The age of the father is 42 and the age of the son is 9. At what age, will the father be twice old as the son?

(Solve by equation system.)

Answer:11/1 11/2 11/3 11/4 11/5  /6

Step-by-step explanation:

Answer: YES, She is correct

Answer:

B. No. Both a and b are incorrect.

Step-by-step explanation:

The transitions are labeled with the input symbol, the symbol to be pushed onto the stack (ε indicates no symbol is pushed), and the symbol to be popped from the stack (ε indicates no symbol is popped).This PDA accepts strings in L where the number of 'a's is twice the number of 'b's.

To draw the state diagram of a PDA that accepts the language L = {w ∈ {a, b}^∗ | w has twice as many a's as b's}, we can design a simple PDA with two states.

State 1: Initial state

Transition: (a, ε, a) -> State 1

Transition: (b, a, ε) -> State 2

Transition: (ε, ε, ε) -> Accepting state

State 2: Secondary state

Transition: (b, a, ε) -> State 2

Transition: (ε, ε, ε) -> Accepting state

Accepting state: Final state to indicate that the input string is accepted.

Here is the state diagram representation of the PDA:

Note: Find the attached image for the state diagram representation of the PDA.

In this PDA, State 1 is the initial state, and State 2 is the secondary state. The transitions are labeled with the input symbol, the symbol to be pushed onto the stack (ε indicates no symbol is pushed), and the symbol to be popped from the stack (ε indicates no symbol is popped).

The PDA works as follows:

This PDA accepts strings in L where the number of 'a's is twice the number of 'b's.

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Let small cups = S

Large cups = L

They bought a total of 8 cups, so S + L = 8

Rewrite as S = 8-L (1st equation)

Then you also have

$3S + $5L = $30 (2nd equation)

Replace the S in the second equation with the first equation:

$3(8-L) + $5L = $30

Simplify:

24 - 3L + 5L = 30

Combine like terms:

24+2L = 30

Subtract 24 from both sides:

2L = 6

Divide both sides by 2:

L = 3

They bought 3 large cups

Since they bought a total of 8 cups, that means they bought 5 small cups ( 8-3=5)

Large = 3 cups, Small = 5 cups

The missing part of the equation is \(-7.0\times10^4 s^2kg⋅m^2 / 1000000.\)

To fill in the missing part of the equation, let's analyze the given information and the desired conversion. The equation is:

\((-7.0\times 10^4 s^2g⋅m^2)\cdot \pi = ? s^2kg\cdot m^2\)

In this equation, we have a quantity expressed in\(s^2g\cdot m^2\) units on the left-hand side. To convert it to \(s^2kg\cdot m^2\) units, we need to multiply it by a conversion factor.

To perform the conversion, we can use the fact that 1 kg is equal to 1000 g. Therefore, the conversion factor we need is:

1 kg / 1000 g

To ensure that the units cancel out correctly, we need to square this conversion factor because we have \(s^2g\cdot m^2\) on the left-hand side. So the missing part of the equation is:

\((-7.0\times 10^4 s^2g\cdot m^2)\cdot \pi = (-7.0\times 10^4 s^2g\cdot m^2)\cdot (1 kg / 1000 g)^2\)

Simplifying this expression, we get:

\((-7.0\times10^4 s^2g\cdot m^2)\cdot \pi = -7.0 \times10^4 s^2kg\cdot m^2 / 1000000\)

Therefore, the missing part of the equation is \(-7.0 \times 10^4 s^2kg\cdot m^2 / 1000000.\)

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Answer:

Step-by-step explanation:

9x-22=11x-54  take 9x from each side

-22=2x-54  add 54 to each side

32=2x  divide by 2

16=x

Answer:

$39,000 a year

Step-by-step explanation:

There are 12 months in a year;

$3,250.00 * 12 = $39,000

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly.

- Heather

Answer:

urmom

Step-by-step explanation:

GAY

In the triangle the line segment joining the midpoints 'S' and 'T' of the sides PQ and PR implies that ST || QR.

