2. The cost of a cell phone is $500. According to the cellular device contract, you will need to be

$0.15 per minute for the first 6oo minutes.

a. Write the function that models the total cost of the cell phone bill for the first 600 minutes

b. Write the domain of the function interval notation).

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:

The mileage must the new model get so that the manufacturer meets the government requirement is 59 mpg.

Step-by-step explanation:

Consider the provided information.

Here it is given that the average mpg for the four models manufactured is 24 mpg.

The total mpg for the four models = 4 × 24 = 96

The manufacturer will add a model and the government standard is 31 mpg.

This can be written as:

[tex]\frac{96+x}{5}=31[/tex]

[tex]96+x=155[/tex]

[tex]x=155-96[/tex]

[tex]x=59[/tex]

Hence, the mileage must the new model get so that the manufacturer meets the government requirement is 59 mpg.

Final answer:

The new model car must achieve 59 mpg in order for the manufacturer to meet the government requirement of an average of 31 mpg when this model is added to the existing four models that average 24 mpg.

Explanation:

The student has asked what mileage a new model car must get so that the manufacturer meets the government requirement of an average of 31 miles per gallon (mpg). Currently, the average mpg for the manufacturer's four models is 24 mpg.

To calculate the required mpg for the fifth model, we use the formula for the average of a set of numbers, which is the sum of all numbers divided by the number of items. In this case, if x is the mpg the new model needs to achieve, the equation is:

(4 ×24 + x) / 5 = 31

Which simplifies to:

96 + x = 155

Therefore:

x = 155 - 96

x = 59 mpg

The new model will need to have an efficiency of 59 mpg for the manufacturer to meet the Corporate Average Fleet Efficiency (CAFE) standard of 31 mpg.

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:

The general solution of the differential equation y' + 3x^2 y = 0 is:

[tex]y=e^{-x^3+C}[/tex]

Step-by-step explanation:

This equation its a Separable First Order Differential Equation, this means that you can express the equation in the following way:

[tex]\frac{dy}{dx} = f_1(x)*f_2(x)[/tex], notice that the notation for y' is changed to [tex]\frac{dy}{dx}[/tex]

Then you can separate the equation and put the x part of the equation on one side and the y part on the other, like this:

[tex]\frac{1}{f_2(x)}dy=f_1(x)dx[/tex]

The Next step is to integrate both sides of the equation separately and then simplify the equation.

For the differential equation in question y' + 3x^2 y = 0 the process is:

Step 1: Separate the x part and the y part

[tex]\frac{1}{y}dy=3x^2}dx[/tex]

Step 2: Integrate both sides

[tex]\int\frac{1}{y}dy=\int 3x^2}dx[/tex]

Step 3: Solve the integrals

[tex]Ln(y)+C=-x^3+C[/tex]

Simplify the equation:

[tex]Ln(y)=-x^3+C[/tex]

To solve the Logarithmic expression you have to use the exponential e

[tex]e^{Ln(y)}=e^{-x^3+C}[/tex]

Then the solution is:

[tex]y= e^{-x^3+C}[/tex]

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.

Answer:

Step-by-step explanation:

a) We want to prove that [tex]f^{-1}(A\cap B)\subset f^{-1}(A)\cap f^{-1}(B)[/tex]. Then, we can do that proving that every element of  [tex]f^{-1}(A\cap B)[/tex] is an element of [tex]f^{-1}(A)\cap f^{-1}(B)[/tex] too.

Then, suppose that [tex]x\in f^{-1}(A\cap B)[/tex]. From the definition of inverse image we know that [tex]f(x)\in A\cap B[/tex], which is equivalent to [tex]f(x)\in A[/tex] and [tex]f(x)\in B[/tex]. But, as [tex] f(x) \in A [/tex] we can affirm that [tex]x\in f^{-1}(A)[/tex] and, because  [tex]f(x)\in B[/tex] we have [tex]x\in f^{-1}(B)[/tex].

Therefore, [tex]x\inf^{-1}(A)\cap f^{-1}(B)[/tex].

b) We want to prove that [tex]f(A\cap B) \subset f(A)\cap f(B)[/tex]. Here we will follow the same strategy of the above exercise.

