This assignment is already late cause I’m terrible with time management but please help

Answer:

She should walk approximately 1,463.34369 feet along the sidewalk going to the east, then walk the remaining straight line distance along the grass.

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

Explanation:

Refer to the diagram below.

Alaina starts at point A. If she stays on the sidewalk the entire time, then she can go from A to C to D in that order.

If she takes the direct line route, then she would go from A to D across the grass entirely.

The two paths have pros and cons. The optimal solution is a mix of the two routes. This means she'll be on the sidewalk for some amount of time, and then cut along the grass once reaching a certain point.

Let's say point B is the point where she decides to cut along the grass. In the diagram below, I made \(\text{BC} = x\) so that I could find \(\text{BD} = \sqrt{x^2+600^2}\) through the pythagorean theorem fairly quickly.

If \(\text{BC} = x\), then the remaining bit of the east/west side walk is \(\text{AB} = 2000-x\) since the two portions must add to 2000 feet.

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

If she travels along the side walk at a rate of 6 ft/sec, and travels 2000-x feet (from A to B), then it will take her

time = distance/speed = \(\frac{2000-x}{6}\) seconds

Then if she cuts across the grass to follow path BD, then she'll take another

time = distance/speed = \(\frac{\sqrt{x^2+600^2}}{4}\) seconds since she's traveling 4 ft/sec here.

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

If Alaina goes from A to B to D in that order, then she takes a total of

\(\text{(time from A to B)}+\text{(time from B to D)}\\ = \frac{2000-x}{6}+\frac{\sqrt{x^2+600^2}}{4}\)

That represents the total time taken when following this path at those specified speeds mentioned.

The goal is to find the minimum of that function. So we'll need to compute the derivative.

\(f(x) = \frac{2000-x}{6}+\frac{\sqrt{x^2+600^2}}{4}\\\\ f \ '(x) = -\frac{1}{6}+2x*\frac{1}{2*4\sqrt{x^2+600^2}}\\\\ f \ '(x) = -\frac{1}{6}+\frac{x}{4\sqrt{x^2+600^2}}\\\\\)

Set the derivative equal to zero and solve for x

\(f \ '(x) = 0\\\\ -\frac{1}{6}+\frac{x}{4\sqrt{x^2+600^2}} = 0\\\\ \frac{x}{4\sqrt{x^2+600^2}} = \frac{1}{6}\\\\ 6x = 4\sqrt{x^2+600^2}\\\\ (6x)^2 = \left(4\sqrt{x^2+600^2}\right)^2\\\\ 36x^2 = 16(x^2+600^2)\\\\ 36x^2 = 16x^2+16*600^2\\\\\)

\(36x^2 = 16x^2+5,760,000\\\\ 36x^2-16x^2 = 5,760,000\\\\ 20x^2 = 5,760,000\\\\ x^2 = 5,760,000/20\\\\ x^2 = 288,000\\\\ x = \sqrt{288,000}\\\\x \approx 536.65631\)

If you were to perform the first derivative test, you should find that the local min occurs at roughly x = 536.65631

This means she must walk a approximately 2000-x = 2000-536.65631 = 1,463.34369 feet when going from A to B such that to minimize the walking time.

Side note: you can use the minimum feature on your calculator to confirm the answer

Answer:

Subtract 3 3/4 from 10 1/2.  Note that the LCD is 4, so 10 1/2 = 10 2/4.

What is    10 2/4

              -  3 3/4

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

                    ?

Since 2/4 is smaller than 3/4, you must borrow 1 from that 10.

Now your problem looks like   9 6/4

                                              -3 3/4

                                            ----------

                                                6 3/4   (answer)

The remnant of the board is 6 3/4 feet long.

