Suppose C is a 3 x 3 matrix such that det (C) = 4. Show that det (C+C) is equal to 32

Answer:

The total resistance is [tex]7.0588\Omega[/tex]

Step-by-step explanation:

Attached please find the circuit diagram. The circuit is composed by a voltage source and two resistors connected in parallel: [tex]R_1=10\Omega [/tex] and [tex]R_2=24\Omega [/tex].

First step: find the total current

For finding the current that the voltage source can provide, you must find the current consumed by each load and then add both. To do that, take first into account that the voltage is the same for both resistors ([tex]R_1[/tex] and [tex]R_2[/tex]).

The total current is:

[tex]I_{TOTAL}=I_{R_1}+I_{R_2}=\frac{V_S}{R_1}+\frac{V_S}{R_2}=\frac{R_2\cdot V_S+R_1\cdot V_S}{R_1\cdot R_2}[/tex]

[tex]I_{TOTAL}=V_S\cdot \frac{R_1+R_2}{R_1\cdot R_2}[/tex]

Now, the total resistance ([tex]R_{TOTAL}[/tex]) would be the voltage divided by the total current:

[tex]R_{TOTAL}=\frac{V_S}{I_{TOTAL}}[/tex]

If you replace [tex]I_{TOTAL}[/tex] by the expression obtained previously, the total resistance would be:

[tex]R_{TOTAL}=\frac{V_S}{V_S\cdot \frac{R_1+R_2}{R_1\cdot R_2}}[/tex]

After simplifying the terms you should get:

[tex]R_{TOTAL}=\frac{R_1\cdot R_2}{R_1 + R_2}}[/tex]

Now, you must replace the values of the resistors:

[tex]R_{TOTAL}=\frac{(10\Omega )\cdot (24\Omega)}{10\Omega + 24\Omega}}=\frac{120}{17}\Omega=7.0588\Omega [/tex]

Thus, the total resistance is [tex]7.0588\Omega[/tex]

Answer:

The total you have to pay for the TV is $115.9

Step-by-step explanation:

When we have a discount we have to make a substraction, when we have tax we have to sum so:

$125.67 * 15 % = 18.85

125.67 - 18.85 = 106.82

Now we have to add the tax

106.82 * 8.5% = 9.08

106.82 + 9.08 = 115.9

Answer: She spend $1.20 for lunch.

Step-by-step explanation:

Let the total amount be 'x'.

Half of her money spend for lunch be [tex]\dfrac{x}{2}[/tex]

Half of her money left for a movie be [tex]\dfrac{x}{2}[/tex]

Amount she has now = $1.20

So, According to question, it becomes ,

[tex]\dfrac{x}{2}=1.20\\\\x=1.20\times 2\\\\x=\$2.40[/tex]

Hence, Amount she spend for lunch is [tex]\dfrac{x}{2}=\dfrac{2.40}{2}=\$1.20[/tex]

Therefore, she spend $1.20 for lunch.

Answer:

A. 1.84

Step-by-step explanation:

We have been given that Karen Price's net worth is $58,000. The face value of her mortgage is $89,000. The face value of the rest of her debt is $18,000.

[tex]\text{Debt to equity ratio}=\frac{\text{Total liabilities}}{\text{Total shareholder's equity}}[/tex]

We know that total liabilities include short term debt and long-term debt.

[tex]\text{Debt to equity ratio}=\frac{\$89,000+\$18,000}{\$58,000}[/tex]

[tex]\text{Debt to equity ratio}=\frac{\$107,000}{\$58,000}[/tex]

[tex]\text{Debt to equity ratio}=1.8448[/tex]

[tex]\text{Debt to equity ratio}\approx 1.84[/tex]

Therefore, Karen's debt-to-equity ratio 1.84 and option A is the correct choice.

By their mutual exclusivity,

[tex]P(A\cup B\cup C)=P(A)+P(B)+P(C)=0.96[/tex]

[tex]P(A\cap B\cap C)=0[/tex]

[tex]P(A\cap B)=0[/tex]

For the last probability, first distribute the intersection:

[tex](A\cup B)\cap C=(A\cap C)\cup(B\cap C)[/tex]

Recall that for two event [tex]X,Y[/tex],

[tex]P(X\cup Y)=P(X)+P(Y)-P(X\cap Y)[/tex]

so that

[tex]P((A\cap C)\cup(B\cap C))=P(A\cap C)+P(B\cap C)-P((A\cap C)\cap(B\cap C))[/tex]

[tex]P((A\cap C)\cup(B\cap C))=P(A\cap C)+P(B\cap C)-P(A\cap B\cap C)=0[/tex]

Answer:

Sample mean tensile strength for 20°C [tex]\bar X_{20} =2.11[/tex]Mp

Sample mean tensile strength for 45°C [tex]\bar X_{45} =2.235[/tex]Mp

Step-by-step explanation:

A dot plot for combined data allows comparison between the responses of an experiment to two or more independent factors. In this case there are 12 experimental observations of tensile strength on silicone rubber for two levels of the curing temperature factor (30°C and 45°C)

The sample mean can be calculated by:

[tex]\bar X_{20} = \frac{1}{n}\sum{x_i}=2.11[/tex]Mp

[tex]\bar X_{45} = \frac{1}{n}\sum{x_i}=2.235[/tex]Mp

The dot plot can be observed in the attached file.

Answer: If A ⊂ B, then A = B \ ( B \ A)

ok, when you do B \ A, you are subtracting all the elements in A∩B from B. So the only elements remaining are those who aren't in A.

If we subtract this of B again, we are subtracting of B all the elements that aren't in A, so the only elements remaining are those who belongs in A.

If A ⊂ B then A U (B \ A) = B.

Again, when you do B \ A you are extracting all the elements that belongs to the A∩B from B. So you are extracting al the elements from A. and when you add all the elements of A again, then you recuperate B.

if AnC = AnC does not imply that B = C.

if A = {1,2}, B = {1,2,3,4,5} and C = {1,2,3}

then AnC = {1,2} and AnB = {1,2} but B and C are different.

Answer:

Step-by-step explanation:

let whole sale cost=100

retail cost=100+40% of 100=100+40=140

to find the ratio

(retail cost)/(whole cost)=140/100=14/10=1.4

so retail cost=1.4*whole cost

or retail cost is 1.4 times the whole cost.

The retail cost of a TV, which is 40% more than its wholesale cost, is 1.4 times the wholesale cost. For instance, if the wholesale cost is $500, the retail cost would be $700.

The retail cost of a TV is 40% more than its wholesale cost. To find out how many times more the retail cost is compared to the wholesale cost, we need to understand percentage increase calculations.

Let the wholesale cost of the TV be represented by 1 (or 100%). An increase of 40% on this cost means the TV now costs:

1 + 0.40 = 1.40.

Therefore, the retail cost of the TV is 1.4 times the wholesale cost.

For example, if the wholesale cost of a TV is $500, then the retail cost would be:

$500 × 1.4 = $700.

Answer:

for all values

Step-by-step explanation:

u = (t - 2, 6 - t, - 4)

v = ( - 4, t - 2, 6 - t)

Angle between them, θ = 120°

Use the concept of dot product of two vectors

[tex]\overrightarrow{A}.\overrightarrow{B}=A B Cos\theta[/tex]

Magnitude of u = [tex]\sqrt{(t-2)^{2}+(6-t)^{2}+(-4)^{2}}[/tex]

                         = [tex]\sqrt{2t^{2}-16t+56}[/tex]

Magnitude of v = [tex]\sqrt{(t-2)^{2}+(6-t)^{2}+(-4)^{2}}[/tex]

                         = [tex]\sqrt{2t^{2}-16t+56}[/tex]

[tex]\overrightarrow{u}.\overrightarrow{v}=-4(t-2)+(6-t)(t-2)-4(6-t)=-t^{2}+8t-28[/tex]

By the formula of dot product of two vectors

[tex]Cos120 = \frac{-t^{2}+8t-28}{\sqrt{2t^{2}-16t+56}\times \sqrt{2t^{2}-16t+56}}[/tex]

[tex]-0.5\times {2t^{2}-16t+56} = {-t^{2}+8t-28}}[/tex]

[tex]{-t^{2}+8t-28}} = {-t^{2}+8t-28}}[/tex]

So, for all values of t the angle between these two vectors be 120.

Answer:

The required expression is y = 1.4 - 0.05x

Step-by-step explanation:

Consider the provided information.

Food mix A contains 2% fat and food mix B contains 7​% fat.

Let x kilograms of food A are​ used, in a 20​-kilogram mixture.

Thus, 20 - x kilograms of food B are​ used, in a 20​-kilogram mixture.

Now It is given that A contains 2% fat and food mix B contains 7​% fat.

2% and 7% can be written as 0.02 and 0.07 respectively. Let represent the total fat with y.

Thus, the required expression is:

y = 2% (x) + 7% (20 - x)

y = 0.02 (x) + 0.07 (20 - x)

y = 0.02x + 1.4 - 0.07x

y = 1.4 - 0.05x

Hence, the required expression is y = 1.4 - 0.05x

Answer:

Take 5 ml of dye and add 3 ml of water

Thus,

The total volume of solution becomes = 8 mL

now,

This solution of 8 mL contains [tex]\frac{\textup{5}}{\textup{8}}[/tex] part of dye and [tex]\frac{\textup{3}}{\textup{8}}[/tex] part of water.

Next step is to take out 2 mL of solution

thus,

Volume of dye in 2 mL solution = [tex]\frac{\textup{5}}{\textup{8}}\times2\ mL[/tex]

or

Volume of dye in 2 mL solution = 1.25 mL

hence,

the 1.25 mL dye is measured.

Step-by-step explanation:

Given:

10-mL graduate calibrated in 1-mL units

dye solution to be measured = 1.25 mL

Now,

take 5 ml of dye and add 3 ml of water

Thus,

The total volume of solution becomes = 8 mL

now,

This solution of 8 mL contains [tex]\frac{\textup{5}}{\textup{8}}[/tex] part of dye and [tex]\frac{\textup{3}}{\textup{8}}[/tex] part of water.

Next step is to take out 2 mL of solution

thus,

Volume of dye in 2 mL solution = [tex]\frac{\textup{5}}{\textup{8}}\times2\ mL[/tex]

or

Volume of dye in 2 mL solution = 1.25 mL

hence,

the 1.25 mL dye is measured.

To measure 1.25 mL of a dye solution using a 10-mL graduate, fill it with water up to the 1 mL mark. Add the dye solution drop by drop until the meniscus reaches the 2.25 mL mark.

To measure 1.25 mL of a dye solution using a 10-mL graduate calibrated in 1-mL units and water as the diluent, you can follow these steps:

https://brainly.com/question/1814591

#SPJ3

Answer:

3x^2-2x+2-x^2-5x+5

2x^2-7x+7

Answer:

4x^2+3x-3

Step-by-step explanation:

(3x^2-2x+2)-(x^2+5x-5)

3x^2+1x^2=4x^2

2x-5x=3x

2-5=3

4x^2+3x-3

Answer:  There are 15 possible ways to fill in answers  .

Step-by-step explanation:

Given : The number of multiple choice questions = 5

The total number of choices for each question {a, b,

and c} = 3

Now by using the fundamental principle of counting , the number of possible ways to fill in answer is given by :-

[tex]5\times3=15[/tex]

Therefore, there are 15 possible ways to fill in answers  .

Answer and explanation :

Unbounded solutions :

Unbounded solution is the case where we can't find the exact solution. In this case there are infinite number of solutions and it is not possible to find exact solution in which these situations occurs.

When we use graphical method to solve the problem then in unbounded solution there is no boundary so that we can determine the maximum possible region in which solution occurs.

Answer:

Sets

Step-by-step explanation:

1) Set can be defined as a collection of objects that are well defined and distinct.

2) Since each idea has its own unique value or characteristic, they can be considered as objects.

3) Thus, a collection of ideas can be considered as a set.

4) In this case we would define the null set as the set with no ideas.

5) The sets can be represented with the help of curly brackets { }.

6) We can represent it in the set form as:

{Idea 1, Idea 2, Idea 3, Idea 4,...}

7) It can be considered a countable set as we can always count the number of ideas.

8) It is a finite set.

Answer:

To break even it  must be molded 1280 handles weekly.

The profit if 1500 handles are produced and sold is $440

Step-by-step explanation:

To break even, the amount of total cost must be the same as the amount of revenues.  

Total Cost is Fixed cost plus unitary variable cost multiplied by the produce quantity.  

Total cost= FC + vc*Q

Where

FC=Fixed cost

vc=unitary variable cos

Q=produce quantity

Revenue= Price * Q

Break even FC + vc*Q=Price * Q

Isolating Q

FC=(Price * Q)-(vc*Q)

FC=(Price-vc) * Q

Q= FC/(Price-vc)

Q= $2560/($3.00-$1.00)=1280

If we sold 1500 handles

Profit = Revenue- Total cost =(Price * Q)-(FC + vc*Q)

P=$3.00 *1500-$2560 - $1.00*1500=

P=$4500-$2560-$1500=440

Final answer:

Northwest Molded must sell 1,280 handles to break even, based on their fixed weekly costs of $2,560 and a variable cost of $1.00 per handle with a selling price of $3.00 each. If they produce and sell 1,500 handles, they will make a profit of $440.

