A math class has 12 students. There are 6 tables in the classroom with exactly 2 students per table. To prevent excessive copying on a certain upcoming quiz, the math professor makes 3 different versions of the quiz with four of each of the three versions. The math professor then shuffles the quizzes and distributes them at random to the students in the class. (a) What is the probability that none of the tables have two of the same version of the quiz? (b) Define a set of tables T = {T₁, T2, T3, T4, T5, T6) Define a sample space S = { all ways to distribute two versions of the quiz to each table T, € T} Define a Bernoulli random variable for each s € S by Jo no tables in s have two of the same version X(s) = at least one table in s has two of the same version Find the probability mass function (pmf) for X. Hint P(X= 0) = the correct answer to part (a). (c) Sketch a graph of the cumulative distribution function (cdf) for X below.

Answer:

-1.14

Step-by-step explanation:

The given information in statement is

mean=μ=69

standard deviation=σ=3.5

Let X be the Ishaan's exam score

X=65

The Z score can be computed as

\(z=\frac{x-mean}{standard deviation}\)

\(z=\frac{65-69}{3.5}\)

z=-1.1429

z=-1.14 (rounded to two decimal places).

Thus, the computed z-score for Ishaan's exam grade is -1.14.

Answer:

-2.67

Step-by-step explanation:

khan academy

We have that, using the Chinese remainder theorem, the number of things is 23

There are certain things whose number is unknown. When divided by 3, the remainder is 2; when divided by 5, the remainder is 3; when dividing by 7, the remainder is 2. To solve this problem, we will have to use the Chinese Remainder Theorem.

It establishes that: Let m1, m2, …, mk be coprime integers greater than 1, and let a1, a2, …, ak be any integers. So, the system of simultaneous congruences:

x ≡ a1 (mod m1)x ≡ a2 (mod m2)…x ≡ ak (mod mk)

It has a unique solution modulo M = m1m2…mk.

The Chinese Remainder Theorem implies that there is only one solution of the system of three congruences such that 0 ≤ x < 3 x 5 x 7 = 105. Using the Chinese Remainder Theorem, we obtain that x ≡ 23 (mod 105). Therefore, the number of things is 23.

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Answer:

a b e f

Step-by-step explanation:The Aztec created music using instruments like drums.

The Aztec used feathers and jewelry to identify social class.

The Aztec wrote complicated poems known as flower songs.

The Aztec expanded existing structures like the Temple of the Sun. i did it

Answer:

The Aztec created music using instruments like drums.

The Aztec used feathers and jewelry to identify social class.

The Aztec wrote complicated poems known as flower songs.

The Aztec expanded existing structures like the Temple of the Sun.

Step-by-step explanation:

The newborn death rate is calculated by dividing the number of newborn deaths by the number of live births and multiplying by 100.

The newborn death rate, also known as the neonatal mortality rate, is a critical indicator used in public health to assess the health and well-being of newborns. It is calculated by dividing the number of newborn deaths within a specified period by the number of live births during the same period and then multiplying the result by 100.

This calculation is performed to express the newborn death rate as a percentage, making it easier to interpret and compare across different populations or time periods. By dividing the number of deaths by the number of live births, we obtain the proportion of newborns who die within a certain timeframe. Multiplying this proportion by 100 provides the rate per 100 live births, which allows for a standardized measure of comparison.

The newborn death rate is a crucial statistic in assessing the quality of healthcare services, identifying areas with high mortality rates, and monitoring the effectiveness of interventions aimed at reducing neonatal deaths. It serves as a vital tool for policymakers, healthcare professionals, and researchers in evaluating and improving newborn health outcomes.

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A 300-kilogram roller coaster car traveling at 25 m/s has the greatest momentum.

A. 0.7kg × 2.5 = 1.75 kg m/s

B. 1000kg × 5m/s = 5000 kg m/s

C. 40kg × 0.5m/s = 20 kg m/s

D. 300kg × 25m/s = 7500 kg m/s

What is momentum?

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The monthly kilowatt-hours (kWh) used by the clothes dryer is approximately 95.38 kWh.

