It takes 41 minutes for 9 people to paint 9 walls.
How many minutes does it take 1414 people to paint 14 walls?

The number of subsets for the set in this problem is given as follows:

16 subsets.

Considering a set with n elements, the number of subsets in the set is the nth power of 2, that is:

[tex]2^n[/tex]

The set in this problem is given as follows:

{C, D, E, F}.

Hence the cardinality of the set is given as follows:

n = 4.

Then the number of subsets is given as follows:

[tex]2^4 = 16[/tex]

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The set intersection X' ∩ Y' is expressed as; {e, 24}

We are given the sets as;

U = {a, b, c, d, e, f, 19, 20, 21, 22, 23, 24}

X = {a, b, c, 20, 21, 22}

Y = {b, d, f, 19, 21, 23}

Union of the sets A and B , denoted A ∪ B , is the defined as the set of all objects that are a member of A , or B , or both. The union of {1, 2, 3} and {2, 3, 4} is the set {1, 2, 3, 4} . Intersection of the sets A and B , denoted A ∩ B , is the set of all objects that are members of both A and B

Thus:

X' ∩ Y' is as follows;

X' = {d, e, 19, 23, 24}

Y' = {a, c, e, 20, 22, 24}

X' ∩ Y' = {e, 24}

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Answer:

  A, D

Step-by-step explanation:

You want to identify the tables that represent inverse functions.

For every ordered pair (x, y) of a function, there is an ordered pair (y, x) of its inverse function.

The first table shown has an ordered pair (x, y) = (4, -14). That means its inverse function must have the ordered pair (-14, 4). The two tables with that characteristic are shown in the attachment.

<95141404393>

The equation that represents the total price of Michigan State University per semester is determined by the number of classes taken (c) and the total cost for the semester, which includes a one-time fee for room and board (t).

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Therefore, the coordinates of point B are (-5.5, -10).

To find the coordinates of point B, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint between two points (x1, y1) and (x2, y2) are given by:

Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)

We are given the midpoint coordinates as (-3, -5) and the coordinates of point A as (-0.5, 0). Let's assume the coordinates of point B as (x, y). Plugging the known values into the midpoint formula, we have:

(-3, -5) = ((-0.5 + x) / 2, (0 + y) / 2)

Simplifying, we get:

-3 = (-0.5 + x) / 2 ... (1)

-5 = y / 2 ... (2)

From equation (2), we can solve for y:

y = -5 * 2

y = -10

Now, substituting this value of y in equation (1), we can solve for x:

-3 = (-0.5 + x) / 2

-6 = -0.5 + x

x = -6 + 0.5

x = -5.5

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The equation of the line that passes through the points (1,0) and (3,6) is y = 3x - 3.

The formula for equation of line is expressed as:

y = mx + b

Where m is slope and b is the y-intercept.

Given that, the line passes through points  (1,0) and (3,6).

First, we determine the slope:

[tex]Slope\ m = \frac{y_2 - y_1}{x_2 - x_1} \\\\Slope\ m = \frac{6 - 0}{3 - 1} \\\\Slope\ m = \frac{6}{2} \\\\Slope\ m = 3[/tex]

Now we plug the  slope m = 3 and one point (1,0)into the point-slope form to find the equation:

( y - y₁ ) = m( x - x₁ )

( y - 0 ) = 3( x - 1 )

y = 3x - 3

Therefore, the equation of the line is y = 3x - 3.

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The two considered triangles JKL and MNP are similar by the AA rule of similarity as the two angles that is ∠K = ∠N and ∠L = ∠P are there.

Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion. We denote the similarity of triangles here by ‘~’ symbol.

It is given that two triangles that are JKL and MNP are considered in which:

Now, from ΔJKL and ΔMNP, we have

∠K = ∠N (Given in the question)

∠L = ∠P(Given in the question)

Thus, by AA rule of similarity,

ΔJKL is similar to ΔMNP.

Therefore, the two considered triangles JKL and MNP are similar by the AA rule of similarity as the two angles that is ∠K = ∠N and ∠L = ∠P are there.

