A pool measuring 18 meters by 30 meters is surrounded by a path of uniform width, as shown in the
figure. If the area of the pool and the path combined is 1900 square meters, what is the width of
the path?

The rectangular distribution f(x) = 1/(b-a) for a ≤ x ≤ b is a valid probability density function.

In mathematics and statistics, a distribution refers to the pattern of values or frequencies of a variable within a set of data. It describes the spread and behavior of data and can be represented by graphs, tables, or mathematical functions.

The rectangular distribution is a continuous probability distribution where the probability density function (PDF) is constant over a certain interval and zero elsewhere. In this case, we have a rectangular distribution with parameters a and b, where a is the lower bound of the interval and b is the upper bound of the interval.

The probability density function (PDF) of this rectangular distribution is given by:

f(x) = 1/(b-a) for a ≤ x ≤ b

and f(x) = 0 elsewhere.

To verify that this function is a valid probability density function, we need to check two conditions:

The first condition is satisfied because f(x) is always positive on the interval [a, b]. The second condition is satisfied because the area under the curve of f(x) from a to b is equal to:

[tex]\int\limits^a_b f(x) dx = \int\limits^a_b (1/(b-a)) dx = [x/(b-a)]_b^a= (b-a)/(b-a) = 1[/tex]

Therefore, the rectangular distribution f(x) = 1/(b-a) for a ≤ x ≤ b is a valid probability density function.

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The value of x when the value of y = 2 is 8 and the value of x when the value of z = 27 is 48 using the direct and inverse variations.

Given that,

x varies directly with the square of y.

For some constant m, x = m y²

x varies inversely with the cube root of z.

For some constant n, x = n ∛z

We have when x = 32, the value of  y = 4.

16m = 32

m = 2

Hence the direct variation equation is, x = 2 y²

We have when x = 32, z = 8.

2n = 32

n = 16

Hence the inverse variation equation is, x = 16 ∛z

When y = 2,

x = 2 × 2² = 8

When z = 27

x = 16 ∛27 = 16 × 3 = 48

Hence the value of x are 8 and 48 respectively when y = 2 and z = 27.

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Yes, the shape can be cut into 3 congruent parts but not 4. This is a whole number division problem. See the attached shape for how to divide the figure into 3 congruent parts.

In mathematics, when two numbers are divided without remainders, it is known as integer division or whole number division.

This specific kind of calculation comes in handy when you desire to find out just the quotient or how many times one number divides into another, disregarding any leftover fraction.

For instance, if we utilize integer division to calculate what happens when ten is divided by two; we're left with five as our answer since two divides equally into ten precisely five times without remaining any leftovers.

Conversely speaking though and in regards to regular arithmetic calculations; dividing ten by three amounts up to three with a remainder value attached since three cannot do so equally.

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The vertex form of the quadratic equation is:

f(x) = 3*(x - 1)² + 12

Remember that for a quadratic equation whose vertex is at (h, k) and the leading coefficient is a, we can write it in the vertex form as:

y = a*(x - h)² + k

Here we have:

f(x) = (3x-9)(x+1)

We can rewrite that as:

f(x) = (3x - 3*3)(x+1)

f(x) = 3(x - 3)*(x + 1)

Thus the leading coefficient is 3.

The x-value of the vertex is the midpoint the two x-intercepts x = 3 and x = -1, then:

h = (3 - 1)/2

h = 2/2

h = 1

And to get the y-value, we need to evaluate in x = 1.

f(2) = 3*(1 - 3)*(1 + 1)

f(2) = 3*-2*2 = -12

So the vertex is (1, 12), then the vertex form is:

f(x) = 3*(x - 1)² + 12

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Answer:

see below

Step-by-step explanation:

50.4 -2.1 = 48.3

48.3/3 = 16.1 each

Answer: $16.10

Step-by-step explanation:

$50.40-$2.10=$48.3

$48.3/3=$16.1

63 mL/Hour should be administered to the patient. Flow rate Q is defined to be the volume V flowing past a point in time t, or Q=Vt where V is volume and t is time.

Here, we have,

One of the oldest theories in biology and medicine is the structure-function relationship, which states that form serves function and that function affects form.

In this article, we derive and validate form-function relations for volume, length, flow, and mean transit time in vascular trees and capillary numbers of different organs and species.