To calculate the monthly kilowatt-hours (kWh) used by the clothes dryer, we need to determine the energy consumption for each load and then multiply it by the number of loads per week and the number of weeks in a month.

Given:

Power of the clothes dryer: 4900 watts

Number of loads per week: 6

Load duration: 45 minutes

First, let's convert the load duration from minutes to hours:

Load duration: 45 minutes / 60 minutes/hour = 0.75 hours

Now, let's calculate the energy consumption for each load:

Energy consumption per load = Power × Load duration

Energy consumption per load = 4900 watts × 0.75 hours = 3675 watt-hours

Next, let's calculate the weekly energy consumption:

Weekly energy consumption = Energy consumption per load × Number of loads per week

Weekly energy consumption = 3675 watt-hours × 6 = 22,050 watt-hours

To convert watt-hours to kilowatt-hours (kWh), we divide by 1000:

Weekly energy consumption in kWh = 22,050 watt-hours / 1000 = 22.05 kWh

Now, let's calculate the monthly energy consumption:

Assuming a month consists of approximately 4.33 weeks:

Monthly energy consumption = Weekly energy consumption in kWh × Number of weeks in a month

Monthly energy consumption = 22.05 kWh × 4.33 = 95.38 kWh

Therefore, the monthly kilowatt-hours (kWh) used by the clothes dryer is approximately 95.38 kWh.

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The range of the inverse function is given by the following interval:

(−∞, 1) ∪ (1, ∞)

The range of a function is the set that is composed by all the output values on a function. Hence, on the graph, the range of a function is composed by the values of y of the function.

For the inverse function, the input and the output are exchanged, hence, given the graph of a function, the range of the inverse function is given by the domain of the original function, that is, the values of x of the graph of the original function.

From the description of the rational function, the asymptote is given as follows:

x = 1.

Hence the domain of the graphed function, which is equivalent to the range of the inverse function, is given by the following interval:

(−∞, 1) ∪ (1, ∞).

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Answer:

=its 29+29+45

Step-by-step explanation:

hope dis helps

Answer:

4/9 16/36 12\27 are all equivalent fraction

Answer:

16/36, 12/27 are equivalent to 4/9.

Step-by-step explanation:

Hope this helps!

The slope of each pair point is listed below:

Case A: m = - 4

Case B: m = 6 / 7

Case C: m = - 3

Case D: m = 4

Case E: m = - 5 / 2

In this problem we find five cases of two points that are part of a line, whose slope (m) can be calculated by means of secant line formula:

m = (y₂ - y₁) / (x₂ - x₁)

Where:

Now we determine the slope for each case:

Case A:

m = (10 - 2) / (7 - 9)

m = 8 / (- 2)

m = - 4

Case B:

m = [- 5 - (- 11)] / [- 1 - (- 8)]

m = 6 / 7

Case C:

m = [3 - (- 6)] / (2 - 5)

m = 9 / (- 3)

m = - 3

Case D:

m = (- 1 - 3) / (5 - 6)

m = - 4 / (- 1)

m = 4

Case E:

m = (2 - 7) / (6 - 4)

m = - 5 / 2

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Answer: X = -85/6

Step-by-step explanation:

The sine of an angle in the second quadrant differs from the sine of its reference angle by a negative sign.

In the unit circle, the reference angle is the acute angle formed between the positive x-axis and the terminal side of an angle measured counterclockwise. The sine of an angle is defined as the y-coordinate of the point on the unit circle corresponding to that angle.

In the second quadrant of the unit circle, angles have values between 90 degrees and 180 degrees (π/2 and π radians). Since the reference angle is always the acute angle, the reference angle for an angle in the second quadrant is the angle formed between the terminal side and the negative x-axis.

When comparing the sine of an angle in the second quadrant to the sine of its reference angle, there is a sign difference. The sine function is positive in the first and second quadrants. However, in the second quadrant, the y-coordinate (sine value) is negative because it lies below the x-axis. This means that the sine of an angle in the second quadrant is the negative value of the sine of its reference angle.

Mathematically, if θ is an angle in the second quadrant, and α is its reference angle, then:

sin(θ) = -sin(α)

This relationship holds true because the y-coordinate (sine value) in the second quadrant is the negative value of the y-coordinate in the first quadrant. So, the sine of an angle in the second quadrant differs from the sine of its reference angle by a negative sign.

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Answer:

789

Step-by-step explanation:

irdk

The matrix B that organizes the data is given as follows:

B = [13, 36, 27,

      10, 15, 0,

       23, 51, 27].

The matrix that shows the total value of each cap size in each location is given as follows:

C = [247, 684, 513,

      190, 285, 0,

      437, 969, 513].

The matrix B is defined considering that it will have three rows and three columns, as follows:

Then the matrix B is defined as follows:

B = [13, 36, 27,

      10, 15, 0,

       23, 51, 27].

The cost of each baseball cap is of $19, thus the cost matrix is obtained multiplying the matrix B by the constant of 19.

When a matrix is multiplied by a constant, all the elements of the matrix are multiplied by the constant, hence the cost matrix is given as follows:

C = [247, 684, 513,

      190, 285, 0,

      437, 969, 513].

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The 10 yearly payments worth is $ 7299806.

The current value of a future sum of money or stream of cash flows at a certain rate of return is known as present value (PV). A discount rate or the interest rate that could be earned if invested is added to the future value for present value.

it is given that

PMT =$ 900000

Rate = 4%

years = 10

using the formula

PV = \(A * \frac{1 - \frac{1}{(1+R)^{N} } }{R}\)

PV = (900000/0.04) × (1 - (1/ (1+0.04)^10))

PV = $ 7299806

the payment you receive today is $7299806

so, it is better to accept 10 annual payments as it has a higher value.

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The total amount of money earned by Nora salary over the 21 years is approximately $1,848,000.

To find the total amount of money earned by Nora over 21 years, we need to calculate the salary for each year and then sum them up.

In the first year, Nora's salary is $40,000.

In the second year, her salary will be increased by 3%, so it will be:

$40,000 + 3% of $40,000 = $40,000 + $1,200 = $41,200.

In the third year, her salary will again increase by 3%, so it will be:

$41,200 + 3% of $41,200 = $41,200 + $1,236 = $42,436.

We can continue this process for each year, adding 3% of the previous year's salary to calculate the next year's salary.

To calculate the total amount of money earned over the 21 years, we need to sum up the salaries for each year. Here's the calculation:

Total = $40,000 + $41,200 + $42,436 + ... (21 terms)

To simplify the calculation, we can use the formula for the sum of an arithmetic series:

Total = (n/2) * (2a + (n - 1)d)

where:

n = number of terms (21 in this case)

a = first term ($40,000)

d = common difference (3% of the previous year's salary)

Plugging in the values:

Total = (21/2) * [2(40,000) + (21 - 1)(0.03)(40,000)]

Simplifying further:

Total = (21/2) * [80,000 + 20(0.03)(40,000)]

= (21/2) * [80,000 + 2,400(40,000)]

= (21/2) * [80,000 + 96,000]

= (21/2) * 176,000

= 21 * 88,000

= 1,848,000

Therefore, the total amount of money earned by Nora salary over the 21 years is approximately $1,848,000.

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Answer:

I think it's. y=-2/1x+2

Answer:

  1.6 qt/s

Step-by-step explanation:

You want the fill rate of 24 gal/min converted to quarts per second.

To convert units, multiply by a factor that has units you want and cancels units you don't want. The numerator value and the denominator value of the conversion factor should be equal:

  4 qt = 1 gal

  1 min = 60 s

Your conversion is ...

  \(\dfrac{24\text{ gal}}{\text{min}}=\dfrac{24\text{ gal}}{\text{min}}\times\dfrac{4\text{ qt}}{1\text{ gal}}\times\dfrac{1\text{ min}}{60\text{ s}}=\dfrac{24\cdot4}{60}\,\dfrac{\text{qt}}{\text{s}}=\boxed{1.6\text{ qt/s}}\)

