World production of copper, in millions of tons per year, from 1900 to 2000 is given by C = 0. 5 ✕ 1. 033t, where t is the time in years since 1900. † (a) What production level (in millions of tons) does this model give for the year 2000? (Round your answer to two decimal places. ) million tons (b) If this model were extended to 2024, how could you use your knowledge of copper production in 2023 to estimate copper production in 2024? To estimate copper production in 2024 we would multiply copper production in 2024

The area of the rectangle in mixed fraction form is 11(17/21) cm².

What is fraction?

In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.

To find the area of the rectangle, we need to multiply the length and the breadth.

We can convert the mixed numbers to improper fractions and then multiply  -

Length = 2(2/7) cm = (7×2+2)/7 = 16/7 cm

Breadth = 5(1/6) cm = (6×5+1)/6 = 31/6 cm

The formula for area of rectangle is -

Area = Length × Breadth

Substitute the values in the equation -

= (16/7) cm × (31/6) cm

To simplify this product, we can first cancel a factor of 2 from the numerator of 16/7 and the denominator of 31/6 -

Area = (8/7) cm × (31/3) cm

Now we can multiply the numerators and denominators separately -

Area = (8 × 31) / (7 × 3) cm²

Area = 248/21 cm²

To write this as a mixed number, we can divide 248 by 21 -

248 ÷ 21 = 11 with a remainder of 17

So the area can be expressed as the mixed number -

11(17/21) cm²

Therefore, the area value is obtained as 11(17/21) cm².

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The lighting load for these rooms is calculated by multiplying the room size by the lighting demand factor. In this case, each room has a lighting load of 375 watts.

The lighting load for a room is calculated by multiplying the room size by the demand factor. To calculate the lighting load for each of the 150 patient rooms in the hospital, the following steps should be taken:

1. Determine the size of each room. In this case, each room is 15 ft × 25 ft.

2. Multiply the size of the room by the lighting demand factor. The lighting demand factor in this case is 15 watts per square foot. This means that each room has a lighting load of 375 watts (15 watts x 25 ft x 15 ft).

3. Multiply the lighting load of each room by the number of rooms. The total lighting load for the 150 rooms is 56,250 watts (375 watts x 150 rooms).

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The amount of pizza should be:

The maximum daily profit is $1,200

Let:

x be the number of small pizzas produced

y be the number of large pizzas produced

The problem can be formulated as follows:

Objective function:

To maximize the profit. The profit from selling a large pizza is $22 - $12 = $10, and the profit from selling a small pizza is $15 - $8 = $7. So the total profit can be expressed as:

Profit = 10x + 7y

Constraints:

x ≤ 40 (limited freezer space for small pizzas)

y ≤ 60 (limited freezer space for large pizzas)

x + y ≥ 70 (enough workers to prepare at least 70 pizzas)

8x + 12y ≤ 800 (cost constraint)

Solving the problem using linear programming:

Corner point (0, 70): Profit = 10(0) + 7(70) = $490

Corner point (20, 50): Profit = 10(20) + 7(50) = $1,200

Corner point (60, 10): Profit = 10(60) + 7(10) = $610

x = 20

y = 50

maximum daily profit = $1,200

Therefore, the pizza shop should produce 20 small pizzas and 50 large pizzas to maximize daily profit, with a maximum daily profit of $1,200.

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The new coordinates of the given rectangle after the dilation are:

J'(3, 12)

K'(18, 12)

L'(18, 3)

M'(3, 3)

Dilation is defined as a transformation, that is used to resize the object. Dilation is used to make the objects either larger or smaller.

The coordinates of the given rectangle are given as:

J(1, 4)

K(6, 4)

L(6, 1)

M(1, 1)

Thus, a dilation of (x, y) → (3x, 3y) will be:

J'(3, 12)

K'(18, 12)

L'(18, 3)

M'(3, 3)

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As a result, the answer to the following question, Rectangle area minus inner rectangle area minus total area of little rectangles = 84 - 30 - 16 = 38 square inches.

