A boat traveled 165 miles each way downstream and back. The trip downstream took 11 hours.
The trip back took 15 hours. What is the speed of the boat in still water? What is the speed of
the current?

Answer:

  a = 1/2

Step-by-step explanation:

You want the solution to 3 +0.5(4a +8) = 9 −2a.

It usually works well to start by simplifying the equation. That is, you eliminate parentheses, combine like terms.

  3 +0.5(4a) +0.5(8) = 9 -2a

  3 + 2a +4 = 9 -2a

  7 +4a = 9 . . . . . . . . . add 2a

  4a = 2 . . . . . . . . . subtract 7

  a = 0.5 . . . . . . divide by 4

The value of a is 1/2.

__

Additional comment

The attached calculator output shows this value of 'a' satisfies the equation.

The expression used to find the surface area of the rectangular prism is given as follows:

S = 2 x (1/2 x 3 x 4) + 4 x 2 + 3 x 2 + 5 x 2.

The prism is composed as follows:

The area of each component is given as follows:

The surface area is given by the addition of all these areas.

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The 59th term of the given arithmetic sequence, is -496

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence. The constant difference is called the common difference of that arithmetic progression.

Given that, an arithmetic sequence 26, 17, 8, we are asked to find the 59th term,

nth term of an arithmetic sequence, is given by :-

aₙ = a₁+(n-1)d

Where n is the asked term, d is the common difference,

Here d = 17-26 = 8-17 = -9

Therefore,

a₅₉ = a₁+(59-1)(-9)

a₅₉ = 26+58×(-9)

a₅₉ = -496

Hence, the 59th term of the given arithmetic sequence, is -496

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Answer:

Step-by-step explanation:the answer is 0.14 pounds

The number of ribbons of length  [tex]1\frac{2}{3}[/tex]  that can be cut out of a piece of ribbon that is 35 ft long, is 21

A division is a process of splitting a specific amount into equal parts.

Given that, a piece of ribbon that is 35 feet long, we need to find that how many [tex]1\frac{2}{3}[/tex] foot pieces of ribbon can you cut from it,

For this we will use the concept of division,

The number of ribbon cut from it = total length / small ribbons length

= 35 /  [tex]1\frac{2}{3}[/tex]

= 35 / 5÷3

= 35×3 / 5

= 21

Hence, the number of ribbons of length  [tex]1\frac{2}{3}[/tex]  that can be cut out of a piece of ribbon that is 35 ft long, is 21

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The new price of the purchase after the 13% discount can also be expressed as 0.87x.

The new price of the purchase after the 13% discount is expressed as x - 0.13x.

We can factor out x as follows to simplify this expression by combining like terms:

x - 0.13x = x(1 - 0.13) (1 - 0.13).

We can simplify the expression in parentheses as follows:

1 - 0.13 = 0.87.

So, by combining like terms, the equivalent expression is:

x - 0.13x = 0.87x.

As a result, the new purchase price after the 13% discount can also be expressed as 0.87x.

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Answer:

Step-by-step explanation:

First, we'll write the cost equations for each house, using the number of months since the initial purchase as the independent variable X:

For the house on Main Street:

Cost = 900X + 10,000

For the house on Empire Road:

Cost = 1050X + 4000

Next, we'll find the rate of change for each house by finding the slope of the respective cost equation:

The slope of the cost equation for the house on Main Street is 900. This means that for every month that passes, the cost of the house will increase by $900.

The slope of the cost equation for the house on Empire Road is 1050. This means that for every month that passes, the cost of the house will increase by $1050.

Now that we have found the rate of change for each house, we can compare them to determine which house has the greater rate of change:

Since the slope of the cost equation for the house on Empire Road is greater than the slope of the cost equation for the house on Main Street (1050 > 900), the house on Empire Road has a greater rate of change.

Finally, we can compare the initial values of each house by comparing the y-intercepts of the respective cost equations:

The y-intercept of the cost equation for the house on Main Street is 10,000, which means that the initial cost of the house is $10,000.

The y-intercept of the cost equation for the house on Empire Road is 4000, which means that the initial cost of the house is $4,000.

Since the y-intercept of the cost equation for the house on Main Street is greater than the y-intercept of the cost equation for the house on Empire Road (10,000 > 4,000), the house on Main Street has a greater initial value.

Answer:

So Ms. Shaw will completely fill 6 fish tanks and have 1 fish left.

