on your desk, there is a very special die with a prime number p of faces, and you throw this die once. show that no two events a and b can be independent unless either a or b is the whole sample space or the empty set.

A Z-score is a metric that quantifies the connection between a value and the mean of a set of values.

z-scores are calculated by (observed value - mean)/standard deviation

Mean = 40

Standard Deviation = 8

Observed Value = 52

z-score = (52 - 40)/8 = 2

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A preimage (the original) is the two-dimensional shape before any transformation. The image (the transferred one) is the figure after transformation.

A transformation is a process that manipulates a polygon or other two-dimensional object an a plane or coordinate system. Mathematical transformations describe how two-dimensional figures move around a plane or coordinate system.

Following are the types of transformations:-

Dilation, Reflection, Rotation, Shear, Translation.

Preimage is the set of all elements of the domain that are mapped into a given subset of the co-domain.

A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.

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Answer: 8 yards

Step-by-step explanation:

15-7=8

The number of people who ranked vanilla first out of total 60 people is 2.

For the stated question-

Total number of people = 60.

vanilla last: 3/5×60 = 36

vanilla before chocolate: 1/10×60 = 6

vanilla before strawberry: 1/3×60 = 20

Rank of 3 flavours are-

    1st place    | 2nd place   | 3rd place

Thus,

vanilla last : 3/5 = 36

C + E = 36   ...eq 1

Vanilla ahead of Chocolate -1/10

A + B + F = 6   ...eq 2

Vanilla ahead of Strawberry- 1/3

A + B + D = 20   ...eq 3

Add all three equations-

A + B + F + A + B + D + C + E = 36 + 6 + 20

A + B + A + B + C + D + E + F = 62

60 people with no ties;

A + B + C + D + E + F = 60

A + B + A + B + C + D + E + F = 62

A + B + 60 = 62

A + B = 62 - 60

A + B = 2

Thus, the number of people who ranked vanilla first is 2.

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The constant of proportionality for the given equation is 7.

What is constant of proportionality?

The ratio that establishes a proportional relationship between any two given values is referred to as the constant of proportionality. The constant of proportionality may also be referred to by the names constant ratio, constant rate, unit rate, constant of variation, or even rate of change.

Given:

The equation C = 7M and represents how many ice cream cones see are sold within a certain number of minutes M add a certain ice cream shop.

We have to find the constant of proportionality.

Since, if the equation is of the form y = kx,

then k is the constant of proportionality.

Here the given equation is

C = 7M

Hence, the constant of proportionality is 7.

Option (B) is the correct answer.

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The answer is 7

...........

Therefore option B is correct

Have a nice day! ( :  > )

Answer: It will reach the ground after 15 seconds. The force is 50.5%

Step-by-step explanation:

Step-by-step explanation:

I just answered this. how often did you post this question ?

the answer is light blue.

The probability that the mean is less than 1,998 milliliters is 0.11%

To solve this problem, it is important to understand the normal probability distribution and the central limit theorem

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean μ and standard deviation σ , the z-score of a measure X is given by:

Z = (X -μ) / σ

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p value, we get the probability that the value of the measure is greater than X.

Central Limit theorem

The Central Limit Theorem establishes that, for a random variable X, with mean  and standard deviation σ, a large sample size can be approximated to a normal distribution with mean μ and standard deviation δ = σ /√n

In this problem, we have that:

μ = 2000, σ = 18

If the manufacturer samples 100 bottles, what is the probability that the mean is less than 1998 milliliters

So n =100,

δ=18/√100 = 1.8

This probability is the p value of Z when X = 1998. So

Z = (X -μ) / σ

By the Central Limit Theorem

Z = (X -μ) /δ

Z = (1998 -2000) / 1.8

Z = -1.11 has a p-value of 0.0011

So, 0.11% probability that the mean is less than 1998 milliliters.

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A person's tendency to believe he/she can predict the outcome of random events is known as the Hindsight bias

An event is the total number of results from a random experiment. Trial results are the outcome. The outcome of an event is the totality of all potential outcomes. To better understand this, let's use an example. Example: Chances of rolling a die and getting the desired number

The three types of outcomes are Organizational outcomes, Team outcomes, and Personal or Individual outcomes.

