A​ salesperson's commission rate is 6​%. What is the commission from the sale of $37,000 worth of​ furnaces? Use pencil and paper. Suppose sales would double. What would be true about the​ commission? Explain without using any calculations.

The total cost of producing 100 bar stools using the left-rectangle approximation with five rectangles is approximately $200.

The marginal cost function for producing the x-th item of a certain brand of bar stool is given by MC(x) = 20 - 0.5x, where 0 ≤ x ≤ 100. To estimate the total cost of producing 100 bar stools using the left-rectangle approximation with five rectangles, we first need to calculate the width of each rectangle.

The width of each rectangle is (100 - 0) / 5 = 20.

Now, we will evaluate the marginal cost function at the left endpoints of each rectangle:
MC(0) = 20 - 0.5(0) = 20
MC(20) = 20 - 0.5(20) = 10
MC(40) = 20 - 0.5(40) = 0
MC(60) = 20 - 0.5(60) = -10
MC(80) = 20 - 0.5(80) = -20

Next, multiply each value by the width (20) and sum the results to approximate the variable cost:
Variable cost ≈ 20(20) + 10(20) + 0(20) + (-10)(20) + (-20)(20) = 400 + 200 - 200 - 400 = 0

Finally, add the fixed cost of $200 to the variable cost:
Total cost ≈ $200 + $0 = $200

So, the total cost of producing 100 bar stools using the left-rectangle approximation with five rectangles is approximately $200.

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The volume of the air in the container is: 3,585.125 in³

The volume of a box or cuboid is given by the formula:

V = L * W * H

Where:

L is length

W is width

H is height

We are given the external dimensions as:

Length = 22 inches

Width = 15 inches

Height = 12 inches

Since the glass is 1/2 inch thick, then the interior dimensions are:

New length = 22 - 1/2 = 21.5 inches

New Width = 15 - 1/2 = 14.5 inches

New height = 12 - 1/2 = 11.5 inches

Thus:

Volume of air in container = 21.5 * 14.5 * 11.5

= 3,585.125 in³

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Answer:

134° + (2x)° = 180°

(2x)° = 46°

x = 23

So angles 1, 2, 3, and 4 all measure 23°.

The teacher originally had [tex]m*c + 13[/tex] notebooks.

If the teacher handed out m packs of notebooks with c notebooks in each pack, then the total number of notebooks that he gave out would be [tex]m*c[/tex].

If he gave out m packs of notebooks with c notebooks in each pack and has [tex]13[/tex] notebooks left, then the total number of notebooks he originally had would be:

[tex]m*c + 13[/tex]

Therefore, the expression for the total number of notebooks originally had by the teacher is [tex]m*c + 13[/tex].

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i) The angle XYZ in which XY= 8.3 cm, YZ= 11.9 cm is constructed.

ii) M the midpoint of XZ where XYZ= 60 is constructed.

iii) The measure of YM is 6.3 cm

Firstly, you are asked to construct an angle XYZ where XY= 8.3 cm and YZ= 11.9 cm. To construct an angle, we need to follow a few steps.

Draw a line segment XY of length 8.3 cm.

At point Y, draw a ray YZ extending in the direction of Z.

Using a compass, draw an arc of radius 11.9 cm from point Y, intersecting the ray YZ at point Z.

The angle XYZ is the angle formed by the line segments XY and YZ.

Now, you need to construct the midpoint M of XZ. The midpoint of a line segment is the point that divides it into two equal parts. To construct the midpoint, we follow these steps:

Draw a line segment XZ joining points X and Z.

Using a compass, draw an arc of radius greater than half of XZ from point X.

Using the same radius, draw another arc from point Z intersecting the first arc at point P.

Draw a line through points X and P, and another line through points Z and P. These two lines will intersect at the midpoint M of line segment XZ.

Finally, you are asked to measure angle YM. To measure an angle, we use a protractor.

Draw a line segment YM.

Place the protractor at point Y with the base line of the protractor aligned with line segment YZ.

