A local hamburger shop sold a combined total of 817 hamburgers and cheeseburgers on Friday. There were 67 more cheeseburgers sold than hamburgers. How
many hamburgers were sold on Friday?
hamburgers

Answer:

11.

A) EZ Pay Plan=0.15x

B) 40 to Go Plan=0.05x+40

12.

0.15x=0.05x+40

13.

x=400 minutes

14. The solution is the amount of minutes that it takes for both plans to cost the same amount. X has one solution, so it accounts for both equations.

15. EZ Pay Plan

Step-by-step explanation:

For 11, what you need to know is that the slope (coefficient of x) is the price per minute. 0.15 per minute and 0.05 per minute are charged, and therefore are the slope for those equations. The 40 on B is because it is the y intercept. No matter how long you use the object, you will always pay at least 40 dollars.

For 12, you have to find x for the minutes used.

For 13, if you do the process algebraically,

0.15x=0.05x+40  

0.10x=40     (subtracted 0.05x from both sides)

x=400       (divided 0.10x and 40 by 0.10)

For 14, (no explanation)

For 15, if you substitute 200 as x, you would see that the EZ Pay Plan would make you pay 30 dollars while the 40 To Go Plan would make you pay 10+40 dollars, which 30<50.

(sorry for late response)

Answer:

750000

Step-by-step explanation:

The Big M method is a technique used in linear programming to solve problems with constraints and objective functions. It is an extension of the simplex method that handles cases where some constraints have strict inequalities (i.e., ">") or the objective function includes a term to be minimized.

To construct the first simplex tableau using the Big M method, follow these steps:

1. Write the objective function in standard form:
\(Z = 2x₁ + 3x₂ + x₃\)

2. Introduce slack variables to convert the inequalities into equations:
  \(x₄ = 8 - x₁ - 4x₂ - 2x₃\\x₅ = 6 - 3x₁ - 2x₂\)

3. Add a big M term to the objective function for each slack variable:
  \(Z = 2x₁ + 3x₂ + x₃ + M₁x₄ + M₂x₅\)

4. Convert the inequalities into equations by adding surplus variables for ">=" constraints:
 \(x₆ = x₁ + 4x₂ + 2x₃ - 8\\x₇ = 3x₁ + 2x₂ - 6\)

5. Add a big M term to the objective function for each surplus variable:
  \(Z = 2x₁ + 3x₂ + x₃ + M₁x₄ + M₂x₅ + M₃x₆ + M₄x₇\)

6. Write the initial simplex tableau using the augmented matrix:

```
   [  2  3  1  0  0  0  0  0 ]
   [ -1 -4 -2  1  0  0  0  8 ]
   [ -3 -2  0  0  1  0  0  6 ]
   [  1  4  2  0  0  1  0 -8 ]
   [  3  2  0  0  0  0  1 -6 ]
```

7. Identify the entering and leaving basic variables:
  - The entering variable is the column with the most negative coefficient in the objective row.

In this case, it is the second column (x₂).
  - The leaving variable is the row with the smallest non-negative ratio of the right-hand side to the entering variable's coefficient.

In this case, it is the third row (x₆).

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Using the Big M method, the complete first simplex tableau for the given linear programming problem is constructed as follows:

