graph the ellipse give by the equation 49^2 + 16^2 = 784. Rewrite the equation i standard form.

The smallest possible number with digits 1 and 2, divisible by 4 and 9 is 22212.

A number that is divisible by both 4 and 9 must be divisible by their least common multiple (LCM), which is 36. To find the smallest possible value of n such that every digit is a 1 or a 2 and the number is divisible by 36, we can start with the smallest possible number that is divisible by 36 and only contains 1s and 2s, which is 11112.

As the number is divisible by 4 and contains only 1 and 2, the last two digits is 12. Now it is divisible by 9 so sum of digits is 9 or multiple of 9.

1 + 2 = 3

So we need digits sum equal 9-3 = 6 to be divisible by 9, so number is 22212.

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I will order a pizza tonight only if we eat dinner at home is a conditional statement.

Sentences are groups of words that convey complete and logical meaning. They have subjects and predicates. It can be in form of exclamation and questions consisting of main and subordinating clauses.

Conditional statements are sentences where the subordinating clause influences whether the action that will be performed or not in the main clause. In these statements, the subordinating clause is also called the antecedent, and the main clause is called the consequent.

There are two types of Conditional statements, they are Implicative and predictive statements. Implicative sentences are based on facts whereas predictive statements depend on a situation dependent on a hypothetical case.

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The intervals on which the function is increasing are: (-∞, -2) and (7, ∞), and the intervals on which the function is decreasing are: (-2, 7). In interval notation, this is written as (-∞, -2), (7, ∞) and (-2, 7).

The given function is h(x) = (x + 2)^2 x (x-7)^1/3. This is a polynomial function with two terms. The first term, (x + 2)^2, is a quadratic function, and the second term, (x-7)^1/3, is a cube root function.

We can use the derivative of the function to determine the intervals on which the function is increasing and decreasing. Taking the derivative of the function yields: h'(x) = 2(x + 2)(x - 7)^1/3 + (x + 2)^2 x (1/3)(x - 7)^-2/3. Setting the derivative equal to zero, we can solve for x and find where the function is not increasing or decreasing. Solving this equation yields x = -2 and x = 7, the points of inflection.

Therefore, the intervals on which the function is increasing are: (-∞, -2) and (7, ∞), and the intervals on which the function is decreasing are: (-2, 7). In interval notation, this is written as (-∞, -2), (7, ∞) and (-2, 7).

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The probability of a customer who gets one piece of fruit from the bowl randomly choosing an orange or a pear is 21/36

What is Probability ?

Probability can be defined as the ratio of number of favourable outcomes and total number of outcomes

Given ,

A bowl at a delicatessen contains a mix of 15 apples, 12 oranges, and 9 pears

so , we have to find  the probability of a customer who gets one piece of fruit from the bowl randomly choosing an orange or a pear.

Choosing orange or a pear ,

= 12c1 + 9c1

= 12+9

= 21

Total = 36.

Probability = 12 + 9 / 36

= 21 / 36 .

Therefore , The probability of a customer who gets one piece of fruit from the bowl randomly choosing an orange or a pear is 21/36

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True. The three numbers can be the measures of the sides of a triangle.

What is the triangle inequality theorem?

The triangle inequality theorem is a fundamental principle in Euclidean geometry that states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. This means that in any triangle, no side can be longer than the sum of the other two sides.

The three numbers 4, 7, and 8 can be the measures of the sides of a triangle. This is because of the triangle inequality theorem which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In other words, for any triangle, the sum of two sides must always be greater than the third side.

For example, in this case,

4 + 7 = 11 > 8,

7 + 8 = 15 > 4,

4 + 8 = 12 > 7

Hence, 4, 7, and 8 can be the measures of the sides of a triangle, so the correct response would be "True".

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The figure of the coterminal angle of 300° on a circle in standard position is attached in the solution.

Coterminal angles are angles in standard position (angles with the initial side on the positive x-axis) that have a common terminal side.

Coterminal angles are two angles in the standard position where one angle is a multiple of 360 degrees larger or smaller than the other. That is, if angle A has a measure of M degrees, then angle B is co-terminal if it measures M +/- 360n, where n=0,1,2,3, ...

