The value of [tex]\sin ^{-1}\left(\frac{\sqrt{3}}{2}\right)-\sin ^{-1}\left(\frac{1}{2}\right)[/tex] is​

The examples of relationship patterns found in mathematics are arithmetic sequence and geometric sequence.

It should be noted that an arithmetic sequence has a common difference. An example is given as: 2, 4, 6, 8. There's a common difference of 2.

For the geometric progression, there's a common ratio. A example is 2, 4, 8, 16, 32. Here, there's a cookie ratio of 2 when the numbers are divided.

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1) Identify the statement you want to prove is true

2) Assume temporarily that the statement is false; assume the opposite is true

3) Obtain statements that logically follow from your assumption.

4) Reason logically until you reach a contradiction of a known fact.

5) Point out that your assumption must be false, and the statement must then be true.

Answer:

$4.5

Step-by-step explanation:

We apply sales tax to the total cost, which in this case is $40 + $50 = $90.

Thus, we have 5% * $90 = $4.5

It even works individually if you apply the tax to both orders separately and add them together:

(50 * 5%) + (40 * 5%) = 4.5

2.5 + 2 = 4.5

Based on the amount the annuity pays per month and the APR, the value of the annuity today is $133,349.85.

First, find the present value of the annuity at 5 years:

= 1,850 x present value interest factor of annuity, 60 months, 8/12%

= 1,850 x 49.32

= $91,242

Then find the present value of the annuity from 5 years till date:

= (1,850 x present value interest factor of annuity, 60 months, 12/12%) + ( 91,242) / (1 + 1%)⁶⁰)

= (1,850 x 44.955) +  ( 91,242) / (1 + 1%)⁶⁰)

= $133,349.85

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Simplify both sides of the inequality.

Add 48 to both sides.

Divide both sides by 2.

Therefore, the correct option is "D".

Solve the inequality. 8(x/4-6)>4

O A. × ≥ 11

O B. × ≥ 5

O C. × ≥ - 22

∅ D. × ≥ 26

Given 8(×/4-6)>4

then simplify both sides of the inequality

[ 2 × - 48 ≥ 4 ]

Add 48 to both sides

[ 2 × ≥ 52 ]

Devide both sides by 2

[ 2×/2 ≥ 52/2 ] = [ × ≥ 26 ]

CarryOnLearning <(￣︶￣)>

Answer:

Step-by-step explanation:

5+16i

Answer:

5 + 16i

Step-by-step explanation:

(2 + 8i) + (3 + 8i)

• Collect the like terms:

2 + 3 + 8i + 8i

⇒ 5 + 16i

[tex]\sf{\qquad\qquad\huge\underline{{\sf Answer}}}[/tex]

An equation is called any equality that contains one or more unknown quantities, which are called unknowns, and that are only generally verified for certain values of the unknowns.

Thus, for example: 4x - 2 = 3x + 1~4x−2=3x+1 is an equation because it is an equality in which there is one unknown, xx .

⇝Equation resolution:

[tex] \qquad \sf \dashrightarrow4x - 2 = 3x + 14x−2=3x+1

[tex] \qquad \sf \dashrightarrow4x - 2 = 3x + 14x−2=3x+1[/tex]

We transpose the term 3x to the first member.

3x to the first member.We will have:

[tex] \qquad \sf \dashrightarrow4x - 2 - 3x = 14x−2−3x=1[/tex]

Next we transpose the term -2 to the second member.

We will have:

[tex] \qquad \sf \dashrightarrow4x - 3x = 1 + 24x−3x=1+2[/tex]

[tex] \qquad \sf \dashrightarrow \: x = 3x = 3[/tex]

Let's check that x = 3x=3 satisfies the given equation:

[tex] \qquad \sf \dashrightarrow4x - 2 = 3x + 14x−2=3x+1[/tex]

[tex] \qquad \sf \dashrightarrow4(3) - 2 = 3(3) + 14(3)−2=3(3)+1[/tex]

[tex] \qquad \sf \dashrightarrow12 - 2 =9+ 112−2=9+1[/tex]

[tex] \qquad \sf \dashrightarrow10 = 10 \: \: \: \: \:10=10[/tex]

That is, 10 = 10, as we wanted to verify.

I hope I've helped : )

Answer:

The value of x is 3

When x = 3 then both the LHS and RHS of the equation equal to the same number; 10.