Explanation:

To calculate the break-even point for Northwest Molded, we need to determine the number of handles that must be sold to cover the total costs, which include both fixed and variable costs.

The fixed cost to operate the molding machine is $2,560 per week, and the variable cost per handle is $1.00.

Each handle is sold for $3.00. The break-even point is reached when total cost equals total revenue, which can be found using the break-even formula:

Break-even point in units = Fixed costs / (Selling price per unit - Variable cost per unit)

Thus, for Northwest Molded:

Break-even point in units = $2,560 / ($3.00 - $1.00) = $2,560 / $2.00 = 1,280 handles

To calculate the profit for producing and selling 1,500 handles, we need to compute the total revenue and subtract the total costs:

Total Revenue = Selling price per unit × Number of units sold = $3.00 × 1,500 = $4,500

Total Costs = Fixed costs + (Variable cost per unit × Number of units sold) = $2,560 + ($1.00 × 1,500) = $4,060

Profit = Total Revenue - Total Costs = $4,500 - $4,060 = $440

Therefore, in order to break even, Northwest Molded must mold and sell 1,280 handles weekly, and the company would make a profit of $440 if they produced and sold 1,500 handles.

Answer:

565 units/hour

Step-by-step explanation:

As given in question,

rate of infusion of pump = 11.3 mL/hr

amount of heparin infusion bag contains = 25,000 units

amount of solution in infusion bag = 500 mL

Since, 500 mL of solution contains 25000 units of heparin

[tex]\textrm{So, 1 mL of solution will contain heparin of amount}=\dfrac{25000}{500}units[/tex]

                                                                                    = 50 units

Since, 11.3 mL of solution can flow in 1 hour

So, the heparin contains in 11.3 mL of solution = 11.3 x 50

                                                                             = 565 units

As, 565 units of heparin can flow in 1 hour so the rate of flow of heparin will be 565 units/hour.

Answer:

x = -1

Step-by-step explanation:

5x - 6 = 3x - 8

-3x        -3x

2x - 6 = -8

+6         +6

2x = -2

----   ----

2      2

x = -1

Hey!

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

Steps To Solve:

5x - 6 = 3x - 8     ​

~Subtract 3x to both sides

5x - 6 - 3x = 3x - 8 - 3x

~Simplify

2x - 6 = -8

~Add 6 to both sides

2x - 6 + 6 = -8 + 6

~Simplify

2x = -2

~Divide 2 to both sides

2x/2 = -2/2

~Simplify

x = -1

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

Answer:

[tex]\large\boxed{x~=~-1}[/tex]

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

Hope This Helped! Good Luck!

Answer:  {1 ,2 ,3 }

Step-by-step explanation:

We know that a sample space is a set of possible occurring oin an experiment.

Given : An die (six faces) has the number 1 painted on three of its faces, the number 2 painted on two of its faces, and the number 3 painted on one face.

We assume that each face is equally likely to come up.

When we toss a dice , then the possible occurring =  1 , 2, 3

Then, the sample space for this experiment will be {1 ,2 ,3 }

Final answer:

Explaining the sample space for an experiment with a die displaying numbers in different frequencies.

Explanation:

An die (six faces) has the number 1 painted on three of its faces, the number 2 painted on two of its faces, and the number 3 painted on one face. The sample space for this experiment would be: {1, 1, 1, 2, 2, 3}.

This means that when you roll the die, the possible outcomes are: 1, 1, 1, 2, 2, 3.

Answer:

  (a) yes, (-2√2, 1) is on the graph

  (b) f(2) = 4/5, the point is (2, 4/5)

  (c) (-2√2, 1), and (2√2, 1)

  (d) all real numbers

  (e) (0, 0)

  (f) (0, 0)

Step-by-step explanation:

You want various points on the graph of the function ...

  [tex]\displaystyle f(x)=\frac{16x^2}{x^4+64}[/tex]

Yes, this point is on the graph. The value of f(x) can be found easily by realizing -2√2 = -√8, so ...

and the function value is ...

  [tex]f(-2\sqrt{2})=\dfrac{16\cdot8}{64+64}=\dfrac{128}{128}=1[/tex]

Substituting 2 for x, we have ...

  [tex]f(2) = \dfrac{16\cdot 2^2}{2^4+64}=\dfrac{64}{16+64}=\dfrac{64}{80}\\\\\boxed{f(2)=\dfrac{4}{5}}[/tex]

The point on the graph is (2, 4/5).

