3. Is the set of rational expressions closed under division? Explain = ________________ p(x) q(x) ÷ r(x) s(x)

The maximum number of people who can stand in each side of the boat is equal to the buoyant force divided by the average mass of a person multiplied by the acceleration due to gravity.

The maximum number of people who can stand in each side of a boat can be determined using Archimedes' Principle. This principle states that the buoyant force on an object is equal to the weight of the fluid it displaces. In the case of a boat, the buoyant force is equal to the weight of the water it displaces.

Using this principle, the maximum number of people who can stand in each side of a boat can be calculated using the equation:

F_B = m_p * g

Where F_B is the buoyant force, m_p is the total mass of all the people standing in the boat, and g is the acceleration due to gravity.

To determine the maximum number of people, we must first calculate the mass of the boat, m_b. We can do this by multiplying the volume of the boat (V) by the density of the material the boat is made of (ρ).

m_b = V * ρ

Next, we can calculate the total mass of all the people standing in the boat, m_p. This can be calculated by multiplying the total number of people (n) by the average mass of a person (m).

m_p = n * m

Finally, we can calculate the maximum number of people who can stand in each side of the boat by rearranging the equation for F_B and solving for n.

n = (F_B) / (m * g)

Therefore, the maximum number of people who can stand in each side of the boat is equal to the buoyant force divided by the average mass of a person multiplied by the acceleration due to gravity.

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Answer:

\(x=-3\)

Step-by-step explanation:

\(-(x+5)=2x+4\)

\(-1(x+5)=2x+4\)

\(-x-5=2x+4\)

     \(+5\)           \(+5\)

\(-x=2x+9\)

\(-2x\) \(-2x\)

\(-3x=9\)

\(\frac{-3x}{-3} =\frac{9}{-3}\)

\(x=-3\)

Hope this helps!

Answer:

To solve the given system of equations using the substitution method, we need to solve one equation for one variable and then substitute that expression into the other equation for that same variable. Let's solve the second equation for y.

-x + y = 4

y = x + 4

Now we can substitute this expression for y into the first equation and solve for x.

-2x + 2(x + 4) = 7

-2x + 2x + 8 = 7

8 = 7

The equation 8 = 7 is not true, which means the system of equations has no solution. We can see this visually by graphing the two lines. They are parallel and will never intersect, which means there is no point that satisfies both equations.

Therefore, the solution to the system of equations is "No solution."

Note: Please be sure to double-check your work to avoid mistakes.

Step-by-step explanation:

Hope this helps you!! Have a wonderful day/night!!

The volumes of the prisms are 12 cm³, 135 cm³ and 1200 cm³

A prism is a polyhedron comprising an n-sided polygon base, a second base which is a translated copy of the first, and n other faces, necessarily all parallelograms, joining corresponding sides of the two bases. All cross-sections parallel to the bases are translations of the bases.

Given are prisms, We need to find their volumes,

Volume of a prism = 1/2 × area of the base × height

1) Area of the base = 1/2 × 3 × 4 = 6 cm²

Height = 4 cm

Volume = 1/2 × 4 × 6 = 12 cm³

2) Area of the base = 1/2 × 5 × 12 = 30 cm²

Height = 9 cm

Volume = 1/2 × 9 × 30 = 135 cm³

3) Area of the base = 1/2 × 15 × 16 = 120 cm²

Height = 20 cm

Volume = 1/2 × 20 × 120 = 1200 cm³

Hence, the volumes are 12 cm³, 135 cm³ and 1200 cm³

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Answer:

−2/3 (10x3 ( raised to the third power) −9 +69)

Step-by-step explanation:

Answer:

3^3+2(3)(7)(-3)-5(-3)^2=-144

hope this is your required answer

Answer:

-144

Step-by-step explanation:

a³ + 2abc - 5c² = (3)³ + 2(3)(7)(-3) - 5(-3)²

= 3³ + (-126) - 5(-3)²

= 27 + (-126) - 45

= (-99) - 45

= -144

your welcome

Recall that the order of the operations PEMDAS

1. Parenthesis

2. Exponents.

3. Multiplication.

4. Division.

5. Addition.

6. Subtraction.

1. Given expression is

Multiply 3 and 5, we get

Divide 6 by 2, we get

Subtract 3 from 8, we get

Add 5 and 15, we get

The answer is

2.Given expression is

Multiply 7 and 3, we get

Divide 15 by 5, we get

Subtract 3 from 21, we get

The answer is

3. Given expression is

First, we need to solve inside the parenthesis, divide 12 by 2, we get

Add 1 and 6, we get

Solve exponent.

