In the data set below, what are the lower quartile, the median, and the upper quartile?
1235588
lower quartile =


median = 5



upper quartile =

In given lines, y = -1/4 x + 7 represents a transversal line.

A transversal is a line that, at two different locations, cuts through two lines in the same plane. Various types of angles in pairs, including successive internal angles, corresponding angles, and alternate angles, are produced by a transversal intersection with two lines.      

Here we have

y = 1/6x - 3  ---- (1)    

y = -1/4 x + 7 ---- (2)  

y = 1/6x - 9 ---- (3)        

Here given lines are in y = mx + c form

The slope of the line (1) is 1/6

The slope of the line (2) is -1/4

The slope of the line (3) is 1/6

As we can see that line (1) and line (3) have the same slope,

Hence, Lines (1) and (3) are two parallel lines

where Line (2) is transversal which cuts the given two parallel lines  

Therefore,

In given lines, y = -1/4 x + 7 represents a transversal line.

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The Durbin-Watson test is used to determine if a regression has autocorrelation and can be corrected by adding lagged values of the independent and dependent variables as additional predictors in the regression model, as represented by the formula AR(t) = ρ * AR(t-1).

a. Both cross-section and time-series multiple regressions should be checked for autocorrelation.

b. Autocorrelation is the correlation of a variable with itself over successive time periods. In the context of a regression, it is the correlation between the residuals or errors of a regression model over successive time periods.

c. The Durbin-Watson test is used to determine if a regression has autocorrelation.

d. Autocorrelation can be corrected by adding lagged values of the independent and dependent variables as additional predictors in the regression model. This is known as the autoregressive model. The formula for calculating the autoregressive coefficient is: AR(t) = ρ * AR(t-1), where ρ is the correlation coefficient.

The Durbin-Watson test is used to determine if a regression has autocorrelation and can be corrected by adding lagged values of the independent and dependent variables as additional predictors in the regression model, as represented by the formula AR(t) = ρ * AR(t-1).

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After 1 week of tutoring and babysitting, Jeremy and Mary will have saved the same amount of money ($28).

Let's start by defining some variables:

We can then use this information to set up two equations that represent how much money each person has saved:

J = 20j + 8

M = 18m + 26

We want to know when J and M are equal, so we can set these equations equal to each other:

20j + 8 = 18m + 26

We can simplify this equation by subtracting 8 from both sides:

20j = 18m + 18

Then, we can divide both sides by 2 to simplify the equation further:

10j = 9m + 9

We want to find the smallest values of j and m that make this equation true. We can start by trying j = 1 and then incrementing j until we find a value that makes the right-hand side of the equation (9m + 9) divisible by 10. We can then solve for m and check that the left-hand side of the equation (10j) is equal to the same value.

If we try j = 1, we get:

10(1) = 9m + 9

Simplifying this equation gives us:

m = 1

So, if Jeremy tutors his cousin for 1 week and Mary babysits her sister for 1 week, they will both have the same amount of money saved. We can check this by plugging j = 1 and m = 1 into the original equations for J and M:

J = 20j + 8 = 20(1) + 8 = 28

M = 18m + 26 = 18(1) + 26 = 44

So, after 1 week of tutoring and babysitting, Jeremy and Mary will have saved the same amount of money ($28).

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We need  9 sophomore girls to make sex and class independent when a student is selected at random.

No. of freshman boys     (fb) = 4

No. of freshman girls      (fg) = 6

No. of sophomore boys (sb) = 6

Let, the no. of sophomore girls = sg

The total number of students in the class T = fb + fg + sb +sg

                                                                     T = 4+6+6+sg

                                                                     T = 16 + sg

The probability of selecting a girl is  P(G) = (fg + sg) / T

                                                                    = (6+sg)/(16+sg)

The probability of selecting a sophomore is  P(S) = (sb + sg)/T

                                                                                  = (6+sg)/(16+sg)

As the events are independent, the probability of selecting a sophomore girl is                       P(sg) = P(G)*P(S)

                       sg/(16+sg) = (6+sg)*(6+sg)/(16+sg)(16+sg)

                       sg(16+sg)  = (6+sg)(6+sg)

                       16sg + [tex]sg^{2}[/tex] = 36 + 6sg + 6sg + [tex]sg^{2}[/tex]

                                 4sg = 36

                                   sg = 9

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Approximately one full tablespoon of coffee powder is required for each 200 ml cup of coffee. We advise using seven teaspoons of ground coffee to produce a full litre of filter coffee at once.

To create coffee, coffee beans must first be roasted. Coffee is a dark-colored, bitter, and slightly acidic beverage that stimulates individuals due to its high caffeine content. In terms of sales, hot beverages have the largest market worldwide. The roasted beans are ground into tiny particles, frequently steeped in hot water, and then filtered to create a cup of coffee. Despite the fact that coffee is typically served hot, it is frequently served cold or iced. Unroasted green coffee beans are made by separating the seeds from the fruits of the Coffea plant. To produce a cup of coffee, the roasted beans are ground into tiny particles, regularly soaked in hot water, and then filtered. Coffee is commonly served cold or iced even though it is traditionally served hot.

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Neglecting friction, a similar ride with 12 passengers aboard would take 6 minutes.

The time it takes for a roller coaster ride is directly proportional to the mass of the passengers. If we assume that each passenger has the same mass, then the time it takes for the ride is proportional to the number of passengers.

Let T1 be the time for the ride with 6 passengers, and T2 be the time for the ride with 12 passengers. Then, we have:

T2 = (12/6) * T1

Simplifying this expression, we get:

T2 = 2 * T1

We are given that T1 = 3 minutes, so we can substitute this value into the equation above to find T2:

T2 = 2 * 3 minutes = 6 minutes

Therefore, a similar roller coaster ride with 12 passengers aboard would take 6 minutes, as opposed to the 3 minutes it takes with 6 passengers aboard. The answer is 6 minutes.

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Answer: 25 inches

Step-by-step explanation:

cos60 = adjacent over hypotenuse

cos60 = a/50

50cos60 = 25

The integer 8 represents the amount lost each time the pass was used.

Division is one of the operation in mathematics where number is divided  into equal parts as that of a definite number.

Given that, every time Ezequiel rides the bus, money is deducted from the value of the pass.

He rode 9 times and $72 was deducted from the value of the pass.

Let x be the integer that represents the amount deducted each time.

The amount deducted after 9 times is 9x.

9x = 72

We have to divide 72 into 9 parts to know the value of x.

x = 72 / 9 = 8

Hence Ezequiel lost $8 each time the pass was used.

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Answer:

-1/6

Step-by-step explanation:

To solve the inequality 4x-(6x+1)≤ 8x + 2(x-3), we can simplify both sides of the inequality and isolate x on one side:

4x - (6x + 1) ≤ 8x + 2(x-3)

4x - 6x - 1 ≤ 8x + 2x - 6

-2x - 1 ≤ 10x - 6

Subtract 10x from both sides:

-12x - 1 ≤ -6

Add 12x to both sides:

-1 ≤ 6x

Divide both sides by 6:

-1/6 ≤ x

The solution to the inequality is x ≥ -1/6. This means that x is greater than or equal to -1/6, so any value of x that is greater than or equal to -1/6 will satisfy the inequality.

The probability that the student is from other majors is 0.40, the probability that the student majors only math is 0.13, and the probability that the student does not major engineering is 0.73.

a) Probability of a student being from other majors = (150-90) / 150 = 0.40

b) Probability of a student majoring only math = (30 - 20) / 150 = 0.13

c) Probability of a student not majoring engineering = (150 - 40 - 20) / 150 = 0.73

Probability = Number of Favorable Outcomes / Total Number of Outcomes

For part a)

Number of Favorable Outcomes = 150-90 = 60

Total Number of Outcomes = 150

Therefore, Probability = 60 / 150 = 0.40

For part b)

Number of Favorable Outcomes = 30-20 = 10

Total Number of Outcomes = 150

Therefore, Probability = 10 / 150 = 0.13

For part c)

Number of Favorable Outcomes = 150-40-20 = 90

Total Number of Outcomes = 150

Therefore, Probability = 90 / 150 = 0.73

The probability that the student is from other majors is 0.40, the probability that the student majors only math is 0.13, and the probability that the student does not major engineering is 0.73.

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Answer:

2(fx-2cosx)

Step-by-step explanation:

regroup terms

factor out the common term 2

Answer:

12 minutes

Step-by-step explanation:

To estimate the time for a trip that is 6 miles long, we need to solve for x in the equation y = 0.467x + 0.417, where y represents the distance in miles.

First, we substitute the value of y, which is 6:

6 = 0.467x + 0.417

Next, we subtract 0.417 from both sides:

5.583 = 0.467x

Finally, we divide both sides by 0.467:

x = 12

So, the estimated time for a trip that is 6 miles long is 12 minutes.

The Olap operations for a data warehouse of a train company contains information about train segments is performed in order to answer the queries with dimension hierarchies when needed.

OLAP operation for first case is Filter on the train dimension to select only Alstom trains. Filter on the departure station dimension to select only French or Belgian stations. Filter on the year dimension to select only 2012. Aggregate the number of kilometers measure across the selected dimensions

Dimension hierarchies for this case is Station dimension: Country > City > Station,  Trip dimension: Year > Month > Day > Trip ID.

OLAP operation for the second case is Filter on the departure station and arrival station dimensions to select only trips that cross country borders. Filter on the year dimension to select only 2012. Aggregate the duration measure across the selected dimensions

Dimension hierarchies for this case is Station dimension: Country > City > Station, Trip dimension: Year > Month > Day > Trip ID.

OLAP operation for third case is Filter on the departure station and arrival station dimensions to select only trips that involve Paris. Filter on the month dimension to select only July 2012. Aggregate the number of trips measure across the selected dimensions.

Dimension hierarchies for this case is Station dimension: Country > City > Station, Trip dimension: Year > Month > Day > Trip ID.

OLAP operation for fouth case is Filter on the departure station and arrival station dimensions to select only trips that involve Belgian stations. Filter on the year dimension to select only 2012.Aggregate the duration measure across the selected dimensions. Calculate the average duration of the segments

Dimension hierarchies for this case is Station dimension: Country > City > Station, Trip dimension: Year > Month > Day > Trip ID.

OLAP operation for fifth case is Aggregate the number of passengers measure across all segments of each trip. Divide by the number of segments per trip to get the average number of passengers per segment

Dimension hierarchies for this case is Station dimension: Country > City > Station, Trip dimension: Year > Month > Day > Trip ID.

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Step-by-step explanation:

so, it starts (year 0 after 2000) with 350 foxes.

after 1 year the number had increased by 5%.

that means : 350×1.05

because 5% is represented by 0.05.

5% of 350 is 350×0.05 (= 17.5)

and to add 5% means that this is added to the original 100% (= 1).

100% + 5% = 105%

means

1 + 0.05 = 1.05

so, again, after the first year we have

350×1.05

foxes.

after the second year we have to multiply that by 1.05 again :

350×1.05×1.05

and so on.

so, what we are doing is multiplying the original number of foxes by powers of 1.05 (with the exponent being the number of years after 2000).

f(x) = 350 × (1.05)^x

Answer:

18 and 3/4 rows of radishes

Step-by-step explanation:

6 + 4 + 7 = 17

3/4 + 3/4 + 1/4 = 7/4

7/4  = 1 3/4

17 + 1 3/4 = 18 3/4

Answer: 18 and 3/4 rows of radishes

Since all the fractions have the same denominator,

you can combine 3/4 + 3/4 + 1/4 together into 1 and 3/4

Adding in the numbers 7 + 4+ 6 and the 1 and 3/4 would amount to 18 and 3/4

Let's first assign variables to the numbers given.

We're given:

Plug the second equation into the first one and solve for y:

[tex]x+y=367\\(y+95)+y=367\\2y+95=367\\2y=272\\y=136[/tex]

Therefore, they sold 136 chocolate cones.

They sold 136 chocolate ice cream cones.

Answer:

15

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given,f(x)=3x^2-x+2

now,f(-4)=3(-4)^2-(-4)+

=3(16)+4+2

=48+4+2

=54

So,f(-4) =

Answer:

The solution is 54

Step-by-step explanation:

f(x) = 3x²-x+2

f(-4) = 3(-4)²-(-4)+2

f(-4) = 48+4+2

f(-4) = 52+2

f(-4) = 54

Answer:

0 over 12

Step-by-step explanation:

3/4 is equal to 9/12

so your basically taking 9/12 from 9/12

Answer:
11i√√3

Step-by-step explanation:

Answer: 1/6 of an hour

Step-by-step explanation: multiply the numerator and denominator by 3 of 1/2 and 1/3 to get 3/6 and 2/6. There is 1/6 more

Answer:

C

Step-by-step explanation:

Answer:

$96

Step-by-step explanation:

We know

$22 if it has 11 attendees.

$22 divided 11 = $2 per attendee

So, we know per attendee costs $2

If there are 48 attendees, how much will the picnic cost?

2 x 48 = $96

So, the picnic cost $96.

If random sample yielded these observed scores: 6 12 5 10 6 9 12 20 5 23 10 20 11 28 13 18. The 99% confidence interval for the mean height of both groups combined is approximately (3.92, 20.58) cm.

To calculate the 99% confidence interval for the mean height of both groups combined, we can use the t-distribution, since the sample size is relatively small (less than 30) and the population standard deviation is unknown.

First, we need to calculate the sample mean and sample standard deviation. The sample mean can be calculated by adding up all the observed scores and dividing by the total number of scores. In this case, the sample mean is (6+12+5+10+6+9+12+20+5+23+10+20+11+28+13+18) / 16 = 12.25 cm.

The sample standard deviation can be calculated using the formula:

s = √((∑(x - x')^2) / (n - 1))

where x is each observed score, x' is the sample mean, and n is the sample size. In this case, the sample standard deviation is approximately 7.05 cm.

Next, we need to calculate the t-value for a 99% confidence level, with 15 degrees of freedom (16 - 1). Using a t-table or a statistical software, we can find that the t-value is approximately 2.947.

Finally, we can calculate the confidence interval using the formula:

Confidence interval = sample mean ± (t-value * (sample standard deviation / √(sample size)))

Plugging in the values, we get:

Confidence interval = 12.25 ± (2.947 * (7.05 / √(16))) = 12.25 ± 8.33

In summary, to calculate the 99% confidence interval for the mean height of both groups combined, we can use the t-distribution and the formula for confidence intervals. We need to calculate the sample mean, sample standard deviation, t-value for the desired confidence level, and then plug these values into the formula to get the confidence interval.

This interval represents the range of values within which we can be 99% confident that the true mean height of both groups combined falls.

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Answer:

654

Step-by-step explanation:

An increase of 9% would mean 1.09 times 600 which equals 654

Answer:

Step-by-step explanation:

You want to know the number of points and the number of turns when Tony and his cousin will have the same score. Tony has 12 points and earns 10 points per turn; his cousin has 0 points and earns 14 points per turn.

The attachment shows a table of points and turns. It shows the score will be tied at 42 points after 3 turns.

Tony's points can be described by ...

  p = 12 +10t . . . . . . . . 12 points in addition to 10 per turn

Cousin's points can be described by ...

  p = 0 + 14t . . . . . . . . . 14 points per turn added to the current score of 0

These will be equal when ...

  p = p

  12 +10t = 0 +14t . . . . substitute for p in both cases

  12 = 4t . . . . . . . . . . subtract 10t

  3 = t . . . . . . . . . . divide by 4

  p = 14·3 = 42 . . . . the scores after 3 turns

The mass of the roller coaster is 800.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 8 is an equation.

We have,

PE = 235,200

Height = h = 30 m

Now,

PE = mhg

We use g = 9.8

So,

Substituting the values.

235,200 = m x 30 x 9.8

m = 235200 / (9.8 x 30)

m = 235200 / 294

m = 800

Thus,

The mass of the roller coaster is 800.

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Ahlam needs to give the shopkeeper $15 more to get a balance of $25.

Word problems in Mathematics are mathematical approaches we make use of in our ongoing day to day activities. Algebra leading to word problems usually consist of numbers, variables, and its arithmetic operations.

Ahlam bought goods worth = $90, If she gave the shopkeeper $100, then she will collect $100 - $90 = $10 back.

But if the shopkeeper did not have an exact balance and Ahlam decided to give the shopkeeper $x to get a balance of $25.

Then we can write the expression as:

10 + x = 25

x = 25 - 10

x = 15

Therefore, we can conclude that Ahlam needs to give the shopkeeper $15 more to get a balance of $25.

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