Handling data 7
2
5
a If Mario buys both newspapers, find the probability that both papers review his
performance.
b If Clarissa buys both newspapers, find the probability that only one paper reviews
her performance.
© Mario buys one of the newspapers at random. What is the probability that it has
reviewed both performances?
4 >

The ordered numbers in this problem are given as follows:

-|-12|, -7, -|5|, -|-4|, |-12|, |-21|

The absolute value function is defined by the following piecewise rule, depending on the input of the function:

It measures the distance of a point x to the origin, hence, for example, |-2| = |2| = 2.

Then the numbers for this problem have their actual value given as follows:

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Answer:

Step-by-step explanation:

Distance traveled by both the planes in 6hrs=10458

let x, x+61 be the speeds of both the planes

Distance traveled = speed*time

10458=(x*6) + [(x+61)*6}

10458=6x+(6x+366)

12x=10092

x=841

Answer:

one plane's rate = 841km/h. other plane's rate = 902km/h

Step-by-step explanation:

Let's say one plane goes to the left and the other to the right.

call the planes L and R, respectively.

L travels at x km/h. R travels at (x + 61)km/h.

after 6 hours, L has travelled 6xkm. R has travelled 6(x + 61)

= (6x + 366)km.

they are 10458 km apart.

so, 6x + 6x + 366 = 10458

12x = 10092

x = 841.

plane L travels at rate of 841 km/h.

plane R travels at rate of 841 + 61 = 902 km/h.

Answer:

Step-by-step explanation:

zeros are the points where curve cuts x-axis

The letters of English alphabet that have parallel lines and intersecting lines and perpendicular lines are: E, F, H, I, L, and T

Parallel lines are demonstrated as the lines that are at the same distance apart from each other. These lines never intersect or meet each other in a plane.

In English alphabet, the letters E, F, H, I, M, N, W, Z are examples of parallel lines.

Intersecting lines are elucidated as the lines that cross or intersect each other at a common point in a plane. Letter X correctly exemplifies this sharing of a common point.

Perpendicular lines are described as the lines which meet or intersect each other at an angle of 90 degrees. The letters E, F, H, I, L, and T demonstrate this intersection.

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The set of points related to an exponential function and matched with set of translated points are, respectively:

(x, y) = (- 1, 0.5) → (x', y') = (2, - 1.5)

(x, y) = (0, 1) → (x', y') = (3, - 1)

(x, y) = (2, 4) → (x', y') = (5, 2)

(x, y) = (3, 8) → (x', y') = (6, 6)

(x, y) = (1, 2) → (x', y') = (4, 0)

(x, y) = (- 2, 0.25) → (x', y') = (1, - 1.75)

According to statemente, we find the case of set of points related to an exponential function and a set of translated points, after a quick inspection we derive the transformation rule:

Horizontal translation: 3 units right, vertical translation: 2 units down.

Now we check the statement on each ordered pair:

(x, y) = (- 1, 0.5):

(x', y') = (- 1, 0.5) + (3, - 2) = (2, - 1.5)

(x, y) = (0, 1):

(x', y') = (0, 1) + (3, - 2) = (3, - 1)

(x, y) = (2, 4):

(x', y') = (2, 4) + (3, - 2) = (5, 2)

(x, y) = (3, 8):

(x', y') = (3, 8) + (3, - 2) = (6, 6)

(x, y) = (1, 2):

(x', y') = (1, 2) + (3, - 2) = (4, 0)

(x, y) = (- 2, 0.25):

(x', y') = (- 2, 0.25) + (3, - 2) = (1, - 1.75)

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Answer:

9 because 18 divided by 2 is 9

The answers are 1) 7/6, 2) 11/15, 3) 11/12 and 4) 3/5.

Given are fractions we need to operate them as mentioned.

1) 1/2 + 2/3 =

To add fractions with different denominators, you need to find a common denominator.

In this case, the common denominator is 6 because both 2 and 3 divide evenly into 6.

Let's convert both fractions to have a denominator of 6:

1/2 = (1/2) x (3/3) = 3/6

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

Now that both fractions have a common denominator, you can add them:

3/6 + 4/6 = 7/6

So, 1/2 + 2/3 = 7/6.

