In five years the sum of Don's and Dan's
ages will be 34. Don's age now is 8 years
less than three times Dan's age. How old
is Don?

By solving this system, we find that there is no unique solution. Therefore, the correct choice is c. There is no solution.

To solve the given system of equations by the method of reduction, we will eliminate variables one by one until we obtain the values of x, y, and z.

First, let's start by eliminating the variable x. We can do this by adding the second equation to the third equation:

(x - 2y - 2z) + (x + y + 2z) = 22 + 1

2x - z = 23    ------(1)

Next, let's eliminate the variable x from the first equation by multiplying the third equation by 3 and subtracting it from the fourth equation:

3x + y + z - (3(x + y + 2z)) = 3 - 3(1)

3x + y + z - 3x - 3y - 6z = 3 - 3

-2y - 5z = 0    ------(2)

Now, let's eliminate the variable y by multiplying the second equation by 2 and adding it to the fourth equation:

2(x - 2y - 2z) + (3x + y + z) = 2(22) + 3

2x - 4y - 4z + 3x + y + z = 44 + 3

5x - 3y - 3z = 47    ------(3)

Now we have a system of three equations (1), (2), and (3) with three variables (x, y, z). We can solve this system to find the values of x, y, and z.

Solving the system of equations, we find:

-2y - 5z = 0     ------(2)

5x - 3y - 3z = 47    ------(3)

2x - z = 23    ------(1)

By solving this system, we find that there is no unique solution. Therefore, the correct choice is c. There is no solution.

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Answer:6,9

Step-by-step explanation:

Answer:

Step-by-step explanation:

y= 5x -7

check:

-2 = 5*1 -7 true

3= 5*2 -7 true

8= 5*3 -7 true

13= 5*4 -7 true

18= 5*5 -7 true

The different simplified two-level gate circuits are as follows:
F(a, b, c, d) = (a'c)(b'd) + (ac)(bd') + (ab'c') + (ab'd') + (a'b'c') + (a'b'd) + (a'bc') + (a'b'd')

(a) F(w, x, y, z) = (x + y′ + z)(x′ + y + z)w
From the expression F(w, x, y, z) = (x + y′ + z)(x′ + y + z)w, the truth table can be derived.

Then Karnaugh Maps (K-map) can be applied to make the equations smaller.

In order to make the equations smaller, there are eight different simplified two-level gate circuits that can be used.

K-Map for (a):

The K-Map above is created for the given function F(w, x, y, z). This K-Map is used to create Boolean equations using the following steps:
1. Combine 1’s wherever possible to get two terms of two variables.
2. There are eight possible combinations of two variable equations.
3. Put these two-variable equations with a common variable together to get four-variable equations.
4. Finally, use the K-Map again to create two-variable equations to use in two-level gate circuits.

The different simplified two-level gate circuits are as follows:

F(w, x, y, z) = (w'z)(xy') + (wz')(x'y)  + (wz)(x + y')  + (wx)(y + z')  + (wx')(y' + z)  + (wy)(x + z')  + (wy')(x' + z)  + (w'x'z)(y + z)

(b) F(a, b, c, d) = Σ m(4, 5, 8, 9, 13)
The given expression F(a, b, c, d) = Σ m(4, 5, 8, 9, 13) can be simplified by using Karnaugh Maps to make the equations smaller. There are eight different simplified two-level gate circuits that can be used for the simplified expressions. K-Map for (b):

The K-Map above is created for the given function F(a, b, c, d). This K-Map is used to create Boolean equations using the following steps:
1. Combine 1’s wherever possible to get two terms of two variables.
2. There are eight possible combinations of two variable equations.
3. Put these two-variable equations with a common variable together to get four-variable equations.
4. Finally, use the K-Map again to create two-variable equations to use in two-level gate circuits.

