An aquarium can be modeled as a right rectangular prism. Its dimensions are 14 in by 7 in by 4 in. If the aquarium contains 153 cubic inches of water, what percent is empty

\(5(x + 3y) \\ y(2x - 3)\)

Answer:

Step-by-step explanation:

(2x + 4x + 6x) * 2  = 360*

2x + 4x + 6x = 180°

12x = 180°

x = 180 : 12

x = 15

(2x + x) * 2 = 360

2x + x = 180

3x = 180

x = 180 : 3

x = 60°

Answer:

x= -7

Step-by-step explanation:

the labeled angles are alternate-interior angles which are congruent

we can solve for 'x' by creating this equation:

x+139 = 132

x = -7

The length of the midsegment of this trapezoid is 8 units. Mid segment of a trapezoid is equal to half of sum of its two parallel sides.

A midsegment of a triangle is defined as a line segment that connects the midpoints or center of two opposite sides of a triangle or adjacent sides of a triangle. The midsegment theorem is defined as a line segment that joins the midpoints of any two sides of a triangle is parallel to the third side of a triangle and is half of it.

The converse of the midsegment theorem states that When a line segment joins two midpoints of two opposite sides of a triangle and is parallel to the third side of a triangle.

So,

Length of mid segment = 1/2(AB+CD)

Applying distance formula,

AB = \(\sqrt{(7-2)^{2} + (4-4)^{2} }\) = \(\sqrt{5^{2} + 0 }\) = 5

CD = \(\sqrt{(9+2)^{2} + (-1+1)^{2} }\) = \(\sqrt{11^{2} + 0 }\) = 11

Hence,

the length of mid-segment = 1/2(5 + 11) = 1/2(16).

⇒ length of mid-segment = 8 unit.

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The value of z such that 0.13 of the area lies to the left of z is z = (1.14). Rounding this to two decimal places gives us z = 1.14 (rounded to two decimal places).

A z-score (aka, a standard score) indicates how many standard deviations an element is from the mean.

A z-score can be calculated from the following formula: z = (X - μ) / σwhere:z = the z-scores = the value of the elementμ = the population meanσ = the standard deviation

Let z be the value such that 0.13 of the area lies to the left of z.

This means that 87% (100% - 13%) of the area lies to the right of z.

Using the standard normal distribution table, we find the z-score that corresponds to an area of 0.87.

We can also solve this using the inverse normal distribution function of a calculator or statistical software.

The z-score that corresponds to an area of 0.87 is 1.14.

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Answer: 21 cups of sugar, 7 cakes

Solve the following proportion:

3/5=x/35

Cross multiply:

5x=35(3)

5x=105

x=21 cups of sugar

3 cups of sugar= 1 cake

21 cups of sugar= x cakes

Cross multiply:

3x=21

21/3

7 cakes

To find dy/dt, we will first differentiate the given equation y = cos(6x) with respect to t using the chain rule.

Differentiating both sides of the equation with respect to t, we get:
dy/dt = -6sin(6x) * dx/dt

Now, we are given that x = π/12 and dx/dt = -4 when x = π/12. Substitute these values into the equation:
dy/dt = -6sin(6(π/12)) * (-4)
dy/dt = -6sin(π/2) * (-4)

Since sin(π/2) = 1, we have:
dy/dt = -6 * 1 * (-4)
dy/dt = 24

So, when x = π/12 and dx/dt = -4, dy/dt = 24.

To find dy/dt, we need to differentiate both sides of the equation y = cos(6x) with respect to t using the chain rule:
dy/dt = -sin(6x) * d(6x)/dt

Since x is a function of t, we can use the chain rule again to find d(6x)/dt:
d(6x)/dt = 6 * dx/dt

Now we can substitute dx/dt = -4 and x = pi/12 into the above equations to get:
d(6x)/dt = 6 * (-4) = -24

and
sin(6x) = sin(6 * pi/12) = sin(pi) = 0

Therefore, we have:
dy/dt = -sin(6x) * d(6x)/dt = 0 * (-24) = 0

So the exact answer is dy/dt = 0.

