a) Si el área de uno de los rectángulos
es de 156 cm2, ¿Cuáles son sus
dimensiones?

Answer:

5,6,7

Step-by-step explanation:

the unfilled circle means that you dony inclued 4, and since the blue line is going u the scale means it can be any number higher than 4

If the school now has 1,378 students enrolled, last year, the number of students enrolled was B. 1,300.

Using the mathematical operations of addition, subtraction, division, and multiplication, we can determine the number of students.

Mathematical operations help us to determine unknown values, given a known domain.

Increase in school enrollment over last year's = 6%

Enrollment for the current year = 1,378

Let last year's enrollment = 100%

And the current year's = 1.06 (100 + 6)

Therefore, the enrollment last year = 1,300 (1,378/1.06)

Thus, the enrollment (number) last school year was B. 1,300.

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The total revenue that will be maximized is 20 - 2a

From the question, we have the following parameters that can be used in our computation:

Qd = 20 - P

The revenue equation is calculated using

Revenue = Quantity * Price

So, we have

R = Qd * P

This gives

R = (20 - P) * P

Expand

R = 20P - P²

Differentiate

R' = 20 - 2P

Next, we have

Q = a

So, we have

R = 20 - 2a

Hence, the total revenue that will be maximized is 20 - 2a

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The equation x/2 = 53 represents the scenario where Mark had a number in mind and halved it to obtain 53.

The number that Mark was thinking of as x. According to the information given, Mark halved the number and obtained an answer of 53. This can be written as:

x/2 = 53

In this equation, x represents the unknown number that Mark was thinking of, and x/2 represents half of that number. The equation states that half of the number is equal to 53.

To solve for x, we can multiply both sides of the equation by 2 to cancel out the division:

2 * (x/2) = 2 * 53

This simplifies to:

x = 106

Therefore, the number that Mark was thinking of is 106.

In the given scenario, Mark had a number in mind and performed an operation on it. By halving the number, he obtained a result of 53. To find the value of the original number, we can set up an equation using x as the variable.

We start by assigning x as the unknown number that Mark was thinking of. Since Mark halved the number, we can represent this operation as x/2. According to the given information, x/2 is equal to 53. This can be expressed in equation form as x/2 = 53.

Now, our goal is to solve for x and find the value of the original number. To isolate x, we can multiply both sides of the equation by 2. This is done to cancel out the division on the left side, allowing us to obtain the value of x alone.

By multiplying both sides of the equation by 2, we have:

2 * (x/2) = 2 * 53

On the left side, the 2 and 1/2 cancel out, leaving us with x. On the right side, 2 multiplied by 53 gives us 106. Therefore, the equation simplifies to x = 106.

As a result, we find that the number Mark was thinking of is 106. This satisfies the condition that when halved, it yields a result of 53.

In summary, the equation x/2 = 53 represents the scenario where Mark had a number in mind and halved it to obtain 53. By multiplying both sides of the equation by 2, we find that the original number Mark was thinking of is 106.

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Answer:

32

Step-by-step explanation:

Hope it helps!!

The conjecture that describes the pattern in the sequence is current term is 2 added to the previous term and the next term is 10

The sequence is given as:

0, 2, 4, 6, 8

In the above sequence, we can see that each current term is 2 added to the previous term

i.e.

Tn = 2 + Tn-1

Using the above conjecture, we have

Next term = 8 + 2

Evaluate

Next term = 10

Hence, the conjecture that describes the pattern in the sequence is current term is 2 added to the previous term and the next term is 10

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The number of ways for filling 4 positions out 17 applicants is 57120

For the local dry cleaner 17 candidates were interviewed.

There are four positions available cashier, washer, salesperson, and delivery driver.

To calculate number of ways by which they can fill those 4 positions first we need to find the no of ways to select 4 candidates out of 17 candidates.

No of ways to select r candidates out of n

= nCr

=( n!) / (r!)(n-r)!

= 17!/( 4! ) ( 17-4)!