Read the angle measurement where line segment YM intersects the protractor.

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To multiply -1(x^2-4x+8), we need to distribute the -1 to each term inside the parentheses:

-1(x^2-4x+8) = -x^2 + 4x - 8

So, the product of -1 and the expression (x^2-4x+8) is -x^2 + 4x - 8.

Layla must pay the agency a fee of $1,426.67 for their services in helping her secure her new job.

One month's pay = Annual salary / 12 months

One month's pay = $53,500 / 12

One month's pay = $4,458.33

Next, we need to determine the agency fee, which is equal to 32% of one month's pay:

Agency fee = 32% x One month's pay

Agency fee = 0.32 x $4,458.33

Agency fee = $1,426.67

Therefore, Layla must pay the agency a fee of $1,426.67 for their services in helping her secure her new job. Layla's agency fee is determined by taking 32% of her monthly pay, which is approximately $4,458.33. This results in a fee of approximately $1,426.67 that Layla must pay to the agency.

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The number of solutions that are there for the pair of equations for lines Q and S is zero solution (no solution) because the lines are parallel with no point of intersection.

In Mathematics and Geometry, no solution is sometimes referred to as zero solution, and an equation is said to have no solution when the left hand side and right hand side of the equation are not the same or equal.

This ultimately implies that, a system of equations would have no solution when the line representing each of the equations are parallel lines and have the same slope i.e both sides of the equal sign are the same and the variables cancel out.

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Answer: So, according to this prediction, a book with 19 chapters would have approximately 950 pages. However, keep in mind that this is just a prediction based on the trend line, and there may be some variability in the actual number of pages for a book with 19 chapters.

Step-by-step explanation:

Unfortunately, I cannot see the scatter plot you are referring to. However, I can explain how to use a trend line to predict the number of pages in a book with 19 chapters.

A trend line is a line that represents the general direction or tendency of the data in a scatter plot. To use a trend line to predict the number of pages in a book with 19 chapters, you would first need to determine the equation of the trend line.

This equation usually takes the form y = mx + b, where y is the dependent variable (in this case, the total number of pages), x is the independent variable (in this case, the number of chapters), m is the slope of the line, and b is the y-intercept (the value of y when x is 0).

Once you have the equation of the trend line, you can plug in the value x = 19 and solve for y to get the predicted number of pages in a book with 19 chapters.

For example, if the equation of the trend line is y = 50x + 200, then the predicted number of pages for a book with 19 chapters would be:

y = 50(19) + 200

y = 950

So, according to this prediction, a book with 19 chapters would have approximately 950 pages. However, keep in mind that this is just a prediction based on the trend line, and there may be some variability in the actual number of pages for a book with 19 chapters.

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At the end of the weekend, Elisa had the most biscuits (168). So, the answer is (E) Elisa baked the most biscuits on Saturday.

To determine who baked the most biscuits on Saturday, we need to calculate how many biscuits each child had at the end of the weekend.

Anna had 24 biscuits, Berta had 25, Charlie had 26, David had 27, and Elisa had 28.

Let's start with the child who had twice as many biscuits as on Saturday. We can divide their total number of biscuits by 2 to get the number they had on Saturday.

If we try this calculation for each child, we find that only Elisa's total number of biscuits (28) is evenly divisible by 2. Therefore, Elisa must be the child who had twice as many biscuits as on Saturday, meaning she had 14 biscuits on Saturday.

We can use a similar process to determine how many biscuits each child had on Saturday:

- The child who had three times as many biscuits as on Saturday must have had a total of 42 biscuits, which means they had 14 biscuits on Saturday.
- The child who had four times as many biscuits as on Saturday must have had a total of 56 biscuits, which means they had 14 biscuits on Saturday.
- The child who had five times as many biscuits as on Saturday must have had a total of 70 biscuits, which means they had 14 biscuits on Saturday.
- The child who had six times as many biscuits as on Saturday must have had a total of 84 biscuits, which means they had 14 biscuits on Saturday.

