car travels along the highway to Yuma at a steady speed when it begins it is 400 miles from Yuma after 7 hours it is 50 miles from Yuma which function describes the cars distance from Yuma ​

Answer:

The solution is x=2, y=4

Step-by-step explanation:

y = 2x

x+y = 6

Using substitution, we can substitute the first equation into the second equation

x + (2x) = 6

3x = 6

Divide by 3

3x/3 = 6/3

x = 2

Now we can find y

y = 2(2)

y = 4

The solution is x=2, y=4

Answer:

Area = 232 in^2

Step-by-step explanation:

Formula

A square's area is found using the following formula

A = S^2

Where A is the area

and S is the length of one side.

Solution

The 2 means that the side is squared and is written as shown above.

s = 2 sqrt(58)

Square both sides

s^2 = 2^2 * sqrt(58)^2

When a square root is squared, you get rid of the square root sign √ and you are left with what is under the square root sign.

s^2 = 4 * 58

s^2 = 232 inches ^2 which is the answer you have chosen.

Answer:

For problem 15 it's y=15/4-7x

For problem 13 it's x=31-5y/6

Step-by-step explanation:

Problem 15:

y(4-7x)=15

y=15/4-7x

Problem 13:

6x=31-5y

x=31-5y/6

Answer:

13) Ans;

\(6x + 5y = 31 \\ 6x = 31 - 5y \\ \\ x = \frac{31 - 5y}{6} \\ \\ x = \frac{31}{6} - \frac{5y}{6} \)

15)Ans;

\(4y - 7xy = 15 \\ y(4 - 7x) = 15 \\ \\ y = \frac{15}{4 - 7x} \)

I hope I helped you^_^

Answer:

No

Step-by-step explanation:

Functions can only have 1 range per domain (Only 1 Y output per X). Another method is by using the vertical line test, and in this case it fails because more than 2 points are on the same vertical line (x = 1 and x = 2)

Profitability index is 1.387. Thus, the correct option is (c) 1.387.

The formula for calculating the profitability index is:

P.I = PV of Future Cash Flows / Initial Investment

Where,

P.I is the profitability index

PV is the present value of future cash flows

The initial investment in the project is $30 million. The cash flow at the end of the first year is $2.85 million.

The present value of cash flows can be calculated using the formula:

PV = CF / (1 + r)ⁿ

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

n is the number of periods

For the first-year cash flow, n = 1, CF = $2.85 million, and r = 11%.

Substituting the values, we get:

PV = 2.85 / (1 + 0.11)¹ = $2.56 million

To calculate the present value of all future cash flows, we can use the formula:

PV = CF / (r - g)

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

g is the constant growth rate

For the subsequent years, CF = $2.85 million, r = 11%, and g = 3.85%.

Substituting the values, we get:

PV = 2.85 / (0.11 - 0.0385) = $39.90 million

The total present value of cash flows is the sum of the present value of the first-year cash flow and the present value of all future cash flows.

PV of future cash flows = $39.90 million + $2.56 million = $42.46 million

Profitability index (P.I) = PV of future cash flows / Initial investment

= 42.46 / 30

= 1.387

Therefore, the correct option is (c) 1.387.

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Answer:

8.

Step-by-step explanation:

Use PEDMAS:

the operations are done in the order

Parentheses Exponents Divide Multiply Add Subtract

8∙4-4^2∙2+2^3         Working on the exponential terms:-

=8.4 - 16.2 + 8          Working on the multiplications:-

= 32 - 32 + 8        

Now working from left to right:

= 0 + 8

= 8.

Total price paid by Michael for the basket of mangoes is $4.48.

For the calculation of total price, price of sales tax will be added with selling price. Forming the equation -

Total price = 4 + 12%×4

Calculating the percentage of sales tax on Right Hand Side of the equation

Total price = 4 + 12×4/100

Solving the percentage part on Right Hand Side of the equation

Total price = 4 + 0.48

Performing addition on Right Hand Side of the equation

Total price = $4.48

Hence, Michael has to pay $4.48 after addition of sales tax for the basket of mangoes.

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The third term of the Taylor series is f''(a)(x-a)². The Taylor series is a mathematical series of infinite sum of terms that is used in expanding functions into an infinite sum of terms.