The different simplified two-level gate circuits are as follows:
F(a, b, c, d) = (a'c)(b'd) + (ac)(bd') + (ab'c') + (ab'd') + (a'b'c') + (a'b'd) + (a'bc') + (a'b'd')

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Step-by-step explanation:

6(-3.8y-11.2)

-22.8y-67.2

answer: -22.8y-67.2

Answer: -22.8y - 67.2

Step-by-step explanation: You multiply the number inside of () by whatever number is on the outside, which is 6.

6 x -3.8

6 x 3 = 18

6 x .8 = 4.8

then add on your negative symbol

-22.8

6 x 11 = 66

6 x .2 = 1.2

add them together

67.2

▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓

\(\sf↦ Product ~of ~numbers = 10000\\\\↦ n × 16n = 10000\\\\↦ 16n² = 10000\\\\↦ n² = \sf \dfrac{10000}{16}\\\\↦ \sf n = \sqrt{\dfrac{10000}{16}}\\\\↦ \sf n = \sqrt{\dfrac{100\:\times\:100}{4\:\times\:4}}\\\\↦ \sf n = {\cancel{\dfrac{100}{4}}}\\\\➦\pmb{\underline{\boxed{\sf{\pink{n = 25}}}}}\)

▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓

Answer:

Step-by-step explanation:

Let the numbers be x and y.

We have:

Substitute y and solve for x:

Then y is:

The numbers are:

Answer:

An equation has equal signs an expresion has nothing much.  

The playground's length and breadth are 12 yards and 17 yards, respectively.

The playground's area is 204 square yards, according to the statistics provided in the inquiry.

204 square yards is the area.

The playground's breadth is 5 yards more than its length.

Let the playground be 'l' yards long.

The playground's width will then be (l + 5) yards.

The formula for the playground area is Length × Width.

A =  Length x width

204 = l (l + 5)

204 = + 5l

+ 5l - 204 = 0

+ 17l - 12l - 204 = 0

l (l + 17) -12 (l + 17) = 0

(l + 17) (l - 12) = 0

(l + 17) = 0 or (l - 12) = 0

l = -17 or l = 12

The length value cannot be negative.

As a result, the length is 12 yards.

The breadth is thus equal to l + 5.

Width = 12 + 5

17 yards wide

As a result, the length is 12 yards and the breadth is 17 yards.

Option (b) is the right answer.

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A playground has a surface area of 204 yd2. The playground's breadth is 5 yards greater than its length. Determine the playground's length and breadth.

a.) 17 yards in length, 22 yards in breadth

b.) 12 yard length, 17 yard breadth

c.) 22 yard length, 17 yard breadth

d.) 17 yard length, 12 yard breadth

The correct answers for the given question are:

1. The remote angles of the triangle are: ∠PQR, ∠PRQ

2. ∠QRU

3. The exterior angle of triangle are : ∠RPS, ∠TQP,  ∠QRU.

4. ∠RPS and ∠QPV are vertically opposite angle. So, ∠RPS = ∠QPV

5. The relation between ∠RPS and ∠RPQ is  ∠RPS + ∠RPQ = 180⁰.

A triangle is a closed shape with 3 angles, 3 sides, and 3 vertices. A triangle with three vertices P, Q, and R is represented as △PQR.

Here,

1. The remote angles of the triangle are: ∠PQR, ∠PRQ

2. ∠QRU

3. The exterior angle of triangle are : ∠RPS, ∠TQP,  ∠QRU.

4. ∠RPS and ∠QPV are vertically opposite angle. So, ∠RPS = ∠QPV

5. The relation between ∠RPS and ∠RPQ is  ∠RPS + ∠RPQ = 180⁰.

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A car travels 500/3 meters in 2 seconds.

What is speed?

The speed at which an object's location changes in any direction. The distance traveled in relation to the time it took to travel that distance is how speed is defined. Given that it just has a direction and no magnitude, speed is a scalar number.

