Select all the expressions which are equivalent to –4/3p – 2/5.
–4/3p + 2/5
–2/5 – 4/3p
4/3p – 2/5
–4/3p + (−2/5)
2/5 + 4/3p

The number that can be equal to 2x² -50 =  2(x + 5)(x - 5).

For the given equation;

= 2x² -50

Take 2 common;

= 2(x² - 25)

This could be written as;

= 2(x² - 5²)

Now use per the property of (a² - b²)  = (a + b)(a - b).

= 2(x + 5)(x - 5)

Thus, the given expression 2x² -50 can be represented as 2(x + 5)(x - 5).

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The best description of a rectangle is " a parallelogram that has four right angles".

From the definition, a rectangle has 4 right angles and opposite sides are parallel.

Then, we can say that,

A parallelogram with 4 right angles best describes the rectangle.

So, option A is correct.

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The lateral surface area of the cylindrical oil storage tank is 2668.36 ft² and the total surface area is 6595.36 ft².

To find the lateral surface area of a cylindrical oil storage tank, we need to find the circumference of the circular base

and multiply it by the height of the tank. The circumference is given by:

C = πd

C = π(50 ft)

C = 157.08 ft (rounded to two decimal places)

Therefore, the lateral surface area is:

Lateral surface area = C x h

Lateral surface area = 157.08 ft x 17 ft

Lateral surface area = 2668.36 ft² (rounded to two decimal places)

To find the total surface area, we need to add the area of the two circular bases to the lateral surface area. The area of

a circle is given by:

A = πr²

The radius of the circular base is half the diameter, so:

r = d/2

r = 50 ft/2

r = 25 ft

Therefore, the area of each circular base is:

A = πr²

A = π(25 ft)²

A = 1963.5 ft² (rounded to one decimal place)

So, the total surface area is:

Total surface area = 2A + Lateral surface area

Total surface area = 2(1963.5 ft²) + 2668.36 ft²

Total surface area = 6595.36 ft² (rounded to two decimal places)

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Therefore, the future value of a three-year uneven cash flow given below, using an 11% discount rate is $1,238.82.

To calculate the future value of a three-year uneven cash flow given below, using an 11% discount rate, we need to use the formula;

Future value of uneven cash flow = cash flow at year 1/(1+discount rate)¹ + cash flow at year 2/(1+discount rate)² + cash flow at year 3/(1+discount rate)³ + cash flow at year 4/(1+discount rate)⁴

Given the cash flows;

Year 0: $0

Year 1: $600

Year 2: $500

Year 3: $400

Then the Future value of uneven cash flow

= $600/(1+0.11)¹ + $500/(1+0.11)² + $400/(1+0.11)³

= $600/1.11 + $500/1.23 + $400/1.36

=$540.54 + $405.28 + $293.00

=$1,238.82

Therefore, the future value of a three-year uneven cash flow given below, using an 11% discount rate is $1,238.82.

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the average number of customers in the barbershop that a guy should expect to see is 5.

To find the average number of customers in the barbershop that a guy should expect to see, we need to calculate the average number of customers present in the system, which includes both those being served by the barber and those waiting in the queue.

Let's denote:

λ = average customer arrival rate per day = 20 customers/day

μ = average service rate per day = 60 minutes/hour / 20 minutes/customer = 3 customers/hour

Since the barber works for 8 hours a day, the average service rate per day is 8 hours * 3 customers/hour = 24 customers/day.

Using the M/M/1 queuing model, where arrival and service times follow exponential distributions, we can calculate the average number of customers in the system (including the one being served) using the following formula:

L = λ / (μ - λ)

L = 20 customers/day / (24 customers/day - 20 customers/day)

L = 20 customers/day / 4 customers/day

L = 5 customers

Therefore, the average number of customers in the barbershop that a guy should expect to see is 5.

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Answer:

The derivative of a function may be used to determine whether the function is increasing or decreasing on any intervals in its domain. If f′(x) > 0 at each point in an interval I, then the function is said to be increasing on I. f′(x) < 0 at each point in an interval I, then the function is said to be decreasing on I.

