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A restaurant investigated the correlation between prices and the number of customers. The linear model below represents this situation,
where x is the average meal price [in dollars), and y is the number of daily customers. Interpret the slope.
y = 437 – 18.5
OA. The average price per meal is $18.
B. The average number of daily customers is 18.
Oc. If the average meal price decreases by $1, the number of daily customers decreases by 18.
D. If the average meal price increases by $1, the number of daily customers decreases by 18.

Answer:

Step-by-step explanation:

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Answer:

Slope Intercept form: y = mx + b

Step-by-step explanation:

mx: the slope

b: y- intercept

To find the slope, use this formula:

y₂ - y₁ / x₂ - x₁

Add in the numbers

1 - (-5) / 0 - 2

-6/2 (or -3) = slope

Use point-slope form to find the Y- intercept

y - y₁ = m (x - x₁)

y - (-5) = -3 (x - 2)

y + 5 = -3x + 6

Subtract 5 from both sides

y = -3x + 1 ← Slope intercept form

Graph the y- intercept at 1, and go down 3 and to the right 1. Your two coordinates will be (0 , 1) and (1, -2) .

Answer:

\(\frac{1}{2} n + 12 \geq 28\)

HOPE THIS HELPS!!!

Answer:

16 is equivalent to 8 12 and 64

Step-by-step explanation:

Answer:

HG = 28

Step-by-step explanation:

The midsegment MN is half the sum of the 2 parallel bases, that is

\(\frac{HG+JF}{2}\) = MN , that is

\(\frac{HG+16}{2}\) = 22 ( multiply both sides by 2 )

HG + 16 = 44 ( subtract 16 from both sides )

HG = 28

Answer:

5.1

Step-by-step explanation:

a² + b² = c²

1² + 5² = c²

1 + 25 = c²

26 = c²

c = 5.1

Answer:

The constant of variation is k =

3/8

When a = 1 and b = 5, what is the value of c?

3/40

The number of students in the survey who said that math was their favorite subject is 42.

This information is obtained from the conditional relative frequency table, which compares the favorite subjects of male and female students at a high school.

The table includes entries for the math favorite subject, other favorite subject, and total number of students in each category.

In the conditional relative frequency table, the second column represents the math favorite subject, with entries of 0.35 for males and 0.45 for females. The third column represents the other favorite subject, with entries of 0.65 for males and 0.55 for females. The fourth column represents the total, with entries of 1.0 for both males and females.

To find the number of students who said that math was their favorite subject, we need to sum the entries in the second column, which correspond to the math favorite subject. Adding 0.35 (males) and 0.45 (females) gives us a total of 0.80.

Since the total probability for each category is 1.0, we can interpret the entries in the table as relative frequencies. Therefore, we can multiply the total number of students in the survey by the relative frequency of the math favorite subject to obtain the number of students who said that math was their favorite subject.

For the math favorite subject, the relative frequency is 0.80. Thus, multiplying 0.80 by the total number of students (120 males + 180 females) gives us 0.80 * 300 = 240.

Therefore, the number of students in the survey who said that math was their favorite subject is 240.

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Step-by-step explanation:

To calculate the value of the investment after 8 years with daily compounding interest, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = Final amount

P = Principal amount (initial investment)

r = Annual interest rate (in decimal form)

n = Number of times interest is compounded per year

t = Number of years

Given:

P = $4140

r = 7% = 0.07

n = 365 (daily compounding)

t = 8 years

Plugging in the values into the formula, we have:

A = 4140(1 + 0.07/365)^(365*8)

Calculating this expression will give us the value after 8 years:

A ≈ 4140(1.000191)^2920 ≈ 4140(1.676793216) ≈ $6944.45

Therefore, the value of the investment after 8 years, rounded to the nearest penny, is approximately $6944.45.

A discrete function is defined on distinct values, while a continuous function is defined on a continuous interval. Discrete functions consist of isolated points, while continuous functions can take on any value within a given range.

The main difference between a discrete function and a continuous function lies in the nature of their domains and ranges. A discrete function is defined on a set of distinct, separate values, while a continuous function is defined on a continuous interval or range of values.

A discrete function can be thought of as a function that consists of isolated points. For example, let's consider a function that represents the number of students in a classroom over the years. The domain of this function would be the set of discrete values representing each year, such as {2010, 2011, 2012, ...}. The range would be the set of corresponding numbers representing the number of students in the classroom each year.

