Complete the frequency table for the following set of data. You may optionally click a number to shade it out.

The completed frequency table is:

Interval   |   Tally   |   Frequency

0-2       |   |||        |   6

3-5       |   |||        |   6

6-8       |   ||||||    |   8

9-11      |   |          |   1

12-14    |   ||        |   2

To complete the frequency table, we need to count the frequency of each interval. We can start by organizing the data in ascending order:

0, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 8, 9, 10, 10, 13, 13

Now, let's count the frequency for each interval:

0-2: 6 (0, 1, 1, 2, 2, 2)

3-5: 6 (3, 3, 4, 4, 5, 5)

6-8: 8 (6, 6, 6, 6, 6, 6, 7, 8)

9-11: 1 (9)

12-14: 2 (10, 10, 13, 13)

Now we can complete the frequency table:

Interval   |   Tally   |   Frequency

0-2       |   |||        |   6

3-5       |   |||        |   6

6-8       |   ||||||    |   8

9-11      |   |          |   1

12-14    |   ||        |   2

The tally marks represent the frequency count in each interval, where each vertical line represents one count. The total frequency is obtained by counting the number of tally marks in each interval.

For more such questions on frequency

https://brainly.com/question/27820465

#SPJ8

Answer:

Step-by-step explanation:

the two other notations can be any from the following,

6/7, 6to7, 6<7

Answer:

The first mechanic worked 5 hours

The second mechanic worked 15 hours

======================================================

Work Shown:

x = number of hours the 1st mechanic worked

y = number of hours the 2nd mechanic worked

75x = total amount charged by the 1st mechanic

95y = total amount charged by the 2nd mechanic

75x+95y = total charged both mechanics combined

75x+95y = 1800 is the first equation to set up

The other equation is x+y = 20 since the total combined time spent was 20 hours.

Solve for y to get y = 20-x

Then plug it into the first equation to solve for x.

75x+95y = 1800

75x+95( y ) = 1800

75x+95(20-x) = 1800   ....... replace y with 20-x

75x+1900-95x = 1800

-20x+1900 = 1800

-20x = 1800-1900

-20x = -100

x = -100/(-20)

x = 5

Now we can determine the value of y

y = 20-x

y = 20-5

y = 15

The first mechanic worked 5 hours.

The second mechanic worked 15 hours.

The angle m∠JIX is 90 degrees.

IX is perpendicular to IJ. Therefore, angle m∠JIX is 90 degrees.

IG bisect CIJ. Hence,

m∠CIG ≅ m∠GIJ

Therefore,

m∠CIX = 150 degrees

Hence, let's find m∠JIX.

Therefore, m∠JIX is 90 degrees because IX is perpendicular to IJ. Perpendicular lines forms a right angle.

learn more on angles here: brainly.com/question/18854964

#SPJ1

The measure of angle m∠JIX is  estimated to be 90⁰.

You should understand that an angle is a figure formed by two straight lines or rays that meet at a common endpoint, called the vertex.

IX is perpendicular to IJ. Therefore, angle m∠JIX is 90⁰.

Frim the given parameters,

IG⊥CIJ.

But;  m∠CIG ≅ m∠GIJ

⇒ m∠CIX = 150⁰

Hence, let's find m∠JIX.

Therefore, m∠JIX is 90⁰ because IX is perpendicular to IJ. Perpendicular lines forms a right angle.

Learn more about bisecting of angles on https://brainly.com/question/23984603

#SPJ1

x = 301/56

Algebra is the branch of mathematics that deals with numbers and values which are represented with letters and symbols.

Sometimes, we do not want to mention a particular number, we can represent the number by a letter or a suitable symbol. This approach is algebraic.

For example, d + d = 2d

This is an example of an algebraic expression

Given the algebraic expression,

[tex]3\frac{1}{8} \div (x - 4 \frac{7}{28} ) = \frac{17}{18} + 1 \frac{5}{6} [/tex]

Step 1:

Simplify the expression by converting the mixed numbers into improper fractions:

25/8 ÷ ( x - 119/28) = 17/18 + 11/6

Step 2: Simplify the right side of the equation

25/8 ÷( x - 119/28) = 17/18 + 33/18

25/8 ÷( x - 119/28) = 50/18

Step 3: Multiply both sides of the equation by (x - 119/28)

25/8 = 50/18 × (x - 119/28)

Step 4: Multiply both sides of the equation by (18/50)

25/8 × (18/50) = (x - 119/28)

Step 5: Simplify the left side of the equation

9/8 = (x - 119/28)

Step 6: Add 119/28 to both sides of the equation

9/8 + 119/28 = x

Step 7: Calculate the value of x:

x = 9/8 + 119/28

= 63/56 + 238/56

= 301/56

Learn more about algebraic expressions from:https://brainly.com/question/395066

#SPJ1

The number of pounds in X kilograms is 2.2X pounds.

