Question 3(Multiple Choice Worth 1 points)
(03.06 LC)
Determine if the sequence is arithmetic or geometric, and find the common difference or ratio.
X
1
2
3 4
f(x) 81 72 63 54
O Arithmetic, common difference = 9
O Arithmetic, common difference = -9
O Gealmetric, common ratio = 9
Geometric, common ratio = -9

a) The area of the first circle is approximately 254.34 square inches

b) The area of the second circle is approximately 70650 square inches.

a) The area of a circle can be calculated using the formula A = πr², where π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.

For the first circle with a diameter of 18 inches, we can find the radius by dividing the diameter by 2:

r = 18/2 = 9 inches

Now we can calculate the area using the formula:

A = πr² = 3.14 x 9² = 254.34 square inches

Therefore, the area of the first circle is approximately 254.34 square inches.

b) For the second circle with a diameter of 25 feet, we need to convert the diameter to inches, since our formula uses radius in inches:

25 feet = 25 x 12 inches = 300 inches

Then we can find the radius by dividing by 2:

r = 300/2 = 150 inches

Now we can calculate the area using the formula:

A = πr² = 3.14 x 150² = 70650 square inches

Therefore, the area of the second circle is approximately 70650 square inches.

Note that the units for the second calculation are in square inches, not square feet, because we used the formula that requires radius in inches.

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a) To find out the speed at which the ball hit the ground, we can use the formula v = u + gt, where v is the final velocity, u is the initial velocity, g is the acceleration due to gravity, and t is the time taken.

Given that the ball was dropped, the initial velocity u is 0. Therefore, the equation simplifies to v = gt.

Using the value of g as 9.8 m/s² and the time taken as 4.2 seconds, we can calculate the final velocity:

v = 9.8 m/s² × 4.2 s = 41.16 m/s.

So, the ball was moving at a speed of 41.16 m/s when it hit the ground.

b) To find the height of the building, we can use the formula h = (1/2)gt², where h is the height, g is the acceleration due to gravity, and t is the time taken for the ball to fall.

Plugging in the values, we get:

h = (1/2) × 9.8 m/s² × (4.2 s)² ≈ 87.15 m.

Rounded to two decimal places, the height of the building is approximately 87.15 m.

c) The acceleration of the ball is the acceleration due to gravity, which is always directed downwards towards the center of the Earth. Its magnitude is 9.8 m/s², meaning that every second, the ball's speed increases by 9.8 m/s in the downward direction. Therefore, the acceleration of the ball is 9.8 m/s² downwards.

2. a) To find the initial velocity of the ball, we can use the equation v = u + gt.

b) To find the maximum height of the ball, we can use the formula h = (1/2)gt², where h is the height, g is the acceleration due to gravity, and t is the time taken for the ball to reach the maximum height.

c) The acceleration of the ball going up is still the acceleration due to gravity, which is always directed downwards towards the center of the Earth. However, since the ball is moving upwards, the acceleration is negative. Therefore, the acceleration of the ball going up is -9.8 m/s².

d) The acceleration of the ball going down is the acceleration due to gravity, which is always directed downwards towards the center of the Earth. Its magnitude is 9.8 m/s², and since the ball is moving downwards, the acceleration is positive. Therefore, the acceleration of the ball going down is +9.8 m/s².

e) The ball is slowing down when it reaches the maximum height because it momentarily stops before starting to fall down. At the maximum height, the ball's velocity is zero, and therefore, its acceleration is also zero. The ball is speeding up when it is thrown upwards and when it is falling down because its velocity is increasing in both cases.

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Options b, d, and e are the true statements about the substitution method.

b. It is useful to solve the integral ∫2x sin x^2 dx.

d. It utilizes the formula ∫ f(u(x))u'(x) dx = ∫ f(u) du.

e. It is based on the chain rule for derivatives.

The true statements about the substitution method are:

b. It is useful to solve the integral ∫2x sin x^2 dx.

The substitution method is commonly used to simplify integrals and make them easier to evaluate. It can be applied to various types of integrals, including the given example.

d. It utilizes the formula ∫ f(u(x))u'(x) dx = ∫ f(u) du.

The substitution method involves making a substitution in the integral by introducing a new variable. This formula represents the fundamental principle of substitution, where the derivative of the substituted function appears in the integral.

e. It is based on the chain rule for derivatives.

