Suppose the expression a(b)n models the approximate number of people who visited an aquarium each day since an aquarium opened, where a is the initial number of people who visited, b is the rate of increase in the number of people who visited each day, and n is the number of days since the aquarium opened.

If the expression below models the number of visitors of a particular aquarium, what is the correct interpretation of the second factor?
54(1.3)^7


A.
There were 9.1 times as many people who visited the aquarium on the 7th day as on the first day.
B.
There were 1.3 times as many people who visited the aquarium on the 7th day as on the first day.
C.
There were 6.27 times as many people who visited the aquarium on the 7th day as on the first day.
D.
There were 10.2 times as many people who visited the aquarium on the 7th day as on the first day.

The 9-1-1 service fee on telecommunications bills is a type of tax such as service tax, fixed tax, business tax. Thus, the option (a), (d) and (e) is correct.

What is tax?

The term tax refers to the government charge the extra money for goods and services. The tax is also called as financial charge. The amount of tax are collect to government account as spent on public welfare. The public pay tax is compulsory. There are two types of tax such as direct tax and indirect tax.

The telecommunications bills are also included tax such as service tax, fixed tax, and business tax etc. The service tax is an indirect tax as charge on exchange of services. The fixed tax are apply on lump sum amount. The business tax is included income tax, and other expenses tax (wages, salaries etc.)

Therefore, option (a) (d) and (e) is correct.

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Answer:

Beneficial terms of trade or trading price between two parties are opportunity costs lower than the cost to manufacture them locally which benefits both parties. They must be less enough to cover the freight charges or additional service charges that may arise.

Answer:

See explanation below

Step-by-step explanation:

In fact, the interval has to be closed (just as [a,b], for b>a). Otherwise, this is not neccesarily true. For example, consider the function f(x) = -1/x defined on the open interval (0.1). f is continuous (quotient of continuous functions) but it does not have a minimum value: it decreases infinitely near zero.

To show this result on the interval [a,b], the idea is the following:

We can use a previous theorem. If f is continuous on [a,b], there exists some N>0 such that N≤f(x) (that is, f is bounded below). Now, we take the biggest N such that N≤f(x) for all x∈[a,b] (this is known as the greatest lower bound)

The number N is the candidate for the minimum value of f. Next, we have to show that there exists some p∈[a,b] such that f(p)=N. To do this, we must use the continuty of f on [a,b]. There are many ways to do it, and usually they require the epsilon-delta definition of continuity.

This is just a description of the ideas involved, but of course, a rigorous proof would need more technical details, depending on the theorems you are allowed to use.  

what's the answer choices

Answer: There is decrease in percent of 26.47% from 2001 to 2008.

Step-by-step explanation:

Since we have given that

Number of runs that chipper had batted in 2001 = 102

Number of runs that chipper had batted in 2008 = 75

So, the year gap = 7 years

Difference in runs = 102- 75 =27

So, the percent change in runs batted from 2001 to 2008 is given by

[tex]\dfrac{27}{102}\times 100\\\\=\dfrac{2700}{102}\\\\=26.47\%[/tex]

Hence, there is decrease in percent of 26.47% from 2001 to 2008.

Answer: 73 songs

Step-by-step explanation:

The online music club has a one- time registration fee of $13.95 and charges $0.49 to buy each song. Let x represent the number of songs that a member buys. This means that the amount that a member who just joins the music club pays for x songs would be

0.49x + 13.95

If Emma has $50.00 to join the club and buy songs, the maximum number of songs she can buy would be expressed as follows

0.49x + 13.95 = 50

0.49x = 50 - 13.95 = 36.05

x = 36.05/0.49 = 73.57

the maximum number of songs she can buy is 73 since the number of songs cannot be a fraction.

50.00 - 13.95 = 36.05 (subtract the registration fee)

36.05/0.49 =  73.57 so she can buy 73 songs

The required cost of a computer Suzie will pay is $545.69.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
The original price of a computer is $599.99.
Suzie has a 15%-off coupon for the computer.
Discounted price = (1 - 0.15)×599.99

Discounted price = 0.85×599.99

A sales tax of 7% will be added to the sale price of the computer.
Price of the computer after taxes = (1 + 0.07)0.85×599.99
                                                   = $545.69

Thus, the required cost of a computer Suzie will pay is $545.69.

