take ω as the parallelogram bounded by x y=0 , x y=4 , x−y=0 , x−y=1 evaluate: ∫∫(x2−y2)dxdy

The probability that they have an average weight of greater than 10 pounds and less than 15 pounds is 0.84134

In this question we have been given there are 250 dogs at a dog show who weigh an average of 15 pounds, with a standard deviation of 6 pounds. of 10 dogs are chosen at random.

We need to find the probability that they have an average weight of greater than 10 pounds and less than 15 pounds.

Given, μ = 12, σ = 8, n = 4

P(X > 8)

= P(z > (8 - 12 / 8/√4))

= P(z > -1)

= 1 - P(z ≤ -1)

= 1 - [1 - P(z ≤ 1)]

=  P(z ≤ 1)

= 0.84134

Therefore, the required probability is 0.84134

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Answer:

Step-by-step explanation:

1

6

10

15

id

id

Answer:

C=24

Step-by-step explanations:

As the x-values go to positive infinity, the function's values go to positive infinity, Option D is the correct answer.

A function is a mathematical statement that relates an independent variable with a dependent variable .

The graph is given in the question and the statement that correctly matches to the behaviour shown is asked .

When X values is increasing , the y value is increasing and

when the x value is decreasing the y value is also decreasing

Therefore the correct Option that can be chosen from the given is Option D

As the x-values go to positive infinity, the function's values go to positive infinity.

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p = The doctor prescribed medicine

q = The patient has recovered

The doctor did not prescribe medicine:

The patient recovered:

The truth table is given by:

Answer:

A

The statement 'when finding a minimum in a linear programming problem, it is possible to find more than one minimum value' is True.

In this question, we have been given a statement - 'when finding a minimum in a linear programming problem, it is possible to find more than one minimum value.'

We need to state whether it is true or false.

We know that, the minimum value of the objective function Z = ax + by in a linear programming problem can also occur at more than one corner points of the feasible region.

Therefore, when finding a minimum in a linear programming problem, it is possible to find more than one minimum value.

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The sample suggests that the school is not believable, as the null hypothesis is rejected.

At the null hypothesis, it is tested if the proportion is of 20%, hence:

\(H_0: p = 0.2\)

At the alternative hypothesis, it is tested if the proportion is different of 20%, hence:

\(H_1: p \neq 0.2\)

We have a two-tailed test, as we are testing if the proportion is different of a value, hence the critical value is of:

|z| = 1.96.

The test statistic is defined by the equation presented as follows:

\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)

In which:

The parameters for this problem are given as follows:

\(p = 0.2, n = 210, \overline{p} = \frac{58}{210} = 0.2762\)

Hence the test statistic is of:

\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)

\(z = \frac{0.2762 - 0.2}{\sqrt{\frac{0.2(0.8)}{210}}}\)

z = 2.76.

The test statistic is greater than the critical value for the two-tailed test, hence the sample suggests that the school is not believable.

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This is due to the fact that the merry-go-round's passengers are being held in orbit by a gravitational force similar to that experienced by stars in a galaxy. People riding on a merry-go-round that is spinning. Thus, option D is correct.

The action that would best model the role gravity plays in the motions of stars within a galaxy is D. People riding on a merry-go-round that is spinning.

This is because, like stars in a galaxy, the riders on the merry-go-round are experiencing a gravitational force that keeps them in orbit around a central point.

This force, which is proportional to the mass of the objects and inversely proportional to the square of the distance between them, is similar to the force that holds stars in orbit around the centre of a galaxy.

The other options do not accurately model this gravitational force in the same way as a spinning merry-go-round.

Therefore, people riding on a merry-go-round that is spinning.

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a) The table of the discrete function is given as follows:

Basketballs - Spending

0 - $0

1 - $15

2 - $30

3 - $45

4 - $60

5 - $75

6 - $90

7 - $105.

b) With the spending of $105, the number of basketballs purchased was of 7.

Discrete and continuous functions depends on the values assumed by the input values of the function, as follows:

In this problem, we have that the number of basketballs purchased is a countable amount, assuming only integers, hence it is a discrete function.

The proportional relationship means that each basketball costs $15, and hence the table is constructed considering it.

Hence the number of basketballs purchased with a cost of $105 is given as follows:

105/15 = 7 basketballs.

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Therefore , the solution of the given problem of variable comes out to be the manager will therefore require a total of 41 pie slices when there are 8 visitors.

A quality who can be assessed and expression assigned different values is called a variable. Variables include things like height, age, wages, province of birth, scholastic standing, and type of housing.

Here,

First, let's define our terms.

Suppose there are x visitors. (independent variable).

Let y represent the overall quantity of pie slices required. (dependent variable).

