Which is the ratio for sin a written as a fraction in simplest form

The formula to find change in entropy is given by :

[tex] Change in entropy = \frac{Q}{T} [/tex]

where Q is change in heat and T is temperature.

We are given Q = 500 joule and T = 20 degree C

Plugging these values in the formula,

[tex] Change in entropy = \frac{500}{20} [/tex]

We get change in entropy = 25 J/Celsius.

The given sequence is a geometric series.

Common ratio can be found as :

(-300/-600) = 0.5

(-150/-300) =0.5

So common ratio is 0.5

First term is -600

The attachment shows the required calculations.

Answer: Sum of eight terms is (-1195.31).

Answer:

The answer is 16.3

Step-by-step explanation:

For a random distribution with an specific mean and standard deviation, the most probable values are the ones that lie between the  ( means + or - standard deviation)

so in this case, the confidence range is:

Low = 15.5-1.5= 14

High = 15.5+1.5= 17

Values that lie between this range are more probable. So in this case 16.3, which is the only value in this range, has higher chance of occuring.

Answer:

The answer is the option C

IV, III,I,II

Step-by-step explanation:

Final answer:

To find the equivalent expression to 6(2m - 1) - 4(m + 8), we first expand and simplify the given expression to 8m - 38, making option A the correct answer.

Explanation:

The question asks which expression is equivalent to 6(2m – 1) – 4(m + 8). To find the equivalent expression, we first expand both terms and then simplify the resulting expression.

Therefore, the expression that is equivalent to 6(2m – 1) – 4(m + 8) is 8m - 38, which corresponds to option A.

Answer:

Step-by-step explanation:

c

Answer:

Compare your personal records to the bank's statement

Answer:

9 is an extraneous solution.

Step-by-step explanation:

Extraneous solution is a solution that when plugged into the equation do not hold true.

Here we are given an algebraic equation in terms of single variable x as:

[tex]\sqrt{x-5}-\sqrt{x}=5-----(1)[/tex]

Now, we will solve this equation to obtain the solution as:

on squaring both side of the equation we obtain:

[tex](\sqrt{x-5}-\sqrt{x})^2=5^2[/tex]

[tex]x-5+x-2\sqrt{x-5}\sqrt{x}=25\\\\2x-5-2\sqrt{x-5}\sqrt{x}=25\\\\2x-30=2\sqrt{x-5}\sqrt{x}\\\\on\ dividing\ both\ side\ by\ 2\ we\ obtain:\\\\x-15=\sqrt{x-5}\sqrt{x}[/tex]

Again on squaring both side of the equation we obtain:

[tex]x^2+225-30x=(x-5)x\\\\\x^2+225-30x=x^2-5x\\\\225=-5x+30x\\\\225=25x\\\\x=9[/tex]

Now when we plug x=9 back to the original equation i.e. equation (1) we get:

[tex]\sqrt{9-5}-\sqrt{9}=5\\\\\sqrt{4}-\sqrt{9}=5\\\\2-3=5\\\\-1=5[/tex]

Hence, the equation does not hold true.

Hence, 9 is a extraneous solution

5x-3(2x+7)=2x+9

This is the equation and Raul had to solve it for x

So he started with simplifying the parenthesis first

To simplify the parenthesis -3 gets multiplied with 2x and 7 , to get rid of parenthesis

So it came out to be

5x-3(2x+7)=2x+9

STEP-1

5x-6x -21 = 2x+9 , So the STEP-1 is correct,

After this in Step -2 , he has combined the like terms on left side, the like terms are 5x and -6x , 5x-6x should combine to -x , because 5-6 = -1

So

STEP-2

-x -21 = 2x+9 , So STEP -2 is INCORRECT

So he made a mistake in STEP-2

After that subtract 2x from both sides

-3x -21 = 9

add 21 to both sides

-3x = 30

divide both sides by -3

x=-10

Hence Option B is correct , he made a mistake in STEP -2

The factored form of the expression 15a + 25b with respect to the Greatest Common Factor (GCF) is 5 (3a + 5b). The GCF of 15 and 25 is 5.

To factor the Greatest Common Factor (GCF) from 15a + 25b, we first have to identify the GCF. The GCF of 15 and 25 is 5. Hence, we divide each term in the expression by this GCF.

We get: 5 (3a + 5b). So, the expression 15a + 25b factored by the GCF is 5 (3a + 5b).

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Answer:

The scale factor is 2.5 and the coordinates of point C are (–2.4, –0.8).

Step-by-step explanation:

Figure 1)

a) The area is A = 36( π - 2) ст²

b) The perimeter is P = 6 (π + 2√2) [tex]cm^2[/tex]

Figure 2)

a) The area is A = 576 cm²

b) The perimeter is P = 24(π+2) [tex]cm^2[/tex]

Figure 1)

a) To find the area of the figure 1 we have to do the substraction

The area of figure 1 is equivalent to the area of a triangle less the area of a quarter circle.

The area of quarter circle is equal to

A = 2

we have

r = 12 cm

Put the  value r as given

A = (12)2

A = 36 [tex]cm^2[/tex]

Area of a triangle formula is

A = (b)(h)

Given information,

b=12 cm

h = 12 cm

substitute

A = (12) (12)

A = 72 cm²

therefore

The area of the figure is

A = (36π - 72) [tex]cm^2[/tex]

Simplify

A = 36(π -2) [tex]cm^2[/tex]

b)

The perimeter of the figure 1 is equal to the circumference of a quarter circle plus the side AC of triangle

The perimeter of a quarter of circle is formula

C = 2πr

simplify

C = r

we have

r=12 cm

substitute

C = (12)

C = 67 cm

Find the length side AC

Applying the Pythagorean Theorem

[tex]AC^2 = 12^2 + 12^2[/tex]

[tex]AC^2 = 144+ 144\\AC^2 = 288\\AC = \sqrt{288}[/tex]

AC = 12√2 cm

P = (6π +12√2) cm

Taking 6 as a common multiplier we get

P = 6(π+2√2)

The perimeter of the figure 1 is

P = 6(π+2√2) cm

Part 2)

a) As we can see,

The area of a semicircle plus the area of a square less the area of a semicircle equals the area of figure 2.

The figure's area and the square's area are equal.

A = [tex]24^2[/tex]

A = 576 cm²

b) Find the perimeter of the figure 2

we know that

The perimeter of the figure 2 is equal to the length side AB plus the length side DC plus the circumference of two semicircles

The perimeter of the figure 2 is equal to two times the length side AB plus the circumference of one circle

P = 2(AB) + π D

P = 2(24) + π(24)

P = 48 +  π(24)

Take out 24

P = 24 (2 + π ) cm

Final answer:

The John Street Barber Shop pays a flat rate of $25 for the first 8,000 gallons of water, with an additional charge of $3.50 per thousand gallons above this threshold. Accordingly, the total costs for using 7,000 gallons is $25, for 10,000 gallons is $32, and for 13,000 gallons is $42.50.

Explanation:

The John Street Barber Shop pays $25 per month for the first 8,000 gallons of water and $3.50 per thousand gallons above 8,000 gallons. To calculate the total water cost when the barber shop uses 7,000 gallons, 10,000 gallons, and 13,000 gallons, we follow this methodology:

Thus, the total costs for using 7,000 gallons, 10,000 gallons, and 13,000 gallons are $25, $32, and $42.50 respectively.

Answer:

r=C/2*pie

Step-by-step explanation:

I got it correct on TTM

Answer:

The correct option would be 6 exterior angles in a Triangle.

Answer:

a=-2 is extraneous solution.

Step-by-step explanation:

Given the equation

[tex]\frac{3}{a+2}+\frac{2}{a}=\frac{4a-4}{a^2-4}[/tex]

we have to find the extraneous solution.

An extraneous solution is a solution to an equation, that emerges from the process of solving the problem but is not a valid solution to the problem.

[tex]\frac{3}{a+2}+\frac{2}{a}=\frac{4a-4}{a^2-4}[/tex]

[tex]\frac{3}{a+2}+\frac{2}{a}=\frac{4a-4}{a^2-4}\\\\\frac{3a+2(a+2)}{a(a+2)}=\frac{4(a-1)}{a^2-4}\\\\\frac{5a+5}{a(a+2)}=\frac{4(a-1)}{a^2-4}[/tex]

On solving, we get

The solution is a=4 and a=-2

Here the solution a=-2 is the valid solution as it makes the denominator 0.

⇒ a=-2 is extraneous solution.

Option 1 is correct.