Today, the sum of Caroline's age and Cameron's age is 73. 5 years ago Cameron was 2 times older than Caroline.

The total number of copies sold is 374,096, calculated using proportion and percentage based on the copies sold in the first month.

Let x be the total number of copies sold to date.

We know that the number of copies sold in the first month represents 8.3% of the total number of copies sold to date, so we can set up the following equation:

31,100 = 0.083x

Solving for x:

x = 31,100 / 0.083

x = 374,096.39

Rounding to the nearest whole number, we get:

x = 374,096

Therefore, approximately 374,096 copies have been sold to date.

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The area of the shaded region is 90 cm².

The space filled by the surface of an object or any flat shape can be thought of as the area in terms of geometry. The quantity of unit squares that cover an object's surface when it is closed is known as the area of the object. Inches, millimeters, square feet, and other square measurements are used to determine the area.

The area of shaded region = area of given square - area of all given triangles

Now, Area of given square = side × side

                                             = 12 × 12

                                             = 144 cm²

Similarly, Area of all triangles

             = 4 × (area of small triangle) + 4 × (area of big triangle)

             = 4 × ( 1/2 × 3× 3) + 4 × ( 1/2 × 3 × 6)

             = 18 + 36

             = 54 cm²

∴ The area of shaded region = 144 - 54

                                                = 90 cm²

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The initial symbol in the Kiran equation is erroneous, and there are two rates for weights of 1, 2, and 3 ounces. In contrast, the prices for 1, 2, and 3 ounces are incorrectly expressed in the Mai equation.

A contract rate, also known as the coupon rate, stated rate, or nominal rate, is the interest rate that is stipulated in a certain contract.

What went wrong for Kiran?

1. For 1, 2, and 3 ounces, there are two rates: Kiran used the wrong symbols to describe the rates for 1, 2, and 3 ounces. Let's look at an illustration:

0.71  1  ≤  w ≤ 2

0.92  2  ≤ w  ≤ 3

Because in the first line the rate is 0.71 for weights less than or equal to 2, and because this also occurs in the second line, it appears that the rate for 2 pounds here can be both 0.71 and 0.92.

2. He chose the wrong initial symbol since it implies that there is a charge even when the weight is 0, which is not conceivable.

0.50 0 ≤ w ≤ 1 (The rate is 0.50 if the weight is less than or equal to 0)

What is Mai's error?

1. Similar to Kiran, she did not express the rate and the pounds. Let's consider one instance:

0.71 1 < w < 2 (The rate is 0.71 if the weight is less than 2; this is false because the rate is 0.71 if the weight is less than or equal to 2)

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Answer:

11

Step-by-step explanation:

Answer:

Step-by-step explanation:

Im not sure I can't see the picture.

Answer: Hence, the width of the path is 4 meters.

First we should find the area of the pool. Our width is 14 and our length is 18. In order to find the area, we must multiply these two numbers. 14 times 18 is 252. This means that the area of the pool is 252.

Since we know that one side of the pool is 18 and one side is 14, we can write out the equation below.

572= (18+2x)(14+2x)

The first thing we should do is combine like-terms.Our equation would now be as below.

x^2+16-80=0

Next we would take our quadratic equation- x=-b+-√b2-4ac/2a and fill it in with the numbers that we had in the first equation, our equation would be like below.  A=1   B=16   C=-80

x=-16+-√16^2-4* 1 * -80 /2 * 1

When then simplify our equation leaving us with x=-16+-√16^2-4*1(-80)/2 * 1, which broken down is x=-16+-√+-24/2.

Lastly we must subtract and add to receive our two answers.

One side is 4 and the other is -20. Since the width of the walk cannot not be a negative number, we know that the width of the path is 4 meters.

Hence, the width of the path is 4 meters.

I hope this helped & Good Luck <3!!!

The match of the terms and correct locations are:

1. A - Amplitude

2. B is compression

3. C is rarefaction

A longitudinal wave is a form of wave in which its direction of propagation is similar to the direction of vibration of the particles of the medium through which the wave is travelling. The waves generated by a stretched or compressed spiral spring produces longitudinal waves.

