chocolate egg either contains a toy or is empty. Assume that each egg contains a toy with probability p, independently of other eggs. You have 5 eggs; open the first one and see if it has a toy inside, then do the same for the second one, etc. Let E1 be the event that you get at least 4 toys and let E2 be the event that you get at least 2 toys in succession. Compute P(E1) and P(E2). Are E1 and E2 independent?

Answer:

x=8

Step-by-step explanation:

(8)2 + 4(8)= 4x + 16

16 + 32 = 4(8) + 16

48= 32+16

48=48

When it comes to the range covered by the decision given that `x<7  Range covered: x<21`, it means that `x` is a non-negative integer, and its range covered is `x<21`.The decision given can be expressed as:x < 7 To indicate the range covered by this decision, it's important to find the largest possible value of x.

Since x is a non-negative integer, the largest possible value would be 6.When x = 6, the inequality becomes:6 < 7, which is true.This means that any value of x that is less than 6 would also make the inequality true.Therefore, the range covered by `x < 7` is:`0 ≤ x < 7`Now, let's consider the second part of the statement: Range covered: x<21`.This means that the range covered by the inequality `x < 7` is also contained within the larger inequality `x < 21`.Since the range of `x<7` is `0 ≤ x < 7`, which is less than 21, then it's true to say that the range covered by `x < 7

Range covered: x<21` is:`0 ≤ x < 21 Therefore, the range covered by the decision `x < 7 // Range covered: x<21` is `0 ≤ x < 21`.

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Answer:

8x²+16x+8=0

x²+2x+1=0

D=4-4=0

x0=-2/2=-1

Answer:

Step-by-step explanation:

\(8x^2+16x+8=0\)                  {divide both sides by 8}

\(x^2+2x+1=0\\\\a=1\,,\quad b=2\,,\quad c=1\\\\x=\dfrac{-2\pm\sqrt{2^2-4\cdot1\cdot1}}{2\cdot1}=\dfrac{-2\pm\sqrt{4-4}}2=\dfrac{-2\pm0}2=-1\)

The student will answer every item that is a multiple of 4 correctly, and every item that is a multiple of 3 will be incorrect.

On a true-false test of 100 items, every fourth item is true, and the rest of the items are false. Thus, there will be 100/4 = 25 correct answers. There are a total of 33 items that are multiples of 3, and the student answers them all wrong. Therefore, the student will answer 100-33 = 67 items correctly. Every item that is a multiple of 4 will be answered correctly by the student because every fourth item is true, and the student marks all true items correctly.

As a result, the student will have 25 correct answers because 100/4 = 25. The rest of the items, which are not multiples of 4, will be answered correctly by the student because they are true, and the student marks all true items correctly. The student will correctly answer 100-33 = 67 items because there are a total of 100 items and 33 multiples of 3 in the exam.

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Answer:

The area of a circle is equal to pi times the square of its Radius

Step-by-step explanation:

Answer:

Pie, Diameter, Circle

Step-by-step explanation:

Answer:

It should be 261 degrees.

Step-by-step explanation:

Answer:

The dimensions of the the party favor bag are;

Height = 14 inches

Width = 2 inches  

Length = 5 inches

Step-by-step explanation:

The given parameters are;

x³ + 6·x² - 27·x = 140

The dimensions of the party-favor bag are;

Height = (x + 9) inches

Width = (x - 3) inches

Length = x inches

The given equation can be rewritten as follows;

x³ + 6·x² - 27·x - 140 = 0

Using an online application, we have;

x³ + 6·x² - 27·x - 140 = 0 = (x + 4)·(x - 5)·(x + 7)

Therefore, x = -4, 5, or -7

Which gives x = 5, as the length of the party favor bag, x inches, cannot be negative;

Therefore, the dimensions of the the party favor bag are;

Height = (x + 9) inches = (5 + 9) inches = 14 inches

Width = (x - 3) inches = (5 - 3) inches = 2 inches  

Length = x inches = 5 inches.

Answer:

Option B

Step-by-step explanation:

Edge 2021

The decibel value of the noise is 50 db.

What is meaning of intensity of sound?

The quantity of energy going across a unit area in a unit time in a direction that is opposite to the direction of the sound waves.

The unit that used to calculate intensity of sound is decibel.

Given equation that represents the relation between intensity of sound and the ratio of the sound to the human hearing threshold is

db = 10 log i

Where i = the ratio of the sound to the human hearing threshold.

Putting i = 100,000 in the given equation:

db = 10 log 100,000

Replace 100,000 by 10⁵ :

db = 10 log 10⁵

Applying the formula of logarithm log 10^{a} = a:

db = 10 × 5

db = 50

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The value of p(y) is -4(y-15)^2 + 2. This is the equation you need to use when determining the value of p(y) for any given value of y.

