A group of students was asked about the number of flights they have taken. The data is shown in the line plot.



Which of the following best describes the spread of the data? Explain its meaning in this situation.


A. The data has a range of 5, which is a wide spread. This means the greatest number of flights was 5.


B. The data has a range of 15, which is a narrow spread. This means that there is not a large difference in the number of flights taken by the students.


C. The data has a range of 5, which is a narrow spread. This means that most of the students have taken a similar number of flights.


D. The data has a range of 15, which is a wide spread. This means that there is a difference of 15 flights between each of the students.

The probability that it takes Jeremiah more than 6 attempts to make his first three-point shot is approximately 0.0479.

The probability that Jeremiah makes a three-point shot is p = 0.25, which means that the probability he misses a shot is q = 1 - p = 0.75.

Let's consider the probability that it takes Jeremiah more than 6 attempts to make his first shot.

This means he must miss the first 6 shots, and make the 7th shot. The probability that he misses a single shot is q = 0.75, so the probability that he misses the first 6 shots is:

P(missing first 6 shots) = q × q × q × q × q × q = (0.75)^6

The probability that he makes the 7th shot is p = 0.25. Therefore, the probability that it takes Jeremiah more than 6 attempts to make his first shot is:

P(MMM > 6) = P(missing first 6 shots) × P(making 7th shot) = (0.75)^6 × 0.25 = 0.0479 (rounded to four decimal places).

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Answer:

5/2

Step-by-step explanation:

[tex]\left[\begin{array}{cccc}-6&-5&-2&-3\\6&5&-1&-3\\4&10&-12&-8\end{array}\right][/tex] is matrix obtained by multiplying row 3 by 2

[tex]\left[\begin{array}{cccc}2&5&-6&-4\\6&5&-1&-3\\6&-5&-2&-3\end{array}\right][/tex] is obtained by interchanging  row 3 and row 1

The given augmented matrix is [tex]\left[\begin{array}{cccc}-6&-5&-2&-3\\6&5&-1&-3\\2&5&-6&-4\end{array}\right][/tex]

The first row operation is given that multiply row 3 by 2

[tex]\left[\begin{array}{cccc}-6&-5&-2&-3\\6&5&-1&-3\\2(2)&5(2)&-6(2)&-4(2)\end{array}\right][/tex]

[tex]\left[\begin{array}{cccc}-6&-5&-2&-3\\6&5&-1&-3\\4&10&-12&-8\end{array}\right][/tex]

Now let us find the matrix by interchanging row 3 and row 1

[tex]\left[\begin{array}{cccc}2&5&-6&-4\\6&5&-1&-3\\6&-5&-2&-3\end{array}\right][/tex]

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In agreement, there is no correlation between the values of the graph because there is no constant that determines the relationship between the average of points and the percentage of failures of three points.

Based on the information in the graph, we can infer that there is no correlation between the values in the graph, since neither influences the other (does not modify it). Due to the above, we can establish that the values have no correlation because they are independent and do not depend on each other.

In this case, we can see that the percentage of 35% is in two values: one below 19 and one above 19. This means that there is no correlation because if there were, the values would have an obvious trend.

To conclude we can say that there is no correlation between these values because there is no a constant relationship that determines the location of the points in the graph.

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Answer:

Sure, here are the steps on how to simplify 2/3 (3x -2) – ¾ (2x -2):

Multiply the factors in the numerator and denominator of each fraction.

2/3 (3x -2) = (2)(3x -2) / (3)(3) = 6x - 4 / 9

¾ (2x -2) = (3/4)(2x -2) / (3) = 3x - 6 / 12

Subtract the numerators of the two expressions.

6x - 4 / 9 - 3x - 6 / 12 = (6x - 4 - 3x - 6) / (9 * 12) = 3x - 10 / 108

Simplify the fraction by dividing the numerator and denominator by 3.

3x - 10 / 108 = (3x - 10) / (3 * 36) = x - 10 / 36

Therefore, the simplified expression is x - 10 / 36.

Step-by-step explanation:

a) The interval in which the height is increasing is given as follows: (0,2).

b) The interval in which the height is decreasing is given as follows: (4,10), .

c) The interval in which the height is constant is given as follows: (2,4), (10, ∞).

d) The height at 14 seconds is of zero, as when the balloon hits the ground, it does not fly anymore.

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Answer:

The answer is 2000

Step-by-step explanation:

The 2 means hundred and the two zeroes mean tens and ones if he added a zero at the end it would be 2000 making the 2 to be a thousand which is the correct answer.

Hello;

4 x 500 = 500 + 500 + 500 + 500 = 1000 + 1000 = 2000

you want 1000 => 2000/2 = 1000

(4 x 500)/2 = 2 x 500 = 500 + 500 = 1000

not 4 x 500 but 2 x 500

If 11 rain jackets were collected. At the end of the the drive, 10 times that number of rain jackets were collected. The number of rain jackets that  were sold is 99.

We must determine the total number of rain jackets gathered at the end of the campaign in order to determine how many were sold.

10 times the original quantity of raincoats gathered is:

= 10 * 11

= 110

So, 110 rain jackets were collected.

Number of raincoats sold:

= 110 - 11

= 99

Therefore 99 rain jackets were sold.

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Answer:

around 3.3 cm

Step-by-step explanation:

The volume of the rectangular prism cake pan can be calculated by multiplying its length, width, and depth:

V = l × w × d

Substituting the given values, we get:

V = 20 cm × 28 cm × d

V = 560d cm³

We are also given that the amount of batter put into the pan is 1848 cm³. So we can set up the following equation:

1848 cm³ = 560d cm³

Solving for d, we get:

d = 1848 cm³ ÷ 560 cm²

d ≈ 3.3 cm

Therefore, the cake batter is about 3.3 cm deep.

The amount at which the cards offer the same deal over the course of a year is a $2,333.33

Since credit card finance charge is the fee associated with using credit.

Credit card issuers use the finance charges to minimize non-payment risks and earn some profits for extending credit to cardholders.

Data and Calculations:

                  Card A         Credit B

APR              20.8%               24.6%

Annual fee  $60                   $0

To calculate the balance required, the required equation is

= 22%x + $40 = 24.6%x

Where x = required balance

Thus,

= 0.208x + $60 = 0.246x

= $60 = 0.03x (0.246x- 0.208x )

= 0.03x = $60

x = $60 /0.03

x = $2,333.33

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ŷ= 6.45x + 31.5 is the equation of the regression line for the given data

Here, we have,

to find the equation of the regression line for a given data:

Construct the table of the data as follows:

x    >>>>     y  >>>>  x²  >>>>  y²  >>>>   xy

1                39            1            1521         39

2               45            4           2025       90

3               52             9          2704       156

4               49            16          2401        196

5               61             25         4096       305

5               72            25          5184        360

................................................................................................

20             318           80          17931       1146

.................................................................................................

∑x = 20,  ∑y = 318, ∑x²= 80, ∑xy = 1146,  n = 6 (number data points)

The linear regression equation is of the form:

ŷ = ax + b

where a and b are the slope and y-intercept respectively

a = ( n∑xy -(∑x)(∑y) ) / ( n∑x² - (∑x)² )

a = (6×1146 - 20×318) / ( 6×80-20² )

a = 6876-6360 / 480-400

a = 516 / 80

a = 6.45

x' =  ∑x/n

x' = 20/6 = 10/3

y' = ∑y/n

y' = 318/6 = 53

b = y' - ax'

b = 53 - 6.45×(10/3)

b = 53 - 21.5

b = 31.5

ŷ = ax + b

ŷ= 6.45x + 31.5

Thus,  the equation of the regression line for the given data is

ŷ= 6.45x + 31.5.

(a) x=3 hours

ŷ= 6.45(3) + 31.5 = 50.85

(b) x=4.5 hours

ŷ= 6.45(4.5) + 31.5 = 60.525

(c) x=13 hours

ŷ= 6.45(13) + 31.5 = 115.35

(d) x=1.5 hours

ŷ= 6.45(1.5) + 31.5 = 41.175

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complete question:

Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line.(The pair of variables have a significant correlation.) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The number of hours 6 students spent for a test and their scores on that test are shown below.

(a) x=3 hours

(b) x=4.5 hours

(c) x=13 hours

(d) x=1.5 hours

The graph of the function f(x) =[x+3] is a linear graph and it is represented on the last graph of the attached image.

A linear equation can be written in the form:

y = mx + c

where:

y = dependent variable (usually on the vertical axis).

x = independent variable (usually on the horizontal axis).

m = slope of the line, which determines its steepness.

c = y-intercept, which is the point where the line crosses the y-axis.

From our question,

f(x) =[x+3]

y = f(x)

m = 1

c = 3

To plot our graph, we use the range of values of x which are:

x = 0, -1, -2, -3

By substituting the value of x into the equation we have the equivalent y values;

f(0) = [0 + 3] = 3

f(-1) = [-1 + 3] = 2

f(-2) = [-2 + 3] = 1

f(-3) = [-3 + 3] = 0

Plotting x against y will give us the graph attached.

