Your friend said that there are exactly 12 different pairs of numbers with a difference of 12 and that he had found them all. How would you respond to him?

Answer:

x=-y/g

Step-by-step explanation:

m-y=m+gx

m-m-y=gx

-y=gx

x=-y/g

Answer:

A) 0.3

B) 0.2

Step-by-step explanation:

We are given the following in the question:

P(Industry in Shanghai) = P(A) = 0.7

P(Industry in Beijing) = P(B) = 0.4

P(Industry in Shanghai or Beijing)  = P(A∪B) = 0.8

a)We need to find the probability that the industry is located in both Shanghai and Beijing that is we need to find P(A∩B)

Formula:

P(A∪B) = P(A) + P(B) - P(A∩B)

Putting the values we get,

0.8 = 0.7 + 0.4 - P(A∩B)

P(A∩B) = 0.3

Thus, the probability that the industry is located in both Shanghai and Beijing is 0.3.

b)Now, we need to find the probability that it is not in either cities

Probability = 1 - Probability(Industry in Shanghai or in Beijing)

                 = 1 - P(A∪B)

                 = 1 - 0.8

                 = 0.2

The probability that the industry will locate in both Shanghai and Beijing is 0.3, while the probability that it will locate in neither of the cities is 0.2.

This problem is solved using the concept of probability in Mathematics. Let's denote A as the event that an industry with locate in Shanghai and B is the event that it will locate in Beijing.

The probability of A, P(A), is given as 0.7 and the probability of B, P(B), is given as 0.4. The probability it will locate in either of the cities, P(A U B), is given as 0.8.

We know, P(A U B) = P(A) + P(B) - P(A ∩ B), where P(A ∩ B) represents the probability the industry will locate in both cities. Using the given probabilities:

0.8 = 0.7 + 0.4 - P(A ∩ B), so P(A ∩ B), the probability the industry will locate in both cities, is equal to 0.3. (a)

The probability the industry will not locate in either of the cities, denoted as P'(A U B), is equal to 1 - P(A U B) = 1 - 0.8 = 0.2. (b).

This means there is a 30% chance the industry will locate in both Shanghai and Beijing, and a 20% chance it will locate in neither city.

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Answer:

4b - 3s = 40

4b = 40 + 3s

b = 40 - 3s/4

4b - 3s = 40

4b - 40 =3s

4b - 40 /3 = s

The age of the brother b = 40 - 3s/4, and the age of the sister is s = 4b - 40/3

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Let the age of the brother be b and the age of the sister be s

If four times the brother's age is subtracted from three times the sister's age, the difference is 40.

So the equation that represents this statement is:

⇒ 4b - 3s = 40

⇒ 4b = 40 + 3s

Divided by 3 into both sides and solve for b,

⇒ b = 40 - 3s/4

Now solve for b,

⇒ 4b - 3s = 40

⇒ 4b - 40 =3s

Divided by 3 into both sides

⇒ s = 4b - 40/3

Hence, the age of the brother b = 40 - 3s/4, and the age of the sister is s = 4b - 40/3

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Answer:

he magnitude of Sarah's displacement is less than the distance she travels

Step-by-step explanation:

Hi!

The magnitude of her displacement is just the difference between her final and initial state, however the distance she traveled is two times the distance she moved in the positive x-direction until she turned around, since she had to move back, plus her displacement.

So:

[tex]displacement = |x_{final} -x_{initial}| \\distanceTraveled = 2|x_{return}-x_{initial}| + displacement\\[/tex]

Since all the terms are positive:

[tex]x_{displacement}<x_{traveled}[/tex]

The given function : [tex]f(x)=x^2+2x-3[/tex]

Using completing the squares, we have

[tex]f(x)=x^2+2x+1-1-3[/tex]        [∵ [tex](x+1)^2=x^2+2x+1[/tex]]

[tex]f(x)=(x+1)^2-4[/tex]      (1)

Comparing (1) to the standard vertex form [tex]f(x)=(x-h)^2+k[/tex] , the vertex of function is at (h,k)=(-1,-4)