The answer to part (a) tells you that one of the points where f(x) = 1 is ...

  (-2√2, 1)

Since the sign of x is irrelevant, another point where x=1 is ...

  (2√2, 1)

There are no values of x that make the denominator of this rational function zero, so its domain is all real numbers.

The only x-value where f(x) = 0 is x = 0.

The x-intercept is (0, 0).

The function crosses the y-axis at the origin.

The y-intercept is (0, 0).

The tank as a cone.

As per the question, the tank is given a shape of an inverted circular cone has a point to the bottom with an height of radius of 4 feet. The tank is full of water the pipe can be cued to pump out the water from the top and until which the tank ill have a level of 5 feet from the bottom.

Thus the answer is W equals to 468832 foot-pound

Learn more about the shape of an inverted.

https://brainly.com/question/23758952.

To calculate the work required to pump water from an inverted circular cone tank, we use a formula that accounts for the weight density of water, volume of water, and height the water is lifted. We integrate from the middle of the tank, where the water level is 5 feet high, up to the top. The work is expressed in foot-pounds and involves an integral that can be solved using calculus.

To calculate the work W required to pump water out of an inverted circular cone tank, we must use the concept of work done against gravity. The formula for work is W = γ x V x h, where γ (gamma) represents the weight density of water, V is the volume of water being lifted, and h is the distance the water is lifted.

Since the tank is a cone and water is being lifted from the current water height to the top of the tank, we have to integrate the work done for each infinitesimally small volume δV of water from the water level at 5 feet to the top at 10 feet. The water has a circular cross-section at any height y, with a radius that can be determined by similar triangles.

As the radius of the tank at the top is 4 feet and the height is 10 feet, the radius r at height y is (4/10)*y. The cross-sectional area A at height y is πr^2, which is (π * (4/10)^2 * y^2). The volume element δV is then A δy, and the work element δW is γ * A * (10 - y) δy. The total work is found by integrating δW from 5 to 10 feet.

The weight density of water γ is typically 62.4 lb/ft^3, so the integral becomes: W = ∫ γ * π * (16/100) * y^2 * (10 - y) dy from 5 to 10. This integral can then be evaluated to find the total work W in foot-pounds.

Answer:

168 of these adults only watched TV last Friday night

Step-by-step explanation:

To solve this problem, we must build the Venn's Diagram of this set.

I am going to say that:

-The set A represents the adults that watched TV

-The set B represents the adults that hung out with friends.

-The set C represents the adults that ate pizza

-The set D represents the adults that did not do any of these three activities.

We have that:

[tex]A = a + (A \cap B) + (A \cap C) + (A \cap B \cap C)[/tex]

In which a is the number of adults that only watched TV, [tex]A \cap B[/tex] is the number of adults that both watched TV and hung out with friends, [tex]A \cap C[/tex] is the number of adults that both watched TV and ate pizza, and [tex]A \cap B \cap C[/tex] is the number of adults that did all these three activies.

By the same logic, we have:

[tex]B = b + (B \cap C) + (A \cap B) + (A \cap B \cap C)[/tex]

[tex]C = c + (A \cap C) + (B \cap C) + (A \cap B \cap C)[/tex]

This diagram has the following subsets:

[tex]a,b,c,D,(A \cap B), (A \cap C), (B \cap C), (A \cap B \cap C)[/tex]

There were 525 adults suveyed. This means that:

[tex]a + b + c + D + (A \cap B) + (A \cap C) + (B \cap C) + (A \cap B \cap C) = 525[/tex].

Solution

We build the sets from what the problem states:

96 did not do any of these three activities:

[tex]D = 96[/tex]

25 watched TV, hung out with friends, and ate pizza:

[/tex]A \cap B \cap C = 25[/tex]

32 hung out with friends and ate pizza, but did not watch TV:

[tex]B \cap C = 32[/tex]

50 watched TV and hung out with friends, but did not eat pizza:

[tex]A \cap B = 50[/tex]

26 watched TV and ate pizza, but did not hang out with friends:

[tex]A \cap C = 26[/tex]

152 ate pizza:

[tex]C = 152[/tex]

[tex]C = c + (A \cap C) + (B \cap C) + (A \cap B \cap C)[/tex]

[tex]152 = c + 26 + 32 + 25[/tex]

[tex]c = 69[/tex]

166 hung out with friends

[tex]B = 166[/tex]

[tex]B = b + (B \cap C) + (A \cap B) + (A \cap B \cap C)[/tex]

[tex]166 = b + 32 + 50 + 25[/tex]

[tex]b = 59[/tex]

How may 18-24 year olds (of these three activities) only watched TV last Friday night?

