How Do You Find a Scale Factor in Similar Figures?

The height of the box in feet is 6 feet.

The surface area of a rectangular prism is the overall region or area that is covered by all of its faces. A three-dimensional shape is a rectangular prism. It has six faces, each of which is rectangular in shape. Consequently, a rectangular prism's two bases must likewise be rectangles.

The surface area of the rectangular prism is given by the formula:

A = 2(wl + hl + hw)

Substitute the value of A = 148, l = 4 and w = 5:

148 = 2((5)(4) + (4)h + (5)h)

148 = 40 + 8h + 10h

148 = 40 + 18h

108 = 18h

h = 6

Hence, the height of the box in feet is 6 feet.

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The missing factor is 9.

Option A is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The factors of 360 are 10 and 36.

360 = 10 x 36

The factors of 10 are 2 and 5.

10 = 2 x 5

The factors of 36 are 4 and 9.

36 = 4 x 9

The factors of 4 are 2 and 2.

The factors of 9 are 3 and 3.

Thus,

9 is the missing factor.

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The simplified expression is (- 5√2 - 5√3 - √6 - 3).

Given is the expression as -

(5 + √3) / (√2 - √3)

The given expression is -

(5 + √3) / (√2 - √3)

We can write -

{(5 + √3) x (√2 + √3)} / {(√2 - √3) x (√2 + √3)}

{5(√2 + √3) + √3(√2 + √3)} / (√2² - √3²)

(5√2 + 5√3 + √6 + 3) / (- 1)

- (5√2 + 5√3 + √6 + 3)

- 5√2 - 5√3 - √6 - 3

Therefore, the simplified expression is (- 5√2 - 5√3 - √6 - 3).

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1.  The area of the scale drawing is  1800 cm².

2. We can multiply the dimensions of the drawing by the scale factor of 5.

3. The area of the actual board is 45000 cm².

We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.

We know, The area of a rectangle is (length×width).

1. Therefore, The area of the scale drawing is (50×36) cm².

= 1800 cm².

2. Given, The scale factor is in the ratio of 5 : 1.

Therefore, The actual length is 50×5 cm = 250 cm and the width is 180 cm.

3. The area of the actual board is 250×180 = 45000 cm².

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Based on the given information, the theorem the paragraph proof offers proof for is: A. Alternate Interior Angles Theorem

The Alternate Interior Angles Theorem states that when two parallel lines are intersected by a transversal (a line that intersects two or more other lines), the pairs of alternate interior angles formed are congruent.

In other words, if you have two parallel lines and a transversal intersecting them, and you draw a line segment connecting two nonadjacent interior angles on opposite sides of the transversal, then those two angles will be congruent. This is because they are alternate (they are on opposite sides of the transversal and between the parallel lines) and interior (they are inside the parallel lines).

Therefore, the theorem the paragraph proof offers is: Alternate Interior Angles Theorem.

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Answer: (A) Alternate Interior Angles Theorem

Step-by-step explanation: cyberia

The rate of change of radius is 2.832 mm per second, when the radius is 6 mm.

A height of cone = 15 mm

An initial radius of cone = 16 mm

The volume of the inverted cone is decreasing at a rate of 534 cubic mm per second, with the height being held constant.

The formula of Volume of cone;

V = 1/3 πr^2h

where, r =  radius of the cone and h = height of the cone

To determine the rate of change of the radius we differentiate the volume with respect to t.

dV/dt = 2/3 πrdr/dt h

Now putting the values

534 = 2/3 × 22/7 × 6 × dr/dt × 15

534 = 3,960/21 × dr/dt

Multiply by 21 on both side, we get

3960 dr/dt = 11,214

Divide by 3960 on both side, we get

dr/dt = 2.832

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The function f(x) = e^(3x) - e^x is increasing on the interval (-∞, +∞).

On the range (-∞, +∞), the function f(x) = e^(3x) - e^x increases. This is because the exponential function e^x is increasing for all x, so the difference of two increasing functions is also increasing.

A mathematical function called an exponential function is applied in numerous instances in the real world. It is mostly used to calculate investments, model populations, and do other tasks like determining exponential growth or decay. In an exponential growth model, the quantity increases initially extremely slowly and subsequently quickly. As time goes on, the rate of change quickens.

Correct Question :

On what interval is the function f (x) = e^(3x)−e^x increasing?

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The amount of the next 50 blogs that are expected to be of pop culture is given as follows:

20 blogs.

The first step in obtaining the expected amount is obtaining the proportion out of the blogs that are of pop culture, dividing the number of blogs that are of pop culture by the total number of blogs.

Considering the data in the table, the proportion is obtained as follows:

p = 26/(20 + 26 + 7 + 12)

p = 0.4.