For x-intercept, put f(x)=0 in (1), we get

[tex]0=(x+1)^2-4\\\\\Rightarrow\ (x+1)^2=4[/tex]    

Square root on both sides, we get

[tex]x+1=\pm2\\\\x+1=-2\ or\ \ x+1=2\\\\=x=-3\ \ or\ x=1[/tex]

∴ x intercepts : x= (-3,0) and (1,0)

For y-intercept put x=0 in (1), we get

[tex]f(1)=(1)^2-4=1-4=-3[/tex]  

∴ y intercept : (0,-3)

Axis of symmetry : [tex]\dfrac{-b}{2a}[/tex]

In [tex]f(x)=x^2+2x-3[/tex] , a=1 and b=2

Axis of symmetry=[tex]\dfrac{-2}{2(1)}=-1[/tex]

A graph of the quadratic equation [tex]f(x) = x^2 + 2x - 3[/tex] with its key features is shown on the coordinate plane in the image below.

In Mathematics and Euclidean Geometry, the standard form of a quadratic function is represented by the following equation;

[tex]y = ax^2 + bx + c[/tex]

Where:

Since the leading coefficient (value of a) in the given quadratic function [tex]f(x) = x^2 + 2x - 3[/tex] is positive one (1), we can logically deduce that the parabola would open upward and the solutions are the x-intercepts. Furthermore, the key features of this quadratic function include the following;

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Complete Question;

Graph [tex]f(x) = x^2 + 2x - 3[/tex], label the function’s x-intercepts, y-intercept and vertex with their coordinates. Also draw in and label the axis of symmetry

Answer:

In x: 4-1=3

In y: -2

Cartesian coordinates: (3,-2)

Step-by-step explanation:

If we move horizontally we must consider only the x axis, if we move to east it is positive, and if we move to west it is negative.

f we move vertically we must consider only the y axis, if we move to north it is positive, and if we move to south it is negative.

Answer:

Parallel

Step-by-step explanation:

All of the other answers give examples of lines that intersect at some point.

Answer:

transversal

Step-by-step explanation:

The line is called transversal. A transversal is a line which intersects two or more parallel lines

Final answer:

Explanation on how to calculate the APR for a mortgage loan based on provided information.

Explanation:

To calculate the APR on the loan, we first need to determine the total amount paid over the life of the loan. The total payment per month is $18,300, and the loan term is 25 years. So, the total payment over 25 years would be $18,300 x 12 months x 25 years = $5,220,000.

Next, calculate the total interest paid by subtracting the loan amount from the total payments: $5,220,000 - 75% of $4,200,000 = $5,220,000 - $3,150,000 = $2,070,000.

Finally, use the formula for APR: APR = (Total Interest Paid / Loan Amount) x 100%. Therefore, APR = ($2,070,000 / $3,150,000) x 100% ≈ 65.71%. So, the APR on this loan is approximately 65.71%.

Answer:

[tex] -1 \frac{1}{2} = m[/tex]

Step-by-step explanation:

3x + 2y = 8

-3x - 3x

___________

2y = -3x + 8

___ _______

2 2

y = -1½x + 4

↑

rate of change [slope]

I am joyous to assist you anytime.

Answer:

Yes

Step-by-step explanation:

Yes it is possible, if the equations are equivalent. For example in one variable, we have x=2 and if we add the equation 2x=4 both considered on the Real numbers, then the system has two equations and one variable, more equations than variables and yet the solution is unique x=2.

Answer:

Yes, it's possible.

Step-by-step explanation:

We know that a linear system has a unique solution if it has the same number of equations than variables (but remember that you musn't have a linear combination of equations).

So it is possible to create a system with more equations than variables, with a unique solution.

Example:

1)  X + Y + Z = 3

2) 2X + 2Y + 2Z = 6

3) X + Y = 2

4) X + Z = 2

This is a 4 equation and 3 variable system.  Pay attention to equation number 1) and 2). They are a linear combination (number 2 is the number 1 multiplied by 2). So, for this system you can basically ignore one of them.

