During a catered lunch, an average of 4 cups of tea are poured per minute. The lunch will last 2 hours. How many gallons of tea should the caterer bring if there are 16 cups in one gallon?

The speed of the baseball when it passes over the home plate is 97.67 mph.

Given :

Differentiate the function x(t) and y(t) with respect to t.

[tex]x'(t)=143[/tex]

[tex]y'(t)= -32t+5[/tex]   ---- (3)

Now, put the value of x(t) in equation (1).

60.5 = 143t

t = 0.423 sec

Now, put the value of t in equation (3).

[tex]y'(t) = -32(0.423)+5=-8.536[/tex]

Now, [tex]s(t) = \sqrt{(x'(t))^2+(y'(t))^2}[/tex]

[tex]s(t)=\sqrt{143^2+(-8.536)^2}[/tex]

[tex]\rm s(t)=\sqrt{20521.8633} = 143.2545\;ft/sec[/tex]

[tex]\rm s(t) = 97.67 mph[/tex]

Therefore, the speed of the baseball when it passes over the home plate is 97.67 mph.

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Answer:

Option C is correct.

Step-by-step explanation:

The formula is = [tex](1+\frac{r}{n})^{n}-1[/tex]

r = rate of interest

n = number of times its compounded

1. 4.0784% compounded monthly

here n = 12

[tex](1+\frac{0.040784}{12})^{12} -1[/tex] = 1.0403-1 = 0.0403

2. 4.0798% compounded semiannually

here n = 2

[tex](1+\frac{0.040798}{12})^{2} -1[/tex] = 1.0066-1 = 0.0066

3. 4.0730% compounded daily

here n = 365

[tex](1+\frac{0.040730}{12})^{365}[/tex] = 3.328-1 = 2.328

The annual value of the employer's contribution towards Trina's health insurance plan is $5,580.

Here, we have to find the annual value of the employer's contribution, we need to determine how much the employer pays towards the health insurance plan in one month.

Trina's employer purchased a health insurance plan that costs $550 per month, and Trina pays $85 toward the plan each month.

Therefore, the employer's contribution is the difference between the total cost of the plan and what Trina pays:

Employer's contribution = Total cost of the plan - Trina's contribution

Employer's contribution = $550 - $85

Employer's contribution = $465 per month

Now, to find the annual value of the employer's contribution, we multiply the monthly contribution by 12 (since there are 12 months in a year):

Annual employer's contribution = $465 * 12

Annual employer's contribution = $5,580

So, the annual value of the employer's contribution towards Trina's health insurance plan is $5,580.

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Answer:

2000 points

Step-by-step explanation:

Topic: Substraction, Addition and Products

You have to organize the problem, as you can see

at Start of Round 3 David Has: - 1500

During Round 3:

5 Questions: 1000 each correctly

so 5 x 1000 = 5000

3 Questions: - 500 each incorrectly

so 3 x -500 = -1500

at the End of Round 3:

Starting: -1500

During Round 3: 5000 - 1500 = 3500

the end of round 3: -1500 + 3500 = 2000

Let

[tex]A(-4,9)\\B(11,9)\\C(5,-1) \\D(-10,-1)\\E(-4.-1)[/tex]  

using a graphing tool  

see the attached figure to better understand the problem

we know that

Parallelogram is a quadrilateral with opposite sides parallel and equal in length

so

[tex]AB=CD \\AD=BC[/tex]

The area of a parallelogram is equal to

[tex]A=B*h[/tex]  

where  

B is the base

h is the height  

the base B is equal to the distance AB

the height h is equal to the distance AE  

Step 1

Find the distance AB

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

[tex]A(-4,9)\\B(11,9)[/tex]  

substitute the values

[tex]d=\sqrt{(9-9)^{2}+(11+4)^{2}}[/tex]

[tex]d=\sqrt{(0)^{2}+(15)^{2}}[/tex]

[tex]dAB=15\ units[/tex]