When a spiral spring is streched or compressed, on removal of the force a series of compression and rarefactions of the sections of the spring are produced. This sections vibrates in the direction of propagation of the waves produced.

Thus the match of the terms and correct locations are:

i. A - Amplitude

ii. B is compression

iii. C is rarefaction

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A student has 8 different choices when choosing a pair of pants and a shirt.

Without using intricate calculations, the likelihood of an event occurring is shown using a probability tree diagram. It shows every consequence that an event might have. A probability tree serves the aim of listing all potential outcomes of an event and calculating the likelihood of each one. A probability tree diagram can be used to indicate conditional probabilities or to show a sequence of independent occurrences.

The student can choose from four shirts and two pairs of pants (black or tan) (yellow, red, green, or white). We multiply the number of options for pants by the number of options for a shirt to get the total number of options:

2 choices for pants × 4 choices for a shirt = 8 total outfit choices

Therefore, a student has 8 different choices when choosing a pair of pants and a shirt.

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Answer:It is given that

In △ABC,

DE∥AC

What is similarity of triangles?

Two triangles are similar if corresponding angles are equal and corresponding sides are in proportion.

Let us consider △BDE and △ABC,

∠B=∠B.....common angles

∠BDE =∠BAC....corresponding angles

so, △BDE∼△ABC

Since △BDE and △ABC are similar so, corresponding sides will be in proportion,

Subtract 1 from both sides,

Thus, we proved   using the similarity of triangles.

Step-by-step explanation:

It appears that Nolan has met the conditions for constructing a confidence interval for the mean birth weight in Somalia. However, he should also check the skewness and presence of outliers in the sample to ensure that the normal approximation is appropriate.

In other words, data with a lower bound are frequently skewed right, and data with an upper bound are typically biased left.

Start-up effects can also cause skewness.

To construct a confidence interval for the mean birth weight in Somalia, we need to ensure that the following conditions are met:

Random Sampling: Nolan used a simple random sample of 100 births, which meets the condition of random sampling.

Independence: Each birth weight in the sample should be independent of the other. This condition is met if the sample size is less than 10% of the total population of births in Somalia.

Sample size: In general, a sample size of at least 30 is recommended to use the normal distribution to approximate the sampling distribution of the sample mean. Since Nolan's sample size is 100, this condition is met.

Skewness and outliers: Nolan mentioned that the sample data was slightly skewed with a few outliers.

Therefore, all the required conditions are given above.

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Answer:

the data is a random sample from the population of interest.

the sampling distribution of x is approximately normal.

individual observations can be considered independent.

Step-by-step explanation:

To find the zeros, set the function equal to 0.  In other words, solve f(x)=0.

             f(x) = 0

x^2 +6x + 8 = 0

 (x+4)(x +2) = 0

x = -4 and x = -2

The vertex will happen when x = -b/2a:

    [tex]x=\dfrac{-6}{2(1)} = -3[/tex]
Then use this x-value of –3 to find the y-value of the vertex:

   y = (-3)^2 + 6(-3) + 8 = 9-18+8 = -1

The vertex is (-3,-1).

Side note: The x-value of the vertex can also be found by finding the average of the two zeros:

    (-4 + (-2)) / 2 = -6/2 = -3

The transformations that have been applied to the parent function y=-(1)/(2)(x-3)^(2)-5 are: horizontal shift, vertical shift, and vertical stretch.

The transformations that have been applied to the parent function y=-(1)/(2)(x-3)^(2)-5 are:

- Horizontal shift: The parent function has been shifted to the right by 3 units. This is indicated by the subtraction of 3 from x in the equation.
- Vertical shift: The parent function has been shifted downward by 5 units. This is indicated by the subtraction of 5 from the entire equation.
- Vertical stretch: The parent function has been stretched vertically by a factor of (1)/(2). This is indicated by the multiplication of the entire equation by (1)/(2).

