After parent teacher conferences, the seventh grade teachers go out to Logan’s for dinner. The total bill comes to $53.79. If they want to leave a 20% tip, about how much should they leave?

Answer:

the answer is 3

90÷3=30

so

10×3=300

10×3=3.00

Step 1

Let the first consecutive integer be n

Then the second will be n+1

The third will be n+2

Step 2

Write an inequality for the problem

Step 3

Solve the inequality

Step 4

Find the possible set of three integers to satisfy the inequality.

One possible set of three integers that satisfy the inequality is;

{4,5,6}

The graph of f(x)=−x^2 is a downward-opening parabola.

The graph of f(x)=−x^2 represents a quadratic function.

In this case, the coefficient of is -1, indicating that the parabola opens downwards. The negative sign in front of reflects the reflection of the graph across the x-axis.

The vertex of the parabola is located at the point (0, 0), which is the origin of the coordinate system. As we move to the left or right from the vertex, the function values decrease since the coefficient of is negative.

The graph is symmetrical with respect to the y-axis, meaning that for every x-value to the right of the vertex, there is a corresponding x-value to the left of the vertex that produces the same function value.

As x approaches positive or negative infinity, the function values also approach negative infinity. This indicates that the graph decreases without bound as x moves further away from the vertex in either direction.

Overall, the graph of f(x)=−x^2 is a downward-opening parabola that is symmetrical with respect to the y-axis and has its vertex at the origin (0, 0). It represents a quadratic function with a negative coefficient of resulting in a decreasing graph as x moves away from the vertex.

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The number of heads tossed on four distinct coins is a discrete random variable.

A discrete random variable can be a count or a finite set of values. Out of the options given in the question, the random variable that is discrete is the number of heads tossed on four distinct coins.

The correct option is: The number of heads tossed on four distinct coins is a discrete random variable.

The time spent waiting for a bus at the bus stop is a continuous random variable because time can take on any value in a given range. The amount of water traveling over a waterfall in one minute is also a continuous random variable because the water can flow at any rate.

The mass of a test cylinder of concrete is also a continuous random variable because the mass can take on any value within a certain range.

The number of heads tossed on four distinct coins, on the other hand, is a discrete random variable because it can only take on certain values: 0, 1, 2, 3, or 4 heads.

Hence, the number of heads tossed on four distinct coins is a discrete random variable.

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The number 0.0098 has two significant digits.In scientific notation, it can be written as 9.8 x 10^(-3), where the digits 9 and 8 are significant.

The leading zeros before the 9 do not contribute to the number of significant digits. Therefore, the correct answer is option a. 2.

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Answer:

Commutative property

Step-by-step explanation:

addition is commutative for example 2+3=3+2

multiplication is also commutative 3*2=2×3

Answer:

Ten thousands place, and its value is fifty thousand (50,000).

Step-by-step explanation:

3,152,308 in written form is:

"Three million, one hundred and fifty two thousand, three hundred and eight."

3,152,308

The underlined number is in the ten thousands place, and its value is 50,000.  In the attached image, I've plugged in your given numbers into the place value chart to show the place value of each digit.

Answer:

  A.  -5

Step-by-step explanation:

You want the slope of a graphed line that crosses grid points (0, 2) and (1, -3).

The sign of the slope is positive if the line goes up to the right. This line goes down to the right, so the sign of its slope is negative. (Eliminates choices C and D)

The magnitude of the slope is the ratio of vertical distance to horizontal distance between two points. This line drops 5 vertical squares for each square to the right, so its slope is ...

  rise/run = -5/1 = -5

The slope is best represented by -5.

__

Additional comment

From a point on the line that is a crossing of grid lines, if the line crosses the next vertical grid line before it crosses the next horizontal grid line, the magnitude of its slope is less than 1.

Here, the line crosses several horizontal grid lines before it crosses another vertical grid line, so its slope has a magnitude greater than 1. When the choice is between -5 and -1/5, the larger magnitude number is -5.

From two points on the line, you can find the slope using the formula ...

  m = (y2 -y1)/(x2 -x1)

  m = (-3 -2)/(1 -0) = -5/1 = -5 . . . . . . using points (0, 2) and (1, -3)

The TVM solver is a tool found in graphing calculators, that solve Time

Value of Money problems.

