Is it possible for the rug to have an area of 71.25 square feet? If it is possible, give approximate dimensions of the rectangle and explain your work. If it is not possible, explain why not.

Solving a set of linear inequalities in several variables is an NP-hard problem, meaning there is no known polynomial-time algorithm to find a satisfying assignment.

Unlike linear equalities, solving a set of linear inequalities in several variables is an NP-hard problem. This means that there is no known polynomial-time algorithm to find a satisfying assignment for all instances of such problems. The complexity arises from the fact that there are infinitely many potential solutions, making it challenging to determine whether a feasible assignment exists or not. To find a satisfying assignment for linear inequalities, algorithms typically use heuristics or approximation techniques that do not guarantee optimality or completeness. Various methods, such as linear programming or constraint satisfaction algorithms, can be employed, but they may have exponential time complexity in the worst case. Therefore, solving a set of linear inequalities generally requires more computational resources and time compared to solving linear equalities.

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The degree form for 3π/4 radians is 135°.The degree form for 3π/4 radians is 135°. To convert radians to degrees, we multiply the radian measure by the conversion factor of 180°/π.

In this case, we have (3π/4) * (180°/π) = (3 * 180°) / 4 = 540° / 4 = 135°. Therefore, 3π/4 radians is equivalent to 135° in the degree form.

To convert an angle from radians to degrees, we use the conversion factor of 180°/π. This conversion factor represents the relationship between a full circle (360°) and 2π radians.

In this case, we want to convert the angle 3π/4 radians to degrees. We multiply the radian measure (3π/4) by the conversion factor (180°/π):

(3π/4) * (180°/π) = (3 * 180°) / 4 = 540° / 4 = 135°

By canceling out the common factor of π and simplifying the expression, we find that 3π/4 radians is equal to 135°.

Therefore, the degree form of the angle 3π/4 radians is 135°.

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The 99% confidence interval for the true proportion of undergraduate college students with home internet access is: 0.872 ± 0.057 or (0.815, 0.929).

To estimate the true proportion of undergraduate college students (18-23 years) with home internet access, we can use a confidence interval.

The point estimate for the proportion is 157/180 = 0.872. To find the margin of error, we can use the formula:

Margin of error = z* (sqrt(p_hat*(1-p_hat)/n))

where z* is the critical value for the desired confidence level, p_hat is the sample proportion, and n is the sample size.

For a 99% confidence level, the critical value is 2.576. Plugging in the values, we get:

Margin of error = 2.576 * (sqrt(0.872*(1-0.872)/180)) = 0.057

Therefore, the 99% confidence interval for the true proportion of undergraduate college students with home internet access is:

0.872 ± 0.057 or (0.815, 0.929)

This means that we are 99% confident that the true proportion of undergraduate college students with home internet access falls between 0.815 and 0.929.

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answer in the picture

Answer:

The illustration below shows the graph of yyy as a function of xxx.

Complete the following sentences based on the graph.

Initially, as xxx increases, yyy

Step-by-step explanation:

(a)  The synchronous reactance of the alternator is 0.001953125 Ω.

The synchronous reactance [tex]X_{s}[/tex] of the alternator can be calculated using the formula:

[tex]X_{s} = (Vt^2) / (3 * VL * S_{base})[/tex]

where [tex]V_{t}[/tex] is the rated line-to-line voltage of the alternator, VL is the rated line-to-neutral voltage of the alternator (which is the same as the rated voltage for a Y-connected alternator), and S_base is the apparent power rating of the alternator (which is equal to the rated power factor of the alternator times the rated apparent power). Substituting the given values, we get:

[tex]X_{s} = (13.5^2) / (3 * 13.5 * 1600) = 0.001953125[/tex] Ω

Therefore, the synchronous reactance of the alternator is 0.001953125 Ω.

(b) The percentage voltage regulation at full-load 0.8 power factor leading is 23.15%.

