in a gp the sixth term is 8 times the third term, and the sum of the seventh and eighth term is 192. determine the common ratio​

Answers

Answer 1

Answer:

common ratio = 2

Step-by-step explanation:

T6 = ar^5

T3 = ar²

T6 = 8 x T³

ar^5 = 8 x ar²

ar^5/ar² = 8

r³ = 8

r = ³√8

r = 2


Related Questions

find the circle through (-4,sqrt(5) with center (0,0)

Answers

Answer:

Circle Equation : x² + y² = 21

Step-by-step explanation:

So we know that this circle goes through the point ( - 4, √5 ), with a center being the origin. Therefore, this makes the circle equation a bit simpler.

The first step in determining the circle equation is the length of the radius. Applying the distance formula, the radius would be the length between the given points. Another approach would be creating a right triangle such that the radius is the hypotenuse. Knowing the length of the legs as √5 and 4, we can calculate the radius,

( √5 )² + ( 4 )² = r²,

5 + 16 = r²,

r = √21

In general, a circle equation is represented by the formula ( x - a )² + ( y - b )² = r², with radius r centered at point ( a, b ). Therefore our circle equation will be represented by the following -

( x - 0 )² + ( y - 0 )² = (√21 )²

Circle Equation : x² + y² = 21

A mail truck traveled 82 miles in 4 1/2 hours. The distance is the product of the rate and the time. To the nearest tenth, what was the average speed of the mail truck?

Answers

Answer:

= 18.2 miles per hour

Step-by-step explanation:

Speed = distance / time

            =82 miles / 4.5 hours

             =18.22222222 miles per hour

             Rounding

             = 18.2 miles per hour

Answer:

Given that

Distance = rate × time

82 = r × 4½

r = 18.2 mph

area please it's easy plzzzzzzzzzz

Answers

a ) Now as you can see, the white region is composed of a triangle and a rectangle. This triangle has a height of 5, as it is composed of the respective blank triangles. It's base is 5 meters as well, by properties of a rectangle - which is sufficient information to solve for the area of the triangle.

Area of Triangle : 1 / 2 [tex]*[/tex] 4 [tex]*[/tex] 5 = 2 [tex]*[/tex] 5 = 10 m²

The area of this rectangle will be 3 [tex]*[/tex] 4 = 12 m², considering it's given dimensions are 3 by 4. Therefore the area of this white region will be 10 + 12 = 22 m²

b ) Now this striped region will be the remaining area, or the area of the white region subtracted from the area of the outer rectangle.

Area of Outer Rectangle : 10 [tex]*[/tex] 4 = 40 m²,

Area of Striped Region : 40 - 22 = 18 m²

Please answer this correctly without making mistakes

Answers

Answer:

1,377/2 and 688 1/17

Step-by-step explanation:

Kelly bought a cup of coffee and drank 58 of it. Write an addition equation to represent how much coffee is remaining.

Answers

Answer:

[tex]L + \frac{5}{8} = 1[/tex]

Step-by-step explanation:

Given

A cup of coffee

Kelly drank 5/8 of the coffee

Required

Determine how much is left

Start by representing the amount of coffee left with L

Because the amount of coffee Kelly drank is in fraction (5/8), the total cup of coffee will equate to 1;

Hence, the addition equation as requested in the question to represent the scenario is

[tex]L + \frac{5}{8} = 1[/tex]

Please help me so confused

Answers

Answer:

m = 15

Step-by-step explanation:

m/9 + 2/3 = 7/3

Subtract 2/3 from each side

m/9 + 2/3  -2/3= 7/3 -2/3

m/9 = 5/3

Multiply each side by 9

m/9 *9 = 5/3 *9

m = 15

The size of a television is the length of the diagonal of its screen in inches. The aspect ratio of the screens of older televisions is 4:3, while the aspect ratio of newer wide-screen televisions is 16:9. Find the width and height of an newer 75-inch television whose screen has an aspect ratio of 16:9

Answers

Answer:

The Width = 65.44 inches

The Height = 36.81 inches

Step-by-step explanation:

We are told in the question that:

The width and height of an newer 75-inch television whose screen has an aspect ratio of 16:9

Using Pythagoras Theorem we known that:

Width² + Height² = Diagonal²

Since we known that the size of a television is the length of the diagonal of its screen in inches.

