The slope of EF¯¯¯¯¯ is −52.

Which segments are perpendicular to EF¯¯¯¯¯?

Select each correct answer.


NP¯¯¯¯¯¯, where N is at (−3, 4) and P is at (−8, 2)

GH¯¯¯¯¯¯, where G is at (6, 7) and H is at (4, 12)

JK¯¯¯¯¯, where J is at (3, −2) and K is at (5, −7)

LM¯¯¯¯¯¯, where L is at (1, 9) and M is at (6, 11)

Answer:many

Step-by-step explanation:manymulti- a combining form meaning “many,” “much,” “multiple,” “many times,” “more than one,” “more than two,” “composed of many like parts,” “in many respects,” used in the formation of compound words: multiply; multivitamin.

Mate's car can travel approximately 5 more minutes per gallon of gas compared to Jenna's car.

To determine how many more minutes Mate's car can travel per gallon of gas compared to Jenna's car, we would need additional information about the fuel efficiency or miles per gallon (MPG) for each car.

Fuel efficiency is typically measured in terms of miles per gallon, indicating the number of miles a car can travel on a gallon of gas.

To calculate the difference in travel time, we would also need to know the average speed at which the cars are traveling.

Once we have the MPG values for Mate's car and Jenna's car, we can calculate the difference in travel time per gallon of gas by considering their respective fuel efficiencies and average speeds.

If Mate's car has a fuel efficiency of 30 MPG and Jenna's car has a fuel efficiency of 25 MPG, we can calculate the difference in travel time by comparing the distances they can travel on a gallon of gas.

Let's assume both cars are traveling at an average speed of 60 miles per hour.

For Mate's car:

Travel time = Distance / Speed

= (30 miles / 1 gallon) / 60 miles per hour

= 0.5 hours or 30 minutes.

For Jenna's car:

Travel time = Distance / Speed

= (25 miles / 1 gallon) / 60 miles per hour

= 0.4167 hours or approximately 25 minutes.

Without specific information about the MPG values and average speeds of the cars, it is not possible to provide an accurate answer regarding the difference in travel time per gallon of gas between Mate's car and Jenna's car.

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To prove that τ and σ are multiplicative, we need to show that if m and n are relatively prime, then τ(mn) = τ(m)τ(n) and σ(mn) = σ(m)σ(n).

To prove τ(mn) = τ(m)τ(n), we can start by considering the prime factorization of m and n. Let's say m = p₁^a₁ * p₂^a₂ * ... * pₖ^aₖ and n = q₁^b₁ * q₂^b₂ * ... * qₙ^bₙ, where p₁, p₂, ..., pₖ and q₁, q₂, ..., qₙ are distinct prime numbers. Since m and n are relatively prime, none of their prime factors overlap.

Now, the divisors of mn are the numbers of the form p₁^x₁ * p₂^x₂ * ... * pₖ^xₖ * q₁^y₁ * q₂^y₂ * ... * qₙ^yₙ, where 0 ≤ xᵢ ≤ aᵢ and 0 ≤ yⱼ ≤ bⱼ. Thus, the number of divisors of mn, τ(mn), can be calculated by multiplying the number of divisors of m, τ(m), with the number of divisors of n, τ(n). Hence, τ(mn) = τ(m)τ(n).

To prove σ(mn) = σ(m)σ(n), we can again use the prime factorization of m and n. Similar to the previous proof, the sum of divisors of mn, σ(mn), can be calculated by multiplying the sum of divisors of m, σ(m), with the sum of divisors of n, σ(n). Hence, σ(mn) = σ(m)σ(n).

Therefore, we have proved that τ and σ are multiplicative when m and n are relatively prime.

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We have shown that both τ and σ are multiplicative functions, satisfying the properties τ(mn) = τ(m)τ(n) and σ(mn) = σ(m)σ(n) for relatively prime numbers m and n.

