The marching band is selling cases of fruit for $13 per case. (a) Write an algebraic expression for the cost of f cases of fruit. (b) Evaluate the expression for 250 cases.

Final answer:

To find the median using quickselect, choose a pivot value, partition the list, and repeat the process with the appropriate partition until the pivot index matches the desired median index.

Explanation:

The median of a list of numbers is the middle value when the numbers are arranged in ascending order. To apply quickselect to find the median, start by choosing a pivot value from the list. Partition the list and move all values smaller than the pivot to the left and all values larger than the pivot to the right. If the pivot index is equal to the desired median index, then the pivot value is the median. Otherwise, if the pivot index is smaller, repeat the process with the right partition; if the pivot index is larger, repeat with the left partition.

In the given example, let's apply quickselect to find the median:

Choose a pivot value, let's say 17.

Partition the list: 5, 8, 9, 12, 17, 20, 30

The pivot index is 4, which is less than the desired median index.

Repeat the process with the right partition: 17, 20, 30

Choose a new pivot value, let's say 20.

Partition the list: 17, 20, 30

The pivot index is 1, which is equal to the desired median index.

Therefore, the median of the list of numbers 9, 12, 5, 17, 20, 30, 8 is 17.

Yes,

If a quadrilateral has four congruent facets and 4 right angles, then it's a square (reverse of the square definition).

If consecutive aspects of a rectangle are congruent, then it is a square neither the reverse of the definition nor the speak of a assets.

If we can display that the slopes of the alternative sides are identical, then the other facets are parallel. The slopes of the opposites have been the same, so ABCD is a parallelogram. Step three: subsequent, show that the parallelogram is a rectangle.

The slope is just the upward thrust over the run, which is defined as the change in y over the change in x meaning the distinction of the y coordinate factors divided with the aid of the distinction of the x-factors? So we have the two x-factors, so this is six minus two, divided by the, the x-factors 3 minus one.

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Final answer:

To find the max value of a line integral over a closed curve using Green's Theorem, consider the curl of the given vector field and apply the theorem to express the result. The maximum value of the line integral is -2y²dy, determined through vector calculus and Green's Theorem application.

Explanation:

Green's Theorem states that for a vector field f in the form given, the max value of the line integral over any positively oriented closed curve C can be found by considering the curl of f.

By applying Green's Theorem, we can find that the maximum value of the line integral is -2 y²dy.

This computation involves utilizing vector calculus and understanding how to apply Green's Theorem to find the extremum of the line integral.

The expected mean square value (E(x^2)) can be found using the formula E(x^2) = μ^2 + σ^2. With the given mean (μ) and standard deviation (σ) as 5, insertion into the formula gives E(x^2) = 5^2 + 5^2 = 50.

The mean square value, often denoted as E(x2), is calculated from the mean (μ) and standard deviation (σ) using this formula: E(x2) = μ2 + σ2. Based on the given distribution values, you're provided with a mean (μ) of 5 and a standard deviation (σ) of 5. By following the formula, you input these values, and it becomes E(x2) = 52 + 52. Thus, E(x2) = 25 + 25 which is equal to 50. So, the mean square value or the expected value of x2 for this distribution is 50.

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110-75+50-85 =

110+50=160

75+85 = 160

160-160=0

her balance is 0

Answer:

A   12 chairs per 3 table

Step-by-step explanation:

4/1 is equivalent to 12 chairs for every 3 tables.

Fractions are used to represent smaller pieces (or parts) of a whole.

Given a statement, 12 chairs for every 3 tables.

The statement represents 12 chairs per 3 tables, which means 12/3 = 4/1

Therefore, there are 4 chairs for every table.

Hence, 4/1 is equivalent to 12 chairs for every 3 tables.

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Answer:

Given the series : 83 , 79 , 75 ,  71 , 67, ?

Difference of two consecutive terms;

79 -83 = -4

75 -79 = -4

71-75 = -4

67-71= -4

Since, you can see that the number is decreases by 4 every time.

Let unknown term be x

then;

x - 67 = -4

x = 67-4

x = 63.

Therefore, the next term in the series is 63.

The next number in the series is 63.

In the given series, each number is decreasing by 4.

We can observe that the first number, 83, is decreased by 4 to get the next number, 79.

Similarly, each subsequent number is obtained by subtracting 4 from the previous number.

Following this pattern, the next number would be obtained by subtracting 4 from the last number in the series, which is 67.

67 - 4 = 63

Therefore, the next number in the series is 63.

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20.25 -18.90 = 1.35

1.35 / 18.90 = 0.071428571

= 7.14%

check:

18.90 x 1.34946 Round to 1.35

18.90 + 1.35 = 20.25

 Sales tax = 7.14%

Value

Depreciation is defined as the reduction in value of an asset over time. In this case, value reduction is due to wear and tear of an equipment (bicycle).

a. The depreciation value would simply be the difference in initial and salvage value divided by time in years.

Depreciation = (Initial value – Salvage value) / Number of years

b. Substituting the given values into the equation where:

Initial value = $1200

Salvage value = $940

Number of years = 10 months = 10/12 years

Calculating:

Depreciation = ($1200 - $940) / (10/12 years)

Depreciation = $312 / year

or

Depreciation = $26 / month

Final answer:

The term 1/2i most likely pertains to complex numbers, where 'i' is the imaginary unit. It's not typically covered in Calculus I or II but in pre-calculus or algebra courses. The principles of working with fractions apply similarly for complex numbers as they do with real numbers.

Explanation:

The term 1/2i likely refers to the fractional unit in the context of complex numbers, where 'i' is the imaginary unit. This concept is not commonly taught in Calculus I or II but is a part of complex number arithmetic, which is sometimes covered in pre-calculus or algebra. When calculating with complex numbers, it is crucial to remember that 'i' represents the square root of -1.

Let's consider the calculation of 'half' of something in more familiar terms. If you have half a pie, and you're looking to find half of that, you would intuitively know that you now have one-quarter of a pie. Likewise, if you are trying to understand how to combine fractions such as 1/2 and 1/3, you look for a common denominator. Multiplying denominators can often provide this common base for addition, just like multiplying 2 and 3 to get 6 as a common denominator.

However, when working with complex numbers and encountering a term like 1/2i, it can seem less intuitive. Nonetheless, the basic principles of fraction manipulation remain the same. The student might be looking at a problem involving complex fractions, which would require familiarity with the algebraic rules governing complex numbers.

total = 450

 parts = 150

450-150 = 300

 50 per hour

300/50 = 6

it took 6 hours

Using the law of sines, the length of side a to the nearest tenth is 58.1 units.

Law of sines states that When we divide side a by the sine of angle A it is equal to side b divided by the sine of angle B, and also equal to side c divided by the sine of angle C.

In ΔABC,

∠A=72°

∠B=16°

∠A + ∠B + ∠C = 180° (angle sum property)

72° + 16° + ∠C = 180°

∠C = 180° - (72° + 16°) = 92°

Using sine law, (refer to the figure attached)

[tex]\frac{sin\ A}{a} = \frac{sin\ B}{b} =\frac{sin\ C}{c} \\\\\frac{sin72}{a} = \frac{sin16}{b} = \frac{sin92}{61} \\\\\frac{sin72}{a} =\frac{sin92}{61} \\\\a = sin72 * \frac{61}{sin92} \\\\= 0.9511 * \frac{61}{0.9994} \\\\=58.05193116\\\\= 58.1[/tex]

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