Each guest will receive two slices of pie, and there will be an extra 25 slices, according to the problem. Thus, we can say:

=> y = 2x + 25

Simply enter x = 8 into the equation and calculate to find y when x = 8.

=> y = 2(8) + 25

=> y = 16 + 25

=> y = 41

The manager will therefore require a total of 41 pie slices when there are 8 visitors.

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Zelda can swim at a speed of 75 meters per minute in still water and the rate of the water current is 25 meters per minute.

Let's call Zelda's speed in still water "s" and the rate of the water current "c".

When swimming upstream, Zelda's speed relative to the ground is s - c. When swimming downstream, her speed relative to the ground is s + c.

We're told that Zelda can swim 50 meters per minute upstream, so we can write the equation:

s - c = 50

We're also told that she can swim twice as fast downstream, so:

s + c = 2(50) = 100

Now we have two equations with two variables. We can solve for s by adding the two equations together:

s - c = 50

s + c = 100

(s - c) + (s + c) = 50 + 100

2s = 150

s = 75

So Zelda can swim at a speed of 75 meters per minute in still water.

To find the rate of the water current, we can substitute s = 75 into either of the two equations we wrote earlier. Let's use the first one:

s - c = 50

75 - c = 50

c = 25

So the rate of the water current is 25 meters per minute.

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Answer:

$8.88

Step-by-step explanation:

5.50+5.50+3.75+3.00=17.75÷2=8.88

Answer:

Its A.

Step-by-step explanation:

Add the price up to find the total: 5.50 + 3.75 + 3 = $12.25. Since there were 2 people and they wanted to split the cost- they pay half half. So 12.25 divided by 2 is $6.12.5 but you gotta round it to get an answer hats there so you round it up to 6.13.

Data collected shows that the more you water, the larger your plant will grow. If you use the following Equation, y = 1/2x + 2 How tall will a plant be at 25 weeks if x is the number of weeks watered and y represents the height of the plant? Show your work.

Answer:

216 in ^2

Step-by-step explanation:

6 time 6 is 36 and 36 times the 6 boxes is 216 therefore your answer is 216in^2

(Answer: 216 in²)

Step-by-step explanation:

Each square is 36in² (6in) (6in)

6 squars are in the shape, so 36in² (6) = 216 in²

\(625=5^{7x-3}\implies 5^4=5^{7x-3}\implies 4=7x-3 \\\\\\ 7=7x\implies \cfrac{7}{7}=x\implies 1=x\)

Option (A) is the correct option and on simplifying the expression by combining like terms we get,

24 - 3p.

Here, we have,

Given, the expression 6(4 - 2p) + 9p

On simplifying, we get

24 - 12p + 9p

24 - 3p

So, on simplifying the given expression, we get

24 - 3p

Hence, Option (A) is the correct option and on simplifying the expression by combining like terms we get,

24 - 3p

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Answer:

C. 77x⁷ + 78x⁶ - 27x⁵

Step-by-step explanation:

Operation of functions

f(x) g(x)

f(x) • g(x) = (11x³ - 3x²)(7x⁴ + 9x³)

Simplify or expand

(11x³ - 3x²)(7x⁴ + 9x³)

Expand the expression

11x³ × 7x⁴ + 11x³ × 9x³ - 3x² × 7x⁴ - 3x² × 9x³

Multiply

77x⁷ + 99x⁶ - 21x⁶ - 27x⁵

Combine like terms

77x⁷ + 78x⁶ - 27x⁵

Hope this helps and have a nice day

The answer is 3.07 (rounded to two decimal places).

We have been given the position of a bug, and we are asked to find the rate of change of temperature at this point (2, 3). We will first calculate the rate of change of temperature in terms of x and y and then evaluate it at the point (2, 3).We are given the temperature function as T(x, y), and the bug's path as follows:x=sqrt(1+t)y=2+1/3tWe know that the temperature function satisfies the following: T_x(2, 3) = 7, and T_y(2, 3) = 4.

To find the rate of change of temperature on the bug's path, we will use the chain rule of differentiation. We have to find dT/dt. Using the chain rule, we can express the derivative of temperature with respect to time as follows: dT/dt = dT/dx * dx/dt + dT/dy * dy/dt Since x = sqrt(1 + t), we can differentiate x with respect to t as follows: dx/dt = (d/dt)(sqrt(1+t))=1/2*(1+t)^(-1/2).

Similarly, we can differentiate y with respect to t as follows:dy/dt = (d/dt)(2 + 1/3t)=1/3Since we are given Tx(2, 3) = 7 and Ty(2, 3) = 4, we can plug in these values to find the rate of change of temperature along the bug's path. Hence, we get:dT/dt = T_x(2, 3) * dx/dt + T_y(2, 3) * dy/dt=7*1/2*(1+3)^(-1/2) + 4*1/3=3.07Hence, the rate of change of temperature along the bug's path after 3 seconds is 3.07 degrees Celsius per second.