A vessel segment is referred to as a "stem," while the vascular tree it supplies is referred to as a "crown."

We show form-function relationships between the volume, length, and blood flow that perfuse a vascular network's crown and the number of capillaries in the network.

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complete question;

an order is given to administer 100. mg of furosemide, a diuretic, over the course of four hours by iv. if a 500. ml bag contains 200. mg of furosemide, what flow rate, in ml/hour, should be administered to the patient?

Answer:

h ≥ -14

Step-by-step explanation:

-1h ≤ 14

h ≥ -14

So, the answer is h ≥ -14

The students that are correct in their approach to solving the problem are Nico, Raj and Sandra.

It should be noted that we can start by simplifying the left side of the equation by distributing the two-fifths:

(2/5)(5) + (2/5)x = 8

2 + (2/5)x = 8

Next, the next thing is that we can isolate the variable term on one side of the equation by subtracting 2 from both sides:

(2/5)x = 6

x = 6 / (2/5)

x = 6 * (5/2)

x = 15

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

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Answer:

$2,738.89/per month

Step-by-step explanation:

this is a loan shark.  15% is robbery.

The Add on Method is an alternative method of paying interest after it is added onto the principal at maturity. In this method, the interest on the loan is calculated annually and multiplied by the number of years left for repayment.

Calculate the annual interest: Multiply the interest rate by the amount you originally borrowed: 15% x $68,000 = $10,200.

Calculate the add-on interest amount: Multiply the annual interest amount by the number of years in the loan: $10,200 x 3 years = $30,600.

so total she'll have to pay over 3 years = 98600

98600/36 months = 2738.89/per month

Answer:

  500

Step-by-step explanation:

You want to know the total number of plantings if 190 trees comprise 38% of them.

The given relationship can be written as the equation ...

  190 = 0.38 × total

  total = 190/0.38 = 500 . . . . . . . divide by the coefficient of 'total'

There are 500 plantings in the garden.

Sasha buys 5 boxes crackers for 12.25 if each box cost the same amount  one box of crackers costs $2.45.

To find the cost of one box of crackers, we can use the concept of unit rate, which is the cost per one unit. In this case, we want to find the cost per one box of crackers.

If Sasha bought 5 boxes of crackers for a total of $12.25, we can set up a proportion to find the cost of one box of crackers:

5 boxes / $12.25 = 1 box / x

Here, "x" represents the cost of one box of crackers. We can solve for "x" by cross-multiplying the proportion:

5 boxes * x = $12.25 * 1 box

5x = $12.25

x = $12.25 / 5

x = $2.45

To check our answer, we can multiply the cost of one box by the number of boxes Sasha bought:

$2.45 * 5 boxes = $12.25

This confirms that our answer is correct.

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Complete question is:

Sasha buys 5 boxes crackers for 12.25, if each box cost the same amount, then how much does 1 box of the crackers cost?

The slope-intercept form of (y - 4) = 3(x - 5) is expressed as:

y = 3x - 11

The slope-intercept form is expressed as y = mx + b, where we have the variables:

m as the slope

b as the y-intercept.

Given the equation in point-slope form as (y - 4) = 3(x - 5), we can convert as follows:

(y - 4) = 3(x - 5)

y - 4 = 3x - 15

y - 4 + 4 = 3x - 15 + 4

y = 3x - 11

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All the points less than -5 will be marked on the number line.

To represent the values of x where x ≤ -2 and x < -5 on a number line, we start by marking a point at -2 and shading everything to the left of it since x is less than or equal to -2. Next, we add another shading to the left of -5 since x is also less than -5. We then mark an open circle at -5 since x is not equal to -5.

Our number line would look like this as image attached below.

The shaded region to the left of -5 represents all values of x that are less than -5. The shaded region between -5 and -2 represents all values of x that are between -5 and -2, including -5 and -2. The open circle at -5 indicates that x cannot equal -5, but can be any other value less than -5.

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a) Assuming no withdrawals are made, the future value in Kareem's account after 3 years is $1,768.74.

b) After 3 years, the interest earned on Kareem's investment is $68.74.

The future value and the interest are determined by the investment (present value) and the interest rate, including the compounding periods.

The future value of a present-value investment can be determined using an online finance calculator, including the total interest earned on the investment.