Then, considering the proportion of 0.4, out of the next 50 blogs, the expected amount of pop culture blogs is given as follows:

0.4 x 50 = 20 blogs.

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The variance of X is (C) 35/12.

The formula for variance of a discrete random variable X is:

Var(X) = E[(X - E[X])^2] = E[X^2] - (E[X])^2

where E[X] represents the expected value of X.

To calculate the variance, we first need to find the expected value of X, which is:

E[X] = (1 + 2 + 3 + 4 + 5 + 6) / 6 = 3.5

Next, we find the expected value of X^2:

E[X^2] = (1^2 + 2^2 + 3^2 + 4^2 + 5^2 + 6^2) / 6 = 91/6

Now we can substitute the values into the variance formula:

Var(X) = E[X^2] - (E[X])^2 = 91/6 - (3.5)^2 = 91/6 - 12.25 = 35/12.

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The vertical asymptote is x = 1 or 7

There is no horizontal asymptote

An asymptote is a straight line that constantly approaches a given curve but does not meet at any infinite distance. In other words, Asymptote is a line that a curve approaches as it moves towards infinity.

To find vertical asymptote we set the denominator to 0 and we find the value of x

:. x² - 8x +7 = 0

x² -7x-x+7 = 0

(x²-7)(-x+7) = 0

x( x-7) -1(x-7) = 0

(x-1)(x-7) = 0

x-1 = 0 or x-7 = 0

therefore x = 1 or 7

to find the horizontal asymptote:

Since the degree of the numerator is higher than the denominator, there is no horizontal asymptote

to find the slant asymptote, we divide the numerator by the denominator.

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The distance from London to Swindon is 81 miles.

We have,

Jenny drives from London to Swindon at an average speed of 54 miles per hour.

Time = 1 1/2 hour = 3/2 hour

Using Speed = distance / Time

Distance = speed x time

Distance = 54 x 3/2

Distance = 27 x 3

Distance = 81 miles

Thus, the distance is 81 miles.

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The error interval needed is [15.375, 15.385)

Given that:

A number 'x' rounded to 2 decimal places = 15.38

According to the rules of the rounding of number, we surely know that

x must be in [ 15.375, 15.385) since if x is outside of this interval, then rounding to two places of decimal won't lead to 15.38.

Since x can't be 15.385 itself since that rounds up to 15.39

Or:

[tex]15.375 \leq x\leq 15.385[/tex]

Thus we have :

Error Interval = [15.375 , 15.385)

The equation of the exponential model is f(x) = 3 * 0.2^x

The opposite of an exponential function is a logarithmic function. A log function and an exponential function both use the same base. An exponent is a logarithm. f(x) = bx is how the exponential function is expressed. The formula for the logarithmic function is f(x) = log base b of x.

Given a data set:

x                                        f(x)

−2                                      71

−1                                       13

 0                                       3

 1                                      0.6

 2                                     0.1

An exponential model is represented as:

f(x) = ab^x

When x= 0 and f(x) = 3;

We have:

ab^0 = 3

This gives

a = 3

When x= 1 and f(x) = 0.6

We have:

ab^1 = 0.6

This gives

ab = 0.6

Substitute 3 for a

3b = 0.6

Divide both sides by 3

b = 0.2

Substitute b = 0.2 and a =3 in f(x) = ab^x

f(x) = 3 * 0.2^x

Hence, the equation of the exponential model is f(x) = 3 * 0.2^x

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The equations that correspond to this situation, that is, the equations that have the value of c as 2 and -3 are: y = - 4/3x + 2 y = 2x -3. Hence, option B is the correct answer.

The point where a graph intersects the y-axis is known as the y intercept. Any point on the y-axis has an x-coordinate of 0, is known as y intercept. Therefore, a x-coordinate of y intercept is 0.

The equation of the line is given by the following formula:

y = mx + c

where, c is the y-intercept of the line.

From the graph we can observe that the y-intercept of the red line is +2 and the y-intercept of the blue line is -3.

Hence, the equations that correspond to this situation, that is, the equations that have the value of c as 2 and -3 are:

y = - 4/3x + 2

y = 2x -3

Hence, option B is the correct answer.

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Combining the given information, ∫51′() = f(5) - f(1) = -7 - (-2) = -5. , the integral of ∫51′() is equal to -5.

In order to evaluate the integral ∫51′(), we need to use the Fundamental Theorem of Calculus. The Fundamental Theorem of Calculus states that the integral of a function's derivative is equal to the function value evaluated from one point to another. For example, if f'(x) is the derivative of a function f(x), then the integral of f'(x) from x = a to x = b is equal to f(b) - f(a).

Using the given information, we can solve the integral ∫51′() as follows. We know that the derivative of our function is 1, so the integral of 1 from x = 1 to x = 5 is equal to f(5) - f(1). Therefore, combining the given information, ∫51′() = f(5) - f(1) = -7 - (-2) = -5. Therefore, the integral of ∫51′() is equal to -5.