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Answer:

(x, y) ⇒ (-y, x)

Step-by-step explanation:

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, rotation, translation and dilation.

Rotation is the flipping of a figure about a point. If a point A(x, y) is rotated 90 degrees counterclockwise about the origin the new location of the point is at A'(-y, x).

Given a triangle with vertices at  E (2, -4). F (3, 6) And G (8, -7). If the triangle is rotated 90 degrees counterclockwise about the origin, the new location is at:

E'(4, 2), F'(-6, 3) and G'(7, 8).

The rule (x, y) ⇒ (-y, x) was used

The shape parameter is 10 and the rate parameter is 1/3.75 = 0.2667.

In a Poisson process, the number of events (in this case, phone calls) occurring in a fixed interval of time follows a Poisson distribution. The shape parameter of the Gamma distribution is related to the number of events, and the rate parameter is related to the rate of occurrence.

In this case, we have an average rate of 4 calls per 15 minutes. The rate parameter of the Gamma distribution is the reciprocal of the average time between events. Since the average rate is 4 calls per 15 minutes, the average time between events is 15 minutes divided by 4 calls, which is 3.75 minutes per call.

The shape parameter of the Gamma distribution is related to the number of events. Here, we are interested in the time until the next 10 phone calls occur. Since the time until the next 10 calls occur is Gamma distributed, the shape parameter is 10.

Therefore, the shape parameter is 10 and the rate parameter is 1/3.75 = 0.2667.

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Answer:

10

Step-by-step explanation:

K is the midpoint between 60 and 80.

Distance between 60 and 80 is,

80 - 60 = 20

Distance between K and H is,

20 / 2 = 10

Answer:

Market price = 3,361.4 (Approx.)

Step-by-step explanation:

Given:

Selling price = 3,430

Discount percentage =2 %

Find:

Market price

Computation:

Market price = Selling price [1-2%]

Market price = 3,430 (1-2%)

Market price = 3,361.4 (Approx.)

The abelian groups (up to isomorphism) of order 360 are:

1. C360: The cyclic group of order 360.2. C2 x C2 x C3 x C3 x C5: The direct product of cyclic groups of orders 2, 2, 3, 3, and 5.

To find all abelian groups of order 360, we need to consider the prime factorization of 360, which is 2^3 × 3^2 × 5. The abelian groups will be direct products of cyclic groups whose orders divide 360.

First, we consider the cyclic groups. Since the order of an element in a cyclic group divides the order of the group, we can have cyclic subgroups of orders 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, and 360.

Now, we can combine these cyclic subgroups to form the abelian groups. We can take direct products of the cyclic groups to obtain different possibilities. The order of the resulting group will be the product of the orders of the cyclic subgroups.

In this case, we can form the following abelian groups of order 360:

C360: This is the cyclic group of order 360 itself.

C2 x C2 x C3 x C3 x C5: This is the direct product of cyclic groups of orders 2, 2, 3, 3, and 5.

These are the two abelian groups (up to isomorphism) that can be formed using the prime factorization of 360.

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Answer: $7.65 for a dozen/12

Step-by-step explanation: 2.55 x 3

Answer:

The correct answer is A

Step-by-step explanation:

2 is exactly 7 units away from -5.

The correct answer is option d. The theoretical Probability of spinning a multiple of 3 with one spin is 0.

The theoretical probability of an event, we need to identify the number of favorable outcomes (the desired event) and the total number of possible outcomes.

In this case, the event is spinning a multiple of 3 on the spinner. Let's examine the possible outcomes and identify the favorable outcomes:

Possible outcomes on the spinner: {1, 2, 3, 4, 5, 6}

Favorable outcomes (multiples of 3): {3, 6}

The total number of possible outcomes is 6, and the number of favorable outcomes is 2.

