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The value of x is  x€ {( x1=- 3/4+(√151)/4 i), (- 3/4  - (√151)/4 i)}

2X^2 + 3X + 20 = 0

Here we will use the Quadratic formula:

Once in standard form, identify a,b and c from the original equation and plug them into the quadratic formula.

2x∧2+ 3x +20=0

Give:

Here,

a= 2

b= 3

c= 20

x= (-3±√(3^2-4.2.20))/2a

x= (-3±√(3^2-4.2.20))/2.2

x= (-3±√(9-160))/(      2^(1+1) )

Now take x1 and x2 , as we have two signs + and -.

x1  = (-3+√(9-160))/(      2^2 )

x2   =   (-3-√(9-160))/(      2^2 )

x1  = (-3+√(-151))/(      2^2 )

x2  = (-3-√(-151))/(      2^2 )

x1   =   (-3+√(-151).  √(-1))/(      2^2 )  

x2   =   (-3-√(-151).  √(-1))/(      2^2 )

x1   =   (-3+√151.  i)/(      2^2 )  

x2   =   (-3-√151.  i)/(      2^2 )

x1   =   (-3+√151.  i)/(      4)  

x2   =  - (3+√151.  i)/(      4)

x1= - 3/4+(√151)/4 i

x2= - 3/4  - (√151)/4 i

x€ {( x1=- 3/4+(√151)/4 i), (- 3/4  - (√151)/4 i)}

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Answer:

to find the answers for the chart, just multiply 2 with the number of kites purchased and add twenty to the total. For example for 4, it would be 4x2 and then add 20 to the total.

For the equation, x stands for the amount of kites purchased. So, it would be 2(x) + 20.

Step-by-step explanation:

The image point is located at (16, 4).

Dilation is a type of transformation where the figure is enlarged or made smaller such that it preserves the shape but not size.

Every dilated image are similar figures to the original figure.

Given that, a point (8, 2) is dilated using a scale factor of 2.

A point (x, y) when dilated by a scale factor of k changes to (kx, ky).

Point (8, 2) will become,

(8 × 2, 2 × 2) = (16, 4).

Hence the dilated point is (16, 4).

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The height of the tree is 38 feet.

Trigonometry is a topic the requires determination of length/ distance or measure of angle of the position of an object from a reference point. Thus the trigonometric functions are required.

In the given question, let distance from Woody's eyes to the top of the tree be represented by x. Then applying the appropriate trigonometric function, we have;

Tan θ = opposite/ adjacent

Tan 70 = x/ 12

x = 12 * Tan 70

  = 12(2.7475)

x = 32.97

x = 33 feet

Thus,

the height of the tree = woody's eyes from the ground + distance from Woody's eyes to the top of the tree

                                    = 5 + 33

                                    = 38 feet

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A jar has 1000 coins, of which 999 are fair and 1 is double-headed. pick a coin at random, and toss it 8 times. given that you see 8 heads,  the probability that the next toss of that coin is also a head  1.

Since the coin is double-headed, each toss will always result in a head. Therefore, the probability of getting a head on the next toss is 1, or 100%.   This is because the coin has been identified as having two heads, and thus it can never land on a tail.

The coin is still subject to the laws of probability, so it is not guaranteed that it will always land on a head, but it does make the probability of getting a head on the next toss one hundred percent.   It is important to note, however, that this probability is only true for the specific coin, and not for any other coin in the jar. The other 999 coins in the jar are all fair coins, meaning that the probability of getting a head on the next toss is still 50-50.

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11,160 cubes can be fit in the prism.

The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

Given:

Cube edge length = 1/2 cm

We have a rectangular prism that measures

= (7 + 1/2)cm by 12cm by (15 + 1/2) cm.

So, the volume is

V = (7 + 1/2)cm x 12cm x (15 + 1/2)cm

   = 1,395 cm³

Now, a cube with an edge length of 1/2 cm has a volume of:

V' = (1/2cm)³

   = 0.125 cm³

Now, the number of cubes fitted

V/V' = ( 1,395 cm³)/(0.125 cm³)

       = 11,160

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So the image of the point (-9, -3) under the translation is (-7, -1).