Reasons:

In the TVM solver, we have;

I = The annual percentage rate

N = n × t

t = The number of years

PV = Present value

PMT = Payment

P/Y = Number of payments per year = n

C/Y = Number of compounding periods per year = n

The formula for monthly payment is presented as follows;

\(M = \mathbf{\dfrac{P \cdot \left(\dfrac{r}{n} \right) \cdot \left(1+\dfrac{r}{n} \right)^{n \times t} }{\left(1+\dfrac{r}{n} \right)^{n \times t} - 1}}\)

Which gives;

\(P = \mathbf{\displaystyle \frac{M\cdot \left(\left(1+\dfrac{r}{n} \right)^{n \times t} - 1 \right) }{\left(\dfrac{r}{n} \right) \cdot \left(1+\dfrac{r}{n} \right)^{n \times t}}}\)

Therefore, we get;

Where;

M = PMT = -415

P = PV

r = I

P/Y = n = 12

Therefore;

\(\displaystyle 0.003 = \frac{I}{12}\)

I = 0.003 × 12 = 0.036 = 3.6%

N = n × t = 24

\(P = \displaystyle \frac{(415)\cdot \left(\left(1+\dfrac{I}{12} \right)^{24} - 1 \right) }{\left(\dfrac{I}{12} \right) \cdot \left(1+\dfrac{I}{12} \right)^{24}} = \mathbf{\displaystyle \frac{(415)\cdot \left(\left(1+0.003\right)^{24} - 1 \right) }{\left(0.003\right) \cdot \left(1+0.003 \right)^{24}}} = ?\)

The value of the equation is the present value, PV = ?

When payment are made based on the PV, we have FV = 0

The group of values the same value as the expression\(\displaystyle \frac{(\$415)\cdot (1 + 0.003)^{24} - 1}{(0.003) \cdot (1 + 0.003)^{24}}\), when plugged into the TVM solver of a calculator is; D. N = 24; I% = 3.6; PV =; PMT = -415; FV = 0; P/Y = 12; C/Y = 12; PMT :END

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Answer:

b = 40 and -40

General form of Perfect square trinomial is

a

2

+

2

a

b

+

b

2

Therefore from

16

x

2

−

b

x

+

25

a

2

=

√

16

x

2

,

b

2

=

25

, then

a

=

±

4

x

,

b

=

±

5

take consideration a=4x and b=-5 (different sign), then

−

b

x

=

2

(

4

x

)

(

−

5

)

−

b

x

=

−

40

x

b

=

40

The perfect square is

(

4

x

−

5

)

2

=

16

x

2

−

40

x

+

25

.

if we consider a=4x and b=5 (same sign), then

−

b

x

=

2

(

4

x

)

(

5

)

−

b

x

=

40

x

b

=

−

40

The perfect square is

(

4

x

+

5

)

2

=

16

x

2

+

40

x

+

25

.

The first solution

(

4

x

−

5

)

2

is the best solution after comparing the expression given.

All the given sets of integers except the set 25,41,49,64 are pairwise relatively prime. This is determined with the help of common factors.

To determine if the integers in each set are pairwise relatively prime, we need to check if each pair of integers in the set share a common factor other than 1. If there is no common factor other than 1, then the integers are pairwise relatively prime.

a. For the set {21, 34, 55}, the greatest common divisor (GCD) of any pair of integers is 1, indicating that they are pairwise relatively prime.

b. Similarly, for the set {14, 17, 85}, the GCD of any pair of integers is 1, indicating that they are pairwise relatively prime.

c. In the set {25, 41, 49, 64}, the integers 49 and 64 have a common factor of 7. Therefore, the integers are not pairwise relatively prime.

d. Finally, for the set {17, 18, 19, 23}, the GCD of any pair of integers is 1, indicating that they are pairwise relatively prime.

In summary, the integers 21, 34, 55 and 14, 17, 85 are pairwise relatively prime, while the integers 25, 41, 49, 64 are not pairwise relatively prime. The integers 17, 18, 19, 23 are also pairwise relatively prime.

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Answer:

I think it's -0.4 but tell me if I'm wrong

\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$1200\\ r=rate\to 0.2\%\to \frac{0.2}{100}\dotfill &0.002\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{weekly, thus fifty two} \end{array}\dotfill &52\\ t=years\dotfill &10 \end{cases} \\\\\\ A = 1200\left(1+\frac{0.002}{52}\right)^{52\cdot 10}\implies A \approx 1224.24\)

Answer: $1248 in compound interest for 10 years

Step-by-step explanation:

Answer:

A or C

Step-by-step explanation:

Using context clues, like "member states" in the key, and "pending withdrawal" on the bottom, it leads me to think it's either A or C. (Kind of leaning towards C)

-hope it helps

The absolute maximum value of f on d is 4, and it occurs when x = 2, y = 0. The absolute minimum value of f on d is -37, and it occurs when x = 1, y = 3.

