You are a screenwriter who is writing a script for an hour-long police drama. You have written 20 1/2 pages for act 1 and 5 1/2 pages for act 2.

How many pages have you written in total?

The impulse developed is\(= 250000*120=30000000 kg.m/s\)

\(\Delta X F\) is not equal to zero the force field \(F=(y^2Z^3-6xz^2) \^i + 2xyz^3 \^j +(3xy^2z^2-6x^2z)\^k\) is not conservative force field.

To find the impulse developed, we first need to find the change in momentum of the object. The initial velocity of the object is 540 \(km/hr\), which is equivalent to 150 m/s (since \(1 km/hr\) = \(1/3.6 m/s\)). The final velocity is 720 \(km/hr\), which is equivalent to 200 m/s.

The change in velocity\(\Delta v\) is the difference between the final velocity (\(v_f\)) and the initial velocity (\(v_i\)): \(\Delta v = v_f-v_i =200m/s-150m/s=50m/s\)

The mass of the object is given as 5000 kg.

The impulse (J) is defined as the product of the change in momentum (Δp) and the time (t): J = Δp × t

Now, we need to find the change in momentum (Δp). The change in momentum is given by the formula:

\(\Delta p=m*\Delta v\)

Substituting the given values:

\(\Delta p=5000*50 = 250000 kg.m/s\)

The time (t) is given as 2 minutes, which is equivalent to 120 seconds.

Finally, we can calculate the impulse (J):

\(J= \Delta p *t\)

= \(250000*120=30000000 kg.m/s\)

Therefore, the impulse developed in this time is 30,000,000 \(kg.m/s\)

Now, let's move on to proving that the force field \(F=(y^2Z^3-6xz^2) \^i + 2xyz^3 \^j +(3xy^2z^2-6x^2z)\^k\) is conservative.

A vector field F = (P, Q, R) is conservative if its curl is zero\((\Delta XF=0)\).

Let's calculate the curl of the given force field F:

\(\Delta X F = (\delta R/\delta y -\delta Q/\delta z)\^i + (\delta P/\delta z-\delta R/\delta x)\^j + (\delta Q/\delta x- \delta P/\delta y)\^k\)

Here,\(P=y^2z^3-6xz^2,\) \(Q=2xyz^3,\) and \(R=3xy^2z^2-6x^2z\)

Substituting these values into the curl equation:

\(\Delta XF = (3y^2z^2-12xz)\^i + (2xz^3-6xy^2z^2)\^j + (6xyz^2-6xy^2z+12xz)\^k\)

Since \(\Delta X F\) is not equal to zero, the force field F is not conservative.

Therefore, the force field \(F=(y^2Z^3-6xz^2) \^i + 2xyz^3 \^j +(3xy^2z^2-6x^2z)\^k\) is not conservative.

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If the best fit line is nearly horizontal, it suggests no significant relationship between height and head circumference.

In this scenario, the explanatory variable is the child's height, as it is being used to predict the head circumference.

The response variable is the head circumference itself, as it is the variable being predicted or explained by the height.

To draw a scatter diagram of the data, you would plot the child's height on the x-axis and the corresponding head circumference on the y-axis. Each data point would represent a child's measurement pair.

Once all the data points are plotted, you can then draw the best fit line, also known as the regression line, that represents the overall trend or relationship between height and head circumference.

By observing the scatter diagram and the best fit line, you can determine the relationship between a child's height and head circumference.

If the best fit line has a positive slope, it indicates a positive relationship, meaning that as height increases, head circumference tends to increase as well.

If the best fit line has a negative slope, it indicates a negative relationship, meaning that as height increases, head circumference tends to decrease.

By assessing the slope of the best fit line in the scatter diagram, you can determine whether the relationship between height and head circumference is positive, negative, or nonexistent.

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Answer:

  3 : 4 ratio of radii

  9 : 16 ratio of areas

Step-by-step explanation:

The ratio of radii is the same as the ratio of diameters:

  one : the other = 6 :8 = 3 : 4

__

The ratio of areas is the square of the ratio of radii:

  one : the other = 3² : 4² = 9 : 16

Answer:

The circumference is 52 ft or 17*pi ft

Answer:

0.12

hope this is the answer you are looking for

Step-by-step explanation:

Answer: 0.12

Step-by-step explanation:

12/100 basically means 12 divided by 100, so it would be 0.12.