17Cr = 2380.

For assigning the four positions to the four candidates there are

17C4 x 4! ways.

So, The number of ways for filling 4 positions out 17 applicants = 2380 x 4!

The answer to this problem is 57120.

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With the given ratio of red to blue cars, which is 3:4, Evan has 16 blue toy cars.

To find the number of cars, follow these steps  -

1: Identify the ratio - Red cars:Blue cars = 3:4

2: Determine the number of red cars - Evan has 12 red toy cars.

3: Find the ratio equivalent to the number of red cars - 12 red cars / 3 (from the ratio) = 4

4: Multiply the ratio of blue cars by the equivalent found in step 3 - 4 (from the ratio) * 4 = 16

So, Evan has 16 blue toy cars.

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Answer:

RQ = 7.4

Step-by-step explanation:

From the right triangle PQR,

m∠Q = 90°

m∠P = 55°

Hypotenuse PR = 9

By applying sine rule in the given triangle,

Sin(55°) = \(\frac{\text{Opposite side}}{\text{Hypotenuse}}\)

0.819152 = \(\frac{\text{RQ}}{\text{PR}}\)

0.819152 = \(\frac{RQ}{9}\)

RQ = 9×0.819152

RQ = 7.37

     ≈ 7.4

Answer: -x+9

Step-by-step explanation:

The total cost of each utility eliminating 450 tons of pollution is $180,000.

To calculate the total cost for each utility to eliminate 450 tons of pollution, we need to multiply the cost per ton of pollution elimination by the number of tons each utility needs to eliminate.

For People's Electric, the cost of eliminating one ton of pollution is $400. So, to eliminate 450 tons, the total cost would be 450 tons * $400/ton = $180,000.

For Municipal Energy, the cost of eliminating one ton of pollution is $350. Again, to eliminate 450 tons, the total cost would be 450 tons * $350/ton = $157,500.

Therefore, the total cost for each utility to eliminate 450 tons of pollution is $180,000 for People's Electric and $157,500 for Municipal Energy.

The cost calculation is based on the given information that each utility is provided with 450 pollution permits by the government. These permits allow them to legally produce a ton of pollution. By setting a limit on the number of permits, the government aims to reduce pollution by half. The utilities have the option to trade permits with each other.

In this scenario, People's Electric has a higher cost of eliminating pollution per ton compared to Municipal Energy ($400 vs. $350). It means that People's Electric would find it more expensive to reduce pollution through internal measures like investing in cleaner technology or implementing environmental initiatives. On the other hand, Municipal Energy has a lower cost, indicating that they have relatively more cost-effective methods for pollution reduction.

Given these costs, it is more beneficial for People's Electric to purchase permits from Municipal Energy rather than eliminating the pollution themselves. By purchasing permits, People's Electric can meet the pollution reduction target at a lower cost. Conversely, Municipal Energy can generate additional revenue by selling their permits.

This permit trading mechanism allows for cost efficiency in achieving the government's pollution reduction goal. The total cost for each utility is determined by multiplying the cost per ton of pollution elimination with the number of tons they need to eliminate.

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Answer:

It depends

Step-by-step explanation:

Does the question specify how many decimal places you are rounding to?

If it's to 1: 0.2, as the next digit is 1 so you round down if it's less than 5

If it's to 2: 0.22 - as the next digit is 8 and you round up if it's greater than or equal to 5.

If it's to 3: 0.218 - as the next digit is 2 so you round down for the reasons above.

If it's to 4: 0.2183 - as the next digit is 5 so you round up for the reasons above.

Hope this helps! Let me know if you have any questions :)

The appropriate form of the partial fraction decomposition for the function 4x/((x-7)^2(x^2 + 2)) is A/(x-7) + B/(x-7)^2 + (Cx + D)/(x^2 + 2).