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Let's arrange the steps for solving the expression using the order of operations (also known as PEMDAS/BODMAS):

Subtract: (42-13) = 29

Multiply: 4 × 3 = 12

Exponentiation: 5² = 25

Multiply: 8 × 3 = 24

Divide: 24 ÷ 29 (result from step 1) = 0.8276 (rounded to 4 decimal places)

Add: 0.8276 (result from step 5) + 25 (result from step 3) = 25.8276 (rounded to 4 decimal places)

Add: 25.8276 (result from step 6) + 12 (result from step 2) = 37.8276 (rounded to 4 decimal places)

The steps should be performed in the following order:

Subtract -> Multiply -> Exponentiation -> Multiply -> Divide -> Add -> Add

So the steps should be performed in this order to evaluate the expression correctly.

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Answer:

The common difference in the given sequence is 5.

Step-by-step explanation:

The common difference in the sequence is 5 because they all add by 5 each time for example 5 + 5= 10 and 10+5=15

Answer:

total age = 84 years

Step-by-step explanation:

mean is calculated as

mean = [tex]\frac{total}{count}[/tex]

here count = 7 and mean = 12 , then

[tex]\frac{total}{7}[/tex] = 12 ( multiply both sides by 7 )

total = 7 × 12 = 84 years

To find the rate at which the light projected onto the wall is moving along the wall, we can use trigonometry and calculus. Let's denote the angle between the rotating light and the wall as θ.

Given:

Distance from the light to the wall, r = 15 feet

Rate of rotation, dθ/dt = 1 rotation every 4 seconds

We need to find the rate at which the light's projection moves along the wall, which is represented by dx/dt.

Using trigonometry, we know that the tangent of the angle θ is equal to the ratio of the distance along the wall (dx) to the distance from the light to the wall (r).

tan(θ) = dx / r

Differentiating both sides of the equation with respect to time t, we get:

sec^2(θ) * dθ/dt = dx/dt

Since we are given that the angle θ is 15 degrees, we can substitute the values and solve for dx/dt.

sec^2(15°) * (1 rotation / 4 seconds) = dx/dt

Simplify and calculate the value to find the rate at which the light's projection moves along the wall in feet per second.

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In 5 years from 2020, the two colleges will have the same enrollment and At that time, both colleges will have an enrollment of 21,200 students.

To determine when the two colleges will have the same enrollment, we can set up an equation based on the given information.

Let's assume "x" represents the number of years from 2020.

For College A, the projected enrollment can be expressed as:

Enrollment_A = 18,700 + 500x

For College B, the projected enrollment can be expressed as:

Enrollment_B = 26,200 - 1000x

To find when the two enrollments will be equal, we set Enrollment_A equal to Enrollment_B and solve for "x":

18,700 + 500x = 26,200 - 1000x

Combining like terms:

1500x = 7,500

Dividing both sides by 1500:

x = 5

Therefore, in 5 years from 2020, the two colleges will have the same enrollment.

To find the enrollment at that time, we substitute "x = 5" into either of the enrollment equations. Let's use Enrollment_A:

Enrollment_A = 18,700 + 500(5)

Enrollment_A = 18,700 + 2500

Enrollment_A = 21,200

At that time, both colleges will have an enrollment of 21,200 students.

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(1) The full payment required on January 22 to reduce the balance on the invoice to zero is $136,294.57.

(2)The full payment required on October 19 to reduce the balance on the invoice to zero is $98,482.75.

(3)The full payment required on April 3 to reduce the balance on the invoice to zero is $48,190.38.

The calculation of the full payment required takes into account the terms specified on the invoice. In the first scenario, the invoice terms are 2/10, n/30, which means that a 2% discount can be applied if payment is made within 10 days, otherwise, the full payment is due within 30 days.

Therefore, the full payment is calculated as the invoice amount minus the discount. Similarly, for the second scenario, the invoice terms are 3/10, 2/20, 1/30, and n/50, which involve multiple discounts based on different payment dates.

The full payment is determined by applying the applicable discounts. Finally, in the third scenario, the invoice terms are ROG (Receipt of Goods), and the full payment is due by April 15. Hence, the full payment required on the specified date is calculated.

