Of the 120 students honored at an academic banquet, 40% won awards for mathematics and 55% for English. Fourteen of these students won awards for both mathematics and English. One of the 120 students is chosen at random to be interviewed for a newspaper article. What is the probability that the student won an award in mathematics or English?

Find the lowest common denominator before adding rational expressions. It is obvious that this is the common denominator because the denominator of the first fraction factors to 2(x+2).

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[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{9a + 3 + 4 + (3a + 1)}\\\mathsf{= 9a + 3 + 4 + 3a + 1}}\\\text{COMBINE the LIKE TERMS}\\\mathsf{= (9a + 3a) + (3 + 4 + 1)}\\\mathsf{= 9a + 3a + 3 + 4 + 1}\\\mathsf{= 12a + 7 + 1}\\\mathsf{= 12a + 8}\\\\\\\huge\text{Therefore, your answer should be: } \\\huge\boxed{\mathsf{12a + 8}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

An average and standard deviation in R is straightforward. The mean() function calculates the average and the sd() function calculates the standard deviation.

In information, the standard deviation is a degree of the quantity of variation or dispersion of a fixed of values. A low standard deviation indicates that the values tend to be near the implied (additionally called the predicted price) of the set, whilst an excessive preferred deviation suggests that the values are spread out over a wider variety.

Popular deviation can be abbreviated SD, and is maximum commonly represented in mathematical texts and equations by means of the decrease case Greek letter σ (sigma), for the population standard deviation, or the Latin letter s, for the sample general deviation.

The standard deviation of a random variable, pattern, statistical population, statistics set, or possibility distribution is the square root of its variance. it's miles algebraically easier, even though in exercise less sturdy, than the common absolute deviation.

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The correct statements are given below.

Exponential growth and decay apply to quantities which change rapidly. Exponential growth and decay have been derived from the concept of geometric progression. Quantities that do not change as constant but change in an exponential manner can be termed as having an exponential growth or exponential decay.

Given here:

Now we know  For exponential growth, the value of b is greater than 1 (b > 1), and for exponential decay, the value of b is lesser than 1 (b < 1), where b is the growth factor and Exponential Growth f(x) = abˣ and Exponential Decay f(x) = ab⁻ˣ

1) f(x)=3×4ˣ

  Clearly b=4>1

Thus the function represents exponential growth.

2) f(x)=4×(1/4)ˣ

  Here b=1/4<1

∴ The function represents exponential decay.

3) f(x)=2×(1/2)ˣ

Again here the growth factor is b=1/2<1 , thus the function represents exponential decay.  

Similarly for equation 4 we have b=12>1 and thus the function represents  

exponential growth.

Hence, equation 1 and 4 represent exponential growth and equations 2 &3 represent exponential decay.

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An inequality is b >  -3 The symbol > represents "greater than OR equal to".

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The number for years that it would take 1600 workers to build 25 ziggurats is 66.67 years.

To find out how many years it would take 1600 workers to build 25 ziggurats, you can use the formula:

(time taken by 1200 workers to build 3 ziggurats) x (1600 workers / 1200 workers) x (25 ziggurats / 3 ziggurats) = time taken by 1600 workers to build 25 ziggurats

Plugging in the given values:

(8 years) x (1600 / 1200) x (25 / 3) = 8 years x (4/3) x (25/3)

= 8*25/3

= 200/3

= 66.67 years

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Three points can define a plane in a three-dimensional space.

Because a plane can be defined as a flat surface that extends infinitely in all directions, three points in space are sufficient to specify a plane. A plane can be determined by any three non-collinear points, i.e., points that are not on the same straight line, as long as they are not on the same line. Imagine three points in space, A, B, and C. We draw straight lines from A to C to create a plane. The triangle formed by these lines is a flat surface. A plane can be made by endlessly extending the flat surface in all directions.

The triangle formed by the three points A, B, and C, which are not collinear, extends in all directions to form a plane. A plane is therefore defined by three points. It's crucial to remember that any new point that lies on the same plane as A, B, and C will also be connected to the three defining points by the same straight line.

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Answer:

[tex](5-2c^{2}) c^{3}[/tex]

Step-by-step explanation:

Factor out [tex]c^{3}[/tex]

[tex](5-2c^{2})[/tex] is not factored since it does not have any rational roots.