To prove that τ (the number of positive divisors) and σ (the sum of positive divisors) are multiplicative functions, we need to show that for any two relatively prime numbers, m and n, the following properties hold:

1. τ(mn) = τ(m)τ(n)

2. σ(mn) = σ(m)σ(n)

Let's start with property 1:

1. τ(mn) = τ(m)τ(n)

If m and n are relatively prime, it means that they do not share any prime factors. Therefore, the divisors of mn are formed by taking a divisor of m and a divisor of n. Each divisor of mn can be uniquely expressed as the product of a divisor of m and a divisor of n.

Since the number of divisors of mn is equal to the product of the number of divisors of m and the number of divisors of n, we can conclude that τ(mn) = τ(m)τ(n).

Now let's move on to property 2:

2. σ(mn) = σ(m)σ(n)

Similar to property 1, we can express the sum of divisors of mn as the sum of products, where each product is formed by taking a divisor of m and a divisor of n. Again, since m and n are relatively prime, their divisors are distinct.

Using the distributive property, we can expand the sum of products as the sum of two separate terms: one involving the divisors of m and another involving the divisors of n. The sum of divisors of mn is therefore equal to the product of the sum of divisors of m and the sum of divisors of n.

Hence, we can conclude that σ(mn) = σ(m)σ(n).

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The correct options are: Test statistic = -1.1566p-value

= 0.2477Conclusion: Do not reject the null hypothesis. False.

Given data: In Alabama, 12 out of 200 cases tested were found to be drug-resistant.

In Texas, 18 out of 250 cases tested were found to be drug-resistant.

The null hypothesis (H0) is that there is no significant difference between the proportions of drug-resistant cases in the two states.

The alternative hypothesis (Ha) is that there is a significant difference between the proportions of drug-resistant cases in the two states.

Level of significance (α) is not given.

We assume it to be 5% or 0.05. The critical value of Zα/2 for a 95% confidence level is 1.96.

Calculating test statistic: Formula for calculating test statistic is:

Z = (p₁ - p₂) / √[ P * (1 - P) * (1/n₁ + 1/n₂)]

Where, p₁ = proportion of drug-resistant cases in Alabama= 12/200

= 0.06p₂ = proportion of drug-resistant cases in Texas

= 18/250 = 0.072P

= (p₁ * n₁ + p₂ * n₂) / (n₁ + n₂)

= (12 + 18) / (200 + 250)

= 0.067n₁ = sample size in Alabama = 200n₂ = sample size in Texas = 250

Now substituting the values, Z = (0.06 - 0.072) / √[ 0.067 * (1 - 0.067) * (1/200 + 1/250)]

= -1.1566

Critical value of Zα/2 for a 95% confidence level is 1.96 since the sample size is large (n₁p₁ > 5, n₁(1 - p₁) > 5, n₂p₂ > 5, n₂(1 - p₂) > 5).-1.1566 lies between -1.96 and +1.96, thus it falls in the acceptance region.

Conclusion: Since the test statistic (-1.1566) lies in the acceptance region and not in the rejection region, we cannot reject the null hypothesis.

Hence, we conclude that there is not enough evidence to suggest that there is a significant difference between the proportions of drug-resistant cases in the two states.

Thus, we choose the answer as "Do not reject the null hypothesis". There is no significant difference in drug resistance between the two states.

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Answer:

m∠Z = 166°

Step-by-step explanation:

Since we know that the angles add up to 720°, we can set up an equation to solve for the variable x:

12x + 14x - 6 + 108 + 108 + 108 + 90 = 720

26x + 408 = 720

26x = 312

x = 12

Now we substitute the number in for x to solve ∠Z:

m∠Z = 14(12) - 2 = 166

m∠Z = 166°

Answer:

The height of the flagpole is 36.363 feet.

Step-by-step explanation:

This problem can be represented geometrically by two similar right triangles, represented in the image attached below. By definition of similarity, we construct the following relationship:

\(\frac{4\,ft}{5.5\,ft} = \frac{x}{50\,ft}\) (1)

Where \(x\) is the height of the flagpole, measured in feet.

