raina swam 8 kilometers against the current in the same amount of time it took her to swim kilometers with the current. the rate of the current was kilometer per hour. how fast would raina swim if there were no current?

The measure of each side of an equilateral triangle is 2 cm whose area is √3 cm square.

Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles. It is one of the fundamental shapes in geometry and is represented by the symbol Δ.

We have been given the measure of each side of an equilateral triangle whose area is √3 cm².

Let the measure of each side would be "a"

We know that,

Area of an equilateral triangle = √3a² / 4

As per the question,

⇒ √3 cm²= √3a² / 4

⇒ √3a² = 4√3 / √3

⇒ a² = 4 = √4

⇒ a = 2 cm

Thus, the measure of each side of an equilateral triangle is 2 cm whose area is √3 cm square.

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For the equation A=s² for s. Assume s > 0, then s = [tex]\sqrt{A}[/tex].

What are squares and square roots?

Squares are the numbers that are produced when a value is multiplied by itself. In contrast, a number's square root is a value that, when multiplied by itself, returns the original value.

For the given equation, A = s², we have to find the value of s.

thus, taking the square root on both sides, we get

                                     s = [tex]\sqrt{A}[/tex].

Hence, the value of s = [tex]\sqrt{A}[/tex].

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The rate of change of the exponential function f(x) = 2(2)ˣ is 2

An equation shows the relationship between two or more numbers and variables.

An exponential function is in the form:

y = abˣ

Where a is the initial value and b is the rate of change.

Given the function:

f(x) = 2(2)ˣ

Hence rate of change = 2

The rate of change is 2

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Caelan must spend a total cost of $ 17 for 10 bowling games.

The total cost consists in the sum of a fixed cost, represented by rent of shoes, and a variable cost, represented by the number of bowling games, whose model is presented below:

c' = c + r · n

Where:

First, construct the system of equations related to Kai and Jack:

Kai

c + 3 · r = 6.50

Jack

c + 5 · r = 9.50

Second, solve the system of linear equations by numerical methods:

(c, r) = (2, 1.5)

Third, write the resulting function:

c' = 2 + 1.5 · n

Fourth, evaluate the function for the situation of Caelan:

17 = 2 + 1.5 · n

1.5 · n = 15

n = 10

Caelan rents 10 bowling games for $ 17.

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The population in 208 years based on the information is 10193600.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.

Since the city doubles its size every 52 years. The number of times that it'll double in 208 years will be:

= 208 / 52

= 4 times

The population in 208 years will be:

= 637100 × 2⁴

= 637100 × 16

= 10193600

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The possible combination of the number of peaches and apricots they can get for $5 is 2 peaches and 5 apricots.

The equation that represents the total cost of peaches and apricots is:

Total cost = (number of peaches x cost of one peach) + (number of apricots x number of apricots)

$5 = ($0.85 x p) + ($0.55 x a)

Total cost of buying 1 peach and 8 apricots:

($0.85 x 1) + ($0.55 x 8) = $5.25

Total cost of buying 2 peaches and 5 apricots:

($0.85 x 2) + ($0.55 x 5) = $4.45

Total cost of buying 3 peaches and 7 apricots:

($0.85 x 3) + ($0.55 x 7) = $6.40

Total cost of buying 4 peaches and 3 apricots:

($0.85 x 4) + ($0.55 x 3) = $5.05

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To move at 100 km/hour at its end, the length of the minute hand that has an angular velocity of 2·π radians per hour, has to be approximately 15.92 kilometers

Angular velocity is the rate and direction of rotation of a body about an axis.

The required linear speed of the minute hand = 100 km/hour

The formula to convert angular speed to linear speed is presented as follows;

Which gives;

The angular speed of the minute hand = 2·π rad/hour

The required length of the minute hand is therefore;

[tex]r = \dfrac{100 \ km/hour}{2\cdot \pi/hour} = \dfrac{50}{\pi}\, km \approx 15.92 \, km[/tex]

The length of the minute hand that that give a motion of 100 km/hour at the end is approximately 15.92 km

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A. The expression in the simplest form that represents the amount (in dollars) it costs to adopt x dogs is 195x

B. The coefficient of the expression in part (a) represents D. The the total amount the animal shelter earns when x dogs are adopted

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

In this situation, to adopt a dog from an animal shelter, you must pay $80 for vaccinations, $65 to spay or neuter the dog, and $50 for a wellness exam by a veterinarian.

Therefore, the expression to adopt x dogs will be:

= 80(x) + 65(x) + 50(x)

= 80x + 65x + 50x

= 195x

This is the cost for x dogs.

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There would be 1024 possible outcomes on a 5 question test with each question having 4 possible answers.

Based on the given information, there are 4 possible ways for each of the 5 questions.

4 possible ways to answer Question # 1

4 possible ways to answer Question # 2

4 possible ways to answer Question # 3

4 possible ways to answer Question # 4

4 possible ways to answer Question # 5

Fundamental Principle of Counting, also called the counting rule, is the method to count how many ways multiple independent events can occur.

Thus, by Fundamental Principle of Counting, the number of possible outcomes is

4 x 4 x 4 x 4 x 4 = 1024

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The information about the graph of the relationship that is given is: E. y-intercept and a point that is not an intercept.

In Mathematics, the y-intercept of any graph such as a linear, quadratic, trigonometric function, generally occurs at the point where the value of "x" is equal to zero (x = 0).

Mathematically, the slope-intercept form of a straight line is generally modeled or represented by this mathematical expression;

y = mx + c

Where:

In this context, we can reasonably infer and logically deduce that the total number of pages (y-intercept) which is equal to 180 is an information that was provided, as well as the number of hours (666 hours), which represents a data point on the x-coordinate of the graph.

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Answer:

Full truck = 18.2 tons

Step-by-step explanation:

FT = ET + 20R. ET (Empty Truck) = 15t

R (refrigerator) = 0.16t

FT = 15t + 3.2t

FT= 18.2t

The value of expression n + p - 2q when n = p = q is 0

In this question, we have been given an expression n+p-2q

We need to find the value of given expression when n=p=q

Consider given expression,

n + p - 2q

Substitute n = p

= p + p - 2q

= 2p - 2q

Now we substitute p = q in above expression,

= 2q - 2q

= 0

Therefore, the value of expression n + p - 2q when n = p = q is 0

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Answer:

14

Step-by-step explanation:

[tex]\frac{4 \text{ miles}}{1 \text{ hour}} \times 3.5 \text{ hours}=14 \text{ miles}[/tex]

The density is the ratio of mass to volume of an object thus the density of the given test sample is 4 g/cm³ thus option (C) will be correct.

Density or mass density is the mass of any object per volume.

For example, if the metal has a 100 kg mass and an area of 10-meter square then 100/10 = 10 kg/meter square will be the density of the given object.

Density can be uniform or non-uniform.

Density is the division of mass and volume and the mass must be for the quantity of the volume only.

Given that,

Mass = 10 g

Volume = 2.5 cm³

Density = 10/2.5 = 4 g/cm³

Hence "The density is the ratio of mass to volume of an object thus the density of the given test sample is 4 g/cm³".

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Radius of Earth's moon is [tex]1.737*10^{8}[/tex]

Very big or very small numbers can be presented in a simpler way using scientific notation. Although whole numbers can be stretched to infinity, humans are unable to write such enormous numbers on paper. Additionally, it was necessary to represent the numbers that appear at the millions place after the decimal in a more straightforward manner. The extended form of a few numbers is therefore difficult to represent. So, we employ scientific notations.

Given, radius of Earth's moon is 173,700,000.

As we know, in scientific notation there is only one number to the left.

So, we need to move the decimal to 8 places.

Therefore, radius of Earth's moon is [tex]1.737*10^{8}[/tex].

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At the rate of variation of 50 days/pound the snake gain 1 pound.

The mathematical expression for the percentage difference change over a predetermined period is called the rate of variation, which also denotes the movement of a variable. It allows us to understand how 2 factors that are changing interact with one another.

A snake takes 25 ÷ 4 days to gain 1 ÷ 8 pounds of weight,

a) Gain 1 pound need take: (25 ÷ 4) × 8 = 50 days

b) In one year = 365 days

= (25 ÷ 4) × (1 ÷ 8)

= (25 ÷ 4) × 8

= 50 days/pound.

So, the snake gained(1 ÷ 50) pounds one day.

In one year: (1 ÷ 50) × 365 = 7.3 pound

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1) Simple interest is $41600, 2) compound interest is $ 43264, 3) Amount at the end of Simple interest is $301600, 4) Amount at the end of Compound interest is $303264, 5) Difference in the amount of simple and compound interest is $ 1664.

Here it is given:

Principle (P) =$ 260000

Time(t) = 2 years

Rate (R) = 8%

1) We have to find the simple interest:

Simple interest(SI) = P× t × R/ 100

                               = 260000× 2× 8/ 100

                               = $41600

2) We have to find Compound Interest

Compound interest(CI) =P( 1 + R/100[tex])^{t}[/tex]- P

                                     = 260000( 1 + 8/100[tex])^{2}[/tex]- 260000

                                     = 260000( 27/25[tex])^{2}[/tex] - 260000

                                     = 303264 - 260000

                                     = $43264

3) Amount at the end of simple interest

Amount = P + SI

             = 260000 + 41600

             =$301600

4) Amount at the end of compound interest

Amount = P + CI

             = 260000+ 43264

             = $303264

5) Difference between the amount at simple interest and compound interest

Difference = 303264 - 301600

                  = $1664

Therefore the simple interest is $41600, the compound interest is $43264, the Amount at the end of simple interest is $ 301600, the amount at the end of the compound interest is $303264, and the difference in the amount of simple interest and compound interest is $1664.

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Total fenced need to replaced is 60 feet

The Perimeter of rectangle is two times the sum length and width.

i.e., Perimeter of rectangle= 2( l+ w)

Given:

Rabbit Pen: Length= 3.5, width= 4.5

Garden: length= 12, width = 10

So, Perimeter of Rabbit Pen = 2( 3.5 + 4.5)

                                               = 2( 8)

                                              = 16 feet

Now, Perimeter of Garden = 2 (12 + 10)

                                              = 2( 22)

                                              = 44 feet.

Total fenced need to replaces= 16 +44 = 60 feet

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Answer:

Step-by-step explanation:

76

Yes, Victor needs to have similar portion of the population in the sample.

What is population size?

The number of objects inside a geographical area that has been arbitrary assigned as the population size.

In a fair, unbiased poll

Population proportion plus random error equals sample proportion.

According to the Normal Approximation, the standard deviation of the distribution of these random mistakes across all feasible samples is

[tex]\sqrt{\frac{\text{Population proportion}(1-\text{Population proportion})}{n}}[/tex]

The sample estimate's variance from the actual population value is known as the random error. Numerous alternative summaries, such as sample averages or discrepancies between two sample proportions or averages, are likewise consistent with the observation that random mistakes follow the normal curve.

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The original function of y = -1/3|x| was translated 2 units to the right and 5 units up.

In Mathematics, there are four (4) main types of transformation and these include the following:

In Mathematics, the translation of a geometric figure (shape) to the right simply means adding a digit to the numerical value on the x-coordinate (x-axis) of the pre-image of a function while a geometric figure (shape) that is translated up simply means adding a digit to the numerical value on the y-coordinate (y-axis) of the pre-image.

In this scenario, the original function was shifted 2 units to the right and then shifted 5 units up to produce the new function as follows:

Original function (x, y)    →     New function (x + 2, y + 5)

y = -1/3|x|                         →        y = -1/3|x + 2| + 5

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The required value of the number of sides ( n ) is 17.

What is polygon?

A closed, two-dimensional object composed of straight lines is called a polygon. In most cases, we can quickly determine the polygon's number of sides from its name.

Given, two of the exterior angles of an n-sided polygon are 25° & 26°

So, the sum of exterior angle = 25° + 26° = 51°

three of its interior angles are 161º each

So, each exterior angle = 180° - 161° = 19° .

sum of three exterior angles = 19*3 = 57° .

Then,

Remaining total angles = n - (2 + 3) = (n - 5).

And, the remaining interior angles are 159° each.

So, each exterior angle of the remaining angles = 180° - 159° = 21°.

sum of all (n -5) exterior angles remaining = 21(n - 5) = (21n - 105°) .

Now,

Sum of all exterior angles = 360°

or, 51° + 57° + (21n - 105°) = 360°

or, 21n + 108° - 105°  = 360°

or, 21n + 3° = 360°

or, 21n = 360° - 3°

or, 21n = 357°

or, n = 357/21 = 17

Hence, The required value of n is 17.

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The axis of symmetry is the line that is relative is vertical goes through the vertex of a parabola so the left and right sides of the parabola are symmetric. To simplify, this line that is relative the graph of a equation that is quadratic two mirror images.

Equation of the Axis of Symmetry of a Parabola:

The equation for the axis of symmetry of a parabola can be expressed as:

[tex]x=\frac{-b}{2a}[/tex]

Remember that every quadratic function can be written in the standard form [tex]y = ax^{2}+bx+c[/tex] . The graph of a quadratic function is called a parabola, where every point on that parabola represents an x and a y that solves the quadratic function.

The vertex of a quadratic function is the highest or lowest point on the graph. The coordinate of the vertex of the parabola, then, is the x and y solution for the lowest or highest point of the parabola.

Calculating the Axis of Symmetry of a Parabola:

Again, the axis of symmetry of the parabola is the line on the graph that passes through the vertex of the parabola and splits the graph into two symmetrical sides.

It is expressed as:

[tex]x=\frac{-b}{2a}[/tex]

Or x = -2 after you substitute in the values for a and b.

Finding the Vertex of a Parabola:

To find the actual coordinates for the vertex of the parabola, simply substitute the x value into the polynomial expression to find the corresponding y value. Remember, each point on the quadratic graph is a solution to the equation.

When we continue with the previous example, we know that x = -2.

We substitute that value for x in the original quadratic function.

[tex]y=x^{2} +4x+3\\y=(-2)^{2}+4(-2)+3\\ y=4+(-8)+3[/tex]

Solving it gives us y = -1. We now know that the vertex of the parabola is the coordinate (-2, -1). Finding the vertex of a parabola couldn’t be easier.

How To Find Axis of Symmetry?

Here's what you need to remember: Whether you’re after the axis of symmetry or the full coordinates of the vertex of the parabola, use this formula to start graphing a quadratic equation.

[tex]x=\frac{-b}{2a}[/tex]

Solving for x gives you the axis of symmetry. This line of symmetry will intersect with the parabola at its vertex, where x is the coordinate you just calculated and y is the coordinate when you substitute x back into the quadratic equation,

[tex]y = ax^{2}+bx+c[/tex].

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Answer:

[tex]\frac{11}{4}[/tex] or 2 [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

Here is one way to solve this problem

2x - [tex]\frac{7}{4}[/tex] = x + 1  (3/3 is another way to write one)  Multiply all the way through by 4

4(2x - [tex]\frac{7}{4}[/tex]) = 4(x + 1)  Distributive property

8x -7 = 4x +4  Subtract 4x from both sides

4x - 7 = 4  Add 11 to both sides

4x = 11  Divide both sides by 4

x = [tex]\frac{11}{4}[/tex]

Answer:717 calories

Step-by-step explanation:

first you need to find what one ounce would be:

430/12=35.83...

then you multiply the answer by 20

35.83*20=716.6...=717

Answer:

5.090 x 10^-5

Step-by-step explanation:

Answer:

e)times by 10

Step-by-step explanation:

collects like term

?=x

x=460÷46

=10

The expected total prize money is $2p/q.

Given that,

You participate as a participant in a game show and respond to questions. You receive $1 for each correct response, and you are disqualified if you first provide two consecutive inaccurate answers. You can answer properly with probability p or wrongly with probability q. Each question stands alone.

Let,

The probability of correctly answering a question is = p

The probability of incorrectly answering a question is = q

The number of failures after which you are eliminated is = 2

Let r = 2 =  No. of failures and

Let q = The probability of failure in a single question

Now, the number of questions that you will attempt will follow a negative binomial distribution whose parameters are r and q.

The expected value of a negative binomial distribution is given by

E[X] = r/q

So, the expected number of questions that you will attempt is = r/q = 2/q

Out of 2/q questions, the expected number of correct questions is = 2p/q

So, the expected total prize money is $2p/q.

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Solving the system of equations we can see that:

We can define the variables:

x = price of a Douglas Fir trees

y = price of a Noble Fir trees.

By using the given information we can write:

6x + 16y = 986

6x + 24y = 1368

That is our system of equations

If we take the second equation and we subtract the first one we get.

(6x + 24y) - (6x + 16y) = 1368 - 986

8y = 382

y = 382/8 = 47.75

now that we know the value of y, we can find the value of x using the first equation.

6x + 16y = 986

6x = 965 - 16y

x = (965 - 16y)/6

x = (965 - 16*47.75)/6 = 33.5

So:

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