Here, we have

Speed of car  = 100 KM/ hour

1 km= 1000m

1 hour = 3600 seconds

Let's find the speed of the car in Meters/second

Speed of car in m/sec = 100*1000 m/3600 second

Here we have taken 1000 for km and 3600 for an hour

Speed of car in m/sec = 100*1000 m/3600 second = 500/18 m/second

Speed of car in m/sec = 250/9  m per sec

We know that

Distance = speed*time

Speed = 250/9  m per sec

Time = 2 second

Distance = 250/9 * 2 meters = 500/3 meters

Hence, a car travels 500/3 meters in 2 seconds.

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The critical value of f(x) = 5x⁶ - 3x⁵ is x = 0.5 which is also its maxima point

f(x) = 5x⁶ - 3x⁵

differentiation w.r.t x

=> f'(x) = 30x⁵ - 15x⁴

Putting f'(x) = 0

30x⁵ - 15x⁴ = 0

=> x⁴(30x - 15) =0

=> 30x - 15 = 0

=> x = 15/30

=> x = 0.5 , 0

Critical number is 0.5 , 0

(B) To find where f(x) is increasing

for x > 0.5 ,

(30x-15) > 0 => x⁴(30x - 15) > 0

Therefore , f(x) is increasing at ( 0.5 , ∞ )

(C)To find where f(x) is decreasing

for x < 0.5 ,

(30x-15) < 0 => x⁴(30x - 15) < 0

Therefore , f(x) is decreasing at ( -∞ , 0.5)

(D) Differentiation f'(x) again w.r.t to x

f'(x) = 30x⁵ - 15x⁴

f"(X) = 150x⁴ - 60x³

Substituting critical values of x

=> 150(0.5)⁴ - 60(0.5)³

=>9.375 - 7.5

=> -1.875 < 0 , Hence , x = 0.5 is point of maxima

(E) no point of minima

Similarly , we can solve other parts

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The wave equation can be written as:

\(\[U_{i,j+1} = 0.073U_{i+1,j} + 1.854U_{i,j} + 0.073U_{i-1,j} - U_{i,j-1}\]\)

To show that the wave equation can be written as the given finite difference equation, we can start by approximating the second-order derivatives in the wave equation using finite differences.

Using the central difference approximation for the second-order partial derivatives with respect to x and t, we have:

\(\( \frac{{\partial^2 U}}{{\partial t^2}} \approx \frac{{U_{i,j+1} - 2U_{i,j} + U_{i,j-1}}}{{(\Delta t)^2}} \)\)

\(\( \frac{{\partial^2 U}}{{\partial x^2}} \approx \frac{{U_{i+1,j} - 2U_{i,j} + U_{i-1,j}}}{{(\Delta x)^2}} \)\)

Substituting these approximations into the wave equation, we get:

\(\( \frac{{U_{i,j+1} - 2U_{i,j} + U_{i,j-1}}}{{(\Delta t)^2}} = 8 \frac{{U_{i+1,j} - 2U_{i,j} + U_{i-1,j}}}{{(\Delta x)^2}} \)\)

Multiplying both sides by \(\( (\Delta t)^2 \)\) and \(\( \frac{1}{{(\Delta x)^2}} \)\), we obtain:

\(\( U_{i,j+1} - 2U_{i,j} + U_{i,j-1} = 8 \frac{{(\Delta t)^2}}{{(\Delta x)^2}} (U_{i+1,j} - 2U_{i,j} + U_{i-1,j}) \)\)

Simplifying the equation further by rearranging the terms, we have:

\(\( U_{i,j+1} = 2U_{i,j} - U_{i,j-1} + 8 \frac{{(\Delta t)^2}}{{(\Delta x)^2}} (U_{i+1,j} - 2U_{i,j} + U_{i-1,j}) \)\)

Now, let's substitute the given values \(\( h = \Delta x = \frac{\pi}{2} \) , \( k = \Delta t = 0.1 \)\) into the equation:

\(\( U_{i,j+1} = 2U_{i,j} - U_{i,j-1} + 8 \frac{{(0.1)^2}}{{(\frac{\pi}{2})^2}} (U_{i+1,j} - 2U_{i,j} + U_{i-1,j}) \)\)

Simplifying the equation further, we get:

\(\( U_{i,j+1} = 0.073U_{i+1,j} + 1.854U_{i,j} + 0.073U_{i-1,j} - U_{i,j-1} \)\)

This matches the given finite difference equation:

\(\( U_{i,j+1} = 0.073U_{i+1,j} + 1.854U_{i,j} + 0.073U_{i-1,j} - U_{i,j-1} \)\)

Therefore, we have shown that the wave equation can be written as the given finite difference equation using the finite difference method.

