The volumes of both containers are 6,912 cubic inches.
What is the height of container 2?
Set up an equation using the width and height from con-
tainer 2 to find the missing height.
V = lwh
Container 1
32 in.
12 in.
18 in.
Container 2
24 in.
? in.
16 in.

the rate of discount is double the rate of VAT. The selling price of the article without VAT is Rs. [tex]7,680.[/tex]

Let's assume that the original selling price of the article is Rs. [tex]8,000.[/tex]

Let the rate of discount be x and the rate of VAT be y.

We know that the selling price of the article with discount and VAT is Rs. [tex]6,689.60.[/tex]

So, we can write the following equation:

Selling price = (Original price - Discount) + VAT

[tex]Rs. 6,689.60 = (Rs. 8,000 - Rs. 8,000 x (x/100)) + (Rs. 8,000 - Rs. 8,000 x (x/100)) x (y/100)[/tex]

Simplifying the equation, we get:

[tex]Rs. 6,689.60 = Rs. 8,000 (1 - x/100 + y/100 - xy/10000)[/tex]

Now, we are given that the rate of discount is double the rate of VAT. So, we can write:

[tex]x = 2y[/tex]

Substituting this value in the equation above, we get:

[tex]Rs. 6,689.60 = Rs. 8,000 (1 - 3y/100 + 2y^2/10000)[/tex]

Simplifying this equation further, we get a quadratic equation in y:

[tex]2y^2 - 3y + 0.41505 = 0[/tex]

Solving this quadratic equation using the quadratic formula, we get:

[tex]y = 10.5 or y = 0.01988[/tex]

Since the rate of VAT cannot be 10.5%, we will take y = 0.01988 (approx. 2%).

Now, we can calculate the rate of discount using x = 2y:

x = 4%

So, the selling price of the article without VAT can be calculated as follows:

Selling price without VAT = Original price - Discount

[tex]= Rs. 8,000 - Rs. 8,000 x\times (4/100)[/tex]

[tex]= Rs. 7,680[/tex]

Therefore, the selling price of the article without VAT is Rs. [tex]7,680.[/tex]

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Therefore, the length of LM is 85.5.

Length is a measure of the size or extent of an object or a distance between two points. It refers to the longest dimension of an object or the distance between two points in space, typically measured in units such as inches, centimeters, meters, or miles. In mathematics, length is also used to describe the size of a line segment or a curve, which can be measured using various techniques such as Euclidean distance, arc length, or fractal dimension. Length is an important concept in many fields, including physics, engineering, geometry, and statistics.

Since LM is the midsegment of ABCD, it is parallel to both AB and DC, and its length is equal to the average of the lengths of AB and DC.

The length of LM can be found using the formula:

[tex]LM = (AB + DC) / 2[/tex]

Substituting the given values, we get:

[tex]LM = (46 + 125) / 2[/tex]

[tex]LM = 171 / 2[/tex]

[tex]LM = 85.5[/tex]

Therefore, the length of LM is 85.5.

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The statement "a) the mean of the sampling distribution of sample mean is always the same as that of x, the distribution from which the sample is taken" is not necessarily true.

While the mean of the sampling distribution of the sample mean is an unbiased estimator of the population mean, it is not always equal to the mean of the original distribution from which the sample is taken. This is because the sample mean will vary from sample to sample, and the sampling distribution will reflect this variability.

For example, if the population distribution is skewed or has outliers, the sampling distribution of the sample mean may be more symmetrical and have a different mean. However, as the sample size increases, the sampling distribution of the sample mean will approach a normal distribution with a mean equal to the population mean. This is known as the Central Limit Theorem.

Therefore, the incorrect statement is a).

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The answer is 2.0625

Answer:

33/16=2.0625

Step-by-step explanation:

33/16=2 rounded to the nearest integer

33/16=2.1 rounded to 1 decimal place

33/16=2.06 rounded to 2 decimal places

33/16=2.063 rounded to 3 decimal places

33/16=2.0625 rounded to 4 decimal places

A sentence to explain how I know this is not a perpendicular bisector is that line AB was not divided into two equal halves.

A possible mistake which Aaron made in his construction is: C. he did not use a pair of compasses to draw his arcs.

In Mathematics and Geometry, a perpendicular bisector can be defined as a type of line that bisects or divides a line segment exactly into two (2) equal halves and forms an angle that has a magnitude of 90 degrees at the point of intersection.