The percentage voltage regulation (%VR) at full-load 0.8 power factor leading can be calculated using the formula:

%VR = (E - Vl) / Vl * 100%

where E is the generated voltage of the alternator, and Vl is the terminal voltage of the alternator at full-load 0.8 power factor leading. We can assume that the armature resistance and inductance are negligible compared to Xs for this calculation. Using the given values, we first calculate the apparent power S of the load:

S = P / pf = 1280 / 0.8 = 1600 kVA

Since the load is at unity power factor, the current drawn from the alternator is also 1600 A. Therefore, the voltage drop across Xs is:

Vx = Xs * I = 0.001953125 * 1600 = 3.125 V

The generated voltage E is equal to the terminal voltage Vl plus the voltage drop across Xs:

E = Vl + Vx

The percentage voltage regulation is then:

%VR = (E - Vl) / Vl * 100% = (Vl + Vx - Vl) / Vl * 100% = Vx / Vl * 100%

Substituting the given values, we get:

%VR = 3.125 / 13.5 * 100% = 23.15%

Therefore, the percentage voltage regulation at full-load 0.8 power factor leading is 23.15%.

(c) If the %VR value is taken at half-load lagging power factor, it will be higher than the %VR value at full-load 0.8 power factor leading. This is because the load impedance at half-load lagging power factor has a lower magnitude than the load impedance at full-load 0.8 power factor leading, which means that the voltage drop across [tex]X_{s}[/tex] will be a larger fraction of the terminal voltage, resulting in a larger %VR value.

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Answer:

x = 49.5°

Step-by-step explanation:

∠ABC = 90°

∠CBD = 45%∠ABC

∠CBD = 0.45(90)

∠CBD = 40.5°

x = ∠ABC - ∠CBD

x = 90 - 40.5

x = 49.5°

71 citizens should be included in the sample to estimate the mean age of the citizens living in your community at a 98% level of confidence.

We need to find out the sample size of citizens that should be included in the sample to estimate the mean age of the citizens living in your community at a 98% level of confidence.

The formula for the Margin of error is

E: E = Zc/2 * (σ/√n)

Where E is the margin of error Zc/2 is the Z-value for the level of confidence cσ is the population standard deviation is the sample size.

So the formula for the sample size n is: n = (Zc/2 / E)² * σ²

We have Zc/2 = Z0.02/2 = Z0.01 = 2.33 (using z-table) σ = 22 years

E = 3 years

n = (2.33 / 3)² * 22²

n ≈ 70.36 ≈ 71 (rounded up)

Therefore, 71 citizens should be included in the sample to estimate the mean age of the citizens living in your community at a 98% level of confidence.

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Answer:

295

Step-by-step explanation:

Answer:

295!

Step-by-step explanation:

72 - 12 = 60

48 x 60 = 2880

2880 - 225 = 2655

2655 / 9 = 295

Have you ever heard of PEMDAS? It is the order in which to solve equations like this one. Here's what it stands for:

Parenthesis

Exponents

Multiplication

Division

Addition

Subtraction

I hope this is helpful for future math equations similar to this one.

Answer:

4 - 12x

Step-by-step explanation:

Use the distributive property.

-6(-2/3 +2x) =

= -6 × -2/3 + (-6) × 2x

= 4 - 12x

a) The 7th percentile of the bill amounts is given as follows: $80.64.

b) The 62nd percentile of the bill amounts is given as follows: $116.24.

c) The median of the bill amounts is given as follows: $110.14.

We first must use the z-score formula, as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In which:

The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, and can be positive(above the mean) or negative(below the mean).

The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure represented by X in the distribution.

The mean and the standard deviation for this problem are given as follows:

[tex]\mu = 110.14, \sigma = 20[/tex]

The median is the same as the mean, hence it is given as follows:

$110.14.

The 7th percentile is X when Z = -1.475, hence:

-1.475 = (X - 110.14)/20

X - 110.14 = -1.475 x 20

X = $80.64.

The 62nd percentile is X when Z = 0.305, hence:

0.305 = (X - 110.14)/20

X - 110.14 = 0.305 x 20

X = $116.24.

