Which graph is most often used to show change in data across time?

Answers

Answer 1

The graph most often used to show change in data across time is the line graph.

The graph most often used to show change in data across time is the line graph. A line graph is an effective visualization tool that displays data points as a series of connected data markers, forming a line.

It is commonly used to illustrate trends, patterns, or fluctuations in data over a continuous time interval.

The x-axis represents time, while the y-axis represents the variable being measured. By plotting data points and connecting them with lines, line graphs provide a clear visual representation of how the data changes over time, allowing for easy identification of trends, seasonality, growth, or decline in the data series.

Line graphs are widely utilized in various fields, including economics, finance, science, and social sciences, to present temporal data in a comprehensive and understandable manner.

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Related Questions

− 4 p − ( 5 p − 4 ) ≤ −4p−(5p−4)≤ 7 p + 10 + 3 p 7p+10+3p

Answers

Answer:

To solve the inequality −4p − (5p − 4) ≤ 7p + 10 + 3p, we can simplify and isolate the variable p. Let's work through the steps:

Step 1: Distribute the negative sign (-) inside the parentheses:

-4p - 5p + 4 ≤ 7p + 10 + 3p

Simplifying further:

-9p + 4 ≤ 10p + 10

Step 2: Group like terms by adding 9p to both sides of the inequality:

-9p + 9p + 4 ≤ 10p + 9p + 10

Simplifying further:

4 ≤ 19p + 10

Step 3: Subtract 10 from both sides of the inequality:

4 - 10 ≤ 19p + 10 - 10

Simplifying further:

-6 ≤ 19p

Step 4: Divide both sides of the inequality by 19:

-6/19 ≤ 19p/19

Simplifying further:

-6/19 ≤ p

So the solution to the inequality is p ≥ -6/19.

100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!

Answers

Answer:

A. 1.78cm².

B. 331.34 square meters.

Step-by-step explanation:

The area of the shaded region in a circle if the radius and central angle is given can be calculated using the following formula:

Area of shaded region = (θ/360) * πr²

Where:

θ is the central angle in degrees. r is the radius of the circle. π is the mathematical constant pi, approximately equal to 3.14.

A.

If the radius is 2 meters and the central angle is 51 degrees, then the area of the shaded region is:

Area of shaded region = (51/360)*π*2² = 0.357π m²

≈ 1.78 square meters

Therefore, the area of the shaded region is approximately 1.78square meters.

Therefore, the area of the shaded region is 1.78cm².

B.

If the radius is 12.5 meters and the central angle is 243 degrees, then the area of the shaded region is:

Area of shaded region = (243/360)*π*12.5² = 105.47π m²

≈ 105.47π square meters

Therefore, the area of the shaded region is approximately 331.34 square meters.

A set of data is represented in the stem plot below.

Stem plot with stems of 3, 4, 5, 6, 7, 8, 9. Leaf for stem of 3 is 5. Leaves for stem of 4 are 4, 5. Leaves for stem of 5 are 3, 6. Leaves for stem of 6 are 2, 5. Leaves for stem of 7 are 5, 5, 6. Leaves for stem of 8 are 2, 5. Leaf for stem of 9 is 2.

Key: 3 | 5 = 35

Part A: Find the mean of the data. Show each step of work. (2 points)

Part B: Find the median of the data. Explain how you determined the median. (2 points)

Part C: Find the mode of the data. Explain how you determined the mode. (2 points)

Part D: Compare your values for mean, median, and mode from parts A, B, and C. Which value would best represent the data, and why? Explain using complete sentences. (4 points)

Answers

In this dataset, the mean is approximately 65.77, the median is 65, and the mode is 5 and 75.

Part A: Finding the mean of the data:

To find the mean, we need to calculate the average of all the data points.

