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In school suspension

The length and the widths are 420.031 yards and 0.031 yards if a rectangular parking lot has a length that is 420 yards greater than the width.

It is defined as two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral.

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

Let L be the length and W be the width of the rectangle.

From the question:

L = 420 + W (based on the data given in the question)

LW  = 13

(420 + W)W = 13

W² + 420W - 13 = 0

After solving the above quadratic equation:

W = 0.031, W = -420.03 (width cannot be negative)

W = 0.031 yards (which is not practical but from a mathematical point of view it can be considered)

L = 420 + 0.031 = 420.031 yards

Thus, the length and the widths are 420.031 yards and 0.031 yards if a rectangular parking lot has a length that is 420 yards greater than the width.

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Answer:

D

Step-by-step explanation:

x coordinate:

8 - -4 = 12

12 / 2 = 6

-4 + 6 = 2

y coordinate:

10 - -8 = 18

18 / 2 = 9

-8 + 9 = 1

(2, 1)

\(\geq\)Answer:

part A---   -9\(\geq\)9

Step-by-step explanation:

Answer:

answer -9>9

Step-by-step explanation:

rbfodnddn bdbndndn

Given sin∠X = cos∠Y and m∠X = 72°, we can find the measure of angle Y to be 18° since angles X and Y are complementary.

The problem states that sin∠X = cos∠Y and m∠X = 72°, and we are asked to find the measure of angle Y.

The first thing to notice is that sin∠X = cos∠Y means that the sine of angle X is equal to the cosine of angle Y. By the definition of sine and cosine, we know that:

sin∠X = opposite/hypotenuse

cos∠Y = adjacent/hypotenuse

where "opposite" and "adjacent" are the lengths of the sides of a right triangle that correspond to angles X and Y, respectively, and "hypotenuse" is the length of the hypotenuse of the triangle.

Since sin∠X = cos∠Y, we can set the two expressions equal to each other:

sin∠X = cos∠Y

opposite/hypotenuse = adjacent/hypotenuse

opposite = adjacent

This tells us that the lengths of the opposite and adjacent sides of the right triangle are equal. Since these sides are opposite and adjacent to angles X and Y, respectively, this means that angles X and Y are complementary angles (i.e., the sum of their measures is 90°).

We know that angle X has a measure of 72°, so we can use the fact that angles X and Y are complementary to find the measure of angle Y:

m∠Y = 90° - m∠X

m∠Y = 90° - 72°

m∠Y = 18°

Therefore, the measure of angle Y is 18°.

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Answer:

D

Step-by-step explanation:

I think

Ava will be charged $180 in interest at the end of one year.

The formula for simple interest is:

I = P x r x t

where I is the interest, P is the principal (the amount borrowed), r is the interest rate, and t is the time period (in years).

In this case, P = $4500, r = 4%, and t = 1 year. Substituting these values into the formula, we get:

I = $4500 x 0.04 x 1 = $180

Therefore, Ava will be charged $180 in interest at the end of one year.

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Given that point T is the center of dilation, we know that the length of line segments TX' and TY' are proportional to the length of line segments TX and TY, respectively.

We can express this as:

TX' = k * TX

TY' = k * TY

where k is the scale factor.

We are given the lengths of TX' and TY':

TX' = 6

TY' = 9

So, we can solve for k:

9 / k = 6

k = 9 / 6 = 3 / 2

Now that we know the value of k, we can find TY:

TY = TY' / k = 9 / (3 / 2) = 6 * (3 / 2) = 9

Next, we are given the length of XX':

XX' = 2

And using the dilation formula, we can find XX:

XX = XX' / k = 2 / (3 / 2) = 2 * (2 / 3)

Finally, we can find TX by using the Pythagorean theorem:

TX^2 = TY^2 + XX^2

TX^2 = 9^2 + (2 * (2 / 3))^2

TX^2 = 81 + (4 / 3)^2

TX^2 = 81 + 16 / 9

TX^2 = 81 + 16 / 9

TX = √(81 + 16 / 9) = √(81 + 16 * 9 / 9) = √(81 + 16) = √97

So, TY = 9 and TX = √97. Therefore, YT = TY - TY' = 9 - 9 = 0.