Step-by-step explanation:

[tex]4x - 2 = 3x + 1 \\ 4x - 3x = 1 + 2 \\ x = 3 \\ [/tex]

When we substitute the value for x in the expression, we see that the expression represents the same number. i.e

[tex]4x - 2 = 3x + 1 \\ 4(3) - 2 = 3(3) + 1 \\ 12 - 2 = 9 + 1 \\10 = 10 \\ [/tex]

Vertical angles theorem (top one): [tex]\angle 1 \cong \angle 3[/tex]

Given: [tex]\angle 1 \cong \angle 2[/tex]

Transitive property of congruence: [tex]\angle 3 \cong \angle 4[/tex]

Vertical angles theorem (bottom one): [tex]\angle 2 \cong \angle 4[/tex]

Answer: 7x-5

Step-by-step explanation:

[tex](f-g)(x)=f(x)-g(x)=(7x+1-8)-(-2)=\boxed{7x-5}[/tex]

Answer:

D. (f-g)(x) = |7x+1|-6

Step-by-step explanation:

f(x) = |7x + 1| - 8

g(x) = -2

(f - g)(x) = f(x) - g(x) = |7x + 1| - 8 - (-2)

(f-g)(x) = |7x + 1| - 6

Answer:What is the magnitude of 3i?

3i invested c.

Step-by-step explanation: $182m in Magnitude Software in 2019 to accelerate its global growth ambitions through new product development and investments in sales & marketing, and to build a more integrated enterprise software business.

Por definición de perímetro y considerando el cambio de unidades, el perímetro de la caja en pulgadas es 12[(g+y)×2].

El perímetro de un figura geométrica plana se denomina a la longitud de su contorno. El perímetro es, por tanto, una medida de longitud.

En otras palabras, el perímetro de una figura de dos dimensiones es la distancia alrededor de la figura y es el resultado de la suma de los lados de una figura geométrica plana. Por lo que para el cálculo del perímetro es necesario conocer el número de lados de la figura y la longitud de cada uno de esos lados.

Una caja se puede considerar como una figura que tiene cuatro lados con dos medidas diferentes (alto y ancho).

El alto de la caja es "y" mientras que su ancho es "g" pies, por lo que su perímetro P es calculado como:

P= 2g + 2y= 2×(g+y) pies

Luego, se puede aplicar la siguiente regla de tres para realizar el cambio de unidades a pulgadas: si 1 pies equivale a 12 pulgadas, 2×(g+y) pies equivales a cuantas pulgadas?

[tex]P=\frac{2x(g+y) piesx12 pulgadas }{1 pie}[/tex]

Resolviendo

P= 12[(g+y)×2] pulgadas

Finalmente, el perímetro de la caja en pulgadas es 12[(g+y)×2].

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The volume of the balloon is 500 cubic inches after 20 seconds

From the given graph, we have:

Also from the graph, we have:

V(20) = 500

This means that:

The volume of the balloon is 500 cubic inches after 20 seconds

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Answer:

n

Step-by-step explanation:

Answer:

7^15

Step-by-step explanation:

7^5^3 = 7^(5*3) = 7^15

The natural antilogarithm of the given logarithm can be evaluated as; 1.014.

The natural logarithm of the number given in the task content can be evaluated by multiplying by 2.303 as follows;

Natural logarithm value is; 2.303 × 0.0058887

= 0.01356.

On this note, it follows that the natural antilogarithm of the result can be evaluated as;

= 1.014.

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The probability that the student will answer 5 correct questions is; P(5) = 0.053

The formula for binomial probability is;

P(X = x) = nCx * p^(x) * (1 - p)^(n - x)

Where;

p = probability of success.

n = number of trials, or the sample size.

x = the number of successes in the probability we are trying to calculate.

Now, we want to find P(5). We are given;

n = 12

x = 5

p = 1/5 = 0.2

Thus;

P(5) = 12C5 * (0.2)⁵ * (1 - 0.2)⁽¹² ⁻ ⁵⁾

P(5) = 0.053

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The minimum that Nolan would have to spend is $33.84  while the maximum he has to spend is $35.94

10 * 0.84 = 8.4

8 * 1.29 = 10.32

8 * 1.89 = 15.12

The minimum is  = 8.4 + 10.32 + 15.12

= 33.84 dollars.

10 * 1.89 = 18.9

8 * 1.29 = 10.32

8 * 0.84 = 6.72

The sum of the maximum is given as 18.9 + 10.32 + 6.72

= $35.94

Edward Nolan has room for 26 bedding plants in his garden. He can get pansies for $1.89 each, marigolds for $1.29 each, and zinnias for $0.84 each. He plans to buy 10 of one type and 8 each of the other two types of plants. (a) What is the minimum (in $) Edward will have to spend? $ Incorrect: Your answer is incorrect. (b) What is the maximum (in $) Edward could spend? $ Incorrect: Your answer is incorrect.