We can find the value of a from the following equation:

[tex]a + 59 + 69 + 96 + 50 + 26 + 32 + 25 = 525[/tex]

[tex]a = 525 - 357[/tex]

[tex]a = 168[/tex]

168 of these adults only watched TV last Friday night

Answer:

(a) 7

(b) -3

(c) [tex]-\frac{9}{8}[/tex]

(d) -1

Step-by-step explanation:

(a) 5x - 7 = 28

5x = 28 + 7

5x = 35

⇒ x = 7

(b) 12 - 5x = x + 30

-5x = x + 30 - 12

-5x = x + 18

-5x - x = 18

-6x = 18

⇒ x = -3

(c) 5(x+2) = 1 - 3x

5x + 10 = 1 - 3x

5x = 1 - 3x - 10

5x + 3x = -9

8x = -9

⇒ x = [tex]-\frac{9}{8}[/tex],

(d) Given system of equations,

Зx-y = -5 ------(1),

x + 2y = 3 ----(2),

Equation (2) + 2 equation (1),

x + 6x = 3 - 10⇒ 7x = -7 ⇒ x = -1

Answer:

[tex]\textrm{Dimension of C }=\ [ML^{-3}T^{0}][/tex]

Step-by-step explanation:

As given in question drag force depends upon the product of the cross sectional area of the object and the square of its velocity

and drag force can be given by

[tex]F=CAv^2[/tex]          (1)

It is given that

Dimension of mass = [M]

Dimension of length = [L]

Dimension of time = [T]

So, by using above dimension we can write

the dimension of force,

[tex]F=[MLT^{-2}][/tex]

dimension of cross-section area,

[tex]A=[L^2][/tex]

and dimension of velocity

[tex]v=[LT^{-1}][/tex]

now, by putting these values in equation (1), we will get

[tex]F=CAv^2[/tex]

[tex]=>[MLT^{-2}]=C[L^2][LT^{-1}]^2[/tex]

[tex]=>C=[ML^{-3}T^0][/tex]

Hence, the dimension of constant C will be,

[tex]C=[ML^{-3}T^0][/tex]

The dimensions of C from the expression above is ML^-3

Given the function that relates drag force with the  cross-sectional area of the object and the square of its velocity expressed as:

[tex]F_{air} = CAv^2[/tex]

Make C the subject of the formula to have:

[tex]C =\frac{F}{Av^2}[/tex]

Given the following dimensions

[tex]M =MLT^{-2}[/tex]

A = L²

v = [tex]LT^{-1}[/tex]

Substitute into the formula. the dimension of C will be given as:

[tex]C=\frac{MLT^{-2}}{L^2L^2T^{ -2}}\\C= ML^{-3}[/tex]

Henc the dimensions of C from the expression above is ML^-3

Learn more on Units and Dimension here: https://brainly.com/question/28464

Answer:

6

Step-by-step explanation:

Given information:

Interior angle of a polygon cannot be more that 180°.

One interior angle = [tex]80^{\circ}[/tex]

Other interior angles are  = [tex]128^{\circ}[/tex]

Let n be the number of sides of the polygon.​

Sum of interior angles is

[tex]Sum=80+128(n-1)[/tex]

[tex]Sum=80+128n-128[/tex]

Combine like terms.

[tex]Sum=128n-48[/tex]           .... (1)

If a polygon have n sides then the sum of interior angles is

[tex]Sum=(n-2)180[/tex]

[tex]Sum=180n-360[/tex]           .... (2)

Equating (1) and (2) we get

[tex]180n-360=128n-48[/tex]

Isolate variable terms.

[tex]180n-128n=360-48[/tex]

[tex]52n=312[/tex]

Divide both sides by 52.

[tex]n=\frac{312}{52}[/tex]

[tex]n=6[/tex]

Therefore the number of sides of the polygon is 6.

Answer:

It takes the frog 7 hours to get out of the well.

Step-by-step explanation:

We know that the well is 11 feet deep and the frog can climb 3 feet per hour.

Each time it climbs, it rests for an hour, and decreases its height by 1 foot.

So, if the frog reaches 3 feet in the first hour, then in the next hour it is 2 feet.

