Differentiation

Please help me! ​

The corresponding answers for each student plan are:

plan A: 15 years

plan B: 5 years

plan C: 10 years

plan D: 9 years

Thus, first, the graph corresponding to each of the plans must be analyzed. The Y-axis corresponds to money and the x-axis corresponds to the time in years.

Thus, in-plane A, it can be observed that to reach the desired value, the graph will be projected in exponential, so it will be close to 15 years. In plan B, this projection will be reached around 5 years. In plans C and D, this projection will be 10 years and 9 years respectively.

To schedule the tasks on two machines in a way that minimizes the time for both machines to finish their tasks, we can use the "Longest Processing Time" algorithm.

1. Sort the list of times in descending order: (18, 16, 12, 8, 6).

2. Assign the tasks one by one to the machine with the currently shorter total processing time.

  Machine 1: (18) -> Total time: 18

  Machine 2: (16) -> Total time: 16

  Machine 1: (12) -> Total time: 30

  Machine 2: (8) -> Total time: 24

  Machine 1: (6) -> Total time: 36

3. The best time for both machines to finish their tasks is the maximum of the two total times: 36.

the correct answer is:

D) 35 (Incorrect)

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Answer:

so confused like what is this

Step-by-step explanation:

Answer:

9363960

Step-by-step explanation:

The calculator says otherwise -.-

but yeah, hope it helps.

Answer:

b

Step-by-step explanation:

it doesn't go to the y or x axis so  B is it

Answer: y = 40 + x

In the morning, Emily studied 40 minutes for an exam

In the evening he studied additional x minutes

The initial minutes he studied = 40 minutes

The additional minutes = x minutes

The total minutes = initial minutes + additional minutes

y = 40 + x

Where y = total minutes studies

Therefore, the total minutes he studied is y = 40 + x

We can arrange the 2023 squares to cover the unit square, with overlaps allowed.

We can prove that a collection of 2023 closed squares of total area 4 can be arranged to cover a unit square by using the pigeonhole principle. Since the total area of the squares is 4, the average area of each square is 4/2023. Let's take a unit square and divide it into 2023 smaller squares of area (1/2023) each. By the pigeonhole principle, we can assign one of the 2023 squares to each of the smaller squares. Since the average area of each square is 4/2023, each of the assigned squares will overlap with at most 4 other squares. Therefore, we can arrange the 2023 squares to cover the unit square, with overlaps allowed.

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Answer:

k = \(\frac{7}{9}\)

Step-by-step explanation:

The equation of proportionality is

y = kx ← k is the constant of proportionality

y = \(\frac{7}{9}\) x ← is in this form

with k = \(\frac{7}{9}\)

Answer:

\(\frac{7}{9}\)

Step-by-step explanation:

A direct variation function is in this general form:

\(y = kx\\\rule{150}{0.5}\\k -\text{ Constant of Proportionality}\)

Since \(\frac{7}{9}\) is in 'k's place, it is the Constant of Proportionality.

Hope this helps you.

Let's call the width of the rectangle "w".

According to the problem, the length of the rectangle is 12 meters more than 5 times the width, so we can write that as:

L = 5w + 12

And the area is given as 32 square meters, so we can write that as:

A = L * w = 32

Now we have two equations:

5w + 12 = L

L * w = 32

We can use the first equation to substitute the value of L in the second equation:

L = 5w + 12

32 = (5w + 12) * w = 5w^2 + 12w

Expanding the right side of the equation, we get:

32 = 5w^2 + 12w

Now we have a quadratic equation that we can solve for w. To do this, we can use the quadratic formula:

w = (-b ± √(b^2 - 4ac)) / 2a

where a = 5, b = 12, and c = -32. Plugging in these values, we get:

w = (-12 ± √(12^2 - 4 * 5 * -32)) / (2 * 5)

w = (-12 ± √(144 + 640)) / 10

w = (-12 ± √(784)) / 10

w = (-12 ± 28) / 10

w = (16 / 10) or ( -40 / 10)

w = 1.6 or -4

Since the width cannot be negative, the width must be 1.6 meters.

To find g(-2), we'll substitute -2 for x in the equation g(x) = -4x² - 5x + 9. So,g(-2) = -4(-2)² - 5(-2) + 9g(-2). The value of g(-2) is -6.