To find the absolute maximum and minimum values of f on the set d, use the following steps:Step 1: Calculate the partial derivatives of f with respect to x and y. f(x, y) = x2 4y2 − 2x − 8y 1∂f/∂x = 2x - 2∂f/∂y = -8y - 8Step 2: Set the partial derivatives to zero and solve for x and y.∂f/∂x = 0 ⇒ 2x - 2 = 0 ⇒ x = 1∂f/∂y = 0 ⇒ -8y - 8 = 0 ⇒ y = -1Step 3: Check the critical point(s) in the given domain d. 0 ≤ x ≤ 2, 0 ≤ y ≤ 3Since y cannot be negative, (-1) is not in the domain d. Therefore, there is no critical point in d.Step 4: Check the boundary of the domain d. When x = 0, f(x, y) = -8y - 1When x = 2, f(x, y) = 4 - 8y - 2When y = 0, f(x, y) = x2 - 2x - 1When y = 3, f(x, y) = x2 - 2x - 37Therefore, the absolute maximum value of f on d is 4, and it occurs when x = 2, y = 0.The absolute minimum value of f on d is -37, and it occurs when x = 1, y = 3.

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function: $f(x,y) = \(x^2 - 4y^2 - 2x - 8y +1$\) , The given domain is \(x^2 - 4y^2 - 2x - 8y +1$\)

Now we have to find the absolute maximum and minimum values of the function on the given domain d.To find absolute maximum and minimum values of the function on the given domain d, we will follow these steps:

Step 1: First, we have to find the critical points of the given function f(x,y) within the given domain d.

Step 2: Next, we have to evaluate the function f(x,y) at each of these critical points, and at the endpoints of the boundary of the domain d.

Step 3: Finally, we have to compare all of these values to determine the absolute maximum and minimum values of f(x,y) on the domain d.

Now, let's find critical points of the given function f(x,y) within the given domain d.To find the critical points of the function \($f(x,y) =\(x^2 - 4y^2 - 2x - 8y + 1$\)\), we will find its partial derivatives with respect to x and y, and set them equal to zero, i.e.\(\($f(x,y) = x^2 - 4y^2 - 2x - 8y + 1$\)\)

Solving these equations, we get:\($x = 1$\) and \($y = -1$\)So, the critical point is \($(1,-1)$.\)

Now, we need to find the function value at the critical point and the endpoints of the boundary of the domain d. We will use these five points:\($(0,0),(0,3),(2,0),(2,3),(1,-1)$\).

Now, let's evaluate the function f(x,y) at each of these five points:\(\($f(x,y) = x^2 - 4y^2 - 2x - 8y + 1$\)\)

Therefore, the absolute maximum value of f(x,y) is 1, and the absolute minimum value of f(x,y) is -67 on the domain d.

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Answer:

rrfgggefgegeegfegefegegeegfgfgfdfefdfefgdfdfdddgedgdfdgedfgfedffdddfgfdgddfddfgdfdgdf

A graph of this system of equations on a coordinate plane is shown in the image attached below.

In order to to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;

y = 2x/5 + 4     ......equation 1.

-2x + 5y = -30     ......equation 2.

Making y the subject of formula in equation 2, we have the following:

5y = 2x - 30

Dividing both sides of the equation by 5, we have:

y = 2x/5 - 30

Based on the graph (see attachment), we can logically deduce that the solution to the given system of equations is non existent because the lines are parallel.

In conclusion, the given system of equations has no solution.

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a) The profit-maximizing output is the level of production where the marginal cost of producing each unit is equal to the marginal revenue earned from selling it.

From the graph, at a price of $12, the profit maximizing output the firm should produce is 10 units.

b) The total cost of production at the profit maximizing quantity can be calculated as:

Total cost = (Average Total Cost × Quantity)

= $7 × 10 units

= $70

c) To find the profit, we need to calculate the total revenue generated by producing and selling 10 units:

Total revenue = Price × Quantity

= $12 × 10 units

= $120

Profit = Total revenue – Total cost

= $120 – $70

= $50

d) The price of $12 is the market price for the product being sold by the firm. It is the price at which the buyers are willing to purchase the good and the sellers are willing to sell it.

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Answer:

used cars can have a lower initial cost

Step-by-step explanation:

it is not a risk/hinder to purchasing a used car

The value of C in the parallelogram B would be = 1.5

To determine the value of C from the parallelogram B, the formula for scale factor should be used and it's given below as follows:

Scale factor = bigger dimension/smaller dimension

where:

bigger dimension = 5.6

smaller dimension = 4.2

scale factor = 5.6/4.2 = 1.33

The value of C = 2/1.33 = 1.5

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Answer:

0.9

Step-by-step explanation:

20/23 = 0.869565217, which rounded to the nearest tenth is 0.9

Answer:

How can we do collaboration

Answer:

x=10

Step-by-step explanation:

Answer:

What is the equation of the graphed line written in standard form?" has four options: 2x + 3y = -6, 2x + 3y = 6, y=-2/3x-2, and y= 2/3x-2. The standard form of a linear equation is Ax + By = C, where A, B, and C are constants. In this case, the first two options, 2x + 3y = -6 and 2x + 3y = 6 are already in standard form. The last two options, y=-2/3x-2 and y= 2/3x-2 are not in standard form. However, without additional information such as a graph or coordinates of points on the line, it is not possible to determine which of these options is the correct equation for the graphed line.

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Answer:

41.6 yd³

Step-by-step explanation:

Volume = lwh

Volume = (2 yd)(4 yd )(5.2 yd) = 41.6 yd³

The correct box-and-whisker plot is the one labeled:

Average Monthly Temperatures

64   74   84  94  

The box ranges from 68 to 90, with the median at 84. The whiskers extend from 64 to 94. So, third option is the right answer.

To create a box-and-whisker plot, we need to organize the data in ascending order:

64, 68, 68, 74, 76, 82, 84, 86, 90, 90, 92, 94

Now, we can identify the key components of the box-and-whisker plot:

Minimum: 64 (the lowest value in the data set)

Lower Quartile (Q1): 68 (the median of the lower half of the data set)

Median (Q2): 84 (the middle value of the data set)

Upper Quartile (Q3): 90 (the median of the upper half of the data set)

Maximum: 94 (the highest value in the data set)

Using these values, we draw a box from Q1 to Q3, with a line marking the median (Q2). We also draw "whiskers" extending from the box to the minimum and maximum values. In this case, the box ranges from 68 to 90, with the median at 84. The whiskers extend from 64 to 94.

Therefore, the correct box-and-whisker plot is the one labeled:

Average Monthly Temperatures

64   74   84  94

The right answer is  third option.

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In linear programming, solutions that satisfy all of the constraints simultaneously are referred to as feasible solutions. These feasible solutions represent all the possible combinations of values for the decision variables that satisfy the constraints of the problem.

The main objective of linear programming is to find the optimal feasible solution that maximizes or minimizes a given objective function. The objective function represents the goal that needs to be achieved, such as maximizing profit, minimizing cost, or maximizing efficiency.

To find the optimal feasible solution, a linear programming algorithm is used to analyze all the possible combinations of decision variables and evaluate their objective function values. The algorithm starts by identifying the feasible region, which is the area that satisfies all the constraints.

Then, the algorithm evaluates the objective function at each vertex or corner of the feasible region to find the optimal feasible solution. The optimal feasible solution is the one that provides the best objective function value among all the feasible solutions.

Therefore, In linear programming, solutions that satisfy all of the constraints simultaneously are referred to as: linear programming

In summary, linear programming involves finding feasible solutions that satisfy all the constraints of the problem, and then selecting the optimal feasible solution that provides the best objective function value.

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Answer:

inequality

Step-by-step explanation:

Emphasis on in because that is the part that negates the equality.

Inequalities fit the description of all of the following.

1) 2 Linear Expressions: 2x ? 5y (EXAMPLE)

Linear expressions are expressions that have a variable to the first power.

2) OR Linear Expression and a Constant: 2x ? 5

A constant is a fixed value. For example, a variable is NOT a constant because if the variable changes, the value changes.

3) Are not equal: >, <, \(\geq\), \(\leq\)

Greater than, less than, greater than or equal to, and less than or equal to, are NOT equality.