Select ALL the correct answers.

Carmen and Matt are conducting different chemistry experiments in school. In both experiments, each student starts with an initial amount of water in a flask. They combine two chemicals which react to produce more water. Carmen's experiment starts with 30 milliliters of water in a flask, and the water increases in volume by 8.5 milliliters per second. Matt's experiment starts with 10 milliliters of water and increases in volume by 28% each second.





Which two conclusions can be made if f represents the volume of water in Carmen's flask and g represents the volume of water in Matt's flask?


The volume of water in Carmen's flask is increasing at a faster rate than the volume of water in Matt's flask over the interval [6, 8].

The volume of water in Carmen's flask is increasing at a slower rate than the volume of water in Matt's flask over the interval [4, 6].

The volume of water in Carmen's flask will always be greater than the volume of water in Matt's flask.

The volume of water in Matt's flask will eventually be greater than the volume of water in Carmen's flask.

The volume of water in Carmen's flask is increasing at a slower rate than the volume of water in Matt's flask over the interval [0, 2].

Answer:

0,95

Step-by-step explanation:

[tex] \frac{19}{20} [/tex]

Multiply the fraction by 5, so that the denominator would be equal to 100:

[tex] \frac{19 \times 5}{20 \times 5} = \frac{95}{100} = 0.95[/tex]

I don't know if I got it right, though...

The inequality c ≥ 20 represents the minimum number of candles that need to be sold to pay for a visit to Knotts costing $100 when each candle is sold for $5.

To write the inequality that represents c, we need to consider the cost of the visit to Knotts and the price of each candle that is being sold. Let's assume that the cost of the visit to Knotts is $100 and each candle is being sold for $5.

We know that the total amount of money she earns from selling c candles is given by 5c, and this amount must be greater than or equal to the cost of the visit, which is $100. Therefore, we can write:

5c ≥ 100

Dividing both sides of the inequality by 5, we get:

c ≥ 20

Therefore, the inequality that represents c is c ≥ 20. This means that she needs to sell at least 20 candles to be able to pay for the visit to Knotts. If she sells fewer than 20 candles, she won't have enough money to cover the cost of the visit.

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Therefore, there are 36 possible values of n to satisfy the given equation.

In mathematics, an equation is a statement that asserts the equality of two expressions. Equations are formed using mathematical symbols and operations, such as addition, subtraction, multiplication, division, exponents, and roots. An equation typically consists of two sides, with an equal sign in between. The expression on the left-hand side is equal to the expression on the right-hand side. Equations can be used to model a wide range of real-world situations, from simple algebraic problems to complex scientific and engineering applications.

Here,

We can use the fact that sin(θ) + i cos(θ) = [tex]e^{(iθ)}[/tex], where e is the base of the natural logarithm.

So, the given equation becomes [tex]e^{(iθ)} ^= e^{(inθ)}[/tex]. Taking the natural logarithm of both sides, we get:

iθ = inθ + 2πik (where k is an integer)

Simplifying, we get:

nθ = (k - i)2π

Since b ≤ 2016, we know that n ≤ 2016. We can also see that k - i must be a multiple of n, so we have:

k - i = nm (where m is an integer)

Substituting this back into the equation, we get:

θ = m(2π/n)

So, the number of possible values of n is equal to the number of divisors of 2016. Prime factorizing 2016 as 2⁵ * 3² * 7, we get:

The number of divisors of 2016 = (5 + 1)(2 + 1)(1 + 1)

= 36

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the sunglasses will never hit the ground.

What is a function?

A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.

The height of the sunglasses at time t is given by the function h(t) = 16t^2 + 5776.

When the sunglasses hit the ground, their height will be 0. So we need to find the value of t that makes h(t) = 0.

16t^2 + 5776 = 0

Dividing both sides by 16, we get:

t^2 + 361 = 0.

This equation has no real solutions since t^2 is always non-negative and can never be equal to a negative number.

Therefore, the sunglasses will never hit the ground.

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Differentiating 8c to the fourth power gives 32c³, not 4 times 8c to the 4-1 power.

What is differentiation?

Differentiation is a mathematical operation that involves finding the derivative of a function with respect to one of its variables.

No, differentiating 8c to the fourth power is not equal to four times 8c to the 4-1 power.

To differentiate a term with a power, we use the power rule of differentiation, which states that:

d/dx [xⁿ] = n*x⁽ⁿ⁻¹⁾

where d/dx denotes differentiation with respect to x, n is the power of x, and x⁽ⁿ⁻¹⁾ is the derivative of xⁿ.

Applying this rule to 8c to the fourth power, we get:

d/dc [8c⁴] = 4*8c³

Notice that the power of c decreased by 1 after differentiation, not by 4 as suggested in the question.

Therefore, differentiating 8c to the fourth power gives 32c³, not 4 times 8c to the 4-1 power.

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The associative property of  (p+7) + 9 =  p+(7 + 9) so that both the sides equals p + 16.

The associative property is a property of binary operations, which are operations that involve two elements. It states that the way we group the elements in an operation does not affect the result of the operation.

For any three elements a, b, and c in a set, and a binary operation *, the associative property states that:

(a * b) * c = a * (b * c)

Addition and multiplication are associative operations.

(a + b) + c = a + (b + c) and (a * b) * c = a * (b * c)

The associative property of addition states that when adding three or more numbers, the way we group them does not affect the sum. More formally, for any three numbers a, b, and c, the associative property of addition can be written as:

(a + b) + c = a + (b + c)

In the case of (p+7) + 9, we can apply the associative property of addition as follows:

[(p+7) + 9] = p + (7 + 9)

p + 16 = p + 16

Here, we have grouped the numbers 7 and 9 together and added them first, and then added the result to p. This gives us the same sum as if we had added p and 7 first and then added 9 to the result.

Therefore, the associative property of addition tells us that we can add (p+7) and 9 in any order or group them differently, and still get the same result (p+16).

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Answer:

3rd degree

3

-4

-(1/2)x³

-1/2

Step-by-step explanation:

1st blank: The largest exponent tells you the degree of the polynomial.

2nd blank: Count how many "parts" (terms) are separated by + or -

3rd: The term without variables is the constant term. Include the sign in front of it!!

4th: The term that includes the highest degree variable. Include the sign in front of it!!

5th: The number preceding the variable in the leading term. Again, include the sign...!!

Answer:to be honest i kinda dont know and i just can give you support so try your best or guess b

Step-by-step explanation:

Using the normal distribution, it is found that this type of fishing line have a breaking strength less than the advertised 6 pounds 27.76% of the time.

The z-score of a measure X of a normally distributed variable that has mean represented by  and standard deviation represented by  is given by the following rule:

Z = X - μ /σ

here, we have,

The z-score measures how many standard deviations the measure X is above or below the mean, depending if the z-score is positive or negative.

From the z-score table, the p-value associated with the z-score is found, and it represents the percentile of the measure X.

The mean and the standard deviation for the breaking strengths are given as follows:

μ = 6.44 and, σ = 0.75

The proportion of times with breaking strength less than 6 inches is given by the p-value of Z when X = 6, hence:

Z = X - μ /σ

Z = (6 - 6.44)/0.75

Z = -0.59

Z = -0.59 has a p-value of 0.2776.

Hence the percentage is of 27.76%.

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What is the missing information?

The question is:

How often will this type of fishing line have a breaking strength less than the advertised 6 pounds.

tower of height 105 feet and a shadow of length 117 feet. We want to find the angle of elevation of the sun, represented by the angle θ. the angle of elevation of the sun to the nearest degree is  [tex]43[/tex] degrees.

We can use the tangent function to find the angle of elevation of the sun:

tan(angle of elevation) = opposite / adjacent

In this case, the opposite side is the height of the tower (105 feet) and the adjacent side is the length of the shadow (117 feet).

tan(angle of elevation) [tex]= 105 / 117[/tex]

We can solve for the angle of elevation by taking the inverse tangent (tan^-1) of both sides:

angle of elevation [tex]= tan^-1(105 / 117)[/tex]

Using a calculator, we get:

angle of elevation  [tex]\approx 42.9[/tex] degrees

Therefore, the angle of elevation of the sun to the nearest degree is  [tex]43[/tex]degrees.

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The area of the region enclosed by the curves can be found to be 1/6 square units.

To find the area enclosed by the curves y = x, y = 5x, and y = -x + 2, we first need to find the points where these curves intersect.

Intersection points of y = x and y = 5x: (0, 0)

Intersection points of y = x and y = -x + 2: Intersection point: (1, 1)

Intersection points of y = 5x and y = -x + 2: Intersection point: (1/3, 5/3)

Now we have the three intersection points: (0, 0), (1, 1), and (1/3, 5/3). The area enclosed by the curves is a triangle with vertices at these points.

To find the area of the triangle, we can use the Shoelace Formula:

Area = (1/2)|x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|

Area = (1/2)|0(1 - 5/3) + 1(5/3 - 0) + (1/3)(0 - 1)|

Area = 1 / 6 square units

The area enclosed by the curves is 1/6 square units.

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the evaluated expressions are: (a) j¹² = 1 ,(b) -1/j⁹ = j ,(c) 5/(2j¹³) = (5/2)j

to solve this use  the properties of the imaginary unit.

what is imaginary unit ?

The imaginary unit is a mathematical concept denoted by i or j (in electrical engineering) that represents the square root of -1. It is called an "imaginary" unit because it does not have a real number counterpart.

In the given question,

To evaluate these expressions, we need to recall the properties of the imaginary unit, j, which is defined as the square root of -1. Specifically, we need to remember that:

j² = -1

j³ = -j

j⁴ = 1

Using these properties, we can simplify the given expressions:

(a) j¹² = (j⁴)³ = 1³ = 1

(b) -1/j⁹ = -1/(j³)³= -1/(-j)³ = -1/(-j³) = -1/(-(-j)) = -1/j = -j/j² = -j/-1 = j

(c) 5/(2j¹³) = 5/(2(j⁴)³*j) = 5/(2*1*j) = 5/(2j) = (5/2) * (1/j) = (5/2) * (-j³/j⁴) = -(5/2)j³ = (5/2)j

Therefore, the evaluated expressions are:

(a) j¹² = 1

(b) -1/j⁹ = j

(c) 5/(2j¹³) = (5/2)j

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. Evaluate the following expression  to simplest form \( j^{12} \); (b) \( -\frac{1}{j^{9}} \); (c) \( \frac{5}{2 j^{13}} \)

the interval over which the graph of f(x) = -(x + 3) - 1 is decreasing is (-∞, +∞).

What is a function?

A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.

The given function is:

f(x) = -(x + 3) - 1

To find the interval over which the function is decreasing, we need to find the values of x where the function's derivative is negative.

The derivative of the function is:

f'(x) = -1

The derivative is a constant, which means the function has a constant slope of -1. Since the slope is negative, the function is decreasing over its entire domain.

Therefore, the interval over which the graph of f(x) = -(x + 3) - 1 is decreasing is (-∞, +∞).

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Answer:61.43

Step-by-step explanation:

yes

Answer:

Louis $61.43 now.

Step-by-step explanation:

Louis sells her bike and helmet for $88.50 and $8.75. Add these together and it gives you the total amount of money she has earned.

[tex]88.50+8.75= 97.25[/tex]

Louis now has $97.25. She then buys something for $35.82, so, subtract the amount of the basketball by the amount of money she earned to find out how much money she has left.

[tex]$97.25- 35.82=61.43[/tex]

Louis now has $61.43.  

let me know if you have any more questions on this problem. :)

The function y = -ln(x + 3) + 7 is a logarithmic function that has undergone multiple transformations like horizontal and vertical shift and reflection and any transformations can not be described for second expression.

What is transformation?

A transformation is a process or operation that changes the position, shape, or orientation of a geometric figure or an object in space.

11. The function y = -ln(x + 3) + 7 is a logarithmic function that has undergone multiple transformations. We can describe these transformations as follows:

Horizontal shift: The argument of the logarithm has been shifted horizontally to the left by 3 units. This means that the graph of the function has been shifted to the left by 3 units relative to the parent function y = -ln(x).

Vertical shift: The entire graph of the function has been shifted vertically upwards by 7 units. This means that the minimum point of the graph has been shifted from y = -∞ to y = 7.

Reflection: The function has been reflected across the x-axis. This means that the values of y will be negative for all positive values of x.

12. The expression 3*+5 - 2 is not a valid mathematical expression or function. It appears to be incomplete, as there is no variable or operation specified. Without additional information, we cannot describe any transformations of this expression.

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The approximate distance across the lake is 6.7 kilometers, which is closest to option D.

What is Pythagorean theorem?

The Pythagorean theorem is a fundamental concept in mathematics that relates to the lengths of the sides of a right triangle.

To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, the distance across the lake is the hypotenuse of a right triangle, and the distances 6 km and 3 km are the lengths of the other two sides. Therefore, we can write:

distance across the lake = √(6 km)² + (3 km)²

distance across the lake = √(36 km² + 9 km²)

distance across the lake = √45 km²

distance across the lake ≈ 6.7 km

Therefore, the approximate distance across the lake is 6.7 kilometers, which is closest to option D.

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The total area is 1570 square units.

Explain area

Area refers to the measurement of the size of a two-dimensional surface. It is typically expressed in square units, such as square meters or square feet. The area of a shape can be calculated by multiplying its length by its width, or by using specific formulas for more complex shapes. Area is an important concept in geometry and is used in many real-life applications, such as calculating the area of a room or a piece of land.

According to the given information

Here the base of the right triangle is 20 and the hypotenuse is 29, so we can set up the equation:

29² = 20² + h²

where h is the height of the triangle(length of dotted line) that we want to find.

Simplifying and solving for h, we get:

h² = 29² - 20²

h² = 841 - 400

h² = 441

h = √(441)

h = 21

Therefore, the length of the dotted line is 21 units

Now,

The area of a right triangle is given by the formula A = (1/2)bh, where b is the base and h is the height. So, the area of the right triangle with base 20 and height 21 is:

A_triangle = (1/2)(20)(21) = 210

The area of a right trapezium is given by the formula A = (1/2)(a+b)h, where a and b are the parallel sides and h is the height. So, the area of the right trapezium with a longer side of 55, smaller side of 21, and height of 40 is:

A_trapezium = (1/2)(55+21)(40) = 1360

Therefore, the total area of the right triangle and right trapezium is:

A_total = A_triangle + A_trapezium = 210 + 1360 = 1570

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Answer: 19.5

Step-by-step explanation:

First order the numbers in ascending order: 105, 106, 107, 117, 118, 123, 125, 127, 136

Next find the median: 118

Then find the median of each quartile: First Quartile: 106.5, Second Quartile: 126

Then subtract 106.5 from 136 to find the range: 126-106.5=19.5

To find the IQR (Interquartile Range) of a set of data, we first need to find the median of the data set. The median is the middle value when the data set is arranged in order.

Arranging the given data set in order:

105 106 107 117 118 123 125 127 136

The median of this data set is the middle value, which is 123.

Next, we need to find the values of the first quartile (Q1) and the third quartile (Q3). Q1 is the median of the lower half of the data set, and Q3 is the median of the upper half of the data set.

The lower half of the data set is: 105 106 107 117 118

The upper half of the data set is: 123 125 127 136

Q1 is the median of the lower half of the data set, which is:

Q1 = (107 + 117)/2 = 112

Q3 is the median of the upper half of the data set, which is:

Q3 = (125 + 127)/2 = 126

Finally, we can calculate the IQR by subtracting Q1 from Q3:

IQR = Q3 - Q1 = 126 - 112 = 14

Therefore, the IQR of the given data set is 14.

Answer:

It can be written in interval notation as [-5,5)

Answer: The simplest form of 564/18 is 94/3.

Step-by-step explanation: Hope this helps

The graphical representations that would best display the data are:

A graph is a visual representation or diagram that organises facts or values. The points on the graph frequently reflect the relationship between two or more objects.

To display the weekly high temperatures in Bartow, Florida for the past six months, the following graphical representations could be used:

Therefore, the graphical representations that would best display the data are:

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The largest possible value for f(4) applying the mean value theorem is 10

According to the Mean Value Theorem, there exists a value c between 0 and 4 such that:

f'(c) = (f(4) - f(0)) / (4 - 0)

Simplifying this equation, we get:

f(4) - f(0) = 4f'(c)

Since f'(x) ≤ 3 for all x, we can substitute 3 for f'(c) to obtain:

f(4) - (-2) ≤ 4(3)

f(4) + 2 ≤ 12

Therefore, we have:

f(4) ≤ 10

So the largest possible value for f(4) is 10.

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Answer: D

Step-by-step explanation:

The values of the given trigonometric functions are 240° and 60° respectively.

What are trigonometric functions?

Trigonometric functions are mathematical functions that relate the angles and sides of a right triangle.

The three primary trigonometric functions are sine, cosine, and tangent.

The sine function (sin) relates the length of the opposite side of an angle to the length of the hypotenuse of a right triangle. It is defined as sin(θ) = opposite/hypotenuse.

The cosine function (cos) relates the length of the adjacent side of an angle to the length of the hypotenuse of a right triangle. It is defined as cos(θ) = adjacent/hypotenuse.

The tangent function (tan) relates the length of the opposite side of an angle to the length of the adjacent side of a right triangle.

Now To find

(a.)  sin⁻¹(-√3/2)

(b.)  cos⁻¹ (1/2)

For a

sin⁻¹(-√3/2)=sin⁻¹(-0.8660)=-⁻60° or 240°

and

For b

cos⁻¹ (1/2)=cos⁻¹ (0.5)=60°

Hence,

             the values of the given trigonometric functions are 240° and 60° respectively.

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Total area = 63 cm² + 33 cm² + 4 cm² + 4 cm² = 104 cm²

The area of a trapezoid is given by the formula:

A = (a + b)h/2

where a and b are the lengths of the parallel sides of the trapezoid and h is the height (the perpendicular distance between the parallel sides).

To use this formula, simply plug in the values of a, b, and h and then solve for A. Note that all measurements must be in the same unit (such as centimeters or inches) for the formula to work correctly.

First, we can find the area of the rectangle with sides 7 cm and 9 cm:

Area of rectangle = length × width = 7 cm × 9 cm = 63 cm²

Next, we can find the area of the trapezoid with bases 2 cm and 5 cm and height 11 cm:

Area of trapezoid = (sum of bases × height) / 2 = ((2 cm + 5 cm) × 11 cm) / 2 = 33 cm²

Finally, we can find the area of the two squares with side lengths 2 cm and 2 cm:

Area of square 1 = side × side = 2 cm × 2 cm = 4 cm²

Area of square 2 = side × side = 2 cm × 2 cm = 4 cm²

Adding up the areas of all the shapes, we get:

Total area = 63 cm² + 33 cm² + 4 cm² + 4 cm² = 104 cm²

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Answer:

about 403.1 miles

Step-by-step explanation:

262 miles is 65% of the distance to the grandmother's house. Let d be that distance.

[tex].65d = 262[/tex]

[tex]d = 403.1[/tex]

The distance from Ken's house to his grandmother's house is about 403.1 miles.

Given the information, the probability that a response is between the ages of 18 and 29 and 30 or older is, respectively, 0.536 and 0.654. There is a 0.265 percent chance that they will say yes—that global warming will affect them over their lifetime. Concern over global warming also seems to vary across people aged 18 to 29 and those over 30.

Probability is the ratio of favourable events to all other potential outcomes in a circumstance. The symbol x can be used to denote how many successful outcomes there were in an experiment with 'n' outcomes. The formula below can be used to determine a given event's probability.

Positive Results/Total Results = x/n = Probability (Event)

The likelihood that a respondent between the ages of 18 and 29 believes that there will be no significant threat from global warming in his or her lifetime is:

P (18-29 and no) = 293/(134 + 293 + 117) = 0.536

The likelihood that a respondent who is 30 years of age or older believes that there will be no significant threat from global warming in his or her lifetime is:

P (30+ and no) = 432/(131 + 432 + 178) = 0.654

The likelihood that a randomly chosen respondent will select "yes"—that is, that they will experience the effects of global warming throughout their lifetimes—is:

P(Yes) = (134 + 131)/(134 + 131 + 293 + 432 + 117 + 178) = 0.265

Yeah, it does seem that younger people (18–29) are less concerned about global warming than older people (30+). In comparison to respondents aged 18 to 29, the likelihood that a respondent aged 30 or older believes that global warming will not constitute a severe hazard during their lifetime is higher (0.654). (0.536). According to this, respondents who are older are less concerned about global warming than respondents who are younger. To confirm this difference, a formal statistical test would be required.

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The complete question is:

Do you think global warming will have an impact on you during your lifetime? A CBS News/New York Times poll of 1000 adults in the United States asked this ques- tion (CBS News website, December, 2014). Consider the responses by age groups shown below Response Age 18-29 30+Yes 134 131No 293 432Unsure a. What is the probability that a respondent 18-29 years of age thinks that global warming will not pose a serious threat during his/her lifetime?b. What is the probability that a respondent 30+ years of age thinks that global warming will not pose a serious threat during his/her lifetime? c. For a randomly selected respondent, what is the probability that a respondent answers yes? d. Based on the survey results, does there appear to be a difference between ages 18-29 and 30+ regarding concern over global warming?

(a) An appropriate sample space S for this experiment is the set of all possible sequences of four children, where each child can be either a boy (b) or a girl (g). So, the sample space S is:

S = {bbbb, bbbg, bbgb, bgbb, gbbb, bggg, bgbg, gbgg, ggbb, gbgb, bggg, gbgg, gggg, gggb, gggg}

There are 2^4 = 16 possible outcomes in the sample space.

(b) The event E that there are three boys and a girl in the family can be represented by the set of all sequences in the sample space S that have three b's and one g. So, the event E is:

E = {bbbg, bbgb, bgbb, gbbb}

There are 4 possible outcomes in the event E.

Answer:

The average adult weighing 150 to 180 pounds should have about 1.2 to 1.5 gallons of blood in their body. 160 ounces.

Step-by-step explanation:

the probability that the student won an award for mathematics or for science is 0.6385 or approximately 64%.

How to solve probability?

To find the probability that the student won an award for mathematics or for science, we need to use the concept of set theory and the inclusion-exclusion principle.

Let A be the set of students who won awards for mathematics, and B be the set of students who won awards for science. We are interested in finding the probability of A union B, which represents the set of students who won awards for either mathematics or science or both.

From the given information, we know that |A| = 115, |B| = 42, and |A intersect B| = 21, where |X| denotes the cardinality of the set X, i.e., the number of elements in the set X.

Using the inclusion-exclusion principle, we can write:

|A union B| = |A| + |B| - |A intersect B|

Substituting the values, we get:

|A union B| = 115 + 42 - 21 = 136

Therefore, there are 136 students who won awards for either mathematics or science or both.

To find the probability of selecting a student who won an award for mathematics or for science, we divide the cardinality of A union B by the total number of students, which is given as 213:

P(A union B) = |A union B| / 213 = 136 / 213 = 0.6385 (rounded to four decimal places)

Therefore, the probability that the student won an award for mathematics or for science is 0.6385 or approximately 64%.

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Answer:

20%

Step-by-step explanation:

Number of phone calls received second month = 4265 + 25% of 4265

                                                                               = 4265 + 0.25 * 4265

                                                                               = 4265 ( 1 + 0.25)

                                                                               = 4265 * 1.25

                                                                               = 5331.25

Number of calls in third month = 6396

Increased calls than second month = 6396 - 5331.25

                                                           = 1034.75

[tex]Increased \ percentage = \dfrac{Increased \ calls}{second \ month \ calls}*100[/tex]

                                   [tex]=\dfrac{1064.75}{5331.25}*100\\\\=19.97 \%\\\\= 20\%[/tex]