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TX' = k * TX

TY' = k * TY

TX' = 6

TY' = 9

So, we can solve for k:

9 / k = 6

k = 9 / 6 = 3 / 2

Now that we know the value of k, we can find TY:

TY = TY' / k = 9 / (3 / 2) = 6 * (3 / 2) = 9

XX' = 2

XX = XX' / k = 2 / (3 / 2) = 2 * (2 / 3)

TX^2 = TY^2 + XX^2

TX^2 = 9^2 + (2 * (2 / 3))^2

TX^2 = 81 + (4 / 3)^2

TX^2 = 81 + 16 / 9

TX^2 = 81 + 16 / 9

TX = √(81 + 16 / 9) = √(81 + 16 * 9 / 9) = √(81 + 16) = √97

So, TY = 9 and TX = √97. Therefore, YT = TY - TY' = 9 - 9 = 0.

In the given figure we have a circle with center J.

By definition, the radius is the distance from its center to a point located on the circle.

a) In the given figure, a radius is JI

A diameter is a chord that passes through the center of the circle and it is twice the radius.

b) A diameter is KL.

A chord is a segment that connects two points on a circle.

c) A chord is HM.

d) If the length of JI (remember this is a radius) is 2 units, then the length of KL is twice this value: 2*2units= 4 units.

Answer:

30 ft

Step-by-step explanation:

h/(40 + 8) = 5/8

h = 30

Answer:

1 hour and 15 minutes.
2 hours and 45 minutes.

Step-by-step explanation:

If a car travels at 56mph, it will take 1 hour and 15 minutes to travel 70 miles.
If a car travels at 56 mph, it will take 2 hours and 45 minutes to travel 154 miles.

Hope this helps!

Step-by-step explanation:

Adair earns 6% commission, and his total sales last week were $ 14,560. How much straight commission did Adair earn?

6% = 0.06

0.06 * $14,560 = $873.60 commission

The best method to assess if sample data fit a normal distribution, assuming a minimum sample size of 125 is available, is the Shapiro-Wilk test.

The Shapiro-Wilk test is a statistical test that evaluates the deviation of the data from a normal distribution. It is commonly used for assessing normality when the sample size is larger than 50. The test provides a p-value, which indicates the likelihood of the data being drawn from a normal distribution. If the p-value is greater than the chosen significance level (e.g., 0.05), it suggests that the data follows a normal distribution.

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In British Columbia, Canada, the number y of purple martin nesting pairs x years since 2000 can be modeled by the equation y = 0.63x² +51.8x + 144 there were about 1000 nesting pairs around the time of year 2011.5.

To find when there were about 1000 nesting pairs, we need to solve the given equation for x.

y = 0.63x² +51.8x + 144

We substitute y = 1000 and solve for x:

1000 = 0.63x² +51.8x + 144

0.63x² + 51.8x - 856 = 0

We can solve this quadratic equation using the quadratic formula:

x = (-b ± sqrt(b² - 4ac)) / 2a

where a = 0.63, b = 51.8, and c = -856.

x = (-51.8 ± sqrt(51.8² - 4(0.63)(-856))) / 2(0.63)

x ≈ -86.3 or x ≈ 11.5

Since we are interested in the time after 2000, we discard the negative solution and get:

x ≈ 11.5

This means that there were about 1000 nesting pairs approximately 11.5 years after 2000. To find the actual year, we add 11.5 to 2000:

2000 + 11.5 = 2011.5

Therefore, there were about 1000 nesting pairs around the time of  year 2011.5.

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Answer:

2/3

Step-by-step explanation:

16/4=4

24/4=6

4/6 divided by 2= 2/3

Answer:

B. -1

Step-by-step explanation:

it is plainly visible.

the dot is one unit to the left (x- or Real-axis), which is -1.

and it is 3 units down (y- or Imaginary-axis), which is -3.

the number is therefore -3i - 1

the question was only for the real part (without any "impact" by an "i"), which again is -1.

It will take 4 months for the total cost for both gyms to be equal.

What is algebra?

Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas. It involves the study of variables, expressions, equations, and functions.

Let's assume that the total cost for both gyms will be equal after "x" months.

For Gym A, the total cost after "x" months can be calculated as follows:

Total cost for Gym A = Joining fee + Monthly charge * Number of months

Total cost for Gym A = $20 + $40x

For Gym B, the total cost after "x" months can be calculated as follows:

Total cost for Gym B = Monthly charge * Number of months

Total cost for Gym B = $45x

Now we can set up an equation to find when the total cost for both gyms will be equal:

$20 + $40x = $45x

To solve for "x", we can first subtract $40x from both sides:

$20 = $5x

Then divide both sides by $5:

x = 4

Therefore, it will take 4 months for the total cost for both gyms to be equal.