The substitution method is based on the chain rule of derivatives. By making an appropriate substitution, the integral can be transformed into a new form that corresponds to a derivative of a simpler function.

Therefore, options b, d, and e are the true statements about the substitution method.

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Answer:

$408.73

Step-by-step explanation:

To determine how much more the SUV will be worth than the car five years after their model years, we first need to calculate how much the car is worth five years after its model year.

The value of the car (in dollars, x years from its model year) can be predicted by the function f(x):

\(f(x)= 12000(0.89)^x\)

Therefore, to calculate how much the car will be worth five years after its model year, substitute x = 5 into the given function f(x):

\(\begin{aligned}x=5 \implies f(5)&=12000(0.89)^5\\&=12000(0.5584059449)\\&=6700.8713388\\&=6700.87\; \sf (nearest\;hundredth) \end{aligned}\)

Therefore, the car will be worth $6,700.87 five years from its model year.

From observation of the given table, the SUV will be worth $7,109.60 five years from its model year.

To calculate how much more the SUV will be worth than the car five years from their model years, subtract the amount the car will be worth from the amount the SUV will be worth:

\(7109.60-6700.87=408.73\)

Therefore, the SUV will be worth $408.73 more than the car five years after their model years.

Answer:

$408.73

Step-by-step explanation:

To determine how much more the SUV will be worth than the car five years after their model years, we first need to calculate how much the car is worth five years after its model year.

The value of the car (in dollars, x years from its model year) can be predicted by the function f(x):

Therefore, to calculate how much the car will be worth five years after its model year, substitute x = 5 into the given function f(x):

Therefore, the car will be worth $6,700.87 five years from its model year.

From observation of the given table, the SUV will be worth $7,109.60 five years from its model year.

To calculate how much more the SUV will be worth than the car five years from their model years, subtract the amount the car will be worth from the amount the SUV will be worth:

Therefore, the SUV will be worth $408.73 more than the car five years after their model years.

Answer:

8

Step-by-step explanation:

FH = FG+GH

15 = FG + 7

FG = 15 -7

FG = 8

False.

When conducting time series forecasting, it is not necessarily safest to utilize regression analysis. Regression analysis is a statistical method used to model the relationship between a dependent variable and one or more independent variables. However, it may not be the most appropriate technique for time series forecasting.

Time series forecasting involves analyzing and predicting patterns and trends in sequential data over time. Techniques specifically designed for time series analysis, such as ARIMA (Autoregressive Integrated Moving Average) models, exponential smoothing methods, or state space models, are generally more suitable for time series forecasting.

Regression analysis assumes that there is a linear relationship between variables, which may not hold in time series data where patterns can exhibit trends, seasonality, or other complex dynamics. Extrapolation, which involves extending a trend beyond the observed data range, can still occur in regression analysis if not properly accounted for.

Therefore, it is important to choose appropriate time series forecasting methods rather than relying solely on regression analysis to ensure accurate and reliable predictions.

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Answer to 2a: The mean of Asset A is 0.235  and the variance is 0.0123

Answer to 2b: The correlation coefficient between Asset A and C is approximately\(\(-0.670\) (Boom), \(-0.187\) (Average), \(-0.670\)\)(Bust).

2a. Mean of Asset A (Expected Value):

The mean of Asset A (E(A)) can be calculated as:

\(\[E(A) = \sum_{i} (x_i \cdot P_i)\]\)

where \(\(x_i\)\) represents the return on Asset A in each state and\(v \(P_i\)\) represents the probability of that state.

Using the given information, we have:

Boom:

\(\(E(A) = (0.35 \cdot 0.30) + (0.20 \cdot 0.50) + (0.05 \cdot 0.20) = 0.235\)\)

Average:

\(\(E(A) = (0.35 \cdot 0.30) + (0.20 \cdot 0.50) + (0.05 \cdot 0.20) = 0.235\)\)

Bust:

\(\(E(A) = (0.35 \cdot 0.30) + (0.20 \cdot 0.50) + (0.05 \cdot 0.20) = 0.235\)\)

Therefore, the mean of Asset A is\(\(E(A) = 0.235\).\)

2b. Correlation Coefficient of A and C:

The correlation coefficient\((\(\rho\))\)between Asset A and C can be calculated using the formula:

\(\[\rho = \frac{{\text{{Cov}}(A, C)}}{{\sigma_A \cdot \sigma_C}}\]\)

where\(\(\text{{Cov}}(A, C)\)\) represents the covariance between Asset A and C, and \((\sigma_A\)\) and\(\(\sigma_C\)\)represent the standard deviations of Asset A and C, respectively.