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Answer:

area = 18.81 m²

Step-by-step explanation:

solving for the 7 sided polygon first:

divide into 7 equal isosceles triangles, each having sides of 10 m and a peak angle of 360°/7 = 51.43°. Drop a line from the peak & perpendicular to the base makes a right triangle with a 25.71° peak angle and a 10 m hypotenuse.

sin 25.71° = x/10, x = 4.34, the base of the full triangle will be 2 x 4.34 = 8.68 m

cos 25.71° = x/10, x = 9.01, the rise of the triangle is 9.01 m

The area of each triangle will be 1/2(8.68)(9.01) = 39.10 m²

39.10 x 7 triangles = 273.72 m²

area of 7 sided polygon = 273.72 m²

Next solve for the inner circle:

The rise of the triangle (9.01) is the radius of the inner circle.

area of inner circle = πr² = 3.14(9.01²) = 254.91 m²

273.72 - 254.91 = 18.81 m²

Answer:

51 degrees

Step-by-step explanation:

As we already know that this triangle is a right triangle.

To find x, you need to subtract both angles.

90 - 39

= 51

Janice needs to be willing to ask at least 16 boys to have a 99.7% chance of getting a "yes" and going to the Sadie Hawkins dance.

To determine how many boys Janice needs to be willing to ask in order to have a 99.7% chance of getting a "yes" and going to the Sadie Hawkins dance, we can use the concept of probability and the binomial distribution.

The probability of a random boy saying yes is 45%, which means the probability of a boy saying no is 55%. Let's assume Janice asks "n" boys.

The probability of at least one boy saying yes can be calculated using the complement rule. The complement of the event "at least one boy saying yes" is the event "all boys saying no."

The probability of all "n" boys saying no is (0.55)^n, as the probability of each boy saying no is 55%.

To find the number of boys Janice needs to ask to have a 99.7% chance of going, we want the complement probability (all boys saying no) to be 0.003. Therefore:

(0.55)^n ≤ 0.003

Taking the logarithm of both sides:

n * log(0.55) ≤ log(0.003)

Solving for "n":

n ≥ log(0.003) / log(0.55)

Using a calculator:

n ≥ 15.154

Since Janice can't ask a fraction of a boy, we need to round up the value of "n" to the nearest whole number.

Therefore, Janice needs to be willing to ask at least 16 boys to have a 99.7% chance of getting a "yes" and going to the Sadie Hawkins dance.

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Answer: 1.2 blocks

Step-by-step explanation:

Timothy walks 12 blocks in 10 minutes so it can be written as

12 blocks = 10 minutes

divide both sides by 10

1.2 blocks per minute

Answer:

3. Likely

Step-by-step explanation:

Answer:

The solution is x = + 0.77 , -0.77

Step-by-step explanation:

The equation is

[tex]x^3 - 3x^2 - 4 = \frac{1}{x} -1 +5\\x^4 -3x^3 -4x = 1-4x\\x^4 - 3x^3 = 1\\x^3 (x-3) = 1\\\\x^4 -3x^3 -1 = 0\\x^4 -3x^3 -1[/tex]

The solutions to the equation is

x = + 0.77 , -0.77

Answer:

0.91 and 3.69

Step-by-step explanation:

Answer:10

Step-by-step explanation:believe me bro

To the nearest minute, it will be 10 minutes until there are 70 grams of the element remaining.

The time the element took to decay can be found by using the following formula:

[tex]F=P(1-r)^{t}[/tex]

Where:

We can find the answer by substituting the values.

[tex]F=P(1-r)^{t}\\\Rightarrow 70=840(1-0.229)^{t}\\\Rightarrow \frac{70}{840} =(1-0.229)^{t}\\0.0833=(1-0.229)^{t}\\t=9.56\\\approx10 \text{ minutes}[/tex]

Therefore, we have found that the element will take around 10 minutes to have 70 grams remaining.

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Answer:

transpose -4 to left

and 5 to left

subtract and and after transpose you will have a sign change

then you can divide

12/4,18/9

so,

x<2,x>3

Answer:

√89

Step-by-step explanation:

√(4+4)2+(0-5)2

√(8)2+(-5)2

√64+25

√89

Answer:

Step-by-step explanation:

3:2 = 2.5:1.5

half of 2 is 1 so if you had 1.5 it would only be half. For a better explanation, 1 minute is 60 seconds half of a minute is 30 seconds. if you have 45 seconds it would be 3/4 of a second. this is hard for me to explain so if you need more examples just tell me in the comments.

i hope this helps

have a nice day/night

mark brainliest please:)

Answer:n=−2

Step-by-step explanation:

The  steps to draw a pipeline diagram for a given program are:

Understand the CPU architecture: This involves knowing pipeline stages, their durations, and relevant instructions/hazards. Step 2: Identify program instructions. Each instruction goes through pipeline stages.

