Working alone at its constant rate, pump X pumped out \small \frac{1}{3} of the water in a pool in 4 hours. Then pump Y started working and the two pumps, working simultaneously at their respective constant rates, pumped out the rest of the water in 6 hours. How many hours would it have taken pump Y, working alone at its constant rate, to pump out all of the water that was pumped out of the pool?

Answer:

47.77778 but really it's just 47

Answer:

The age of Sleepy is 1 .

Then the age of Scoopy is 9.

The age of Doc would be 45.

Step-by-step explanation:

We have to find the ages of all the three people based on the given equations.

Let the age of Sleepy be  x. Since Scoopy is 8 years older than Sleepy, the age of Scoopy would be (x+8).

Also Doc is 5 times as old as Scoopy so his age is 5(x+8).

Now the sum of the ages of all three is 55.

Writing equation for this,

x + x + 8 + 5(x+8) = 55

7x + 48 = 55

7x = 7

x = 1

So the age of Sleepy is 1 .Then the age of Scoopy is 9.

The age of Doc would be 45.

By solving the linear equations given by the problem, it is found that Scoopy is 10 years old, Sleepy is 2 years old, and Doc is 50 years old.

This problem is a system of linear equations, a topic in the field of mathematics. The task is to find out the age of Sleepy, Scoopy, and Doc. Let's denote Scoopy's age as 'S', Sleepy's age as 'S - 8' (since Sleepy is eight years younger than Scoopy), and Doc's age as '5S' (since Doc is 5 times as old as Scoopy). The equations can be written as below:

It is known that the sum of their ages is 55, which gives us our second equation:

S + (S - 8) + 5S = 55

By solving this equation, we find that S = 10. So Scoopy is 10 years old. Accordingly, Sleepy is 10 - 8 = 2 years old and Doc is 5 * 10 = 50 years old.

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Answer:

$12

Step-by-step explanation:

72/6=12

Each of the suitcases cost 12 dollars and in total, all 6 suitcases equated to 72 dollars.

Answer: the cost for each piece of luggage is $12

Step-by-step explanation:

The total number of suitcases that the Taylor family brought on their trip to Italy is 6. They paid $72 to check their luggage in with the airport. Therefore, the cost for each piece of luggage would be

Total amount paid for 6 pieces of luggage divided by the total number of pieces of luggage. It becomes

72/6 = 12

Answer:

A.) Multiply 46 by 5/9

Step-by-step explanation:

The formula to convert Fahrenheit degrees to Celsius degrees is as follows:

[tex]\\ C = \frac{5}{9}*(F-32) [/tex]

So, converting 78°F to °C, according this previous equation is:

[tex]\\ C = \frac{5}{9}*(78-32) [/tex] [Barbara subtracts 32 from 78]

[tex]\\ C = \frac{5}{9}*(46) [/tex]  [Barbara multiplies 46 by 5/9]

[tex]\\ C = \frac{5*46}{9} [/tex]

[tex]\\ C = \frac{230}{9} = 25.56 [/tex] or 25.56°C

Answer:

A) multiply 46 by 5/9

Step-by-step explanation:

Answer:35%

Step-by-step explanation:

Lizzie's answer is not right as two sides are not equal.

Step-by-step explanation:

Given equation is;

2+3x+3=3(x+3)+2x

Lizzy got;

x=2

We will put this value of x in Equation to determine if the sides are equal or not.

[tex]2+3(2)+3=3(2+3)+2(2)\\2+6+3=3(5)+4\\11=15+4\\11\neq 15[/tex]

Lizzie's answer is not right as two sides are not equal.

Keywords: linear equation, addition

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Answer:

Total Number of Coconuts which fell from tree are 14.

Step-by-step explanation:

Given:

Some coconuts fall out of a tree.

Mercy is greedy and takes half,

Joe grabs what he can, and gets five more than Frank.

Frank gets one coconut.

We need to find Total number of coconuts fell from tree.

Number of Coconuts franks has = 1

Now Given that Joe grabs what he can, and gets five more than Frank.

Number of Coconuts Joe has = Number of Coconuts franks has + 5 = 1 + 5 = 6

Also Given Mercy is greedy and takes half.

