in a ping pong tournament consisting of twelve teams, each team plays every other team once. how many games are there?

Fuel consumption rate = Fuel used / Distance traveled

First, let's convert the fuel used from liters to milliliters (ml) for convenience in calculations:

Fuel used = 120 L = 120,000 ml

Now we can substitute the given values into the formula:

Fuel consumption rate = 120,000 ml / 3000 km

Simplifying this expression, we get:

Fuel consumption rate = 40 ml/km

This means that the vehicle uses 40 milliliters of fuel to travel 1 kilometer. To convert this to a more commonly used unit of fuel consumption, we can use the conversion factor of 1 L = 1000 ml:

Fuel consumption rate = 0.04 L/km

Finally, to find the rate of fuel consumption in km/h, we need to divide this value by the vehicle's speed in km/h. However, the problem does not provide information about the vehicle's speed, so we cannot determine the fuel consumption rate in km/h.

Step-by-step explanation:

Answer: The number is 42

Step-by-step explanation:

difference of 19 & 5 = 19 - 5
                                   = 14
One less than = 14-1
                         = 13

=> 13*3
= 39

The expressions with the options that will give 4^-12 are

The expression is an exponent of negative integer. The options are simplified further to their simplest forms as shown below

A. 4^-10 * 4^-2

The equation is multiplied to give a result of 4^-12

B. (1/4^-3)^4

= (4^3)^4

= 4^12

C. (4^-16)^4

= 4^(-16+4)

= 4^-12

D. 4^3 / 4^15

= 4^(3 - 15)

= 4^-12

E. (4^-7 * 4^-2) / 4^3

= 4^(-7 + (-2) + 3)

= 4^6

Hence the expression that will result to 4^-12 are A, C, and D

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Purple is the color with an angle closest to the 40 degrees; 175 people did not choose a rainbow color; the percentage of people that prefer red is 20%.

By considering a circle is 360°, let's analyze the percentage 40 degrees would represent.

40/360 x 100% =11.1%

This percentage is closer to the purple color.

People surveyed:: 500

The percentage that did not choose a rainbow color: 35%

500 x 0.35 =175 people

Percentage of people who chose a rainbow color:64%

Percentage that chose red: 13%

13 x 100/ 64 = 20.3%

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The number of ways Steve can buy  bottles of orange juice is equal to  1.3176 x 10¹⁸ ways.

Number of  bottles of orange juice Steve wants to buy = up to 20  

⇒ He can buy any number of bottles from 0 to 20, inclusive.

Number of available different brands = 8

For each number of bottles he decides to buy, he can choose from 8 different brands.

Use the sum rule of counting to find the total number of ways Steve can buy the bottles.

Number of ways

= number of ways to buy 0 bottles + number of ways to buy 1 bottle + ... + number of ways to buy 20 bottles

The number of ways to buy a specific number of bottles use the product rule of counting.

Number of ways to buy x bottles

= number of ways to choose a brand for each bottle is 8ˣ

Putting everything together, we get,

⇒ Number of ways = 8⁰ + 8¹ + 8² + ... + 8²⁰

This is a finite geometric series with a first term 'a' of 1 and a common ratio 'r' of 8.

Use the formula for the sum of a finite geometric series to simplify,

Sum = a ( 1 -rⁿ⁺¹)( 1 - 4)

Sum = (1 - 8²¹) / (1 - 8)

       = (1 - 8²¹) / (-7)

       = 1.3176 x 10¹⁸ ways.

Therefore, Steve can buy the bottles in 1.3176 x 10¹⁸ ways.

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Answer:

(2,-6)

Step-by-step explanation:

x=2 y=-6

Answer:

divide d by 1

6.7÷1 so it will be the answer

Mr. William's class has a higher rate of students with afterschool jobs because 9 over 30 is less than 8 over 25. Therefore, the second statement is correct.

Comparing the ratios of students with afterschool jobs in Ms. Talley's and Mr. William's classes.

Ms. Talley's class

Students have afterschool jobs = 9 out of 30

Ratio = [tex]\frac{9}{30}[/tex]

Mr. William's class

Students have afterschool jobs = 8 out of 25

Ratio = [tex]\frac{8}{25}[/tex]

Let us now compare the ratios:

9/30 = 0.3

8/25 = 0.32

Comparing the ratios, we can see that 0.32 is greater than 0.3.

As a result, compared to Ms. Talley's class, Mr. William's class has a higher percentage of students who have afterschool jobs.

Therefore, the correct statement is: Mr. William's class has a higher rate of students with afterschool jobs because 9 over 30 is less than 8 over 25.

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The value of the given exponential expression 2⁴·3⁵/(2.3)⁵ is 1/2.

1) Given that, (3·2)⁴·3⁻³/2³·3

Here, 3⁴·2⁴·3⁻³/2³·3

= 3·2⁴/2³·3

= 2

2) 3²·4³·2⁻¹/(3·4)²

= 3²·4³·2⁻¹/3²·4²

= 4·2⁻¹

= 2²·2⁻¹

= 2

3) 3⁻³·2⁻³·2⁻¹/(4⁰)²

= 3⁻³·2⁻⁴/1

= 1/3³·2⁴

= 1/27×16

= 1/432

4) 2⁴·3⁵/(2.3)⁵

= 2⁴·3⁵/2⁵.3⁵

= 1/2

Therefore, the value of the given exponential expression 2⁴·3⁵/(2.3)⁵ is 1/2.

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Answer:

  10

Step-by-step explanation:

You want the minimum value of c = x +y, subject to the constraints {2x +y ≥ 20, 2x +3y ≥ 0, x ≥ 0, y ≥ 0}.

The attached graph shows the relevant vertices of the feasible region are (0, 20) and (10, 0). The value of c is minimized when (x, y) = (10, 0). At that point, c = 10 + 0 = 10.

The minimum value of c is 10.

The area of the shaded sector of the circle is 3π ft².

A sector of a circle is simply a region bounded by two radii of the circle and an arc of the circle.

The area of a sector can be found using the formula:

A = (θ/360) × πr²

Where A is the area of the sector, θ is the central angle in degrees, r is the radius of the circle, and π is pi.

From the image:

Central angle θ =  360° - 90° = 270°

Radius r = 2ft

Plug the given values into the above formula and solve for area.

A = (θ/360) × πr²

A = (270/360) × π × (2ft)²

A = (270/360) × π × 4ft²

A = 3/4 × π × 4ft²

A = 3π ft²

Therefore, the area is 3π ft².

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Answer:

The length of the rectangular field is 77 meters.

Step-by-step explanation:

We can use the formula for the area of a rectangle to solve this problem:

Area = length x width

We are given that the area is 4235 m² and the width is 55 m. We can substitute these values into the formula and solve for the length:

4235 = length x 55

To isolate the variable "length" on one side of the equation, we can divide both sides by 55:

4235/55 = length

Simplifying the right side gives:

77 = length

Answer:

y intercept is -2

Step-by-step explanation:

y intercept is when x is 0.

original equation:

If you want to make it into something solvable, you want to move everything but y to one side.

1. x+4y+8=0

2. 4y+8=-x

3. 4y=-x-8

4. y=-1/4x-2

5. Since this is a linear function, all you have to do to find the y intercept is plug x in with 0. (mentioned above)

6. y=-1/4(0)-2

7.y=-2

8. y int=-2

The probability that their mean total body protein is between 12.2 and 12.4 kg is 0.6826.

We know that the conveyance of the test mean is additionally ordinary with the mean breaking even with the populace mean and standard deviation rising to the populace standard deviation isolated by the square root of the test measure.

Let X be the whole body protein in sound grown-up men.

At that point, we have:

X ~ N(12.3, 0.4²) (populace conveyance)

X bar ~ N(12.3, 0.4²/4) = N(12.3, 0.2²) (dissemination of test cruel)

We need to discover P(12.2 ≤ X bar ≤ 12.4) for a test measure of n=4.

Utilizing standardizing the dispersion of the test mean, we have:  

 z = (X bar - μ) / (σ / √(n))

where μ = 12.3, σ = 0.2, n = 4

z = (12.2 - 12.3) / (0.2 / √(4)) = -1

z = (12.4 - 12.3) / (0.2 / √(4)) = 1

Employing a standard ordinary dispersion table, we are able to discover the likelihood:

P(-1 ≤ z ≤ 1) = P(z ≤ 1) - P(z < -1) = 0.8413 - 0.1587 = 0.6826

In this manner, the likelihood that the mean adds up to body protein of a test of 4 solid grown-up men is between 12.2 and 12.4 kg is 0.6826. 

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The probability of being enrolled in AP Physics given of Key Club is equal to 0.826, or 82.6%.

Probability of member of key club 'K'= 2.3%

Probability of enrolled in AP Physics, P = 2.3%

Probability of both = 1.9%

Use the formula for conditional probability to find the probability of P given K,

P(P|K) = P(P ∩ K) / P(K)

where P(P ∩ K) represents the probability of being in both P and K,

and P(K) represents the probability of being in K.

Here,

since 2.3% of the senior class are members of Key Club

⇒ P(K) = 0.023

Since 1.9% of the senior class are in both P and K.

⇒ P(P ∩ K) = 0.019

Substituting these values into the formula for conditional probability, we get,

P(P|K) = P(P ∩ K) / P(K)

         = 0.019 / 0.023

         ≈ 0.826

Therefore, the probability of being enrolled in AP Physics given that a senior is a member of Key Club is approximately 0.826, or 82.6%.

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Answer: Mean: 40.2, Median: 41

Step-by-step explanation: 37, 43, 41, 36 and 44 added all together is 201 / 5 = 40.2 (70 is the outlier). The middle of 37 43 41 36 44 is 41, because the numbers lined up is 36, 37, 41, 43, 44 the middle is 41.

The probability that the point lies in the region is 21.5%

Note that percentage is the ratio of a number and 100.