The theoretical probability of spinning a multiple of 3 can be calculated as:

P(multiple of 3) = (Number of favorable outcomes) / (Total number of possible outcomes)

P(multiple of 3) = 2 / 6

Simplifying the fraction, we get:

P(multiple of 3) = 1 / 3

Therefore, the correct answer is option d. The theoretical probability of spinning a multiple of 3 with one spin is 0.

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The statements are as follows: The two-point forward difference requires two nodes to approximate the derivative. (True)

The two-point forward difference always requires two consecutive nodes to approximate the derivative. (False)

The three-point forward difference requires three consecutive nodes to approximate the derivative. (True)

The two-point forward difference method indeed requires two nodes to approximate the derivative. This method calculates the derivative using the difference between the function values at two neighboring points.

The two-point forward difference method does not always require two consecutive nodes. It can be used with any two nodes, regardless of whether they are consecutive or not. However, using consecutive nodes is a common and straightforward approach.

The three-point forward difference method requires three consecutive nodes to approximate the derivative. It calculates the derivative using the difference between the function values at three consecutive points. This method provides higher accuracy compared to the two-point forward difference method.

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The inverse of the table is (5 - x) / 2

The inverse of the function is y = -9x/2.

What is linear equation?

The standard linear equation is represented as y = mx + b

where: m is the slope

           b is the Y- intercept

Now, Using the coordinate points (-2, 9) and (-1, 7) from the table;

Slope = 7 - 9/-1 - (-2)

Slope =-2/1

Slope = -2

Hence, The equation of the table is,

y - 9 = - 2 (x + 2)

y - 9 = -2x - 4

y - 9 + 2x + 4 = 0

2x + y = 5

y = -2x + 5

So, The equation of the table will be y = -2x + 5

Now, Find the inverse as,

y = -2x + 5

x = -2y + 5

2y = 5 - x

y = (5-x)/2

f⁻¹(x) = (5-x)/2

And, The function is;

f (x) = -2/9 x

So, Inverse for the function,

f(x) = -2/9 x

x = -2/9 y

9x = -2y

y = -9x/2

Hence, The inverse of the table is (5 - x) / 2

The inverse of the function is y = -9x/2.

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The simplified form of the exponential expression \(64^{\frac{1}{4} }\) is  \(2\sqrt{2}\)

The given expression = \(64^{\frac{1}{4} }\)

The exponential function is the function in the form of f(x)= \(a^{x}\), where x is the variable and a is the constant. The constant term is the base of the exponential function.

The given expression = \(64^{\frac{1}{4} }\)

Here we have to use the power rule of the exponents

\((a^{m})^{n}=a^{mn}\)

To increase a number with an exponent to the power, we have to multiply the exponent times the power

We know

64 = \(2^{6}\)

Then

\(64^{\frac{1}{4} }\) = \((2^{6})^{\frac{1}{4} }\)

Apply the power rule of the exponent

\((2^{6})^{\frac{1}{4} }\) = \(2^{(6)(\frac{1}{4} )}\)

= \(2^{\frac{3}{2} }\)

= \(2\sqrt{2}\)

Hence, the simplified form of the exponential expression \(64^{\frac{1}{4} }\) is  \(2\sqrt{2}\)

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Answer:

Step-by-step explanation:

8(-1) +4 = -8 +4 = -4 . . . . regardless of the definition of g(x).

__

Perhaps you want

  g(-1) +4

  = (-1)^2 -(-1) +4

  = 1 +1 +4

  g(-1) +4 = 6

Answer:

It costs $0.49 for each avocado and $0.36 for each tomato.

Step-by-step explanation:

This is a system of equations problem.