On the other hand, a continuous function is one that can take on any value within a given interval. For instance, consider a function that represents the temperature in a room over time. The domain of this function would be a continuous interval, such as [0, 24] representing the 24-hour day. The range would be the set of possible temperature values within that interval.

To summarize, a discrete function is defined on distinct values, while a continuous function is defined on a continuous interval. Discrete functions consist of isolated points, while continuous functions can take on any value within a given range.
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The maximum value of f(x, y) = x + y, subject to the budget constraint 2x + 4y = 8, is 4.

To solve the constrained maximization problem:

Maximize f(x, y) = x + y

Subject to the budget constraint: 2x + 4y = 8

We can use the method of Lagrange multipliers to find the solution.

Step 1: Set up the Lagrangian function:

L(x, y, λ) = f(x, y) + λ(g(x, y) - c)

Where:

f(x, y) = x + y (objective function to maximize)

g(x, y) = 2x + 4y (budget constraint)

c = 8 (constant in the budget constraint)

λ is the Lagrange multiplier.

Step 2: Take partial derivatives of L(x, y, λ) with respect to x, y, and λ:

∂L/∂x = ∂f/∂x + λ∂g/∂x = 1 + 2λ

∂L/∂y = ∂f/∂y + λ∂g/∂y = 1 + 4λ

∂L/∂λ = g(x, y) - c = 2x + 4y - 8

Step 3: Set the partial derivatives equal to zero and solve the resulting system of equations:

1 + 2λ = 0 --> λ = -1/2

1 + 4λ = 0 --> λ = -1/4

2x + 4y - 8 = 0

Solving the last equation:

2x + 4y - 8 = 0

x + 2y = 4

x = 4 - 2y

Substituting x in terms of y into the budget constraint:

2(4 - 2y) + 4y = 8

8 - 4y + 4y = 8

8 = 8

The constraint equation is satisfied.

Step 4: Plug the values of x and y back into the objective function to find the maximum value:

f(x, y) = x + y

f(x, y) = (4 - 2y) + y

f(x, y) = 4 - y

Therefore, the maximum value of f(x, y) = x + y, subject to the budget constraint 2x + 4y = 8, is 4, which occurs when x = 4 - 2y.

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The account's interest rate for deposit $1,198.00 into an account 7.00 years from today and worth $1,639.00 after 12 years from today, is equals to the 6.47%.

Future value (FV) is defined as the value of a current value at a future date based on an assumed rate of growth. Formula is written as FV = P× (1 + i)ⁿ

where, FV --> future value

P --> present value or principal

i --> interest rate

n --> number of periods (in years )

We have, present value = $1,198.00

future value, FV = $1,639.00

number of time periods, n = 12 years - 7 years = 5 years

We have to calculate the account's interest rate. Substutes the known values in above formula, we get,

$1,639.00 = $1,198.00( 1 + i)⁵

=> 1639/1198 = (1+i)⁵

=> 1.368124 = (1 + i) ⁵

=> (1.368124)⅕ = 1 + i

=> 1.064693 = 1 + i

=> i = 1.064693 - 1

=> i = 0.064693 ~ 6.47%

Hence, the required interest rate is 6.47%.

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Answer:

-0.7 is the answer to your question

Answer:

Answer:

-0.7 is the answer to your question

Step-by-step explanation:

Answer:

x = 2.5, y = 0.5

Step-by-step explanation:

\(10x - 16y = 17\\3x + 3y = 9\)

Isolate for x or y on the equation of choice (Just choose a random one)

\(3y = 9 - 3x\\y = 3 - x\)

Sub new equation into the other equation

\(10x - 16(3-x) = 17\\10x -48 + 16x = 17\\26x = 65\\x = 2.5\)

Sub x into new equation

\(y = 3 - x\\y = 0.5\)

Answer:

\(x=0\)

Step-by-step explanation:

STEP 1: Since x is on the right side of the equation, switch the sides so it is on the left side of the equation.

\(3.6x+1.8x=11.52x\)

STEP 2: Add  3.6x  and  1.8x.

\(5.4x=11.52x\)

STEP 3: Move all terms containing x to the left side of the equation.

\(-6.12x=0\)

STEP 4: Divide each term by  −6.12  and simplify.