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The question attached here is inappropriate, the correct question is (attached)

The investment's expected return is 5.95%.

The expected return of an investment is calculated by multiplying the probabilities of each possible return by their respective returns and summing them up. In this case, Gautney Enterprises has provided the probabilities and returns for the investment. By applying the formula, we find that the expected return is 5.95%.

To calculate the standard deviation, we need to determine the variance first. The variance is computed by taking the difference between each possible return and the expected return, squaring those differences, multiplying them by their respective probabilities, and summing them up. Once we have the variance, the standard deviation is simply the square root of the variance. The standard deviation measures the degree of risk associated with an investment.

In this scenario, the expected return of the investment is 5.95%, but we need to consider the standard deviation as well to assess the risk. If the standard deviation is high, it indicates a greater level of uncertainty and potential volatility in returns. A low standard deviation implies a more stable investment.

Without the specific values for each return and their respective probabilities, we cannot calculate the exact standard deviation. However, Gautney Enterprises should compare the calculated expected return and the associated standard deviation to their risk tolerance and investment objectives. If the expected return meets their desired level of return and the standard deviation aligns with their risk appetite, they may consider investing in this security.

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The ratio of the weight to the mass and the value of x in the table is B) The ratio is 10/98, x = 110.

The quantity of matter in an object is measured by its mass, which is commonly expressed in kilogrammes or grammes. Since mass is a scalar quantity, the gravitational field has no effect on it. The force of gravity acting on an object is quantified by weight, which is commonly expressed in newtons or pounds. Weight is a vector quantity that is influenced by the strength of the gravitational field. While an object's mass is constant, its weight might vary depending on the gravitational field.

The ratio of weight to mass according to the given table is:

weight / mass = 196 / 20 = 98/10

The ratio is constant thus for x we have:

1078 / x = 98 / 10

Using cross multiplication we have:

x = 1078 (10) / 98 = 110

Hence, the ratio of the weight to the mass and the value of x in the table is B) The ratio is 10/98, x = 110.

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The complete question is:

Answer:

volume = 45 yd³

Step-by-step explanation:

5 x 3 x 3 = 45 yd³

The volume of the cuboid will be 45 cubic yards.

Volume is defined as the space occupied by any object in the three-Dimensions. All three parameters are required for the volume like length, width, and height of cube or cubes.

Given that the cuboid is having small cubes of side 1 yard. The length width and height of the cuboid is 5yd, 3yd, and 3yd respectively.

The volume will be calculated as:-

Volume = L x W x H

Volume = 5 x 3 x 3

Volume = 45 yards

Therefore, the volume of the cuboid will be 45 cubic yards.

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The value of the integral is 64/3 ln(2).

The integral we are given is:

∫⁴₀ ∫⁴₂ y³ 1 dy dx / x

To reverse the order of integration, we need to write the integral in terms of the other variable. Since the region is bounded by the lines x = 0, x = 4, y = 2, and y = 4, we can write the limits of integration as follows:

2 ≤ y ≤ 4

0 ≤ x ≤ y/4

The integral can now be written as:

∫⁴₂  ∫y/4 0 y³ / x dx dy

Note that we have swapped the order of integration and changed the limits of integration accordingly. The integral can now be evaluated using standard techniques.