The Taylor series is very important in many areas of mathematics such as analysis, numerical methods, and more. The third term of the Taylor series can be obtained by using the general formula of the. In this question, we have given the first two terms of the Taylor series and we are required to find the third term. The first two terms of the Taylor series are: f(x)=f(a)+f′(a)(x−a)+…+…The third term can be found by looking at the general formula of the Taylor series and comparing it with the given expression. Therefore, the third term is f''(a)(x-a)².

The third term of the Taylor series is f''(a)(x-a)². The Taylor series is a mathematical tool that is used to represent a function as an infinite sum of terms. This series is used to expand the functions and determine their values at different points. The Taylor series has many applications in various fields of mathematics such as calculus, analysis, numerical methods, and more.The third term of the Taylor series is f''(a)(x-a)². This term is obtained by looking at the general formula of the Taylor series and comparing it with the given expression. The third term is essential in determining the values of the function at different points. By expanding the function using the Taylor series, we can easily determine the values of the function and its derivatives at different points. The Taylor series is a very important tool that is used in many areas of mathematics and science.

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Answer:

B. y = 2/3x + 5

Step-by-step explanation:

(3,7) (6,9) Find the distance

(3,2)

Slope: y/x = 2/3x

you can subtract now using slope from one of the coordinates till x is zero so you can find the y-intercept.

(3,7) use slope 2/3x

(0,5)

y-intercept: (0,5)

Write the equation in standard form now that you have the slope and y-intercept.

Slope-intercept form: y = mx + b

Equation: y = 2/3x + 5

Your option is B

Answer:

2.81

Step-by-step explanation:

\(4*1.6^x=15\\\\1.6^x=\dfrac{15}{4} \\\\x*ln (1.6)=ln (3.75)\\\\x=\dfrac{ln(3.75)}{ln(1.6)} \\\\x=2.81222475...\approx{2.81}\)

The amount of storage required to represent a simple graph with n vertices and m edges can vary depending on the chosen representation. Here's the storage requirement for each representation:

a) Adjacency lists:

In an adjacency list representation, we typically use an array of size n to store the vertices, and for each vertex, we maintain a linked list or an array to store its adjacent vertices. The space complexity of this representation is O(n + m), where n is the number of vertices and m is the number of edges.

Each vertex requires constant space, and each edge is represented by a link or entry in the adjacency list.

b) Adjacency matrix:

In an adjacency matrix representation, we use a 2D matrix of size n x n to represent the graph. Each entry (i, j) in the matrix represents whether there is an edge between vertices i and j. The space complexity of this representation is O(n^2), as we need to store n^2 entries for the complete matrix. However, if the graph is sparse (few edges compared to vertices), the space complexity can be reduced to O(n + m) by only storing the entries corresponding to the existing edges.

c) Incidence matrix:

In an incidence matrix representation, we use a 2D matrix of size n x m, where n is the number of vertices and m is the number of edges. Each entry (i, j) in the matrix represents whether vertex i is incident to edge j. The space complexity of this representation is O(n * m), as we need to store n * m entries for the matrix.

Similar to the adjacency matrix, if the graph is sparse, the space complexity can be reduced to O(n + m) by storing only the entries corresponding to the existing edges.

In summary:

a) Adjacency lists: O(n + m)

b) Adjacency matrix: O(n^2) or O(n + m) for sparse graphs

c) Incidence matrix: O(n * m) or O(n + m) for sparse graphs

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When two tables have a one-to-many relationship, you typically need to add a foreign key to the table on the "many" side to link the records to the corresponding record in the "one" table.

In a one-to-many relationship, the table on the "one" side is usually the primary key table, and the table on the "many" side is usually the foreign key table. The foreign key is used to link the records in the "many" table to the corresponding record in the "one" table. This is done by adding a column to the "many" table that contains the primary key value from the "one" table.

When designing a database, it is important to establish relationships between tables to ensure data integrity and avoid redundant data. In a one-to-many relationship, one record in the primary key table can be associated with many records in the foreign key table. To establish a one-to-many relationship, you need to create a primary key in the "one" table and a foreign key in the "many" table. The foreign key is a column that contains the primary key value from the "one" table. For example, if you have a "customers" table and an "orders" table, the "customers" table would be the primary key table and the "orders" table would be the foreign key table. Each record in the "orders" table would have a foreign key column that contains the customer ID from the "customers" table.