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Joint Distribution of x and y is 25.

Joint Distribution is based on joint probability, which can be simply defined as the probability of two events happening together.

We know the formula for joint distribution

F(x,y) = P(X ≤ x and Y ≤ y) = ∑∑p(xi,yi)

Here x is the number of aces and y is the number of kings in a poker hand.

That means x can take values from 0 to 4 and y can take values from 0 to 4.

∴ F(x,y) = P(X ≤ 4 and Y ≤ 4)

⇒ F(x,y) = p(0,0) + p(0,1) + p(0,2) + p(0,3) + p(0,4) + p(1,0) + p(1,1) + p(1,2) + p(1,3) + p(1,4) + p(2,0) + p(2,1) + p(2,2) + p(2,3) + p(2,4) + p(3,0) + p(3,1) + p(3,2) + p(3,3) + p(3,4) + p(4,0) + p(4,1) + p(4,2) + p(4,3) + p(4,4).

To find all these values we will construct a table as follows;

P(x,y)           Y=0      Y=1         Y=2      Y=3    Y=4

X=0              0          1/4          1/2        3/4       1      

X=1               1/4        1/2        3/4         1        5/4

X=2             1/2         3/4         1            5/4     3/2

X=3             3/4          1          5/4         3/2      7/4      

X=4               1          5/4         3/2       7/4       2

Now the joint distribution will become,

F(x,y) = 0 + 1/4 + 1/2 + 3/4 + 1 + 1/4 + 1/2 + 3/4 +1  + 5/4 + 1/2 + 3/4 + 1 + 5/4 + 3/2 + 3/4 + 1 + 5/4 + 3/2 + 7/4 + 1 + 5/4 + 3/2 + 7/4 + 2

F(x,y) = 25

Therefore the joint distribution of x and y is 25.

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Answer:

15.16

Step-by-step explanation:

14.58 x 1.04

Answer:

0.5832 or 0.58

Step-by-step explanation:

14.58 / 0.04 =  0.58

The position \( u(t) \) of the mass at any time \( t \) is given by the equation \( u(t) = R \cos(\omega_0 t + \delta)\).

To determine the position of the mass at any time \( t \), we need to find the values of \( R \), \( \omega_0 \), and \( \delta \).

1. Given that the mass weighs 8 lb and stretches the spring 2 in, we can use Hooke's Law to find the spring constant \( k \):

  - \( F = kx \), where \( F \) is the force, \( k \) is the spring constant, and \( x \) is the displacement.

  - The weight of the mass is \( F = 8 \) lb, and the displacement is \( x = 2 \) in.

  - Converting the units to pounds and inches, we have \( 8 \) lb \( = k \cdot 2 \) in.

  - Therefore, \( k = 4 \) lb/in.

2. The angular frequency \( \omega_0 \) can be found using the formula \( \omega_0 = \sqrt{\frac{k}{m}} \), where \( m \) is the mass of the object.

  - In this case, the mass is not given, so we'll need to convert the weight of the mass to mass using the conversion factor \( 1 \) lb \( = 32.2 \) lb-ft/s\(^2\).

  - The weight of the mass is \( 8 \) lb, so the mass is \( m = \frac{8}{32.2} \) slugs.

  - Plugging the values into the formula, we get \( \omega_0 = \sqrt{\frac{4 \, \text{lb/in}}{\frac{8}{32.2} \, \text{slugs}}} \).

3. To find the amplitude \( R \), we can use the maximum displacement of the mass, which is given as 9 in.

4. The phase \( \delta \) is determined by the initial conditions of the system. Since the mass is set in motion with a downward velocity, the phase is \( \delta = 0 \) rad.

5. With the values of \( R \), \( \omega_0 \), and \( \delta \), we can write the equation for the position \( u(t) \):

  - \( u(t) = R \cos(\omega_0 t + \delta) \).

6. The frequency \( \omega_0 \) can be used to calculate the period \( T \) using the formula \( T = \frac{2\pi}{\omega_0} \).

7. Substitute the given values to find the exact answers for \( u(t) \), \( \omega_0 \), \( T \), \( R \), and \( \delta \).

In summary, the position \( u(t) \) of the mass at any time \( t \) is given by the equation \( u(t) = R \cos(\omega_0 t + \delta) \), and the frequency \( \omega_0 \), period \( T \), amplitude \( R \), and phase \( \delta \) can be determined based on the given information.

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Answer:

A

Step-by-step explanation:

Range = Highest value - Lowest value

At Park Zoo:

R = 44 - 38

= 6

At Countryside Zoo;

R = 45 - 38

= 7

So, it cannot be D, because the ranges are not the same and it cannot be B because the range is greater at countryside zoo

The mode is the value that appears the moat frequently.