Hence, for this new TV

Width² + Height² = 75²

We are given ratio: 16:9 as aspect ratio

Width = 16x

Height = 9x

(16x)² +(9x)² = 75²

= 256x² + 81x² = 75²

337x² = 5625

x² = 5625/337

x² = 16.691394659

x = √16.691394659

x = 4.0855103303

Approximately x = 4.09

For the newer 75 inch tv set

The Height = 9x

= 9 × 4.09

= 36.81 inches

The Width = 16x

= 16 × 4.09

= 65.44 inches.

PLEASE HELP!!! Determine the domain and range of the following function. Record your answers in set notation.

Answers

Answer:

Ok so to help you out, first, off you need to be sure that the sets domain and range use the proper variable. After that, you are going to want to just plug it into the equation. I am going to link a screenshot to the correct answer if you are still have trouble finding it.

Anyways hoped this helped and I got to this question in time c:

A researcher wishes to determine whether people with high blood pressure can lower their blood pressure by performing yoga exercises. A treatment group and a control group are selected. The sample statistics are given below. Construct a 90% confidence interval for the difference between the two population means, Would you recommend using yoga exercises? Treatment Group Control Group n1 = 100 n2 = 100 1 = 178 2 = 193 s1 = 35 s2 = 37

Answers

Answer:

90% confidence interval for the difference between the two population means

( -23.4166 , -6.5834)

Step-by-step explanation:

Step(i):-

Given first sample size n₁ = 100

Given mean of the first sample x₁⁻ = 178

Standard deviation of the sample S₁ = 35

Given second sample size n₂= 100

Given mean of the second sample x₂⁻ = 193

Standard deviation of the sample S₂ = 37

Step(ii):-

Standard error of two population means

        [tex]se(x^{-} _{1} -x^{-} _{2} ) = \sqrt{\frac{s^{2} _{1} }{n_{1} }+\frac{s^{2} _{2} }{n_{2} } }[/tex]

       [tex]se(x^{-} _{1} -x^{-} _{2} ) = \sqrt{\frac{(35)^{2} }{100 }+\frac{(37)^{2} }{100 } }[/tex]

        [tex]se(x^{-} _{1} -x^{-} _{2} ) = 5.093[/tex]

Degrees of freedom

ν  = n₁ +n₂ -2 = 100 +100 -2 = 198

t₀.₁₀ = 1.6526

Step(iii):-

90% confidence interval for the difference between the two population means

[tex](x^{-} _{1} - x^{-} _{2} - t_{\frac{\alpha }{2} } Se (x^{-} _{1} - x^{-} _{2}) , x^{-} _{1} - x^{-} _{2} + t_{\frac{\alpha }{2} } Se (x^{-} _{1} - x^{-} _{2})[/tex]

(178-193 - 1.6526 (5.093) , 178-193 + 1.6526 (5.093)

(-15-8.4166 , -15 + 8.4166)

( -23.4166 , -6.5834)

se pueden calcular las edades de Juanita y de su madre si se sabe que:
1) actualmente la suma de sus edades es 44 años
2) dentro de 11 años la edad de juanita será la mitad de la edad de su mamá

Answers

Responder:

Juanita = 11, madre = 33

Explicación paso a paso:

Dado lo siguiente:

Suma de sus edades = 44

En 11 años, Juanita tendrá la mitad de la edad de su madre

Sea la edad de la madre = my la edad de juanita = j

m + j = 44 - - - - (1)

(j + 11) = 1/2 (m + 11)

j + 11 = 1/2 m + 5,5; j - 1/2 m = - 5,5; 2j - m = - 11

2j - m = - 11 - - - - (2)

Desde (1): m = 44 - j

Sustituyendo m = 44- j en (2)

2j - (44 - j) = - 11

2j - 44 + j = - 11

3j = - 11 + 44

3j = 33

j = 11

De 1)

m + j = 44

m + 11 = 44

m = 44 - 11

m = 33

what is ap in math abreviation and explain my math teacher was drunk so he couldn't teach nothing ​

Answers

Step-by-step explanation:

n mathematics, an arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. ... For instance, the sequence 5, 7, 9, 11, 13, 15, . . . is an arithmetic progression with common difference of 2.