Multiply 2 and 49, we get

Add 8 and 98, we get

The answer is

Answer:

6n+12z

Step-by-step explanation:

then we got this bc we do like terms so 6n from 2 x3n then 12z bc 2x6

Answer:

-1/5

Step-by-step explanation:

To find the slope of the line using two points, you have to use the slope formula:

\(\frac{y2-y1}{x2-x1}\)

10 is x1

1 is y1

5 is x2

2 is y2

\(\frac{2-1}{5-10} =\frac{1}{-5} =-\frac{1}{5}\)

The probability that at least one of them has been vaccinated is equal to 98.5% if 65% of the people have been vaccinated.

Considering P to be the probability that at least one is vaccinated and q to be the probability that none of the four are vaccinated; the sum of all the probabilities must equal 1; therefore,

P = 1 - q

As 65% of the population is vaccinated, therefore 35% are not vaccinated. Thus any person has a probability of 0.35 of not being vaccinated;

q = 0.35^4 = 0.015

P = 1 - 0.015

P = 0.985

Converting it into percentage;

P = 0.985 × 100 = 98.5%

Therefore the probability that at least one of them has been vaccinated is calculated to be 98.5%

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The case-fatality rate among residents with TB over the course of the year is approximately 33.3%. None of the answer choices provided (25.0%, 14.3%, 20.0%) match this calculated value, so the correct answer is "None of the above."

The case-fatality rate among residents with TB over the course of the year can be calculated by dividing the number of residents who died from TB by the total number of residents with TB at the start of the study. Let's calculate it based on the given information.

On January 1st, there were 30 residents with existing cases of TB. On July 1st, 10 of these residents died from their disease.

Case-Fatality Rate = (Number of TB deaths / Number of residents with TB) * 100%

Case-Fatality Rate = (10 / 30) * 100% ≈ 33.3%

Therefore, based on the given information, the case-fatality rate among residents with TB over the course of the year is approximately 33.3%. None of the answer choices provided (25.0%, 14.3%, 20.0%) match this calculated value, so the correct answer is "None of the above."

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Answer:

22

Step-by-step explanation:

5(7)=35

3(8)=24

35-24+11=22

Answer:

22

Step-by-step explanation:

\(5c - 3d + 11\\\rule{150}{0.5}\\5(7)-3(8)+11\\\\35 - 24 + 11\\\\11 + 11\\\\\boxed{22}\)

Hope this helps!

Answer:

w= -44

Step-by-step explanation:

The probability that at least one of the randomly selected 5 people has been vaccinated is 0.9502.

The probability of at least one vaccinated person from a population where 51% of people are vaccinated and 5 people are chosen randomly is calculated as follows:Since the probability of a person who has been vaccinated is 51%, and the probability of a person who has not been vaccinated is 49%, the probability of at least one person being vaccinated from 5 people who are selected randomly is given by the formula:P(at least one vaccinated person) = 1 - P(no vaccinated person)The probability of no vaccinated person is calculated as follows: P(no vaccinated person) = 0.49 × 0.49 × 0.49 × 0.49 × 0.49 = 0.0498

The probability of at least one vaccinated person is calculated as follows:P(at least one vaccinated person) = 1 - P(no vaccinated person)P(at least one vaccinated person) = 1 - 0.0498P(at least one vaccinated person) = 0.9502Therefore, the probability that at least one of the randomly selected 5 people has been vaccinated is 0.9502.

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joe runs each lap in 6 minutes, we can express the total time as 6n where n is the number of laps.

A relationship that compares two numbers or other mathematical expressions in an unequal way is known as an inequality. It is most frequently used to compare the sizes of two numbers on the number line.

A less than symbol a < b indicates that an is less than b.

A greater than b is indicated by the notation a > b.

He will run at most 66 minutes, "at most" means less than or equal.

Forming an inequality will be :

\(6n\) \(\leq\) \(66\)

Since he won't exceed 66 minutes.

The value of n will be :

\(6n\) \(\leq\) \(66\)

\(n\) \(\leq\)  \(\frac{66}{6}\)

\(n \leq 11\)

The answer is n ≤ 11

Hence, the possible number of laps he will run today  is 11

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Answer:

\(m = \frac{14 - 7}{2 - 0} = \frac{7}{2} \)

\(14 = \frac{7}{2} (2) + b\)

\(14 = 7 + b\)

\(b = 7\)

\(y = \frac{7}{2} x + 7\)

the missing coefficients are approximately c = 0.5, d = 0.7, e = -1.6, and f = -9.9.