As given in the question,

Diagram is attached.

As per the attached diagram  we have,

Given : In triangle PQR with midpoints S and T of sides PQ and PR respectively.

To prove : ST is parallel to QR.

Proof : First construct a line through R parallel to PQ such that it meet the extended line of ST at point 'U'

In triangle PST and triangle RTU,

PQ|| RU and SU is the transversal

∠PST ≅ ∠RUT ( alternate angles )

∠PTS ≅ ∠RTU ( vertically opposite angles)

PT ≅TR ( 'T' is the midpoint of PR )

By AAS we have

ΔPST ≅ΔRTU

By congruent part of congruent triangle we have,

PS ≅ RU

⇒ SQ ≅ RU

In quadrilateral QSUR,

SQ ≅ RU

SQ || RU ( as PQ || RU by construction )

Quadrilateral with one pair of opposite side congruent and parallel implies it is a parallelogram.

Quadrilateral QSUR is a parallelogram.

⇒ SU || QR

S - T - U

⇒ ST is parallel to QR

Therefore, in the given triangle line segment formed by joining the midpoints of the other two sides is parallel to third side.

The above question is incomplete , the complete question is :

Prove theorem 8.9 : The line segment joining the midpoints of the two sides of the given triangle is parallel to the third side .

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Answer:

R and Z

Step-by-step explanation:

A point that "touches" the circle once.

Answer:

Yes, he can.

Step-by-step explanation:

To find the sale, you need to times the sale percentage by the original price so

60 x 0.50 = 30

Then you subtract the original price by the sale price so

60 - 30 = 30

So the with the sale, the price is $30.

Now the tax

Do the same

30 x 0.045 = 1.35

Now instead of subtracting you add so

30 + 1.35 = $31.35

Yes, he can afford it.

The right response is that the two linear equation never intersect , because the graph of these two linear equation will be two parallel lines.

How many types of solution are there for two linear equations ?

There are 2 types of solution :
Consistent :

A consistent system is said to be an independent system if it has a single solution.

A consistent system is said to be a dependent system if the equations have the same slope and the same y-intercepts. In other words, the lines coincide, so the equations represent the same line. Each point on the line represents a pair of coordinates that fits the system. So there are an infinite number of solutions.

Non-consistent :

Another type of system of linear equations is the inconsistent system, in which the equations represent two parallel lines. The lines have the same slope and different y-intercepts. There are no common points for both lines; therefore, there is no solution to the system and if we draw the graph of these equations then the graphs of both equation becomes parallel to each other.

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The two linear equations never intersect.

When a system of two linear equations in two variables has no solution, it means that there is no set of values for the variables that satisfies both equations simultaneously. Geometrically, this corresponds to the two lines represented by the equations being parallel. Since parallel lines never intersect, the statement "The two linear equations never intersect" accurately describes the situation.

If the two linear equations were graphed on a coordinate plane, they would appear as two distinct lines that run parallel to each other without ever crossing or intersecting. This indicates that there is no common point of intersection between the lines, and therefore no solution exists for the system of equations.

It is important to note that this scenario is different from the case where the two linear equations represent the same line. In that case, the equations would be equivalent, and every point on the line would satisfy both equations. However, when there is no solution, it means that the lines do not share any common points and never intersect.

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I) f is continuous at x=2

II) f is differentiable at x=2

These both f (function ) are true

The given limit can be recognized as the definition of the derivative of f at x=2. Specifically, it states that the derivative of f at x=2 is equal to 5.

Using this information, we can make the following conclusions:

I) We cannot say for sure whether f is continuous at x=2 based on the given limit alone. While a function being differentiable at a point implies that it is also continuous at that point, the converse is not necessarily true. Therefore, we would need additional information to determine whether f is continuous at x=2.

II) The given limit implies that f is differentiable at x=2, since the limit exists and is finite. Specifically, we can say that the derivative of f at x=2 exists and is equal to 5.

III) The given limit also implies that the derivative of f is continuous at x=2. This is because the limit defines a continuous function at x=2, and it is well-known that if a function is differentiable at a point, then it is also continuous at that point.