Answer:

30%

Step-by-step explanation:

Represent 15 out of 50 in fractions:

15/50

Simplify the fraction if you can and multiply by 100:

15/50 = 3/10

3/10 × 100 = 30%

The amount of water in the tank at 0 minutes is equal to 150 liters.

As time increases, the amount of water in the tank increases by 100 liters per minute.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

Next, we would determine the linear equation representing the line which passes through the points (0, 150) and (2, 350) by using the point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 150 = (350 - 150)/(2 - 0)(x - 0)

y - 150 = 100(x - 0)

y = 100x + 150

When x = 0 minutes, the amount of water in the tank is given by;

y = 100(0) + 150

y = 150 liters.

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The Sun transfer its energy to areas A and B by radiation.

The statement compares how much heat is absorbed

by areas A and B : Area A absorbs more heat.

The statement compares the temperatures of areas A

and B : Area A is warmer than area B.

Energy transfer by radiation is a way that energy travels through space without anything touching it. Just like the Sun sends energy to Earth without touching it. The Sun sends energy to Earth in the form of light and heat. This energy travels through the empty space between the Sun and Earth and reaches our planet. When this energy reaches the Earth, it helps plants grow, warms the air and water, and helps create the weather.

Heat absorption is the process by which an object or material takes in or absorbs heat energy from its surroundings. This can happen in a variety of ways, including conduction, convection, and radiation.

The temperature in different areas is determined by a complex interplay of factors, including latitude, altitude, proximity to bodies of water, and local weather patterns. Understanding these factors can help us make predictions about future temperatures and prepare for potential climate change.

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4 is not a perfect number because the sum of its factors (besides 4 itself), 1+2, is less than 4. Numbers like 4 are known as deficient numbers.

In number theory, a natural number is called deficient if it is greater than the sum of its divisors, excluding itself. For example, the number 8 is deficient because its divisors are 1, 2, and 4, and 1 + 2 + 4 = 7, which is less than 8. A number that is not deficient is called abundant.

The concept of deficient numbers was first studied by the ancient Greek mathematician Nicomachus of Gerasa in his work "Introduction to Arithmetic". He classified numbers into three categories: abundant, perfect, and deficient numbers. He defined a perfect number as a number whose divisors (excluding the number itself) sum up to the number and abundant if the sum of divisors (excluding the number itself) is greater than the number.

The study of deficient numbers is closely related to the study of divisors of numbers, which is a fundamental area of number theory. The study of deficient numbers also has connections to other areas of mathematics such as algebraic number theory and the theory of quadratic forms. In addition, the study of deficient numbers has applications in computer science and cryptography.

It is important to note that only a small percentage of numbers are deficient, and the study of deficient numbers is not as widely studied as the study of prime numbers or perfect numbers, but it is still an interesting area of research in number theory.

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When a die is thrown, getting an even number, The probability of getting an even number when a die is thrown is 1/2.

Some number cards with a whole number on each are in Charlotte's possession. There is a 4/9 chance that the card she chooses at random will have an even number on it.

Charlotte's balance of even to odd cards. Your response should be as brief as possible. Three out of six, or three-sixths, of a die will provide an even number.

As both the numerator and denominator of this fraction can be divided by three, it can be simplified. A definition of an even number An even integer is one that can be divided by two while leaving a 0 as the final digit. Two, four, six, eight, ten, and other even numbers are examples. The first and present definitions are equivalent.

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The graph of f(x) translated 3 units down.

correct option is D.

What is a graph of a function?

The graph of a function is a visual representation of the function that shows the relationship between the input (x) and output (y) values. It is typically plotted on a coordinate plane, with the x-axis representing the input values and the y-axis representing the output values. Each point on the graph corresponds to an (x, y) pair that satisfies the equation of the function.

The given options are:
A. It is the graph of f(x) translated 3 units up.

B. It is the graph of f(x) translated 3 units to the right.

C. It is the graph of f(x) where the slope is decreased by 3.

D. It is the graph of f(x) translated 3 units down.

Let y = f(x) then f(x)-3 means y-3. Subtracting 3 from the y coordinate of each point will move the entire curve down 3 units.