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The loan will be (ln(Time) - ln(136,000) + ln(1,180)) / ln(1 + 6.5 / 12) repaid.

What is interest ?

Interest is payment from a borrower or deposit-taking financial institution to a lender or depositor of an amount above repayment of the principal sum, at a particular rate.

Time = Loan Amount * (1 + Interest Rate / 12)^(12 * Number of Payments) / Monthly Payment

Given the loan amount ($136,000), interest rate (6.5%), and monthly payment ($1,180), we can plug these values into the formula:

Time = 136,000 * (1 + 6.5 / 12)^(12 * Number of Payments) / 1,180

To find the number of payments, we need to take the natural logarithm of both sides:

ln(Time) = ln(136,000 * (1 + 6.5 / 12)^(12 * Number of Payments) / 1,180)

ln(Time) = ln(136,000) + ln((1 + 6.5 / 12)^(12 * Number ofPayments)) - ln(1,180)

ln(Time) = ln(136,000) + 12 * Number of Payments * ln(1 + 6.5 / 12) - ln(1,180)

Next, we can isolate the number of payments on one side:

12 * Number ofPayments * ln(1 + 6.5 / 12) = ln(Time) - ln(136,000) + ln(1,180)

The loan will be (ln(Time) - ln(136,000) + ln(1,180)) / ln(1 + 6.5 / 12) repaid.

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The height of the rectangular prism is 5 feet.

A box is in the shape of a right rectangular prism. The area of one of the bases is shown.

Let's find the height of the box.

Using the volume of a rectangular prism,

volume of a rectangular prism = Bh

where

V = B × h

where V is the volume of the right rectangular prism, B is the area of the base, and h is the height.​

Hence,

h = V / B

h = 60 / 12

Therefore,

h = 5 ft

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This is a pond in the shape of a prism. It is completely full of water. Colin has to wait for the pond to completely empty is 2hrs and 30minutes.

We have a pond which is completely filled with the water.

Area of the side face ( trapezium shaped)

= 1/2 x (1.4 + 0.6) x 2

= 2 m²

Volume = area x height (here width)

V = 2x1 = 2 m³

The level goes down by 20cm in the first 30 mins

Volume of water that will be taken down =

=0.2 x 1 x 2

=0.4 m³ ( upper water will form cuboid face)

Now,

⇒0.4 m³ water is taken out in 30 minutes

⇒1 m³ water is taken out in 30/0.4 minutes

⇒2 m³ water is taken out in 30/0.4 x 2 minutes

⇒30x2/0.4

⇒150 minutes.

So the pond will be completely empty in 150 min that is 2hrs30mins.

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The area of the shaded part is 50(2-π)

Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.

The area of the shaded part = area of a square - area of a semi circle

area of square = l× l = 10 × 10 = 10²

=100 squared units

the area of the semi circle = πr²/2

= π ×10²/2

= 50π

Therefore the area of the shaded part in term of π is 100-50π

= 50( 2-π) units

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The value of the current 'I' for the given relation of current , impedance, and voltage  I = E/ Z is equal to I = ( 4.5 + 5.4i ) / ( 6 + 4i ).

Here R=6, and XL=4

Impedance Z = R+ XL i

⇒ Z = 6 + 4i  __(1)

Where

E = 7(cos 50 degrees +i sin 50 degrees)

Simplify the above expression to get the value of voltage E.

⇒ E = 7 ( 0.6428 + i 0.7660 )

⇒ E = 4.4996 + i( 5.362 )

⇒ E = 4. 5 + 5.4i ____(2)

Now alternating current  ,

I = E / Z

Substitute the value of E and Z from (1) and (2) we get,

⇒ I = ( 4.5 + 5.4i ) / ( 6 + 4i )

Therefore, the value of the current I is equal to ( 4.5 + 5.4i ) / ( 6 + 4i ).

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When two or more roads or lines cross each other, they come together. You may also remark that two roads or lines cross.

They are referred to be intersecting lines when two or more lines in a plane cross each other.The common point shared by all intersecting lines is known as the point of intersection, and it can be found on all of them. Point O in this case represents the intersection of lines P and Q.

A line is something that is made up of indivisible points that stretch in many directions, to put it simply. Let's use the two points A and B as an example. Now, a line connecting points A and B can be drawn.