Therefore, the correct answers are horizontal shift, vertical shift, and vertical stretch.

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Answer:

Starting with the given equation:

√x³ - 100 = 5

Adding 100 to both sides:

√x³ = 105

Squaring both sides:

x³ = 11025

Taking the cube root of both sides:

x = 15

Therefore, the exact solution to the given equation is x = 15.

Note that no inverse functions were needed to solve this equation

Step-by-step explanation:

The set W represents the x-axis and y-axis in the plane. Any vector with one of its components equal to 0 will satisfy the equation x⋅y = 0, and these vectors lie on either the x-axis or y-axis.

(a) The set W is closed under standard scalar multiplication in the plane. This is because for any scalar c and any vector u = (x,y) in W, the product of the components of cu = (cx,cy) is (cx)(cy) = c2(xy) = c2(0) = 0, so cu is also in W.

(b) The set W is not closed under standard vector addition in the plane. For example, the vectors u = (1,0) and v = (0,1) are both in W, but their sum u + v = (1,1) is not in W because the product of its components is 1(1) = 1, which does not satisfy the equation x⋅y = 0.

Since the set W is not closed under standard vector addition, it does not form a vector space. A set must be closed under both scalar multiplication and vector addition in order to be a vector space.

Geometrically, the set W represents the x-axis and y-axis in the plane. Any vector with one of its components equal to 0 will satisfy the equation x⋅y = 0, and these vectors lie on either the x-axis or y-axis.

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The parent function f(x) = 2^(x) is transformed into the function g(x) = 2^((x+3)) by shifting the graph 3 units to the left.

This means that the maximum value on the interval [-2,2] for the parent function will now occur at the point (-2+3) = 1 for the transformed function.

Therefore, the maximum value for the transformed function on the interval [-2,2] will be 2^(1) = 2.

In summary, the transformation shifts the graph of the parent function 3 units to the left, causing the maximum value on the interval [-2,2] to occur at x = 1 and have a value of 2.

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Therefore , the solution of the given problem of unitary method  comes out to be the height of the table in the scale model because we lack any measurements to base our calculations on.

Divide the measures of just this microsecond portion by two in order to complete the task using the unitary variable technique. Briefly stated, the characterised by a group and colour subgroups are both removed from the unit method when a wanted item is present. For example, 40 pens subset with a changeable price would cost Rupees ($1.01). It's possible that one country will have total influence over the approach taken to accomplish this. Almost every living creature has a distinctive quality.

Here,

We could use the scale factor to determine the height of the table in the scale model if we knew the measurements of the actual table and the scale model. The scale factor is the ratio of the actual object's dimensions to the scale model's dimensions. For instance, if the scale factor is 1:12 and the actual table is 48 inches tall, the scale model table would be 12 inches tall.

12 times 48 inches, or 4 inches,

However, we are unable to calculate the height of the table in the scale model because we lack any measurements to base our calculations on.

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The coordinates (2,1) will be on graph but (1,3) is not on graph.

What is a coordinate?

A coordinate is a set of two or more numbers or variables that identify the position of a point, line, or plane in a space of a given dimension. Coordinates are used to pinpoint a particular location, such as a specific point on a map or a specific point in a mathematical equation.

This means that for every 1.5 cups of dried fruit, there is 1 pound of granola. The graph of this proportional relationship would be a line that goes through the origin and has a slope of 1.5. For the point (2,1), the x-coordinate (2) is exactly 1.5 times the y-coordinate (1). This means that if you used 2 cups of dried fruit, you would get 1 pound of granola. Therefore, this point would be on the graph of the proportional relationship, so the answer is Yes. However, for the point (1,3), the x-coordinate (1) is not 1.5 times the y-coordinate (3). This means that if you used 1 cup of dried fruit, you would not get 3 pounds of granola.

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From left to right, function f has zeros at x = 0, x = 3, x = -3, x = 1/2, and x = -3/2.

An expression, rule, or law in mathematics that explains how one independent variable and one dependent variable are connected (the dependent variable).