Given that a random variable X is normally distributed with a mean of 2 and a variance of 4, find the value of x such that P(X < x)

Answers

Given that a random variable X is normally distributed with a mean of 2 and a variance of 4, find the value of x such that P(X < x)=0.99   using the cumulative standard normal distribution table

Answer:

6.642

Step-by-step explanation:

Given that mean = 2

standard deviation = 2

Let X be the random Variable

Then X [tex]\sim[/tex] N(n,[tex]\sigma[/tex])

X [tex]\sim[/tex] N(2,2)

By Central limit theorem;

[tex]z = \dfrac{X - \mu}{\sigma} \sim N(0,1)[/tex]

[tex]z = \dfrac{X - 2}{2} \sim N(0,1)[/tex]

P(X<x) = 0.09

[tex]P(Z < \dfrac{X-\mu}{\sigma })= 0.99[/tex]

[tex]P(Z < \dfrac{X-2}{2})= 0.99[/tex]

P(X < x) = 0.99

[tex]P(\dfrac{X-2}{2}< \dfrac{X-2}{2})=0.99[/tex]

[tex]P(Z< \dfrac{X-2}{2})=0.99[/tex]

[tex]\phi ( \dfrac{X-2}{2})=0.99[/tex]

[tex]( \dfrac{X-2}{2})= \phi^{-1} (0.99)[/tex]

[tex]( \dfrac{X-2}{2})= 2.321[/tex]

X -2 = 2.321 × 2

X -2 = 4.642

X = 4.642 +2

X = 6.642

more math questions if you would

Answers

Answer:

A.

Step-by-step explanation:

So we are given the function:

[tex]f(x)=7x+8[/tex]

To find the inverse of the function, we simply need to flip f(x) and x and then solve for f(x). Thus:

[tex]x=7f^{-1}(x)+8\\x-8=7f^{-1}(x)\\f^{-1}(x)=\frac{x-8}{7}[/tex]

So the answer is A.

Answer:

[tex]\large \boxed{\mathrm{Option \ A}}[/tex]

Step-by-step explanation:

f(x) = 7x+8

Write f(x) as y.

y = 7x + 8

Switch variables.

x = 7y + 8

Solve for y to find the inverse.

x - 8 = 7y

[tex]\frac{x-8}{7}[/tex] = y

a data set includes 110 body temperatures of healthy adult humans having a mean of 98.1F and a standard deviation of 0.64F. Construct a 99% confidence interval estimate of the mean body temperature of all healthy humans

Answers

Answer:

The 99%  confidence interval is  [tex]97.94 < \mu < 98.26[/tex]

Step-by-step explanation:

From the question we are told that

    The sample size is  n =  110

     The  sample mean is  [tex]\= x = 98.1 \ F[/tex]

       The standard deviation is  [tex]\sigma = 0.64 \ F[/tex]

Given that the confidence level is  99% the level of significance i mathematically evaluated as

                  [tex]\alpha = 100 - 99[/tex]

                  [tex]\alpha = 1\%[/tex]

                  [tex]\alpha = 0.01[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution, the values is  

          [tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.01 }{2} } = 2.58[/tex]

Generally the margin of error is mathematically represented as

           [tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }[/tex]

substituting values

          [tex]E = 2.58 * \frac{ 0.64}{\sqrt{110} }[/tex]

          [tex]E = 0.1574[/tex]

Generally the  99% confidence interval  is mathematically represented as

               [tex]\= x - E < \mu < \= x + E[/tex]

substituting values

             [tex]98.1 - 0.1574 < \mu < 98.1 + 0.1574[/tex]