Let x represent the avocados and y represent tomatoes:

4x + 5y = 3.76  <--- scenario 1

6x + 3y = 4.02 <---- scenario 2

If we graph these out on a graphing calculator, the lines will intersept at point (0.49,0.36)

The x coordinate represents how much it costs for each avacado and the y coordinate represents how much it costs for each tomato

Answer: Terminating decimal

Step-by-step explanation:

change the fraction 58 into a decimal.

58=0.625 .

If y1 and y2 are linearly independent solutions of the equation t^2y'' + 3ty' + 5y = 0 and the Wronskian w(y1, y2)(1) = 2, you want to find w(y1, y2)(4) rounded to two decimal places.

Using Abel's Identity, we know that the Wronskian is constant for linearly independent solutions of a homogeneous linear differential equation with variable coefficients. So, w(y1, y2)(t) = w(y1, y2)(1) = 2 for all t.

Therefore, w(y1, y2)(4) = 2. In decimal form, the answer is 2.00.

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the series Σ(6k/k!) converges.To determine whether the series Σ(6k/k!) from k = 1 to infinity converges or diverges, we can apply the ratio test.

Let's calculate the ratio of consecutive terms:

R = [(6(k+1))/(k+1)!] / [(6k)/k!]

Simplifying this expression:

R = (6(k+1)(k!)) / [(k+1)(k!)(6k)]
 = 6/(6k)
 = 1/k

As k approaches infinity, 1/k approaches 0. Since the ratio R is less than 1 for all k, the series converges.

Therefore, the series Σ(6k/k!) converges.

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After the 6-for-1 stock split, the stock price will be $16.41 per share, assuming no market imperfections or tax effects.

A stock split is a process in which a company increases the number of shares outstanding while proportionally reducing the price per share. In this case, the company plans a 6-for-1 stock split, which means that for every existing share, shareholders will receive six new shares.

To determine the post-split stock price, we divide the original stock price by the split ratio. The original stock price is $98.48, and the split ratio is 6-for-1. Therefore, we calculate:

$98.48 / 6 = $16.41

Hence, after the 6-for-1 stock split, the stock price will be $16.41 per share. This means that each shareholder will now hold six times more shares, but the value of their investment remains the same.

It is important to note that in practice, market imperfections, investor sentiment, and other factors can influence the stock price after a split. However, assuming no market imperfections or tax effects, the calculated value of $16.41 represents the theoretical post-split stock price.

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Answer: 24 model airplanes can be made in 2 hours.

Step-by-step explanation:

Answer:I believe its 24 because each plane takes 5 minutes so that's  12 in an hour so multiply by 2 and you get 24

Step-by-step explanation:

Answer: c and e are correct answer.

Step-by-step explanation:

The sampling technique used in this scenario is known as cluster sampling.

Cluster sampling involves dividing the population into groups or clusters and then randomly selecting entire clusters to include in the sample.

In this case, the population is all the passengers on different cruises, and the clusters are the five randomly selected cruises.

Cluster sampling is a practical and efficient method when it is difficult or costly to obtain a complete list of all individuals in the population.

By selecting entire clusters (in this case, cruises) rather than individual passengers, the researcher can simplify the sampling process and reduce costs.

However, it's important to note that cluster sampling introduces a potential source of bias.

If there are significant differences between the clusters, such as varying demographics or preferences among different cruises, the sample may not be fully representative of the entire population.

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Answer:

the answer is c 1.2

Step-by-step explanation:

to calculate the iqr you have to do the following:

q3 - q1 = answer

4.5 - 3.3 = 1.2

The IQR(interquartile range) for the distribution of the song length is 1.2.

Interquartile range gives information on the spread of the middle half of your distribution.

Mathematically, the interquartile range can be represented as follows:

IQR = Q₃ - Q₁

where

Q₃ = 4.5

Q₁ = 3.3

Therefore,

IQR = 4.5  - 3.3

IQR = 1.2

Therefore, the interquartile range is 1.2.

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Answer:

y- 7 x = 5 answer of this question

Answer:

18m

Step-by-step explanation:

Answer:

18 m would be the answer.......