Thus, the graph of f(x) translated 3 units down.

correct option is D.

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First of all, we will need to find the set of values of x for which we will get the possible value of y. This is comprehended as the domain of a function. Secondly, to find the range, we need to find all the possible values of y, which we will get after putting the values of x.

Now, to find the domain:-

Case 1: If the equation doesn’t have a denominator, then the domain will be (−∞,∞).

Case 2: If the equation has a denominator, then the domain will be all values other than those where the denominator will become 0.

Case 2: If the equation has a root in the denominator, the domain will be all values except the ones where the value is inside root<0.

To find the range:-

Case 1: If the equation doesn’t have a denominator, the range will be [0,∞). This is because whenever the value of y tends to be negative, the modulus sign will make it positive.

Case 2: If the equation has a denominator, then the range will be all values above 0 except the points where the denominator is equal to 0.

Case 3: If the equation has a root in the denominator, the domain will be all values more than 0 except the ones where the value is inside root<0.

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The value of x is 7 in the equation ∛x+1 - 2 =0

Two or more expressions with an Equal sign is called as Equation.

The given equation is ∛x+1 - 2 =0

The first step is to figure out what the equation is. When unconventional math symbols are used, and when there are no grouping symbols identifying operands, that can be the most difficult step

∛x+1 - 2 =0

Add 2 on both the sides

∛x+1  = 2

Take cube on both the sides

x+1=2³

x+1=8

Subtract 1 from both sides

x=7

Hence, the value of x is 7 in the equation ∛x+1 - 2 =0

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Answer:

66

Step-by-step explanation:

2m = 11

m = 11/2

m = 5.5

m² - 1 = 29.25

m² + 1 = 31.25

The perimeter = 29.25+31.25+5.5 = 66

In the equation for acceleration, a, equals final velocity - original velocity/time, acceleration would be negative if the numerator is negative.

The object is slowed down by the acceleration, which is acting against the motion. In this situation, your acceleration is negative. Positive value will be returned if your end velocity is lower than your initial velocity. The equation for acceleration can be related as:

Acceleration, a = [tex]v_{f}[/tex] - [tex]v_{i}[/tex] × [tex]\frac{1}{t}[/tex]

The general equation a = v/t denotes acceleration (a), which determines the change in velocity (v) over the change in time (t). This enables you to calculate the change in velocity in meters per second squared ([tex]m/s^{2}[/tex]). Since acceleration has both its magnitude and direvtion, it is a vector quantity.

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C.) right and isosceles, but not equilateral

Answer:

C.) right and isosceles, but not equilateral

Step-by-step explanation:

The Real Zeros of the polynomial can be found by equating the given polynomial to zero(0) .

The polynomial function is  a function that involves only non negative integer exponents of a variable in the equation .

For example :  3x+6 is a polynomial which has the exponent equal to 1.

The process to find the real zeros of a polynomial is :

(i) we write the polynomial expression based on what is  given.

(ii) Equate the polynomial equal to zero.

(iii) Solve for the variable(s) by using the polynomial factorization.

The degree of the polynomial tells us about the maximum number of distinct zeros that the polynomial can Have . For example, x - 4 has a degree of 1 . Therefore , it has only one real zero .

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equation of circle : (x - h)² + (y - k)² = r²

h = x coordinate of center

k = y coordinate of center

hence h = 10, k = 8

center - (10 , 8)

For the above case, the graph of the linear equation y = 20 + 10x

Each solution inside the scenario involving two variables may be thought of as the Cartesian coordinates of a specific point on the Euclidean plane.The answers to a linear equation create a line inside the Euclidean plane, and each line may be considered as the sum of all solutions to a linear model with two variables.

This is how this type of equation became known as “linear.” The solutions to an equation system with integer variables form a hyperplane in Euclidean space with size n (a subdomain of dimension n1).

Because linear equations typically properly reflect nonlinear systems, they are widely employed in all fields.

Mathematics as well as in physics and engineering.

Here the equation is given as  y = 20 + 10x

Therefore at x = 0 ,  y = 20 and at y = 0, x = -2

This represents that the fixed monthly fee is 20 and the daily fee is 10.