Step-by-step explanation:

Ms. Shaw has 16 fish and each fish tank can hold 3 fish. To find out how many fish tanks she needs, we can divide the total number of fish by the capacity of each tank:

16 fish / 3 fish per tank ≈ 5.33 tanks

Since we cannot have a fraction of a tank, we need to round up to the nearest whole number. Therefore, Ms. Shaw needs 6 fish tanks to completely fill all her fish.

To find out how many fish are left, we need to subtract the number of fish in the full tanks from the total number of fish:

16 fish - (5 tanks * 3 fish per tank) = 1 fish left

So Ms. Shaw will completely fill 6 fish tanks and have 1 fish left.

The height of a cone is equal to 1.91 feet.

Mathematically, the volume of a cone can be calculated by using this formula:

Volume of a cone, V = 1/3 × πr²h

Making "h" the subject of formula, we have:

Height, h =3V/(πr²)

Substituting the given parameters into the height of a cone formula, we have;

Height, h =3(18)/(3.142 × 3²)

Height, h = 54/(28.278)

Height, h = 1.91 feet.

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" The value of the mean is always greater than the value of the standard deviation" is not a characteristic of the normal distribution

The curve of a normal distribution is known as the bell curve. The curve in statistical analysis represents the occurrence of some particular result as a product of the experiment. The normal curve is always symmetrical. This implies that the results of the trials will produce results near the mean value of the distribution.

Characteristics of a normal distribution involve:

1. The total area beneath the symmetric curve is 1: Since the area under the curve represents the chances of all the experiments; hence the summation must be 1.

2. The two tails of the curve extend indefinitely: The tails of the normal distribution never touch the horizontal axis; it is extended indefinitely.

4. The curve is symmetric about the mean: In a normal curve, the mean value of the distribution lies in the centre dividing the distribution curve into two symmetric parts.

Not a characteristic of a normal curve:

3. The value of the mean is always greater than the value of the standard deviation. The mean of the data can be negative as well as positive, but the value of the standard deviation is always positive. The small value of standard deviation implies the presence of more clustered data around the mean. The large value of the standard deviation indicates that the data is more spread out.

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The square pyramid is having a height of 89 units.

A pyramid is a three-dimensional shape. A pyramid's flat triangular faces unite at a common point known as the apex and have a polygonal base. The bases are joined to the peak to create a pyramid.

As per the given data:

length of the base ([tex]a[/tex]) = 20.8 units

slant height of the pyramid ([tex]s[/tex]) = 89.6 units

Height of the pyramid ([tex]H[/tex]) = [tex]\sqrt{s^2 - (\frac{a}{2})^2}[/tex]

=  [tex]\sqrt{(89.6)^2 - (\frac{20.8}{2})^2}[/tex]

=  [tex]\sqrt{(89.6)^2 - (\frac{20.8}{2})^2}[/tex]

=  [tex]\sqrt{(89.6)^2 - (10.4)^2}[/tex]

=  [tex]\sqrt{(8028.16) - (108.16)}[/tex]

= [tex]\sqrt{7920}[/tex]

= [tex]89[/tex] units

The height of the square pyramid is 89 units.

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The electric potential at the center of the circle formed by the plastic rod is -1.644V.

We know that the formula to find the electric potential V = KQ/R,

where K is Coulombs constant, Q is the charge, and R is the radius of the circle.  

According to the question,

The radius of the circle formed by the plastic rod on bending = 8.20 cm

(Converting cm to m by dividing by 100)               = (8.20)/100 = 0.082m

We know that Coulombs constant (K) =  8.99 × 10 ^ 9 N m^2/C^2

It is given that along one quarter of its circumference (Q1) =  +3.00 pC

and along the remaining circumference, the charge (Q2) = -6Q1

Therefore, electric potential (V) = K (Q1+KQ2) /R

= (8.99 × 10 ^ 9) (Q1 + (-6Q1)) / 0.082 = (8.99 × 10 ^ 9) (-5Q1)/ 0.082

= -5 (8.99 × 10 ^ 9) (3 X 10 ^ -12) / (0.082) = -1.644512V ≈ -1.644V

The given question is incomplete, the complete question is:

A plastic rod has been bent into a circle of radius R = 8.20 cm. It has a charge Q1 = +3.00 pC uniformly distributed along one-quarter of its circumference and a charge Q2 = -6Q1 uniformly distributed along the rest of the circumference. Take V = 0 at infinity.

What is the electric potential at the center C of the circle?

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We can write the quadratic equation as -

y = 3(x - 2)² - 7.

A function is a relationship between a dependent {y} and independent variable {x}.

An expression is a combination of terms both constants and variables.

Given is the quadratic function as shown in the image.

The general equation of a quadratic equation is -

y = ax² + bx + c

We can writ the equation of a parabola from the vertex as -

y = a(x - h)² + k

We have (2, - 7) as the coordinates of vertex. So, we can write -

y = a(x - 2)² - 7

For the point (3, - 4), we can write -

- 4 = a(3 - 2)² - 7

- 4 = a x 1 - 7

a = - 4 + 7

a = 3

So, we can write the quadratic equation as -

y = 3(x - 2)² - 7

Therefore, we can write the quadratic equation as -

y = 3(x - 2)² - 7.

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Answer:

b

Step-by-step explanation:

T2÷T1=r and T3÷T2=r and T4÷T3=r

The hypotenuse of the right triangle has a length of 19.24 cm.

For a right triangle whose catheti are A and B, and the hypotenuse is C, then the Pythagorean's theorem says that:

A^2 + B^2 = C^2

The lengths of the legs are:

A = 9cm

B = 17cm

Then the length of the hypoten use is given by:

(9cm)^2 + (17cm)^2 = C^2

√((9cm)^2 + (17cm)^2) = C

19.24 cm = C

The length of the hypotenuse is 19.24 cm.

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Answer:It is 45

Step-by-step explanation:Take 1,530 and divid it by 34 using a calculator.

The false statement involving p, and the arbitrary events A and B are e) P(Ac ∩ B) = P(B) - P(A ∩ B).

When two events cannot happen simultaneously or at the same time, they are said to be mutually exclusive in probability theory. In other words, discontinuous occurrences are described as being mutually exclusive. The likelihood of two occurrences occurring simultaneously is 0 if they are regarded as separate events. based on an impulse, notion, or chance rather than on logic: Despite being a random pick, her clothing was ideal. 1. Dependent solely upon one's discretion; open to individual will or judgment without limitations. a choice made at random. 2. made by a court or arbitrator as opposed to a law or statute.

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The algebraic expression is 2x - 5 > 6

The given equation can be written in a verbal phrase as:

"Twice a number, decreased by five, is equal to a number greater than negative six."

When represented as an expression, we have

Hence, the expression is 2x - 5 > 6

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Based on the simulation, we can say that, 95% of proportion of the 95 percent confidence intervals capture the population proportion of 0.3.

Confidence interval in statistics is defined as the certain range of values that you estimate for the unknown parameter lies within.

This means that, if you do your experiment more than once and do resampling, then this is the percentage that the parameters falls within a range.

If we say that the confidence interval is A% for a certain parameter like proportion, mean, standard deviation, etc. to be fall within a range of x and y, then this can be interpreted as that we are A% confident that the parameters fall within x and y.

In other words, A% of the intervals capture the parameters.

Therefore, here, we can say that, 95% of the 95% confidence intervals will capture the population proportion of 0.3.

Hence 95% of proportion of the 95 percent confidence intervals capture the given proportion.

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It is impossible to get 8 aces from a standard 52 cards deck.

What is probability and its formula?

The formula for probability states that the possibility of an event happening, or P(E), equals the ratio of the number of favorable outcomes to the number of total outcomes. Mathematically, it looks like this: P(E) = favorable outcomes/total outcomes.

Now, According to the question:

There are four aces in total in a 52 card deck.

Therefore the probability of getting 8 aces can be expressed as:

P(8A) = 7/52 × 6/51 × 5/50 × 4/49 × 3/48 × 2/47 × 1/46 × 0/45 = 0

The probability getting is zero.

Therefore, it is impossible to get 8 aces from a standard 52 cards deck.

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The equation of the function is g(x) = √(x + 5) - 2

From the question, we have the following parameters that can be used in our computation:

f(x)=√(x + 2) - 3

The transformation is given as:

3 units left and 1 unit up

This is represented as

(x + 3, y + 1)

Substitute the known values in the above equation, so, we have the following representation

g(x) = √(x + 2 + 3) - 3 + 1

Evaluate

g(x) = √(x + 5) - 2

Hence, the equation is g(x) = √(x + 5) - 2

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Answer:

B

Step-by-step explanation:

The graph has to start at  - 4   and get  smaller ( more negative...'less than')   but NOT INCLUDE -4   ( should be hollow dot at -4)

Answer:

--------------------------------------

Every 3 clovers out of 10 have four leaves and the rest 7 have three leaves.

This gives us the ratio of clovers with four leaves by the total number:

If the total number is 100, then Lucy has:

If there are 200 clovers, then the number of four-leaf clovers is doubled:

Typically, the group of objects in which data is collected from is called the population

The first 10 Pythagorean triples are: (3, 4, 5), (5, 12, 13), (8, 15, 17), (7, 24, 25), (20, 21, 29), (12, 35, 37), (9, 40, 41), (28, 45, 53), (11, 60, 61), and (16, 63, 65).

Pythagorean triples are sets of three positive integers that satisfy the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The first 10 Pythagorean triples, listed in ascending order of their hypotenuse lengths, are (3, 4, 5), (5, 12, 13), (8, 15, 17), (7, 24, 25), (20, 21, 29), (12, 35, 37), (9, 40, 41), (28, 45, 53), (11, 60, 61), and (16, 63, 65). There are infinitely many Pythagorean triples, and they have important applications in mathematics, physics, and engineering.

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The formula to calculate the magic number in MLB is: Magic number = 163 - (number of wins by leading team) + (number of losses by trailing team) - 1.

The "magic number" in Major League Baseball (MLB) represents the combination of wins by the leading team and losses by the trailing team required for the leading team to clinch a playoff spot. To calculate the magic number, follow these steps:

1. Determine the total number of games in the season. In MLB, this is typically 162 games.

2. Subtract the number of games in the season from 163. For example, 163 - 162 = 1.

3. Subtract the number of wins by the leading team from 163. For example, if the leading team has 90 wins, 163 - 90 = 73.

4. Add the result from step 2 to the result from step 3. For example, 73 + 1 = 74.

5. Finally, subtract the number of losses by the trailing team from the result of step 4. For example, if the trailing team has 80 losses, 74 - 80 = -6. In this case, the magic number is zero, meaning that the leading team has already clinched a playoff spot.

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The area of rectangle in expanded quadratic form is; is 20x² - 10x - 30.

The area of rectangle is given by the formula;

Area = length × width.

Area = 5  × (4x² - 2x - 6)

= (5 × 4x²) - (5 × 2x) - (5 × 6)

= 20x² - 10x - 30

Therefore, the area of rectangle is 20x² - 10x - 30.

Upon solving the above quadratic equation, we get,

20x² - 10x - 30 = 0

2x² - x - 3 = 0

x = 3/2, x = -1

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Complete question is;

A rectangle has a height of 5 and a width of 4x² - 2x - 6. Find the area of rectangle.

Answer:

20x² - 10x - 30

Step-by-step explanation:

The exact value of a trig function can be found by using the unit circle, the trigonometric identities, tables or a calculator.

To find the exact value of a trigonometric function, there are several methods you can use. Below are a few:

1. Using the Unit Circle: The unit circle is a circle with radius 1 centered at the origin in the coordinate plane. The angles in the unit circle are measured in radians and the coordinates of points on the circle can be used to find the exact values of trigonometric functions. For example, given an angle θ in the unit circle, the x-coordinate of the point on the circle corresponding to θ is cos(θ) and the y-coordinate is sin(θ).

2. Using the Trigonometric Identities: There are several trigonometric identities that relate the values of the six trigonometric functions to one another. These identities can be used to find the exact value of a trigonometric function for certain angles. For example, the Pythagorean identity states that for any angle θ, sin²(θ) + cos²(θ) = 1.

3. Using Tables or a Calculator: Trigonometric tables or a scientific calculator can be used to find the exact values of trigonometric functions for certain angles. The values are often given in degrees, so it is important to convert the angle to radians if necessary.

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The value of 6½ - 1⅓ is 5 ⅙

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

To solve 6½ - 1⅓ ;

we make the mixed fraction improper fraction

= 13/2 - 4/3

= (39-8)/6

= 31/6

= 5 1/6

therefore The value of 6½ - 1⅓ = 5 1/6

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Step-by-step explanation:

[tex]6 \frac{1}{2} - 1\frac{1}{3} = 5 \frac{1}{6} [/tex]

Answer:

it is the 4th and 5th

Step-by-step explanation:

by following the laws of BODMAS

Brackets

of

Division

Multiplication

Addition

Subtraction

(5×6)+2=5×6+2

(30)+2=30+2

32=32

5×6+2=2+5×6

30+2=2+30

32=32