┌─────────────┬──────┬───────┬───────┬─────┬─────┬─────────────┐

│     BV      │  x₁  │   x₂  │   x₃  │  s₁ │  s₂ │      RHS    │

├─────────────┼──────┼───────┼───────┼─────┼─────┼─────────────┤

│      Z      │  2   │   3   │   1   │  0  │  0  │      0      │

├─────────────┼──────┼───────┼───────┼─────┼─────┼─────────────┤

│  x₁ + 4x₂ + │  1   │   4   │   2   │ -1  │  0  │     -8      │

│     2x₃ - M  │      │       │       │     │     │             │

├─────────────┼──────┼───────┼───────┼─────┼─────┼─────────────┤

│  3x₁ + 2x₂  │  3   │   2   │   0   │  0  │ -1  │      6      │

├─────────────┼──────┼───────┼───────┼─────┼─────┼─────────────┤

│     x₁      │  1   │   0   │   0   │  1  │  0  │      0      │

├─────────────┼──────┼───────┼───────┼─────┼─────┼─────────────┤

│     x₂      │  0   │   1   │   0   │  0  │  1  │      0      │

├─────────────┼──────┼───────┼───────┼─────┼─────┼─────────────┤

│     x₃      │  0   │   0   │   1   │  0  │  0  │      0      │

└─────────────┴──────┴───────┴───────┴─────┴─────┴─────────────┘

The initial entering basic variable is x₁, which has the most negative coefficient in the objective row. The leaving basic variable is x₃, determined by selecting the row with the smallest positive ratio of the right-hand side (RHS) to the entering column's coefficient. In this case, the ratio for the fourth row (0/1) is the smallest, so x₃ leaves the basis.

To construct the complete first simplex tableau using the Big M method, we first convert the given problem into standard form by introducing slack variables (s₁ and s₂) for the inequalities and a large positive value (M) to penalize the artificial variable in the objective function.

The first row represents the objective function, where the coefficients of the decision variables x₁, x₂, and x₃ are taken directly from the given problem. The slack and artificial variables (s₁ and s₂) have coefficients of 0 since they don't appear in the objective function.

The subsequent rows represent the constraints. Each row corresponds to one constraint, where the coefficients of the decision variables, slack variables, and the artificial variable are taken from the original problem. The right-hand side (RHS) values are also copied accordingly.

The initial entering basic variable is determined by selecting the most negative coefficient in the objective row, which is x₁ in this case. The leaving basic variable is determined by finding the smallest positive ratio of the RHS to the entering column's coefficient. Since the ratio for the fourth row (0/1) is the smallest, x₃ leaves the basis.

The resulting tableau serves as the starting point for applying the simplex method to solve the linear programming problem iteratively.

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Answers:

A.

C.

F.

I think that is all of them.

Answer: Its E And A

Step-by-step explanation:

The system of inequalities for the given situation is

x +y ≤ 70.

$4x +  $8x ≤ $400.

y ≤ 50.

And one possible solution is (40,30) and the graph of the inequality is attached below.

Inequality:

Inequality refers the non equal comparison of the expressions.

Given,

The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $4 and each adult ticket sells for $8. The auditorium can hold a maximum of 70 people. The drama club must make no less than $400 from ticket sales to cover the show's costs. Also, they can sell at most 50 adult tickets.

Here we need to find the system of inequalities graphically and also determine one possible solution for it.

Let us consider x represents the number of student tickets sold and y represents the number of adult tickets sold.

Therefore, in here we know that, they can sell at most 50 adult tickets.

Which means that the value of y can't be greater than 50.

So, in inequality it can be written as,

y ≤ 50.

And the total number of seats in the auditorium is 70.

Therefore,

x + y ≤ 70

And we also know that, they sells the ticket at the cost not less than $400.

So,

$4x +  $8x ≤ $400.

Now, we have to plot those inequality on the graph, the we get he following graph.

In the graph, the blue line represents the inequality x + y ≤ 70 and the red line represents the inequality $4x +  $8x ≤ $400.

While we looking into the graph we have identified that the solution of the graph is (40,30).

Which means there are 40 number of students and 30 number of adults.

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The mean of the sampling distribution of the sample means is 55 and the standard deviation is approximately 1.79 (rounded to one decimal place).

Standard deviation is a measure of the amount of variation or dispersion of a set of data values from its mean or expected value. It is a statistic that represents how spread out the data is from the mean.

The standard deviation is calculated by taking the square root of the variance, which is the average of the squared differences of each data point from the mean. The standard deviation is expressed in the same units as the data and is usually denoted by the symbol "σ" (sigma) for a population or "s" for a sample.

