By first finding tan 8, calculate the size of angle 0.
Give your answer in degrees to the nearest integer.

The dimensions of the closed rectangular box with a square base and volume of 8000 cubic centimeters that can be constructed with the least amount of material are 20 cm.

Let the length and width of the rectangular box with a square base be x.

and the height is y.

The volume, V = 8000 = [tex]x^{2} y[/tex]       --------(1)

The surface area, S = 2[tex]x^{2}[/tex] + 4xy .   -------(2)

S =  2[tex]x^{2}[/tex] + 4xy and  8000/ [tex]x^{2}[/tex] =y     -------( from 1 and 2)

so, S= 2[tex]x^{2}[/tex] + 4x(8000/ [tex]x^{2}[/tex])

S= 2[tex]x^{2}[/tex] + 32000/x

to find the least amount of material to be used, we will differentiate the surface area w.r.t x.

ds/dx= 0 = 4x - 32000/[tex]x^{2}[/tex]

therefore, we have, 4x = 32000/[tex]x^{2}[/tex]

                                 4[tex]x^{3}[/tex] =32000

                                   [tex]x^{3}[/tex] =8000

                                     x=20

Hence, The dimensions of the closed rectangular box with a square base and volume of 8000 cubic centimeters that can be constructed with the least amount of material are 20 cm.

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Answer:

y-intercept: -3

slope: 3

Step-by-step explanation:

Slope can be found by using rise/run

The equation: y = 3x - 3

Answer: x= -13

y= -18.5

When you plug these into the first equation, you will find the answer of 9.

Hope this helps.

9.028 many resonances will be observed when a tuning fork with a frequency of 321 Hz is used in air with a sound speed of 342 m/s.

Given that,

When a tuning fork with a frequency of 321 Hz is used in air with a sound speed of 342 m/s, how long is the tube utilized in our experiment, 4 m?

We have to find what many of resonances will be seen.

We know that,

The length of the tube is Lₙ=4 m

Frequency is ν = 321 hz

Speed of sound is v = 342 m/s

We know that,

ν=vλ

321=342λ

λ=321/342

λ=0.938

Now,

Lₙ=(2n+1/4)λ

4=(2n+1/4)0.938

n=8.028

We get,

N=n+1=8.028+1=9.028

Therefore, 9.028 many resonances will be observed when a tuning fork with a frequency of 321 Hz is used in air with a sound speed of 342 m/s.

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The circle is partitioned into 9 parts and arc GH is only one of the parts, therefore, the length of arc GH is a ninth of the circumference of the circle which has the radius as a factor.

The circumference of a circle is the perimeter of the circle which is equal to the product of twice the radius and π.

The circumference of the circle is C = 2·π·r

The circle is divided into 9 parts

The arc GH is the arc to one part of the circle

The length of the arc GH = 2·π·r/9

The ratio of the arc GH to the radius, r = n is therefore;

When r = n,

Measure of arc length [tex]\widehat{GH}[/tex] = 2·π·n/9

Ratio of [tex]\widehat{GH}[/tex] to r = n is obtained using the formula;

[tex]Ratio = \dfrac{Measure \ of \ arc\ length \ GH }{n}[/tex]

[tex]\dfrac{\dfrac{2\cdot \pi\cdot n}{9} }{n} = \dfrac{2\cdot \pi }{9}[/tex]

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By working with the given percentage, we can see that the amount of the markup is $6.90

Suppose that the original price is P, and we have a markup (in percentage form) of X, then the amount of the markup is:

M = P*(X/100%)

Here we know that the original price of a hoodie is P = $23.00, while the percentage of the markup is 30%.

Then the amount of the markup in these hoodies is:

M = $23.00*(30%/100%)

M = $23.00*0.3

M = $6.90

The amount of the markup is $6.90

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The value of y shown in the parallelogram given in question is 7.

What is parallelogram?

In Euclidean geometry, a parallelogram is an easy quadrilateral with two sets of parallel sides. The confronting\opposed sides and the opposing angles of a parallelogram are of equal length. To show the congruence of opposed sides and opposite angles, the Euclidean parallel postulate or one of its equivalent formulations must be utilized because both criteria follow directly from this postulate.

To find the value of y we need to use one the property of the parallelogram.

It is property of the parallelogram that it's diagonals bisects each other.

So,

In the given figure,

4y-7 = y + 14

3y = 21

y = 21/3

y = 7

Therefore, the value of y is 7.

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For the given geometric progression, the nth term of the given GP is [tex]A_n=2.3^{n-1}[/tex].

Option (C) is correct.

What is the Geometric Progression?

