The mean number of sit-ups


done by a group of students is


46 with a standard deviation


of 7. If Rylee's Z-score was


1. 8, how many sit ups did she


do?

a) It is verified that the situation is binomial

b. Probability of exactly coining 4 times is 1.83 × 10⁻³

c. Probability of winning atleast 3 times is 0.0234

d. Mean number of wins is 0.555

The total number of outcomes per toss is 6×6×6=216

a) Number of trails n = 20

Probability of win P = 6/216 = 1/36

Probability of lost Q = 1 - P

= 1 - 1/36

= 35/36

The outcome has two possibilities with P = 1/36, Q = 35/36  and with n = 20 times. Hence, it is binomial.

(B) Probability of exactly coining 4 times

[tex]P= C^{20}_{4} P^4Q^{16}[/tex]

= 4845 × (1/36)⁴ × (35/36)¹⁶

= 1.83 × 10⁻³

(C) Probability of winning atleast 3 times

[tex]P= 1-C^{20}_{0} P^0Q^{20}-C^{20}_{1} P^1Q^{19}-C^{20}_{2} P^2Q^{18}[/tex]

= 1 - 1 × (1/36)⁰ × (35/36)²⁰ - 20 × (1/36)¹ × (35/36)¹⁹ - 190 × (1/36)² × (35/36)¹⁸

= 1 - 0.5692 - 0.3252 - 0. 0882

= 0.0234

(D) Mean number of wins = nP

= 20 × (1/36)

= 0.555

a) It is verified that the situation is binomial

b. Probability of exactly coining 4 times is 1.83 × 10⁻³

c. Probability of winning atleast 3 times is 0.0234

d. Mean number of wins is 0.555.

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One way to model this situation is by using a probability distribution, such as the binomial distribution. The binomial distribution models the probability of a certain number of successes (in this case, rain) in a fixed number of trials (in this case, school days during springtime).

Let's say we want to simulate whether it will be raining when school is dismissed on a particular day during springtime. We can define a success as rain and a failure as no rain. Then, the probability of success (rain) is 0.4, and the probability of failure (no rain) is 0.6.

To simulate whether it will be raining on a particular day, we can use a random number generator to generate a value between 0 and 1. If the value is less than or equal to 0.4, we can consider it a success (rain) and if it's greater than 0.4, we can consider it a failure (no rain).

We can repeat this process for a large number of trials (school days during springtime) to simulate the probability of rain over a given period of time. By keeping track of the number of successes (rainy days) and failures (non-rainy days), we can estimate the probability of rain during springtime when school is dismissed.

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The length of SQ to the nearest tenth of a foot is approximately 2.1 feet.

To find the length of SQ, we can use trigonometry. First, we can find the measure of angle R by subtracting the measures of angles Q and S from 180°:

R = 180° - 90° - 6° = 84°

Then, we can use the sine function to find the length of SX (which is equal to SQ):

sin(Q) = SQ / RS

sin(6°) = SQ / 20

SQ = 20 * sin(6°)

SQ ≈ 2.07 feet (rounded to the nearest tenth of a foot)

Therefore, the length of SQ to the nearest tenth of a foot is approximately 2.1 feet.

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The length of the main span of the George Washington Bridge is 3500 feet.

Let x be the length of the main span of the George Washington Bridge.

We know that the main span of the Walt Whitman Bridge is 600 feet longer than two-fifths of the length of the main span of the George Washington Bridge, so we can write the equation:

2000 = (2/5)x + 600

To solve for x, we can start by isolating the term with x on one side of the equation:

(2/5)x = 2000 - 600

(2/5)x = 1400

Then, we can solve for x by multiplying both sides by the reciprocal of (2/5):

x = 1400 / (2/5)

x = 3500

Therefore, the length of the main span of the George Washington Bridge is 3500 feet.

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Answer:

$444.89

Step-by-step explanation:

PV = $400

i = 2.15%

n = 5

Compound formula:

FV = PV (1 + i)^n

FV = 400 (1 +2.15%)^5

FV = $444.89 (round to nearest cents)

The probability that Lucky will get different colored socks is 1/6 or 1 out of 6.

To solve this problem, we can use the concept of probability and combinations.

Step 1: Determine the total number of possible outcomes.

When Lucky selects two socks without replacement, there are a total of 13 socks in the bag (5 red + 8 blue). So, the total number of possible outcomes is given by selecting 2 socks out of 13, which is represented as C(13, 2) or 13 choose 2.

