A store purchased a DVD for $12.00 and sold it to a customer for 50% more than the purchase price.The customer was charged a 7% tax when the DVD was sold.What is the customer's total cost for the DVD?

Answers

Answer 1

Answer:

The customer's total cost for the DVD is $19.26

Step-by-step explanation:

Store buy the dvd for $12.00.

The store price is $12.00+50% more

The store price= $12.00 *(1+0.5)= $18.00

Final price (tax added)= $18.00 + 7%

Final price= $18.00 * (1 + 0.07)= $19.26

Answer 2

Answer:

The total cost of the DVD for the consumer was 19.26 $

Step-by-step explanation:

The sales price for the DVD was the price paid by the store plus 50%. To discover this value we will transform the percentage in a real number, by dividing it by 100, like following:

50/100 = 0.5

We then multiply this value by the price paid by the store (12) to find out how much is 50% of that. Then we add this value to the price paid by the store and we obtain the price of the DVD before taxes. So we do as following:

Price before taxes = price paid by the store + (price paid by the store)*0.5

Price before taxes = 12 + 12*0.5 = 18 $

On top of that there was 7% of tax for the consumer. We must repeat the same steps as before but using 7 instead of 50. So we have:

Final price = Price before taxes + (Price before taxes)*(7/100)

Final price = 18 + 18*0.07 = 19.26 $

The total cost of the DVD for the consumer was 19.26 $


Related Questions

WILL MARK BRANLIEST! 10 POINTS!
show work for #5

Answers

Step-by-step explanation:

ok so your gonna need to set up a proportion, specifically

25 is to x as x is to 16

mathematically, it's a cross multiplying problem:

25                X

           =          

X                   16

cross multiply and you get 400 = x²

which when solved is 20.

Have a good night dude.

If a standard dartboard's diameter is 17.75 inches, what is the area of once sector?

Answers

Answer:

  12.37 square inches

Step-by-step explanation:

The area of the dartboard can be figured from the diameter as ...

   A = (π/4)d² = (π/4)(17.75 in)² ≈ 247.4495 in²

There are 20 sectors, all the same size, so the area of one of them is ...

  sector area = (1/2)(247.4495 in²) ≈ 12.37 in²

find the area of a rectangle that has a base of (4a) cm and a height (2a + b)

Answers

Answer:

area = 8a^2 +4ab

Step-by-step explanation:

Area = (4a)(2a + b)

= 8a^2 +4ab

Step-by-step explanation:

[tex]Area of rectangle \\ = base \times height \\ = (4a) \times (2a + b) \\ = 4a \times 2a + 4a \times b \\ = 8 {a}^{2} + 4ab \\ [/tex]

X-1 0 1 2 fx 18 6 2 2/3 what is the decay factor of the exponential function represented by the table 1/3 2/3 2 6

Answers

Final answer:

The decay factor of the exponential function represented by the provided table is 1/3 as the ratio of the consecutive y-values of the function is consistently 1/3.

Explanation:

The decay factor of an exponential function can be found by comparing the ratio of the y-values of the function.

In the given question, a table of x/f(x) values is provided.

A decay happens if the ratios of the consecutive y-values (outputs) are consistently less than 1.

Let's find the ratio between successive y-values. Between 18 and 6, the ratio is 6/18 = 1/3. Going from 6 to 2, the ratio is 2/6 = 1/3. Lastly, transitioning from 2 to 2/3, the ratio is (2/3)/2 = 1/3.

Since we find the ratio of successive outputs (y-values) to consistently be 1/3, it is safe to say that 1/3 is the decay factor for the exponential function represented by the given table.

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Give a big-O estimate for the number of operations, where an operation is a comparison or a multiplication, used in this segment of an algorithm (ignoring comparisons used to test the conditions in the for loops, where a1, a2, ..., an are positive real numbers). m :

Answers

Answer:

O(n2)

Step-by-step explanation:

the first iteration algorithm of the i-for loop (the outer loop), the j-for loop (the inner loop) will run 2 to

n times which is represented as

(n − 1 times).

the second iteration algorithm of the i-for loop, the j-for loop will run 3 to n times represented as

(n − 2 times).

the third to the last iteration algorithm of the i-for loop, the j-for loop will run n − 1 to n times (2 times).