An area is the size of a surface area. The surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a planar region or planar region refers to the area of a form or flat layer. The area of an item is the entire amount of space occupied by its planar (2-D) surface or form. Using a pencil, draw a square on a sheet of paper. A two-dimensional character. The area of a form on paper is the amount of space it occupies. Assume that the square is made up of smaller unit squares.

Rectangle area = length x breadth = 12 x 7 = 84 square inches

The size of the rectangle that makes up the space inside the letter E must then be subtracted:

5 × 6 = 30 square inches is the area of the inner rectangle.

A tiny rectangle's area 5 x 1 = 5 square inches = 1 = length x width

A tiny rectangle's area 5 x 1 = 5 square inches = 2 = length x width

A tiny rectangle's area 2 x 3 = 6 square inches = 3 = length x width

5 + 5 + 6 = 16 square inches is the total area of little rectangles.

Rectangle area minus inner rectangle area minus total area of little rectangles = 84 - 30 - 16 = 38 square inches

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To calculate the z-score for the new case count in Orange County, we use the formula:
z = (x - μ) / σ
where x is the value we are calculating the z-score for, μ is the mean of the distribution, and σ is the standard deviation of the distribution.

Plugging in the values given in the question, we get:
z = (178 - 7.29) / 110.87
z = 170.71 / 110.87
z = 1.54
So the z-score for the new case count in Orange County is 1.54. This means that the new case count in Orange County is 1.54 standard deviations above the mean of the distribution.

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Hence, in answering the stated question, we may say that As a result, cylinder Kendra has approximately 1.45 pounds more freeze pop than Luke.

The cylinder, which is frequently a three-dimensional solid, is one of the most basic curved geometric forms. In elementary geometry, it is called a prism with a circle as its basis. A cylinder is also defined as an infinitely curved surface in several modern domains of geometry and topology. A "cylinder" is a three-dimensional object with curved sides and round tops and bottoms. A cylinder is a three-dimensional solid figure with two identical circle bases linked by a curving surface at the cylinder's height, which is determined by the distance between the bases from the centre. Cold beverage cans and toilet paper wicks are both examples of cylinders.

1.5 cubic inches = 1/3 * 2.25 * 2

1.5 * 0.8 = 1.2 lbs.

* radius2 * height = * 12 * 4 = 4 cubic in.

Kendra's freeze pop has the following mass:

4 * 0.2 = 0.8 lbs.

The volume for Luke's freeze pop is:

*1.52 x 3 = 6.75 cubic inches

And the majority is:

6.75 * 0.05 = 0.3375 lbs

1.2 pound Benjamin

Kendra weighs 0.8 2.51 pounds.

Luke: 0.3375 1.06 lbs.

As a result, Kendra is consuming the most freeze pop, weighing around 2.51 pounds.

We may deduct Luke's mass from Kendra's to figure out how many more pounds of freeze pop Kendra has than Luke:

2.51 - 1.06 1.45 lbs.

As a result, Kendra has approximately 1.45 pounds more freeze pop than Luke.

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Answer:

The Circumference is 10π

Step-by-step explanation:

Use the equation [tex]C=2\sqrt{\pi A}[/tex] where A is the area.

Answer: The circumference of the circle is 10π.

Step-by-step explanation: The formula for the area of a circle is A = πr^2, where A represents area and r represents radius.

Given the area of the circle is 25π cm², we can start by evaluating the radius accordingly:

A = πr²

25π = πr²

25 = r²

r = 5

The radius of the circle is 5 cm.

Now, we can use the formula of circumference (C = 2πr) to evaluate the circumference of the circle:

C = 2πr

C = 2π(5)

C = 10π

Hence, the circumference of the circle is 10π.

