If using the method of completing the square to solve the quadratic equation x^2-19x-39=0x 2 −19x−39=0, which number would have to be added to "complete the square"?​

At most, they can wash 96 cars and mow 96 lawns.

To determine the maximum number of cars they can wash and lawns they can mow, we need to consider the work rates of each person and the total number of hours they work.

Huey can wash 6 cars or mow 3 lawns in one hour, so in 8 hours, he can wash 6 \(\times\) 8 = 48 cars or mow 3 \(\times\) 8 = 24 lawns.

Dewey can wash 3 cars or mow 3 lawns in one hour, so in 8 hours, he can wash 3 \(\times\) 8 = 24 cars or mow 3 \(\times\) 8 = 24 lawns.

Louie can wash 3 cars or mow 6 lawns in one hour, so in 8 hours, he can wash 3 \(\times\) 8 = 24 cars or mow 6 \(\times\) 8 = 48 lawns.

Since two of them wash cars and one mows lawns, the maximum number of cars they can wash is the sum of the maximum cars each person can wash, which is 48 + 24 + 24 = 96 cars.

The maximum number of lawns they can mow is the sum of the maximum lawns each person can mow, which is 24 + 24 + 48 = 96 lawns.

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The correct option is A, the lower quartile (Q1) and it is 75.

We must comprehend the quartiles of the box plot in order to calculate the number below which 25% of the data lies.

A box plot's interquartile range (IQR), which contains the middle 50% of the data, is represented by the box.

The median, which splits the data into two equally sized half, is shown by the line inside the box.

Here, the box has a line at 79 and spans from 75 to 82.

Accordingly, the lower quartile (Q1) and the upper quartile (Q3) are both situated near the box's boundary, which is 75 and 82, respectively.

The line inside the box, which is 79, is the median (Q2).

The first quartile (Q1) or the 25th percentile must be identified in order to establish the number below which 25% of the data lies.

The first quartile in a box plot symbolizes the number below which 25% of the data is found.

Since Q1 is located at the lower boundary of the box, which is 75, 25% of the data lies below the score of 75.

Hence the correct option is A.

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a)  The 95% confidence interval for µd is [2.32, 6.88].

b) There is strong evidence that µd differs from 0.

(a) To calculate a 95% confidence interval for µd, we use the formula:

Confidence interval = [d¯ - t*sd/√n , d¯ + t*sd/√n]

Where d¯ is the sample mean, t is the t-value corresponding to the desired level of confidence and degrees of freedom (df = n-1), sd is the sample standard deviation, and n is the sample size.

For a 95% confidence interval with 49-1=48 degrees of freedom, the t-value is 2.01 (from a t-table).

Plugging in the given values, we get:

Confidence interval = [4.6 - 2.01*7.6/√49 , 4.6 + 2.01*7.6/√49]

Confidence interval = [2.32 , 6.88]


Since the entire interval is greater than 0, we can be 95% confident that the difference between µ1 and µ2 is greater than 0.

(b) To test the null hypothesis H0: µd = 0 versus the alternative hypothesis Ha: µd ≠ 0, we use a t-test.

The test statistic is:

t = (d¯ - µd)/(sd/√n)

Where d¯ is the sample mean, µd is the hypothesized mean difference, sd is the sample standard deviation, and n is the sample size.

Plugging in the given values, we get:

t = (4.6 - 0)/(7.6/√49)

t = 4.24

We then compare this t-value to the critical t-values for the different levels of significance (α = .10, .05, .01, and .001) and 48 degrees of freedom (from a t-table).

The critical t-values are:

t(.10) = 1.68

t(.05) = 2.01

t(.01) = 2.68

t(.001) = 3.50

Since our calculated t-value (4.24) is greater than all of the critical t-values, we reject the null hypothesis at all levels of significance.

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Answer:

(5,3) and (5,9)

Step-by-step explanation:

When two parallel lines are cut by a transversal, eight angles are formed. Interior angles are supplementary to corresponding exterior angles and the sum of an interior and its corresponding exterior angle is 180 degrees.

Two parallel lines are cut by a transversal, eight angles are formed. Four of these angles are interior angles, which are the angles formed between the two lines and the transversal that lie within the region bounded by the parallel lines. The other four angles are exterior angles, which are the angles formed between the two lines and the transversal that lie outside the region bounded by the parallel lines. Interior angles are equal in measure and are supplementary to the corresponding exterior angles. In other words, the sum of an interior angle and its corresponding exterior angle is equal to 180 degrees. Understanding the properties of interior and exterior angles is important in geometry, as they can be used to prove the parallelism of lines.