Using the given information, we have:

Boom:

\(\(\text{{Cov}}(A, C) = (0.35 - 0.235) \cdot (0.10 - 0.25) = -0.017\)\)

Average:

\(\(\text{{Cov}}(A, C) = (0.20 - 0.235) \cdot (0.15 - 0.25) = -0.005\)\)

Bust:

\(\(\text{{Cov}}(A, C) = (0.05 - 0.235) \cdot (0.35 - 0.25) = -0.017\)\)

Now, we calculate the standard deviations of Assets A and C:

\(\(\sigma_A = \sqrt{{\text{{Var}}(A)}} = \sqrt{0.0123} \approx 0.1108\)\)

\(\(\sigma_C = \sqrt{{\text{{Var}}(C)}} = \sqrt{0.0517} \approx 0.2274\)\)

Finally, we can calculate the correlation coefficient:

Boom:

\(\(\rho = \frac{{-0.017}}{{0.1108 \cdot 0.2274}} \approx -0.670\)\)

Average:

\(\(\rho = \frac{{-0.005}}{{0.1108 \cdot 0.2274}} \approx -0.187\)\)

Bust:

\(\(\rho = \frac{{-0.017}}{{0.1108 \cdot 0.2274}} \approx -0.670\)\)

Therefore, the correlation coefficient between Asset A and C is approximately\(\(\rho \approx -0.670\) (Boom), \(\rho \approx -0.187\) (Average), and \(\rho \approx -0.670\) (Bust).\)

Answer to 2a: \(The mean of Asset A is \(0.235\) and the variance is \(0.0123\.\)

Answer to 2b: The correlation coefficient between Asset A and C is approximately\(\(-0.670\) (Boom), \(-0.187\) (Average), \(-0.670\)\)(Bust).

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At 8000 feet MSL in the teardrop could a descent to 3,200 feet commence.

What is aircraft?

A vehicle that can fly is known as an aircraft. It does so by getting help from the air. It does this by either employing static lift, the dynamic lift of an airfoil or, in a few rare instances, the downward push from jet engines. Aerial vehicles include, but are not limited to, planes, helicopters, airships (including blimps), gliders, paramotors, and hot air balloons.

As given, your aircraft was cleared for the ils rwy 18 at Lincoln municipal and crossed the Lincoln Vortac at 5,000 feet MSL.

Therefore, at 8000 feet MSL in the teardrop could a descent to 3,200 feet commence.

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so hmmm tripling $380 we end up with $1140, now, since 7/8 is 0.875, that means that Layla's rate is 5.875, whilst Brandon's is 6.125.

\(~~~~~~ \stackrel{ \textit{\LARGE Layla}}{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 1140\\ P=\textit{original amount deposited}\dotfill &\$380\\ r=rate\to 5.875\%\to \frac{5.875}{100}\dotfill &0.05875\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years \end{cases}\)

\(1140 = 380\left(1+\frac{0.05875}{4}\right)^{4\cdot t} \implies \cfrac{1140}{380}=1.0146875^{4t} \\\\\\ 3=1.0146875^{4t}\implies \log(3)=\log(1.0146875^{4t}) \\\\\\ \log(3)=t\log(1.0146875^{4})\implies \cfrac{\log(3)}{\log(1.0146875^{4})}=t\implies \boxed{18.84\approx t} \\\\[-0.35em] ~\dotfill\)

\(~~~~~~ \stackrel{ \textit{\LARGE Brandon}}{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 1140\\ P=\textit{original amount deposited}\dotfill &\$380\\ r=rate\to 6.125\%\to \frac{6.125}{100}\dotfill &0.06125\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years \end{cases}\)

\(1140 = 380\left(1+\frac{0.06125}{12}\right)^{12\cdot t} \implies \cfrac{1140}{380}=\left( \cfrac{9649}{9600} \right)^{12t}\implies 3=\left( \cfrac{9649}{9600} \right)^{12t} \\\\\\ \log(3)=\log\left[ \left( \cfrac{9649}{9600} \right)^{12t} \right]\implies \log(3)=t\log\left[ \left( \cfrac{9649}{9600} \right)^{12} \right]\)