Similarly,

2) 9/10 - 1/6 =

Let's convert both fractions to have a denominator of 30:

9/10 = (9/10) x (3/3) = 27/30

1/6 = (1/6) x (5/5) = 5/30

Now we can subtract the fractions:

27/30 - 5/30 = (27 - 5)/30 = 22/30 = 11/15

3) 3/4 + 3/18 =

Let's convert both fractions to have a denominator of 36:

Now that both fractions have the same denominator, we can add them together:

(3/4) x (9/9) = 27/36

(3/18) x (2/2) = 6/36

27/36 + 6/36 = 33/36 = 11/12

4) 3/4 - 3/20 =

LCM of 4 and 20 is 20. We can convert both fractions to have a denominator of 20:

3/4 = (3/4) x (5/5) = 15/20

3/20 remains as it is.

Now, we can subtract the two fractions:

15/20 - 3/20 = (15 - 3) / 20 = 12/20 = 3/5

Hence the answers are 1) 7/6, 2) 11/15, 3) 11/12 and 4) 3/5.

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Answer:

The ratios are given in the explanation for both part a and b

Step-by-step explanation:

we take the two part to part ratios as blue/white and white/blue

and the part to whole ratio as blue/whole and white/whole

we take 1 box as 1 (look below for clarity)

a.

blue/white = 5 boxes/4 boxes

white/blue = 4 boxes/5 boxes

(we omit the word "boxes" from now on)

blue/whole = 5/9

white/whole = 4/9

b.

blue/white = 8/7

white/blue = 7/8

blue/whole = 8/15

white/whole = 7/15

The value of function at x= -4 is f(-4) = -24.

We have the function,

f(x) = 3x² - 6x

Now, to find f(-4), we substitute -4 for x in the given function f(x) = -3x² - 6x:

f(-4) = -3(-4)² - 6(-4)

= -3(16) + 24

= -48 + 24

= -24

Therefore, the value of function at x= -4 is f(-4) = -24.

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Answer:

2

Step-by-step explanation:

To find the width of the path surrounding the rectangular pool, we can start by calculating the area of the rectangular plot and the area of the pool.

Given:

Dimensions of the rectangular plot: 12m by 10m

Step 1: Calculate the area of the rectangular plot

Area of the plot = length × width

Area of the plot = 12m × 10m = 120m²

Step 2: Calculate the area of the pool

Let's assume the width of the path surrounding the pool is denoted by "x."

The dimensions of the pool will be smaller than the plot by twice the width of the path.

Length of the pool = 12m - 2x

Width of the pool = 10m - 2x

Area of the pool = (length of pool) × (width of pool)

Area of the pool = (12m - 2x) × (10m - 2x)

Given that the area of the pool is 2/3 of the area of the plot, we can set up the equation:

(12m - 2x) × (10m - 2x) = (2/3) × 120m²

Step 3: Solve the equation for x

Expand the equation and simplify:

(120m - 24xm - 20xm + 4x²) = (2/3) × 120m²

120m - 44xm + 4x² = (2/3) × 120m²

Multiply both sides by 3 to remove the fraction:

360m - 132xm + 12x² = 240m²

Rearrange the equation to get it in the standard form of a quadratic equation:

12x² - 132xm + (240m² - 360m) = 0

Simplify further:

12x² - 132xm + 120m(2m - 3) = 0

Now, we can solve this quadratic equation for x using factoring, completing the square, or the quadratic formula. However, it seems that there might be an error in the problem statement or calculation because there is a missing value for the length "m" in the given information.

Please double-check the given dimensions or provide any missing information so that I can assist you further in finding the width of the path surrounding the pool.

The coordinates of point A are,

A = (-24, -4).

Now, For the coordinates of point A, we use the fact that

⇒ vector AB + vector BC = vector AC.

So, We get;

AB + BC = (20, 10) + (16, -14)

             = (36, -4)

Now, we know that vector AC is equal to (36, -4)

since vector BC points from B to C.

We also know that point C has coordinates (12, -8).