Step-by-step explanation:

jmryhnrfthyj4u5ikjhgtrfrgthyjunr

\(circumference \: of \: circle \: = 2 \: \pi \: r\)

38 = 2πr

r = 38/2π

r = 38÷6.28

r = 6 cm

Answer:15 i think

Step-by-step explanation:

mode is the number that occurs the most

Answer:

x=9

y=27

Step-by-step explanation:

the scale factor is \(\frac{4}{3}\) so 6 × \(\frac{4}{3}\) is x - 1

x-1 is 8

so x is 9.

Answer:

202.5 miles

Step-by-step explanation:

We find the unit rate of the mile per gallon

135/6

= 22.5

We multiply 22.5 by 9 to get the miles they can drive on 9 gallons

22.5 * 9

= 202.5

Answer:

202.5 miles

Step-by-step explanation:

135 miles  divided by 6 = 22.5 x 9 = 202.5 miles

6 gallons  divided by 6 = 1 gallon x 9 = 9 gallons

Answer:

Quadrants: 1, 3, 4. (See explanation for further details)

Step-by-step explanation:

The graphic of the linear function is included below as attachment. The line covers the following quadrants: 1, 3, 4

Answer:

1, 2, 3

Step-by-step explanation:

To find the reference angle of a negative angle, follow these steps:

Determine the positive equivalent: Add 360 degrees (or 2π radians) to the negative angle to find its positive equivalent. This step is necessary because reference angles are always positive.

Subtract from 180 degrees (or π radians): Once you have the positive equivalent, subtract it from 180 degrees (or π radians). This step helps us find the angle that is closest to the x-axis (or the positive x-axis) while still maintaining the same trigonometric ratios.

For example, let's say we have a negative angle of -120 degrees. To find its reference angle:

Positive equivalent: -120 + 360 = 240 degrees

Subtract from 180: 180 - 240 = -60 degrees

Therefore, the reference angle of -120 degrees is 60 degrees.

In summary, to find the reference angle of a negative angle, first, determine the positive equivalent by adding 360 degrees (or 2π radians). Then, subtract the positive equivalent from 180 degrees (or π radians) to obtain the reference angle.

know more about negative angle.

https://brainly.com/question/29090895

#SPJ11

The value of the new home is $142000.

It is important to note that mean simply means the average of a set of numbers that are given. In this situation, Seven houses on a block have values of $105,000, $110,000, $110,000, $117,000, $125,000, $135,000and $138,000.

The addition of the values will be $840000.

When an eighth home is built on the block, the average home value for the block is $122,750. The total will be:

= $122750 × 8

= $982000

The value of the new house will be:

= $982000 - $840000

= $142000

The value is $142000.

Learn more about mean on:

brainly.com/question/1136789

#SPJ1

41.18% of students chose cats, 65.88% chose dogs, and 10.59% chose fish as their favorite pets.

We can analyze the favorite pets among 7th and 8th grade students. There are three pets to consider: cats, dogs, and fish.

In total, there were 70 students in 7th grade and 100 students in 8th grade, making a combined total of 170 students. Out of these students, 36 in 7th grade and 34 in 8th grade preferred cats, totaling 70 students. For dogs, 55 students in 7th grade and 57 in 8th grade chose them as their favorite, totaling 112 students. Lastly, 9 students from each grade preferred fish, which gives us a total of 18 students.

Now, let's list the pets in order from most favorite to least favorite:
1. Dogs (112 students)
2. Cats (70 students)
3. Fish (18 students)

To calculate the percentage of students who chose each pet as their favorite, we will use the following formula: (Number of students who chose the pet / Total number of students) * 100.

- Cats: (70/170) * 100 = 41.18%
- Dogs: (112/170) * 100 = 65.88%
- Fish: (18/170) * 100 = 10.59%

So, 41.18% of students chose cats, 65.88% chose dogs, and 10.59% chose fish as their favorite pets.

To learn more about percentage  click here

brainly.com/question/26352729

#SPJ11

The x.length is the number of rows, which is 4. x[2].length is the number of columns in the 3rd row, which is 5. The expression "new double[4][5]" creates a 2D array of doubles with 4 rows and 5 columns. The correct answer is (b) 4 and 5.

