multiplications, 6 additions, and 4 divisions are required.
Clearly, Gauss-Jordan Elimination is the method that requires the least computational work, so it would probably be used for this question.
FlowersThe attachment shows the order to be ...
80 carnations50 roses70 daisies__
Additional comment
The estimates of computational load presented by each of the solution methods are not intended to be exact counts. For this specific problem, some of the operations can be avoided due to the fact that some coefficients are already 1. Also, some computations are not needed simply because they are intended to produce an outcome that is already known. The intention is to give an idea of the relative difficulty of using these different methods.
In some cases, computationally less-efficient methods may be preferred because they are simpler to describe.
Point G lies between points F and H on Line segment F H.
A line contains points F, G, H. The space between F and G is 4 x. The space between G and H is 2 x.
If the length of FH is 18 units, what is the value of x?
3
4
6
12
The value of x is 3 units.
We know that a portion of a line with two endpoints is referred to as a line segment. A line segment, in contrast to a line, has a known length. A line segment's length can be calculated using either metric measurements like millimeters or centimeters, or conventional measurements like feet or inches.
Given that FH is a line segment and FH = 18 units. G is a point on FH such that FG = 4x units and GH = 2x units.
So, we can write
4x + 2x = 18
i.e. 6x = 18
i.e. x = 18/6 = 3
Then, the value of x is 3 units. So, the first option is correct.
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Answer: A / 3
Step-by-step explanation: edge 2022
need help with this asap
There is no relationship between the number of hours cycled and the number of hours worked (Option D).
What is a scatterplot?A scatterplot is a graph that is used to show the association between two variables. The relationship between the variables is shown by the use of line of best fit.
From the scatterplot shown, we can conclude that there is no relationship between the number of hours cycled and the number of hours worked (Option D).
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Which choice is equivalent to the expression below? √-12 A. 214√3 B. -12/ C. 12/ OD. -2√3 E. 2/3/
The equivalent expression of [tex]\sqrt{-12}[/tex] is [tex]2\sqrt{-3}[/tex]
How to determine the equivalent expression?The expression is given as:
[tex]\sqrt{-12[/tex]
Express -12 as 4 * -3
[tex]\sqrt{-12} = \sqrt{4 * -3}[/tex]
Expand the expression
[tex]\sqrt{-12} = \sqrt{4} * \sqrt{-3}[/tex]
Take the positive square root of 4
[tex]\sqrt{-12} = 2 * \sqrt{-3}[/tex]
Evaluate the product
[tex]\sqrt{-12} = 2\sqrt{-3}[/tex]
Hence, the equivalent expression of [tex]\sqrt{-12}[/tex] is [tex]2\sqrt{-3}[/tex]
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The length of a rectangle is 27 meters and the width is 4 meters. Find the area. Give your answer without units.
Answer:
[tex]108 m^{2}[/tex]
Step-by-step explanation:
[tex]27\times4=108[/tex]
On Friday, a local hamburger shop sold a combined total of 376 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold. How many hamburgers were sold on Friday?
Answer:
94 hamburgers
Step-by-step explanation:
Let's solve this question through the use of equations.
Start by defining the variables used.
Let the number of hamburgers and cheeseburgers sold on Friday be h and c respectively.
Form 2 equations using the given information.
Given that the total sold is 376,
h +c= 376 -----(1)
The number of cheeseburgers sold was thrice the number of hamburgers sold.
c= 3h -----(2)
Solving by substitution:
Substitute (2) into (1):
h +3h= 376
Now that we have an equation expressed only in terms of h, we can find the value of h.
4h= 376
Divide both sides by 4:
h= 376 ÷4
h= 94
Thus, 94 hamburgers were sold on Friday.
What is the slope and y- intercept in the equation y=4x+6?
The slope is 4 and the y-intercept is 6.
The slope-intercept form is [tex]y=mx+b[/tex], where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept.
Attached is an image of the graph.
Suppose a graphic designer earns $52,000 and is not self-employed. How much will the designer have to pay in FICA taxes?
The amount that the designer will have to pay in FICA taxes is:$3,978.
