Which of the following is true? O (LS - ES) >= 0 O (LF-LS) > (EF - ES) Slack = (LF-LS)

The difference between the three variances, Var(x), Var(y), and Var(x + y), can be determined analytically in the context of the bus ridership example.

In the given context, let's consider two variables: x represents the ridership on line l2, and y represents the ridership on line l1. The statement mentions that intuitively, l1 and l2 are not independent, meaning they are related in some way.

To determine the difference between the variances, we need to calculate the variances of x, y, and the sum of x and y, which is x + y.

Var(x): This represents the variance of the ridership on line l2. It quantifies the spread or variability in the data points of x. To calculate Var(x) analytically, you can use the formula: Var(x) = E[(x - μx)^2], where E represents the expectation (mean) operator and μx represents the mean of x.

Var(y): This represents the variance of the ridership on line l1. Similar to Var(x), it quantifies the spread or variability in the data points of y. Var(y) can be calculated using the same formula as Var(x): Var(y) = E[(y - μy)^2], where μy represents the mean of y.

Var(x + y): This represents the variance of the sum of ridership on both lines l1 and l2. It measures the combined variability of the two variables. To calculate Var(x + y), you can use the formula: Var(x + y) = E[(x + y - μ(x + y))^2], where μ(x + y) represents the mean of the sum of x and y.

By analytically calculating the three variances, Var(x), Var(y), and Var(x + y), you can compare them to understand their differences and the relationship between the ridership on line l1 and line l2.

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Answer:

Step-by-step explanation

Left at 6:15 am

How many hours until 2:15pm? 8 hours

How many minutes from 2:15 until 2:30? 15

So it took 8 hours and 15 minutes

Answer:

11.6

Step-by-step explanation:

In a right-angled triangle, a ² + b ² = c ². This is Pythagoras' Theorem.

Let's call unknown side A.

we have A² +  11² = 16².

subtract  11² from both sides:

A² = 16² - 11²

= 256 - 121

= 135

A = √135

= 11.6 to nearest tenth

Answer:

like terms

1.-2x-p+7z

2.7m+5n-3

3.6t+2+3s

Distribute and simplify

1.-24t-30x-12+3x

-24t-27x-12

2.10x+15y+35-5x-3y

5x+12y+35

3.24x-12-2x

22x-12

Answer:

points for points

Step-by-step explanation:

aint gotta explain $ hit.

The simplification is correct.

The expression $n 2\binom{n}{2}$ can be simplified using the definition of binomial coefficients and the properties of factorials. First, we can rewrite the binomial coefficient as follows:

$\binom{n}{2} = \frac{n!}{2!(n-2)!}$

Next, we can substitute this into the original expression and simplify:

$n 2\binom{n}{2} = n 2\frac{n!}{2!(n-2)!} = n\frac{n!}{(n-2)!}$

Now, we can cancel out the $n!$ terms in the numerator and denominator:

$n\frac{n!}{(n-2)!} = n\frac{n(n-1)(n-2)!}{(n-2)!} = n(n-1)$

Finally, we can simplify the expression to get our final answer:

$n(n-1) = n^2 - n$

Therefore, the simplified expression is $n^2 - n$.

To prove this simplification using a counting argument, we can think about what the original expression represents. The binomial coefficient $\binom{n}{2}$ represents the number of ways to choose 2 items from a set of n items. Multiplying this by 2 gives us the number of ways to choose 2 items and then choose one of those 2 items again. Finally, multiplying by n gives us the number of ways to choose 2 items, choose one of those 2 items again, and then choose one of the n items. This is equivalent to choosing 2 items from a set of n items and then choosing one of the n items, which is represented by the simplified expression $n^2 - n$. Therefore, the simplification is correct.

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\(~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 30000\\ P=\textit{original amount deposited}\dotfill & \$20000\\ r=rate\to 9\%\to \frac{9}{100}\dotfill &0.09\\ t=years \end{cases} \\\\\\ 30000 = 20000[1+(0.09)(t)] \implies \cfrac{30000}{20000}=1+0.09t\implies \cfrac{3}{2}=1+0.09t \\\\\\ \cfrac{3}{2}-1=0.09t\implies \cfrac{1}{2}=0.09t\implies \cfrac{1}{2(0.09)}=t\implies 5.6\approx t\)

Answer:

x-y

Step-by-step explanation:

Answer:

Explanation:

The number 43 is basically 40+3

We read "43" as "forty three", in which you can think of having 40 and then an additional 3 on top of that to get 40+3 = 43 overall.

As for the decimal portion, we do the same sort of thing.

The 0.205 breaks up into 0.2 + 0.005

0.2 = 2 tenths

0.005 = 5 thousandths

So that's why 43.205 breaks down into 40+3+0.2+0+0.005; each place value digit corresponds to a term in that expanded sum.

Answer:

They never touch

Step-by-step explanation:

BEcause they dont touch because they are at a 90 degree angle forever so therefor it will not touch

The equation in slope intercept form is y=-1/5x +13/5.

The given equation is y-3=-1/5(x+2).

We need to write this equation in the form of slope intercept form.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

y-3=-1/5(x+2).

y-3=-x/5 -2/5

Add 3 on both sides:

y=-x/5 -2/5 +3

y=-x/5 +13/5.

Hence, the equation in slope intercept form is y=-1/5x +13/5.

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Answer:

C. 6.8, because |6.8|= 6.8

Step-by-step explanation:

The magnitude of a directed number is a property that turns the number to a positive of its value. Thus, the magnitude of a negative number equals its positive value. Examples:

Find the magnitude of the following numbers:

i. -20

ii. 10

iii. -5

iv. 2

The magnitudes of the numbers can be expressed as:

i. |-20| = 20

ii. |10| = 10

iii. |-5| = 5

iv. |2| = 2

Therefore, the magnitude of 6.8 = 6.8, because |6.8|= 6.8.

A correlation coefficient based on an observational study cannot be used to support a claim of cause and effect. The correct answer is A: never.

Correlation does not imply causation, and while a strong correlation between two variables may suggest that there is a relationship between them, it does not prove that one variable causes the other. Observational studies are particularly susceptible to confounding variables, which can make it difficult or impossible to determine whether a relationship between two variables is causal or not.

To establish causality between two variables, a randomized controlled experiment is required. In a randomized controlled experiment, the experimenter can manipulate the independent variable and observe the effect on the dependent variable, while controlling for other variables that might affect the outcome. By randomly assigning subjects to different treatment groups, the experimenter can ensure that any differences in the outcome between groups are due to the treatment, rather than some other factor.

Therefore, while a correlation coefficient can be a useful tool for describing the relationship between two variables, it cannot be used to establish causality.

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To prove that if n is composite, then 2^n - 1 is composite, we can use the concept of prime factorization. We assume that n is composite and express it as a product of two integers a and b. By applying the identity (a - b)(a^(n-1) + a^(n-2)b + ... + ab^(n-2) + b^(n-1)) to the expression 2^n - 1, we can show that it is divisible by a - b, which implies that 2^n - 1 is composite.

Let's assume that n is composite, which means it can be expressed as n = ab, where a and b are positive integers greater than 1. Now we can rewrite 2^n - 1 as (2^a)^b - 1. Using the identity for the difference of squares, we have (2^a)^b - 1 = (2^a - 1)((2^a)^(b-1) + (2^a)^(b-2) + ... + 2^a + 1).

Here, (2^a - 1) is a factor of 2^n - 1 since it divides into the expression without a remainder. Additionally, the second factor is a sum of terms, each of which is greater than or equal to 2^a + 1. Hence, both factors are greater than 1, and 2^n - 1 is composite.

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Answer:

A 3.14159.......

Step-by-step explanation:

We need a non rational number

3.14159 is pi which is an irrational number

1/7, .27(repeating) and .83333(repeating) can be written in the form

a/b where a and b are integers, which makes them rational

Answer:

its a

Step-by-step explanation:

....

The town's Population in 2025 is estimated to be approximately 5643.

The town's population in 2025, we need to calculate the population growth over the 20-year period from 2005 to 2025.

Given that the population in 2005 was 3800, and it grows at a rate of 2% every year, we can calculate the population for each year using the formula:

Population = Initial Population * (1 + Growth Rate)^Number of Years

Substituting the given values into the formula:

Population in 2025 = 3800 * (1 + 0.02)^20

Calculating this expression:

Population in 2025 = 3800 * (1.02)^20

Using a calculator or software, we can find the population in 2025:

Population in 2025 ≈ 3800 * 1.485947

Population in 2025 ≈ 5643.47

Therefore, the town's population in 2025 is estimated to be approximately 5643.

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Answer:

-232

Step-by-step explanation:

9+12=21

21-219= -198

-198-22= -232

In 1973, one could buy a popcom for $1.25. If adjusted in today's dollar the price of popcorn today will be b. $7.22.

To adjust the price of popcorn from 1973 to today's dollar, we can use the Consumer Price Index (CPI) ratio. The CPI ratio is the ratio of the current CPI to the CPI in 1973.

Given that the CPI in 1973 was 45 and the CPI today is 260, the CPI ratio is:

CPI ratio = CPI today / CPI in 1973

= 260 / 45

= 5.7778 (rounded to four decimal places)

To calculate the adjusted price of popcorn today, we multiply the original price in 1973 by the CPI ratio:

Adjusted price = $1.25 * CPI ratio

= $1.25 * 5.7778

≈ $7.22

Therefore, the price of popcorn today, adjusted for inflation, is approximately $7.22 in today's dollar.

The correct option is b. $7.22.

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Answer:

No it is not a collection of well defined and distinct objects

Hope this helps <3

The standard deviation is a useful tool in understanding the spread of data and making inferences about the population mean based on sample means.

The standard deviation is a measure of how spread out the data is from the mean.

In this case, the mean recycled material collected per household in other local authorities is 40kg with a standard deviation of 15kg.

In part a, the probability of a randomly selected household recycling less than 30kg in a given week is calculated. In part b, the probability of the sample mean recycled material collected in a given week being less than 30kg for a sample of 100 households is calculated.

In part c, it is explained that finding a sample mean of 30kg for 100 households on a single street does not necessarily mean that the recycling scheme of local authority A is not working.

Finally, in part d, a 95% confidence interval for the mean amount of recycled material per household in local authority A is constructed after an advertising campaign.

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Answer:

JL = 32

Step-by-step explanation:

We are told in the above question that:

In triangle △JKL, ∠JKL is right angle, and KM is an altitude. JK=24 and JM=18, find JL.

From the attached diagram, we can see that

JL : JK = JK: JM

Therefore,

JL/ JK = JK /JM

Where JL = Unknown

JK = 24

JM = 18

JL/ 24 = 24/18

Cross Multiply

24 × 24 = JL × 18

Divide both sides by 18

JL = (24 × 24) /18

JL = 576/18

JL = 32

The statement "confidence intervals are useful when trying to estimate unknown statistics" id True.

Confidence intervals are valuable tools for estimating unknown statistics. When dealing with limited data, it is often impossible to determine the true value of a population parameter with absolute certainty. Confidence intervals provide a range of plausible values within which the true parameter is likely to fall.

A confidence interval consists of two components: a point estimate and a margin of error. The point estimate is the best guess of the parameter's value based on the available data, while the margin of error reflects the uncertainty associated with the estimate. By specifying a confidence level, typically expressed as a percentage (e.g., 95% confidence interval), we can quantify the level of confidence we have in capturing the true parameter within the interval.

Confidence intervals allow researchers and decision-makers to make informed conclusions about population parameters while acknowledging the inherent uncertainty. They provide a range of plausible values, taking into account sampling variability and the variability of the data. Confidence intervals also facilitate hypothesis testing, as they help determine whether a hypothesized value falls within the interval.

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Answer:

13.75 foot

- - - - - - - -

Use Pythagoras theorem where hypotenuse is 15 feet and base is 6 feet.

- - - - - - - -

Let the length of building be h.

a² + b² = c²

h² + 6² = 15²

h² + 36 = 225

h² = 225 - 36

h² =  189

h = √189

h = 3√21

h ≈ 13.75 foot

Answer:

\(\rm 3\sqrt{21}\approx 13.75\:\:ft\:\:(nearest\:hundredth)\)

Step-by-step explanation:

The given scenario can be modeled as a right triangle, where the distance from the foot of the ladder to the base of the building is the base of the triangle, and the ladder is the hypotenuse of the triangle.

To find the height of the building, and therefore the height of the triangle, use Pythagoras Theorem.

Pythagoras Theorem

\(\rm a^2+b^2=c^2\)

where:

Given:

Substitute the given values into the formula and solve for a:

\(\implies \rm a^2+6^2=15^2\)

\(\implies \rm a^2+36=225\)

\(\implies \rm a^2+36-36=225-36\)

\(\implies \rm a^2=189\)

\(\implies \rm \sqrt{a^2}=\sqrt{189}\)

\(\implies \rm a=\sqrt{9 \cdot 21}\)

\(\implies \rm a=\sqrt{9}\sqrt{21}\)

\(\implies \rm a=3\sqrt{21}\)

\(\implies \rm a \approx 13.75\:\:ft\:\:(nearest\:hundredth)\)

Therefore, the height of the building is 13.75 ft  (nearest hundredth).

Answer:

\(-1\frac{7}{9}\)

Step-by-step explanation:

Rewriting our equation with parts separated

\(2+\frac{8}{9} -4+\frac{2}{3}\)

Solving the whole number parts

\(2-4=-2\)

Solving the fraction parts

\(\frac{8}{9} -\frac{2}{3} =?\)

Find the LCD of 8/9 and 2/3 and rewrite to solve with the equivalent fractions.

LCD = 9

\(\frac{8}{9} -\frac{6}{9} =\frac{2}{9}\)

Combining the whole and fraction parts

\(-2+\frac{2}{9} =-1\frac{7}{9}\)

Hence, -1 7/9 is the correct Answer.

[RevyBreeze]

Answer:

(f-g)(x)=4x^2+1-x^2+5

=3x^2+6

=3(x^2+2)

We are given that:

Circumference = 19.4 cm

Formula:

2πr = Circumference

Rewrite the equation:

The "r" variable represents the radius of the circle. Thus, we need to isolate it on one side to determine the radius. This can be done with the four mathematical operations (+  -  ×  ÷). Since the "÷" is included, we can divide both sides by 2π to isolate the "r" variable.

Divide both sides by 2π:

Substitute the radius as 22/7:

There are 2 common factors of 9 and 24, that are 1 and 3. Therefore, the greatest common factor of 9 and 24 is 3.

In mathematics, the greatest common divisor of two or more nonzero integers is the largest positive integer that divides each integer

. The greatest common divisor (GCF) of a set of numbers is the greatest factor of division of all numbers.

GCF by listing factor method :-

Factors of 9: 1, 3, 9

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

There are 2 common factors of 9 and 24, that are 1 and 3. Therefore, the greatest common factor of 9 and 24 is 3.

other two methods are attached below .

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A random sampling method could be used to find the percentage of students in your grade who eat five servings of fruit and vegetables each day.

This method involves selecting a random sample of students from the entire population of your grade and surveying them about their eating habits.

In other word, its involves randomly selecting a subset of students from the entire grade population and collecting data on their eating habits. By selecting students at random, the sample is more likely to be representative of the entire grade. This cam provide accurate insights into the percentage of students meeting the desired dietary recommendation.

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The farmer walks a total of 68 + 51 = 119 yards but the actual distance that the farmer walks is 85 yards.

However, since she walks diagonally across the field, the actual distance is much shorter. To find the actual distance, we can use the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. If we call the diagonal distance d, then d^2 = 51^2 + 68^2. Simplifying, we get

d^2 = 2601 + 4624 = 7225, so d = sqrt(7225) = 85 yards.

This is the actual distance that the farmer walks, so the answer is 85 yards.

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A farmer has just tilled her 51-yard by 68-yard field. To survey her field, the farmer begins in one corner and walks the length of the field. She then turns and walks the width before crossing diagonally across the field to the original corner. How far does the farmer walk?

Answer:

B

Step-by-step explanation:

We have to look at the full dot

(i) When testing whether girls who attended girls-only high schools do better in math, it is important to control for various factors that could potentially influence math scores.

Some factors to consider are:

(ii) The equation relating the math score (score) to girlhs (dummy variable indicating girls-only high school attendance) and other factors can be written as:

score = β0 + β1 * girlhs + β2 * socioeconomic status + β3 * prior academic performance + β4 * school quality + β5 * peer effects + β6 * teacher quality + β7 * access to resources + ε

This equation represents the structural relationship between the math score and the factors being controlled for. The coefficients β1, β2, β3, β4, β5, β6, and β7 represent the respective effects of girlhs and the other factors on the math score.

(iii) Parental support and motivation, which are unmeasured factors, may be correlated with girlhs. This is because parents who choose to send their daughters to girls-only high schools might have certain preferences or beliefs regarding education, which could include providing higher levels of support and motivation. However, without directly measuring parental support and motivation, it is difficult to establish a definitive correlation.

(iv) To ensure that numghs (the number of girls-only high schools within a 20-mile radius of a girl's home) is a valid instrumental variable (IV) for girlhs, certain assumptions are needed:

(v) If the coefficient estimate on the chosen IV numghs is negative and statistically significant in the reduced form estimation, it suggests a strong relationship between the instrumental variable and the attendance at girls-only high schools. This provides some confidence in the validity of the IV. However, the decision to proceed with IV estimation should also consider other factors such as the strength of the instruments, the overall model fit, and the robustness of the results to alternative specifications.

It is important to carefully evaluate the assumptions and limitations of the IV estimation approach before drawing conclusions in math.

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