The expression double[][] x = new double[4][5] creates a 2D array x with 4 rows and 5 columns. Therefore, x.length gives the number of rows, which is 4. And x[2].length gives the number of columns in the 3rd row (since array indices start at 0), which is 5. Therefore, the correct option is (b) 4 and 5.

To know more about length:

https://brainly.com/question/28478858

#SPJ4

Answer:

a/4b = 0.075

Step-by-step explanation:

a = 30% of b

a = 30/100 × b

a = 0.3b

The value of a/4b is calculated as:

= 0.3b/4b

= 0.075

Answer:

$4.50 for French Roast

$7.60 for Columbian

Step-by-step explanation:

tried substitution and elimination method but got different answers to I graphed these equations and found the point of intersection

5/3x + 25/8y = 31.25

29/12x + 9/16y = 15.15

point of intersection (4.5, 7.6)

Answer:

Step-by-step explanation:

Thus Markus buy 3.19 pounds of coffee altogether.

Answer:

n = -34/7

Step-by-step explanation:

So what you want to do is find n, which means you have to get n by itself. So first you want to subtract 10 from both sides.

-7n + 10 = -24

      - 10    - 10

-7n = -34

We got a negitive 34 because a negitive - negitive = a negitive

Now, you want to divide -7 from both sides.

-7n = -34

---      ----

-7       -7

n = -34/7

This cannot be simplified so you will keep it as a fraction.

Exponential smoothing is a popular forecasting technique used to predict future trends in time-series data. It works by assigning weights to historical data points, with more recent data points receiving higher weights. The level of smoothing is controlled by a smoothing parameter called alpha, which ranges between 0 and 1. As alpha increases, the influence of older data points decreases, and the model becomes more reactive to recent changes in the data.

When alpha is high, the exponential smoothing model group of answer choices tends to produce sluggish forecasts. This is because the model gives more weight to recent data points, which can cause it to overreact to short-term fluctuations in the data. As a result, the model may miss important trends or patterns in the data that would have been captured by a more balanced weighting scheme.

On the other hand, when alpha is low, the model tends to be more stable and less reactive to short-term changes in the data. This can be useful for predicting long-term trends or for smoothing out noisy data sets.

In summary, the choice of alpha in an exponential smoothing model depends on the characteristics of the data and the goals of the forecast. A high alpha value may be appropriate for short-term forecasting or for data sets with high volatility, while a low alpha value may be more suitable for long-term forecasting or for data sets with low volatility.

Learn more about smoothing here:

https://brainly.com/question/31358866

#SPJ11

The question is to determine whether the given relation on Z is reflexive, symmetric, transitive and forms a partition of integers into 23 equivalence classes, and to explain the answer.

1. Reflexive: A relation is reflexive if x is related to itself for all x in Z.
For this relation, x - x = 23k => 0 = 23k => k = 0.
Since k is an integer, the relation is reflexive.

2. Symmetric: A relation is symmetric if x is related to y implies y is related to x for all x, y in Z.
If x is related to y, then x - y = 23k for some integer k.
Then y - x = -(x - y) = -23k = 23(-k).
Since -k is also an integer, the relation is symmetric.

3. Transitive: A relation is transitive if x is related to y and y is related to z implies x is related to z for all x, y, and z in Z.
If x is related to y, then x - y = 23k1 for some integer k1.
If y is related to z, then y - z = 23k2 for some integer k2.
Then, x - z = (x - y) + (y - z) = 23k1 + 23k2 = 23(k1 + k2).
Since (k1 + k2) is an integer, the relation is transitive.

Since the relation is reflexive, symmetric, and transitive, it is an equivalence relation.

Moreover, this relation forms a partition of the integers into 23 equivalence classes. Each equivalence class contains related elements, each pair of which differs by a multiple of 23. Each class can be represented by one of the possible remainders when dividing an integer by 23. We may perform arithmetic on the classes, similar to how we may perform arithmetic with a clock.