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(a) To compute the experimental probability of rolling a 1 or 6 from Latoya's results, we need to determine the number of times a 1 or 6 was rolled and divide it by the total number of rolls Latoya made.

Let's assume that Latoya rolled the dice 100 times and obtained 20 1's and 10 6's. The total number of successful outcomes (rolling a 1 or 6) is 20 + 10 = 30.

Therefore, the experimental probability of rolling a 1 or 6 is 30/100 = 0.3 or 30%.

(b) Assuming the cube is fair, the theoretical probability of rolling a 1 or 6 can be determined by considering the favorable outcomes (rolling a 1 or 6) divided by the total possible outcomes (rolling any number from 1 to 6).

Since there are two favorable outcomes (1 and 6) out of six possible outcomes (1, 2, 3, 4, 5, 6), the theoretical probability is 2/6 = 1/3 or approximately 0.3333.

(c) The correct statement is B. As the number of rolls increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal. This is due to the law of large numbers, which states that as more trials are conducted, the experimental probability tends to converge towards the theoretical probability. However, it is not necessary for them to be exactly equal. Random variations can cause some discrepancy, but with a larger number of rolls, the experimental probability should approach the theoretical probability more closely.

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Answer:

x² - 11x + 5 = 0

Step-by-step explanation:

the standard form of a quadratic equation is

ax² + bx + c = 0 ( a ≠ 0 )

given

- 3x² + 2 - 11x = - 4x² - 3 ( add 4x² to both sides )

x² + 2 - 11x = - 3 ( add 3 to both sides )

x² + 5 - 11x = 0 , that is

x² - 11x + 5 = 0 ← in standard form

Answer:

The interval from -12 to -7

The interval from 6 to 12.

Step-by-step explanation:

The equation is log(x + 9) + log(x 9) = log[(x + 9)(x 9)]. = log(x² − 81)

Here is the equation:

log(x² - 81) = 0.47712

This can be expressed in exponential form:

x² - 81 = 10^(0.47712)

x² = 81 + 3.02343

x² = 84.02343

x ≈ ± 9.1658

The answers are therefore x -9.1658 and x 9.1658.

These intervals are where these solutions occur:

The answer, x -9.1658, can be found in the range from -12 to -7.

- The answer x = 9.1658 is found in the range of 6 to 12.

The appropriate choices are:

- The range between -7 and -12; - The range between 6 and 12.

Step-by-step explanation:

I am going to assume that = sign should be the ≅.

For the Statements :

1. AB=DC

AB ll DC

2. Line AC is the transversal of AB and CD

3. Angle BAC ≅ Angle DCA

4. Angle BCA ≅ Angle DAC

5. Line AC=Line AC

6. Triangle ABC ≅ Triangle CDA

For the Reasons:

1. Given

2. Definition of a transversal

3. Alternate Interior Angles

4. Alternate Interior Angles

5. Reflexive Property

6. ASA

The expression which represents the quotient of the model is x² + 5x.

The correct answer choice is option B.

The quotient of a number is the number resulting from the division of one number by another.

There is one x²

There are 5 x

Hence, the quotient of the expression is x² + 5x

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Work Shown:

y = 5x+8

0 = 5*8+8

0 = 40+8

0 = 48

The last equation is false, so the original equation is false when x = 8 and y = 0. This means the point (8,0) is NOT found on the line.

Visual confirmation is shown below.

The system of equations that is represented by the graph include:

D. y = x - 4

   [tex]y=\frac{x-4}{x+2}[/tex]

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of the red line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (0 + 5)/(4 + 1)

Slope (m) = 5/5

Slope (m) = 1

At point (4, 0) and a slope of 1, a linear equation for C can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 0 = 1(x - 4)

y = x - 4

Since the rational function has a y-intercept of (0, -2), it would have a vertical asymptote and the denominator would be undefined at x = 2;

[tex]y=\frac{x-4}{x+2}[/tex]

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

11 yards and 3 feet

Therefore, the quotient when x³ - x² - 3x + 2 is divided by x - 2 is x² - 2x - 5 with a remainder of -3.