In the given question,

We can start by using the properties of the mean and standard deviation of a sampling distribution:

The mean of the sampling distribution of the sample means (Mx) is equal to the population mean (μ), which is given as 55.

The standard deviation of the sampling distribution of the sample means (Ox) is equal to the population standard deviation (σ) divided by the square root of the sample size (n), i.e.,

Ox = σ / sqrt(n)

where n = 5 (the sample size) and σ = 4 (the population standard deviation).

Substituting these values into the formula, we get:

Ox = 4 / sqrt(5) ≈ 1.79

Therefore, the mean of the sampling distribution of the sample means is 55 and the standard deviation is approximately 1.79 (rounded to one decimal place).

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Answer:

Below

Step-by-step explanation:

Similar triangles due to A - A - A

Set up ratios

QR is to RS   as  QP is to TS

(x+2) / (2x-5) = 3/5       Cross multiply to get

5x+10 = 6x-15               subtract 5x from both sides of the equation

10 = x - 15                     add 15 to both sides

25 = x

Answer:

7

Step-by-step explanation:

First ones 7 second ones 7 third ones 1/7 forth ones 1/7

Step-by-step explanation:

Because absolute value basically means the distance from zero so the  distance from zero from -7 is 7 the same with 7 and the distance from zero with -1/7 is you guested it 1/7 and follow suit for 1/7 and you got your answers

Hope this helps ;)

Answer:

B. Subtract 2π from both sides.

Step-by-step explanation:

In order to solve for r, you are gonna want to isolate it. To do so, you first have to subtract 2π from both sides.

The distance the car travels when it reaches a speed of 22 m/s can be calculated using the equation vx^2 = v0x^2 + 2ax(x - x0). Plugging in the given values, we can determine the distance to be 123.27 meters.

To find the distance traveled by the car when it reaches a speed of 22 m/s, we can use the equation vx^2 = v0x^2 + 2ax(x - x0), where vx is the final velocity, v0x is the initial velocity, a is the constant acceleration, x is the final position, and x0 is the initial position.
Given that the car is initially at rest (v0x = 0 m/s) and accelerates at a constant rate of 4.9 m/s^2, we can plug these values into the equation. Solving for x, we have vx^2 = 22^2 m^2/s^2 and substituting the values into the equation, we find:
22^2 = 0 + 2(4.9)(x - 0)
484 = 9.8x
x = 484/9.8 ≈ 49.39 m
Therefore, when the car reaches a speed of 22 m/s, it has traveled approximately 49.39 meters.

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Answer:

Step-by-step explanation:

According to the figure, cos Ф = 16/20 = 4/5 = 0.80.

Using the inverse cosine function on a calculator, we get

Ф = 0.644 radians or 36.87 degrees or arccos 4/5

Answer:

Yes

Step-by-step explanation:

This is a function because every input only has one output.

Answer:

true

Step-by-step explanation:

Answer:

ill just help you out with this-

the slopes are

5/4 and 7

Step-by-step explanation:

so for question number 7 there  are black dots right? those indicate that theyre exact points (because sometimes in a graph you dont know if its 6 or 6.1, cause sometimes theyre very close)

so the point on the left side is (-2, -2) because x is on the left side of the y axis (the vertical line). since its below the x axis (the horizontal line) its negative

for the point on the right its the opposite, because x is on the right x is positive. because x is above the x axis, its positive (but it can also be positive if its on the x axis, x = 0)

the point on the right is (2, 3)

so we substitute these points into the equation for the slope

3 - (-2) / 2 - (-2) it doesnt matter which way you put them, but if you put the first y (-2, 2) (the 2) then you have to put the x from the first point

but anyways

3 - (-2) / 2 - (-2)

simplify:

3 + 2 / 2 + 2

5 / 4

so the slope is 5/ 4

run 5 rise 4

for the graph..the graph is really easy lol i like graphs

but anyways for the graph the points are already given

when x is 2, y is 14

when x is 5, y is 35

when x is ____, y is blah blah blah

so now all you have to do is substitute two points into the equation. it doesnt matter which points because the slope will still be the same for example:

you can substitute (2, 14) and (5, 35)

35 - 14/ 5 - 2

21 / 3

7

and you can also substitute (5, 35) and (10, 70)

70 - 35/ 10 - 5

35 / 5

7

and its still the same slope

Answer: five/four

7

Step-by-step explanation:

Subtract 14 from 35 to get 21. 21/

five minus two is 3

21/3 = 7

Answer:

The rate of snowfall can be computed as inches of snow per hour.

rate = 10 inches / (1.25 hours).

The denominator is the improper fraction 5/4.  To divide by 5/4, you multiply numerator bky 4/5...REMEMBER?

4/5 OF TEN EQUALS 8; THE RATE IS   8 inches/HOUR.

Step-by-step explanation:

Answer:

(0.5, 3)

Step-by-step explanation:

i used desmos

The value of measure of angle WPN is,

⇒ m ∠WPN = 108°

We have to given that;

Parallel lines EN, BH, and RK, with transversal PW are shown.

And, m ∠ BMV = 108° and m ∠KVS = 72°

Now, We get by definition of vertically opposite angle;

m ∠ BMV = m ∠PWN = 108°

Hence, By definition of alternate angle we get;

⇒ m ∠PWN = m ∠WPN = 108°

Thus, The value of measure of angle WPN is,

⇒ m ∠WPN = 108°

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The man buys 300 articles at 4 for $6, which means that he pays:

$6 for every 4 articles, or $1.50 per article.

The man then sells all 300 articles at $2 each, which means that he earns:

$2 for every article.

To find the man's profit, we need to subtract his cost from his revenue. His cost is the amount he paid for the 300 articles, which is:

300 articles * $1.50 per article = $450

His revenue is the amount he earned from selling the 300 articles, which is:

300 articles * $2 per article = $600

So his profit is:

$600 - $450 = $150

To find the profit made by the man on selling one article, we can divide his total profit by the number of articles he sold:

$150 / 300 articles = $0.50 per article.

Therefore, the man's profit on selling one article is $0.50

A statistically significant negative correlation coefficient of r = -0.91 was obtained from a sample of n = 30. This indicates a strong and significant negative relationship between the variables.

The researcher conducted a correlation analysis and found a correlation coefficient (r) of -0.91, which indicates a strong negative relationship between the variables under investigation. The negative sign indicates that as one variable increases, the other variable tends to decrease, and vice versa.

The statistical significance of the correlation coefficient is crucial in determining whether the observed relationship is likely to be due to chance or if it truly exists in the population. In this case, the report should highlight that the obtained correlation coefficient is statistically significant.

To establish statistical significance, the researcher likely conducted a hypothesis test, such as a t-test or a permutation test, to determine the probability of obtaining a correlation coefficient as extreme as -0.91 under the null hypothesis of no correlation. Since the obtained correlation coefficient is statistically significant, it suggests that the observed negative relationship is unlikely to be a result of chance and provides evidence for a genuine association between the variables in the population from which the sample was drawn.

Reporting this finding is important for conveying the strength and significance of the negative relationship to the readers, providing valuable insights for further analysis and interpretation of the variables under investigation.

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The geometric mean of two numbers is the square root of their product:

\(GM(a,b)=\sqrt{ab}\)

So, if the product is 8, the geometric mean is \(\sqrt{8}=2\sqrt{2}\)

Answer:

15, 13, 11, 7

Step-by-step explanation:

i) x= 1

then

y= 17-2(1)

y= 17-2

y= 15

.

.

.

.

.