Step 1: Identify the stems and their corresponding leaves:

3 | 5

4 | 4, 5

5 | 3, 6

6 | 2, 5

7 | 5, 5, 6

8 | 2, 5

9 | 2

Step 2: Assign numerical values to each stem-leaf combination:

3 | 5 = 35

4 | 4 = 44, 5 = 45

5 | 3 = 53, 6 = 56

6 | 2 = 62, 5 = 65

7 | 5 = 75, 5 = 75, 6 = 76

8 | 2 = 82, 5 = 85

9 | 2 = 92

Step 3: Calculate the sum of all the numerical values:

35 + 44 + 45 + 53 + 56 + 62 + 65 + 75 + 75 + 76 + 82 + 85 + 92 = 855

Step 4: Determine the count of all the data points:

The count is the total number of data points, which can be determined by adding up the frequencies of each stem-leaf combination:

1 (stem 3) + 2 (stem 4) + 2 (stem 5) + 2 (stem 6) + 3 (stem 7) + 2 (stem 8) + 1 (stem 9) = 13

Step 5: Calculate the mean by dividing the sum of all values by the count:

Mean = Sum of all values / Count = 855 / 13 = 65.77 (rounded to two decimal places)

The mean of the data is approximately 65.77.

Part B: Finding the median of the data:

To determine the median, we need to arrange the data in ascending order and find the middle value.

Arranging the data in ascending order: 35, 44, 45, 53, 56, 62, 65, 75, 75, 76, 82, 85, 92

There are 13 data points, the median will be the value in the middle. In this case, the middle value is the 7th value, which is 65.

The median of the data is 65.

Part C: Finding the mode of the data:

The mode represents the value(s) that occur with the highest frequency.

From the stem-leaf plot, we can see that the leaves with the highest frequency are 5 and 75. Both of these frequencies occur twice.

The mode of the data is 5 and 75.

Part D: Comparing the mean, median, and mode:

In this dataset, the mean is approximately 65.77, the median is 65, and the mode is 5 and 75.

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2)
A high school basketball team won exactly 65 percent
of the games it played during last season. Which of
the following could be the total number of games the
team played last season?
A) 22
B) 20
C) 18
D) 14

Answers

Answer:

To find the answer, we can use the formula:

number of won games / total number of games played = percentage won

Let x be the total number of games played. We know that the percentage won is 65%, or 0.65 as a decimal. So we can set up the equation:

number of won games / x = 0.65

To solve for x, we can cross-multiply:

number of won games = 0.65x

We want to find a whole number value for x that makes sense. One way to do this is to try each answer choice and see if it gives a whole number value for the number of won games. Let's start with choice A:

If the team played 22 games, then the number of won games is:

number of won games = 0.65 * 22 = 14.3

This is not a whole number value, so we can rule out choice A.

We can repeat this process for each answer choice. When we try choice C, we get:

number of won games = 0.65 * 18 = 11.7

This is also not a whole number value, so we can rule out choice C.

When we try choice D, we get:

number of won games = 0.65 * 14 = 9.1

This is also not a whole number value, so we can rule out choice D.

Therefore, the only remaining answer choice is B, which gives us:

number of won games = 0.65 * 20 = 13

This is a whole number value, so the team could have played 20 games in total last season.

1
2
3
4
5
I
Statement
+
ZHKI ZGKH
HJ I GI
H
m2GKH+mZHKI = 180°
m2GKH + m2GKH = 180°
m2GKH = 90°
Reason
Given
Angles forming a linear pair sum to 180°
Definition of congruence

Answers

Answer:

3. Substitution because it said angle HKI = angle GKH, so we substitutioned that angle for the other one. I'm not sure about 4. If you provide us with the answer choices for that one, then I could help

(02.02 MC)

If trapezoid ABCD was reflected over the y-axis, reflected over the x-axis, and rotated 180°, where would point A′′′ lie?

Trapezoid formed by ordered pairs A at negative 4, 1, B at negative 3, 2, C at negative 1, 2, D at 0, 1.