             [tex]97.94 < \mu < 98.26[/tex]

                 

         

Answer:

Step-by-step explanation:

janice is buying paint to paint her new apartment

Answers

Answer:

I canot answer this

Step-by-step explanation:

The U.S. National Whitewater Center in Charlotte uses a pump station to provide the flow of water necessary to operate the rapids. The pump station contains 7 pumps, each with a capacity to deliver 80,000 gallons per minute (gpm). The water channels and ponds in the facility contain 13 million gallons of water. If the pump station is operating 5 pumps simultaneously, assuming ideal conditions how long will it take to completely pump the volume of the system through the pump station

Answers

Answer:

t = 32,5 minutes

Step-by-step explanation:

Volume to fill =  13000000 Gal

5 pumps delivering  80000 gal/min

5 * 80000 = 400000 gal/min

If we divide the total volume by the amount of water delivered for the 5 pumps, we get the required time to fill the volume, then

t =  13000000/ 400000

t = 32,5 minutes

Why is a rhombus considered a type of quadrilateral?

Answers

Answer:

Well a rhombus is considered a quadrilateral because it has 4 sides and 4 angles.

Just like a square and rectangle they both are quadrilaterals with 4 angles and sides.

A rhombus is considered a type of quadrilateral because it has four sides and four angles

How to determine the reason?

As a general rule, a shape that is considered a quadrilateral must have:

4 sides4 angles

Since a rhombus has four sides and four angles, then it is considered a type of quadrilateral

Read more about rhombus at:https://brainly.com/question/20627264

#SPJ6

A baseball player has a batting average (probability of getting on base per time at bat) of 0.215. Based on this: What is the probability that they will get on base more than 6 of the next 15 at bats

Answers

Answer:

[tex]\mathbf{P(x>6) = 0.0265}[/tex]

Step-by-step explanation:

Given that:

A baseball player has a batting average (probability of getting on base per time at bat) of 0.215

i.e

let x to be the random variable,

consider [tex]x_1 = \left \{ {{1} \atop {0}} \right.[/tex]  to be if the baseball player has a batting average or otherwise.

Then

p(x₁ = 1) = 0.125

What is the probability that they will get on base more than 6 of the next 15 at bats

So

[tex]\mathtt{x_i \sim Binomial (n,p)}[/tex]

where; n =  15 and p = 0.125

P(x>6) = P(x ≥ 7)

[tex]P(x>6) = \sum \limits ^{15}_{x=7} ( ^{15 }_x ) \ (0.215)^x \ (1 - 0.215)^{15-x}[/tex]

[tex]P(x>6) = 1 - \sum \limits ^{6}_{x=7} ( ^{15 }_x ) \ (0.215)^x \ (1 - 0.215)^{15-x}[/tex]

[tex]P(x>6) = 1 - \sum \limits ^{6}_{x=0} ( ^{15 }_x ) \ (0.215)^x \ (1 - 0.215)^{15-x}[/tex]

[tex]P(x>6) = 1 -0.9735[/tex]

[tex]\mathbf{P(x>6) = 0.0265}[/tex]

60 is x% of 12. Find the value of x.

Answers

Answer:

20

Step-by-step explanation:

We can set up a percentage proportion to find the value of x.

[tex]\frac{12}{x} = \frac{60}{100}[/tex]

Now we cross multiply:

[tex]100\cdot12=1200\\\\1200\div60=20[/tex]

Hope this helped!

Can anyone help me please??

Answers

Answer:

-20x / (x-12) = y

Step-by-step explanation:

3/x  - 5/y  = 1/4

Multiply each side by 4xy to clear the fractions

4xy ( 3/x  - 5/y  = 1/4)

Distribute

12y - 20x = xy

Subtract 12y from each side

-20x = xy -12y

Factor out y

-20x = y(x-12)

Divide each side by (x-12)

-20x / (x-12) = y

Which phrase represents t times 33 he quotient of a number and 33 the product of a number and 33 the quotient of 33 and a number the difference of a number and 33

Answers

Answer:

  the product of a number and 33

Step-by-step explanation:

The operation "times" is what is used to form the product of two operands.

