Two trains leave towns 476 kilometers apart at the same time and travel toward each other. One train travels 22 km/h faster than the other. If they meet in 2 hours, what is the rate of each train?

The probability that the mean height of a random sample of 56 ten-year-old males will be greater than 53 inches is approximately 0.9991, or 99.91% when rounded to three decimal places.

What is the central limit theorem?

The central limit theorem, which states that the sample means of large samples (n > 30) from a population with any distribution approaches a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

We can solve this problem by using the central limit theorem,

In this case, the sample size is n = 56, which is larger than 30, so we can assume that the sample means are normally distributed. The mean of the sample means is equal to the population mean, which is 55.5 inches, and the standard deviation of the sample means is equal to the population standard deviation divided by the square root of the sample size:

standard deviation = 6 / √(56) = 0.801

To find the probability that the mean height of the sample will be greater than 53 inches, we can standardize the sample mean using the standard deviation calculated above:

z = (sample mean - population mean) / (standard deviation)

= (53 - 55.5) / 0.801

= -3.12

Using a standard normal distribution table or calculator, we can find the probability that a standard normal random variable is greater than -3.12:

P(Z > -3.12) = 0.9991 (rounded to four decimal places)

Therefore, the probability that the mean height of a random sample of 56 ten-year-old males will be greater than 53 inches is approximately 0.9991, or 99.91% when rounded to three decimal places.

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The student is trying to construct a bisector of a given Angle i.e. A.

what is a bisector?

In Geometry, a “Bisector” is a line that divides the line into two different or equal parts. It is applied to the line segments and angles. A line that passes through the midpoint of the line segment is known as the line segment bisector, whereas the line that passes through the apex of an angle is known as the angle bisector. The bisector of a segment always contains the midpoint of the segment. There are two types of bisectors based on what geometrical shape it bisects.

Line Segment Bisector (Perpendicular Bisector Theorem)

Angle Bisector (Triangle Bisector Theorem)

Now,

As we can see from the figure given that the bisector is dividing the angle in two equal segments.

Hence,

          The student is trying to construct a bisector of a given Angle.

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Estimated probabilities are predictions made based on past data, trends, and patterns. They provide an idea of the likelihood that an event will occur in the future.

Part A:

Answer: The probability of a drought within the next 4 years if the probability of a drought in any one year is 12% is approximately 48%.

Part B:

Answer: Pairs of digits starting at 00 and ending at 11 represent a drought happening. Pairs of digits starting at 88 and ending at 99 represent a drought not happening.

Part C:

Answer: Using the random numbers, the estimated probability that a drought happens at least once over the next 4 years is 68%.

Part D:

Answer: The probability that was calculated is greater than the probability predicted. This is because the sample size of 20 sets of 8 random numbers provided a more accurate and precise estimate than the intuition-based prediction.

Part E:

Answer: Yes, the estimated probability changes when the pairs of digits that represent a drought happening are changed so that they start at 10 instead of 00. Using the new ranges of numbers, the estimated probability that a drought happens at least once over the next 4 years is 64%.

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Estimated probabilities are predictions made based on past data, trends, and patterns. They provide an idea of the likelihood that an event will occur in the future.

Predictions based on historical data, patterns, and trends are known as estimated probability. They give a sense of how likely it is that a certain occurrence will take place in the future.

Estimated probabilities calculation Part A:

If the likelihood of a drought in any given year is 12%, the likelihood that one will occur within the next four years is roughly 48%.

Part B:

Answer: The drought is represented by pairs of numerals beginning at 00 and ending at 11. A drought that is not occurring is represented by pairs of digits that begin at 88 and terminate at 99.

Part C:

According to the random numbers, there is a 68% chance that a drought will occur at least once over the next four years.

Part D:

Answer: The calculated probability is higher than the expected probability. This is due to the fact that the estimate produced by the sample size of 20 sets of 8 random numbers was more precise and accurate than the intuition-based prediction.

Part E:

Answer: When the pairs of digits that represent the occurrence of a drought are modified so that they begin at 10 instead of 00, the predicted likelihood does indeed change. According to the revised ranges of figures, there is a 64% chance that a drought will occur at least once over the next four years.

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Answer:

D. I centimeter

Step-by-step explanation:

Since it is only 0.128 nm wide

0.128 nm x 100,000,000 =

1.28 centi meters

Answer:

D)  1 centimeter

Step-by-step explanation:

The SI base unit for length is meters (m).