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There exist points c1, c2, ..., cn in [a, b] such that f(c1) = f(p1), f(c2) = f(p2), ..., f(cn) = f(pn). f is continuous on [a, b], g is continuous on [a, b] as well.

To prove the statement, we will use the intermediate value theorem. Consider the function g(x) = f(x) - f(p1). Since f is continuous on [a, b], g is continuous on [a, b] as well.

Now, we have g(p1) = f(p1) - f(p1) = 0. Also, g(a) = f(a) - f(p1) and g(b) = f(b) - f(p1). Without loss of generality, assume that g(a) ≤ 0 and g(b) ≥ 0. (If not, swap a and b.)

Since g is continuous on [a, b] and g(a) ≤ 0 ≤ g(b), there exists a point c in [a, b] such that g(c) = 0. That is, f(c) - f(p1) = 0, or f(c) = f(p1). Therefore, we have found a point c in [a, b] such that f(c) = f(p1).

Repeating this argument for p2, p3, ..., pn, we can find points c2, c3, ..., cn in [a, b] such that f(c2) = f(p2), f(c3) = f(p3), ..., f(cn) = f(pn).

Therefore, we have proved that there exist points c1, c2, ..., cn in [a, b] such that f(c1) = f(p1), f(c2) = f(p2), ..., f(cn) = f(pn).

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Answer:

Step-by-step explanation:

Given,

5x + 6 = 1

=> 5x = 1 - 6

=> 5x = -5

\( = > x = \frac{ - 5}{5} \)

=> x = -1 (Ans)

Answer:

I can help u. don't worry i don't really want to be payed. I'll help u for free if I can. What's ur question.

Step-by-step explanation:

Answer with explanation:

Given: Charlie is laying down mulch in his front yard. It takes Charlie 4 minutes to lay down 11 cubic yards of mulch and  16 minutes to lay down 44 cubic yards of mulch.

Here, Time(Independent variable (x)) is directly proportion to the Volume of mulch(dependent variable (y)) lied by Charlie.

Let k be the constant of proportionality, such that

\(k=\dfrac{y}{x}\)

For x= 4 and k= 11, \(k=\dfrac{11}{4}\)

Required equation: \(y=\dfrac{11}{4}x\)                        

Two points are given in question: (4,11) , (16,44).

Take x= 8 , \(y=\dfrac{11}{4}(8)=22\)i.e. point (8,22)

Similarly, for x= 12, y=33 i.e. point (12, 33)

For x= 20 , y= 55 i.e. point (20,55)

Five data points: (4,11) , (16,44), (8,22),  (12, 33), (20,55).

Now, we plot these points on graph and join them

Answer:

Here

Step-by-step explanation:

Answer:

24 dollars per liter

Step-by-step explanation:

Take the number of dollars and divide by the number of liters

60 dollars / 2.5 liters

24 dollars per liter

Answer:$24 per litter

Step-by-step explanation:

Answer:

Step-by-step explanation:

6y - y = y(6 - 1) = y * 5

The answer is 5y.

We are given a differential equation: 2(1 - x^2)dy/dx + y = x(y - 2ln(xy)) + xy + C, where C is a constant. Our goal is to solve this differential equation. y^2 - 2xy + 2y = 1/2x^2y^2 - 2xyln(xy) + Cx + K.This is the solution to the given differential equation

To solve the given differential equation, we will use various methods of integration and manipulation.

First, we rearrange the equation to separate variables:

2(1 - x^2)dy = (x(y - 2ln(xy)) + xy + C)dx.

Next, we integrate both sides of the equation with respect to their respective variables:

∫2(1 - x^2)dy = ∫(x(y - 2ln(xy)) + xy + C)dx.

Simplifying the integrals and combining terms, we get:

2y - 2∫x^2dy = ∫xydx - ∫2ln(xy)dx + ∫xydx + ∫Cdx.

Further simplifying, we have:

2y - 2xy + 2∫xydx = ∫xydx - 2∫ln(xy)dx + ∫Cdx.