Step-by-step explanation:

Answer:

your answer is > or the second choice

Step-by-step explanation:

-7+2=-5  > 3+(-9)=-6

Answer:

the second option is correct. -5 > -6

The speed of boat is 5/6 meter per second and height of boat is 50\(\sqrt{3}\) meter.

An angle is a shape created by two rays or lines that meet at the same terminal. The Latin word "angulus" (which means "corner") is where the term "angle" first appeared. The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle. It is not necessary for the angle to be in Euclidean space if it lies in the plane. Angles are referred to as dihedral angles if they are created by the intersection of two planes in a space other than Euclidean. The sign "" is used to denote angles. The Greek letter,,, etc. can be used to represent the angle between the two beams.

The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.

After solving the figure:

The speed of boat is 5/6 meter per second and height of boat is 50\(\sqrt{3}\) meter.

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The speed of the boat from point C to point B is approximately 10.82 meters per second.

What is speed ?

Speed is a measure of how fast an object is moving. It is the rate at which an object covers distance.

We can use trigonometry to solve for h and the speed of the boat. Let's start with h:

From the right triangle CLB, we have:

tan 30° = h / CB

where CB is the distance between points C and B, which is given as 50 meters. Solving for h, we get:

h = CB * tan 30° = 50 * tan 30° ≈ 28.87 meters

So the height of the lighthouse is approximately 28.87 meters.

Now let's find the speed of the boat. We know that the boat travels from point C to point B in 1 minute, which is equivalent to 60 seconds. Let's define the speed of the boat as v, in meters per second. Then we have:

v = CB / t

where t is the time it takes for the boat to travel from point C to point B. We can find t using the distance formula:

\(CB = \sqrt{(x_B - x_C)^2 + (y_B - y_C)^2\)

where x and y are the coordinates of each point. From the diagram, we can see that:

\(x_C = 0\)

\(y_C = 0\)

\(x_B = BL * cos \theta\)

\(y_B = BL * sin \theta\)

where BL is the distance from point B to the foot of the lighthouse, which is equal to h / tan θ. Therefore:

CB \(= \sqrt{((BL * cos \theta)^2 + (BL * sin \theta)^2)\)

     \(= \sqrt{(BL^2 * (cos^2 \theta + sin^2 \theta))\)

     \(= BL = h / tan \theta\)

Substituting the values we have found, we get:

v = CB / t = (h / tan θ) / 60 ≈ 10.82 meters per second

Therefore, the speed of the boat from point C to point B is approximately 10.82 meters per second.

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Answer: 18

Step-by-step explanation:

The maximum number of electrons in the n = 3 level can be found using the formula for the maximum number of electrons in an energy level, which is given by:

Here, n = 3, so we can substitute this value into the formula and solve for the maximum number of electrons:

Therefore, the maximum number of electrons in the n = 3 level is 18.

________________________________________________________

The maximum number of electrons in the n = 3 level can be found using the formula:

where:

Substituting n = 3, we get:

Simplifying this expression, we get:

\(\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}\)

Answer:6

Step-by-step explanation:

The two stores at points A and C would serve the residents of Miniville, providing them access to essential goods and services, with residents in the middle mile having the flexibility to choose between the two stores.

If one store is located at point A and the other store is located at point C, it means that the stores are located at the extremes of the 3-mile stretch of Lake Shore Drive in Miniville. Point B would be the midpoint between points A and C.

Given that the 300 residents of Miniville are evenly distributed along the 3 miles of shoreline on the lake, it implies that there are approximately 100 residents per mile.

Therefore, the store located at point A would serve the residents living in the westernmost mile of Lake Shore Drive, while the store located at point C would serve the residents living in the easternmost mile of Lake Shore Drive.

The residents living in the middle mile, between points A and C, would have the option to shop at either store, depending on their preference or convenience.

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Answer:

5

Step-by-step explanation:

First, we can add the whole numbers together.

1 + 3 = 4

Next, we know that the denominators (base/bottom of fraction) of the fractions are the same, meaning we simply add the numerators (top of fraction).

1/3 + 2/3 = 3/3

3/3 is equal to 1.

Now, we add the 4 from above to this 1 to get our answer, 5.

Feel free to comment down if this doesn't make sense, and I can explain it in a different way.

The system of equations is:

x + y = 10

4x + 3y = 36

The solution is x = 6 and y = 4.