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The multiplier that would be used to calculate the depreciation of the car is 0.83^y.

Depreciation is when the value of an asset declines due to wear and tear.

The equation that can be used to represent depreciation is:

Value of the asset x (1 - rate of depreciation)^years

$31,000 x 0.83^y.

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Answer:

4/5+14%15

4×3/5+14×1/15

12+14/15

26/15

(26/5)/2

13/15

Answer:ay

Step-by-step explanation:

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Subtract how much more angle 1 is from the total. :

112 - 48 = 64

Divide by 2:

64/2 = 32

Angle 2 = 32 degrees

Answer:

measure of angle 2 is 32 degrees.

Step-by-step explanation:

I will refer to the measure of the angles as m1 and m2 (I don't have the angle symbol on my keyboard).

we are looking for measure of angle 2, so let's call m2 "x".

so,

m2 = (x)

m1 = (48 + m2) or m1 = (48 + x)

and we know that:

m1 + m2 = 112

so we substitute the values above into the equation.

m1 + m2 = 112

(48 + x) + (x) =  112

combine like terms:

42 + x + x = 112

42 + 2x = 112

subtract 42 from both sides, leaving us with

2x = 64

divide by 2, giving us

x = 32

remember that we are looking for m2, which is x, so m2 is 32 degrees. hope this helped! (:

Unit rate of students per tent = Total number of students / Number of tents for students
= 36 / 12
= 3

Therefore, the answer is B) 3 students per tent.

A) There were 5 teachers, and each teacher had 2 tents, so there were 5 x 2 = 10 tents for the teachers. In total, there were 36 students + 5 teachers = 41 people on the trip. Therefore, there were 12 tents for the students + 10 tents for the teachers = 22 tents in total.

So, the answer is A) 2 tents, 5 teachers.

B) To find the unit rate of students per tent, we need to divide the total number of students by the number of tents for the students.

The total number of students is 36, and the number of tents for the students is 12, so:

Unit rate of students per tent = Total number of students / Number of tents for students
= 36 / 12
= 3

Therefore, the answer is B) 3 students per tent.

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Answer:

isosceles right triangle

Explanation

To graph, or plot, points we use two perpendicular lines called the x-axis and the y-axes. The horizontal number line is the x-axis and the vertical line is the y- axis

so, a coordinate has this form

where x indicantes the position ( horizonta) and y the vertical position, so

the point (x,y)

hence

Step 1

the, plot the points

Step 2

B)(2, -1.5)

I hope this helps you

Answer: To check a solution, you can substitute the solutions into the equations and verify that both equations are true.

Step-by-step explanation:

Answer:

the first one for sure.

Step-by-step explanation:

Answer:

Definitions, postulates, and theorems.

Step-by-step explanation:

- Definition: This is a statement that describe the meanings of the terms being used.

- Postulate: This is a statement that is assumed true without proof. It is a statement that is taken to be "clearly true".

- Theorem: This is a statement that is never assumed to be true until it is proven so. It depends strongly on proofs.

Answer:

0.011865211

Step-by-step explanation:

5.9/497.252 =0.011865211

Answer:

84.28

Step-by-step explanation:

The line plot shows the favorite color of the students in the class. Option A, 9 students liked red or blue.

The line plot presents four columns with red, blue, orange, and yellow colors at the bottom. The number of students liking the color is represented by the x variable. The line plot presents five x in the column of red and four x in the column of blue. Therefore, a total number of students liking the color red and blue are option 9.

A line plot or line chart presents a chart along the number line. Line dots are often used in the line chart but variables can be presented by alphabet as well. It presents the frequency of the number of times the variable is presented in the data. If the data is big in numbers, the legend is used to present the variable. For instance, the legend of the line plot is x. Therefore, x = 5 students.