#SPJ11

Answer:

Step-by-step explanation:

800-160=640

640/800=64/80

64/80=16/20

16/20=4/5

Answer=4/5

The fraction of his original money does he have left = 4/5 .

What is a fraction in math?

A boy has = 800 and spends = 160

800-160=640

640/800=64/80

64/80=16/20

16/20=4/5

Therefore, his original money left =4/5

Learn more about fraction

brainly.com/question/10354322

#SPJ4

Answer:

–5 + 8 = 3. Find each sum. 1. –4 + (–8). 2. 14 + 16. 3. –43 + (–12). –12. 30. –55. 4. ... 1. Change the minus sign to a plus. 2. Find the opposite of the 2nd number. 3. Add ... –8 + –2. –3. –8. –10. 4. –3 – 24. 5. 10 – 17. 6. 13 – 9. = –3 + –24. = 10 + –17 ... 30. 5 + 4 x 3 = ____46_______. 12. (7)(9) +. 9. 3 – 20 x 3 = ____6______.

Step-by-step explanation:

The average wattage supplied during a 24 hour time interval is 24 Watts. This is equal to the total energy supplied divided by the time interval, which is 24 hours.

To calculate the total energy supplied, we need to integrate the power function over the 24 hour time interval:

where P(t) is the power function in megawatts.

Alternatively, if we have a table of values of the power function at regular intervals (e.g. every hour), we can estimate the average wattage supplied by taking the average of those values.

Learn more about Wattage:

https://brainly.com/question/25781540

#SPJ4

To find the critical points of the function f(x,y) = x' + y - 6y - 3x + 9, we need to take the partial derivatives with respect to x and y and set them equal to zero.

∂f/∂x = -3 = 0

∂f/∂y = 1 - 6 = -5 = 0

So the system of equations is:

-3 = 0

-5 = 0

These equations have no solutions, which means there are no critical points for this function.

Therefore, the list of critical points is empty.
Hello! I'd be happy to help you find the critical points of the given function. The function is:

f(x,y) = x' + y - 6y? - 3x + 9

To find the critical points, we need to find the partial derivatives of the function with respect to x and y, and then set them equal to zero:

∂f/∂x = ∂(x' + y - 6y? - 3x + 9)/∂x
∂f/∂y = ∂(x' + y - 6y? - 3x + 9)/∂y

Now, let's calculate the partial derivatives:

∂f/∂x = 1 - 3
∂f/∂y = 1 - 12y

The system of equations is:

1. ∂f/∂x = 1 - 3 = 0
2. ∂f/∂y = 1 - 12y = 0

Now let's solve the system of equations:

1. 1 - 3 = 0 → -2 = 0 (this equation cannot be satisfied)

Since the first equation cannot be satisfied, there are no critical points for the given function.

To learn more about function visit;

brainly.com/question/12431044

#SPJ11

Answer:

Answer:

A. 2

Step-by-step explanation:

slope formula is :  or the difference in y-coordinates in 2 points divided by the difference in x-coordinates in 2 points.

in this question, they have given you both the difference in x and difference in y.

therefore this question is saying :  =

= 2

therefore, the correct slope value is A. 2

Step-by-step explanation:

Answer:

12 km

Step-by-step explanation:

20 minutes = 20 * 60 = 1200 second

distance = velocity * time

car 1 = 1200 * 20 = 24000 m = 24km

car 2= 1200 * 10 = 12000 m = 12km

so distance between them after 20 minutes is 24 -12 = 12 km

Given that;

Liana takes 2 pages of notes during each hour of class. ​

To write a proportional relationship, let x represent the time in class and y represent the number of pages.

according to the question, the constant of proportionality is equal to 2. ( 2 pages per hour).

So, the equation becomes;

Therefore, an equation to represent the proportional relationship is;

We can represent the equation on the graph as;

We can also represent it on the table as;

Where x is in hours and y is in pages.