If you do that, you will have 3 equations and 3 variables, with a unique solution. In this case solution is X = 1, Y = 1, Z = 1.

Now, let's see if equation number 2 satisfies:

2x1 + 2x1 + 2x1 = 6

                     6 = 6

With this simple example we proved that you can have a linear system with a unique solution if it has more equations than variables.

Answer:

The term used to describe this type of survey is - voluntary response sample or self elected sample.

The thing that is wrong with this type of sampling is that only those people will respond who have a strong interest in the particular topic.

Also, it is quite possible that only 38% responses do not reflect the opinions of the whole general population.

The price per quart of a 3-gallon container of laundry detergent is $1.73.

To find the price per quart, we need to convert the 3-gallon container into quarts. Since there are 4 quarts in a gallon, there are 4 x 3 = 12 quarts in a 3-gallon container

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Final answer:

The answer calculates the price per quart of laundry detergent from a 3-gallon container and provides estimated costs for 40 oz. and 90 oz. sizes. All calculations are based on the given information and formula.

Explanation:

Price of 3-gallon container: $20.76
Price per quart: $20.76 / 12 quarts = $1.73 per quart

If the detergent were sold in a 40 oz. size: Estimated cost = $1.73 x 3.33 = $5.76

If the detergent were sold in a 90 oz. size: Estimated cost = $1.73 x 7.5 = $12.98

Answer:

#1. 408% of 568

We get two equations from this

408% = x

568 = 100%

568/x=100%/408%

Solve and you'll get

408% of 568

=2317.44

2. New - Original = % change

712500 - 950000 = -237500

3. 10 at $1, 7 at $5

4. 2.2 lb. of raisins, 7.8 lb. of nuts

As per the given conditions we have

1. Number which is 408% of 568 is equals to 2317.44 ( nearest hundredth).

2. Total decrease in percentage of the population of Detroit is equals to 25%.

3.Cash box contain bill of $1 is equals to 10 and bill of $5 is equals to 7.

4. Raisins is equals to 2.2 pounds and nuts is equals to 7.8 pounds for the trail mix.

" Equation is defined as the relation between the variables using sign of equality."

" Percentage is defined as the hundredth part of the given number."

According to the question,

1. 'x' represents the number

As per given condition,

x = 408% of 568  

⇒ [tex]x= \frac{408}{100} (568)[/tex]

⇒ [tex]x = 2317.44[/tex]

Therefore, the number which is 408% of 568 is equals to 2317.44.

2. Total population of Detroit = 950,000

Population after 10 years = 712,500

Decrease in population = 950,000 - 712,500

                                       = 237,500

Total percentage decrease in population = [tex]\frac{237500}{950,000}(100)[/tex]

                                                                     = 25%

Therefore, total  decrease in percentage of the population of Detroit is equals to 25%.

3. 'x' represents the bill of $1

  'y' represents the bill of $5

As per the condition given equation we have,

$1x + $5y = $45                  ______(1)

x = y + 3                              ______(2)

Substitute the value of  equation (2) in (1) we get,

[tex]1(y + 3) + 5y = 45\\\\\implies 6y = 45-3\\\\\implies y \frac{42}{6} \\\\\implies y = 7[/tex]

Substitute the value y in (2) we get,

[tex]x= 7 + 3\\\\\implies x =10[/tex]

Therefore , cash box contain bill of $1 is equals to 10 and bill of $5 is equals to 7.

4.  'x' represents the pounds of raisins

  '10- x ' represents the pounds of nuts

Cost of trail mix from raisins and nuts per pound = $6.96

Therefore,

Cost of 10 pounds of  trail mix of raisins and nuts = $(6.96 ×10)

                                                                                  = $69.6

Cost per pound of raisins = $3.45

Cost per pound of nuts = $7.95

Equation formed as per given condition we get,

[tex]3.45x + 7.95(10-x) = 69.6\\\\\implies 3.45x + 79.5 -7.95x = 69.6\\\\\implies -4.5x = 69.6 - 79.5\\\\\implies-4.5x= -9.9\\\\\implies x =\frac{9.9}{4.5}\\ \\\implies x = 2.2 pounds[/tex]

Pounds of raisins  = 2.2pounds

Pounds of nuts = 10 - 2.2

                         = 7.8 pounds

Therefore,  pounds of raisins is equals to 2.2 and pounds of nuts is equals to 7.8 for the trail mix.

