evaluate the expression 4(3-2)^3+2(-8) and justify each step

The width of the rectangle is 2 units when length of the rectangle is 10 units.

As per the given data:

The length of a rectangle varies inversely with its width.

The length of the rectangle is 5 units when its width is 4 units

The length of the rectangle when its width is 10 units

Here we have to determine the width of a rectangle.

Let l be the length and w be the width of the rectangle.

Now, from the given direction, we have

[tex]$l=\frac{k}{w}[/tex]

Substitute l = 5 units, w = 4 units, to find the constant k

5 = [tex]$\frac{k}{4}[/tex]

k = 20 units

Now, we have to find the width of the rectangle when l = 10 units

10 = [tex]$\frac{20}{w}[/tex]

w = [tex]$\frac{20}{10}[/tex]

w = 2 units.

Therefore the width of the rectangle is 2 units.

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The length of a rectangle varies inversely with its width. if the length of the rectangle is 5 units when its width is 4 units , find the width of the rectangle when its length is 10 units?

None of the points listed are solutions to the equation y = 12x^3.

The equation y = 12x^3 is a polynomial equation, which describes a curve in a graph. The points listed are just random points and do not satisfy the equation. To find the solutions to the equation, we need to find the x-values that make y equal to the given value.

The equation y = 12x^3 is a cubic equation, which is a polynomial equation with degree 3. It describes a curve in a graph, where the x-values are inputs and the y-values are outputs. To find the solutions to the equation, we need to find the x-values that make y equal to the given value.

For example, if we plug in x = 1 into the equation, we get y = 12 * 1^3 = 12. This means that the point (1, 12) is a solution to the equation y = 12x^3. We can repeat this process for different x-values to find all the solutions.

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In a dataset or graph, outliers are extreme values that greatly deviate from the dominant pattern of values.

In order to identify the outlier, search for a value that is significantly greater or smaller than all the other values. Due to its extreme size compared to all other numbers, the number 267 is an outlier.

a value that "lies outside" (i.e., is significantly smaller or substantially bigger) most of the other values in a set of data For instance, both 3 and 85 in the scores 25, 29, 3, 32, 85, 33, 27 and 28 are "outliers".

A data point that is an outlier in a data graph or dataset you are dealing with is one that is extraordinarily high or extraordinarily low in comparison to the nearest data point and the rest of the nearby coexisting values. Outliers in a dataset or graph are extreme values that stand out significantly from the main pattern of values.

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Costs that do not change with output are called fixed costs.

Hence the correct option is D.

Fixed costs are the costs that does not change when output gets changed. Fixed cost is also known as overhead cost. For example, insurance, rent, profit, depreciation, and normal cost.

Fixed costs are indirect costs and must be paid irrespective of the level of production, that is, these costs can be incurred even when the level of production is zero. The best example for this is rent of the factory and payment on the lease for the equipment of the factory must be paid even if the level of production is zero.

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Answer:

Step-by-step explanation:true

Answer:

False

Step-by-step explanation:

To find the interquartile range, compute the positive difference between the first and third quartiles.

The conditional probability that the first and fourth balls drawn will be white given that the sample drawn contains exactly 3 white balls will be  [C(5, 3) * C(2, 2) / C(12, 5)] / (C(12, 3) / C(12, 5))

The conditional probability of the first and fourth balls drawn being white given that the sample drawn contains exactly 3 white balls can be calculated as follows:

Let A be the event that the first and fourth balls drawn are white and B be the event that the sample drawn contains exactly 3 white balls. We want to find P(A|B), the probability of A given B.

Using the formula for conditional probability:

P(A|B) = P(A and B) / P(B)

To calculate P(A and B), we can use the formula for the number of combinations:

C(n, k) = n! / (k! (n - k)!)

Where n is the total number of balls, k is the number of white balls, and ! denotes the factorial symbol.

In this case, n = 5 (the sample size), k = 3 (the number of white balls), and m = 2 (the number of white balls in the first and fourth positions).

P(A and B) = C(5, 3) * C(2, 2) / C(12, 5)

P(B) = C(12, 3) / C(12, 5)

Putting it all together:

P(A|B) = P(A and B) / P(B)

= [C(5, 3) * C(2, 2) / C(12, 5)] / (C(12, 3) / C(12, 5))
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The home's price is worth today's compared to the original price, which increased by 9% per year, equal to $803,310.