This ultimately implies that, the steps taken by Aaron for the construction of the perpendicular bisector for line AB is incorrect because it was not divided into two equal halves, even though it formed an angle that has a magnitude of 90 degrees at the point of intersection.

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To solve the inequality -6x < 36, we need to isolate x on one side of the inequality sign. We can do this by dividing both sides of the inequality by -6, remembering to reverse the inequality sign because we are dividing by a negative number:

-6x < 36

x > -6

Therefore, the solution set for the inequality is {x | x > -6}.

The answer of the given question based on Algebric notation is when x=4 and y=2, the value of 3x + 5y is 22.

An expression is combination of numbers, variables, and mathematical operations like addition, subtraction, multiplication, division, exponentiation, and others. Expressions can be simple or complex, and they can be used to represent a wide range of mathematical concepts, such as equations, inequalities, functions, and formulas. For example, "3x + 5y" is an expression that involves the variables x and y, and the operations of multiplication and addition.

In algebra, expressions are often used to represent relationships between variables, and to solve problems by manipulating the expressions to obtain a desired result.

To find the value of 3x + 5y when x=4 and y=2, we simply substitute these values into the expression and evaluate:

3x + 5y = 3(4) + 5(2) = 12 + 10 = 22

Therefore, when x=4 and y=2, the value of 3x + 5y is 22.

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Find 3x + 5y when x=4 and y=2 (algebric notation)?

Answer:

172.5

Step-by-step explanation:

1/2(perimeter)(Apothem)

10+10+10+10+10=50

1/2(50)(6.9)

172.5

Answer:

273/500

Step-by-step explanation:

54.6% can be changed into a fraction by making it over 100.
This gives us 54.6/100
However, you can change it by making it into an integer by multiplying both sides by 10.
This gives us 546/1000
You can then go on by simplifying this by dividing both sides by 2

273/500.

Hope this helped,
No problem

The passage and Aylmer's dialogue describe his obsession with perfection and his attempts to remove a birthmark from his wife's face.

Aylmer's language is formal and scientific, using technical terms and precise language to describe his work. This enhances the meaning of the passage by highlighting Aylmer's belief in the power of science and his desire to control nature.

For example, Aylmer says, “Georgiana, I have spent much thought upon the subject,” and “I feel myself fully competent to render this dear cheek as faultless as its fellow.”

This language conveys Aylmer's confidence in his abilities and his belief that he can achieve perfection through scientific means. The precise language also reinforces the idea that Aylmer sees his wife's birthmark as a flaw that needs to be eradicated.

Therefore, the diction in Aylmer's dialogue enhances the meaning of Passage 2 by highlighting the theme of obsession with perfection and the power of science to control nature.

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The probability that a randomly selected student studies Hindi or Maths is 0.60 or 60%.

We can use the formula P(A or B) = P(A) + P(B) - P(A and B) to find the probability that a randomly selected student studies Hindi or Maths is calculated by adding the probabilities of studying Hindi and Maths and subtracting the probability of studying both Hindi and Maths.

P(Hindi or Maths) = P(Hindi) + P(Maths) - P(Hindi and Maths)

P(Hindi or Maths) = 0.30 + 0.45 - 0.15

P(Hindi or Maths) = 0.60

Therefore, if a student is selected randomly, then the probability that he/she studies Maths or Hindi is 0.60 or 60%.

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The probability of selecting a pen from the first box is 1/8 (since there is only 1 pen out of 8 items in the box). The probability of selecting a crayon from the second box is 3/6 (since there are 3 crayons out of 6 items in the box).

To find the probability of both events happening together, we multiply the probabilities:

P(pen and crayon) = P(pen) x P(crayon)

P(pen and crayon) = (1/8) x (3/6)

Simplifying the fraction 3/6 to 1/2:

P(pen and crayon) = (1/8) x (1/2)

Multiplying the numerators and denominators:

P(pen and crayon) = 1/16

Therefore, the probability of selecting a pen from the first box and a crayon from the second box is 1/16.

Answer:

These triangles are congruent by AAS.

Answer:

C

Step-by-step explanation:

the nth term of a geometric sequence is

[tex]a_{n}[/tex] = a₁ [tex]r^{n-1}[/tex]

where a₁ is the first term and r the common ratio

here a₁ = - 1 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{-5}{-1}[/tex] = 5

then nth term is

[tex]a_{n}[/tex] = - 1 [tex](5)^{n-1}[/tex]

Answer: 21

In order to find the answer you have to multiply FJ and JH which is equal to 6x+24.

