Find the perimeter of the figure

Answer:

33 , 39

Step-by-step explanation:

given

9 , 15 , 21 , 27

there is a common difference between consecutive terms, that is

15 - 9 = 21 - 15 = 27 - 21 = 6

to obtain terms in the sequence add 6 to the preceding term

27 + 6 = 33

33 + 6 = 39

the next two terms are 33 and 39

The third term (a3) of the sequence is -8, the fourth term (a4) is 35, and the fifth term (a5) is -183. These values are obtained by applying the given formula recursively and substituting the previous terms accordingly. The calculations follow a specific pattern and are derived using the provided formula.

The sequence is defined by the following formula:

a1 = 1, a2 = 3,

and

an = (-1)nan - 1 + an - 2 for n ≥ 3.

To find the third term (a3), we substitute n = 3 into the formula:

a3 = (-1)(3)(a3 - 1) + a3 - 2.

Next, we simplify the equation:

a3 = -3(a2) + a1.

Since we know a1 = 1 and a2 = 3, we substitute these values into the equation:

a3 = -3(3) + 1.

Simplifying further:

a3 = -9 + 1.

Therefore, the third term (a3) is equal to -8.

To find the fourth term (a4), we substitute n = 4 into the formula:

a4 = (-1)(4)(a4 - 1) + a4 - 2.

Simplifying the equation:

a4 = -4(a3) + a2.

Since we know a2 = 3 and a3 = -8, we substitute these values into the equation:

a4 = -4(-8) + 3.

Simplifying further:

a4 = 32 + 3.

Therefore, the fourth term (a4) is equal to 35.

To find the fifth term (a5), we substitute n = 5 into the formula:

a5 = (-1)(5)(a5 - 1) + a5 - 2.

Simplifying the equation:

a5 = -5(a4) + a3.

Since we know a4 = 35 and a3 = -8, we substitute these values into the equation:

a5 = -5(35) + (-8).

Simplifying further:

a5 = -175 - 8.

Therefore, the fifth term (a5) is equal to -183.

In summary, the third term (a3) is -8, the fourth term (a4) is 35, and the fifth term (a5) is -183.

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Step-by-step explanation:

The solution would be 6

The exact value of the specified trigonometric identity found using the the trigonometric identity for tan(A - B) and tan(arccos(x)) and tanarcsin(x)) is presented as follows;

\(tan\left(sin^{-1}\left(\dfrac{3}{4} \right) - cos^{-1}\left(\dfrac{1}{5}\right) \right) =\dfrac{32\cdot \sqrt{6}- 75\cdot \sqrt{7} }{209}\)

A trigonometric identity is an equality that involves trigonometric functions that is valid for all values of the arguments of the equation

The required trigonometric identities are;

\(tan (A - B) = \dfrac{tan(A) -tan(B)}{1-tan(A)\cdot tan(B)}\)

\(tan(sin^{-1}(x)) = \dfrac{x}{\sqrt{1-x^2} }\)

\(tan(cos^{-1}(x)) = \dfrac{\sqrt{1-x^2}}{x }\)

Therefore;

\(tan\left(sin^{-1}\left(\dfrac{3}{4} \right) - cos^{-1}\left(\dfrac{1}{5}\right) \right) = \dfrac{tan\left(sin^{-1}\left(\dfrac{3}{4} \right)\right)-tan\left(cos^{-1}\left(\dfrac{1}{5} \right)\right)}{1-tan\left(sin^{-1}\left(\dfrac{3}{4} \right)\right)\times tan\left(cos^{-1}\left(\dfrac{1}{5} \right)\right)}\)

Which gives;

\(\dfrac{\dfrac{\frac{3}{4} }{\sqrt{1-\left(\frac{3}{4} \right)^2} } -\dfrac{\sqrt{1-\left(\frac{1}{5} \right)^2}}{\frac{1}{5} } }{1+\dfrac{\frac{3}{4} }{\sqrt{1-\left(\frac{3}{4} \right)^2} } \times \dfrac{\sqrt{1-\left(\frac{1}{5} \right)^2}}{\frac{1}{5} }}=\dfrac{\dfrac{3\cdot \sqrt{7}-14\cdot \sqrt{6} }{7} }{\dfrac{7+6\cdot \sqrt{42} }{7} }\)

\(\dfrac{\dfrac{3\cdot \sqrt{7}-14\cdot \sqrt{6} }{7} }{\dfrac{7+6\cdot \sqrt{42} }{7} }=\dfrac{32\cdot \sqrt{6}- 75\cdot \sqrt{7} }{209}\)

Which indicates that we have;

\(tan\left(sin^{-1}\left(\dfrac{3}{4} \right) - cos^{-1}\left(\dfrac{1}{5}\right) \right) =\dfrac{32\cdot \sqrt{6}- 75\cdot \sqrt{7} }{209}\)

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Answer:

A bag contains 8 red marbles, 3 blue marbles and 7 green marbles.