N (# of periods) = 3 years

I/Y (Interest per year) = 1.33%

PV (Present Value) = $1,700

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $1,768.74

Total Interest = $68.74

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Answer: a = 9

Step-by-step explanation:

The triangle follows the 45-45-90 rule, meaning:

- This is the only isosceles triangle where the Pythagorean theorem can be used.

There are 2 ways to solve this problem...

The easy way is to identify the fact that the sides of a 45-45-90 triangle will be:

– the sides opposite the 45° angles will be 'a'

– the hypotenuse is a•[tex]\sqrt{2[/tex]

The hard way will help visualize this:

Since there's a right angle, you can use the Pythagorean theorem

a² + a² = c² = [tex](9\sqrt{2})^{2}[/tex]

2a² = [tex](9\sqrt{2})^{2}[/tex]

2a² = (9²•2) = 162

a² = 81

a = 9

for the first one 225÷5=45. For the second one to do 363÷5 you have to decrease 363 to the closest number divisible by 5 and that number is 360 so 360÷5=72 then for the remaining 3 instead of doing 3÷5 you can do 30÷5 then bring the decimal point 1 digit forward so 30÷5=6 then when you bring the decimal point forward its 0.6 then add both and its 72.6. for the third one its the same thing so 372÷3=124 but since you cant do 10÷3 you have to use fractions so 1÷3 means 1/3 then add both of them together and its 124 1/3

a) The function that represents the volume of the trough in terms of x is  V(x) = 88x - 8x².

b) x = 5.5 inches.

c) The maximum volume is 0 cubic inches.

A function is a mathematical concept that describes a relationship between two sets of values, typically represented as variables. A function maps each element of the first set, called the domain, to a unique element of the second set, called the range. In other words, a function assigns a single output value to each input value.

For example, consider the function f(x) = x². The domain of this function is all real numbers, and the range is all non-negative real numbers. For each value of x, the function f(x) returns the square of that value.

(a) Let x be the distance in inches that the homeowner makes the fold along the two long sides of the rectangular piece of aluminum. Then, the height of the resulting trough will be x inches, and the length of the trough will be 22 - 2x inches (since the fold reduces the length by 2x inches). The width of the trough will still be 4 inches.

The volume of the trough can be found by multiplying its length, width, and height:

V(x) = (22 - 2x) * 4 * x

V(x) = 88x - 8x²

So, the function that represents the volume of the trough in terms of x is V(x) = 88x - 8x².

(b) To find the value of x that maximizes the volume of water that can be carried by the gutter, we need to find the maximum point of the function V(x). We can do this by taking the derivative of V(x) with respect to x, setting it equal to zero, and solving for x:

V'(x) = 88 - 16x

88 - 16x = 0

16x = 88

x = 5.5

Therefore, the value of x that maximizes the volume of water that can be carried by the gutter is x = 5.5 inches.

(c) To find the maximum volume, we substitute x = 5.5 into the function V(x):

V(5.5) = 88(5.5) - 8(5.5)^2

V(5.5) = 242 - 242

V(5.5) = 0

Therefore, the maximum volume of water that can be carried by the gutter is 0 cubic inches.

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Solving the equation, the calculated value of the width of the border is 3 feet

From the question, we have the following parameters that can be used in our computation:

140 (202x)(16-2x)

Express properly

So, we have

(20 - 2x)(16 -2x) = 140

The above equation can be solved graphically

When the equation (20 - 2x)(16 -2x) = 140 is entered in a graphing tool, we have the solution to be

x = 3 and x =15

The value 15 would make the lengths invalid

So, we have

x = 3

Hence, the width of the border is 3 feet

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According to the concept of compound interest, the effective annual yield on your investment of $1800 at a 6.3% interest rate compounded daily is 6.49%.

To find the effective annual yield, we need to use the formula for compound interest:

A = P(1 + r/n)ⁿˣ

Where A is the amount of money at the end of the investment period, P is the principal amount invested, r is the annual interest rate, n is the number of times the interest is compounded in a year, and t is the number of years.

In this case, we know that the principal amount P is $1800, the annual interest rate r is 6.3%, and the interest is compounded daily, which means that n is 365 (the number of days in a year). We need to find the effective annual yield, which is the total amount of interest earned in one year.

