Mathematics College

Two cable ferries start moving towards each other from shores A and B. When the pass each other for the first time the distance to shore B is 100 meters. Once they reach their destinations and start traveling back at the same time. When they meet for the second time, the distance to shore A is 50 meters. What is the distance between the shores Aand B?

Answers

Answer 1
Final answer:

The first meeting point of the ferries represents half of the total roundtrip, while the second meeting point represents a quarter of it. Knowing this proportion and the distances at which the meetings happen, we conclude that the distance between shores A and B is 200 meters.

Explanation:

This problem can be solved using rates and proportions. Consider the total round trip of each ferry. The first meeting is at 100 meters from shore B and the second meeting is  50 meters from shore A.

Imagine a full roundtrip travel, from A to B and back to A. When the ferries meet for the first time, they have collectively completed one full round trip (distance A to B and B back to A). At their second meeting, they have collectively made two full round trips.

This means that the first meeting happened at 1/2 of the round trip distance and the second meeting happened at 1/4 of the round trip distance, meaning that the second meeting point was half the distance of the first meeting point. Based on where the second meeting point is (50 meters from shore A), we know that the first meeting point (100 meters from shore B) is twice the distance of the second meeting point from shore A.

Now, we understand the distances as follow: the total distance from shore A to shore B is the sum of the distance from the first meeting point to shore B (100 meters) and twice the distance from the second meeting point to shore A (2*50 meters), which sums up to 200 meters. Therefore, the distance between shores A and B is 200 meters.

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Related Questions

Solve the system using the substitution method
2x+y=6
3x+5y=9
branliest offered

Answers

[tex]\left\{\begin{array}{ccc}2x+y=6&|-2x\\3x+5y=9\end{array}\right\\\left\{\begin{array}{ccc}y=6-2x\\3x+5y=9\end{array}\right\\\\substitute\ to\ second\ equation\\\\3x+5(6-2x)=9\\3x+30-10x=9\\-7x+30=9\ \ \ \ |-30\\-7x=-21\ \ \ \ |:(-7)\\x=3\\\\substitute\ the\ value\ of\ x\ to\ first\ equation\\\\y=6-2\cdot3\\y=6-6\\y=0\\\\\boxed{ \left\{\begin{array}{ccc}x=3\\y=0\end{array}\right}[/tex]

If two cylinders are similar and the ratio between the lengths of their edges is 2:5 what is the ratio of their volumes

Answers

we know that
[scale factor] is equal to the ratio between the lengths of their edges
so
scale factor=2/5

volume smaller cylinder/volume larger cylinder=[scale factor]³
volume smaller cylinder/volume larger cylinder=[2/5]³---> 8/125

the answer is
8/125

Answer: Thou answer shalt be Le letter B. 8:125




lori is 3 times as old as 7 more than ron's age if ron is a years old how old is lori

Answers

21 I think because 3 times 7 is 21 so you multiply 3 times 7.

hey can you please help me posted picture of question

Answers

The correct answer  for the exercise shown in the figure attached is the first option (Option A), which is:

 A. y=(x-2)^2-4

 1. As you can see in the figure attached, the red parabola has the function f(x)=x^2. This is the patern function.  By definition, which is the most basic function of the quadratics functions.

 2. The blue parabola is shifted 2 units at x axis and 4 units in the -y axis. Therefore, the correct function that represents this parabola is the function of the option A.

 3. If you want to verify it, you can give values to x and plot each point on a graph.
 

Hey can you please help me posted picture of question

Answers

The correct answer fot the problem shown in the figure attached is the option B, which is:

 B. Empirical

The empirical probability is the one that is determined experimentally, repeating once many times under the same conditions.
 When performing more repetitions, the empirical probability tends to establish a value that coincides with the theoretical probability of the event.
 In this case, when the coin was tossed 10 times, it could be determined that the probability of occurrence of heads or tails was not 50%.
 Therefore, the answer is:
 B: Empirical

ASAP
The equation of the linear regression line represents the relationship between the number of cars washed for charity, x, and the amount earned for charity, y. yˆ=10x+20 How much money can the charity expect to earn if 50 cars come in for a wash?