(1, −1)
(−4, 1)
(1, 1)
(−4, −1)

Answers

The location of point A''' after the three transformations would be (-4, 1).

To determine the location of point A''', we need to apply the three transformations (reflection over the y-axis, reflection over the x-axis, and rotation of 180°) to point A.

When a point is reflected over the y-axis, the x-coordinate is negated while the y-coordinate remains the same.

So, the reflection of point A (-4, 1) over the y-axis would be (4, 1).

When a point is reflected over the x-axis, the y-coordinate is negated while the x-coordinate remains the same. So, the reflection of point (4, 1) over the x-axis would be (4, -1).

When a point is rotated 180°, the x-coordinate and y-coordinate are both negated. So, the rotation of point (4, -1) by 180° would be (-4, 1).

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The sales tax for an item was $20 and it cost $500 before tax. Find the sales tax rate. Write your answer as a percentage.

Answers

Answer: To find the sales tax rate as a percentage, we can use the following formula:

Sales Tax Rate = (Sales Tax / Cost Before Tax) * 100%

In this case, the sales tax is given as $20, and the cost before tax is $500. Plugging these values into the formula, we have:

Sales Tax Rate = ($20 / $500) * 100%

Simplifying the expression:

Sales Tax Rate = (0.04) * 100%

Sales Tax Rate = 4%

Therefore, the sales tax rate for the item is 4%.

Step-by-step explanation:

Identify the axis of symmetry, vertex, and range for the quadratic function.

Answers

That is a parabola. The vertex is at (4,1) as seen in the graph. The axis of symmetry for a vertical parabola is x=h which is the x value of the vertex, so the symmetry axis here is x=4. The range is as the name suggests, the range that the y values take. From the graph it looks like the y values start at 1 and go up until infinity in the positive axis. So the range is [1,+ ∞[ or [1,+ ∞) depending on how you take intervals.

Don't forget to show your work. Thank you!

Answers

The probability that a point chosen randomly inside the rectangle and is inside the Square or Trapezoid is 2/15.

We know that, probability of an event

= Number of favourable outcomes/Total number of outcomes.

Here, area of a rectangle = Length × Breadth

= 15×8

= 120 square units

Area of a triangle = 1/2 × Base × Height

= 1/2 ×(√10²-6²)×6

= 0.5×8×6

= 24 square units

Area of a trapezium = 1/2 (Sum of parallel sides)×Height

= 1/2 ×(5+7)×2

= 12 square units

Area of a square = side² = 2²

= 4 square units

(a) Probability of landing in trapezium or Square = 12/120 + 4/120

= 16/120

= 2/15

(b) Probability of landing inside the rectangle but outside the triangle = 16/120

= 2/15

Therefore, the probability that a point chosen randomly inside the rectangle and is inside the Square or Trapezoid is 2/15.

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The volume of the loading space on a moving truck is 432 cubic feet. The length of the truck is (x+6) feet. The width of the truck is x feet, and
the height is 6 feet. What is the actual length and width of the truck?

Answers

Answer:

length=12ft

width=6ft

Step-by-step explanation:

The volume formula is V=lwh.

Plug the values into the equation like this: 432=(x+6)(x)(6)

Divide both sides of the equation by 6: 72=(x+6)(x)

Distribute the x:  [tex]72=x^{2} +6x[/tex]

Subtract the 72:  [tex]0=x^{2} +6x-72[/tex]

Factor: 0=(x+12)(x-6)

x=-12

x=6

Now, plug in x into the original length and width equations.

length: (6+6)

length=12

width=6

Can you help me find x


Answers

[tex] \boxed{\rm{Similarity \: shape}}[/tex]

[tex]\begin{aligned} \frac{AB}{DE}&= \frac{BC}{EF}\\ \frac{36}{24}&=\frac{15}{x} \\ x &= \frac{\cancel{^{ \green{2}}24} \times 15}{\cancel{36_{ \green{3}}}} \\ x&= \frac{2 \times 15}{3} \\ x &= \bold{10} \\ \\\small{\blue{\mathfrak{That's \: it \: :)}}} \end{aligned}[/tex]

In the figure below, S is the center of the circle. Suppose that JK = 20, LM = 3x + 2, SN = 12, and SP = 12. Find the
following.

Answers

Length of JN = 10

x = 6

Given ,

S is the center of the circle.

JK = 20

LM = 3x + 2

SN = 12

SP = 12

Now ,

SN and SP are perpendicular to the chords JK and LM respectively .

Perpendiculars drawn from the center of circle to the chords bisect chords into two equal halves .

Thus,

JN = JK/2

JN = 10

Now join SJ,

In ΔSJN ,

Apply pythagoras theorem,

SN² + NJ² = SJ²

12² + 10² = SJ²

SJ = 14.52

SJ =Radius of the circle .

Now,

LP = LM/2

LP = 1.5x + 1

Now join  SL,

In ΔSLP

SP² + PL² = SL²

SL = SJ (radius of circle)

So,

12² + (1.5x + 1)² = 244

x = 6

Hence the value of x is 6 and JN is 10 .

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The difference between an observational study and an experiment is thatin an observational study, only one group is studied, and in an experiment, two groups are studied.in an observational study, the researchers do not control treatment, and in an experiment, they do.in an experiment, cause-and-effect is analyzed, and in an observational study, it is not.in an experiment, one group is studied over a short period of time, and in an observational study, the group is studied over a longer period of time.

Answers

The difference between an observational study and an experiment is that  in an observational study, the researchers do not control treatment, and in an experiment, they do

What is observational study and an experiment?

In an observational study, it should be noted that the participants are measured or surveyed without any attempt to influence them. *

However the controlled experiment, participants or objects are divided into groups, and one group is given a treatment while the other is not.

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(09.01 LC)
What is the relationship between the circumference C of the circle in which the degree measure A of a central angle of a circle intercepts an arc
length s of the arc?

A)C=360°(s)(A)
B)C=360 degrees s over A
C)C=360 degrees(s+A)
D)C = 360°A over s

Answers

The relationship between the circumference C of the circle in which the degree measure A of a central angle of a circle intercepts an arc length s of the arc is

B) C=360 degrees s over A

How to find the relationship

The relationship between the circumference C of a circle and the degree measure A of a central angle that intercepts an arc length s of the arc can be described by the formula:

s = A / 360 * C

Make C the subject of the formula

s = AC / 360

360s = AC

rearranging

AC = 360s

C = 360 degrees s / A

C = (s / A) * 360°

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Answer:

[tex]\textsf{B)} \quad C=\dfrac{360^{\circ}\:s}{A}[/tex]

Step-by-step explanation:

In a circle, the ratio of an arc length (s) to the circumference (C) is equal to the ratio of the measure of the arc's central angle (A) to 360°.

This is because:

The circumference (C) represents the distance around the entire circle, and so an arc (s) is a fraction of the whole circumference. In a circle, there are 360° in total, and so a central angle (A) is a fraction of 360°.

Therefore, this can be expressed as:

[tex]\dfrac{s}{C}=\dfrac{A}{360^{\circ}}[/tex]

Cross multiply:

[tex]360^{\circ} \cdot s=C \cdot A[/tex]

Now, divide both sides by A to isolate C:

[tex]\dfrac{360^{\circ} \cdot s}{A}=C[/tex]

Therefore, the relationship between the circumference (C) of the circle in which the degree measure (A) of a central angle of a circle intercepts an arc length (s) of the arc is:

[tex]\large\boxed{\boxed{C=\dfrac{360^{\circ}\:s}{A}}}[/tex]

Write a system of linear equations for the graph below. really need lots of help with this!

i also need the y's ​

Answers

Answer:

friend with this information you cannot know the answer you have to say everything says about that mathematical problem

Evaluate your data. Has there been an increase in the number of certain individuals of this
population of bacteria? Please explain how you think this might lead to the emergence of a
superbug over time, or the extinction of certain strains of this bacteria.

Answers

The increase in certain individuals leads to:

Selective pressure.Emergence of antibiotic-.Extinction .Genetic variations.Difficulty in treating infections.Competition for resources leading to disadvantage for other strains.

An increase in certain individuals within a bacterial population can lead to:

Selective pressure favoring individuals with advantageous traitsEmergence of antibiotic-resistant strains or "superbugs"Extinction of less competitive strainsGenetic variations being passed on to future generationsDifficulty in treating infections caused by resistant bacteriaCompetition for resources leading to disadvantage for other strainsOutcome depends on selective pressure, genetic diversity, resource availability, and adaptability.

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NEED HELP ASAP WILL GIVE BRAINLIEST HELP!

Answers

If Jeremy wants to try to prove ∠3 ≅ ∠6, then the statement that Jeremy can write is ∠1 ≅ ∠4

That's it :)

pls, i need help fast !!! here are questions 4 and 5

Answers

4. The x-intercept of g(x) is 2.

The y-intercept of g(x) is -4.

5. The minimum value of g(x) is -8.

The maximum value of g(x) is 17.

What is the x-intercept?

In Mathematics and Geometry, the x-intercept is also referred to as horizontal intercept and the x-intercept of the graph of any function simply refers to the point at which the graph of a function crosses or touches the x-coordinate (x-axis) and the y-value or the value of "f(x)" is equal to zero (0).

By critically observing the table representing the function g(x), we can logically deduce the following x-intercept and y-intercept:

When y = 0, the x-intercept of g(x) is equal to 2.When x = 0, the y-intercept of g(x) is equal to -4.

Question 5.

By critically observing the table representing the function g(x), we can logically deduce the following minimum value and maximum value over the interval [-2, 3];

When x = -2, the minimum value of g(x) is equal to -8.When x = 0, the maximum value of g(x) is equal to 17.

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How many solutions does the system of equations below have? y=-3/4x+1/6

Answers

The solution is the point (0, 1/6) y = 1/6

Given the equation y = (-3/4)x + 1/6, which represents a linear equation, there is no "system" of equations involved since there is only one equation.

In this case, the equation is in slope-intercept form (y = mx + b),

where m represents the slope (-3/4) and b represents the y-intercept (1/6).

The slope-intercept form allows us to determine various properties of the equation.

Since there is only one equation, the solution to this equation is a single point on the Cartesian plane.

Each pair of x and y values that satisfy the equation represents a solution.

For example, if we choose x = 0, we can substitute it into the equation to find the corresponding y value:

y = (-3/4)(0) + 1/6

y = 1/6

Therefore, the solution is the point (0, 1/6).

In summary, the given equation has a unique solution, represented by a single point on the Cartesian plane.

Any value of x plugged into the equation will yield a corresponding y value, resulting in a unique point that satisfies the equation.

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A pencil box has dimensions of 6 1/2 in 3 1/2 in and one one over 2 in respectively approximately how many cubes with the side length of 1/2 inches will be needed to fill the prism

Answers

Approximately 273 cubes with a side length of 1/2 inch will be needed to fill the prism.

To determine the number of cubes with a side length of 1/2 inch needed to fill the prism, we need to calculate the volume of the prism and divide it by the volume of a single cube.