Step 2

Find the distance AE

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

[tex]A(-4,9)\\E(-4.-1)[/tex]  

substitute the values

[tex]d=\sqrt{(-1-9)^{2}+(-4+4)^{2}}[/tex]

[tex]d=\sqrt{(-10)^{2}+(0)^{2}}[/tex]

[tex]dAE=10\ units[/tex]

Step 3

Find the area of the parallelogram

The area of a parallelogram is equal to

[tex]A=B*h[/tex]

[tex]A=AB*AE[/tex]

substitute the values

[tex]A=15*10=150\ units^{2}[/tex]

therefore

the answer is

the area of the parallelogram is [tex]150\ units^{2}[/tex]

The area of the parallelogram is 0 units.

To find the area of a parallelogram, we can use the formula A = base * height. We can find the length of the base by finding the distance between points A and D, which is 11 units. To find the height, we can find the distance between points A and B, which is 0 units. Therefore, the area of the parallelogram is 0 units.

Answer:16

Step-by-step explanation:

Final answer:

Using the formula for the confidence interval of a proportion, and after calculating standard error and margin of error, the 98% confidence interval for the proportion of 8th graders involved in after school activities is [0.799, 0.981]. Therefore, option a is correct.

Explanation:

To find the 98% confidence interval for the proportion of 8th graders involved in some type of after school activity, we can use the formula for the confidence interval of a proportion:

CI = ± z * √((p*(1-p))/n), where p is the sample proportion, n is the sample size, and z is the z-score corresponding to the confidence level.

In this case, we have p = 0.89 (since 89% of the sample is involved in after school activities), n = 64, and for a 98% confidence interval, the z-score (from z-tables or statistical software) is approximately 2.33.

First, let's calculate the standard error (SE): SE = √((0.89*(1-0.89))/64) = √((0.89*0.11)/64) = √(0.0989/64) = 0.0392.

Next, calculate the margin of error (ME): ME = z * SE = 2.33 * 0.0392 = 0.09136.

Now we can calculate the confidence interval: the lower limit is p - ME = 0.89 - 0.09136 = 0.79864 and the upper limit is p + ME = 0.89 + 0.09136 = 0.98136.

After rounding to three decimal places, the 98% confidence interval for the proportion is [0.799, 0.981]. Hence, option a is correct.

The probability that both alternators fail is approximately 0.0004, the probability that neither fails is approximately 0.9612, and the probability that at least one fails is approximately 0.0388, all rounded to four decimal places.

(a) The probability that both Alternator will fail is calculated by multiplying the probabilities of each failing:
P(Both Fail) = P(Alternator 1 Fails) x P(Alternator 2 Fails) = 0.019 x 0.019 ≈ 0.000361 = 0.0004 (rounded to four decimal places).

(b) The probability that an alternator does not fail is 1 minus the probability that it fails.
P(Neither Fail) = (1 - P(Alternator Fails))^2 = (1 - 0.019)^2 ≈ 0.9612 (rounded to four decimal places).

(c) To find the probability of at least one alternator failing, we subtract the probability of neither failing from 1:
P(At Least One Fails) = 1 - P(Neither Fail) = 1 - 0.9612 ≈ 0.0388 (rounded to four decimal places)

It takes Robert 13 minutes and 36 seconds to complete a 400 meter swimming race when he swims the first 50 meters in 1 minute and slows down by 12 seconds for each subsequent 50 meters.

In this mathematical problem, Robert swims the first 50 meters in 1 minute. He slows down by 12 seconds for each subsequent 50 meters of the race. The total distance Robert needs to swim is 400 meters. The 400 meters is split into eight 50 meter increments.

For the first increment, it takes Robert 1 minute (or 60 seconds). For the next seven increments, Robert swims each in 12 seconds slower than the previous increment.

Therefore, the total time in seconds for Robert to complete the 400 meters swimming race is:

60 + 72 + 84 + 96 + 108 + 120 + 132 + 144 = 816 seconds

This is equivalent to 13 minutes and 36 seconds.

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65*8 = 520 miles traveled

520/80 = 6.5 hours for the car

Answer:

The automobile would take 6.5 hours to complete the trip.