Geometric Progression (GP) is a type of sequence in mathematics in which each succeeding term is produced by multiplying each preceding term by a fixed number known as a common ratio. This progression is also known as a pattern-following geometric sequence of numbers.

The given sequence is 2, 6, 18, 54

here the first term(a) = 2 and the common ratio(r) = 6/2 =3

Then by using the formula for the nth term of a GP, we get

                               [tex]A_n=ar^{n-1}\\\\A_n=2.3^{n-1}[/tex]

Hence the nth term of the given GP is [tex]A_n=2.3^{n-1}[/tex].

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Check the picture below.

[tex]\cos(63^o)=\cfrac{\stackrel{adjacent}{x}}{\underset{hypotenuse}{16}}\implies 16\cos(63^o)=x\implies 7.3\approx x[/tex]

Make sure your calculator is in Degree mode.

The required value of the given function  f(a) = -2a^2 - 5a + 4 at a = -3 is 1

Function is characterized as a connection between a bunch of data sources having one result each. In straightforward words, a capability is a connection between inputs where each info is connected with precisely one result. Each Function has a domain and co-domain or range. A capability is by and large meant by f(x) where x is the information.

Function, f(a) = -2a^2 - 5a + 4

To find value of f(-3),

f(a) = -2a^2 - 5a + 4

Put a = -3 in th function

F(-3) = -2(-3)^2-5×-3+4

F(-3) = -18+15+4=1

F(-3) = 1

Thus, required value of f(-3) is 1

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Coorect Question:

What is f(-3) for the function f(a) = -2a2 - 5a + 4?

Yes, angry is considered to be a tone in a paper.

The tone of writing appears an author’s attitude or intent. The tone is the essence of the voice, which is how a writer passes on their thoughts to the peruser. Tone can be found through particular words, expressions, and sentence structure. The tone is broadly depicted as the author’s demeanor toward his or her subject. It can be enthusiastic, far off, irate, and cheerful, among numerous other possibilities. Tragically there are as well numerous possibilities for us to cover, and without knowing your subject, we cannot allow the foremost particular advice possible. The obvious pitfalls incorporate sounding condescending or silly, whereas sounding energetic and eager could be a definite positive. An angry tone is ordinarily utilized when the author needs to communicate a sense of frustration or outrage. It can take diverse forms such as passive-aggressive, protective, or sarcastic.

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The equivalent expression of 4(x + 2) + 4. is 4x + 12.

Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.

In other words, two algebraic expressions are said to be equivalent if their values obtained by substituting the values of the variables are same.

Therefore, let's find the equivalent expression of 4(x + 2) + 4.

Let's simplify the expression to find it's equivalent.

4(x + 2) + 4 = 4x + 8 + 4 = 4x + 12

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The scale factor used to create the travel version of the piece is 1: 0.16

0.6 is the scale factor used to reduce the dimensions of the original piece having sides measuring 3 inches each.

Scale factor is calculated by dividing the new reduced scale by original scale. Hence:

0.5/3 = 0.166

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).

Scale Factor = New Shape Dimension / Original Shape Dimension

Enlarging a small form into a huge one is known as scaling up. Upscaling always uses a scale factor greater than 1. A scale factor 2 means the figure is enlarged twice the original figure's size.

A large number gets scaled down in order to become a smaller one. Scaling down always results in a scale factor less than 1.

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Percentage of the sales price to the given purchase price is equal to 180% .

As given in the question,

Purchase price of the each coat bought by owner is equal to  $55

Selling price of each coat sold by owner is equal to  $99

Percentage of sales price of purchase price is equal to

= ( Selling price / Purchase price )  × 100

Substitute the value of the selling price and the purchase price we get,

= ( 99 / 55 ) × 100

= ( 1.8 ) × 100

= 180%

Therefore, the sales price is 180 percent of the given purchase price.

The complete question is:

Owner buys coats for $55 each and sell them for $99 each. The sales price is what % of the purchase price.

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Using percentage to calculate the actual amount, we found out that the real percentage were off.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

In this case, we have to find 70% of the original price and see if it's true.

70% of $49.99 will be;

70 / 100 = x / 49.99

0.7 = x / 49.99

x = 49.99 * 0.7

x = 34.993

The new price is supposed to be $34.99 and not $30

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A sample of 81 business students over a one-week period with the population standard deviation is 1.2 hours. We calculate the following using the standard formulae:

a) Standard error of the mean is 0.13.

b) Margin of error is 0.975.

c) If the sample mean is 9 hours, then 95% confidence interval is (8.608 , 9.392).