Given that,

Number of pounds in 1 kilogram = 2.2 pounds

1 kilogram = 2.2 pounds

X kilograms =?

After cross-multiplication,

Number of pounds = 2.2X

Therefore, there will be 2.2X pounds in 1 kilogram.

To learn more about unit conversion,

https://brainly.com/question/4736731

Answer:

2x^3-5x^2-28x+15 -------------------------expanded

2x^3-5x^2-28x+15--------------------simplified

Step-by-step explanation:

\left(2x-1\right)\left(x+3\right)\left(x-5\right)

=2x^2x+2x^2\left(-5\right)+5xx+5x\left(-5\right)-3x-3\left(-5\right)

simplyfied

\left(2x^2+5x-3\right)\left(x-5\right)

=2x^2x+2x^2\left(-5\right)+5xx+5x\left(-5\right)-3x-3\left(-5\right)

=2x^3-5x^2-28x+15

The identity for cos in terms of cos²x is cos 2x = 2cos²x - 1. Solve the identity for cos²x to obtain the power-reducing identity, cos²x =  (1 + cos(2x)) / 2

We need to know that there are six different trigonometric identities.

They are listed as;

From the information given, we have that;

The identity for cos 2x in terms of cos^2x is given by the double-angle identity:

cos 2x = 2 × cos²x - 1

Also, following the power reducing identity, we have that;

cos²x = (1 + cos(2x)) / 2.

Learn more about trigonometric identities at: https://brainly.com/question/7331447

#SPJ1

Answer:

x = 9

Step-by-step explanation:

Sum of angles in a polygon with n sides : (n - 2)*180

If the n sides are equal then each angle will be : sum/n

n = 6

sum = (6 - 2)*180

= 4*180

sum  = 720

each angle = 720/6 = 120

⇒ 11x + 21 = 120

⇒ 11x = 120 - 21

⇒ 11x = 99

⇒ x = 99/11

⇒ x = 9

to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below.

[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{-6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-6}-\stackrel{y1}{4}}}{\underset{\textit{\large run}} {\underset{x_2}{6}-\underset{x_1}{(-6)}}} \implies \cfrac{-10}{6 +6} \implies \cfrac{ -10 }{ 12 } \implies - \cfrac{5}{6}[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{- \cfrac{5}{6}}(x-\stackrel{x_1}{(-6)}) \implies y -4 = - \cfrac{5}{6} ( x +6) \\\\\\ y-4=- \cfrac{5}{6}x-5\implies {\Large \begin{array}{llll} y=- \cfrac{5}{6}x-1 \end{array}}[/tex]

a) Comparing the two functions, Scooter's business has a lower slope of 15 compared to Karissa's business with a slope of 35. b) Both Scooter and Karissa earned a total of $500 in that month. Therefore, they had an equal month in terms of total money earned.

a) In the context of Scooter's business, the slope of the function f(x) = 200 + 15x represents the rate at which the total money earned increases with each additional sale. Each unit increase in x (number of sales) results in an increase of $15 in total money earned. The y-intercept of 200 represents the initial amount of money Scooter already had before making any sales.

In the context of Karissa's business, the slope of the function f(x) = 80 + 35x represents the rate at which the total money earned increases with each additional repair job. Each unit increase in x (number of repairs) results in an increase of $35 in total money earned. The y-intercept of 80 represents the initial amount of money Karissa already had before doing any repair jobs.

Comparing the two functions, Scooter's business has a lower slope of 15 compared to Karissa's business with a slope of 35. This means that Karissa's business earns more money per repair job compared to Scooter's business per t-shirt sale.

b) To determine who had the better month, we need to calculate the total money earned by each individual based on the given sales/repairs.