And the second to the last iteration of the i-for loop, the j-for loop will run from n to n times (1 time)

For the last iteration of the i-for loop, the j-for loop will run 0 times because i + 1 > n.

Now we know that the number of times the loops are run is

1 + 2 + 3 + . . . + (n − 2) + (n − 1) = n(n − 1)/2

So we can express the number of total iterations as n(n − 1)/2.

Since we have two operations per loop (one comparison and one multiplication), we have

2 ·n(n−1)/2 = n

2 − n operations.

So f(n) = n2 − n

f(n) ≤ n2

for n > 1.

Therefore, the algorithm is O(n2) with

C = 1 and k = 1.

Line l is parallel to line m. The slope of line l is . What is the slope of line m? 4/9

Answers

Final answer:

The slope of Line m that is parallel to Line l is also 4/9.

Explanation:

The slope of a line determines its steepness and direction. When two lines are parallel, they have the same slope. In this case, Line l is parallel to Line m, and the slope of Line l is 4/9. Therefore, the slope of Line m is also 4/9.

The mean of the sampling distribution of the sample mean is: Select one: a. equal to the population mean b. greater than the population mean c. less than the population mean d. not equal to the population mean but the direction cannot be determined

Answers

Answer:

Correct option is (a) equal to the population mean.

Step-by-step explanation:

According to the Central limit theorem if a large sample is selected from an unknown population with mean μ and standard deviation σ then the sampling distribution of sample means follows a normal distribution.

The mean and standard deviation of this sampling distribution is:

[tex]\mu_{\bar x}=\mu[/tex]

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]

This standard deviation of the sampling distribution of mean is known as the standard error.

Thus, the correct option is (a) equal to the population mean.

Final answer:

The mean of the sampling distribution of the sample mean is equal to the population mean, as stated by the Central Limit Theorem, when the sample size is sufficiently large.

Explanation:

The correct answer to the student's question is: a. equal to the population mean. This principle is a key concept in statistics, known as the Central Limit Theorem. According to the theorem, if the size (n) of the sample is sufficiently large, the distribution of the sample means will be approximately normal, with the mean of these sample means equalling the population mean. Another important point to note is that the standard deviation of this distribution, called the standard error of the mean, is the population standard deviation divided by the square root of the sample size (n). Therefore, as the sample size increases, the standard deviation of the sampling distribution of the means decreases, leading to more precise estimations of the population mean.

The president of a college has been told that when they raised their tuition by 15 percent the previous year, total revenue from tuition remained unchanged. Assuming the change in revenue is due to the change in tuition only, the president could conclude that demand for that college, over that tuition range, must be:

Answers

Answer:

= 1

Step-by-step explanation:

The demand for that college will be equal to 1 or it can be said as unit elastic demand over the tuition range. This means that the demand for the college would move proportionately with the tuition range of that college, since the change in revenue is due to the change in tuition only.

Hope this helps.

Good luck and cheers.

Answer:

demand for the college is equal to 1

Step-by-step explanation:

- We know that the change in Total Revenue is only the function of change in tuition fee only.

- The change in tution fee is subjected to 15% last year multiplied by the corresponding change in demand for the college will lead to a change in total revenue.

- The relation can be expressed as:

                                         ΔTR =  Δ P *ΔD

Where,

         ΔTR : Change in Total Revenue

         Δ P : Change in tuition fee

         ΔD : Change in demand.

- For TR to remain unchanged then ΔTR = 0. Hence,

                                         ΔTR = 0 = Δ P *ΔD

- We are given a change in Δ P = 15%, so that means for ΔTR = 0, the change in demand ΔD = 0.

- ΔD = 0, also means that the elasticity of the demand curve is perfectly elastic or in other words the demand for the college is equal to 1.