Total = 18 marbles.

Probability of drawing three red marbles = probability of drawing one red without replacement + probab of drawing another without reeplacement + probab of drawing a third without replacement.

Probability of drawing three red marbles = 8/18 + 7/17 + 6/16 = 0.4444 + 0.4118 + 0.3750 = 1.2312.

Answer:

0.043

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Answer:

6.3

Step-by-step explanation:

so first we find the radi

2 pi radi=4

4/pi=radi=1.27

1.27 sqaured times pi=5

Answer:

1:

26

24

57

47

59

61

16

23

2:

58.5

56.556

49.75

93.75

62.2857142857

98.667

28.223

57.5

56.5714285714

19.28

57.75

Answer:

100r1

Step-by-step explanation:

Answer:

4 1/10 when u have a inproper fraction like that every 10 is one whole number

The values of m and n are m = 123,000 and n = (123,000 - m1) / 2 + 1.

The given number is 123,000 which is the mth number in the nth row.

The rows contain two more numbers than the previous row.

Let us assume that the first row has m1 numbers.

Therefore, the second row has m1 + 2 numbers, the third row has m1 + 4 numbers, and so on.

We can represent the above information in a general formula as;

m1 + 2 (n - 1) = m

where m1 is the number of elements in the first row and n is the row number in which 123,000 is present.

By solving the above equation, we get

m1 = m - 2 (n - 1)

Now, we can calculate the value of n as;

n = (m - m1) / 2 + 1

Substituting the values of m and m1, we get

n = (123,000 - m1) / 2 + 1

Therefore, the values of m and n are m = 123,000 and n = (123,000 - m1) / 2 + 1.

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answer:

sale price: $5

explanation:

total price is always 100%

sale price is 80% off,

sale price: 100% - 80% = 20%

solve:

→ 20% * $25

→ $5

Answer:

$5

Step-by-step explanation:

\(25\times(1-80)\\25\times(1-0.8)\)

Calculate the sum or difference

\(25\times0.2\)

Calculate the product or quotient

\(5\)

I hope this helps you

:)

The correct option is,

⇒ −3 > −11; the bass is at a higher elevation than the flounder.

Option B is true.

What is Elevation?

Elevation is distance above the sea.

Given that;

A stripes bass is swimming at an elevation of −3 feet.

And, A flounder is swimming at an elevation of −11 feet.

Clearly, The bass is at higher elevation than the flounder.

So, -3 > -11

Hence, The correct option is,

⇒ −3 > −11; the bass is at a higher elevation than the flounder.

Option B is true.

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Solution:

Given:

The equation of the population can be gotten using the formula;

Hence, the equation is:

The population of the town 8.5years from now will be:

Answer:

\(2,712 \: {yd}^{2} \)

Step-by-step explanation:

Height of cylinder (h) = 24 yd

radius of cylinder (r) = 6 yd

Lateral surface area of the cylinder

\( = \pi {r}^{2} h \\ \\ = 3.14 {(6)}^{2}(24) \\ \\ = 2,712.96 \: {yd}^{2} \\ \\ \approx \: 2,712 \: {yd}^{2} \)

Answer:

The volume of 1 bucket is 2.4 liters.

Step-by-step explanation:

We know that the volume of 12 buckets is the same as the volume of 9 bottles:

\( 12B = 9b \)  

\( B = \frac{9}{12}b = \frac{3}{4}b \)   (1)

Where B is for buckets and b is for bottles.

Also, that the total volume of 3 bottles and 5 buckets is 21.6 liters:

\( 5B + 3b = 21.6 \)   (2)

We can calculate the volume of 1 bucket by entering equation (1) into (2):

\( 5(\frac{3}{4}b) + 3b = 21.6 \)

By solving for "b" we have:

\( b = \frac{21.6*4}{27} = 3.2 \)

Now, the volume of 1 bucket is:

\( B = \frac{3}{4}b = \frac{3*3.2}{4} = 2.4 \)

Therefore, the volume of 1 bucket is 2.4 liters.