First, we integrate with respect to x:

∫⁴₂ ∫y/4 0 y³ / x dx dy = ∫⁴₂  [y³ ln(x)]y/4 0 dy

Next, we integrate with respect to y:

∫⁴₂  [y³ ln(y/4)] dy = 64/3 ln(2)

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Answer:

$39.59

Step-by-step explanation:

37 increase 7% =

37 × (1 + 7%) = 37 × (1 + 0.07) = 39.59

Answer:

l don't understand please explain ppppppppp

Answer:

Check pdf

Step-by-step explanation:

Answer:

6:05PM

Step-by-step explanation:

did the math , three hours and 5 minutes

Answer:

3:00 pm + 1 hr 55 min = 4:55 pm

4:55 pm + 1hr 10 min= 6:05 pm

Scott and his family finished setting up their campsite at 6:05 pm.

Answer:

y= -3x+2

Step-by-step explanation:

Mode

2 x 5 = 10

6 x 5 = 30

5 x 5 = 25

3 x 5 = 15

7 x 5 = 35

8 x 5 = 40

9 x 5 = 45

2 x 5 = 10

4 x 5 = 20

7 x 5 = 35

4 x 5 = 20

7 x 5 = 35

The mode is 35 because it is repeated 3 times.

Answer:

B

Step-by-step explanation:

Answer:

the answer is c :)

Step-by-step explanation:

Answer:

Step-by-step explanation:

2(x+y)=32  means :

x+y =16

The lifetime cost of Ellen's dishwater is $1,030.44

What is Number system?

A system of writing to express the number is called number system.

Given that;

Cost of dishwasher before sales tax 9.22% is = $315

And, Sales tax = 9.22%

Hence, Total cost = 315 *( 1 + 0.0922) = 315 * 1.0922 = 344.043

And, Average of 10 times per week for the next 6 years before replacing it.

Since, There are 52 weeks in a year.

So, Average uses is calculated as,

10  * 52  * 6 = 3120

Since, cost for water = $0.09

Cost for electricity = $0.13

Total cost per uses = $0.22

Hence, Cost of uses = 0.22 * 3120 = $686.40

Now, Purchase cost = $344.043

And, Cost of uses =  $686.40

Hence, Lifetime cost =  $344.043 + $686.40 = $1,030.443

So, The lifetime cost of Ellen's dishwater is $1,030.44.

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The estimated regression model shows that as advertising increases by $1,000, the estimated mean sales increase by $80,000.

The estimated regression model is a mathematical equation that relates the dependent variable (sales) to the independent variable (advertising) based on a given set of data. In this case, the estimated regression model indicates that for every increase of $1,000 in advertising, the estimated mean sales increase by $80,000. This means that there is a positive correlation between advertising and sales, and the model predicts that increasing advertising expenditure will result in higher sales.

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Answer:

Step-by-step explanation:

2. Subtraction property of equality

3. Simplification

4. Subtraction property of equality

5. Simplification

Yes, y = e^xy  is an implicit solution of the differential equation

(1-xy)y'=y^2

Here,

The differential equation (1-xy)y' = y^2

And,  y = e^xy is an implicit solution of the differential equation

(1-xy)y'=y^2.

What is Differential equation?

A differential equation is a mathematical equation that relates some function with its derivatives.

Now,

To show y = e^xy is an implicit solution of the differential equation

(1-xy)y'=y^2, we have to find the solution of differential equation.

The differential equation is;

\((1-xy)y'=y^2\\\\\\\\\)

\((1-xy) \frac{dy}{dx} = y^2\)

\(\frac{dx}{dy} + \frac{x}{y} = \frac{1}{y^{2} }\)

It is form of  \(\frac{dx}{dy} + Px = Qy\),

Where, P is the function of y and Q is the function of x.

Hence, Integrating factor = \(e^{\int\limits {\frac{1}{y} } \, dy} = e^{lny} = y\)

The solution is;

\(x y = \int\limits {\frac{1}{y^{2} }y } \, dy + c\)

\(xy = lny + c\)

Take c = 0, we get;

\(xy = lny\\\\y = e^{xy}\)

Hence, y = e^xy  is an implicit solution of the differential equation

(1-xy)y'=y^2

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Answer:

Rate of change = 2 & Initial value = -1