Now we can add up the number of biscuits each child had on Saturday:

- Anna had 24 biscuits.
- Berta had 25 biscuits.
- Charlie had 26 biscuits.
- David had 27 biscuits.
- Elisa had 14 biscuits.

Therefore, David baked the most biscuits on Saturday with 27.
To determine who baked the most biscuits on Saturday, we need to consider the information given about the multiplication factors (twice, 3 times, 4 times, 5 times, and 6 times) and the initial number of biscuits baked by each child.

1. Anna baked 24 biscuits.
2. Berta baked 25 biscuits.
3. Charlie baked 26 biscuits.
4. David baked 27 biscuits.
5. Elisa baked 28 biscuits.

Now, let's apply the multiplication factors and see which child had the most biscuits at the end of the weekend:

1. Anna: 24 x 2 = 48
2. Berta: 25 x 3 = 75
3. Charlie: 26 x 4 = 104
4. David: 27 x 5 = 135
5. Elisa: 28 x 6 = 168

At the end of the weekend, Elisa had the most biscuits (168). So, the answer is (E) Elisa baked the most biscuits on Saturday.

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If the commission rate is ​%6.5 for the real estate agency, the real estate agency made $20,475 on the house. The agent earned $4,095 in commission.

First, let's determine the commission earned by the real estate agency. To do this, we'll multiply the house price ($315,000) by the commission rate (6.5%).

$315,000 * 6.5% = $20,475

The real estate agency made $20,475 on the house.

Next, let's determine the commission earned by the agent. We'll multiply the commission earned by the real estate agency ($20,475) by the agent's commission rate (20%).

$20,475 * 20% = $4,095

The agent earned $4,095 in commission.

So, the real estate agency made $20,475 on the house, and the agent earned $4,095 in commission.

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The total number of students who were surveyed is 575

The graph likely displays a horizontal axis and a vertical axis.

In this graph, the horizontal axis may indicate two categories, such as "juniors" and "seniors," and the vertical axis shows the number of students in each category who responded "yes," "no," or "not sure."

To find the total number of students surveyed, we need to look for the bar that represents the entire group of juniors and seniors. Typically, this bar will be labeled as "total," "all," or something similar. Once we locate this bar, we can add up the number of students represented by the bar. The value will be displayed on the vertical axis, and it should correspond to the sum of the bars for juniors and seniors separately.

=> 100 + 200 + 125 + 150 = 575

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If Shen drives fewer than 80 miles, the first plan will be cheaper. If he drives more than 80 miles, the second plan will be cheaper.

Let's denote the number of miles driven by "m".

Under the first plan, Shen will pay an initial fee of $40, and then an additional $0.30 for each mile driven. So the total cost, C1, can be expressed as:

C1 = 0.3m + 40

Under the second plan, Shen will not have to pay an initial fee, but he will be charged $0.80 for each mile driven. So the total cost, C2, can be expressed as:

C2 = 0.8m

To determine which plan is cheaper for a given number of miles driven, we can set the two expressions for cost equal to each other and solve for "m":

0.3m + 40 = 0.8m

Subtracting 0.3m from both sides, we get:

40 = 0.5m

Dividing both sides by 0.5, we get:

m = 80

So if Shen drives fewer than 80 miles, the first plan will be cheaper. If he drives more than 80 miles, the second plan will be cheaper.

It's worth noting that this assumes that Shen is only considering the cost of the rental when making his decision. If there are other factors he is considering, such as convenience or availability, he may choose a different plan even if it ends up being slightly more expensive.

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Answer:

it should be 1/10 if that helps you

Answer:

0.01 does not have the same value as the others.

Step-by-step explanation:

10/100, 10%, and 1/10 is all the same. 0.01 is NOT the same because it is equal to 1/100, or 1% while the others were all equal to 10%. To figure this out, you must multiply 0.01 by 100 (or move the decimal point one space to the right two times) and we will get 1. This means that 0.01 is 1% which is also equal to 1/100, therefore it does not obtain the same value as the others.

