Experimental and theoretical probability

The median salary of the workers is P11,000.

In statistics, the median is a measure of central tendency that represents the middle value of a data set when the data set is ordered from least to greatest (or vice versa). If the data set has an odd number of values, the median is the middle value. If the data set has an even number of values, the median is the average of the two middle values. The median is used as a measure of central tendency when the data set has outliers or is not normally distributed.

To calculate the median of a set of numbers:

In the given question,

To find the median salary of the workers, we need to arrange the salaries in order from lowest to highest.

The salaries are:

P9,000, P9,000, P10,500, P10,500, P11,000, P11,000, P11,000, P11,000, P12,500, P12,500, P12,500, P12,500

There are 12 workers, so the median salary will be the average of the 6th and 7th salaries when arranged in order.

Median salary = (P11,000 + P11,000)/2

= P11,000

Therefore, the median salary of the workers is P11,000.

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In response to the stated question, we may respond that As a result, the expressions laboratory should be closed for 5.19 days to allow the radon gas to decline to a safe level.

An expression in mathematics is a combination of numbers, elements, and mathematical (like addition, reduction, multiplication, division, algebraic, and so on) that expresses an amount or value. Expressions may well be simple, such as [tex]"3 + 4"[/tex], or complicated, such as [tex]"(3x2 - 2) / (x + 1)"[/tex]. They might additionally contain functions like "sin(x)" or "log(y)". Expressions can be assessed by substituting variables with their values and performing the arithmetic operations in the specified sequence. For example, if x = 2, the ratio [tex]"3x + 5" equals 3(2) + 5 = 11.[/tex]Expressions are commonly used in mathematics to describe real-world situations, generate equations, and simplify complicated mathematical concerns.

We must apply the notion of radioactive decay and the half-life of radon gas to address this dilemma.

Begin by calculating the percentage of the safe radiation level that corresponds to the 40% increase. This can be written as:

[tex]1 + 0.4 = 1.4[/tex]

As a result, the resultant radiation level is 1.4 times that of the safe threshold.

To compute the proportion of the original amount of radon gas that remains after a certain period t, we may use the following formula:

[tex]N/NO = (1/2) t/T1/2)1/2 t/3.8) = 1/1.42 t/3.8) 1.4t / 3.8 = log(2) * (1.4)(1.4)t = 3.8x * log(2) * (1.4)t = 5.19[/tex]

As a result, the laboratory should be closed for 5.19 days to allow the radon gas to decline to a safe level.

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For all values of x, y, and z, the expression 56x + 40y - 48z = 8(7x + 5y - 6z) holds true.

As an illustration, the phrase x + y is one where x and y are terms with an addition operator in between. There are two sorts of expressions in mathematics: numerical expressions, which only contain numbers, and algebraic expressions, which also include variables.

Indeed, for all values of x, y, and z, the expression 56x + 40y - 48z = 8(7x + 5y - 6z) holds true.

We can simplify both sides of the equation to understand why:

56x + 40y - 48z = 8(7x + 5y - 6z)

56x + 40y - 48z = 56x + 40y - 48z

As we can see, the equation is true for all values of x, y, and z because both sides are identical.

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Answer: The poster should have width 17.50 CM

Step-by-step explanation:

Given that boasted I have a total area 245 cm square area of a poster is 200 and 45 20 m square. And it is in the rectangle format. So we know that the poster is always in the rectangle format and the area of rectangular area is equal to L N T W. So 245 will be equal to Ln tW. From this. We need to find L. So L is equal to 245 divided by W. Now consider the diplomatic representation of the poster. So it has mentioned that there is a margin around the edges of six cm at the top. This is 6cm and four cm at the sites. All the four sides 3 sides are four cm. So from this we need to find land and the doctor posted area that is printed area. The first wine printed with www. Z. Quilter. Now let this be total birth will be W. And this will be four and this will be four. Therefore posted with will be we need to find this part alone. So W -4 -4 will give the this part with. So W -4 -4. So post printed with PW will be equal to W -8. Similarly printed lunch will be equal to The total length is already we have found 245 by W. And we need to find this part length. So we have to subtract six and four from the total length so that that will give them this part length, So -6 -4. So printed length will be equal there 245 Divided by W -10. And we know that formula for area of a rectangle. Urz D is equal to L W. Now substitute the printed with and printed length in the area formula. We have to find the printed area. So Printed area Zeke Walter W -8 into 245 Divided by W -10. To simplify this, we get 325 minus 10. W -100 and 30,960 W. to the power of -1. Now fine D A by D. T. Not D D. This is D. W. So this is equal to differentiation of constant alma zero, this is minus 10 plus 900 and 60 W. to the power of -2 and equate this to be equal to zero. We out to find the maximum width so D A by D W is equal to zero, therefore minus 10 1960 W. To the power of -2 will be equal to zero. To simplify this, we get them maximum with value the W is equal term I wrote off 196. Therefore the value of W. Z quilter plus or minus 14. We will neglect the negative values since we cannot be negative. So one we assume the positive values. So what will be equal to 14 and length will be equal to 245 divided by 14, So which will be equal to 17.50 centimeters. And they have concluded that At W is equal to 14 cm and lunch will be equal to 17.50 cm needed to print the largest area. I hope you found the answer to school. Thank you.

Answer:

A

Step-by-step explanation:

∠ o and ∠ z are alternate exterior angles and are congruent, that is

∠ z = ∠ o = 125°

The critical values, the intervals of increasing or decreasing and the maximum and minimum points of the f(x) is (-1.5, -16), x < -1.5 and x = -1.5 and for b (4,6) and (2,10), (2,4).

A) Critical values

We will find out the critical value by solving for f ' (x) = 0

therefore, taking the derivative of given function we get,

f ' (x) = 4(2x) + 12 = 0

        = 8x + 12 = 0

therefore, 8x = -12

                 x = -12/8

                 x= -1.5

x = -1.5 is the only critical value in x-coordinate. Now to determine the y-coordinate, simply put the value of x in the function f(x) = 4x2 + 12x - 7

we get, f(-1.5) = 4(-1.5)2 + 12 (-1.5) - 7

                      = 4(2.25) - 18 - 7

                      = 9 - 25 = -16  

therefore, the critical value of the function f(x) = 4x2 + 12x - 7 is (-1.5, -16)

f(x) =x3 - 9x2 + 24x - 10.

Intervals of increasing and decreasing function is i.e. f decreases for

x < -1.5.

Therefore, f has minimum value at x = -1.5.

B) Critical values

We will find out the critical value by solving for f ' (x) = 0

therefore, taking the derivative of given function we get,

f '(x) = 3x2 - 9(2x) + 24

       = 3x2 - 18x + 24 = 0

therefore, 3 ( x2 - 6x + 8) = 0

   i.e x2 - 6x + 8 = 0

        (x-4) (x-2) = 0

So, x = 4 or x = 2 are the two critical values in x-coordinate. Now to determine the y-coordinate, simply put the values of x in the function f(x) =x3 - 9x2 + 24x - 10

we get, Substituting x = 4

f(4) = 43 - 9 (4)2 +24 (4) -10

     = 64 - 144 + 96 - 10

     = 6

Now, Substituting x = 2

f(2) = 23 - 9(2)2 + 24(2) - 10

     = 8 - 36 + 48 - 10

     = 10

Therefore, the critical values of the function f(x) =x3 - 9x2 + 24x - 10 are (4,6) and (2,10).

Intervals of increasing and decreasing functions is f decreases in (2,4).

therefore, f has minimum at x = 4 and maximum at x = 2.

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Complete question:

For each function determine: i) the critical values ii) the intervals of increasing or decreasing iii) the maximum and minimum points.

a. f(x) = 4x²+12x–7 (3 marks)

b. F(x) = x°-9x²+24x-10 (3 marks)

Answer:

1. basement: 1,4,7,10,13

middle : 2,5,8,11,14

top: 3,6,9,12,15

2. you just need to skip count ten  times then we will have 30. so she lives in apartment 30.    

Step-by-step explanation:

Answer:

[tex]96 \: {m}^{2} [/tex]

The correct answer is B

Step-by-step explanation:

First, we have to find the area of one side of the cube:

[tex]a(side) = 4 \times 4 = 16[/tex]

Now multiply this number by 6 (since the cube has 6 sides in total):

[tex]a(surface) = 16 \times 6 = 96[/tex]

Answer: B - 96 sq m

Step-by-step explanation:

The surface area is the area of all the squares added up. To find the area of one square, you multiply 4 x 4, which equals 16. Then, count the number of sides on the cube. There are 6 sides on this cube. So, you multiply        16 x 6. 96 is your total. And you can eliminate C because it says meters instead of square meters.

The solution to the compound inequality -3+b> 7 OR b +9 <17 is given as follows:

b < 8 or b > 10.

