Case Study 2: (remember to include your calculations. Just an answer will not receive full credit.) You are the owner of a chain of 3 successful restaurants with the following number of seats at each location: airport – 340 seats; downtown – 218 seats; and suburban – 164 seats. 1. If the liability insurance premium is $16,000 per year, how much of that premium should be allocated to each of the restaurants based on percent of total seating capacity. 2. If you open a fourth restaurant at the beach that has 150 seats and the liability insurance premium increases by 18%, what is the new allocation of insurance premium among the 4 locations?

the expression describing all the angles that are coterminal with 8° is: θ = 8° + 360°k, where k is an integer.

How to solve and what is angle?

An angle of 8° has an initial side on the positive x-axis and rotates counterclockwise by 8°.

Any angle coterminal with 8° can be expressed as:

θ = 8° + 360°k

where k is an integer.

Therefore, the expression describing all the angles that are coterminal with 8° is:

θ = 8° + 360°k, where k is an integer.

An angle is a geometric figure formed by two rays, called the sides of the angle, that share a common endpoint, called the vertex of the angle. Angles are typically measured in degrees or radians and are used to measure the amount of rotation or turn between two intersecting lines or planes.

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Answer:

-9.7

Step-by-step explanation:

Given

x + y when x =2.1 and y = -11.8​



Solution

x+y

substitute x=2.1 and y=-11.8

2.1+(-11.8)

2.1 - 11.8 = -9.7



The final answer is -9.7

The extremas of the function f(x) = x³ - 7x² + 10x are given as follows:

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Answer:

The rewritten equation is: \(x = \ln{4}\)

Step-by-step explanation:

The inverse operation of the exponential is the natural logarithm, \(\ln\), and the following property is used to solve this question:

\(\ln{e^x} = x\)

In this question, we have that:

\(4e^x = 16\)

\(e^x = \frac{16}{4}\)

\(e^x = 4\)

Applying the natural logarithm to both sides:

\(\ln{e^x} = \ln{4}\)

\(x = \ln{4}\)

The rewritten equation is: \(x = \ln{4}\)

The equivalent logarithmic equation is: \(x = \log(4)\)

The exponential equation is given as:

\(4e^x=16\)

Divide both sides of the equation by 4

\(e^x=4\)

Next, take the logarithm of both sides (to convert the expression to a logarithmic expression)

\(\log(e^x)=\log(4)\)

The logarithm of e^x is x.

So, we have:

\(x = \log(4)\)

Hence, the equivalent logarithmic equation is: \(x = \log(4)\)

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The computer can occupy a maximum of 1200 bytes of memory.

To determine the maximum memory capacity of a computer that can execute 300 instructions, we need to consider the representation of integers and the storage requirements for instructions.

If each instruction is stored in the entire memory word, it implies that each instruction occupies one memory word. Therefore, the number of instructions executed (300) directly corresponds to the number of memory words required.

The memory capacity of a computer is typically measured in bytes. However, since we are assuming each instruction occupies one memory word, we can consider the memory capacity in terms of memory words.

Hence, the maximum memory capacity this computer can occupy would be 300 memory words.

To convert this capacity into bytes, we need to know the size of a memory word. If we assume the computer uses a 32-bit word size, which is common in many systems, each memory word would consist of 4 bytes (32 bits / 8 bits per byte). Therefore, the maximum memory capacity in bytes would be:

300 memory words * 4 bytes per word = 1200 bytes.

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Answer:

20000

Step-by-step explanation:

Answer:

Hello, just a slight bit confused by your phrasing?

I would love to help, I just can't seem to understand how.

Step-by-step explanation:

Just let me know, here to help!

a) The percentage is 73%.

b) The ratio is 73:27

d) The decimal form is 0.73

e) The fraction is 73/100

The percentage of the model that is shaded is given by:

P = 100%*(shaded squares)/(total number of squares)

There are 100 squares in total, of these 73 are shaded, then the percentage is:

P = 100%*(73)/100 = 73%

b) The ratio is "shaded squares to non shaded squares"

There are 73 shaded squares and 27 non-shaded ones, then the ratio is 73:27

c) To get the equivalent decimal to a percentage, just divide it by 100%.

p = 73%/100%  =0.73

d) The equivalent fraction is the fraction we wrote on the first step, it is:

fraction = 73/100

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Using the concept of word problems and quadratic equation it will take 1 year until the sum of square of their ages be 45.

Word problems are mathematical problems that are delivered in ordinary words, instead of mathematical symbols.