C(13, 2) = (13!)/(2!(13-2)!) = (13 * 12)/(2 * 1) = 78

Step 2: Determine the number of favorable outcomes.

For Lucky to get different colored socks, there are two cases to consider: selecting a red sock first and a blue sock second, or selecting a blue sock first and a red sock second.

Case 1: Red sock first, then blue sock:

The number of ways to select one red sock out of five is C(5, 1) = 5. After selecting one red sock, there are eight blue socks remaining, and Lucky needs to select one blue sock out of eight, which is C(8, 1) = 8.

Case 2: Blue sock first, then red sock:

The number of ways to select one blue sock out of eight is C(8, 1) = 8. After selecting one blue sock, there are five red socks remaining, and Lucky needs to select one red sock out of five, which is C(5, 1) = 5.

So, the total number of favorable outcomes is 5 + 8 = 13.

Step 3: Calculate the probability.

The probability of getting different colored socks is the ratio of the number of favorable outcomes to the total number of possible outcomes:

P(Different Colored Socks) = Number of Favorable Outcomes / Total Number of Possible Outcomes

= 13 / 78

= 1/6

Therefore, the probability that Lucky will get different colored socks is 1/6 or 1 out of 6.

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Therefore , the solution of the given problem of equation comes out to be False.

In order to demonstrate consistency between two opposing statements, variable words are frequently used in sophisticated algorithms. Equations are academic phrases that are used to demonstrate the equality of different academic figures. Consider expression the details as y + 7 offers. In this case, elevating produces b + 7 when partnered with building y + 7.

Here,

False.

The order of operations we use to solve two-step equations is the same order we use to solve every other mathematical statement,

which is commonly recalled by the acronym PEMDAS. (parentheses, exponents, multiplication and division from left to right, and addition and subtraction from left to right).

The fundamental distinction is that we are carrying out the operations against the equation's representation. For instance, consider the following equation:

=> 2x + 5 = 11

To get the following result, we would first subtract 5 from both sides, then divide by 2.

=> x = 3

In order to "undo" the operations that were carried out on the variable in the original equation, we are utilising the same series of operations as usual, but in reverse order.

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Answer:

-7x^2 + 15x +7

Step-by-step explanation:

-7x^2 + 5x + 10 - (-10x + 3)

-7x^2 + 5x + 10 + 10x -3.......when u distribute it multiple by -1

-7x^2 + 15x +7 ...... simplify by collecting like term.

Answer:  In order least to greatest, our answer would be-

2.704 ,  2.74  ,  4.2  , 4.27  ,  4.72

.70 is less than .74. In the second set of numbers .2 is less than .27, while they are all less than .72, which gives us the number arrangement above.

I hope this helped & Good Luck!!!

Answer: The answer is 2.704, 2.74, 4.2, 4.27, 4.72

Step-by-step explanation:

The height of the cone is 30 cm

The first step is to write out the parameters given in the question

Volume of the cone= 2560π cm³

Diameter of the circular base is 32 cm

radius= diameter/2

= 32/2

= 16

The formula for calculating the height of the cone is

Height= volume ÷ 1/3 πr²

height= 2560 πcm³ ÷ 1/3 πr²

height= 2560 ÷ 0.333(16²)

height= 2560 ÷ 0.333(256)

height= 2560÷ 85.248

height= 30

Hence the height of the cone is 30 cm

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Answer:

height = 9.54cm

Step-by-step explanation:

Volume of a cone = 2560cm³

Radius = diameter/ 2 = 32/2 = 16

height = ?

volume of a cone =

[tex]volume \: of \: a \: cone = \frac{1}{3} \pi {r}^{2} h \\ 2560 = \frac{1}{3} \times \frac{22}{7} \times 16 \times 16 \times h \\ 2560 = \frac{22}{21} \times 256 \times h \\ 2560 = \frac{5,632h}{21} \\ 21 \times 2560 = 21 \times \frac{5632h}{21} \\ 53,760 = 5632h \\ \frac{53760}{5632} = \frac{5632h}{5632} \\ 9.54cm = h[/tex]

height = 9.54cm

The inequailty y < m + 4 would be true when m = -4 and all values of y are less than 0

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

The statement that m = -4

The above value implies that we substitute -4 for m in an inequality and solve for the other variable (say y)

Take for instance, we have

y < m + 4

Substitute the known values in the above equation, so, we have the following representation

y < -4 + 4

Evaluate

y < 0

This means that the inequailty y < m + 4 would be true when m = -4 and all values of y are less than 0

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Answer:  325

Step-by-step explanation:

15*30-5*5-20*5=325

Answer: 875 square feet.

