The change between outputs found by dividing one output by its previous output is called...​

Answer:

Amount = $ [tex]2080[/tex]

Step-by-step explanation:

Given ,

To Find : The Amount

We can derive the SI i.e the Simple Interest by the formula,

[tex]SI = \frac{PRT}{100}[/tex]

Applying the values into the given equation we get,

[tex]SI = \frac{2000X8X5}{100}[/tex]

Substituting we get,

[tex]SI = 80$[/tex]

[tex]Amount =[/tex] [tex]SI + Principal[/tex]

[tex]Amount = 80 + 2000[/tex]

[tex]Amount = $2080[/tex]

The solution of the inequality is less than 1.75 which is shown on the diagram.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The inequality is given below.

5/8 > (1/2)x - 1/4

Simplify the inequality, then we have

5/8 > (1/2) x - 1/4

5/8 + 1/4 > (1/2) x

(5 + 2)/8 > (1/2) x

7 / 8 > (1/2) x

(1/2) x < 7 / 8

x < 7 / 4

x < 1.75

The solution of the inequality is less than 1.75 which is shown on the diagram.

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Answer:

  (f/g)(x) = -(x²+7x)/(x²-9)

Step-by-step explanation:

Given f(x) = x^2 +7x and g(x) = 9 -x^2, you want f/g(x).

The rational function (f/g)(x) is ...

  [tex](f/g)(x)=\dfrac{f(x)}{g(x)}=\dfrac{x^2+7x}{9-x^2}\\\\\\\boxed{(f/g)(x)=-\dfrac{x^2+7x}{x^2-9}}[/tex]

__

Additional comment

We simply use the values of f(x) and g(x) in the desired ratio. No simplification is possible.

A unit vector u in the direction opposite of ⟨−9,−2,−8⟩  is  ⟨-9/√(149) , -2/√(149) , -8/√(149) ⟩

What are vector equations ?

Vector equations allow for the creation of parametric curves. That is, points in space are formed for each value of the parameter by the equation of a vector, where each of its elements has a function with an independent variable that we refer to as a parameter.

Let unit vector u be = k⟨−9,−2,−8⟩.

√(81k^2 + 4k^2 + 64k^2) = 1

SO k = 1/√(149)

So a unit vector u in the direction opposite of v=⟨−9,−2,−8⟩ = (-9/√(149) , -2/√(149) , -8/√(149))

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The system of inequalties on the graph is:

x  + 4y ≤ 15

y ≥ 0

First, we can see a solid line at y = 0 and we have the region above that line shaded, so one of the inequalities is:

y ≥ 0.

The other inequality is a solid line with a negative slope and the shaded region is below the line.

The only option that has these characteristics is:

x  + 4y ≤ 15

4y ≤ - x + 15

y ≤ (-1/4)x + 15/4

Then the system of inequalities is:

x  + 4y ≤ 15

y ≥ 0

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The value of the expression P(x) in the function for the weight of a thin water layer between heights x and Δx, P(x)·Δx, is;  P(x) = 47040·x N/m

A function is a rule that defines the relationship between a set of input and outputs variables, such that each input variable is mapped to only one output variable.

The parameters of the right prism are presented as follows;

Height of the isosceles triangular face = 5 meters

Width of the triangle = 4 meters

The length of the right prism = 6 meters

The function for the weight of a thin water layer between height x and height x + Δx = P(x)·Δx

Weight = Density × Volume × Gravity

Volume = Cross sectional area × Height

Cross sectional area = Width × Length = Width × 6

Using similar triangles, we get;

Width, W = (4/5)×x

Therefore; Cross sectional area = (4/5)×x × 6

Weight = Density × Cross sectional area × Gravity × Height

The height of the section = Δx, therefore;

Weight = Density × Cross sectional area × Gravity × Δx = P(x) × Δx

Therefore; Density × Cross sectional area × Gravity = P(x)

P(x) = ρ × (4/5) × x × 6 × g

The density of water, ρ = 1000 kg/m³

g = 9.8 m/s²

P(x) = 1000 kg/m³ × (4/5) × x × 6 m × 9.8 m/s² = 47040·x N/m

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Answer:

71

Step-by-step explanation:

the circle standard form is

(x - h)² + (y - k)² = r²

r being the radius, (h, k) being the coordinates of the center.

fully multiplied that is

x² - 2hx + h² + y² - 2ky + k² = r²

we have here

4x² + 12x + 4y² - 40y - B = 0

our first step is to bring this back to an excision in x² and y². so, we divide everything by 4.

x² + 3x + y² - 10y - B/4 = 0

by comparing this to the general equation we see

3 = -2h

h = -3/2 = -1.5

-10 = - 2k

k = 5

-B/4 = h² + k² - r² = 9/4 + 25 - (3×sqrt(5))² =

= 9/4 + 25 - 9×5 = 9/4 + 25 - 45 = 9/4 - 20

-B = 9 - 80 = -71

B = 71

The new equation is y=-1/2x+5.  An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used.

Our first line in this equation is y=2x-1. By applying the equation y=mx+b, where "m" stands for the slope, we can see that our "m" in this instance is 2. then negate 2. It turns into -2.

Change the denominator and numerator after that. Since -2 is actually -2/1, let's change it to -1/2. The perpendicular line's slope is that.

We must now make it pass through (-2,6). We just have a line like this to work with at the moment: y=-1/2x

Plugging in the x-coordinate of our target location, -2, yields y=-1/2(-2), or 1. But hold on, because the y-coordinate we were given is 6, shouldn't y be equal to 6 as well? Yes! The only thing left to do is to add 5 to get from 1 to 6!

The complete question  is,

Write an equation for a line perpendicular to y = 2 x − 1 and passing through the point (-2,6)

Write an equation for a line perpendicular to y=2x−1 and passing through the point (-2,6)

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Answer:

6

Step-by-step explanation:

Given logarithmic expression:

[tex]\log_{4}\left(4\right)+\log_{4}\left(16\right)+\log_{4}\left(64\right)[/tex]

Rewrite 16 as 4² and 64 as 4³:

[tex]\implies \log_{4}\left(4\right)+\log_{4}\left(4\right)^2+\log_{4}\left(4\right)^3[/tex]

[tex]\textsf{Apply the log power law}: \quad \log_ax^n=n\log_ax[/tex]

[tex]\implies \log_{4}\left(4\right)+2\log_{4}\left(4\right)+3\log_{4}\left(4\right)[/tex]

[tex]\textsf{Apply log law}: \quad \log_aa=1[/tex]

[tex]\implies 1+2(1)+3(1)[/tex]

Simplify:

[tex]\implies 1+2+3[/tex]

[tex]\implies 3 + 3[/tex]

[tex]\implies 6[/tex]

Answer: 222 gallons of gasoline to travel 444 miles.

Step-by-step explanation: To find how much gasoline the boat needs to travel 444 miles, we need to use the formula:

distance = rate x time

Where distance is the total distance to be traveled, rate is the distance per unit of fuel (370 miles/185 gallons) and time is the amount of fuel required to travel 444 miles.

So we can calculate the fuel required as:

Fuel = (distance) / (rate)

Fuel = (444 miles) / (370 miles/185 gallons) = 444/ (370/185) = 444/2 = 222 gallons.

So the boat needs 222 gallons of gasoline to travel 444 miles.

Answer: So, after 3 years and 5 months, the total amount of simple interest earned on an investment of $2500 at a 6% interest rate would be $525.

Step-by-step explanation:

To calculate the simple interest on an investment of $2500 at a 6% interest rate for 3 years and 5 months, you would use the formula:

Simple Interest = (Principal x Interest Rate x Time in Years)

In this case, the time in years would be 3.5 (3 years and 5 months)

Simple Interest = (2500 x 0.06 x 3.5) = $525

So, after 3 years and 5 months, the total amount of simple interest earned on an investment of $2500 at a 6% interest rate would be $525.

Answer:

-320

Step-by-step explanation:

Use the formula

Tₙ = a + (n - 1)d where

a is the first term (in this case, -2)

n is the required term ( in this case, 54)

d is the common difference (in this case, -6)

54th term = -2 + 53 x -6 = -320

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Answer:

The slope is 3

Step-by-step explanation:

y = mx + b  The slope is the m.  It is the number before the letter x.