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Answer:

We conclude that the volume of a regular octahedron will be:

Step-by-step explanation:

Given

The length of one of the side or edge of a regular octahedron = a = 4 cm

To determine

The volume of a regular octahedron = V

Using the formula to determine the volume of a regular octahedron

\(V\:=\:\frac{\sqrt{2}}{3}a^3\)

substituting a = 4 in the volume equation

\(V=\frac{\sqrt{2}\cdot \:4^3}{3}\)

\(V=\frac{64\sqrt{2}}{3}\)         ∵ 4³ = 64

\(\:\:V\:\approx \:30.17\) cm

Therefore, we conclude that the volume of a regular octahedron will be:

Answer:

Literal equations, simply put, are equations containing two or more variables. Your goal is to solve for just one variable with respect to others

Step-by-step explanation:

literal literal equations are equations that contain more than one variable

Answer:

12(x+4)

Step-by-step explanation:

12(x+4)

Answer:

Area & Circumference = 12.56ft

Step-by-step explanation:

The formula for area of a circle is πr^2

r = 2

π = 3.14

(3.14) x (2^2)

(3.14) x (4) = 12.56

The formula for circumference of a circle is 2πr

r = 2

π = 3.14

2 x (3.14) x 2

(3.14) x (4) = 12.56

Answer:

26400 ft^3

Step-by-step explanation:

basement: 60*35*10=21000

crawl space: 30*(35-20)*4=30*15*4=1800

garage: 20*30*6=3600

total: 21000+1800+3600=26400

Tom can paint the room alone in 12 hours.

Let's assume that the work required to paint the room is equivalent to 1 unit of work. If John can paint the room alone in 6 hours, his work rate per hour is 1/6.

Similarly, if John and Tom together can paint the room in 4 hours, their combined work rate per hour is 1/4. Let x be Tom's work rate per hour.

Then, we can set up the following equation:1/6 + x = 1/4

To solve for x, we can simplify the equation as follows:

Multiplying both sides by 12 (the LCM of 6 and 4) yields:2 + 12x = 3Solving for x gives:12x = 1x = 1/12Therefore, Tom's work rate per hour is 1/12, which means he can paint the room alone in 12 hours.

Summary:Tom can paint the room alone in 12 hours

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Avery interpreting the Probability is wrong because 0.40 represents probability in the long run over many visits to the site

Probability: The chance that a given event will occur. The ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes

given that the probability that a randomly selected visitor to a certain website will be asked to participate in an online survey is 0. 40

Avery claims that for the next 5 visitors to the site, 2 will be asked to participate in the survey

Avery interpreting the Probability is wrong because 0.40 represents probability in the long run over many visits to the site

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Answer:

Because 0.40 represents likelihood over many visits to the site in the long term, Avery's interpretation of the probability is incorrect.

Step-by-step explanation:

What does the term probability mean?

Probability: The likelihood that a specific occurrence will take place. the proportion between the total number of conceivable outcomes and the number of outcomes in a comprehensive collection of equally likely outcomes that result in a specific event

Given that there is a 0. 40 percent chance that a randomly chosen website visitor will be requested to take an online survey

Avery asserts that of the following 5 site visits, 2 will be required to complete the survey.

Because 0.40 represents chance over the long term and several visits to the site, Avery's interpretation of the probability is incorrect.

Answer: x= 4/1289 not sure if this was what you were looking for.

Step-by-step explanation:

Step 1: Subtract 143x from both sides.

1432x−3−143x=143x+1−143x

1289x−3=1

Step 2: Add 3 to both sides.

1289x−3+3=1+3

1289x=4

Step 3: Divide both sides by 1289.

1289x/1289 = 4/1289

x= 4/1289

Answer:

2

Step-by-step explanation:

Using the graph of tanx attached, we know that each period starts and restarts after each π. I've contrasted the periods of the functions in blue versus what we have between the two points in green.

From -3π/4 to 5π/4, we have.....

1/4 of a period

1 full period

3/4 of a period

1/4 + 1 + 3/4 = 2 periods

I hope this helps!

Using quantifiers; a) ∀ student ∈ this class, ∃ exactly 2 mathematics classes ∈ this school that the student has taken and b) ∃ person, ∀ country ∈ the world (country ≠ Libya), the person has visited that country.

a) "Every student in this class has taken exactly two mathematics classes at this school."

In this statement, we have two main quantifiers:

Universal quantifier (∀): This quantifier denotes that we are making a statement about every individual student in the class. It indicates that the following condition applies to each and every student.

Existential quantifier (∃): This quantifier indicates the existence of something. In this case, it asserts that there exists exactly two mathematics classes at this school that each student has taken.

So, when we combine these quantifiers and their respective conditions, we get the statement: "For every student in this class, there exists exactly two mathematics classes at this school that the student has taken."

b) "Someone has visited every country in the world except Libya."

In this statement, we also have two main quantifiers:

Existential quantifier (∃): This quantifier signifies the existence of a person who satisfies a particular condition. It asserts that there is at least one person.

Universal quantifier (∀): This quantifier denotes that we are making a statement about every individual country in the world (excluding Libya). It indicates that the following condition applies to each and every country.

So, when we combine these quantifiers and their respective conditions, we get the statement: "There exists at least one person who has visited every country in the world (excluding Libya)."

In summary, quantifiers are used to express the scope of a statement and to indicate whether it applies to every element or if there is at least one element that satisfies the given condition.

Therefore, Using quantifiers; a) ∀ student ∈ this class, ∃ exactly 2 mathematics classes ∈ this school that the student has taken and b) ∃ person, ∀ country ∈ the world (country ≠ Libya), the person has visited that country.

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Answer:

n=36

Step-by-step explanation:

To isolate n you need to subtract 15 from both sides giving you

2n=72

Then to further isolate n you need to divide 2 from both sides giving you the answer

n=36

Answer:

Since the ratio of the altitudes of the two triangles ABC and DEF is 1:3, we can say that the altitude of triangle DEF is three times that of triangle ABC.

Let's assume the altitude of triangle ABC is h, then the altitude of triangle DEF is 3h.

Now, we know that the area of a triangle is given by the formula:

Area = (1/2) * base * height

Let's apply this formula to both triangles:

Area of triangle ABC = (1/2) * base * altitude

= (1/2) * 7cm * h

= 3.5h cm^2

Area of triangle DEF = (1/2) * base * altitude

= (1/2) * 7cm * 3h

= 10.5h cm^2

Since the two triangles are similar, their areas are proportional to the squares of their corresponding sides. That is:

Area of triangle ABC / Area of triangle DEF = (AB / DE)^2

Substituting the values, we get:

3.5h / 10.5h = (AB / DE)^2

1/3 = (AB / DE)^2

Taking the square root of both sides, we get:

AB / DE = 1 / sqrt(3)

AB = (1 / sqrt(3)) * DE

Now, we know that the sides of triangle ABC are 3cm, 5cm, and 7cm.

Let's assume that the sides of triangle DEF are a, b, and c.

Since the sides of the two triangles are proportional, we can write:

a / 3 = b / 5 = c / 7 = 1 / sqrt(3)

Solving for a, b, and c, we get:

a = 3 / sqrt(3) = sqrt(3) cm

b = 5 / sqrt(3) = (5 * sqrt(3)) / 3 cm

c = 7 / sqrt(3) = (7 * sqrt(3)) / sqrt(3) = 7 cm

Therefore, the measures of the sides of triangle DEF are sqrt(3) cm, (5 * sqrt(3)) / 3 cm, and 7 cm.

Answer:

n = 3/25

Step-by-step explanation:

5(n-1/10)=1/2

5n = 6/10

n = 3/25

Answer:

Step-by-step explanation:

lets remove the parenthesis

5n- 5/10=1/2

5n=1/2+1/2

5n=1

n=1/5

Answer:(a) The smallest possible distance between the two towns would be 12km (the distance to Bergville) + 15km (the distance to Reddington) = 27km. The largest possible distance would be 12km + 15km + 1km (the margin of error for each distance being given to the nearest kilometer) = 28km.

(b) The possible difference in the distance the two walkers walk would be the difference in the distances given on the sign, which is 15km - 12km = 3km. However, this difference would also be affected by the margin of error of 1km for each distance given on the sign, so the possible difference in distance could range from 2km to 4km.

it's easy

Step-by-step explanation:

use the formula for finding a slope and equate it to 7

The position value, r(t) is equals to the (t³/6)k + 2j and velocity value, v(t) is equals to ( t²/2 )k + 4i , for a(t) = tk, v(0) = 4i, r(0) = 2j.

Acceleration is defined as the rate of change of the velocity of an object with respect to time. Accelerations are vector quanty.

a = dv/dt

We have the following informations are available,

Initial velocity, v(0) = 4i

Initial position, r(0) = 2j

Acceleration at any time "t",

a(t) = tk

we have to determine the value of v(t) and r(t).

