several people form groups with eight people in each group. write an expression for the number of groups formed by p people. how many groups are formed if there are 96 people?

Probability of at least one people behind taller person = n-1/n.

From the question, we have

n people of different heights are lined up in a queue

Probability of at least one people behind taller person = 1 - 1/n =n-1/n

Probability:

The term probability refers to possibility. The occurrence of a random event is the focus of this mathematical field. There is a 0 to 1 value range. To determine the possibility of certain events, probability has been employed in mathematics. The likelihood of anything happening is often referred to as probability. You can better understand the outcomes of a random experiment by applying this fundamental theory of probability, which also holds true for the probability distribution. Utilize probability to gauge a situation's likelihood of happening. Numerous factors are difficult to forecast with absolute precision. Using it, we can only speculate on whether or how likely it is that an event will occur.

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The equivalent expression of -5 + 4(-3x+6) -4x is -29 - 16x

From the question, we have the following parameters that can be used in our computation:

-5 + 4(-3x+6) -4x

Open the bracket in the above expression

This gives

-5 + 4(-3x+6) -4x = -5 - 12x - 24 -4x

Collect the like terms in the above expression

This gives

-5 + 4(-3x+6) -4x = -5 - 24 - 12x  -4x

Evaluate the like terms in the above expression

This gives

-5 + 4(-3x+6) -4x = -29 - 16x

Hence, the equivalent expression is -29 - 16x

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The highest score is 32 points.

Given,

Mean score of 8 players =14.5

After removing highest score then,

Mean score of 7 players =12

let

the sum of all score be 'x'

highest score be 'y'

At first,

[tex]Mean=\frac{sum\ of\ all\ scores}{total\ number\ of\ scores}\\\\14.5=\frac{x}{8}\\\\x=116[/tex]

after removing the highest score, mean  will be

[tex]Mean=\frac{sum\ of\ all\ scores-highest\ score}{number\ of\ scores}\\\\12=\frac{x-y}{7}\\\\x-y=84[/tex]

substituting 'x'

[tex]116-y=84\\\\116-84=y\\\\y=32[/tex]

Thus, the highest score is 32 points.

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After evaluating , we get that the number of feet of fencing that Luke needs is 40 ft .

In the question ,

it is given that ,

Luke if fencing his garden ,

and the gate across the narrow end is not replaced .

From the figure given below ,

we see that , the lengths of the garden are , 3 ft , 14 ft , 14 ft and 12 ft .

So , the perimeter of the figure is = 3 + 14 + 14 + 12

Since , the gate is not fenced , length of the gate (3 ft) will be subtracted .

So , we get ,

= 14 + 14 + 12

= 40 ft .

Therefore , the Luke need to fence 40 ft of the garden.

The given question is incomplete , the complete question is

Luke needs a new fence around his garden, but the gate across the narrow end of the garden will not be replaced. Write and evaluate a numerical expression to find how many feet of fencing Luke needs .

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The numbers for 9 faculty members who will be included in the sample are 26, 17, 58, 68, 2, 1, 29, 33, 51

What is a simple random sample?

A subset of a statistical population called a simple random sample is one in which each member has an equal chance of being chosen. A straightforward random sample is intended to offer an unbiased representation of a group.

Given, the President uses technology to produce the following numbers:

26 17 58 68 2 17 1 29 33 51

Now, 9 faculty members will be included in the sample is:

26, 17, 58, 68, 2, 17, 1, 29, 33, 51

In the above data, 17 occurs with repeated frequency then we will make 17 once.

Hence, the required answer is 26, 17, 58, 68, 2, 1, 29, 33, 51

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Step-by-step explanation:

um, I'm going to use elimination method to solve this simultaneous equation

x+2y=-6.......... equation 1

6x+2y=4........ equation 2

subtract equation 2 from equation 1

-5x = -10

x = -10/-5

x=2

substitute x=2 in equation 1

therefore equation 1 becomes

2+2y=-6

2y=-6-2

2y=-8

y=-8/2

y=-4

The mean and standard deviation of the sampling distribution is 70 and 2 respectively.

Given a random sample of 25 measurements means

n = 25.

Population with mean(µ)  70 means

µ = 70.

Population with standard deviation(σ) 10 means

σ = 10.

mean of sampling distribution is itself same as mean of population

so mean of sampling distribution is 70.

standard deviation of sampling distribution is

σ/[tex]\sqrt{n}[/tex].

put the value of σ= 10 and n =25.

10/[tex]\sqrt{25}[/tex] = 10/5 = 2

So mean of sampling distribution is 70 and standard deviation of sampling distribution is 2.

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The truth about the quotient -11/10 is that it is written as an improper fraction, which can also be written as a mixed number.

The quotient is the result of a division operation.

To determine the quotient, the dividend is divided by the divisor.

The dividend is the number being divided while the divisor is the number dividing.

Division operation is one of the basic mathematical operations.  Other mathematical operations are subtraction, addition, and multiplications.

These basic mathematical operations determine mathematical results undertaken by manipulating numbers, constants, and variables using mathematical operands.

An improper fraction is one that whose numerator is greater than the denominator.

Improper fractions can be converted to mixed numbers (whole numbers and proper fractions).

Thus, we can conclude that the quotient -11/10 is written as an improper fraction.

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324 is the maximum value of the product of these three numbers

What is maxima and minima?

The curve of a function has peaks and troughs called maxima and minima. A function may have any number of maxima and minima. Calculus allows us to determine any function's maximum and lowest values without ever consulting the function's graph. Maxima will be the curve's highest point within the specified range, and minima will be its lowest.

The extrema of a function are the maxima and minima. The maximum and minimum values of a function inside the specified ranges are known as maxima and minima, respectively. Absolute maxima and absolute minima are terms used to describe the function's maximum and minimum values, respectively, over its full range.

Let the three nonnegative numbers are x,y,z

According to the question

x+y+z=36

and y=2x

therefore, 3x+z=36--------------------------------------------------(1)

z=36-3x

Let 3xz= u--------------------------------------------------------------(2)

differentiating equation 2

du/dx=3z + 3xdz/dx

or

du/dx= z + xdz/dx

differentiating equation 1

3 + dz/dx = 0

dz/dx = -3

du/dz = 36-3x + x(-3)

du/dx = 12 - 2x--------------------------------------------------------------(3)

for maxima put du/dx = 0

x=6-------------------------------------------------------------------------------(4)

again differentiating du/dx = 12 - 2x

d2u/dx2=-2

which means 3xz= u is maximum at x=6

from equation 1 and 4

we get 18+z=36

z=18

Therefore 3xz= 3(6)(18)=324

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Answer:

The volume increases 8-fold or by 700%.

Step-by-step explanation:

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The expression in terms of x that represents the total amount that Zoe paid is 1.2x

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

A tax of 5% is applied to the bill.

Zoe decides to leave a tip of 15% on the entire bill (including the tax).

let the bill cost $x.

So, the price after tax and tip

= x+ 5% of x+ 15% of x

= x + 0.05x + 0.15x

= x + 0.20x

= 1.2x

Hence, the expression in terms of x that represents the total amount that Zoe paid is 1.2x

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The probability that a randomly selected jury of 12 people is all male is 2.1 × 10⁻⁵.

What is the probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

An order does not matter so it is a Combination.

There are 16 men and we are going to choose 12 --> ₁₆C₁₂

There are 30 people and we are going to choose 12  --> ₃₀C₁₂

₁₆C₁₂ / ₃₀C₁₂

[tex]= \frac{16!}{(16 - 12)!} \div \frac{30!}{(30 - 12)!}[/tex]  

= 0.00002104211

= 2.1 × 10⁻⁵

Hence, the probability that a randomly selected jury of 12 people is all male is 2.1 × 10⁻⁵.

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If we pay 12.5 percent for 10 years, our monthly payment for a $6000 loan will be about (C) $55.58.

In mathematics, a percentage is a number or ratio that is expressed as a fraction of 100. Although "pct," "pct," and occasionally "pc" are also used as abbreviations, the percent symbol "%" is most usually used to denote it.

A % is a number that has neither dimensions nor a defined unit of measurement.

To calculate the percentage, we must divide the value by the entire amount and then multiply the result by 100.

So, if the interest rate is 12.5%, our total loan payment would be:

112.5/100 × 6,000 = $6,750.

The monthly payment would be if there was no buildup and other agreement in payment:

6750/12*10

6750/120

$56.25

Therefore, if we pay 12.5% for 10 years, our monthly payment for a $6000 loan will be about (C) $55.58.

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Complete question:

How much would you pay monthly on a $6,000 loan if you pay 12.5 percent for 10 years?

a. $87.90

b. $70.32

c. $55.58

d. $125.00?

Answer:

I think it would be 13.42 because round 13.41640786… would be 13.42

I hope this helps

Answer: 15

 9             60

-------   =   -------

 ?             100

Multiply 9 and 100, then divide by 60

You will get 15

Since 9 beings preferred joogh juice and that was 60% of the beings who were surveyed, that must mean 15 beings were surveyed in total.

the spread data is dispersed across the entire range of data.

What is range of data?

In statistics, we must put the given values, set of data, or set of observations in ascending order in order to determine the range. That indicates that you should start by writing the observations from lowest to highest value. The formula must now be used to determine the range of observations. As a result, the range may alternatively be thought of as the distance between the highest and lowest observation. The range of observation is the name given to the outcome. Statistics' range reflects the variety of observations.

When we plot data, we are considering the shape of the data. We plot the data based on the histogram, for example. The data's shape is Shape.

Outliers are different observations from the majority of the observations and are clustered in the center. Spread is the dispersion of the data throughout the entire range.

Hence, the spread data is dispersed across the entire range of data.

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The container put 320 ml amount of the acid in 60 seconds.

Given, a robotic machine fills containers with an acid solution at the rate of 140 + 3t milliliters ( ml ) per second, where t is in seconds and 0 ≤ t ≤ 60 .

we have to find the amount of acid solution put into the container in 60 sec

As, Amount of acid be A(t)

A(t) = 140 + 3t

A(60) = 140 + 3(60)

A(60) = 140 + 180

A(60) = 320

So, the container put 320 ml amount of the acid in 60 seconds.

Hence, the container put 320 ml amount of the acid in 60 seconds.

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The value of f(t) are 48000, 52200, 54300, 56400, and g(t) are 48000, 49776, 51617.71, and 53527.56.

She was given a starting wage of $48,000 from Company A, with annual raises of $2100.

The formula for Company A is

f(t) = 48000 + 2100t

She was given a starting wage of $48,000 from Company B, with an annual rise of 3.7%.

The formula for Company B is

g(t) = 48000 × [tex](1 + 0.037)^t[/tex]

The value of f(t) and g(t),

t ------- f(t) ------- g(t)

0 ----- 48000 ----- 48000

1 ------ 52200 ----- 49776

2 ----- 54300 ----- 51617.71

3 ----- 56400 ----- 53527.56

The graphical representation of both the linear equations of company A and company B.

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Answer:

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Reports that describe how many customers shared positive comments about the gardening magazine on social media in the past year. Reports that compare past weather patterns to the number of people asking gardening questions to their social media. Reports that examine how a recent 50%-off sale affected the number of subscription purchases. Reports that predict the success of sales leads to secure future subscribers.

In order to find relevant information, support inferences, and help decision-making, data analysis is the process of analyzing, cleaning, manipulating, and modeling data. A data analyst examines data to find significant consumer insights and potential uses for the information. They also advise the company's management and other stakeholders of this information. Although it is recommended that data analysts have a basic understanding of statistics and mathematics, many of their tasks may be completed without it. However, data analysts often need to be familiar with statistics, linear algebra, and calculus.

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The probability of rolling a die 10 times and obtaining odd digit 8 or less of the rolls is 529/512 = 1.033

Let us call, getting an odd no. on a roll of die, Success.

The, clearly, the probability p of Success is 3/6 = 1/2.

Hence, q = 1 −p = 1/2

If, X = x denotes the no. of success in n trials, then, X is a

Binomial Random Variable, with parameters

n = 10, and, p = 1/2.

Binomial Random Variable:

This is a specific type of discrete random variable. A binomial random variable counts how often a particular event occurs in a fixed number of tries or trials. For a variable to be a binomial random variable, ALL of the following conditions must be met:

Then, the Probability of x success out of n trials, i.e.,

P (X = x), is,

P (X = x) = p(x) =ⁿCₓ pˣ , qⁿ⁻ˣ, x = 0,1,2, ........, n

In our case,

P (X = x) = ¹⁰Cₓ (1/2)ˣ (1/2)¹⁰⁻ˣ ,x = 0,1,2,..., 10, i.e.,

P (X = x) = p(x) = ¹⁰Cₓ (1/2)¹⁰ = ¹⁰Cₓ /1024, x = 0, 1, ..., 10.