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Final answer:

To find how much Suzie will pay for a computer with a 15% discount and a 7% sales tax, first calculate the discount, then subtract it from the original price, calculate the sales tax on the sale price, and add it to the sale price. The total payment is the original price reduced by the discount and increased by the sales tax, rounded to the nearest cent would be approximately $545.69.

Explanation:

Calculation of Total Payment for the Computer with a Discount and Sales Tax

To calculate how much Suzie will pay for the computer after applying a 15%-off coupon and adding a 7% sales tax, you will need to perform two main calculations. First, calculate the discount amount by converting the percentage to a decimal and multiplying it by the original price. Second, calculate the sales tax on the discounted price by again converting the percentage to a decimal and multiplying it. Finally, add the sales tax to the discounted price to arrive at the total cost.

Here's a step-by-step breakdown of the calculations:

Add the sales tax to the sale price to find the total cost: $509.9915 + $35.699405 = $545.690905.

Therefore, the expression to calculate Suzie's total payment for the computer is ($599.99  times (1 - 0.15))  times (1 + 0.07). When actually performing the calculation, the total payment, rounded to the nearest cent, would be approximately $545.69.

Answer:

Therefore the lengths of the opposite side pairs, AB and BC are 12 units and 6 units .

Step-by-step explanation:

Given:

[] ABCD is a Parallelogram.

∴ pairs of opposite sides are congruent

∴ AB = DC and

  BC = AD

To Find:

Length of AB = ?

Length of BC = ?

Solution:

[] ABCD is a Parallelogram. .............Given

∴ pairs of opposite sides are congruent

∴ AB = DC        and          BC = AD

On substituting the values we get

For 'x' i.e AB = DC  

[tex]4x=x+9\\\\4x-x=9\\\\3x=9\\\\x=\frac{9}{3}\\ \\x=3[/tex]

For 'y' i.e BC = AD

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

Now substituting 'x' and 'y' in AB and BC we get,

[tex]Length\ AB=4\times 3 =12\ units\\\\Length\ BC=2\times 3 =6\ units[/tex]

Therefore the lengths of the opposite side pairs, AB and BC are 12 units and 6 units .

C) 12, 6

Set opposite sides equal to each other and solve for x or y.

AB = DC → 4x = x + 9 → 3x = 9 → x = 3

So, AB = DC = 12

And,

AD = BC → 6 = 2y → y = 3

So, AD = BC = 6

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

Work Shown:

Let P and Q be two concentric circles

P = area of circle with radius 19

P = pi*r^2

P = pi*19^2

P = 361pi

-------

Q = area of circle with radius 29

Q = pi*r^2

Q = pi*29^2

Q = 841pi

-------

R = area of shaded region between circle P and circle Q

R = region outside circle P, but inside circle Q

R = Q - P

R = 841pi - 361pi

R = 480pi

------

S = area of circle with area equal to region R's area

S = 480pi

S = pi*r^2

pi*r^2 = 480pi

r^2 = 480

r = sqrt(480)

r = sqrt(16*30)

r = sqrt(16)*sqrt(30)

r = 4*sqrt(30)

Answer: z= kxy

Step-by-step explanation:

There are three types of variation. We have direct, inverse and joint.

Variation has to do with the manner in which we relate two mor more variables either directly or inversely.

For joint variation, we relate two or more variables to one another. A variable among those variables is written in terms of the remaining variables directly.

According to the question, since we have three variables z, x and y and we are to express z joint as x and y.

Joint variation is a "direct relationship" between variables i.e z will be directly proportional to the product of x and y making k as constant of proportionality. Mathematical relationship will give us;

Z=kxy

Answer:

Dog Pogo will fetch the frisbee 12 times in 4 minutes.

Step-by-step explanation:

Given:

Number of minutes required =2 minutes.

Number of times frisbee fetch by dog = 6 times

We need to find Number of times the dog can fetch the frisbee in 4 minutes.

First we will find number of frisbee fetch in minute.

In 2 minutes = 6 times frisbee fetched by the dog

so in 1 minute = Number of times frisbee fetched by the dog in 1 minute.

