-353.92 - (-283.56) -131.29

By solving a simple equation we can see that Chris earned $192.50.

We know that Chris wins $10 per hour plus the 12.5% of the total amount he solds in computers.

So, if he works 5.5 hours and sold $1,100 in computers, the amount that he earns is given by the equation:

E = $10*5.5 + $1,100*( 12.5%/100%)

E = $10*5.5 + $1,100*(0.125) = $192.50

Then we conclude that Chris earned $192.50 today.

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The values that match the various trigonometric identity are;

1) sin²/₅π cos π/₁₀ + cos²/₅π sin π/₁₀ = 1

2) cos 13 cos 47 + sin 13 sin 47 = 0.5

3) sin²/₅π cos ⁸/₅π + cos²/₅π sin ⁸/₅π = 0

Trigonometric identities are defined as the equations that involves the trigonometric functions that are true for every value of the variables involved.

1) We know that the trigonometric identity sin(A + B) is expressed as;

sin(A + B) = sinAcosB + cosAsinB

We are given;

sin²/₅π cos π/₁₀ + cos²/₅π sin π/₁₀

Applying the trigonometric identity above, gives us;

sin(²/₅π + π/₁₀)

= sin(5π/10)

= sin(π/2)

= 1

2) We know that the trigonometric identity sin(A + B) is expressed as;

cos(A + B) = cosAcosB − sinAsinB.

We are given;

cos 13 cos 47 + sin 13 sin 47

Applying the trigonometric identity above, gives us;

cos(13 + 47)

= cos 60

= 0.5

3) We know that the trigonometric identity sin(A + B) is expressed as;

sin(A + B) = sinAcosB + cosAsinB

We are given;

sin²/₅π cos ⁸/₅π + cos²/₅π sin ⁸/₅π

Applying the trigonometric identity above, gives us;

sin(²/₅π + ⁸/₅π)

= sin(¹⁰/₅π)

= sin(2π)

= 0

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The difference between the sum of first 10 terms of AP and GP where the first term and second term is 2 and 4 respectively is -932

What is Arithmetic Progression and Geometric Progression?

An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"

The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁

Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]

A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.

The general form of a GP is a, ar, ar2, ar3 and so on

Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )

Given data ,

First term = -2

Second term = 4

A)

For Arithmetic Progression

First term a = -2

Second term = 4

Common difference d = Second term - First term

                                     = 4 - ( -2 )

                                     = 6

And Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]

n = 10 terms

Sₙ = ( 10/2 ) [ (2x- 2) + ( 9 ) x 6]

Sₙ = 5 [ -4 + 54 ]

Sₙ = 5 x 50

Sₙ = 250

Therefore , Sum of first 10 terms of an AP is 250

B)

For Geometric Progression

First term a = -2

Second term = 4

Common ratio = Second term / First term

                        = 4 / -2

                        = -2

And Sum of first n terms of an GP : Sₙ =  a( 1 - rⁿ ) / ( 1 - r )

n = 10

Sₙ = 2( 1 - ( -2 )¹⁰ ) / 1 - ( -2 )

Sₙ = 2 ( 1 - 1024 ) / 3

Sₙ = ( 2 x (-1023) ) / 3

Sₙ = 2 x ( - 341 )

Sₙ = - 682

Therefore , Sum of first 10 terms of an GP is -682

The difference between the sum of first 10 terms of AP and GP is GP - AP

= -682 - 250

= -932

Hence , The difference between the sum of first 10 terms of AP and GP where the first term and second term is 2 and 4 respectively is -932

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Answer: There is no solution

Step-by-step explanation:

The formatting of the question isn't clear, but I'll still explore both possibilities. If the square root is only applied to x, we can solve for the variable by adding 4 to both sides and then squaring both sides, which would give us 4. Since that is not an answer choice, it means the square root applies to x-4. With this problem, we square both sides right away. That gives us x=0, but plug 0 back into the original equation. Doing so gives us the square root of -4, which is not possible with real numbers, only with imaginary numbers.