\(x=0\)

Answer:

See Below

Step-by-step explanation:

Ok, this is just like the systems of equations.

x-7 = 5x-31

Solve

x-7 = 5x-31

-x     -x

-7 = 4x -31

+31       +31

24 = 4x

24/ 4   = 4x/ 4

x=6

Hope this helps!=)

Correct option is A,  f(x) -2 has changed the parent function f(x) = (0.5)x to its new appearance.

The parent function f(x) = log5x has been modified by reflecting it over the x-axis, extending it vertically by a factor of three, and moving it down by three units.

In the picture below you can see the blue line is the graph of the function

f(x) = log(5x) and the green line is the graph of the function

g(x) = log[5(x + 4)] - 2

Since the function f passes at point (2, 1), we must reduce it by 2 units to ensure that it also passes at position (-2, -1). To do this, we add 2 to the function f.

We only need to add 4 to the variable x to have the function go left when we obtain log(5x) - 2.

The function shifts to the left when you add a number to x;

The function moves to the right when you remove a number from x;

The function increases when you add a number to it;

The function decreases when you take a number away from it.

Then we get a function g(x) = log[5 (x + 4)] - 2.

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Answer:

y = 4/6x - 4

Step-by-step explanation:

y = mx + b, m = slope and b = y intercept

Rise over run

Rise = +4

Run = +6

This means the slope is 4/6.

The y intercept is at -4.

Now, plug in the numbers for y = mx + b

y = 4/6x - 4

A relative frequency is obtained with the division of the number of desired outcomes by the number of total outcomes.

For hamburguers, the outcomes are given as follows:

Hence:

58/300 x 100% = 19.33%.

For cheeseburger and onion rings compared to the total amount of orders for onion rings, the outcomes are given as follows:

Hence:

74/103 = 71.84%.

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The term for the value that occurs most often in a series of numbers is called the mode.

The mode is one of the three main measures of central tendency, along with the mean and the median. It is a useful descriptive statistic that can provide insights into the characteristics of a dataset.

To find the mode of a set of data, you first need to arrange the data in order, either in increasing or decreasing order. Then, you simply identify the most frequent data point, which is the mode. In some cases, there may be more than one mode if multiple data points occur with the same maximum frequency.

The mode is particularly useful when dealing with categorical or nominal data, where there are distinct categories or values that cannot be ordered in a meaningful way. For example, the mode can help identify the most popular color among a group of people or the most common type of car on a given street. It can also be used for continuous data, although it may be less useful in this case than the mean or median.

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Answer:

6

Step-by-step explanation:

The sine , cosine and tangent of an acute angle can be find by using:

Acute Angle:

Acute angles are defined as angles less than 90 degrees, i.e. angles between 0° and 90°. Examples include 60°, 30°, 45°. A triangle with all interior angles less than 90° is called an acute triangle. For example, an equilateral triangle is an acute triangle because its interior angles are 60°.

Sine of an Acute Angle :

The sine of an angle in a right triangle is the ratio of the opposite side of the angle to the hypotenuse. The sine function is the important periodic function in trigonometry, with period 2π. To understand the derivation of sin x, consider the unit circle centered at the origin of the coordinate plane. On the boundary (perimeter) of this circle the variable point P moves. Note that P is in the first quadrant and OP makes an acute angle of x radians with the positive x-axis. PQ is the perpendicular from P to the horizontal axis.

Cosine:

Cosine or cos x is the trigonometric periodic function. Imagine a unit circle centered at the origin of the coordinate plane. The variable point P moves on the circumference of this circle. From the figure, we can see that P is in the first quadrant and OP forms an acute angle of x radians with the positive x-axis. PQ is the perpendicular from P to the horizontal axis. A triangle is therefore formed by connecting the points O, P, and Q as shown. where OQ is the base and PQ is the height of the triangle.

Tangent:

The tangent function is one of the six most important trigonometric functions, commonly written as tan x. It is the ratio of the opposite side to the adjacent side of the angle considered in a right triangle. There are various trigonometric identities and formulas related to the tangent function that can be derived using various formulas. The period expression for the tangent function f(x) = a tan (bx) is given by Period = π/|b|. The tangent function tan x is periodic, with period π/1 = π (because b = 1 for tan x).

So the formula for tan x is:

tan x = sin x/cos x

tan x = opposite side/adjacent side

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Answer:-1.93939393939

Step-by-step explanation:

To show that the matrix A = [XX - X'Z(ZZ)^(-1)Z'X] is positive definite, we need to demonstrate two properties: (1) A is symmetric, and (2) all eigenvalues of A are positive.