By using Using Unitary method we get;

Number of times frisbee fetched by the dog in 1 minute = [tex]\frac{6}{2} =3[/tex]

Hence in 1 minutes the dog can fetch frisbee 3 times.

for 1 min = 3 times frisbee is been fetched by dog

So for 4 minutes = Number of times frisbee is been fetched by dog in 4 min.

Again by using Unitary Method we get;

Number of times frisbee is been fetched by dog in 4 min = [tex]3\times4 = 12[/tex]

Hence Dog Pogo will fetch the frisbee 12 times in 4 minutes.

Answer:12

Step-by-step explanation:

Answer:

The answer to your question is   -3x² + 29x -150

Step-by-step explanation:

                                -3x² + 29x -150

  x³ + 6x² - 3x - 5     -3x⁵ + 11x⁴ + 33x³ - 26x² - 36x - 6

                                +3x⁵ +18x⁴ -   9x³  - 15x²

                                   0     29x⁴ +24x³ - 41x² - 36x

                                         -29x⁴ - 174x³ +87x²+145x

                                            0     -150x³ +46x² +109x - 6

                                                  +150x³ +900x²-450x -750

                                                       0       946x² -341x -756

Quotient =   -3x² + 29x -150

Remainder = 946x² -341x -756

Answer:

10%

Step-by-step explanation:

Machine out put power =100 watt

Machine input power=1000 watt

We have to find the efficiency of the machine.

We know that

Efficiency of machine=[tex]\frac{O.p}{I.p}[/tex]

Where O.p=Output power

I.p=Input power

By using the formula

Efficiency of machine=[tex]\frac{100}{1000}=0.1[/tex]

Efficiency of machine (in percent)[tex]0.1\times 100=[/tex]10%

Hence, the efficiency of machine=10%

The efficiency of the machine is 10%, as it is calculated by dividing the output power, 100 watts, by the input power, 1000 watts, and then multiplying by 100 to express it as a percentage.

The efficiency of a machine is calculated by dividing the useful output power by the input power and then multiplying the result by 100 to get a percentage. For the given machine, which puts out 100 watts for every 1000 watts put into it, the calculation would look like this:

Efficiency (Eff) = (Wout / Ein) times 100%

Efficiency (Eff) = (100W / 1000W) times 100%

Efficiency (Eff) = 0.1 times 100%

Efficiency (Eff) = 10%

This means the efficiency of the machine is 10%.

In this bacterial growth problem, the population after 24 hours under normal conditions would be approximately 19136 bacteria. With a reduced growth rate due to antibiotics, the population would be approximately 79 bacteria.

The subject of the question relates to the concept of exponential growth, as demonstrated by a bacteria population. Given that the initial population is 24, the population P after time t, in this case in hours, is given by the formula P = P0 * (1 + r/100)^t, where P0 is the initial population, r is the relative growth rate (percentage), and t is time.

Under normal growth conditions, after 24 hours the population would be P = 24 * (1 + 15/100)^24 = approximately 19136, rounded to the nearest whole number. However, with the introduction of antibiotics, reducing the growth rate to 5%, after 24 hours the population would be P = 24 * (1 + 5/100)^24 = approximately 79, rounded to the nearest whole number.

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Yes, you are correct.

From the image, we can see 3 triangles, the large triangle and the two triangles that make the larger triangle.

All 3 of these triangles are similar since they're angle measurements are the same (can be proven by geometry).

We can gather the following information from the given information.

We know the hypotenuse to corresponding leg ratio must be equal since these two triangles are similar. Thus, we have the equation:

12/x = x/9

Using the cross product property gives us:

x² = 9 × 12

x² = 108

Taking the square root of both sides gives us:

x = √108

= 6 √3

Thus, your answer is correct. Great job!

Let me know if you need any clarifications, thanks!

188 children and 155 adults were admitted that day.