\(\cfrac{\log(3)}{ ~~ \log\left[ \left( \frac{9649}{9600} \right)^{12} \right] ~~ }=t\implies \boxed{17.98\approx t} \\\\[-0.35em] ~\dotfill\\\\ 18.84~~ - ~~17.98 ~~ \approx ~~ \text{\LARGE 0.86}\)

The effective interest method is used to amortize the bond premium. The carrying value of the bond increases by the effective interest each period, and the premium is amortized over the life of the bond. The journal entry for bond issuance is as follows: Dr. Cash 205,000, Dr. Premium on Bonds Payable 5,000, Cr. Bonds Payable 210,000

The effective interest method is a method of amortizing bond premium or discount that takes into account the time value of money. The effective interest is the interest that would be earned if the bond were purchased at its market value and held to maturity. The carrying value of the bond increases by the effective interest each period, and the premium is amortized over the life of the bond.

The journal entry for bond issuance records the proceeds from the sale of the bonds, the premium on bonds payable, and the bonds payable. The proceeds from the sale of the bonds are equal to the face value of the bonds plus the premium.

The premium on bonds payable is a liability that represents the excess of the issue price of the bonds over their face value. The bonds payable account is a long-term liability that represents the amount that the company owes to the bondholders.

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The Pythagorean theorem is a fundamental concept in geometry that relates the lengths of the sides of a right triangle. It states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Mathematically, it can be expressed as:

a² + b² = c²

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

The converse of the Pythagorean theorem states that if the square of the length of one side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.

The Pythagorean theorem is a powerful tool in solving problems involving right triangles. It allows us to calculate unknown side lengths or determine whether a triangle is a right triangle based on the lengths of its sides. It has numerous applications in various fields, including engineering, architecture, physics, and navigation.

Understanding the Pythagorean theorem and its converse is essential for working with right triangles and applying geometric principles. It provides a foundation for further exploration of trigonometry and advanced geometric concepts.

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The expression given is 30 x [(9 x 2) - (4 + 3)]. In order to find which expression has a value of 1, we must simplify the expression. First, we must solve the parentheses by adding 4 and 3 together, which equals 7, and multiplying 9 and 2 together, which equals 18.

So, the expression now becomes 30 x [18 - 7]. Next, we must solve the brackets by subtracting 7 from 18, which equals 11. So, the expression now becomes 30 x 11. Finally, we must multiply 30 and 11 together to get the final answer, which is 330. Therefore, the given expression does not have a value of 1.
Hello! Let's solve the given expression and check if its value is 1.

Expression: 30 x [(9 x 2) - (4 + 3)]

Step 1: Perform operations within the parentheses first.
9 x 2 = 18
4 + 3 = 7

Step 2: Substitute these values back into the expression.
30 x (18 - 7)

Step 3: Perform subtraction inside the parentheses.
30 x (11)

Step 4: Perform the final multiplication.
30 x 11 = 330

The given expression has a value of 330, not 1.

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The graph of 3x-2y≤6 is the third graph, for 3x-2y<6 is the first graph, for 3x-2y>6 is the fourth graph and for 3x-2y≥6 is the second graph. The solution has been obtained using concept of linear inequality.

What is linear inequality?

A linear inequality is one that would produce a linear equation if the equals relation were used instead of the inequality. When multiplying or dividing both sides by a negative number in order to solve the inequality, the direction of the inequality is reversed. The entire set of solutions to an inequality is known as the solution set.

We are given for graphs, of which two graphs are dotted and two are simple straight line graphs.

The dotted graphs are drawn for the inequalities having < or >

Whereas the simple straight line graphs are drawn for the inequalities having ≤ or ≥.

Now, to notice the shaded pattern, we will see whether the equations are true for (0,0) or not

1. 3x-2y≤6

⇒ 0≤6

So, the equation is true for the point.

Hence, the third graph represents this equation.

2. 3x-2y<6

⇒ 0<6

So, the equation is true for the point.

Hence, the first graph represents this equation.

3. 3x-2y>6

⇒ 0>6

So, the equation is false for the point.

Hence, the fourth graph represents this equation.

4. 3x-2y≥6

⇒ 0≥6

So, the equation is false for the point.

Hence, the second graph represents this equation.

Hence, the graphs are matched with the inequalities.

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Since, there are multiple questions so, the question answered above is attached below.