To find g(-2), substitute -2 for x in the equation

g(x) = -4x² - 5x + 9 to get

g(-2) = -6 + 9g(-2)

We are given three functions as follows:

f(x) = (1/3)x - 5, g(x)

= -4x² - 5x + 9, and

h(x) = 1/(x - 8) + 3.

We are asked to find g(-2), which is the value of g(x) when x = -2.

Substituting -2 for x in the equation g(x) = -4x² - 5x + 9, we get

g(-2) = -4(-2)² - 5(-2) + 9.

This simplifies to g(-2) = -16 + 10 + 9 = -6.

Hence, g(-2) = -6.

The value of g(-2) is -6.

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From the graph, we can observe that as x increases, T(x) also increases.

To sketch the graph, we need to select appropriate values of x and then use these values to calculate the corresponding values of y. Then we can plot these ordered pairs and join them to get the graph.

The function given is: \[ T(x)=130 x+32,000 \]

So, let us select some values of x and use them to calculate the corresponding values of y.

Let us choose the values of x from 0 to 20:

Year since 1996,

                      x 0, 1, 2, 3, 4, 5, 10, 15, 20

Value of T(x), y 32000, 13130, 26260, 39390, 52520, 65650, 138000, 209350, 280700

Now, let us plot these ordered pairs and join them to get the graph:

From the graph, we can observe that as x increases, T(x) also increases.

This is because the amount of trash in a landfill increases with time.

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Problem 1

Part (a)

It is possible to find the equation of the line of best fit by hand, but it's much more efficient to use technology. That could mean a graphing calculator, an online tool, or some computer software installed. I'm going to use GeoGebra. Specifically, I'm using the "FitLine" command to find the regression line.

The equation of line of best fit is y = -2.45x + 11.83

There's not much to say in terms of steps, since it's basically a calculator problem. Doing this by hand would take a lot longer than it should be.

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

Part (b)

Plug in x = 2.3 and evaluate

y = -2.45x + 11.83

y = -2.45*2.3 + 11.83

y = 6.195

Answer: 6.195

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

Part (c)

We'll compare the result from the previous part (6.195) to the y value in the table (6.2)

The difference is 6.2 - 6.195 = 0.005

This means the estimated value is off by 0.005 and this is an underestimate (since 6.195 is smaller than 6.2)

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

Problem 2

To be perfectly honest, I'm not sure what's going on here. It seems like there's missing context to the problem. Perhaps a data table that got cut off or this is referring to a previous problem.

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

Problem 3

Recall that y = mx+b is the slope intercept form

m = slope

b = y intercept

We simply read off the values of the given equation y = 0.404x - 5.18 to see that 0.404 is the slope and -5.18 is the y intercept

The slope tells us that each time x goes up by 1, y will increase by an estimated amount of 0.404; this represents the unit rate or speed. In this context, it means the height goes up by about 0.404 cm per day. This is an estimated value because the regression line itself is a collection of estimated points.

The y intercept is where the graph crosses the y axis. It always occurs when x = 0. The x refers to the day number. Day 0 is basically the starting day. So the y intercept being -5.18 means the estimated height is -5.18 cm on the starting day. At first glance, it might not seem possible to have a negative height. But simply think of negative heights as below ground level, much like how the negative y values are below the x axis.

In other words, the plant is estimated to start off at about 5.18 cm below ground level. This is a reasonable assumption because the seed is buried into the ground (assuming at this level more or less) and it then grows upward.

Answer: 8/9

Step-by-step explanation:

The time the train takes to travel and the 45 miles distance from Ashford to Bromley indicates that the average speed and the difference between the average speeds are;

a) 30 mph

b) 3 mph

The speed is the rate at which the position of the train is changing with time.