Options A and C are ruled out because they don't even represent legitimate expressions for a prism's surface area.   [tex]12 + 12 + 12 + 3 + 3.[/tex]Thus, option D is correct.

The expression that represents the surface area of the prism depends on the dimensions of the prism. However, we can use the formula for the surface area of a rectangular prism, which is:

Surface Area [tex]= 2lw + 2lh + 2wh[/tex]

where l is the length, w is the width, and h is the height of the prism.

Looking at the answer choices:

A)[tex]2.6 + 12 + 8 + 8 = 28.6[/tex]

B)[tex]2.3 + 3.8 = 6.1[/tex]

C)[tex]3 + 3 + 12 + 8 + 8 = 34[/tex]

D)[tex]12 + 12 + 12 + 3 + 3 = 42[/tex]

We can eliminate options A and C because they are not even valid expressions for the surface area of a prism.

Option B is a valid expression for the surface area, but it is not simplified.

Option D is also a valid expression for the surface area, and it is simplified.

Therefore, the answer is (D)  [tex]12 + 12 + 12 + 3 + 3.[/tex]

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The characteristics of the hyperbola with equation (x+12)²/36-(y-15)²/100=1 are:

Comparing the given equation with the standard form, we have:

(h, k) = (-12, 15)

a² = 36

b² = 100

Taking the square root of a² and b², we get:

a = 6

b = 10

c² = 36 + 100

c² = 136

c ≈ 11.66

The foci of the hyperbola are located at (-12, 15 + 11.66) and (-12, 15 - 11.66), which are approximately (-12, 26.66) and (-12, 3.34).

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The lower and upper quartiles are calculated by finding the average of two values when there is an even number of data points in the dataset. Specifically, the lower quartile (Q1) is the average of the middle two values when the dataset is sorted in ascending order, and the upper quartile (Q3) is the average of the middle two values when the dataset is sorted in descending order.

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Answer:

m = -3

Step-by-step explanation:

We Know

Slope = rise/run or (y2 - y1) / (x2 - x1)

Pick 2 points (0,15) (2,9)

We see the y decrease by 6, and the x increase by 2, so the slope is

m = -6/2 = -3

So, the slope of the line representing the data is -3.

The type of transformation shown is a vertical transformation

In mathematics, a vertical translation refers to a transformation of a function or graph that involves moving it up or down along the y-axis without changing its vertical transformation.

From the attached figure, we can see that the polygons are moved up or down to map them to one another

This means that the transformation is a vertical transformation

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Complete question

Use the image to determine the type of transformation shown.

Image of polygon ABCD and a second polygon A prime B prime C prime D prime below.

Vertical translation

Reflection across the x-axis

180° counterclockwise rotation

Horizontal translation

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The dice has eight sides, hence the theoretical probability of rolling a six is given as follows:

1/8 = 0.125 = 12.5%.

The experimental probabilities are obtained considering the trials, hence:

The more trials, the closer the experimental probability should be to the theoretical probability.

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Answer: 48 inches

Step-by-step explanation:

Note that the first coordinate of M is -1. (Option D)

Given :- coordinates of F = (-4,-2) = (x1,y1)

coordinates  of G = (2,-2) = (x2,y2)

coordinates of P = (2,-8) = (x3,y3)

and distance between point M and P is half of the distance between FG

To find :- first coordinate of point M

solution :- let the coordinate of M be (x4,y4)

as we know that distance between of the opposite point of parallel line segments are equal

so, second coordinate of M = -8

now by distance formula

FG = √(x2-x1)² + (y2-y1²)

= √[2-(-4)]² + [-2-(-2)]²

= √(2+4)² + (2-2)²

= √(6)² + (0)²

=√36

F G = 6

so, distance between point M and P = 1/2 × F G

= 1/2 × 6

= 3units

again, by distance formula

MP = √(x3-x⁴)² + (y3-y4)²

3 = √(2-x⁴)² + [-8-(-8)]²

squaring on both side

(3)² = (√(2-x⁴)² + [-8-(-8)]²)²

9 = (2-x⁴)² + [-8-(-8)]²

9 = (2-x⁴)²+(0)²

9 = (2-x⁴)²

√9 = 2-x⁴

3 = 2-x⁴

x⁴ = 2-3

x⁴ = -1

Hence the first coordinate of M is -1

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Full Question:

Although part of your question is missing, you might be referring to this full question:

Point M is located in the third quadrant.