Answer:

(x-1)(x-2)

x=1, x=2

Step-by-step explanation:

The rate of increase of the depth of the water (W(t)) is constant.

What is rate ?

In mathematics and physics, the rate is a measure of change of a certain quantity with respect to another quantity. The rate can be a number, a ratio or a derivative. It is often represented by the symbol "d" or "dx/dt" or "dy/dt" and it measures how fast a quantity is changing.

Water is poured into the top half of a spherical tank at a constant rate, this means that the rate of increase of the depth of the water (W(t)) is constant.

In this case, W(t) is constant.

It is important to keep in mind that the rate of change of the function doesn't indicate the shape of the function, it just tells us the change of the dependent variable with respect to the independent variable. The shape of the function can be visualized by creating a graph of the function.

So , The rate of increase of the depth of the water (W(t)) is constant.

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Answer:

Step-by-step explanation:

30 boxes

The total number of boxes in which both the apples and snack bars can be evenly divided is 6.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that Xavier has 30 apples and 54 snack bars he is dividing up evenly in supply boxes that will contain both apples and snack bars.

Total item = 30 + 54 = 84

A common number between 30, 54 and 84 is 6. The number of apples in each box will be 5 and the snack bars will be 9.

Sum = 5 + 9 = 14

Total boxes = 84 / 14

Total boxes = 6

Therefore, the total number of boxes in which both the apples and snack bars can be evenly divided is 6.

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To prove the identity sinh(2x) = 2 sinh(x) cosh(x), we can use the definitions of sinh(x) and cosh(x) and apply trigonometric identities for exponential functions.

We start with the left-hand side of the identity, sinh(2x). Using the definition of the hyperbolic sine function, sinh(x) = (e^x - e^(-x))/2, we can substitute 2x for x in this expression, giving us sinh(2x) = (e^(2x) - e^(-2x))/2.

Next, we focus on the right-hand side of the identity, 2 sinh(x) cosh(x). Again using the definitions of sinh(x) and cosh(x), we have 2 sinh(x) cosh(x) = 2((e^x - e^(-x))/2)((e^x + e^(-x))/2).

Expanding this expression, we get 2 sinh(x) cosh(x) = (e^x - e^(-x))(e^x + e^(-x))/2.

By simplifying the right-hand side, we have (e^x * e^x - e^x * e^(-x) - e^(-x) * e^x + e^(-x) * e^(-x))/2.

This simplifies further to (e^(2x) - 1 + e^(-2x))/2, which is equal to the expression we derived for the left-hand side.

Hence, we have proved the identity sinh(2x) = 2 sinh(x) cosh(x) by showing that the left-hand side is equal to the right-hand side through the manipulation of the exponential functions.

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Answer:

4

Step-by-step explanation:

For this, you need to find the scale factor of two sides that are already given to you.

So, we will have to use the hypotenuse and one of the legs to make sure there is an accurate scale factor.

Hypotenuse:

15 / 5 = 3

Leg:

6 / 2 = 3

____________

So the scale factor is 3.

Using the leg (with the x) we need to divide 12 by the scale factor (3) to give us what x is equal to.

12 / 3 = 4

So, the answer is 4.

The total amount due on the invoice is $324.18

What is meant by amount?

The term "quantity" refers to the amount or total amount of something, usually expressed in numbers or measures. It can refer to physical objects, money, time, or abstract concepts such as energy or effort.

What is meant by invoice?

An invoice is a document that lists the goods or services provided by a seller to a buyer and the amount to be paid. It contains details such as the description of the item, the quantity, the price and the terms of payment.

According to the given information

For the first item, the unit price is $4.89 and 20 units were bought, so the cost of this item is:

20 x $4.89 = $97.80

For the second item, the unit price is $5.49 and 10 units were bought, so the cost of this item is:

10 x $5.49 = $54.90

For the third item, the unit price is $6.19 and 15 units were bought, so the cost of this item is:

15 x $6.19 = $92.85

For the fourth item, the unit price is $1.89 and 20 units were bought, so the cost of this item is:

20 x $1.89 = $37.80

The total cost of the items before taxes and shipping charges are applied is:

$97.80 + $54.90 + $92.85 + $37.80 = $283.35

To calculate the total amount due on the invoice, we need to add the sales tax and shipping charges to the total cost of the items. The sales tax is 7% of the total cost of the items:

7% x $283.35 = $19.83

The shipping charge is $21.00.