Now, we integrate each term individually:

2y - 2xy + xy^2 = 1/2x^2y^2 - 2xyln(xy) + Cx + K,

where K is the constant of integration.

Finally, we can rearrange the equation to solve for y:

y^2 - 2xy + 2y = 1/2x^2y^2 - 2xyln(xy) + Cx + K.

This is the solution to the given differential equation. The equation represents a relationship between x and y that satisfies the original equation.

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To find the value of 'a' such that P(0 < Z < a) = 0.2324, follow these steps:

Step 1: Identify the given probability
The given probability is P(0 < Z < a) = 0.2324.

Step 2: Understand the context of the problem
This is a problem involving the standard normal distribution (Z-distribution), where Z represents the standard normal variable.

Step 3: Use a Z-table or calculator
To find the value of 'a', you can use a standard normal (Z) table or a calculator with a Z-table function. Since P(0 < Z < a) = 0.2324, we can rewrite it as P(0 < Z) + P(Z < a) = 0.5 + P(Z < a) = 0.2324.

Step 4: Calculate the cumulative probability
Solve for P(Z < a) by subtracting 0.5 from both sides: P(Z < a) = 0.2324 - 0.5 = -0.2676.

Step 5: Find the Z-value
Look for -0.2676 in the Z-table or use the calculator's inverse Z-function. You will find that the corresponding Z-value (to two decimal places) is approximately -0.64.

Step 6: Provide the answer
The value of 'a' that satisfies P(0 < Z < a) = 0.2324 is approximately -0.64.

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Answer:

A handtowel costs $2.00 and a bathtowel is $9.00

Step-by-step explanation:

Let h equal the cost of a handtowel. And let b equal the cost of a bathtowel.

In Campbell, they spent:

255 = 6h + 27b

In Lowell, they spent:

343 = 50h + 27b

Solve the system.

see image.

The maximum profit if the profits per acre are $75 for corn and $40 for soybeans is $371,255.83. Therefore, the correct option is c.

To find the maximum profit from planting corn and soybeans, we can use linear programming. Let's first define the variables and write the constraints.

Let x be the number of acres of corn and y be the number of acres of soybeans.

1. Total acre constraint: x + y ≤ 6,000

2. Fertilizer/herbicide constraint: 9x + 3y ≤ 40,501

3. Labor constraint: 0.75x + y ≤ 5,250

The objective function to maximize is the profit function: P(x,y) = 75x + 40y

Now, we will use the Solver to find the maximum profit:

Step 1: Set up a spreadsheet with the constraints and the objective function.

Step 2: Go to the Data tab and click on Solver. If Solver is not available, you may need to add it in Excel Options.

Step 3: Set the objective function by selecting the cell with the profit function.

Step 4: Choose "Max" for the objective.

Step 5: Add the constraints by selecting the corresponding cells.

Step 6: Click on "Solve" and the Solver will find the optimal values for x and y.

After using Solver, we find that the optimal values are x = 4,363.89 (corn) and y = 1,636.11 (soybeans), which yields a maximum profit of $371,255.83. Therefore, the correct answer is c: $371,255.83

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Answer:

Well the equation of the line is -3x+4, so we know the slope is -3/1

Answer:

1/3

Step-by-step explanation:

Rise = 1

Run    3

The age of the artifact is 3523.77 years.

What is radioactive decay?

The process of radioactive decay is how an unstable atomic nucleus loses energy through radiation. A substance that has unstable nuclei is regarded as radioactive.

Here,

The half-life of the reaction is defined as the time required by a substance to reach half its initial concentration. It is represented by t(1/2)

 All radioactive decay processes follow the first-order reaction.

The equation for the half-life for first-order reaction follows:

t(1/2) = 0.693/k....(1)

where,

k = rate constant of a first-order reaction

Given value:

t(1/2) = 5715 years

Put the value of t in equation (1), and we get

k = 0.693/5715

k = 1.21×10⁻⁴yr

The integrated rate law expression for first-order reaction follows:

t = 2.303/k×㏒(a/(a-x))

where,

t = time period

a = initial concentration of the reactant = 58.2 counts per minute

(a-x) = Concentration of reactant left after time t = 38.0 counts per minute

k = rate constant of a first-order reaction

Put the values in the equation and we get

t = 2.303/1.21×10⁻⁴㏒58.2/38

t = 3523.77 years.

Hence, the age of the artifact is 3523.77 years.

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