Part of the problem with dealing with word problems that they first need to be translated into mathematical equations, and then the equations need to be solved.In this problem;

let x represent the number of years from now when the sum of square of their respective age will be

45.(x + 2)² + (x + 5)² = 45

Expanding the brackets;

x² + 4x + 4 + x² + 10x + 25 = 45

2x² + 14x + 29 = 45

2x² + 14x + 29 - 45 = 0

2x² + 14x - 16 = 0

Solving the quadratic equation for x;

x = 1, x = -8

Taking the positive value, the value of x is 1

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Answer:

y = -1 - 2/1x

Step-by-step explanation:

Glad to help! :)

Answer:157.5

Step-by-step explanation:becuase mutilpy 4.5x35 that equals 157.5

Answer:

The original tax credit was $2500, so 15% of that is:

0.15 x $2500 = $375

Therefore, buyers would receive a $375 tax credit if they purchased the vehicle one year after the sales reached the 60,000 unit threshold.

Answer:

\(\frac{3}{8}\)

Step-by-step explanation:

To make this a fraction, you do \(\frac{4.5}{12}\). This is now a simple division problem. 4.5 ÷ 12 = .375

.375 as a fraction is \(\frac{375}{1000}\). When you simplify, you get \(\frac{3}{8}\)

An example of a one-to-one function that is an isomorphism between sets P and Q is the function f: P -> Q defined as f(x) = 2x, where P and Q are the sets of integers.

An example of a one-to-one function that is an isomorphism between sets P and Q is the function f: P -> Q defined as f(x) = 2x, where P and Q are the sets of integers.

This function is one-to-one because for every element x in P, there is a unique element 2x in Q. It is onto because every element y in Q has a preimage x in P such that f(x) = y (e.g., y/2 = x).

Furthermore, this function preserves the group structure between P and Q, as it satisfies the properties of an isomorphism. In this case, the group structure is addition, and the function f preserves addition: f(x + y) = 2(x + y) = 2x + 2y = f(x) + f(y) for all x, y in P.

Therefore, the function f: P -> Q defined as f(x) = 2x is an example of a one-to-one function that is an isomorphism between sets P and Q.

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Answer:

The answer is number 3.

Step-by-step explanation:

-15 - 8 = -23

12 + 11 = 23

When you subtract -23 from 23 you have a sum of 0

Therefore the answer is 0

Answer:

x = 7

Step-by-step explanation:

Answer:

x= 1

Step-by-step explanation:

Add four to both sides of the equation:

10x-4+4 = 2x+4+4

Simplify:

10x = 2x+8

Subtract 2x from both sides:

8x = 8

Cancel out terms:

x=

Simplify:

x=1

Answer:

75-42=33

Step-by-step explanation:

We know that 70-40=30 and that 5-2=3, so this means that 30+3=33

A)78°

135°+a° =180°

a°=45°

57°+x°+a°=180°

57°+x°+45°=180°

102°+x°=180°

x°=180°-102°

x°=78°

the closest answer choice to this value is 372.32 yd2.

How to solve the question?

The given shape is a trapezoid, where the two parallel sides are the base and the top, and the height is the perpendicular distance between them. We can divide this trapezoid into a rectangle and a right triangle, as shown below:

 A (bottom     B (bottom

 left vertex)   right vertex)

We can find the length of the top side by adding the portions given on each side of the perpendicular, as follows:

top side = 6.4 yards + 14.9 yards = 21.3 yards (same as the base)

The area of the rectangle (ABCD) is the product of the base (21.3 yards) and the height (12.8 yards):

area of rectangle = 21.3 yards * 12.8 yards = 272.64 square yards

The area of the right triangle (BCD) is half the product of the height (12.8 yards) and the difference between the base and the top (21.3 yards - 6.4 yards = 14.9 yards):

area of triangle = 0.5 * 12.8 yards * 14.9 yards = 95.36 square yards

Therefore, the total area of the figure is the sum of the area of the rectangle and the area of the triangle:

total area = 272.64 square yards + 95.36 square yards = 368 square yards

Therefore, the closest answer choice to this value is 372.32 yd2.

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\((\stackrel{x_1}{8}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{8}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{5}-\underset{x_1}{8}}} \implies \cfrac{ 3 }{ -3 } \implies - 1\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{- 1}(x-\stackrel{x_1}{8}) \\\\\\ y-5=-x+8\implies {\Large \begin{array}{llll} y=-x+13 \end{array}}\)

Answer: below

Step-by-step explanation: 2 small toys

Answer:

2 toys.

Step-by-step explanation:

That would be 5/8 divided by 5/16

= 5/8 * 16/5

= 16/8

= 2.