Purchase price of the house bought by Sunita in 1992 = $289,000

Percent increase in the average home price from 1992 to today per year

= 9% per year.

Let us consider 'y' be the home price worth today.

Total number of years = 2023 - 1992

                                     = 31 years

Todays price = 289,000 × 9 % × 31

                      = ( 289,000 × 9 × 31 )/100

                      = $803,310

Therefore, for the increased in home price by 9% per year the worth todays home price is equal to $803,310.

The given question is incomplete, I answer the question in general according to my knowledge:

From 1992 to today the average home price increased by 9% per year. In 1992 Sunita Bath bought a house for $289,000. What was it worth today?

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The coordinates of the point on the unit circle corresponding to a central angle of 21 degrees are (0.93, 0.36), which is answer choice c.

The point on the unit circle corresponding to a central angle of 21 degrees can be found using the trigonometric functions sine and cosine.

In this case, the x-coordinate is equal to the cosine of the angle and the y-coordinate is equal to the sine of the angle.

Converting degrees to radians, we have:

x = cos(21) = 0.93

y = sin(21) = 0.36

A unit circle in mathematics is a circle with a radius of one, or one unit. The unit circle is frequently the circle with radius 1 that is located at the origin (0, 0) in the Cartesian coordinate system on the Euclidean plane, notably in trigonometry.

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The value of x and y are 4.24 units and 4.24 units respectively in the right angled triangle.

An equation is an expression that shows the relationship between two or more numbers and variables.

Trigonometric ratio shows the relationship between the sides and angles of a right angled triangle.

For the triangle shown, using trigonometric ratio:

sin(45) = x / 6

x = 4.24 units

Also:

cos(45) = y / 6

y = 4.24 units

The value of x and y are 4.24 units and 4.24 units respectively

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Answer: 21.5%

Step-by-step explanation:

this is for number 25.

Answer:

Step-by-step explanation:

Figure 1

Total area = Area of square = 12 * 12 =144

Area of Shaded region =

Area of Square – Area of circle =

144 - pi r^2 = 144 – π 6*6=144-36π = 30.96

(Here the value \pi  of is 3.14)

Probability = Area of Shaded region/Total area = 30.96/144=0.215

Rounded to the nearest 10th the answer is 21.5%

Area of circle = pi{10}^2=100 \pi=314

Area of arc AB = Area of quarter circle – Area of triangle OAB

=( pi{10}^2\ *1/4)-1/2 * 10*10 = 25pi – 50 = 28.5

 Probability = Area of arc/Area of circle = 28.5/314 = 0.090

   Rounded to nearest 10th the answer is 9%

The required probability that the hand is a full house is; 0.00144 or 0.144%.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

Consider the provided information we have Five cards are drawn from an ordinary deck of 52 playing cards.

Thus full house is a hand that consists of two of one kind and three of another kind.

The total number of ways to draw 5 cards are 78 was.

Now we want two of one kind and three of another.

Therefore, the hand has the pattern AAABB, where A and B are from distinct kinds. The number of such hands are:

3744/25989611

= 0.00144

Hence, the required probability is 0.00144 or 0.144%.

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For the given category,  there are three individuals with a score of 0, meaning they are married.

In this scenario, we want to convert the marital status of individuals into category scores where Single = 1 and Married = 0.

The score assigned to each person will indicate whether they are single or married.

To calculate the category score, we look at the marital status of each individual. If they are single, they are assigned a score of 1. If they are married, they are assigned a score of 0. So, in the given data, we have:

Married 24 $45,000 with a score of 0

Single 26 $33,000 with a score of 1

Single 33 $53,000 with a score of 1

Single 28 $59,000 with a score of 1

Married 36 $62,000 with a score of 0

Married 29 $48,000 with a score of 0.

We can see that there are three individuals with a score of 1 and three individuals with a score of 0.  