Line AB is the name of this line, which stretches in both directions. Arrows are used to represent lines to show that they have no ends and go on forever.

solve log(x)=-x+6

log(x)=-x+6 it can be written as

⇒log(x)+x+6=0

⇒log(1/x+6)=0

It will  be in the form of lod(1/a+b)

so we can write log(x)+log(1+6/x)

Therefore, if modulus of 6/x <0 then it can be written as

                        ∞ =log(x)-∑xn/n

            n-1

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The factorization case for each polynomial is listed below:

In this problem we find six cases of polynomials, whose factorization case must be found. Now we proceed to show and indicate what kind of factorization case is used for each polynomial:

Case 1: z² + z - 90 (Sum and product)

z² + z - 90

z² - (- 10 + 9) · z + (- 10) · 9

(z + 10) · (z - 9)

Case 2: x² - 4 · x + 6 · x - 24 (Grouping)

x² - 4 · x + 6 · x - 24

x · (x - 4) + 6 · (x - 4)

(x + 6) · (x - 4)

Case 3: 16 · x² + 24 · x · y + 9 · y² (Perfect square trinomial)

16 · x² + 24 · x · y + 9 · y²

(4 · x + 3 · y)²

Case 4: 49 · x² - 100 · y² (Difference of two squares)

49 · x² - 100 · y²

(7 · x - 10 · y) · (7 · x + 10 · y)

Case 5: 121 · m² + 64 (None)

Case 6: 8 · x³ · y² + 4 · z³ (GCF)

8 · x³ · y² + 4 · z³

4 · (2 · x³ · y² + z³)

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The sum of cubes identity states that a^3 + b^3 = (a+b)(a^2 - ab + b^2). To find the factors of 8x^6 + 27y^3, we can apply this identity to the expression by identifying a and b:

What is the identity of the sum of cubes?

What Does the Algebraic Sum of Cubes Formula Mean? One of the key algebraic identities is the sum of cubes formula. Its symbol is written as a3 + b3 and is interpreted as a cube plus a cube. A3 + b3 = (a + b) (a2 - ab + b2) is how the sum of cubes formula (a3 + b3) is written.

8x^6 + 27y^3 = (2x^2)^3 + (3y)^3

We can then apply the identity to get:

(2x^2)^3 + (3y)^3 = (2x^2 + 3y)((2x^2)^2 - 2x^2*3y + (3y)^2)

This gives us the factors of 8x^6 + 27y^3 as (2x^2 + 3y)(4x^4 - 6x^2y^2 + 9y^2).

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57  times more material was used to build the Hoover dam than the American falls .

A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.

Given:

Volume of Hover dam = 4 x [tex]10^6[/tex]

Volume of American Falls dam = 7 x [tex]10^4[/tex]

So, the number of times more material used

= Volume of Hover dam / Volume of American Falls dam

= 4 x [tex]10^6[/tex] / 7 x [tex]10^4[/tex]

= 400 x  [tex]10^4[/tex] / 7 x [tex]10^4[/tex]

= 57.14

Hence, 57.14 times more material used.

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The value given is from a continuous data set because there are infinitely many possible values.

In statistics, a discrete data set is a set of data that can only take certain values, typically whole numbers, that can be counted. A continuous data set is a set of data that can take any value within a certain range, and the values can't be counted as they are infinite in number.

In the given scenario, the weight of a car can take any value within a certain range, and there are infinitely many possible values between any two values. For example, between 1628.3 kg and 1628.4 kg, the car's weight could be an infinite number of values. Hence, the weight of the car is a continuous variable, and the given value of 1628.3 kg is part of a continuous data set.

Hence, the correct answer is d.

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In mathematical terms, if X is the sum of successes in n different Bernoulli trials, and p is the likelihood of success in each trial, then X may be represented as a normal distribution with mean increasing as n rises.

μ = np

variance σ^2 = np(1-p)

The binomial distribution is a discrete probability distribution that produces just two outcomes in an experiment: success or failure. In a binomial distribution, the chance of success must remain constant during the trials under consideration. For example, because there are only two possible outcomes when tossing a coin, the chance of flipping a coin is 1/2 or 0.5 for each experiment we do.

Here,

When the sample size (n) is high, the distribution of the total of successes (k) in n separate Bernoulli trials approaches a normal distribution, according to the normal approximation for the binomial distribution.

In mathematical terms, if X is the total of successes in n separate Bernoulli trials, with p being the chance of success in each trial, then X may be represented by a normal distribution with mean as n increases.

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Answer:

The equation H(x) = (-4x-5)(-x+5) can be simplified to H(x) = 4x^2 + 25.

The lesser value for x is -5, and the greater value for x is 5.

The relative size of the samples from each school should be proportional to the square root of the enrollment at each school.

The relative size of the samples from each school should be proportional to the square root of the enrollment at each school. So, for Wabash College, we would want to sample approximately √(900) = 30 students, and for Purdue University, we would want to sample approximately √(36,000) = 180 students.

This would ensure that the standard deviation of the sample proportions from each school would be approximately the same.

So, the relative size of the samples from each school should be proportional to the square root of the enrollment at each school.

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