A lake contains 4 distinct types of fish. Suppose that each fish caught is equally likely to be any one of these types. Let Y denote the number of fish that need be caught to obtain at least one of each type.
(a) Give an interval (a, b) such that (b) Using the one-sided Chebyshev inequality, how many fish need we plan on catching so as to be at least 90 percent certain of obtaining at least one of each type?

2,598,960 many different hands consisting of four queens and one king.

What is combination?

A combination is a choice made in mathematics from a group of different elements when the order of the choices is irrelevant (unlike permutations). For instance, if three fruits, such as an apple, an orange, and a pear, are supplied, there are three possible pairings of the two: an apple and a pear. Formally speaking, a k-combination of a set S is a subset of S's k unique components. In other words, two combinations are the same if and only if they have the same members. (It is not important how the individuals in each set are arranged.) The quantity of k-combinations for a set with n components

To choose 4 kings, there is only one way, and to choose a queen, there are four.

Thus, there are 4 different methods to draw the 5 cards as instructed.

The probability of drawing cards is taken into account while calculating the number of ways to draw 5 cards from a typical 52-card deck.

= 52!/(47!)(5!) = 2,598,960.

Hence,  2,598,960 many different hands consisting of four queens and one king.

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Answer:

$21.6

Step-by-step explanation:

[tex]720*\frac{3}{100} =720*0.03=21.6[/tex]

The value of c that will make the expression x² + 24x + c  a perfect trinomial is 144.

The perfect squared trinomial as a perfect binomial is (x + 12)²

An expression obtained from the square of the binomial equation is a perfect square trinomial.

In other words, perfect square trinomials are algebraic expressions with three terms that are obtained by multiplying a binomial with the same binomial.

If a trinomial is in the form ax² + bx + c is said to be a perfect square, if and only if it satisfies the condition b² = 4ac.

Therefore,

x² + 24x + c

where

Therefore,

b² = 4ac

24² = 4 × 1 × c

4c = 576

divide both sides by 4

c = 576 / 4

c = 144

Therefore,

c = 144

The perfect squared trinomial as a perfect binomial is as follows:

x² + 24x + 144

x² + 12x + 12x + 144

x(x + 12) + 12(x + 12)

(x + 12)(x + 12)

(x + 12)

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Answer:

would it not be 26? I honestly don't know

A quadrilateral is a closed shape with four sides and the four angles add up to 360 degrees.

The value of x is 47

The value of y is 10.6

The four angles for the given quadrilateral are,

96, 94, 76, and 94.

A quadrilateral is a closed shape with four sides and the four angles add up to 360 degrees.

We have,

A an isoceles trapezium.

Where one pair of sides are equal and parallel.

Two angles are equal.

Now,

94 = 2x

x = 47

Now,

The four angles sum is 360.

94 + 94 + 96 + 3y + 44 = 360

328 + 3y = 360

3y = 360 - 328

3y = 32

y = 32/3

y = 10.7

Now,

3y + 44 = 3 x 10.7 + 44 = 32 + 44 = 76

Thus,

The four angles for the given quadrilateral are,

96, 94, 76, and 94.

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The mean and standard deviation of sampling distribution are 0.0187 and 0.010 respectively

The mean is a measure of location which tells us the average of observation.

Standard deviation tells us how dispersed a data is or how much variation our data contains.

According to question,

The population size : N = 1500

Number of fraudulent in a month : 28

Population proportion : P = 28/1500

=> P = 0.0187

Sample size: n = 180

Sample proportion : p = 28 / 180

=> p = 0.156

Therefore The mean of sampling distribution for the sample size 28,

μ = P

=> μ = 0.0187

The standard deviation will be

=> σ = [tex]\sqrt{\frac{p(1-p)}{n}}[/tex]

Substituting the value,

=>  σ = [tex]\sqrt{\frac{0.0187(1-0.0187)}{180}}[/tex]

=>  σ  = 0.010

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(7, 5) are the required coordinates of the diner.

A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates.

You do the reverse to determine a point's coordinates in a coordinate system.

Start at the point, then move up or down a vertical line until you reach the x-axis. Your x-coordinate is shown there.

To find the y-coordinate, repeat the previous step while adhering to a horizontal line.

So, we must discover the halfway point between Lan's house and Joe's house in order to get the diner's coordinates.

The following equation will determine the midway between any two points:

M(x1 + x2/2, y1 + y2/2)

There are (4, 4), the point, and the point replaces the specified values:

M(4+10/2, 4+6/2)

M(7, 5)

Therefore, (7, 5) are the required coordinates of the diner.

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The year 2029 written as a roman numeral is MMXXIX.

Roman numerals are mathematical representations of numbers in the Roman alphabet. Roman numerals are a numeral system that originated in ancient Rome and remained the standard way of writing numbers in Europe until the late Middle Ages.

Roman numerals are the symbols used in a system of numerical notation based on the ancient Roman system. The symbols are I, V, X, L, C, D, and M, which stand for 1, 5, 10, 50, 100, 500, and 1,000, respectively.

In this case, it should be noted that 2029 is MMXXIX.

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The length of the median of the trapezoid ABCD is  12 .

In the question ,

it is given that ,

the area of the trapezoid ABCD is = 60 ,

the height of the trapezoid ABCD is = 5 ,

let one base of the trapezoid ABCD be = a ,

So, b = a + 4 ,

Substituting the value in the formula for Area of the trapezoid = A =(a+b)h/2

(a + a + 4)5/2 = 60

(2a + 4)5 = 120

2a + 4 = 120/5

2a + 4 = 24

2a = 24 - 4

2a = 20

a = 20/2

a = 10 units

and other base = 10 + 4 = 14 units

So , the length of the median will be = (10 + 14)/2

= 24/2 = 12 units

Therefore , the length of median is = 12  .

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It is true, that the most level of confidence used in creating confidence intervals is 90%.

What is confidence interval?

A confidence interval (CI) for an unknown parameter in frequentist statistics is a range of estimations. The most popular confidence level is 95%, but other levels, such 90% or 99%, are occasionally used for computing confidence intervals. The fraction of related CIs over the long run that actually contain the parameter's true value is what is meant by the confidence level. The degree of confidence, sample size, and sample variability are all factors that might affect the width of the CI. A larger sample would result in a narrower confidence interval if all other factors remained constant. A wider confidence interval would also be required by a higher confidence level and would be produced by a sample with more variability.

We have given,

Given n = 93, u =24, x' = 23, α=5.5

z = x'- u / α(/√n) = 1.645

Hence the answer choice is true.

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Answer:130.09

Step-by-step explanation:

Using the formulas

A=2AB+(a+b+c)h

AB=s(s﹣a)(s﹣b)(s﹣c)

s=a+b+c

2

Solving forA

A=ah+bh+ch+1

2﹣a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4=5·7.2+8·7.2+3.5·7.2+1

2·﹣54+2·(5·8)2+2·(5·3.5)2﹣84+2·(8·3.5)2﹣3.54≈130.08536

Check the picture below.

[tex]tan(x)=\cfrac{\stackrel{opposite}{50}}{\underset{adjacent}{42}}\implies tan(x)=\cfrac{25}{21}\implies x=tan^{-1}\left( \cfrac{25}{21} \right)\implies x\approx 50^o[/tex]

Make sure your calculator is in Degree mode.

The minimum value of the function occurs between 4 and 5.

A function is a relation where every input is connected to only one possible output from a set of available inputs.

Given the table of values.

Note that the value of the function is a minimum of between 4 and 5.

Hence, the minimum value of the function occurs between 4 and 5.

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Answer: 1 1/5

Step-by-step explanation: you can write it as 1.5/1 times 4/5.

multiply by numerator and denominator so 1.5*4 which is 6

and 1*5 which is 5.

Now you have 6/5

6 can go into 5 once and you have 1 extra so 1 1/5

Answer:This is not a proportional relationship.

Step-by-step explanation:

At a confidence interval of 95%, if a polling result states that a president has an approval rating of 55%, the value of a margin of error of x is 1.534%.

In the given question, at a confidence interval of 95%, if a polling result states that a president has an approval rating of 55%, with a margin of error of x, then we have to explain how should we interpret that.

The given confidence interval = 95%.

We can write it as CI = 0.95.

An approval rating is 55%.

We can write it as(p) = 0.55

A margin of error is x.

Let the value of sample size n = 1000.

So the margin of error;

ME = z× {p(1-p)}/√n

The value of z for confidence interval of 95% is 1.96.

Now putting the value

x = 1.96× {0.55(1-0.55)}/√1000

x = 1.96× {0.55×0.45}/31.623

x = 1.96× 0.2475/31.623

x = 1.96×0.00783

x = 0.01534

x = 1.534%

So the margin of error should be 1.534%.

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The right question is:

At a confidence interval of 95%, if a polling result states that a president has an approval rating of 55%, with a margin of error of x, how should you interpret that?

Answer:

$40.8

Step-by-step explanation:

You would do 3.40 * 12 because a dozen is 12 roses.

So 3.40 × 12 = 40.8

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The GCF can be applied to problems requiring the division of something into equal groups or an equal number of groups, as well as problems requiring the simplification of a fraction.

The LCM can be used to solve problems involving the overlap of two activities or something similar, as well as problems involving the addition of two or more fractions with different denominators.

The greatest common factor of two or more integers that are not all zero in mathematics is the largest positive integer that divides each of the integers.

A set's greatest common factor (GCF) is the largest factor that all of the numbers share.

For example, the numbers 12, 20, and 24 all have two common factors: 2 and 4. The greatest is 4, so the GCF of 12, 20, and 24 is 4. The LCM, or smallest common multiple, is the smallest common number or multiple of any two numbers. The least common multiple of 3 and 5 is 15, for example.

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The values for random variables in a Monte Carlo simulation area that were chosen at random from probability distributions are the right answer.

What is Monte Carlo Simulation ?

The Monte Carlo Method, also referred to as the Monte Carlo Simulation or a multiple probability simulation, is a mathematical method for predicting potential outcomes of an uncertain event. To help people make better decisions when faced with uncertainty, John von Neumann and Stanislaw Ulam developed the Monte Carlo Method during World War II.

Therefore, the values for random variables in a Monte Carlo simulation area that were generated at random from probability distributions are the right answer.

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The correct response is the set of values for random variables in a Monte Carlo simulation region that were randomly selected from probability distributions.

In order to represent uncertainty in a model that represents a real system and computes the values of model outputs, a Monte Carlo technique is used. During World War II, John von Neumann and Stanislaw Ulam created the Monte Carlo Method to aid people in making better judgments when faced with uncertainty.

As a result, the correct response is the random values for random variables that were produced using probability distributions in a Monte Carlo simulation area.

Determine the distance covered by a car traveling 80 km/h for each unit and time given. The answer should be in meter in one hour.

What is a kilometer?

1,000 meters is one metric unit of measurement (approximately 0.62 miles).

The car is travelling at the speed of 80 kilometers per hour.

One hour is  60 minutes.

So car will travel in ideal conditions 80 kilometers in one hour which is 60 minutes.

So just convert the kilometers into meters.

1 kilometer = 1000 meters,

Thus,

80 kilometers = 80,000 meters.

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The largest integer that is a divisor of (n + 1)(n + 3)(n + 5)(n + 7)(n + 9)  for all positive even integers is 15

The correct answer is an option (d)

In this question, we need to find the largest integer that is a divisor of (n + 1)(n + 3)(n + 5)(n + 7)(n + 9)  for all positive even integers n.

We can observe that (n + 1), (n + 3), (n + 5), (n + 7) and (n + 9)  are 5 consecutive odd integers

In every 5 consecutive odd positive integers, one of them is always divisible by 3 and one of them is always divisible by 5.

This means, (n + 1)(n + 3)(n + 5)(n + 7)(n + 9) will be divisible by both 3 and 5

i.e., (n + 1)(n + 3)(n + 5)(n + 7)(n + 9) will also divisible by 15 (3 * 5 = 15)

Therefore, the largest integer that is a divisior of (n + 1)(n + 3)(n + 5)(n + 7)(n + 9)  = 15

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For the function, [tex]h(x) = \frac{50}{5.5 + 8e^{-0.9x} }[/tex], the value of h(4) is h(4) ≈ 8.7

From the question, we are to determine the value of h(4) in the given function.

The given function is

[tex]h(x) = \frac{50}{5.5 + 8e^{-0.9x} }[/tex]

To determine the value of h(4), substitute 4 for x in the given function

[tex]h(x) = \frac{50}{5.5 + 8e^{-0.9x} }[/tex]

[tex]h(4) = \frac{50}{5.5 + 8e^{-0.9(4)} }[/tex]

[tex]h(4) = \frac{50}{5.5 + 8e^{-3.6} }[/tex]

[tex]h(4) = \frac{50}{5.5 + 8(0.0273237) }[/tex]

[tex]h(4) = \frac{50}{5.5 + 0.21859 }[/tex]