It means mercy took half of coconuts and rest half were took by Frank and Joe

Hence Number of Coconuts Mercy has = Number of Coconuts franks has +  Number of Coconuts Joe has = 6 + 1 = 7

Now Total Number of Coconuts is equal to sum of Number of Coconuts Mercy has and Number of Coconuts Joe has and Number of Coconuts frank has.

Total Number of Coconuts = 7 + 1 + 6 = 14

Hence Total Number of Coconuts which fell from tree are 14.

Answer:

120 seconds

Step-by-step explanation:

if the elevator is moving at a constant rate, then it takes 10 seconds to move up one floor, to travel from the 4th to the 16th floor, it will take 120 seconds total to travel 10 floors

Answer:

The number of runners is [tex]\dfrac{4 }{35}[/tex] of Total number of the member in team .

Step-by-step explanation:

Given as :

The Total number of the member in team = x

The number of boys in team = [tex]\dfrac{3}{5}[/tex] of x

I.e  number of boys in team = [tex]\dfrac{3 x}{5}[/tex]

Again

The number of sixth-grade boys = [tex]\dfrac{4}{7}[/tex] of total boys in team

I.e The number of sixth-grade boys = [tex]\dfrac{4}{7}[/tex] × [tex]\dfrac{3 x}{5}[/tex]

Or, The number of sixth-grade boys = [tex]\dfrac{12 x}{35}[/tex]

Again

The number of runners =  [tex]\dfrac{1}{3}[/tex] of number of sixth-grade boys

i.e The number of runners =  [tex]\dfrac{1}{3}[/tex] × [tex]\dfrac{12 x}{35}[/tex]

Or, The number of runners =  [tex]\dfrac{4 x}{35}[/tex]

So, The number of runners = [tex]\dfrac{4 }{35}[/tex] of Total number of the member in team

Hence,The number of runners is [tex]\dfrac{4 }{35}[/tex] of Total number of the member in team . Answer

Answer:

The New world colonization enabled by the vessel affect the European economy as it increased the amount of gold and silver brought into Europe, this lead to the development of the banking sector and also helped to promote the transition of Europe into a capitalist economy.

it brought a great deal of gold and silver into Europe, stimulating the banking industry and promoting Europe’s transition of capitalism

Answer:

Total Amount made by Mailing in a week is $3395.

Step-by-step explanation:

Given:

Fixed Salary = $385

Percentage of Commission on Sale = 70%

Total Sale = 4300

we need to find Total amount made by Mailing in a week.

We will first find the amount made on commission.

Amount made on commission  = [tex]\frac{70}{100} \times 4300 = \$3010[/tex]

Now Total Amount made by Mailing in a week is equal to sum of Fixed Salary and  Amount made on commission.

Framing in equation form we get;

Total Amount made by Mailing = $385 + $3010 = $3395.

Hence Total Amount made by Mailing in a week is $3395.

Answer:

0

Step-by-step explanation:

Slope of a line which passes through two points (x1,y1) and (x2,y2) is given by:

\frac{y2-y1}{x2-x1}

(x1,y1) = (-3,2)

(x2,y2) = (1,2)

Substituting the values in the equation to determine the slope of the line:

= \frac{2-2}{1-(-3)}

= \frac{0}{4}

=0

So the slope of the given line is 0.

This is intuitively evident as well as the y coordinates of the two given points are the same.

Answer: Second triangle.

Step-by-step explanation:

For this exercise you need to use the Pythagorean Theorem. Based on it, you know that in a right triangle:

[tex]a^2=b^2+c^2[/tex]

Where "a" is the hypotenuse of the right triangle and "b" and "c" are the legs.

In this case you can identify that the legs of the first triangle and the legs of the second triangle are equal. These are:

[tex]b=7\\c=3.3[/tex]

Knowing their values, you can substitute them into the Pythagorean Theorem and solve for "a":

[tex]a^2=(7)^2+(3.3)^2\\\\a=\sqrt{(7)^2+(3.3)^2}\\\\a=7.738[/tex]

Therefore, you can conclude that the triangle that is closest to being a right triangle is the second one.