Answers

The given regression shows the relationship between the numbers of car washed(x) and the amount earned for charity(y).

y = 10x + 20

We are to calculate the amount of charity if 50 cars are washed. Number of cars are represented by x, so by substituting x = 50 in above equation we can find the amount of charity that is earned by washing 50 cars.

y = 10(50) + 20 = $ 520

Thus, the charity can earn $520 if 50 cars come in for a wash.

£54 in the ratio 5:4

Answers

add the ratio together: 5:4 becomes 5+4 = 9

divide the amount by 9:

54 / 9 = 6

multiply 6 by both 5 and 4

6 *5 = 30
6 * 4 = 24
 30 and 24 are two amounts

Solve for e.

9e^2f=49

e=±√7f/3

e=±7√f/3

e=±7√f/3f

e=±√7f/3f

Answers

[tex]9e^{2}f=49[/tex]
Divide by the coefficient of e², multiply by f/f, then take the square root.
[tex]e^{2}=\dfrac{49}{9f}=\dfrac{49}{9f}\cdot \dfrac{f}{f}=\dfrac{49f}{9f^{2}}\\\\e=\pm \dfrac{\sqrt{7^{2}f}}{\sqrt{(3f)^{2}}}\\\\e=\pm \dfrac{7\sqrt{f}}{3f}[/tex]

The appropriate selection is ...
   e = ±7√f/(3f)

Find the sum of the first 10 terms for the sequence {21, 63, 189, . . . }.

5.2 × 1010

620,004

206,661

2730

Answers

The sum of n terms of a geometric sequence with first term "a" and common ratio "r" is given by
[tex]S_{n}=a\dfrac{r^{n}-1}{r-1}[/tex]
You have a=21, r=3, so the sum of 10 terms is
[tex]S_{10}=21\cdot \dfrac{3^{10}-1}{3-1}=620004[/tex]

The appropriate choice is the 2nd one:
   620,004

The sum of the first 10 terms for the sequence given is 620,004.

What is Geometric sequence?

A geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

Given is a geometric sequence, 21, 63, 189, . . . we need to find the sum of the first 10 terms,

Sum of n terms of GP = aₙ = arⁿ-1 / r-1,

a₁ = 21

r = 3

So,

a₁₀ = 21 × 3¹⁰-1 / 3-1

a₁₀ = 21 × 29,524

a₁₀ = 620,004

Hence the sum is 620,004.

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A sandwich shop offers the following toppings. How many two topping sandwiches can you make? -lettuce -tomato -bacon -cheese -mustard

A) 8
B) 10
C) 12
D) 20
Please include steps or explain how you got your answer! :)

Answers

The correct answer is:  B) 10

Step 1:

To calculate the number of two-topping sandwiches you can make from the given toppings, you can use the combination formula:

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

Where:

- [tex]\(n\)[/tex] is the total number of toppings available (5 in this case).

- [tex]\(k\)[/tex] is the number of toppings you want to choose (2 in this case).

- [tex]\(C(n, k)\)[/tex] represents the number of combinations.

Step 2:

Substituting the values:

[tex]\[C(5, 2) = \frac{5!}{2!(5-2)!}\][/tex]

[tex]\[C(5, 2) = \frac{5!}{2!3!}\][/tex]

[tex]\[C(5, 2) = \frac{5 × 4}{2 × 1}\][/tex]

[tex]\[C(5, 2) = \frac{20}{2}\][/tex]

[tex]\[C(5, 2) = 10\][/tex]

So, you can make [tex]\(10\)[/tex] two-topping sandwiches from the given toppings.