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The reasons why our bags would differ from the expected distribution are sampling error, measurement error, selection bias, quality control issues, human error, environmental factors and external factors

There are several reasons why the distribution of bags might differ from the expected distribution. Some possible causes include:

1. Sampling error: If the sample size of bags is small, the distribution of bags may not accurately reflect the overall population.

2. Measurement error: If the bags were not measured or counted correctly, the distribution may be affected.

3. Selection bias: If the bags were not selected randomly or if certain bags were excluded from the sample, the distribution may not reflect the true population.

4. Quality control issues: If there were issues with the production of the bags, such as variations in size or weight, the distribution may be affected.

5. Human error: If mistakes were made in the handling, counting, or measuring of the bags, the distribution may not be accurate.

6. Environmental factors: External factors, such as temperature, humidity, or transportation, could cause changes in the weight of bags.

7. External factors: The distribution could also differ because of external factors such as competition, marketing, seasonality, etc.

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The unit rate for the speed of the snail is 4/3 cm/s

A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate.

Given is a graph of distance vs time for the speed of a snail,

We need to find, unit rate for the speed of the snail by the given graph,

Since, we are given a coordinate (12, 16) therefore, the snail covers a distance of 16 cm in 12 sec,

Therefore, in 1 sec, it will cover = 16 / 12 = 4/3 cm/s

Hence, the unit rate for the speed of the snail is 4/3 cm/s

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The solution of RR(A) is (-3, -4).

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Answer:

k=0.6

Step-by-step explanation:

y=kx

42=k(70)

42=70k

k=0.6

The number being divided is known as the dividend, the number dividing it is known as the divisor, and the result of the division is known as the quotient.

Factors are the numbers that are being multiplied, and the result of the multiplication is known as the product. Dividend, divisor, and quotient are the terms used to describe the three numbers involved in division: the dividend, the divisor, and the result of the division, the quotient.

The arithmetic procedures of multiplication and division are related and developed from commonplace situations. Multiplication is the same as repeated addition for whole numbers, hence repeated addition exercises are frequently used to teach multiplication.

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A right triangle is a triangle with one right angle (90 degrees). The hypotenuse of a right triangle is the side opposite the right angle and is usually the longest side of the triangle.

To find the area of the triangle, you will need to use the base and the height of the triangle. In this case, the base of the triangle is 48cm and the height is the length of the side opposite to the right angle.

To find the length of the side opposite to the right angle, you can use the Pythagorean Theorem, which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides. The theorem can be written as:

c^2 = a^2 + b^2

where c is the hypotenuse, and a and b are the other two sides.

So, substituting the values we have:

50^2 = a^2 + 48^2

2500 = a^2 + 2304

a^2 = 2500 - 2304

a^2 = 196

a = 14

Area of the triangle = (1/2) * base * height

= (1/2) * 48 * 14

= 336 cm^2

So, the area of the triangle is 336 cm^2

The area of the triangle is 336 cm²

The area of a triangle can be found using the formula:

Area = (1/2) × base × height

In this case, we know the base is 48cm and the hypotenuse is 50cm. To find the height, we can use the Pythagorean theorem, which states that the square of the length of the hypotenuse (a) is equal to the sum of the squares of the lengths of the other two sides (a and b) in the right triangle.

c² = a² + b²

So in this case, we have:

50² = 48²  + b²

Solving for b, we get:

b =√ 50² - 48²

b = √2500 - 2304

b = √196

b = 14 cm

So the height of the triangle is 14cm.

Now we can use this information to find the area:

area = (1/2) ×48 ×14 = 336 cm²

Hence, we can say the area of the triangle is 336 cm²

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The graphing method is used to solve a system of linear equations by multiplying and adding.

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Arcs with the same radius from each endpoint will help you locate the midpoint of the segment more accurately.

When constructing a perpendicular bisector of a segment, it is important to make arcs with the same radius from each endpoint. This will help you to locate the midpoint of the segment more accurately. By using arcs of the same radius, you can ensure that the bisector is perfectly perpendicular to the segment. When the two arcs intersect, the midpoint of the segment will be the point of intersection. This will also ensure that the bisector is exactly in the middle of the segment, as the two arcs with the same radius will be of equal length. By constructing arcs with the same radius, you can achieve a precise and accurate perpendicular bisector of the segment.

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