Answer:

A. 18%

Step-by-step explanation:

For independent events:

P(A and B) = P(A) × P(B)

P = 0.30 × 0.60

P = 0.18

There is an 18% probability that it will rain on both days and the game will be canceled.

Answer:

(2, 2)

Step-by-step explanation:

According to the distance formula, the distance between two points is:

d² = (x₂ − x₁)² + (y₂ − y₁)²

If one point is (x, y) and the other point is (1, 4), then:

d² = (x − 1)² + (y − 4)²

We know y² = 2x, so x = ½ y².  Substituting:

d² = (½ y² − 1)² + (y − 4)²

The minimum distance is when dd/dy equals 0.  We can either simplify first by distributing, or we can immediately take the derivative using chain rule.

If we distribute and then take the derivative:

d² = ¼ y⁴ − y² + 1 + y² − 8y + 16

d² = ¼ y⁴ − 8y + 17

2d dd/dy = y³ − 8

If we use chain rule instead without distributing:

2d dd/dy = 2(½ y² − 1) (y) + 2(y − 4)

2d dd/dy = y³ − 2y + 2y − 8

2d dd/dy = y³ − 8

Setting dd/dy equal to 0:

0 = y³ − 8

y = 2

x = ½ y²

x = 2

(2, 2) is the point on the parabola closest to (1, 4).

Graph: desmos.com/calculator/m4apqwsduk

Multiplying is simply the same as repeated addition. For example:

[tex]5 \times 3 = 5 + 5 + 5[/tex]

Or:

[tex]4 \times 7= 4 + 4 + 4 + 4 + 4 + 4 + 4[/tex]

Answer:

Below.

Step-by-step explanation:

Adding the number the same number of times as the multiplier.

For example

2 * 3  = 2 + 2 + 2.

Answer:

857164 magnetic block.

Step-by-step explanation:

Given: Each cube constructed with 1331 magnetic block.

          Mrs. cady has 256 student in her school and 388 student in another school make an identical cube.

First lets find out total number of students in both schools.

Total student= [tex]256+388= 644\ students[/tex]

∴ Total number of students is 644, who make identical cube.

Now, finding number of magnetic blocks do student use in all.

We will use unitary method.

Each cube require 1331 magnetic blocks.

As there are total 644 students making each cube

∴ 644 cubes require = [tex]644\ cubes\times 1331\ magnetic\ block= 857164[/tex]

∴ 857164 magnetic blocks, student use in all.

Answer:

A =    441  in²  

Step-by-step explanation:

An isosceles right triangle is a triangle with two equals sides (the legs ). In this particular case the base of the triangle will be the length of one side and at the same time the height of the triangle will be the other leg.  Hypotenuse as always is the opposite side to the right angle.

The area of a triangle is

A =  (1/2) * b* h

If we are going to compute the area of such triangle we have to find the length of one side That will be the base of the triangle and at the same time that will be the height of the triangle.

In any right triangle  hypotenuse is:

H²  = L₁²  +  L₂²    (1)

As was explain before  in this particular case  L₁  = L₂

Then

H²  =  L₁² +  L₁²    ⇒    H²  =  2 L₁²        H  =  √2 * L₁      ⇒   L₁  =  42/√2  

Then area of the  

A = (1/2)* ( 42/√2) *   ( 42/√2 )    ⇒     A = 1/4 * (42)²  

A =    441  in²    

Final answer:

Using the Central Limit Theorem, the probability that the stock's price will exceed $105 on the 10th day is calculated to be approximately 13.14%, assuming that the daily change of the stock price is a random variable with a mean of 0 and a variance of 2 and starting from a stock price of $100.

Explanation:

The question is asking to calculate the probability that a company's stock price will exceed $105 on the 10th day, given that the stock price today is $100 and that the daily change of price is a random variable with a mean of 0 and a variance of 2. To answer this, we can use the Central Limit Theorem (CLT) since we have a sum of independent and identically distributed random variables. According to the CLT, the sum of these random variables (or the stock price on the 10th day) will approximate a normal distribution as the number of days increases. For the 10th day, the expected price is the initial price (which is $100) plus 10 times the expected daily change (10*0 = 0), so the expected price is still $100. The variance of the sum of the daily changes is 10 times the variance of a single day (10*2), which equals 20, and the standard deviation is the square root of the variance, which is approximately 4.47.