I hope it helps you!

Answer:  No, we don't have a right triangle

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

Explanation:

If a triangle with sides a,b,c makes the equation a^2+b^2 = c^2 true, where c is the longest side, then this triangle is a right triangle. This is the converse of the pythagorean theorem.

Here we have a = 2, b = 5 and c = 7.

So...

a^2+b^2 = c^2

2^2+5^2 = 7^2

4+25 = 49

29 = 49

The last equation is false, so the first equation is false for those a,b,c values. Therefore, we do not have a right triangle.

------------

In contrast, consider the classic 3-4-5 right triangle

a = 3, b = 4 and c = 5 would make a^2+b^2 = c^2 true because 3^2+4^2 = 5^2 is a true equation (both sides lead to 25).

Answer:

Step-by-step explanation:

for 1 they give us an angle and the side next to that angle.. or the Adjacent side and they want to know the Opposite side from the angle sooo let's use ..

SOH CAH TOA    

hmm TOA seems good , it's got the adj and Opp in it ,

Tan(Ф) = Opp / Adj

Tan(67) = Opp / 26

26 * Tan(67) = Opp

61.2521 = Opp

61.3  ( rounded to nearest 10th )    does this seem big to you?  well it should be quite a bit bigger than the 25 on the base, seems about right to me

for 2 they give us one angle, 48 , and one side, 35 , that is opposite from that angle,  and ask what is the Hyp.  So find a trig function that has those pieces in it.     SOH seems good

sin(Ф) = Opp / Hyp

sin(48) = 35 / Hyp

Hyp = 35 / sin(48)

Hyp = 47.0971  ( and that seems about right for the Hypotenuse )

x = 47.1  ( rounded to the nearest 10th )

for 3  they are asking us to imagine a triangle, I'll draw it and attach it as a picture.    Looking at the picture helps a lot, we can see we have the angle and the adj side and want to find the Opposite side of that big triangle. sooo   use TOA  , it's got those pieces in it

Tan(17) = Opp / 200

200*Tan(17) = Opp

61.1461  =Opp

so the height of the radio mast is  61.1 meters  ( rounded to nearest 10th )

Does this seem a bit easier when you think about how the parts of the trig functions fit on the triangles?    :)   ask if you have any questions

Answer: 60(30) + 16h) = 79(15h)

Let's call the height of the rectangular prism "h".

The surface area of a rectangular prism is given by the formula:

SA = 2lw + 2lh + 2wh

The volume of a rectangular prism is given by the formula:

V = lwh

We're given that the ratio of the surface area to the volume is 79:60. So, we can write:

SA/V = 79/60

Substituting the values for the length, width, and height of the prism, we get:

(2(5)(3) + 2(5)(h) + 2(3)(h)) / (5)(3)(h) = 79/60

Simplifying the left-hand side, we get:

(30 + 10h + 6h) / 15h = 79/60

Combining like terms on the numerator, we get:

(30 + 16h) / 15h = 79/60

Cross-multiplying, we get:

60(30 + 16h) = 79(15h)

Expanding and simplifying, we get:

1800 + 960h = 1185h

Subtracting 960h from both sides, we get:

1800 = 225h

Dividing both sides by 225, we get:

h = 8

So, the height of the rectangular prism is 8 inches.

To solve for the height using a proportion, we can set up the following proportion:

(2lw + 2lh + 2wh) / lwh = 79/60

Substituting the given values, we get:

(2(5)(3) + 2(5)(h) + 2(3)(h)) / (5)(3)(h) = 79/60

Simplifying the left-hand side, we get:

(30 + 10h + 6h) / 15h = 79/60

Cross-multiplying, we get:

60(30 + 16h) = 79(15h)

We can then solve for h using algebraic manipulation as shown earlier.

Using Chebyshev's theorem, the percentage of recent graduates with salaries between $21300 and $29100 is 88.9%

Chebyshev's theorem states that for any given dataset, at least 1 - 1/k^2 of the data falls within k standard deviations from the mean. In this case, we want to find the minimum percentage of recent graduates who have salaries between $21,300 and $29,100, so we need to find the range of salaries that are k standard deviations from the mean.