To find the value of p(y), we first need to know what y is. Unfortunately, the question does not provide us with a value for y. Therefore, we cannot provide a specific answer to this question.However, we can use the given equation to determine some general information about the function p(x). The equation tells us that p(x) is a quadratic function with a vertex at (15,2). The negative coefficient of the squared term (-4) indicates that the parabola opens downwards. Additionally, the value of p(x) at the vertex is 2.

In summary, we cannot provide a specific answer to the question of what p(y) is without knowing the value of y. However, we can determine some general information about the function p(x) using the given equation. This information includes the fact that p(x) is a quadratic function with a vertex at (15,2) and that it opens downwards.
To find the value of p(y), we need to replace the variable x with y in the given equation. The given equation is p(x) = -4(x-15)^2 + 2.
The answer for p(y) can be obtained by substituting y for x in the equation. So, the new equation becomes p(y) = -4(y-15)^2 + 2.

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Similar shapes may or may not be congruent

The length of DE is 42 units

The given parameters are:

\(\mathbf{AC = 84}\)

\(\mathbf{BA = 2BD}\) --- Because DE is at the midpoint

The equivalent ratio is then represented as:

\(\mathbf{BD : DE = BA : AC}\)

Substitute \(\mathbf{BA = 2BD}\)

\(\mathbf{BD : DE = 2BD : AC}\)

Express as fraction

\(\mathbf{\frac{DE}{BD }= \frac{AC}{2BD }}\)

Make DE the subject

\(\mathbf{DE= \frac{AC}{2BD } \times BD}\)

\(\mathbf{DE= \frac{AC}{2 }}\)

Substitute 84 for AC

\(\mathbf{DE= \frac{84}{2 }}\)

\(\mathbf{DE= 42}\)

Hence, the length of DE is 42 units

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Answer:

number 1

Step-by-step explanation:

The volume of a sphere can be calculated as

Where r is the radius of the sphere

We want to calculate half of the volume, then we must divide that volume by 2

Now we must find the radius of our sphere, the segment AB is the diameter of the sphere, and the radius is half od the diameter, then

Let's put it into our equation

The problem says to use

Then

Final answer:

The formula that can be used to calculate the volume of water inside the fish bowl is

Answer:

if a joke i dont know

If the evidence against the null hypothesis is statistically significant at level α, it means that there is enough evidence to reject the null hypothesis and support the alternative hypothesis.

When conducting a statistical test of hypotheses, the aim is to determine whether there is enough evidence to reject the null hypothesis. In this case, if the evidence against the null hypothesis is statistically significant at a certain level, it means that the results obtained are highly unlikely to have occurred by chance.
If the evidence against the null hypothesis is statistically significant at level α (usually set at 0.05 or 0.01), it means that the p-value obtained from the test is less than α. The p-value represents the probability of obtaining a result as extreme or more extreme than the one observed, assuming the null hypothesis is true. Therefore, a p-value less than α means that it is highly unlikely that the observed result occurred due to chance, and the null hypothesis can be rejected.
In conclusion, if the evidence against the null hypothesis is statistically significant at level α, it means that there is enough evidence to reject the null hypothesis and support the alternative hypothesis. This implies that the observed effect or relationship is real and not due to chance, and can be considered statistically significant. It is important to note, however, that statistical significance does not necessarily imply practical significance or importance, and further analysis and interpretation of the results is required.

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Therefore, we would anticipate finding 150,000x golden fish throughout the entire lake based on the class average.

Volume is the measure of room within a particular 3D entity in mathematics. For illustration, a fish aquarium measures three feet long by one foot wide by two feet high. The capacity is calculated by multiplying the length, the breadth, and the height, or 3x1x2, that also equals six. The fish aquarium therefore has a 6 cubic foot capacity.

Let's say the class average is "x" yellow fish per liter of water.

If the sample contained 500 liters of water, we can estimate the number of yellow fish in the sample as:

500 * x = 500x

Now that we have an approximation, we can use it to determine the anticipated number of yellow fish in the 150,000,000-liter pool as a whole.

The expected number of yellow fish in the whole lake would be:

(500x / 500) * 150,000,000 = 150,000x

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Answer:80

Step-by-step explanation:

All angles in a triangle add up to 180.

70+30= 100

180-100= 80

There you have it

An equation for a rational function with the given intercepts, vertical and horizontal asymptotes is \(f(x)=\frac{-6(x+5)(x-2)}{(x+2)(x-4)}\).

Any equation with at least one fraction in which both the numerator and denominator are polynomials is said to be rational. Let f(x) represent the required function. Given that x=1 and x=3 are vertical asymptotes. Therefore, the rational function's denominator includes the terms (x-1) and (x-3). Then, the required function is written as,

\(f(x)=\frac{g(x)}{(x+2)(x-4)}\)

Given that function f(x) has a horizontal asymptote, the degree of g(x), which is in the numerator, must match that of the denominator.