The distance between point M and point P is half the distance between point F and point G.

• Segment MP is parallel to segment FG. What is the first coordinate of point M?

Service fee for the over the counter deposit of R700: R10.50

Service fee for the ATM withdrawal of R500: R11.50

To determine the service fee that Tilly will incur for the given transactions,

Over the Counter Deposit of R700:

Tilly is depositing R700, the fee will be:

Fee = R3.50 + (R1.00 per R100) x (R700 / R100)

= R3.50 + R7.00

= R10.50

Therefore, the service fee for the over the counter deposit of R700 is R10.50.

ATM Withdrawal of R500:

The fee for an ATM withdrawal at own bank is calculated as R6.50 + R1.00 per R100.

Since Tilly is withdrawing R500, the fee will be:

Fee = R6.50 + (R1.00 per R100) x (R500 / R100)

= R6.50 + R5.00

= R11.50

Therefore, the service fee for the ATM withdrawal of R500 is R11.50.

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The mean absolute deviation is 6.25.

To find the mean absolute deviation (MAD), we first need to find the mean of the scores:

Mean = (68 + 76 + 63 + 58 + 64 + 75 + 78 + 78) / 8 = 69.5

Next, we need to find the absolute deviation of each score from the mean. The absolute deviation is the absolute value of the difference between the score and the mean.

For example, the absolute deviation of the first score (68) is:

|68 - 69.5| = 1.5

We can calculate the absolute deviation for each score:

|68 - 69.5| = 1.5

|76 - 69.5| = 6.5

|63 - 69.5| = 6.5

|58 - 69.5| = 11.5

|64 - 69.5| = 5.5

|75 - 69.5| = 5.5

|78 - 69.5| = 8.5

|78 - 69.5| = 8.5

To find the MAD, we take the average of the absolute deviations:

MAD = (1.5 + 6.5 + 6.5 + 11.5 + 5.5 + 5.5 + 8.5 + 8.5) / 8 = 6.25

Therefore, the mean absolute deviation is 6.25.

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By using Pythagoras' theorem, triangle 3 and 4 is a right triangle, and others are not.

What is the triangle?

A triangle is a three-sided polygon with three vertices. The angle produced within the triangle is 180 degrees.

What is right-angled triangle?

A right-angled triangle is one with one of its interior angles equal to 90 degrees, or any angle is a right angle.

According to the given information:

The Pythagorean theorem states that " In a right-angled triangle, the square of the hypotenuse is equal to the sum of squares of the other two sides"

Let's check fig (3)

[tex]15^{2} =12^{2} +9^{2}[/tex]

225 = 144 + 81

225 = 225

both sides are equal, Therefore it is a right-angled triangle.

Let's check fig (4)

[tex]48.5^{2}=39^{2}+32.5^{2}[/tex]

2352.25 = 1521 + 1056.25

2352.25 ≠ 2577.25

Both sides are not equal, Therefore it is not a right-angled triangle.

Let's check fig (5)

[tex]11^{2}=9^{2}+\sqrt{115} ^{2}[/tex]

121 = 81 + 115

121 ≠ 196

Both sides are not equal, Therefore it is not a right-angled triangle.

Let's check fig (6)

[tex]16^{2} = 10^{2} + (2\sqrt{39}) ^{2}[/tex]

256 = 100 + 156

256 = 256

both sides are equal, Therefore it is a right-angled triangle.

Hence figure 3 and 6 is right angle triangle, others are not.

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BD = CA is proved using the Pythagorean theorem.