Hope this helps :)

We know that 1 gallon = 3.785 L,Therefore, 24.1364 L = 24.1364/3.785 gallons= 6.3781 gallons (rounded to four decimal places)Therefore, the car will use approximately 6.3781 gallons of gas on this trip.

The car travels for 3.0 hours at a velocity of 55 miles per hour. The gas mileage of the car is 11 km/L. We have to find how many gallons of gas will be used on this trip. We can solve this problem by using the following steps:Step 1: Convert the velocity from miles per hour to km/hourWe know that 1 mile

= 1.609 km Therefore, 55 miles per hour

= 55 × 1.609 km per hour

= 88.5 km per hour Step 2: Calculate the distance traveled by the car We know that distance = velocity × time Therefore, distance traveled by the car

= 88.5 km/hour × 3.0 hours

= 265.5 km

Step 3: Convert the distance from kilometers to miles We know that 1 mile

= 1.609 km Therefore, 265.5 km

= 265.5/1.609 miles

= 165.1287 miles (rounded to four decimal places)Step 4: Calculate the fuel consumption in liters We know that fuel consumption

= distance traveled/gas mileage Therefore, fuel consumption

= 265.5 km/11 km/L

= 24.1364 L (rounded to four decimal places)Step 5: Convert the fuel consumption from liters to gallons.We know that 1 gallon

= 3.785 L,Therefore, 24.1364 L

= 24.1364/3.785 gallon

s= 6.3781 gallons (rounded to four decimal places)Therefore, the car will use approximately 6.3781 gallons of gas on this trip.

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Answer:

Step-by-step explanation:

6:00 a.m. in Philadelphia comes 1 hour before 6:00 a.m. in Chicago, so it is the Philadelphia train that leaves first.

Substitute "n" for 8.

2(8)^2 - 3(8) - 6

2*64 -24 -6

128 - 30

98

Therefore T₈ = 98

The price of the article tomorrow will be #4.95.

If an article cost #5 yesterday and has risen by 10% today, it will now cost #5.50. To calculate the price tomorrow, we need to consider that the price will fall by 10%.

To do this, we can first calculate what 10% of #5.50 is, which is #0.55. This means that the price will fall by #0.55 tomorrow, bringing the price down to #4.95.

Therefore, the price of the article tomorrow will be #4.95. This calculation highlights the importance of understanding the impact of percentage changes on prices and how they can impact the overall cost. It also demonstrates the need for individuals to be aware of such changes when making financial decisions.

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the calculation of the chi-square statistic and give the p-value for the test.0.05 < p-value ≤ 0.1.The correct answer is (d)

The chi-square test is used to test the hypothesis that two categorical variables are independent of each other. The null hypothesis is that there is no association between the two variables.

The test statistic is the chi-square statistic, which is calculated by comparing the observed frequencies in each category to the expected frequencies under the null hypothesis.

In this case, the chi-square statistic is calculated as follows: (16-10.25)²/10.25 + (8-10.25)²/10.25 + (6-5.125)²/5.125 + (3-2.5)²/2.5 = 6.98.

The degrees of freedom for this test are 3, which is the number of categories minus 1. The p-value for this test is less than 0.05, which means that the data provide evidence of a color preference.

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Answer:

Step-by-step explanation:

The root which is 2 is the fractional portion of your exponent

\(\sqrt{x^{7} y^{12} }\)

=\((x^{7} y^{12} )^{\frac{1}{2} }\)              >You can distribute 1/2 to each term by multiplying

\(=x^{\frac{7}{2} } y^{6\)

Answer:

Step-by-step explanation:

Perimeter of a rectangle = 2L +2W

L is the length

W is the width

If the length of a rectangle is 2 cm less than 7 times the width, then;

L = 7W-2 .... 2

Substitute eqn into the formula for finding the perimeter

P = 2(7W-2)+2W

P = 14W-4+2W

P = 16W-4

If P =60cm

60 = 16W-4

16W = 60+4

16W = 64

W = 64/16

W = 4cm

Hence the width of the rectangle is 4cm

Since l = 7w-

l = 7(4)-2

L = 28-2

L = 26cm

You can proceed and draw a rectangle with the dimension of 4cm by 26cm

Answer:

#1

mean=7

median=8

range=9

mode=3

#2

mean=15

mode=17

range=14

median=14

#3

mean=11

mode=none

range=10

median=4.5

#4

mean=6

mode=4

range=13

median=4

Step-by-step explanation:

there you go, I think that's right but it's been awhile since I've had to do mode mean median and range

The volume common to two spheres, each with radius r, if the distance between their centres is r/2 is V = (11/12)×π×r³.