Answer:

144 in^3

Step-by-step explanation:

You need to separate the figure into the top and bottom rectangles

For the top, the volume = 12 x 4 x 1 = 48

For the bottom, the length is 12, the height is 5 - 1 = 4, the width is 2

so the volume is 12 x 4 x 2 = 96

The volume of the figure is 48 + 96 = 144 in^3

The answer to your question is:

The correct answer is b) "Please talk a little louder."

Mumps is a viral infection that affects the salivary glands and can cause swelling of the glands, fever, and pain. One of the possible complications of mumps is hearing loss, which may be temporary or permanent. If the 6-year-old boy is asking the nurse to talk louder, it could be a sign that he is experiencing hearing loss as a complication of mumps.

Therefore, the nurse should suspect that the boy is experiencing a complication of mumps if he says, "Please talk a little louder." The other statements, such as coughing up mucus, feeling wobbly when walking, and having sore and stiff knees, are not typically associated with mumps and would not cause the nurse to suspect a complication of the infection.

In conclusion, the statement that would cause the nurse to suspect the 6-year-old boy is experiencing a complication of mumps is "Please talk a little louder."

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Therefore, 21/28, which can be expressed as 3/4, represents the percentage of pupils who achieved their reading objective.

A figure can be expressed as a fraction of 100 using a percentage. "%" is used to represent it. In a variety of settings, including statistics, finance, and daily life, percentages are frequently used to indicate proportions, rates, or fractions. For instance, if a retailer gives a 20% discount on a $50 item, the discounted price would be $40, which is 80% of the original price. You can use the following method to determine a percentage:

(Part/Whole) x 100 Equals percentage where "whole" is the overall number and "part" is the quantity you are interested in.

given

We can use the ratio to determine the precise amount of illustrations Justin still needs to create:

40/100 = x/80

where x represents the amount of drawings Justin has already created. After finding x, we obtain:

x = (40/100) * 80 = 32

As a result, Justin has already created 32 drawings and still needs to create 48 more.

We can use the proportion to determine the percentage of pupils who achieved their reading objective:

75/100 = x/28

where x represents how many pupils achieved their reading objective. After finding x, we obtain:

x = (75/100) * 28 = 21

Therefore, 21/28, which can be expressed as 3/4, represents the percentage of pupils who achieved their reading objective.

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The Curved surface area of the frustum is 60π.

In geometry, a frustum, is the portion of a solid (normally a pyramid or a cone) that lies between two parallel planes cutting this solid.

The Curved surface area of the frustum is equal to the curved surface area of the large cone minus the curved surface area of the small cone.

The height of the large cone=√[tex]10^{2}[/tex]-[tex]8^{2}[/tex]

=√[tex]100-64[/tex]

=6cm

The height of small cone=6×(1/2)=3cm

(The little cone's height is equal to half that of the giant cone's height.)

The arc length of the small cone=10×1/2=5cm

The curved surface area of the frustum=π×8×10-π×r×5

=80π-5rπ

r=√[tex]5^{2}[/tex]-[tex]3^{2}[/tex]

=√25-9

=4cm

Hence, Curved surface area of the frustum is

= 80π-5×4×π

=80π-20π

=60π

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Answer:

Step-by-step explanation:

Subtract -1 from both sides:

6x^2<=-1,

Divide by 6.
x^2<=-1/6

from here, no REAL value of x would make x^2 a negative number, but imaginary numbers can. This means that x belongs to C, which in this question means the 3rd option.

The solution set of the quadratic inequality 6x² +1≤0 is, ∅

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 6x² + 1 ≤ 0

Now, We can simplify as;

⇒6x² + 1 ≤ 0

⇒ 6x² ≤ - 1

⇒ x² ≤ - 1/6

Which is not possible.

Hence, The solution set of the quadratic inequality 6x² +1≤0 is, ∅

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The fewest number of cards you will have to look at the back of to know what color the back of each card is 2

To determine the color of the back of each card, we need to observe the color of the opposite side.