The equivalent equation to (2/3)x - 5/6 = (-5/12)x + 1/4 is x = 13/9.

To find an equation equivalent to the given equation, we can start by simplifying both sides and rearranging the terms. Let's go step by step:

Given equation: (2/3)x - 5/6 = (-5/12)x + 1/4

First, let's eliminate the fractions by multiplying the entire equation by the least common denominator (LCD) of the fractions involved. In this case, the LCD is 12.

12 * [(2/3)x - 5/6] = 12 * [(-5/12)x + 1/4]

Simplifying:

4x - 10 = -5x + 3

Now, let's gather like terms on each side of the equation:

4x + 5x = 3 + 10

Combining like terms:

9x = 13

Finally, to isolate x, divide both sides of the equation by 9:

(9x)/9 = 13/9

x = 13/9

So, the equivalent equation to (2/3)x - 5/6 = (-5/12)x + 1/4 is x = 13/9.

for such more question on equivalent

https://brainly.com/question/9657981

#SPJ8

Null hypothesis: Gender and flight destination preference are independent.

Alternative hypothesis: Gender and flight destination preference are not independent.

The null and alternative hypotheses for this chi-square test can be stated as follows:

Null hypothesis (H0): Gender and flight destination are independent variables. There is no association between gender and preferred flight destination

Alternative hypothesis (H1): Gender and flight destination are dependent variables. There is an association between gender and preferred flight destination.

To calculate the chi-square statistic, we need to first construct the observed and expected contingency table. The degrees of freedom for a chi-square test in this case can be calculated as (number of rows - 1) * (number of columns - 1), which in this case is (2 - 1) * (4 - 1) = 3.

Using the chi-square table or a statistical software, we can find the critical chi-square value at a 2% significance level with 3 degrees of freedom.

The decision rule at the 2% significance level is: If the calculated chi-square statistic is greater than the critical chi-square value, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

After calculating the chi-square statistic and comparing it with the critical chi-square value, we can make a decision. If the calculated chi-square statistic is greater than the critical chi-square value, we reject the null hypothesis, indicating that there is a significant association between gender and preferred flight destination. If the calculated chi-square statistic is less than or equal to the critical chi-square value, we fail to reject the null hypothesis, suggesting that there is no significant association between gender and preferred flight destination

A graph can be created to illustrate the decision, with the calculated chi-square statistic compared to the critical chi-square value at the 2% significance level. The key numerical values, such as the observed and expected frequencies, can be included in the graph.

Based on the decision made, there are two types of errors that can occur:

Type I error: Rejecting the null hypothesis when it is actually true, indicating a false positive result.

Type II error: Failing to reject the null hypothesis when it is actually false, indicating a false negative result.

The conclusion of the test should be interpreted in the context of the specific hypothesis and the significance level chosen.

Learn more about independent

brainly.com/question/4273396

#SPJ11

The result of multiplying 40 by the distance to the finish line is equal to the total distance covered.

To calculate the product of 40 and the distance to the finish line,

1. Determine the distance to the finish line. This could be measured in any unit of length, such as meters or feet.

2. Take the value of the distance to the finish line and multiply it by 40. This can be done by simply multiplying the two numbers together.

  Result = Distance to finish line * 40

3. Perform the multiplication to find the product. The result will be the total distance covered from the starting point to the finish line.

For example, if the distance to the finish line is 100 meters:

  Result = 100 * 40

         = 4000 meters

  Therefore, the product of 40 and the distance to the finish line is 4000 meters.

Remember to adjust the units of the result based on the units used for the distance to the finish line.

For more such questions on distance, click on:

https://brainly.com/question/30395212

#SPJ8

Answer:

g(4)= 25-12g

Step-by-step explanation:

g(r)= 25-3rg

g(4)= 25-3(4)g

g(4)= 25-12g

Answer:

13

Step-by-step explanation:

Khan