To find the magnitude of r prime of quantity pi over 3 end quantity, we first need to take the derivative of r of t. r prime of t = a vector with two components, sec^2(t) and 2csc(2t) .Then, we can evaluate r prime of pi/3 using these components: r prime of pi/3 = a vector with two components, sec^2(pi/3) and 2csc(2(pi/3)).
Using the fact that sec^2(pi/3) = 4 and csc(2(pi/3)) = -2sqrt(3)/3, we can simplify the vector to: r prime of pi/3 = a vector with two components, 4 and -4sqrt(3)/3
Now, we can find the magnitude of this vector using the formula:

magnitude of a vector = square root of (sum of squares of its components)

magnitude of r prime of pi/3 = square root of (4^2 + (-4sqrt(3)/3)^2)

= square root of (16 + 16/3)

= square root of (64/3)

= 4/square root of 3

Multiplying this by the given constants (1/3 square root of thirty four, 1/2 square root of nineteen, 2 square root of thirteen over three, 4/3 square root of ten), we get the final answer:

magnitude of r prime of quantity pi over 3 end quantity = (4/square root of 3) * (1/3 square root of thirty four) * (1/2 square root of nineteen) * (2 square root of thirteen over three) * (4/3 square root of ten)

= 16/square root of (3 * 34 * 19 * 13 * 10/9)

= 16/square root of 2,583.49

= 16/50.83

= 0.3147 (rounded to four decimal point)

To find the magnitude of r'(π/3), we need to take the square root of the sum of the squared components:

Magnitude of r'(π/3) = √[sec^4(π/3) + (2*cot(2(π/3))*csc^2(2(π/3)))^2]

Once you evaluate the trigonometric functions at π/3 and simplify the expression, you will have the magnitude of r'(π/3).

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Answer:

11:27 am.

Step-by-step explanation:

The time which has passed when Tom overtakes Hazel is after Hazel has walked 1 hr 15 minutes and in that time Hazel has walked

1.25 * 4.8

= 6 km.

So, Tom runs 6 km in 10:15 - 9.39 = 36 minutes

= 0.6 hrs.

So, Tom's speed is 6/0.6 = 10 km/hr.

,

and Tom will take 18/10 = 1.8 hours to finish the route,

= 1 hr 48 minutes

So he finishes the route at

9:39 + 1:48

= 11:27 am.

Answer:

x=4

Step-by-step explanation:

3x+4=x+12

     -4    -4

3x=x+8

-x   -x

2x=8

/2   /2

x=4

Answer:

b

Step-by-step explanation:

Answer:

the answer is b

Step-by-step explanation:

Due to the presence of two rectangles with sides of lengths a and b, Square G's area in Step 2 should equal \(a^2+2ab+b^2\).

According to the Pythagorean Theorem, the squares on the hypotenuse of a right triangle, or, in conventional algebraic notation, \(a^2+b^2\), are equal to the squares on the legs. The Pythagorean Theorem states that the square on a right-angled triangle's hypotenuse is equal to the total number of the squares on its other two sides.

The Pythagoras theorem, often known as the Pythagorean theorem, explains the relationship between each of the sides of a shape with a right angle. According to the Pythagorean theorem, the square root of a triangle's the hypotenuse is equal to the sum of the squares of its other two sides.

Area of square \(G=a^2+2ab+b^2\)

\(a^2+2ab+b^2=c^2+2ab\\\\a^2+2ab-2ab+b^2=c^2+2ab-2ab\\\\a^2+b^2=c^2\)

[ The Pythagorean theorem]

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Answer is 2nd answer

Thus, the area of the shaded part is found to be 50 sq. ft.

The shaded region's area is most frequently found in common geometry problems. Such problems always have a minimum of two forms, and you must determine the area for each shape as well as the darkened zone by deducting the smaller shape's area from the larger.

Rectangle's area :

Area has two dimensions: length and width. Square units like square inches, square feet, or square metres are used to measure area.

Length of shaded part = 5 ft

width of shaded part = 10 ft

Area = 5*10

Area = 50 sq. ft

Thus, the area of the shaded part is found to be 50 sq. ft.

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Correct question:

For the given figure find the area of the shaded region.

Length BC = 18 ft

Length CD = 10 ft

Answer:

1+2-3+4-5+6-7+8-9=3-3+4-5+6-7+8-9=-1+6-7+8-9=5-7+8-9=6-9=-3

Step-by-step explanation:

Answer: 45

Step-by-step explanation: Add all the digits