Help ASAP Please




The following two-way frequency table shows information collected from a survey of students regarding their grade level and how they spend their screen time.
Grade vs.
Screen Time Uses the
Internet Watches
TV Plays Video
Games Total
7th Grader 6 3 6 15
8th Grader 8 3 2 13
Total 14 6 8 28
What is the probability that a student uses the Internet, given that he or she is in eighth grade?

Enter your answer rounded to two decimal places, like this: 0.42

Enter your answer as a fraction in simplest form, formatted like this: 3/14

Answers

Final answer:

The probability of an eighth-grade student using the Internet, based on the data provided, is approximately 0.62, or simply 8/13 as a fraction.

Explanation:

To calculate the probability that a student uses the Internet given he or she is in eighth grade, we look at the eight graders' behaviors in the table. There are 13 students in total in the eighth grade, and 8 of these use the Internet.

So, the probability can be expressed as P(Internet|8th grader) = number of internet users in 8th grade / total number of 8th graders = 8 / 13.

When rounded to two decimal places, this probability would be approximately 0.62. In terms of fractions, it can simply be left as 8/13.

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The probability that a student uses the Internet, given that he or she is in eighth grade, is 2/3.

We are asked for the probability that a student uses the Internet, given that he or she is in eighth grade. This is the conditional probability [tex]$P({\text{Internet}} | {\text{8th Grade}})$[/tex], which can be calculated using Bayes' Theorem: \begin{align*}

[tex]P({\text{Internet}} | {\text{8th Grade}}) &= \frac{P({\text{8th Grade}} | {\text{Internet}})P({\text{Internet}})} {P({\text{8th Grade}})} \\&= \frac{\frac{8}{28} \cdot \frac{14}{28}} {\frac{13}{28}} \\&= \frac{2}{3}[/tex]

\end{align*}

Therefore, the probability that a student uses the Internet, given that he or she is in eighth grade, is [tex]$\boxed{\frac{2}{3}}$[/tex].

Here is a more detailed explanation of how we arrived at our answer:

Step 1: Calculate the probability of being in eighth grade, given that the student uses the Internet. This is the conditional probability [tex]$P({\text{8th Grade}} | {\text{Internet}})$[/tex], which can be calculated from the table as follows: [tex]$P({\text{8th Grade}} | {\text{Internet}}) = \frac{8}{14}$[/tex]

Step 2: Calculate the probability of using the Internet.** This is the marginal probability [tex]$P({\text{Internet}})$[/tex], which can be calculated from the table as follows: [tex]$P({\text{Internet}}) = \frac{14}{28}$[/tex].

Step 3: Calculate the probability of being in eighth grade.This is the marginal probability [tex]$P({\text{8th Grade}})$[/tex], which can be calculated from the table as follows: [tex]$P({\text{8th Grade}}) = \frac{13}{28}$[/tex].

Step 4: Apply Bayes' Theorem to calculate the conditional probability [tex]$P({\text{Internet}} | {\text{8th Grade}})$[/tex].

Therefore, the probability that a student uses the Internet, given that he or she is in eighth grade, is[tex]$\boxed{\frac{2}{3}}$[/tex].

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Choose the correct molecular geometry of the phosphorus atom in each of these ions from the list below: A) square plane B) T-shape C) icosahedral D) seesaw E) trigonal pyramid F) bent G) octahedron H) square pyramidal I) linear J) tetrahedron K) trigonal bipyramid L) None of the above Enter two letters that correspond to PCl4+ and PCl6− in order, e.g. AB, DC, EA, etc.

Answers

Answer:

See attached picture.

Step-by-step explanation:

See attached picture.

For remaining parts resubmit question.  

hey, help me with this pls i only have 10 minutes. 30 points each :)

Answers

Answer:

y=-2x

Step-by-step explanation:

First you want to remember rise over run. Your rise is -2 and your run is 1. So -2/1 is your answer. And -2/1 is equal to -2.

Answer:

[tex]\frac{2} {-1}[/tex]=-2

Step-by-step explanation:

The top five test scores in Mr. Rhodes's class were: 98, 92, 96, 97, and 97. What is
the mean absolute deviation?





plz help I'm lost!!​

Answers

The mean of the top five test scores is 96. Then the mean absolute deviation is zero.

