Please help me with this math problem. Find the equation for the line below.

The value of S₃ is 65/9.

A geometric series is the sum of an infinite number of terms that have a constant ratio between successive terms. S=  a + ar + ar² + ar³+ . . .

a=start term r =common ratio

Given here, the nth term is 5(1/3)ⁿ⁻¹

therefore the sum of the first 3 terms of the geometric series is

S₃ = 5(1/3⁰) +5(1/3)¹+5(1/3)²

   = 1+ 5/3 + 5/9

   = 65/9

Hence the final answer is 65/9

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Answer:

C. [tex]32.7cm^{2}[/tex]

Step-by-step explanation:

Area = (Perimeter x apothem) / 2

Area = 21.8 x 3 / 2

Area = 65.4 / 2

Area = [tex]32.7cm^{2}[/tex]

C. The area of the regular pentagon, rounded to the nearest tenth is 32.7 cm².

The area of the regular pentagon is calculated as follows;

Area = aP/2

where;

Area = (3 x 21.8)/2

Area = 32.7 cm²

Thus, the area of the regular pentagon, rounded to the nearest tenth is 32.7 cm².

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Answer:

(5,0) and (-1,0)

Step-by-step explanation:

Answer:

[tex]y = 9[/tex]

Step-by-step explanation:

[tex]28 + 7y = 91 \\ 7y = 91 - 28 \\ 7y = 63 \\ \frac{7y}{7} = \frac{63}{7} \\ y = 9[/tex]

Answer:

Y=9

Step-by-step explanation:

28 + 7y =91

first subtract 28 from both sides

28-28+7y=91-28

7y= 63

then divide both sides by 7

7y/7=63/7

y=9

ANSWER CHECK

to see if the answer is correct substitute the answer you got for the variable

y=9

28 + 7(9)

multiply 7 and 9

7(9)=63

63+28= 91

Answer:

f(8) = 3^8  = 6561

Step-by-step explanation:

f(x) = 3^x

Let x =8

f(8) = 3^8

     = 6561

Answer:

f(8) = 6561

Step-by-step explanation:

f(x) = 3^x        Substitute x = 8

f(8) = 3^8       Simplify the exponent

f(8) = 6561

To simplify the expression 5.2 + 3.6x - 8 + x, combine like terms to get -2.8 + 4.6x, which is the final simplified expression.

The student's question involves simplifying the expression 5.2 + 3.6x – 8 + x. To simplify the given algebraic expression, combine like terms. Like terms in this expression are the constant terms (5.2 and -8) and the variable terms (3.6x and x).

First, add the constant terms together:

5.2 - 8 = -2.8

Then, combine the variable terms:

3.6x + x = (3.6 + 1)x = 4.6x

Now, put the constants and variable terms together to get the simplified expression:

-2.8 + 4.6x

To check if the simplified expression is reasonable, ensure that all like terms have been correctly combined. There is no further simplification possible, so this is the final answer.

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Answer:

100 degrees

Step-by-step explanation:

Arc QM = Arc QN = 130°

Arc MN = 360 - Arc QM - Arc QN

= 360 - 2(130)

= 360 - 260

= 100°

Answer:

1120 grams

Step-by-step explanation:

The amount of sea water is directly proportional to the amount of salt in the water.

Let the amount of sea water be W and the amount of salt be S.

This means that:

W α S

=> W = kS

where k = constant of proportionality

2 liters of sea water contain 70 grams of salt Therefore:

2 = k * 70

k = 2 / 70 = 1/35

Therefore, for 32 liters of sea water:

32 = 1/35 * S

S = 35 * 32

S = 1120 grams

There are 1120 grams of salt in 32 liters of water.

Answer:

47.16 Square centimeters

Step-by-step explanation:

Width=7.2cm

Length =19cm

Height =32cm

Surface Area=2(LW+LH+WH)

=2(19*7.2+19*32+7.2*32)

Surface Area [tex]=1950.4 cm^2[/tex]

When the height is increased by 0.9cm

Height =32.9cm

Surface Area=2(LW+LH+WH)

=2(19*7.2+19*32.9+7.2*32.9)

Surface Area [tex]=1997.56 cm^2[/tex]

Difference in Surface Area=1997.56-1950.4

=47.16 Square centimeters

An alternative way is to calculate the surface area dealing with the height only using the height difference,

Difference=2(LH+WH)

=2(19*0.9+7.2*0.9)

=47.16 Square centimeters

Answer:

I am 99% sure it's [tex]x = 100[/tex]°, here's why (down)

Step-by-step explanation:

The total is 180°. When adding 57° + 23° = 80°. To get [tex]x[/tex], you have to subtract 80° from 180°. The difference is 100°, which is the answer of this problem.