So, to find the coordinates of point A, we can use the formula:

A = C - AC

Substituting in the values we have:

A = (12, -8) - (36, -4) = (-24, -4)

Therefore, the coordinates of point A are (-24, -4).

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Answer: 1/4

Step-by-step explanation:

Rate of change is same as slope

Rate of change = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

Rate of change = [tex]\frac{10-9}{6-2}[/tex]

Rate of change = [tex]\frac{1}{4}[/tex]

Volume of Cylinder B is,

⇒ V = 2.67π

We have to given that;

Two cylinders A nd B are shown in figure.

Here, In cylinder A;

Diameter = 4 cm

Volume of cylinder = 24π

Since, Volume of cylinder is,

V = πr²h

For cylinder A;

⇒ 24π = π (2²) × h

⇒ 24 / 4 = h

⇒ h = 6

Since, Cylinder A and B are similar.

Here, Height of B = 2 cm

And, Height of A = 6 cm

So, Scale factor is,

⇒ 6 / 2

⇒ 3

Hence, Radius of B  = 2/3

So, Volume of Cylinder B is,

⇒ V = π × (2/3)² × 2

⇒ V = 2.67π

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The probability of selecting a matching donut on the second try is 7/23.There is a 10.14% chance of selecting two ​-filled donuts in a row from Elizabeth's box of two dozen donuts.

To find the probability of selecting two ​-filled donuts in a row, we first need to determine the total number of donut combinations.

Since there are three different fillings, there are three possible outcomes for the first donut and three possible outcomes for the second donut. Therefore, the total number of combinations is 3 x 3 = 9.

Next, we need to determine the number of combinations where both donuts are filled. There are 24 donuts in the box, and eight of them are jelly-filled, eight are lemon-filled, and eight are custard-filled.

So, the probability of selecting a filled donut on the first try is 8/24, or 1/3. Once the first donut is eaten, there are only 23 donuts left, and seven of them are filled with the same type of filling as the first donut.

To find the probability of selecting two ​-filled donuts in a row, we multiply the probabilities of each event. So, the probability of selecting two matching ​-filled donuts in a row is (1/3) x (7/23) = 7/69, or approximately 0.1014.

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The length of arc ADC is 29.33 units.

Let us take the measure of angle ADC to be 60 degrees.

We know that,

the angle formed by an arc on the center of a circle is twice the magnitude of the angle formed by the same arc on the circumference of the circle.

Now, arc AC forms angle ABC at the center and angle ADC at the circumference.

∴ angle ABC = 2 × angle ADC

                     = 2 × 60 degrees

                     = 120 degrees

Or, the magnitude of reflex angle ABC = 360 - 120 degrees.

                                                                 = 240 degrees.

Also, the circumference of the circle = 2πr

                                                       = 2 × 22/7 × 7

                                                       = 44 units.

∴ the length of arc ADC = magnitude of reflex angle ADC/total angle × circumference

                                         = 240/360 × 44

                                         = 29.33 units.

Hence, the length of arc ADC is 29.33 units.

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The complete question is:

Use the image of circle B to answer the question. Choose a measure for angel ADC. Use your choice for angle ADC to determine the measure of arc ADC. The radius of the circle is 7 units.

If Darryl uses small unit cubes to make a big cube that is 3 units high, he would need 27 small cubes to complete the task.

Darryl is using small unit cubes to make a big cube that is 3 units high. To complete the big cube, Darryl would need to determine the total number of small unit cubes required.

A cube is a three-dimensional figure that has six faces, eight vertices, and twelve edges of equal length. The small cubes are placed one on top of the other, in layers, to create a larger cube.

Therefore, if the big cube is 3 units high, there will be three layers of small cubes in the vertical direction, each with the same dimensions as the base.

The base of the cube would be a square, and each side would have three small cubes lined up next to each other.

So, the base of the cube would have dimensions of 3 units by 3 units. To fill one layer of the cube, Darryl would need 3 x 3 x 1 = 9 small cubes.

Since there are three layers in total, Darryl would need 9 x 3 = 27 small cubes to complete the big cube.

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Answer:

x = 110°

y = 110°

z = 70°

Explanation:

A rhombus' interior angles (the ones we're looking for) always equal to 360°.

A rhombus also has the same degree as the side opposite of it, so since z is the opposite side of the current 70°, we also know that z is equal to 70°.

This also means that x and y are equal to each other, so to find these sides, we need to subtract the other known values from 360.

70° + 70° = 140°

360° - 140° = 220°

Since the amount we have left is 220°, and our last 2 values are equal to each other, we can divide this by 2 in order to find their individual degrees.

220/2 = 110°

Both x and y are equal to 110°.

The diagonals of ABCD do not intersect. There is no intersection point for the diagonals CD.

To discover the coordinates of the intersection of the diagonals of ABCD, we want to calculate the factor of intersection between the line section connecting factors C and D and the line section connecting factors A and B.

Given the coordinates:

A(0, 3)

B(10, 3)

C(8, -1)

D(-2, -1)

We first locate the equations of the two lines:

Line AD:

The slope of line AD can be calculated as (change in y) / (change in x):

m_AD = (3 - (-1)) / (0 - (-2))

= four / 2

= 2

Using the point-slope form, we have the equation of line AD as:

y - three = 2(x - 0)

y - three = 2x

Line BC:

The slope of line BC can be calculated as (change in y) / (change in x):

m_BC = (3 - (-1)) / (10 - 8)

= four / 2

= 2

Using the point-slope form, we have the equation of line BC as:

y - three = 2(x - 10)

y - three = 2x - 20

Now, we have the equations:

y = 2x (Equation for line AD)

y = 2x - 17 (Equation for line BC)

To discover the intersection point, we set these two equations equal to every other:

2x = 2x - 17

This equation is contradictory and has no solution, indicating that the strains AD and BC are parallel and do now not intersect.

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Answer:

[tex]115 \dfrac{1}{2}\:cm^3[/tex]

Step-by-step explanation:

The volume of a rectangular prism is the product of each of the sides of the prism

Given the sides have lengths
[tex]3\dfrac{1}{2}, 6 \;and\; 5 \dfrac{1}{2} cm[/tex]

the volume would be
[tex]3\dfrac{1}{2} \times 6 \times 5 \dfrac{1}{2}[/tex]

To perform this multiplication, convert mixed fractions to improper fractions first

Use the rule that mixed fraction
[tex]a\dfrac{b}{c}=\dfrac{a\times \:c+b}{c}[/tex]

[tex]3\dfrac{1}{2}=\dfrac{3\times 2+1}{2} = \dfrac{7}{2}[/tex]

[tex]5\dfrac{1}{2}=\dfrac{5\times 2+1}{2}= \dfrac{11}{2}[/tex]

Therefore
[tex]3\dfrac{1}{2}\times \:6\times \:5\dfrac{1}{2}\\\\= \dfrac{7}{2}\times \:6\times \dfrac{11}{2}\\\\= \dfrac{7}{2}\times \dfrac{6}{1}\times \dfrac{11}{2} \quad(6 = \dfrac{6}{1})[/tex]

[tex]=\dfrac{7\times \:6\times \:11}{2\times \:1\times \:2}\\\\= \dfrac{462}{4}\\[/tex]

Divide numerator and denominator by 2 to get
[tex]\dfrac{231}{2}\\[/tex]

Convert improper fraction [tex]\dfrac{231}{2}[/tex] to mixed fraction using quotient/remainder

[tex]\dfrac{231}{2} \\\\\rightarrow Quotient: 115\\\\\rightarrow Remainder = 231 - 115 \times 2 = 231 - 230 = 1[/tex]

[tex]\dfrac{231}{2} = 115 \dfrac{1}{2}[/tex]

The number x will be a rational number if (m/n) and (a/b) are both rational numbers, x will be a rational number. Otherwise, if either (m/n) or (a/b) (or both) are irrational numbers, x will be an irrational number.

Given data ,

Let the number y be a irrational number

Let the number x be an irrational number such as,

y = ( a/b ) , where m and n are integers and b ≠ 0.

The sum of x + y = m/n , where n ≠ 0.