We are trying to find the probability that the stock price is greater than $105. To do this, we convert the stock price into a z-score using the formula:

z = (X - μ) / σ

where X is the stock price we are interested in ($105), μ is the mean of the stock price on the 10th day ($100), and σ is the standard deviation (approximately 4.47). So we have:

z = (105 - 100) / 4.47 = 1.12

Using standard normal distribution tables or a calculator, we find that the probability of a z-score being greater than 1.12 is approximately 0.1314 (or 13.14%). Therefore, the probability that the stock's price will exceed $105 on the 10th day is about 13.14%.

Answer:the two equations that model the situation are

x + y = 48

3x + 2y = 15

Step-by-step explanation:

Let x represent the total number of hours that Derek worked.

Let y represent the total number of hours that Donnie worked.

Derek and Donnie mow 15 lawns over two 2 days. There are 24 hours in a day. Therefore, the number of hours in 2 days would be 2 × 24 = 48 hours. Therefore

x + y = 48 - - - - - - - - - -1

If Derek mows 3 lawns per hour and Donnie mows 2 lawns per hour, it means that

3x + 2y = 15 - - - - - - - - - 2

Answer:

At 20 miles both companies cost will be same.

Step-by-step explanation:

Let Number of miles be 'x'.

Given:

Quick movers charges $50 a day and $0.50 per mile .

So we can say Total charge is equal to sum of per day charge plus number of miles multiplied by cost of per mile.

framing in equation form we get;

Quick movers charges = [tex]50+0.5x[/tex]

Also Given:

ABC movers charges $45 a day and $0.75 per mile .

So we can say Total charge is equal to sum of per day charge plus number of miles multiplied by cost of per mile.

framing in equation form we get;

ABC movers charges = [tex]45+0.75x[/tex]

We need to find the number of miles at which both companies cost are are same.

Solving to find the same we get;

[tex]50+0.5x=45+0.75x[/tex]

Combining like terms we get;

[tex]0.75x-0.5x=50-45\\\\0.25x=5[/tex]

By Division property of equality we will divide both side by 0.25 we get;

[tex]\frac{0.25x}{0.25} =\frac{5}{0.25} \\\\x= 20 \ miles[/tex]

Hence at 20 miles both companies cost will be same.

Final answer:

By setting up an equation to equate the charges of Quick Movers and ABC Movers, it is determined that at 20 miles, the costs for both companies will be the same.

Explanation:

To find at how many miles the cost for both Quick Movers and ABC Movers is the same, we set up an equation where the cost of each company is equal. Quick Movers charges $50 a day plus $0.50 per mile, and ABC Movers charges $45 a day plus $0.75 per mile. Let's use m to represent the miles.

The equation based on the costs given will be:

50 + 0.50m = 45 + 0.75m

To solve the equation, we first bring all the m terms to one side and the constants to the other:

0.50m - 0.75m = 45 - 50

This simplifies to:

-0.25m = -5

Dividing both sides by -0.25, we find:

m = 20

Therefore, the cost for both companies is the same at 20 miles.

Answer:Michael spent 53 1/4 hours

training.

Step-by-step explanation:

Over the course of four weeks Mia spent 35 1 2 hours training for a race. This can be written in decimal point as 35.5 hours.

Michael spent 1 1 2 times that amount training for the same race. Converting 1 1 2 to decimal, it becomes 1.5 hours.

This means that the number of hours that Michael spent training will be 35.5 × 1.5 = 53.25 hour.

Converting 53.25 hours to mixed fraction, it becomes

53 1/4 hours

Answer:

The answer is B

Step-by-step explanation:

Answer:3 gallons of water would be mixed with 1/2 gallon of the chemical

Step-by-step explanation:

If the mix ratio for certain chemical is 1:6 when it is mixed with water. This means that for every 1 gallon of the chemical, 6 gallons of water is required.