What is the mean absolute deviation?

It is the average distance between each data point and the mean.

The top five test scores in Mr. Rhodes's class were: 98, 92, 96, 97, and 97.

Then the mean (μ) will be

[tex]\mu = \dfrac{98+92+96+97+97}{5}\\\\\mu = \dfrac{480}{5}\\\\\mu = 96[/tex]

Then the mean absolute deviation will be

[tex]\rm MAD = \dfrac{\Sigma (X_i - \mu)}{n}\\\\MAD = \dfrac{(98-96)+(92-96)+(96-96)+(97-96)+(97-96)}{5}\\\\MAD = \dfrac{2-4+0+1+1}{5}\\\\MAD = 0[/tex]

The mean absolute deviation is zero and the mean is 96.

More about the mean absolute deviation link is given below.

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Final answer:

Calculating the mean absolute deviation of the top five test scores in Mr. Rhodes's class involves finding the mean score and then the average of the absolute deviations from this mean. The result is a MAD of 1.6, indicating the average dispersion of the top scores from the class mean.

Explanation:

The question involves calculating the mean absolute deviation (MAD) of the top five test scores in Mr. Rhodes's class, which are 98, 92, 96, 97, and 97. First, we find the mean (average) of these scores by adding them together and dividing by the number of scores, which gives us (98 + 92 + 96 + 97 + 97) / 5 = 96. Next, we calculate the absolute deviation of each score from the mean, which are 2, 4, 0, 1, and 1 respectively. The mean absolute deviation is then the average of these absolute deviations, calculated as (2 + 4 + 0 + 1 + 1) / 5 = 1.6.

The result of these calculations shows that the mean absolute deviation of the test scores is 1.6. This value represents how much, on average, each of the top five scores deviates from the mean score of the class, providing an understanding of the variability or dispersion within the top scores. The MAD is a useful measure in understanding how spread out the scores are from the mean.

The second side of a triangular deck is 3 feet longer than the shortest​ side, and the third side is 3 feet shorter than twice the length of the shortest side. If the perimeter of the deck is 80 ​feet, what are the lengths of the three​ sides?

Answers

Answer: the lengths are 20 feet, 23 feet and 37 feet

Step-by-step explanation:

Let x represent the length of the shorter side of the triangular deck.

The second side of a triangular deck is 3 feet longer than the shortest​ side. This means that the length of the second side is (x + 3) feet.

The third side is 3 feet shorter than twice the length of the shortest side. This means that the length of the third of the triangle is (2x - 3) feet.

If the perimeter of the deck is 80 ​feet, it means that

x + x + 3 + 2x - 3 = 80

4x = 80

x = 80/4

x = 20

The length of the second side is

20 + 3 = 23 feet

The length of the third side is

20 × 2 - 3 = 40 - 3 = 37 feet

What is the distance between point (6, -1) and point (5, 3) rounded to the nearest tenth?


4.6 units


1.4 units


17 units


4.1 units

Answers

Answer:

4.6

Step-by-step explanation:

Use the distance formula:

d = [tex]\sqrt{(x-x)^{2}-(y-y)^{2} }[/tex]

plug in the numbers

[tex]\sqrt{(6-1)^{2} -(5-3)^{2} }\\[/tex]

PEMDAS says do parenthisee first

[tex]\sqrt{(5)^{2} -(2)^{2} }[/tex]

now square it

[tex]\sqrt{25-4}[/tex]

subtract

[tex]\sqrt{21}[/tex]

do the calculator for this part

4.582575695

round it to get

4.6

Steve, an entrepreneur, decides to open a flower shop and looks for an appropriate location for his shop. He wants to use the center-of-gravity method for the purpose. He researches the zip codes in his area and finds the following information: Identify a true statement about the best center of gravity for the possible shop location.
A) The x-axis and the y-axis are less than 5.0.
B) The x-axis is less than 7.0 and the y-axis is more than 7.0.
C) The x-axis is more than 7.0 and the y-axis is less than 7.0.
D) The x-axis and the y-axis are more than 7.0.