Hence,

The Required Probability = P( X< 8),

⇒ P (X = 0)+ P( X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) +P(X = 6) +  P(X= 7) +  P(X =8)

⇒ 1/1024 ( 1 + 10 + 45 + 120 +210 + 252 + 210 + 120 +90)

⇒ 1/1024 ×1058

⇒ 529 / 512

⇒ 1.033

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Answer:

if 5x + 2 = 7x - 7 then the answer is x = 9/2.

The inequalities are y ≥ (2/3)x + 1 and y < (-1/4)x + 2 and (−6, −3) satisfied the inequality.

A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.

In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.

As per the given phrase,

y is greater than or equal to two-thirds times x plus 1 ⇒ y ≥ (2/3)x + 1

y is less than negative one-fourth times x plus 2 ⇒ y < (-1/4)x + 2

Substitute, point (−6, −3)

-3 ≥ (2/3)(-6) + 1

-3 ≥ -3  

Substitute in second inequality,

-3 < (-1/4)(-6) + 2

-3 < 7/2

Hence "The inequalities are y ≥ (2/3)x + 1 and y < (-1/4)x + 2 and (−6, −3) satisfied the inequality".

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Answer:

1) 312

2) 20

Step-by-step explanation:

4x78=312

78 divided by 4=19.5 rounded up =20

Type I error is:

" Reject the claim that the proportion of people who write with their left hand is 0.29 when the proportion is actually 0.29 "

Type II error is:

"Fail to reject the claim that the proportion of people who write with their left hand is 0.29 when the proportion is actually different from 0.29 "

What is proportion?

An equation in which two ratios are made equal is called a proportion. For instance, you could write the ratio as 1: 3 (for every one boy, there are three girls), which means that 14 of the population is made up of boys and 34 of the population is made up of girls.

In Statistics, a  type I error is the rejection of a true null hypothesis

and  a type II error is the non-rejection of a false null hypothesis

Given that p = 0.29 is accepted

Now type I error is

C. Reject the claim that the proportion of people who write with their left hand is 0.29 when the proportion is actually 0.29

i.e. (false positive)

and type II error here is

B. Fail to reject the claim that the proportion of people who write with their left hand is 0.29 when the proportion is actually different from 0.29.

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The combined sample mean for sample one, whose size equals 8 scores and mean equals 2, and for sample second, whose size equals 4 scores and mean equals 8, is 4..

A combined sample mean is calculated by taking the mean of each group and combining (adding) the results of each average.

We have given that,

For First sample :

Sample size ,n₁ = 8 scores

sample mean, m₁ or X₁-bar = 2

Sample 2 :

Sample size, n₂ = 4

sample mean , m₂ or X₂-bar = 8

Combined sample mean is given by,

M or X-bar =( n₁× x₁-bar + n₂ × x₂-bar)/(n₁+n₂)

plug all the known values in above formula

=> M = (8×2 + 4×8 )/12

=> M = 48/12 = 4

Hence, combined sample mean is 4 .

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Answer:

To make the expression 3(x + 4) - 2(x + 4) + 0.5(x + 4)  equals 1.5, we make x in the linear equation equals -3

A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always results in a straight line. This is the reason why it is named as a 'linear equation'.

There are linear equations in one variable and linear equations in two variables.

In this problem given we have to simplify and equation the expression to 1.5 to make it an equation.

3(x + 4) - 2(x + 4) + 0.5(x + 4) = 1.5

3x + 12 -2x -8 + 0.5x + 2 = 1.5

3x - 2x + 0.5x + 12 - 8 + 2 = 1.5

1.5x + 6 = 1.5

Collect like terms

1.5x = 1.5 - 6

x = -3

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A polynomial equation is used to analyze the behavior of the problem's solutions and is known as the characteristic equation of a second-order differential equation.

It is frequently used to simulate real-world events, such as the operation of electrical circuits. The behavior of the differential equation's solutions may be predicted when the characteristic equation's roots are 2 and -3. The roots of the characteristic equation can be used to identify the properties of an unforced circuit when a second-order differential equation is used to represent it.

The circuit will behave oscillatory when the roots are 2 and -3. As a result, the output of the circuit will oscillate frequently, with the frequency of the oscillations being defined by the variation between the roots. The oscillations in this instance will occur at a frequency of 5 Hz.

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The correct question is-

What behavior of the differential equation's solutions can be determined when the roots of the characteristic equation are 2 and -3?

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