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The total number of beads in the two boxes: is: 20

The parameters given are:

Number of white beads in box A = 7

Number of black beads in box A = x - 7

Number of white beads in box B = 4

Number of black beads in box B = x - 4

The probability of getting white from both boxes is:

P(W & W) = (7/x) * (4 + 1)/(x + 1)

P(W & W) = 35/(x(x + 1)

We are given that P(W & W) = 7/22

Thus:

35/(x(x + 1) = 7/22

Solving gives x = 10

Thus:

Box A has 10 beads and box B has 10 beads.

Total number of beads = 20 beads

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The SUV is the more cost-effective choice for the trip than Sedan

To determine which vehicle is the more cost-effective choice for the trip, Belle needs to consider both the rental cost and the fuel cost for each option.

Let's assume the trip is a round-trip of 500 miles.

For the sedan:

Rental cost: $180

Fuel cost: 500 miles x $0.11/mile = $55

Total cost: $180 + $55 = $235

For the SUV:

Rental cost: $200

Fuel cost: 500 miles x $0.06/mile = $30

Total cost: $200 + $30 = $230

Based on these calculations, the SUV is the more cost-effective choice for the trip.

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Answer:

400

Step-by-step explanation:

The measure of the unknown sides is equivalent to 12.6

The given figure is a circle geometry with the perpendicular lines intersecting both segments of the circle.

We need to determine the measure of x. Since the measure of the perpendicular lines are equal, hence the measure of the line of the segments will also be equal.

Hence:

x = 6.3 + 6.3

x = 12.6

Therefore the measure of x from the given diagram is equivalent to 12.6

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After considering the given set of options we conclude that a large sample was used in the evaluation, which means the correct option is Option A.

1/2 is the evaluated expected probability for the given case under the condition that when the die was rolled an even number came out with face number 1 out of 6.

In the event that the cube was rolled 20 times, an even number came up 15 times, or 3/4 of the time. Now the same cube was again rolled 100 times, an even number came up on the recent throw which showed 51 times even, or almost 1/2 the time.

Therefore we can say that the actual results are closer to the expected probability of 1/2 when rolling the cube 100 times because a larger sample size was used.
Hence we are dealing with  larger  sample size, this means that the actual results will be much closer to the expected probability.
This is due to the law of large numbers which states that as the sample size increases, the average of the results will get closer and closer to the expected value .
Therefore, option (a) is correct.
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Answer:

Step-by-step explanation:

start by listing the prime numbers which are {2,3,5,7,11,13...}

now we need to find the divisibility test of 819 it can't be divisible by 2 so we shall go for 3 let check

divisible by 3

a number is divisible by 3 if when the digits are added it gives a number which is a multiple of 3

check divisible by 3

819=8+1+9=18

18÷3=6

18 is divisible by 3

now divide 819 by 3 getting 273

273=2+7+3=12

12 is divisible by 3

273÷3=91

91 is not divisible by 3 so we try the other numbers 5

a number is divisible by 5 if only the last digit is a 0 or 5

and 91 doesn't end with 0 or 5 so it is not divisible by 5

divisible by 7

a number is divisible by seven only when u remove the last digit, double it then subtract it from the remaining number and get a multiple of 7

the best way of finding the divisibility of seven is by long division

91÷7=13

we have 13 and 13 is a prime number

13÷13=1

now let's multiply the factors

3×3×7×13=819

therefore the factors are {3²,7,13}

To find the prime factorization of 819, we divide by prime numbers until we can no longer divide. The prime factorization of 819 is 3 x 3 x 7 x 13.

To find the prime factorization of 819, we need to determine the prime numbers that multiply together to give 819. We start by dividing 819 by the smallest prime number, which is 2. Since 819 is an odd number, it is not divisible by 2. So, we move on to the next prime number, which is 3. 819 divided by 3 gives us 273.

Next, we continue dividing 273 by prime numbers until we can no longer divide. Dividing 273 by 3 again gives us 91. Continuing this process, we divide 91 by 7 to get 13. Since 13 is a prime number, we cannot further divide it.

Therefore, the prime factorization of 819 is 3 x 3 x 7 x 13.

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A total of 7 33 inches of rain fell over the course of 11 hours

The rate of rain on thursday was two inches every three hours which means it rained 2/3 inches per hour

After 11 hours of consistent rain the total amount of rain that fell can be calculated by multiplying the rate of rain per hour by the number of hours

total amount of rain  = 2/3 inches hour x 11 hours

total amount of rain = 22/3 inches

total amount of rain = 7 33 inches )rounded to the nearest hundredth)

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The computation of the interest and the maturity value of the loan, using ordinary interest, is as follows:

Interest = $54.30

Maturity value = $1,404.30.