Also given that the x-intercepts are at (-5, 0) and (2, 0), the numerator can be expressed as \(f(x)=\frac{(x+5)(x-2)}{(x+2)(x-4)}\). Now substituting the horizontal asymptote at y=-6, we get, \(f(x)=\frac{-6(x+5)(x-2)}{(x+2)(x-4)}\).

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r = 5% = 0.05

t = 4 years

n = 4 (quarterly)

A = 1000

P = ?

1000 = P (1.2199) ==> P = 1000/1.2199 = 819.74

Answer:

$819.74

The probability of a 6-card hand with three hearts and three spades is 0.001862, or 1/535

Probability is the mathematics of chance; it is the study of calculating the likelihood of certain outcomes in any given situation.

Here we have to find the probability of a particular 6-card hand consisting of three hearts and three spades is determined first by the fact that there are 13 hearts and 13 spades in a standard deck of 52 cards.

To calculate the probability of a 6-card hand consisting of three hearts and three spades, one must first consider that the order of the cards in a hand does not matter.

The total number of combinations of three hearts and three spades that can be drawn from a standard deck of cards is

=> 4,824.

This number can be calculated by an equation that uses the number of hearts, spades, and cards in a standard deck

=> (13 x 13 x 52).

Then the probability of a 6-card hand consisting of three hearts and three spades is calculated by dividing the number of combinations of three hearts and three spades

=>  (4,824) / (2,598,960).

This equation yields a probability of 0.001862, or a 1 in 535 chance of getting a 6-card hand with three hearts and three spades.

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In the following question, A linear system is ill-conditioned if its solution is highly sensitive to small changes in the problem data is said to be True.

What is a linear system? In mathematics, a linear system refers to a system of linear equations that can be expressed in matrix form as Ax = b. A is a matrix, x is a vector, and b is a constant vector. When working with linear systems, we must keep track of the numerical accuracy of the computations. When a small change in the matrix or constant vector produces a large change in the solution, the matrix is said to be ill-conditioned.

The mathematical concept of condition numbers measures the sensitivity of a matrix to changes in the problem data. If a matrix has a high condition number, it is said to be ill-conditioned, whereas if it has a low condition number, it is said to be well-conditioned. An ill-conditioned matrix is difficult to solve numerically because a small error in the input data can produce a large error in the computed solution.

Therefore, the statement that "a linear system is ill-conditioned if its solution is highly sensitive to small changes in the problem data" is correct, and it is true.

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The probability of the committee consisting of only civil engineers and aerospace engineers is then:70/98,010 ≈ 0.034

a) The committee of size 4 can be selected in 98,010 different ways. Here's how to solve:

Total number of people = 14 + 3 + 4 + 3 = 24 (since there are 3 industrial engineers, 4 civil engineers, 4 aerospace engineers, and 3 biomedical engineers)

Then we use the formula for combinations: nCk = n! / (k! (n-k)!)

We want to select 4 people from 24. Therefore, n = 24 and k = 4nCk = 24C4 = 24! / (4! (24-4)!) = 10626

Ck = the number of ways to choose k objects out of n distinct objects.

b) The probability that the committee of size 4 will consist of 1 engineer from each major is 0.154. Here's how to solve:

We first find the total number of ways to select 4 people from 24 people (as in part a), which is 98,010.Then, we need to find how many ways to choose 1 engineer from each of the 4 groups. There are 3 ways to choose 1 industrial engineer, 4 ways to choose 1 civil engineer, 4 ways to choose 1 aerospace engineer, and 3 ways to choose 1 biomedical engineer. By the multiplication principle, the total number of ways to choose 1 engineer from each of the 4 groups is 3 x 4 x 4 x 3 = 144.

The probability of the committee consisting of 1 engineer from each major is then: 144/98,010 ≈ 0.154

c) The probability that the committee of size 4 will consist of 2 civil engineers and 2 aerospace engineers is 0.170. Here's how to solve:

We use the same formula as before to find the total number of ways to choose 4 people from 24 people: 98,010.Next, we need to count how many ways there are to choose 2 civil engineers from the 4 available and how many ways there are to choose 2 aerospace engineers from the 4 available. We use combinations for each: 4C2 = 6. By the multiplication principle, the total number of ways to choose 2 civil engineers and 2 aerospace engineers is 6 x 6 = 36.

The probability of the committee consisting of 2 civil engineers and 2 aerospace engineers is then:

36/98,010 ≈ 0.170

d) The probability that the committee of size 4 will consist of only civil engineers and aerospace engineers is 0.034. Here's how to solve:

First, we use the formula from part a to find the total number of ways to choose 4 people from 24 people: 98,010. Next, we need to count how many ways there are to choose 4 people from the 8 available (4 civil engineers and 4 aerospace engineers). We use combinations: 8C4 = 70.