Step-by-step explanation: (25x30)+(5x20)+25

a) We can conclude that there is significant evidence that the probability of heads is not 0.5.

b) A 95% confidence interval for the true probability of heads is (0.4872, 0.5262).

a) To test whether the probability of heads is significantly different from 0.5, we can use a two-tailed z-test with a significance level of 0.05. The null hypothesis (H₀) is that the probability of heads is 0.5, while the alternative hypothesis (Hₐ) is that it is not 0.5.

The test statistic is given by:

z = (x - np) / √(np(1-p))

where x is the number of heads observed (5067), n is the total number of coin tosses (10,000), and p is the hypothesized probability of heads under the null hypothesis (0.5).

Plugging in the values, we get:

z = (5067 - 5000) / √(10,000 * 0.5 * 0.5) = 2.20

The P-value for this test is the probability of getting a z-score greater than 2.20 or less than -2.20, which is approximately 0.0287. Since the P-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is significant evidence that the probability of heads is not 0.5.

b) To find a 95% confidence interval for the true probability of heads, we can use the formula:

p ± z*√(p(1-p)/n)

where p is the sample proportion (5067/10000), n is the sample size (10,000), and z is the critical value from the standard normal distribution corresponding to a 95% confidence level (1.96).

Plugging in the values, we get:

p ± 1.96*√(p(1-p)/n) = 0.5067 ± 0.0195

So a 95% confidence interval for the true probability of heads is (0.4872, 0.5262). This means that we can be 95% confident that the true probability of heads falls within this interval based on the observed sample proportion.

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Answer:

Based on the given information, we can conclude that the graph represents a quadratic function. The vertex of the parabola is located at (0, 9) and the function passes through several points including (-4, -7), (-3, 0), (3, 0), and (4, -7).

To find the equation of the function, we need to determine the value of "a" in the equation f(x) = ax^2 + bx + c. Since the vertex is located at (0, 9), we know that the x-coordinate of the vertex is 0. Therefore, we can use the vertex form of the equation, which is f(x) = a(x - 0)^2 + 9, or simply f(x) = ax^2 + 9.

Next, we can use one of the given points to solve for "a". Let's use the point (-3, 0).

0 = a(-3)^2 + 9

0 = 9a - 9

9 = 9a

a = 1

Therefore, the value of "a" in the equation of the function is B. 1.

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According to the above, the fishing population is divided into 53% prefer fresh water and 47% prefer salt water.

To find the percentage of people that make up each group, we must find the total number of people who were surveyed:

228 + 245 + 242 + 285 = 1,000

Once we find the total number of people who took the survey, we can find the percentage of each value by making rules of three as shown below:

Age 30 and younger and Saltwater fishing:

1,000 = 100%

228 = ?%

228 * 100 / 1,000 = 22.8%

Age 30 and younger and Freshwater fishing:

1,000 = 100%

245 = ?%

245 * 100 / 1,000 = 24.5%

Over 30 years old and Saltwater fishing:

1,000 = 100%

242 = ?%

242 * 100 / 1,000 = 24.2%

Over 30 years old and Freshwater fishing:

1,000 = 100%

285 = ?%

285 * 100 / 1,000 = 28.5%

To find the other percentages we must find the total number of fishermen by age ranges and by fishing preference:

Age ranges

228 + 245 = 473

242 + 285 = 527

1,000 = 100%

473 = ?%

473 * 100 / 1,000 = 47.3%

1,000 = 100%

527 = ?%

527 * 100 / 1,000 = 52.3%

Fishing mode preferences

228 + 242 = 470

245 + 285 = 530

1,000 = 100%

530 = ?%

530 * 100 / 1,000 = 53%

1,000 = 100%

547 = ?%

470 * 100 / 1,000 = 47%

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Answer:

A = P(1 + r/n)^(n*t) is the formula

Where:

A = the account balance after t years

P = the principal amount (initial investment)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time in years

P = $6,154

r = 0.08 (8% expressed as a decimal)

n = 52 (compounded weekly)

t = 10

A = 6154(1 + 0.08/52)^(52*10)

A ≈ $14,239.44

Therefore, the account balance after 10 years will be approximately $14,239.44.