Therefore, the correct answers are II and III.

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Answer:

I really hope this help! Some may call it front end rounding while others call is front end estimating, even though they mean the same thing. When rounding a place value, you need to look to the number to the right of it. Example: Most often a teacher may as you round the number 452 to the nearest ten’s. That number will than be 450. But why? Well as we look at the number, we know we need to round to the nearest ten. So in our case it would be 52. Our rule to remember when rounding is 5 and higher we round-up. Since we are looking at the portion of the number 52, we go right of the tens place to find the number 2. Since the number 2 is not 5 or higher, we round down making it 50. Don’t forget to finish the problem by adding the hundreds back to the original number. Your answer for this problem is 450.

Step-by-step explanation: I really hope this helps i will post the rest in the comment!

This value of v into the formula for centripetal acceleration, we have:14.7 = (2πr/45)2Solving for r, we get:r = 77 meters (rounded to the nearest whole number). Therefore, the radius of the loop is 77 meters.

A loop is created by having an airplane follow a circular path in a vertical plane. This means that the acrobatic plane has centripetal acceleration, which is directed towards the center of the circular path. The acceleration depends on the speed of the plane, the mass of the plane, and the radius of the circular path. The acceleration can be calculated using the formula a = v2/r where v is the velocity and r is the radius of the circular path.

The given centripetal acceleration, a = 14.7 m/s2, is equal to v2/r. The velocity of the plane is not given, but we can use the fact that the pilot takes 45 seconds to complete the loop to find the velocity. During the loop, the plane travels a distance equal to the circumference of the circular path.

Therefore, the velocity of the plane is given by the formula v = 2πr/t where t is the time taken to complete one loop, which is 45 seconds.

Substituting this value of v into the formula for centripetal acceleration, we have:14.7 = (2πr/45)2Solving for r, we get:r = 77 meters (rounded to the nearest whole number) Therefore, the radius of the loop is 77 meters.

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Answer:

y = 3x - 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (3, 6 ) and (x₂, y₂ ) = (- 1, - 6 )

m = \(\frac{-6-6}{-1-3}\) = \(\frac{-12}{-4}\) = 3 , then

y = 3x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (3, 6 )

6 = 3(3) + c = 9 + c ( subtract 9 from both sides )

- 3 = c

y = 3x - 3 ← equation of line

The metric unit from pounds to tons is 250 pounds = 0.125 tons

From the question, we have the following parameters that can be used in our computation:

250 pounds = how many tons

As a general rule, we have

1 pound = 0.0005 tons

Multiply both sides of the equation by 250

So, we have

250 * 1 pound = 0.0005 tons * 250

Evaluate the products

250 pounds = 0.125 tons

Hence, the conversion is 250 pounds = 0.125 tons

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To find the joint probability distribution function f(u, v) of two random variables U and V, follow these steps:
1. Identify the support: Determine the range of values that the random variables U and V can take. The support is the set of all possible (u, v) pairs for which f(u, v) > 0.
2. Define the joint probability function: Using the support, create an equation that describes the probability of each (u, v) pair occurring. The equation should satisfy the conditions of a valid probability distribution function. That is, f(u, v) ≥ 0 for all (u, v) pairs in the support, and the sum (for discrete variables) or integral (for continuous variables) of f(u, v) over the entire support should be equal to 1.
3. Calculate probabilities: Use the defined joint probability distribution function f(u, v) to compute the probabilities of events involving U and V.

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Answer:

8 inches

Step-by-step explanation:

The volume of a hemisphere is half the volume of a sphere.

Therefore, the sum of the volumes of the two hemisphere-shaped scoops of ice cream (with diameters of 4 inches), is equal to the volume of a sphere with diameter of 4 inches.

If the melted ice cream fills the cone exactly to the top without overflowing, the volume of the cone with diameter of 4 inches must be equal to the volume of a sphere with diameter of 4 inches.