Answers

Answer:

C

Step-by-step explanation:

The x-axis is more than 7.0 and the y-axis is less than 7.0.

Cheers

A light house operator is 34m above sea level. He spots a sailboat in the distance. The angle of depression of the sighting is 10. How far is the boat from the base of the lighthouse?

Answers

Answer: the distance of the boat from the base of the lighthouse is 192.9 m

Step-by-step explanation:

The scenario is represented in the right angle triangle shown in the attached photo.

Looking at triangle ABC, the height of the light house operator above sea level represents the opposite side of the right angle triangle.

Angle A = 10° because it is alternate to the angle of depression.

To determine AB, the distance of the boat from the base of the lighthouse, we would apply

the tangent trigonometric ratio which is expressed as

Tan θ, = opposite side/adjacent side. Therefore,

Tan 10 = 34/AB

AB = 34/Tan 10 = 34/0.1763

AB = 192.9 m

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.2, -4, and 1 3i

Answers

Answer:

[tex]f(x)=x^{4}+x^{3}-10x^{2} +8x[/tex]

Step-by-step explanation:

A number is a factor of f(x) if and only if f(x) is zero for that value/number.

For the factors of a function we write the factors as x-a where a is the zero of function i.e. value at which f(x) is zero.

To write the polynomial function of minimum degree with real coefficients whose zeros include 2, -4, and 1, 3i, we find the f(x) is the product of all factors i.e x-a where a will represent the given zeros.

[tex]f(x)=(x-2)(x-(-4))(x-1)(x-3i)\\f(x)=(x-2)(x+4))(x-1)(x-3i)\\f(x)=(x^{2} +4x-2x-8)(x^{2} -3xi-x+3i )\\f(x)=(x^{2} +2x-8)(x^{2} -x-(3x+3)i)\\[/tex]

As it is stated that polynomial should have real coefficients so skipping the terms with 'i' we get

[tex]f(x)=(x^{2} +2x-8)(x^{2} -x)\\f(x)=x^{4}-x^{3}+2x^{3}-2x^{2} -8x^{2} +8x\\f(x)=x^{4}+x^{3}-10x^{2} +8x[/tex]

Answer:

f(x) = x4 - 2x2 + 36x - 80

Step-by-step explanation:

What is the answer to this question??

Answers

Option B:

Point R on the number line best represents [tex]\frac{-6}{2}[/tex]

Solution:

In the number line,

The numbers which are left side of 0 are -1, -2, -3, -4, -5, -6, -7, -8.

The numbers which are right side of 0 are 1, 2, 3, 4, 5, 6, 7, 8.

Q is 6 points left of 0. That is Q = -6

R is 3 points left of 0. That is R = -3

S is 2 points left of 0. That is s = -2

T is 3 points right of 0. That is T = 3

[tex]$\frac{-6}{2}=-3[/tex]

In the number line -3 is the point of R.

Therefore point R on the number line best represents [tex]\frac{-6}{2}[/tex].

Option B is the correct answer.

Please help me with these rotation problem.​

Answers

Answer:

  see below

Step-by-step explanation:

In the attachment, the points are listed in the order given in the problem statement. (They are listed to the right of the "rotation matrix", with x-coordinates above y-coordinates.)

__

I really don't like to do repetitive calculations, so I try to use a graphing calculator or spreadsheet whenever possible. Angles are measured CCW.

As always, the rotation transformations are ...

  180° — (x, y) ⇒ (-x, -y)

  270° — (x, y) ⇒ (y, -x)

A plastic rod 1.5 m long is rubbed all over with wool, and acquires a charge of -9e-08 coulombs. We choose the center of the rod to be the origin of our coordinate system, with the x-axis extending to the right, the y-axis extending up, and the z-axis out of the page. In order to calculate the electric field at location A = < 0.7, 0, 0 > m, we divide the rod into 8 pieces, and approximate each piece as a point charge located at the center of the piece. 1. What is the length of one of these pieces? 2. What is the location of the center of piece number 2? 3. How much charge is on piece number 2?