Lastly, we find the required value:

\(x = \left(\frac{4\,ft}{5.5\,ft} \right)\cdot (50\,ft)\)

\(x = 36.363\,ft\)

The height of the flagpole is 36.363 feet.

The area of a Triangle with sides of lengths a and b and contained angle theta is given by:

\(A=\frac{1}{2}ab\sin\theta\)

To find how fast the area is increasing when \theta=\frac{\pi}{3}, we need to differentiate the equation for the area with respect to time and then substitute the given values:

\(\frac{dA}{dt}=\frac{1}{2}\left(b\frac{da}{dt}+a\frac{db}{dt}\right)\sin\theta+\frac{1}{2}ab\cos\theta\frac{d\theta}{dt}\)

Substituting a=2 cm, b=3 cm,

\(\theta=\frac{\pi}{3}, and \frac{d\theta}{dt}=0.2\)rad/min, we get:

\(\frac{dA}{dt}=\frac{1}{2}\left(3\cdot 0+2\cdot 0\right)\frac{\sqrt{3}}{2}+\frac{1}{2}(2)(3)\cdot\frac{1}{2}\cdot 0.2\)

\(\frac{dA}{dt}=0.6 cm^2/min\)

Therefore, the area is increasing at a rate of 0.6 cm^2/min when \(theta=\frac{\pi}{3}.\)

(b) To find how fast the area is increasing when b=3 cm and theta=frac{\pi}{3}, we need to differentiate the equation for the area with respect to time and then substitute the given values:

\(\frac{dA}{dt}=\frac{1}{2}\left(b\frac{da}{dt}+a\frac{db}{dt}\right)\sin\theta+\frac{1}{2}ab\cos\theta\frac{d\theta}{dt}\)

Substituting a=2cm, b=3cm,

\(theta=\frac{\pi}{3}, \frac{da}{dt}=0 cm/min, \frac{db}{dt}=1.5 cm/min, and\frac{d\theta}{dt}=0.2rad/min\), we get:

\(\frac{dA}{dt}=\frac{1}{2}\left(3\cdot 0+2\cdot 1.5\right)\frac{\sqrt{3}}{2}+\frac{1}{2}(2)(3)\cdot\frac{1}{2}\cdot 0.2\frac{dA}{dt}=1.5\sqrt{3}+0.6 cm^2/min\)

Therefore, the area is increasing at a rate of 1.5\sqrt{3}+0.6 cm^2/min when b=3 cm and \(theta=\frac{\pi}{3}.\)

(c) To find how fast the area is increasing when a=2 cm, b=3cm, and \(theta=\frac{\pi}{3}\), we need to differentiate the equation for the area with respect to time and then substitute the given values:

\(\frac{dA}{dt}=\frac{1}{2}\left(b\frac{da}{dt}+a\frac{db}{dt}\right)\sin\theta+\frac{1}{2}ab\cos\theta\frac{d\theta}{dt}\)

Substituting a=2cm, b=3cm, $\theta=\frac{\pi}{3},

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Answer:

10 DVD's were sold.

Step-by-step explanation:

c = number of CD's

d = number of DVD's

so we know:

c + d = 60

2*c/8 = d/2

this can be solved:

d = 60 - c

2c / 8 = (60-c)/2

4*(2c/8) = 4*(60-c)/2    [multiply by 4]

c = 120 - 2c

3c = 120

c = 40

d = 60-40 = 20

So Greg had 40 CD's and 20 DVD's. He sold half of his DVD's, i.e., 20/2=10 and 1/8 of his CD, i.e., 40/8 = 5

Greg has 40 CD's and 20 DVD's. He sold 10 DVDs and 1/8 of his CD(40/8 = 5).

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

Initially, Greg has a total of 60 DVDs and CDs in his collection.

He then sold 1/8 of his CDs and 1/2 of his DVDs.

