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RATIONAL EQUATION

x = 6 is the value of x does f(x) = 2.

What is a function?

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.

Here, we have

Given function:  f(x) = −1 + 0.5x

We have to find the value of x does f(x) = 2.

For this, we put the different values of x and see what value satisfies the given function.

For x = -6

f(x) = −1 + 0.5(-6)

f(x) = -4

For x = 5

f(x) = −1 + 0.5(5)

f(x) = 1.5

For x = 6

f(x) = −1 + 0.5(6)

f(x) = 2

Hence, x = 6 is the value of x does f(x) = 2.

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The solution is A = 37

The value of the equation A = 8a + 3b - 10 + c² is A = 37

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is given by

A = 8a + 3b - 10 + c²

When the value of a = 2 , the value of b = 5 and the value of c = 4 ,

The equation A is given as

Substitute the value of a , b and c in the equation , we get

A = 8a + 3b - 10 + c²

A = 8 ( 2 ) + 3 ( 5 ) - 10 + 4²

A = 16 + 15 - 10 + 16

On simplifying the equation , we get

A = 31 + 6

The value of A = 37

Therefore , the value of A is 37

Hence , The value of the equation A = 8a + 3b - 10 + c² is A = 37

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Answer:

Step-by-step explanation:

There are 4 kings in a deck of playing cards.

There are 52 cards in a deck.

So the probability is 4 out of 52.

Which is 4/52,

Which can be reduced to 1/13.

4 divided by 4 = 1 and 52 divided by 4 =13.

Answer:

The function g(x) = log(-3x - 9) - 1 is obtained from the parent function f(x) = log(x) through two transformations: a shift to the right and a shift downward. The shift to the right is achieved by multiplying x by -3 and subtracting 9, which results in a rightward shift in the function's graph. The shift downward is achieved by subtracting 1 from the final result, which results in a downward shift in the function's graph. These transformations result in a graph that is shifted to the right and downward compared to the graph of the parent function.

[tex]log( - 3x - 9) = log( 3( - x - 3)) \\ = log( 3) + log( - (x + 3))[/tex]

A vertical shift by 1 unit downwards

A vertical shift by log(3) units upwards

A horizontal shift by 3 units to the left

A reflection along the line x=-3

The statement supported by the plot is that the IQR of the distribution is roughly 10. It is possible to estimate the median from the plot, and the distribution appears to be unimodal, with the mean being smaller than the median. There are no outliers shown in the plot.

The relative frequency histogram provides a visual representation of the distribution of the data. From the plot, it is possible to estimate the median, which is the middle value of the distribution, as well as the interquartile range (IQR), which is the difference between the upper and lower quartiles. The IQR of the distribution is roughly 10, which can be seen by the distance between the upper and lower quartiles in the plot. Additionally, the distribution appears to be unimodal, which means that it has only one mode or peak. It is also apparent that the mean of the distribution is smaller than its median, as the peak is shifted to the left of the median. Finally, there are no outliers shown in the plot, as all of the values appear to be within the range of the distribution.

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A stable sorting algorithm is one that keeps the relative order of two equal elements. Quicksort is a sorting algorithm that has a high degree of instability, which means that it may alter the relative order of two equal components.

The Merge Sort, Timsort, Counting Sort, Insertion Sort, and Bubble Sort are just a few examples of popular sorting algorithms that are by their very nature stable. Others, like Quicksort, Heapsort, and Selection Sort, are erratic. Stable sorting algorithms can be modified to be more efficient.

Because we swap elements according on the location of the pivot, QuickSort is an unstable algorithm (without considering their original positions). A sorting algorithm is said to sort in-place if it never stores more than a fixed number of input array members outside of the array. If the order of elements with the same value is not altered by a sorting technique, it is stable. Binary insertion sort is the only stable algorithm available from the options offered.

Therefore the correct answer is false.

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Answer:

15 stairs would be needed

Step-by-step explanation:

10x12= 120

15 x 8 = 120

Answer: No

Step-by-step explanation:

To determine whether the college graduate will have $200,000 saved in their retirement account after 25 years, we can use the formula for compound interest:

A = P * (1 + r/n)^(nt)

where A is the total amount of money in the account after the specified time, P is the initial amount of money deposited in the account, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years the money is invested.

