A group of three friends ate dinner at a
restaurant. When they settled the check andtip, Peter paid 4/5 as much as John paid, and
John paid 1/3 as much as Ralph paid. What
fraction of the check and tip did John pay?

Answer:

0.125 in decimal 12.5 in percent

Step-by-step explanation:

in percent it will be 12.5

Answer:

  x = -4/3 or 3

Step-by-step explanation:

You want the solution to 3x² -5x -12 = 0 using the quadratic formula.

The given equation is written in standard form:

  ax² +bx +c = 0

Comparing the equations, we see that ...

The formula for the solution of the equation is ...

  [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

To find the values of x, use the numerical values of a, b, c in this formula:

  [tex]x=\dfrac{-(-5)\pm\sqrt{(-5)^2-4(3)(-12)}}{2(3)}=\dfrac{5\pm\sqrt{25+144}}{6}\\\\x=\dfrac{5\pm\sqrt{169}}{6}=\dfrac{5\pm13}{6}=\left\{\dfrac{-8}{6},\ \dfrac{18}{6}\right\}\\\\\boxed{x=\left\{-\dfrac{4}{3},\ 3\right\}}[/tex]

0.25 recurring can be expressed as the fraction 25/99.

A fraction is a mathematical expression representing a part of a whole, or a ratio between two numbers. It consists of a numerator, which represents the part or ratio being considered, and a denominator, which represents the whole or total.

To express 0.25 recurring as a fraction, we can use the following method:

Let x = 0.25 recurring

Then 100x = 25.25 recurring (multiply both sides by 100 to move the decimal point)

Subtracting the first equation from the second equation, we get:

100x - x = 25.25 recurring - 0.25 recurring

99x = 25

x = 25/99

Therefore, 0.25 recurring can be expressed as the fraction 25/99.

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From the statements, the expression is    1 inch/2.2 ft =    x/16 ft

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

We can use ratios to solve

Changing 11/5 into a decimal

1 inch              x

-------------- = -----------

2.2 ft            16 ft

Using cross products

16 = 2.2 x

Divide each side by 2.2

16/2.2 = x

7.2727 =x  Since this is less than 8.5 inches   Yes

1 inch              x

-------------- = -----------

2.2 ft            15 ft

Using cross products

15 = 2.2x

Dividing each side by 2.2

6.8 =x

Yes

1 inch              x

-------------- = -----------

2.2 ft            20 ft

Using cross products

20 = 2.2x

9.09 =x

If this is the 11.5 inch side   (15 ft   is  6.8 inches which is less than 8.5 inches)

yes

1 inch              x

-------------- = -----------

2.2 ft            12 ft

12 = 2.2x

5.4 inches  yes since 16 is 6.8 inches

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The critical value for a two-tailed test with a significance level of 0.01 and 13 degrees of freedom is approximately ±0.532.

A critical value is a point on a statistical distribution that is compared to a test statistic to determine whether to reject the null hypothesis

It is based on a significance level, which is the probability of rejecting the null hypothesis when it is actually true.

To find the critical value for a correlation coefficient at a significance level of 0.01 and 13 degrees of freedom, we can use Table A-6 in the textbook or online resources.

To determine if the data set has a statistically significant correlation, we need to calculate the correlation coefficient r and compare it to the critical value. We can use a calculator or spreadsheet software to calculate the correlation coefficient. Using the data from the table, we find that:

The mean of the age variable is 41.47, and the standard deviation is 19.16.

The mean of the resting heart rate variable is 66.73, and the standard deviation is 8.53.

The correlation coefficient between age and resting heart rate is 0.439.

Since the correlation coefficient (r=0.439) is greater than the critical value (±0.532), we can conclude that there is not a statistically significant correlation between age and resting heart rate at the 0.01 level of significance. This means that we cannot reject the null hypothesis that there is no correlation between age and resting heart rate in the population.

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The earning of an employee is 8.25 dollars per hour and hourly pay rate is 8.25 dollars.

What is pay rate?

Pay rate refers to the amount of money an employer pays an employee for their work, typically expressed as an hourly, weekly, or monthly rate. It is the rate at which an employee is compensated for their time and labor, and can be influenced by a number of factors, such as job skills, experience, industry, location, and market demand for the particular role. The pay rate may also be subject to deductions for taxes, insurance, and other benefits provided by the employer.