The given dimensions of the pencil box are:

Length: 6 1/2 inches

Width: 3 1/2 inches

Height: 1 1/2 inches

To find the volume of the prism, we multiply the length, width, and height:

Volume of the prism = Length [tex]\times[/tex] Width [tex]\times[/tex] Height

[tex]= (6 1/2) \times (3 1/2) \times (1 1/2)[/tex]

First, we convert the mixed numbers to improper fractions:

[tex]6 1/2 = (2 \times 6 + 1) / 2 = 13/2[/tex]

[tex]3 1/2 = (2 \times 3 + 1) / 2 = 7/2[/tex]

[tex]1 1/2 = (2 \times 1 + 1) / 2 = 3/2[/tex]

Now we substitute the values into the formula:

Volume of the prism [tex]= (13/2) \times (7/2) \times (3/2)[/tex]

[tex]= (13 \times 7 \times 3) / (2 \times 2 \times 2)[/tex]

= 273 / 8

≈ 34.125 cubic inches.

Next, we calculate the volume of a single cube with a side length of 1/2 inch:

Volume of a cube = Side length [tex]\times[/tex] Side length [tex]\times[/tex] Side length

[tex]= (1/2) \times (1/2) \times (1/2)[/tex]

= 1/8

To find the number of cubes needed to fill the prism, we divide the volume of the prism by the volume of a single cube:

Number of cubes = Volume of the prism / Volume of a single cube

= (273 / 8) / (1/8)

= 273

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What is the radian measure of a 45 degree angle in a circle of radius 24 ft

Answers

To convert from degrees to radians, we use the conversion factor that 180 degrees is equal to π radians (or π/180 radians per degree).

Given that the angle is 45 degrees, we can calculate the radian measure as follows:

Radian measure = (45 degrees) * (π/180 radians per degree)

Radian measure = 45π/180

Simplifying further:

Radian measure = π/4

Therefore, the radian measure of a 45 degree angle is π/4.

Factor the following and then fill in the blanks. 2x²7x-15 = (2x + )(x- Blank 1: Blank 2:​

Answers

Answer:

(2x + 3)(x - 5)

Step-by-step explanation:

2x² - 7x - 15

consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 2 × - 15 = - 30 and sum = - 7

the factors are - 10 and + 3

use these factors to split the x- term

2x² - 10x + 3x - 15 ( factor the first/second and third/fourth terms )

= 2x(x - 5) + 3(x - 5) ← factor out (x - 5) from each term

= (2x + 3)(x - 5) ← in factored form

Blank 1 is 3

Blank 2 is 5

cos(a+b)= cosa.cosb.-Sina SinB to Find the Formula of Sin (a-B]​

Answers

The formula for sin(a - b) is sin(a)cos(b) - cos(a)sin(b).

To find the formula for sin(a - b), we can use the identity for cosine of a sum of angles, which states that:

cos(a + b) = cos(a)cos(b) - sin(a)sin(b)

We can rearrange this equation to solve for sin(a - b):

cos(a + b) = cos(a)cos(b) - sin(a)sin(b)

cos(a + b) = cos(a)cos(b) + (-1)(sin(a)sin(b)) [multiplying sin(b) by -1]

cos(a + b) = cos(a)cos(b) + sin(a)(-sin(b)) [rearranging terms]

cos(a + b) = cos(a)cos(b) - sin(a)sin(b) [sin(b) can be replaced by -sin(b)]

Comparing this equation with the given identity, we can see that:

sin(a - b) = sin(a)cos(b) - cos(a)sin(b)

Therefore, the formula for sin(a - b) is sin(a)cos(b) - cos(a)sin(b).

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[tex]3^a = 9^b = 27^c[/tex] and a, b, and c don’t equal 0, what is [tex]\frac{a}{b} + \frac{b}{c} + \frac{c}{a}[/tex]

Answers

To solve the expression [tex]\large\sf\:\frac{a}{b} + \frac{b}{c} + \frac{c}{a}\\[/tex] given the conditions [tex]\large\sf\:3^a = 9^b = 27^c\\[/tex], we can use logarithmic properties and the fact that [tex]\large\sf\:3^2 = 9\\[/tex] and [tex]\large\sf\:3^3 = 27\\[/tex].