To determine the missing coefficients in the equation x² + cy² + dx + ey + f = 0, we can use the given points on a vertical ellipse and substitute them into the equation. This will create a system of equations that we can solve to find the values of c, d, e, and f.

Let's substitute the given points into the equation:

For the point (3.75, 0):

(3.75)² + c(0)² + d(3.75) + e(0) + f = 0

14.06 + 3.75d + f = 0            -- Equation 1

For the point (0, 2.71):

(0)² + c(2.71)² + d(0) + e(2.71) + f = 0

7.35c + 2.71e + f = 0            -- Equation 2

For the point (1, -7):

(1)² + c(-7)² + d(1) + e(-7) + f = 0

1 + 49c + d - 7e + f = 0        -- Equation 3

For the point (-1, -5.725):

(-1)² + c(-5.725)² + d(-1) + e(-5.725) + f = 0

1 + 32.86c - d - 5.725e + f = 0 -- Equation 4

We now have a system of equations with four variables (c, d, e, f). By solving this system, we can find the missing coefficients.

Solving the system of equations using a numerical solver or by hand, we find the following approximate values:

c ≈ 0.5

d ≈ 0.7

e ≈ -1.6

f ≈ -9.9

Therefore, the missing coefficients are approximately c = 0.5, d = 0.7, e = -1.6, and f = -9.9.

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The graph represents the set of all solutions to the inequality -6x + y ≥ 3, which includes the line -6x + y = 3 and all points above the line.

Jenna created the graph below to represent the solution to the inequality -6x + y ≥ 3:Jenna has graphed a linear inequality, -6x + y ≥ 3, on a coordinate plane. The graph indicates that all points on the line -6x + y = 3 are solutions to the inequality; in addition, any point above the line (i.e. in the shaded region) is also a solution to the inequality.To determine whether a point is a solution to the inequality, one can plug in the x and y values of the point into the inequality and see if the resulting inequality is true.

For example, consider the point (3, 1), which lies in the shaded region above the line. Plugging in x = 3 and y = 1, we get:-6(3) + 1 ≥ 3Simplifying, we get:-17 ≥ 3This inequality is false, so the point (3, 1) is not a solution to the inequality -6x + y ≥ 3. On the other hand, consider the point (2, 5), which also lies in the shaded region above the line. Plugging in x = 2 and y = 5, we get:-6(2) + 5 ≥ 3Simplifying, we get:-7 ≥ 3This inequality is true, so the point (2, 5) is a solution to the inequality -6x + y ≥ 3.

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Answer: 15.83%

Step-by-step explanation: To find the percentage of the original bill saved with the coupon, you need to find how much of the original bill is reduced by. 31.58 - 26.58 = 5. And 5 is what percentage of 31.58. So you do 5/31.58 and multiply by 100% to get the answer in percent.

Answer:

32

Step-by-step explanation:

You have to use pythagorean theorem for this, where a and b represent the 2 sides while c represents the hypoteneuse.

a²+b²=c²

If the diagonal of a square is 8, it divides the square into 2 triangles, both with a hypoteneuse of 8. Since it is a square, that means the other 2 sides will have equal lengths. So input 8 into the equation:

a²+b²=8²

a²+b²=64

Then you can change a and b into the same variable, since you know they will be equal due to you working with a square.

a²+a²=64

simplify: 2a²=64

divide both sides by 2: a²= 32

square root both sides: a = \(\sqrt{32}\)

then you know the length of each side is \(\sqrt{32}\)

to find the area of a square, you must multiply both sides by each other, so do \(\sqrt{32}\)*\(\sqrt{32}\), which will give you 32 since you are essentially doing this:

\((\sqrt{32})^2\) in which the square and square root cancel out.

Answer:

1/3

Step-by-step explanation:

There are 12 boys and 6 girls, meaning there are 18 students. The girls are 1/3 out of those 18.

The value of ∫[6, -10]g(x)dx is 2.

We are given two integrals: ∫[-104, -10]g(x)dx = -3 and ∫[6, 4]g(x)dx = 5.

We need to find the value of ∫[6, -10]g(x)dx.

Notice that the desired integral's interval is just the union of the given intervals.

Therefore, we can obtain the value of the desired integral by summing the values of the two given integrals: ∫[6, -10]g(x)dx = ∫[-104, -10]g(x)dx + ∫[6, 4]g(x)dx = -3 + 5 = 2.

Thus, the value of ∫[6, -10]g(x)dx is 2.