Answer: No there isn't

Explanation:

A score of 53.7% is quite close to 50% and this is a true or false exam. Charlie could have easily gotten this result by indeed guessing and not studying. This test mark is therefore not high enough to disregard the teachers's claim. Were the results to be significantly high enough above 50% then it could be said that indeed Charlie does study for his exams.

Answer:

1/4

Step-by-step explanation:

Answer:

1/4

Step-by-step explanation:

1/8+1/8=2/8 simplified its 1/4 but if you dont want it simplified its 2/8

The percent of the increase, rounded to the nearest tenth of a percent, concerning the sales of boxes of cookies that Molly sold last month and this month, is 11.5%.

The percentage increase can be determined by finding the difference or the amount of increase in sales.

This difference is divided by the previous month's sales and multiplied by 100.

The total number of boxes of cookies Molly's Scout Troop sold last month = 148

The total number sold this month = 165

The increase = 17 (165 - 148)

Percentage increase = 11.5% (17 ÷ 148 x 100)

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The linear function is of:

P(t) = 3265t + 34687.

Using the linear function, the estimate for 2016 is of:

54,277.

The exponential function is of:

P(t) = 34687(1.0941)^t.

Using the exponential function, the estimate for 2016 is of:

59,499.

The linear function is defined as follows:

P(t) = mt + b.

The coefficients of the function are given as follows:

In the context of this problem, these parameters are given as follows:

Hence the function is:

P(t) = 3265t + 34687.

2016 is 6 years after 2010, hence the estimate is given as follows:

P(6) = 3265(6) + 34687 = 54,277.

The exponential function is defined as follows:

P(t) = ab^t.

In which the coefficients are given as follows:

Hence the parameters are given as follows:

Hence the function is of:

P(t) = 34687(1.0941)^t.

Then the estimate for the year of 2016 is of:

P(6) = 34687(1.0941)^6 = 59,499.

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The linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

To determine the linear function with the same y-intercept as the graph, we need to find the equation of the line passing through the points (3, 4) and (5, 0).

First, let's find the slope of the line using the formula:

slope (m) = (change in y) / (change in x)

m = (0 - 4) / (5 - 3)

m = -4 / 2

m = -2

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Using the point (3, 4) as our reference point, we have:

y - 4 = -2(x - 3)

Expanding the equation:

y - 4 = -2x + 6

Simplifying:

y = -2x + 10

Now, let's check the given options to find the linear function with the same y-intercept:

Option 1: The table with x-values (-3, -1, 1, 3) and y-values (-4, 2, 8, 14)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 2: The table with x-values (-4, -2, 2, 4) and y-values (-26, -18, -2, 6)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 3: The table with x-values (-5, -3, 3, 5) and y-values (-15, -11, 1, 5)

The y-intercept is the same as the given line (10). So, this option is correct.

Option 4: The table with x-values (-6, -4, 4, 6) and y-values (-26, -14, 34, 46)

The y-intercept is not the same as the given line. So, this option is not correct.

Therefore, the linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

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Answer:

436.42 m

Step-by-step explanation:

We are to determine the perimeter of the field

perimeter = perimeter of rectangle + perimeter of the two semicircles

Perimeter of a rectangle = 2 x (length + breadth)

2 x (82 + 53) = 270m

Perimeter of a semicircle = 1/2πD

perimeter of the 2 semicircles = 2 x (1/2 x 3.14 x 53) = 166.42

Perimeter = 270 + 166.42 = 436.42 m

Answer:

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

Taking the inverse tangent (arctan) of the given ratio 7/9.

Use a calculator or trigonometric table to find:

The approximate value of θ is 37.9°.

The vertex form of the quadratic function f(x) = 2x^2 + 8x + 7 is f(x) = 2(x + 2)^2 - 25.

Take a look at the quadratic function:

f(x) = 2x^2 + 8x + 7

In this situation, a = 2 and b = 8, yielding:

f(x) = 2(x^2 + 4x) + 7

It shtbe noted that to determine the value to add and subtract, multiply (b/2a)2 by (8/2(2))2 = 42 = 16. Inside the parenthesis, we add and subtract 16:

f(x) = 2(x^2 + 4x + 16 - 16) + 7

The expression inside the parenthesis can now be written as a perfect square:

f(x) = 2((x + 2)^2 - 16) + 7

Finally, the phrase is simplified by spreading the 2:

f(x) = 2(x + 2)^2 - 32 + 7

f(x) = 2(x + 2)^2 - 25

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What is the vertex form of the quadratic function f(x) = 2x^2 + 8x + 7