FICA taxes
FICA taxes comprises of:
Social Security tax= 6.2%
Medicare tax= 1.45%
Hence:
FICA taxes=($52,000×6.2%)+($52,000×1.45%)
FICA taxes=$3,224+$754
FICA Taxes=$3,978
Therefore the amount that the designer will have to pay in FICA taxes is:$3,978.
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You have $1,300 in savings for retirement. If your investments earn 12% annually, how much will you have in your retirement account in 11 years?
Step-by-step explanation:
Answer :- Amount (after 11 years) = $4522.11
You are training your dog to catch a frisbee. You are playing in a large field, and you are standing next to your dog when you throw the frisbee. If the path of the frisbee is y=-x²
+7x+1 and the path of the dogis modeled by y = 2x + 5, will the dog catch the frisbee? If so, what are the coordinates of the point or points where they meet?
A: Yes, they intersect at the coordinates (1,7) and (4, 13)
B: Yes, they intersect at the coordinates (1,9) and (2, 9)
C: Yes, they intersect at the coordinates (2, 11) and (3, 11)
D: No, the paths do not cross
the intersection points are (1, 7) and (4, 13), So the correct option is A.
Will the dog catch the frisbee?
To see that, we need to see when the two equations:
y = -x²+7x+1
y = 2x + 5
Can be solved simultaneously for a point (x, y). So we need to solve a system of equations.
y = -x²+7x+1
y = 2x + 5
We can rewrite:
-x²+7x+1 = y = 2x + 5
Then we can solve this for x:
-x²+7x+1 = 2x + 5
x² - 5x + 4 = 0
This is just a quadratic equation, the solutions are:
[tex]x = \frac{-(-5) \pm \sqrt{(-5)^2 - 4*(1)*(4)} }{2} \\\\x = \frac{5 \pm 3 }{2}[/tex]
So we have two values of x:
x = (5 + 3)/2 = 4x = (5 - 3)/2 = 1The correspondent values of y are:
y = 2*(4) + 5 = 13
y = 2*(1) + 5 = 7
Then the intersection points are (1, 7) and (4, 13)
Then the correct option is A. The dog will catch the frisbee.
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Why is the angle of elevation for two parasailing boats traveling at the same speed
The angle of elevation for two parasailing boats traveling at the same speed is equal because they have the same length of tow line.
What is parasailing?Parasailing is also referred to as parascending and it can be defined as a recreational activity which involves a person wearing an open parachute (canopy wing) and gliding through the air, while being towed by a boat.
By critically observing the image shown below, we can infer and logically deduce that the reason why the angle of elevation for two parasailing boats traveling at the same speed is equal, is simply because they have the same length of tow line.
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Complete Question:
Why is the angle of elevation for two parasailing boats traveling at the same speed equal?
Given that 1/x+1/y=3 and xy+x+y=4, compute x^2y+xy^2.
Answer:
3
Step-by-step explanation:
[tex]\frac{y+x}{xy} =3\\x+y=3xy\\xy+x+y=4\\xy+3xy=4\\4xy=4\\xy=1\\x^2y+xy^2=xy(x+y)=xy(3xy)=3(xy)^2=3(1)^2=3[/tex]
Answer:
3
Step-by-step explanation:
So we're given: [tex]\frac{1}{x} + \frac{1}{y} = 3[/tex] and that: [tex]xy+x+y=4[/tex]. And now we need to solve for: [tex]x^2y+xy^2[/tex].
Original equation:
[tex]\frac{1}{x} + \frac{1}{y} = 3[/tex]
Multiply both sides by xy
[tex]y+x=3xy[/tex]
Now take this and plug it as x+y into the second equation:
Original equation:
[tex]xy+x+y=4[/tex]
Substitute 3xy as x+y
[tex]xy + 3xy = 4[/tex]
Combine like terms:
[tex]4xy = 4[/tex]
Divide both sides by 4
[tex]xy=1[/tex]
Divide both sides by x:
[tex]y=\frac{1}{x}[/tex]
Original equation:
[tex]x^2y+xy^2[/tex]
Substitute 1/x as y
[tex]x^2(\frac{1}{x})+x(\frac{1}{x})^2[/tex]
Multiply values:
[tex]\frac{x^2}{x}+\frac{x}{x^2}[/tex]
Simplify:
[tex]x+\frac{1}{x}[/tex]
Substitute y as 1/x back into the equation:
[tex]x+y[/tex]
so now we just need to solve for x+y
Look back in steps to see how I got this:
[tex]y+x=3xy[/tex]
Divide both sides by 3
[tex]\frac{x+y}{3}=xy[/tex]
Original equation:
[tex]xy+x+y=4[/tex]
Substitute
[tex]\frac{x+y}{3}+x+y=4[/tex]
Multiply both sides by 3
[tex]x+y+3x+3y=12[/tex]
Combine like terms:
[tex]4x+4y=12[/tex]
Divide both sides by 4
[tex]x+y=3[/tex]
So now we finally arrive to our solution 3!!!!! I swear I felt like I was going in circles, and I was about to just stop trying to solve, because I had no idea what I was doing, sorry if I made some unnecessary intermediate steps.
