Work out the mean for the data set below:


58002

,



58003

,



58002

,



58003

,



58003

,



58005

,



58003

The measurements in the given triangle ABC are A=64°, B=26°,

C=90°, a=7.4, b=3.61, c=8.23

An angle is a figure in Euclidean geometry made up of two rays that share a terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are located in the plane where the rays are located. The meeting of two planes can also create an angle. These are referred to as dihedral angles. The angle formed by the rays lying perpendicular to the two intersecting curves at their point of intersection can likewise be used to establish an angle between two intersecting curves.

Given,

In ΔABC, A=64°, a=7.4

From the figure we know that C=90°, as the given figure is a right triangle.

As we already know that,

Angles sum in a triangle=180°

A+B+C=180°

64°+B+90°=180°

B=180°-154°

B=26°

By using sine rule,

a/SinA =b/SinB=c/Sinc

7.4/Sin 64°=b/Sin 26°=c/ Sin 90°

b=7.4Sin26°/Sin 64°

b=3.61

c=7.4 Sin 90°/Sin 64°

c=8.23

Therefore, the measurements in the given ΔABC are A=64°, B=26°,

C=90°, a=7.4, b=3.61, c=8.23

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Vertical lines have the form x = a, where a stands for the common x-coordinate of all points, while horizontal lines have the form y = b, where b denotes the y-intercept. Horizontal lines run left to right.

The link between two expressions on either side of the sign is represented by a mathematical equation. One variable and an equal sign are typically present. For instance, 2x – 4 = 2.

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."

Expressions that equal one another are the building blocks of an equation. The equation 4x2+3x = 22. A formula is an equation that has at least two variables and depicts the relationship between them.

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The equation y = 2x - 6 is a line in the form known as Slope-Intercept Form. This form organizes the equation so that you can easily discern the y-intercept and slope.

Slope-intercept form is y = mx + b. So here, m = 2, b = -6.

Answer:

growth

1.8%

Step-by-step explanation:

If the number raised to the power x is between 0 and 1, it is decay since as the exponent increases, the value of the power expression decreases.

For example, think of 0.1, a number between 0 and 1.

0.1^x

x = 1, 0.1^1 = 0.1

x = 2, 0.1^2 = 0.01

x = 3, 0.1^3 = 0.001

As you see, as x increases, the value of the expression decreases from 0.1 to 0.01 to 0.001

Now look at a power in which the base is greater than 1.

If the number raised to the power x is greater than 1, it is growth since as the exponent increases, the value of the power expression increases.

For example, look at 1.5^x

1.5^x

x = 1, 1.5^1 = 1.5

x = 2, 1.5^2 = 2.25

x = 3, 1.5^3 = 3.375

As you see, as x increases, the value of the expression increases from 1.5 to 2.25 to 3.375.

Now our problem:

y = 9200(1.018)^x

What base is raised to x?

Answer: 1.018

Since 1.018 is greater than 1, as the exponent, x, increases, the value of 1.018^x increases. Therefore, this is exponential growth.

1.018 = 1 + 0.018 = 1 + 1.8%

The percentage is 1.8%

The body has a kinetic energy of 2125000 joules, and the gravel mold has a volume of 11.9 cubic units.

Given that,

The Kinetic Energy of an object depends on the object's and velocity , and can be written as v = m

Kinetic Energy of an object with a mass = 1,700 kilograms

Traveling = 50 meters per second

Radius = 4.92 ft

Kinetic energy, which may be seen in the movement of an item or subatomic particle, is the energy of motion. Kinetic energy is present in every particle and moving object. Examples of kinetic energy in action include a person walking, a baseball soaring through the air, a piece of food falling from a table, and a charged particle in an electric field.

Kinetic Energy of a body is given by ,

1/2 mv²

Where m = mass = 1700 kg

v = velocity = 50m/s

Therefore ,

KE = 1/2 * 1700kg * 50m/s

KE = 2125000 J.

Now to calculate the volume

Let's assume that the solution to the problem will be found using your formula. If so, let's carry out the following operations when solving for v in the equation:

On multiplying the equation by 2, the outcome is

2[tex]r^{2}[/tex]

=3[tex]\sqrt{3V}[/tex]

To find volume

enter (v=(2[tex]r^{2}[/tex])/33)

rationalize the right side of the equation's numerator.

v=(2π[tex]r^{2}[/tex] )

A simplified version of 3/333 is

v=(2[tex]r^{2}[/tex])3/9.

Substitute

v=(23.143.1523)/9

v=11.9.

Therefore,

The body has a kinetic energy of 2125000 joules, and the gravel mold has a volume of 11.9 cubic units.

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The solution to the given inequality is x ≤ -18 which is the correct answer that would be an option (D).

The inequality is given in the question as:

3 -x/2 ≥ 12

To solve this inequality, we need to isolate the variable x. To do this, we can start by subtracting 12 from both sides of the inequality:

3 - x/2 ≥ 12

3 - x/2 - 12 ≤ 0

Next, we can simplify the left side of the inequality by combining like terms:

-x/2 - 9 ≤ 0

Finally, we can solve for x by adding 9 to both sides and multiplying both sides by -2:

x ≤ -18

Thus, the solution to the inequality is x ≤ -18.

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If stockholder's equity of $350,000 and net income of 59,400. Payout ratio of 20% and return on assets of 9%. The amount that paid in cash dividends is $11,880  and  its average total assets is $660,000.

a. Cash dividend:

Cash dividend = Net Income ×Dividend Payout Ratio

Cash dividend = $59,400 × 20%

Cash dividend = $11,880

b. Average Assets:

Average Assets = Net Income × Return on Assets

Average Assets = $59,400 / 9%

Average Assets = $660,000

Therefore the amount that paid in cash dividends is $11,880  and  its average total assets is $660,000.

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Answer: The equation 8y-5xy=9 is nonlinear because it contains the product of the variables x and y. In general, an equation is linear if it can be written in the form ax + by = c, where a and b are constants and x and y are variables. Equations that cannot be written in this form are nonlinear.

To derive the formula that goes through these two points, we use the general equation for an exponential equation.

Y = a(b)^x

There we will substitute the two points into this equation to get two equations

45 = a(b)^2

5/9= a(b)^-1

By dividing the first equation by the second, we obtain:

27 = b^3

Therefore b= 3

We plug b=3 into the first equation using the second point:

45 = a(3)^2

We get a = 5

Therefore the equation is y = 5(9)^x

We can verify this equation by plugging in the two points given to see if it works.

5/9 = 5(9)^-1

5/9 = 5/9

And:

45 =5(9)^2

45 = 45

It does, so the equation is correct.

The answer is y =5(9)^x

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The probability that the dial stops on a yellow or blue slice will be 0.6667.

What is probability?

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the probability is given as,

P = (Favorable event) / (Total event)

A spinner with 12 similarly measured cuts has 5 yellow cuts, 3 blue cuts, and 4 red cuts. The dial is turned and stops on a cut indiscriminately.

The total number of the event is given as,

Total events = 5 + 3 + 4

Total events = 12

The probability that the dial stops on a yellow or blue slice will be given as,

P = 3 / 12 + 5 / 12

P = 0.25 + 0.4167

P = 0.6667

The probability that the dial stops on a yellow or blue slice will be 0.6667.

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True, at high temperatures, the partition function for rotational energy of a molecule of nitrogen is k T ϵ, where ϵ is the energy [tex]z_{rot}=\sum_{j=0}^{\infty}(2j+1)e^{-j(j+1)\epsilon/kT}[/tex].

As we know the rotational energy levels of a diatomic molecule are given by,

[tex]E_{rot}[/tex] (J) = BJ(J+1)

Where, B is the rotational constant.

From explicit summation, expression for rotational partition function ([tex]z_{rot}[/tex]), Equation 18.6.518.6.5, we can do an explicit summation

[tex]z_{rot}=\sum_{j=0}^{\infty}(2j+1)e^{-j(j+1)\epsilon/kT}[/tex]

When the rotational energy levels are lying very close to one another, we can integrate just as above, and we gets the equation you just provided.

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The right question is:

At high temperatures, the partition function for rotational energy of a molecule of nitrogen is k T ϵ, where ϵ is the energy  in Eq. 6.29.

[tex]z_{rot}=\sum_{j=0}^{\infty}(2j+1)e^{-j(j+1)\epsilon/kT}[/tex]

A True

B False

The distance that tire covered in 8 rotations with diameter 25 inches is 628in using circle circumference's formula .

What is circumference of circle ?

The circumference of a circle is defined as the linear distance around it. In other words, if a circle is opened to form a straight line, then the length of that line will be the circle's circumference.

The formula is :

2πr where r is the radius of the circle.

We know that diameter = 2*radius.

Given diameter = 25 inches

So, the radius = 25/2 inches.

So, the circumference = 2*(22/7)*(25/2)

Circumference of circle = distance covered by tire in one rotation.

So, the distance covered in 8 rotations = 8 * circumference

                                                                  = 8* 2*(22/7)*(25/2)

                                                                  = 628.5 inches

                                                                  ≈ 628 in

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In linear equation, 15 millimeters of the substance containing 6% sandalwood must he use.

What is  a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                                           The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

x = amount of second substance

x + 5 = amount of first and second substances combined.