At Park zoo, the mode is 41 since it has the most dots.

At Countryside zoo, the mode is 40, since it has the most dots

So, it cannot be C because Park zoo has a greater Mode.

so, the only answer is A

Answer:

((3 / 14) * 3) / 14 = 9 / 196

Step-by-step explanation:

Reduce 9/196 to lowest terms 9 196 is already in the simplest form. It can be written as 0.045918 in decimal form (rounded to 6 decimal places).

A shelving company shipped 2,483 shelving units to each of 417 warehouses 1035411 shelving units did the company ship in all.

Total shelving to one = 2483

Total shelving to 417 warehouse = 417 x 2483 = 1035411

A flexible display system that can be moved and altered to meet various product dimensions is a shelving unit. A gondola is an open-sided island shelving unit. Overstocks are kept on the riser, the top shelf atop a shelving unit.

Pallet racks are used for products placed onto pallets, whereas used shelving is often used for single things or boxes. The styles of used shelving include enclosed, nut and bolt, modular, wire, clip, and record storage, among others.

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If Last year, Milan opened an investment account with $5200. At the end of the year, the amount in the account had decreased by 7%.  the year-end amount in terms of the original amount is $364.00 and the year-end amount in Milan's account is $4,836.00.

a. Year end amount in terms of original amount

Year end amount = Principal × Percentage decrease

Year end amount = $5,200 × 7%

Year end amount = $364.00

b. Year end amount in Milan account

Year end amount = $5,200 -$364

Year end amount = $4,836.00

Therefore the year-end amount in terms of the original amount is $364.00 and the year-end amount in Milan's account is $4,836.00.

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Answer: The equation can also be used to find the perimeter of the rectangle  P = 4 × ( l + w).

Step-by-step explanation:

Given data,

A rectangle has a length of 6 feet and a width of 4 feet.

The perimeter of the rectangle can be found using the equation =2×6+2×4.

                        P = 2×6+2×4

Let l be the length and w be the width of a rectangle.

Since there four sides of a rectangle, the perimeter is given by adding all the sides.

Therefore perimeter of the rectangle is given by

                    = l + l + b + b

                    = 2×l +2×w

                    = 2 × ( l + w).

The equation given by 2 × ( l + w) can also be used to find the perimeter of any given rectangle.

We can use,

                          P = 4x4x6

Therefore perimeter of the rectangle is given by

                           = l + l + b + b

                           = 4×l +4×w

                           = 4 × ( l + w).

substitute l and w values,

Then,

                           = 4 × ( l + w)

                        P = 4 × ( 6 + 4).

The equation given by 4 × ( l + w) can also be used to find the perimeter of any given rectangle.

Therefore,

The equation can also be used to find the perimeter of the rectangle P = 4 × ( l + w).

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The sandbox will not be covered. 450ft² is the area of the shredded tire portion of the playground.

Modern mathematics heavily relies on the concept of area. A two-dimensional figure, form, or planar lamina's area is a measurement of how much space it takes up in the plane. Simply put, the area is the amount of fabric or material with the specified thickness needed to build an accurate representation of the shape and the quantity of paint required to cover the shape's surface in a single layer, or one coat.

area = 15×30

       =450ft²

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The equation of the line with slope m and y-intercept b is given by:

In this case the slope is 5 and the y-intercept is -2; then we have that the equation of the line is:

Now that we have the equation of the line we can use it to find points on the line, we do that by given values to x (whichever values we want) and use the equation to determine its corresponding y value.

If x=0, then we have:

Hence, the line passes through the point (0,-2).

If x=1, then we have:

Hence, the line passes through the point (1,3).

Now that we have two points on the line we graph them on the plane:

Finally, we join the points with a straight line. Therefore, the graph of the line is:

Answer:

So to get the answer we need to find both of the rays. So first we need to find the end points for the horizontal one. That would be D and E for the horizontal. Those are points, do the same for the diagonal one. AC would be it. AC and DE would be the answer

The Euler equation represents the relationship between current-period consumption and future-period consumption in the optimum. It is derived from intertemporal optimization in economics.

In the context of consumption, the Euler equation can be expressed as:

u'(Ct) = β * u'(Ct+1)

where:

- u'(Ct) represents the marginal utility of consumption in the current period,

- Ct represents current-period consumption,

- β is the discount factor representing the individual's time preference,

- u'(Ct+1) represents the marginal utility of consumption in the future period.

This equation states that the marginal utility of consumption in the current period is equal to the discounted marginal utility of consumption in the future period. It implies that individuals make consumption decisions by considering the trade-off between present and future utility.

Note: The Euler equation assumes a constant discount factor and a utility function that is differentiable and strictly concave.

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