In this case, the initial amount deposited each month is $150, the annual interest rate is 10%, the number of times the interest is compounded per year is 12 (once per month), and the number of years the money is invested is 25. Plugging these values into the formula above gives us:

A = $150 * (1 + 10%/12)^(12*25) = $150 * (1.0083)^300 = $150 * 3.4955 = $524.33

Since the goal is to have $200,000 saved in the account after 25 years, the college graduate will not have enough money in their account if they contribute $150 per month at 10% interest. In order to reach their goal, they would need to save more money each month or earn a higher interest rate on their contributions.

LCL would be 4 minutes and UCL would be 6 minutes if the company uses 2-sigma control limits instead.

The average of a group of variables is referred to as the mean in mathematics and statistics. There are several methods for calculating the mean, including simple arithmetic means (adding the numbers together and dividing the result by the number of observations), geometric means, and harmonic means. The arithmetic mean, also known as the arithmetic average or simply the mean or average, is the sum of a set of numbers divided by the total number of numbers in the set. The collection frequently consists of a series of findings from a survey, experiment, or observational study.

Given

LCL = 3.5 minutes

UCL = 6.5 minutes

Mean = LCL + UCL/2

Mean = 3.5 + 6.5/2

Mean = 5

Standard deviation = UCL - LCL/6

Standard deviation = 6.5 - 3.5/6

Standard deviation = 0.5

LCL = 5 - 2(0.5)

LCL = 4

UCL = 5 + 2(0.5)

UCL = 6

LCL = 4 minutes and UCL = 6 minutes

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On solving the provided question, we can say that - the instantaneous rate of change of the function at the given value, by solving the equation  y = 11 - 5x, f'(1) = 3-8 = -5

A mathematical equation is a formula that uses the equals symbol (=) to link two expressions and represent their equivalence. A mathematical statement that demonstrates the equality of two mathematical expressions is an equation in algebra, in its most basic form. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."

y = f(x) =

[tex]x^3 - 4x^2 + 7 \\at x =1[/tex]

f(x) = 3-4+7

= 6

F'(x) = [tex]3x^2 - 8x[/tex]

f'(1) = 3-8 = -5

equation = y - 6 = -5(x-1)

y = 11 - 5x

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Answer:

Below

Step-by-step explanation:

Area of square - area of circle = remnant               area of circle = pi r^2

(40 x 40) - pi (20^2) = 343 . 4 in^2  left over

( this assumes the circle touches the edges of the square)

The equation of a line is typically given in the form y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis). To find the equation of the line that passes through the points (3, 4) and (5, 8), we need to first calculate the slope of the line.

The slope of a line is given by the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line. In this case, we have:

m = (8 - 4) / (5 - 3) = 4/2 = 2

Now that we know the slope of the line, we can use one of the given points to find the y-intercept. Let's use the point (3, 4). If we plug the values of x and y into the equation y = mx + b, we get:

4 = 2 * 3 + b

4 = 6 + b

-2 = b

Therefore, the equation of the line that passes through the points (3, 4) and (5, 8) is:

y = 2x - 2

Answer:

[tex]\ln (y) = 0.210x-2.601[/tex]

Step-by-step explanation:

Given table:

[tex]\begin{array}{|c|c|}\cline{1-2} \sf Length & \sf Diameter \\x & y\\\cline{1-2} \vphantom{\dfrac12} 2 & 0.113\\\cline{1-2} \vphantom{\dfrac12} 3& 0.151\\\cline{1-2} \vphantom{\dfrac12} 4& 0.192\\\cline{1-2} \vphantom{\dfrac12} 5& 0.222\\\cline{1-2} \vphantom{\dfrac12} 6& 0.262\\\cline{1-2} \end{array}[/tex]

To convert  y = abˣ  to linear form, take natural logs of both sides and rearrange:

[tex]\begin{aligned}y=ab^x \implies \ln y &= \ln ab^x\\\implies \ln y &= \ln a + \ln b^x\\\implies \ln y &= \ln a + x \ln b\\\implies \ln y &=x \ln b+ \ln a\end{aligned}[/tex]

This is in the straight-line form y = mx + c.

Substitute the first and last values of x and y from the table into the natural log formula:

Subtract the first equation from the second equation to eliminate ln(a);

[tex]\implies \ln 0.262 - \ln 0.113 = 6 \ln b - 2 \ln b[/tex]

[tex]\implies \ln 0.262 - \ln 0.113 = 4 \ln b[/tex]

Apply the quotient log law:

[tex]\implies \ln \dfrac{0.262}{0.113} = 4\ln b[/tex]

Rearrange and solve for ln(b):

[tex]\implies \ln b = \dfrac{1}{4}\ln \dfrac{0.262}{0.113}[/tex]

[tex]\implies \ln b = 0.210\; \sf (3\;d.p.)[/tex]

Substitute the found value of ln(b) into one of the equations and solve for ln(a):

[tex]\implies \ln 0.262 = 6 \cdot \dfrac{1}{4}\ln \dfrac{0.262}{0.113}+\ln a[/tex]

[tex]\implies \ln a=\ln 0.262 -\dfrac{6}{4}\ln \dfrac{0.262}{0.113}[/tex]

[tex]\implies \ln a = -2.601\; \sf (3\;d.p.)[/tex]

Substitute the found values of ln(a) and ln(b) into the formula to create an equation for ln(y):

[tex]\boxed{\ln (y) = 0.210x-2.601}[/tex]

The series of transformations that would map Figure T onto Figure U are:

What is rigid transformation?

Transformation is a process in which the dimensions of an object is resized, or its orientation is changed.

Rigid transformation is a topic that involves resizing an object, or changing its orientation. Some common methods used in transformation are: reflection, dilation, rotation and translation.

Reflection is the process in which a given object is turned about a reference point or line.Dilation involves changing the dimensions of a given object. Thus its size will be affected.

Rotation involves turning an object at a certain angle. Translation implies moving a whole object in a given direction and number of units.

In the given question, the required series of transformation are:

i. First rotating figure T at an angle of 90 degrees using its base as the reference line.

ii. Then translating the image some units.

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The correct statement regarding the unit circle is given as follows:

x = cos(θ) and y = sin(θ), and both functions have a period of 2π.

For an angle [tex]\theta[/tex] the unit circle is a circle with radius 1 containing the following set of points: [tex](\cos{\theta}, \sin{\theta})[/tex].

These points are contained according to the following identity:

[tex]\cos^2{\theta} + sin^2{\theta} = 1[/tex]

(standard identity of trigonometry).

From the x-coordinate and the y-coordinate of each point on the unit circle, the function definitions are given as follows:

The period of both functions is of 2π, as the entire unit circle forms an angle of 360º = 2π.

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Answer:

Step-by-step explanation:

Answer:

To round a number to the nearest thousand, we first need to identify the thousands digit in the number. In this case, the thousands digit is 8, because 87388 is between 80000 and 90000.

To determine whether to round up or down, we need to look at the hundreds digit, which is 7 in this case. If the hundreds digit is 5 or greater, we round up. If the hundreds digit is less than 5, we round down. In this case, the hundreds digit is 7, which is greater than or equal to 5, so we need to round up.

To round up, we add 1000 to 87388, which gives us 88388. So, 87388 rounded to the nearest thousand is 88000.

The value of the trigonometric expression will be 1. Then the correct option is C.

Mathematical capabilities inspect the collaboration between the aspects and points of a three-sided structure.

The meaning of straightforwardness is simplifying something to accomplish or get a handle on while likewise making it somewhat less troublesome.

The expression is given below.

⇒ tan²x / sec²x + cot²x / cosec²x

Simplify the expression, then the value of the expression is given as,

⇒ tan²x / sec²x + cot²x / cosec²x

⇒ (sin²x × cos²x) / cos²x + (cos²x × sin²x) / sin²x

⇒ sin²x + cos²x

⇒ 1

The worth of the mathematical articulation will be 1. Then, at that point, the right choice is C.

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1) Nominal GDP = Current year price* Current year quantity

= 500*3000 + 400,000*20

= 1,500,000 + 8,000,000

= $9,500,000

2) Real GDP = Base year price* Current year quantity

= 500*2000 + 400,000*10

=1,000,000 + 4,000,000

= $5,000,000

3) GDP Deflator = Nominal GDP/Real GDP

=9,500,000/5,000,000

Answer:

Step-by-step explanation:

So your first point has x=325.0 and y=1.10, your second point has x=348.9 and y=1.40, and so on.

The graph should look something like this:

The conclusion that you would draw from your plot is that the power seems to vary linearly with the speed. The data points are almost in a straight line. They are not perfectly aligned, of course. There is always some variability in real data, but you can see a trend.

Answer:

Step-by-step explanation:

To find the minimum number of daisies and lilies that Manuel must have watered, we need to find the least common multiple (LCM) of 11 and 12. The LCM of two numbers is the smallest positive integer that is a multiple of both numbers.

To find the LCM of 11 and 12, we can list the multiples of each number and find the smallest number that appears in both lists. The multiples of 11 are 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, etc. The multiples of 12 are 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, etc.

We can see that the smallest number that appears in both lists is 11, which is the LCM of 11 and 12. Therefore, the minimum number of daisies and lilies that Manuel must have watered is 11. If he watered the same number of each flower, he must have watered at least 11 daisies and 11 lilies.

Measure of angle VTK is 90°.

Angles come in many different varieties in geometry. Angle is among the most crucial and fundamental units. Two rays or lines are linked at their shared terminus when they create an angle. We use angles in many facets of our daily lives, starting with the construction of buildings, dams, and monuments, not only in mathematics. The study of angles is essential to civil engineering. Two rays (half-lines) combined into an angle have a single terminal. The latter is known as the vertex of the angle, while the rays are known as its sides, occasionally as its legs, and occasionally as its arms.

Given

∠VTK = 90°

∠VMK = 90°

∠VTK is given

∠VTK = 90°

Measure of angle VTK is 90°.

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On solving the provided question, we can say that The $289,000 in fixed overhead that was used in production at that time

In accounting and economics, expenses for a firm are referred to as "fixed costs," often known as "indirect costs" or "overhead costs" since they are independent of the volume of goods or services the organization produces. They often have a periodic nature, such monthly rent or interest payments. These expenses are frequently capital costs as well.

The fixed overhead rate equals the budgeted amount Budgeted hours / Fixed overhead costs

Fixed overhead rate (predetermined) = 300,000/60,000

The fixed overhead rate (predetermined) is $5 per hour.

Applied Standard hours permitted with a predetermined overhead rate equals fixed overhead (fixed)

Fixed overhead applied = 57,800 * $5 per hour

$289,000 for applied fixed overhead

Therefore, $289,000 in fixed overhead was allocated to production during that time.

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We can say that whenever x changes by 1, the value of y becomes 1.7 times as large as its previous value.

Given that,

With respect to x, the value of y varies exponentially, and the 1-unit growth factor is 1.7.

We have to find which of the following best describes the significance of this growth factor.

We know that,

The required expression for y with respect to x is

y=(1.8)ˣ------>equation(1)

1.8=1- unit growth factor.

Whenever x changes by 1.

x=x-1----->equation(2)

Putting equation (2) in (1)

y'=1.8ˣ⁺¹

y'=1.8ˣ×1.8----->equation(3)

Here [ y is new value after increase]

Taking ratio of (3) and (1)

y'/y= (1.8)ˣ×(1.8)/(1.8)ˣ

y'=(1.8)y

Therefore, We can say that whenever x changes by 1, the value of y becomes 1.8 times as large as its previous value.

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y=(1.8)ˣ               equation(1)

1.8=1- unit growth factor.

Whenever x changes by 1.

x=x-1                     equation(2)

y'=1.8ˣ⁺¹

y'=1.8ˣ×1.8              equation(3)

Here [ y is new value after increase]

Taking ratio of (3) and (1)

y'/y= (1.8)ˣ×(1.8)/(1.8)ˣ

y'=(1.8)y

Therefore, We can say that whenever x changes by 1, the value of y becomes 1.8 times as large as its previous value.

The megabytes that have been downloaded will be 48 megabytes.

Based on the information, percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

Since 273 megabytes is being download if the download is 17.7%, the megabytes that have been downloaded will be:

= 17.7% × 273

= 48 megabytes.

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The Solution for the given problem is 6x² +4x

What is Polynomial?

A polynomial is a mathematical statement made up of indeterminates and coefficients that solely includes the operations of addition, subtraction, multiplication, and positive-integer powers of variables.

Solution:

We are given with the values of the following terms f(x), g(x), and m(x)

f(x) = 3x² + 5x - z

g(x) = 5x² - 3x + z

m(x) = 2x² - 2x

To find: f(x) + [g(x) - m(x)]

so, we need to put the respective values in the equation and simplify it

3x² + 5x - z + [5x² - 3x + z - 2x² + 2x]

3x² + 5x - z + [3x² - x + z]

6x² +4x

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a) probability that a randomly selected resident has red hair is 0.16

b) probability that a randomly selected resident has brown or black hair   is  0.67

c) probability that a randomly selected resident does not have blonde hair is 0.8.

P(black hair color) = 0.17

P (Brown hair)  = 0.47

P (blonde hair)  = 0.20

a) Probablity that a randomly chosen resident has red hair is:

P(red hair) = 1 - P(black hair) - P(brown hair) - P(blonde hair)

=> 1 - 0.17 - 0.47 - 0.20

=> 0.16

b) P(brown hair) + P(black hair) is the likelihood that a randomly chosen resident has brown or black hair (black hair)

= 0.47 + 0.20

= 0.67

c) The Probability that a randomly chosen resident does not have blonde hair is equal to 1 - P (blonde hair)

=> 1 - 0.20

=> 0.8

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The probability that a randomly selected resident has red hair and brown or black and  black, brown, or blonde hair is 0.16, 0.80 and 0.20

The probabilities of a randomly selected resident having black, brown, or blonde hair are 0.17, 0.47, and 0.20 respectively.

P (black hair) = 0.17

P (brown hair) = 0.47

P (blonde hair) = 0.20

The probability is the measure of the likelihood of an event to happen. It measures the certainty of the event. The formula for probability is given by; P(E) = Number of Favourable Outcomes/Number of total outcomes.

(a). Probability that a randomly selected resident has red hair is

P (red hair) = 1 -P(black hair)-P (brown hair)-P (blonde hair)

 = 1 - 0.17 - 0.47 - 0.2

 = 0.16

(b).  Probability that a randomly selected resident has brown or black hair

  = P (brown hair) + P (black hair)

  = 0.47 + 0.20  

  = 0.67

(c). Probability that a randomly selected resident does not have blonde hair

   = 1 - P (blonde hair)

   = 1 - 0.20

   = 0.80

Therefore, the probability is 0.16, 0.80 and 0.20.

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There are two groups of [tex]\dfrac{7}{4}[/tex], an integer which is equal to 1, and 0.75 which is decimal.

A fraction is a numeral that represents a rational number.

Let a and b be two numbers, then their fraction can be represented as a/b.

The given fraction is,

[tex]\dfrac{7}{4}[/tex].

To find the groups of fraction,

Simplify the fraction,

[tex]\dfrac{7}{4} = 1 \dfrac{3}{4}\\\\ = 1.75[/tex]

There are two groups in the fraction of  [tex]\dfrac{7}{4}[/tex] ,

Integer part which is 1.

And decimal part which is 0.75.

Hence, there are two groups of fraction [tex]\dfrac{7}{4}[/tex].

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Answer:

GCF: 50

Step-by-step explanation:

Let's test

50 ( 5 + 6)

= 250 + 300

So, my answer is correct!

The answer is 3.03

A sample mean is an average of a set of data . The sample mean can be used to calculate the central tendency, standard deviation and the variance of a data set.

Given here μ=62 σ=7 sample mean x = 65 and n=50

now the formula given is z= x-μ / σ÷√n

                                            = 65-62 / 7÷√50

                                            = 3√50/7

                                            = 3.03

Hence the final answer is 3.03

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