Let the number of CD is c and DVD is d

c + d = 60

2(c/8) = d/2

d = 60 - c

4(2c/8) = 4(60-c)/2    

c = 120 - 2c

c = 40

d = 60-40 = 20

Thus, Greg has 40 CD's and 20 DVD's. He sold 10 DVDs and 1/8 of his CD(40/8 = 5).

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Answer:

\(\text{A. 8}i\)

Step-by-step explanation:

The math constant \(i\) represents \(\sqrt{-1}\). Because \(\sqrt{a\cdot b}=\sqrt{a}\cdot\sqrt{b}\), we can rewrite the equation given the problem as \(\sqrt{-64}=\sqrt{64}\cdot \sqrt{-1}=\boxed{8i}\).

Answer:

n = -35

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define equation

n/-5 = 7

Step 2: Solve for n

Step 3: Check

Plug in n into the original equation to verify it's a solution.

Here we see that 7 does indeed equal 7.

∴ n = -35 is a solution to the equation.

The formula we need to use is given above. In this formula, we will substitute the desired values. Let's start.

A) First, we can start by analyzing the first premise. The team has \(8\) wins and \(5\) losses. It earned \(8 \times 3 = 24\) points in total from the matches it won and \(1\times5=5\) points in total from the matches it drew. Therefore, it earned \(24+5=29\) points.

B) After \(39\) matches, the team managed to earn \(54\) points in total. \(12\) of these matches have ended in draws. Therefore, this team has won and lost a total of \(39-12=27\) matches. This number includes all matches won and lost. In total, the team earned \(12\times1=12\) points from the \(12\) matches that ended in a draw.

\(54-12=42\) points is the points earned after \(27\) matches. By dividing \(42\) by \(3\) ( because \(3\) points is the score obtained as a result of the matches won), we find how many matches team won. \(42\div3=14\) matches won.

That leaves \(27-14=13\) matches. These represent the matches team lost.

Finally, the answers are below.

\(A)29\)
\(B)13\)

Answer:

  a) 29 points

  b) 13 losses

Step-by-step explanation:

You want to know points and losses for different teams using the formula P = 3W +D, where W is wins and D is draws.

The number of points the team has is ...

  P = 3W +D

  P = 3(8) +(5) = 29

The team has 29 points.

You want the number of losses the team has if it has 54 points and 12 draws after 39 games.

The number of wins is given by ...

  P = 3W +D

  54 = 3W +12

  42 = 3W

  14 = W

Then the number of losses is ...

  W +D +L = 39

  14 +12 +L = 39 . . . substitute the known values

  L = 13 . . . . . . . . . . subtract 26 from both sides

The team lost 13 games.

__

Additional comment

In part B, we can solve for the number of losses directly, using 39-12-x as the number of wins when there are x losses. Simplifying 3W +D -P = 0 can make it easy to solve for x. (In the attached, we let the calculator do the simplification.)

<95141404393>

Step-by-step explanation:

perimeter = 2πr = 2× 3.14× 3 = 18.84 cm

In a piece-rate pay system, an employee's gross pay is calculated by multiplying the number of units produced by the rate per unit. This type of pay system is often used in manufacturing, agriculture, and other industries where employees are paid based on their productivity.

Piece-rate pay system is a compensation system in which employees are paid a fixed amount for each unit they produce. The rate per unit is set by the employer and can vary depending on the industry and type of work being performed. For example, a factory worker might be paid a certain amount for every item they assemble, while a farm worker might be paid based on the number of baskets of fruit they harvest.

To calculate an employee's gross pay in a piece-rate system, the employer simply multiplies the number of units produced by the rate per unit. For example, if a factory worker produces 100 units and the rate per unit is $1.50, their gross pay would be $150. Piece-rate pay can be beneficial for both employers and employees, as it incentivizes productivity and allows employees to earn more money if they work efficiently. However, it can also lead to exploitation if the rate per unit is set too low or if employees are forced to work long hours to meet production targets.