Now , In the equation x + (a/b) = (m/n), we have a rational number (a/b) and a sum on the left side equal to a fraction (m/n).

To find the type of number x, we can rearrange the equation as follows:

x = (m/n) - (a/b)

Now, let's consider the right side of the equation. When subtracting two fractions, the result can be either a rational number or an irrational number, depending on the specific values of (m/n) and (a/b).

And , If (m/n) and (a/b) are both rational numbers, then their subtraction will result in a rational number. This means x would also be a rational number.

Hence , the number x depends on the values of ( m/n ) and ( a/b).

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The area of the triangle is 52.32 square units

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

The triangle (see attachment)

The base of the triangle is calculated as

base = 12 * tan(36)

The area of the triangle is then calculated as

Area = 1/2 * base * height

Where

height = 12

So, we have

Area = 1/2 * base * height

Substitute the known values in the above equation, so, we have the following representation

Area = 1/2 * 12 * tan(36) * 12

Evaluate

Area = 52.32

Hence, the area of the triangle is 52.32 square units

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The researcher should obtain a sample size of 1700 to estimate the percentage of adults who support abolishing the penny with a 95% confidence level and a margin of error of 4 percentage points.

To determine the sample size needed to estimate the percentage of adults who support abolishing the penny with a 95% confidence level and a margin of error of 4 percentage points, we can use the following formula:

Sample size = (Z^2 * P * (1 - P)) / E^2

Where:

Z = Z-score for the desired confidence level (for 95% confidence level, Z ≈ 1.96)

P = Estimated proportion (expressed as a decimal)

E = Margin of error

Given:

Estimated proportion (P) = 27.5% (0.275 as a decimal)

Margin of error (E) = 0.04

Substituting the values into the formula:

Sample size = (1.96^2 * 0.275 * (1 - 0.275)) / 0.04^2

Sample size = (3.8416 * 0.275 * 0.725) / 0.0016

Sample size ≈ 1699.63

Rounding up to the next integer, the required sample size is 1700.

Therefore, the researcher should obtain a sample size of 1700 to estimate the percentage of adults who support abolishing the penny with a 95% confidence level and a margin of error of 4 percentage points.

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Topic: Data Handling - Collecting and Representing Data

Objective: Students will learn how to collect and represent data using different methods and graphical representations.

Teaching Approach: Meaning of Doing Mathematics

1. Introduction (5 minutes):

- Begin the lesson by asking students to think about why data is important and how it can be used in everyday life.

- Engage students in a discussion about the different types of data they encounter in their daily lives (e.g., favorite colors, sports, ice cream flavors, etc.).

2. Data Collection Activity (15 minutes):

- Explain to students that they will collect data on a topic of their choice, such as favorite animals, hobbies, or TV shows.

- Provide each student with a data collection sheet and ask them to survey their classmates to gather data.

- Emphasize the importance of asking clear and specific questions and recording responses accurately.

3. Data Representation (20 minutes):

- Once the data is collected, guide students in representing the data using different methods.

- Discuss the importance of selecting appropriate representations based on the type of data collected (e.g., tally marks, bar graphs, pictographs).

- Model how to create a bar graph or pictograph using the collected data on the board or chart paper.

- Encourage students to interpret the graphs, identify patterns, and draw conclusions from the data represented.

4. Analyzing and Interpreting Data (15 minutes):

- Engage students in a class discussion about the different patterns and trends they notice in the data represented.

- Guide them in making comparisons, finding the most common and least common responses, and discussing the significance of the findings.

- Encourage students to express their thoughts and reasoning behind their observations.

5. Application and Reflection (10 minutes):

- Provide students with additional data sets or ask them to create their own data sets to practice representing and interpreting data.

- Ask students to reflect on the importance of collecting and representing data accurately and how it helps in understanding and making informed decisions.

6. Wrap-up and Extension (5 minutes):

- Summarize the key concepts covered in the lesson and highlight the importance of data handling in real-life situations.

- Assign a small project or task where students can apply their data collection and representation skills in a different context.