If Sebastian filled 10 gallons of gas, the total amount he spent at the gas station was C. $40.50.

Using the mathematical operations of multiplication and addition, we can compute the total amount that Sebastian spent at the gas station.

We first determine the total cost of gas that Sebastian bought by multiplying the unit cost by the quantity.

Secondly, we add the above total cost to the total cost of other items he bought at the station to arrive at the total amount spent.

The cost of gas per gallon = $2.91

The number of gallons of gas bought = 10

The total cost of gas = $29.10 ($2.91 x 10)

The total cost of granola bars and tissues = $11.40

The total amount spent = $40.50 ($29.10 + $11.40)

Thus, mathematically, Sebastian spent C. $40.50 at the gas station.

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The percent increase from 2,500 pounds this week to 2,525 pounds is 1% increase

From the question, we have the following parameters that can be used in our computation:

Initial weight = 2500 pounds

New weight = 2525 pounds

The percentage increment is then calculated as

Percentage = (Final value - Initial value)/Initial value * 100%

Substitute the known values in the above equation

Percentage = (2525 - 2500)/2500 * 100%

Evaluate the difference

So, we have

Percentage = 25/2500 * 100%

Evaluate the quotient

So, we have

Percentage = 0.01 * 100%

Evaluate the product

So, we have

Percentage = 1%

Hence, the percent increase is 1% increase

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The order for the extra materials that are ordered by the man will be between 17.31 ft² and 23.08 ft².

From the information, the man is ordering new tile for her kitchen floor the area of the floor is 115.4 ft.² and wants to order between 15% and 20% extra of the material.

It should be noted that 15% of the material will be:

= 15% × 115.4

= 17.31 ft²

It should be noted that 20% of the material will be:

= 20% × 115.4

= 23.08 ft²

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Answer:

ln A / ln 2

Step-by-step explanation:

Using the change of base rule: ln A / ln 2

Answer:

25% or 35 rocks.

Step-by-step explanation:

To find this answer, simply add up 40% and 35% to get 75%. Now, 100% is the most we can have. So, 100 - 75 = 25%.

To find even more in depth of exactly how much 25% of 140 is, we can simply move the decimal point from 25 over twice to get 0.25. The term "of" means multiply:

0.25 x 140 = 35 rocks.

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Answer: 8

Step-by-step explanation:

(Sum of first 5 quizzes) / 5 quizzes = 8

Sum of 1st 5 quizzes = 8 x 5 = 40

let x = score on the 8th quiz

(40 + 7 + 5 + x) / 8 = 7.5

52 + x = (7.5)(8) = 60

x = 60 - 52 = 8

Answer:cap

Step-by-step explanation:C A P

The graph of inequalities equation on coordinate plane is given below ↓↓↓

Difference between equality and inequality equations

Both mathematical phrases, equality and inequality , are created   by connecting two expressions.The equal sign (=) indicates that two expressions in an equation are believed to be equivalent. The symbols show that the two expressions in an inequality are not always equal: >, <, ≤ or ≥. Or in simple words the equation which has '=' sign is an equality equation while the inequality equation has the signs are >, <, ≤ or ≥.

The inequalities equation is ,

y> 2x+4

x+y≤6

so, the graph is ↓↓↓

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Answer:

p=-10

Step-by-step explanation:

-10-20=-30

Subtracting a negative from a negative will result in a higher negative, the same can be said for -10-20. Removing 10 from -20 will result in a lower answer. This is 20.

Answer:

The new value is $8,272

Step-by-step explanation:

8800 x (1 - 0.06) = 8272

[tex]\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{"y" varies with "x"}}{y=kx}\hspace{5em} \textit{we know that} \begin{cases} y=0.1\\ x=0.2 \end{cases} \\\\\\ 0.1=k(0.2)\implies \cfrac{0.1}{0.2}=k\implies 0.5=k\hspace{5em}\boxed{y=0.5x}[/tex]

Answer:

the answer is down there