A)

Let's define the variables:

We can write the system of equations:

x + y = 10

4x + 3y = 36

Isolate x on the first equation to get:

x = 10 - y

Replace that in the other one:

4*(10 - y) + 3y = 36

40 - 4y + 3y = 36

40 - y = 36

40 - 36 = y

4 = y

And thus, the value of x is:

x = 10 - y = 10 - 4 = 6

They bought 6 cheese wafers and 4 chocolate ones.

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Answer:

B.) \(6^{\frac{1}{2}}\)

Step-by-step explanation:

Use the exponent rule that states \(a^{\frac{1}{m}}=\sqrt[m]{a}\).  For this problem, let

a=6

m=2

So,

\(\sqrt6=6^{\frac{1}{2}}\)

If it takes 10 workers 2.5 years to build a 20 story building, it will take 2.5 sec 20 workers to build a 40 story building.

Given that a skyscraper's height and the number of workers needed to build it determine how long the project takes, We must make the time.

Allow the time t, height h, and number of workers to be ω.

Then, based on the relationship,

t = kh/ω

where k is constant.

The formula in the term of k is:

k = tω/h

Additionally, it takes 10 employees t0 2.5 years to construct a 20-story skyscraper.

Now putting the value

k = (2.5 × 10)/20

k = 25/20

k = 5/4

If a 40-story skyscraper requires 20 workers to construct, we have

t = kh/ω

t = (5/4) × (40/20)

t = 5/2

t = 2.5 sec

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The complete question is:

The time is takes to build a skyscraper is proportional to its height and inversely proportional to the number of construction workers. If it takes 10 workers 2.5 years to build a 20 story building, how long will it take 20 workers to build a 40 story building?

PreAlg students spend significantly less time doing homework compared to ElemAlg and InterAlg students, while there is no significant difference in homework time between ElemAlg and InterAlg students.

What is significantly ?

Significantly" is the keyword that indicates a notable or meaningful difference or result in the context of statistical analysis. It is often used to describe findings that have a high level of confidence and statistical significance, indicating that the observed difference or relationship is unlikely to have occurred by chance.

Based on the given data and statistical analysis, the conclusion is as follows:

PreAlg compared to ElemAlg:

The sample mean for PreAlg (1.32) is significantly different from the sample mean for ElemAlg (3.18) with a t-value of 5.08 and a p-value of 0.000. Therefore, we can conclude that PreAlg students spend significantly less time doing homework compared to ElemAlg students.

PreAlg compared to InterAlg:

The sample mean for PreAlg (1.32) is significantly different from the sample mean for InterAlg (4.42) with a t-value of 3.64 and a p-value of 0.003. Hence, we can conclude that PreAlg students spend significantly less time doing homework compared to InterAlg students.

ElemAlg compared to InterAlg:

The sample mean for ElemAlg (3.18) is not significantly different from the sample mean for InterAlg (4.42) with a t-value of 1.49 and a p-value of 0.163. Therefore, we fail to reject the null hypothesis, and we cannot conclude a significant difference in homework time between ElemAlg and InterAlg students.

In summary, the PreAlg students have significantly lower homework time compared to both ElemAlg and InterAlg students. However, there is no significant difference in homework time between ElemAlg and InterAlg students.

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: The problem requires formulating two given problems as linear programming problems in standard form. In problem (a), we need to minimize a linear objective function subject to linear inequality

(a) To formulate problem (a) as a linear programming problem in standard form, we define the decision variables x₁, x₂, and x₃. The objective function becomes: min 5x₁ - x₂.

The constraints are as follows:

- x₁ + 3x₂ + 2x₃ ≥ 7 (linear inequality constraint)

- x₁ + 2x₂ + |x₂| ≤ 4 (linear inequality constraint with absolute value)

- x₁ ≤ 0 (linear inequality constraint)

The problem can be expressed in standard form by introducing slack variables and converting the absolute value constraint into two separate constraints. The objective function, inequality constraints, and non-negativity constraints for the slack variables will form the linear programming problem in standard form.

(b) Problem (b) is already in the form of a linear programming problem with a linear objective function 2x + 3y. Since there are no constraints mentioned, we can assume that the decision variables x and y can take any real values. Thus, the problem is already in standard form.