The ordinary interest method is based on the use of 360 days as the ordinary days in a calendar year.

The ordinary interest contrasts with the exact interest, which uses 365 days or the normal calendar days.

Principal = $1,350

Interest rate = 8%

Date borrowed = July 21

Date repaid = January 18

The number of days between July 21 and January 18 = 181 days

Total Interest = Principal x Rate x Time

= $54.30 ($1,350 x 8% x 181/360)

Maturity value = Principal + Total Interest

= $1,404.30 [$1,350 + ($1,350 x 8% x 181/360)]

Thus, based on the ordinary interest method, the maturity value of the loan is $1,404.30.

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Answer:

i think its

x^2 + (y + 2)^2 = 21.

Step-by-step explanation:

According to van Hiele's levels of geometric thought, the Intermediate Phase corresponds to level 3, which is called the Informal Deduction stage.

The learner appears to be at level 3, known as the "Informal Deduction" stage. This is evident from their ability to use geometric properties in their reasoning.

At this phase, students start employing logical thinking to understand the connections and characteristics of geometry, using informal explanations and visual aids. Their ability to draw conclusions from particular instances is evident, though they may face difficulties when attempting to extrapolate their findings to broader contexts.

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Answer:

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

Let the number be n.

Twice the difference of a number and 9 is 3, set up an equation:

Hence the number is 10.5.

Answer: 57 cm²

Step-by-step explanation:

To answer this question, we need to find the surface area of the figure.

First, we will find the surface area of the bottom part, the rectangular prism. We will use the given formula. However, we do not count the top side since it is connected to the bottom part. We will subtract this.

       SA = 2(wl + hl + hw)

       SA = 2((3 cm)(3 cm) + (2 cm)(3 cm) + (2 cm)(3 cm))

       SA = 42 cm²

       SA = 42 cm² - 9 cm² = 33 cm²

Next, we will find the surface area of the top part, the square pyramid. We know we have four congruent triangles. We will not count the square base since it is connected to the bottom part.

       SA = 4 * ([tex]\frac{bh}{2}[/tex])

       SA = 2 * (bh)

       SA = 2 * ((3 cm)(4 cm))

       SA = 2 * (12 cm²)

       SA = 24 cm²

Lastly, we will add these two parts together.

        33 cm² + 24 cm² = 57 cm²

The greatest common factor of the polynomial 2x³ - 10 is 2.

By extracting the greatest common factor, we obtain:

= 2(x³/2 - 5)

Therefore, the factored form of the polynomial is 2(x³/2 - 5).

Thus, the greatest common factor of the polynomial 2x³ - 10 is 2.

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It is likely that the contractor's true, on-time completion rate is still around 90%.

Based on the provided dot plot and the sample of last month's on-time completions, the conclusion that can be drawn is:

The dot plot does not provide convincing evidence that the contractor's true, on-time completion rate is less than 90% because 7 or fewer on-time completions happened 19% of the time in the simulation.

This means that the observed 7 out of 10 jobs completed on time in the last month is not significantly different from what would be expected based on the assumption of a 90% completion rate.

Therefore, it is likely that the contractor's true, on-time completion rate is still around 90%.

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Option B, three 2-liter tins, is the most cost-effective choice.

1.7.1: To convert 5 litres to cm³, multiply by 1000 cm³ per litre:

5 litres * 1000 cm³/litre = 5000 cm³.

1.7.2: If 1 litre covers 8m², and you need to paint 14.4m² with three coats: 14.4m² * 3 coats = 43.2m².

Divide by 8m²/litre to find litres needed: 43.2m² / 8m²/litre = 5.4 litres.

To find the most cost-effective combination, consider the options:

A: One 5-liter tin and one 2-litre tin.

B: Three 2-liter tins.

Calculate costs including VAT: A: (1 * 439.99 + 1 * 189) * 1.15 = 723.63, B: (3 * 189) * 1.15 = 651.45.

Option B, three 2-liter tins, is the most cost-effective choice.

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The Complete Question

Paint is sold in different sizes as shown below A B 2 litre tin R189 5 litre tin at 439.99 Prices excludes VAT of 15% 1.7.1 Convert the capacity of a 5-litre tin to its volume in cm³ NOTE: 1 litre 1 000 cm³ 1.7.2

According to a paint specialist one needs at least two coats of pain therefore decided that she will paint three coats just to be sure that covered. Remember that the area that needs to be covered is 14.4 How many litres of paint will be needed if 1 litre of paint covers 8m- Looking at the paint quantity diagram and using your answer in QUI 1.7.2 A make use of different combinations of the tins of paint, ther Prudence of which combination will be the most cost effective. Inclu your calculations. 8,84 cm