Answer: The hour hand of a clock makes one complete rotation, 360 degrees, in 12 hours or 720 minutes.

The hour hand of a clock turns 30 degrees in one hour or 0.5 degrees in one minute.

In this case, the hour hand is turned anticlockwise from 2 pm to 9 am, which is 21 hours.

So, it will have turned 21 * 30 = 630 degrees.

It is important to note that this answer only accounts for the rotation of the hour hand and does not take into account the rotation of the minute hand.

Step-by-step explanation:

The respective answers are 5 and 4

Addition in math is a process of combining two or more numbers. Addends are the numbers being added, and the result or the final answer we get after the process is called the sum.

Given: 5 means 5+0+0 which equals to 5

4 means 4+0+0+0 which equals 4

Hence the respective answers are 5 and 4

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Answer:

Let's call the total amount of the lottery winnings x.

If Kelly took one half of the earnings, then she took 1/2x and Toey took 1/2x as well.

Toey spent 1/4 of his earnings, so he spent 1/4*(1/2x) = 1/8x

So Joey spent 1/8 of the total lottery winnings.

After evaluating the expression 58 + (4x12-40) to the power of 2, we get 4356 or 4.356 ×10³ in scientific notation.

An expression or mathematical expression is a finite combination of symbols that are well-formed in accordance with context-dependent rules. To help define the logical syntax and order of operations, mathematical symbols can be used to represent variables, operations, functions, brackets, punctuation, and grouping.

Authors frequently distinguish between a formula and an expression, with the former referring to a mathematical object and the latter to a statement about such an object.

We have been asked to evaluate the Expression

​58 + (4x12-40) to the power of 2

⇒ (​58 + (4x12-40))²

Use (a + b)² = a² + b² + 2ab

= 58² + (4x12-40)² + 2(​58)(4x12-40)

= 3364 + (4x12-40)² + 116(4x12-40)

= 3364 + (48-40)² + 116(48-40)

= 3364 + (8)² + 116(8)

= 3364 + 64 + 928

= 4356

= 4.356 ×10³

Thus, After evaluating the expression 58 + (4x12-40) to the power of 2, we get 4356 or 4.356 ×10³ in scientific notation.

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Explanation:

The points do not fall on the same line, but the points trend upward as we move to the right. This means that a straight line can get somewhat close to all of the points to represent the average trend of what's going on.

Answer:

linear :)

Step-by-step explanation:

ive already answered this question and got it right <3

The standard deviation of the number of restaurants that failed within a year is 3.46.

The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data distant from the mean. The normal distribution will show as a bell curve on a graph.

Given that the probability that an independent restaurant will fail in the first year is 48%. Therefore, the probability can be written as,

p = 48% = 0.48

q = 1-p = 1-0.48 = 0.52

Also, Kristen obtains a random sample of 66 independent restaurants that opened in her city more than one year ago and determines if each one had closed within a year. Therefore, the sample size is 53.

n = 53

Now, the standard deviation can be calculated as,

Standard deviation, σ = √(npq)

                                    = √(53 × 0.48 × 0.52)

                                    = √11.9808

                                    = 3.46

Hence, the standard deviation is 3.46.

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The average rate of change of g(x) =5x^3+4/x^2 on the interval [-1,2] is -2

A function can be defined as a law, rule or expression explaining the relationship between two variables.

These variables are called;

From the information given, we have the function;

g(x) =5x^3+4/x^2

For the interval, {1, -2}

Let's substitute the value of x as 1

g(1) = 5(1)³ + 4/(1)²

find the values

g(1) = 5 + 4/1

g(1) = 9/1 = 9

For x = -2

g(-2) = 5(-2)³ + 4/(-2)²

find the values and substitute

g(-2) =5(-8) + 4/ -8

g(-2) = -40 + 4/-8

add the numerators

g(-2) = -36/8

divide the values

g(-2) = -9/2

The average change = 9 ÷ -9/2 = 9 × 2/-9 = -2

Hence, the value is -2

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The group of 20 students will save $144 by using the promotional deal. Half of the group, or 10 students, will get the free cotton candy, so that's $30 saved. 14 of the students will get the free soda, so that's another $28 saved. Added together the group of 20 students will save $58 on the cotton candy and $28 on the soda for a total savings of $144.