Assume that [tex]y\in f(A\cap B)[/tex]. Then, there exists [tex]x\in A\cap B[/tex] such that [tex]y=f(x)[/tex]. But, as [tex]x\in A\cap B[/tex] we know that [tex]x\in A[/tex] and [tex]x\in B[/tex]. From this, we deduce [tex]f(x)=y\in f(A)[/tex] and [tex]f(x)=y\in f(B)[/tex]. Therefore, [tex]y\in f(A)\cap f(B)[/tex].

c) Consider the constant function [tex]f(x)=1[/tex] for every real number [tex]x[/tex]. Take the sets [tex]A=(0,1)[/tex] and [tex]B=(1,2)[/tex].

Notice that [tex]A\cap B = (0,1)\cap (1,2)[/tex]=Ø, so [tex]f(A\cap B)[/tex]=Ø. But [tex]f(A) = \{1\}[/tex] and [tex]f(B) = \{1\}[/tex], so [tex]f(A)\cap f(B) =\{1\}[/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:

1. ∀ y ∈ Z such that ∃ x ∈ Z, ¬R (x + y)

2. ∃ x ∈ Z, ∀ y ∈ Z such that ¬R(x + y)

Step-by-step explanation:

If we negate a quantified statement, first we negate all the quantifiers in the statement from left to right, ( keeping the same order ) then we negative the statement,

Here, the given statement,

1. ∃y ∈Z such that ∀x ∈Z, R (x + y)

By the above definition,

Negation of this statement is ∀ y ∈ Z such that ∃ x ∈ Z, ¬R (x + y),

2. Similarly,

The negation of statement ∀x ∈Z, ∃y∈Z such that R(x + y),

∃ x ∈ Z, ∀ y ∈ Z such that ¬R(x + y)

Final answer:

The negation of a mathematical statement involving existential and universal quantifiers involves switching the quantifiers and negating the inner statement. An example of a statement and its negation is 'All swans are white' and its negation 'Not all swans are white.' The law of noncontradiction implies the law of the excluded middle by rejecting the possibility of a middle ground.

Explanation:

When negating mathematical statements involving existential and universal quantifiers, the negation of an existential quantifier ∃ (there exists) becomes a universal quantifier ∀ (for all), and vice versa. Additionally, the statement inside the quantifiers gets negated. Here is the negation of each statement:

1. The original statement is ∃y ∈Z such that ∀x ∈Z, R(x + y). The negation becomes ∀y ∈Z, ∃x ∈Z such that ¬R(x + y).

2. The original statement is ∀x ∈Z, ∃y∈Z such that R(x + y). The negation becomes ∃x ∈Z, ∀y∈Z such that ¬R(x + y).

For an example of a statement and its negation: "All swans are white" is a universal affirmative statement, which can be negated to "Not all swans are white," or equivalently "There exists at least one swan that is not white."

The law of noncontradiction states that a statement and its negation cannot both be true simultaneously. The law of the excluded middle asserts that for any proposition, either the proposition is true, or its negation is true. The law of noncontradiction logically implies the law of the excluded middle, as if a statement and its negation can't both be true, then one of them must be true, rejecting the possibility of a middle ground.

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]

Answer:

The correct answers are marked.

Step-by-step explanation:

Line k is indicated as perpendicular to RX by the little square at their point of intersection.

Congruence of different line segments will be indicated by marks on them, or by the nature of the geometry containing them (a parallelogram, for instance). There is nothing in this diagram indicating RZ is congruent to GR.

The named points, X, B, V, N, are all shown as being in plane F, so are coplanar.

A plane contains an infinite number of points. In the diagram, there are 5 named points in plane F.

The endpoint of ray RH is point R, which is on line K. However, that is the extent of their intersection. Ray RH heads off in a different direction than line k, so is not part of it.

Segment VN is in plane F; ray RH is not in the plane, but is skew to segment VN. They are not headed in the same direction.

Points R and G are both on line k, so line RG is the same as line k.

In the given figure, line K is perpendicular to RX, points X, B, V, and N are coplanar in plane F, and line RG is the same as line K.