For Scooter, with x = 20 (number of shirts sold):

f(x) = 200 + 15x

f(20) = 200 + 15 * 20

f(20) = 200 + 300

f(20) = 500

For Karissa, with x = 12 (number of repairs):

f(x) = 80 + 35x

f(12) = 80 + 35 * 12

f(12) = 80 + 420

f(12) = 500

Both Scooter and Karissa earned a total of $500 in that month. Therefore, they had an equal month in terms of total money earned.

learn more about functions at https://brainly.com/question/11624077

#SPJ1

Step-by-step explanation:

I hope this answer is helpful ):

Answer:

x = 28

Step-by-step explanation:

40x + 42 = 1162 ( subtract 42 from both sides )

40x = 1120 ( divide both sides by 40 )

x = 28

Answer:x=-1

Step-by-step explanation:

y+2=(x+3)

0+2=x+3

to find out x intercept make y 0

2=x+3

2-3=x

-1=x

The expression [tex]\displaystyle\sf \cos^{2}(x)+\sin^{2}(x)[/tex] represents the fundamental trigonometric identity known as the Pythagorean identity. It states that the square of the cosine of an angle plus the square of the sine of the same angle is always equal to 1.

Therefore, [tex]\displaystyle\sf \cos^{2}(x)+\sin^{2}(x)=1[/tex].

This identity holds true for any value of [tex]\displaystyle\sf x[/tex].

There are no roots of the given functions in common.

To find the roots of the functions in common, the two given functions will have to be equated to each other. So the answer to the given question will be determined by finding the roots of the given equations. The given equations are: (�)=�2−9f(x)=x2−9

Here, the first equation is a linear equation and the second one is a quadratic equation. The number of roots of these two functions in common will be the number of solutions to the equation obtained by equating these two given equations.

Now, equating the given equations, we have (�) = f(x)2 - 9 ⇔ � - f(x)2 = 9.The equation obtained by equating the two given equations is a quadratic equation. Let p(x) = � - f(x)2, then the above equation can be written as p(x) = 9.

Since the discriminant, D = b^2 - 4ac = 0 - 4(1)(9) = - 36 < 0, this means the quadratic equation doesn't have any real solutions. Hence, there are no roots of the given functions in common.

For more such questions on functions, click on:

https://brainly.com/question/11624077

#SPJ8

A study based on a population sample that includes 2000 respondents would be the most reliable out of the given options.

In statistical analysis, the reliability of a study depends on the representativeness and size of the sample.

A larger sample size generally provides more reliable results as it reduces the sampling error and increases the precision of the estimates.

Given that the population contains 20,000 people, we need to consider which number of respondents would yield the most reliable study.

Option A: 200 respondents

This represents only 1% of the population.

While it is better than having just 2 respondents, it may not be sufficient to accurately capture the characteristics of the entire population.

Option B: 20 respondents

This represents only 0.1% of the population.

With such a small sample size, the study would likely suffer from a high sampling error and may not provide reliable results.

Option C: 2000 respondents

This represents 10% of the population.

While it is a larger sample size compared to the previous options, it still only captures a fraction of the population.

The study may provide reasonably reliable results, but there is room for potential sampling error.

Option D: 2 respondents

This represents an extremely small sample size, accounting for only 0.01% of the population.

With such a small sample, the study would be highly susceptible to sampling bias and would likely yield unreliable results.

Based on the options provided, option C with 2000 respondents would be the most reliable study.

Although it does not include the entire population, a sample size of 2000 respondents provides a larger representation of the population and reduces the potential for sampling error.

However, it's important to note that the reliability of a study depends not only on sample size but also on the sampling method, data collection techniques, and other factors that ensure representativeness.

For similar question on population sample.

https://brainly.com/question/27859177  

#SPJ8

Answer:

[tex]\begin{aligned}v &= \dfrac{33}{13} \approx 2.5\end{aligned}[/tex]

Step-by-step explanation:

First, we can reciprocate (flip) both sides.

[tex]\dfrac{13}{3}=\dfrac{11}{v}[/tex]

[tex]\implies \dfrac{3}{13} = \dfrac{v}{11}[/tex]

Next, we can multiply both sides by 11.

[tex]\implies 11\cdot \dfrac{3}{13} = \dfrac{v}{\not{11}} \cdot \not{11}[/tex]

[tex]\implies \dfrac{33}{13} = v[/tex]

[tex]\implies \boxed{v = \dfrac{33}{13}}[/tex]

Answer:

50

Step-by-step explanation:

In trapezium STUV, SV║TU

Since ST = UV, this is an isosceles trapezium and by property,

∠SVU = ∠VST

⇒ ∠SVU = 50

There are 50 employees in total at the shop.

Let's assume the total number of employees at the shop is 'x'.

According to the given information, 8% of the employees work part-time. This means that 8% of 'x' equals the number of part-time employees.

We can set up the following equation to represent this relationship:

(8/100) * x = 4

To solve for 'x', we first simplify the equation by dividing both sides by 100:

(8/100) * x = 4

0.08 * x = 4

Next, we isolate 'x' by dividing both sides of the equation by 0.08:

x = 4 / 0.08

Performing the division, we find:

x = 50

Therefore, the total number of employees at the shop is 50.

For more such questions on employees, click on:

https://brainly.com/question/29678263

#SPJ8

Answer:

x = 53

Step-by-step explanation:

BCDE is a trapezoid

Therefore diagonals are equal

BD = EC

8x-27 = 2x+33

8x-2x = 33+27

6x = 60

x = 10

DB = 8x-27

= 8*10 - 27

= 80 - 27

= 53

Answer:

1.) inverse proportion : 1kx = y

2) direct proportion. y = kx

The length of EB is approximately 14.6 units when rounded to the nearest tenth.

To find the length of EB, we can use the property of similar triangles in this diagram. By looking at triangle DFE and triangle CFB, we can see that they are similar triangles.

Using the similarity ratio, we can set up the proportion:

DF / CF = DE / EB

Plugging in the given values, we have:

13.1 / 10.9 = 17.5 / EB

To find EB, we can cross-multiply and solve for EB:

13.1 * EB = 10.9 * 17.5

EB = (10.9 * 17.5) / 13.1

EB ≈ 14.6

Therefore, the length of EB is approximately 14.6 units when rounded to the nearest tenth.

for such more question on length

https://brainly.com/question/20339811

#SPJ8

Answer:

[tex]\displaystyle -\frac{3}{e^2}[/tex]

Step-by-step explanation:

Find f'(x)

[tex]\displaystyle f(x)=\frac{3x}{e^x}\\\\f(x)=3xe^{-x}\\\\f'(x)=3e^{-x}-3xe^{-x}[/tex]

Find f'(2) to get the slope

[tex]f'(2)=3e^{-2}-3(2)e^{-2}\\f'(2)=3e^{-2}-6e^{-2}\\f'(2)=-3e^{-2}\\f'(2)=-\frac{3}{e^2}[/tex]

Answer:

[tex]-\dfrac{3}{e^{2}}[/tex]

Step-by-step explanation:

Differentiation is an algebraic process that finds the slope of a curve. At a point, the slope of a curve is the same as the slope of the tangent line to the curve at that point. Therefore, to find the slope of the line tangent to the given function, differentiate the given function.

Given function:

[tex]f(x)=\dfrac{3x}{e^{x}}[/tex]

Differentiate the given function using the quotient rule.

[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Quotient Rule for Differentiation}\\\\If $f(x)=\dfrac{g(x)}{h(x)}$ then:\\\\\\$f'(x)=\dfrac{h(x)g'(x)-g(x)h'(x)}{(h(x))^2}$\\\end{minipage}}[/tex]

[tex]\textsf{Let\;$u=x^2}[/tex][tex]\textsf{Let\;$g(x)=3x$}\implies g'(x)=3[/tex]

[tex]\textsf{Let\;$h(x)=e^{x}$}\implies h'(x)=e^{x}[/tex]

Input the values into the quotient rule to differentiate the function:

[tex]\begin{aligned}f'(x)&=\dfrac{e^x \cdot 3 - 3x \cdot e^x}{(e^{x})^2}\\\\&=\dfrac{e^x(3 - 3x)}{(e^{x})^2}\\\\&=\dfrac{3 - 3x}{e^{x}}\end{aligned}[/tex]

To find the slope of the tangent line at x = 2, substitute x = 2 into the differentiated function:

[tex]\begin{aligned}f'(2)&=\dfrac{3 - 3(2)}{e^{2}}\\\\&=\dfrac{3 -6}{e^{2}}\\\\&=-\dfrac{3}{e^{2}}\\\\\end{aligned}[/tex]

Therefore, the slope of the line tangent to the graph of f(x) = 3x/eˣ at the point where x = 2 is:

[tex]\boxed{-\dfrac{3}{e^{2}}}[/tex]

[tex]\hrulefill[/tex]

Differentiation rules used:

[tex]\boxed{\begin{minipage}{4 cm}\underline{Differentiating $ax$}\\\\If $y=ax$, then $\dfrac{\text{d}y}{\text{d}x}=a$\\\end{minipage}}[/tex]

[tex]\boxed{\begin{minipage}{4 cm}\underline{Differentiating $e^{x}$}\\\\If $y=e^{x}$, then $\dfrac{\text{d}y}{\text{d}x}=e^x$\\\end{minipage}}[/tex]

Part 1: The base fee charged by the ride-share service is $4.