The attached diagram shows 2 circumferences with radius r and separated centres by r/2.

Let´s call circumferences  1 and 2; by symmetry, rotating area A will produce a volume V₁ identical to a V₂, Obtained by rotating area B ( both around the x-axis), then the whole volume V will be:

V = 2× V₁

V₁ = ∫π×y²×dx         (1)

Now

( x - r/2)²  +  y² = r²       the equation of circumference 1

y² = r² - ( x - r/2)²

Plugging this value in equation (1)

V₁ = ∫π×[  r² - ( x - r/2)²]×dx        with integrations limits    0 ≤ x ≤ r/2

V₁ = π×∫ ( r² - x² + (r/2)² - r×x )×dx

V₁ = π× [  r²×x - x³/3 + (r/2)²×x - (1/2) × r × x²]    evaluate between 0 and r/2

V₁ = π× [(5/4)×r²×x - x³/3 - (1/2) × r × x²]

V₁ =  π× [(5/4)×r² × ( r/2 - 0 ) - (1/3)×(r/2)³ -  (1/2) × r × (r/2)²]

V₁ =  π× [ (5/8)×r³ - r³/24 - r³/8]

V₁ =  π× (11/24)×r³

Then

V = 2× V₁

V = 2×π×11/24)×r³

V = (11/12)×π×r³

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Answer:

Step-by-step explanation:

COPY PASTE I WROTE THE ANSWER ON THERE!!! :)))

The lengths of LV and OE are 15cm, and the lengths of LD and EV are 3√7 cm and 9/√7 cm, respectively.

Since LOVE is a kite, LV and OE are perpendicular bisectors of each other. Let the length of LD be x, and the length of EV be y. Then, we can use the Pythagorean theorem and the fact that the diagonals bisect each other to set up two equations:

x² + (LV/2)² = DV²/4

y² + (OE/2)² = LE²/4

Simplifying each equation and substituting the given values, we get:

x² + (LV/2)² = 81/4

y² + (OE/2)² = 225/4

We also know that the diagonals bisect each other, so we can set up another equation:

LV/2 + OE/2 = LO = VE

Substituting the given value for LE, we get:

LV/2 + OE/2 = 15

Solving this equation for one of the variables, we get:

LV = 30 - OE

Substituting this expression into the first equation above, we get:

x² + ((30 - OE)/2)² = 81/4

Simplifying and rearranging, we get:

OE² - 60OE + 675 = 0

Using the quadratic formula, we get:

OE = (60 ± √(3600 - 2700)) / 2

OE = 15 or 45

If OE = 15, then LV = 30 - 15 = 15, and we can solve for x and y:

x² + 7.5² = 81/4

y² + 7.5² = 225/4

Solving these equations, we get:

x = 3√7

y = 9/√7

If OE = 45, then LV = 30 - 45 = -15, which is impossible for a length. Therefore, the solution is:

LV = OE = 15

x = 3√7

y = 9/√7

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Complete question:

LOVE is a kite. LV and OE are diagonals. The segments DV = 9cm and LE = 15cm are given. Find the lengths of the other segments of the diagonals, DV, OE, and LV.

Answer:

Step-by-step explanation:

Midpoint theorem : The line joining midpoint of  any two side of a triangle is parallel to third side and is half of it.

1) AI = 10.5

MC = 2*AI = 2*10.5

MC = 21

I solved for MC using midpoint theorem.

2) MC = 32

AI = \(\frac{1}{2}*32\)

AI = 16

I solved for AI using midpoint theorem.

Answer:

AI is 16

Step-by-step explanation:

The dimensions of the room will be 12m x 6m.

So, now calculate the dimensions of the room as follows:

Solve as shown:

Therefore, 12m x 6m will be the dimensions of the room.

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Answer:

Option D

Answer:

4d-16/1, 8d-32/2, 12d-48/3, etc.

Step-by-step explanation:

Just throw a denomiator under the expression and adjust the expression accordingly.

Answer:

48

Step-by-step explanation:

All the angles of a triangle add up to 180

180-45-87=48

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Answer:

Divide by 39 on both sides

Step-by-step explanation:

y = 6

Answer:

Divide by 39 on both sides y=6

Answer:

60

Step-by-step explanation:

I hope this helps

The diameter of the  cylinder is equal to 59.98 units.