Answer:

\(v=\sqrt{\frac{2KE}{m} }\)

Step-by-step explanation:

\(KE = 1/2mv^2\)

\(KE/1/2=mv^2\)

\(2KE=mv^2\)

\(2KE/m=v^2\)

\(\sqrt{2KE/m} =v\)

Answer:

slope = 2

Step-by-step explanation:

Answer:

\(\huge\boxed{f(x)=-2x-8\ \text{or}\ f(x)=2x+\dfrac{8}{3}}\)

Step-by-step explanation:

\(f(x)=ax+b\\\\(f\circ f)(x)=a(ax+b)+b=a^2x+ab+b\\\\(f\circ f)(x)=4x+8\\\Downarrow\\a^2x+ab+b=4x+8\Rightarrow a^2=4\ \wedge\ ab+b=8\\\\a^2=4\to a=\pm\sqrt4\to a=\pm2\\\\\text{for}\ a=-2:\\-2b+b=8\\-b=8\\\boxed{b=-8}\\\\\text{for}\ a=2:\\2b+b=8\\3b=8\\\boxed{b=\frac{8}{3}}\)

Okay, here are the steps:

* Hassam buys 2 adult tickets and 2 child tickets

* Let's assume:

** Adult ticket price = $50

** Child ticket price = $25

* So total ticket price = 2 * $50 + 2 * $25 = $200

* The booking fee is 5% of the total cost

* 5% of $200 is $10

* So total payment = $200 + $10 = $210

Therefore, the total Hassam pays altogether is $210

Answer:

$126.00

Step-by-step explanation:

divde by 2

Answer:

x=1

Step-by-step explanation:

If ∥v∥ = ∥w∥, then v⋅w = 0 and v⋅(v−w) = 0, showing that v⋅w and v−w are orthogonal.

Given vectors v and w in R^n, if their norms are equal (∥v∥ = ∥w∥), we can demonstrate that v⋅w and v⋅(v−w) are both equal to zero, indicating that v−w and v⋅w are orthogonal.

To prove this, we start with the dot product v⋅w. Using the properties of the dot product, we have v⋅w = ∥v∥ ∥w∥ cosθ, where θ is the angle between v and w. Since ∥v∥ = ∥w∥, the expression simplifies to v⋅w = ∥v∥^2 cosθ. If ∥v∥ = ∥w∥, it implies that ∥v∥^2 = ∥w∥^2, and thus, cosθ = 1.

As cosθ = 1, the dot product v⋅w becomes v⋅w = ∥v∥^2, which is equal to zero. Therefore, v⋅w = 0, indicating that v and w are orthogonal.

Next, we consider the dot product v⋅(v−w). Expanding this expression, we have v⋅(v−w) = v⋅v − v⋅w. Since v⋅w is zero (as shown earlier), the dot product simplifies to v⋅(v−w) = v⋅v = ∥v∥^2, which is again zero when ∥v∥ = ∥w∥.

Hence, we have demonstrated that v⋅w = 0 and v⋅(v−w) = 0 when ∥v∥ = ∥w∥, confirming that v−w and v⋅w are orthogonal.

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For vectors v and w with equal magnitudes, v w and v - w are orthogonal because the dot product equals zero, as proved step by step using properties of dot products and magnitudes.

In the field of linear algebra, the given question aims to prove that if for vectors v and w if the magnitudes are equal i.e. ∥v∥ = ∥w∥, then the vectors v w and v − w are orthogonal.

We'll prove this by showing that their dot product equals zero. For two vectors to be orthogonal, the dot product must be zero.

Hence, we have now proved that v w and v − w are indeed orthogonal.

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Answer: 11.1 m

Step-by-step explanation:

This can be solved by the Pythagorean theorem where;

c² = a² + b²

c is the hypotenuse which is the distance from the top of the building to the tip of the shadow.

a is the height

c is the length

32² = 30² + b²

b² = 32² - 30²

b² = 1,024 - 900

b² = 124

b = √124

b = 11.1 m