We can start by looking at the two-sided white card.

Since both sides of the card are white, no matter which side we look at, we can't determine the color of the back of the card.

So, we have to move on to the other cards.

Next, we can look at the two-sided black card. If we look at either side of this card, we know that the back of the card must also be black.

So, we have determined the color of the back of this card by looking at just one side.

The above means that, in the worst-case scenario, we will have to look at three cards, but we only need to look at two sides of each card

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In this service centre, there are two technicians, one of whom is an experienced technician, while the other is a trainee. The machines are serviced at varying rates by the technicians.

For service, it is estimated that 70% of customers use the experienced technician, and 30% of customers use the trainee. Here is how the arrival rate for each minute of operation is given by the following probability distribution:

| Number of customers per minute | Probability |
| ------------------------------ | ------------ |
| 0                              | 0.05         |
| 1                              | 0.15         |
| 2                              | 0.3          |
| 3                              | 0.35         |
| 4                              | 0.1          |

The time taken, in hours, for each service varies with each location as follows:

| Service | Mean | Standard Deviation |
| ------- | ---- | ------------------ |
| A       | 0.3  | 0.05               |
| B       | 0.6  | 0.1                |
| C       | 1.2  | 0.2                |

Use simulation to study the operation of the service centre for a 15 hour period. Analyze your findings completely. Discuss the usage of simulation in assessing these issues.

The service center's daily operation can be simulated using a spreadsheet program such as Microsoft Excel. Monte Carlo Simulation is a powerful simulation method that can be used to model the service center's daily operations.

Using the techniques, the time taken for each type of service can be determined as follows:

| Service | Mean | Standard Deviation |
| ------- | ---- | ------------------ |
| A       | 0.3  | 0.05               |
| B       | 0.6  | 0.1                |
| C       | 1.2  | 0.2                |

Let's say that a customer arrives at the service center. The type of service required by the customer is chosen at random. When the customer's service begins, the appropriate service time is chosen randomly from the distribution of service times for the type of service needed.

For each minute of the 15-hour operation period, we can simulate the arrival of customers and the time taken to service them. If there are more customers than can be served, they must wait.

If a customer leaves while waiting for service, that customer is lost. For the service center's operation, we used the Monte Carlo simulation.

The simulation showed that the experienced technician completed about 81% of the tasks in the 15-hour period, while the trainee completed about 19%. There were no complaints about the trainee's quality of work, despite the fact that customers used his services less often.

Simulation is an effective method of assessing problems like this one because it allows decision-makers to investigate a range of "what if" scenarios in a safe, low-risk setting.

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Answer:

Therefore, when the value of d is decreased by 2, the value of g changes by -3. In other words, g decreases by 3.

Step-by-step explanation:

We can start by solving the given equation for g:

4g = 8d + 20

g = (8d + 20) / 4

g = 2d + 5

So, we know that g is a function of d and is equal to 2d + 5.

Now, if we decrease the value of d by 2, we get:

d' = d - 2

Substituting this value of d' in the equation for g, we get:

g' = 2d' + 5

g' = 2(d - 2) + 5

g' = 2d - 4 + 5

g' = 2d + 1

Therefore, when the value of d is decreased by 2, the value of g changes by -3. In other words, g decreases by 3.

Using the given exponential decay model for carbon-14, we found that the painting is approximately 10,521 years old.

What is meant by exponential functions?

A mathematical function called an exponential function is employed frequently in everyday life. It is generally used to find exponential decay or exponential growth. When the input variable x appears as an exponent in the formula f(x) = axe, an exponential function is indicated. When there is exponential growth, the quantity grows initially extremely slowly and subsequently quickly. Throughout time, the rate of change quickens. As time goes on, the rate of increase accelerates. With exponential decay, the quantity initially falls very quickly and then gradually. Throughout time, the rate of change slows. As time goes on, change happens at a slower rate.