The probability of the committee consisting of only civil engineers and aerospace engineers is then:70/98,010 ≈ 0.034

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On solving the provided question, we can say that - so, percentage - 400/500 X 100 = 80%

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.

here,

total is 500

obtained is 400

so, percentage - 400/500 X 100 = 80%

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The total area of the given shape is 71cm².

The size of a section on a surface is determined by its area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina. A shape's area can be calculated by contrasting it with squares of a known dimension. The square meter (abbreviated as m²), which is the area of a square whose sides are one metre long, is the common measure of area in the International System of Units (SI). Three such squares would be the same size as a shape with a three square metre surface.

The following figure can be divided into a rectangle 7cm x 8cm and a triangle of height and base 6 cm and 5 cm respectively.

Area of rectangle= 7*8= 56 cm²

Area of triangle= 1/2* base*height= 1/2*6*5 = 15 cm²

Total area of shape = 56+15= 71 cm²

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To find the required sample size for a margin of error less than 3%, we can rearrange the formula for the margin of error:

\(n = (Z^2 * p * (1 - p)) / (E^2)\)

Here, Z represents the critical value, p is the estimated proportion (0.51), and E is the desired margin of error (0.03)

To determine the margin of error for the 95% confidence interval, we need to use the formula:

Margin of Error = Critical value * Standard error

The critical value for a 95% confidence level can be obtained from the standard normal distribution table, which corresponds to 1.96. The standard error can be calculated using the following formula:

Standard error = \(\sqrt{(p * (1 - p) / n)}\)

Given that the proportion of North Carolina residents planning to set off fireworks is estimated to be 51% (0.51) based on the survey, we can substitute the values into the formula. However, the sample size (n) is not provided in the question, so we need to determine it in the next part.

To find the required sample size for a margin of error less than 3%, we can rearrange the formula for the margin of error:

\(n = (Z^2 * p * (1 - p)) / (E^2)\)

Here, Z represents the critical value, p is the estimated proportion (0.51), and E is the desired margin of error (0.03). Substituting these values into the formula, we can solve for the required sample size.

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The length and breadth of the given rectangle is 17 cm and 8 cm, respectively.

Let's suppose the breadth of the given rectangle is 'b' cm.

So, the length of the rectangle will be '(b+9)'.

According to the problem, if we increase the length and breadth by 3 cm each, then the area of the new rectangle will be 84 sq cm more than the given rectangle.

Area of the given rectangle = lb = (b+9)b = b²+9b

Area of the new rectangle = (l+3)(b+3)

Area of new rectangle = lb + 3l + 3b + 9 [Since lb = area of the given rectangle]

Area of new rectangle = (b²+9b) + 3(b+9) + 3b + 9

Area of new rectangle = b² + 15b + 36

Let's consider the difference in area of the new rectangle and the given rectangle:

84 sq cm = (b²+15b+36) - (b²+9b)84 sq cm = 6b+3684 sq cm - 36 = 6b84 sq cm - 36 = 6b48 = 6bb = 8 cm

Therefore, the length of the rectangle will be '8+9=17 cm'.

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Therefore, the compound interest of the annuity due of BD 400 paid each 4 months for 6.2 years at a nominal rate of 3% per annum is BD 40,652.17.

Compound interest of an annuity due can be calculated using the formula:A = R * [(1 + i)ⁿ - 1] / i * (1 + i)

whereA = future value of the annuity dueR = regular paymenti = interest raten = number of payments First, we need to calculate the effective rate of interest per period since the nominal rate is given per annum. The effective rate of interest per period is calculated as

:(1 + i/n)^n - 1 = 3/1003/100 = (1 + i/4)^4 - 1

(1 + i/4)^4 = 1.0075i/4 = (1.0075)^(1/4) - 1i = 0.0303So,

the effective rate of interest per 4 months is 3.03%.Next, we can substitute the given values in the formula:

A = BD 400 * [(1 + 0.0303)^(6.2 * 3) - 1] / 0.0303 * (1 + 0.0303)A = BD 400 * [4.227 - 1] / 0.0303 * 1.0303A = BD 400 * 101.63A = BD 40,652.17

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The value of x in the given figure is 93 degrees.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Let us find the interior angle of the triangle SQR.

By angle sum property the sum of three angles is 180 degrees.

35+58+x=180

93+x=180

Subtract 93 from both sides

x=180-93

x=87 degrees

Now let us find the x degrees.

The sum of interior angle of vertex Q and exterior angle is 180 degrees

87+x=180

x=180-87

x=93 degrees

Hence, the value of x in the given figure is 93 degrees.

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