PLEASE HELP


1. What is the length of the unknown leg in the right triangle? with sides
sqrt 23yd and sqrt 87 yd
a. 8yd
b. sqrt 110yd
c. 64 yd
d. sqrt 7040yd

Answers

we know that
in a right triangle
Applying the Pythagoras Theorem
c²=a²+b²

in this problem
c=√87 yd
a=√23 yd
b=?
so
b²=c²-a²-----> b²=(√87)²-(√23)²----> b²=87-23----> b²=64----> b=8 yd

the answer is
8 yd

A local company employs a varying number of employees each year, based on its needs. The labor costs for the company include a fixed cost of $41,949.00 each year, and $28,826.00 for each person employed for the year. For the next year, the company projects that labor costs will total $1,483,249.00. How many people does the company intend to employ next year?

Answers

Answer:

50

Step-by-step explanation:

Let

x = number of employees each yeary = labor costs

The relationship between x and y can be represented through a linear equation.

y = a . x + b

where,

a is the slope

b is the y-intercept

The slope represents the cost per each person employed, that is, a = $28,826.00/person.

Then,

y = ($28,826.00/person) . x + b

Even if no person is hired (x = 0), there is a fixed cost of $41,949.00 (y = $41,949.00).

$41,949.00 = ($28,826.00/person) . 0 + b

b = $41,949.00

The final equation is

y = ($28,826.00/person) . x + $41,949.00

If the company will spend $1,483,249.00 (y = $1,483,249.00.),

$1,483,249.00 = ($28,826.00/person) . x + $41,949.00

1,441,300 = ($28,826.00/person) . x

x = 50 person (50 people)

The company intends to employ 50 people next year.

y = |x| translated half a unit to the left

Answers

Answer:|

y=|x+.5|

Step-by-step explanation:

I found my answer by drawing a graph and then moving 2 spaces left then you need to do absolute values

you also need to plot some points on the graph to see where there is a straight line

I hope this helps

Solve the system of equations algebraically 5x - 3y = 6 6x - 4y = 2

Answers

Answer:

[tex]x=9[/tex] and [tex]y=13[/tex]

Step-by-step explanation:

We have been given a system of equations. We are asked to solve our given system algebraically.

[tex]5x-3y=6...(1)[/tex]

[tex]6x-4y=2...(2)[/tex]

From equation (1), we will get:

[tex]x=\frac{6+3y}{5}[/tex]

Upon substituting this value in equation (2), we will get:

[tex]6(\frac{6+3y}{5})-4y=2[/tex]

[tex]\frac{36+18y}{5}-4y=2[/tex]

[tex]\frac{36+18y}{5}-\frac{5*4y}{5}=2[/tex]

[tex]\frac{36+18y-20y}{5}=2[/tex]

[tex]\frac{36-2y}{5}=2[/tex]

[tex]\frac{36-2y}{5}*5=2*5[/tex]

[tex]36-2y=10[/tex]

[tex]36-36-2y=10-36[/tex]

[tex]-2y=-26[/tex]

[tex]\frac{-2y}{-2}=\frac{-26}{-2}[/tex]

[tex]y=13[/tex]

Upon substituting [tex]y=13[/tex] in equation (1), we will get:

[tex]5x-3(13)=6[/tex]

[tex]5x-39=6[/tex]

[tex]5x-39+39=6+39[/tex]

[tex]5x=45[/tex]

[tex]\frac{5x}{5}=\frac{45}{5}[/tex]

[tex]x=9[/tex]

A 12 pack of soda is roughly $3.75. What is the cost per can of soda?

Answers

So you just need to divide the cost of 12 pack of soda by 12 pack of soda.

That would be $3.75 / 12 = $0.3125

So answer is $0.3125 per can of soda or you can round it to approximately $0.31 per can of soda.

Hope this helps.

My son is trying to figure out how to decompose 8/12 and what he has to work with is x/2 + x/2 =8/12

Answers

x/2 + x/2 = 2x / 2 or just x. So x = 8/12 which can be simplified by their greatest common factor of 4. Divide both top and bottom by 4. This gives you x = 2/3. 

Your answer for that equation is x = 2/3

Not sure what you mean by "decompose" though. 

I need help on this please

Answers

Answer: the points that show the maximum and you have to draw are:

(0, 1.5); (2, 1.5); (4, 1.5);(6,1.5),...

Explanation:


1) formula given:

h(t) = 0.5 sin (πt + π/2) + 1

2) You want the points (t, h) where h is maximum.

3)  The mamimum of 0.5 sin (πt + π/2) + 1 is when 0.5 sin (πt + π/2) is maximum, and the  maximum of 0.5 sin (πt + π/2) is when sin (πt + π/2) is maximum.

4) Now, the maximum of the sine function is 1, so you must solve this equation:

 sin (πt + π/2) = 1.

5) As you know, sine function is equal to 1 when the argument is π/2 + 2nπ

So, find the first positive value of t doing

πt + π/2 = π/2

⇒ πt = 0 ⇒ t = 0

So, the first solution is t = 0.

Since the periodicity is 2π, the same value is obtained for t = 0, 2, 4, 6, ... 2n

6) The corresponding height is the same for all those t:

h(0) = 0.5 sin ( 0×t + π/2) + 1 = 0.5×1 + 1 = 1.5.

7) Therefore the points that you have to draw are: (0, 1.5); (2, 1.5); (4, 1.5);(6,1.5)...

I attach a figure just in case you need more help to visualize the answer.



which situation is represented by the following equation?45w+123.95=753.95

Answers

45w+123.95=753.95
subtract 123.95 from both sides
45w+123.95-123.45=753.95-123.95
simplifying gives us:
45w=630
multiply both sides by 1/45
1/45×45w=630×1/45
simplifying we get
w=14

1¼ gallons equals how many pints?

Answers

Answer:

10 pints

Step-by-step explanation:

There are 8 pints in a gallon, so ...

(1.25 gal) × (8 pt/gal) = 10 pt

How many different ways can a family visit Philadelphia, Baltimore, and Washington? 3 6 12

Answers

This is a problem regarding permutation. 

     [tex]P\left(3,3\right)=3!=3\times 2\times 1=6[/tex]

There are 6 different ways. 

Answer:

Answer is 6 ways

Step-by-step explanation:

Given that a family wants to visit three different places as Philadelphia, Baltimore, and Washington.

We have to find the number of ways these three can be visited.

Here this is a question of permutation since order matters.

There are 3 cities and these can be visited in 3P3 ways =3!

=3x2x1 =6 ways

There are in total 6 different ways that the family can visit three different places as Philadelphia, Baltimore, and Washington.

A line passes through the ordered pairs (4,1) and (2,8) . What is the slope? Please help

Answers

Final answer:

The slope of the line that passes through the points (4,1) and (2,8) is calculated using the slope formula and results in a slope of -3.5.

Explanation:

To find the slope of a line passing through the ordered pairs (4,1) and (2,8), you can use the slope formula:

m = (y2 - y1) / (x2 - x1). Here, (x1, y1) is the first point (4,1) and (x2, y2) is the second point (2,8).

Plugging in the values, we get:

m = (8 - 1) / (2 - 4) = 7 / (-2) = -3.5

Therefore, the slope of the line that passes through the points (4,1) and (2,8) is -3.5.

The slope of the line passing through the given points is -3.5.

Let’s find the slope of the line passing through the points (4, 1) and (2, 8).

The slope of a line can be calculated using the following formula:

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

where:

• [tex](x_1) and (y_1)[/tex] are the coordinates of the first point (in this case, (4, 1)).

• [tex](x_2) and (y_2)[/tex] are the coordinates of the second point (in this case, (2, 8)).

Let’s compute the slope:

1. Difference in (x)-coordinates: [tex](x_2 - x_1 = 2 - 4 = -2)[/tex]

2. Difference in (y)-coordinates:[tex](y_2 - y_1 = 8 - 1 = 7)[/tex]

Now, calculate the slope:

[tex]\text{slope} = \frac{7}{-2} = -3.5[/tex]

Therefore, the slope of the line passing through the given points is -3.5.

Mias dog weighs 32.6 pounds. Letties dog weighs 3.8 times as much as Mias you. What does Letties dog weigh in pounds?

Answers

Hello!

We are given the weight of Mia's dog and told to find the weight of Lettie's dog based on the known relationship. Using these given values, we can create the following equation (let "w" represent the total weight of Lettie's dog):

w = 32.6(3.8)

Simplify the right side of the equation:

w = 123.88

We have now proven that Lettie's dog weighs 123.88 lbs.

I hope this helps!

Final answer:

Lettie's dog weighs 123.88 pounds, calculated by multiplying Mia's dog's weight of 32.6 pounds by 3.8.

Explanation:

Calculating Lettie's Dog's Weight:

To find out how much Lettie's dog weighs, we need to perform a simple multiplication calculation because we are told Lettie's dog weighs 3.8 times as much as Mia's dog. Mia's dog weighs 32.6 pounds, so the weight of Lettie's dog will be:

32.6 pounds × 3.8 = 123.88 pounds.

It's important to remember that when we're dealing with measurements such as weight, we need to ensure that we stick to the same unit for a proper comparison. Given that we're talking about the weight of dogs, the pound is the most suitable unit of measurement for this context. Thus, we would not be using ounces or tons here, as those units are suitable for much lighter or heavier items, respectively.

Hey can you please help me posted picture of question

Answers

The code contains 4 letters and 3 numbers

Number of ways to select a letter = 26
So, number of ways to select 4 letters = 26 x 26 x 26 x 26 = 26⁴

Number of ways to select a number = 6
So, number of ways to select 3 numbers = 6³

Number of key code combinations = 26⁴ x 6³ = 98706816

So, option C is the correct answer

i need help with this

Answers

8. The mean of the grades (74) is substantially below the median (88), so the distribution is not symmetrical. Of course, half the grades are below the median, just as half are above the median. However, the mean being 88-74 = 14 points below the median means that the lower half of the grades will have an average at least twice that much, or 28 points, below the median. The distribution of grades must extend quite a bit further to the left of the median than it does to the right. Hence ...
  B. The distribution is skewed left.

9. It seems likely the distribution has a number of low grades pulling the average down. There certainly exists the possibility that at least one of them qualifies as an outlier by being more than 1.5 times the IQR below the first quartile. That rule, however, only applies when the distribution is relatively symmetrical, which this one is not. There does not appear to be any recommended way to describe an outlier when the distribution is skewed and has a long tail.*
  TRUE: The distribution likely has an outlier.

_____
* Math instruction these days rarely recognizes such subtleties. Since it is probable that at least one value is well below the bottom quartile, I've shown my guess at the expected answer as TRUE. In a real set of grades, I expect the tail of the distribution to have enough low grades that they cannot be considered to be outliers.

who help me is a genius

Answers

[tex]\bf \textit{arc's length}\\\\ s=r\theta ~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad radians\\ ------\\ r=6\\ s =\frac{3\pi }{4} \end{cases}\implies \cfrac{3\pi }{4}=6\theta \implies \cfrac{3\pi }{24}=\theta \\\\\\ \stackrel{simplified}{\cfrac{\pi }{8}=\theta }[/tex]

Mary has been $50 to spend on T-shirts from an online store. there is $10 shipping and handling fee and each t-shirt cost $5 which inequality represents the number of t-shirts s Mary can buy the answer choices are 5S + 10 greater than equal to 50, 5S + 10 less than equal to 50, 10s + 5 greater than equal to 50, 10s - 5 greater than equal to 50, 5S - 10 greater than equal to 50

Answers

Hello there!
The inequality that represents this situation is 5S + 10 is less than or equal to 50.
The $10 is just a fee, and you don't have to multiply it by anything. However, when the problem says each it means that you have to multiply the given number.
Hope this helped!

i need help finding the perimeter of a rectangle

Answers

Perimeter Formula= 2L + 2W
L= length
W= width

Plug in the width and length into the formula above to solve for perimeter.