Lets calculate with the same pattern:

1st hour: 3 feet

2nd hour: [tex]3-1=2[/tex] feet

3rd hour: [tex]2+3=5[/tex] feet

4th hour: [tex]5-1=4[/tex] feet

5th hour: [tex]4 +3= 7[/tex] feet

6th hour: [tex]7-1=6[/tex] feet

5th hour: [tex]6+3=9[/tex] feet

6th hour: [tex]9-1=8[/tex] feet

7th hour:  [tex]8+3= 11[/tex] feet

Therefore, it takes the frog 7 hours to get out of the well.

Final answer:

To find out how long it takes for a frog to climb out of an 11-foot deep well, we calculate the net gain of height over time considering its climbing rate and slipping back. It will take the frog a total of 11 hours to escape the well.

Explanation:

The question involves a frog climbing out of a well and deals with a sequence of movements that include climbing and slipping back. Each hour, the frog climbs 3 feet but then slips back 1 foot during the rest hour.

To solve this, we perform a step-by-step calculation to determine the total time required for the frog to climb out of an 11-foot deep well. The frog makes a net gain of 2 feet for every 2 hours (3 feet up in the first hour and slips back 1 foot in the next hour).

However, on the final climb, the frog does not slip back since it will climb out of the well. Therefore, in the 11th hour, the frog climbs the remaining 1 foot and escapes the well.

So, the total time taken is 11 hours.

Answer:

a. [tex]y=\frac{2}{3}x^7+cx^4[/tex]

b. [tex]y=2e^{7x}-ce^{5x}[/tex]

c. [tex]y=e^{-2x}arctan(e^{2x})+ce^{-2x}[/tex]

d. [tex]i=e^{-2t}\left(\frac{8\left(3e^{2t}\sin \left(3t\right)+2e^{2t}\cos \left(3t\right)\right)}{13}+C\right)[/tex]

Step-by-step explanation:

a) xy' -4y = 2 x^6

[tex]xy'-4y=2x^6\\y'-\frac{4}{x}y=2x^5\\p(x)=\frac{-4}{x}\\Q(x)=2x^5\\\mu(x)=\int P(x)dx=\int \frac{-4}{x}dx=Ln|x|^{-4}\\y=e^{-\mu(x)}\int {e^{\mu(x)}Q(x)dx}\\y=x^4 \int {x^{-4}2x^6}dx\\y=\frac{2}{3}x^7+cx^4[/tex]

b) y' - 5y = 4e^7x

[tex]y'-5y=4e^{7x}\\p(x)=-5\\Q(x)=4e^{7x}\\\mu(x)=\int P(x)dx=\int-5dx=-5x\\y=e^{-\mu(x)}\int {e^{\mu(x)}Q(x)dx}\\y=e^{5x}\int {e^{-5x}4e^{7x}}dx\\y=2e^{7x}-ce^{5x}[/tex]

c) dy/dx + 2y = 2/(1+e^4x)

[tex]\frac{dy}{dx}+2y=\frac{2}{1+e^{4x}}\\p(x)=2\\Q(x)=\frac{2}{1+e^{4x}}\\\mu(x)=\int P(x)dx=\int 2dx=2x\\y=e^{-\mu(x)}\int {e^{\mu(x)}Q(x)dx}\\y=e^{-2x}\int {e^{2x}\frac{2}{1+e^{4x}}}dx\\y=e^{-2x}arctan(e^{2x})+ce^{-2x}[/tex]

d) 1/2 di/dt + i = 4cos(3t)

[tex]\frac{1}{2}\frac{di}{dt}+i=4cos(3t)\\\frac{di}{dt}+2i=8cos(3t)\\p(t)=2\\Q(t)=8cos(3t)\\\mu(t)=\int P(t)dt=\int 2dt=2t\\i=e^{-\mu(t)}\int {e^{\mu(t)}Q(t)dt}\\i=e^{-2t}\int {e^{2t}8cos(3t}dt\\i=e^{-2t}\left(\frac{8\left(3e^{2t}\sin \left(3t\right)+2e^{2t}\cos \left(3t\right)\right)}{13}+C\right)[/tex]

People who didn't travel by any mode = 45

In the question,

Total number of people included in survey = 250

People who traveled by plane but not by train = 70

i.e.

a + e = 70

People who traveled by train but not by plane = 70

i.e.

c + d = 70

People who traveled by Bus but not by Plane or Train = 20

i.e.

f = 20 ..........(1)

People who traveled by bus and plane both = 45

i.e.

e + g = 45

People who traveled by all three = 20

i.e.

g = 20

People who traveled by Plane or Train = 185

i.e.