Answer:

C.

D.

E.

Step-by-step explanation:

The two options that yield the same value for 'x' as the equation 'Three-fifths (30 x minus 15) = 72' are '3 (6 x minus 3) = 72' and 'x = 4.5'. The confusion can be eliminated by simply breaking down and solving the initial equation for 'x', and then substituting the calculated value for 'x' into the optional equations.

To discover which options yield the same value as 'Three-fifths (30 x minus 15) = 72', we first need to solve the given equation for 'x'. This can be done as follows:

Substitute x = 4.5 into each option:

Therefore, '3 (6 x minus 3) = 72' and 'x = 4.5' provide the same value for x as the initial equation 'Three-fifths (30 x minus 15) = 72'.

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Answer:

27218

Step-by-step explanation:

y= 17000 (1.04) ^12

y=27217.54772

y= 27218

If a town has a population of 17000. The population after 12 years, to the nearest whole number is 27,218.

Using this formula

A=P(1+r/100)^n

Let plug in the formula

A= 17000 (1+.04) ^12

A= 17000 (1.04) ^12

A=17000×1.601032

A=27217.54

A=27218 (Approximately)

Therefore the population after 12 years, to the nearest whole number is 27,218.

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Answer:

The absolute value of a number is a distance /2/=2

Step-by-step explanation:

The absolute value of the absolute expression |2| will be 2.

When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.

The absolute function is also known as the mode function. The value of the absolute function is always positive.

The absolute expression is given below.

⇒ |2|

The value will be always positive when the value inside the mode is taken out. Then we have

⇒ |2|

⇒ 2

The absolute value of the absolute expression |2| will be 2.

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Answer:

The circumference of a circle is not the same as the area of the circle because the circumference represents the distance around the circle while the area represents the amount of space within the circle. Hope this helps.

Answer:

No

Step-by-step explanation:

The circumference of a circle is the distance around the outside of the circle. It is similar to the perimeter of other shapes such as squares.

Hope this helps! :)

Answer:

7.68 s

Step-by-step explanation:

The vertical motion formula is:

[tex] h_{t} = h_{0} + v_{0}t - \frac{gt^{2}}{2} [/tex]

Where:

h(t): is the final height = 0

h(0): is the height of the cliff = 104 foot

v(0): is the initial velocity = 110 ft/s

g: is the gravity = 9.8 m/s² = 32.15 ft/s²

Hence, from the vertical motion formula we can find the time that will take the rocket to hit the ground:

[tex] 0 = 104 + 110*t - \frac{32.15t^{2}}{2} [/tex]

[tex] 0 = 104 + t(110 - 16.08t) [/tex]

We have two solutions:

t₁= -0.84 s

t₂ = 7.68 s

We will take the positive value, thus the time that will take the rocket to hit the ground is 7.68 s.

I hope it helps you!

Answer:

[tex]P(H|P) = \frac{P(H \cap P)}{P(P)}[/tex]

And replacing we got:

[tex] P(H|P) =\frac{0.28}{0.64}= 0.4375[/tex]

And the probability required for this case is 0.4375

Step-by-step explanation:

For this case we define the following events:

H = represent that the student is honorable

P= represent that the student have a part time job

And we have the following probabilities:

[tex] P(H) = 0.42 , P(P) = 0.64, P(H \cap P) =0.28[/tex]

And we want to find this probability:

[tex] P(H|P)[/tex]

And we can use the following probability:

[tex]P(H|P) = \frac{P(H \cap P)}{P(P)}[/tex]

And replacing we got:

[tex] P(H|P) =\frac{0.28}{0.64}= 0.4375[/tex]

And the probability required for this case is 0.4375

Answer:

Step-by-step explanation:

[tex]Width=\frac{Area}{length}\\\\=\frac{36}{9}\\\\[/tex]

= 4 inches

Answer:

9×W=36 or 36÷9=W

Step-by-step explanation:

to find the area of a figure you multiply L×W in this situation you only have length. soo find what times 9 = 36 or 36÷9 to find Width

Answer:

-62.5008

Step-by-step explanation:

Find the pattern first: -75/15 = -5

Find the first 7 terms: -3/-5, 3/25, -3/125, 3/625

Add: -62.5008

Answer:

  -62.5008

Step-by-step explanation:

The terms form a geometric sequence with first term -75 and common ratio -1/5. The sum of n terms of such a sequence is...

  Sn = a1(1 -r^n)/(1 -r)

For the values of a1, r, and n, this sum is ...

