if n people of different heights are lined up in a queue, what is the probability that at least one person is just behind a taller person?

Answer:

7/3 or 3

Step-by-step explanation:

Step by step explanation is shown in the picture attached.

Hope it helps

From the origin (6,18,36) to the tip, the exact length of the curve is 42.

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance.

Equations come in a variety of forms, including linear, quadratic, cubic, and others.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. The statement is not an equation if there is no "equal to" sign in it.

According to our question-

let x = t

x^2= 2y

y = t^2

44/3

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After covering 194 miles, Mr. Etrada's car can go a maximum of 316 miles with the gas still in the tank and the inequality that represents the given situation is x + m ≤ 510.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another.

The equation-like form of the formula 5x 4 > 2x + 3 has an arrowhead in place of the equals sign.

It is an illustration of inequity.

This shows that the left half, 5x 4, is bigger than the right part, 2x + 3.

Finding the x numbers for which the inequality holds true is what we are most interested in.

So, the inequality that can represent the given situation is:
x = total distance traveled

m = miles that the gas will allow you to go

The maximum number of miles per full tank is 510.

Then,

x + m ≤ 510

194 + m ≤ 510

m ≤ 510 - 194

m ≤ 316

Therefore, after covering 194 miles, Mr. Etrada's car can go a maximum of 316 miles with the gas still in the tank and the inequality that represents the given situation is x + m ≤ 510.

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In general, there are n>3 lines in the plane. Show that at least n - 2 triangles are formed by these lines.

Let's consider the following diagram, where each line is labelled with a letter:

A-B-C-D-E

Since each line intersects with at least one other line, there are at least n-2 triangles that can be formed. For example, triangle ABC, triangle ABD, triangle ABE, triangle BCD, triangle BDE, and triangle CDE are all triangles that can be formed from our five lines.

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To calculate the probability that there will be at least four accident in no accident occur before the forth month in which at least one accident occurs

If a month with one or more accidents is regarded as success and let the

k = the number of failures before the fourth success, and  then k follows a negative binomial distribution and the requested probability is

1. success taken as a month with no accident

2. k = the number of failure before the fourth success

Alternatively the solution is where [tex]Pr[k\leq 3][/tex]

which is derived directly as a negative binomial distribution

Therefore, the probability that there will be at least four months in which no accidents occur before the fourth month in which at least one accident occurs is 0.2898

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The amount of interest earned quarterly at 0.5% interest rate compounded quarterly are;

a. Interest for the first quarter = $8.125

b. First quarter ending balance = $6,508.125

c. Interest for the second quarter = $8.13515625

d. Second quarter ending balance = $6,516.26015625

e. Interest for the third quarter = $8.1432520325

f. Third quarter closing balance = $6,524.40548145

g. Interest for the fourth quarter = $8.15550685975

h. The amount of interest earned in a year is about $32.56

An interest is the amount a borrower pays to a lenders as to make use of the lender's funds.

The amount Fred deposited, P = $6,500

The interest paid by the account, r = 0.5% compounded quarterly

a. The first quarter interest can be found by the formula;

[tex]C.I. = P\cdot \left(1 + \dfrac{r}{4} \right)^{4\times \dfrac{1}{4} }- P[/tex]

Therefore;

[tex]C.I. = 6500\times \left(1 + \dfrac{\frac{0.5}{100} }{4} \right)^{4\times \dfrac{1}{4} }- 6500 = 8.125[/tex]

The interest after the first period is $8.125

b. The first quarter ending balance is therefore;

A = P + C.I.

A = $6,500 + $8.125 = $6,508.125

c. The second quarter's interest can be found from the formula;

[tex]C.I. = P\cdot \left(1 + \dfrac{r}{4} \right)^{4\times t} - P[/tex]

Here, P = The balance from the first quarter = $6,508.125

t = 1/4 for one quarter

Therefore;

[tex]C.I. = 6508.125\times \left(1 + \dfrac{\frac{0.5}{100} }{4} \right)^{4\times \dfrac{1}{4} }- 6508.125 = 8.13515625[/tex]

The second quarter's interest is $8.13515625

d. The second quarter ending balance is therefore;

A = $6,508.125 + $8.13515625 = $6,516.26015625

The second quarter ending balance is $6,516.26015625

e. The third quarters interest is therefore;

[tex]C.I. = 6516.26015625\times \left(1 + \dfrac{\frac{0.5}{100} }{4} \right)^{4\times \dfrac{1}{4} }- 6516.26015625 = 8.1432520325[/tex]

The third quarter's interest is about $8.1433

f. The third quarter's ending balance is therefore;

A ≈ $6516.26015625 + $8.1432520325 = $6,524.40548145

The third quarter's ending balance is $6,524.40548145

g. The fourth quarter's interest can be found as follows;

[tex]C.I. = 6,524.40548145 \times \left(1 + \dfrac{\frac{0.5}{100} }{4} \right)^{4\times \dfrac{1}{4} }- 6524.40548145 = 8.15550685975[/tex]

The fourth quarter's interest is; $8.15550685975

h. The balance at the end of one year is therefore;

Balance = C.I. fourth quarter + Principal for the fourth quarter

Therefore;

Balance = $6,524.40548145 + $8.15550685975 = $6,532.56098831

i. The interest the account earns in a year is therefore;

$6,532.56098831 - $6,500 = $32.5609883

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Distinct value of x, y, z are will be 3

Consider the function will be f(x) = x3 - x2 - 2x +2 = ( x - 1 ) (x2 - 2 )

we have three real roots and ,

x + y + z = - 1/ (-1)

= 1 ,

1/x + 1/y + 1/z = -2 /(-2)

= 1

Consider the function

f(x) = x3 - x2 - 40 + 20.

Set the derivation equal 0 we get x = 4 and x = -10/3

are two local extrema. When x= 4 , f(x)<0,when x = -10/3 . f(x) >0 there are three real roots . we have x + y + z = 1 and 1/x + 1/y + 1/z = - (-40)/ 20 = 2

consider the function

f(x) = x3 - x2- 40x + 40/3 .

we still have same local extrema as (2) and we have x= 4 , f(x) < 0 and we

x= -10/3 , f(x) > 0 so there are three real roots. We have x+ y + z = 1 and 1/x + 1/y + 1/z = -(-40)/40/3 = 3

So, there are 3 distinct values

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Answer:

20/50

Step-by-step explanation:

40% is equal to 40/100

40/100 is equal to 20/50

Mary Beth Mars, develops a Pareto chart using the information. The recommendations that you would make is as follows:

A graph containing both bars and a line, the bars representing individual values in descending order and the line representing the cumulative total, is known as a Pareto chart. The Pareto chart allows us to concentrate on it when we need to. The Pareto chart is built upon the 80%-20% run of the show. The Pareto chart states that 20% of arrangements assist in resolving 80% of issues. The complex manager, Mary Beth Marrs, must concentrate on issues with the pool, the ground, and the stopping part in order to satisfy the majority of residents and reduce complaints.

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The equation is P = 1700x + 22,000 and the population in 2009 is 32,200.

Here we have to find the equation to get to know the population after x years.

Data provided:

Population in 2003 = 22,000

Year = x year

Population increases every year = 1700

Let P be the population after x year.

So the equation is:

P = 1700x + 22,000

Now we have to find the population in 2009.

So 2009 - 2003 = 6

Put x = 6

P = 1700 × 6 + 22,000

  = 10200 + 22,000

  = 32,200

Therefore the equation is P = 1700x + 22,00 and in 2009 population is 32,200.

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109.5° is the bond angle between two nearby hybrid orbitals. sp3 will be the hybridization.

The hybridization would be sp3. This is because the bond angle of 109.5° is characteristic of hybridized orbitals with four sp3 orbitals, which form an angle of 109.5°. sp3 hybridization occurs when one s orbital and three p orbitals mix to form four sp3 hybrid orbitals.

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The total number of students participating in a school club or sport is 105.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers. On the other hand, a fraction appears in the numerator or the denominator of a complex fraction.