Starting from that position, 300° is drawn by moving around the circle to the left "counter-clockwise" and ending at the 300° measure.

The negative coterminal angle is the angle that would end in the same place if we went to the right instead of right on the circle. It is equal to the original 300° minus 360°

Coterminal angles Ac to angle A may be obtained by adding or subtracting k⋅360° or k × (2π)

Hence, Ac = A + k⋅360°, if A is given in degrees.

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We can find the coordinates of the point that partitions a line segment into a ratio of 1 to 5 by using the formula:

(x, y) = (x1 + r * (x2 - x1), y1 + r * (y2 - y1))

Where (x1, y1) and (x2, y2) are the coordinates of the endpoints of the line segment, and r is the ratio of the distance from the starting point to the point of interest, to the total distance of the line segment. In this case, r = 1/(1 + 5) = 1/6.

We know the coordinates of the two endpoints of the line segment:

(x1, y1) = (-10, 9)

(x2, y2) = (-4, 3)

So, we can substitute these values into the formula and find the coordinates of the point that partitions the line segment into a ratio of 1 to 5:

(x, y) = (-10 + (1/6) * ((-4) - (-10)), 9 + (1/6) * (3 - 9))

= (-10 + (1/6) * (-6), 9 + (1/6) * (-6))

= (-10 -1/6, 9 -1)

= (-10/6 -1/6, 3/2 -1)

= (-16/6, 3/2 -1)

= (-8/3,-1/2)

So, the coordinates of the point on the directed line segment from (-10, 9) to (-4, 3) that partitions the segment into a ratio of 1 to 5 is (-8/3,-1/2)

It is important to notice that this point is a vector and not a point in the Cartesian plane

Axis of Symmetry: This function is not symmetric with respect to the x-axis, y-axis, or the origin.

To check for symmetry with respect to both the x-axis and the y-axis, we need to check whether the function is even or odd. To do this, we can substitute -x for x in the equation and check if the equation remains the same.

y = x^4 - x^2 + 3

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

y = x^4 - x^2 + 3

Since the equation remains the same, the function is neither even nor odd and therefore is not symmetric with respect to either the x-axis or the y-axis.

To check for symmetry with respect to the origin, we need to check if the equation is symmetric when x and y are both substituted with -x or -y.

y = x^4 - x^2 + 3

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

y = x^4 - x^2 - 3

Since the equation is not the same, the function is not symmetric with respect to the origin.

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Chung is going to be able to get the representative sample by carrying out a random selection.

It would be helpful to get the multiple samples because it is a way w=of getting the true representation of sample.

Chung could generate a representative sample by randomly selecting a group of teachers from the school population and surveying them about their hobbies.

It would be helpful to generate multiple samples because, with only one sample, there's always a chance that the sample is not truly representative of the population. By generating multiple samples, Chung can compare the results and see if there is a consistent pattern among the samples, which would increase the likelihood that the results are representative of the population.

Additionally, by comparing multiple samples, Chung can also estimate the degree of variability in the population and the sample, this allow him to have more robust conclusions.

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The impact on the salesperson’s broker when the salesperson’s violations are brought to the attention of the real estate commission is that the employing broker may be disciplined by the real estate commission for failure to supervise.

Real estate commission is defined as the agency that is responsible for the stating the rules and regulations regarding the selling and acquisition of land and other related properties.

The rules and regulations enacted by them helps to prevent different forms of violations which includes blockbusting and discrimination on the basis of disability.

Therefore, salesperson’s broker would be disciplined by the real estate commission for failure to supervise the salesperson.

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Millimeter and meter are units of length. 1.2 meters are equal to 1200.O millimeters. Significant figures means writing all the certain digit along with an uncertain or estimated digit.

The SI unit of length is meters. There are different units like millimeters, centimeters, kilometers, inches etc. All these values are interconvertible.

1 Meter = 100 centimeters

1 centimeter = 10 meter

So 1 meter = 100× 10 = 1000 millimeter.

So 1.2 meter = 1.2× 1000 = 1200 millimeters.

1200 has only two significant. To increase the number of significant figures we can add two decimal places. 1200.00 have 6 significant figures.

So 1.2 meters is 1200.00 millimeter.

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Answer:

w = 0, z = − 2

Step-by-step explanation:

The solution for the given system of equations is: w = 0 and z = -2.

What is a system of equations?

A system of equations is a collection of two or more equations with the same set of unknowns. For a system to have a unique solution, the number of equations must equal the number of unknowns.

The equations are as follows:

[tex]3w-4z=8[/tex]-------- (1)

[tex]2w+3z=-6[/tex]-------(2)

The solution for the above equation,

Multiply the equation 1 by 2,

⇒([tex]3w-4z=8[/tex]  )*2 --------- (3)

Multiply the equation 2 by 3,

⇒([tex]2w+3z=-6[/tex] )*3 --------(4)

Now solve equations 3 and 4 to get,

⇒ [tex]-17z=34[/tex]

⇒ [tex]z= -2[/tex]

Now substitute the value of z in equation 1,

⇒  [tex]3w-4(-2)=8[/tex]

⇒ [tex]\\3w=0[/tex]

⇒ [tex]w=0\\[/tex]

Hence we can conclude that the solution for the given system of equations is w = 0 and z = -2.

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The function is undefined for those values of x where the denominator is zero.

The reciprocal identity for sine, cosine, and tangent states that:

sin(x) = 1/csc(x)

cos(x) = 1/sec(x)

tan(x) = 1/cot(x)

It is important to note that csc, sec, and cot are only defined for values of x where the denominator is not equal to zero.

For example, csc(x) is defined as 1/sin(x), so it is undefined for x = kπ where k is any integer and sin(x) = 0.

Similarly, sec(x) is defined as 1/cos(x) and is undefined for x = (k+1/2)π where k is any integer and cos(x) = 0. Finally, cot(x) is defined as 1/tan(x) and is undefined for x = kπ where k is any integer and tan(x) = 0.

Therefore, the reciprocal identity for sine, cosine, and tangent is only defined for certain input values, and it is undefined for those values of x where the denominator is zero.

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Transformation includes changing the position of a shape.

The sequence of metamorphosis is 90 degrees counterclockwise gyration, followed by a vertical restatement to the right by 2 units.

What's meant by sequence?

The ordered brace- rule for each are :

(x,y)⇒ (-y,x) and (x,y)⇒(x+2,y)

The sequence of metamorphosis.

From the figure, we observed that ABC was rotated and also restated

So, the sequence of metamorphosis on ABC are

90 degrees counter clockwise gyration.

Vertical restatement to the right by 2 units.

The ordered brace rule :

When a point is rotated 90 degrees counter clockwise, the rule of metamorphosis is :

x, y)->(- y, x)

When a point is restated 2 units right, the rule of metamorphosis is :

x, y)->( x 2, y)

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Transformation includes changing the position of a shape.

The sequence of metamorphosis is 90 degrees counter clockwise gyration, followed by a vertical restatement to the right by 2 units.

The ordered brace- rule for each are :

(x,y)⇒ (-y,x) and (x,y)⇒(x+2,y)

The sequence of metamorphosis.

From the figure, we observed that ABC was rotated and also restated

So, the sequence of metamorphosis on ABC are

90 degrees counter clockwise gyration.

Vertical restatement to the right by 2 units.

The ordered brace rule :

When a point is rotated 90 degrees counter clockwise, the rule of metamorphosis is :

x, y)->(- y, x)

When a point is restated 2 units right, the rule of metamorphosis is :

x, y)->( x 2, y)

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(a) log₂(x) is a logarithmic function, (b) ∜x is a root function, (c) 2x^3/(1 - x^2) is a rational function, (d) 1 - 1.1t + 2.54t^2 is a polynomial of degree 2, (e) 5^t is an exponential function and (f) sin θ cos^2 θ is a trigonometric function.

A power function has the form f(x) = x^n, where n is a constant.

A root function has the form f(x) = √x or f(x) = x^(1/n), where n is a constant.

A polynomial is an algebraic function that can be written in the form f(x) = a_n x^n + a_{n-1} x^{n-1} + ... + a_2 x^2 + a_1 x + a_0, where a_i are constants and n is the degree of the polynomial.

A rational function is a function that can be written as the ratio of two polynomials, i.e., f(x) = (p(x))/(q(x)), where p(x) and q(x) are polynomials and q(x) ≠ 0.

An algebraic function is a function that can be expressed as the solution to a polynomial equation, i.e., it can be written as a polynomial, a root, or a combination of polynomials and roots.

A trigonometric function is a function that involves the ratios of sides in a right triangle, such as sine, cosine, tangent, etc.

An exponential function has the form f(x) = a^x, where a is a positive constant greater than 1.

A logarithmic function has the form f(x) = logₐx, where a is a positive constant greater than 1.

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after 20 hours the clock will show 3*20 = 60 min = 1 hr more

since the clock is analogue after 12 hours it will show the same time hat is 6 am and 6 pm are shown the same way.

after 20*12 = 240 hr = 10 days the clock will show 12 hr more but since 6 am and 6 pm are shown the same after 240 hr = 10 days the clock will show the correct time again.

the correct time will be shown on Monday 6 pm.

Answer:

The probability of (B|A) is 0.25 which is correct option(B).

What is probability?

The probability is defined as the possibility of an event is equal to the ratio of the number of outcomes and the total number of outcomes.

P(A)=0.40

P(B)= 0.50

P(A ∩ B) = 0.10

In order to find the probability of (B|A),

Condi

Step-by-step explanation:

According to the Greek geocentric paradigm, a planet moves retrogradely when it actually goes backward in its orbit around Earth. So the option b is correct.

The geocentric paradigm, also known as geocentrism, which is frequently and particularly shown by the Ptolemaic system, is an outdated explanation of the cosmos that places Earth at its center. The Sun, Moon, stars, and planets all orbit Earth according to the majority of geocentric models.

Since humans have been gazing up at the stars for thousands of years, our perception of what the Universe looks like has undergone a significant transformation.

In time, humanity also realized that the Earth was a sphere and developed logical justifications for how other heavenly bodies behaved. By classical antiquity, scientists had developed theories about how the planets moved and how all the celestial bodies interacted. This led to the development of the now-defunct Geocentric model of the cosmos, which described how the Sun, Moon, and firmament revolved around our earth.

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The complete question is:

In the Greek geocentric model, the retrograde motion of a planet occurs when (a) Earth is about to pass the planet in its orbit around the Sun. (b) the planet actually goes backward in its orbit around Earth. (c) the planet is aligned with the Moon in our sky.

Answer: 17

Step-by-step explanation:it goes -1 then x2 so after ten is 9 then 18 then 17

As per the given standard deviation, the interval in which she can be 68% sure that the sample mean will lie is 98.75 ± 10.45/ √60

In math the term called standard deviation is defined as a statistic that measures the dispersion of a dataset relative to its mean and is calculated as the square root of the variance.

Here we have given that the population mean is $98.75 with a standard deviation of $10.45 and the a sample size of 60.

Now, here we need to find the equation that Susan can use to find the interval in which she can be 68% sure that the sample mean will lie.

Here the distribution of the sample mean is approximately normal distribution with mean $98.75 and standard deviation approximately written as 10.45/√60

Here we have Symbolically written as,

=> X~ N(98.75, 10.45/√60) 2

Here by using empirical rule, then we find the limits for sample mean for which we're 68% sure that the sample mean will lie in that interval as one standard deviation away from its mean, then it can be written as

=> P (98.75 -10.45/√60 < x <98.75 +10.45/√60) ≈ 68%

Hence the equation is written as

=>98.75 ± 10.45/ √60

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The linear function that models the graph is given as follows:

a) y = -2x/3 - 4.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The graph crosses the y-axis at y = -4, hence the intercept b is obtained as follows:

b = -4.

When x increases by 6, y decays by 4, hence the slope m is obtained as follows:

m = -4/6

m = -2/3.

Hence the function is defined as follows:

y = -2x/3 - 4.

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It will take 51 days to fill the Olympic sized pool.

Time and work have a relationship that is

Work Completed is equal to Time x Rate of Work.

Alternately, Rate of Work = Time Taken / 1.

Alternatively, Time Taken = 1 / Rate of Work

Considering that,

Pool volume is 6.6043 x 105 gallons, or 6,600,430 gallons.

9 litres of water are delivered through a hose every minute.

Therefore, the amount of water delivered by hose every hour is equal to (9 * 60) gallons.

Water provided by hosen each day is equal to (9 * 60 * 24) gallons, or 12,960 gallons.

Thus, the amount of time needed to fill the pool is equal to 6,600,430/12960.

There are 50.9 days needed to fill the pool.

51 days were needed to fill the swimming pool.

The Olympic-sized pool will therefore fill in 51 days.

The Complete Question is Olympic sized pool.

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C ((6.5) (3, 2), (2, 4), (6, 3), (1, 0)) , this relation is not a function

C ((6.5) (3, 2), (2, 4), (6, 3), (1, 0)) is not a function because it does not pass the vertical line test.

The vertical line test states that if a vertical line crosses the graph of a relation more than once, then the relation is not a function.

In this example, a vertical line drawn at x=6.5 will cross the graph twice, at (6.5, 3) and (6.5, 2).

Since a vertical line passes the graph twice, it does not pass the vertical line test and is not a function.
The theory used in this question is the Vertical Line Test,

which states that if a vertical line crosses the graph of a relation more than once, then the relation is not a function.

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C ((6.5) (3, 2), (2, 4), (6, 3), (1, 0)) , this relation is not a function

Because C ((6.5) (3, 2), (2, 4), (6, 3), and (1, 0) fail the vertical line test, they are not functions.

According to the vertical line test, a relation is not a function if a vertical line crosses its graph more than once.

A vertical line drawn at x=6.5 in this example will cross the graph twice at (6.5, 3) and (6.5, 2).

A vertical line fails the vertical line test and is not a function because it traverses the graph twice.

The Vertical Line Test is the hypothesis employed in this query.

which implies that a vertical line crossing a relation's graph more than once is a sign that the relation is not a function.

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5-year projected budget total is brought forward from the Project Budget and Projection sheet, using an Excel formula.

P is equal to PMT [((1 + r)n - 1)/r]

Taking into account a certain amount of compounded interest earnings that progressively accumulate during the measurement period, this figure represents the sum that a stream of future payments will increase to.

One of the financial functions, FV, determines the investment's future value using a constant interest rate. Future Value (FV )can be used with either a series of regular, recurring payments or a single, one-time payment. To determine the future worth of a sequence of payments, use the Excel Formula Coach.

Your interest rates correctly match the corresponding entries from the table for theyears and months given.Your 5-year projected budget total is brought forward from the Project Budget andProjection sheet, using an Excel formula.

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The  difference in the account balances at the end of the loan terms is, $1770.87. So option B is correct

Simple interest is an amount which is calculated for a certain period of time and for a certain rate, in simple interest calculation there are three factors which we consider: principal amount(P), rate(R) and time(T).

Every time we calculate simple interest the principal values will be the same unlike compound interest.

Formula;    Simple Interest(I) =  P × R × T/100

Given that,

Offer 1-  5.99% annual simple interest, with a total account balance of $32,487.50 after a 60-month term Offer

Offer 2-  3.75% annual interest compounded monthly for a 66-month term

In offer 1,

Total amount A  = $32487.50

In offer 2,

Total amount =

[tex]A = P[ 1 + r/n]^{nt}[/tex]

[tex]A = 25000[ 1 + 0.0375/12]^{12*5.5}[/tex]

A = $30,716.63

Difference = 32487.50 - 30716.63

                  = $1770.87

Hence, the difference in account balance is $1770.87

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Answer:

18/5 or 3 3/5

Step-by-step explanation:

Turn 6 into a fraction -> 6/1

Hence, 6/1 × 3/5

Multiply the numerators and denominators.

(6×3)/(1×5) = 18/5

Simplify = 3 3/5

Answer:

= 18/5

Step-by-step explanation:

6 × 3 = 18

Then:

6 × 3/5

= 18/5

...

Answer:

x > 0

Step-by-step explanation:

An open circle means less than or greater than the number it is on.

A closed circle means less than or equal to, or greater than or equal to the number it is on.

This graph has an open circle on zero with the arrow pointing to the right.

so x>0