a + b + c + d + e + g = 185 ........(2)

So,

e = 45 - g = 45 - 20 = 25

e = 25

Now, on putting in eqn. (2) we get,

a + b + c + d + 25 + 20 = 185

a + b + c + d = 140 .......(3)

Now,

We need to find out,

Number of people travelling with any of these three is,

a + b + c + d + e + f + g

So,

On putting from eqn. (3) and (1), we get,

a + b + c + d + e + f + g = 140 + 25 + 20 + 20 = 205

So,

Number of people who didn't travel by any mode =Total people - Number of people travelling by any three

People who didn't travel by any mode = 250 - 205 = 45

Final answer:

By analyzing the given data and using set theory, we determined that 90 adults did not travel by plane, train, or bus in the last year.

Explanation:

To solve this question, we need to find out how many adults did not travel by plane, train, or bus. We are given several subsets of people who use various combinations of these modes of transportation, and we can use a principle in set theory to determine the answer.

We know that 185 adults traveled by plane or train. This number includes those who traveled by both modes. There is an overlap of people who used all three modes, which is 20. So, to find the sole plane and train travelers, we subtract the people who used all three modes from those who traveled by plane but not by train and vice versa.

We calculate the number of plane-only and train-only travelers: 70 (plane only) + 70 (train only) - 20 (all three) = 120.

Since 185 traveled by either plane or train, the number that traveled by either without the bus is 185 - 20 (all three) = 165. The number that traveled by plane or train only is 165 - 45 (bus and plane) = 120.

Adding those who traveled by bus but not by plane or train (20) to those who traveled by all three (20) gives us 40. Therefore, 120 (plane or train only) + 40 = 160. To find out the number of adults who did not travel by any of these three modes, we subtract 160 from the total number of surveyed adults (250).

Finally, the number of adults who did not travel by any mode is 250 - 160 = 90.

Therefore, 90 adults did not travel by plane, train, or bus.

Answer:

[tex]1.36\times 10^{-6}:1[/tex]

Step-by-step explanation:

We have been given that the United States has 435 members of the House of Representatives in Congress. There are 325.7 million people in the country.

To find the ratio of members to the people, we will find compare both numbers.

1 million equals 1,000,000.

[tex]\text{325.7 million}=325.7\times 1,000,000[/tex]

[tex]\text{325.7 million}=3257,000,000[/tex]

Ratio of members to the people:

435: 3257,000,000

[tex]0.0000013355848941:1[/tex]

[tex]1.3355848941\times 10^{-6}:1[/tex]

[tex]1.36\times 10^{-6}:1[/tex]

Therefore, our required ratio would be [tex]1.36\times 10^{-6}[/tex] members per person.

Answer:

Cos x = 1 - [tex]\frac{x^2}{2!}[/tex] + [tex]\frac{x^4}{4!}[/tex] - [tex]\frac{x^6}{1!}[/tex] + ...

Step-by-step explanation:

We use Taylor series expansion to answer this question.

We have to find the expansion of cos x at x = 0

f(x) = cos x, f'(x) = -sin x, f''(x) = -cos x, f'''(x) = sin x, f''''(x) = cos x

Now we evaluate them at x = 0.

f(0) = 1, f'(0) = 0, f''(0) = -1, f'''(0) = 0, f''''(0) = 1

Now, by Taylor series expansion we have

f(x) = f(a) + f'(a)(x-a) + [tex]\frac{f''(a)(x-a)^2}{2!}[/tex] + [tex]\frac{f'''(a)(x-a)^3}{3!}[/tex] + [tex]\frac{f''''(a)(x-a)^4}{4!}[/tex] + ...

Putting a = 0 and all the values from above in the expansion, we get,

Cos x = 1 - [tex]\frac{x^2}{2!}[/tex] + [tex]\frac{x^4}{4!}[/tex] - [tex]\frac{x^6}{1!}[/tex] + ...

Final answer:

The expansion of cos x about the point x=0 is given by the Maclaurin series of cos x, which is 1 - (x^2)/2! + (x^4)/4! - (x^6)/6! + ...

Explanation:

The expansion of cos x about the point x=0 is given by the Maclaurin series of cos x. The Maclaurin series is a special case of the Taylor series, which is a way to approximate a function using a sum of terms.

The Maclaurin series of cos x is:

cos x = 1 - (x^2)/2! + (x^4)/4! - (x^6)/6! + ...

This series can be derived by expanding the cosine function using its power series representation and evaluating it at x = 0.