The distance between Ashford and Bromley = 45 miles

The time it takes the train = 20:05 - 18:35 = 1 hour 30 minutes = 1.5 hours

a) The average speed = Total distance ÷ Time taken

Therefore;

Average speed of the train = 45 miles ÷ 1.5 hours = 30 miles per hour

b) The time the train leaves Ashford the following day = Normal time = 18:35

The time the train arrives Bromley = 10 minutes late = 10 + 20:05 = 20:15

The time it takes the train = 20:15 - 18:35 = 1 hours 40 minutes = 1 2/3 hours = 5/3 hours

The average speed of the train the following day is therefore;

Average speed = 45 miles ÷ 5/3 hours = 27 miles per hour

The difference between the average speed of the train on the two days is therefore; 30 mph - 27 mph = 3 mph

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The magnitude of the earthquake in India can be found by multiplying the magnitude of the earthquake in Japan (7.2) by 25.

The Richter scale is used to measure the magnitude of earthquakes. It is a logarithmic scale, which means that each whole number increase on the Richter scale represents a tenfold increase in the amplitude of the seismic waves.

Given that the earthquake in Japan registered 7.2 on the Richter scale, and the earthquake in India was 25 times as intense, we can find the magnitude of the earthquake in India by multiplying the magnitude of the earthquake in Japan by 25:

Magnitude of earthquake in India = Magnitude of earthquake in Japan * 25

Magnitude of earthquake in India = 7.2 * 25 = 180

It's important to note that the Richter scale measures the amplitude of seismic waves and not the actual energy released by the earthquake. The Richter scale is logarithmic, so each whole number increase represents a tenfold increase in the amplitude and approximately 31.6 times more energy released.

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Answer: x = 12, y = 15

Step-by-step explanation: 12/15 reduces to 4/5 because 12 divided by 3 is 4 and 15 divided by 3 is 5. 12 + 3 is 15 so if you add 3 to the numerator, you get 15/15, which is equal to 1.

Answer:

Step-by-step explanation:

We need to subtract that sum from the total number of miles Hannah needs to drive on her trip:450.5 - 251 = 199.5 Therefore, Hannah has 199.5 miles left to drive on the third day of her trip.

Here's an example problem that falls under problem type 1:Problem: Hannah is going on a road trip. She will be driving a total of 450.5 miles. On the first day, she drives 120.25 miles and on the second day, she drives 130.75 miles.

To solve this problem, we need to first add the number of miles Hannah drove on the first and second day:120.25 + 130.75 = 251.

Then, we need to subtract that sum from the total number of miles Hannah needs to drive on her trip:450.5 - 251 = 199.5 Therefore, Hannah has 199.5 miles left to drive on the third day of her trip.

In this problem, we needed to perform multiple decimal operations (addition and subtraction) to arrive at the solution.

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Answer:

2. 240     3. 100

Step-by-step explanation:

2. Create a chart 3/4 and 180/x and place them side by side

multiply 4 times 180 then divide by 3 to get 240

3 Create another chart 3/5 then 60/x and multiply 5 times 60 and divide that by 3 to get 100

Answer:

1/5 or 0.2

Step-by-step explanation:

Conversion a mixed number 1 1/ 5

to a improper fraction: 1 1/5 = 1 1/ 5

= 1 · 5 + 1/ 5

= 5 + 1/ 5

= 6/ 5

To find a new numerator:

a) Multiply the whole number 1 by the denominator 5. Whole number 1 equally 1 * 5/ 5

= 5/ 5

b) Add the answer from previous step 5 to the numerator 1. New numerator is 5 + 1 = 6

c) Write a previous answer (new numerator 6) over the denominator 5.

One and one fifth is six fifths

Subtract: 6/ 5

- 2/ 5

= 6 - 2/ 5

= 4/ 5

For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(5, 5) = 5. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 5 × 5 = 25. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - six fifths minus two fifths = four fifths.

Multiple: the result of step No. 2 * (-3/ 4

) = 4/ 5

* (-3/ 4

) = 4 · (-3)/ 5 · 4

= -12/ 20

= -3 · 4/ 5 · 4

= -3/ 5

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(-12, 20) = 4. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - four fifths multiplied by minus three quarters = minus three fifths.

Multiple: the result of step No. 3 * 3 = -3/ 5

* 3 = -3 · 3/ 5 · 1

= -9/ 5

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(-9, 5) = 1. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - minus three fifths multiplied by three = minus nine fifths.

Divide: the result of step No. 4 : (-9) = -9/ 5

: (-9) = -9/ 5

· -1/ 9

= -9 · (-1)/ 5 · 9

= 9/ 45

= 9 · 1/ 9 · 5

= 1/ 5

Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of -9/ 1

is 1/ -9

) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, cancel by a common factor of 9 gives 1/ 5

.