The inequality for this problem is defined as follows:

-3+b> 7 OR b +9 <17.

The or operation means that the we must solve each operation separately, and then the solution set to the compound inequality is given by the union of the solution set of each of the inequalities.

The solution set for the first inequality is given as follows:

-3+b> 7

b > 10.

The solution set for the second inequality is given as follows:

b + 9 < 17

b < 8.

Hence the solution for the entire inequality is of:

b < 8 or b > 10.

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Answer:

Step-by-step explanation:

Let's assume that 'a' adults and 'c' children attended the concert.

From the problem statement, we know that:

a + c = 107 ---(1) (The total number of people who attended the concert is 107)

3.75a + 3.5c = 391.25 ---(2) (The total revenue generated from the concert is $391.25)

Now, we need to solve these two simultaneous equations to find the values of 'a' and 'c'.

To do this, we can use the elimination method to solve these equations.

First, we will multiply equation (1) by 3.5 to eliminate 'c':

3.5a + 3.5c = 374.5 ---(3)

Next, we will subtract equation (3) from equation (2):

3.75a + 3.5c - (3.5a + 3.5c) = 391.25 - 374.5

0.25a = 16.75

a = 67

Now that we know the value of 'a', we can substitute it into either equation (1) or (2) to find the value of 'c':

a + c = 107

67 + c = 107

c = 40

Therefore, there were 67 adults and 40 children at the concert.

Answer:

888.4 mL.

Step-by-step explanation:

To solve this problem, we can use the following formula:

Amount of drug (in mg) = concentration (in mg/mL) × volume (in mL)

We are given the concentration of the drug as 5.315 mg per 3.743 mL. To find the volume of the drug needed to give 4.719 g, we need to rearrange the formula to solve for volume:

Volume (in mL) = amount of drug (in mg) ÷ concentration (in mg/mL)

First, we need to convert 4.719 g to mg by multiplying by 1000:

4.719 g × 1000 mg/g = 4719 mg

Now we can substitute the given concentration and the calculated amount of drug into the formula and solve for volume:

Volume (in mL) = 4719 mg ÷ 5.315 mg/mL

Volume (in mL) ≈ 888.5 mL

Therefore, approximately 888.5 mL of the drug are needed to give 4.719 g. Rounded to 1 decimal, the answer is 888.4 mL.

1. a. Rolling fair die, Flipping fair coin ; b. does not affect the occurrence of the other event; c. 1/4; 2. a. Picking red card, Picking another red card; b. affects the probability of the second event, c. use of conditional probability.

Probability can be used to make predictions, analyze data, and make informed decisions in a wide range of fields, including science, economics, finance, engineering, and social sciences. It is often used in conjunction with statistical methods to make inferences about populations based on samples, and to test hypotheses about the relationships between variables.

There are many different types of probability, including classical probability, empirical probability, subjective probability, and conditional probability. Probability theory also includes concepts such as random variables, probability distributions, and statistical inference.

1. a. Two independent events:

Rolling a fair die and getting an even number.

Flipping a fair coin and getting heads.

b. These events are independent because the occurrence of one event does not affect the occurrence of the other event. In other words, the outcome of rolling the die does not influence the outcome of flipping the coin, and vice versa.

c. The probability of both events occurring is found by multiplying the individual probabilities of each event.

P(getting an even number on a die) = 3/6 = 1/2

P(getting heads on a coin) = 1/2

P(rolling an even number on a die AND flipping heads on a coin) = (1/2) * (1/2) = 1/4

2. a. Two dependent events:

Picking a red card from a standard deck of playing cards.

Picking another red card without replacing the first card.

b. These events are dependent because the occurrence of the first event affects the probability of the second event. If a red card is picked on the first draw, there are fewer red cards remaining in the deck for the second draw, which changes the probability of picking another red card.

c. The probability of both events occurring in this case would require the use of conditional probability. We would need to find the probability of picking a red card on the second draw given that a red card was picked on the first draw. This conditional probability would be affected by the number of red cards remaining in the deck after the first draw, which changes with each draw.

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Answer:y=x-5

Step-by-step explanation:this is the answer for sure

Answer:

[tex]y=x-5[/tex]

Step-by-step explanation:

Notice for every X you do increase your Y by 1, this is the slope must be 1, to check you can use the slope equation with any two points

[tex]m= \frac{-4-(-3)}{1-(2)} =-1[/tex]
The lets use one point and the line equation:

[tex]y-yo=m(x-xo)[/tex]
[tex]y+4=-1(x-1)[/tex]

Solving for Y you can obtain

[tex]y=x-5[/tex]

You can input any X value and check the Y value to be sure, for example, for X=3 you can check Y=3-5=-2. In the table for X=3 the Y value is -2, so this checks.