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Answer:

see explanation

Step-by-step explanation:

the equation of proportion is of the form

y = kx ← k is the constant of proportionality

(a)

- [tex]\frac{5}{2}[/tex] x = y , or

y = - [tex]\frac{5}{2}[/tex] x ← is in standard form

thus x and y are directly proportional

with constant of proportionality k = - [tex]\frac{5}{2}[/tex]

(b)

y = x ← is in standard form

thus x and y are directly proportional

with constant of proportionality k = 1

Answer:

5.5−5x (sorry if i got it wrong i tried)

Answer:

-5x+5.5

Step-by-step explanation:

3.5−4x+2−3x+2x

-4x-3x+2x+3.5+2

-5x+5.5

The equation of the tangent line to the curve at the point (x1,y1) is

  y - y1 = - 3.54(x - x1)

What is a tangent?

The straight line that just touches the curve at a given location is referred to as the tangent line to a plane curve in geometry.

Given parametric equations,

x(t)=sin(8t)

y(t)=−8cos(−5t)

We now differentiate the above equations with respect to t.

dx/dt = 8cos(8t)

dy/dt = -8 * -5 * -sin(-5t) = -40sin(-5t)

the slope of tangent =  dy/dx of the curve.

dy/dx = (dy/dt)/(dx/dt) = -40sin(-5t) / 8cos(8t) = -5[ sin(-5t)/cos(8t) ]

Equation of a tangent to the curve

y - y1 = dy/dx (x-x1)

When t = (3π/4)

dy/dx = -5[ sin(-5*3π/4) / cos(8* 3π/4) ] = -5[ 0.707/1] = - 3.54

Therefore the equation of the tangent line at point (x1,y1) is

  y - y1 = - 3.54(x - x1)

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For every additional atmosphere of pressure applied to 1 mole of carbon dioxide at a volume of 10 L,  the volume will decrease by 9.5633 L.

The van der Waals equation is an important tool for understanding the behavior of gases. It is a mathematical equation that relates the pressure, volume, and temperature of a gas.

To find the rate of change of volume with respect to pressure, we use implicit differentiation.

This means that we take the derivative of both sides of the equation with respect to pressure (dP) while keeping all other variables constant.

After some algebraic manipulation, we find that

=> dV/dP = (V - nb)/(P + n'aV2).

This result tells us how the volume of a gas changes as the pressure changes.

To calculate the rate of change of volume with respect to pressure for 1 mole of carbon dioxide, we use the values of

V= 10 L, P=2.5atm, a=3.592 L2-atm/mole², and b=0.04267 L/mole.

Plugging in these values, we find that

=> dV/dP = (10 L - 0.04267 L)/(2.5atm + 3.592 L2-atm/mole² x 10 L2)

=> 9.5633 L/atm.

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Calculating the correlation coefficient, which runs from -1 to 1, will reveal how strong a correlation is.

Positive Correlation, A relationship between two variables such that as one variable increases, the other variable also increases.

Negative Correlation, A relationship between two variables such that as one variable increases, the other variable decreases.

No Correlation, A relationship between two variables such that there is no relationship or pattern between the two variables.

The strength of a correlation can be determined by calculating the correlation coefficient, which ranges from -1 to 1. A value of -1 indicates a perfect negative correlation, a value of 1 indicates a perfect positive correlation, and a value of 0 indicates no correlation. The closer the correlation coefficient is to either -1 or 1, the stronger the correlation is.

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Answer:

First option: ∠I = ∠K

Step-by-step explanation:

The translation dilates ΔGHI about point G using a positive scale factor to generate ΔGJK.

We can use process of elimination(POE) to get rid of obviously wrong choices

∠I = ∠K is a correct choice since dilation preserves the original shape so the angles two triangles are equal and therefore the first choice appears to be the correct answer

Let's look at the other choices to make sure:

GH is smaller than GJ so GH = 2GJ is obviously false

∠G cannot be equal to ∠K unless it is an isoscles triangle and such information is not provided

HI is less than JK so the last option is also not true

Correct answer:
First option: ∠I = ∠K

The additional information would you need to complete the boxplot are option (A), (B) and (C).

A boxplot is a visual representation of a dataset that provides information about the distribution of the data. It shows the median, quartiles, range, and any outliers in the data.

To complete the boxplot, a few additional pieces of information are required.

A. The largest value inside the fence: The high whisker on a boxplot represents the largest value that is within 1.5 times the interquartile range (IQR) of the data. To plot this, the largest value inside the fence is needed

D. The smallest value inside the fence: Similar to the high whisker, the low whisker represents the smallest value within 1.5 times the IQR of the data. To plot this, the smallest value inside the fence is needed.

C. Outliers: Outliers are values that fall outside the fences, and are plotted as individual points. To complete the boxplot, any outliers that are above the top fence and below the maximum value need to be included.

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The probability of Margo being paired with Irma will be = 1/29

As per the data given,

Total number of students participated in the quiz = 30

Since each student must be paired with exactly one other student, there are 29 possible students that Margo could be paired with.

Since Irma is Margo's best friend, there is only one possibility for Margo's pairing that would result in her being paired with Irma.

The probability of Margo being paired with Irma is 1 out of 29 possible pairings, so the answer is = 1/29

This is the exact probability, expressed as a common fraction.

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Answer: 31 quarters and 47 dimes

Step-by-step explanation:

Please refer to the image below:

An equation of the question is 250 × 0.94^n = 150 and in approx 8 years it will have about 150 students.

The population of its high school decreases by 6% each year.

The senior class has 250 students now.

Each year decrease in population = 6% = 0.06

So it can be = 1 - 0.06 = 0.94

Total student now = 250

Let n be the number of years before the class will have  students.

So the equation should be = 250 × 0.94^n

After years left students = 150.

Now the equation should be

250 × 0.94^n = 150

Now solving the equation.

Divide by 250 on both side, we get

0.94^n = 150/250

0.94^n = 3/5

Taking log on both side, we get

log(0.94^n) = log(3/5)

Using the formula log(m^n) = n logm and log(m/n) = log m - log n

n log(0.94) = log3 - log5

Now finding the value of log using calculator

n (-0.062) = 1.099 - 1.61

(-0.062)n = -0.511

Divide by (-0.062) on both side, we get

n = 8.242

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The complete question is:

As a town gets smaller, the population of its high school decreases by 6% each year. The senior class has 250 students now. In how many years will it have about 150 students? Write an equation. Then solve the equation without graphing. Write an equation to represent this situation. Let n be the number of years before the class will have  students.

Answer:

the answer is 2a and 4b

Step-by-step explanation:

The possible approximate lengths of b are: 2.3 units and 7.8 units

We know that the law of sines for triangle is:

The ratios of the length of all sides of a triangle to the sine of the respective opposite angles are in proportion.

This means, for triangle ABC,

[tex]\frac{sin~ A}{a} =\frac{sin~B}{b} =\frac{sin~ C}{c}[/tex]

where a is the length of side BC,

b is the length of side AC,

c is the length of side AB.

For triangle ABC consider an equation from sine law,

[tex]\frac{sin~ A}{a} =\frac{sin~ C}{c}[/tex]

here, c = 5.4, a = 3.3, and m∠A = 20°

[tex]\frac{sin~ 20}{3.3} =\frac{sin~ C}{5.4}\\\\\frac{0.3420}{3.3} =\frac{sin~ C}{5.4}[/tex]

0.3420 × 5.4 = 3.3 × sin(C)

sin(C) = 0.5596

∠C = arcsin(0.5596)

∠C = 34.03°  OR 145.9°

∠C ≈ 34° OR 146°

We know that the sum of all angles of triangle is 180 degrees.

so, ∠A + ∠B + ∠C = 180°

when m∠C = 34°,

20° + ∠B + 34.03° = 180°

∠B = 125.97°

m∠B = 126°

when m∠C = 146°,

20° + ∠B + 146° = 180°

m∠B = 14°

Now consider equation,

[tex]\frac{sin~ A}{a} =\frac{sin~ B}{b}\\\\\frac{sin~20^{\circ}}{3.3} =\frac{sin~ 126^{\circ}}{b}[/tex]

b × 0.3420 = 0.8090 × 3.3

b = 7.8 units

when m∠B = 14°,

[tex]\frac{sin~20^{\circ}}{3.3} =\frac{sin~ 14^{\circ}}{b}[/tex]

b × 0.3420 = 0.2419 × 3.3

b = 2.3 units

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The complete question is:

Law of sines: StartFraction sine (uppercase A) Over a EndFraction = StartFraction sine (uppercase B) Over b EndFraction = StartFraction sine (uppercase C) Over c EndFraction

In ΔABC, c = 5.4, a = 3.3, and measure of angle A = 20 degrees. What are the possible approximate lengths of b? Use the law of sines to find the answer.

2.0 units and 4.6 units

2.1 units and 8.7 units

2.3 units and 7.8 units

2.6 units and 6.6 units

The graph would be a straight line with points (1,4), (2,6), (3,8), (4,10), and (5,12).

A graph is a visual representation of data. It is a pictorial representation of a set of numerical values, in which individual values are plotted as points on the graph. Graphs are used to show trends, patterns and relationships between different data sets. Graphs are used in various fields including mathematics, science, economics, and statistics. Graphs can be used to represent a variety of data such as linear, nonlinear, and even categorical data. Graphs are also used to display financial data, like stock prices and currency exchange rates.

The graph would be a straight line with points (1,4), (2,6), (3,8), (4,10), and (5,12). This indicates that for 1 cart the total length is 4 feet, for 2 carts the total length is 6 feet, for 3 carts the total length is 8 feet, for 4 carts the total length is 10 feet, and for 5 carts the total length is 12 feet.

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The combination of two linear equation (x-1) and (x-3) is equal to zero according to the extended equation (x2 - 4x + 3) = 0.

1. Expand (x-1)²: x² - 2x + 1

2. Multiply the result with (x-3): x² - 2x + 1 * x - 3 = x³ - 5x² + 3x - 3

3. Simplify the equation: x³ - 5x² + 3x - 3 = 0

It is possible to solve the equation (x-1)2(x-3) = 0 by multiplying the two linear equations (x-1) and (x-3). (x-1) can be expanded as x2 - 2x + 1 since it is a square. This value will be obtained by multiplying it by (x-3): x3 - 5x2 + 3x - 3. This indicates that the two linear expressions (x-1) and (x-3) have the same product, which is equal to zero. We can make the extended form equal to zero and then solve for x to solve the equation. As a result, we will have two solutions: x = 1 and x = 3. This indicates that the equation will be true when either x = 1 or x = 3. The product of two linear expressions (x-1) and (x-3) is equal to zero, as shown by the expansion of the equation (x-1)2(x-3) = 0 to (x2 - 4x + 3) = 0. Set the expanded form equal to zero and search for x to solve the equation. This will yield two answers: x = 1 and x = 3.

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The questions are:

Is the prize in the first five boxes?

Is the prize in the first two and a half boxes?

Is the prize in the first or second box?

To find the prize with the fewest number of questions, we can use the binary search algorithm.

The algorithm works as follows:

Ask if the prize is in the first five boxes or the last five boxes.

Based on the answer, eliminate half of the boxes from consideration.

Repeat this process until only one box remains.

The fewest number of questions you can ask is log base 2 of the number of boxes, which in this case is log base 2 of 10, or approximately 3 questions.

The questions are:

Is the prize in the first five boxes?

Is the prize in the first two and a half boxes?

Is the prize in the first or second box?

Note that the exact wording of the questions may differ depending on the specific rules of the game show, but the principle remains the same.

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Answer:

Step-by-step explanation:

12.6x-4.9x=123.2

63x over 5 -4.9x-123.2

If 7 out of every 9 people had Internet access, then 2 out of every 9 people did not have Internet access. The fraction of the world population that did not have Internet access in that year would be 2/9.

A fraction represents a portion of a whole or, more broadly, any number of equal pieces; a fraction describes the number of parts of a specific size, for example, one-half.

A fraction is a portion of a larger total. The number is stated in arithmetic as a quotient, which is the numerator divided by the denominator. Both are integers in a simple fraction. A complicated fraction contains a fraction in either the numerator or the denominator. A suitable fraction has a numerator that is smaller than the denominator.

There are three primary forms of fractions in mathematics. Proper fractions, improper fractions, and mixed fractions are the three types. Fractions are phrases that have a numerator and a denominator. We describe its kinds based on these two concepts.

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