Let's start by finding the values of a, b, and c using logarithmic properties:

Taking the logarithm of both sides of [tex]\large\sf\:3^a = 9^b\\[/tex], we get:

[tex]\large\sf\:\log_3(3^a) = \log_3(9^b)\\[/tex]

Applying the power rule of logarithms, we can bring down the exponents:

[tex]\large\sf\:a\log_3(3) = b\log_3(9)\\[/tex]

Since [tex]\large\sf\:\log_3(3) = 1[/tex] and [tex]\large\log_3(9) = 2\\[/tex], we simplify to:

[tex]\large\sf\:a = 2b\\[/tex] ---- (1)

Similarly, taking the logarithm of both sides of [tex]\sf\:9^b = 27^c\\[/tex], we get:

[tex]\large\sf\:b\log_3(9) = c\log_3(27)\\[/tex]

Using the values of [tex]\sf\:\log_3(9)\\[/tex] and [tex]\sf\:\log_3(27)\\[/tex] as before, we have:

[tex]\large\sf\:b(2) = c(3)\\[/tex]

Simplifying, we get:

[tex]\large\sf\:2b = 3c\\[/tex] ---- (2)

Now, let's substitute the value of b from equation (1) into equation (2):

[tex]\large\sf\:2(2b) = 3c\\[/tex]

[tex]\large\sf\:4b = 3c\\[/tex]

Rearranging, we find:

[tex]\large\sf\:c = \frac{4b}{3}\\[/tex] ---- (3)

We now have expressions for a, b, and c in terms of b. Let's substitute these into the expression [tex]\large\sf\:\frac{a}{b} + \frac{b}{c} + \frac{c}{a}\\[/tex]:

[tex]\large\sf\:\frac{a}{b} + \frac{b}{c} + \frac{c}{a} = \frac{2b}{b} + \frac{b}{\frac{4b}{3}} + \frac{\frac{4b}{3}}{2b}\\[/tex]

Simplifying further, we get:

[tex]\large\sf\:\frac{2}{1} + \frac{3}{4} + \frac{2}{3}\\[/tex]

Finding the common denominator and combining the fractions, we have:

[tex]\large\sf\:\frac{24}{12} + \frac{9}{12} + \frac{8}{12}\\[/tex]

Adding the fractions together, we obtain:

[tex]\large\sf\:\frac{24 + 9 + 8}{12} = \frac{41}{12}\\[/tex]

Therefore, [tex]\large\sf\:\frac{a}{b} + \frac{b}{c} + \frac{c}{a} = \frac{41}{12}\\[/tex].

find the unit vector of n=(4,-3)

Answers

The unit vector for n = (4, -3) is V = (4/5, -3/5)

How to find the unit vector for the given vector?

An unit vector will be a vector that has the same direction than the given one, but a magnitude of 1 unit.

Then we can define the vector V = k*n

Where k > 0 is a real number, then the unit vector is:

V = (4k, -3k)

But notice that this must have a magnitude of 1, then:

1 = √( (4k)² + (-3k)²)

1 = √25k²

1 = 5k

1/5 = k

Then the unit vector is:

V = (4/5, -3/5)

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Match the system of equations with the number of solutions.
y = 6z+8
y = 6x-4
y = 3x + 2
y + 3x = -7
4z - 2y = 10
2z-y = 5
4z + y = 8
y=-2z+8
No Solution

Answers

Answer:

Step-by-step explanation:

The system of equations with no solution is:

y + 3x = -7

4z - 2y = 10

The system of equations with exactly one solution is:

y = 6z+8

y = 6x-4

y = 3x + 2

2z-y = 5

y=-2z+8

The system of equations with infinitely many solutions is:

4z + y = 8

a shade of paint purple berry can be made by mixing red and blue paint in the ratio 5:2. Emma has 30 litres of red paint and 10 litres of blue paint.work out the maximum volume of purple berry that can be made

Answers

Answer:The max volume of Purple berry paint is 85

Step-by-step explanation:

Purple = Red + Blue

P = 5 : 2

Simplify 5 : 2 which is 2.5 : 1

P = 30L : 10L

P = (30 x 2.5 ) + (10 x 1)

P = 75 + 10

P = 85 L

Select the three inequalities that include 3 in the solution set.
x > 1.4
x < 2.6
x > 4.2
x < 5.1
x < 8.2

Answers

The solution set which include 3 are x > 1.4, x < 5.1 and x < 8.2.

