in her kayak bunny can travel 70 miles downstream with the current in 5 hours. the return trip against the current takes 7 hours. find the speed of the kayak in Stillwater and the speed of the current​

{5x + 2(x - 1) = 6(x + 1) +x}------------------------No solution

{5x + 2(x - 1) = 6(x - 1) - x}------------------------- x = -2

{5x + 2(x - 3) = 6(x - 1) - x}-------------------------x = 0

{5x + 2(x - 3) = 6(x - 1) + x}-------------------------All real numbers

What is linear equation?

A linear equation is an algebraic equation of the shape y= mx + b. regarding simplest a consistent and a first-order (linear) term, wherein m is the slope and b is the y-intercept.

Solution:

Simplifying First equation,

5x + 2x - 2 = 6x + 6 + x

⇒7x - 2 = 7x + 6

⇒ -2 = 6, which is not possible

Similarly second equation,

5x + 2x - 2 = 6x - 6 -x

⇒ 7x - 2 = 5x - 6

⇒ 2x = -4

⇒ x = -2

Similarly third equation,

5x + 2x - 6 = 6x - 6 - x

⇒7x - 6 = 5x -6

⇒ 2x = 0

⇒ x = 0

Similarly fourth equation,

5x + 2x - 6 = 6x - 6 + x

⇒ 7x - 6 = 7x - 6

⇒ 0 = 0

It means all real numbers are the solutions.

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Answer:

  B.  216 in²

Step-by-step explanation:

You want to know the area of a triangle with a base of 36 inches and a height of 12 inches.

The area of a triangle is given by ...

  A = 1/2bh

where b is the base of the triangle (one side), and h is the height to the opposite vertex, measured perpendicular to the base.

The figure shows a base of 36 inches and a height of 12 inches. Using these values in the formula, we have ...

  A = 1/2(36 in)(12 in) = 216 in²

The area of the triangle is 216 in².

Answer: 216

Step-by-step explanation: I got it right sorry for the late comment

The correct interpretation is (a) I am 95% confident that the confidence interval for mean weight of apples in the orchard will be between 147 grams to 151 grams

A confidence interval, refers to the probability that a population parameter will fall between a set of values for a certain proportion of times.

A 95% confidence interval is a range of values that you can be 95% certain contains the true mean of the population.

Since the 95% confidence interval for the mean weight of apples in an orchard at a specific given time is between 147 grams to 151 grams.

This follows that from our definition of confidence interval and 95 % confidence interval, that there is a 95 % confidence that the mean weight of the apples in the orchard lies between 147 grams to 151 grams.

So, the correct interpretation is (a) I am 95% confident that the confidence interval for mean weight of apples in the orchard will be between 147 grams to 151 grams

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The equation is y = 15x + 90. The initial value is 90. Rate of change is: 15.

To host a party at a local restaurant, you must pay $90 to rent it and $15 per guest.

To write a linear equation that models a situation in slope-intercept form, y = mx + b, find the following:

Given the table above, the value of y when x = 0 is 90. This means the initial value (b) = 90.

Using two pairs of values from the table, (0, 90) and (6, 180):

Rate of change (m) = (180 - 90) / (6 - 0) = 15

Substitute m = 15 and b = 90 into y = mx + b, to write the equation:

y = 15x + 90.

The graph of y = 15x + 90 is shown below.

The complete table is:

x   |  y  

0    90

3    135

6    180

9    225

12   270

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Class members that should be the public are: Constructors, accessors/ mutators and methods the user needs to manipulate the objects of the class. The correct answer is c. I, III, V.

All members declared in a class as well as all members (apart from constructors and finalizers) defined in all classes in its inheritance structure are considered to be members of the class. Although they are inherited, derived classes cannot access private elements of base classes.

Class members are all the members (apart from constructors and destructors) defined in the class, as well as all the classes in its inheritance structure. Members of a class may be any of the following: Constant values represented by constants. Variables represented by fields.