This function is an example of exponential decay because the base of the exponential term (2/7) is between 0 and 1. and the y-intercept is 8.

To find the y-intercept, we need to evaluate the function when x=0, which gives:

y = 8 (2/7)^0 = 8

The given function is an example of exponential decay. In an exponential function, if the base of the exponent is between 0 and 1, the function shows exponential decay, and if it is greater than 1, the function shows exponential growth.

In the given function y = 8 (2/7)^x, the base of the exponent is 2/7, which is less than 1. This means that as the value of x increases, the value of the function decreases at a decreasing rate, which is the characteristic of exponential decay.

To find the y-intercept of the function, we can substitute x=0 in the given function. When x=0, we have:

y = 8 (2/7)^0

y = 8 x 1

y = 8

This means that the y-intercept of the function is (0, 8), which is the point where the function intersects the y-axis. In this case, it represents the initial value of the function when x=0.

Therefore, This function is an example of exponential decay because the base of the exponential term (2/7) is between 0 and 1. and the y-intercept is 8.

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The surface area of the cylindrical food storage container given by the formula SA = 2πrh + 2πr² is 954. 56 inch².

The region is the space taken up by a flat, two-dimensional surface. Its unit of measurement is the square. A three-dimensional object's surface area is the area occupied by its outside surface. It is also measured in square units.

Surface area and volume are calculated for each geometric object in three dimensions. The surface area of an object refers to the space that it takes up.

As, we Know the Surface Area of Cylinder

= 2πr² + 2πrh

Radius of the base = 8 inches

Height of the cylinder = 11 inches.

Now, putting the values we get

= 2πr² + 2πrh

= 2 x 3.14 x 8 x 8 + 2 x 3.14 x 8 x 11

= 401.92 + 552.64

= 954. 56 inch²

Therefore, the surface area of the cylinder is 954. 56 inch².

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Complete question

Use the formula SA = 2πrh + 2πr2 to find is the surface area of the cylindrical food storage container. Use 3. 14 for π. Round your answer to the nearest hundredth of a square inch

To find the slope of the tangent line to the polar curve, we need to find the derivative of the equation with respect to θ.

First, we can convert the polar equation into rectangular coordinates using the conversions rcos(θ) = x and rsin(θ) = y:
rcos(θ) = (1-2sin(θ))cos(θ)
r = x/cos(θ)
x/cos(θ) = 1 - 2sin(θ)
x = cos(θ) - 2sin(θ)cos(θ)
y = sin(θ) - 2sin^2(θ)

Next, we can find the derivative of y with respect to x using the chain rule:
dy/dx = (dy/dθ) / (dx/dθ)
dy/dθ = cos(θ) - 4sin(θ)cos(θ)
dx/dθ = -sin(θ) - 2cos^2(θ)
Plugging in the value of e for θ, we get:
dy/dθ = cos(e) - 4sin(e)cos(e)
dx/dθ = -sin(e) - 2cos^2(e)

Finally, we can find the slope of the tangent line by taking the ratio of dy/dθ to dx/dθ:
slope = (cos(e) - 4sin(e)cos(e)) / (-sin(e) - 2cos^2(e))
This is the slope of the tangent line to the polar curve at the point specified by the value of e.
Hi! I'd be happy to help you with your question. To find the slope of the tangent line to the polar curve r = 1 - 2sin(θ) at a specific value of θ, we'll first need to convert the polar equation into Cartesian coordinates.
Let's recall the conversion formulas:
x = r*cos(θ)
y = r*sin(θ)

Now, substitute the polar curve equation into these formulas:
x = (1 - 2sin(θ))*cos(θ)
y = (1 - 2sin(θ))*sin(θ)
To find the slope, we need the derivative of y with respect to x, which is dy/dx. To do this, we'll first find dy/dθ and dx/dθ.
Differentiating both x and y with respect to θ:
dx/dθ = -2cos(θ)^2 + 2sin(θ)cos(θ)
dy/dθ = -2sin(θ)^2 + 2sin(θ) - 2sin(θ)cos(θ)
Now, we find the derivative of y with respect to x:
dy/dx = (dy/dθ) / (dx/dθ)
dy/dx = (-2sin(θ)^2 + 2sin(θ) - 2sin(θ)cos(θ)) / (-2cos(θ)^2 + 2sin(θ)cos(θ))

Now, you can plug in the specific value of θ for which you want to find the slope of the tangent line to the polar curve, and simplify the expression to obtain the final answer.