Runner A finished 200 meter race in 5/12 of a minute. Runner B ran it in 21/25 of runner A's time. How much time did it take runner B to finish the race?
The time it will take runner B to finish the race is 7/15 of a minutes
FractionRunner A = 200 meters in 5/12 minutesRunner B = 21/25 of runner A timeTime taken by runner B = 21/25 × 5/12 minutes
= (21 × 5) / (25 × 12)
= 105 / 300
= 7/15 minutes
Therefore, it takes runner B 7/15 of a minutes to run the same race as runner A.
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If you are just given the two points it is the same formula. Find the midpoint between the
points (4,-5) and (-4, 5).
Solution
Let's begin by applying the Midpoint Formula:
(217-22,
+32
2
Looking at our x values first we have:
+(-4))/
And looking at our y values we have:
(-5+
)/2 = (0/
So our midpoint would be the point (
4
/2) =
Given :
Point 1 = (4, -5)Point 2 = (-4, 5)Midpoint formula :
[tex]\boxed {M = (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})}[/tex]
Let's input the values !
⇒ M = (4 - 4 / 2, -5 + 5 / 2)
⇒ [tex]\boxed {M = (0,0)}[/tex]
The midpoint between the points is (0, 0).
If three times a number added to 2 is divided by the number plus 4 the result is eight thirds. Find the number
Answer:
26
Step-by-step explanation:
(3a+2)/(a+4) = 8/3
(3a+2) = (8/3)(a+4)
(3a+2) = a*8/3 + 4*8/3
(3a+2) = 8a/3 + 32/3
3a - 8a/3 = 32/3 - 2
9a/3 - 8a/3 = 32/3 - 6/3
9a - 8a = 32 - 6
a = 26
Check:
(3*26 + 2) / (26+4) = 8/3
(78+2) / 30 = 8/3
80 / 30 = 8/3
Use the diagram to complete the statements.
This is circle .
If the distance from A to C is 6 units, then the distance from C to B is units.
A circle is a curve sketched out by a point moving in a plane. If the distance from A to C is 6 units, then the distance from C to B is 6 units.
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.
If the distance from A to C is 6 units, then the distance from C to B is 6 units. This is because AC and BC are the radii of the circle, therefore, both are equal to each other.
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Answer: c and 6
Step-by-step explanation:
(3√5)(10√3) help me pls
Mrs. evans has 5 spaces in which to display 5 baskets. how many ways can mrs. evans display the baskets?
Factorial of a positive integer is the result of the repeated multiplication of all the integers from 1 to that considered integer. The number of ways Mrs Evans can display the 5 baskets is 120.
What is factorial?Factorial of a positive integer is the result of the repeated multiplication of all the integers from 1 to that considered integer.
Thus, if we want to take the factorial of 'n',(n being a positive integer), then:
[tex]n! = 1 \times 2 \times \cdots \times (n-1) \times n[/tex]
We usually write it in reverse order because, in calculations, its cancellation comes useful. Thus, we have:
[tex]n! = n \times (n-1) \times \cdots \times 2 \times 1[/tex]
Mrs. evans has 5 spaces in which to display 5 baskets. Therefore, the number of ways Mrs Evans can display the 5 baskets are,
Number of ways = 5! = 5×4×3×2×1 = 120
Hence, the number of ways Mrs Evans can display the 5 baskets is 120.
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