Confidence Interval

The error introduced during the random sampling process is the sampling error described in the estimation procedure in the form of margin of error (MOE). MOE is expressed by the following formula:

MOE = CV ×SE

where,

CV = critical value of distribution

SE = standard error Solution

Note that, Population standard deviation(σ) is known. So we use z distribution.

we have given that

Sample size, n = 81

Standard deviations, σ = 1.2 h

a)

Standard error = σ /√n

=> S.E = 1.2/√81 = 1.2/9

=> S.E = 0.13

b) We have to construct 95% confidence interval.

therefore, c = 0.95

=> α= 1 - c = 1- 0.95 = 0.05

then, α/2 = 0.05/2 = 0.025 and 1- α/2 = 0.975

the probability or P-vale is 0.975 then from Z-table the corresponding z value is 1.96

The margin of error formula:

MOE = Zα/2 (σ/√n)

= 1.96 (0.13 )

= 0.2548

Margin of error = 0.2548

c) Now , confidence interval for mean(u) formula

(X-bar - E ) < μ < (X-bar + E)

=> ( 9 - 0.392) < μ < (9 + 0.392)

=> 8.608 < μ < 9.392

=>(8.608 , 9.392)

Hence, standard error is 0.13

Margin of error is 0.2548 and confidence interval is (8.608 , 9.392).

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There are 4 fundamental main properties of numbers: commutative, associative, distributive, and identity. You must be acquainted with every of those.

Commutative Property: a. Addition. When numbers are added, the sum is the equal irrespective of the order wherein the numbers are added. b. Multiplication. When all numbers are accelerated together, the product is the equal irrespective of the order wherein the numbers are accelerated. Identity Property. Addition. The sum of any wide variety and 0 is that wide variety.

Associative Property : a. Addition. When 3 or greater numbers are added, the sum is the equal irrespective of the manner wherein the numbers are grouped. b. Multiplication. When 3 or greater numbers are accelerated, the product is the equal irrespective of the manner wherein the numbers are grouped. Distributive Property: The sum of numbers instances a 3rd wide variety is identical to the sum of every addend instances the 1/3 wide variety.

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The total cheese production in 2006 was about 7.7 billion pounds and the total cheese production in 2014 was about  9.7 billion pounds

The function that can be used in our computation is given as

y = 7(1.03)ˣ

Such that

x = Number of years after 2003 and y is the amount of cheese

The value of x can be calculated using

x = year - 2003

Substitute 2006 for year

x = 2006 - 2003

Evaluate

x = 3

Substitute x = 3 in the equation y = 7(1.03)ˣ

y = 7(1.03)³

Evaluate

y = 7.7

In the year 2014, the value of x is calculated as

x = Current year - 2003

So, we have

x = 2014 - 2003

Evaluate

x = 11

Substitute x = 11 in the equation y = 7(1.03)ˣ

y = 7(1.03)¹¹

Evaluate

y = 9.7

Hence, the amount of cheese is 9.7 billion pounds

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The marginal revenue in the interval between six and seven jet skis is $300.

Here we are given that total revenue from six jet skis is $2,400

and total revenue from seven jet skis is $2,700

Now, marginal revenue is defined as the revenue gained or lost by producing one more additional unit of a good.

Here, the total revenue increases from $2,400 to $2,700 as we go from producing 6 jet skis to 7 jet skis.

Thus, the change in total revenue will be-

2700 - 2400

= 300

This means that the gain in revenue is $300.

Thus, the marginal revenue in the interval between six and seven jet skis is $300.

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The legend defines architectural symbols and notations used in the plans.

Floor plan symbols make up their own language, just as construction workers have their own vocabulary that they use to communicate when working on projects as it’s essential for architects, designers and builders to understand this language, a floor plan includes an important element called a legend, which acts as a key that helps viewers interpret the drawing.

Therefore, the The legend defines architectural symbols and notations on the plan. Many standard symbols usually appear there for specific projects. However, there can be variations in how symbols look and what they represent, which makes consulting the legend  for each project is essential.

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Answer: c approximately normal

Step-by-step explanation:

because the graph states that there is 100 random sample people with the rash using the cream and this ask what best describes the shape .

a.) W=31.9J

b.) Normal force=0

c.) Gravitational force = 0

We apply the definition of "work by a constant force" in the first three part  and in the fourth part, we total the results. The work performed by the overall (net) force is equal to the sum of the separate forces' respective amounts of work.

Work by a constant force is defined as W=FΔrcosθ.

Work, in general, is the result of force and the displacement it produces. W = FX is the formula used to express how much work a force has produced. Here, x is the body's displacement as a result of the force F. The dot product informs us that only the force that causes displacement is taken into account when calculating the work done.

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Answer:

17 yards and 31 yards.

