Which expression is a perfect cube

Using the uniform distribution, considering that the novel has 435 pages, the probability that the page is numbered something between 21 and 31 is:

[tex]p = \frac{10}{435}[/tex]

It is a distribution with two bounds, a and b, in which each outcome is equally as likely.

The probability of finding a value between c and d is:

[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]

Researching the problem on the internet, it is found that the novel has 435 pages, hence a = 0, b = 435, and the probability that the page is numbered something between 21 and 31 is given by:

[tex]P(21 \leq X \leq 31) = \frac{31 - 21}{435 - 0} = \frac{10}{435}[/tex]

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the exact value of sin A  to the nearest ten- thousandth is 0. 6625

a² + b² = c²

The opposite side is unknown, so use the pythagorean theorem to find it

c = hypotenuse = 4

a= opposite site = ?

b= adjacent side = 3

Substitute into the formula

4² = a² + 3²

16 = a² + 9

a² = 16 -9 = 7

Find the square root

a =√7 = 2. 65

To find Sin A, use

Sin A = opposite side ÷ hypotenuse

Sin A = 2. 65 ÷ 4 = 0. 6625

Thus,  the value of sin A is 0. 6625

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Option d is the correct answer. All real numbers are greater than or equal to 2.

Domain of a function--The domain of the function is the set or collection of all the x-values for which the function is well defined.

Range of a function--The range of a function is the set of all the values which are attained by a function in its defined domain.

By looking at the graph we observe that the function is continuously increasing and the function takes all the real values greater than as well as equal to 2( since there is a closed circle at (1,2). Hence, the range is: [2,∞).

Thus Option d is the correct answer. All real numbers are greater than or equal to 2.

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The function f(x) = 2x -14 is a polynomial function

The equation of the function is given as:

f(x) = 2x -14

A polynomial is represented as:

f(x) =ax^n + bx^(n - 1)....... + c

Where n is at least 1.

The function f(x) = 2x -14 is a polynomial with a degree of 1

Hence, the function f(x) = 2x -14 is a polynomial function

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The first term of an arithmetic progression of 4 terms and ratio equal to 4 whose sum is 100 is 19.

The first term of an arithmetic progression can be calculated using the following expression:

Sn = n/2 [2a + (n − 1)d]

Where;

100 = 2 [2a + (4 - 1)4]

100 = 4a + 24

4a = 100 - 24

a = 76/4

a = 19

Therefore, the first term of an arithmetic progression of 4 terms and ratio equal to 4 whose sum is 100 is 19.

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Answer: 0.5 or - 0.834

Step-by-step explanation: Here is the explanation!

The scale model of a building 3 inches tall if the building is 90 feet tall is 2:5

Scaling is the way of enlarging or reducing the image of an object.

Given scale model of a building is 3 inches, if the building is 90feet tall, to write the scale;

Convert both measures to same units

Since 1 feet. = 12 in

90 feet = 90/12 in = 7.5 in

Take the ratio

3 : 7.5 = 30: 75

Reduce to lowest term

30: 75 = 2 : 5

Hence the scale model of a building 3 inches tall if the building is 90 feet tall is 2:5

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Answer:

6

Step-by-step explanation:

Answer:

One way is that there can each be 99 for each. 99x3= 297 which, isn't too far from 360. Another way is that they can each have 50. 50x3=150. The last way is to have them each have 30. 30x3=90.

Step-by-step explanation: Hope I helped at least a little bit. Give brainliset to best answer. I don't think my answer was that good. Let me know if it helped at all.

Given the following formula, w=x-y/2 -z. The value of y is y = x - 2w + wz .

Usually, simplification involves proceeding with the pending operations in the expression.

Like, 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form.

Simplification usually involves making the expression simple and easy to use later.

Given the following formula,

w=x-y/2 -z

We need to solve for y.

[tex]w = \dfrac{x-y}{2 -z}[/tex]

By cross multiplication

[tex]w\times (2 -z)= {x-y}\\\\2w - wz = x - y[/tex]

subtract x both side

2w - wz -x = x - y -x

y = x - 2w + wz

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Answer:

[tex]4*6^\frac{5}{2}[/tex]

Step-by-step explanation:

Use [tex]\sqrt[n]{a^x}=a^{\frac{x}{n} }[/tex] to rewrite [tex]\sqrt{6^5}[/tex] as [tex]6^\frac{5}{2}[/tex].

[tex]4*6^\frac{5}{2}[/tex]

Answer:

[tex]1.25332[/tex]

Step-by-step explanation:

[tex] tan(30 times tan(60 ) \div \tan(60 \div + 30) [/tex]

Answer:

m = -1/3

Step-by-step explanation:

Find two points in order to calculate slope:

Slope (m) =

ΔY /ΔX= -1/ 3= -0.33333333333333

Slope intercept:

y = -0.33333333333333x + 2

Answer:

Slope = - 1/3

Step-by-step explanation:

Choose the point on the right and move upwards. How many times did you move upwards until you were at the same level as the point on the left? You moved once, which means your rise is 1.