1. Line K is perpendicular to RX:

  - This statement is true because there is a right-angle symbol (∟) at the intersection point of lines K and RX, indicating that line K is perpendicular to line RX.

2. RZ is congruent to GR:

  - There is no information or markings in the given description that suggest RZ is congruent to GR. Congruence typically requires specific markings or information about the lengths or angles of the line segments, which are not provided in this description.

3. Points X, B, V, and N are coplanar:

  - This statement is true. Coplanar points are points that lie in the same plane. In the description, it's mentioned that all these points are in plane F, so they are indeed coplanar.

4. Plane F contains six points:

  - This statement is not true. Plane F contains only five named points (R, X, B, V, N) as indicated in the description.

5. Ray RH is part of line K:

  - This statement is not true. While the endpoint of ray RH is point R, which is on line K, ray RH heads off in a different direction than line K and does not extend along line K, so it's not considered part of line K.

6. VN is headed the same direction as RH:

  - This statement is not true. Segment VN and ray RH are not headed in the same direction. VN is a line segment in plane F, while RH is a ray that extends from point R but does not align with VN.

7. Line RG is the same as line K:

  - This statement is true. Both line RG and line K coincide and are represented by the same line in the figure, indicating that they are the same line.

So, statements 1, 3, and 7 are the accurate descriptions of the figure based on the information provided.

To know more about coplanar, refer here:

https://brainly.com/question/17688966

#SPJ3

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:

  (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:

3,500,000,000

Step-by-step explanation:

The total number of human genomic characters is 3.5 billion.

Expressing this quantity numerically without using a decimal we can write it as ;

3,500,000,000

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:

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 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:

11.78 hours.

Step-by-step explanation:

We are asked to find the time that an "H" cylinder will last having 1350 PSI of gas in it at a flow of 6 LPM.

[tex]\text{Duration of tank (in minutes)}=\frac{\text{Tank pressure (in PSI)}\times\text{Conversion factor}}{\text{Flow (LPM)}}[/tex]

[tex]\text{Duration of H tank (in minutes)}=\frac{1350\times 3.14}{6}[/tex]

[tex]\text{Duration of H tank (in minutes)}=\frac{4239}{6}[/tex]

[tex]\text{Duration of H tank (in minutes)}=706.5[/tex]

To convert the time in hours, we will divide 706.5 by 60 as i hour equals 60 minutes.

[tex]\text{Duration of H tank (in hours)}=\frac{706.5}{60}[/tex]

[tex]\text{Duration of H tank (in hours)}=11.775[/tex]

Therefore, it will take 11.78 hours to last the given cylinder.

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:[tex]x-2y-2=0[/tex]

Step-by-step explanation:

Given :

[tex]f(x) = x^2 - 4 \\ g(x) = - 3x^2 + 2x + 8[/tex]

Point of intersection :

[tex]f(x)=g(x)\\x^2-4=-3x^2+2x+8\\4x^2-2x-12=0\\2x^2-x-6=0\\2x^2-4x+3x-6=0\\2x(x-2)+3(x-2)=0\\(x-2)(2x+3)=0\\x=2\,,\,\frac{-3}{2}[/tex]

[tex]x=2\,;f(2)=2^2-4=0\\x=\frac{-3}{2}\,; f\left ( \frac{3}{2} \right )=\left ( \frac{3}{2} \right )^2-4=\frac{-7}{4}=-1.75[/tex]

So, we have points [tex]\left ( 2,0 \right )\,,\,\left ( -1.5,-1.75\ \right )[/tex]

Equation of line passing through two points [tex]\left ( x_1,y_1 \right )\,,\,\left ( x_2,y_2 \right )[/tex] is given by [tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}\left ( x-x_1 \right )[/tex]

Let [tex]\left ( x_1,y_1 \right )=\left ( 2,0 \right )\,,\,\left ( x_2,y_2 \right )=\left ( -1.5,-1.75\ \right )[/tex]

So, equation is as follows :

[tex]y-0=\frac{-1.75-0}{-1.5-2}\left ( x-2 \right )\\y=\frac{-1.75}{-3.5}\left ( x-2 \right )\\y=\frac{1}{2}(x-2)\\2y=x-2\\x-2y-2=0[/tex]

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:

Square of a rational number is a rational number.

