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Each person eats at least one fruit. Hence 39% of people eat both orange and apple using the probability.

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics. From the given data

n(O)=0.63

n(A)=0.76

n(A∪O)=1 as every person eats at least one fruit

n(A∪O)=n(A)+n(O)−n(A∩B)

1=0.63+0.76−n(A∩B)

n(A∩B)=1.39−1

n(A∩B)=0.39

A∩B=0.39×100=39

Hence 39% of people eat both orange and apple

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The data analyst should a)investigate the outlier to determine if it can lead to any important observations and b)use a filter to highlight the outlier, as it is more important than the rest of the data.

When analyzing data, it is important to look at outliers as they can provide valuable information. Outliers can point to an unexpected correlation or reveal a hidden trend that could be missed if they were removed. By investigating the outlier, a data analyst can look for any important observations the outlier might reveal.

Additionally, using a filter to highlight the outlier allows the analyst to focus on the outlier and compare it to the other data points. This can help the analyst to understand how the outlier differs from the rest of the data and draw any relevant conclusions.

Removing the outlier should be avoided as it can lead to data bias and remove important information from the analysis.

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The area of the state of Nevada which had the shape of a right trapezoid would be = 110,622 miles²

The area of a trapezoid can be calculated using the formula of the following;

A = ( a + b ) x h/2

where;

a = 205

b = 511

h = 309

Area (A) = (205+511) × 309/2

= 716 × 154.5

= 110,622 miles²

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The area of the state of Nevada with the shape of a right trapezoid is; 110622 miles²

The area of a trapezoid can be calculated with the formula :

Area = ¹/₂(a + b) * h

where;

a and b are parallel sides

h is height

The parameters are;

a = 205

b = 511

h = 309

Thus;

Area = ¹/₂(205 + 511) * 309

Area = 716 * 154.5

Area = 110622 miles²

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Answer:

A) (3x + y)^4:

The Binomial Theorem states that for any real numbers a and b, and any positive integer n, the expansion of (a + b)^n is given by the sum of n terms of the form:

C(n,k)a^(n-k)b^k

where C(n,k) is the binomial coefficient (n choose k).

So, expanding (3x + y)^4:

(3x + y)^4 = C(4,0)(3x)^4(y)^0 + C(4,1)(3x)^3(y)^1 + C(4,2)(3x)^2(y)^2 + C(4,3)(3x)^1(y)^3 + C(4,4)(3x)^0(y)^4

Using the binomial coefficients:

C(4,0) = 1, C(4,1) = 4, C(4,2) = 6, C(4,3) = 4, C(4,4) = 1

Expanding the terms:

(3x + y)^4 = 1(3x)^4(y)^0 + 4(3x)^3(y) + 6(3x)^2(y)^2 + 4(3x)(y)^3 + 1(y)^4

= 1(81x^4) + 4(27x^3y) + 6(9x^2y^2) + 4(3xy^3) + 1(y^4)

= 81x^4 + 108x^3y + 54x^2y^2 + 12xy^3 + y^4

B)

The Binomial Theorem states that for any real numbers a and b and any positive integer n, the expansion of (a + b)^n is given by:

(a + b)^n = C(n, 0)a^n * b^0 + C(n, 1)a^(n-1) * b^1 + C(n, 2)a^(n-2) * b^2 + ... + C(n, n-1)a^1 * b^(n-1) + C(n, n)a^0 * b^n

where C(n, k) represents the binomial coefficient, which can be calculated as n! / (k! (n - k)!).

Applying this to (x - 2y)^6, we get:

(x - 2y)^6 = C(6, 0)x^6 * (-2y)^0 + C(6, 1)x^5 * (-2y)^1 + C(6, 2)x^4 * (-2y)^2 + ... + C(6, 5)x^1 * (-2y)^5 + C(6, 6)x^0 * (-2y)^6

Expanding each term:

C(6, 0) = 6! / (0! 6!) = 1

C(6, 1) = 6! / (1! 5!) = 6

C(6, 2) = 6! / (2! 4!) = 15

C(6, 3) = 6! / (3! 3!) = 20

C(6, 4) = 6! / (4! 2!) = 15

C(6, 5) = 6! / (5! 1!) = 6

C(6, 6) = 6! / (6! 0!) = 1

Now we can substitute each value into the equation:

(x - 2y)^6 = 1x^6 - 12x^5 * 2y + 90x^4 * (-2y)^2 - 360x^3 * (-2y)^3 + 720x^2 * (-2y)^4 - 720x * (-2y)^5 + 1 * (-2y)^6

Answer:

(x - 2y)^6 = x^6 - 12x^5 * 2y + 90x^4 * (-2y)^2 - 360x^3 * (-2y)^3 + 720x^2 * (-2y)^4 - 720x * (-2y)^5 + (-2y)^6.

Answer: The rate of revolutions per minute is 308.8 revolutions per minute.

Step-by-step explanation: To find the rate of revolutions per minute, we need to convert the number of degrees of rotation per second to the equivalent number of full rotations per minute.

First, divide the number of degrees of rotation per second by 360, which is the number of degrees in one full rotation:

1848 / 360 = 5.13

Next, multiply the number of full rotations by 60 to get the number of rotations per minute:

5.13 * 60 = 308.8

So, the rate of revolutions per minute is 308.8 revolutions per minute.

Ximena wants to decrease 350 by 4%, here the complete statement is:

350 × 4% = 14.

When the denominator is 100, percentages are really just fractions. We place the percent sign (%) next to the number to indicate that the number is a percentage.

Comparing two amounts while rebasing the second amount to 100 is the simplest way to use percentages. The word percentage comes from the Latin term per centum, which means "by the hundred." In the 16th century, the Latin term made its way into English. It was later abbreviated to %.

b)

= 350 × 4%

= 350 × (4/100)

= 14

19. a)

5 (x - 6) = 15

or, 5x - 30 = 15

or, 5x = 45

or, x = 9

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Answer:

p= 77

Step-by-step explanation:

Answer:

answer for the expression 5(–4+k) + –2(–3+–10k) is -5k - 6.

To arrive at this answer, we used the order of operations (PEMDAS) as follows:

Parentheses first: (–4+k) = k-4 and (–3+–10k) = –10k-3

Next, the multiplication: 5(k-4) = 5k-20 and -2(-10k-3) = 20k+6

Finally, the addition: -5k-20 + 20k+6 = -5k - 6 + 20k

And then we simplify further by combining the like terms:

-5k - 6 + 20k = -5k + 20k - 6 = 15k - 6

So the final answer is -5k -6

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An example of a pure exact number is "3".

In mathematics, pure exact numbers are also known as mathematical constants or closed-form numbers. Unlike approximations, such as those obtained through measurement or estimation, exact numbers have a fixed and well-defined value.

A pure exact number is a number that has a fixed, precise value and is not subject to any estimation or measurement error.

Examples of pure exact numbers include integers (e.g. 3, 42), rational numbers (e.g. 1/2, -3/7), and some real numbers that can be expressed as a ratio of integers (e.g. pi, e).

These numbers have a definite value and do not change, regardless of the measurement or calculation method used.

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Answer:

80

Step-by-step explanation:

Hope it helps! =D

Answer: 80

Step-by-step explanation: When rounding to the nearest 10, you need to examine the number you are trying to round. If the number has a 1's place that is 4 or lower, you round to 70, but if the 1's position is 5 to 9, you round to 80. In this case, 77 can be rounded to 80, since the 1's place number is between 5 and 9.

Hope this helps! :)

By the property of exponents, the value of the above equation is 2*10^7.

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is the expression. A number, a variable, or a combination of numbers, variables, and operation symbols constitutes an expression. An equation consists of two expressions joined by an equal sign. Example of a word: the sum of 8 and 3. Example of a word: The sum of 8 and 3 equals 11. 8 + 3 is an expression.

Here,

=1.2 x 10^5/6 x 10^-3

=(12/6)*10^7

=2*10^7

The value of given expression is 2*10^7 by property of exponents.

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from the given information in the question we have found that all the three sets form a partition from the universal sets

What is a set?

A set is a mathematical model for a collection of items; it comprises elements or members, which may be any mathematical object: numbers, symbols, points in space, lines, other geometrical structures, variables, or even other sets.

As it is given that there are 3 sets where the first set A1 has 10 or more elements, A2 has 20 or more elements, and A3 has 15 or more elements.

1. If A1 ⊆ A2 and A2 ⊆ A3 then the union of these three will contain the same number of elements as that of A3.

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The required solution for the given inequalities has been shown in the graph.

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Here,
4x + y < 8
x - y > 3

Illustrate the graph of the inequality, the overlapped region on the graph is the solution of a system of inequalities.

Thus, the required solution for the given inequalities has been shown in the graph.

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Height is a interval - level variable typically in statistics.