Step-by-step explanation:

This is a case of a inverse variation relationship because when you increase the speed of traveling the time of arriving will reduce, now we have to define the equation and the variables:

Inverse variation equation: [tex]x1y1=x2y2[/tex]

[tex]x1[/tex]: speed of the bus, 65 miles per hour

[tex]y1[/tex]: time to Austin by bus, 8 hours

[tex]x2[/tex]: speed of the automobile, 80 miles per hour

[tex]y2[/tex]: time to Austin by automobile, unknown

Now we can replace the values in the equation and clear [tex]y2[/tex], this is:

[tex]65*8=80*y2\\y2=\frac{65*8}{80} =\frac{520}{80} =6.5\\[/tex]

The automobile would take 6.5 hours to complete the trip.

Answer:

the answer is .15

Step-by-step explanation:

To find the area of the surface above the given rectangle, we need to determine the intersection of the cylinder with the plane of the rectangle. The surface area above the rectangle is equal to the area of the rectangle multiplied by the range of the z-coordinate.

To find the area of the surface that lies above the given rectangle, we need to determine the intersection of the cylinder with the plane of the rectangle. The equation of the cylinder is y^2+z^2=9, and the vertices of the rectangle are (0,0), (4,0), (0,2), and (4,2). At the x=0 and x=4 cross sections, we can see that the y-coordinate ranges from 0 to 2 and the z-coordinate ranges from -3 to 3. Therefore, the surface area above the rectangle is equal to the area of the rectangle multiplied by the range of the z-coordinate.

The area of the rectangle is (4-0)(2-0) = 8 square units. The range of the z-coordinate is -3 to 3, so the surface area above the rectangle is 8 * (3 - (-3)) = 48 square units.

Answer:

Step-by-step explanation:

1. The total amount of oil in the two tanks at the start is ...

  total oil = n + (n +150) + 0 = 2n+150 . . . . litres

The amount of oil in tank C at the end is 1/3 this amount, or

  oil in tank C = (total oil)/3 = (2n+150)/3 . . . . litres

The amount pumped into tank C was 500 litres, so we have ...

  (2n +150)/3 = 500

  2n +150 = 1500 . . . . . . multiply by 3

  2n = 1350 . . . . . . . . . . . subtract 150

  1350/2 = n = 675 . . . . . divide by the coefficient of n

___

2. Let x represent the amount remaining in container A. Then 4x is the amount in tank B. Before the transfer, the amount in each container was the same, so ...

  x +120 = 4x -120 . . . . . A had 120 more than remains; B had 120 less

  240 = 3x . . . . . . . . add 120-x

  240/3 = x = 80 . . . divide by the coefficient of x

The amount of liquid left in container A is 80 mL.

Answer and explanation:

Use the distributive property in two different ways to find the product of 127 and 32.

Distributive property says that,

[tex]a(b+c)=ab+ac[/tex]

We have to find product of 127 and 32,

1) Split 127 as 100+27

[tex]127\times32=(100+27)\times 32[/tex]

Apply distributive property,

[tex]127\times32=100\times 32+27\times 32[/tex]

[tex]127\times32=3200+864[/tex]

[tex]127\times32=4064[/tex]

2) Split 32 as 30+2

[tex]127\times32=127\times (30+2)[/tex]

Apply distributive property,

[tex]127\times32=127\times 30+127\times 2[/tex]

[tex]127\times32=3810+254[/tex]

[tex]127\times32=4064[/tex]

The Java Rectangle class implements both the Shape and Serializable interfaces. Therefore, Rectangle r can be legally assigned to Rectangle, Shape, Serializable, and Object data types. It can't be assigned to a String, Measurable, and ActionListener as Rectangle doesn't implement these.

In Java, the Rectangle class implements the Shape and Serializable interfaces. Therefore, the legal assignments would be:

The rest assignments are not legal because the Rectangle class doesn't implement Measurable, ActionListener interfaces and it cannot be assigned to a String.

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