To find the quotient when x³ - x² - 3x + 2 is divided by x - 2, we will use the long division method. Here is the solution:  

Step 1: The first term of the quotient is x². Multiply x² by x - 2 to get x³ - 2x². Subtract this product from x³ - x² to get: x² - 3x² = -2x²

Step 2: Bring down the next term of the dividend, which is -3x. The new dividend is -2x² - 3x.

Step 3: The second term of the quotient is -2x. Multiply -2x by x - 2 to get -2x² + 4x. Subtract this product from -2x² - 3x to get -5x.

Step 4: Bring down the last term of the dividend, which is +2. The new dividend is -5x + 2. Step 5: The third term of the quotient is -5. Multiply -5 by x - 2 to get -5x + 10. Subtract this product from -5x + 2 to get -3.

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Answer: $2.21

Step-by-step explanation:

To calculate the cost per pound of mushrooms, we need to use the yield factor given in the question. The yield factor tells us the percentage of the total weight of the mushrooms that can be used for cooking or sale. Here, the yield factor is 90%, which means that 90% of the weight of the mushrooms can be used. Let's begin with the calculation:

First, we need to find out how much of the weight of the mushrooms is usable: 90% of 15 pounds = 0.9 x 15 = 13.5 pounds

Now, we can find out the cost per pound of the mushrooms:

Cost per pound = Total cost / Total usable weight

Total cost = $29.85

Total usable weight = 13.5 pounds

Therefore, the cost per pound of mushrooms = $29.85 / 13.5 pounds ≈ $2.21 per pound

Therefore, the cost per pound of mushrooms is $2.21 per pound.

The amount that can be withdrawn immediately after the last deposit is approximately $8,876.80.

We can use the formula for the future value of an ordinary annuity. The formula is given by:

[tex]FV = P * [(1 + r/n)^(^n^t^) - 1] / (r/n)[/tex]

Where

Given:

Plugging in the values, we have:

[tex]FV = 480 * [(1 + 0.045/2)^(^2*^8^) - 1] / (0.045/2)[/tex]

Calculating the expression inside the brackets

[tex](1 + 0.045/2)^(^2^*^8^) = 1.0225^1^6[/tex]≈ 1.4197

Substituting this value back into the formula:

FV = 480 * (1.4197 - 1) / (0.045/2)

FV = 480 * 0.4197 / 0.0225

FV ≈ $8,876.80

So, the amount that can be withdrawn immediately after the last deposit is approximately $8,876.80.

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The area of the trapezium with bases 20cm and 10cm and a height of 16cm is 240 square centimeters.

A trapezium is simply a two-dimensional quadrilateral that has one pair of parallel sides.

The area of a trapezium is expressed as:

Area = 1/2 × ( a + b ) × h

Where a and b are the base measure and h is the height.

From the diagram:

Base a = 20 cm

Base b = 10 cm

Height h 16 cm

Area = ?

Plug the values into the above formula and solve for the area:

Area = 1/2 × ( a + b ) × h

Area = 1/2 × ( 20 + 10 ) × 16

Area = 1/2 × ( 30 ) × 16

Area = 15 × 16

Area = 240 cm²

Therefore, the area of the trapezium is 240 square centimeters.

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The arrow is at a height of 48 ft after approx. 3 - √6 s and after 3 + √6 s.

To find the time it takes for the arrow to reach a height of 48 ft, we can use the formula for the height of the arrow:

s = v0t - 16t^2

Here, s represents the height of the arrow, v0 is the initial velocity, and t is the time.

Given that the initial velocity, v0, is 96 ft/s and the height, s, is 48 ft, we can set up the equation:

48 = 96t - 16t^2

Now, let's solve this equation to find the time it takes for the arrow to reach a height of 48 ft.

Rearranging the equation:

16t^2 - 96t + 48 = 0

Dividing the equation by 16 to simplify:

t^2 - 6*t + 3 = 0

We now have a quadratic equation in the form of at^2 + bt + c = 0, where a = 1, b = -6, and c = 3.

Using the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / (2a)

Plugging in the values:

t = (6 ± √((-6)^2 - 413)) / (2*1)

t = (6 ± √(36 - 12)) / 2

t = (6 ± √24) / 2

Simplifying the square root:

t = (6 ± 2√6) / 2

t = 3 ± √6

Therefore, the arrow reaches a height of 48 ft after approximately 3 + √6 seconds and 3 - √6 seconds.

In summary, the arrow takes approximately 3 + √6 seconds and 3 - √6 seconds to reach a height of 48 ft, assuming an initial velocity of 96 ft/s.

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Note the complete question is

The height of an arrow shot upward can be given by the formula s = v0*t - 16*t², where v0 is the initial velocity and t is time.How long does it take for the arrow to reach a height of 48 ft if it has an initial velocity of 96 ft/s?  

Solve (t-3)^2=6

The arrow is at a height of 48 ft after approx. ___ s and after ___ s.

The top left graph represents the weight of the radioactive isotope over time.

An exponential function has the definition presented according to the equation as follows:

[tex]y = ab^x[/tex]

In which the parameters are given as follows:

The parameter values for the function in this problem are given as follows:

a = 96, b = 0.5.

Hence the function is given as follows:

[tex]y = 96(0.5)^x[/tex]

Two points on the graph of the function are given as follows:

(1,48) and (2, 24).

Hence the top left graph represents the weight of the radioactive isotope over time.

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Answer:

Graph W

Step-by-step explanation:

The given information describes a radioactive decay process, where the weight of the isotope decreases by half at regular intervals. This type of decay is characteristic of exponential decay.

Based on the description, the graph that represents the weight of the radioactive isotope over time would be a decreasing exponential curve, where the y-axis represents the weight of the isotope (in grams), and the x-axis represents time (in hours).

The initial weight of the isotope is 96 grams, and after each subsequent hour, the weight becomes half of what it was in the previous hour. Therefore, the correct graph would start at 96 grams (the initial weight when x = 0) and then decrease by half every hour. It would be a curve that gets closer and closer to zero but never quite reaches it.

Initial weight: 96 grams

After 1 hour: 96 / 2 = 48 grams

After 2 hours: 48 / 2 = 24 grams

After 3 hours: 24 / 2 = 12 grams

After 4 hours: 12 / 2 = 6 grams

After 5 hours: 6 / 2 = 3 grams

So, the points on the graph would be:

Therefore, the graph that represents the weight of the radioactive isotope over time is Graph W.

a) The experimental probability of landing on red or yellow is:

P(red or yellow) = 33/40

b) The theoretical probability can be computed as follows:

P(red or yellow)  = 8/10

c) As the number of spins increases: Option A: we expect the experimental and theoretical probabilities to become closer, though they might not be equal.

Theoretical probability represents the likelihood of an event occurring. The theoretical probability of getting heads is 1/2, because we know that the probability of heads and tails on a coin is equal. Experimental probability describes how often an event actually occurred in an experiment.  

a) The experimental probability of landing on red or yellow is:

P(red or yellow) = (20/40) + (13/40) = 33/40

b) The theoretical probability can be computed as follows:

P(red or yellow) = (4/10) + (4/10) = 8/10

c) As the number of spins increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal.

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The statement "there exists x ∈ S ∖ m" means that there exists an element x that belongs to the set S but does not belong to the set m. In other words, x is an element that is present in S but is not present in m.

The phrase "m ⊊ m ∪ {x} ∈ X" states that the set m is a proper subset of the set m ∪ {x}, and this union belongs to the set X. This implies that the set m ∪ {x} contains all the elements of m along with the additional element x.

The phrase "a contradiction" indicates that the statement or assumption being made leads to a logical inconsistency or contradiction. In this context, the contradiction arises from the fact that the assumption that x is not in m contradicts the statement that m ∪ {x} is a proper superset of m.

Overall, the given statement implies that the existence of an element x in S, which is not in m, leads to a contradiction when considering the relationship between m and m ∪ {x}.

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Answer:

24 u jus gotta multiply by 3 cuz it is 1 out of 3

Step-by-step explanation: hi :)