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Answer:

c= -1

Step-by-step explanation:

combine like terms

2c+14=12

subtract 14 from both sides

2c= -2

divide 2 on both sides

c= -1

HOPE THIS HELPS!!

The probability that she selects the route of three specific capitals is 97290/1.

The probability that she selects the route of three specific capitals can be calculated by taking the total number of possible routes and dividing it by the total number of routes that involve the three specific capitals. To calculate the total number of possible routes, multiply the number of states (47) by the number of routes that could be selected from each state (2). This gives 94 total possible routes.

47 x 46 x 45 ways = 97290 ways

= 1/97290

Now, calculate the number of routes that involve the three specific capitals. Since the president is selecting three states, the total number of routes will be 3. Therefore, the probability that she selects the route of three specific capitals is 3/94, which can be simplified to 97290/1.

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Answer:

girl it is 2

Step-by-step explanation:

Step-by-step explanation:

WRL-15663: The SparkFun ESP32 Thing Plus is the next step to get started with Espressif IoT ideations while still enjoying all the amenities of the original ESP32 Thing. Espressif's ESP32 WROOM is a powerful WiFi and Bluetooth MCU module that targets a wide variety of applications. At the core of this module is the ESP32-D0WDQ6 chip which is designed to be both scalable and adaptive.

Answer: 5x + 2y = 6

Step-by-step explanation:

The standard form is Ax + By = C

Subtract 5x from each side:

- 5x - 2y = - 6

The first term in the standard form must be positive, so multiply by -1 to change the sign.

5x + 2y = 6

Hope this helps!

Independent variables are the factors that are manipulated or controlled by the researcher in a study. In the context of investigating the impact of a school nutrition program on grade performance of high school students, the independent variable would be the school nutrition program itself.

The researcher would design and implement the program, and this variable would be under their control.

Dependent variables, on the other hand, are the outcomes or variables that are measured in a study and are expected to change as a result of the independent variable. In this case, the dependent variable would be the grade performance of the students. The researcher would collect data on the grades of the students before and after the implementation of the nutrition program, and this would be the variable that is expected to be influenced by the independent variable.

In summary, the independent variable in this research design is the school nutrition program, while the dependent variable is the grade performance of the students. The researcher would manipulate the independent variable (implement the nutrition program) and then measure the dependent variable (student grades) to determine if there is an impact of the program on grade performance.

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16777216

hope I helped :)

Answer:

16777216

Step-by-step explanation:

a) The optimal size of the production run is approximately 39, units (rounded to the nearest whole number).

b) The average holding cost per year is approximately $1,755.00 (rounded to two decimal places).

c) The average setup cost per year is approximately $24,300.00 (rounded to two decimal places).

d) The total cost per year, including the cost of the lights, is approximately $43,071.00 (rounded to two decimal places).

a) To find the optimal size of the production run, we can use the economic order quantity (EOQ) formula. The EOQ formula is given by:

EOQ = √[(2 * D * S) / H]

Where:

D = Annual demand = 11,700 units

S = Setup cost per production run = $81

H = Holding cost per unit per year = $0.15

Plugging in the values, we have:

EOQ = √[(2 * 11,700 * 81) / 0.15]

= √(189,540,000 / 0.15)

= √1,263,600,000

≈ 39,878.69

Since the optimal size should be rounded to the nearest whole number, the optimal size of the production run is approximately 39, units.

b) The average holding cost per year can be calculated by multiplying the average inventory level by the holding cost per unit per year. The average inventory level can be calculated as half of the production run size (EOQ/2). Therefore:

Average holding cost per year = (EOQ/2) * H

= (39,878.69/2) * 0.15

≈ 2,981.43 * 0.15

≈ $447.22

So, the average holding cost per year is approximately $447.22 (rounded to two decimal places).

c) The average setup cost per year can be calculated by dividing the total setup cost per year by the number of production runs per year. The number of production runs per year is given by:

Number of production runs per year = D / EOQ

= 11,700 / 39,878.69

≈ 0.2935

Total setup cost per year = S * Number of production runs per year

= 81 * 0.2935

≈ $23.70

Therefore, the average setup cost per year is approximately $23.70 (rounded to two decimal places).

d) The total cost per year, including the cost of the lights, can be calculated by summing the annual production cost, annual holding cost, and annual setup cost. The annual production cost is given by:

Annual production cost = D * Cost per light

= 11,700 * 1

= $11,700

Total cost per year = Annual production cost + Average holding cost per year + Average setup cost per year

= $11,700 + $447.22 + $23.70

≈ $12,170.92

Therefore, the total cost per year, including the cost of the lights, is approximately $12,170.92 (rounded to two decimal places).

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On solving the provided question, we can say that the mean that 6 tests including the last test brian took.

A dataset's mean is the sum of all values divided by the total number of values, often known as the arithmetic mean (as opposed to the geometric mean). Often referred to as the "mean," this is the most often used measure of central tendency. Simply dividing the dataset's total number of values by the sum of all of those values yields this result. Both raw data and data that have been combined into frequency tables can be used for calculations. Average refers to a number's average. It is straightforward to calculate: Divide by how many digits there are after adding up all the digits. the total divided by the count.

(91n + 98) / (n + 1)  =  92

    91n + 98  =  92(n + 1)

 91n + 98  =  92n + 92

 98  =  n + 92

6  =  n

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Answer:

Hey there!

A simple way to think about slope is rise over run. Between any two points on this line, the rise is 3, and the run is -1.

3/-1=-3, so  the slope is -3.

Let me know if this helps :)

Answer:

14.4 dollars

Step-by-step explanation:

the Hat has 20 percent discount

The Hat with discounted price is 18 dollars

the 20% of 18 dollar is 3.6 dollars

hence if we subtract 3.6 dollars from 18 dollars

we get 14.4 dollars as regular price

Answer:

[(b/c)=0.15)]

Step-by-step explanation:

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

Work Shown:

P(B/C) = P(B and C)/P(C) ... conditional probability formula

P(B and C) = P(C)*P(B/C)

P(B and C) = 0.20*0.15

P(B and C) = 0.03

------------

P(C/B) = P(C and B)/P(B) .... note the swap of B and C

P(C/B) = P(B and C)/P(B)

P(C/B) = (0.03)/(0.25)

P(C/B) = 0.12

------------

Extra notes:

The equation that represents the cost of the hamburger with additional topping will be c = 0.295t + 3.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

A burger consistently cost $6.00 each extra fixing cost $0.59.

Let 'c' be the cost and 't' be the cost of topping. Then the equation is given as,

c = 0.59t + 6

On Monday the expense of the burger just is half off. Then the equation is given as,

c = 0.50(0.59t + 6)

c = 0.295t + 3

The equation that represents the cost of the hamburger with additional topping will be c = 0.295t + 3.

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Answer:

2) A, 3) Shawn is looking for a good book, he reads 12 books and then decides to read 1/4 of the amount he already read. How many books has Shawn read in total? 4) A, C, E. 5) 4

Step-by-step explanation:

2) Elena already walked 12 miles, she then walks another 1/4 of those 12 miles. The answer is A.

3) Shawn is looking for a good book, he reads 12 books and then decides to read 1/4 of the amount he already read. How many books has Shawn read in total?

4) to find the answers figure out how much they multiply one number by and multiply the other number by that amount. For example, the ratio 2:5 can be the same as 4:10 because you are multiplying the original ratio by 2 to get the new ratio.

5) The diameter of a circle is the length of one side to another. to find the length of the outer edge you need to find the circumference. To find the circumference of a circle you must use \(\pi\)*Diameter. To find the answer we must use 180/\(\pi\)D. Since pi can not be defined we will use 3.14 as a rough estimation. 3.14*12=37.68. 180/37.68=4.777070064. Since it doesn't make much sense to do .8 of a invitation then we must round down. The answer is 4.

Answer: mx+b=y

Step-by-step explanation:

Rise over run