  "t times 33" is "the product of t and 33"

15 < −5x can someone please solve for x?

Answers

Answer:

x <-3

Step-by-step explanation:

15 <-5x

divide both sides by 5 but since the coefficient of x is negative after dividing the sign changes.

x <-3

Answer:

x < −3

I hope this helps!

Let x represent the number of times a student visits a gym in a one month period. Assume that the probability distribution of X is as follows:
x 0 1 2 3
p(x) 0.37 0.29 0.22 0.12
Find the mean, of this distribution. Report your answer to two decimal places.

Answers

Answer:

1.86

Step-by-step explanation:

Given the following :

X : - - - - 0 - - - - 1 - - - - 2 - - - - - 3 - - - - 4

P(x) - 0.37 - - 0.28 - - 0.22 - - 0.22 - - 0.12

The mean of the distribution can be calculated by evaluated by determining the expected value of the distribution given that the data above is a discrete random variable. The mean value can be deduced multiplying each possible outcome by the probability of it's occurrence.

Summation of [P(x) * X] :

(0.37 * 0) + (0.28 * 1) + (0.22 * 2) + (0.22 * 3) + (0.12 * 4)

= 0 + 0.28 + 0.44 + 0.66 + 0.48

= 1.86

(a) Find the standard error of the mean for each sampling situation (assuming a normal population). (Round your answers to 2 decimal places.) (a) σ = 18, n = 9 (b) σ = 18, n = 36 (c) σ = 18, n = 144

Answers

Answer:

a) 6.00

b) 3.00

c) 1.50

Step-by-step explanation:

Sample error of the mean is expressed mathematically using the formula;

SE = σ /√n where;

σ  is the standard deviation and n is the sample size.

a) Given σ = 18, n = 9

Standard error of the mean = σ /√n

Standard error of the mean = 18/√9

Standard error of the mean = 18/3

Standard error of the mean = 6.00

b) Given σ = 18, n = 36

Standard error of the mean = σ /√n

Standard error of the mean = 18/√36

Standard error of the mean = 18/6

Standard error of the mean = 3.00

c) Given σ = 18, n = 144

Standard error of the mean = σ /√n

Standard error of the mean = 18/√144

Standard error of the mean = 18/12

Standard error of the mean = 3/2

Standard error of the mean = 1.50

PLEASE HELP!!!
Evaluate the expression when b=4 and y= -3
-b+2y

Answers

Answer: -10

Step-by-step explanation: All you have to do is plug the values into the equation. -4+2(-3). Then you solve the equation using PEDMAS.

1. -4+2(-3)

2. -4+(-6)

3.-4-6

4.-10

Answer:

8

Step-by-step explanation:

-b + 2y

if

b = 4

and

y = 3

then:

-b + 2y = -4 + 2*6 = -4 + 12

= 8

GCF/LCM of 8 and 24 the reduce 8/24

Answers

Answer:

GCF(8, 24) = 8LCM(8, 24) = 248/24 = 1/3

Step-by-step explanation:

Since 8 is a factor of 24, 8 is the GCF of the pair, and 24 is the LCM of the pair.

__

The ratio 8/24 is reduced by observing that 24 = 8·3:

  8/24 = 8/(8·3) = (8/8)·(1/3)

  8/24 = 1/3

Find the work done by the force field F(x,y,z)=6xi+6yj+6k on a particle that moves along the helix r(t)=3 cos(t)i+3sin(t)j+2 tk,0≤t≤2π.