Answer:

A)  0.374

Step-by-step explanation:

Let event A be that the person is female.

Let event B be that the person does not take vitamins.

[tex]\boxed{\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}}[/tex]

Therefore, from the given table:

   [tex]\sf P(A) = \dfrac{288}{500}=0.576[/tex]

   [tex]\sf P(B) = \dfrac{107}{500}=0.214[/tex]

   [tex]\sf P(A \cap B)=\dfrac{40}{500}=0.08[/tex]

To calculate the probability that someone is female (Event A), given that they do not take vitamins (Event B), use the conditional probability formula for A given B:

[tex]\boxed{\begin{minipage}{5 cm}\underline{Conditional Probability formula}\\\\A given B:\\\\$\sf P(A|B)=\dfrac{P(A \cap B)}{P(B)}$\\\end{minipage}}[/tex]

[tex]\sf \implies P(A|B)=\dfrac{0.08}{0.214}=0.374\;(3\;s.f.)[/tex]

Upon letting x variable be the amount of money Cristiano has. Cristiano has $55, Ozias has $30, Jaydon has $110

A variable is a symbol used to represent an unknown or changing value in an equation or expression. Variables can take on different values and are used to solve equations, simplify expressions, and model real-world situations.

According to the question

Let us use variables to represent the amount of money each child has:

Let x be the amount of money Cristiano has.

Then Jaydon has twice as much, that is 2x

And Ozias has $25 less than Cristiano, that is x - $25.

We know that the three children have a total of $195, so we can make an equation:

x + 2x + (x - $25) = $195

Simplify and solve for x:

4x - $25 = $195

4x = $220 x = $55

So Cristiano has $55, Jaydon has twice as much or $110, and Ozias has $25 less than Cristiano.

So Ozias has $55-$25= $30.

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300 is the correct answer.

The middle 50% data of the boxplot will be calculated between the value of 7 to 14.

The data set ranges are:

4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17

Divide the given data in 4 quartiles Qs;

Q1 = 4 - 6

Q2 = 7 - 10

Q3 = 11 - 14

Q4 = 15 - 17

Thus, 50% data will be lying in Q2 and Q3.

Range - 7 - 14

Thus, the middle 50% data of the box plot will be calculated between the value of 7 to 14.

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Answer:

F) 12

Step-by-step explanation:

To answer, we use the perfect square formula:

(a + b)² = a² + 2ab + b²

(√3 + √3)² = (√3)² + 2(√3)(√3) + (√3)²

Simplify:

√3² = 3

2(√3)(√3) = 2 x (√3)² = 2 x 3 = 6

Plug in:

(√3 + √3)² = 3 + 6 + 3 = 12

The correct option is (C). In nonlinear models, the expected change in the dependent variable for a change in one of the explanatory variables is given by: ΔY = f(x₁ + ΔX₁, X₂ + ΔX₂, ..., Xk + ΔXk) - f(x₁, X₂, ..., Xk)

where ΔX₁, ΔX₂, ..., ΔXk are the changes in the respective explanatory variables. This equation represents the change in Y due to a simultaneous change in all the explanatory variables by ΔX₁, ΔX₂, ..., ΔXk. Option (C) represents the same equation in a slightly different notation. Option (A) only considers one explanatory variable, and option (B) does not include the baseline value of the function. Therefore, option (C) is the correct answer.

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Complete question:

In nonlinear models, the expected change in the dependent variable for a change in one of the explanatory variables is given by

A. ΔY= f(x₁ +Xq, X2, Xx) = f(Xq, X2....XK). 1 1'

B. ΔY = F(X,+ ΔX₁₁ X2, Xx) - F(X₁₁ X2, Xk). ---

C. ΔY = f(x,+ ΔX₁₁ X₂ + ΔX2, Xx+ ΔX x) - F(X₁₁ X2, Xx). 1°

D. ΔY = f(x₁ +Xq, X2, Xk).

Answer:

if u want total price then,

=Rs.35×80=Rs.2800

Answer:

The maximum number of students to whom 48 apples, 60 bananas, and 96 guavas can be distributed equally is 20. Each student will receive 2 apples, 3 bananas, and 4 guavas.

