The final exam grade of a mathematics class has a normal distribution with mean of 81 and standard deviation of 6.6. If a random sample of 40 students selected from this class, then what is the probability that the average final exam grade of this sample is between 77 and 82? Answer: (round to 4 decimal places)

Answer: 6.5%

Step-by-step explanation:

Interest = Amount repaid - Amount borrowed

= 226 - 200

Interest = 26

Si = ( prt) / 100

26 = (200 x r x 2) / 100

26 = 4r

r = 6.5%

Answer:

On a coordinate plane, a dashed straight line with negative slope goes through (negative -5/3, 0) and (0, negative 5). Everything to the right of the line is shaded

Step-by-step explanation:

6x + 2y > –10

Solve for y

Subtract 6x from each side

2y > -6x -10

Divide by 2

y > -3x - 5

The y intercept is -5 and the slope is -3

The x intercept is -5/3

The line is dashed  and shaded to the right

Answer:

Graph A i'm right e2020

Step-by-step explanation:

just took the test plz give brainliest heres link to graph

Answer:

The diagram of the question is missing, I found a matching diagram, and it is attached to this answer

The 3D object produced is a cone with height 8 and diameter 8 (radius 4)

Step-by-step explanation:

A 3 dimensional solid figure can be formed when a 2 dimensional object is rotated about a line without displacing the object.

when the object in the diagram is rotated about line m, the rotation forms an object with a circular base of diameter 8 units (radius 4) from the base of the triangle and height 8 units, and the 3D object formed is called a cone.

Answer:

Step-by-step explanation:

2x² + 5x - 3 = 2x² - x + 6x - 3*1

                  =x(2x - 1) + 3(2x - 1)

                 = (2x -1)(x + 3)

[tex]\frac{x+3}{\frac{2x^{2}+5x-3}{x+1}}=(x+3)*\frac{x+1}{2x^{2}+5x-3}\\\\=(x+3)*\frac{(x+1)}{(2x-1)(x+3)}\\\\=\frac{x+1}{2x-1}\\\\5+\frac{x+3}{\frac{2x^{2}+5x-3}{x+1}}=5+\frac{x+1}{2x-1}\\\\=\frac{5*(2x-1)+(x+1)}{2x-1}\\\\=\frac{10x-5+x+1}{2x-1}\\\\=\frac{11x-4}{2x-1}[/tex]

Answer:

x=2

Step-by-step explanation:

x + 4 = 3(3x - 4)

Distribute

x+4 = 9x -12

Subtract x from each side

x+4 -x = 9x-x-12

4 = 8x-12

Add 12 to each side

4+12 = 8x-12+12

16 = 8x

Divide by 8

16/8 = 8x/8

2 =x

Answer:

x = 2

Step-by-step explanation:

x + 4 = 3(3x - 4)

Expand the brackets.

x + 4 = 9x - 12

Add -x and 12 on both sides.

4 + 12 = 9x - x

16 = 8x

Divide 8 into both sides.

16/8 = x

2 = x

Switch sides.

x = 2

Answer:

B. -2t^2+3t+4

Step-by-step explanation:

The standard form as

ax^2 + bx + c

Option B meets that requirement, even though it has a '-' in front

Answer:

y = 1/2x + 1

Step-by-step explanation:

Step 1: Find slope

(1-0)/(0+2) = 1/2

Step 2: Write equation

y = 1/2x + 1

Answer:

The intensity of the beam 16 feet below the surface is 0.06% of the initial intensity of the incident beam.

Step-by-step explanation:

"When a vertical beam of light passes through a transparent medium, the rate at which its intensity I decreases is proportional to I(t), where t represents the thickness of the medium (in feet).

This means that the intersity can be modeled by the following differential equation:

[tex]\frac{dI(t)}{dt} = -kt[/tex]

In which k is the decrease rate.

This differential equation leads to the following solution:

[tex]I(t) = I(0)e^{-kt}[/tex]

In which I(0) is the initial intensity.

The intensity 3 feet below the surface is 25% of the initial intensity I0 of the incident beam.

This means that I(3) = 0.25I(0). We use this to find k. So

[tex]I(t) = I(0)e^{-kt}[/tex]

[tex]0.25I(0) = I(0)e^{-3k}[/tex]

[tex]e^{-3k} = 0.25[/tex]

[tex]\ln{e^{-3k}} = \ln{0.25}[/tex]

[tex]-3k = \ln{0.25}[/tex]

[tex]k = -\frac{\ln{0.25}}{3}[/tex]

[tex]k = 0.4621[/tex]

So

[tex]I(t) = I(0)e^{-0.4621t}[/tex]

What is the intensity of the beam 16 feet below the surface

This is I(16). So

[tex]I(16) = I(0)e^{-0.4621*16} = 0.0006I(0)[/tex]

The intensity of the beam 16 feet below the surface is 0.06% of the initial intensity of the incident beam.

Hi

abswer is  : 0

any number a ^0 = 1  by convention if  a≥ 0 , and  0^3 = 0  

as you have a succsession of multiplication , and one  0 , so 0.

Answer:

[tex]0[/tex]

Step-by-step explanation:

[tex](3^0 \times 0^3) \times 2[/tex]

[tex](1 \times 0) \times 2[/tex]

[tex](0) \times 2[/tex]

[tex]=0[/tex]

Answer:

Step-by-step explanation:

A type I error occurs when one rejects the null hypothesis when it is actually true.

A type II error occurs when one fails to reject the null hypothesis when it is false.

In this study, the null hypothesis is 91 ​% of all jurors in the population were convinced that the suspect is guilty this he is convicted.

Failure of the jury to then convict the guilty suspect results in a type I error: The error is a Type I error because the null hypothesis is​ true, but the jury concluded that it is not true.

Answer:

The null hypothesis should not be rejected.

Step-by-step explanation:

We are given that the contents of a sample of 26 cans of beer showed a standard deviation of 0.06 ounce.

Let [tex]\sigma^{2}[/tex] = population variance

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\sigma^{2} \leq[/tex] 0.003      {means that the variance of the population is significantly less than or equal to 0.003}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\sigma^{2}[/tex] > 0.003      {means that the variance of the population is significantly more than 0.003}

The test statistics that would be used here One-sample chi-square test statistics;

                           T.S. =  [tex]\frac{(n-1)\times s^{2} }{\sigma^{2} }[/tex]  ~  [tex]\chi^{2}__n_-_1[/tex]

where, [tex]s^{2}[/tex] = sample variance = [tex]0.06^{2}[/tex] = 0.0036 ounces

            n = sample of cans of beer = 26

So, the test statistics  =  [tex]\frac{(26-1)\times 0.0036 }{0.003 }[/tex]  ~ [tex]\chi^{2}__2_5[/tex]

                                     =  30

The value of chi-square test statistics is 30.

Since in the question, we are not given with the level of significance so we assume it to be 5%. Now at 5% level of significance, the ch-square table gives a critical value of 37.65 for right-tailed test.

Since our test statistics is less than the critical value of chi as 30 < 37.65, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.

Therefore, we conclude that the variance of the population is significantly less than or equal to 0.003.

Answer:

Step-by-step explanation:

Here is the complete question.

The cylinder contains mw = 1.80 kg of water at just under 100°C. The piston has a radius of r = 6.35 cm, mass of mp = 2.70 kg, and initially rests on the surface of the water. The heater transfers energy to the water at the rate of 150 W. The latent heat of vaporization of water is Lvap = 2.26 ✕ 106 J/kg, and the specific heat of steam is csteam = 2,010 J/(kg ° C). The top of the piston is exposed to atmospheric pressure.

Once the water  begins  boiling, how fast does the piston rise ( in mm/s)?

Answer:

thus, once the water begins boiling, the speed of the piston rise is 8.73  mm/s

Step-by-step explanation:

Given that:

[tex]m_w =[/tex] 1.80 kg

radius  r = 6.35 cm

[tex]m_p =[/tex] 2.70 kg

rate of energy transfer = 150 W

latent heat of vaporization of water [tex]L_{vap} = 2.26 * 10^6 J/kg[/tex]

specific heat of steam is [tex]c_{steam} = 2,010 J/(kg ^0 C)[/tex]

From the given information;

the speed rise of the piston can be perceived to be of the same rate at which the height of the steam above the water is also increasing due to boiling.

Thus; volume of the gas  [tex]v = \dfrac{dh}{dt}[/tex]

[tex]v = \dfrac{d}{dt}(\dfrac{V}{A})[/tex]

Using the ideal gas law to replace the volume of the gas where the pressure and temperature are constant: we have;

[tex]v = \dfrac{1}{A} \dfrac{d}{dt}(\dfrac{nRT}{P})[/tex]

[tex]v = \dfrac{RT \ \ dn}{PA \ \ dt}[/tex]

However; the number of moles n in the mass [tex]m_g[/tex] of the gas to the molecular mass [tex]M_w[/tex] is ; [tex]n = \dfrac{m_g}{M_w}[/tex]

Replacing that into the above velocity formulae; we have:

[tex]v = \dfrac{RT \ \ d}{(m_pg+ P_oA)}( \dfrac{m_g}{M_w})[/tex]    

where F  = PA and F is the product of atmospheric pressure and area of piston plus the weight of the piston; i.e [tex]F = m_pg+ P_oA[/tex]

[tex]v = \dfrac{RT \ \ d}{(m_pg+ P_oA)}( \dfrac{m_g}{M_w})[/tex]    

[tex]v =[\dfrac{RT }{(m_pg+ P_oA)M_w}]( \dfrac{dm_g}{dt})[/tex]

where;

[tex]Q = \pm (\Delta mL)[/tex]

[tex]\dfrac{dm_g}{dt}= \dfrac{d}{dt}( \dfrac{Q}{L_v})[/tex]

Again;

[tex]v =[\dfrac{RT }{(m_pg+ P_oA)M_w}]( \dfrac{d}{dt})(\dfrac{Q}{L_v})[/tex]

[tex]v =[\dfrac{RT }{(m_pg+ P_oA)M_w * L_v}]( \dfrac{dQ}{dt})[/tex]

[tex]v =[\dfrac{RT \ \ Power}{(m_pg+ P_oA)M_w * L_v}][/tex]

[tex]v =[\dfrac{(8.314*373)(150)}{((2.70*9.8)+ (1.013*10^5)(\pi*0.0635^2))(0.0180 * 2.26*10^6}][/tex]

[tex]v = 8.73*10^{-3} \ m/s\\[/tex]

[tex]v = 8.73 \ \ mm/s\\[/tex]

Answer:

4

Step-by-step explanation:

there are a total of 16 home runs

there are a total of 4 teams

divide the homeruns by the teams to get the mean

16÷ 4 = 4

Answer:

4

Step-by-step explanation:

L-7

H-2

G-4

R-3

mean is 7+2+4+3= 16

16 / 4

the 4 represents the 4 teams

4 is the answer

i hope this helped

Answer:

$300

Step-by-step explanation:

Let [tex]x[/tex] be the original price.

[tex]x \times (1-0.04)=288[/tex]

[tex]0.96x=288[/tex]

[tex]x=\frac{288}{0.96}[/tex]

[tex]x=300[/tex]

Answer:

$300

Step-by-step explanation:

If it was a 4% reduction then we get:

[tex]x*0.96=288\\[/tex]

Divide both sides by 0.96

[tex]x=300[/tex]

The original suit price was $300

Answer:

Step-by-step explanation:

Step 1: Consider P(1) that is n = 1

[tex]1^2 = \frac{1(1+1)(2*1+1)}{6}=\frac{6}{6}=1 \checkmark[/tex]

Step 2: Suppose the equation is true up to n. That is

[tex]1^2 + 2^2+3^2+........+n^2 = \dfrac{n(n+1)(2n+1)}{6 }[/tex]

Step 3: Prove that the equation is true up to (n+1). That is

[tex]1^2 + 2^2+3^2+........+n^2 + (n+1)^2 = \dfrac{(n+1)(n+2)(2n+3)}{6 }[/tex]

The easiest way to prove it is to expend the right hand side and prove that the right hand side = the right hand side of step 2 + (n+1)^2

From step 2, add (n+1)^2 both sides. The left hand side will be the left hand side of step 3, now, the right hand side after adding.

[tex]\dfrac{n(n+1)(2n+1)}{6 }+(n+1)^2 = \dfrac{2n^3+3n^2+n}{6}+\dfrac{6n^2+12n+6}{6}[/tex]

[tex]=\dfrac{2n^3+9n^2+13n+6}{6}[/tex]

If you expend the right hand-side of the step 3, you will see they are same.

Proof done

Answer:

see below

Step-by-step explanation:

1^2+2^2+3^2+...+n^2=n(n+1)(2n+1)/6

Step1

Verify it for n=1

1^2= 1(1+1)(2*1+1)/6= 1*2*3/6= 6/6=1 - correct

Step2

Assume it is correct for n=k

1^2+2^2+3+2+...+k^2= k(k+1)(2k+1)/6

Step3

Prove it is correct for n= k+1

1^2+2^2+3^2+...+(k+1)^2= (k+1)(k+2)(2k+2+1)/6

prove the above for k+1

1^2+2^2+3^2+...+k^2+(k+1)^2= k(k+1)(2k+1)/6 + (k+1)^2=

= 1/6(k(k+1)(2k+1)+6(k+1)^2)= 1/6((k+1)(k(2k+1)+6(k+1))=

=1/6((k+1)(2k²+k+6k+6))= 1/6(k+1)(2k²+4k+3k+6))=

= 1/6(k+1)(2k(k+2)+3(k+2))=

=1/6(k+1)(k+2)(2k+3)

Proved for n= k+1 that:

the sum of squares of (k+1) terms equal to  (k+1)(k+2)(2k+3)/6

Answer:

By the Empirical Rule, 68% of IQ scores are between 87 and 121

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 104

Standard deviation = 17

Using the empirical rule, what percentage of IQ scores are between 87 and 121

87 = 104 - 1*17

So 87 is one standard deviation below the mean

121 = 104 + 1*17

So 121 is one standard deviation above the mean

By the Empirical Rule, 68% of IQ scores are between 87 and 121

Answer:

The sampling method that was used in the scenario is systematic sampling.

Step-by-step explanation:

Systematic sampling is a kind of probability sampling method in which individuals from a larger population are nominated according to a random initial point and following a static, periodic interval.  

For instance, consider a study where the researcher first selects a name randomly from the alphabetized order and then follow a fixed pattern of selecting every 10th person from the population.

In this case, a study was done to determine the age, the number of times per week, and the duration (amount of time) of residents using a local park in San Antonio, Texas.

The first house was randomly selected from the neighborhood around the park.

Then, the resident of every 8th house in the neighborhood around the park was interviewed.

So, the researcher selects a random house and then keep on selecting the houses in an interval of 8. This way the next house selected with be the 8th, the next the 16th, and so on.

Thus, the sampling method that was used in the scenario is systematic sampling.

Answer:

1/4 gallon, 1/6 gallon, 1/8 gallon, 1/10 gallon, 1/12, gallon

Step-by-step explanation:

You just take 1/2 and divide it my number of bowls

for 2 bowls: 1/2 Divided by 2

= 1/2 * 1/2 = 1/4 gallon per bowl, same with other bowls

Amount of yogurt in each bowl is [tex]\frac{1}{4},\frac{1}{6},\frac{1}{8},\frac{1}{10},\frac{1}{12}[/tex] gallons respectively.

Given in question,

Expression used to calculate the amount of frozen yogurt in each bowl,

Amount of yogurt in each bowl = [tex]\frac{\text{Total amount of yogurt}}{\text{Number of bowls}}[/tex]

If Number of bowls = 2

Amount of yogurt in each bowl = [tex]\frac{\frac{1}{2} }{2}[/tex] = [tex]\frac{1}{4}[/tex] gallons

If the number of bowls = 3

Amount of yogurt in each bowl = [tex]\frac{\frac{1}{2} }{3}[/tex] = [tex]\frac{1}{6}[/tex] gallons

If the number of bowls = 4

Amount of yogurt in each bowl = [tex]\frac{\frac{1}{2} }{4}[/tex] = [tex]\frac{1}{8}[/tex] gallons

If the number of bowls = 5

Amount of yogurt in each bowl = [tex]\frac{\frac{1}{2} }{5}[/tex] = [tex]\frac{1}{10}[/tex] gallons

If the number of bowls = 6

Amount of yogurt in each bowl = [tex]\frac{\frac{1}{2} }{6}=\frac{1}{12}[/tex] gallons

       Hence, amount of yogurt in each bowl is [tex]\frac{1}{4},\frac{1}{6},\frac{1}{8},\frac{1}{10},\frac{1}{12}[/tex] gallons respectively.

Learn more about the property of division here,

https://brainly.com/question/14047371?referrer=searchResults

Answer:

B (-1,0), (3,0)

Step-by-step explanation:

Quadratic Formula

Answer:

The 90% confidence interval for the mean production rate fro the new method is (75.9, 84.1).

Step-by-step explanation:

We have to calculate a 90% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=80.

The sample size is N=18.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{10}{\sqrt{18}}=\dfrac{10}{4.24}=2.36[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=18-1=17[/tex]

The t-value for a 90% confidence interval and 17 degrees of freedom is t=1.74.

The margin of error (MOE) can be calculated as:

[tex]MOE=t\cdot s_M=1.74 \cdot 2.36=4.1[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M-t \cdot s_M = 80-4.1=75.9\\\\UL=M+t \cdot s_M = 80+4.1=84.1[/tex]

The 90% confidence interval for the mean production rate fro the new method is (75.9, 84.1).

Answer:

ANSWER: - 3

Step-by-step explanation:

1.8 - 3.7 x = - 4.2 x + 0.3

    + 3.7 x   + 3.7 x

(add 3.7 x on both sides)

  1.8  = - 0.5 x + 0.3

- 0.3                 - 0.3

  1.5 = - 0.5 x

-------  ---------    <- Divide both sides by 0.5

 - 0.5   - 0.5

     - 3 = x

ANSWER: - 3

Hope this helps :)

Mark as brainliest if it helped

Answer:

[tex]x=-3[/tex]

Step-by-step explanation:

[tex]1.8-3.7x=-4.2x+0.3\\1.5-3.7x=-4.2x\\1.5=-0.5x\\-0.5x=1.5\\-x=3\\x=-3[/tex]

Answer:

4. s = -2 cos 4t/pi + 4

Step-by-step explanation:

The position is the integral of the velocity.

In this question:

[tex]v(t) = \frac{8}{\pi}\sin{(\frac{4t}{\pi})}[/tex]

So

[tex]s(t) = \int {v(t)} dt[/tex]

[tex]s(t) = \int {\frac{8}{\pi}\sin{(\frac{4t}{\pi})}} dt[/tex]

Integrating by substitution:

[tex]u = \frac{4t}{\pi}[/tex]

[tex]du = \frac{4}{\pi}dt[/tex]

[tex]dt = \frac{\pi du}{4}[/tex]

So

[tex]s = \int {\frac{8}{\pi}\sin{u} (\frac{\pi du}{4})[/tex]

[tex]s = 2 \int {\sin{u}} du[/tex]

[tex]s = -2 \cos{u} + C[/tex]

Since [tex]u = \frac{4t}{\pi}[/tex]

[tex]s(t) = -2 \cos{\frac{4t}{\pi}} + C[/tex]

Since s(pi^2) = 2 .

[tex]s(t) = -2 \cos{\frac{4t}{\pi}} + C[/tex]

[tex]2 = -2 \cos{\frac{4\pi^{2}}{\pi}} + C[/tex]

[tex]2 = -2\cos{4\pi} + C[/tex]

The cosine of 4pi is the same as the cosine of 0 = 1. So

[tex]2 = -2 + C[/tex]

[tex]C = 4[/tex]

So the correct answer is:

4. s = -2 cos 4t/pi + 4

Step-by-step explanation:

I will do 12 and 14 as examples.

12) Angles of a triangle add up to 180°.

m∠P + m∠Q + m∠R = 180

5x − 14 + x − 5 + 2x − 9 = 180

8x − 28 = 180

8x = 208

x = 26

m∠P = 5x − 14 = 116

m∠Q = x − 5 = 21

m∠R = 2x − 9 = 43

14) If two sides of a triangle are equal, then the angles opposite those sides are also equal.

(Conversely, if two angles are equal, then the sides opposite those angles are also equal.  Such a triangle is called an isosceles triangle.)

BC ≅ BD, so m∠C = m∠D.