Hence, As per the given conditions we have

1. Number which is 408% of 568 is equals to 2317.44 ( nearest hundredth).

2. Total decrease in percentage of the population of Detroit is equals to 25%.

3.Cash box contain bill of $1 is equals to 10 and bill of $5 is equals to 7.

4. Raisins is equals to 2.2 pounds and nuts is equals to 7.8 pounds for the trail mix.

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Answer:

A. simpson's paradox

Step-by-step explanation:

The Simpson's paradox was named after Edward Simpson, the person who described this paradox for the first time in 1951. In this paradox, you find two contrary patterns. For example, a positive and a negative correlation, depending on how data is analyzed. The differences in the analyses are how data are grouped. This paradox is observed often in social researches. Most of the times, results are affected by the sample on each group or additional information related to the data.

Answer:

Multicollinearity

Step-by-step explanation:

Answer:

y = [tex]\frac{3}{4}[/tex] x + 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ( = (0, 2) and (x₂, y₂ ) = (4, 5) ← 2 points on the line

m = [tex]\frac{5-2}{4-0}[/tex] = [tex]\frac{3}{4}[/tex]

Note the line crosses the y- axis at (0, 2) ⇒ c = 2

y = [tex]\frac{3}{4}[/tex] x + 2 ← equation of line

Answer:

Step-by-step explanation:

For the first two parts, you need to know the number of hours in a day, and the number of days in 30 days (!?). No doubt, these numbers are familiar to you.

Part A.

The distance traveled in 24 hours (1 day) is 24 times the distance traveled in one hour.

  distance per day = (27,600,000 m/h)×(24 h/day) = 662,400,000 m/day

Since you are familiar with place value and powers of 10, you know you can write this as ...

  662,400,000 m/day = 6.624×100,000,000 m/day = 6.624×10⁸ m/day

__

Part B.

Using the result from Part A, we know that 30 days' travel will be 30 times one day's travel:

  distance in 30 days = (30 days)×6.624×10⁸ m/day = 198.72×10⁸ m

     = 1.9872×10¹⁰ m

__

Part C.

Your judgment is required to determine a "suitable unit." I might choose gigameters, abbreviated Gm. "giga-" is a prefix meaning 10⁹, so the distance traveled in 30 days could be written as ...

  1.9872×10¹⁰ m = 19.872×10⁹ m = 19.872 Gm = 1.9872×10¹ Gm

_____

Comment on "suitable unit"

In my engineering career, I would often choose units from the list of SI prefixes, so that exponents were a multiple of 3. That means any given measurement or calculation result ranged from 1 to 999, multiplied by some suitable choice of units. Here, the distance traveled in 30 days would be left as (about) 19.9 Gm. The choice of units is intended to avoid the need for scientific notation.

The meaning of "a more suitable unit in scientific notation" is unclear in this context. I would say a "more suitable unit" is Gm, whose value in scientific notation is 10^9 m or 10^6 km.

Answer:

A neuropsychologist​ is most likely to be administering the tests.

Step-by-step explanation:

Mr. Spindero periodically visits a hospital clinic where he takes various paper and pencil tests that document the progression of his dementia.

A neuropsychologist​ is most likely to be administering the tests.

Certain disorders within the brain and nervous system can alter the normal  behavior and cognitive function of a person.

So, a neuropsychologist deals with such patients. He specializes in understanding the relationship between the physical brain and behavior.

Answer:

(a) 349.34

(b) 77.63 km/h

Step-by-step explanation:

Distance you covered before it rain S =  180 km

Speed v = 95/km

Time taken to cover 180 km = [tex]\frac{S}{v}[/tex]

                                               =  [tex]\frac{180}{95}[/tex]

                                               = 1.89473 hrs.

Total time to cover the distance between school to home T = 4.5 hrs.

Remaining time t = T - t

                             = 4.5 - 1.89473

                             = 2.60527 h.

Velocity after travel 180 km. v' = 65 km/h

Distance traveled in this velocity S' = v'(t)

                                                           = 2.60527 × 65

                                                           = 169.34 km

(a) distance of hometown from school = 169.34 + 180 = 349.34 km.

(b) Your average speed V =  [tex]\frac{S}{T}[/tex]

                                           =  [tex]\frac{349.34}{4.5}[/tex]

                                           = 77.63 km/h

Answer:

The answer is 40a+14c

Step-by-step explanation:

Step 1: Open the brackets

7a-9c+12a+33c+21a-10c

Step 2: Group all the like terms

Like terms are terms with similar variables, for example;

(7a, 12a, 21a) are all like terms since they have a common variable (a)

(-9c, 33c,-10c) are also like terms since they have a common variable (c)

Step 2: Solve

(7a+12a+21a)+(33c-10c-9c)=40a+14c

The answer is 40a+14c

Answer:

  A.  $16,079

Step-by-step explanation:

You are given the income of a married couple and the tax table applicable to married couples. To find the amount of tax owed, you first find the applicable line in the table, then do the computation it tells you.

The applicable line for an income of $110,000 is the one that says ...

  "77,401 to 165,000"

The left (Tax Rate) column of that line has "22%", and the right (Tax Owed) column tells you the computation you need to make.

You find "the excess over $77,400" by subtracting that amount from the $110,000 income:

  the excess over $77,400 = $110,000 -77,400 = $32,600

__

Then the tax owed is 22% of this amount plus $8907:

  tax owed = $8,907 + 0.22 × 32,600

  = $8,907 + 7,172

  tax owed = $16,079

Answer:

The coordinates of point H' are (-2 , 0) ⇒ answer B

Step-by-step explanation:

* Lets revise the vertical stretch

- A vertical stretching is the stretching of the graph away from the  

 x-axis  

- If k > 1, then the graph of y = k • f(x) is the graph of f(x) vertically

 stretched by multiplying each of its y-coordinates by k

* Lets solve the problem

- Square EFGH stretches vertically by a factor of 2.5 to create

 rectangle E′F′G′H′

∴ k = 2.5

- The square stretches with respect to the x-axis

∴ The square stretches vertically

∴ The y-coordinates of each vertex of the square EFGH are

  multiplied by 2.5 to get the vertices of the rectangle E'F'G'H'

∵ Point H located at (-2 , 0)

∵ The image of point (x , y) after stretched vertically by k is (x , ky)

∴ Point H' located at (-2 , 0 × 2.5) ⇒ (-2 , 0)

∴ The coordinates of point H' are (-2 , 0)

∴ Point H' located at (-2 , 0)

Answer:

B.   (-2, 0)

Step-by-step explanation:

Answer:

30 parts

Step-by-step explanation:

We are given that machine produces 100 parts twice as  fast as machine B does.

Machine produces 100 parts in 40 minutes.

We have to find number of parts produces by machine A in 6 minutes.

According to question

Machine A  takes time to produce 100 parts =[tex]\frac{40}{2}=20 minutes[/tex]

Machine A and machine B produces parts at constant rate.

Machine A produces parts at the rate=[tex]\frac{100}{20}=5 parts /minute[/tex]

In one minute,Machine A produces =5 parts

In 6 minutes , machine B produces =[tex]5\times 6=30[/tex] parts

Hence, machine A produce parts in 6 minutes=30

Answer:

The answer to your question is: 800.4 km

Step-by-step explanation:

Data:

111 km to east

444 km to north

555 km to east

How far is from her starting position?

See the picture please

To do this problem, we must to find the hypotenuse of a right triangle where one cathetus is 444 km and the other one is the sum of 111 and 555km.

them the pythagorean theorem says c² = a² + b²

                                                              c² = 444² + (111+555)²

                                                               c² = 444² + 666²

                                                                c² = 197136  + 443556

                                                               c² = 640692

                                                                c = 800.4 km

Answer: 7.211

Step-by-step explanation:

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Answer:

There are 795 combinations.

Step-by-step explanation:

The number of ways or combinations in which we can select k element from a group of n elements is given by:

[tex]nCk=\frac{n!}{k!(n-k)!}[/tex]

So, if Miriam want to choose 3 movies with at least two comedies, she have two options: Choose 2 comedies and 1 foreign film or choose 3 comedies.

Then, the number of combinations for every case are:

1. Choose 2 Comedies from the 10 and choose 1 foreign film from 15. This is calculated as:

[tex]10C2*15C1=\frac{10!}{2!(10-8)!}*\frac{15}{1!(15-14)!}[/tex]

[tex]10C2*15C1=675[/tex]

2. Choose 3 Comedies from the 10. This is calculated as:

[tex]10C3=\frac{10!}{3!(10-3)!}=120[/tex]

Therefore, there are 795 combinations and it is calculated as:

675 + 120 = 795

Answer:

20,000,000,000 or 200

Step-by-step explanation:

depending on which 2 you are asking for

The place value of 2 in the number 24,398,407,268 is 20 billion, as it is in the ten billion place.

The place value of 2 in the number 24,398,407,268 refers to the position of 2 in the number and its corresponding value. In this case, the 2 is in the ten billion place. To find the value of 2 in that position, we multiply it by 10 billion (109). Therefore, the place value of 2 in this number is 20 billion (2 x 10^9).

Answer:

The probability that the student is going to pass the test is 0.0545

Step-by-step explanation:

The variable that says the number of correct questions follows a Binomial distribution, because there are n identical and independent events with a probability p of success and a probability 1-p of fail. So, the probability of get x questions correct is:

[tex]P(x)=\frac{n!}{x!(n-x)!} *p^{x} *(1-p)^{n-x}[/tex]

Where n is equal to 10 questions and p is the probability of get a correct answers, so p is equal to 1/2

Then, if the student pass the test with at least 8 questions correct, the probability P of that is:

P = P(8) + P(9) + P(10)

[tex]P=(\frac{10!}{8!(10-8)!}*0.5^{8}*(0.5)^{10-8})+(\frac{10!}{9!(10-9)!} *0.5^{9} *(0.5)^{10-9})+(\frac{10!}{10!(10-10)!} *0.5^{10} *(0.5)^{10-10})[/tex]

P = 0.0439 + 0.0097 + 0.0009

P = 0.0545

Answer:

After 7 months

Step-by-step explanation:

DATA:

⇒ Sign-up fee = $25

⇒ Monthly fee = $25

⇒ Number of months = y

⇒ Gift card = $200

Form an equation to calculate when the total spent on gym would exceed the amount of the gift card

Sign-up fee + (monthly fee x number of months) = Gift card amount

25 + 25y = 200

25y = 200-25

25y = 175

y = 7

Therefore, the total spent on your gym membership exceeds the amount of your gift card after 7 months.

Answer:

h = [tex]\frac{2A}{b}[/tex]

Step-by-step explanation:

Given

A = [tex]\frac{1}{2}[/tex] bh

Multiply both sides by 2 to clear the fraction

2A = bh ( isolate h by dividing both sides by b )

h = [tex]\frac{2A}{b}[/tex]

Answer: h = 2a/b

Step-by-step explanation:

Answer:

The answer to your question is: P(A) = 0.47

Step-by-step explanation:

Data

7 red flowers

3 white flowers

5 yellow flowers

Probability  that he select a red one

Formula

 P(A) = Number of favorable cases of A / total number of outcomes

Number of favorable cases = 7

Total number of outcomes = 7 + 3 + 5 = 15

Substitution

                      P(A) = 7 / 15

                      P(A) = 0.47