To find the appropriate form of the partial fraction decomposition for the function 4x/((x-7)^2(x^2 + 2)), we follow a systematic approach. First, we factorize the denominator to identify the distinct linear and irreducible quadratic factors:

Denominator: (x-7)^2(x^2 + 2)

The denominator consists of two linear factors: (x-7) and (x^2 + 2). Since the quadratic factor, x^2 + 2, cannot be factored further over real numbers, we treat it as an irreducible quadratic.

Now, we proceed to the partial fraction decomposition by assuming the numerator of the original function as:

4x = A/(x-7) + B/(x-7)^2 + (Cx + D)/(x^2 + 2)

To determine the unknown coefficients A, B, C, and D, we perform the common denominator operation:

4x = A(x-7)(x^2 + 2) + B(x^2 + 2) + (Cx + D)(x-7)^2

Next, we simplify this equation by expanding and collecting like terms:

4x = A(x^3 - 5x^2 - 14x + 14) + B(x^2 + 2) + (Cx^3 - 7Cx^2 - 14Cx + Dx^2 - 14Dx + 49C - 49D)

Now, we group the terms with the same powers of x:

4x = (A + C)x^3 + (-5A - 7C + D)x^2 + (-14A - 14C - 14D)x + (14A + 2B + 49C - 49D)

By comparing the coefficients of x^3, x^2, x, and the constant term on both sides of the equation, we can form a system of equations to solve for the unknown coefficients A, B, C, and D.

The resulting system of equations is:

A + C = 0          (coefficients of x^3)

-5A - 7C + D = 0  (coefficients of x^2)

-14A - 14C - 14D = 4 (coefficients of x)

14A + 2B + 49C - 49D = 0 (constant term)

By solving this system of equations, you can find the appropriate values for A, B, C, and D, which will complete the partial fraction decomposition of the given function.

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The population size of mantis shrimp will be approximately 266 individuals after 5 years.

The intrinsic rate of increase is an essential concept in population biology. It is the rate at which a population is growing at a particular moment in time. The population size after a particular period can be calculated using the intrinsic rate of increase with the help of this formula:

Nt = N0e^(rt)

where Nt is the future population size, N0 is the initial population size, r is the intrinsic rate of increase, and t is the time in years.

The population size of mantis shrimp is 475 individuals and the intrinsic rate of increase is -0.10.

We can calculate the population size after 5 years using the above formula as follows:

Nt = N0e^(rt)

Nt = 475 * e^(-0.10 * 5)

Nt = 475 * e^(-0.50)

Nt ≈ 266

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Answer:

13.2 g

Step-by-step explanation:

let x = grams sugar in a 200 ml glass

16.5 g sugar / 250 ml = x g sugar / 200 ml

x(250) = (16.5)(200)

x =  (16.5)(200) / (250) = 3300 / 250 = 13.2

Answer:  there are 13.2 g sugar in a 200 ml glass of juice

\(\text{Hi there! :D}\)

\(\boxed{\text{There is a horizontal shift of 1 unit left and 5 units down.}}\)

\(\text{Recall that the transformations form of a quadratic function is:}\\\\y = \pm a(b(x-h))+k \text{ where:}\\\\a = \text{ vertical stretch/compression}\\\\b = \text{ horizontal stretch/compression}\\\\h = \text{ shift left/right}\\\\k = \text{ shift up/down}\\\\\text{Therefore, in this instance:}\\\\h = -1\\\\k = -5, \text{ so:}\\\\\text{There is a horizontal shift of 1 unit left and 5 units down.}\)

Answer: 5 1/4

Step-by-step explanation:

hope this helps!

The translation from figure 1 to figure 2 is 4 units to the left and one unit up.

Here we have two figures, the blue one is figure 1 and the orange one is figure 2.

Clearly we have a translation here, to identify the translation just analyze one of the vertices.

The top vertex at the blue figure is (2, 1)

The top vertex at the orange figure is (-2, 2)

The translation is given by:

T = (-2, 2) - (2, 1) = (-4, 1)

So we have a translation of 4 units to the left and one unit up.