In a diagram,

Then,

[tex]\dfrac{DE}{BC}=n[/tex]

For example, suppose that n=2; thus,

[tex]DE=2BC\longrightarrow2\times CA[/tex]

We can form a new triangle DEF whose side EF is parallel to CA; therefore,

[tex]\longrightarrow EF=2CA[/tex]

The given argument is Valid because the conclusion follows the argument logically.

The argument is that "Every nonzero real number has a reciprocal. Zero(0) does not have a reciprocal. Therefore, zero is not a non-zero real number."

The argument can be expressed in logical form as:

⇒ Premise 1: For every nonzero real number x, there exists a reciprocal 1/x.

⇒ Premise 2: Zero does not have a reciprocal.

⇒ Conclusion: Therefore, zero is not a nonzero real number.

This argument is valid because the conclusion logically follows from the premises.

The premises establish that every nonzero real number has a reciprocal, and that zero does not have a reciprocal.

The conclusion then follows logically, as zero is explicitly excluded from the set of nonzero real numbers based on the definition of a reciprocal.

Therefore, the argument is valid.

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The given question is incomplete, the complete question is

Is The Following Argument Valid Or Invalid?

Every nonzero real number has a reciprocal. Zero does not have a reciprocal. Therefore, zero is not a nonzero real number.

Step-by-step explanation:

that height splits GK (32) into 2 parts :

8 and 32-8 = 24

then we use the geometric mean theorem for right-angled triangles

height = sqrt(p×q)

with p and q being the parts of the Hypotenuse.

so,

height = sqrt(8×24) = sqrt(192)

and now we can use Pythagoras

c² = a² + b²

with c being the Hypotenuse (the side opposite of the 90° angle), a and b are the legs,

to get HK.

HK² = height² + 24² = 192 + 576 = 768

HK = sqrt(768)

The result of the cross breeding between the heterozygous and homozygous pea plant is  the offspring will have a 50% chance of inheriting the dominant "G" allele and displaying yellow color, and a 50% chance of inheriting the recessive "g" allele and displaying green color.

In this problem, the heterozygous pea plant with yellow color is represented as "Gg" (where "G" is the dominant allele for yellow color and "g" is the recessive allele for green color). The homozygous pea plant with green color is represented as "gg" (where both alleles are recessive).

When these two plants are crossed, their offspring will inherit one allele from each parent, which will determine their phenotype (observable trait).

The possible combinations of alleles that the offspring can inherit from their parents are:

Gg x gg

Therefore, in this cross, the offspring will have a 50% chance of inheriting the dominant "G" allele and displaying yellow color, and a 50% chance of inheriting the recessive "g" allele and displaying green color.

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The mathematical model that represents the general price movement of mortgages is:     ΔPM = f(Δk, ΔPrin, ΔC)

Where ΔPM is the change in the price of the mortgage, Δk is the change in the required rate of return, ΔPrin is the change in the principal payment, and ΔC is the change in the interest payment.

This means that the change in the price of a mortgage is a function of the change in the required rate of return, the change in the principal payment, and the change in the interest payment.

The securities that are issued to financial institutions to increase liquidity in the secondary mortgage market by financing the origination of mortgages are:

Financial institutions may also receive private-label pass-through securities, although these are not guaranteed by government entities like Ginnie Mae, Freddie Mac, or Fannie Mae.

They are not backed by the government, but by private institutions, which can make them riskier.

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Answer:

The critique of the sample method and survey used by the guild is as follows:

In summary, the survey used by the guild suffers from various types of bias, which may affect the validity and generalizability of the results. To improve the validity and reliability of the survey, the guild should use random sampling and address issues such as non-response and response bias.

The standard normal areas are given as follows:

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Considering the second bullet point, the areas are given as follows:

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The surface area of the sphere ball is 1817.74 square centimeters.

Every geometric shape has a different surface area formula, but the goal of all of them is to determine the total area occupied by all of the objects' faces. While the lateral surface area is calculated to determine the area occupied by the shape's curved surface, the total surface area takes into account all faces of the 3D shape, including the flat and curved surfaces. The area of the bases is excluded. One 3D shape called a sphere has just one round surface and no flat base.

Given that the surface area is related using the relation r = √(S/12.6).

Also, the value of r = 12.04, substituting the value we have:

(12.04) = √(S/12.6)

Squaring on both sides:

Hence. the surface area of the ball is approximately 1817.74 square centimeters.

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The complete question is: