what is the domain and range

Assuming,

Question: what is the simplest form of the expression  [(X/6) + X³] * (1/2) ?

Solution:-

The simplest form of the expression  [(X/6) + X³] * (1/2) is,

An expression is a sentence with at least two numbers or variables having mathematical operation. Maths operations can be addition, subtraction, multiplication, division.

For example, 2x+3

Given that,

The expression,

[(X/6) + X³] * (1/2)

To simplify the expression [(X/6) + X³] * (1/2),

we can first simplify the two expressions in the parentheses:

(X/6) + X³ = X/6 + X³

(1/2) * (X/6 + X³) = X/12 + X³/2

So the simplified form of the expression [(X/6) + X³] * (1/2) is X/12 + X³/2.

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On solving the provided question, we can say that Length of rectangle = 50 m and Area of rectangle = 300 m.sq and the breadth of the garden is 6 m.

A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.

Length of rectangle = 50 m and Area of rectangle = 300 m.sq

Since, Area of rectangle = length x breadth

Therefore, Breadth = 300/6

Thus, the breadth of the garden is 6 m.

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The exposure time when x = 560 is: 13.66 hour

A method of simulating the relationship between two sets of variables is quadratic regression. The outcome is a regression equation that may be applied to the data to generate predictions. The formula for the equation is: y = ax² + bx + c, where a ≠ 0. Situations that may be approximated by quadratic functions include tossing a ball, firing a cannon, jumping from a platform, and striking a golf ball. Researchers may find the quadratic model to be a useful tool for data analysis in identifying the combined impact of success objectives on academic accomplishment. We anticipate that future studies on the impact of academic performance objectives will frequently use the quadratic model to analyse their data.

Given that,

T = 0.0002x² - 316x + 127.9

exposure time = T

Now, calculate exposure time when x = 560

So, T = 0.0002x² - 0.316x + 127.9

T = 0.0002×(560)² - 0.316 × (560) + 127.9

T = 62.72 - 176.96 + 127.9

T = 13.66 hour

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the equation for the line perpendicular will be y = -5x +11.

What is the equation straight line?

The formula for a straight line is generally expressed as Y = mx + c, where m stands for the slope and c for the y-intercept. In geometry, it is the straight-line version of the equation that is most usually utilised. A straight-line's equation can be expressed in a variety of forms, including point-slope form, slope-intercept form, general form, standard form, etc. An infinitely long straight line has two dimensions and is a geometrical object with two ends. The equations for a straight line that are used the most frequently are y = mx + c and axe + by = c. Point-slope, slope-intercept, standard, general, and other forms are more variations.

The given line is y = x/5 +3

the slope is m = 1/5

So the slope of the perpendicular line will be -5

So the equation of line will be y-3 = m1(x-1)+3

y-3 = -5x+5+3

y = -5x +11

Hence the equation for the line will be y = -5x +11.

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Answer:

Step-by-step explanation:

when does this come into play? what year??

the voltage across the circuit ([tex]V_{0}[/tex]) is 80 volts.

In the superposition theorem, the voltage across any element in a linear circuit is equal to the sum of the voltages caused by each source acting independently. In other words, in a linear circuit, each source is treated as the only source, and the other sources are replaced with their internal resistances.

With the resistance value of 8 ohms, we can calculate the voltage across the circuit using the superposition theorem.

First, consider [tex]I_{1}[/tex] as the only source, and set [tex]I_{2} = 0 A[/tex]. The voltage across the circuit can be found using Ohm's law (V = IR), where R is the resistance in the circuit.

[tex]V_{1} = i1 * R = 6 A * 8 ohms = 48 V[/tex]

Next, consider [tex]I_{2}[/tex] as the only source, and set [tex]I_{1} = 0 A[/tex]. The voltage across the circuit can be found using Ohm's law (V = IR), where R is the resistance in the circuit.

[tex]V_{2} = i2 * R = 4 A * 8 ohms = 32 V[/tex]

Finally, the voltage across the circuit ([tex]V_{0}[/tex]) is the sum of the voltages found in steps 1 and 2.

[tex]V_{0} = V_{1} + V_{2} = 48 V + 32 V = 80 V[/tex]

So, the voltage across the circuit ([tex]V_{0}[/tex]) is 80 volts.

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None. The discriminant of the quadratic equation is [tex]b^{2}[/tex]-4ac = [tex]11^{2}[/tex] - 4(1)(18) = 121 - 72 = 49, which is not a perfect square.

A perfect square is a number that can be expressed as the product of two equal integers. For example, 9 is a perfect square because it can be written as 3 x 3.

The zeros of this quadratic function can be found by setting the equation equal to 0 and solving for x.