From the information given, we have that;

The total area of the figure = 22(22 ×2)

expand the bracket

Total area = 22(44)

Total area = 968 units square

Area of the shaded area is expressed as;

= Total area - 2area of a circle

substitute the values

= 968 - 2πr/2²

=968 - 2(3.14 × 11²)

find the square

= 968 - 759. 88

= 208. 12 units square

The probability is;

Area of shaded are/total area × 100/1

208. 12/968 × 100/1

21. 5%

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Answer:

D

Step-by-step explanation:

Answer:

Step-by-step explanation:

||y + 6|| = 10

Next, we can consider the two possible cases:

Case 1: y + 6 ≥ 0

If y + 6 is non-negative, then the absolute value of y + 6 is just y + 6 itself. So we have:

y + 6 = 10

y = 4

Case 2: y + 6 < 0

If y + 6 is negative, then the absolute value of y + 6 is the opposite of y + 6, which is -(y + 6). So we have:

-(y + 6) = 10

y + 6 = -10

y = -16

Therefore, the solutions to the equation 3||y + 6|| = 30 are y = 4 and y = -16.

Answer:

F(2)= 3

Step-by-step explanation:

The equation of a circle centered at the origin with a radius of 12, which is x² + y² = 144.

To find the equation of the circle, we use the standard form of the equation of a circle, which is:

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the center of the circle, and r is the radius.

In our problem, the center of the circle is at the origin, which means h = 0 and k = 0. The radius is given as 12, so we have r = 12. Substituting these values into the standard form equation, we get:

(x - 0)² + (y - 0)² = 12²

Simplifying, we get:

x² + y² = 144

Therefore, the equation of the circle centered at the origin with a radius of 12 is x² + y² = 144.

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Answer:

An investment of $10000 today invested at 6% for five years at simple interest will be $13,000.

Answer:

20 days for 8 people to do the work Assuming that the rate of work is the same.

the answer is 4/3, because the angles are complementary".

What is Trigonometric Functions?

Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.

To find the value of sin 54°, we can use the identity: sin 54° = cos (90° - 54°).

Since the angles are complementary, we know that cos 36° = sin (90° - 36°) = sin 54°.

We are given that cos 36° = three fourths, so we can substitute this value in the above equation to get:

sin 54° = cos (90° - 36°) = cos 54° = three fourths / sin 36°

We know that sin²x + cos²x = 1, so we can solve for sin 36°:

sin²36° + (3/4)² = 1

sin²36° = 1 - (3/4)² = 7/16

sin 36° = √(7/16)

Now we can substitute the value of sin 36° in the equation for sin 54°:

sin 54° = (3/4) / √(7/16) = 4/3

Therefore, the answer is "four thirds, because the angles are complementary".

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Answer:

I would say -F=0.4

Step-by-step explanation:

if F=-0.4 and -F is the opposite of F then the opposite of -0.4 is 0.4

The correct conclusion we can draw from the circle graph is an option (D) "Together, Walk and Streetcar are the preferred transportation for 165 residents."

As per the information provided, it is given that:

Bicycle is the preferred transportation for 8% of 300 residents, which is 0.08 x 300 = 24 residents.

Therefore, option (B) "Bicycle is the preferred transportation for 48 residents" is not correct, as it represents twice the actual number.

Option (A) "Bus is the preferred transportation for 25 residents" is not supported by the information in the graph, as the bus section represents 10% of the graph, but we don't know the actual number of residents who prefer the bus.

Option (C) "Together, Streetcar and Cable Car are the preferred transportation for 42 residents" is not correct, as the cable car section alone represents 27% of the graph, which is more than 42 residents.

Option (D) "Together, Walk and Streetcar are the preferred transportation for 165 residents" is supported by the information in the graph, as the walk section represents 40% of the graph, which is 0.4 x 300 = 120 residents, and the streetcar section represents 15% of the graph, which is 0.15 x 300 = 45 residents.

Therefore, the total number of residents who prefer walking or streetcar is 120 + 45 = 165.

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We can determine that the necessary angle ∠a is 15° using the provided secant line.

A secant crosses a circle at precisely two points in a case of a circle.

Mathematicians refer to a line that cuts through the points P and Q of any arbitrary curve whose equation is y=f as a secant, from the Latin term secant, which means to cut (x).

So, we know that:

c = 55° and b = 25°

And, the formula is:

∠a = c - b/2

Now, substitute values as follows:

∠a = c - b/2

∠a = 55 - 25/2

∠a = 30/2

∠a = 15°

Therefore, using the given secant line, we know that the required angle ∠a is 15° respectively.

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Complete question:

We would need to toss the coin 46,316 times to be sure that our confidence interval has a margin of error of no more than plus or minus 0.001.

To calculate the sample size needed for our desired margin of error, we use the following formula:

n = (z² x p x (1-p)) / E²

where n is the sample size, z is the z-score corresponding to the desired level of confidence (in our case, 1.96 for 95% confidence), p is our estimate of the probability of a head, and E is the margin of error we want (in our case, 0.001).

Since we don't know the true probability of a head, we can use our best estimate based on past experience or a preliminary study. Let's assume we believe the probability of a head is 0.52.

Plugging in these values, we get:

n = (1.96² x 0.52 x 0.48) / 0.001² ≈ 46,316

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