After, multiply GJ and JE which is equal to 90.

After doing all these steps equal your findings:

6x+24= 90

x= 11

The length of FH is asked so, you have found x, which is equal to 11

FH= 6+(11+4)= 21

Answer: See attachment (enlarge line)

Step-by-step explanation:

y = 2x

When x = -1

y = 2(-1)

y = -2

When x = 2

y = 2(2)

y = 4

Plot the points on the graph (-1, -2) and (2, 4)

S is not a basis for R3 because: c. S is linearly dependent and does not span R3.

A basis for a vector space is a set of vectors that are linearly independent and span the space.

Let's check if S = {(1, 1, 1), (0,1,1), (1,0,1), (0, 0, 0)} satisfies this definition of the basis or not.

Here, we have to find if the set is linearly dependent or not. If the set is linearly dependent, then it can't be a basis. To check the linearity of the set, we will set the equation for the linear combination of vectors of set S.

Then α1(1, 1, 1) + α2(0,1,1) + α3(1,0,1) + α4(0, 0, 0) = 0

For the above equation to hold true, α1 + α3 = 0α1 + α2 = 0α1 + α3 = 0

By solving the above equations, we get

α1 = -α3α2 = -α1α4 = 0

The above equation shows that α4 = 0 means there is always a trivial solution which makes it linearly dependent.

Therefore, it is not a basis.

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Answer:

x = -10

Step-by-step explanation:

To solve the equation:

x - 4 = 16 + 3x

Collect like terms:

x - 3x = 16 + 4

Then solve:

-2x = 20

x = -10

Answer: x is -10

Step-by-step explanation:

x - 4 = 16+3x

Transposing the x, and arranging in one side of equation

x - 3x = 16 + 4

now we changed the positions of x and we can simplify it.

so,

x - 3x = -2x -----------------(1)

16 + 4 = 20 ----------------(2)

Therefore the x - 3x = 16 + 4 will change into -2x = 20

Then x = 20 ÷ -2 = -10

x = -10

Based on the data given, the probability of the next roll of the die being a 4 is 30%.

what is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

To find the probability of rolling a 4 on the next roll, we need to divide the number of times 4 was rolled by the total number of rolls. In this case, 4 was rolled 9 times out of a total of 30 rolls.

So the probability of rolling a 4 on the next roll is:

9/30 = 3/10 = 0.3 = 30%

Therefore, based on the data given, the probability of the next roll of the die being a 4 is 30%.

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The expression in terms of x and/or y for

a) angle OAC = y

b) angle OBA = 2x

A circle is a shape consisting of all points in the plane that are at a specified distance from a specified point (center). Correspondingly, it is a curve drawn by points moving in the plane at a constant distance from a point. The distance from any point of the circle to the center is called the radius. Normally the radius should be a positive number.

Specifically, a circle is a simple closed curve that divides a plane into two regions inside and outside. In everyday use, the term "circle" can be used interchangeably to refer to the entire shape, including the boundary or interior of the shape. In strict technical usage the circle is just the boundary and the whole figure is called the disk.

In ΔOCA;

OC = OA  [Radius of circle]

So, m∠OCA = m∠OAC

y = m∠OCA

y = m∠OAC

Similarly in ΔAOB;

m∠OAB = 2x

m∠OAB = m∠OBA

2x = m∠OBA

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The complete question is as follows:

The diagram shows a circle with centre O.

Write an expression in terms of x and/or y for

a) angle OAC.

b) angle OBA.

The rate of change of y when x = 1 is 0.005 unit/sec.