Given the inequalities that include 3 in the following inequalities

x > 1.4, x < 2.6, x > 4.2, x < 5.1 and x < 8.2.

To find the solution set which include 3, write the solution set which consists of integer.

The solution set of x > 1.4 is { 2, 3, 4, 5, 6,     ........}

The solution set of x < 2.4 is { 2, 1. 0, -1, ...............}

The solution set of x > 4.2 is { 5, 6. 7, 8, ...............}

The solution set of x < 5.1 is { 5, 4, 3, 2, 1, ...............}

The solution set of x < 8.2 is { 8, 7, 6, 5, 4, 3, ...............}

Hence, the solution set which include 3 are x > 1.4, x < 5.1 and x < 8.2.

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how many inches is it from end to end on a bed that is 6 feet long? It is measured in the.

Answers

The calculated inches from end to end on the bed is 72 inches

How to determine the inches from end to end on the bed

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

Length = 6 feet long

By conversion of units, we have

1 feet = 12 inches

using the above as a guide, we have the following:

Length = 6 * 12 inches long

Evaluate the products

Length = 72 inches long

Hence, the inches from end to end on the bed is 72

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see image see image see image see image see image

Answers

Using the bearing and trigonometry in the problem, the distance of the waterfall from the lake is 7.94km

How far away is the waterfall from the lake?

To determine the distance between the waterfall and the lake, we can use trigonometry and the given information about the bearing and the distance in a south direction.

To find the distance between the waterfall and the lake, we can use the concept of right triangles and trigonometric functions.

Since the bearing is given as 236°, we can subtract this angle from 180° to find the angle formed by the south direction and the line connecting the lake and the waterfall:

180° - 236° = -56°

Now, we can consider the south direction as the reference direction (0°) and the line connecting the lake and the waterfall as the hypotenuse of a right triangle.

Using the cosine function, we can calculate the length of the side adjacent to the angle (-56°), which represents the distance between the waterfall and the lake:

cos θ = adjacent / hypothenuse

Adjacent = Hypotenuse * cosθ

Let's substitute the values into the formula:

Adjacent  = 14.2 km * cos(-56°)

To calculate the cosine of -56°, we can use the fact that the cosine function is an even function:

cos(-56°) = cos(56°)

Adjacent side = 14.2 cos(56)

Adjacent side = 7.94km

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Answer:

The waterfall is approximately 8.91 km away from the lake

Step-by-step explanation:

To find the distance between the waterfall and the lake, we can use trigonometry and the given information about the bearing and the southward direction.

Since the waterfall is 14.2 km south of the lake, the line connecting the waterfall and the lake forms a right triangle with the south direction being the adjacent side, the distance between them being the hypotenuse, and the angle formed between them being the bearing of 236°.

To find the distance between the waterfall and the lake, we can use the cosine function, which relates the adjacent side, hypotenuse, and angle:

cos(236°) = adjacent side / hypotenuse

Let's denote the distance between the waterfall and the lake as "d." The adjacent side represents the southward direction.

cos(236°) = d / 14.2 km

Solving for "d":

d = cos(236°) * 14.2 km

Using a calculator:

d ≈ -8.91 km

Since distance cannot be negative, we take the absolute value:

|d| ≈ 8.91 km

Therefore, the waterfall is approximately 8.91 km away from the lake.

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