The required transformations are

A function is a mathematical equation which shows the relationship between two variables.

Transformation is the performing of the mathematical operations of dilation, translation, relection and rotation on a function.

Given the function [tex]f(x) = 2^{3\sqrt{x} }[/tex] which is transformed into the function [tex]g(x) = 2^{3\sqrt{x - 4}} + 5[/tex], we describe the transformations as follows.

First Since we have x - 4,  [tex]f(x) = 2^{3\sqrt{x} }[/tex] is shifted four units to the right. So, we have , [tex]g(x) = 2^{3\sqrt{x - 4}}[/tex].

Also, since 5 is added  to [tex]g(x) = 2^{3\sqrt{x - 4}}[/tex].   [tex]g(x) = 2^{3\sqrt{x - 4}}[/tex]. is shifted 5 units up to get    [tex]g(x) = 2^{3\sqrt{x - 4}} + 5[/tex],

So, the required transformations are

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Answer:

The answer is b.

Step-by-step explanation:

For first row first column=18+72+10=100

For first row second column=-9+48-7=32

For first row third column=27-96+7=-62

Repeat this for the rest.

Hope this helps you.

15ft

Step-by-step explanation:

bc I said so..............

Answer:

To determine how much you should invest to receive $100,000 on the maturity date, you will need to calculate the present value of the cash flows at the beginning of the investment. The present value is the amount of money you would need to invest today to receive a certain amount at a future date, taking into account the time value of money and the interest rate.

You can calculate the present value by using the formula:

PV = CF / (1 + r)^t

Where:

PV = present value

CF = cash flow (the amount you will receive at the maturity date)

r = interest rate

t = time (in years)

The first 18 months, the interest rate is 8% per year, which is equivalent to 8/12 = 0.67% per month.

The next 6 months, the interest rate is 1.5% per quarter, which is equivalent to 1.5/4 = 0.375% per month.

The last 12 months, the interest rate is 2% per semi-annual, which is equivalent to 2/2 = 1% per month.

For the first 18 months, the present value of the cash flow is:

PV = 100,000 / (1 + 0.0067)^(18/12) = 95,167

For the next 6 months, the present value of the cash flow is:

PV = 95,167 / (1 + 0.00375)^(6/12) = 94,853

For the last 12 months, the present value of the cash flow is:

PV = 94,853 / (1 + 0.01)^(12/12) = 94,853

So, to receive $100,000 on the maturity date, you should invest 94,853 dollars to the nearest dollar.

There is no difference between the population mean customer satisfaction scores for the two retailers, according to p-value: 0.33049.

chosen at random (purely random, unpredictable). Every person in the demographic being surveyed should have an equal chance of being chosen. She gave an example of a simple representative sample, choosing 25 names at random from a group of 250 employees. The sampling in this case is random since there are 250 of her coworkers in total, and every one has an equal chance of being picked. Researchers select people at random from a population using simple random sampling, which is a type of probability sampling. Every member of the population is given an equal chance at selection.

Given that,

mean(x)=86

standard deviation , σ1 =12

number(n1)=250

y(mean)=85

standard deviation, σ2 =12

number(n2)=300

null,  u1 = u2

alternate, H1: μ1 != u2

level of significance, alpha = 0.05

we got |zo | =0.973  & | z alpha | =1.96

(b) test statistic: 0.97

There is no difference between the population mean customer satisfaction scores for the two retailers, according to p-value: 0.33049.

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The model shows that there are 10 pieces that are each 0. 2 ft long.

From the given model, we see that Devin cut the ribbon in equal proportions. The number of proportions can be found by summing the different sections on the ribbon.

This number comes to 10 sections which means that Devin cut the ribbon into 10 pieces.

The length of each of these pieces is:

= Length of entire ribbon / Number of pieces

= 2 / 10

= 0. 2 ft long

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Answer: 90

Step-by-step explanation:

If you're looking for the number of times she has to visit the movie theater in order to have 310 points for the free movie ticket then;

310-85 = 225

225/2.5 = 90

Eva needs 90 visits before she can get a free movie ticket.