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Recall the following property of exponents:

[tex]a^b\cdot a^c=a^{b+c}[/tex]

[tex]\implies 216^{-3k}\cdot 216^{-2k}=216^{-3k-2k}=216^{-5k}[/tex]

Now, notice that 6² = 36 and 6³ = 216, which means that

[tex]216^{-5k}=36^{2k-1} \iff (6^3)^{-5k}=(6^2)^{2k-1}[/tex]

Recall another property of (real) exponents:

[tex](a^b)^c=a^{bc}[/tex]

[tex]\implies(6^3)^{-5k}=6^{3(-5k)}=6^{-15k}\text{ and }(6^2)^{2k-1}=6^{2(2k-1)}=6^{4k-2}[/tex]

So we have

[tex]216^{-5k}=36^{2k-1} \iff 6^{-15k}=6^{4k-2}[/tex]

Since both sides are equal powers of 6, that must mean that the exponents must be equal, so

[tex]-15k=4k-2[/tex]

Solve for k :

[tex]-15k-4k=(4k-4k)-2[/tex]

[tex]-19k=-2[/tex]

[tex]k=\dfrac{-2}{-19}=\boxed{\dfrac2{19}}[/tex]

Answer:

18

Step-by-step explanation:

We know that line FH total length is 49. We also know that the length of line GH is 31.

To find FG, all we need to do is subtract 49-31 to find the length of FG.

Line FG total length is 18.

Answer:

4 2/3

Step-by-step explanation:

7/9 multiplied by 6/1 = 42/9

Simplify: 14/3

Turn it into a mixed number: 4 2/3

Answer:

0.78

Step-by-step explanation:

Answer:

0.78

Step-by-step explanation:

because...

0.78 = 0.780

so,

0.780 > 0.708

have a nice day! <3

The value of the function f(x) at x = - 2 is equivalent to 32.

Given is that the average rate of change of the function f(x) on the interval -2 is less than or equal to [x] which is less than or equal to 4 is -3.5.

In the range of {- 2 ≤ x ≤ 4}, the rate of change of f(x) is -3.5. This means we can write -

r = {f(4) - f(-2)}/(4 + 2)

f(4) = 11 and [r] = - 3.5. So, we can write -

- 3.5 = {11 - f(-2)}/6

11 - f(-2) = -3.5 x 6

11 - f(-2) = - 21

f(-2) = 11 + 21

f(-2) = 32

Therefore, the value of the function f(x) at x = - 2 is equivalent to 32.

To solve more questions on functions, expressions and polynomials, visit the link below -

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Tanmayi will need $30 more to reach her goal.

$120 + n = $150

$150 - $120 = 30

n = 30

Answer:

( 1 ; -2 )

Step-by-step explanation:

x + 3y = -5..............1

5y - 10 = -20x........2

x = -5 - 3y..............3

5y - 10 = -20( -5 - 3y)

5y - 10 = 100 + 60y

-55y = 110

y = -2

x = 1

Answer:

230

Step-by-step explanation:

You should multiply 345 by 2/3 or you can divide 345 by 3, which equaks 115 and then multiply 115 by 2 which equals 230.

The number of boys in the school is 207.

Given

The ratio of girls to boys in a school simplifies to 2:3.

We need to find out how many boys are there if there are 345 students in the school.

The ratio gives us an idea between two quantities.

It is denoted by a:b

Example:

The ratio of apple and mango in the basket is 1:2.

The total number of fruits is 12.

Apple = [ 1 / (1+2) ] x 12 = (1/3) x 12 = 4

Mango = [ 2/(1+2) ] x 12 = (2/3) x 12 = 2 x 4 = 8

We have,

Total number of students = 345

The ratio of girls to boys = 2:3

The number of boys :

= [ 3 / (2+3) ] x 345

= [ 3/5 ] x 345

= 3 x 69

= 207

Thus the number of boys in the. school is 207.

Learn more about ratios here:

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Answer: 7 and a 1/2

Step-by-step explanation: 1 and 1/4 times4 = 5 plus 2 and a 1/2 = 7 and a 1/2

Answer:

(a) [tex]\text{P(n)} = \text{p} \times \text{(1 - p)}^{n-1} ; \text{ n} = 1, 2, 3,....[/tex]

(b) P(1) = 0.740, P(2) = 0.192, and P(3) = 0.050.

(c) The probability that n ≥ 4 is 0.018.

(d) The expected number of residents in the village you must meet before you encounter the first person of Hawaiian ancestry is 3.

Step-by-step explanation:

We are given that on the leeward side of the island of Oahu, in a small village, about 74% of the residents are of Hawaiian ancestry.

Let n = 1, 2, 3, … represent the number of people you must meet until you encounter the first person of Hawaiian ancestry in the village.

(a) We can observe that the above situation can be represented through the geometric distribution because the geometric distribution states that we will keep on going with the trials until we achieve our first success,

Here also, n represent the number of people you must meet until you encounter the first person of Hawaiian ancestry in the village.

So, the probability distribution of the geometric distribution is given by;

[tex]\text{P(n)} = \text{p} \times \text{(1 - p)}^{n-1} ; \text{ n} = 1, 2, 3,....[/tex]

where, p = probability that the residents are of Hawaiian ancestry = 74%

(b) The probabilities that n = 1, n = 2, and n = 3 is given by;

[tex]\text{P(n)} = \text{p} \times \text{(1 - p)}^{n-1}[/tex]

P(1) = [tex]\text{0.74} \times \text{(1 - 0.74)}^{1-1}[/tex] = 0.74

P(2) = [tex]\text{0.74} \times \text{(1 - 0.74)}^{2-1}[/tex] = 0.192

P(3) = [tex]\text{0.74} \times \text{(1 - 0.74)}^{3-1}[/tex] = 0.050

(c) The probability that n ≥ 4 is given by = P(n ≥ 4)

     P(n ≥ 4) = 1 - P(n = 1) - P(n = 2) - P(n = 3)

                   = 1 - 0.74 - 0.192 - 0.050

                   = 0.018

(d) The expected number of residents in the village you must meet before you encounter the first person of Hawaiian ancestry is given by = E(n)

We know that the mean of the geometric distribution is given by;

           Mean = [tex]\dfrac{p}{1-p}[/tex] = [tex]\dfrac{0.74}{1-0.74}[/tex]

                     = [tex]\dfrac{0.74}{0.26}[/tex] = 2.85 or 3 (approx).

Answer:

5.73

Step-by-step explanation:

Answer:

He should have $5.73 as change

Step-by-step explanation:

First add 85.43 with 21 and 7.84 and then do 120 - 114.27.

Answer:

a.) DomainL: -2 ≥ x < 1        Range:   1 ≥ y < 2

b.) DomainL: -2 > x < 2        Range:   -2 > y < 2

Step-by-step explanation:

look up what the open and closed dots mean

understand how to determine values on the y or x axis

Answer:

[tex]4(x^2+4x-1)[/tex]

Step-by-step explanation:

The greatest common factor is 4

[tex]4(x^2+4x-1)[/tex]

Answer: X=6

you would do 30 - 12 witch equals 18

than you would do 18 divided by 3 witch is 6 so it is x = 6

Answer:

.

Step-by-step explanation:

Answer: y=-3x+17

b = 17

Answer:

  24√3 square units

Step-by-step explanation:

The side length of a regular hexagon is 2/√3 times the length of the apothem. For an apothem of 2√3, the side length is ...

  s = (2/√3)(2√3) = 4

The perimeter P of the hexagon is 6 times the side length, so is 6×4 = 24.

The area is given by ...

  A = 1/2Pa

where P is the perimeter and 'a' is the apothem.

  A = 1/2(24)(2√3) = 24√3

The area of the hexagon is 24√3 square units.

_____

A hexagon can be divided into 6 congruent equilateral triangles. The apothem will be the altitude of one of those, so will divide the triangle into two triangles with angles 30°, 60°, and 90°. The ratios of the side lengths of such a triangle is something you might want to remember: 1 : √3 : 2. The altitude corresponds to the "√3" side, and the side length of the equilateral triangle corresponds to the "2" side. That is, we have the proportion ...

  apothem : hexagon side = √3 : 2

Multiplying by 2 gives the actual values in the hexagon of this problem:

  apothem : hexagon side = 2√3 : 4

Answer:

Step-by-step explanation:

2(x+y)=60

2x+2y=60

The second is the same  as the 1st but with the distribution

                    perimeter formula: P=2(W+L)

 We can distribute .Then P =  2W+2L

Answer:

waala kang jowa sabi ko

Answer:

Step-by-step explanation:

Simplifying

3x + 5 = 2x + 1

Reorder the terms:

5 + 3x = 2x + 1

Reorder the terms:

5 + 3x = 1 + 2x

Solving

5 + 3x = 1 + 2x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2x' to each side of the equation.

5 + 3x + -2x = 1 + 2x + -2x

Combine like terms: 3x + -2x = 1x

5 + 1x = 1 + 2x + -2x

Combine like terms: 2x + -2x = 0

5 + 1x = 1 + 0

5 + 1x = 1

Add '-5' to each side of the equation.

5 + -5 + 1x = 1 + -5

Combine like terms: 5 + -5 = 0

0 + 1x = 1 + -5

1x = 1 + -5

Combine like terms: 1 + -5 = -4

1x = -4

Divide each side by '1'.

x = -4

Simplifying

x = -4

Answer:

x = -4

Step-by-step explanation:

To solve the given equation, we must find a value of x that satisfies the equation.

3x + 5 = 2x + 1

Subtract 2x from both sides.

x + 5 = 1

Subtract 5 from both sides.

x = -4

So the value of x that satisfies the equation is -4. So the solution to the equation would be x = -4.

I hope you find my answer and explanation to be helpful. Happy studying.

Answer:

About $2.85 per gallon

Step-by-step explanation:

We can set up a proportion [tex]\frac{45.3}{15.9}[/tex]=[tex]\frac{x}{1}[/tex] we can then cross multiply, getting 15.9x=45.3. When you divide you get about $2.85

Answer:

98$ in savings

Step-by-step explanation:

If you do all the spending combined you would do $700+$325=$1025 $420+$182=$602 add those = $1627+$300=$1927  if his monthly take-home pay is $2025 you would have to do $2025-$1927=$98 remanding.

Answer:

36

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

We can use d to find out how much x equals which therefore would solve the rest of the equation. We also know that half of a parallelogram= 180 degrees so we know that it wouldn't be c and it wouldn't be any of the others either.

Hope this helps!

Answer:

150

Step-by-step explanation: one apple cost $0.50, so 75/ $0.50= 150