Answers

Answer:

Answer:

a) k = 0.1875 m

b) r2 = 0.46875 m

c) q = -1.125*10^-8 C

Step-by-step explanation:

Given:

- The total Length of rod L = 1.5 m

- The total charge of the rod Q = -9 * 10^8 C

- Total section of a rod n = 8

Find:

1. What is the length of one of these pieces?

2. What is the location of the center of piece number 2?

3. How much charge is on piece number 2?

Solution:

- The entire rod is divided into 8 pieces, so the length of each piece would be k:

                                     k = L / n

                                     k = 1.5 / 8

                                     k = 0.1875 m

- The distance from center of entire rod and center of section 2 is 2.5 times the section length

                                     r2 = 2.5*k

                                     r2 = 2.5*(0.1875)

                                     r2 = 0.46875 m

- Assuming the charge on the rod is uniformly distributed. The the charge for each section of rod is given by q:

                                     q = Q / n

                                     q = -9 * 10^8 / 8

                                     q = -1.125*10^-8 C

Final answer:

The length of one of the eight pieces of the rod is 0.1875 m. The center of piece number 2 is at <0.28125, 0, 0> m. The charge on piece number 2 is -1.125e-08 Coulombs.

Explanation:

The problem involves the concepts of electric field, charge distribution, and coordinate system in Physics. Let's answer the question part by part:

The length of one of these pieces is the total length divided by the number of pieces. That is, 1.5 m / 8 = 0.1875 m.The center of piece number 2 would be one and a half times the length of one piece, to the right of the origin in the x-direction; hence, it is at <0.28125, 0, 0> m.The charge on piece number 2 is the total charge divided by the number of pieces. That is, -9e-08 C / 8 = -1.125e-08 Coulombs.

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Jesse takes his dog and cat for Their annual vet visit. Jesse's dog weigh's 23 pounds. The vet tells him his cat weighs 5/8 as much as his dogs weighs. How much does his cat weigh

Answers

Answer:

14.375 pounds

Step-by-step explanation:

Jesse's dog: 23 lb

Cat: 5/8*23=115/8

Therefore, Jesse's cat weighs 14.375 pounds

To find the depth of a well, a farmer lowers a 50-foot rope vertically into the well. If 15 feet of rope remain above the well, how deep (in feet) is the well?

Answers

The well is 35 feet deep.

Step-by-step explanation:

Given,

Length of rope = 50 feet

Length of remaining rope = 15 feet

Let,

x be the depth of well.

Total length of rope = Length of remaining + Depth of well

[tex]50=15+x\\50-15=x\\x=35[/tex]

The well is 35 feet deep.

Suppose a firm has a net profit margin of 15%, sales of $155 million, assets of $312 million, and owner's equity of $223 million. If the dividend payout ratio is 10%, what is the firm's sustainable growth rate?

Answers

Answer:

2.7%.

Step-by-step explanation:.

Given:

Net profit margin ( profitability rate) =  15%

Total sales = $155 million

Total assets = $312 million

Total equity = $223 million.

Dividend rate = 10%

Question asked:

What is the firm's sustainable growth rate ?

First of all we will find these thing.

1. Asset utilization rate = [tex]\frac{Total \ sales}{Total \ assets}[/tex]

                                     = [tex]\frac{155}{312} = 0.496\ million= 0.5\%[/tex]

2. Financial utilization rate   =   [tex]\frac{Total\ debt}{Total\ equity} \\[/tex]

  Total debt = Total asset - Total equity

                   = $312 million -   $223 million = $89 million

                                           = [tex]\frac{89}{223} = 0.4\%[/tex]

3. Return on equity rate = Asset utilization rate [tex]\times[/tex] profitability rate

Return on equity rate = [tex]0.5\times15\times0.4=3\%[/tex]

4. Business retention rate = 100 - Dividend rate

                                           = 100 - 10 = 90%

Now, finally we will calculate sustainable growth rate :

Sustainable growth rate =  Return on equity rate [tex]\times[/tex]  Business retention rate

                                        = [tex]3\%\times90\%=2.7\%[/tex]

Therefore, firm's sustainable growth rate is 2.7%

                                             

Give the coordinates of each point under the given transformation.​

Answers

Answer:

  see below

Step-by-step explanation:

The rotation transformations are ...

