Suppose that you are swimming in a river while a friend watches from the shore. In calm water, you swim at a speed of 1.25 m/s . The river has a current that runs at a speed of 1.00 m/s.Note that speed is the magnitude of the velocity vector. The velocity vector tells you both how fast something is moving and in which direction it is moving.Part AIf you are swimming upstream (i.e., against the current), at what speed does your friend on the shore see you moving?Express your answer in meters per second.

we know that Bob can do the whole job in 14 hours, how much of the work has he done in 1 hour only?  well since he can do the whole lot in 14 hours in 1 hour he has only done 1/14 th of the job.

we know that James can do it in 18 hours, a bit slower, so in 1 hour he has done only 1/18 th of the job.

let's say it takes both of them working together say "t" hours, so in 1 hour Bob has done (1/14) of the work whilst James has done (1/18) of the work, the whole work being t/t or 1 whole, so for just one hour that'd 1/t done by both Bob and James.

[tex]\bf \stackrel{Bob}{\cfrac{1}{14}}~~+~~\stackrel{James}{\cfrac{1}{18}}~~=~~\stackrel{total~for~1~hour}{\cfrac{1}{t}} \\\\\\ \stackrel{\textit{using an LCD of 126}}{\cfrac{9+7}{126}=\cfrac{1}{t}}\implies \cfrac{16}{126}=\cfrac{1}{t}\implies 16t=126\implies t=\cfrac{126}{16} \\\\\\ \stackrel{\textit{7 hrs, 52 minutes and 30 seconds}}{t=\cfrac{63}{8}\implies t=7\frac{7}{8}}\implies \stackrel{\textit{rounded up}}{t=7.88}[/tex]

Answer:

  24

Step-by-step explanation:

The greatest common divisor of 72 and 96 is 24. Robert can make any number of bags that is a divisor of 24. If he wants to make the largest number possible, then he can make 24 bags with 4 balloons and 3 pieces of candy in each one.

__

  72 = 2³·3²

  96 = 2⁵·3

The greatest common divisor is the product of the common factors: 2³·3 = 24.

Answer:

-46 feet/min

Step-by-step explanation:

Initial elevation = 1,380 ft

Final Elevation = 0 feet

Change in elevation

= Final elevation - Initial Elevation

= 0 - 1,380

= - 1,380 feet

Given that the journey took 30 min,

rate of descent = Change in elevation / time

= -1,380 / 30

= - 46 feet/min

Answer:

27.32 m

Step-by-step explanation:

We are given that

Height of window from the ground=18 m

Height of rock  form the ground=2 m

Speed of thrown rock=30 m/s

We have to find the horizontal distance from the window from which rock was release.

Difference between window and rock=18-2=16 m

Initial vertical velocity component=[tex]30sin40^{\circ}=19.28 [/tex]m/s

Initial horizontal velocity component=[tex]30cos 40^{\circ}=22.98 m/s[/tex]

If the rock is reached to maximum height

Then, maximum height=[tex]\frac{v^2}{2g}=\frac{(19.28)^2}{2\times 9.8}=18.9731 m[/tex]

Time taken by rock to reach maximum height=[tex]\frac{v}{g}=\frac{19.28}{9.8}=1.96775 s[/tex]

Distance between window and maximum height at which rock reached=18.9731-16=2.973 m

Time to drop 2.973 m=[tex]\sqrt{\frac{2h}{g}}=\sqrt{\frac{2\cdot 2.973}{9.8}}=0.77893 s[/tex]

Time to be at 16 m=1.96775-0.77893=1.189 s

Horizontal distance=[tex]1.189\times 22.98=27.32 m[/tex]

Hence, horizontal distance of rock from the window from which rock was released=27.32 m

The rock was released approximately 71.1 meters horizontally from the window. This calculation is based on the rock's initial speed of 30.0 m/s, launch angle of 40.0°, and the fact that it struck the window on its upward trajectory with no air resistance.

To solve this problem, we can use the kinematic equations of motion. We need to find the horizontal distance the rock was released from the window.

1. First, we can find the time it takes for the rock to reach its maximum height. We can use the following kinematic equation:

[tex]\[v_y = u_y + at\][/tex]

  Where:

  - [tex]\(v_y\)[/tex] is the final vertical velocity (0 m/s at the maximum height),

  - [tex]\(u_y\)[/tex] is the initial vertical velocity (30.0 m/s, since it's thrown vertically),

  - \(a\) is the vertical acceleration due to gravity (-9.81 m/s²),

  - \(t\) is the time.

  Rearrange the equation to solve for t:

 [tex]\[0 = 30 - 9.81t\]\\\\[/tex]

[tex]\[t = \frac{30}{9.81} \approx 3.06 \, \text{s}\][/tex]

2. Now, we can find the horizontal distance using the horizontal motion equation:

 [tex]\[d_x = u_x \cdot t\][/tex]

  Where:

  - [tex]\(d_x\)[/tex] is the horizontal distance we want to find.

  - [tex]\(u_x\)[/tex] is the horizontal component of the initial velocity                                    
[tex](30.0 m/s * cos(40°)).[/tex]

  - \(t\) is the time calculated in step 1.

  Plug in the values:

[tex]\[d_x = (30 \cdot \cos(40°)) \cdot 3.06 \approx 71.1 \, \text{m}\][/tex]

So, the rock was released approximately 71.1 meters horizontally from the window.

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Answer:

the easyiest way for me to explain why the answer is A 0.077

Step-by-step explanation:

first add all your numbers it comes up to 1112 then youre going to take that number and put it aside then you dived 86 (the total for anyone at least 31+) and it gices you 0.077

Total shoppers 255.

Number of shoppers who did not shop at the store = 20+70 = 90

Probability = 90/255 = 0.353

Answer:

The answer is (d) "None of the these alternatives are correct"

Step-by-step explanation:

If two events A and B are independent, the probability of the intersection [tex]P(A\cap B)[/tex] is defined as:

[tex]P(A\cap B)=P(A)\cdot P(B)[/tex]

Therefore, in the exercise:

[tex]P(A\cap B)=P(A)\cdot P(B)=0.5\cdot 0.5\\P(A\cap B)=0.25[/tex]

which give (d) "None of the these alternatives are correct"

For independent events A and B with P(A) = 0.5 and P(B) = 0.5, the probability of both events occurring, P(A ∩ B), is the product of their probabilities, which is 0.5 × 0.5 = 0.25. The correct answer is 'd. None of these alternatives are correct.'

The question revolves around the concept of independent events in probability. Since events A and B are independent, the probability of both events occurring together, P(A ∩ B), is the product of their individual probabilities. Thus, using the given probabilities P(A) = 0.5 and P(B) = 0.5, the probability of both A and B occurring is found by multiplying these probabilities together.

P(A ∩ B) = P(A) × P(B) = 0.5 × 0.5 = 0.25.

Therefore, the correct answer is not listed among the provided alternatives, so the correct choice would be 'd. None of these alternatives are correct.'

Answer:

May

Step-by-step explanation:

Let x be the sales in January,

∵ Sales were 10% greater in February than in January,

So, the sales in February = (100 +10)% of x

= 110% of x

= [tex]\frac{110x}{100}[/tex]

= 1.1x

∵  it is 15% less in March than in Feb,

Sales in march = (100-15)% sales in February

= 85% of 1.1x

= 0.935x

∵ It is 20% greater in April than in March,

Sales in April = (100+20)% of sales in march

= 120% of 0.935x

= 1.122x,

∵ It is 10% less in May than in April

Sales in May = (100-10)% of sales in march

= 90% of 1.122x,

= 1.0098x,

∵ It is 5% greater in June than in May

Sales in June = (100+5)% of sales in march

= 105% of 1.0098x,

= 1.5147x

∵ 1.0098x is much closure to x than 1.1x, 0.935x, 1.122x and 1.5147x

Hence, the sales in May is closest to sales in January.

Answer:

The equation of the line is [tex]y=45.25t+545[/tex]

Step-by-step explanation:

The general for of a line is:

[tex]y=mt+n[/tex]       (1)

where:

[tex]m[/tex] is the slope of the line and [tex]m[/tex] is the intercept with the axis of the dependent variable, [tex]y[/tex] in this case.

In order to obtain the value of the slope ([tex]m[/tex]) we can use the corresponding slope formula:

[tex]m=\frac{y_{2}-y_1 }{t_2-t_1}[/tex]         (2)

where [tex]t_1, t_2, y_1[/tex] and [tex]y_2[/tex] are the corresponding coordinates of the given points. In this case:

[tex]t_1=0\\t_2=4\\y_1=545\\y_2=726\\[/tex]

Substituting these values in equation (2) we obtain:

[tex]m=\frac{726-545}{4-0}=\frac{181}{4}=45.25\\m=45.25[/tex]

Hence, the line equation is now:

[tex]y=45.25t+n[/tex]     (3)

Now to obtain the value of [tex]n[/tex] you can follow two options:

Note that for this question, it is easier to select point A because of having the independent variable equals to zero [tex]t=0[/tex]. Hence, substituting point A in equation (3):

[tex]45.25*0+n=545\\n=545[/tex]

Therefore, the line equation is: [tex]y=45.25t+545[/tex]

The second option to find [tex]n[/tex] is to think of the meaning of the intercept. The intercept of a line is defined as the point in which the line crosses the axis of the dependent variable, which also means that the value of the independent variable for this point is zero. From this, we could have automatically said that [tex]n[/tex] is equal to [tex]545[/tex].

See the attachment for a plot of the line.

Final answer:

To derive the equation of the line through A(0, 545) and B(4, 726), calculate the slope (45.25) and use the point-slope form to get the final equation: [tex]\(y = 45.25t + 545\).[/tex]

Explanation:

To derive an equation of the line passing through points A(0, 545) and B(4, 726), first we need to find the slope of the line. The slope, usually represented as[tex]\(m\),[/tex] is given by the change in \(y\) over the change in \(x\), which is [tex]\(\Delta y / \Delta x\).[/tex]We use the formula [tex]\(m = (y_2 - y_1) / (x_2 - x_1)\).[/tex]

Substituting the given points into the formula:

[tex]\[m = \frac{726 - 545}{4 - 0} = \frac{181}{4} = 45.25\][/tex]

Now that we have the slope, we use the point-slope form of a line's equation, which is [tex]\(y - y_1 = m(x - x_1)\), where \((x_1, y_1)\)[/tex]is a point on the line. Since one point we have is A(0, 545), we can substitute the values in:

[tex]\[y - 545 = 45.25 \cdot (x - 0)\][/tex]

Therefore, the equation simplifies to:

[tex]\[y = 45.25x + 545\][/tex]

This is the equation of the line in slope-intercept form, with \(t\) being the independent variable and \(y\) being the dependent variable.

Answer:

y = [tex]\frac{1}{2}[/tex] x + 1

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, 1) and (x₂, y₂ ) = (4, 3)

m= [tex]\frac{3-1}{4-0}[/tex] = [tex]\frac{2}{4}[/tex] = [tex]\frac{1}{2}[/tex]

Note the line crosses the y- axis at (0, 1) ⇒ c = 1

y = [tex]\frac{1}{2}[/tex] x + 1 ← equation of line

Answer:

38

Step-by-step explanation:

1/3+1/4=7/12

7/12*24=12

24+12=26

Answer:

It's a bit unclear with the table this way, but I count fifteen points, fifteen lines of the table, each a pair of numbers.

That's 15 degrees of freedom in the data.   When modeling, each parameter in the model uses up one degree of freedom, so you'd use a smaller number of degrees of freedom when calculating t statistics, etc.

The value of 5 in 5,476,807,139 is five billion, as it is positioned in the billions place. This is explained by the concept of place value.

The value of 5 in the number 5,476,807,139 refers to its place value in the numerical system. In this case, the 5 is in the billions place. This means that, in terms of place value, that 5 actually represents [5 × 1,000,000,000], which is 5,000,000,000 or five billion. The concept of place value is important in mathematics, it tells you how much each digit in a number is worth according to its position.

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Answer:

x + y = 4 or y = -x + 4

Step-by-step explanation:

0 = -1[4] + b

4 = b

y = -x + 4

If you want it in Standard Form:

y = -x + 4

+x +x

_________

x + y = 4 >> Line in Standard Form

* Since the rate of change [slope] is -1 and that parallel lines have SIMILAR SLOPES, -1 remains the same.

I am joyous to assist you anytime.

Answer:

A. [tex]150+75h>600[/tex]

B. More than 6 hours

Step-by-step explanation:

A plumber earns $50 for a repair job, so he will earn $150 for three repair jobs.

Let h be the number of hours the plumber worked on Tuesday. He earns $75 per hour worked, so he will earn $75h in h hours.

In total, the plumber earned $(150 + 75h)

A. On Tuesday, he completed 3 repair jobs and earned a total of more than $600. Thus

[tex]150+75h>600[/tex]

B. Solve this inequality. Subtract 150:

[tex]150+75h-150>600-150\\ \\75h>450[/tex]

Divide by 75:

[tex]h>\dfrac{450}{75}\\ \\h>6[/tex]

This means, the plumber worked more than 6 hours.

Answer:

c

Step-by-step explanation:

it is the total cost for the lawn servic3

Answer:

B

Step-by-step explanation:

f(x)= the total of the equation

The constant term is the $25 which is what they charge along with the hours determined by x

Answer:

  (x, y) = (-1, -3)  or  (4, 12)

Step-by-step explanation:

A graphing calculator can show the solutions to this system.

__

You can equate expressions for y and solve for x.

  3x = x^2 -4

  x^2 -3x = 4 . . . . add 4-3x

  x^2 -3x +2.25 = 6.25 . . . . complete the square by adding (-3/2)^2 where -3 is the coefficient of x.

  (x -1.5)^2 = 2.5^2 . . . . . . rewrite as squares

  x -1.5 = ±2.5 . . . . . . . . . . take the square root

  x = 1.5 ± 2.5 = -1, +4

  y = 3x = -3, +12, respectively

Solutions are ...

  (x, y) = (-1, -3) . . . . and . . . . (4, 12)

Answer:

12 seconds

Step-by-step explanation:

75 t=66t+108

75t-66t=108

9t=108

t=108/9=12

Answer:

The answer to your question is: 12 seconds

Step-by-step explanation:

Lion v = 75 ft/s

wildebeest = 66 ft/s and is 108 feet behind the lion

t = time = ?

Formula

v = d/ t    solve for d   d = vt

Process

lion      d = 75t

wildebeest =   d = 108 + 66t

Now

                    75t = 108 + 66t

solve for t     75t - 66t = 108

                     9t = 108

                       t = 12 s

[tex]\bf (\stackrel{x_1}{-6}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{-3}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{9}}}{\underset{run} {\underset{x_2}{-3}-\underset{x_1}{(-6)}}}\implies \cfrac{-8}{-3+6}\implies -\cfrac{8}{3}[/tex]

Answer:

  42 = the number of hats Paula can knit from one yard of yarn

Step-by-step explanation:

The way this problem is written, the constant 42 is the multiplier of yards to get hats. That is, it has units of hats per yard, so represents the number of hats that can be knit from 1 yard of yarn.

_____

Comment on the problem

It seems more likely that the proportion should be written as ...

  y = 42h

or

  h = y/42

Then the constant would be the number of yards of yarn required for each hat.

In order to get the answer to this question you will have to rearrange and solve the question step by step.

[tex]10=7-m[/tex]

Rearrange:

[tex]10-(7-m)=0[/tex]

[tex]10-7=3[/tex]

Rearrange once more:

[tex]m+3=0[/tex]

[tex]-3 -3[/tex]

[tex]m=-3[/tex]

Therefore the answer is "m=-3."

Hope this helps.

Answer:

The answer to your question is: 10. 1 miles

Step-by-step explanation:

data

P = (-1, 3)

Q = (3, -3)

Formula

d = √((x2-x1)² + (y2-y1)²)

d = √)(3- -1)² + (-3-3))

d = √ (4² + -6²)

d = √ (16 + 36)

d = √ 52

d = 7.21 units

but

           1 units ----------------------- 1.4 miles

        7.21 units ---------------------     x

              x = 7.21 x 1.4/1 = 10.1 miles

Check the picture below.

make sure your calculator is in Degree mode.

The angle that the ladder makes with the ground would be 66.42 degrees.

Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.

We are given that  ladder is leaning against a building. The ladder is 10m long and it is sitting on the ground 4m out from the building.

The side adjacent to the angle is given, and the hypotenuse of the triangle is the unknown.

The cosine relation applies

 Cos = Adjacent/Hypotenuse

We are given the hypotenuse = ladder length

Cos (∅)= (4 )/10

Cos (∅)≈ 2/5

(∅)≈ [tex]Cos^{-1}[/tex]2/5

(∅) = 66.42

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Answer:

They are intersecting line segments ⇒ answer b

Step-by-step explanation:

* Lets explain the types of the lines

- Parallel lines lie in the same plane and never intersect each other

- Intersecting lines are lines that meet each other in exactly one point

- Skew lines are lines that are in different planes and never intersect

* Now lets solve the problem

- The line segments that cut sides of a wedge of apple pie

∵ The wage of apple pie could represent a plane

∵ The line segments cut the sides of the wedge

∴ The lines are in the same plane

∵ Skew lines are in different planes and never intersect

∴ The lines can not be skew

∵ The line segments that cut sides of the wage must be intersected

   at exactly one point

∵ Parallel lines never intersected

∴ The lines can not be parallel lines

∴ They are intersecting line segments

Answer: 11,658.45

Step-by-step explanation:

First multiply 305 x 620 to determine the square footage

divide that answer by 16.22 to get your answer

The required amount of electricity produced by a field of solar panels which is 305 feet by 620 feet, is 3,067,202 watt.

Given that,
A field of solar panels yields 16.22 watts per square foot.
T0 determines the amount of electricity produced by a field of solar panels that is 305 feet by 620 feet.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Here,
A field of solar panels yields 16.22 watts per square foot.
The amount of electricity produced by a field of solar panels is 305 feet by 620 feet,
= 16.22 * 305 * 620
= 3,067,202 watt,

Thus the required amount of electricity produced by a field of solar panels that is 305 feet by 620 feet, is 3,067,202 watt.

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Answer:

The height that make the surface area as small as possible is 10 cm

Step-by-step explanation:

Let

L -----> the length of the base of the box

W -----> the width of the base of the box

H ----> the height of the box

we know that

The volume of the box is equal to

[tex]V=LWH[/tex]

we have

[tex]V=4,500\ cm^3[/tex]

so

[tex]4,500=LWH[/tex] ----> equation A

[tex]L=2W[/tex] ------> equation B

substitute equation B in equation A

[tex]4,500=(2W)WH[/tex]

[tex]4,500=2W^2H[/tex]

Solve for H

[tex]H=\frac{2,250}{W^{2}}[/tex] -----> equation C

The surface area of a open box is equal to

[tex]SA=2(L+W)H+LW[/tex] ----> equation D  

Substitute equation B and equation C in equation D

[tex]SA=2(2W+W)(\frac{2,250}{W^{2}})+(2W)W[/tex]

[tex]SA=6W(\frac{2,250}{W^{2}})+2W^2[/tex]

[tex]SA=6(\frac{2,250}{W})+2W^2[/tex]

[tex]SA=\frac{13,500}{W}+2W^2[/tex]

Convert to function notation

[tex]f(W)=\frac{13,500}{W}+2W^2[/tex]

Find the derivative

[tex]f'(W)=-\frac{13,500}{W^2}+4W[/tex]

set equal to zero

[tex]f'(W)=0[/tex]

[tex]0=-\frac{13,500}{W^2}+4W[/tex]

Solve for W

[tex]\frac{13,500}{W^2}=4W[/tex]

[tex]W^3=\frac{13,500}{4}[/tex]

[tex]W=15\ cm[/tex]

Find the value of L (equation B)

[tex]L=2(15)=30\ cm[/tex]

Find the value of H (equation C)

[tex]H=\frac{2,250}{15^{2}}=10\ cm[/tex]

therefore

The height that make the surface area as small as possible is 10 cm

Answer:

Option D. No solutions

Step-by-step explanation:

we have

[tex]3x+2y=1[/tex] -----> equation A

[tex]-9x-6y=3[/tex] ----> equation B

Multiply by -3 both sides equation A

[tex]-3(3x+2y)=-3(1)[/tex]

[tex]-9x-6y=-3[/tex] -----> equation C

Compare equation B and equation C

Equation B and equation C are parallel lines with different y-intercept

Verify

For x=0

Equation C

[tex]-9(0)-6y=-3[/tex] ----->[tex]y=0.5[/tex]

The y-intercept is the point (0,0.5)

Equation B

[tex]-9(0)-6y=3[/tex] ----->[tex]y=-0.5[/tex]

The y-intercept is the point (0,-0.5)

therefore

Lines do not intersect

The system has no solution

see the attached figure to better understand the problem

Final answer:

The system of equations has infinitely many solutions because the second equation is an exact multiple of the first, indicating that both equations are equivalent and represent the same line.

Explanation:

To determine how many solutions the system of equations has, we can look at the coefficients of the variables x and y in both equations.

The first equation is 3x + 2y = 1.

The second equation is -9x - 6y = 3. If we multiply the first equation by -3, we obtain -9x - 6y = -3.

We notice that the second equation is an exact multiple of the first equation after our manipulation. This means that the two equations are equivalent, and every solution to one equation is also a solution to the other. Thus, the system does not have a unique solution, but rather infinitely many solutions, as both lines represented by these equations would perfectly overlap on a graph.

The correct answer to the question is A. Infinitely many solutions.

Answer:12.5 seconds

Step-by-step explanation:hconsidering Runner 1 with a speed of 10m/s

and Runner 2 with a speed of 4 m/s

the equation of displacement for a uniform movement is

x=V*t

so x1=V1*t

and x2=V2*t

and the problem condition is x2=x1+75m

so we proceed to solve the equations.

from equation 2 t=x2/V2

substituting in equation 1 we have

x1=V1(x2/V2) and then the 3 equation

x1=V1((x1+75m)/v2

finally x1=75*(V1/(V2-V1)) =75*(10/(10-4))=125m

then t=(x1/v1)=125/10=12.5 seconds

Answer:

12.5 seconds

Step-by-step explanation:

Speed of the first person = 10 meter per second

Speed of the second person = 4 meter per second

Relative velocity of faster person = 10 - 4 = 6 meter per second

since distance between both the person is = 75 meter.

Therefore, time to cover this distance by faster person = [tex]\frac{Distance}{Speed}[/tex]

[tex]\frac{75}{6}[/tex]

= 12.5 seconds.

Faster runner catches the slower runner after 12.5 seconds.

Answer:

In this case study we have following groups:

1. Population: It had all the cars which passed the bicyclist. Out of which 3000 cars were taken.

2. Who:  Each instance of a car passing a rider, means the drivers passing by.

That is the 3000 cars which passed the researcher on his bicycle.

3. What: The distance at which cars pass the bicycle rider. The distance the drivers stayed away from his bike.

The subject of this question is the cars in the study.

The Who in this study refers to the cases under study. In this case, the cases under study are the cars. The researcher rigged his bicycle with an ultrasonic sensor to measure how close each car was that passed him, and he observed that when he wore a helmet, motorists passed closer to him compared to when his head was bare. Therefore, the cars are the subject of this study.