Part A

Create a random triangle, ΔABC. Measure and record its angles.

Answer:

let the position vector of A,B,C,D and E be OA,OB,OC,OD andOE respectively.

IN triangle OBD , OE = OD+OB/2

OE=OA+AB+OD/2. (in triangle,OB=OA+AB)

OE=OA+OD+DC/2

OE=OA+OC/2. (in triangle ODC,OD+DC=OC)

proved....

It is important to look at many companies to invest and compare their advantages to one another before investing money in a company by purchasing stock.

It's crucial to research a variety of businesses before investing your money in them because you can compare their advantages to one another and determine which one will provide you with a higher return on your investment in addition to a guaranteed return.

It's crucial to take into account a company's financial fundamentals when choosing stocks, such as earnings, operating margins, and cash flow. When considered collectively, these elements can provide a fair picture of the company's current financial situation as well as its prospects for short- and long-term profitability.

Diversification is a portfolio's greatest asset. With diversity, you can more easily manage risk, weather market downturns, and generate better long-term returns. Due to these factors, you'll need a variety of stocks in various industries that can counteract one another.

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The examples that represent the importance of determining the number of bacteria in a sample are determining the quality of milk, assessing the purity of food or water , testing to see if a patient has a bladder infection.

It is necessary to count the number of organisms present in a sample of a material, such as water, food, or a bacterial culture. Bacterial pathogens, for instance, can enter food at any point, including during growth/production at the farm, processing, handling, and packaging, as well as when the food is prepared in the kitchen . While pathogenic bacteria in tiny quantities are typically not harmful, poor storage and/or cooking practices can cause these germs to grow to dangerously high concentrations .Another method bacteria can be introduced into water is by faecal contamination . Gram-negative, non-spore-forming bacteria called coliforms can ferment lactose to create acid and gas. Fecal coliforms are a subset of these bacteria that are prevalent in both human and animal intestines. Other fecal coliform bacteria are frequently utilized as indicator species since they are rarely observed thriving in nature when there is no fecal pollution. The presence of E. coli signals the presence of feces, which raises the possibility of the presence of dangerous pathogens including Salmonella species and Campylobacter species.

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Answer:

the second option

Step-by-step explanation:

the limit coming to x = 4 from the left (the '-' side) is -4.

the limit coming to x = 4 from the right (the '+' side) is 2.

it does not matter that the point itself is excluded. but the tendency of the function coming from the right is clear and defined.

the one-sided limit would not exist, if the function violently oscillates at the limit point.

or if the limit is infinite. then officially it does not exist, but we can write ±infinite.

for the case of the violent oscillation there is nothing else we can write but DNE.

The expression of the nth term of the sequence is 1/n

From the question, we have the following parameters that can be used in our computation:

The sequence definition

From the sequence, we can see that only the denominator increaes by 1

The numerator is constant at 1

Using the above as a guide, we have the following:

Tn = 1/n

Hence, the expression is 1/n

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The expression that represents how much he will spend would be = y ( 5p + 1d)

The amount of money that each pizza(p) is sold = $5 each.

The amount of money that each drink(d) is sold = $1.

The total money that Matthew may spend on the party is represented by = y.

Therefore the expression that will show how much he will spend would be = y ( 5p + 1d).

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Answer: The equation to find the time when the ball is 4 feet above the ground is:

-16t^2 + 10 = 4

We can solve for t by subtracting 4 from both sides:

-16t^2 + 6 = 0

And then dividing both sides by -16:

t^2 = -6 / -16

t^2 = 3/8

Taking the square root of both sides:

t = ±√(3/8)

Since time cannot be negative, we choose the positive solution:

t = √(3/8)

So the ball will be 4 feet above the ground after √(3/8) seconds.

Step-by-step explanation:

The expression that will be not equal to -{-20} are -20,{-20}. The correct options are B and D.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is -(-20). The not equivalent expressions are written below,

-(-20) ≠ 20

-(-20) ≠ {-20}

Therefore, expressions like -20, and -20 will not be equal to —20. B and D are the appropriate choices.

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The actual dimensions of the walk-in closet are 4 feet × 6.67 feet.  

To find actual dimensions multiply the given measurement with the measurement given in scale.

In the given problem, given that 1 in = 10 feet which is the scale given, we need to multiply the given measurements that are in the plan with the scale measurement 10 feet.

Here we have

A floor plan is given for the first floor of a new house.

One inch represents 10 feet.

The walk-in closet is 2/5 in. × 2/3 in. on the floor plan  

As we know 1 inch  = 10 feet

=> 2/5 in = (2/5) × 10 feet = 4 feet

=> 2/3 in = (2/3) × 10 feet = 6.67 feet

Therefore,

The actual dimensions of the walk-in closet are 4 feet × 6.67 feet.  

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Robert W. Fogel, in his famous article, used data from one year, 1890, to make inferences about a longer time period, 1850-1890. He did so through the use of statistical methods, including regression analysis and comparative economic growth analysis.

The basic idea behind this approach is to use the data from 1890 as a snapshot of the state of the economy at that time and to use this information to make inferences about the longer time period. The assumption behind this approach is that the data from 1890 is representative of the economy over the entire period 1850-1890, and that the underlying trends and patterns that existed in 1890 were also present in the earlier period.

Fogel used a combination of economic theory, demographic data, and historical information to validate his assumptions and to support his conclusions. He also conducted extensive sensitivity analysis to ensure that his results were robust to different assumptions and data sources.

In conclusion, while using data from one year to draw conclusions about a much longer time period might seem unconventional, it was a valid approach used by Robert W. Fogel in his research and allowed him to make important contributions to our understanding of the economic history of the United States.

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Ethan deposited 400 each month into his IRA for 31 years.

This totals 148,800 (400 x 31 years = 12,400 x 12 months = 148,800). Upon retirement, Ethan's total savings was 709,165.25. To determine the amount of interest he made, we subtract the total deposits from the total savings: 709,165.25 - 148,800 = 560,365.25. This shows that Ethan made 560,365.25 in interest on his retirement savings over the 31 years. The formula used to calculate the amount of interest Ethan made is: Interest = Total Savings - Total Deposits.Ethan deposited $400 each month into his IRA for 31 years.

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Answer:

Soup B

Step-by-step explanation:

Soup A = 5 grams sodium = 12 cups

Soup B = 8 grams of sodium = 13 cups

Find the unit rate, so, soup B has more sodium.

I hope this helps.

Also, next time can you write the question entirely?

Answer:

Step-by-step explanation:

To determine whether VY is parallel to ZW, we need to see if the ratio of their corresponding sides is equal.

The ratio of corresponding sides of two parallel lines is constant, so we can set up an equation to compare the ratios:

ZV/ZX = WX/YX

6/18 = 24/16

Simplifying the fractions, we get:

1/3 = 3/2

Since the two sides of the equation are not equal, VY is not parallel to ZW.

Answer:

1/6

Step-by-step explanation:

You can change 1.5 into a fraction.
1.5 = 3/2
Now you can multiply the two fractions easily: the two numerator values multiply and the two denominator values multiply.
1/9 * 3/2 = 3/18.

You can further simply this fraction by noting that 3 divides into 18.

So the answer is 1/6.

Answer:

it will take approximately 3 and 1/3 days for 12 chickens to lay 100 eggs.

Answer:

Step-by-step explanation:

12, 28, 44, 60

1, 3, 5, 7, 11

9, 25, 49, 81

4, 8, 15, 16, 20

Answer:

1. 12 , 24 , 36 , 48 , 60

2. 1, 3, 5, 7, 9

3. 9, 27, 45, 63, 81

4. 1, 2, 15, 16, 20

Step-by-step explanation:

1. The rule is +12, or add 12.

2. The rule is +2, or add 2.

3. The rule is +18, or add 18.

4. The rule is +1, +13, +1, +4, or add 1, add 13, add 1, add 4.

Precession and nutation are two distinct motions of a spinning top or gyroscope. Precession is a slow, uniform motion that results from the gravitational force acting on a spinning top or gyroscope.

It is a slow, uniform motion in which the spinning object's axis of rotation moves in a cone-like motion.

Nutation is a fast, non-uniform motion that is caused by the torque of a nearby force. It is a rapid, irregular motion that causes the spinning object's axis of rotation to wobble back and forth.

Precession is a regular, predictable motion, whereas nutation is an unpredictable, irregular motion. Precession is typically used to describe the motion of a satellite or planet in its orbit, while nutation is used to describe the motion of a spinning top or gyroscope.

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Precession and nutation are two different types of rotational movements in astronomy.

Precession refers to the slow, conical movement of an object's rotational axis, which changes the orientation of the object over time. In the case of Earth, precession causes the direction of the North Pole to change over time.

Nutation, on the other hand, is a rapid, irregular movement of an object's rotational axis. It is caused by the combined gravitational forces of the Sun, Moon, and other celestial bodies on the Earth. Unlike precession, nutation occurs in small, cyclical changes in the orientation of the rotational axis, causing the axis to move slightly back and forth.

In summary, precession is a slow, systematic change in the orientation of an object's rotational axis, while nutation is a rapid, irregular movement of the axis caused by external forces.

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On solving the provided question, we can say that value of the equation , h = [tex]\frac{M}{Zg} + f[/tex]

Two assertions in a mathematical equation are joined by the equal sign (=), which stands for equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places a space between the variables 3x + 5 and 14. The connection between the two sentences on either side of a letter is explained by a mathematical formula. Typically, there is only one variable, which also serves as the symbol. In this case, 2x4=2.

here,

the equation

[tex]Z=\frac{M}{g(h-f)}[/tex]

[tex]for, h , \\h - f = \frac{M}{(Zg)}\\h = \frac{M}{Zg} + f[/tex]

value of the h will be [tex]\frac{M}{Zg} + f[/tex]

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The end behavior of the function f(x) = 2ˣ - 5 will be increasing only.

Let a be the initial value and x be the power of the exponent function and b be the increasing factor.

The exponent is given as

y = a(b)ˣ

The function is given below.

f(x) = 2ˣ - 5

We know that the function is an exponential function. And the exponential function is always inceasing.

Thus, the end behavior of the function f(x) = 2ˣ - 5 will be increasing only.

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Answer:

D

Step-by-step explanation:

AD≅AB because they are tangent segments from the same point, A

x² + 2 = 11

x² = 9

x = √9 = 3, -3  (two solutions of [tex]\sqrt{9}[/tex])

Answer:

70

Step-by-step explanation:

Find the number pattern (check image)

The shape consisting of 28 squares will have 812 sticks.

From the given data, we can see that the number of squares is increasing by consecutive odd numbers, starting from 1:

1, 3, 6, 10, 15, ...

Also, the number of sticks is increasing by consecutive even numbers, starting from 4:

4, 10, 18, 28, 40, ...

This suggests that the number of sticks required to make a pattern of n squares can be found using the formula:

sticks = 2n + (n-2) + (n-4) + ... + 4

This formula represents the sum of the first n even numbers, which can be simplified to:

sticks = n(n+1)

Using this formula, find the number of sticks required to make a pattern of 28 squares:

sticks = 28(28+1) = 28(29) = 812

Therefore, a shape consisting of 28 squares will have 812 sticks.

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The equation [tex]$x^2-13x+4=0$[/tex] is a quadratic equation and can be solved using the quadratic formula.

The sum of the squares of the solutions of the equation [tex]$x^2-13x+4=0$[/tex]can be found in the following steps:

Solve for the solutions: The equation can be solved using the quadratic formula. The solutions are given by

[tex]$x = \frac{13 \pm \sqrt{13^2 - 4 \cdot 4}}{2 \cdot 1} = \frac{13 \pm \sqrt{169 - 16}}{2} = \frac{13 \pm \sqrt{153}}{2} = \frac{13 \pm 9}{2} = 11$ or $-6$.[/tex]

Square the solutions: Find the square of each solution by raising it to the power of 2.

[tex]$11^2 = 121$ and $(-6)^2 = 36$.[/tex]

Sum the squares: Add the squares of the solutions together to get the final answer: 121 + 36 = 157.

Therefore, the sum of the squares of the solutions of

[tex]$x^2-13x+4=0$[/tex] is 157.

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For the values 44. 4, 43. 8, 45. 6, 45. 9, 44. 1, 45. 6, 44. 0, 44. 9, 45. 8, the mean of the data set is 49.52. The Mean Absolute Deviation (MAD) of the data set is 4.83.

To find the mean of the given data set, we add up all the values and divide by the number of values:

Mean = (44.4 + 43.8 + 45.6 + 45.9 + 44.1 + 45.6 + 44.0 + 44.9 + 45.8) / 9 = 445.7 / 9 = 49.52

So, the mean of the data set is 49.52.

To find the Mean Absolute Deviation (MAD), we first find the absolute difference between each value and the mean, and then find the mean of these absolute differences:

Absolute Difference = |44.4 - 49.52|, |43.8 - 49.52|, ..., |45.8 - 49.52|

MAD = (Absolute Difference1 + Absolute Difference2 + ... + Absolute Difference9) / 9

Calculating the MAD gives:

MAD = (5.12 + 5.72 + 3.92 + 3.62 + 5.42 + 3.92 + 5.52 + 4.62 + 5.32) / 9 = 43.5 / 9 = 4.83

So, the Mean Absolute Deviation (MAD) of the data set is 4.83.

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Answer:

  P ∈ {3, 5, 6, 8}

Step-by-step explanation:

You want the possible perimeter values such that there can only be one triangle with that perimeter and integer side lengths.

The requirement that the triangle satisfies the triangle inequality means the longest side must be shorter than P/2.

The smallest triangle with integer side lengths is the {1, 1, 1} equilateral triangle.

  P=3, {1, 1, 1}

For P=4, the longest side can be neither 1 nor 2, so P=4 is not an option.

For P=5, the longest side can be 2, requiring the other sides to be 2 and 1:

  P = 5, {2, 2, 1}

For P=6, the longest side must be less than 3, so all sides must be 2.

  P = 6, {2, 2, 2}

For P=7, two triangles are possible: {3, 3, 1} and {3, 2, 2}.

For P = 8, the longest side must be less than 4, so will be 3. The other two sides must be 3 and 2.

  P = 8, {3, 3, 2}

For all values of P above 8, there are at least two possible triangles.

Possible values of P are 3, 5, 6, 8.

Answer:

1.25a

Step-by-step explanation:

Original value = a

An increase of 25% can be found by a x 25/100 = 0.25a

The resulting increased value = Original value + Increase in value

= a + 0.25a

= 1.25a

Sometimes it is a more direct approach to use the final value as original value(1 + increase%/100) in which case it would be a(1+25/100) = a(1 + 0.25) = a(1.25) = 1.25a

The minimum height of the cone is 17.87 in (approx)

In geometry, the cylinder is a fundamental 3 dimension shape that has two parallel circular bases at a distance. The two circular bases are joined by a curved surface, at a fixed distance from the center.  

Total surface area, A = 2πr²+ 2πrh square units

The volume of the Cylinder, V = πr²h cubic units

Here we have

A cylindrical can with an open top is to be constructed so that

The volume of the cone is 167 in³  

As we know volume of cone = (1/3) πr²h

=> (1/3) πr²h = 167

=> h = 501/πr²  

As we know Surface Area of the cone = 2πrh + 2πr²  

Substitute h = 501/πr² in Surface Area of cone  

=> SA = 2πr(501)/πr² + 2πr²  

=> SA = 1002r⁻¹+ 2πr²        

Differentiate SA with respect to r

=> SA' = (-1) 1002r⁻²+ 4πr  

=> SA' = - 1002r⁻² + 4πr  

Here  - 1002r⁻² + 4πr = 0

=>  - 501r⁻² + 2πr = 0  

=>  - 501/r² + 2πr = 0  

=>  [-501 + 2πr³ ]/r² = 0

=>  [-501 + 2πr³ ] = 0  

=>  2πr³ = 501

=>  πr³ = 250.5

=>  r³ = 79.70

=>  r = 8.92  (approx)

Hence the height of the cone, h = 501/πr²    

= 501/π(8.92)

= 17.87 (approx)

Therefore,

The minimum height of the cone is 17.87 in (approx)  

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Answer:

379.25

Step-by-step explanation:

20.5% of 1850 means 20.5/100 × 1850

0.205×1850

= 379.25

therefore 20.5% of 1850 is 379.25

Answer:

x= -3

Hope this helped

Answer:

90,217.77

Step-by-step explanation:

We can use the equation S+RS=M to figure this out where S is the initial salary before the raise, R being the rate at which the salary is increased, and M being the Salary after the raise.

By plugging it in for the first year we get

77,000+2%*77,000=M

Solving it, we get 78,540 and since there is a new salary increase 78,540 is the new starting salary

78,540+78,540*2%=80,110.8

80,110.8+80,110.8*2%=81,713.016

83,347.27632

85,014.2218464

86,714.506283328

88,448.796408995

90,217.772337175

Or rounded up

90,217.77