It is a quadrilateral that has one pair of parallel sides and a height.

The area is calculated as 1/2 x the sum of the parallel sides x height.

Examples:

Area of a trapezium that has the parallel sides as 3 cm and 4 cm and a heght o 5 cm.

Area = 1/2 x (3 + 4) x 5

Area = 1/2 x 7 x 5

Area = 35/2 = 17.5 cm^2

We have,

From the trapezium ABCD,

BA = CD ______(A)

Now,

We can have two triangles:

ΔABD and ΔACD

Using the Pythagorean theorem.

BD² = AB² + AD² _____(1)

And,

CA² = CD² + AD² ______(2)

From (1), (2), and (A).

BD² = BA² + AD²

CA² = BA² + AD²

This means,

BD² = CA²

BD = CA

Proved

Thus,

BD = CA can be Proven as above.

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Answer:

Step-by-step explanation:

Faith needs a prosthetic hand because she lost her left hand at birth and requires assistance holding objects.

According to the article "7-Year-Old Girl Gets New Hand from 3-D Printer," Faith is a young girl who was born with a condition that caused her to lose her left hand. As a result, she has difficulty holding onto objects such as paper and bicycle handlebars. Faith had been waiting for an opportunity to design her own prosthetic hand, but the waiting list for other types of treatment was too long. Fortunately, a team of students and educators at a local university were able to create a prosthetic hand for her using a 3-D printer. The new hand will allow Faith to have greater independence and mobility, and she is excited to be able to participate in activities she was previously unable to do. This story is an example of how technology can be used to improve the lives of individuals with disabilities and provide them with greater opportunities to participate fully in everyday life.

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The system of inequalities that has a solution set that is a line is [x + y ≥ 3; x + y ≤ 3]; option A

A system of inequalities is a set of two or more inequalities that are solved simultaneously to find the values of variables that satisfy all the inequalities in the system.

Considering the given system of inequalities:

The system of inequalities that has a solution set that is a line is:

[x + y = 3;]

This is because the solution set of this equation is a line with slope -1 passing through the point (3, 0) and (0, 3).

Therefore, the system of inequalities [x + y ≥ 3; x + y ≤ 3] has a solution set that is a line.

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Answer:

3 cm.

Step-by-step explanation:

Let's use the formula for the perimeter of a rectangle, which is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.In this case, we have:P = 16 cm (given)

l = k cm (given)

w = 5 cm (given)Substituting these values into the formula, we get:

16 cm = 2(k cm) + 2(5 cm)

Simplifying, we get:

16 cm = 2k cm + 10 cm

Subtracting 10 cm from both sides, we get:6 cm = 2k cm

Dividing both sides by 2, we get:

3 cm = k

Therefore, the value of k is 3 cm.

The customer can choose from 21 different gifts if they want to order only 1 item, 138 different gifts if they want to order 2 items of different kinds, and 280 different gifts if they want to order 3 items of different kinds.

To find the different number of gifts, we use the fundamental counting principle, which states that the total number of ways to choose a sequence of items is equal to the product of the number of choices available for each item.

⇒ If a customer wants to order only 1 item, they can choose from:

10 varieties of "greeting-cards"

4 types of "fruit-baskets"

7 flower arrangements

So, total number of different gifts that can be created is: 10 + 4 + 7 = 21.

⇒ If a customer wants to order 2 items of different kinds, they can choose from:

10 varieties of greeting-cards and 4 types of fruit baskets :

(10 × 4 = 40 choices)

10 varieties of greeting cards and 7 flower arrangements :

(10 × 7 = 70 choices)

4 types of fruit-baskets and 7 flower arrangements :

(4 × 7 = 28 choices)

So, number of different gifts that can be created is: 40 + 70 + 28 = 138.

⇒ If a customer wants to order 3 items of different kinds, they can choose from:

10 varieties of greeting cards, 4 types of fruit baskets, and 7 flower arrangements (10 × 4 × 7 = 280 choices),

So, the total number of different gifts that can be created is : 280.

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