Therefore, the total amount due on the invoice is:

$283.35 + $19.83 + $21.00 = $324.18

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Given:

a.) A person had 14,000 infested in two accounts.

b.) One paying 9% simple interest.

c.) One paying 10% simple interest.

Let,

x = the amount invested at 9% simple interest

y = the amount invested at 10% simple interest

1.) We know the total amount of money invested is $14,000. We get,

x + y = 14,000

2.) We know that the total interest for the year for the two accounts is $1432. We get,

0.09*x + 0.1*y = 1,339

Let's equate the two equations,

x = 14,000 - y (Substitute for x)

0.09*(14,000 - y) + 0.1*y = 1,339

1,260 - 0.09y + 0.1y = 1,339

0.1y - 0.09y = 1,339 - 1,260

0.01y = 79

0.01y/0.01 = 79/0.01

y = 7,900

Therefore, $7,900 was invested at the rate of 10% simple interest.

Let's determine x, substituting y = 7,900 in x + y = 14,000.

x + y = 14,000

x + 7,900 = 14,000

x = 14,000 - 7,900

x = 6,100

Therefore, $6,100 was invested at the rate of 9% simple interest.

Answer:

y = 3x + 4

Step-by-step explanation:

Because $4 is your base pay, it is your y-intercept. And because it is $3 per child, then that is your slope. "x" represents how many objects/people/etc. there could be.

Answer:

The triandgle

Step-by-step explanation:

10 (11.3) + 4 = 113 + 4  = 117

Perimeter = square's side times 4

117 * 4 = 468 cm

15 (11.3) - 5 = 169.5 - 5 = 164.5

Perimeter = triangle's side times 3

164.5 * 3 = 493.5 cm

Answer:

1952

Step-by-step explanation:

Just add lol

a. The rectangle with dimensions 5 cm × 5 cm has the minimum perimeter of 20 cm.

b.  There is no maximum value for the perimeter of rectangles with a fixed area of 25 cm^2.

(a) To minimize the perimeter of rectangles with area 25 cm^2, we can use the fact that the perimeter of a rectangle is given by P = 2(l + w),  . We want to minimize P subject to the constraint that lw = 25.

Using the constraint to eliminate one variable, we have:

l = 25/w

Substituting into the expression for the perimeter, we get:

P = 2(25/w + w)

To minimize P, we need to find the value of w that minimizes this expression. We can do this by finding the critical points of P:

dP/dw = -50/w^2 + 2

Setting this equal to zero and solving for w, we get:

-50/w^2 + 2 = 0

w^2 = 25

w = 5 or w = -5 (but we discard this solution since w must be positive)

Therefore, the width that minimizes the perimeter is w = 5 cm, and the corresponding length is l = 25/5 = 5 cm. The minimum perimeter is:

P = 2(5 + 5) = 20 cm

So the rectangle with dimensions 5 cm × 5 cm has the minimum perimeter of 20 cm.

(b) There is no maximum perimeter of rectangles with area 25 cm^2. As the length and width of the rectangle increase, the perimeter also increases without bound. Therefore, there is no maximum value for the perimeter of rectangles with a fixed area of 25 cm^2.

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Answer:

1.823835

If this is what you are looking for

Answer:

E

Step-by-step explanation:

Answer:

125/1000

Step-by-step explanation:

Answer:

Im really sorry if this is wrong, i'm just trying to help cause everyone is giving you fake answers

I think the answer may be 336/55

(Decimal: 6.10909)

Step-by-step explanation:

Karen that has a piece of fabric that is 1 187/240 yards long needs to trim 227/240 yards

Is a number that expresses the portion of some number over a total. The number that expresses the portion is known as the numerator and the number that expresses the total is known as the denominator.

To solve this problem we must perform the corresponding algebraic operations with mixed fraction.

Data of the problem:

A mixed operation is solved as follows:

For the denominator: the same denominator is placed.

For the numerator:

The value of the denominator is multiplied by the integer component.

The result is added to the numerator of the fraction.

We transform the mixed fractions into improper fractions and we have:

1 187/240 =

[(240*1) + 187)] /240=

[240+ 187] /240=

427/240

Calculating how many yards should she trim:

Yards to trim: 427/240 - 5/6

Yards to trim: (427 - 200) / 240

Yards to trim: 227/240

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