Answers

Answer:

the work done by the force field = 24 π

Step-by-step explanation:

From the information given:

r(t) = 3 cos (t)i + 3 sin (t) j + 2 tk

= xi + yj + zk

x = 3 cos (t)

y =  3 sin (t)

z = 2t

dr = (-3 sin (t)i + 3 cos (t) j + 2 k ) dt

Also F(x,y,z) = 6xi + 6yj + 6k

∴  F(t) = 18 cos (t) i + 18 sin (t) j +6 k

Workdone = 0 to 2π ∫ F(t) dr

[tex]\mathbf{= \int \limits ^{2 \pi} _{0} (18 cos (t) i + 18 sin (t) j +6k)(-3 sin (t)i+3cos (t) j +2k)\ dt}[/tex]

[tex]\mathbf{= \int \limits ^{2 \pi} _{0} (-54 \ cos (t).sin(t) + 54 \ sin (t).cos (t) + 12 ) \ dt}[/tex]

[tex]\mathbf{= \int \limits ^{2 \pi} _{0} 12 \ dt}[/tex]

[tex]\mathbf{= 12 \times 2 \pi}[/tex]

= 24 π

Why would a linear function be an appropriate model?

Answers

Answer:

I know the answer

Step-by-step explanation:

Linear functions are those whose graph is a straight line. A linear function has the following form. y = f(x) = a + bx. A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.

Find the minimum sample size needed to estimate the percentage of Democrats who have a sibling. Use a 0.1 margin of error, use a confidence level of 98%, and use the results from a prior Harris poll that gave a confidence interval of (0.44, 0.51) for the proportion of Democrats who have a sibling.

Answers

Answer:

The minimum sample size is  [tex]n =135[/tex]

Step-by-step explanation:

From the question we are told that

   The confidence interval is [tex]( lower \ limit = \ 0.44,\ \ \ upper \ limit = \ 0.51)[/tex]

    The margin of error is  [tex]E = 0.1[/tex]

   

Generally the sample  proportion can be mathematically evaluated as

     [tex]\r p = \frac{ upper \ limit + lower \ limit }{2}[/tex]

    [tex]\r p = \frac{ 0.51 + 0.44}{2}[/tex]

    [tex]\r p = 0.475[/tex]

Given that the confidence level is  98% then the level of significance can be mathematically evaluated as

         [tex]\alpha = 100 - 98[/tex]

        [tex]\alpha = 2\%[/tex]

        [tex]\alpha =0.02[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table  

   The value is

        [tex]Z_{\frac{\alpha }{2} } = 2.33[/tex]

Generally the minimum sample size is evaluated as

      [tex]n =[ \frac { Z_{\frac{\alpha }{2} }}{E} ]^2 * \r p (1- \r p )[/tex]

     [tex]n =[ \frac { 2.33}{0.1} ]^2 * 0.475(1- 0.475 )[/tex]

     [tex]n =135[/tex]

The length of the sides of the triangle are in the ratio 3:4:5 and it’s perimeter is 144 cm find its area and height corresponding to the longest side

Answers

3:4:5 is one of Pythagorean’s triplets, meaning this is a right triangle.

144 = 3x + 4x + 5x (combine like terms)
144 = 12x (divide both sides by 12)
x = 12
To find the side lengths, multiply 3, 4 and 5 by 12. This means the triangle has sides of 36, 48 and 60 centimetres.

Because this is a right triangle, two of the sides are the base and the height. The hypotenuse (longest side) is not the base nor the height because it is not directly adjacent to the right angle. In this case, the hypotenuse is 60 cm.
A = bh/2
A = (36 cm)(48 cm)/2
A = 864 cm^2
Therefore the area is 864 cm^2.

I’m not sure what is meant by the “height corresponding to the longest side”, sorry.

