Which could be the function?

f(x) = (x + 4)2
f(x) = x2 + 4
f(x) = (x – 4)2
f(x) = x2 – 4.

The solution of the given problem of probability comes out to be P(not same color) = 236/361.

Calculating the likelihood that a statement is true or that an event will take place is the focus of probability theory, a branch of mathematics. Any number range between 0 and 1, where 1 is frequently used to describe certainty and 0 is commonly used to denote possibility, can be used to represent chance. A probability diagram shows the likelihood that a particular event will occur.

Here,

There are three cases to consider:

Case 1: both marbles are red

Case 2: both marbles are yellow

Case 3: both marbles are blue

The probability of drawing two red marbles can be found by multiplying the probability of drawing a red marble on the first draw (5/19) by the probability of drawing a red marble on the second draw (5/19):

P(red and red) = (5/19) ×  (5/19) = 25/361

Similarly, the probability of drawing two yellow marbles is:

P(yellow and yellow) = (6/19) × (6/19) = 36/361

And the probability of drawing two blue marbles is:

P(blue and blue) = (8/19) ×  (8/19) = 64/361

So, the probability of drawing two marbles that are the same color is:

P(same color) = P(red and red) + P(yellow and yellow) + P(blue and blue)

P(same color) = (25/361) + (36/361) + (64/361)

P(same color) = 125/361

d.

There are three cases to consider:

Case 1: one marble is red and one marble is yellow

Case 2: one marble is red and one marble is blue

Case 3: one marble is yellow and one marble is blue

The probability of drawing one red marble and one yellow marble can be found by multiplying the probability of drawing a red marble on the first draw (5/19) by the probability of drawing a yellow marble on the second draw (6/19), and then multiplying by 2 (since the order of the marbles doesn't matter):

P(red and yellow) = 2 × (5/19) × (6/19) = 60/361

Similarly, the probability of drawing one red marble and one blue marble is:

P(red and blue) = 2  × (5/19) × (8/19) = 80/361

And the probability of drawing one yellow marble and one blue marble is:

P(yellow and blue) = 2 × (6/19) × (8/19) = 96/361

So, the probability of drawing two marbles that are not the same color is:

P(not same color) = P(red and yellow) + P(red and blue) + P(yellow and blue)

P(not same color) = (60/361) + (80/361) + (96/361)

P(not same color) = 236/361

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Symbolab is the best derivative calculator that solves first derivatives, second derivatives, higher order derivatives, one point derivatives, partial derivatives, implicit derivatives, derivatives with definition and more.

Symbolab Derivative Calculator is free online tool for calculating derivatives of functions. It allows users to input the equations and then calculates the derivatives of those equations for the user. This tool is useful for students and professionals who need to calculate derivatives quickly and accurately.

The calculator supports a variety of mathematical functions, including exponential, polynomial, logarithmic and trigonometric functions. It also allows users to graph derived functions. The calculator is easy to use and can also save users time and effort. It can also be used to check the correctness of the derivative of a function.

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The coordinates of Room 1314 are given as follows:

(2, 13).

We are going to label the rooms are follows:

Then the coordinates of Room 1314 are obtained applying the proportions in the context of the problem.

Room 1314 is located five-sevenths of the distance from Room 1305 to Room 1324, hence the equation is given as follows:

Z - X = 5/7(Y - X).

Then the x-coordinate is obtained as follows:

x + 8 = 5/7(6 + 8)

x = 10 - 8

x = 2.

The y-coordinate is obtained as follows:

y + 2 = 5/7(19 + 2)

y + 2 = 15

y = 13.

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The probability of selecting the integer 318 is 0

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

Sample space = 1 to 50

The integer 318 is not in the range of integers that the random number generator can select from (1 to 50).

Hence, the required probability of selecting the integer 318 is 0.

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Members of Baby Boomers generation are retiring at a rate of 10,000 every 24 hours and will all be 65 or older by 2030.

There are 4 generational cohorts :

Baby Boomers(1946-1964)

Thirteeners/Gen X(1965-1980)

Millenials/Gen Y(1981-1996)

Centennials/Gen Z(1997-Present)

So , by the above stated data one can clearly say that the Baby Boomers are the oldest generational cohorts. They are the generation born after Second World War.

According to the last census which was taken in 2010 , none of them turned 65 but after that about 10,000 a day have attained that threshhold and by 2030 , all of the boomers are going to attain at least the age 65.

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Answer:

Multiply the denominator of the fractional part by the whole number, and add the result to the numerator.

For example, suppose you want to convert the mixed number to an improper fraction. First, multiply 3 by 5 and add 2:

(3 · 5) + 2 = 17

Use this result as your numerator, and place it over the denominator you already have.

Place this result over the denominator:

This method works for all mixed numbers. Furthermore, if you start with the fractional part reduced, the answer will also be reduced.

Step-by-step explanation:

Using trigonometric ratios the approximate horizontal distance from the observatory to the island is option A: 322 feet.

What is trigonometric ratio?

Triangle side length ratios are known as trigonometric ratios. In trigonometry, these ratios show how the ratio of a right triangle's sides to each angle. Sine, cosine, and tangent ratios are the three fundamental trigonometric ratios.

We can use trigonometry to solve this problem.

Let's call the horizontal distance from the observatory to the island "x".

Since we know the opposite side (150 ft) and the angle of depression (25 degrees), we can use the tangent function -

tan(25) = opposite / adjacent

tan(25) = 150 / x

Solving for x, we get -

x = 150 / tan(25)

Using a calculator, we find that -

x ≈ 322 feet

Therefore, the horizontal distance value is 322 feet.

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Answer:

Step-by-step explanation:

Using trigonometric ratios the approximate horizontal distance from the observatory to the island is option A: 322 feet.

What is trigonometric ratio?

Triangle side length ratios are known as trigonometric ratios. In trigonometry, these ratios show how the ratio of a right triangle's sides to each angle. Sine, cosine, and tangent ratios are the three fundamental trigonometric ratios.

We can use trigonometry to solve this problem.

Let's call the horizontal distance from the observatory to the island "x".

Since we know the opposite side (150 ft) and the angle of depression (25 degrees), we can use the tangent function -

tan(25) = opposite / adjacent

tan(25) = 150 / x

Solving for x, we get -

x = 150 / tan(25)

Using a calculator, we find that -

x ≈ 322 feet

Therefore, the horizontal distance value is 322 feet.

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Answer:

25 / 2

Step-by-step explanation:

12.5% = 125 / 10 ( simplify the fraction with 5 )

= 25 / 2

At 95% confidence, the margin of error for the population mean is:

3.920

The margin of error for the population mean can be calculated using the formula:

margin of error = (z-score)*(standard deviation/√(sample size))

Where z-score is the value that corresponds to the desired confidence level, standard deviation is the square root of the variance, and sample size is the number of items in the sample.

Given that the variance is 900, the standard deviation is √(900) = 30. The sample size is 225, and the z-score for a 95% confidence level is 1.96.

Plugging these values into the formula, we get:

margin of error = (1.96)*(30/√(225))

margin of error = (1.96)*(30/15)

margin of error = (1.96)*(2)

margin of error = 3.92

Rounding to three decimal places, the margin of error is 3.920.

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The negation of the proposition posed the statement is:

"Every student in this class has seen a computer."

The negation of the proposition "There is a student in this class who has never seen a computer" can be expressed using quantifiers as follows:

∀ x ∈ S, ∃ y ∈ C (x has seen y)

This means "For all students x in the class S, there exists a computer y in the set of computers C such that x has seen y."

In English, the negation of the proposition can be expressed as "Every student in this class has seen a computer."

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Press fit is calculated by determining the required force to assemble two cylindrical parts, using the interference between them and their material properties.

Press fit is calculated by determining the amount of interference between two cylindrical parts and their material properties. The interference is the difference between the diameter of the shaft (male part) and the diameter of the hole (female part). The required force to assemble the parts is then calculated using the material properties of both parts and the amount of interference. The interference is typically expressed as a percentage of the shaft diameter, and the required force is expressed in pounds or newtons.

Calculating the press fit is important for ensuring that the parts are securely and correctly assembled, and for preventing excessive stress or deformation in either part. Press fit calculations are commonly used in mechanical engineering and manufacturing applications.

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A. Two equivalent expressions that represent the new average are x = v - 0.12v and x = 0.88v.

B. Another way to find the new average directly using:

x = 0.88v (using the second expression )

In mathematics, an expression is a combination of numbers, symbols, and/or operators that represent a value or a relationship between values. Expressions can be as simple as a single number, variable, or symbol, or they can be complex combinations of terms, functions, and operations.

For example, the expression "2x + 3" is a combination of the number 2, the variable x, and the operators + and *. It represents a relationship between x and a value that is 3 more than twice x.

Expressions can be used in a wide range of mathematical contexts, including algebra, calculus, geometry, and statistics, to name a few. They are an essential tool for describing and solving mathematical problems.

A. Let x be the new acreage after the sale. Then we have:

x = v - 0.12v (12% decrease means 0.12v decrease from v)

x = 0.88v (Simplify by factoring out v)

So, two equivalent expressions that represent the new average are x = v - 0.12v and x = 0.88v.

B. Another way to find the new acreage is to multiply the original acreage by the decimal equivalent of the percent decrease. In this case, the percent decrease is 12%, which is equivalent to 0.12 as a decimal. So, we have:

x = v - 0.12v (using the first expression above)

x = 0.88v (simplify)

x = (1 - 0.12)v (factor out v)

x = 0.88v (simplify)

Alternatively, we can calculate the new average directly using:

x = 0.88v (using the second expression above)

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Answer:A.Two equivalent expressions that represent the new average are x = v - 0.12v and x = 0.88v.B.Another way to find the new average directly using:x = 0.88v (using the second expression )What is expression ?In mathematics, an expression is a combination of numbers, symbols, and/or operators that represent a value or a relationship between values. Expressions can be as simple as a single number, variable, or symbol, or they can be complex combinations of terms, functions, and operations.For example, the expression "2x + 3" is a combination of the number 2, the variable x, and the operators + and *. It represents a relationship between x and a value that is 3 more than twice x.Expressions can be used in a wide range of mathematical contexts, including algebra, calculus, geometry, and statistics, to name a few. They are an essential tool for describing and solving mathematical problems.A. Let x be the new acreage after the sale. Then we have:x = v - 0.12v (12% decrease means 0.12v decrease from v)x = 0.88v (Simplify by factoring out v)So, two equivalent expressions that represent the new average are x = v - 0.12v and x = 0.88v.B. Another way to find the new acreage is to multiply the original acreage by the decimal equivalent of the percent decrease. In this case, the percent decrease is 12%, which is equivalent to 0.12 as a decimal. So, we have:x = v - 0.12v (using the first expression above)x = 0.88v (simplify)x = (1 - 0.12)v (factor out v)x = 0.88v (simplify)Alternatively, we can calculate the new average directly using:x = 0.88v (using the second expression above)

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The conversion of 65 kilos in pounds is equivalent to approximately 143.3 pounds.

Its name derives from the Latin word "poundus" meaning "weight". The £ symbol comes from an ornate L in Libra. The pound was a unit of currency as early as 775AD in Anglo-Saxon England, equivalent to 1 pound weight of silver.The approximation we use for kilograms (kg) to pounds (lb) is 1 kg = 2.2 lb. To convert from kilogram to pound, we multiply by 2.2. To convert from pound to kilogram, we divide by 2.2.

To convert 65 kilograms to pounds, you can use the conversion factor of 1 kilogram = 2.20462 pounds.

Therefore,65 kilograms = 65 x 2.20462 pounds= 143.3003 pounds (rounded to 4 decimal places)

So, 65 kilograms is equivalent to approximately 143.3 pounds.