  90° : (x, y) ⇒ (-y, x)

  180° : (x, y) ⇒ (-x, -y)

  270° : (x, y) ⇒ (y, -x)

Applying these to the given points, you get ...

9) A'(6, 9)

10) A'(15, 11)

11) A'(9, 6)

12) A'(-11, 15)

13) A'(6, -9)

14) A'(15, -11)

Gerry has two different part-time jobs, and he had work 20 hours per week at each job. He earns $8 per hour at one job. Which expression represents how much Gerry earned last week if he earns d dollars per hour at this other job? A- 20+20d B- 160+ 20d C- 40+ d D- 160+ 8d PLZZZZZZ ANSWER THX!!!!!!

Answers

Answer:The answer is B. 160 + 20d

Step-by-step explanation: first find out the total for how much he makes at the first job. 20 x 8 = 160 then you just write out the equation

Find the indicated sum for each sequence. S9 of –9, 36, –144, 576, ...

Answers

Answer:

-471,861

Step-by-step explanation:

The sum of 9 terms in the sequence –9, 36, –144, 576, ... is -471861.

What is a sequence?

An ordered collection of objects that allows repetitions is referred to as a sequence. It has members, just like a set does. The length of the sequence is determined by the number of items.

Given:

–9, 36, –144, 576, ...

Calculate the ratio of the sequence as shown below,

ratio = 36 / -9

ratio = -4

Calculate the sum of 9 terms as shown below,

S₉ = -9 (1 - (-4)⁹) / (1 - (-4))

S₉ = -9 (1 + 262144) / 5

S₉ = -9 (262145) / 5

S₉ = -2359305 / 5

S₉ = -471861

To know more about the sequence:

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James folds a piece of paper in half several times,each time unfolding the paper to count how many equal parts he sees. After folding the paper about six times, ti becomes too difficult to fold it again,but he is curious how many parts the paper would be broken into if he could continue to fold it. He decides to employ the modeling cycle to predict how many parts the paper would be folded into if he were able to fold it 11 times.

Answers

Answer:

There will be total 2048 parts of the given paper if James if able to fold the paper eleven times.

The needed function is [tex]y = 2 ^n[/tex]

Step-by-step explanation:

Let us assume the piece of paper James decides to fold is a SQUARE.

Now, let us assume:

n : the number of times the paper is folded.

y : The number of parts obtained after folds.

Now, if the paper if folded ONCE ⇒  n = 1

Also, when the pap er is folded once, the parts obtained are TWO equal parts.

⇒  for n = 1 , y = 2       ..... (1)

Similarly, if the paper if folded TWICE  ⇒  n = 2

Also, when the paper is folded twice, the parts obtained are FOUR equal parts.

⇒  for n = 2 , y = 4       ..... (2)

⇒[tex]y = 2^2 = 2^n[/tex]

Continuing the same way, if the paper is folded SEVEN times  ⇒  n = 7

So, [tex]y = 2^ n = 2^7 = 128[/tex]

⇒  There are total 128 equal parts.

Lastly,  if the paper is folded ELEVEN  times  ⇒  n = 11

So, [tex]y = 2^ n = 2^{11} = 2048[/tex]

⇒  There are total 2048 equal parts.

Hence, there will be total 2048 parts of the given paper if James if able to fold the paper eleven times.

And the needed function is [tex]y = 2 ^n[/tex]

Gina's literacy bucket weighs 6 pounds. Her novel weighs 1 4/6 pounds, and her chrome book weighs 2 1/6 how much would her bucket weigh if she took out the two items.

Answers

Answer:

[tex]2\frac{1}{6}[/tex] pounds.