If you want the class to be instantiated from anywhere, you must make the constructor public. If you want a class to be inheritable and its inherited classes to be instantiated, you must make the constructor protected.

A technique used to regulate changes to a variable is known as a mutator method. They're also frequently referred to as setter methods. A getter, often referred to as an accessor, frequently follows a setter and returns the value of the private member variable.

Therefore, the correct answer is (c). I, III, V.

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Answer:

The average high temperatures in degrees for a city are listed.

58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57

If a value of 110.5° is added to the data, how does the mean change and by how much?

80.41 to 82.7

The mean increases by 2.7°.

The means stays at 80.4°.

The mean stays at 82.7°.

The average high temperatures in degrees for a city are listed.

58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57

If a value of 58° is changed to 101°, which of the following measures changes the most and what is the new value?

Mean 84°

Range 48°

IQR 32°

The average high temperatures in degrees for a city are listed.

58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57

If a value of 101° is added to the data, how does the mean change?

80.42 to 82

The mean decreases by 1.6°.

The mean decreases by 8.4°.

The mean increases by 8.4°.

Step-by-step explanation:

Answer:

11/20

Step-by-step explanation:

4/5 - 1/4

find greatets common denominator aka 20 cuz 5 and 4 can go into 20

multiply that many tiems it goes into 20 for the numerator

you now have 16/20 - 5/20
the answer is 11/20

Answer:

25%

Step-by-step explanation:

we know that you have to do amount of error/ correct amount

so the amount of error is 10 and the correct amount is 40, so its 10/40.

10 divided by 40 is 0.25.  They want the answer as a percent, so in order to turn 0.25 to a percent, you have to move the decimal 2 times over. It then turns into 25%

The system of equation to describe Tammy and Luke's outcome is as follows:

5x + y = 23

8x + 5y = 30

Tammy and Luke take part in a game in which they earn the same number of points for each catch and lose the same number of points for each miss.

let

x =  number of points for a catch

y = the number of points for a miss.

Tammy makes 5 catches and misses 1, ending the game with 23 points.

Therefore,

5x + y = 23

Luke earns 8 catches and has 5 misses. Luke ends the game with 30 points. Therefore,

8x + 5y = 30

Hence, the combine equation to describe the outcome is as follows:

5x + y = 23

8x + 5y = 30

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The graph which correct shows an image and pre-image after reflecting across the line; y = -x as required in the task content is; Option 1.

It follows from the task content that the answer choice which correctly represents an image ajd pre-image after reflecting across the line; y = -x.

First it is noteworthy to know that the line; y = -x is one which passes through the origin and has a negative slope of; -1.

On this note, by observation; when the line y = -x is drawn; the graph which represents the image and pre-image after reflecting across the line; y = -x is; Option 1.

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Using the Leading Coefficient Test the end behavior of the function  f(x) = 1234999x as the values of x increase towards infinity, ∞ is the functin also tends to infinity

The end behavior of function typically says the characteristics of the function at the ends

The given function is:

f(x) = 1234999x

The end behavior is determined by the leading Coefficient = 1234999, the problem has only one variable and hence the leading coefficient

x ⇒ ∞ f(x) ⇒ ∞

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Answer:

693.2

Step-by-step explanation:

6.932 · 100

Move the point two times to the right

693.2

The horizontal force that the student exert on the boat is 120 N toward the front of the boat.

What is third law of Newton ?

As per the third law of Newton, the force exerted by the boat over the student is equal in magnitude to the force that the student exerted on the boat.

So, calculate the force on the student using the second law of Newton, Force = mass * acceleration.

Force on the student = 60 kg * 2.0 m/s^2 = 120 N.

=> horizontal force exerted by the student on the boat = 120 N

Answer: option d. 120 N. toward the back of the boat.

Of course it is toward the back because that is where the student jumped from..

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Answer:

54.33

Step-by-step explanation:

Answer:

54.33

Step-by-step explanation:

Addition or a calculwtor can be used

While China has pulled hundreds of millions out of poverty, it has done so at the expense of the right to free speech and government.

China is a Communist country ruled by the Communist Party in a one-party state.

As a result, there are few political liberties because everything must adhere to the party's criteria. This means that while China's economy has been flourishing for decades, lifting people out of poverty has come at the expense of their freedom.

This is why Tiananmen Square movements for democracy were crushed, and Hong Kong protesters are being suppressed.

China is giving its people economic rights by lifting them from poverty, but has taken their political rights away.

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Answer:

b

Step-by-step explanation:

when the object is on the ground then h = 0 , then

- 16t² + 140 = 0 ( subtract 140 from both sides )

- 16t² = - 140 ( divide both sides by - 16 )

t² = [tex]\frac{-140}{-16}[/tex] = 8.75 ( take square root of both sides )

t = [tex]\sqrt{8.75}[/tex] ≈ 2.96 seconds ( to the nearest tenth )

The amount of money earned by Zach each week will be equal to $9 per week.

The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.

They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.

As per the given data in the question,

Total amount earned by Zach = $36

The time taken to earn the amount = 4 weeks

Then, the amount earned each week will be.

= $36/4

= $9 per week

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Answer:

x = 9

Step-by-step explanation:

Use Vertical Angles and Supplementary Angles to put all the given information inside the triangle.

Then use the idea that the three angles in a triangle add up to 180° to write an equation.

see image.

Actually also--shortcut! The 150° is an exterior angle, so it is equal to the

90° + 5x+15

90 + 5x + 15 = 150

this calculation comes out the same as the other.

Answer:

  x = 9

Step-by-step explanation:

Given a right triangle with an exterior angle of 150°, and a vertical angle to the other acute angle marked as 5x+15, you want to solve for x.

The exterior angle is equal to the sum of the remote interior angles. One of those is the right angle; the other is a vertical angle with respect to the one marked 5x+15. So, we have ...

  150 = 90 + (5x +15)

  45 = 5x . . . . . subtract 105

  9 = x . . . . . . divide by 5

The value of x is 9.

The equation of line that passes through point (-8, 1) and parallel to x - 4y = 4 is x - 4y + 12 = 0.

A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system.

The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line.

The given equation is,

x - 4y = 4.

The slope of the given equation,

m = 1/4

The slope of the required line will be equal to given line if line is parallel.

The equation of line that passes through point (-8, 1) and parallel to line x - 4y = 4.

y - 1  = m (x - (-8))

y - 1 = 1/4.(x + 8)

4y - 4 = x + 8

x - 4y + 12 = 0

The required equation of line is x - 4y + 12 = 0.

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The volume of a sphere is 33409.6 cm³ and the volume of a cube is 8000 cm³. Therefore, the volume of water 8000 cm³ can fit in the sphere.

Given that, a cube with an edge of 20 cm is filled with water.

Volume is the measure of the capacity that an object holds.

Formula to find the volume of the object is Volume = Area of a base × Height.

We know that, the volume of cube =a³, where a=edge

Here, volume of cube =20³

= 8000 cm³

Radius of sphere is 20 cm

As we know, the volume of sphere = 4/3πr³

= 4/3 ×3.14×20³

= 1.33×3.14×8000

= 33409.6 cm³

The volume of a sphere is 33409.6 cm³ and the volume of a cube is 8000 cm³. Therefore, the volume of water 8000 cm³ can fit in the sphere.

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The number of goals scored in a hockey game is a discrete random variable.

A discrete random variable has a countable number of different possible values, such as 0,1,2,3,4, etc. Usually, but not always, discrete random variables are counted. If a random variable has a limited range of possible values, it is discrete.

The number of children in a household, the Friday night movie attendance, the number of patients at a doctor's office, and the number of faulty light bulbs in a box of ten are a few examples of discrete random variables. A discrete random variable's probability distribution is a table of the probabilities connected to each of its potential values.

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Yes, the deviation is greater than it was in tossing them 40 times.

A standard deviation (or σ) is a measure of how widely distributed the data is in reference to the mean. A low standard deviation suggests that data is grouped around the mean, whereas a large standard deviation shows that data is more spread out.

Given:

n= 400 trials

Tossing 2 coins 400 times gives 800 trials

so, [tex]\sigma_1[/tex]² = np(1- p)

        = 800 x 1/2 x 1/2

      [tex]\sigma_1[/tex]  = √200

      [tex]\sigma_1[/tex] = 10√2

Now, n=40

and,  [tex]\sigma_2[/tex]² = np(1- p)

        = 80 x 1/2 x 1/2

      [tex]\sigma_2[/tex]  = √20

      [tex]\sigma_2[/tex] = 2√5

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Answer: x = 11

Step-by-step explanation: set both angles equal to 90 bc a triangle is 180 minus the 90 degree angle

Answer:

The answer is $14.224.

Step-by-step explanation:

The distance between  Bowtown to Dovebury is 39.

The total distance Dave will drive is 54 miles.

What is meaning of  total distance?

Total distance refers to the actual travel distance between the origin and destination locations of the material.

Given table is

Aranville

24                 Bowtown

37                        20           Cliffton

18                         39               17           Dovebury

From the table, the distance from Bowtown to Dovebury is 39miles.

The distance between Aranville to Cliffton is 37 miles.

The distance between Cliffton to Dovebury is 17 miles.

Dave wants to drive from Aranville to Cliffton and then from Cliffton to Dovebury.

Total distance is (37 + 17) miles = 54 miles

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Answer:

AB - [tex]\frac{2}{1}[/tex]

BC - [tex]\frac{4}{2}[/tex]

AC - [tex]\frac{6}{3}[/tex]

Slope = 2

Step-by-step explanation:

For AB the rise (counting upwards) is 2 and the run (counting to the right) is 1. If you simplify it, it would be 2. The reason why it's not a negative is that the slope is going upwards not downwards.

Answer:

1.135,

3.718,

and 8.389

Step-by-step explanation:

Answer:

[tex]x=-2,\;y\approx\boxed{1.135}[/tex]

[tex]x=1,\;y\approx\boxed{3.178}[/tex]

[tex]x=2,\;y\approx\boxed{8.389}[/tex]

Step-by-step explanation:

Euler's number, denoted as the letter "e", is a mathematical constant approximately equal to 2.7182818 ( 7 d.p.).

To evaluate [tex]y=e^x+1[/tex] for the given values of x, substitute the value of x into the equation and evaluate using a calculator, rounding the final answer to 3 decimal places (nearest thousandth).

[tex]\begin{aligned}x = -2\implies y&=e^{-2}+1\\y&=0.135335...+1\\y&=1.135335...\\y&=1.135\end{aligned}[/tex]

[tex]\begin{aligned}x =1\implies y&=e^1+1\\y&=2.7182818...+1\\y&=3.7182818...\\y&=3.718\end{aligned}[/tex]

[tex]\begin{aligned}x = 2\implies y&=e^{2}+1\\y&=7.389056...+1\\y&=8.389056...\\y&=8.389\end{aligned}[/tex]

The ways to assign for different people is 126 ways

From the question, we have

Total number of questions, n = 9

Numbers to people, r = 4

The number of ways of selection could be drawn is calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 9 and r = 4

Substitute the known values in the above equation

Total = 9C4

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have

Total = 9!/5!4!

Evaluate

Total = 126

Hence, the number of ways is 126

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We have proved that the ray FE is parallel to the ray GC.

What is meant by parallel lines?

In geometry, parallel lines are coplanar straight lines that do not intersect at any point. Parallel planes are planes in the same three-dimensional space that never meet. Parallel curves are curves that do not touch each other or intersect and keep a fixed minimum distance.

Angle DEF intersects at B

which results in angle DEF corresponding to the angle  ACG.

As DEF = 45 so angle ACG = 45

So by the above discussion, we can say that the ray FE is parallel to the ray GC.

Hence, we have proved that the ray FE is parallel to the ray GC.

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