As we know, a(t) = dv(t)/dt = tk

integrating the above equation ,

v(t) = ∫tk dt = ( t²/2 )k + c

at t = 0 , v(0) = 0 + c = 4i ( since, v(0) = 4i

=> c = 4i

So, v(t) = ( t²/2 )k + 4i

Also, velocity is calculated by derivative of postion (r) with respect to time.

=> v(t) = dr(t) /dt

=> r(t) = ∫ v(t) dt

=> r(t) = ∫ ( t²/2 )k dt

integrating value of the right hand side,

r(t) = ( t³/2×3 )k +d

= (t³/6)k + d

At t = 0, r(0) = (0/6)k + d

=> r(0) = d = 2j

so, r(t) = (t³/6)k + 2j

Hence, the required position and velocity are

(t³/6)k + 2j and ( t²/2 )k + 4i.

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If we shuffle a deck of cards ,turn over first card, then

(a) "Sample-Space" of this experiment is set of all 52 cards.

(b) Number of outcomes in event that the first card is a heart is 13 .

Part (a) : The "Sample-Space" of this experiment refers to all possible outcomes that occur when "first-card" from a shuffled deck of cards is turned over.

In a "standard-deck" of 52 playing cards, the sample space consist of all 52 cards, which includes 4 suits (hearts, diamonds, clubs, spades) each with 13 cards (Ace - 10, Jack, Queen, King).

So, the sample space of this experiment will be set of all 52 possible cards that could be turned over as "first-card".

Part (b) : The event that "first-card" is a heart will consist of all outcomes where the first card turned over is a heart.

In a "standard-deck" of 52 "playing-cards", there are 13 hearts (Ace of Hearts, 2 of Hearts, 3 of Hearts, ..., 10 of Hearts, Jack of Hearts, Queen of Hearts, and King of Hearts).

Therefore, there are 13 outcomes in the event .

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The given question is incomplete, the complete question is

Shuffle a deck of cards and turn over the first card.

(a) What is the sample space of this experiment?

(b) How many outcomes are in the event that the first card is a heart?

Answer:

2:1

Step-by-step explanation:

4 pineapples, 2 bananas

4:2

2:1 (If reduced)

Answer:

Step-by-step explanation:

4m - 8 = 10 - 2m

6m - 8 = 10

6m = 18

m = 3

Answer:

m=3

Step-by-step explanation:

4m-8=10-2m

+2          +2

6m-8=10

     +8  +8

6m=18/6

m=3

4(3)-8=10-2(3)

4=4

Solution

The question would like us to evaluate the following:

- The solution is given below:

Final Answer

The answer is -3

Answer:

Step-by-step explanation:

Comparing

This is not same as u = v, so the answer is false

Answer:

41

Step-by-step explanation:

2021 eng

A lift ratio of 1.52 implies that identifying a person who purchases coffee and a breakfast sandwich is 52% better than guessing that a random person will purchase a breakfast sandwich.

Stronger relationships are indicated by higher lift values.We divide the confidence ratio by the support of the consequent to arrive at the lift ratio.

Lift ratios greater than one are typically thought to imply a significant link between the components. Lift ratios below 1 indicate that a purchase of the items is unlikely. Lift is simply the ratio of target response divided by the average response.

Carmen analyzed data from the month of March to see if there was a link between coffee and breakfast sandwich purchases. She calculated the lift ratio to be 1.52 after running confidence and expected confidence calculations.

In this case, she wants to know the association between coffee and breakfast sandwich purchases. There's 52% better off than a random individual.

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Answer:

16

Step-by-step explanation:

Answer:

a: -1/2

b: 15

Step-by-step explanation:

A system that has infinite solutions is the same line on top of itself.

Hope that helps

Therefore, the solar flux density for mercury after the calculation is 9.12 x 10⁻³ W/m².

The solar flux density also referred to as the solar constant is the total amount of energy derived from the sun per unit area per given unit of time. It is considered to be equal to solar luminosity divided by the surface area of a given sphere that has a radius equivalent to the distance between the respective planet from the sun.

using the formula for finding the solar flux density,

solar flux density =  solar luminosity /(4 x π x distance between mercury and the sun)

solar flux density =  3.865 x \(10^{26}\) /(4 x π x ( 5.791 x \(10^{10}\)))

solar flux density = 9.12 x 10⁻³ W/m²

Therefore, the solar flux density for mercury after the calculation is 9.12 x 10⁻³ W/m².

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