[tex]h(4) = \frac{50}{5.71859 }[/tex]

h(4) = 8.7434

h(4) ≈ 8.7

Hence, the value of h(4) is 8.7

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Answer:

If 6a = 5b then the ratio of 2a : 7b is 5 : 21

Explanation:

Given that 6a = 5b

We have to find the ratio of 2a : 7b

Let us first solve the given expression and find values of a and b

6a = 5b

So we have found that a = 5 and b = 6

Finding ratio of 2a : 7b

2a : 7b = 2(5) : 7(6)

2a : 7b = 10 : 42

On simplifying to lowest terms,

2a : 7b = 5 : 21

Thus the ratio of 2a : 7b is 5 : 21

Dilating a triangle by - 3 with vertices (3, 4), (3, 5), and (5, 5) will be

(- 9, - 12), (- 9, - 15) and (- 15, - 15).

Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.

Dilation: The preimage is scaled up or down to create the image.

Reflection: The picture is a preimage that has been reversed.

Rotation: Around a given point, the preimage is rotated to create the final image.

Translation: The image is translated and moved a fixed amount from the preimage.

Given, A triangle with vertices (3, 4), (3, 5) and (5, 5).

Now dilating by a scale factor of - 3 will have every point multiplied by - 3 and the new vertices will be (- 9, - 12), (- 9, - 15) and (- 15, - 15).

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Due to construction, approximately 5 minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit.

Given that,

length of highway is 8 miles

Reduced length is 55 miles

Hours taken is 35 miles per hour.

Let t₁ is time taken is 55 mph

t₁ = 8/55

Let t₂ is time taken is 35 mph

t₂ = 8/35

Difference in time = 8/35 - 8/55

= 8 × 20 / (35 * 55) hour

= 160 × 60 / (35 × 55) mins

= 4.7

= 5 minutes (approximately)

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If there are 58 nominees, then the number of ways in which scholarships can be awarded is 4,24,270.

What are the Permutation and Combination?

Permutations and combinations are the various ways in which objects from a set can be selected to form subsets, generally without replacement. When the order of selection is a factor, this selection of subsets is called a permutation; when it is not, it is called a combination.

If there are 58 nominees, and Blackhawk can give only four scholarships then the number of ways is =

                        [tex]=^nC_r\\\\=^{58}C_4\\\\=\frac{58!}{4!*54!}\\\\=\frac{58 * 57 * 56 * 55}{4 * 3 * 2 *1}\\\\=4,24,270[/tex]

Hence, if there are 58 nominees, then the number of ways in which scholarships can be awarded is 4,24,270.

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Answer:

60 degrees

Step-by-step explanation:

The arc length is 1/6th of the total ....the angle will be 1/6th of the total 360° of the circle

1/6th  X 360 = 60 °

Answer:

60 degrees

Step-by-step explanation:

1.) Figure out which portion of the circle that the arc is. Since the total circumference is 6, and the arc is 1, that means that the arc is 1/6 of the circle.

2.) Now, figure out the measure of the angle. Since the total angle measure in a circle is 360 degrees, we multiply 1/6*360 to figure out the measure. This is equal to 60 degrees.

Applying the formula of the lateral surface area of a cylinder, the number of gallons needed to paint the top and the lateral surface is: 314,901 gallons.

The lateral surface area of a cylinder = 2πrh, where h is the height, r is the radius of the cylinder.

Given the following:

Lateral surface area of the cylinder = 2 × π × 1.5 × 24 = 226.19 yards²

Area of the top = area of circle = πr² = π(1.5²) = 7.07 yards²

Area to be painted = 226.19 + 7.07 = 233.26 yards²

Convert square yards to square feet:

1 square yard = 1 square feet

233.26 square yards = 2099.34 square feet

Gallons of paint needed = 2099.34 × 150 = 314,901 gallons.

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Answer:

Y = 7x + 51

Step-by-step explanation:

Point-slope form is in this form: y = mx + b where b is the y-intercept and m is the slope. We have the slope, and we already have a point that must be on the line. The only thing we need is the y-intercept, so we can plug in the given point and the slope to solve for b.

Plug in (-7, 2) for x and y and the slope(7) for m. This gives: [tex]2 = 7*-7 + b[/tex], or [tex]2 = -49 + b[/tex]. Now add 49 to both sides to isolate x, and we get that [tex]b = 51[/tex]. We have everything we need for the equation now, so plug in the slope and y-intercept for m and b, giving us y = 7x + 51.\

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