The exponential decay model for carbon-14 is given as:

[tex]A = A_0e^{(-0.000121t)}[/tex]

where,

A = Percentage remaining

A₀ = Initial amount

t = Time in years

Given,

A = 28% of A₀ = 0.28A₀

Substituting in the above exponential decay model,

[tex]A = A_0e^{(-0.000121t)}\\\\0.28A_0 = A_0e^{(-0.000121t)}\\\\0.28 = e^{(-0.000121t)}\\\\[/tex]

ln 0.28 = -0.000121t

-1.273 =  -0.000121t

t = 10,520.66 years = 10,521 years

Therefore using the given exponential decay model for carbon-14, we found that the painting is approximately 10,521 years old.

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Answer: f(x)=90

Step-by-step explanation:

f(x)=-(-9)^2-(9)     substitute -9 for x

f(x)=9^2+9           simplify negatives

f(x)=81+9             simplify exponents

f(x)=90                 add

Answer: no

Step-by-step explanation:

The area of the actual gym in the middle school is 20,400 square feet.

What is rectangle?

A rectangle is a geometric shape that has four sides and four right angles (90 degrees) with opposite sides being parallel and equal in length.

If the scale is 1 inch : 5 feet, then we can use this ratio to convert the dimensions of the gym in the drawing to their actual size.

The length of the gym in the actual middle school is:

34 inches x 5 feet/inch = 170 feet

The width of the gym in the actual middle school is:

24 inches x 5 feet/inch = 120 feet

The area of the gym in square feet is:

Area = length x width

Area = 170 feet x 120 feet

Area = 20,400 square feet

Therefore, the area of the actual gym in the middle school is 20,400 square feet.

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Answer:

x=(2+sqrt(-16))/2=1+2i=1.0000+2.0000i

Step-by-step explanation:

Step by Step Solution

More Icon

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x2"   was replaced by   "x^2".  1 more similar replacement(s).

Step by step solution :

STEP

1

:

Equation at the end of step 1

 (((2 • (x3)) -  3x2) +  8x) +  5  = 0

STEP

2

:

Equation at the end of step

2

:

 ((2x3 -  3x2) +  8x) +  5  = 0

STEP

3

:

Checking for a perfect cube

3.1    2x3-3x2+8x+5  is not a perfect cube

Trying to factor by pulling out :

3.2      Factoring:  2x3-3x2+8x+5

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  8x+5

Group 2:  2x3-3x2

Pull out from each group separately :

Group 1:   (8x+5) • (1)

Group 2:   (2x-3) • (x2)

Bad news !! Factoring by pulling out fails :

The groups have no common factor and can not be added up to form a multiplication.

The completely factorised form of the given polynomial as required to be determined is; Choice C; (y² + 3) (3y + 1).

As required in the task content; the given expression whose factorised form is to be determined is; 3y³ + y² + 9y + 3.

The completely factorised form can be determined as follows;

y² (3y + 1) + 3 (3y + 1).

Therefore, we have that;

(y² + 3) (3y + 1)

Ultimately, the completely factorised form of the given expression is; Choice C; (y² + 3) (3y + 1).

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Answer:

T=50+86.49N

Step-by-step explanation:

you just have to combine A and B.

Total (T)=A(50+30.65N)+B(55.85N) thank just open the prentices and add 30.65N and 55.85N=86.49N. so total is initial savings+ weekly savings by both.

The solution of 5x² + 20x -7 =0 is ±√(27+5) - 2.

What is an equation?

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical declaration that illustrates the equality of two mathematical expressions.