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The value of x is 10

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

The large triangle is divided into 2 similar triangles

The ratios of corresponding sides are equal

8/12 = x+4/2x+1

=> 8( 2x+1) = 12( x+4 )

=>  16x+8 = 12x+48

=> 16x-12x = 48-8

=> 4x = 40

=> x= 40/4 = 10

The value of x is 10

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Answer:10 cm

Step-by-step explanation:

Answer:B 24 cm

Step-by-step explanation:

Applying the angles addition postulate, m<KJL = 132°.

The Angles Addition Postulate is a fundamental property of angles in geometry that explains how to find the measure of an angle that is formed by two adjacent angles. According to this postulate, the measure of the larger angle, which is formed by two adjacent angles, is equal to the sum of the measures of the two smaller adjacent angles.

Given the following:

m <1 =79°

m<2 = 53°

Thus, we have:

m<KJL = m<1 + m<2

Substitute:

m<KJL = 79 + 53

m<KJL = 132°

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The angles m∠1 = 79° and m∠2 = 53° make up the angle m∠KJL and the measure of m∠KJL = 132°.

We can observe that the angles m∠1 and m∠2 are between the angle m∠KJL hence the sum of the two angles m∠1= 79° and m∠2 = 53° will give the measure of m∠KJL as follows:

m∠1 + m∠1 = m∠KJL

79° + 53° = 132°

m∠KJL = 132°

Therefore, the angles m∠1 = 79° and m∠2 = 53° make up the angle m∠KJL and the measure m∠KJL = 132°

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The height of the silo, to the nearest meter is, 84.9 m

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

A surveyor needs to determine the height of a large grain silo.

And,  He positions his transit 65 m from the silo and records an angle of elevation of 52º.

Now, By the given condition we can formulate;

tan 52° = x / 65

x = 83.2 m

Here, the height of the transit is 1.7 m,

Thus, The height of the silo, to the nearest meter is,

83.2 + 1.7 m

84.9 m

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190 pounds is approximately equal to 86.1826 kg ( rounded to four decimal places )

To convert 190 pounds to kg, we can use the following formula:

1 pound = 0.453592 kg

The conversion factor is 0.453592

The conversion is the process of changing the unit of one quantity to another units  

The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing

Therefore,

The mass in kg = conversion factor × The mass in pounds

Substitute the values in the equation

The mass in kg = 0.453592 × 190

Multiply the numbers

= 86.1826 kg  ( rounded to four decimal places )

Therefore, 190pounds is 86.1826 kg

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Answer:

6 US tablespoons

Step-by-step explanation:

A = [1 0 0; 0 1 0; 0 0 0] and B = [1 1 0; 0 0 0; 0 0 0] are two integer matrices that are not multiples of each other such that Nul(A) = Nul(B) and Col(A) = Col(B).

To find integer matrices A and B that are not multiples of each other such that Nul(A) = Nul(B) and Col(A) = Col(B), we can start with the following matrices:

A = [1 0 0; 0 1 0; 0 0 0]

B = [1 1 0; 0 0 0; 0 0 0]

The null space of A consists of all vectors of the form [x; y; 0], where x and y are integers. Similarly, the null space of B also consists of all vectors of the form [x; y; 0]. Therefore, Nul(A) = Nul(B).

The column space of A consists of all vectors of the form [x; y; 0], where x and y are integers. Similarly, the column space of B also consists of all vectors of the form [x; y; 0]. Therefore, Col(A) = Col(B).

We can verify that A and B are not multiples of each other by computing their determinants. The determinant of A is 0, while the determinant of B is 0 as well. However, A and B are not multiples of each other because the first column of A is [1; 0; 0], while the first column of B is [1; 0; 0] + [0; 1; 0], which is a linear combination of the columns of A.

Therefore, A = [1 0 0; 0 1 0; 0 0 0] and B = [1 1 0; 0 0 0; 0 0 0] are two integer matrices that are not multiples of each other such that Nul(A) = Nul(B) and Col(A) = Col(B).

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Find integer matrices A, B not multiples of each other such that Nul(A)=Nul(B)andCol(A)=Col(B)?