By adopting the "Meaning of Doing Mathematics" approach, students actively engage in the process of collecting and representing data. They develop a deeper understanding of the purpose and significance of data handling in real-life situations. The emphasis is on hands-on activities, critical thinking, and making connections between mathematics and their everyday experiences.

The number of cats that company take to care of on Saturday night = 72.

The given system of equation is,

       x + y = 16     .....(i)  

18x + 30y = 432  .....(ii)

Where x represents the number of dog

And y represents the number of cat

One strategy for solving a system of linear equations is the elimination method. To get the equation in one variable, either add or subtract the equations. If the coefficients of one of the variables are the same and their signs are opposite, we can use the equation to delete the variable. Similarly, if the coefficients of one of the variables are the same, as well as their sign, we can subtract the equation to yield the equation in one variable.

Now  multiply 18 with (i) we get,

18x + 18y = 288    .....(iii)

Subtract (iii) from (ii)

⇒ 2y = 144

⇒   y = 72

Hence,

there were 72 cats.

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√(126539.1 / 171) =

To calculate the appropriate measure of skewness for the given data, we can use the formula:

Skewness = [3(mean - median)] / standard deviation

First, we need to find the mean, median, and standard deviation of the data set.

To find the mean, we use the formula:

mean = (Σ(xi * fi)) / N

where xi is the midpoint of each class, fi is the frequency of each class, and N is the total number of workers.

Calculating the midpoint of each class:

5, 15, 25, 35, 45, 55

Multiplying each midpoint by its corresponding frequency, and summing the results:

(5*10) + (15*12) + (25*25) + (35*35) + (45*40) + (55*50) = 6300

Dividing by the total number of workers:

6300 / 172 = 36.63

So the mean is approximately 36.63.

To find the median, we need to first calculate the cumulative frequency for each class:

Class: 0-10 10-20 20-30 30-40 40-50 50-60

Frequency: 10 12 25 35 40 50

Cumulative: 10 22 47 82 122 172

The median is the middle value of the data set, which is the 86th value in this case. Looking at the cumulative frequencies, we see that the median falls in the 30-40 class. So the median class is 30-40, with a cumulative frequency of 82. The width of the class interval is 10, and the frequency of the median class is 35.

Using the formula:

median = L + [(N/2 - CF) / f] * w

where L is the lower limit of the median class, N is the total number of workers, CF is the cumulative frequency of the class preceding the median class, f is the frequency of the median class, and w is the width of the median class interval.

Substituting in the values, we get:

median = 30 + [(86/2 - 82) / 35] * 10 = 31.71

So the median is approximately 31.71.

To find the standard deviation, we can use the formula:

standard deviation = √[Σ(fi * (xi - mean)²) / (N - 1)]

where xi and fi are as before, mean is the mean of the data set, and N is the total number of workers.

Calculating the squared deviation of each midpoint from the mean, and multiplying by the frequency of each class:

[(5 - 36.63)² * 10] + [(15 - 36.63)² * 12] + [(25 - 36.63)² * 25] + [(35 - 36.63)² * 35] + [(45 - 36.63)² * 40] + [(55 - 36.63)² * 50] = 126539.1

Dividing by (N-1) and taking the square root:

√(126539.1 / 171) =

We have to remember that 60 seconds in a minute, 60 minutes in an hour, and 24 hours in a day and the base unit for capacity is the liter (L).

There are 1,000 milliliters (mL) in a liter, and 1,000 liters in a kiloliter (kL).

Time Conversions:

There are 60 seconds in a minute, 60 minutes in an hour, and 24 hours in a day.

To convert from smaller to larger units, divide the value by the appropriate conversion factor.

To convert from larger to smaller units, multiply the value by the appropriate conversion factor.

Capacity Conversions:

In the metric system, the base unit for capacity is the liter (L).

There are 1,000 milliliters (mL) in a liter, and 1,000 liters in a kiloliter (kL).

To convert from smaller to larger units, divide the value by the appropriate conversion factor.

To convert from larger to smaller units, multiply the value by the appropriate conversion factor.

Remembering these conversion factors and units will help ensure accurate conversions when dealing with time and capacity measurements.

To learn more on Conversions click:

https://brainly.com/question/9414705

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