The interval of an integral refers to the range over which the integration is performed.

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The more plausible explanation for the association between diet soda consumption and weight gain is that people who drink diet soda may have other factors or behaviors that contribute to weight gain.

For example, individuals who drink more diet soda may have a higher intake of calorie-dense foods or may engage in less physical activity.

Additionally, people who are already overweight or at risk of gaining weight.

May be more likely to choose diet soda as a way to manage their weight.

While the large sample size may provide strong statistical evidence of the association between diet soda consumption and weight gain.

It does not necessarily prove a causal relationship.

Further research is needed to establish a cause-and-effect relationship between diet soda consumption and weight gain.

Such as randomized controlled trials or longitudinal studies.

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Labor productivity in this case is equal to 10 baskets.

When eight weavers are employed, and output is 80 baskets, labor productivity is equal to 10 baskets.

A labor productivity measure is a way of estimating the amount of output generated per unit of labor.

The following formula is used to calculate labor productivity:

                               Total output produced / Total number of workers involved in the production.  

Therefore, in this case, labor productivity will be equal to the total output produced divided by the total number of weavers employed.

Mathematically, Labor productivity = Total output produced / Total number of weavers employed

Given,The number of weavers employed, n = 8Output produced, Y = 80 baskets

Substitute the above values into the formula for labor productivity,

                        Labor productivity = Total output produced / Total number of weavers employed

                                                   = 80 / 8= 10

Thus, labor productivity in this case is equal to 10 baskets.

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Answer:

Profit obtained by X =  Rs. 2,976.64

Profit obtained by Y = Rs. 2,545.58

Profit obtained by Z = Rs. 2,777.78

Step-by-step explanation:

Total capital for the first 6 months = Rs 5000 + Rs.4500 + Rs.6500 = Rs. 16,000

Total capital for the next 3 months = Rs. 16,000+ Rs 5000 = Rs. 21,000

Total capital for the last 3 months of the year = Rs. 21,000 + (Rs 4500 * 2) = Rs. 30,000

Share of profit of each partner is the sum of all the ratios of his capital to total capital of the business at each point in time multiply by the ratio of the numbers of months covered by each capital to 12 months and then multiply by RS.8300.

Profit obtained by X = ((Rs 5000 / 16,000) * (6 / 12) * Rs. 8300) +  ((Rs 10,000 / 21,000) * (3 / 12) * Rs. 8300) + ((Rs 10,000 / 30,000) * (3 / 12) * Rs. 8300) =  Rs. 2,976.64

Profit obtained by Y = ((Rs 4500 / 16,000) * (6 / 12) * Rs. 8300) +  ((Rs 4500 / 21,000) * (3 / 12) * Rs. 8300) + ((Rs 13,500 / 30,000) * (3 / 12) * Rs. 8300) = Rs. 2,545.58

Profit obtained by Z = ((Rs 6500 / 16,000) * (6 / 12) * Rs. 8300) +  ((Rs 6500 / 21,000) * (3 / 12) * Rs. 8300) + ((Rs 6,500 / 30,000) * (3 / 12) * Rs. 8300) = Rs. 2,777.78

Confirmation of total profit shared = Rs. 2,976.64 + = Rs. 2,545.58 + Rs. 2,777.78 = Rs. 8,300

Answer:

S = 180C²

18,000 lbs

Step-by-step explanation:

Assuming the table attached with C in inches and S in pounds, we see that the first differences in S are ...

 180, 540, 900

These are not constant, so the relation is not linear.

Second differences are ...

 360, 360

These are constant, so the relation is quadratic. With a short trial, we find that a suitable equation is ...

 S = 180·C²

__

The safe load for C=10 is then ...

 S = 180·10² = 18,000 . . . pounds

better?

about what there is no question here....?

Answer:

I think it is the first one

Step-by-step explanation:

To determine the sample size needed to construct a 95% confidence interval with a margin of error of 9 ounces and assuming a standard deviation of 0.05 ounces, we can use the formula:

n = (Z * σ / E)^2

where n is the sample size, Z is the z-score corresponding to the desired confidence level (95% corresponds to a z-score of approximately 1.96), σ is the standard deviation, and E is the margin of error.

Substituting the given values into the formula, we have:

n = (1.96 * 0.05 / 9)^2

n = (0.098 / 9)^2

n ≈ 0.0109^2

n ≈ 0.000119

Rounding up to the nearest integer, the required sample size is 1.

The sample size needed to construct a 95% confidence interval with a margin of error of 9 ounces, assuming a standard deviation of 0.05 ounces, is 1.

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