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The statements that are always true for geometric shapes are:

1) Always

2) Always

3) Sometimes

4) Never

1) A square is a type of rectangle in which all four sides are equal. Therefore, all of the properties that apply to rectangles (such as having four right angles and opposite sides that are parallel) also apply to squares, making the statement "A square is a rectangle" always true.

2) The diagonals of a rhombus are always perpendicular to each other. This is because a rhombus has opposite sides that are parallel, and the diagonals bisect each other at a right angle.

3) The diagonals of a rectangle are sometimes equal. This is true only if the rectangle is a square (where all four sides are equal) or if the rectangle is a "golden rectangle" (where the ratio of the longer side to the shorter side is equal to the golden ratio).

4) The diagonals of a trapezoid are never equal unless the trapezoid happens to be an isosceles trapezoid (where the legs are equal in length). In general, the diagonals of a trapezoid will have different lengths, and there is no special relationship between them.

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The probability that the first 5 seasons you receive in the mail are the first 5 seasons that were made, in the correct order is given as follows:

p = 1/30240.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

5 seasons are going to be shown from a set of 10, and the order is relevant, hence the permutation formula is used to obtain the total number of outcomes, as follows:

P(10, 5) = 10!/5!

P(10, 5) = 30240.

Only one of the outcomes has the correct seasons and order, hence the probability is given as follows:

p = 1/30240.

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The area of the shaded region of the circle is A = 57,918.5 feet²

Given data ,

First, we need to find the area of the quarter circle:

Area of quarter circle = (1/4)  π ( r )²

= (1/4)  π ( 290 )²

= 66,018.5 feet²

Next, we need to find the area of the square:

Area of square = side²

= 90²

= 8,100 feet²

Now, we can find the area of the shaded section by subtracting the area of the square from the area of the quarter circle:

Area of shaded section = Area of quarter circle - Area of square

= 66,018.5 feet² - 8,100 feet²

= 57,918.5 feet²

Hence , the area of the shaded section of the field is 57,918.5 feet²

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The net present value of this investment, assuming a required 8% return, is approximately $13,829.

To calculate the net present value (NPV) of this investment, we'll first find the present value of the net cash flows and the salvage value, then subtract the initial investment.

For the net cash flows, we'll use the Present Value of Annuity (PVA) formula:

PVA = Net Cash Flow * [(1 - (1 + r)^(-n)) / r]

Where:
- Net Cash Flow is $11,000
- r is the required return (0.08)
- n is the number of years (7)

PVA = 11,000 * [(1 - (1 + 0.08)^(-7)) / 0.08]
PVA = 11,000 * 4.99271
PVA ≈ $54,920

Next, we'll find the present value of the salvage value at the end of year 7:

PV_salvage = Salvage Value / (1 + r)^n
PV_salvage = 6,700 / (1 + 0.08)^7
PV_salvage ≈ $3,909

Now, we can calculate the NPV by adding the present values and subtracting the initial investment:

NPV = (PVA + PV_salvage) - Initial Investment
NPV = (54,920 + 3,909) - 45,000
NPV ≈ $13,829

The net present value of this investment, assuming a required 8% return, is approximately $13,829.

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Answer:

Step-by-step explanation:

the point at which the lines representing the linear equations intersect

The volume of the cylinder is 3811.7 cubic units when the radius is 9 and the width is 15.

Volume = π × radius² × height

Substitute the given values:
Volume = π × (9)² × 15

Squaring the radius:
Volume = π × 81 × 15

Multiplying the values together:
Volume = π × 1215

Calculating the volume using the approximate value of π (3.14):
Volume ≈ 3.14 × 1215

Calculating the final volume:
Volume ≈ 3811.7 cubic units

So, the volume of the cylinder with a radius of 9 and a height of 15 is approximately 3811.7 cubic units.

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The fraction, David used 13/8 cups of blueberries for the pancakes.

Let's solve it step-by-step using the given information.

1. David has 3 1/2 cups of blueberries.
2. He uses 1/4 cup for a breakfast smoothie.
3. He uses 1/2 of the remaining blueberries for pancakes.