The factors of the function f(x) can be found by factoring the expression:

f(x) = 2x⁴ - x³ - 18x² + 9x = x(2x³ - x² - 18x + 9)

To find the zeros of f(x), we need to find the values of x that make the expression in the parentheses equal to zero:

2x³ - x² - 18x + 9 = 0

We can use synthetic division or other methods to factor this polynomial and find its zeros. Alternatively, we can use the Rational Zeros Theorem to test possible rational zeros:

Possible rational zeros: ±1, ±3, ±9, ±1/2, ±3/2, ±9/2

Testing x = 1: 2(1)³ - (1)² - 18(1) + 9 = -8, not a zero

Testing x = -1: 2(-1)³ - (-1)² - 18(-1) + 9 = 28, not a zero

Testing x = 3: 2(3)³ - (3)² - 18(3) + 9 = 0, a zero

Testing x = -3: 2(-3)³ - (-3)² - 18(-3) + 9 = 0, a zero

Using polynomial division or factoring by grouping, we can factor the polynomial further:

2x³ - x² - 18x + 9 = (x - 3)(2x² + 5x - 3)

The quadratic factor can be factored using the quadratic formula or other methods:

2x² + 5x - 3 = (2x - 1)(x + 3)

Therefore, the zeros of f(x) are:

x = 0 (from the factor x)

x = 3 (from the factor x - 3)

x = -3 (from the factor x + 3)

x = 1/2 (from the factor 2x - 1)

x = -3/2 (from the factor 2x - 1)

So the completed statement is:

From left to right, function f has zeros at x = 0, x = 3, x = -3, x = 1/2, and x = -3/2.

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a)91.44 m

b)51.18 in

c)372.85 W

d)2383186.955 Pa

e)10000 ????????/m3

f)0.4667 T????/ℎ

g)41840 J

300 ft = m

1 ft = 0.3048 m, so 300 ft = 300 * 0.3048 m = 91.44 m



130 cm = in

1 in = 2.54 cm, so 130 cm = 130/2.54 in = 51.18 in



0.5hp = W

1 hp = 745.7 W, so 0.5 hp = 0.5 * 745.7 W = 372.85 W



350psi = Pa

1 psi = 6894.757 Pa, so 350 psi = 350 * 6894.757 Pa = 2383186.955 Pa



10 ????????/????????3 = ????????/m3

1 ????????/????????3 = 1000 ????????/m3, so 10 ????????/????????3 = 10 * 1000 ????????/m3 = 10000 ????????/m3



350 W = ????T????/ℎ

1 W = 0.00134 T????/ℎ, so 350 W = 350 * 0.00134 T????/ℎ = 0.4667 T????/ℎ



10,000 cal = ????

1 cal = 4.184 J, so 10,000 cal = 10,000 * 4.184 J = 41840 J

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The sin of the angle is 0.6 and the cos of the angle is 0.8.

In a right triangle, the sine (sin) of an angle is the ratio of the length of the side opposite to the angle to the length of the hypotenuse. The cosine (cos) of an angle is the ratio of the length of the side adjacent to the angle to the length of the hypotenuse.

In this case, the side opposite to the angle is 6 and the side adjacent to the angle is 8. To find the hypotenuse, we can use the Pythagorean theorem:

a^2 + b^2 = c^2

Where a and b are the lengths of the two legs of the right triangle, and c is the length of the hypotenuse.

Plugging in the given values:

6^2 + 8^2 = c^2

36 + 64 = c^2

100 = c^2

c = 10

So the hypotenuse of the right triangle is 10.

Now we can find the sin and cos of the angle:

sin = opposite/hypotenuse = 6/10 = 0.6

cos = adjacent/hypotenuse = 8/10 = 0.8

Therefore, the sin of the angle is 0.6 and the cos of the angle is 0.8.

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Answer: 8 times per minute

Step-by-step explanation: 50 (1-84%) = 8

The greatest common factor of 8m2 and 7b3 is the largest monomial that can divide both 8m2 and 7b3. So, the greatest common factor of 8m^(2) and 7b^(3) is 1.