Here,

The hourly pay rate of the employee can be calculated by dividing the earnings by the number of hours worked. Using the given equation, we can rewrite it as E = 8.25h

Dividing both sides by h,

E/h = 8.25

Therefore, the hourly pay rate of the employee is 8.25 dollars per hour.

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The area covered by the label is 188.4cm² and total surface area is 244.92cm².

A cylinder's total surface area is equal to the sum of all of its faces' surface areas. The cylinder's total surface area—the sum of its curved and circular areas—has a radius of "r" and a height of "h."

Here, we have

Given: A can of soup in the shape of a cylinder is 10 centimeters tall and has a diameter of 6 centimeters.

We have to find the total surface area of the can including the top and bottom.

The area covered by the label = πd×height

= π(6)×10

= 3.14×6×10

= 188.4

Total surface area =  πr² +  πr³ + 188.4

= 3.14(3)² +  3.14(3)³ + 188.4

= 244.92

Hence, the area covered by the label is 188.4cm²

and total surface area is 244.92cm².

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Answer:

Step-by-step explanation:

v = π · r² · h

v = π · 5² · 10

v = 25· 10π

v = 250π

v =785.39816339

v =785.4

The equation that expresses the relationship between the two variables is 6x = y.

Let's assume that Chad runs 'x' laps, then Kyle runs 6 times as many laps as Chad, which means Kyle runs 6x laps. Therefore, the equation expressing the relationship between Chad's laps and Kyle's laps can be written as:

Kyle's laps = 6 times Chad's laps

or                              

6x = the number of laps Kyle runs

So, the equation is: 6x = y, where 'x' represents the number of laps Chad runs i.e. he ran six times more, and 'y' represents the number of laps Kyle runs i.e. he ran six times lesser than Chad.

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The tree stump is approximately 2.64 feet tall. This is solved using the Tangent Function.

Let's assume that the height of the tree stump is h feet.

Since the roots of the tree extend out from the base of the tree the same distance that the stump is tall, the distance between the end of the roots and the top of the stump is also h feet.

Therefore, the total distance covered by the 2x4's is 2h feet (h feet up to the top of the stump and h feet down to the end of the roots).

We can use the tangent function to find the angle of incline. The tangent of an angle is equal to the opposite side divided by the adjacent side.

In this case, the opposite side is h and the adjacent side is 5 feet. So, we have:

tan θ = h/5

To maximize the angle of incline, we want to maximize the value of θ. This occurs when tan θ is as large as possible.

Since the tangent function is an increasing function, we can find the largest possible value of tan θ by finding the largest possible value of h.

Solving for h in the equation tan θ = h/5, we get:

h = 5 tan θ

Since the length of the boards is 5 feet, we know that:

2h = 5

Substituting for h, we get:

2(5 tan θ) = 5

10 tan θ = 5

tan θ = 0.5

Using a calculator or a table of tangent values, we can find that the angle whose tangent is 0.5 is approximately 26.57 degrees.

Therefore, the height of the tree stump is:

h = 5 tan θ

h = 5 tan 26.57

h ≈ 2.64 feet

So, the tree stump is approximately 2.64 feet tall.

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Based on the IQR values, we can see that Player B is more consistent than Player A. Thus option B is correct.

To find the best measure of variability for the data, we need to compare the range and interquartile range (IQR) for both players.

For Player A:

Range = maximum value - minimum value [tex]= 7 - 1 = 6[/tex]

[tex]IQR = Q3 - Q1 = 3 - 1.5 = 1.5[/tex]

For Player B:

Range = maximum value - minimum value [tex]= 10 - 1 = 9[/tex]

[tex]IQR = Q3 - Q1 = 5 - 1.5 = 3.5[/tex]

The IQR is generally considered a better measure of variability than the range because it is not influenced by extreme values. Therefore, the best measure of variability for this data is the interquartile range (IQR).

Based on the IQR values, we can see that Player B is more consistent than Player A.

Therefore, the correct answer is: Player B is the most consistent, with an IQR of  [tex]3.5[/tex]  .

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Answer:

Step-by-step explanation: The answer is to be calculated with help of taking out averages of the households' Tvs.

In order to calculate the expected value we multiply each value of the random variable by its probability and then add the results.

(1 TV times 350/1000) + (2 TV times 500/1000) + (3 TV times 120/1000) + (4 TV times 30/1000) = 1.83.

on average, each household has 1.83 TVs.

As per the data given, a television channel conducted a study on the number of TVs per household in their service area. Out of 1000 households surveyed, 350 have one TV, 500 have two TVs, 120 have three TVs and 30 have four TVs. We need to determine the number of TVs each household has on average.To calculate the average number of TVs, we need to calculate the total number of TVs and divide that by the number of households.

Totals TVs = (Number of households with 1 TV × 1) + (Number of households with 2 TVs × 2) + (Number of households with 3 TVs × 3) + (Number of households with 4 TVs × 4)Total TVs

= (350 × 1) + (500 × 2) + (120 × 3) + (30 × 4)Total TVs = 350 + 1000 + 360 + 120

Total TVs = 1830

Average number of TVs per household = Total TVs / Number of households

Average number of TVs per household = 1830 / 1000

Average number of TVs per household = 1.83

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Answer:    The computer Lea wants to buy is listed at a regular price of $400.00.

During the sale, the computer will be discounted by 30%. So, the price after the discount will be:

$400.00 - (30% of $400.00) = $400.00 - $120.00 = $280.00

If Lea buys the computer before 9:00 a.m. on that same Saturday, she will get an additional 10% discount. So, the price after both discounts will be:

$280.00 - (10% of $280.00) = $280.00 - $28.00 = $252.00

Therefore, Lea will pay $252.00, without tax, when she buys the computer that Saturday before 9:00 a.m.

Step-by-step explanation:

Answer:

240

Step-by-step explanation:

The relative frequency of business majors in the given table survey is: 0.24

Relative frequency is defined as the number of times an event occurs divided by the total number of events occurring in a given scenario

To calculate the relative frequency the following must be known:

- Number of total events/trials

- Frequency count for a category/subgroup

We want to find the relative frequency of business majors in the given table.

Total number of business majors = 37 + 38 = 75

Total number of students in the survey = 318

Thus:

Relative Frequency = 75/318 = 0.2358 ≈ 0.24

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Answer: It's the third rectangle

Step-by-step explanation: If you cut from the vertex vertically it would be a triangle but if you cut a pyramid horizontally its either a square or rectangle.

The data is collected on two different populations of people: those that use the internet, and those that don't, and the data was collected over a 10-year time period. Therefore, the correct option is A.

A scatter plot is a graphical representation of data in which two variables are plotted on the x-axis and y-axis,

respectively.

It is used to visualize the relationship between two quantitative variables. In the scatter plot, each point represents a

value for each variable.

A scatter plot is the most appropriate visualization of this bivariate relationship because one variable is quantitative,

and one variable is categorical.

Both variables are numeric, and we know both their age and how often they use the internet each week.

This explains why scatter plot is the most appropriate visualization of this bivariate relationship.

Therefore, the correct option is A. The data is collected on two different populations of people: those that use the

internet, and those that don't, and the data was collected over a 10-year time period.

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Part A: The function s(w) = 15w represents the number of seeds planted by the botanist as a function of the number of weeks w that planting occurs at the garden. The units of measurement for this function are seeds and weeks.

Part B: The function f(s) = 3s + 35 represents the number of flowers that can be expected to bloom as a function of the number of seeds planted by the botanist. The units of measurement for this function are flowers and seeds.

Part C: The composite function that represents the number of flowers the botanist can expect to bloom over a certain number of weeks is f(s(w)) = 3(15w) + 35 = 45w + 35.

Part D: To evaluate the composite function for 36 weeks, we substitute w = 36 into the function: f(s(36)) = 45(36) + 35 = 1635. Therefore, the botanist can expect 1635 flowers to bloom after 36 weeks of planting. The units of measurement for this answer are flowers.

1. Part A: What does the function s(w) = 15w represent in terms of the garden? What are the units of measurement for this function?

ANSWER: The function s(w) = 15w represents the total number of seeds planted by the botanist as a function of the number of weeks (w) that planting occurs at the garden. The units of measurement for this function are seeds.

2. Part B: What does the function f(s) = 3s + 35 represent in the context of the garden? What are the units of measurement for this function?

ANSWER:  The function f(s) = 3s + 35 represents the total cost (in dollars) of supplies needed to plant s seeds in the garden. The units of measurement for this function are dollars.

3. Part C:What composite function represents the number of flowers the botanist can expect to bloom over a certain number of weeks?

ANSWER:   the composite function that represents the number of flowers the botanist can expect to bloom over a certain number of weeks is f(s(w)) = 45w + 35.

4. Part D: Evaluate the composite function in Part C for 36 weeks.

ANSWER: the botanist can expect 1,655 flowers to bloom over 36 weeks.

The probability that an international flight leaving the US is delayed in departing given that the flight is a transpacific flight is approximately 0.1964.

We can use Bayes' theorem to calculate the probability that an international flight leaving the United States is delayed in departing given that the flight is a transpacific flight. Bayes' theorem states that:

P(D|P) = P(P|D) * P(D) / P(P)

where P(D|P) is the probability that a flight is delayed given that it is transpacific, P(P|D) is the probability that a flight is transpacific given that it is delayed, P(D) is the probability of a flight being delayed, and P(P) is the probability of a flight being transpacific.

Using the given values, we can calculate:

P(P and D) = 0.11 (the probability that a flight is both transpacific and delayed)

P(P) = 0.56 (the probability that a flight is transpacific)

P(D) = 0.28 (the probability that a flight is delayed)

To find P(D|P), we need to calculate P(P and D) / P(P):

P(D|P) = P(P and D) / P(P) = 0.11 / 0.56 = 0.1964

Therefore, the probability that an international flight is delayed in departing is approximately 0.1964 (rounded to 4 decimal places).

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--The given question is incomplete, the complete question is given

"The probability that an international flight leaving the United States is delayed in departing (event D) is .28. The probability that an international flight leaving the United States is a transpacific flight (event P) is .56. The probability that an international flight leaving the U.S. is a transpacific flight and is delayed in departing is .11. (a) What is the probability that an international flight leaving the United States is delayed in departing given that the flight is a transpacific flight? (Round your answer to 4 decimal places.)"--

The value of x and y in the figure are

5. x = 29

6. y = 5 and x = 5

5. The value of x is found knowing that angles in a straight line is supplementary hence we have that

6x + 4 + 10x = 180

16x = 180 - 4

6x = 174

x = 174 / 6 = 29

6. Applying vertical angle theorem and angles in a straight line is supplementary

155 + 5y = 180

5y = 180 - 155

5y = 25

y = 5

also

5y + 13x = 90

5(5) + 13x = 90

13x = 90 - 25

13x = 65

x = 65 / 13 = 5

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Answer:

35

Step-by-step explanation:

The equation can be written as:

p - 10 = 25

To solve for p, we can add 10 to both sides of the equation:

p - 10 + 10 = 25 + 10

Simplifying the left side by canceling out -10 and +10, we get:

p = 35

Therefore, the number we are looking for is 35.

Scarlett was charged $33 when she received her bill at the restaurant. She chose to tip 26% for the service she received. She must multiply the bill amount by 0.26 to determine the tip.

Tip = 0.26 x $33 = $8.58 Thus the total cost of the dinner plus the tip is: Total = $33 + $8.58 = $41.58  before tax for the lunch and tip. It should be noted that tax is not included in this computation. The tip amount may be calculated by multiplying the meal cost by the tip percentage: Tipping rate = 33 * 0.26 = 8.58 Therefore the entire cost of the lunch, including the tip, is: Cost total = 33 + 8.58 = 41.58 As a result, Scarlett's lunch plus tip, before tax, was $41.58.Scarlett was charged $33 when she received her bill at the restaurant. She chose to tip 26% for the service she received. She must multiply the bill amount by 0.26 to determine the tip: Tip = 0.26 x $33 = $8.58 Thus the total cost of the dinner plus the tip is: Total = $33 + $8.58 = $41.58  before tax for the lunch and tip. It should be noted that tax is not included in this computation. The tip amount may be calculated by multiplying the meal cost by the tip percentage: Tipping rate = 33 * 0.26 = 8.58 Therefore the entire cost of the lunch, including the tip, is Cost total = 33 + 8.58 = 41.58 As a result, Scarlett's lunch plus tip, before tax, was $41.58.Scarlett was charged $33 when she received her bill at the restaurant. She chose to tip 26% for the service she received. She must multiply the bill amount by 0.26 to determine the tip. Tip = 0.26 x $33 = $8.58 Thus the total cost of the dinner plus the tip is: Total = $33 + $8.58 = $41.58.

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The type of error that occurs when potential respondents are improperly excluded before the sample is taken is called selection bias

The type of error that occurs when potential respondents are improperly excluded before the sample is taken is called "selection bias". Selection bias occurs when the sample is not representative of the population, leading to an overrepresentation or underrepresentation of certain groups. This can happen when certain individuals or groups are systematically excluded from the sample, either intentionally or unintentionally.

Selection bias can lead to inaccurate conclusions and invalid results, which can undermine the validity and reliability of the study. Therefore, it is essential to use appropriate sampling techniques and ensure that the sample is representative of the population of interest to avoid selection bias.

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Answer:

Angle A: 49 degrees

Angle B: 139 degrees

Step-by-step explanation:

- Since Angles Y and A are vertical angles, they are congruent. Since Angle Y measures 49 degrees, Angle A also measures 49 degrees.

- Since Angle A, an unnamed angle, and the right angle in the triangle must sum up to 180 degrees, solve for the remaining angle that we don't know the measure of. We know the measure of the right angle is 90 degrees and Angle A measures 49 degrees, and 90 + 49 = 139, so the other angle measures 41 degrees because 180 - 139 = 41. That 41-degree unnamed angle is supplementary to Angle B because they are adjacent, so 180 - 41 = 139. Therefore, Angle B measures 139 degrees.

Value of x is 9.

In geometry, two figures or objects are said to be congruent if their shapes and sizes same, or if one is the mirror image of the other. Congruent involves comparing two numbers, .In, two line segments are congruent implies that the two lines have equal measurements.

Triangle congruence; If all three corresponding sides and all three corresponding angles are equal . two triangles are said to be congruent If Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved.

if,ΔABC≅ΔDEC

than ∠B=∠E

So, 3 x = 6 x-39

⇒6 x = 3 x+39

⇒6 x -3 x=39

⇒3 x = 39

⇒x=13.

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Their corresponding side's ratio will not change. Then, x has a value of 4.

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes.

ABC refers to a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

With three sides, three angles, and three vertices, a triangle is a closed, two-dimensional object.

A polygon also includes a triangle.

Triangle ABC is shown in the image above.

So, it is made up of two triangles: DEF and XYZ.

The similarity between the DEF and XYZ is assumed.

When it happens, the ratio of their corresponding side will not change. Which is:
5/10 = 2x-1/14 = 11/5x+2

The first two are what we have.

5/10 = 2x-1/14

Then, we have:
x = 4

Therefore, their corresponding side's ratio will not change. Then, x has a value of 4.

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Correct question:

Find the value of x that makes Triangle DEF~ triangle XYZ.

The area of the circle is decreasing at a rate of 0.2 cm³/s. We simply multiply dA/dr by dr/dt, giving us dA/dt.

A line segment connecting the center of the circle to a point on the circle, and is equal in length to all other line segments connecting the center to points on the circle.

The three variables involved in the question are the area of a circle (A), the radius of a circle (r), and the rate of change of the radius (dr/dt). Using the chain rule, we can link all of these rates together with the equation dr/dt = dA/dr x dA/dt.

We know that the area of a circle is equal to r², so we can rewrite the equation as

dr/dt = 2r x dA/dt.

We are given the value of dr/dt, which = 0.4 cm/s, and so we can use this to calculate the value of dA/dr.

To do this, we first divide both sides of the equation by 2r, giving us dA/dr = dr/dt/2r.

Plugging in the values for dr/dt and r (which is 8 cm) gives us a value of dA/dr = 0.05 cm²/cm.

We can use this to calculate the rate at which the area of a circle is decreasing when its radius= 8 cm and decreasing at 0.4 cm/s.

To do this, we simply multiply dA/dr by dr/dt, giving us dA/dt = 0.2 cm³/s. This means that the area of the circle is decreasing at a rate of 0.2 cm³/s.

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