As the diameter of a circle is twice its radius, then the radius of the sphere and cone is r = 2 inches.

The formulas for the volume of a cone and the volume of a sphere are:

\(\boxed{\begin{minipage}{4 cm}\underline{Volume of a cone}\\\\$V=\dfrac{1}{3} \pi r^2 h$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}\)   \(\boxed{\begin{minipage}{4 cm}\underline{Volume of a sphere}\\\\$V=\dfrac{4}{3} \pi r^3$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius.\\\\\end{minipage}}\)

The depth of the cone is its height.

Therefore, to calculate how deep the cone must be so that the melted ice cream will fill the cone exactly to the top without overflowing, set the two equations equal to each other, substitute r = 2, and solve for h (the depth of the cone).

\(\begin{aligned}\textsf{Volume of a cone}&=\textsf{Volume of a sphere}\\\\\dfrac{1}{3} \pi (2)^2 h & = \dfrac{4}{3} \pi (2)^3\\\\\dfrac{1}{3} \pi \cdot 4 h & = \dfrac{4}{3} \pi \cdot 8\\\\\dfrac{4}{3} \pi h& = \dfrac{32}{3} \pi \\\\\dfrac{4}{3} h& = \dfrac{32}{3} \\\\4 h& = 32 \\\\h&=\dfrac{32}{4}\\\\h&=8\; \sf inches\end{aligned}\)

Therefore, the depth of the cone must be 8 inches.

The cone must be at least 8 inches deep in order for the melted ice cream to fill the cone exactly to the top without overflowing.

1. The opening of the ice cream cone has a diameter of 4 inches. This means that the radius of the cone's opening is 4/2 = 2 inches.

2. The two hemisphere-shaped scoops of ice cream have diameters of 4 inches each. This means that the radius of each scoop is 4/2 = 2 inches.

3. When the ice cream melts, it will take up the space between the scoops and fill the cone. In order for the melted ice cream to fill the cone exactly to the top without overflowing, the depth of the cone must be equal to the combined height of the two ice cream scoops.

4. The height of each hemisphere-shaped scoop can be calculated using the formula for the volume of a sphere, which is (4/3)πr³, where r is the radius.

  - For each scoop, the radius is 2 inches, so the height of each scoop is (4/3)π(2)³ = (4/3)π(8) = (32/3)π.

5. Since there are two scoops, the combined height of the two scoops is 2 * (32/3)π = (64/3)π.

6. Therefore, the cone must be at least (64/3)π inches deep in order for the melted ice cream to fill the cone exactly to the top without overflowing. This is approximately equal to 67.03 inches.

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None of the given options matches this general solution, so the answer is E. None of the options.

To solve the given ordinary differential equation:

y'' + 2y' + 5y = e^t sin(t)

We first find the characteristic equation:

r^2 + 2r + 5 = 0

Using the quadratic formula, we find the roots to be:

r = (-2 ± sqrt(4 - 4(1)(5))) / 2

r = -1 ± 2i

The characteristic equation has complex roots, so the general solution is:

y(t) = e^(-t)(Acos(2t) + Bsin(2t))

Next, we find the particular solution by guessing a solution of the form:

y_p(t) = Ae^t sin(t) + Be^t cos(t)

Taking the first and second derivatives, we get:

y_p'(t) = Ae^t sin(t) + Ae^t cos(t) + Be^t sin(t) - Be^t cos(t)

y_p''(t) = 2Ae^t cos(t) - 2Be^t sin(t)

Substituting these expressions into the original equation and simplifying, we get:

(2A - B) e^t sin(t) + (-2B - A) e^t cos(t) = e^t sin(t)

We need the coefficients of e^t sin(t) and e^t cos(t) to be equal to 1 and 0, respectively, in order to obtain a particular solution. This gives us the system of equations:

2A - B = 1

-2B - A = 0

Solving for A and B, we get:

A = 1/5

B = -2/5

Therefore, the particular solution is:

y_p(t) = (1/5) e^t sin(t) - (2/5) e^t cos(t)

The general solution is then the sum of the homogeneous and particular solutions:

y(t) = e^(-t)(Acos(2t) + Bsin(2t)) + (1/5) e^t sin(t) - (2/5) e^t cos(t)

To solve for the constants A and B using the initial conditions, we can substitute y(0) = 0 and y'(0) = 1 into the general solution and solve the resulting system of equations. However, since the question asks us to avoid solving for the constants, we can simply write the general solution as:

y(t) = e^(-t)(Acos(2t) + Bsin(2t)) + e^t (Csin(t) + Dcos(t))

where A, B, C, and D  are constants that we do not need to solve for.