To calculate the effective annual yield, we can use the following formula:

Effective Annual Yield = (1 + r/n)ⁿ - 1

Plugging in the values, we get:

Effective Annual Yield = (1 + 0.063/365)³⁶⁵ - 1

Effective Annual Yield = 0.0649 or 6.49%

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Note that the lateral area of the right prism is 16cm²

The first step is to convert    the sides of the paralllogram to the same unit

6cm = 60mm

so

Perimeter of base = 2( 60 + 20) = 160 mm

Thus, the lateral area of the prism is

A = p x h = 160 x 0.3dm

But we cant have different units, so we say:

160 mm x 30mm
= 4,800mm

Converting this to centimeters, we have

480cm²

hence, the lateral area of the right prism  480cm²

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Answer: The lateral area of the prism is 48 cm²

Work:

We have,

Lateral area is the surface area of the sides or lateral faces of a three-dimensional object, excluding the surface area of the bases.

Now,

From the figure,

There are 4 rectangular-shaped sides.

And,

1 dm = 10 cm

0.3 dm = 3 cm

Now,

Lateral area of the prism.

= 4 x 3 + 3 x 3 + 4 x 3 + 5 x 3

= 12 + 9 + 12 + 15

= 48 cm²

Thus,

The lateral area of the prism is 48 cm²

Answer:

Based on the patient's chart, the percentage of their body burned is:

(0 + 0 + 1 + 1 + 1 + 1 + 0 + 1 + 1 + 1 + 0) / 11 = 7 / 11 = 0.64

Using the Parkland formula, we can calculate the fluid intake needed in the first 24 hours as:

4 mL x weight in kg x % body burned = 4 x 97 x 0.64 = 248.32 mL

Since the patient has already been in treatment for 8 hours, we need to calculate the fluid intake needed for the remaining 16 hours:

248.32 mL / 24 hours x 16 hours = 132.22 mL

Therefore, the patient should receive approximately 132.22 mL of fluid per hour in the next 16 hours of their care. Rounded to two decimal places, this is 132.22 mL per hour.

Certainly!

The text is asking how to solve the equation x² - 14x + 9 = 0 using the factoring method. Factoring is a method of finding the roots of a quadratic equation by expressing it as a product of two linear factors. The roots of a quadratic equation are the values of x that make the equation equal to zero. In this case, we are trying to find the values of x that satisfy the equation x² - 14x + 9 = 0.

Based solely on financial considerations, Vim Cola should be discontinued.

We have,

Differential analysis to determine whether Vim Cola should be continued or discontinued:

Differential Analysis:

Continue vs. Discontinue Vim Cola table is given below.

The differential analysis shows that if Vim Cola is continued (Alternative 1), the company will have sales of $235,000, a cost of goods sold of $111,000, and operating expenses of $143,000.

This will result in a gross profit of $124,000 and an operating loss of $19,000.

If Vim Cola is discontinued (Alternative 2), the company will have no sales or cost of goods sold related to Vim Cola, but will still have $25,000 of fixed operating expenses.

This will result in an operating loss of $25,000.

The difference between the two alternatives is an operating income(loss) of ($6,000).

Since the difference is negative, discontinuing Vim Cola would result in a better financial outcome for the company.

Therefore,

Based solely on financial considerations, Vim Cola should be discontinued.

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Here's a differential analysis for Lavonia Beverage Inc. to decide whether Vim Cola should be continued or discontinued:

Differential Analysis

Alternative 1: Continue Vim Cola

Alternative 2: Discontinue Vim Cola

Sales revenue $235,000 $0

Cost of goods sold:

Variable costs (111,000) 0

Fixed factory overhead costs (16,650) 0

Total cost of goods sold (127,650) 0

Gross profit $107,350 $0

Operating expenses:

Variable expenses (114,400) (28,800)

Fixed expenses (28,600) 0

Total operating expenses (143,000) (28,800)

Operating income (loss) $(35,650) $(28,800)

The analysis shows that if Lavonia Beverage Inc. continues to sell Vim Cola, it will generate sales revenue of $235,000 and incur total variable costs of $111,000.

Additionally, 15% of the cost of goods sold, or $16,650, is fixed factory overhead costs. Total cost of goods sold for Vim Cola is $127,650 ($111,000 + $16,650).

On the other hand, if Vim Cola is discontinued, the company will lose the sales revenue of $235,000 but will also save on the variable and fixed costs associated with the product.