Step 1: Calculate the remaining blueberries after making the smoothie.
3 1/2 - 1/4 = (7/2) - (1/4)

To subtract the fractions, they need a common denominator, which in this case is 4.

(7/2) * (2/2) - (1/4) = (14/4) - (1/4) = 13/4 cups

Step 2: Calculate the amount of blueberries used for the pancakes.
David uses 1/2 of the remaining blueberries for the pancakes, so:

(13/4) * (1/2) = 13/8 cups

David uses 13/8 cups of blueberries for the pancakes.

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The limit of Ln as n approaches infinity is -1/2, and it can be expressed as the definite integral ∫0¹ (x - 1) dx over the interval [0, 1].

To express the limit of Ln as n approaches infinity as a definite integral, we can use the definition of the definite integral as the limit of a Riemann sum. We can divide the interval [0, 1] into n subintervals of equal width Δx = 1/n, and evaluate Ln as the limit of the Riemann sum:

Ln = 1/n * [f(0) + f(Δx) + f(2Δx) + ... + f((n-1)Δx)]

where f(x) = x - 1 is the function being integrated.

Taking the limit as n approaches infinity, we have:

lim(n→∞) Ln = lim(n→∞) 1/n * [f(0) + f(Δx) + f(2Δx) + ... + f((n-1)Δx)]

= ∫0¹ (x - 1) dx

where we have used the fact that the limit of the Riemann sum is equal to the definite integral of the function being integrated.

Therefore, the limit of Ln as n approaches infinity is equal to the definite integral of (x - 1) over the interval [0, 1].

So,

lim(n→∞) Ln = ∫0¹ (x - 1) dx = [x¹ - x] from 0 to 1

= [1/2 - 1] - [0 - 0]

= -1/2

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If Polly reduced the price and sold 3 of the remaining necklaces for £8 each, she sold the remaining necklaces for £6.70 each.

First, let's find the original cost of the necklaces:
50 necklaces * £5 = £250

Now, let's calculate the profit Polly made:
£250 * 70% = £175

So, the total amount she made from selling the necklaces is:
£250 + £175 = £425

Polly sold 40% of the necklaces for £11 each:
50 necklaces * 40% = 20 necklaces
20 necklaces * £11 = £220

She sold 3 necklaces for £8 each:
3 necklaces * £8 = £24

Now let's find the amount left after selling these necklaces:
£425 - £220 - £24 = £181

Polly has 50 - 20 - 3 = 27 necklaces remaining. Let's find the price at which she sold each of the remaining necklaces:
£181 / 27 = £6.70

So, Polly sold the remaining necklaces for £6.70 each.

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The best point estimate is 15 hours. The 95% confidence interval for the population mean is (14.71, 15.29).

The best point estimate of the population mean is the sample mean, which is 15 hours since it was stated in the problem that the average time spent by college students on computer gaming is 15 hours.

To calculate the 95% confidence interval for the population mean, we use the formula:

CI = [tex]\bar{X}[/tex] ± z*(σ/√n)

where [tex]\bar{X}[/tex] is the sample mean, z is the z-score corresponding to the desired level of confidence (in this case, 95% corresponds to a z-score of 1.96), σ is the population standard deviation (given as 3), and n is the sample size (given as 350).

Plugging in the values, we get:

CI = 15 ± 1.96*(3/√350)

Simplifying, we get:

CI = 15 ± 0.29

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The width of the swamp is 12 feet, and the length is 50 feet.

length is 10 less than 5 times its width. We can write that as:

Equation for length:

L = 5W - 10

We also know that the perimeter of the swamp is 124 feet. The formula for the perimeter of a rectangle is:

Perimeter = 2(Length + Width)

So, we have:

124 = 2(L + W)

Now, we can substitute the expression for L from the first equation into the second equation:

124 = 2((5W - 10) + W)

Now, we can solve for W:

Step 2: solving for width

124 = 2(6W - 10)

62 = 6W - 10

72 = 6W

W = 12

Now that we have the width (W = 12 feet), we can find the length by plugging the width back into the equation for L:

Step 1: solving for length

L = 5W - 10

L = 5(12) - 10

L = 60 - 10

L = 50

So, the width of the swamp is 12 feet, and the length is 50 feet.

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The swamp has a perimeter 124 feet the length L of the swamp is 10 less than 5 times it width What are the length and the width of the swamp