Step-by-step explanation:

Since length is 14 more than width, lets call width: w and length: w+14

So perimeter is 96 so: 2w+2(w+14)=96

2w+2w+28=96 so 4w+28=96

4w=68 and finally w=17

So 17 yards and 31 yards.

The simplified numerator of the sum is 4x + 6

Given,

We have the following expression for this situation:

x / (x² + 3x + 2) + 3/(x + 1)

And here's where we can start:

x(x + 1) + 3(x² + 3x + 2) / (x² + 3x + 2) (x + 1)

We may now factor the terms x² + 3x + 2 = (x + 1) (x + 2) on the denominator and distribute the terms on the numerator to get:

x² + x + 3x² + 9x + 6 / (x + 2) (x + 1)²

4x² + 10x + 6 / (x + 2) (x + 1)²

Now, the numerator can be factored as follows:

4x² + 10x + 6 = (2x + 2) (2x + 3)

And if we substituted that, we got:

(2x + 2) (2x + 3) / (x + 2) (x + 1)²

We can now apply common factor 2 to the numerator as follows:

2(x + 1) (2x + 3) / (x + 2) (x + 1)²

Additionally, the x+1 can be cancelled on the numerator and denominator as follows:

2(2x + 3) /  (x + 2) (x + 1) = 4x + 6/ (x + 2) (x + 1)

Therefore,

The simplified numerator of the sum is 4x + 6

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#6

z =(-2,-3)

y =(-1,-1)

b =(-3,1)

w =(-4,-2)

#7

r =(3,-2)

j =(4,-4)

e =(3,-4)                                                          

#8

v = (-1,-5)

c = (0,0)

r = (-3,-3)

#9

z = (2,0)

l = (4,-3)

n =(1,-4)

#10

r =(-3,-2)

z =(0,-2)

j =(-1,3)

y =(2,2)

Hope those are all correct! Good luck on the HW!

Using the Indifference curve , the slope of ambrose indifference curve is -2.

Indifference Curve

A bunch of places of consumption where consumer tastes are indifferent is an indifference curve. Indifference curves are usually convex towards the origin.

Rewriting algebraically the equation of the indifference curve U(t, y)=c in the form y=g(t, c),

where g(t, c) is a decreasing convex function of t for c given .

Indifference curve is given by:

x₂ = C − 4x₁¹/²

Slope of the indifference curve = dx₂/dx₁

Hence, Slope of the Ambrose indifference curve = dx₂/dx₁ = -(1/2)(4/x₁¹/²)

=> Slope of the Ambrose indifference curve = -2/x₁¹/²

At (1,6), Slope of the Ambrose indifference curve = -2/x₁¹/² = -2/1= -2

Hence, Slope of the Ambrose indifference curve = -2

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Carpetland not $8,000 in step with week in earnings. Vice President, proposes a plan with new selling incentives with the want that the plan will increase the not earnings in step with earnings are more than $8,000 in step with week.

It implies, The null hypothesis, H: μ≤$8,000 in step with week. The possibility hypothesis, H: μ>$8,000 in step with week where μ is the whole not unusual place earnings in step with week.

Type II mistakes is defined due to the fact the opportunity of now now not rejecting the false-null hypothesis i.e. now now not rejecting the null whilst it is false. Therefore, if we do now now not reject that the not earnings are a great deal much less than or same to $8000 (and end that the not unusualplace earnings may be a great deal much less than same to $8000) whilst in fact it is more than $8000 then we are growing a type II mistakes.

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The correct statement is option (B) the market for paper is growing faster than the market for all other

The given statement is

Paper production accounts for approximately 40 percent of the world's industrial use of wood, and the market for paper is growing faster than it is for all major wood products.

The first option is a sentence that in the question but its not conveying the proper meaning of the given statement. Option C, D and E is not saying about the paper market, therefore it is not conveying the correct meaning of the statement

Hence, the correct statement is option (B) the market for paper is growing faster than the market for all other

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The larger of population1 and population2 by calling max.

max(population1, population2)

Since the function max returns a large integer among two integers, max(population1,population2) will give us the large one among population1 and population2. Now if we compare that value with population2 using another max, then that will provide us with the large among maximum (population1,population2) i.e it will be the largest among these three variables.

Therefore the required expression will be:

max(population1,population2).

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Answer: Correct, 4.4 is the answer when rounded, but to be more exact, it would be 4.420

Step-by-step explanation:

The only discrepancy is the rounding, the rest of the work is correct. It is subjective to the teacher whether the answer is sufficient or not, but you did a great job otherwise. If your teacher does want preciseness, however, I would not round to 4.5, it would be more accurate as 4.44 when setting up your equation.