Given the following data:

To determine the diameter of the  cylinder:

First of all, we would find the radius of the circular base of this cylinder.

Mathematically, the volume of a cylinder is given by the formula:

\(Volume = \pi r^2h\)

Making r the subject of formula, we have:

\(r=\sqrt{\frac{V}{\pi h} }\)

Substituting the given parameters into the formula, we have;

\(r=\sqrt{\frac{33912}{3.142 \times 12} }\\\\r=\sqrt{899.43}\)

Radius, r = 29.99 units.

For the diameter:

\(Diameter = 2 \times radius\\\\Diameter = 2 \times29.99\)

Diameter = 59.98 units.

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Answer:

The correct option is;

E) The average wait time to make payment and the number of cashiers working in a store

Step-by-step explanation:

An inversely proportional relationship is a relationship between two variables one where the increase in the magnitude one variable leads to the reduction in the magnitude of a second variable written mathematically as follows;

y ∝ 1/x

Therefore, given that as the number of cashiers at a store increases, the number of customers attended to per unit time by all the cashiers together increases, and the number of wait time observed by a customer to pay for the goods bought decreases.

Answer:

B.) The total number of stores visited and the average time spent in each store

E.) The average wait time to make a purchase and the number of cashiers working in a store

Step-by-step explanation:

It is correct I just took the test :)

Answer:

It is not infront of the 5 because when mutiplying it goes above a whole number so the . has to move back.

Step-by-step explanation:

Answer:

It has to be in front of the 5 since you have to move the decimal 2 places to the right and it lands beside the 5

Answer:

49%

Step-by-step explanation:

465 + 485 = 950

465/950 = .489

.489 * 100 = 48.9, round up for 49 to get 49%, since it's only focused on people who tested positive, you would only have to compare the people in that column

Answer: b

Step-by-step explanation:

Kermit will likely enjoy Peggy's iced tea as it has the same concentration as his favorite iced tea.

Let's compare the ratios of tea bags to water in Kermit's favorite iced tea and Peggy's iced tea to determine what Kermit might think of Peggy's iced tea.

1. Kermit's favorite iced tea ratio:
Kermit uses 15 tea bags in every 2 liters of water. So, the ratio is 15:2.

2. Peggy's iced tea ratio:
Peggy made a 12-liter batch of iced tea with 90 tea bags. So, the ratio is 90:12.

Now, let's simplify both ratios:

1. Kermit's ratio:
15:2 can be simplified to 7.5:1 by dividing both numbers by 2.

2. Peggy's ratio:
90:12 can be simplified to 7.5:1 by dividing both numbers by 12.

Both iced tea recipes have the same ratio of 7.5:1 (tea bags to water), and the tea bags are in the water for the same amount of time. Therefore, Kermit will likely enjoy Peggy's iced tea as it has the same concentration as his favorite iced tea.

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The probability is the same for each outcome since they are equally likely.

Let's assume there are n gift cards in total in the bag. When a student selects two gift cards without replacement, the total number of possible outcomes is the number of ways to choose 2 cards out of n, which can be calculated using the combination formula:

C(n, 2) = n! / (2! * (n - 2)!)

Each of these outcomes has an equal probability of being selected since the gift cards were mixed well, and the selection is random

The probability of each outcome in the sample space can be calculated by dividing 1 by the total number of possible outcomes:

P(outcome) = 1 / C(n, 2).

For example, if there are 4 gift cards in the bag, the total number of possible outcomes is C(4, 2) = 6. Therefore, the probability of each outcome in this case would be 1/6.

In general, the probability of each outcome in the sample space for the random selection of two gift cards is 1 divided by the total number of possible outcomes, ensuring that all outcomes have an equal chance of occurring.

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The statement is true.

When the block is in equilibrium, each spring is stretched an additional ∆x. This implies that the forces from the two springs are balanced, and the block is not experiencing any net force in the equilibrium position.

When the block is set into oscillation with amplitude a, it will pass through its equilibrium point during the oscillation. At the equilibrium point, the displacement of the block is zero, and it changes direction. At this point, the block has its maximum speed v, as it is accelerating towards the equilibrium position.

The speed of the block decreases as it moves away from the equilibrium position, reaches zero at the maximum displacement (amplitude), and then starts accelerating towards the equilibrium point again. Therefore, when the block passes through its equilibrium point, it has its maximum speed v.

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