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Answer:

A

Step-by-step explanation:

The system of linear inequalities to model the situation is 10x + 20y ≤ 100 and y > 2x

From the question, we have the following parameters that can be used in our computation:

Using the following representations:

We have the following system of inequalities from the given statements

10x + 20y ≤ 100

y > 2x

Hence, the system of inequalities is 10x + 20y ≤ 100 and y > 2x

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The value of m or Mia's time is 11.34 seconds.

Let Mia's time is m.

Thomas's time = 8+m

Jasmine's time = 21 + 8+ m

m + 8 + m + 21 + 8 + m = 71

3m + 37 = 71

3 m = 71 - 37

m = 34/3

m = 11.34

Therefore, the value of m or Mia's time is 11.34 seconds.

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Using strong induction, we can prove that the square root of -2 is irrational by showing that it cannot be expressed as a fraction of coprime odd integers.

To prove that √-2 is irrational using strong induction, we need to show that for any natural number n, if the square root of -2 can be expressed as a fraction a/b, where a and b are coprime integers, then a and b must be odd.

We can start by using the base case, n = 1. Assume that √-2 can be expressed as a fraction a/b where a and b are coprime integers. Then, we have

√-2 = a/b

Squaring both sides gives

-2 = a^2/b^2

Multiplying both sides by b^2 gives

-2b^2 = a^2

This implies that a^2 is even, and therefore a is also even. We can express a as 2k for some integer k, which means

-2b^2 = (2k)^2

Simplifying, we get

-2b^2 = 4k^2

Dividing both sides by -2 gives

b^2 = -2k^2

This implies that b^2 is even, which means that b is also even. However, this contradicts our assumption that a and b are coprime integers. Therefore, √-2 cannot be expressed as a fraction a/b where a and b are coprime integers.

Now, let's assume that for all n ≤ k, the square root of -2 cannot be expressed as a fraction a/b where a and b are coprime integers with a and b odd. We want to prove that this also holds for n = k+1.

Assume that √-2 can be expressed as a fraction a/b where a and b are coprime integers with a and b odd. Then, we have

√-2 = a/b

Squaring both sides gives

-2 = a^2/b^2

Multiplying both sides by b^2 gives

-2b^2 = a^2

This implies that a^2 is even, and therefore a is also even. We can express a as 2k for some integer k, which means

-2b^2 = (2k)^2

Simplifying, we get

-2b^2 = 4k^2

Dividing both sides by -2 gives

b^2 = -2k^2

This implies that b^2 is even, which means that b is also even. However, this contradicts our assumption that a and b are coprime integers with a and b odd. Therefore, √-2 cannot be expressed as a fraction a/b where a and b are coprime integers with a and b odd.

By strong induction, we have proven that for any natural number n, the square root of -2 cannot be expressed as a fraction a/b where a and b are coprime integers with a and b odd. Therefore, √-2 is irrational.

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To forecast using data that has seasonality, one commonly used method is seasonal decomposition of time series (STL). This method separates the time series data into three components: trend, seasonality, and residuals. By isolating the seasonal component, you can forecast future values by extrapolating the pattern observed in previous seasons.

Another approach is the use of seasonal autoregressive integrated moving average (SARIMA) models. SARIMA models are an extension of ARIMA models that incorporate seasonal patterns. These models capture both the trend and seasonality in the data and can be used to make forecasts.

To control volatility in various time series models, a common technique is to use a volatility model, such as the generalized autoregressive conditional heteroskedasticity (GARCH) model. This model estimates the volatility of the time series by incorporating past volatility and squared residuals. By modeling and forecasting the volatility, you can better understand and manage the potential fluctuations in the time series data.

A simple moving average method is a technique used to smooth out fluctuations and identify trends in time series data. It involves calculating the average of a fixed number of data points, often referred to as the window size or period. As new data becomes available, the oldest data point in the window is dropped, and the newest data point is included in the calculation. This process is repeated for each subsequent data point. The resulting moving average values can provide insights into the overall trend of the data, helping to identify patterns or changes over time.

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0.67

1) Given that we've got the following data:

We can plug them all together into the Z score formula:

Thus, the Z-score is 0.67

Answer:

(-8,2)

Step-by-step explanation:

This is because when you reflect a point across the x-axis, the x-coordinate fo the point remains the same and the y-coordinate's sign gets switched.

(x,y) --> (x,-y)

(-8,-2) --> (-8,2)