The greatest common factor (GCF) of two monomials is the product of the greatest common factor of their coefficients and the greatest common factor of their variables. In this case, the greatest common factor of the coefficients is 1, since 8 and 7 have no common factors other than 1. The GCF of the variables is 1, since m and b have no common factors. Therefore, the GCF of 8m^(2) and 7b^(3) is 1*1 = 1.

Here is a step-by-step explanation:
1. Find the GCF of the coefficients: GCF(8,7) = 1
2. Find the GCF of the variables: GCF(m^(2),b^(3)) = 1
3. Multiply the GCF of the coefficients and the GCF of the variables: 1*1 = 1
4. The GCF of 8m^(2) and 7b^(3) is 1.

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(a) The possible number of positive real zeros of P(x) can be determined using Descartes' Rule of Signs. The Rule of Signs states that a polynomial with real coefficients can have at most as many positive real zeros as its leading coefficient has sign changes in the coefficients. This means that the polynomial has at most 3 positive real zeros.

(b) Descartes' rule of signs can also be used to prove that 1-2 cannot be a zero of P(x). According to the Rule of Signs, the number of positive real zeros of P(x) is limited to 3. However, if 1-2 is a zero of P(x), then the polynomial would have 4 sign changes, which is not possible. Therefore, 1-2 cannot be a zero of P(x).

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The simplified expression  is log_(w)(16x^6)

To rewrite the logarithmic expression as a single logarithm with the same base, we need to use the properties of logarithms. The properties we will use are:

1) log_b(x)+log_b(y) = log_b(xy)

2) a*log_b(x) = log_b(x^a)

Using the first property, we can combine the two terms with the same base:

2log_(w)x+4log_(w)2x = log_(w)x^2+log_(w)(2x)^4

Using the second property, we can simplify the exponents:

log_(w)x^2+log_(w)(2x)^4 = log_(w)x^2+log_(w)16x^4

Using the first property again, we can combine the two terms with the same base:

log_(w)x^2+log_(w)16x^4 = log_(w)(x^2*16x^4)

Simplifying the expression inside the logarithm:

log_(w)(x^2*16x^4) = log_(w)(16x^6)

Therefore, the final expression is:

2log_(w)x+4log_(w)2x = log_(w)(16x^6)

Answer: log_(w)(16x^6)

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radius of the circle is sqrt(3)x.

The radius of the circle can be found by using the Pythagorean Theorem. The side lengths of each equilateral triangle created by the diagonals is 2x, so the hypotenuse of the triangle is sqrt(3)x. Since the hypotenuse of each triangle is the same as the radius of the circle, the radius of the circle is sqrt(3)x.

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After using the properties of logarithms to rewrite and simplify the logarithmic expression  ln((e⁸)/7) simplifies to 1.

What are natural logarithms?

Natural logarithms are a type of logarithm that uses the number e as its base. The natural logarithm of a positive number x (written as ln(x)) is the exponent to which e must be raised to get x. In other words, ln(x) represents the power to which e must be raised to obtain x.

The number e is a mathematical constant that is approximately equal to 2.71828. It is a special number that appears in many areas of mathematics, science, and engineering. Natural logarithms have a variety of applications in fields such as calculus, probability theory, and statistics.

Some properties of natural logarithms include:

ln(1) = 0

ln(e) = 1

ln(xy) = ln(x) + ln(y) for any positive numbers x and y

ln(x/y) = ln(x) - ln(y) for any positive numbers x and y

ln(xᵃ) = a ln(x) for any positive number x and any real number a

Natural logarithms can be evaluated using a calculator or by using the properties of logarithms to simplify expressions. They are commonly used in mathematical and scientific calculations that involve exponential growth or decay.

We can use the property of logarithms that states: log(aᵇ) = b log(a) for any base a and any real number b.

Using this property, we can rewrite ln((e⁸)/7) as:

ln((e⁸)/(e⁷))

[tex]= ln(e^{(8-7)})[/tex]

= ln(e)

= 1

Therefore, ln((e⁸)/7) simplifies to 1.