A psychological phenomenon called hindsight bias enables people to persuade themselves after an occurrence that they correctly predicted it before it occurred. People may get the conclusion that they can foresee subsequent occurrences with accuracy as a result.

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The number of tomatoes weight between 73 grams and 178 grams is 978.

A data set's mean provides the average  and the standard deviation provides information on the range (dispersion) of values around the mean. Squaring is used to determine standard deviation but not mean.

The mean changes when the same value is added to each data point, but the standard deviation remains unchanged.

The standard deviation (SD, also represented by the Greek letter sigma σ or the Latin letter s) is a measure that is used to quantify the amount of variation or dispersion of a set of data values.

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The maximum number of intersections for the graphs is two.

A quadratic equation is any equation in algebra that may be rearranged in standard form as:

When x denotes an unknown value while a, b, and c denote known numbers In general, one assumes that a = 0; equations with a = 0 are considered degenerate since the equation becomes linear or even simpler. The numbers a, b, and c are the equation's coefficients, which can be separated by referring to them as the quadratic coefficient, linear coefficient, and constant or free term, respectively.

The task material indicates that the two graphs involved are linear and quadratic graphs.

A quadratic graph produces a parabola, while a linear graph produces a straight line. As a result, the best instance of intersection is when the straight line crosses over the parabola, resulting in two points of intersection.

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Answer:

Step-by-step

pp

Answer:

7 2/5=2/3x-4 1/2

37/5=2/3x-9/2 /×30

30×37/5=30×2/3x+30×(-9/2)

222=20x-135

-20x=-135-222

-20x=-357

20x=357

x=357/20

x=17 17/20

The smallest whole number of inches that could be my sister's height will be equal to 55 inches.

Equations are mathematical expressions that have two algebras on either side of an equal (=) sign. The expressions on the left and right are shown to be equal to one another, demonstrating this relationship. L.H.S. = R.H.S. (left-hand side = right side) is a fundamental simple equation.

As per the given information in the question,

Let me be n inches tall, while my sister is m inches tall.

I'm my sister's tallest by over $2 inches.

So, the equation obtained is,

n = 2 + m             (1)

However, if we treble her height, it would be more than 51 inches taller than I am.

So, the equation will be,

3m = 51 + 2n            (2)

We need to find the value of m.

In the equation, n should be replaced with the aforementioned value (2)

3m = 51 + 2(2 + m)

3m = 51 + 4 + 2m

3m - 2m = 51 + 4

m = 55 inches

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Alpha, Beta and Positron carries charges.

What are Nuclear Reactions?

When a more stable element is to be formed, nuclear reactions frequently produce or capture particles or radiation. The names of several nuclear reactions are given using these particles since they play a significant role in the reaction.

Alpha carries high energy helium nuclei consisting of two protons and two neutrons which makes it a positive particle.

Beta is a high energy electron which is a Negative particle.

Positrons are particles with the same mass as an electron but with 1 unit of positive charge which makes it a Negative particle.

Gamma rays are not particles but carries a very high-energy electromagnetic radiation.

Hence, Alpha is a positive charged particle, Beta is a negative charged particle and Positron is a negative charged particle.

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The number line is shown in figure.

What is Number line?

Number line is a horizontal line where numbers are marked at equal intervals one after another form smaller to greater.

Given that;

Stock in Boomer Branding, Inc. started the week at $26.50 per share.

During the week, the following changes in the share price were registered. (+$2.75),(+$3.00),(−$9.25),(+$1.50),(−$5.25)

Now,

Since, During the week, the following changes in the share price were registered. (+$2.75),(+$3.00),(−$9.25),(+$1.50),(−$5.25)

Hence, All the number is shown in figure on that place.

Thus, The number line is shown in figure.

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Two events are mutually exclusive if the probability of their intersection is 0 and they have no sample points in common. Hence, option D is the correct answer.

The two events are called mutually exclusive when they have no sample points in common. Thus, the probability of event A and event B happening is zero. this means that their intersection set is the empty set.

let us take an example-

Let A be a set of odd numbers and B be a set of even numbers.

A = {1,3,5,7,9}

B = {0,2,4,6,8}

A ∩ B = { }

Hence, the two sets - A and B are mutually exclusive of each other.

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Answer: 2n-1

Step-by-step explanation:

Answer:

The answer is the third one. It means less than 3 degrees. So X is less than 3 degrees meaning the degrees of the freezer is below 3 degrees.

Step-by-step explanation:

The probability that fewer than 20 customers in the sample buy coffee during their visit on that certain day of the week is 59.87%

What is the normal distribution?

A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution appears as a "bell curve" on a graph.

The formula for z-score is z = (x -μ)/σ

Where,

Z is standard score.

X is observed value.

μ is mean of the sample.

σ is standard deviation of the sample

Given that 55% of the customers buy coffee, hence p = 55% = 0.55

Sample of 35 customers, hence n = 35.

For the normal distribution μ = np, σ = √[np(1-p)]

The mean and the standard deviation of the approximation are:

μ = 35 ˣ 0.55 = 19.25

σ = √[35 ˣ 0.55(1-0.55)] =2.943

Using continuity correction, the probability that fewer than 20 customers in the sample buy coffee during their visit on that certain day of the week is P(X < 20 - 0.5) = P(X < 19.5), which is the p-value of Z when X = 19.5, hence:

z = (20 -19.25)/2.943

z = 0.25 has a p-value of 0.5987.

0.5987 =59.87%

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Answer:

20 seconds

Step-by-step explanation:

Answer:

Step-by-step explanation:

So let’s look at the hundredths place. You round .08 to the tenth. So that would be 504.1 then you round the tenths place (the one) to the nearest whole number. But you can’t do that so the answer will be 504. No decimal needed. Or you could’ve just looked at the original number, 504.08 and understood that since there is no number in the tenths place then the answer would be 504.

Answer: 504

Step-by-step explanation:

The summation for the indicated value of the variable is 23.

What is factorial?

The product of all positive integers less than or equal to n in mathematics is known as the factorial of a non-negative integer, indicated by the symbol n!. Additionally, the factorial of n is equal to the sum of n and the subsequent smaller factorial: For instance, According to the convention for an empty product, the value of 0! is 1.

Here, we have

Given

1(1!) +2(2!) +3(3!) + 4(4!)+......... m(m!)

By applying summation,

For m = 3, it will become,

= 1(1!) +2(2!) +3(3!)

Now we open factorization and we get

= 1(1) +2(2×1) +3(3×2×1)

= 1 + 4 + 18

= 23

Hence, the summation for the indicated value of the variable is 23.

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Answer:

Step-by-step explanation:

- Hint: In this question we asked to find the Simple interest. Here, we will calculate simple interest for 4 years at 8% per annum by using the formula of simple interest (SI) =PRN100 .

Complete step-by-step solution -

To find the simple interest first we will know about simple interest.

Simple interest is based on principal amount for a fixed period of time. The amount which we deposit or take loan from the bank is known as principal amount. The period of time for which the money is lent is known as time on interest.

Now, we will calculate here simple interest,

SI =PRN100

Where P (principal amount) = Rs. 3000

R (Rate of interest) = 8%

N (number of period) = 4 years

So, finding simple interest by putting all the value, we get

=3000×8×4100

=30×8×4

=960 Rs.

Answer:

a = [tex]\frac{8}{29}[/tex]

Step-by-step explanation:

May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 3 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!

You must count the instances of each rule and the instances of each item in each rule separately using the data in the Excel file in order to determine the support, confidence, and lift of a rule.

Open the Excel file and look for the information on the options ordered for the specific model of car. This information will probably be presented as a table or a group of columns, where each row represents a distinct order and each column a different choice.

You must count the instances of the rule's components occurring together in the data in order to calculate the support for a rule. You would need to track how frequently the fastest engine choice and the traction control option are selected together, for instance, if the rule is "If the quickest engine, then traction control." This can be accomplished by counting the number of cells in a range that satisfy a specific condition using Excel's COUNTIF function.

The confidence in a rule is calculated by dividing the total number of times the items in the premise (the "if" component of the rule) occur by the total number of times the items in the rule. The number of times the fastest engine and traction control options are selected together must be divided by the total number of times the fastest engine option is ordered, for instance, if the rule is "If the fastest engine, then traction control."

You must divide the rule's confidence by the support of the item in the rule's conclusion to determine the lift of a rule (the "then" part of the rule). You would need to divide the rule's confidence by the support for the traction control option, for instance, if the rule is "If the quickest engine, then traction control."

To calculate the support, confidence, and lift for each of the rules, you can use the Excel formulas indicated above together with any other Excel functions or tools you are familiar with.