Every point in the plane is translated by shifting it a predetermined distance in one direction to a new position. The translation moves the point (x1, y1) by the same horizontal and vertical distances to reach to point (x2, y2) if the image of the point (x1, y1) under a translation is (x2, y2) (x2, y2).

We can observe that the translation shifts the point -2 units to the right and 2 units up if we consider that the image of point (-3, -6) under a translation is (-1, -8).

By shifting the point -9 units to the right and -3 units up by 2 units, the image of the point (-9, -3) under the same translation may be found:

(-9 + 2, -3 + 2) = (-7, -1) (-7, -1)

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6. The costs are given as follows:

4 kites - $28.

7 kites  - $34.

10 kites - $40.

7. The linear function is defined as follows:

y = 20 + 2x.

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

y = mx + b.

In which:

From the table, the intercept b is given as follows:

b = 20.

When x increases by one, y increases by two, hence the slope m is given as follows:

m = 2.

Then the function is given as follows:

y = 2x + 20.

The costs are given as follows:

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The number of whole numbers that are less than n are n.

A horizontal line with uniformly spaced numerical increments is referred to as a number line.

The way the number on the line can be replied will depend on the numbers on the line.

The number's intended use is described in the question that goes with it, such as when graphing a point.

Locating numbers, comparing numbers, fractions and mixed numbers, decimals, integers, absolute value, addition, subtraction, inequalities, multiples, common denominators, and other mathematical concepts may all be taught using number lines, which are incredibly versatile manipulatives.

Here, we do not have the bounds of n.

Let the number n = m.

Then the number of whole number is m.

Example - the number is 5.

Then,

n > 5.

The whole numbers are 4, 3, 2, 1, 0.

Therefore, the explanation is given above.

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Answer:

To solve the inequality - 3x ≤ 3, using the table provided, we can see that when x = -2, the value of 3x is -6, which is less than 3. So the solution of the inequality -3x ≤ 3 is x ≤ 1.

The stated statement indicates that the item's new cost of goods sold is $37.7.

Exempt and non-exempt workers are the two basic categories into which employees fall. Your business may need to hire a variety of workers in order to function effectively and complete the task. This varies according to the type of organization.

A store manager gives his staff the order to mark up every item by 30%. The retailer paid $29 for the item, and 30% is shown in decimal form.

30/100 = 0.30

30% of the $29 = 0.30 × 29

                         = $8.7

Selling price of the item = Original price of item + 30% of the $29

                                       = $29 + $8.7

                                      = $ 37.7

Consequently, the item's new selling price is $37.7.

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Answer:

Divide 192 (students) by 3 ( buses).

192/ 3 = 64

Step-by-step explanation:

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The probability of getting exactly two heads when three coins are tossed is 25%, and the probability of getting one heads and one tail when three coins are tossed is 37.5%.

The probability of getting exactly two heads when three coins are tossed is 1/4 or 25%. This can be calculated using the formula for probability of an event: P(E) = Number of favorable outcomes / Total number of outcomes. In this case, the favorable outcome is two heads, and the total number of outcomes is 8 (2^3) since each coin has two possible outcomes (head or tail). So P(E) = 1/8 = 0.125 = 25%.

The probability of getting one heads and one tail when three coins are tossed is 3/8 or 37.5%. This can be calculated using the same formula as above. In this case, the favorable outcome is one heads and one tail, and the total number of outcomes is 8 (2^3). So P(E) = 3/8 = 0.375 = 37.5%.

The probability of getting exactly two heads when three coins are tossed is 25%, and the probability of getting one heads and one tail when three coins are tossed is 37.5%.

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Answer: (f∘g)(x)=15x

Step-by-step explanation:

The expression of (f∘g)(x) in the simplest form is (f∘g)(x)=15x and this can be determined by using the arithmetic operations.

Given :

f(x)=3x

g(x)=5x

The following steps can be used in order to determine the expression of (f∘g)(x):

Step 1 - Write the given function.

f(x)=3x

g(x)=5x

Step 2 - Now, replace 'x' with g(x) in order to determine the expression of (f∘g)(x).

(f∘g)(x)=3g(x)

(f∘g)(x)=3x5x

Step 3 - Simplify the above expression.

(f∘g)(x)=15x

The expression of (fog)(x) in the simplest form is (f∘g)(x)=15x

Answer:

see below

Step-by-step explanation:

Put first equation into second

18x+3*(-6x+7) =21

open up the bracket

18x -18x+21=21

21 = 21

so infinite many solutions

The required probability P(x< 75) is given as 0.8943, as of the given condition.

A Z-score is stated as the fractional model of data point to the mean using standard deviations.

here,
z = x - μ / σ

where, μ = mean and σ = standard daviation

From the question put the value in the above expression,
z = 75 - 60 / 12
z = 1.25

From z score table,
P(x < 75) = p(z < 1.25)
P(x< 75) = 0.8943

Thus, the required probability P(x< 75) is given as 0.8943.

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Answer:

143.2 L

Step-by-step explanation:

1 pm: 1870 L

Each hour, 14% is drained.

x - 14% of x = x - 0.14x = 0.86x

To decrease a number by 14%, multiply the number by 0.86

2 pm: 0.86 × 1870 L = 1608.2 L

3 pm: 0.86 × 1608.2 L = 1383.052 L

4 pm: 0.86 × 1383.052 L = 1189.4247 L

5 pm: 0.86 × 1189.4247 L = 1022.9052 L

6 pm: 0.86 × 1022.9052 L = 879.69847 L

From 5 pm to 6 pm, the volume decreased from 1022.9052 L to 879.69847 L:

1022.9052 L - 879.69847 L = 143.2068 L

Answer: 143.2 L

The side WX is perpendicular to side XY,

similarly,  XY is perpendicular to side YZ, YZ is perpendicular to side WZ, and side WX is parallel to size YZ.

so WXYZ is a square.

A line's slope is defined as the ratio of the change in the y coordinates to the change in the x coordinate.

Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.

Given the slope of WX = [4 - 1] / [3 - (-1)] = 3/4

the slope of XY = [0 - 4] / [6 - 3]

slope of XY = -4/3

the slope of YZ = [-3 - 0] / [2 - 6]

the slope of YZ = 3/4

slope of WZ = [-3 - 1] / [2 - (-1)] = -4/3

for the perpendicular slope, m₁m₂ = -1

or m₁ = -1/m₂

where m₁ is perpendicular to m₂

so the slope of WX = -1/(the slope of XY)

so WX is perpendicular to side XY,

similarly,  XY is perpendicular to side YZ, YZ is perpendicular to side WZ, and side WX is parallel to size YZ.

so the coordinates form a square.

Hence WXYZ is a square.

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The expected number of schools that will be attended by at least one top applicant is [tex]( M \cdot \left( 1 - \left( \frac{M-1}{M} \right)^N \right))[/tex].

If there are N top applicants and M schools to choose from, then the expected number of schools that will be attended by at least one top applicant is [tex]\frac{M \choose N}{M^N}[/tex]. This is because each of the N top applicants can choose any of the M schools independently, and the probability of any one top applicant attending any given school is[tex](\frac{1}{M})[/tex]. Thus, the probability of at least one top applicant attending any given school is[tex](1 - \left( \frac{M-1}{M} \right)^N)[/tex]. Therefore, the expected number of schools that will be attended by at least one top applicant is [tex]( M \cdot \left( 1 - \left( \frac{M-1}{M} \right)^N \right)).[/tex]

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Literally nothing occurs. On the off chance that the two terminals are at an equivalent voltage, no ongoing streams, any more than if you contacted two impartial bits of metal together.

Cases 1 and 3 are basically something very similar. There's a voltage difference, so current normally streams. In any case, you don't have a circuit, so when electrons stream from the lower positive voltage (which is zero assuming it's released) to the higher positive terminal, the electrons develop and make a static charge that balances the voltages. This occurs in a small part of a second, so the current is negligible, and voltage promptly stops.

The standard metric unit on electric potential difference is the volt, truncated V and named to pay tribute to Alessandro Volta. One Volt is identical to one Joule per Coulomb. In the event that the electric potential difference between two areas is 1 volt, one Coulomb of charge will acquire 1 joule of potential energy when moved between those two areas. In the event that the electric potential difference between two areas is 3 volts, one coulomb of charge will acquire 3 joules of potential energy when moved between those two areas.