0 = [tex]x^{2}[/tex] + 11x + 18

To solve for x, we can use the quadratic formula:

x = [-b ± √([tex]b^{2}[/tex] - 4ac)]/2a

Substituting in our values from the equation above, we get:

x = [-11 ± √([tex]11^{2}[/tex] - 4(1)(18))]/2(1)

x = [-11 ± √(-63)]/2

Since the square root of a negative number is not a real number, there are no zeros.

Therefore, the answer is None.

So, there are no real solutions.

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We can tell that Mike thought the difference would be 72, but it is actually 72.74 by rounding off.

A number is simplified when it is rounded off, preserving its value while moving it closer to the next number.

It is done for whole numbers as well as decimals at various places of hundreds, tens, tenths, etc.

When numbers are rounded off, the important numbers are kept.

To determine how to round a number, look at the next digit in the appropriate position; if it is less than 5, round down, and if it is greater than 5, round up.

So, Mike determined 79 to be 79.44 and 7 to be 6.7, so he determined the difference as follows:

79 - 7 = 72

Actual numbers that vary are:

79.44 - 6.7 = 72.74

Therefore, we can tell that Mike thought the difference would be 72, but it is actually 72.74 by rounding off.

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Correct question:

Mike estimated the difference of 79.44 and 6.7 by rounding each number to the nearest whole. What was Mike's estimate, and what is the actual difference of the numbers? Enter your answers in the boxes. Mike estimated the difference to be. The actual difference is __.

The solution for the given equation is C) [tex]x=\frac{-1+-\sqrt{33} }{4}[/tex]

What does a quadratic function mean?

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other words, a "polynomial function of degree 2" is a quadratic function.

The formula for the solution of a quadratic equation [tex]ax^{2} +bx+c=0[/tex] is

[tex]x=\frac{-b+-\sqrt[2]{b^{2}-4ac } }{2a}[/tex].

So, the solution for the equation [tex]2x^{2} +x-4=0[/tex] is

[tex]x=\frac{-1+-\sqrt[2]{1^{2}-4*2*(-4) } }{2*2}\\x=\frac{-1+-\sqrt[2]{1+32 } }{4}\\x=\frac{-1+-\sqrt{33} }{4}[/tex]

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The value of x in function cos(3pi/2+2x/3)=1/2 is  x= pi/4 + 3pi*n, 5pi*/4 + 3pi*n.

Trigonometric ratios for a right angled triangle are from the perspective of a particular non-right angle.

In a right angled triangle, two such angles are there which are not right angled(not of 90 degrees).

The slant side is called hypotenuse.

From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called base.

From that angle (suppose its measure is θ),

[tex]\sin(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of Hypotenuse}}\\\cos(\theta) = \dfrac{\text{Length of Base }}{\text{Length of Hypotenuse}}\\\\\tan(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}}\\\\\cot(\theta) = \dfrac{\text{Length of base}}{\text{Length of perpendicular}}\\\\\sec(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of base}}\\\\\csc(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of perpendicular}}\\[/tex]

We are given;

6sinx=5, 6cosx=7, sin2x=0, sin(x+pi/3)+1=0, cos(2x/3-pi/4)=[tex]\sqrt{2} /2[/tex], cos2x-1=0, 2sin3x=-1, cos(3pi/2+2x/3)=1/2

Now,

1. 6sinx=5

sinx=5/6

x=0.98511078

2. sin2x=0

x=n*pi/2

3. sin(x+pi/3)+1=0

x-intercept= (pi/6+2n*pi)

y-intercept= (0, [tex]\sqrt{3}[/tex]/2 -1)

4. cos(2x/3-pi/4)=[tex]\sqrt{2}/2[/tex]

x= (pi/4+n*pi, pi+n*pi)

6. cos2x-1=0

x=n*pi

7. 2sin3x=-1

x= 7pi/18 + 2pi*n/3, 11pi/18+2pi*n/3

8. cos(3pi/2+2x/3)=1/2

x= pi/4 + 3pi*n, 5pi*/4 + 3pi*n

For any value of integer n

Therefore, the answer of trigonometric function will be x= pi/4 + 3pi*n, 5pi*/4 + 3pi*n.

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Answer: =x^4+7x^3+7x^2-3x+19

Step-by-step explanation:

= 10x^3 -x^2 +6x +3 +x^4 -3x^3 +8x^2-9x+16

Step 1. Group like-terms. x^4+10x^3-3x^3-x^2+8x^2+6x-9x+3+16

Step 2. Add similar elements. x^4+7x^3-x^2+8x^2+6x-9x+3+16

Step 3. Keep adding similar elements. x^4+7x^3+7x^2+6x-9x+3+16

Step 4. Add similar elements, again. x^4+7x^3+7x^2-3x+3+16

Step 5. Final adding elements. x^4+7x^3+7x^2-3x+19

The following data represent the dividend yields of a random sample of 28 publicly traded stocks. The five number summary is: 0, 0.185, 0.72, 2.30, 3.58

The term "trade shocks" refers to changes in the amount of commodities and services exchanged globally as well as in international pricing that result in net profits or losses from trade. It has to do with changes in international marketplaces that frequently occur independently of national influences. Conventional wisdom is that terms-of-trade shocks are a significant contributor to business cycles in developing and underdeveloped nations. This viewpoint is founded in great part on the examination of calibrated business-cycle models.

(a) From the given table it is shown that,

0,3.58,0.37/2, (0.69+0.85)/2, (2.11 + 2.49)/2

The five number summary is: 0, 0.185, 0.72, 2.30, 3.58

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Answer:

In feet: [tex]\boxed{158,892 \textrm{ feet}}[/tex]

In miles: [tex]\boxed{\textrm{ 3.11 \;miles}}[/tex]

Step-by-step explanation:

A diagram really helps here and so I have drawn one for your understanding

From the diagram we see that Point A refers to the location of the plane when it is 50 miles away from the airport at am altitude of 30,500 feet

In a 2D coordinate system where x refers to the horizontal distance from the airport value and y refers to the altitude,
=> Point A has coordinates (50, 30500)

When the plane is 20 miles away from the airport, the altitude has dropped down to 18000 feet

This location is represented as point B(20, 18000)

The horizontal distance traveled by the plane is 50 - 20 = 30 miles

The vertical distance traveled by the plane(drop in altitude) is 30,500 - 18,000 = 12, 500

These two form the legs of a right triangle with the actual path of descent as the hypotenuse of the right triangle (see figure)

The distance c traveled by the plane is the distance from Point A to Point B which can be computed using the Pythagorean theorem given the two legs of the right triangle

The general formula is :

[tex]\mbox{\large c = \sqrt{a^{2} + b^{2}}}[/tex]

where c is the length of the hypotenuse, a and b are the lengths of the other two sides

We have a = 12, 500 feet and b = 30 miles

Convert miles to feet to get same units:

a = 12, 500 feet

b = 30 miles = 30 x 5280 feet = 158400

[tex]\mathbox{ c = \sqrt{158400^{2} + 12500^{2}}}[/tex]

[tex]c = \sqrt{25090560000 + 156250000}[/tex]

[tex]c = \sqrt{25246810000}[/tex]

[tex]\mathrm{c = 158,892.45 \;feet}\\[/tex]

[tex]\mathbox{ \textrm{c = 158,892 feet (to the nearest foot)}}[/tex]

So the distance traveled by the plane is 158, 992 feet (to the nearest foot)

This works out to 158992/5280 miles = 30.11 miles which is pretty close to 3.09

Maybe you are required to answer in feet and not in miles.

I don't know

The probability of drawing one blue marble on the first draw is 4/10. Since we do not replace the marble, there are only 9 marbles left in the bag, so the probability of drawing a green marble on the second draw is 2/9.

The probability of drawing one blue marble and one green marble is the product of the probabilities of each event:

(4/10) x (2/9) = 8/90 = 4/45

Therefore, the probability of drawing one blue marble and one green marble is 4/45.

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1 4/5 bags of dog food will last the LPS for approximately 8 and 3/10 days, or 8.3 days.

The Logan pet store uses 9/10 of a bag of dog food every day, which means they need 9/10 * 1 bag = 9/10 bags of dog food per day. To determine how many days 1 4/5 bags of dog food will last,

we need to divide the total amount of dog food by the amount used per day: 1 4/5 bags / (9/10 bags/day) = (9/10)*(18/5) / (9/10) = 18/5 days. Therefore, 1 4/5 bags of dog food will last for 18/5 days.

One 4/5 bags of dog food will last the Logan Pet Store (LPS) for approximately 8 and 3/10 days. This is because if the LPS uses 9/10 of a bag of dog food every day, then they are using 9/10 * 5/5 = 9/10 bags of dog food per day. If we divide 1 4/5 bags of dog food by 9/10 of a bag per day, we get (1 4/5) / (9/10) = (18/5) / (9/10) = 18/5 * 10/9 = 20/9 days. Therefore, 1 4/5 bags of dog food will last the LPS for approximately 8 and 3/10 days, or 8.3 days.

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Answer:

97 R=26

Step-by-step explanation:

Andrew's training plan can be modeled by an exponential function, and Sebastian's training plan can be modeled by a linear function. So, correct option is c) .

A linear function is a mathematical function that maps a set of inputs to a set of outputs in such a way that the output is proportional to the input. In other words, if the input changes by a certain amount, the output changes by a constant factor.

The equation of a linear function has the form:

y = mx + b

where x is the input variable, y is the output variable, m is the slope of the line, and b is the y-intercept. The slope represents how much the output changes for each unit change in the input, and the y-intercept represents the output value when the input is zero.

Linear functions are represented by straight lines on a graph. If you plot the input and output values for a linear function on a graph, the resulting points will form a straight line. The slope of the line represents the rate of change of the output with respect to the input, and the y-intercept represents the initial value of the output.

In Andrew's training plan, the weight he lifts is increasing by a constant percentage each week, which is characteristic of exponential growth. In Sebastian's training plan, the weight he lifts is increasing by a constant amount each week, which is characteristic of linear growth.

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The complete question is:

Andrew and Sebastian are training for a weightlifting competition. In order to prepare, each of them has created their own personal training plan as follows:

Which of the following statements are true?

a) Andrew and Sebastian both increase the weight they lift each week by the same amount.

b) Andrew's training plan can be modeled by a linear function, and Sebastian's training plan can be modeled by an exponential function.

 c) Andrew's training plan can be modeled by an exponential function, and Sebastian's training plan can be modeled by a linear function. 

d) Andrew increases the weight he lifts each week by equal factors, and Sebastian increases the weight he lifts each week by equal differences

e)  Andrew increases the weight he lifts each week by equal differences, and Sebastian increases the weight he lifts each week by equal factors.

Answer:

x = 45

Step-by-step explanation:

the sum of the interior angles of a quadrilateral = 360°

sum the angles and equate to 360

x + 3x + 90 + 90 = 360

4x + 180 = 360 ( subtract 180 from both sides )

4x = 180 ( divide both sides by 4 )

x = 45

The probability distribution function of Y is the set of all probabilities P(Y), for all possible values of Y[tex]P(Y) = (C(7, Y) * (12/52)^Y * (40/52)^{(7-Y)} /C(7, 52)[/tex]. Option E is correct.

Let Y be the discrete random variable that counts the number of face cards in a seven-card hand drawn from a standard 52-card deck. The possible values for Y are 0, 1, 2, 3, 4, 5, 6, and 7.

The number of ways to get Y face cards in a seven-card hand is given by the binomial coefficient C(7, Y), where C(7, Y) represents the number of combinations of 7 things taken Y at a time.

The probability of getting Y face cards in a seven-card hand is given by:

[tex]P(Y) = (C(7, Y) * (12/52)^Y * (40/52)^{(7-Y)} /C(7, 52)[/tex]

where [tex](12/52)^Y[/tex] represents the probability of drawing Y face cards and [tex](40/52)^{(7-Y)}[/tex] represents the probability of drawing the remaining 7-Y cards from the 40 non-face cards.

Thus, the probability distribution function of Y is the set of all probabilities P(Y), for all possible values of Y:

[tex]P(Y) = (C(7, Y) * (12/52)^Y * (40/52)^{(7-Y)} /C(7, 52)[/tex]

Y = 0, 1, 2, ..., 7

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Answer:

3(x)+4-8

find x.

Step-by-step explanation:

Answer:

5

6

[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\dotfill & \$ 500\\ P=\textit{initial amount}\dotfill &3300\\ r=rate\to 75\%\to \frac{75}{100}\dotfill &0.75\\ t=years \end{cases}[/tex]

[tex]500 = 3300(1 - 0.75)^{t} \implies \cfrac{500}{3300}=0.25^t\implies \cfrac{5}{33}=0.25^t \\\\\\ \log\left( \cfrac{5}{33} \right)=\log(0.25^t)\implies \log\left( \cfrac{5}{33} \right)=t\log(0.25) \\\\\\ \cfrac{\log\left( \frac{5}{33} \right)}{\log(0.25)}=t\implies 2\approx t\qquad \qquad \textit{to be exact, about 1 year and 131 days}[/tex]

Answer:

Non-linear

Step-by-step explanation:

y = 10/x is non-linear!

Because a linear equation is an equation of a straight line, which means the degree of a linear equation must be 0. In this case, the degree of variable y is 1; the degrees of the variables in the equation violate the linear equation definition, which means that the equation is not linear.

Answer:

hey

Step-by-step explanation:

Answer:

17

a. 5^4 = 625

b. 3^4 = 81

18

a. log base 10000 , 10 = -4

b. log base 2, 1/2 = -1

19. Inverse represent opposite functions, when you plug one into the other using variables, the result should be x.

Step-by-step explanation: Remember that when converting, use the base of the log function as the base of exponent. The answer to the log function represents the value of the exponent. Hope this helps!

Answer:

252 dollars

Step-by-step explanation:

so $3,500 * 2.4% is $84 * 3 gives you $252

Answer:

4:5

Step-by-step explanation:

Answer:

80% shining

20% not shining