A boat travels downstream at an average speed of 30 mph. The boat makes the same trip back upstream at an average speed of 18 mph. What is the speed of the boat? What is the speed of the water current?

Answer: a. In this situation, 0 likely represents sea level or the baseline from which water levels are measured.

b. To find the average water level relative to high tide, you need to take the average of high tide and low tide.

Since high tide is 5 feet higher than low tide, you can assume that low tide is 0 ft. Therefore, the high tide is 5 ft.

The average of two values is the sum of the values divided by the number of values. So average of 0ft and 5ft is (0+5)ft / 2 = 2.5 ft.

Therefore, an integer that represents the average water level relative to high tide would be 2.5 ft.

It's worth noting that relative to high tide means how much the average water level varies (higher or lower) from the high tide, so the answer was not an integer in this case.

Answer:

(-3,5)

Step-by-step explanation:

8x+3(23+6x)=-9

x=-3

y=23+6x(-3)

y=5

(-3,5)

The equation of the polynomial function is (a)  h(x) = x^3 - 2x^2 - 5x - 6

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

x –2 0 1 2 3

h(x) 0 –12 0 8 0

The x-intercepts are where y = 0

So, we have

x = -2, x = 1 and x = 3

The multiplicity is 1

So, we have

h(x) = (x + 2)(x - 1)(x - 3)

Expand

= (x + 2)(x^2 - 4x + 3)

This gives

= x(x^2 - 4x + 3) + 2(x^2 - 4x + 3)

So, we have

= x^3 - 4x^2 + 3x + 2x^2 - 8x + 6

Evaluate the like terms

= x^3 - 2x^2 - 5x - 6

So the equation is h(x) = x^3 - 2x^2 - 5x - 6

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The 4 types of triangle with respect to angle measurement :

Acute Triangle

Obtuse Triangle

Right triangle

Equivalent triangle

A triangle is said to be equilateral if each of its three sides is the same length. In the well-known Euclidean geometry, an equilateral triangle is also equiangular, meaning that each of its three internal angles is 60 degrees and congruent with the others.

A triangle having three acute angles is known as an acute triangle. A triangle having one obtuse angle and two acute angles is known as an obtuse triangle. No Euclidean triangle may contain more than one obtuse angle because in Euclidean geometry, a triangle's angles must add up to 180°.

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or previously rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.

Obtuse-angled triangles or obtuse triangles are triangles with any one of its angles being an obtuse angle or more than 90°. Only 180° is equivalent to the internal angles of an acute triangle.

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There are four different triangles for measuring angles:

sharp triangle

Sharp triangle

correct triangle

comparable triangle

If all three sides of a triangle are the same length, the triangle is equilateral. Equiangular triangles are equilateral triangles in well-known Euclidean geometry. His three internal angles, which are all 60 degrees, are therefore consistent with one another.

An acute triangle is a triangle having three acute angles. Obtuse triangles are those with one obtuse angle and two acute angles. Euclidean geometry mandates that the total of all the angles of a triangle be 180°, hence a triangle cannot have more than one obtuse angle.

A right triangle, also known as a right triangle, right triangle, right triangle, right triangle, right triangle, or formerly right triangle, is a triangle with one or two right sides. The basis of trigonometry is the relationship between the sides of a right triangle and different angles.

An obtuse or obtuse triangle is a triangle with one of its angles obtuse or greater than 90°. An acute triangle has only 180° interior angles.

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The option that describes the center and variability of simulation A and simulation B is The centers will roughly be equal, and the variability of simulation A will be less than the variability of simulation B. The correct answer is C.

Considering the details provided in the query,

The two simulations will be run with sampling proportions from a population with a true percentage of 0.325.

Simulacrum A:

100 samples were used.

Tests: 1500

Exercise B -

50 samples total.

2000 trials

Due to the relationship between simulations A and B, they are now nearly equal.

1500 x 100 is the overall sample size for Simulation A.

= 150000

The simulation B sample size is 2000 x 50.

= 100000

We can observe from the simulations A and B calculations above that when comparing the,

Sample Size = Comparison of Simulations A and B

Simulation B + Simulation = Variability

Your question is incomplete but most probably your full question was

In a recent survey, the proportion of adults who indicated mystery as their favorite type of book was 0.325. Two simulations will be conducted for the sampling distribution of a sample proportion from a population with a true proportion of 0.325. Simulation A will consist of 1,500 trials with a sample size of 100. Simulation B will consist of 2,000 trials with a sample size of 50. Which of the following describes the center and variability of simulation A and simulation B?

A) The centers will roughly be equal, and the variabilities will roughly be equal.

B) The centers will roughly be equal, and the variability of simulation A will be greater than the variability of simulation B.

C) The centers will roughly be equal, and the variability of simulation A will be less than the variability of simulation B.