Given that three out of 5 students at Maria's school participate in a school club or sport and there are 175 students at the school.

In this situation, the number of people that participate will be:

= Fraction utilized × Total number of students

= 3/5 × 175

= 105

The number of people is 105.

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Answer:

y=5x+53

Step-by-step explanation:so all i did was go into the demos app and typed in y=5x-7 and then i entered y=5x+30 and i kept going up until i found the right answer

The pass numbers are independent of the school of study.

Given that a high  school offers math placement exams for incoming freshmen to place students into the appropriate math class during their freshman year

Set up hypotheses as

H₀ : Pass independent of school

Hₐ : Pass independent on school

Two tailed chi square test for independence)

Contingency table is shows as below

School A B C Total

Pass 42 29 45 116

Expected 38.6667 38.6667 38.6667 116.0000667

Obs-exp)^2/observed 0.2874 2.4167 1.0373 3.74138208

df 2    

p value = 0.154

Since p > alpha(0.1) we accept null hypothesis

The pass numbers are independent of the school of study.

Hence we get the required answer.

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Answer:

-4t ≥ -2/5

Step-by-step explanation:

t≥0.1

Sample error is ±2.9872 from the sample mean of 22 inch and standard deviation of 8 inch and sample size of 30 inch.

An analyst makes a statistical error known as a sampling error when they choose a sample that does not accurately represent the complete population of data. As a result, the sample's findings do not accurately reflect the findings from the total population.

Here,

mean=22 inch

standard deviation=8 inch

sample size=30 inch

degree of freedom=29 inch

The sampling error is calculated by dividing the standard deviation of the population by the square root of the size of the sample, and then multiplying the resultant with the Z-score value, which is based on the confidence interval.

By using this,

sampling error=±2.9872 inch

With a sample mean of 22 inches, a standard deviation of 8 inches, and a sample size of 30 inches, the sample error is 2.9872 inches.

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Answer:

y = -5x -8

Step-by-step explanation:

The slope must be the negative reciprocal(-5). So we have y = -5x + b, where we need to find b. To do that, we will plug in the known point. This gives us [tex]-3 = -1 * -5 + b[/tex], or[tex]-3 = 5 + b[/tex]. We subtract 5 from both sides to get b = -8.

The equation that doesn't belong is (c) 12(p + 8) = 3(20 - 2p)

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

Options A to D

Looking through the options, we can see that:

However, three of the equations have their variables on one side

While the last has its variable on both sides

Hence, the one that does not belong is (c) 12(p + 8) = 3(20 - 2p)

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The explanation for each condition of the question is given below in which the activation record for the function is deallocated for Option (A).

What is an activation record?

Information required for just one execution of a procedure is managed by an activation record. When a procedure is called, an activation record is pushed into the stack, and it is popped when the control is returned to the calling function.

From the question, Languages typically group all activation-specific function validation under the umbrella of an activation record.

Whenever the block is entered, extend the function activation record.

a. fun f x = x + 1;

b. fun f x = y =>x y;

Take fun f

x=fun y

x+y

c. fun.f x = fn y => y+ 1;

fun f

x => fn

y => y+1

d. fun f x = map ~ x

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In the year 2002 the exports of Chinese's automobile parts will $5.3 billion.

The exponential function for the given export of Chinese's automobile parts is-

5.3 = 1.8208 e^0.3387x

5.3/1.8208 = e^0.3387x

Taking ln both sides-

ln(5.3/1.8208) = ln e^0.3387x

ln(5.3/1.8208) = 0.3387x

Further simplifying

x = ln(5.3/1.8208)/0.3387

x =  3.15

x ≈ 3 year ad some months

Add 3 years to 1998 to get the required year.

Year = 1998 + 3

Year = 2001 and months

Year = 2002

Thus, in the year 2002 the exports of Chinese's automobile parts will $5.3 billion.

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The correct question is-

The value of China's exports of automobiles and parts (in billions of dollars) is approximately f(x) = 1.8208e^.3387x, where x = 0 corresponds to 1998.

In what year did/will the exports reach $5.3 billion?

The percent of Hispanics that prefer to read catalogs in Spanish is equal or higher than 30%

What is percentage ?

A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.

%, which is a relative figure used to denote hundredths of any quantity. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.

By dividing the value by the entire value and multiplying the result by 100, one may determine the percentage. The percentage calculation formula is (value/total value)100%.

The percent of Hispanics that prefer to read catalogs in Spanish is equal or higher than 30%

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There is sufficient data to back up the assertion that salespeople with college degrees generate much higher average sales than salespeople without.

Given,

This is a test of the hypothesis that the means of the two populations differ.

The assertion is that salespeople with college degrees generate much higher average sales than salespeople without.

The alternative and null hypothesis are then:

H₀ ; μ₁ - μ₂ = 0

Hₐ ;  μ₁ - μ₂ > 0

The level of significance is 0.05.

The mean and standard deviation for sample 1 (college degree), with n1=14, are 3542 and 468, respectively.

The mean and standard deviation of sample 2 (non-college degree), with n2=17, are 3301 and 642, respectively.

Now,

Md = M₁ - M₂ = 3542 - 3301 = 241

Md=241 is the difference between the sample means.

The following formula is used to calculate the estimated standard error of the difference between means:

S Md = √(σ₁²/n₁ + σ₂²/n₂) = √(468²/14 + 642²/17) = √(15644.6 + 24244.94) = 199.72

Then, we can calculate the t-statistic as:

t = (Md - (μ₁ - μ₂) / S Md = 241 - 0 / 199.72 = 241/199.72  = 1.21

The degrees of freedom for this test are:

Df = n₁ + n₂ - 2 = 14 + 17 - 2 = 29

Right-tailed tests have 29 degrees of freedom and t=1.21, so the following formula is used to determine the P-value for this test:

P Value = P(t > 1.21) = 0.118025

The effect is significant since the P-value (0.118025) is less than the 0.05 standard of significance.

The null hypothesis is rejected.

Therefore,

The idea that salespeople with college degrees generate much higher average sales than those without is supported by sufficient data.

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The equation of the perpendicular line to x + 6y = 42 is: y = 6x + 1.

The lines that are perpendicular to each other will have slope values that have a product of -1, which means one is a negative reciprocal of the other.

Given the equation, x + 6y = 42, it can rewritten in slope-intercept form as shown below:

6y = -x + 42

6y/6 = -x/6 + 42/6

y = -1/6x + 7

The slope of the line is -1/6. The negative reciprocal of -1/6 is 6. Therefore, the slope of the line that is perpendicular to x + 6y = 42 is 6.

Substitute m = 6 and (x, y) = (1, 7) into y = mx + b to find the y-intercept (b):

7 = 6(1) + b

7 = 6 + b

7 - 6 = b

b = 1

Tp write the equation of the perpendicular line, substitute m = 6 and b = 1 into y = mx + b:

y = 6x + 1

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The probability that they will have exactly one affected child is 9/64.

What is probability?

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

The likelihood that a population parameter will be less than a given value when the null hypothesis is true is expressed as the p-value, also known as a probability value or a measure of significance, for a particular statistical model.

Probability of affecting for 1 child = 3/4  = q

Probability of not affecting on 1 child =p=1/4

Formula:

P( exactly one affected child )

= [tex]^{3}C_{1}[/tex] * * (1/4)² * (3/4) = 9/64

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Dividing the class by using Coin flip , The instructor has created minimal group

Researchers employ a technique called the minimal group paradigm to instigate new social groups in the lab. The objective is to classify people into groups using minimal, meaningless, or arbitrary criteria.

A minimal group is a a group lacking interdependence, group cohesion, structure, and other characteristics typically found in social groups.

An example is a group of people disembarking from a bus.

According to the question ,

The instructor is dividing the class by means of coin

Here, the flipping of coin is an arbitrary criteria . Also , the group formed will be anonymous

Hence , the formed group will be minimal group

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