Symmetry: To show that A is symmetric, we need to prove that A' = A, where A' represents the transpose of A. Taking the transpose of A: A' = [XX - X'Z(ZZ)^(-1)Z'X]'. Using the properties of matrix transpose, we have:

A' = (XX)' - [X'Z(ZZ)^(-1)Z'X]'. The transpose of a sum of matrices is equal to the sum of their transposes, and the transpose of a product of matrices is equal to the product of their transposes in reverse order. Applying these properties, we get: A' = X'X - (X'Z(ZZ)^(-1)Z'X)'.  The transpose of a transpose is equal to the original matrix, so: A' = X'X - X'Z(ZZ)^(-1)Z'X. Comparing this with the original matrix A, we can see that A' = A, which confirms that A is symmetric.  Positive eigenvalues: To show that all eigenvalues of A are positive, we need to demonstrate that for any non-zero vector v, v'Av > 0, where v' represents the transpose of v. Considering the expression v'Av: v'Av = v'[XX - X'Z(ZZ)^(-1)Z'X]v

Expanding the expression using matrix multiplication : v'Av = v'X'Xv - v'X'Z(ZZ)^(-1)Z'Xv. Since X and Z have full column rank, X'X and ZZ' are positive definite matrices. Additionally, (ZZ)^(-1) is also positive definite. Thus, we can conclude that the second term in the expression, v'X'Z(ZZ)^(-1)Z'Xv, is positive definite.Therefore, v'Av = v'X'Xv - v'X'Z(ZZ)^(-1)Z'Xv > 0 for any non-zero vector v. Implications in econometrics: In econometrics, positive definiteness of a matrix has important implications. In particular, the positive definiteness of the matrix [XX - X'Z(ZZ)^(-1)Z'X] guarantees that it is invertible and plays a crucial role in statistical inference.

When conducting econometric analysis, this positive definiteness implies that the estimator associated with X and Z is consistent, efficient, and unbiased. It ensures that the estimated coefficients and their standard errors are well-defined and meaningful in econometric models. Furthermore, positive definiteness of the matrix helps in verifying the assumptions of econometric models, such as the assumption of non-multicollinearity among the regressors. It also ensures that the estimators are stable and robust to perturbations in the data. Overall, the positive definiteness of the matrix [XX - X'Z(ZZ)^(-1)Z'X] provides theoretical and practical foundations for reliable and valid statistical inference in econometrics.

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The distribution for X is a negative binomial distribution, denoted as nb(x;6, 188​), with parameters r = 6 (number of successes), p = 8/18 (probability of success in each trial).

To compute the probabilities:

P(X = 2): nb(2;6, 8/18)

P(X ≤ 2): nb(0;6, 8/18) + nb(1;6, 8/18) + nb(2;6, 8/18)

P(X ≥ 2): 1 - P(X < 2) = 1 - P(X ≤ 1)

To calculate the mean value and standard deviation of X:

Mean (μ) = r * (1 - p) / p

Standard Deviation (σ) = sqrt(r * (1 - p) / (p^2))

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Answer:

576 feet

Step-by-step explanation:

I'm going directly off the graph but it looks like the y-coordinate of the vertex is 576, which would make 576 feet the maximum height. Hope that helps :)

Answer: where's the table..

Step-by-step explanation:

The missing description is (i) Multiply 3 on LHS  

                                            (ii) subtract 3 form both side

                                            (iii) subtract 20t form both the side

                                            (iv) divide both side by 34

What is Fraction ?

Given expression,

3(18t + 1) = 20t + 3

First, Multiply 3 on LHS

54 t + 3 = 20t + 3

After this it's written subtract 3 from both side. Let's do that

54t + 3 - 3 = 20t + 3 -3

54t = 20t

Now, subtract 20t form both the side

54t - 20t = 20t - 20t

34t = 0

Now, divide both side by 34

34t/34 = 0/34

t = 0    

Hence, the value we get of t = 0 which is correct with mentioned description.

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The calculated value of x in the pentagon is 121

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

The pentagon (see attachment)

The sum of angles in a pentagon is

Sum = 180 * (n - 2)

Where

n = 5

So, we have

Sum = 180 * (5 - 2)

Evaluate

Sum =  540

Algebraically, we have

x + 87 + 92 + 105 + 135 = 540

So, we have

x + 419 = 540

Subtract 419 from both sides

x = 121

Hence, the value of x is 121

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