Hope this helps! :)

we have 8 yards of wrapping paper if we use two feet for each present how many presents can we wrap

Answers

1 yard = 3 feet

Mulitply 8 × 3 = 24
You have 24 feet of wrapping paper.

Divide 24 by 2 = 12

You can wrap 12 presents.

Determine the measure of an angle (in radians) that cuts off an arc length of 6.4 inches in a circle with a 6.4 inch radius.

Answers

1 radian
because s= r × angle measurement in radian
we have s= arc , r = radian so we got the value

Q # 6 find the measure please

Answers

Angle AEB and angle BEC are supplementary angles, which means that they sum is 180°. knowing this we can subtract the measure of angle BEC from 180° to get the measure of angle AEB:
angle AEB=180°-127°=53°

We can conclude that the measure of angle AEB is 53°
Hello!

Angles AEB and BEC are examples of supplementary angles. Supplementary angles are two angles whose measures add to a sum of 180 degrees. This can be represented using the following formula:

A1 + A2 = 180

In this case, the formula can be rewritten to state the following:

∠AEB + ∠BEC = 180

Insert any values given in the problem above:

∠AEB + 127 = 180

Now subtract 127 from both sides of the equation:

∠AEB = 53

We have now proven that ∠AEB has a measure of 53 degrees.

I hope this helps!

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The time it takes me to wash the dishes is uniformly distributed between 10 minutes and 15 minutes. what is the probability that washing dishes tonight will take me between 11 and 13 minutes? Write the equation of the line with the following characteristics.A horizontal line through the point (0,3) What is the Value of Y? If you divided 26 objects into sets of 6, how many sets of 6 could you make, and how many are left over? Ender uses the jeers of the onlookers as a teaching tool. what does this reveal about the character of ender? Find the relative rate of change of the function f(x)=150-0.08x^2 How does HIV/AIDS affect the economics of Africa? When north korean communist leader kim il sung attempted to reunify korea under a communist government by invading the south, how did the us government respond? Laura recently ended a 10-year relationship when she learned her partner was cheating on her. the situation most likely caused ____________ work problems exhaustion distress. eustress Zola is very skilled with Microsoft and Apple, and she knows different methods of programming. This knowledge will help make Zola a successful candidate for a Hospitality and Tourism career. Which type of qualification does she have?A}professional appearanceB}flexibility in handling unexpected tasksC}good computer skillsD}expertise in problem solving Please answer and explain What is the value of x? sin(x+21)=cos(2x+21) given a mean of 7.6 and a standard deviation of 3.1 what is the z-score of the value 10 rounded to the nearest tenth ? A)0.8B)0.9C)1.7D)5.7 Why was Japan able to colonize Korea, Taiwan and parts of China? The star spangled banner written by frances scott commemorates what event in 1812 : how do network effects help facebook fend off smaller social-networking rivals? What prevented early plants from moving far from water? After the conclusion of the Spanish-American War, the United States faced stiff oppositionin the form of a guerrilla warfrom which of their newly acquired territoriesA)CubaB)GuamC)MexicoD)Philippines What strategies can i use with keywords to help narrow down the search results? The norm of reciprocity select one:a. suggests that when we receive something from another person we should respond in the future with a favor for them.b. plays only a nominal role in negotiations.c. applies only to favors of the same size.d. is prevalent only in western culture.e. none of the above statements describe the norm of reciprocity.