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Answer:

c/13 - 10

Step-by-step explanation:

Answer:

y = 5

Step-by-step explanation:

1) Simplify 7y+8+8y+7 to 15y + 15.

90 = 15y + 15

2) Subtract 15 from both sides.

90 - 15 = 15y

3) Simplify 90 - 15 to 75.

75 = 15y

4) Divide both sides by 15.

75/15 = y

5) Simplify 75/15 to 5.

5 = y

6) Switch sides.

y = 5

The transformation of a function may involve any change. The function f(x) is vertically stretched and shifted 5 units upwards to form h(x).

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Vertical shift

Stretching:

The function f(x)=x^(1/3) is transformed to form the function of  h(x)=(2x)^(1/3)+5. Therefore, the transformation made to the function is,

Vertically stretched by a factor of 2^(1/3) ⇒ 2^(1/3) × x^(1/3) = (2x)^(1/3)

Up by 5 units ⇒ (2x)^(1/3) + 5

Hence, the function f(x) is vertically stretched and shifted 5 units upwards to form h(x).

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Answer:

Step-by-step explanation:

The volume of the cylinder is [tex](\pi)(14^{2})(42)=8232\pi[/tex].

The volume of the hemisphere is [tex]\frac{2}{3}(\pi)(14^{3})=\frac{5488}{3}\pi[/tex].

Adding these together gives the exact volume to be [tex]\frac{30184\pi}{3}[/tex].

To the nearest tenth, this is 31608.6 square feet.

The statement, square of the product of 6 and a number can be written as 6x²

let

x = unknown number

= 6 × x

= 6x

= 6x²

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Answer!!

it would be a

Step-by-step explanation:

The total surface area of the cuboid is 143.52 cubic cm

The formula for calculating the surface area of a cuboid is expressed as:

SA = 2(lw + wh + lh)

where

l is the length = 7.2cm

w is the width = 3.1cm

h is the height = 4.8cm

Substitute

SA = 2(7.2*3.1 + 7.2*4.8 + 3.1*4.8)

SA = 2(22.32 + 34.56 + 14.88)

SA= 143.52 square cm

Hence the total surface area of the cuboid is 143.52 cubic cm

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The basic market graph is attached below.

A market is said to have reached equilibrium price when the supply of goods matches demand.

The equilibrium price is the only price where the plans of consumers and the plans of producers agree, where the amount consumers want to buy of the product, quantity demanded, is equal to the amount producers want to sell, quantity supplied. This common quantity is called the equilibrium quantity.

Quantity of gasoline:

Explanation of graph: The demand curve, D, and the supply curve, S, intersect at the equilibrium point E, with an equilibrium price of 1.4 dollars and an equilibrium quantity of 600.

The equilibrium is the only price where quantity demanded is equal to quantity supplied. At a price above equilibrium, like 1.8 dollars, quantity supplied exceeds the quantity demanded, so there is excess supply.

At a price below equilibrium, such as 1.2 dollars, quantity demanded exceeds quantity supplied, so there is excess demand.

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Based on the mixtures of the four students in the art class, the student with a different shade of purple would be Aiden.

In order to solve this question, look at the ratio of red paint to blue paint for all the students:

Alec:

1¹/₃ : ²/₃

2 : 1

Rosa:

2¹/₂ : 1 ¹/ ₄

2  :  1

Aidan:

4¹/₂  : 2

2.25 :  2

Zoe:

5 : 2¹/₂

2 : 1

Notice that Aidan's mixture is the only one that is different and so will have a different shade of purple as a result.

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Answer:

its aidan

Step-by-step explanation:

Considering the definition of an equation and the way to solve it, a person will devote 28 years watching TV and 6 years sleeping.

An equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear in addition to certain known data.

The members of an equation are each of the expressions that appear on both sides of the equal sign while the terms of an equation are the addends that form the members of an equation.

The solution of a equation means determining the value that satisfies it. In this way, by changing the unknown to the solution, the equality must be true.

To solve an equation, keep in mind:

Being "x" the number of years watching TV, and knowing that:

the equation in this case is:

x + (x+22) =34

Solving:

x + x =34 -22

2x= 12

x= 12 ÷ 2

x=6

As the number of years sleeping will exceed the number of years watching TV by 22, then x +22= 6 +22= 28 years.

Finally, a person will devote 28 years watching TV and 6 years sleeping.

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