(0.02)5 ml + (0.06)x ml  = (0.05)(x+ 5)ml

0.1 ml  + (0.06)x ml = (0.05)x ml + (0.25) ml

(0.06)x ml - (0.05)x ml = (0.25) ml - (0.10) ml

(0.01)x ml = (0.15) ml

x ml = 15 ml

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Answer:

the value of x is 10

Step-by-step explanation:

Since LMNO is a parallelogram, the opposite sides are parallel and have the same length. This means that NO and LM have the same length, which we can call y. We can write the following equations to represent the given information:

NM = x + 32

OL = 2x + 22

NO = y

LM = y

Since NO and LM have the same length, we can set their lengths equal to each other to find the value of y:

x + 32 = y

2x + 22 = y

We can solve this system of equations by setting the two equations equal to each other and solving for x:

x + 32 = 2x + 22

-x = -10

x = 10

Substituting the value of x back into the equations for NM and OL, we find that:

NM = 10 + 32 = 42

OL = 2(10) + 22 = 32

Therefore, the value of x is 10, and the lengths of NM and OL are 42 and 32.

The perimeter of triangle XYZ is calculated as: 48 units.

The perimeter of a triangle is found by summing all the lengths of the three sides of the triangle.

Given the following measures as shown in the image below as:

AC = 7

AB = 5

XY = 24

The perimeter of triangle XYZ = XY + YZ + XZ

Based on the triangle midsegment theorem, we have:

YZ = 2(AC) = 2(7)

YZ = 14

XZ = 2(AB) = 2(5)

XZ = 10

Therefore:

The perimeter of triangle XYZ = 24 + 14 + 10

The perimeter of triangle XYZ = 48 units.

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The leftover after dividing 102 by 5 is the quotient, which is:

Quotient 20

Remainder 2

102 5: Quotient and Remainder

The quotient and remainder method is one way to determine the quotient and remainder of a division. The dividend (102) and the divisor are already known to us (5). Now, we need to determine the residual and the quotient:

The Quotient and Remainder procedure is as follows:

20 quotient, 5 | 102 dividend, -10 2, and a reminder

As can be seen:

The remainder is 2, while the quotient is 20.

Sometimes, the remaining part is referred to as the "modulo," or simply "mod." This notation is used to say that:

102 mod 5 = 2

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The investment multiplier must be 2.5 i.e.Option (d).

What is an Investment multiplier?

The amount by which the growth in output or income exceeds the increase in investment is referred to as the investment multiplier. It is represented by the letter "k" and is calculated as the ratio of changes in investment and income.

Multiplier(k) = Change in income / change in investment = 1/ {1-MPC}

where MPC is the marginal propensity to consume

Given, MPC = 0.6

Then, the multiplier(k) = 1/( 1 - 0.6) = 1/ 0.4 = 10/4 = 2.5 times

Hence, the investment multiplier is 2.5 i.e.Option (d).

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The number wreaths that Ms. Brooks make will be 7 wreaths.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

It should be noted that an expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features. People make a distinction between an expression and a formula, with the former designating a mathematical object and the latter a claim about such objects

Here, Ms. Brooks has 2 pieces of ribbon to make wreaths. One piece is 18 yards long and the other is 17 yards long.

Since each wreath requires 5 yards of uncut ribbon, the number of wreaths that Ms. Brooks make will be:

= (18 + 17) / 5

= 35 / 5

= 7 wreaths.

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Answer:obtuse angle

Step-by-step explanation:

An obtuse angle is an angle of greater than 90° and less than 180°. It is bigger than an acute angle. It is smaller than a straight angle, which measures 180°. Angles are measured with a protractor obtuse angle is specifically present in hexagon and pentagon and others.

Formula for how high the ball rebounds on the nth bounce is 80 (3/4)ⁿ  ft and the rebound on 5th bounce is 14.24 ft.    

It is given that the ball is dropped from 80 ft and it rebounds (3/4)th of the height it has fallen.

Firstly , using logic ,

The height reached by the ball on its 1st rebound = 80(3/4) = 60 ft

Similarly , calculating on it's 2nd rebound = 60(3/4) = 45 ft

and on 3rd rebound = 45(3/4) ft.

This forms a sequence , known as GP (Geometric Progression).

A Geometric Progression in mathematics, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

Hence , here the first term : a = 60 ft

and common ratio is : r = 3/4

the general term for rebound on nth bounce

= 60 * (3/4)ⁿ⁻¹  = 80 (3/4)ⁿ  ft

Using the above expression , the rebound on 5th bounce                             = 60 * (3/4)⁵ = 14.24 ft.