We can start by converting the salary range to standard deviations from the mean:

$21,300 - 25,200 = -3,900$

$-3,900 / 1,300 = -3$

$29,100 - 25,200 = 3,900$

$3,900 / 1,300 = 3$

So, the salary range $21,300 to $29,100 is equivalent to 3 standard deviations from the mean in either direction.

Now, using Chebyshev's theorem, we can find the minimum percentage of recent graduates who have salaries within this range:

$1 - 1/k^2 = 1 - 1/3^2 = 1 - 1/9 = 8/9$

So, at least 8/9 or 88.9% of recent graduates have salaries within the range of $21,300 and $29,100.

Rounding to one decimal place, the minimum percentage of recent graduates with salaries between $21,300 and $29,100 is 88.9%.

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Here you go!

Also, if you could label this brainliest that would be a great help!

Thanks xx 

-Dante

Answer:

Divide 4.50 by 5 to find the unit rate for the 5-pound bag, and compare that number to $0.80 per pound.

Step-by-step explanation:

The type of sytudy that we have here is the observational study.

In an observational study, the researcher observes and analyzes data from individuals without actively intervening or manipulating any variables.

In this case, the researcher is observing and comparing the health outcomes of two groups of individuals: those who have eaten a vegan diet for the past five years and those who have not.

The participants are not randomly assigned to the groups, and the researcher does not actively control or manipulate the diet of the individuals.

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Answer:

See below

Step-by-step explanation:

1/2 mile   /   1/4 hr   =   1/2  / 1/4   mph =  1/2 * 4/1 = 2 mi/hr

The result of the number 1 trillion to the 10th power as required to be determined is; 10¹²⁰.

The result of the number 1 trillion to the 10th power is as follows;

Recall; 1 trillion = 1,000,000,000,000 = 10¹²

Hence; 1 trillion to the 10th power is; ( 10¹² )¹⁰.

From the laws of indices; we therefore have that;

= 10¹²⁰

Ultimately, the result is; 10¹²⁰.

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Answer:

I think the answer are C, B, C, and A.

Answer:

FG=11.6 feet

Step-by-step explanation:

cos 77 degrees=2.6/FG (because this is a right triangle)

.22495=2.6/FG

FG=11.558 feet

Answer:

11.3

Step-by-step explanation:

Answer:

48 feet

Step-by-step explanation:

1 yard equals 3 feet, so you'll just need to multiply 16 x 3.

16 x 3 = 48

Answer:

48 feets

Step-by-step explanation:

1yard=3feets

hope this helps

Answer:

x=2

Step-by-step explanation:

4x + 2(x - 4) is equivalent to x +2

first, distribute. 4x+2x-8

next, combine like terms. 6x-8

6x-8 = x+2

we need to group all the variable terms on one side, and all the constant terms on the other side of the equation. (6x-8)+(8-x)=(x+2)+(8-x)

get rid of the parenthesis. 6x-8+8-x=x+2+8-x

combine like terms. 6x-x-8+8=x-x+2+8

solve. 5x=10

divide both by 5. 5x/5=10/5

x=2

Answer: The answer is 3

Step-by-step explanation:

The image of A about O after 90 degrees rotation is C

Rotation refers to the movement of an object around an axis or center point.

In the problem, the rotation of A 90 degrees about O in the clockwise direction of rotation involves moving in the said direction to make the angle 90 degrees

In an octagon, each angle in the center is solved by

= 360 / 8

= 45

Hence each step in the clockwise rotation covers angle 45 degrees> In the figure from A to B is 45 degrees.

Moving from A to C in clockwise direction is equal to 90 degrees

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Answer:

\(y=-x+1\)

Step-by-step explanation:

It helps to write the equation in slope-intercept formula to find the slope of an equation in the form: \(y=mx+b\) where "m" is the slope of the equation. We can take the equation given: \(-7x-7y=7\) and solve for "y" to get the equation in slope-intercept form:

\(-7x-7y=7\)

add 7x to both sides:

\(-7y=7x+7\)

Divide both sides by -7

\(y=-x-1\)

Now in this form we can tell that the coefficient of "x" (the m value) is our slope, which is -1. We need this slope to determine a parallel line as parallel lines share the same slope but different y-intercepts. So a general equation for a parallel line would be:

\(y=-x+b\text{ where b }\ne -1\)

We're given the point (-1, 2) and we can use it to solve for that "b" value.

We plug in -1 as x and 2 as y

\(2=-1(-1)+b\implies 2=1+b\implies 1=b\)

Now we just plug this into the general equation to get: \(y=-x+1\)