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Option B is correct, the missing length is 12.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

We know that the corresponding sides are in proportion .

Let x be the missing length

9/6=x/8

Apply cross multiplication

72=6x

Divide both sides by 6

x=72/6

x=12

Hence, Option B is correct, the missing length is 12.

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Step-by-step explanation:

I don't understand explain further

The variables for this problem are classified as follows:

a) The number of songs on a randomly chosen ipod is discrete.

b) The number of people in line at the bank at a randomly chosen time is discrete.

c) The time it takes to drive to the airport is continuous.

d) The amount of rain during the next thunderstorm is continuous.

Variables are classified as continuous or discrete depending if they can assume decimal values, as follows:

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The value of cos(a - B) is 63/65.

option C.

The value of cos(a - B) is calculated by applying the following formula as shown below.

sina = 3/5,

sinb = 5/13

The values of cos(a) and cos(b) is determined by applying Pythagoras tipple.

sin = opp/hypo

third side = adj

if sin (a) = 3/5, cos (a) = 4/5

if sin (b) = 5/13, cos (b) = 12/13

cos (a - b) = cos(a)cos(b) + sin(a)sin(b)

cos (a-b) = (4/5 x 12/13)  +  ( 3/5 x 5/13)

cos ( a -b ) = ( 48 / 65 )  +  ( 3/13 )

cos ( a - b ) = ( 63/65)

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The claim that a random sample is representative of the population of interest is only true under certain conditions.

The concept of population and sample is crucial in conducting a survey. In a survey, a sample is a smaller group of individuals selected from a larger group, also known as the population.

When a sample is selected randomly from a population, it is said to be representative of the population of interest.

However, just because a sample is selected randomly does not guarantee that it is representative of the population.

Therefore, the claim that the sample of 500 students selected from the statistics classes is representative of the population of interest (all the students enrolled in the university) is only partially true.

If the population of all students enrolled in the university is homogeneous with respect to their opinions on foreign language classes, and if the random sampling process was carried out correctly, then it is possible that the sample is representative of the population.

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Answer:x = 7

Step-by-step explanation:

To solve the equation 9x = 7(x + 2), we can first expand the expression inside the parentheses:

9x = 7x + 14

Next, we can isolate x by subtracting 7x from both sides:

2x = 14

Finally, we can divide both sides by 2 to find the solution:

x = 7

The value of [tex]i^5[/tex] is i.

The correct option is (A).

Complex Numbers in Maths. Complex numbers are the numbers that are expressed in the form of a+ib where, a,b are real numbers and 'i' is an imaginary number called “iota”.

Given:

[tex]i^5[/tex]

Now, we have to expand the complex number

[tex]i^5[/tex] = i x i x i x i x i

   = (i)² x (i)² x i

As, the value of i² = -1

[tex]i^5[/tex] = (i)² x (i)² x i

   = (-1) x (-1) x i

   = 1 x i

   = i

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The probability that the average final exam grade of a sample of 45 students selected from this class is between 80 and 83 is approximately 0.0922.

The standard error of the mean is given by the formula: [tex]standard error=standard deviation / \sqrt{sample size}\\\\ = 8.2/\sqrt{45} \\\\ = 1.935[/tex]

Next, we can calculate the Z-scores for 80 and 83:

Z1 = (80 - 79.8) / 1.935 = 0.512

Z2 = (83 - 79.8) / 1.935 = 2.056

Finally, we can use a Z-score table or calculator to find the cumulative probability of a standard normal distribution between Z1 and Z2:

P(80 < Xbar < 83) = P(0.512 < Z < 2.056) = 0.0922

So the probability that the average final exam grade of a sample of 45 students selected from this class is between 80 and 83 is approximately 0.0922.

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If the right triangle has side lengths of 12 feet and 5 feet then the length of hypotenuse is 13 feet.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given that a right triangle has side lengths of 12 feet and 5 feet

We need to find the length of the hypotenuse.

By using pythagoras theorem we find hypotenuse.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides

12²+5²=x²

144+25=x²

169=x²

Take square root on both sides

x=13

Hence, if the right triangle has side lengths of 12 feet and 5 feet then the length of hypotenuse is 13 feet.

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