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Answer:

Step-by-step explanation:

answer is a

Answer:

The answer is X = 18

Step-by-step explanation:

2x/3 - 7 = 5

Multiply both sides if the equation by 3 : 2x - 21 = 15

Move the constant to the right hand side and change its sign : 2x = 15 + 21

Calculate 2x = 15 + 21

2x = 36

Divide both sides of the eqaution by 2 : 2x = 36

x = 18

Answer X = 18

Answer:

f(x)=3x-4

Step-by-step explanation:

just replace the y with f(x)

Answer:

2+2%2%5+51%895%+8+81%9+61%+5%+8+%15+%

Answer:

(- 8, - 6 )

Step-by-step explanation:

y = 2x + 10 → (1)

y = x + 2 → (2)

substitute y = 2x + 10 into (2)

2x + 10 = x + 2 ( subtract x from both sides )

x + 10 = 2 ( subtract 10 from both sides )

x = - 8

substitute x = - 8 into either of the 2 equations and evaluate for y

substituting into (2)

y = - 8 + 2 = - 6

solution is (- 8, - 6 )

Answer:

Answer:-

Your answer is D)81

Step-by-step explanation:

As 81 is an odd number so the square of 81 will also be odd

hence proved

Step-by-step explanation:

To find the consumer surplus, we need to first find the equilibrium quantity at the given sales level of 800. To do this, we set the demand function equal to 800 and solve for q:

770 - 0.3q - 0.0004q^2 = 800

0.0004q^2 + 0.3q - 30 = 0

Using the quadratic formula, we get:

q = (-0.3 ± sqrt(0.3^2 - 4(0.0004)(-30))) / (2(0.0004))

q = 387.97 or q = -77.47

Since the negative quantity doesn't make sense in this context, we can disregard it and conclude that the equilibrium quantity at a sales level of 800 is approximately 388.

To find the consumer surplus, we need to calculate the area between the demand curve and the price line up to the quantity of 388. We can do this by taking the integral of the demand function from q = 0 to q = 388 and subtracting the total revenue earned at the quantity of 388:

CS = ∫[770 - 0.3q - 0.0004q^2]dq - (770 - 0.3(388)) * 388

CS = 217,829.32 - 66,224 = 151,605.32

Rounding to two decimal places, the consumer surplus is $151,605.32.

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Answer: 3/52

Step-by-step explanation:

You want to pick a diamond jack, diamond queen or diamond king

There are only 3 of those so

P(DJ or DQ or DK) = 3/52        There are 3 of those out of 52 total

Answer:

The slope is \(\frac{2}{3}\)

Step-by-step explanation:

The slope formula: \(m=\frac{y2-y1}{x2-x1}\)

The two coordinates given: (1, -9) and (4, -7)

-

Let's substitute and solve:

\(m = \frac{-7-(-9)}{4-1} \\m = \frac{2}{3}\)

Step-by-step explanation:

the sum of all angles in a triangle is 180 degrees.

so,

x + (x - 6) + (2x + 34) = 180

x + x - 6 + 2x + 34 = 180

4x + 28 = 180

4x = 152

x = 38 degrees

x - 6 = 32 degrees

2x + 34 = 110 degrees

Answer and explanation:

Take the area formula:

A = L * W

Then manipulate it to fit the context of which unknown you are finding:

Problem 1

\(\dfrac{36 = 4 * W}{4}\)

\(9 = W\)

So, the length of side c is 9 mm.

Problem 2

\(\dfrac{21 = W * 21}{21}\)

\(1 = W\)

So, the length of side a is 1 m.

Problem 3

\(\dfrac{49 = 7 * W}{7}\)

\(7=W\)

So, the length of side t is 7 cm.

Answer:

-3

Step-by-step explanation:

Order of Operations: BPEMDAS

Step 1: Parenthesis

(105 ÷ -5)/(45 ÷ -9 + 12)

Step 2: Divide

-21/(-5 + 12)

Step 3: Parenthesis

-21/7

Step 4: Divide

-3