Part 2: The rate of increase in cost in dollars per mile is $2.7.

Part 3: The slope and y-intercept of the equation are $2.7 and $4 respectively.

Part 4: The slope-intercept equation of the line in the graph is y = 2.7x + .

Part 5: The cost of a 20-mile ride is $58.​

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + b

Where:

Part 1.

The base fee is the initial fee or y-intercept, and based on the graph, it is equal to $4.

Part 2.

Rate of increase = (y₂ - y₁)/(x₂ - x₁)

Rate of increase = (12 - 4)/(3 - 0)

Rate of increase = $8/3 or $2.7.

Part 3.

The slope and y-intercept of the equation in this graph are $2.7 and $4 respectively.

Part 4.

Next, we would write the slope-intercept equation of the line as follows;

y = mx + b

y = 2.7x + 4

Part 5.

When x = 20 miles, the cost is given by;

y = 2.7x + 4

y = 2.7(20) + 4

y = $58.

Read more on slope-intercept here: brainly.com/question/7889446

#SPJ1

Answer:

x = 7

Step-by-step explanation:

Each angle is a square is 90°

Also the diagonals bisect each angle

⇒ ∠ACB = 90/2

⇒ 11x - 32 = 45

⇒ 11x = 45 + 32

⇒ 11x = 77

⇒ x = 77/11

⇒ x = 7

The electrical resistance varies directly as the square of the voltage and inversely as the electric power, and the equation that relates them isR ∝ V²/PR = kV²/PR = V²/P. This relationship can be used to calculate the electrical resistance of the wire or component for any given voltage and power.

The electrical resistance is the measure of the difficulty in passing electric current through a wire or an electrical component. It depends on various factors, such as the material, dimensions, and temperature of the wire.The given statement says that the electrical resistance varies directly as the square of the voltage and inversely as the electric power.

In mathematical terms, this relationship can be expressed as R ∝ V²/PR = kV²/P where R is the electrical resistance, V is the voltage, P is the electric power, and k is the constant of proportionality. The constant k depends on the material, dimensions, and temperature of the wire or component.

The given statement implies that the constant k is the same for the given wire or component, and it is not affected by the voltage or the power.To find the value of k, we can use the given values of V, P, and R.

According to the statement, if the voltage is 20 volts and the electric power is 5 watts, then the electrical resistance is 80 ohms. Therefore,R = kV²/PR = k(20²)/5R = 400k/5R = 80 ohms

Substituting the value of R in the equation, we get80 = 400k/5k = (80 x 5)/400k = 1. Therefore, the equation that relates the electrical resistance, voltage, and power isR = V²/PThe constant of proportionality k is 1 for the given wire or component.

Therefore, the electrical resistance varies directly as the square of the voltage and inversely as the electric power, and the equation that relates them isR ∝ V²/PR = kV²/PR = V²/P. This relationship can be used to calculate the electrical resistance of the wire or component for any given voltage and power.

For more such questions on electrical resistance, click on:

https://brainly.com/question/30609640

#SPJ8

Answer:

(B) reduction

Step-by-step explanation:

A dilation with a scale factor of 1/4 is a reduction.

A dilation is a transformation that enlarges or reduces a figure by a certain scale factor. The scale factor is a number that tells you how much bigger or smaller the image will be compared to the original figure. A scale factor of 1/4 means that the image will be 1/4 the size of the original figure. This is a reduction, because the image is smaller than the original figure.

3.1.1 The basic property of operations used is the commutative property of multiplication.

3.1.2 The basic property of operations used is the additive inverse property.

3.1.3 The basic property of operations used is the associative property of addition.

3.1.1 The basic property of operations used in this calculation is the commutative property of multiplication. It states that the order of the factors in a multiplication problem can be rearranged without changing the product. In this case, the numbers 25 and 4 were swapped, resulting in the same product of 100.

3.1.2 The basic property of operations used in this calculation is the additive inverse property. It states that for any number, there exists an additive inverse such that when the number and its additive inverse are added together, the result is zero. In this case, adding 412 and its additive inverse (-412) results in zero.

3.1.3 The basic property of operations used in this calculation is the associative property of addition. It states that the grouping of numbers being added does not affect the sum. In this case, the numbers 25, 37, 20, 5, 30, and 7 were regrouped to facilitate easier mental addition. By grouping 25 and 37, and then grouping 20, 5, 30, and 7, the final sum of 62 is obtained, which is the same as adding all the numbers together in the original order.

for such more question on commutative property

https://brainly.com/question/2475734

#SPJ8