The radius of a copper atom is 128 pm.

Picometer (pm) is a unit of length equal to 1 × 10⁻¹² meters.

Therefore, the radius of a copper atom in the SI base unit for length is:

[tex]\implies \sf 128 \times 10^{-12} = 1.28 \times 10^{-10}\;m[/tex]

One hundred million = 100,000,000 = 1 × 10⁸

Therefore, the length of a line of one hundred million copper atoms in meters is:

[tex]\implies \sf 1 \times 10^{8} \times 1.28 \times 10^{-10}[/tex]

[tex]\implies \sf 1.28 \times 10^{-10} \times 10^{8}[/tex]

[tex]\implies \sf 1.28 \times 10^{-10+8}[/tex]

[tex]\implies \sf 1.28 \times 10^{-2}\;\;m[/tex]

Centimeter (cm) is a unit of length equal to 1 × 10⁻² meters.

To convert meters to centimeters, divide by 1 × 10⁻²:

[tex]\implies \sf \dfrac{1.28 \times 10^{-2}}{1 \times 10^{-2}}=1.28\;cm[/tex]

Therefore, a reasonable estimate for the length of one hundred million copper atoms arranged in a line is 1 centimeter.

The domain is: a = -4, and b = 1 and the y = mx + b rule that makes the left (red) piece of the graph is given by y = -0.5x - 2.

The range of values that can be plugged into a function is known as its domain. In a function like f, this set represents the x values (x).

The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set. They are the values for y.

The domain of the left (red) graph is determined using the x-coordinates of the line. The x-coordinates give the input of the function of the graph, which forms the domain.

The domain is:

a = -4, and

b = 1

Hence, the domain of the function of the graph is: -4 < x <1.

The y = mx + b is the equation of the linear function where, m is the slope and b is the point where the line intersects the y-axis.

The value of m - slope is given by:

m = (y2 - y1) / (x2 - x1)

m = (-2.5 - 0) / (1 - (-4))

m = -2.5/ 5

m = - 0.5

The value of b from the graph is:

b= -2

Substituting the values of m and b in the equation we have:

y = mx + b

y = -0.5x - 2

Hence, the y = mx + b rule that makes the left (red) piece of the graph is given by y = -0.5x - 2.

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Between 5:15 pm to 6:30 pm, Beth is decreasing her distance from home. Hence option c is the correct answer.

Distance between two points or objects can sometimes be measured qualitatively and sometimes quantitatively.

In physics, the concept of distance can refer to a physical length or, more commonly, to an approximation based on several other considerations.

The term is frequently used metaphorically to denote a measure of the degree of separation or statistical distance between two similar objects (such as edit distance between strings of text or distance between probability distributions), given that spatial cognition is a rich source of probability metaphors in human thought (as exemplified by distance between people in a social network).

Most of these literal and figurative concepts of distance are defined in terms of a mathematical idea called a metric space.

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A Pareto diagram assists a team in focusing its efforts on the variables that have the biggest influence by separating the important few from the unimportant many. Additionally, it facilitates the team's ability to explain why specific areas are important.

The following situations call for the use of scatter plots.

In the case of paired numerical data

when more than one value of the dependent variable is associated with a particular value of the independent variable

When determining the relationships between variables, it might be helpful to look for potential problem-solving causes, see if two products that seem connected both have the same root cause, and so on.

A histogram is a graphic depiction of a frequency distribution with continuous classes that has been grouped. A series of rectangles with bases equal to the distances between class boundaries and areas proportional to frequencies in the associated classes make up the area diagram. Since the base in such representations spans the spaces between class boundaries, every rectangle is neighbouring. Rectangle heights are inversely correlated with comparable frequencies for similar classes, and inversely correlated with frequency densities for other class.

A run chart, also known as a run-sequence plot is a graph that displays observed data in a time sequence. Often, the data displayed represent some aspect of the output or performance of a manufacturing or other business process. It is therefore a form of line chart.

The complete question is :-

Which of the following charts would be best to justify focusing on a few large problems and ignoring many smaller ones?

1) run chart  (2) pareto diagram  

(3) histogram (4) scatter plot

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a) The bigger the value, each box plot is spread out. The ages of the top 50% of customers are more varied than 50% of lower consumers. Hence, each plot is slanted to the right.

b) The BMW 3 series is likely to have an outlier. It has the longest whisker.

c) When comparing median age, younger people are likely to purchase the BMW 3 series and while older people are more likely to purchase the BMW 7 series. However, because each data set is so dissimilar, this is not a rule.

d) The spread is the smallest in the second quarter of the box. The difference between the first quartile and the median seems to be barely three years.

