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Dovator [93]
3 years ago
13

It costs $60 to reserve a movie theater for a party. There is also a charge of $3 for each person. Write an expression that repr

esents the total cost to reserve a movie theater for (n) persons?
Mathematics
1 answer:
dimulka [17.4K]3 years ago
6 0

Answer

Now I'm not the best at this so don't go with mine but i'm gonna say

the expression could be n x 3 + 60

Step-by-step explanation:

if n = 4 then multiply 3 x 4 = 12 then 12 + 60 = 72

I don't know sorry i tried

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Find all solutions to 0= 2x^4+5x^3+38x^2+125x-300
Mariana [72]
2x^4+5x^3+38x^2+125x-300=0\\\\2x^4+5x^3-12x^2+50x^2+125x-300=0\\\\x^2(2x^2+5x-12)+25(2x^2+5x-12)+0\\\\(2x^2+5x-12)(x^2+25)=0\\\Updownarrow\\1^o\ 2x^2+5x-12=0\ \vee\ 2^o\ x^2+25=0\\\\\\1^o\ \Delta=5^2-4\cdot2\cdot(-12)=25+96=121\\\\\sqrt\Delta=\sqrt{121}=11\\\\x_1=\frac{-5-11}{2\cdot2}=\frac{-16}{4}=-4;\ x_2=\frac{-5+11}{2\cdot2}=\frac{6}{4}=\frac{3}{2}\\\\\\2^o\ x^2=-25-false\\\\\\Answer:x=-4\ or\ x=\frac{3}{2}
3 0
3 years ago
Surface area and volume of a regular triangular pyramid that has a base edge of 16 cm and a slant height of 15 cm
Schach [20]

Answer:

a) Surface area = 616 cm²

b) Volume = V = 1083 cm³

Step-by-step explanation:

Surface area and volume of a regular triangular pyramid that has a base edge of 16 cm and a slant height of 15 cm

a) Formula for surface area = Base area × 1/2(perimeter × slant height)

Base area = Base edge²

=( 16 cm)² = 256 cm²

Perimeter = Base edge × 3

= 16 cm × 3 = 48 cm

Hence:

Surface Area = 256 cm² + 1/2(48 × 15)

= 256 cm² + 360 cm²

= 616 cm²

b) Volume = 1/3 × Base area × Height

1082.758616785cm³

Approximately = 1083 cm³

8 0
3 years ago
Jan wants to protect the wooden box in question 4a by painting varnish on all of the outside surfaces, including the bottom. Wil
Dafna1 [17]

Answer:

As this question is incomplete, but we will try to solve this question by adding our own data to understand the concept of the problem.

Explanation is given below

Step-by-step explanation:

As this question is incomplete, but we will try to solve this question by adding our own data to understand the concept of the problem.

In order to answer this question we need to have the dimensions of the box.

Let's suppose there are 6 outside surfaces of the box and are equal in dimension including the bottom side which Jan wants to varnish.

So,

Let's suppose,

Surface area of the cube = 6a^{2}

Here, Surface area = 275 square inch

Surface area of the cube = 6a^{2} = 275 square inch

a^{2} = 275/6 = 45.833

a = \sqrt{45.833}

a = 6.77 inches

Now, for the amount of the varnish, we need the spreading rate of the varnish to be used on the box,

Let's suppose it is = 11 square incher per litre.

So,

Required Varnish = Surface area / Spreading rate

Required varnish = 275 / 11

Required varnish = 25 liters

If the 1 container of varnish contains 25 liters then it will be sufficient to protest the outside surfaces of the box.

6 0
3 years ago
1400 dollars is placed in an account with an annual interest rate of 5.5%. to the nearest year, how long will it take for the ac
olga_2 [115]

It will take 19 years and 6 months for the account value to reach 2900 dollars

Step-by-step explanation:

Given

Principal amount = 1400 dollars

Rate = 5.5 %

Final value = A = 2900

We have to find t

So,

The formula for simple interest is:

A = P(1+rt)

Putting values

2900 = 1400(1+0.055.t)\\\frac{2900}[1400} = 1+0.055t\\2.071 = 1+0.055t\\2.071-1=0.055t\\1.071 =0.055t

Dividing both sides by 0.055

\frac{0.055t}{0.055} = \frac{1.071}{0.055}\\t = 19.47\ years

Rounding off to nearest tenth

19.5 years

Hence,

It will take 19 years and 6 months for the account value to reach 2900 dollars

Keywords: Interest, simple interest

Learn more about interest at:

  • brainly.com/question/2654504
  • brainly.com/question/2654231

#LearnwithBrainly

6 0
3 years ago
Provide an example of optimization problem
Mashutka [201]

Answer:

a. Convex solutions ,GO Methods

b. market efficiency

Explanation :

Step-by-step explanation:

A globally optimal solution is one where there are no other feasible solutions with better objective function values. A locally optimal solution is one where there are no other feasible solutions "in the vicinity" with better objective function values. You can picture this as a point at the top of a "peak" or at the bottom of a "valley" which may be formed by the objective function and/or the constraints -- but there may be a higher peak or a deeper valley far away from the current point.

In convex optimization problems, a locally optimal solution is also globally optimal. These include LP problems; QP problems where the objective is positive definite (if minimizing; negative definite if maximizing); and NLP problems where the objective is a convex function (if minimizing; concave if maximizing) and the constraints form a convex set. But many nonlinear problems are non-convex and are likely to have multiple locally optimal solutions, as in the chart below. (Click the chart to see a full-size image.) These problems are intrinsically very difficult to solve; and the time required to solve these problems to increases rapidly with the number of variables and constraints.

GO Methods

Multistart methods are a popular way to seek globally optimal solutions with the aid of a "classical" smooth nonlinear solver (that by itself finds only locally optimal solutions). The basic idea here is to automatically start the nonlinear Solver from randomly selected starting points, reaching different locally optimal solutions, then select the best of these as the proposed globally optimal solution. Multistart methods have a limited guarantee that (given certain assumptions about the problem) they will "converge in probability" to a globally optimal solution. This means that as the number of runs of the nonlinear Solver increases, the probability that the globally optimal solution has been found also increases towards 100%.

Where Multistart methods rely on random sampling of starting points, Continuous Branch and Bound methods are designed to systematically subdivide the feasible region into successively smaller subregions, and find locally optimal solutions in each subregion. The best of the locally optimally solutions is proposed as the globally optimal solution. Continuous Branch and Bound methods have a theoretical guarantee of convergence to the globally optimal solution, but this guarantee usually cannot be realized in a reasonable amount of computing time, for problems of more than a small number of variables. Hence many Continuous Branch and Bound methods also use some kind of random or statistical sampling to improve performance.

Genetic Algorithms, Tabu Search and Scatter Search are designed to find "good" solutions to nonsmooth optimization problems, but they can also be applied to smooth nonlinear problems to seek a globally optimal solution. They are often effective at finding better solutions than a "classic" smooth nonlinear solver alone, but they usually take much more computing time, and they offer no guarantees of convergence, or tests for having reached the globally optimal solution.

5 0
4 years ago
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