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Cara has consumed 139/425 of her 212 1/2 liter water goal.

To find the fraction of her 212 1/2 liter goal that Cara has consumed, we can divide the amount she has consumed by her total goal

Fraction consumed = amount consumed / total goal

Fraction consumed = 34 3/4 / 212 1/2

To make it easier to work with, we can convert the mixed numbers to improper fractions

Fraction consumed = (434 + 3) / (2212 + 1)

Fraction consumed = 139 / 425

Therefore, water consumed 139/425 of cara is 212 1/2 liter goal.

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--The given question is incomplete, the complete question is given

" Cara is trying to drink more water. She wants to drink 212 1/2 liters of water today. So far, she has consumed 34 3/4 of a liter of water.

What fraction of her 212 1/2 liter goal has Cara consumed thus far? "--

Answer:

x = -1/11.

Step-by-step explanation:

I am interpreting this as:

(2x+4)/ 3 - (5x-7)/2 = 5

Multiply through by the LCM of 2 and 3 ( that is 6):

2(2x + 4) - 3(5x - 7) = 30

4x - 15x + 8 +21 = 30

-11x = 30 - 21 - 8

-11x = 1

x = -1/11.

Answer:

96 ÷ 3 = 32

Step-by-step explanation:

96 ÷ 3 is equivalent to 96 thirds

The goal of the equation is to find how many 3rds fit into 96.

One easy way to break 96/3 down is to first divide 90 by 3, which is 30.

Divide the remaining 6 by 3 to get 2

Add your two answers together and you get 32.

Answer:

B super you can try my answer

Answer:

C

Step-by-step explanation:

That's the graph of the absolute value function.

Answer:

51x^5 y^3 z^6

Step-by-step explanation:

(-3×^2 y^3 z^2) × (-17 × ^3 z^4)

3x^2 y^3 z^2 × 17×^3 z^4

51x^5 y^3 z^6

Answer:

f(-5)=20

Step-by-step explanation:

f(x)=x^2-x

=f(-5)=-5^2-5

=f(-5)=25-5

=f(-5)=20

The change in equilibrium real GDP is B220.

To calculate the change in equilibrium real GDP resulting from an increase in autonomous investment, we need to use the expenditure-output model. In this model, equilibrium real GDP (Y) is determined by the aggregate expenditure (AE), which is the sum of consumption (C), investment (I), government spending (G), and net exports (NX). The equation is:

Y = AE = C + I + G + NX

Given the information provided, let's calculate the initial equilibrium real GDP (Y) using the given values:

C = 80 + (9/10)Y

DI = 1800

G = 1600

TR = 10

T = (1/3)Y

Substituting the values into the equation:

Y = (80 + (9/10)Y) + 1800 + 1600 + 10 - (1/3)Y

Simplifying the equation:

Y = 3490 + (5/6)Y

Multiplying through by 6 to remove the fraction:

6Y = 6(3490) + 5Y

6Y = 20940 + 5Y

Y = 20940

The initial equilibrium real GDP is 20940.

Now, let's calculate the equilibrium real GDP after the B220 increase in autonomous investment (ΔI):

Y' = Y + ΔI

Substituting the values:

Y' = 20940 + B220

Calculating the change in equilibrium real GDP:

Change in Y = Y' - Y

Change in Y = (20940 + B220) - 20940

Change in Y = B220

The change in equilibrium real GDP is B220.

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Answer:

\( \boxed{C}\)