Step-by-step explanation:

Given,

Cost of one children admission = $2.50

Cost of one adult admission = $5.80

Number of people entered = 343

Total admission fees collected = $1369

Let,

Number of children admission = x

Number of adult admission = y

According to given statement;

x+y=343     Eqn 1

2.50x+5.80y=1369     Eqn 2

Multiplying Eqn 1 by 2.50

[tex]2.50(x+y=343)\\2.50x+2.50y=857.50\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 3 from Eqn 2

[tex](2.50x+5.80y)-(2.50x+2.50y)=1369-857.50\\2.50x+5.80y-2.50x-2.50y=511.50\\3.30y=511.50[/tex]

Dividing both sides by 3.30

[tex]\frac{3.30y}{3.30}=\frac{511.50}{3.30}\\y=155[/tex]

Putting y=155 in Eqn 1

[tex]x+155=343\\x=343-155\\x=188[/tex]

188 children and 155 adults were admitted that day.

Keywords: linear equation, subtraction

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Gallons of water are leaked in one year is 94.253 gallons

Given that leaky faucet drips 356,755 mL of water over the course of the year

There are approximately 3,785 mL in 1 gallon.

To find: gallons of water are leaked in one year

From given information,

Amount of water leaked in one year in ml = 356,755 mL

Also given in question that,

[tex]1 \text{ ml} = \frac{1}{3785} \text{ gallons}[/tex]

Now we can convert 356,755 mL to gallons

[tex]356,755 \text{ ml} = \frac{1}{3785} \times 356755 \text{ gallons}\\\\356,755 \text{ ml} = 94.253 \text{ gallons}[/tex]

Thus gallons of water are leaked in one year is 94.253 gallons

Answer:

x = -0.5.

Step-by-step explanation:

x^2 = 16^x

One way to do this is to use 2 graphs  y = x^2 and y = 16^x  .

The solution  is where the 2 graphs intersect.

The answer is x = -0.5.

Answer:

Option D) It is flawed because it is a voluntary response sample.

Step-by-step explanation:

We are given the following information in the question:

The subjects of the survey were internet users who responded to a question that was posted on a news website.

A total of 714 subjects responded to this question, answering the question, how often he or she read a book.

Option D) It is flawed because it is a voluntary response sample.

Voluntary response sample:

Answer:28 square shaped tiles of area 25 m^2 would be needed to cover the rectangular plot.

Step-by-step explanation:

The area of the rectangular plot is 700m^2

The area of each square tiles is 25m^2

The number of tiles needed to cover a rectangular plot would be

700/25 = 28 square shaped tiles

Set up the equation and solve for x:

11x-2 = 9x +2 + 10

11x-2 = 9x +12

2x = 14

X = 7

BOC = 9x +2 = 9(14) +2 = 126+2 = 128

Answer:

In 9 days will the second warehouse have 1.5 times more coal than the first one

Step-by-step explanation:

The coal left in warehouses after x days can be found using the equation:

Let the second warehouse have 1.5 times more coal than the first one after n days then  

Answer:

3 units below the y-intercept of g(x) is the y-intercept of f(x)

Step-by-step explanation:

[tex]g(x)=x+2[/tex] and [tex]f(x)=x-1[/tex]

In f(x)= mx+b the y intercept is b

In [tex]g(x)=x+2[/tex], the y intercept value is 2

In [tex]f(x)=x-1[/tex], the y intercept value is -1

the difference in y intercept is +2-(-1)=+3

3 units below the y-intercept of g(x) is the y-intercept of f(x)

Answer:

cash = $450000                                 ........... debit

common stock =  1000                       .......... credit

paid in capital amount =  $449000 ............ credit

Step-by-step explanation:

given data

share = 100000

par value = $0.01

total selling price = $450,000

solution

here

here total selling price is $450000

so cash = $450000    ........... debit

and common stock will be

common stock = 100000 × 0.01

common stock =  1000       .......... credit

and paid in capital amount will be

paid in capital amount = selling price - common stock

paid in capital amount =  $450000 - $1000

paid in capital amount =  $449000 ............ credit

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slope = difference in y / difference in x

slope = (12 - 0) / (6 - 0)

slope = 12/6

slope = 2

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slope

Done

Height of the water after 3 minutes is 31.25 inches

Given that height of the water in a fish pond is 42.5 inches

Water is being drained from the pond at a rate of 3.75 inches per minute

To find:  height of the water after 3 minutes

According to given information,

Water drained in 1 minute = 3.75 inches

So height of the water after 3 minutes is calculated by following steps:

1) find how much water is drained in 3 minutes

2) subtract value obtained in step 1 from total height of water in fish pond

water is drained in 3 minutes = Water drained in 1 minute x 3

[tex]\text {water is drained in } 3 \text { minutes }=3.75 \times 3=11.25[/tex]

Thus water drained in 3 minutes is 11.25 inches

height of the water after 3 minutes = total height of water in fish pond - water drained in 3 minutes

height of the water after 3 minutes = 42.5 - 11.25 = 31.25 inches

Thus height of the water after 3 minutes is 31.25 inches

Final answer:

After draining water at a rate of 3.75 inches per minute for 3 minutes, the height of the water in the pond decreases from 42.5 inches to 31.25 inches.

Explanation:

The question is asking for the height of the water in a pond after draining some amount of water for a specified time. Initially, the pond has a water height of 42.5 inches. Water is being drained at a rate of 3.75 inches per minute. To find the height of the water after 3 minutes, we need to calculate the total amount of water drained and subtract it from the initial height.

Total water drained in 3 minutes = Drain rate per minute × number of minutes = 3.75 inches/minute × 3 = 11.25 inches.

Height of water after 3 minutes = Initial height - Total water drained = 42.5 inches - 11.25 inches = 31.25 inches.

Therefore, the height of the water in the pond after 3 minutes is 31.25 inches.

Answer:

d. x < 9.02 or x > 9.48 because |x − 9.25| > 0.23

Step-by-step explanation:

Given,

The standard weight of the pack = 9.25 oz,

The pack must weigh within 0.23 oz of the target weight to be accepted.

i.e. if x represents the weight of the pack,

If x > 9.25 oz

then x - 0.925 ≤ 0.23  ......(1)

if x < 9.25

then 9.25 - x ≤ 0.23

⇒ -(x-9.25) ≤ 0.23   .......(2)

From equation (1) and (2),

The accepted range of mass is,

|x-9.25| ≤ 0.23

Hence, the rejected range mass would be,

|x-9.25| > 0.23

⇒ x - 9.25 > 0.23 or -x + 9.25 < 0.23

⇒ x > 0.23 + 9.25 or -x > 0.23 - 9.25

⇒ x > 9.48 or - x > −9.02

⇒ x > 9.48 or  x < 9.02

Since in the question, there are no ordered pairs given so you can consider the below explanation to check which ordered pairs satisfies the inequality 3x-4y>12

Step-by-step explanation:

We need to identify which ordered pair(x,y) satisfies the inequality 3x-4y>12

The ordered pair (x,y) which satisfies the inequality will be the values of x and y that satisfies the inequality given 3x-4y>12

So, if x= 2 and y = 2 then the inequality will be:

3x-4y>12

3(2)-4(2)>12

6-8>12

-2>12 is false because -2 is not greater than 12

So, ordered pair (2,2) doesn't satisfy the inequality 3x-4y>12

Now if x = 10 and y = 2 then the inequality will be:

3x-4y>12

3(10)-4(2)>12

30-8>12

22>12 is true because 22 is greater than 12.

So, ordered pair (10,2) satisfies the inequality 3x-4y>12

Since in the question, there are no ordered pairs given so you can consider the above explanation to check which ordered pairs satisfies the inequality 3x-4y>12

Keywords: Solving inequalities

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To find the order pair (x,y) satisfying the inequality 3x - 4y > 12, substitute potential order pairs for x and y and evaluate. If the result is greater than 12, then the order pair satisfies the inequality.

The inequality given is 3x - 4y > 12. To find the order pair (x,y) that satisfies this inequality, let's plug in some potential solutions and see which one works.

For example, let's try the order pair (6, 1): 3(6) - 4(1) = 18 - 4 = 14, which is greater than 12, so (6,1) does satisfy the inequality.

But if we try the order pair (2, 3): 3(2) - 4(3) = 6 - 12 = -6, which is not greater than 12, so (2,3) does not satisfy the inequality.

Through these examples, you can see how we can find potential solutions to the inequality by substituting different order pairs for x and y.

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