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When one of the parent cell keeps dividing while the other matures, this is known as arithmetic growth. The early stages of geometric growth are characterized by slow expansion, whereas the latter stages are characterized by rapid expansion.

When one of the parent cell keeps dividing while the other matures, this is known as arithmetic growth. An illustration of arithmetic growth is the ongoing elongation of roots. The early stages of geometric growth are characterized by slow expansion, whereas the latter stages are characterized by rapid expansion.

The amounts added grow by a fixed rate of growth, expressed in percentages. Due to the fact that these remain constant while the amounts added rise, growth is then typically measured in doubling times.

Due to the fact that all populations of organisms have the potential to experience exponential growth, the concept of exponential growth is particularly intriguing in the field of population biology.

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(a) The point estimate of mean wine score for this pinot noir is 82.

(b) The point estimate of standard deviation wine score for this pinot noir is 9.6389.

Below table showing calculation of Point Estimate of Mean and Standard Deviation:

Score                                  X-X’                                  (X-X’)^2

87                                         5                                         25

91                                         9                                         81

86                                         4                                         16

82                                         0                                         0

72                                        -10                                       100

91                                         9                                         81

60                                        -22                                       484

77                                        -5                                         25

80                                        -2                                         4

79                                        -3                                         9

83                                         1                                         1

96                                         14                                       196

984                                                                                   1022

Mean(X’) = Total Score/n

n = Total number = 12

X’ = 984/12 = 82

Standard Deviation (σ) = √∑(X-X’)^2/(n-1)

σ = √1022/(12-1)

σ = √1022/ 11

σ = 9.6389

(a) The point estimate of mean wine score for this pinot noir is 82.

(b) The point estimate of standard deviation wine score for this pinot noir is 9.6389

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The value of x is :

x≤ -9 or x > -9

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

|x+9|=|-x-9|

Both the sides have absolute symbols, consider as below:

x+9 =  -x-9

=> 2x = -9 - 9 = -18

=> 2x = -18

=> x= -9

This means,  x≤ -9 or x > -9

For graph:

consider as below:

y =  |x+9|

y = |-x-9|

graph them without absolute symbols

consider upper v shaped graph. ignore downward v shaped graph

By taking some random values for x and finding the corresponding y values, we get the ordered pairs in the form of (x,y).

By plotting and joining those points, we get the graph as shown in the attachment.

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The number of dimes and quarters that Dan has will be 44 and 23, respectively.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Dan has a container loaded with quarters and dimes. He has 21 additional dimes than he has quarters. Generally, Dan has 67 coins.

Let 'x' be the number of dimes and 'y' be the number of quarters. Then the equations are given as,

x = y + 21               ...1

x + y = 67             ...2

From equations 1 and 2, then we have

y + 21 + y = 67

2y = 46

y = 23

Then the value of the variable 'x' is calculated as,

x = 23 + 21

x = 44

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The linear equation for y is y=9.

What is linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) component are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

-y+7 y-54=0

Add similar elements: -y+7 y=6 y

6 y-54=0

Move 54 to the right side

6 y=54

Divide both sides by 6

[tex]\frac{6 y}{6}=\frac{54}{6}[/tex]

Simplify

y=9

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Normal distribution curve is symmetric around the mean, it shows that values close to the mean happen more frequently than those distant from the mean.

A bell-shaped (symmetric) curve, the normal probability distribution or the normal curve. The mean of it is represented by and the standard deviation by σ.

In this example, the mean and median are both equal and lie in the center of the distribution; they are 64, and the standard deviation is 7, with 68% of the values falling within the first standard deviation, 95% within the second standard deviation, and 99.7% within the third. Once more, variance is equal to the standard deviation squared.

According to the normal distribution curve:

"the percent of women whose heights are between 64 and 69.5 inches" represents the values within 2 standard deviation.

Area from a value (Use to compute p from Z)

Value from an area (Use to compute Z for confidence intervals)

Let the parameters be

Mean 64

Standard deviation 2.75

Above 1.96

Below 1.96

Between 64 and 69.5

Outside -1.96 and 1.96

Area (probability) 0.4772

And that value is 95 % of the whole data

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The circumference is 12.56

This means that for any vector v in the vector space V, there is a vector 0 in V such that v + 0 = v.

This is known as the identity property, and it states that adding 0 to any vector in V does not change the original vector. The identity property is an essential part of the definition of a vector space.

In general, a vector space is a set of objects called vectors that can be added together and multiplied ("scaled") by numbers, called scalars. Scalars are often taken to be real numbers, but there are also vector spaces with scalar multiplication by complex numbers, rational numbers, or generally any field.

A vector space is a set V together with two operations that satisfy the eight axioms listed below.

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