It is crucial to keep in mind that the precise formulas and processes you will need to follow will depend on the exact data and rules you are working with, so you might need to modify the following instructions to suit your personal needs.

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The rate of change of the perimeter of a rectangle is 4 in/sec.

What is the perimeter of a rectangle?

The whole length of the outline is referred to as the perimeter of a two-dimensional shape. We add the lengths of all four corners of a rectangle to find its perimeter. Since the opposite sides of a rectangle are always equal, we must determine the length and width of the rectangle in order to determine its perimeter. The rectangle's perimeter can be expressed as twice the sum of its length and width.

Given, the length of a rectangle, L = 1 inches

width of a rectangle, W = 6 inches

rate of increasing length, dL/dt = +4 in/sec

rate of decreasing width, dW/dt = -2 in/sec

Now, the perimeter of a rectangle is given by

P = 2L + 2W

Then, the rate of change of the perimeter is

dP/dt = 2 * ( dL/dt) + 2*(dW/dt )

         = 2*(+4) + 2*(-2)

         = 8-4

         = 4 in/sec

Hence, the rate of change of the perimeter is 4 in/sec.

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Answer: 88

Step-by-step explanation:

x^2 - xy

8^2-(8(-3))

64-(-24)

64+24

88

It reaches a high of 51.8 degrees Fahrenheit. There is a 59.4 degree F range. 12.6 degrees Fahrenheit is the standard deviation. The average temperature is 33.8°F. The median temperature is 35.6 °F. IQR is 60.8 degrees Fahrenheit.

The study of statistics focuses on gathering, organizing, organizing, analyzing, interpreting, and presenting data. It is customary to start with a statistical population or a statistical model to be researched when applying statistics to a scientific, industrial, or social problem. The study of gathering, analyzing, interpreting, presenting, and organizing data in a particular way is the focus of the mathematic branch known as statistics. The process of gathering data, classifying it, presenting it in a way that makes it understandable, and then conducting additional analyses of the data is known as statistics.

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By using Probability, it can be calculated that

a) Probability that the person test positive for HIV is infected with HIV = 0.54

b) Probability that the person test positive for HIV is not infected with HIV = 0.46

c) Probability that the person test negative for HIV is infected with HIV = 0.0056

d) Probability that the person test negative for HIV is not infected with HIV (P(not HIV|-ve)) = 0.9944

What is Probability?

Probability gives us the information about how likely an event is going to occur

Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.

Probability of any event is greater than or equal to zero and less than or equal to 1.

Probability of sure event is 1 and probability of unsure event is 0.

Probability that the person is infected with HIV (P(HIV)) = 0.08

Probability that the person is not infected with HIV (P(not HIV)) = 0.92

Probability that the person infected with HIV test positive (P(+ve|HIV)) = 0.94

Probability that the person infected with HIV test negative (P(-ve|HIV)) = 0.06

Probability that the person not infected with HIV test positive (P(+ve|not HIV)) = 0.07

Probability that the person not  infected with HIV test negative (P(-ve|not HIV)) = 0.93

By using Baye's Theorem of probability,

a) Probability that the person test positive for HIV is infected with HIV (P(HIV|+ve))  =

[tex]\frac{0.94 \times 0.08}{0.94 \times 0.08 + 0.92 \times 0.07}[/tex] = 0.54

b) Probability that the person test positive for HIV is not infected with HIV   (P(no HIV|+ve)) = 1 -  0.54 = 0.46

c) Probability that the person test negative for HIV is infected with HIV (P(HIV|-ve) =

[tex]\frac{0.06 \times 0.08}{0.06 \times 0.08 + 0.93 \times 0.92}[/tex] = 0.0056

d) Probability that the person test negative for HIV is not infected with HIV (P(not HIV|-ve))  = 1 - 0.0056 = 0.9944

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Complete Question

Suppose that 8% of the patients tested in a clinic are infected with hiv. furthermore, suppose that when a blood test for hiv is given, 94% of the patients infected with hiv test positive and that 7% of the patients not infected with hiv test positive. what is the probability that

a) The person test positive for HIV is infected with HIV

b) The person test positive for HIV is not infected with HIV

c) The person test negative for HIV is infected with HIV

d) The person test negative for HIV is not infected with HIV