D) The center of simulation A will be greater than the center of simulation B, and the variability of simulation A will roughly be equal to the variability of simulation B.

E) The center of simulation A will be less than the center of simulation B, and the variability of simulation A will be greater than the variability of simulation B.

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A 3:2 image ratio refers to the proportion of the width to the height of an image or screen. It means that for every 3 units of width, there are 2 units of height.

The aspect ratio 3:2 is commonly used in digital photography, particularly for DSLR cameras and some mirrorless cameras.

In photography, the 3:2 aspect ratio is considered a standard format, it's the same as the traditional 35mm film frame, it's also the same as the aspect ratio of most modern digital cameras. It allows photographers to capture a wide range of scenes and subjects, and it's also a good option for cropping and printing photos.

For example, if an image's resolution is 3000x2000 pixels, it means that it has a 3:2 aspect ratio. The width of the image is 3000 pixels and the height is 2000 pixels, so 3000/2000 = 3/2

It's worth noting that the aspect ratio of 3:2 is a compromise between the wider aspect ratio of 16:9, used for video and some photography, and the taller aspect ratio of 4:3, used for more traditional photography.

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Yes, rectangles and squares are similar polygons.

Similar polygons are two or more polygons with the same shape but different sizes. This means that the sides of the polygons are proportional, and the angles are congruent. The formula to determine if two polygons are similar is A/a = B/b = C/c = D/d = …, where A, B, C, and D are the sides of one polygon and a, b, c, and d are the sides of the other polygon. For instance, if a rectangle has sides of 4 and 8, and a square has sides of 6 and 6, the ratio of the sides of the rectangle to the sides of the square is 4/6 = 8/6. This means that the two shapes are similar.

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David's annual gross pay is $2 730.00 * 12 = $32 760.00.

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The volume of the biggest possible cube inside the right cylinder is approximately 1193.243 cubic centimeters.

Cubes are hexahedrons with one same side length and only right angles. In this case, the cube is constrained by cross area of right cylinder in accordance to image attached below. The maximum possible volume for a cube inside the cylinder is described by following expression:

V = (√2 / 2)³ · R³

Where:

If we know that R = 15 cm, then the volume of biggest possible cube is:

V = (√2 / 2)³ · (15 cm)³

V ≈ 1193.243 cm³

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Equation  that represents Chris's total income I = ($5.75+$17.5)h , where X is the number of hours he works in a day.

Equation is a mathematical statement that expresses the equality between two or more expressions.

Equation are different types such as equation with one variables and equation with two variables. The equation is used to determine the unknown values.

Chris salary  $5.75 per hour.

During his work time he serves two groups.

The average tip per group = $8.75

Tips earned from two groups = $8.75 × 2 = $17.5

Then Chris total income in one hour = $5.75 + $8.75

Let Chris works h hours

Chris total income if he works total h hours in a day

I = ($5.75+$17.5) h

Hence, I = ($5.75+$17.5) h is the equation that determines Chris total income.

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the other equation is missing, the solution cannot be found.

What is Rate?

A rate in arithmetic is a ratio that contrasts two separate values with various unit systems. For instance, if John types 50 words per minute, that means he types 50 words per minute. We are dealing with a rate because the word "per" is there. The symbol "/" can be used in place of the word "per" in issues.

When two or more similar amounts or numbers are being compared using the same units, a ratio is utilized. When referring to the ratio of one quantity "to" the second quantity in spoken language, it is frequently written with a colon.

Determined to finish her milkshake before Diego, Lin now drinks her 12 ounce milkshake at a rate of an ounce per second.

Rate= 1/3 ounce milkshake per second

Initial = 20 ounces

Lin's condition is thus represented by the equation:

[tex]y = \frac{1}{3} x +20[/tex]

Since the other equation is missing, the solution cannot be found.

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The 4 physical properties of solutions are:

1) Concentration

2) Solubility

3) Viscosity

4) Transparency

In chemistry, a solution is a homogeneous mixture of two or more substances. The four common physical properties of solutions are:

1) Concentration: The amount of solute present in a given amount of solvent, typically measured in molarity, molality, or mass percentage.

2) Solubility: The maximum amount of solute that can be dissolved in a given amount of solvent at a specific temperature and pressure.

3) Viscosity: The resistance of a fluid to flow, which can be affected by the presence of a solute.

4) Transparency or Opacity: The property of a solution by which it allows light to pass through it or not.

These are the 4 common physical properties of solutions, but there are many other physical properties that can be used to describe solutions depending on the context.

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The area of the triangle is 54 square centimetres, which is calculated by multiplying the base (12 cm) and height (9 cm) and dividing by 2.

A = (12 cm * 9 cm) / 2

A = (108 cm²) / 2

A = 54 cm²

The area of a triangle is calculated by multiplying the base of the triangle and its height, and then dividing the result by 2. To calculate the area of the triangle with a base of 12 cm and a height of 9 cm, first the base and height must be multiplied together. 12 cm multiplied by 9 cm equals 108 cm². Then, the result of the multiplication, 108 cm², must be divided by 2. 108 cm² divided by 2 equals 54 cm². Therefore, the area of the triangle is 54 cm². To summarize, the area of a triangle is found by multiplying the base and height of the triangle, and then dividing the result by 2. In this case, the area of the triangle with a base of 12 cm and a height of 9 cm is 54 cm².

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The correct measure of center to determine which shop typically sells the most amount of coffee per hour will be C. Coffee Ground, with a mean value of about 5 gallons.

The mean is calculated by adding all the data points together and dividing by the number of data points.

When comparing the mean values of the two shops, Coffee Ground has a higher value of 5 gallons compared to Wide Awake's mean value of about 4.5 gallons. This indicates that Coffee Ground typically sells more coffee per hour on average.

The correct option is C.

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Answer:

see explanation

Step-by-step explanation:

given the system of equations

x + 3y = 76 → (1)

x + y = 36 → (2)

1

subtracting (2) from (1) term by term will eliminate x

(x - x) + (3y - y) = 76 - 36

0 + 2y = 40

2y = 40 ( divide both sides by 2 )

y = 20

3

substitute y = 20 into either of the 2 equations and solve for x

substituting into (2)

x + 20 = 36 ( subtract 20 from both sides )

x = 16

4

that is 16 students bought orange juice and 20 bought a sandwich

As a check

substitute the values for x and y into the equations and if both sides are equal then they are the solution

(1) :  16 + 3(20) = 16 + 60 = 76 ← True

(2) : 16 + 20 = 36 ← True

since both equations are true, then

x = 16 and y = 20 are the solutions to the system

Solutions can be divided into supersaturated, unsaturated, and saturated solutions based on how well the solute dissolves in the solvent.

A homogeneous mixture with the major ingredients solute and solvent is referred to as a solution.

Solutions can be divided into supersaturated, unsaturated, and saturated solutions based on how well the solute dissolves in the solvent.

Supersaturated solution: The excess solute will crystallize quickly in a supersaturated solution because it contains a lot of solute at a temperature where it will be decreased.

Unsaturated solution: When a solvent can dissolve any more solute at a specific temperature, the solution is said to be unsaturated.

Saturated solution: A saturated solution is one in which a solvent can no longer dissolve any more solute at a particular temperature.

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Claire's current account balance would be -$50.

The amount that Clare has in his bank account initially = $150

The amount that he used from his bank account to buy the bike =  $200

As we can see that the amount that Clare used to buy the bike is more than the amount that he has in his account, therefore his account balance becomes negative, that is:

$150 - $200 = -$50

Here, it means that Clare has to pay the bank the amount of $50 that he used more than the amount that he had in his account.

Therefore, Claire's account balance would be -$50.

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A digital clock will show that the number of the hour is less than the number of the minute for 12 different displays, starting at 10:00 AM and ending at 4:00 PM.

These displays are:

10:01 AM, 10:12 AM, 10:23 AM, 10:34 AM, 10:45 AM, 11:02 AM, 11:13 AM, 11:24 AM, 11:35 AM, 12:03 PM, 12:14 PM, and 12:25 PM.

For example, 10:01 AM and 11:23 AM.

From 10:00 AM to 12:59 PM, the hour will always be a single digit, so we can check the minutes to see if they are double digit.

From 10:00 AM to 10:59 AM, the minute has to be greater than the hour. So, we can pick the minutes starting from 01 to 59 and check whether the hour is less than the minute which gives us 12 such displays

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A system of equations consisting of a linear equation and a quadratic equation has infinitely many solutions is not true.

Linear equations are equations that graph as a line, while the quadratic equations are that graph as a parabola. Lines and parabolas in the xy-plane are convenient representations of linear and quadratic systems, respectively. One solution to the system is shown by each point where the line and parabola intersect. It is possible for a line and a parabola to intersect zero, one, or two times. This indicates that a linear and quadratic system may have zero, one, or two solutions.

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A quadrilateral is a four-sided shape. The perimeter of a quadrilateral is the sum of all its sides. If the perimeter of a quadrilateral is 54 cm, and we know that all four sides are equal, we can divide 54 by 4 to find the length of each side.

54 cm / 4 = 13.5 cmTherefore, the length of each side of the quadrilateral is 13.5 cm.

It's important to note that this is only one possibility, since quadrilaterals can have different shapes and different side lengths.

The total playground area is 280 square meter, if the dome cover an area of 1+2/3 = 5/3 square meter.

The area covered by the dome = 5/3 square meter

The area covered by the dome is 5/840 times of the total playground area.

Let the total area of the playground = A

5/3 = 5/840 × A

A = (5 × 840)/(3 × 5)

A = 280 square meter

--The given question is incomplete, the complete question is " Ben like to go in the covered dome, when he feels overexcited. The dome covers an area of 5/3 square meter, which is 5/840 of the total playground area. What is the total playground's area?"--

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The equation of the line perpendicular to the line A is given by the

x-4y +29=0

What is the general equation of a Straight line?

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line can be also written as -

Ax + By + C = 0

By = - Ax - C

y = (- A/B)x - (C/A)

Given is a  Line A pass through the point (1,5) and (5,7).

Find the equation of the line perpendicular to A that pae through point (-1,7)

line A is y= 1/4 x+c

x-4y +4c=0

it passes through ( -1,7)

c= 29/4

equation becomes x-4y +29=0

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Answer:

9/4

Step-by-step explanation:

Use the process of elimination. Divide each number's numerator by its denominator; if the outcome repeats itself, it isn't a terminating decimal. Therefore, when you divide 9/4, it equals 2.25, which is a terminating decimal.

Answer:

I don't care for the points

Step-by-step explanation:

The answer is the last one

3/4 divided by 2 in the fraction is equal to 3/8.

A fraction is used to represent the portion of the whole quantity. Also, we know that every integer is a rational number and any whole number can be written in the form of n/1, where n is any whole number.

On the given data, we need to use the concept of the division of fractions.

3/4 ÷ 2

=3/4 × 1/2 [ Reciprocal of 2 is 1/2]

=3/8

Therefore, 3/4 divided by 2 in the fraction is equal to 3/8.

Once you have your final fraction, just divide the numerator by the denominator to get your answer in decimal form: 3/8=0.375

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Answer:

the answer is 45°

Step-by-step explanation:

because they mirror eachother

Answer:

Step-by-step explanation:

I'm not sure but I think that is 45

The angles are congruent and the ratios of sides are equal, then the polygons are similar.

What is the similarity of polygons?

The similarity of polygons refers to the relationship between two or more polygons in which the corresponding angles are congruent (equal in measure) and the corresponding side lengths are in proportion.

We have,

Polygon 1:

Opposite Sides 24 = 24, 12=12,

Angles = 90°

Polygon 1:

Opposite Sides 16 = 16, 8=8,

Angles = 90°

This means that if two polygons are similar, their corresponding angles will have the same measure, and their corresponding side lengths will be in the same ratio. In other words, the ratio of any pair of corresponding sides of similar polygons will be the same.

For example, two triangles are similar if the ratio of their corresponding sides is the same, and their corresponding angles are equal. Similarly, two quadrilaterals are similar if the ratio of their corresponding sides is the same and their corresponding angles are equal.

It's important to note that similarity is a stronger relationship than congruence, because in congruence all the sides and angles must have the same measure, while in similarity only the angles and ratios of sides are the same.

Additionally, the similarity of a polygon can be determined by measuring the angles of the polygon, and comparing the ratios of the corresponding sides.

If the angles are congruent and the ratios are equal, then the polygons are similar.

Hence, the angles are congruent and the ratios of sides are equal, then the polygons are similar.

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Answer:

See below

Step-by-step explanation:

I'm guessing this is what you're looking for:

[tex]45^2=(40+5)^2=(40+5)(40+5)=40(40)+2(40)(5)+5(5)=1600+400+25=2025[/tex]

Step-by-step explanation:

1.y = x * (1-0.4)

2.y = x - 0.4x

3.x = y / (1-0.4)

4.x = y + 0.4y

The equation 1 and 2 correctly represent the situation. In the first equation, we are multiplying the initial amount of water (x) with (1-0.4) which is the percentage of the water that is remaining after drinking 40% of it. In the second equation, we are subtracting 0.4x from x, which is equivalent to multiplying x by (1-0.4).

The equation 3 and 4 are not correct, as they are trying to calculate the initial amount of water from the remaining amount, but it's not possible to know the initial amount once it has been consumed.

You have 0.6X amount water remaining.

The amount of water remaining in the water bottle is X minus 40%. This means that if you had X amount of water at start you now have 60% of X left.  That is, you have 0.6X amount of water remaining.

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The equation written is: x + 18 + x = 84

The lengths of each piece of the cable are: 33 meters and 51 meters.

To write an equation, let the unknown quantity be represented as a variable, which would be used in creating an algebraic expression.

For example, we are given the following:

Length of a cable = 84 meters

The length of one the pieces that the cable is cut into is represented as x.

The second pieces = x + 18 meters.

The equation that would be created for this problem would be:

x + 18 + x = 84

Solve for x:

2x + 18 = 84

2x = 84 - 18

2x = 66

2x/2 = 66/2

x = 33

The length of one of the pieces = 33 meters

Length of the second piece = x + 18 = 33 + 18 = 51 meters.

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