Now from the point where you are at now, move right or left depending on where the point is. In this case, it's on the left which means our run will be negative. Now move left until you reach that point on the left. How many times did you move left? You moved three times, which means your run is 3.

Rise/Run = -1/3

Slope = Rise/Run

Slope: - 1/3

hope this helps!! p.s. i really need brainliest :)

The correct answer is option A. which is the right triangle shown. The length of the hypotenuse is 6.7 and the length of another side is 4.3. The angle between the 2 sides is x.

The complete figure is attached with the answer below.

The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

In the given figure of option A, we can see that the hypotenuse is 6.7 and the base is 4.3 and the angle between both the sides is x. Now we will calculate the angle of cosine x.

Cos(x)= Base / Hypotenuse

Cos(x) = ( 4.3 / 6.7 )

(x) = Cos⁻¹ ( 4.3 / 6.7)

Therefore the correct answer is option A. which is the right triangle shown. The length of the hypotenuse is 6.7 and the length of another side is 4.3. The angle between the 2 sides is x.

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Answer:

The answer is A

Step-by-step explanation:

Just took the test

Answer:

[tex] - \infty < x < \infty [/tex]

Step-by-step explanation:

Answer:

The angle shows 90° so that means

90° - 42° = 48°

Therefore the angle of the depression is 48°

The angle of depression from C to point A 48°. The correct option is c. 48°

From the question, we are to determine the angle of depression from C to point A

The angle of depression is the angle formed between the horizontal line and the line of sight when an observer looks downwards at an object

Thus, in the given diagram

The angle of depression is 90° - 42°

Angle of depression = 48°

Hence, the angle of depression from C to point A 48°. The correct option is c. 48°

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Answer:

  Adult market

  Junior market

  Total profit: 13000

  Total consumer surplus: 14600

Step-by-step explanation:

Given Adult (a) and Junior (j) demand equations Pa = 200 -Qa and Pj = 160 -Qj, and cost equation C = 20Q, you want to find the price in each market that maximizes profit, the sales in each market, and the consumer surplus, and a graph of profit-maximizing sales and prices.

Each demand equation is of the form P = Pmax -Q, where P is the price that will result in sales of Q tickets. The revenue (R) in each case is the product of numbers of tickets sold (Q) and the price at which they are sold (P).

  R = QP = Q(Pmax -Q)

The profit is the difference between revenue and cost.

  Profit = R - C = Q(Pmax -Q) -20Q

  Profit = Q(Pmax -20 -Q)

Writing the demand equation in terms of P, we find ...

   Q = Pmax -P

Substituting this into the Profit equation gives ...

  Profit = (Pmax -P)(Pmax -20 -(Pmax -P))

  Profit = (Pmax -P)(P -20)

The profit function describes a downward-opening parabolic curve with zeros at P=Pmax and P=20. The maximum profit is on the line of symmetry of this curve, halfway between these values of P:

  Price for maximum profit = (Pmax +20)/2 = Pmax/2 +10

In the adult market, Pmax = 200, so the profit-maximizing ticket price is ...

  Pa = 200/2 +10 = 110 . . . . price for maximum profit in Adult market

In the Junior market, Pmax = 160, so the profit-maximizing ticket price is ...

  Pj = 160/2 +10 = 90 . . . . price for maximum profit in Junior market

Using the revenue equation, we find the sales in each market to be ...

  Qa = 200 -Pa = 200 -110 = 90

  Ra = Qa·Pa = 90(110) = 9900 . . . . sales in Adult market

  Qj = 160 -Pj = 160 -90 = 70

  Rj = Qj·Pj = 70(90) = 6300 . . . . sales in Junior market

The profit in each market is ...

  Adult market profit = 90(110 -20) = 8100

  Junior market profit = 70(90 -20) = 4900

The overall profit will be the sum of the profits in each market:

  Overall profit = 8100 +4900 = 13000

The consumer surplus in each market is the area below the demand curve and above the price point. It is half the product of the maximum price and the quantity actually sold.

  CSa = (1/2)(200)Qa = 100(90) = 9000

  CSj = (1/2)(160)(Qj) = 80(70) = 5600

The total consumer surplus is ...

  CS = CSa +CSj = 9000 +5600 = 14,600 . . . . total consumer surplus

The first attachment shows the sales (output) in each market (red=Adult, purple=Junior) as a function of ticket price. It also shows the corresponding profit (orange=Adult, blue=Junior). The profit-maximizing price point is marked on each curve. You will note that it is different from the output-maximizing price point.

The second attachment illustrates the consumer surplus in each market. That graph has price on the vertical axis, and quantity on the horizontal axis. The colors correspond to the colors on the graph in the first attachment.

The lateral area of the prism is 270cm²

What is the lateral area of a prism?

The lateral area of a prism is defined as the sum of the areas of its lateral faces.