Answer:

1,188

Step-by-step explanation:

15x360=5,400

5,400-22%=4212

5,400-4,212=1,188

Josiah invested $96,000 in an account paying an interest rate of 3.5% compounded continuously. Assuming no deposits or withdrawals are made, the value of the account will reach $153,400 after 9 years.

To calculate this, we can use the formula for the future value of a single sum invested with an inverted interest rate compounded continuously.

Future Value = Present Value × (1 + r)n

Where:

We can solve for n to find out how many years it will take to reach $153,400.

153,400 = 96,000 × (1 + 0.035)n

153,400/96,000 = (1 + 0.035)n

Taking the natural log of both sides and simplifying:

ln(153,400/96,000) = n × ln(1.035)

n = ln(153,400/96,000)/ln(1.035)

n ≈ 8.99

To the nearest year, it will take 9 years for the value of the account to reach $153,400.

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The required number of dollars in a year per 37 dollars in an hour equals 324,120 dollars.

Number of dollars in one hour is equal to 37 dollars.

Relation between year and hour .

1 year = 12 months

1 month = 31, 30 or 28 days

Total number of days in a year = 365 days

Number of hours in 1 day = 24 hours

Number of hours in 365 days = ( 365 × 24 ) hours

                                                 = 8760 hours

In 1 hour = 37 dollars

⇒ 8760 hours = ( 37 × 8760 ) dollars

⇒ 8760 hours = ( 324,120 ) dollars

⇒ 1year = (  324,120  ) dollars

Therefore, the number of dollars in a year is equal to  324,120 dollars.

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A long division polynomials calculator is an online tool used to perform polynomial long division for dividing polynomials.

A long division polynomials number cruncher is an internet based device that performs polynomial long division, a strategy used to separate one polynomial by another. This cycle is like long division with numbers, yet rather than partitioning by single-digit numbers, it includes separating by a polynomial of at least one terms. The interaction includes partitioning the most extensive level term of the profit by the most extensive level term of the divisor, then increasing the divisor by the remainder and taking away the outcome from the profit. The subsequent articulation is the rest of the division. The interaction is then continued involving the rest of the new profit, until the level of the rest of not exactly the level of the divisor. An internet based long division polynomials mini-computer robotizes this interaction, permitting clients to enter the profit and divisor polynomials and get the remainder and remaining portion. This can be helpful for understudies and experts in fields like math, physical science, and designing, who need to partition polynomials for computations and critical thinking.

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Of these three examples, height and weight are more likely to be normally distributed.

What is continuous variable ?

A continuous variable is a type of quantitative variable that can take on any value within a certain range. Continuous variables can be measured to any degree of precision, meaning they can be broken down into smaller and smaller increments.

Three real-life examples of a continuous variable are:

Height: Height is a continuous variable that can take any value within a certain range. It can be measured to any degree of precision, making it a continuous variable.

Time: Time is another continuous variable that can be measured to any degree of precision, from milliseconds to years.

Weight: Weight is also a continuous variable that can take any value within a certain range. It can be measured to any degree of precision, making it a continuous variable.

This is because these variables tend to follow a bell-shaped curve when plotted, with most values clustering around the mean and fewer values appearing further away from the mean. Time, on the other hand, may not be normally distributed because it can have different distributions depending on the situation, such as a bimodal distribution for the time of day people go to sleep or wake up. However, it's important to note that the normal distribution is just one of many possible distributions for continuous variables and may not always be the most appropriate or accurate for real-life situations.

Therefore, Of these three examples, height and weight are more likely to be normally distributed.

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The Volume 12 oz on converting to millimeter is equivalent to 354.9  milliliters .

The Ounces (oz) is a unit of volume which is used in the US customary system of measurement.

The Milliliters (mL) is a metric unit of volume.

We have to convert 12 ounces to milliliters, we need to use a conversion factor.

⇒ 1 fluid ounce (oz) is = 29.5735 milliliters (mL).

So , to convert 12 ounces to milliliters , we write :

⇒ 12 ounces × 29.5735 mL/ounce = 354.882 mL ≈ 354.9 mL .

Therefore , 12 ounces is approximately equal to 354.9 milliliters.

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