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The complete question is:

A survey was conducted of 130 purchasers of new BMW 3 series cars, 130 purchasers of new BMW 5 series cars, and 130 purchasers of new BMW 7 series cars. In it, people were asked the age they were when they purchased their car. The following box plots display the results.

a. In complete sentences, describe what the shape of each box plot implies about the distribution of the data collected for that car series.

b. Which group is most likely to have an outlier? Explain how you determined that.

c. Compare the three box plots. What do they imply about the age of purchasing a BMW from the series when compared to each other?

d. Look at the BMW 5 series. Which quarter has the smallest spread of data? What is the spread?

Using the arithmetic operation, the number of worker in San Diego is obtained as 260, and the number line which represents the same is option 1.

What is arithmetic operation?

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

The number of offices are = 3

The number of workers in the company is = 480

The number of workers in New York city = 90

The number of workers in Denver city = 130

The number of workers in San Diego city = x

To find the number of workers in San Diego use the formula -

Number of workers in San Diego = Total Number of Workers - (Number of workers in New York + Number of workers in Denver)

The arithmetic operation of addition and subtraction is used.

Substitute the values into the equation -

Number of workers in San Diego = 480 - (90 + 130)

Number of workers in San Diego = 480 - 220

Number of workers in San Diego = 260

The number line which represents the number of workers in San Diego is  option 1.

Therefore, the number of workers in 260.

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A company has offices in 3 different cities and a total of 480 workers. There are 90 workers in New York and 130 workers are in Denver. Which number line represents the number line represents the number of workers in San Diego?

The probability hat 1st winner lives in Guston and the 2nd living in Pikes = 3/25

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

1. P(E) = [Number of favorable outcomes of E]/[Total number of potential outcomes of E] is the formula for calculating an event's probability.

2. The likelihood of a given occurrence or a sure thing happening is 1.

3. There is no chance that an impossible occurrence will occur.

4. A number P(E) that has the formula 0 P(E) 1) represents the probability of an occurrence E. The probability scale is always positive.

5. If events A and B are two occurrences that can never occur together, then P(AB) = P(A) + P (B).

6. An basic event is one that has just one result. The total likelihood of such outcomes in an experiment is 1, or 1.

7. The probability of an event plus the probability of its complementary occurrence equals one. P(A) + P(A').

Total number of Customers = 10

Customers lives in Guston = 6

Customers living in Pikes = 2

Customers living in Wells = 2

Probability that 1st winner lives in Guston and the 2nd living in Pikes = 6/10 * 2/10 = 3/25

The probability hat 1st winner lives in Guston and the 2nd living in Pikes = 3/25

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The maximum error in the volume of the cone is approximately 20π cubic centimeters.

In this problem we must estimate the maximum error in the volume of the cone, based on uncertainties in radius and height of a circular cone. The volume formula for a circular cone is:

V = (π / 3) · R² · h

Where:

And the maximum error formula (ΔV), in cubic centimeters, is found by total differentials:

ΔV = (dV / dR) · ΔR + (dV / dh) · Δh

Where:

All first derivatives are shown below:

dV / dR = (2π / 3) · R · h

dV / dh = (π / 3) · R²

If we know that R = 10 cm, h = 25 cm, ΔR = 0.1 cm and Δh = 0.1 cm, then the maximum error in volume of circular cylinder is:

dV / dR = (2π / 3) · (10 cm) · (25 cm)

dV / dR = 500π / 3 cm²

dV / dh = (π / 3) · (10 cm)²

dV / dh = 100π / 3 cm²

ΔV = (500π / 3 cm²) · (0.1 cm) + (100π / 3 cm²) · (0.1 cm)

ΔV = 20π cm³

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The given circumstance is represented by the linear equation 2y = x, and the graph is included below.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given, A student traveled a distance of 68 miles in 136 minutes.

From the general formula of a linear equation:

y = mx + c

where,

m = slope

c = y-intercept

Since At 0 minutes, he started traveling so at 0 minutes total distance he traveled is 0. So the graph will pass through origin.

Thus, the y-intercept will be zero

And Slope of the graph that passes through the origin is always the ratio of the y and x values at any point of the line.

Thu, m = 68/136

m = 1/2

Therefore, a linear equation that represents the given situation is 2y = x, and the graph is attached below.

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Complete question:

174 number of students must be in the 8th grade class.

A relationship between two expressions or values that are not equal to each other is called 'inequality.

Given that The eight grade class is planning a trip to Washington, D.C. this spring.

They need a minimum of 75 people to attend in order to reserve busses.

1/3 of the 8th grade class plus 17 parent chaperones have signed up and this is enough to satisfy the requirement,

We need to find the number of students must be in the 8th grade class

1/3x+17≤75

Subtract 17 on both sides

1/3x≤58

x≤174

Hence, 174 number of students must be in the 8th grade class.

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Answer:

all

Step-by-step explanation:

all of them

As per the given ratio Mina's age is 12 years old.

Ratio in math is defined as shows how many times one number contains another.

Here we have given ratio information as written as

=> Lev's age : Mina's age = 1 : 2

And the ratio between is written as

=> Mina's age : Naomi's age = 3 : 4

Here we have given the condition that the sum of all three ages is written as,

=> Lev + Mina + Naomi = 30 to 50

Here let us consider Lev's age as L, Mina's age as M and Naomi's age as N

Then the ratio is calculated as,

=> L = 1/2M

=> N = 4/3M

And the sum of all value is written as

=> L + M + N = 30 to 50

When we apply the values on it, then we get,

1/2M + M + 4/3M = 30 to 50

When we simplify it by multiply all by 6, then we get

=> 3M + 6M + 8M = 180 to 300

=> 17M = 180 to 300

Therefore, here we have to find a number between 180 and 300 that divisible by 17 and 6.

So let us consider that that number is 204.

Then the value of M is calculated as,

=> 17M = 204

=> M = 12

Complete question:

Let us consider that suppose the ratio of lev's age to mina's age is 1 : 2 and the ratio of mina's age to Naomi's age is 3 : 4. if the sum of all three ages is between 30 and 50, then how old is mina?

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Answer:

4 cm.

Step-by-step explanation:

Area = pi r^2, so:

pi r^2 = 4 / pi

(pi)^2 r^2 = 4

r^2 = 4/ (pi^2)

r = 2/pi

Therefore, the circumference

= 2 pi r

= 2* pi * 2/pi

= 4

The value of the z-test statistic = 1.16667

When told the question that a random number of samples is tested

z test statistic formula = x - x bar(x with bar above it) /Standard error

From the question

x = raw score = 46 pounds

x bar (x with bar above it)= sample mean = 45.5 pounds

Standard Error = σ/√n

Standard deviation = σ = 3

n = random number of samples = 49

z = 46 - 45.5/3/√49

z = 0.5/ 3/7

z =0.5/ 0.4285714286

z = 1.16667

Therefore, the value of the z-test statistic = 1.16667

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Answer:

E = 36

Step-by-step explanation:

1. Add 7 to both sides of the equation

3e - 7 = 101

    +7     +7

------------------

3e = 108

2. Isolate the variable e by dividing by 3 on both sides

[tex]\frac{3e}{3} = \frac{108}{3}[/tex]

3. Simipfy the equation

[tex]e = 36[/tex]

The value of y is 11/3 when the value of x = 3

What is inverse function?

A function that returns the initial value for which a function has produced output is called an inverse function. If f(x) is a function that produces the value y, then f-1(y), which is the inverse function of y, will produce the value x. Inverse and reciprocal functions should not be confused. The output's original value is returned by the function's inverse, which is represented by the symbol f-1 (x). While the reciprocal of a function is represented by 1/f(x) or f(x)-1

Those that do are referred to as invertible. For a function f: X Y to have an inverse, it must possess the characteristic that there is exactly one x in X such that f(x) = y for every y in Y. This characteristic guarantees the existence of a function g: Y X that has the required connection to f.

If y varies inversely as x^2, and y=11/9 when x=9

when x =3,

y = 11/9 *x²

y = 11/3

Hence, the value of y is 11/3 when the value of x = 3

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The absolute values of inequality equations totally depend on the symbols.

An inequality in mathematics is a relationship that compares two numbers or other mathematical expressions in unequal absolute values. By comparing the absolute valuesof two numbers on the number line, inequality is most frequently utilized. Different types of inequality are represented by a variety of different notations, including:

The symbol a b indicates that an is less than b.