In other words - minus nine fifths divided by minus nine = one fifth.

Answer:

y=2x-4

Step-by-step explanation:

sorry if I get this wrong I'm slowly understanding slope intercept form

Answer:

Step-by-step explanation:

Answer: $156.25

Step-by-step explanation:

You need to find the cost of the carpet. Then, to find the service fee, take 5% of the carpet cost. After that, add 100 to that product.

Step 1: Set the value of x to the number of square feet.

x = 150

f(150) = 7.5 * 150.

Step 2: Multiply

7.5 * 150 = 1125

Step 3: Find 5% of 1125.

5% = 0.05

0.05 * 1125 = 56.25

Step 4: Add 100 to the product.

56.25 + 100 = $156.25

Answer:

$17.60

Step-by-step explanation:

We know that Emma spent $16.00 on her food.

There is a 10% tax.

Therefore, the total bill will be the price without tax plus the tax.

The price without tax is $16.00.

Tax is 10%. So, the tax will be 10% of 16.

10% of 16 is the same as 0.1(16) or 1.6.

So, the tax is $1.60.

Therefore, the total bill is:

$16.00+$1.60=$17.60.

Emma’s total bill comes to $17.60

The 95% confidence interval for the true proportion of all auto accidents involving teenage drivers is approximately (0.1205, 0.1927).

To find the 95% confidence interval for the true proportion of all auto accidents involving teenage drivers, we can use the formula for the confidence interval for a proportion.

The formula for the confidence interval is:

CI = p1 ± Z * √((p1 * (1 - p1)) / n)

Where:

CI is the confidence interval,

p1 is the sample proportion (proportion of accidents involving teenage drivers),

Z is the Z-score corresponding to the desired confidence level (95% confidence level corresponds to Z ≈ 1.96),

n is the sample size (number of accidents checked).

Given:

Number of accidents checked (sample size), n = 582

Number of accidents involving teenage drivers, x = 91

First, we calculate the sample proportion:

p1 = x / n = 91 / 582 ≈ 0.1566

Now we can calculate the confidence interval:

CI = 0.1566 ± 1.96 * √((0.1566 * (1 - 0.1566)) / 582)

Calculating the standard error of the proportion:

SE = √((p1 * (1 - p1)) / n) = √((0.1566 * (1 - 0.1566)) / 582) ≈ 0.0184

Substituting the values into the formula:

CI = 0.1566 ± 1.96 * 0.0184

Calculating the values:

CI = 0.1566 ± 0.0361

Finally, we can simplify the confidence interval:

CI = (0.1205, 0.1927)

Therefore, the 95% confidence interval for the true proportion of all auto accidents involving teenage drivers is approximately (0.1205, 0.1927).

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The length of the arc s is 6.283 inches.

The length of an arc is given by the formula,

\(\rm{ Length\ of\ an\ Arc = 2\times \pi \times(radius)\times\dfrac{\theta}{360}\)

where

θ is the angle, which arc creates at the center of the circle in degrees.

Radius, r = 8 in.

Angle, θ = 45°,

\(\rm{ Length\ of\ an\ Arc = 2\times \pi \times(radius)\times\dfrac{\theta}{360}\)

\(\rm{ Length\ of\ the\ Arc\ s = 2\times \pi \times(8)\times\dfrac{45}{360}\)

\(\rm{ Length\ of\ the\ Arc\ s =6.283\ inches.\)

Hence, the length of the arc s is 6.283 inches.

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The approximate length of arc s on the given circle is; 6.28inches

The length of an arc is given by the formula;

Therefore,

Length, L = (45/360) × 2 × 3.14 × 8

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Answer:

4 feet

Step-by-step explanation:

2 feet = 24 inches

6 inches = 1/2 foot

There are 12 months in a year.

12*(1/2) = 6 feet (72 inches)

OR

12*6 = 72 inches (6 feet)

If it rained 6 inches or 1/2 foot every month of a year, it would rain 6 feet or 72 inches that year.

6-2 = 4 feet

This would be 4 feet of rain more than Springfield's world record.

Answer:

30 squares?

Step-by-step explanation: