The equation p=t/3 is used to calculate the individual profit,p, made by each of three brothers operating a lemonade stand with total profit, t

Answer:

Step-by-step explanation:

By applying the exponential properties, it can be concluded that the simplest rational exponent is [tex]x^{\frac{3}{4} }[/tex]

Exponential is a repeated multiplication method with the same number, which is notated in the form aⁿ, where a is called the base and n is the exponent or power.

Some properties of exponent:

[tex]a^{x}[/tex] x [tex]a^{y}[/tex] = [tex]a^{x+y}[/tex]

[tex]a^{x}[/tex] : [tex]a^{y}[/tex] = [tex]a^{x-y}[/tex]

[tex](a^{x}) ^{y}[/tex] = [tex]a^{xy}[/tex]

[tex](\frac{a}{b} )^{x}[/tex] = [tex]\frac{a^{x} }{b^{x} }[/tex]

a⁰ = 1

a⁻ˣ = 1 / aˣ

In mathematics, a radical is described as [tex]\sqrt[n]{x}[/tex], where n is a positive integer ≥ 1 and x is a real number. Then n is called the index of the radical, x is the radicand, and the symbol √ is the radical.

The radical can be written as a rational exponent as follows:

[tex]\sqrt[n]{x} = x^{\frac{1}{n} }[/tex]   or [tex]\sqrt[n]{x^{m} } = x^{\frac{m}{n} }[/tex]

From the problem, we can denote the expression as follows:

square root of x = √x  

the fourth root of x = ⁴√x

The product of the two expressions will be:

(√x)   x  (⁴√x)  = [tex]x^{\frac{1}{2}}[/tex]  x  [tex]x^{\frac{1}{4} }[/tex]

                       = [tex]x^{\frac{3}{4} }[/tex]

Thus the simplest rational exponent is [tex]x^{\frac{3}{4} }[/tex]

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The value of x is 900 and value of y is 300.

Two or more expressions with an Equal sign is called as Equation.

From the given information we form a system of linear equations.

1.4x+1.6y=1740..(1)

x-3y=0..(2)

x=3y

Plug in x =3y in the equation 1.

1.4(3y)+1.6y=1740

4.2y+1.6y=1740

5.8y=1740

Divide both sides by 5.8

y=300

x=3(300)=900

Hence, the value of x is 900 and value of y is 300.

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a. 45 m S and 35 m S: This vector combination resolves to 10 m S.

b. 15 m N and 60 m S: This vector combination resolves to 45 m S.

c. 5 m S, 10 m E, and 7m W: This vector combination resolves to 8 m E.

Vectors can be added, subtracted, and multiplied by scalars (numbers) to create new vectors. In physics, vectors are used to represent quantities such as velocity, force, and acceleration.

They can also be used in other fields such as engineering, computer graphics, and economics. Vectors can be represented in different ways, such as in Cartesian coordinates (x, y, z) or polar coordinates (magnitude, angle).

a. The vector combination of 45 m S and 35 m S is 10 m S. This is because the vectors are pointing in the same direction (south) and the magnitude of the resultant vector is the sum of the magnitudes of the individual vectors.

b. The vector combination of 15 m N and 60 m S is 45 m S. This is because the vectors are pointing in opposite directions (north and south) and the magnitude of the resultant vector is the difference of the magnitudes of the individual vectors.

c. The vector combination of 5 m S, 10 m E, and 7 m W is 8 m E. This is because the vectors are pointing in different directions (south, east, and west) and the magnitude of the resultant vector is found using the Pythagorean theorem.

The east and west vectors can be viewed as the legs of a right triangle, with the resultant vector being the hypotenuse. The magnitude of the resultant vector is the square root of the sum of the squares of the individual vectors.

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X and Y don't have a proportionate relationship.No, not all yx ratios are equal.

If the ratios of two or more numbers or variables are equal to one another, they are said to be in proportion.

The answer to the query is

8; 10, 12; 14, given x

y : 5, 7, 9, 11

Ratios between various x and y values are not comparable.

( 8 /5)

≠ (10 / 7)

≠ (12 /9)

≠(14 /11)

We get to the conclusion that x and y have no proportional relationship.

Hence, Option(1) is the correct answer.

X and Y don't have a proportionate relationship.No, not all yx ratios are equal.

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The probability that at least one of the five female high school friends born in 2003 lives to be 100 years old is 0.054 or 5.4%.

Probability refers to the chance, odds, or likelihood that an expected outcome occurs when there are many possible outcomes.

Probability is a fractional value, lying between one and zero when the expected event is not 100% certain or uncertain.

Probability is computed as the quotient or ratio that results from dividing the expected value by the total weight.

The chance of British women born in 2003 living at least 100 years according to The Guardian website = 0.27

The probability that at least one of five female high school friends born in 2003 lives to be 100 years old = 0.27 x 1/5

= 0.054

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The sample mean can be classified as a random variable because it is calculated from the sample which is built as random.

The mean of a data-set is obtained as the sum of all observations in the data-set divided by the number of observations.

Hence the sample mean is obtained as the sum of all observations of the sample divided by the sample size.

As the observations of the sample are taken at random, the sum of these observations will be a random variable, and so will the sample mean.

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Answer:

C)  To know whether 2 triangles are similar, it is enough to know the measure of 2 angles in each triangle.

Step-by-step explanation:

Two triangles are said to be similar if:

As there are three interior angles in a triangle, and the sum of the interior angles is always 180°, we need to know the measure of at least 2 angles in each triangle to determine if they are similar.  The known angles don't have to be corresponding angles, as we can calculate the third angle and then compare all three angles to determine if the triangles are similar.

With regards to the sides of a triangle, it is not enough to know the measure of 2 sides to determine if they are similar. We would need to know at least one interior angle in this case.

to find a given term, substitute the corresponding value of n into the ninth term formula. For example, if the ninth term is 3n + 2, the 10th term of the sequence can be found by substituting n = 10 into the ninth term. 3 x 10 + 2 = 32 and so, the tenth term of the sequence is 32.

To find the nth term of an arithmetic sequence, use the following formula:

[tex]an = a + (n - 1)d[/tex]

an(nth term) = a(first term) + (n(term you are looking for) - 1) * d(common difference)

The equation does not define a linear function

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

y = -x³ - 11

As a general rule, a linear equation is any equation that has a degree of 1

The given equation above has a degree of 3

Hence, it is not a linear equation

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s3+5s2+8s+4

Step-by-step explanation:

Answer:

(1-e^(-2t))*u(t) - (1-e^(-t))*u(t)

Where u(t) is the step function

Step-by-step explanation:

use partial fraction decomposition. This involves expressing the rational function as the sum of simpler fractions, each with a pole at a different point in the complex plane. Once we have done this, we can use the formula for the inverse Laplace transform of a simple pole to find the inverse Laplace transform of the original function.

The chi-square goodness-of-fit test requires a comparison of the observed values with their expected values in the f2 generation.

The chi-square goodness-of-fit test is used to determine how well observed values fit a model of independent assortment. The test requires a comparison of the observed values with their expected values in the f2 generation.

Option A is the best choice for this comparison, as it provides a direct comparison of the observed and expected values. This comparison allows for an assessment of the goodness-of-fit of the model, as any differences between the observed and expected values can be attributed to the model's performance.

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Since divisions by zero is ill-defined, the domain for F(x)=8/x includes any real integers other than x=0. F(xdomain )'s is therefore (-infinity, 0) U (0, +infinity).

Describe domain. The term "domain," which is unique to the internet, can apply to both the structure of the internet and the organization of a company's network resources. A domain is typically a sphere of information or a governing region.

A function's domain is the set of all potential inputs. For instance, the domain of f(x)=x2 and g(x)=1/x are all real integers with the exception of x=0.

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Answer:

[tex]9x^2+14x+1[/tex]

Step-by-step explanation:

Hey there!

In order to find the answer to this problem, we must first form an equation; then we can solve/simplify it further

Our Equation:

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

[tex](9x^2+5x+8)+(9x-7)[/tex]

1. Distribute the positive sign: positive and positive make positive, positive and negative make negative, negative and negative make positive

[tex]9x^2+5x+8+9x-7[/tex]

2. Combine like terms in each parenthesis: This means combining the x values and the constants.

[tex]9x^2+14x+1[/tex]

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

This means that when you add the two given values, the answer you get is: [tex]9x^2+14x+1[/tex]

Please see the image attached below to know a representation of linear function y = - (1 / 3) · x - 6 in Cartesian plane.

Linear functions are polynomials of the form:

y = m · x + b

Where:

Graphically speaking, linear functions represents lines and lines can be generated from two points on Cartesian plane. The procedure is described below.

First, obtain two points from linear function:

x = 0

y = - (1 / 3) · 0 - 6

y = - 6

x = 1

y = - (1 / 3) · 1 - 6

y = - 1 / 3

Second, add the points on Cartesian plane.

Third, construct a line that passes through the two points added. Please see the image attached below.

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Answer:

50h(5h - 2)

Step-by-step explanation:

Open up all the parenthesis on each answer

only the first one is correct

Answer:

50h(5h-2)

Step-by-step explanation:

Solution given

250h² - 100h

50*5*h*h-50*2*h

taking common

50*h(5*h-2)

50h(5h-2)

here taking common and keeping remaining on bracket

50h(5h-2)

Answer: To find the surface area of the cylindrical vase, we can use the formula:

SA = B + Ph

Where B is the area of the base (the circular top of the vase), P is the perimeter of the circular top of the vase, and h is the height of the vase.

We know that the diameter of the vase is 4.3 inches and the height of the vase is 11 inches. To find the radius of the base, we can divide the diameter by 2:

r = 4.3 inches / 2 = 2.15 inches

The area of the base is given by πr², so:

B = πr² = π * 2.15² = 14.65 square inches

To find the perimeter of the circular top we can use 2πr:

P = 2πr = 2 * 3.14 * 2.15 = 13.64 inches

Now we can substitute these values into the formula:

SA = B + Ph = 14.65 + 13.64 * 11 = 260.04 square inches

Rounded to the nearest tenth, the surface area of the vase is 260.0 square inches.

Step-by-step explanation:

The improper integrals are i and ii.

An improper integral is the limit of a definite integral in mathematical analysis when either one endpoint of the interval of integration approaches a limit, such as a real number, positive or negative infinity, or, in rare cases, when both endpoints approach limits.

According to the question

The first integral, the integral from 2 to 5 of dx over amount x squared minus 1, is incorrect because the denominator x2-1 becomes 0 at x=1, meaning the integrand expands to infinity at these places and the integral is not convergent across the range [2,5]. Since the interval of integration extends from 1 to infinity and the function is not limited, the second integral, the integral from 1 to infinity of amount x minus 1 dx, is incorrect. The integrals I and ii are both incorrect. The third integral, which is a standard integral and is the integral from negative 2 to 3 of dx over amount x + 1, is convergent.

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Explanation:

ASA = angle side angle

The marked side is between the marked angles.

The markings on the angles tell us which angles pair up to be congruent. The tickmark on the sides tell us the sides are congruent.

AAS is similar to ASA, but with AAS the marked side isn't between the marked angles.

We cannot use SAS since we don't know anything about another pair of sides.

The value of x and y obtained when multiplying equations to eliminate variable is y = -62/40 and x = -18/16.

The elimination approach involves taking one variable out of the system of linear equations by utilizing addition or subtraction together with multiplication or division of the variable coefficients.

The given equations are:

5x - 3y = 6, and

2x + 5y = -10

Isolate the value of x in the following equation:

5x - 3y = 6

5x = 6 + 3y

x = (6 + 3y)/5

Substitute the value of x as follows:

2x + 5y = -10

(2) (6 + 3y)/5 + 5y = -10

12 + 15y + 25y = -50

40y = -50 -12

40y = -62

y = -62/40

Substitute the value of y to find the value of x:

2x + 5(-62/40) = -10

16x - 62 = -80

16x = -80 + 62

16x = -18

x = -18/16

Hence, the value of x and y obtained when multiplying equations to eliminate variable is y = -62/40 and x = -18/16.

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The factorisation of  20xy - 54 can be expressed as 2( 10xy - 27 ).

The concept here is the factorisation . The breaking or decomposition of an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication results in the original number, matrix, etc., is known as factorization or factoring in mathematics.

A number or other mathematical object is factorized or factored when it is written as the product of numerous factors, typically smaller or simpler things of the same kind.

We were given, 20xy - 54, we can see that that factor of 2 is common for both 20xy and 54.

Then we can factorize as 2( 10xy - 27 ).

2( 10xy - 27 )

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The joint frequency of adults who voted for chocolate is given as follows:

0.1148.

A relative frequency is calculated as the division of the number of desired outcomes by the number of total outcomes.

A joint frequency is calculated considering a combination of two events.

In the context of this problem, we have that out of 122 people, there are 14 adults who voted for chocolate, hence the joint frequency of adults who voted for chocolate is obtained as follows:

14/122 = 0.1148.

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Answer:

Linear equation with one variable

Step-by-step explanation:

Here, that one variable is x.

- 11x - 14x - 26 = - 25 - 25x - 1

- 25x - 26 = - 25x - 25 - 1

- 25x - 26 = - 25x - 26

Multiply - 1 on both sides,

25x + 26 = 25x + 26

This equation has infinite solutions.

Where value you substitute in place of x, you will the same answer on the both the sides.

The domain of the function f(x) = √(x - 5) is x ≥ 5, thus, x = 3 is not in the domain.

Remember that for a function y = f(x), we define the domain as the set of the possible inputs.

Here we have the square root function:

f(x) = √(x - 5)

Remember that the argument of a square root needs to be zero or larger, then the domain of the given function is:

x - 5 ≥ 0

Solving for x:

x ≥ 5

The domain is the set of values equal to or larger than 5, thus, the value 3 is not in the domain.

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Answer:

y = -5x + 7

Step-by-step explanation:

Parallel lines on a graph have the same slopes/gradients.

m1=m2

First you want to rewrite the equation of the graph given. So put the 5x to the other side and you will have:

y = -5x -2

This means that the equation that we need must have the gradient -5 (bc it is m in y=mx+c)

The equation will be y = -5x + c

However we must still find c aka the y intercept.

Sub the point we are given (1,2) into the equation

We will have:

2 = -5(1) + c

2 = -5 + c

7 = c

Now that we know c, we know what the equation of the line is. Just sub it in (without 1 and 2)

y = -5x + 7

The greatest number that evenly divides the sum of any three consecutive whole numbers is three.

This is referred to as a whole number that can be positive, negative, or zero and we should note that it doesn't a fractional number and examples include 0, 2, -3 etc.

The product of any three consecutive integers is always divisible by 3 and the addition of any 3 consecutive numbers together it will always equal a multiple of 3 which is therefore the reason why it was chosen as the correct choice.

An example is  n+2 is an integer, 3(n+2) is divisible by 3 in this scenario hence 3 is the correct choice.

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The value of the constant rate of change of y with respect to x is 20.

A formula that expresses change in y in terms of change in x is y = kx.

Suppose that y = 1.5 when x = 1, a formula that expresses y in terms of x is k = 1.5.

In Geometry, the rate of change of any straight line simply refers to its gradient or slope and it can be calculated by using this mathematical expression;

Rate of change (slope), m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Rate of change (slope), m = (y₂ - y₁)/(x₂ - x₁)

Assuming that both the x-axis and the y-axis have a scale of 1:20, the constant rate of change is given by:

Constant rate of change = 20/1 = 20.

When y = 1.5 and x = 1, a formula that expresses y in terms of x is given by:

y = kx

k = y/x

k = 1.5/1

k = 1.5.

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