Assign cycle numbers sequentially to each instruction. Visualize pipeline progress over time. Draw pipeline stages. Draw a horizontal line divided into cycles to represent time. Each cycle = 1 clock cycle duration. Place cycle numbers below the line.

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Answer:

m = 4.7

Step-by-step explanation:

If you plug in these values in the slope formula, this is what happens:)

Answer:

47/10x

**Do not leave your answer as a decimal, slope is usually in fraction form**

Step-by-step explanation:

Slope Formula: [tex]\frac{\text{rise}}{\text{run}} / \frac{y_2 - y_1}{x_2 - x_1}[/tex] In this formula, subtract the 1st coordinate from the second. So, the 2nd y coordinate goes first, place a "minus" sign, and then the 2nd y-coordinate. This is the same for the x coordinates.

Finding the Answer: To find the answer, we just plug the numbers correctly into the equation, just as I explained above. We would do 55-8 first, which is 47, and then 12-2 which is 10.

Combined, the answer is 47/10x. You always place an x after the slope, which can be used to plug in other numbers. The answer cannot be simplified anymore, so this is simplfied.  

Therefore, the decimal representations of irrational numbers satisfy conditions 1 and 2; that is, irrational numbers are decimals that do not terminate and do not repeat. Knowing these properties, it is now possible for us to construct irrational numbers in decimal form at will.

for spanish people

Por lo tanto, las representaciones decimales de números irracionales cumplen las condiciones 1 y 2; es decir, los números irracionales son decimales que no terminan y no se repiten. Conociendo estas propiedades, ahora es posible para nosotros construir números irracionales en forma decimal a voluntad.

Answer:

$33,040

Step-by-step explanation:

Hope this helps and have a wonderful day!!!

Answer:

$30520

Step-by-step explanation:

Answer:

Where is ur question??

plss put ur question I will give correct answer

If the ship is travelling at a constant rate of 17 mph, the distance between the ship and San Francisco is changing at a rate of approximately 1 mile per hour. So, the rate of change is 1mph.

What is the concept of related rates?

The concept of related rates is a fundamental topic in calculus that deals with how the rates of change of different variables are related to each other. It involves analyzing how the rates of change of two or more related quantities are connected through their derivatives.

To solve this problem, we can use the concept of related rates. Let's assume that the cruise ship starts at point A, the port 3 miles directly south of San Francisco, and moves towards the west.

Let's denote the position of the cruise ship at a given time as point B. We are interested in finding the rate at which the distance between point B and San Francisco (let's call it point C) is changing.

We can create a right triangle with points A, B, and C, where the distance between A and C is the constant 3 miles. Let's call the distance between B and C as "x" (in miles).

We are given that the ship is traveling at a constant rate of 17 mph, which means its speed is 17 miles per hour.

To find how fast the distance between the ship and San Francisco is changing, we need to find dx/dt (the rate at which "x" is changing) when 1 hour has passed.

Using the Pythagorean theorem, we have:

[tex]x^2 + 3^2 = (distance\ traveled \ by\ the\ ship)^2[/tex]

Taking the derivative of both sides with respect to time (t):

2x(dx/dt) = 2(distance traveled by the ship)(speed of the ship)

Plugging in the given values:

2x(dx/dt) = 2(17 mph)

Simplifying:

x(dx/dt) = 17 mph

Now, we need to find x when 1 hour has passed. The ship is traveling at a constant speed of 17 mph for 1 hour, so the distance it travels is 17 miles.

Plugging in x = 17 and solving for dx/dt:

17(dx/dt) = 17 mph

dx/dt = 1 mph

Therefore, 1 hour after leaving port, the distance between the ship and San Francisco is changing at a rate of approximately 1 mile per hour.

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