Therefore, the number of gallons of water that would be mixed with 1/2 gallon of the chemical becomes

1/2 × 6 = 3 gallons of water.

Answer: 3 gallons of water would be mixed with 1/2 gallon of the chemical

Step-by-step explanation:

If the mix ratio for certain chemical is 1:6 when it is mixed with water. This means that for every 1 gallon of the chemical, 6 gallons of water is required.

Therefore, the number of gallons of water that would be mixed with 1/2 gallon of the chemical becomes

1/2 × 6 = 3 gallons of water.

Answer:

a) has the same probability of being selected

Step-by-step explanation:

A simple random sampling means that each possible sample of size n has the same probability of being selected.

Then your answer is:

a) has the same probability of being selected

The definition of a simple random sampling method implies that each possible sample of a given size has an equally likely chance of being selected. Hence, option a. 'has the same chance of being selected' is the correct answer.

The simple random sampling method is a statistical method used to select individual samples from a large population where each sample is given an equal chance of being selected. In a simple random sampling of size n from a finite population of size N, each possible sample of size n would have the same probability of being selected. Therefore, the correct answer is a. has the same probability of being selected.

It is crucial to note that the probability of a sample being selected is not dependent on its size (n) nor the total size of the population (N), as options b, c, and d suggest. Instead, it is determined solely by the sampling method, i.e., simple random sampling.

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Answer: a=70°

              b=45°

              c=65°

              d=45°

              e=70°

               f=110°

Step-by-step explanation:

a=70°

b=180°-135°=45°

c=180-(70+45)=180-115=65°

c=65°

e=70°

d=180-(c+e)=180-(65+70)=180-135=45°

d=45°

f=180-e=180-70=110°

Answer:

His conclusion was incorrect.

Step-by-step explanation:

Since, slope of a line passes through [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is,

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Thus, the slope between (-1, 4) and (0, 0),

[tex]m_1=\frac{0-4}{0+1}=-4[/tex]

Also, the slope between (2, 7) and (3, 3),

[tex]m_2=\frac{3-7}{3-2}=\frac{-4}{1}=-4[/tex]

Now,

There are two cases possible,

Case 1 : line passes through (-1, 4) and (0, 0) is parallel to line passes through (2, 7) and (3, 3)

Case 2 : (-1, 4), (0, 0), (2, 7) and (3, 3) are on the same line

Hence, we can not say that they are on same line only after getting same slope.

i.e. his conclusion was incorrect.

Answer:

Okay so this picture is basically the answer for anyone who needs it...

Step-by-step explanation:

Answer:

Amount returned will be $14.80

So option (D) will be correct answer

Step-by-step explanation:

We have given the purchase price of store = $80

To sell the dress price is marked up by 19 %

So marked up price [tex]=80+\frac{80\times 19}{100}=$95.2[/tex]

He give the $110 to clerk

We have to find the amount which is returned by clerk

So the amount will be equal to $110-$95.2 = $14.8

So option (d) will be correct answer

Answer:

Mary buy $30 / $ 2 = 15 grilled cheese sandwiches

Step-by-step explanation:

five hamburgers cost 42 x 5 = $10

money left for grilled cheese sandwiches = $40 - $ 10 = $ 30

each grilled cheese sandwiches cost $2

Mary buy $30 / $ 2 = 15 grilled cheese sandwiches

Answer:

Check it down.

Step-by-step explanation:

Injective functions or One to one functions are functions in each one element of A set is is mapped to another element of B set

1) Let's start by listing supposition and their respective Reasons

Suppose:

[tex]g\circ f[/tex] is injective then [tex]f:A\rightarrow B[/tex] is also injective.

Reason: Given

2) Since we are dealing with injective (one to one) functions,  we can rightly proceed:

[tex]f(x)=f(y) \:such \:as\: x,y \in A[/tex]

[tex]g(f(x))=g(f(y))[/tex]

Given the fact that [tex]g\circ f[/tex]

[tex]x=y[/tex]

Then we can say that since [tex]g\circ f[/tex]  f: A is an injective too ("one to one" ) function.

Answer:

B

Step-by-step explanation:

210=1200*.035*5