A bigger value for a than a lesser value for b is indicated by the notation a > b.

a is not equal to b in either situation. These relationships are referred to be stringent inequalities since an is either strictly less than or strictly greater than b. Equivalence is not included.

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The unit square that covers the figure is attached

The quantity of unit squares necessary to completely cover a shape is its area.

Consequently, area is represented and measured in square units.

The attached figure shows the 9 squares that makes up the figure

Each side has 3 squares and hence

= 3 squares * 3 squares

= 9 squares

The image is attached

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To find the percentile, we need to calculate what percentage of the data falls below the $78 thousand dollars wage.

To find the percentile, we sort the data in ascending order and find the percentage of the data that falls below $78 thousand dollars. Here's one way to do this:

69 58 43 43 43 51 57 57 62 68 69 75 76 78 78 80 91 97 102 124 130 135 144 157 185 217

Out of 28 observations, 22 of them are below $78 thousand dollars. So, the percentile for someone who earns $78 thousand dollars is 22/28 * 100 = 78.5714.

In this context, the value of the percentile represents the percentage of the population of full-time employed people who hold at least a Bachelor's degree and earn less than $78 thousand dollars. So, someone who earns $78 thousand dollars is in the 78.5714th percentile of this population.

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The equation that represents the quotient of -100 and twice 10 equal to -5 is; -100 ÷ 2(10) = -5

The quotient of an algebraic operation is defined as a result that is obtained by dividing one quantity by another.

We are told that the quotient of -100 and twice 10 is equal to -5. Thus, we can express the given expression as;

-100 ÷ 2(10) = -5

This is because quotient means answer that is produced from dividing 2 numbers and since the product is a whole number and not a proper fraction, then it means that the larger number will be the numerator while the smaller number will be the denominator.

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The fraction of a pound of granola that Marty bought is 3/4 pounds.

A fraction is a non-integer that is made up of a numerator and a denominator. The numerator is the number above and the denominator is the number below. An example of a fraction is 3/4.

The unit of conversion of ounces to pounds is :

1 pound = 16

12 ounces of granola =  12/16 pounds = 3 /4 pounds

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When calculating the finance charges, the monthly interest rate (MPR) is multiplied by the D. average daily balance.

The finance charge refers to the interest and other fees a borrower pays on a credit card.

To compute the finance charge, the annual percentage rate (APR) or the monthly percentage rate (MPR) is multiplied by the balance owed.

The balance commonly used for this calculation is the average daily balance.

Thus, Option D is multiplied by the MPR to compute the finance charges.

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The equation of the plane  passing through point P with normal vector n A(x-2) + B(y-3) + C(z-4) = 0

(a) Normal Form:

The equation of the plane passing through point P with normal vector n can be written in normal form as:

n • (r - p) = 0

where r is a position vector in three-dimensional space and n is the normal vector of the plane.

Given n = (1,2,3) and p = (2,3,4).

Therefore, n • (r - p) = (1,2,3) • (r - (2,3,4)) = r1 + 2r2 + 3r3 -2 - 3 - 4 = 0

=> r1 + 2r2 + 3r3 - 8 = 0

=> Plane equation in normal form: 1x + 2y + 3z - 8 = 0

(b) General Form:

The equation of the plane passing through point P with normal vector n can also be written in general form as:

A(x-x0) + B(y-y0) + C(z-z0) = 0

where A, B and C are the components of the normal vector n and (x0,y0,z0) are the coordinates of the point p.

Given n = (1,2,3) and p = (2,3,4).

Therefore, A(x-2) + B(y-3) + C(z-4) = 0

=> 1(x-2) + 2(y-3) + 3(z-4) = 0

=> Plane equation in general form: x - 2y + 3z - 8 = 0

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Provide complete question here:Write the equation of the plane passing through p with normal vector n in (a) normal form and (b) general form.

Systematic random sampling is used when selecting every nth item from a list of items. In this example, every 49th student starting with the 3rd student is selected.

In systematic random sampling, a list of items is created and every nth item is selected for the sample. This technique is useful when selecting a representative sample from a large population of items. In the example given, 496 students were listed and every 49th student starting from the 3rd student was selected. This is a systematic random sampling technique because the items were selected in a systematic and random fashion. The selection of every 49th student starting from the 3rd student ensures that the sample is representative of the population while also randomizing it so that all students have an equal chance of being selected.

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Answer:

-0.50, -0.10, 0.60, 0.68, 0.98