5x − 19 = 2x + 14

3x = 33

x = 11

m∠B = 13x − 35 = 108

m∠C = 5x − 19 = 36

m∠D = 2x + 14 = 36

Answer:

I don't know

Step-by-step explanation:

sorry I can't help,use a calculator

Answer:

58.5 miles

Step-by-step explanation:

Let's Use unitary Method

8 hours = 52 miles

Then,

1 hour = 52/8 miles

1 hour = 6.5 miles

Multiplying both sides by 9, We'll get

9 hours = 6.5 × 9 miles

9 hours = 58.5 miles

Answer:a^2/b

Step-by-step explanation:

(a^6b^−3)1^/3

a^6 ^ 1/3  b ^ -3 ^ 1/3

using the power of power rule we can multiply the exponents

a ^ (6*1/3) b ^ (-3* 1/3)

a^ 2 b ^ -1

the negative exponent flips it from the numerator to the denominator

a^2* 1/ b^1

a^2/b

Answer:

A. -18b^-4

second answer is B. -18/b^-4

Step-by-step explanation:

Answer:

20 m

Step-by-step explanation:

First find the side length

A = s^2 for a square garden

200 = s^2

Take the square root of each side

sqrt(200) = sqrt(s^2)

sqrt(2) sqrt(100) = s

10 sqrt(2) = s

Now we can use the Pythagorean theorem to find the diagonal

a^2 + b^2 = c^2  where  a and b are the side lengths a c is the hypotenuse

s^2 + s^2 = c^2

200 + 200 =c^2

400 = c^2

Take the square root of each side

sqrt(400) = sqrt(c^2)

20 = c

First find the lenght of a side:

[tex]a=\sqrt{200}\implies a\approx 14.14[/tex]

Then multiply the approximated side by [tex]\sqrt{2}[/tex] and obtain the lenght of diagonal:

[tex]d\approx14.14\sqrt{2}=\boxed{20\mathrm{m}}[/tex]

Hope this helps.

The slope of Jeremy's function is 12 and the y-intercept of the function is 50.

A linear function is a mathematical function that can be written in the form y = mx + b, where x and y are variables, m is the slope, and b is the y-intercept.

The linear function that represents the grade G (in points out of 100) that Jeremy can earn on an exam as a function of the number of hours h he spends studying for the exam is given by:

G = 12h + 50

In this equation, the coefficient of h is 12, which represents the slope of the function.   The slope indicates that for each additional hour Jeremy spends studying, his grade on the exam is expected to increase by 12 points.

The y-intercept of the function is 50. In the context of the problem, this means that if Jeremy doesn't spend any time studying for the exam (i.e., h = 0), he can still earn 50 points out of 100 on the exam

To know more about variables, visit:

https://brainly.com/question/17344045

#SPJ1

Answer:

Option B is correct.

The statement is false.

The term for the differential that expresses the differential changes in all the variables is the Total differential and not ordinary differential.

Step-by-step explanation:

Truly, for a multivariable function, that is, one which depends on two or more variables, the partial differential represents the change in the function with one of the variables as the other variables are held constant.

For example, a function z which has x and y as its independent variables

z = f(x, y)

The function has partial derivatives (∂f/∂x) (which is the derivative of the function with respect to x, holding y constant) and (∂f/∂y) (the derivative of the function with respect to y, holding x constant).

But to obtain the differential changes in all the variables, a differential known as the total differential is used.

The total differential, for our example function z, is given as

dz = (∂f/∂x) dx + (∂f/∂y) dy

This isn't called the ordinary differential.

Hope this Helps!!!

Answer: 1456

Step-by-step explanation:

For this problem, there is a short cut you can use to solve it. In order to understand the meaning of summation, I will do it the long way to show how a summation works. This sum is from n=1 to n=6. We plug in the values of n into the expression, then add together the sums.

n=1

4(3)¹⁻¹

=4(3)⁰

=4

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

n=2

4(3)²⁻¹

=4(3)¹

=12

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

n=3

4(3)³⁻¹

=4(3)²

=4(9)

=36

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

n=4

4(3)⁴⁻¹

=4(3)³

=4(27)

=108

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

n=5

4(3)⁵⁻¹

=4(3)⁴

=4(81)

=324

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

n=6

4(3)⁶⁻¹

=4(3)⁵

=4(243)

=972

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Now that we have all our values, we can add them together to get the sum.

4+12+36+108+324+972=1456

The sum is 1456. You can also notice that the values multiply by 3 each time.