Step-by-step explanation:

Let m be a rational number. Thus, m can be written in the form of  fraction [tex]\frac{x}{y}[/tex], where x and y are integers and [tex]y \neq 0[/tex].

The square of m = [tex]m\times m = m^2[/tex]

[tex]m^2 = \frac{x}{y} \times\frac{x}{y} = \frac{x^2}{y^2}[/tex]

It is clearly seen, that [tex]m^2[/tex], can be easily written in the form of fraction and the denominator is not equal to zero.

Hence, [tex]m^2[/tex] is a rational number.

This can also be understood with the help of the fact that rational numbers are closed under multiplication that is product of a rational number is also a rational number.

Answer:

There are 4,148,350,734,528 ways

Step-by-step explanation:

We have

(a) How many ways are there to select a committee of 10 senate members with the same number of Demonstrators and Repudiators?

We want to choose 5 Demonstrators and 5 Repudiators. The number of ways to do this is [tex]{44} \choose {5}[/tex] and [tex]56 \choose 5[/tex] respectively. Therefore, the number of ways to select the committee is given by:

[tex]{{44}\choose {5}} \times {{56}\choose{5}}=\frac{44!}{39!5!}\times\frac{56!}{51!5!}=\frac{44!56!}{51!39!5!5!}=\frac{44\times43\times42\times41\times40\times56\times55\times54\times53\times52}{5!5!}=\\\\=\frac{44\times43\times42\times41\times8\times56\times11\times54\times53\times52}{4!4!}= \frac{11\times43\times42\times41\times2\times56\times11\times54\times53\times52}{3!3!}=\\\\\frac{11\times43\times14\times41\times2\times56\times11\times18\times53\times52}{2!2!}=[/tex]

[tex]11\times43\times14\times41\times28\times11\times18\times53\times52=4,148,350,734,528[/tex]

(b) Suppose that each party must select a speaker and a vice speaker. How many ways are there for the two speakers and two vice speakers to be selected?

[tex]44\times43\times56\times55=5,827,360.[/tex]

This is because there are (in the case of Demonstrators) 44 possibilities to choose an speaker and after choosing one, there would be 43 possibilities to choose a vice speaker. The same situation happens in the case of Repudiators.

[tex]5\times4\times5\times4=400[/tex].

Final answer:

To select a committee with an equal number of members from both parties, we use the combination formula to calculate the number of ways to choose 5 out of 44 Demonstrators and 5 out of 56 Repudiators, and then multiply these numbers together. For selecting speakers and vice speakers, we multiply the number of possible choices for each position within each party. The committee selection results in 4,149,395,102,528 ways, and selecting speakers and vice speakers yields 5,825,760 ways.

Explanation:

For part (a), if the committee requires an equal number of members from both parties, and we have 44 Demonstrators and 56 Repudiators, we need to select 5 members from each party to have a committee of 10 with an equal number of senators from both parties.

The number of ways to select 5 Demonstrators from 44 is given by the combination formula C(44, 5), which represents the number of ways to choose 5 members out of 44 without regard to order. Similarly, the number of ways to select 5 Repudiators from 56 is C(56, 5).

To find the total number of ways to form the committee, we multiply the two results:

The total number of ways is 1,086,008 * 3,819,416 = 4,149,395,102,528 ways.

For the selection of speakers and vice speakers, for each party, we can choose 1 speaker and 1 vice speaker. There are 44 Demonstrators, so there are 44 choices for the speaker and 43 choices for the vice speaker since the same person cannot hold both positions. Similarly, there are 56 Repudiators, so there are 56 choices for the speaker and 55 for the vice speaker.

The total number of ways to select the speakers and vice speakers for both parties is:

Final calculation: (44 * 43) * (56 * 55) = 1,892 * 3,080 = 5,825,760 ways.

Answer:

True

Step-by-step explanation:

Yes, In Descriptive Statistics we are most often interested in the summary of data in words. It is done by describing the features of the data. Mostly we explain the five-number summary of the data, central tendency of data, dispersion, skewness, etc. Overall we summarize the quantitative data in words.

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:

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:

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:

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:

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

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