Using the formula;

Lateral area = (a+ b+ c) h

Where a, b, c, are all the lateral faces and h is the height

Lateral area = (8 + 6 + 13) × 10 = 27 × 10 = 270cm²

Therefore, the lateral area of the prism is 270cm²

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Answer:

108°

Step-by-step explanation:

From the diagram,

Angle X + Angle CXD = 180°

Angle X + 72° = 180°

Angle X = 180° - 72° = 108°

To expand an expression, use FOIL method.

-7y and y are the first terms in each expression.

(-7y)(y) = -7y²

-7y is the first term in the first expression

-4 is the last term of the second expression

(-7y)(-4) = 28y

-8 is the last term in the first expression

y is the first term in the second expression

(-8)(y) = -8y

-8 is the last term of the first expression

-4 is the last term of the second expression

(-8)(-4) = 32

Combine all simplified terms.

Answer:

Wxndy~~

Answer:

[tex]x=\frac{3}{4},\:x=-1[/tex]

Keys:

For this problem, you need the quadratic formula(listed below).

When you see ± in a quadratic equation, you must know there is going to be at least 2 solutions.

Step-by-step explanation:

solving for x₁ and x₂

[tex]4x^2+x=3\\4x^2+x-3=3-3\\4x^2+x-3=0\\x_{1,\:2}=\frac{-1\pm \sqrt{1^2-4\cdot 4\left(-3\right)}}{2\cdot 4}\\[/tex]

[tex]1^2=1\\=\sqrt{1-4\cdot \:4\left(-3\right)}\\=\sqrt{1+4\cdot \:4\cdot \:3}\\=\sqrt{1+48}\\=\sqrt{49}\\=\sqrt{7^2}\\\sqrt{7^2}=7\\=7[/tex]

[tex]x_{1,\:2}=\frac{-1\pm \:7}{2\cdot \:4}\\x_1=\frac{-1+7}{2\cdot \:4},\:x_2=\frac{-1-7}{2\cdot \:4}\\[/tex]

solve for x₁

[tex]\frac{-1+7}{2\cdot \:4}[/tex]

[tex]=\frac{6}{2\cdot \:4}[/tex]

[tex]=\frac{6}{8}[/tex]

[tex]= \frac{6\div2}{8\div2}[/tex]

[tex]=\frac{3}{4}[/tex]

solve for x₂

[tex]\frac{-1-7}{2\cdot \:4}[/tex]

[tex]=\frac{-8}{2\cdot \:4}[/tex]

[tex]=\frac{-8}{8}[/tex]

[tex]=-\frac{8}{8}[/tex]

[tex]=-1[/tex]

Hope this helps!

All the numbers follow a pattern of division by 2

Therefore the next number is 3/2 which is equal to 1.5

Answer:

11.25

Step-by-step explanation:

6 3/4 + 4 1/2

The surface area of the given shape is 285.01 ft²

From the question, we are to calculate the surface area of the given shape.

The given shape in the diagram is a cone.

The surface area of a cone is given by the formula,

[tex]S = \pi r(r+l)[/tex]

Where S is the surface area

r is the radius

and [tex]l[/tex] is the slant height

First, we will calculate the slant height of the cone

[tex]l^{2}=9^{2} +5.6^{2}[/tex] (Pythagorean theorem)

[tex]l^{2}=81+31.36[/tex]

[tex]l^{2}=112.36[/tex]

[tex]l}=\sqrt{112.36}[/tex]

[tex]l=10.6 \ ft[/tex]

∴ The slant height is 10.6 ft

Now, for the surface area

[tex]S = \pi \times 5.6(5.6+10.6)[/tex]
[tex]S = \pi \times 5.6(16.2)[/tex]

[tex]S = 90.72\pi \ ft^{2}[/tex]

[tex]S = 285.0053 \ ft^{2}[/tex]

S ≅ 285.01 ft²

Hence, the surface area of the given shape is 285.01 ft²

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Answer:

hope you can understand

Answer:

3m²n⁴

Step-by-step explanation:

Given :

⇒ [tex]\sqrt[4]{81m^{8}n^{16} }[/tex]

=============================================================

Solving :

⇒ [tex]\sqrt[4]{81}[/tex] × [tex]\sqrt[4]{m^{8} }[/tex] × [tex]\sqrt[4]{n^{16} }[/tex]

⇒ [tex]\sqrt[4]{3^{4} }[/tex] × [tex]\sqrt[4]{(m^{2})^{4} }[/tex] × [tex]\sqrt[4]{(n^{4})^{4} }[/tex]

⇒ 3 × m² × n⁴

⇒ 3m²n⁴

Answer:

In terms of Pi: [tex]3\pi + 6[/tex] km

Exact value (rounded): 15.42477 km

Approximated (3.14): 15.42 km

Step-by-step explanation:

Hello!

A semicircle's perimeter can be found using the formula: [tex]P = \pi r + 2r[/tex]

We can plug in the values to solve for the perimeter.

In terms of Pi, it is [tex]3\pi + 6[/tex],

Exact value of Pi, it is 15.42477

Approximation of Pi (3.14), it is = 15.42