To find the rate of change of y when x = 1 and given that x increases at a rate of 0.02 unit/sec, we'll first find the derivative of the equation y = (2x - 5)/(x + 1) with respect to x, and then multiply it by the rate of change of x (0.02 unit/sec). Differentiate the equation with respect to x:

y = (2x - 5)/(x + 1)

To differentiate this function, we'll use the quotient rule: [tex](u'/v) - (uv')/v^2[/tex], where u = (2x - 5) and v = (x + 1).

u' = derivative of (2x - 5) = 2

v' = derivative of (x + 1) = 1

Now, apply the quotient rule:

dy/dx =[tex](2\times(x + 1) - (2x - 5)\times1) / (x + 1)^2[/tex]

Plug in x = 1:

dy/dx =[tex](2\times(1 + 1) - (2\times1 - 5)\times1) / (1 + 1)^2[/tex]

dy/dx = (4 - 3) / 4

dy/dx = 1/4

Multiply the derivative by the rate of change of x:

The rate of change of x is 0.02 unit/sec, so the rate of change of y when x = 1 is:

Rate of change of y = (dy/dx) × (rate of change of x)

Rate of change of y = (1/4) × 0.02 = 0.005 unit/sec

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Answer:

238

Step-by-step explanation:

Formula: 2(aXb + bXc + cXa)

let, a = 7 m

     b = 7 m

     c = 5 m

then,

      2(7X7 +7X5 + 7X5)

      = 2(49 + 35 + 35)

      = 2 X 119

      = 238

We want a circle that has center (-1,4) and just skims y=2. We can find the equation of the circle knowing its center and its radius. Knowing that it skims y=2 the radius=4-2=2 (Do you know why? Think visually). Then, the standard form of a circle is given by (x-h)^2+(y-k)^2=r^2 where (h,k) is the center and r is the radius. So the equation is (x+1)^2+(y-4)^2=4

Answer:

The area of the rectangle is 24x^5 y^2.

Step-by-step explanation:

To find the area of a rectangle when the length is represented by 8x³y² and the width is represented by 3x²yº, you need to multiply the length by the width.

8x³y² represents the length and 3x²yº represents the width.

Therefore, the area (A) of the rectangle can be calculated as:

A = length x width

A = 8x³y² x 3x²yº

To simplify this expression, you can use the laws of exponents:

A = 8x³y² x 3x²y°

A = 8 x 3 x x³ x x² x y² x yº

A = 24x^(3+2) y^(2+0)

Simplifying further:

A = 24x^5 y^2

Therefore, the area of the rectangle is 24x^5 y^2.

Answer:

I'm going to make it more simple for you so you don't have to read his book (no offence to that guy)

the area of the rectangle is 24x^5 y^2.

For expression a(x+2) = b(x-1), x will be (-b - 2a)/(a - b).

What exactly are expressions?

In mathematics, an expression is a combination of numbers, variables, operators, and/or functions that can be evaluated to produce a numerical value. Expressions can range from simple calculations involving only arithmetic operations such as addition, subtraction, multiplication, and division, to more complex combinations of algebraic expressions and functions.

Now,

To solve for x in the equation a(x+2) = b(x-1), we can use algebraic manipulation:

a(x+2) = b(x-1)

ax + 2a = bx - b [distribute the terms]

ax - bx = -b - 2a [subtract bx and 2a from both sides]

x(a - b) = -b - 2a [factor out x]

x = (-b - 2a)/(a - b)

Therefore,

                 x = (-b - 2a)/(a - b).

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Answer:

Step-by-step explanation:

75

Answer:$75

Step-by-step explanation:

Answer: The variables h and k in the general formula for a cube root function affect the graph by causing a horizontal and vertical shift, respectively. The value of h determines the horizontal position of the graph by shifting it to the right or left along the x-axis. If h is positive, the graph will shift to the right, and if h is negative, the graph will shift to the left. On the other hand, the value of k determines the vertical position of the graph by shifting it up or down along the y-axis. If k is positive, the graph will shift upward, and if k is negative, the graph will shift downward. It is important to note that these shifts do not affect the shape of the graph, only its position on the coordinate plane. Therefore, changing the values of h and k in the general formula for a cube root function will cause the graph to shift, but the overall shape of the graph will remain the same.

Step-by-step explanation:

The domain of the expression is (−∞,−5)∪(−5,7)∪(7,∞).

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input.

Here the given expression is,

=> [tex]\frac{3}{x+5}-\frac{1}{7-x}[/tex]

Now simplifying the expression then,

=> [tex]\frac{3(7-x)-1(x+5)}{(x+5)(7-x)}[/tex]

=> [tex]\frac{21-3x-x-5}{7x-x^2+35-5x}[/tex]

=> [tex]\frac{-4x-26}{-x^2+2x+35}[/tex]

Now to find domain then x≠-5 and x≠7.

The domain is (−∞,−5)∪(−5,7)∪(7,∞).

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