Step-by-step explanation:

We have been given that Gina's literacy bucket weighs 6 pounds. Her novel weighs 1 4/6 pounds, and her chrome book weighs 2 1/6.

To find weight of bucket after taking out the two items, we will subtract weight of each item from 6 pounds as:

[tex]\text{Weight of bucket}=6-1\frac{4}{6}-2\frac{1}{6}[/tex]

Let us convert mixed fractions into improper fractions as:

[tex]1\frac{4}{6}=\frac{6\cdot 1+4}{6}=\frac{10}{6}\\\\2\frac{1}{6}=\frac{6\cdot 2+1}{6}=\frac{12+1}{6}=\frac{13}{6}[/tex]

[tex]\text{Weight of bucket}=6-\frac{10}{6}-\frac{13}{6}[/tex]

[tex]\text{Weight of bucket}=\frac{6\cdot 6}{6}-\frac{10}{6}-\frac{13}{6}[/tex]

[tex]\text{Weight of bucket}=\frac{36}{6}-\frac{10}{6}-\frac{13}{6}[/tex]

Combine numerators:

[tex]\text{Weight of bucket}=\frac{36-10-13}{6}[/tex]

[tex]\text{Weight of bucket}=\frac{13}{6}[/tex]

[tex]\text{Weight of bucket}=2\frac{1}{6}[/tex]

Therefore, the weight of the bucket is [tex]2\frac{1}{6}[/tex] pounds.

Which equations represent the line that is parallel to 3x − 4y = 7 and passes through the point (−4, −2)? Select two options.
y = 3/4x + 1
3x − 4y = −4
4x − 3y = −3
y – 2 = –3/4(x – 4)
y + 2 = 3/4 (x+4)

Answers

Option A: [tex]y=\frac{3}{4}x+1[/tex] is the equation of the line.

Option E: [tex]y+2=\frac{3}{4}(x+4)[/tex] is the equation of the line.

Explanation:

Given that the line is [tex]3 x-4 y=7[/tex] and passes through the point [tex](-4,-2)[/tex]

We need to determine the equation of the line.

Formula:

The equation of the line can be determined using the formula,

[tex]y-y_1=m(x-x_1)[/tex]

Slope:

Since, the lines are parallel, from the equation [tex]3 x-4 y=7[/tex], we shall determine the slope.

Thus, we have,

[tex]-4 y=-3x+7[/tex]

   [tex]y=\frac{3}{4} x+\frac{7}{4}[/tex]

Thus, the slope of the equation is [tex]m=\frac{3}{4}[/tex]

Equation of line:

Substituting [tex]m=\frac{3}{4}[/tex] and the point [tex](-4,-2)[/tex] in the formula, we get,

[tex]y+2=\frac{3}{4}(x+4)[/tex]

Hence, the equation of line is [tex]y+2=\frac{3}{4}(x+4)[/tex]

Thus, Option E is the correct answer.

Let us write the equation of line [tex]y+2=\frac{3}{4}(x+4)[/tex] in slope - intercept form.

Thus, we have,

[tex]y+2=\frac{3}{4}x+3[/tex]

     [tex]y=\frac{3}{4}x+3-2[/tex]

     [tex]y=\frac{3}{4}x+1[/tex]

Thus, the equation of the line is [tex]y=\frac{3}{4}x+1[/tex]

Hence, Option A is the correct answer.

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Bob placed three regular pentagons together at a vertex, thinking he might be able to form a tessellation. However, they left a gap. What is the number of degrees in the measure indicated?

Answers

Answer:

36

Step-by-step explanation:

The angles of a pentagon sum to 180(5-2) = 540 degrees, so each angle of a regular pentagon is 540/5 = 108. Therefore, three of these angles sum to $3 * 108 = 324, which means the indicated angle measures 360 - 324 = 36.

Answer:

36

Step-by-step explanation:

The angles of a pentagon sum to 180(5-2) = 540 degrees, so each angle of a regular pentagon is 540/5 = 108. Therefore, three of these angles sum to 3* 108 = 324, which means the indicated angle measures 360 - 324 = 36

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