Hope this helps!
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Group of answer choices Which describes a grizzly bears habitat? all the biotic factors in the ecosystem all the abiotic factors in the ecosystem the role of the bear in the ecosystem the physical area where the bear lives What is the number of square units in the area of the triangle whose vertices are points A(2,0), B(6,0), and C(8,5)? "A little while after you arrive home from a traffic fatality accident, you receive a telephone call from your captain. A critical incident stress debriefing has been set up for your crew tomorrow. You know that your participation is on a completely voluntary basis, but you realize you should participate because:" Write a SELECT statement that selects all of the columns for the catalog view that returns information about foreign keys. How many foreign keys are defined in the AP database? As the workforce becomes more diverse, why does performance appraisal become a more difficult process? 0.69 points eBookPrintReferences Check my work Check My Work button is now enabledItem 1Item 1 0.69 points Fresh Veggies, Inc. (FVI), purchases land and a warehouse for $410,000. In addition to the purchase price, FVI makes the following expenditures related to the acquisition: broker's commission, $21,000; title insurance, $1,100; and miscellaneous closing costs, $4,200. The warehouse is immediately demolished at a cost of $21,000 in anticipation of building a new warehouse. Determine the amount FVI should record as the cost of the land. 5. How were Earth's core and mantle formed? Lott Company uses a job order cost system and applies overhead to production on the basis of direct labor costs. On January 1, 2020, Job 50 was the only job in process. The costs incurred prior to January 1 on this job were as follows: direct materials $21,200, direct labor $12,720, and manufacturing overhead $16,960. As of January 1, Job 49 had been completed at a cost of $95,400 and was part of finished goods inventory. There was a $15,900 balance in the Raw Materials Inventory account. During the month of January, Lott Company began production on Jobs 51 and 52, and completed Jobs 50 and 51. Jobs 49 and 50 were also sold on account during the month for $129,320 and $167,480, respectively. The following additional events occurred during the month. 1. Purchased additional raw materials of $95,400 on account. 2. Incurred factory labor costs of $74,200. Of this amount $16,960 related to employer payroll taxes. 3. Incurred manufacturing overhead costs as follows: Indirect materials $18,020 Indirect labor $21,200 Depreciation expense on equipment $12,720 Various other manufacturing overhead costs on account $16,960. 4. Assigned direct materials and direct labor to jobs as follows. Job No. Direct Materials Direct Labor 50 $10,600 $5,300 51 41,340 26,500 52 31,800 21,200Calculate the predetermined overhead rate for 2020, assuming Lott Company estimates total manufacturing overhead costs of $ 882,000, direct labor costs of $735,000, and direct labor hours of 21,000 for the year. Georgia is the primary shareholder in Acme, Inc., a small corporation. After its corporate certificate was issued by the state, there were no other formalities or documentation. In fact, Georgia does not keep separate books for the corporation, and sometimes combines her personal assets with those of the corporation. If she is sued individually by a corporate creditor, what would be the likely outcome When an LRC series circuit is driven at resonance, which of the following statements about the circuit are correct? (There may be more than one correct choice.)a) The impedance of the circuit has its minimum value.b) The inductive reactance and the capacitive reactance are exactly equal to each other.c) The impedance of the circuit is zero.d) The inductive reactance and the capacitive reactance are both zero.e) The impedance of the circuit has its maximum value. Find the degree, leading coefficient, and the constant term of the polynomial. Who formed the record label Death Row? Steelcase Inc. (SCS) is one of the largest manufacturers of office furniture in the United States. In Grand Rapids, Michigan, it assembles filing cabinets in an Assembly Department. Assume the following information for the Assembly Department: Direct labor per filing cabinet 18 minutes Supervisor salaries $250,000 per month Depreciation $18,500 per month Direct labor rate $28 per hourRequired:Prepare a flexible budget for 70,000, 80,000, and 90,000 filing cabinets for the month ending February 28 in the Assembly Department. Entries for Investments in Bonds, Interest, and Sale of Bonds Kalyagin Investments acquired $220,000 of Jerris Corp., 7% bonds at their face amount on October 1, 20Y2. The bonds pay interest on October 1 and April 1. On April 1, 20Y3, Kalyagin sold $80,000 of Jerris bonds at 103. Journalize the entries to record the following: a. The initial acquisition of the Jerris Corp. bonds on October 1, 20Y2.b. The adjusting entry for three months of accrued interest earned on the Jems Corp. bonds- or December 11, 20Y2. c. The receipt of semiannual interest on April 1. 20Y3. d. The sale of 580,000 of Jerris Corp. bonds on April, 20Y3, at 103.