In summary, to formulate problem (a) as a linear programming problem in standard form, we need to introduce slack variables and convert the absolute value constraint into separate constraints. Problem (b) is already in standard form as it contains a linear objective function without any constraints.

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The equation of the graphed function is given as follows:

f(x) = x³ + 2x² - 5x - 6.

The equation of the function is obtained considering the Factor Theorem, as a product of the linear factors of the function.

From the graph, the zeros of the function are:

Hence the function is:

f(x) = a(x + 3)(x + 1)(x - 2).

In which a is the leading coefficient.

Expanding the product, we have that:

f(x) = a(x² + 4x + 3)(x - 2)

f(x) = a(x³ + 2x² - 5x - 6).

When x = 0, y = -6, hence the leading coefficient a is obtained as follows:

-6a = -6

a = 1.

Hence the function is:

f(x) = x³ + 2x² - 5x - 6.

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To answer this question, solve the given expression for calculating velocity for a, this way:

The correct answer is B.

If the null hypothesis is true and there is no treatment effect, the expected value on average for the F-ratio would be 1.00. The correct answer is option (b) 1.00

In hypothesis testing using the F-test, the F-ratio is calculated by dividing the variance between groups (treatment effect) by the variance within groups (random variation). When the null hypothesis is true and there is no treatment effect, the numerator (variance between groups) and the denominator (variance within groups) would be similar, resulting in an F-ratio close to 1.

Therefore, the correct answer is b. 1.00, as the expected value for the F-ratio would be around 1 when the null hypothesis is true and there is no treatment effect.

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Answer:

7) \( \dfrac{25c^2}{d^4} \)

8) \( 4w^6r \)

Step-by-step explanation:

You must use the laws of exponents.

7)

\( (\dfrac{5c}{d^2})^2 = \)

When you raise a fraction to an exponent, raise the numerator and the denominator to that exponent.

\( = \dfrac{(5c)^2}{(d^2)^2} \)

When you raise a product to an exponent, raise each factor to that exponent.

When you raise an exponent to an exponent, multiply the exponents.

\( = \dfrac{5^2c^2}{d^4} \)

\( = \dfrac{25c^2}{d^4} \)

8)

\( \dfrac{-16w^7r^2}{-4wr} = \)

To divide powers with the same base, subtract the exponents. Remember that a plain variable, such as w is the same as w^1.

\( =\dfrac{-16}{-4}w^{7-1}r^{2-1} \)

\( = 4w^6r \)

The critical heat flux (CHF) is the maximum heat flux that can be transferred from a surface to a boiling liquid before the boiling process transitions from a stable regime to an unstable regime. The CHF is an important parameter in the design of heat transfer systems, as exceeding the CHF can lead to boiling crisis, which can cause severe damage to the system.

The CHF for a fluid depends on various factors such as fluid properties, surface properties, and flow conditions. One of the commonly used correlations for calculating CHF is the Kutateladze number (Ku) correlation, which is given by:

q_c = C (ρ_L^2 g Δh_f)^0.5 (σ/ρ_L)^0.1

where q_c is the critical heat flux, ρ_L is the liquid density, g is the acceleration due to gravity, Δh_f is the latent heat of vaporization, σ is the surface tension, and C is a constant that depends on the surface properties and flow conditions.

Using this correlation, we can calculate the CHF for the given fluids at 1 atm:

For mercury at 1 atm:

Density of mercury, ρ_L = 13,534 kg/m^3

Latent heat of vaporization of mercury, Δh_f = 2.66 x 10^5 J/kg

Surface tension of mercury, σ = 0.48 N/m

Acceleration due to gravity, g = 9.81 m/s^2

Using the Kutateladze number correlation with a constant value of C = 0.028, we get:

q_c = 0.028 * (13,534^2 * 9.81 * 2.66 x 10^5)^0.5 * (0.48/13,534)^0.1

q_c = 2.44 x 10^6 W/m^2

For ethanol at 1 atm:

Density of ethanol, ρ_L = 789 kg/m^3

Latent heat of vaporization of ethanol, Δh_f = 8.51 x 10^5 J/kg

Surface tension of ethanol, σ = 0.022 N/m

Acceleration due to gravity, g = 9.81 m/s^2

Using the Kutateladze number correlation with a constant value of C = 0.027, we get:

q_c = 0.027 * (789^2 * 9.81 * 8.51 x 10^5)^0.5 * (0.022/789)^0.1

q_c = 1.17 x 10^6 W/m^2

For refrigerant R-134a at 1 atm:

Density of R-134a, ρ_L = 1245 kg/m^3

Latent heat of vaporization of R-134a, Δh_f = 2.03 x 10^5 J/kg

Surface tension of R-134a, σ = 0.011 N/m

Acceleration due to gravity, g = 9.81 m/s^2

Using the Kutateladze number correlation with a constant value of C = 0.026, we get:

q_c = 0.026 * (1245^2 * 9.81 * 2.03 x 10^5)^0.5 * (0.011/1245)^0.1

q_c = 1.35 x 10^6 W/m^2

For water at 1 atm:

Density of water, ρ_L = 1000 kg/m^3

Latent heat of vaporization of water, Δh_f = 2

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Answer:

x=29

Step-by-step explanation:

3x+15+2x+20=180

3x+2x+15+20=180

5x+35=180

5x=180-35

5x=145

x=145/5

x=29

To find out how long it would take to fill the swimming pool using both the hose and the pipe, we can use the concept of work rate. The work rate is the amount of work done per unit of time. In this case, the work is filling the swimming pool, and the time is the duration it takes to fill it.

If we let x represent the time it takes to fill the pool using both the hose and the pipe, we can set up the following equation:

1/12 + 1/30 = 1/x

In summary, we can solve the equation 1/12 + 1/30 = 1/x to find the time it would take to fill the swimming pool using both the hose and the pipe.

To explain further, the equation is derived from the fact that the work rates of the pipe and the hose are additive when used together. The work rate of the pipe is 1 pool per 12 hours, and the work rate of the hose is 1 pool per 30 hours. Adding these rates together gives us the combined work rate when both the hose and the pipe are used. The equation 1/12 + 1/30 = 1/x represents the combined work rate of filling the pool using both the hose and the pipe. By solving this equation, we can find the value of x, which represents the time it would take to fill the pool using both methods.

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The 1000th term in Cai's list is 1505.

A writing system used to express numbers is known as a number system. It is the mathematical notation used to consistently express the numbers in a particular set using digits or other symbols. It represents the arithmetic and algebraic structure of the numbers and offers a distinctive representation for each number.

Now, For the 1000th term in Cai's list of positive integers excluding squares and cubes, we need to continue the sequence until we reach the 1000th term.

Starting with 2, we skip 1 and 4 (which is 2 squared),

so 3 is the third positive integer.

Next, we skip 8 (which is 2 cubed) and include 5, 6, and 7.

Skipping 9 (which is 3 squared), we add 10 and 11.

Skipping 16 (which is 2 to the fourth power), we include 12, 13, 14, and 15.

Skipping 25 (which is 5 squared), we add 17, 18, 19, 20, 21, 22, 23, and 24.

Skipping 27 (which is 3 cubed), we add 26 and 28.

Skipping 36 (which is 6 squared), we include 29, 30, 31, 32, 33, 34, 35, and 37.

Skipping 49 (which is 7 squared), we add 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, and 48.

Skipping 64 (which is 2 to the sixth power), we include 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, and 63.

Skipping 81 (which is 3 to the fourth power), we add 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 82, 83, 84, 85, 86, 87, 88, and 89.

Skipping 100 (which is 10 squared), we include 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 101, and so on.

By the time we reach the 1000th term, we will have found the first 999 positive integers excluding squares and cubes.

Therefore, the 1000th term in Cai's list is 1505.

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Answer:

Square! #N#The sides and angles of a square: The sides of a square are all congruent (the same length.) The angles of a square are all congruent (the same size and measure.) Remember that a 90 degree angle is called a "right angle.". So, a square has four right angles. Opposite angles of a square are congruent.

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Step-by-step explanation:

Answer:

4.3

Step-by-step explanation:

the length wont be negitive because things cant be negitively long and you would add -3.5 and 7.8 and you need to remember that it is a negitive 3.5

Answer: 70%

Step-by-step explanation:

Please tell me if I am wrong.