  S7 = -75(1 -(-1/5)^7)/(1 -(-1/5)) = -75(1 +1/78125)/(1 +1/5)

  = -75(13021/15625) = -62 313/625

  = -62.5008

The sum of the first 7 terms of the sequence is -62.5008.

Answer:

80% confidence interval for the proportion of homes that are "eclectic" is [0.59 , 0.78].

Step-by-step explanation:

We are given that James takes a random sample of 42 homes form the Austin MLS (that's where Realtors go for information) and finds that 29 of them are listed as "eclectic" style.

Firstly, the pivotal quantity for 80% confidence interval for the population proportion is given by;

                              P.Q. =  [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = sample proportion of homes that are "eclectic" = [tex]\frac{29}{42}[/tex] = 0.69

            n = sample of homes = 42

            [tex]\mu[/tex] = population proportion of homes that are "eclectic"

Here for constructing 80% confidence interval we have used One-sample z proportion statistics.

So, 80% confidence interval for the population proportion, p is ;

P(-1.282 < N(0,1) < 1.282) = 0.80  {As the critical value of z at 10% level

                                                     of significance are -1.282 & 1.282}  

P(-1.282 < [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < 1.282) = 0.80

P( [tex]-1.282 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < [tex]{\hat p-p}[/tex] < [tex]1.282 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.80

P( [tex]\hat p-1.282 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < p < [tex]\hat p+1.282 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.80

80% confidence interval for p = [ [tex]\hat p-1.282 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex],[tex]\hat p+1.282 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]]

= [ [tex]0.69-1.282 \times {\sqrt{\frac{0.69(1-0.69)}{42} } }[/tex] , [tex]0.69+1.282 \times {\sqrt{\frac{0.69(1-0.69)}{42} } }[/tex] ]

= [0.59 , 0.78]

Therefore, 80% confidence interval for the proportion of homes that are "eclectic" is [0.59 , 0.78].

Answer:

18/m - 3

Step-by-step explanation:

Answer:

[tex]d = \frac{t - 7c}{ - 2} [/tex]

Hope this helps at all. :)

To solve for d in T = 7c - 2d, isolate the variable d by moving the term with d to the other side of the equation and simplifying.

To solve for d in the equation T = 7c - 2d, we need to isolate the variable d. First, we'll start by moving the term with d to the other side of the equation.

Step 1: Add 2d to both sides of the equation.

T + 2d = 7c

Step 2: Now, we'll isolate the variable d by subtracting T from both sides of the equation.

2d = 7c - T

Step 3: Finally, divide both sides of the equation by 2 to solve for d.

d = (7c - T)/2

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Answer:

Step-by-step explanation:

The total number of paint used = 8.8pints

If 4/5 of this amount is white paint, then the amount of white pint is expressed as;

[tex]= \frac{4}{5}*8.8\\= \frac{35.2}{5}\\[/tex]

= 7.04

This means the amount of white paint used is 7.04pints.

amount of blue paint used = Total amount of paint - amount of white paint

amount of blue white paint used = 8.8 - 7.04

amount of blue paint used = 1.76pints of paint

Answer:

Depends on the angel needed, I'll provide all answers

Step-by-step explanation:

Angel A is 93, because a straight line has an angel total of 180, so in order to find angel A you would just need to subtract

180-87 = 93

Angel B is 87, because angels opposite each other have the same value.

The Angel without a character would be 93 for the same reason :3

Answer:

The nth term can be represented by;

Tn = 5n- 1

Step-by-step explanation:

In this question, we are concerned with finding an expression in terms of n for then the term of the sequence.

Mathematically, the nth term of a sequence Tn can be represented by the formula;

Tn = a + (n-1)d

where a is the first term in the sequence which is 4 , and d is the common difference which is the difference between 2 consecutive terms which is 9-4= 5

our n is n, since we do not know the number of terms we are finding for

Plugging these values, we have;

Tn = 4 + (n-1)5

Tn = 4 + 5n -5

Tn = 5n- 1

Answer:

constant or constant polynomial

Some call is the zero polynomial

Step-by-step explanation:

Let x be raised to the 0 power

x^0 = 1

This is constant

3x^0 = 3*1 = 3

This is still constant

Answer:

Constant

Step-by-step explanation:

Degree 0 means the highest power of the variable is 0, which also means there's only one term

(Because the powers have to non-negative integers, and 0 is the smallest)

Ax⁰ is the form of a degree-0 polynomial

x⁰ = 1

Ax⁰ = A

Which is a constant

Answer:

2

Step-by-step explanation:

12a+6b

factor out 6

6(2a+b)

Answer:

The answer is this.

[tex]y = 4x {}^{2} [/tex]

Hope this helps ya.

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