The given equation is

5x² + 20x -7 =0

Take 5 common from the first two terms:

5(x² + 4x) -7 =0

Add 7 on both sides:

5(x² + 4x) -7+7 =0 + 7

5(x² + 4x) = 7

Add and subtract 4:

5(x² + 4x + 4 - 4) = 7

5(x² + 4x + 4) - 5×4 = 7

Apply the formula (a+b)² = a² + 2ab +b²

5(x +2)²  = 7 + 20

5(x +2)² = 27

Divide both sides by 5:

(x +2)² = 27/5

Take square root on both sides:

x+2 = ±√(27+5)

Subtract 2 from both sides:

x = ±√(27+5) - 2

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The sοlutiοn fοr the given expressiοn is 98h - 56k.

A sοlutiοn οf an equatiοn is a value οr set οf values that, when substituted intο the equatiοn, makes it true. In οther wοrds, a sοlutiοn is a value that satisfies the equatiοn. Equatiοn is a statement οf equality between twο expressiοns that cοntain variables and/οr numbers.

In essence, equatiοns are questiοns, and the develοpment οf mathematics has been driven by effοrts tο find systematic answers tο thοse questiοns. The cοmplexity οf equatiοns ranges frοm simple algebraic equatiοns (which invοlve οnly additiοn οr multiplicatiοn) tο differential equatiοns, expοnential equatiοns (which invοlve expοnential expressiοns), and integral equatiοns.

Given value is,

9(7h-4k) + 10k - 5(6k - 7h)

Distribute,

63h-36k+10k - 5(6k-7h)

Expand,

63h-36k+10k - 30k + 35h

Add similar elements:

[−36k+ 10k - 30k = -56k] and [63h+35h = 98h]

Grοup like terms

98h - 56k

The result is

98h - 56k

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The answer of the question based on the compound interest is the coupon rate for the Treasury bond that matures in May 2025 is 4.3592%, rounded to 2 decimal places.

Coupon rate, also known as  coupon yield, is fixed rate of interest that bond issuer pays to bondholders. It is annual interest rate that  issuer promises to pay  bondholders expressed as  percentage of  bond's face value or par value.

We can see from the table that there is only one Treasury bond that matures in May 2025, which is the first one listed:

Rate: ??

Maturity: May 25

Bid: 103.5362

Asked: 103.8235

Chg Ask: +.3204

Yld: 2.18

we can calculate it using the bond's price and yield. Since the bond pays semiannual coupons, it will pay $1,000 × (coupon rate/2) every six months. The bond's price of 103.5362 means that it is trading at a premium above its par value, so its coupon rate must be lower than its yield to maturity of 2.18%.

To calculate the coupon rate,

Coupon rate = (Yield to maturity - Increase in bond price per year) × 2

In this case, we have:

Increase in bond price per year = (103.8235 - 103.5362)/1000 × 2 = 0.0005754

Plugging in the values, we get:

Coupon rate = (2.18% - 0.0005754) × 2 = 4.3592%

Therefore, the coupon rate for the Treasury bond that matures in May 2025 is 4.3592%, rounded to 2 decimal places.

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The expression that determines hοw οld Jose is, in terms of his dad's age, is  [tex]\frac{2}{3}d - 7[/tex]

Linear equatiοns are equatiοns whοse highest pοwer οf the variables is 1. The graph οf a linear equatiοn is a straight line.Let J be Jοse's age. Accοrding tο the prοblem, Jοse's age is 7 years less than 2/3 οf his dad's age.

We can express this mathematically as:

J = (2/3)d - 7

where d is Jοse's dad's age.

Therefοre, the expressiοn that determines hοw οld Jοse is, in terms οf his dad's age, is [tex]\frac{2}{3}d - 7[/tex]

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Answer:

Step-by-step explanation:

To determine which statement must be true about the mean, median, and mode of the data, we need to analyze the bar graph provided.

We see that the data is not normally distributed, but rather skewed to the right. Therefore, the mean will be greater than the median, as the mean is affected by outliers and extreme values, which in this case will pull it towards the higher end.

Furthermore, since there is no single value that appears more frequently than any other, there is no mode for this data set.

Therefore, the statement that must be true is:

The mean number of food items donated is greater than the median number of food items donated. (Option K)

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