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If we consider the number line with rational number marked on it, then the number of parts to be present between 1 and 2 and -1 and -2 will be one part each.

A number line is a pictorial representation or drawing of numbers in which there are equal intervals between each number and is used to represent the real numbers on it. Real numbers are those numbers which may be positive or negative integers, rational numbers or irrational numbers. In general, a quantity which can be expressed as an infinite decimal expansion is called as a real number.

If we draw a number line and mark the points as 1, 2, 3,...,∞ and -∞,..., -3, -2, -1 on the right and left hand side of 0, then the intervals between each real number is equal to 1. Hence the number of parts between 1 and 2 is one part and -1 and -2 is one part. However, these parts may be subdivided into more parts to get more fine value (smaller value).

This value will be a fractional value between 1 and 2 or -1 and -2. Hence parts between two numbers on a number line can be infinity, but for sake of simplicity, one is taken in general case.

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To write a quadratic function f whose zeros are -2 and 9 , we have to factor the function by (x+2) and (x-9).

A quadratic function is a second-degree mathematical function whose graph is a parabola. The general form of a quadratic function is given by f(x) = ax² + bx + c, where a, b and c are constants and a cannot be equal to zero. The variable x represents the input of the function and f(x) represents the output or result of the function. To find the quadratic function of f we first need to multiply these factors, like this:

So the quadratic function whose zeros are -2 and 9 is:

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Answer:

Let's assume that the number of text messages sent in a day is x. Then the cost of Michelle's phone plan is:

Cost of Michelle's plan = 0.22x

And the cost of Jeff's phone plan is:

Cost of Jeff's plan = 0.12x + 1

We want to find the number of text messages for which the two plans have the same cost. So we can set the two expressions for the cost equal to each other and solve for x:

0.22x = 0.12x + 1

0.1x = 1

x = 10

Therefore, for 10 text messages per day, the cost of Michelle's plan and Jeff's plan will be the same.

We can also verify this by plugging x = 10 into the two expressions for the cost:

Cost of Michelle's plan = 0.22(10) = $2.20

Cost of Jeff's plan = 0.12(10) + 1 = $2.20

So the cost of the two plans is indeed the same for 10 text messages per day.

Answer:

Step-by-step explanation:

cost m = 0.22x

cost j = 0.12x+1

0.22x=0.12x+1

0.1=1

x=10

cost m = 0.22(10) = $2.20

cost J =0.12(10)+1=$2.20

So the answer is 10

The minimum total cost for the gas station to store, ship, and purchase 22,032 gallons of diesel for one year is $199,152.87.

The gas station has a steady annual demand for 22,032 gallons of diesel. The cost to store 1 gallon for 1 year is $9, the cost to ship each order of diesel is $34, and the cost to purchase each gallon is $19. To calculate the total cost of storing, shipping, and purchasing the diesel for one year, we can use the following formula:

Total cost = (storage cost per gallon x annual demand) + (shipping cost per order x number of orders) + (purchase cost per gallon x annual demand)

To find the number of orders, we can divide the annual demand by the number of gallons per order. In this case, the number of gallons per order is not given, so we will use the variable "x" to represent it:

Number of orders = 22,032 / x

Plugging this back into the formula, we get:

Total cost = (9 x 22,032) + (34 x 22,032 / x) + (19 x 22,032)

Simplifying, we get:

Total cost = 198,288 + (748,288 / x)

To minimize the total cost, we can take the derivative of the total cost with respect to x and set it equal to zero:

d(Total cost) / dx = -748,288 / x^2 = 0

Solving for x, we get:

x = sqrt(748,288 / 0) = 865.12

Therefore, the gas station should order 865.12 gallons of diesel per order to minimize the total cost. The minimum total cost is:

Total cost = 198,288 + (748,288 / 865.12) = $198,288 + $864.87 = $199,152.87

The minimum total cost for the gas station to store, ship, and purchase 22,032 gallons of diesel for one year is $199,152.87.

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