Variable operating expenses are estimated to be 20% of total operating expenses, or $28,800. Fixed operating expenses associated with Vim Cola are estimated to be 20% of total fixed operating expenses, or $28,600.

Thus, based on the analysis, it appears that Vim Cola is generating a loss of $35,650 if it continues to be sold, while discontinued it would result in a loss of $28,800. Therefore, it may be advisable to discontinue Vim Cola.

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The probability that all three murders were committed with a gun is: 0.252.

The probability that one murder was committed with a gun is:

P(Gun) = (6368 + 364 + 200 + 3326)/13927 = 0.632

Therefore, the probability that all three murders were committed with a gun is:

P(3 Guns) = P(Gun) * P(Gun) * P(Gun) = [tex]0.632^3[/tex] = 0.252

The probability that a murder was committed with a handgun given that a gun was used is:

P(Handgun | Gun) = P(Handgun and Gun) / P(Gun)

We need to find P(Handgun and Gun). From the table, we see that 6368 murders were committed with a handgun and 6368 + 364 + 200 = 6932 murders were committed with a gun. Therefore:

P(Handgun and Gun) = 6368/13927

And:

P(Handgun | Gun) = (6368/13927) / (6368 + 364 + 200 + 3326)/13927 = 0.542

The probability that two murders involved a gun and two involved a cutting instrument is:

P(2 Guns and 2 Cutting instruments) = (C(4,2) * C(6932,2) * C(1476,2)) / C(13927,4)

Where C(n,r) is the number of combinations of n things taken r at a time.

Thus, calculating this gives: P(2 Guns and 2 Cutting instruments) = 0.150

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a. The polyhedron is a triangular prism

b. The polyhedron a pentagonal pyramid

From the question, we are to determine the names of the given polyhedra.

a. The given polyhedra is a three-dimensional geometric shape that consists of two congruent parallel triangles as the base and three rectangular faces that connect the corresponding sides of the triangles.

This shape is known as a triangular prism.

b. The polyhedra is a three-dimensional geometric shape that consists of a pentagonal base and five triangular faces (also known as lateral faces) that meet at a common vertex point above the base. The lateral faces connect the corners of the pentagonal base to the apex, forming five triangular sides that taper upwards to meet at a single point.

This shape is known as a pentagonal pyramid.

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Where the function f(x) = (9/10)ˣ is given, all the functions are correct with the EXCEPTION of option D.

A. The range of f(x) is y > 0 since any positive number raised to any power is positive.

Therefore, f(x) = (9/10)ˣ >  0.

  B. Since the base of the exponential function, 9/10, is less than 1, f(x) is a decreasing  function. Therefore, it is not always increasing

C. To find the y-  i ntercept of f(x ), we substitute x=0 into the equation:

f(0) = (9/10)⁰ = 1.

Therefore, the y- intercept is ( 0, 1).

D. The domain of f(x) is x ≥ 0, not x > 0. The function is defined for all non  negative real numbers since any non-negative number can be raised to any power.

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Answer: one solution x=3

Step-by-step explanation:

this problem is very simple, we need to figure out out what number(x) when multiplied by 2, and then you minus 3 (2x-3)

we need to then multiply this number by 5 to get 15, so 5x3 is what we need to find, so then we need to have the number 6 as 2x, or 3 as x.

so we end up with equation 5(2*3-3) or, 5(6-3), which equals 5*3= 15.

When be graph the functions given, we find that option A is correct.

What is meant by to graph a function?

To graph a function, you have to select x-values and plug them into the equation. Once you plug those values into the equation, you will get a y-value. Your x-values and your y-values make up your coordinates for a single point. Keep plugging in x-values to get coordinates to plot more points on the graph, and then you will see your graphed function once the dots are connected.

Using the graph,

For x < = -2, y = 5.

For -2 < x < 1, the function is a polynomial.

We have two options, either y = x² - 5 or y = x² + 5

The polynomial must have the point (0,-5) on it.

For y = x² - 5 , when x = 0, y = -5.

Hence, it is the correct option.

For x >= 1,

Using graph, we see that when y = 0, x lies between 3 and 4.

For equation, y = 2⁽ˣ⁻²) - 2 , when y = 0, x = 3, so it is not correct.

For equation, y = 2⁽ˣ⁻²) - 3 , when y = 0, x = 3.584, hence it is correct.

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