Height is typically considered an interval-level variable in statistics. This means that height has a meaningful zero point, but the difference between two height measurements does not have a meaningful interpretation. For example, if one person is 6 feet tall and another person is 5 feet tall, the difference of 1 foot is meaningful, but the ratio of their heights is not.

In contrast, ratio-level variables have a meaningful zero point and the ratio of two values also has a meaningful interpretation. For example, weight is a ratio-level variable because a weight of 0 pounds has a well-defined meaning, and the ratio of two weights (such as two people each weighing 150 pounds) is meaningful and can be compared.

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The marks in paper 2 would be 100.

Given is a pupil who scored 50 in his paper 1 exam got ill and missed paper 2.

Assume the equation of the line of best fit is of the form -

y = mx + c

Let {c} = 0

Now, for the point (1, 50), we can write -

50 = m

So, the equation will be of the form -

y = 50x

Now, for {x} = 2, we can write -

y = 100

Therefore, the marks in paper 2 would be 100.

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The resulting equation is 14√3x - 47 = 0.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 8 is an equation.

We have,

√3x + 4 = 1 + √3x -11

√3x + 4 = √3x - 10

Squaring both sides

(√3x + 4)² = (√3x - 10)²

3x² + 16 + 8√3x = 3x² - 20√3x + 100

16 - 100 + 8√3x + 20√3x = 0

28√3x - 94 = 0

2(14√3x - 47) = 0

14√3x - 47 = 0

Thus,

14√3x - 47 = 0 is the resulting equation.

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When both sides of the given equation are squared, the resulting equation is x = 20.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

The equation is given in the question, as follows:

√(3x+4) = 1+√(3x-11)

Squaring both sides of the equation:

3x + 4 = (1 + √(3x - 11))²

Expanding the square on the right side:

3x + 4 = 1 + 2√(3x - 11) + (3x - 11)

Simplifying the above equation, we get

196 = 12x - 44

12x = 196 + 44

12x = 240

x = 20

So the value of x that satisfies the equation is 20.

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The graph of the sequence may pass toward the vertical line test.

Functions are defined as a fundamental part of the calculus in mathematics. These are the special types of relations. A function is visualized as a rule, which gives a unique output for every input x.

Given the information that, he gives two away on day 1, four away on day 2, and eight away on day 3. He continues this pattern for 10 days.

Let x be the number of days and f(x) be the number of cards.

So, the pattern is

f(x)=2, when x=1

f(x)=4, when x=2

f(x)=8, when x=3

Then, the function will be f(x)=2ˣ

The equation of the graph is passing through a vertical line.

The vertical line test is a graphical method that determines whether a curve in the plane represents the graph of a function by visually examining the number of intersections of the curve with vertical lines.

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The required number of songs that can be put in the final CD are 5 song.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
A band expects to put 16 songs on their next CD. The band writes and records ​25% more songs than they expect to put on the CD. During the editing​ process, 75​% of the songs are removed.

According to the question,
Song added to CD = 16 + 25% of 16
                               = 20 songs

Song added to Final CD = 20 - 75% of 20
                                        = 5 songs

Thus, the required number of songs that can be put in the final CD are 5 song.

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The required simplified value of the given expression is [A × B] ×10².

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given expression,
=  A x 10 ×  B × 10

Applying distributive property, a (bc) = (ab) c
= A × B × 10 × 10

Applying associative property in the exponents of 10, 10 × 10 = 10²
= [A × B] × 10²

Thus, the required simplified value of the given expression is [A × B] ×10².

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From given data, equation of line will be x - 2y = -16.

To find points on the line y = mx + b, choose x and solve the equation for y, or. choose y and solve for x.

The two-point form of a line is used for finding the equation of a line given two points (x1,y1) ( x 1 , y 1 ) and (x2,y2) ( x 2 , y 2 ) on it. The two point-form of a line is:y−y1=y2−y1x2−x1(x−x1) y − y 1 = y 2 − y 1 x 2 − x 1 ( x − x 1 ) OR y−y2=y2−y1x2−x1(x−x2) y − y 2 = y 2 − y 1 x 2 − x 1 ( x − x 2 ) .

It's called this because it clearly identifies the slope and the y-intercept in the equation. The slope is the number written before the x. The y-intercept is the constant written at the end. Let's look at an example: y = 3x + 2.

Given,

x represent how old the baby is in weeks

y represent the baby's weight in pounds.

At 2 weeks old, baby Nellie weighed 9 pounds. When she was 8 weeks old, she weighed 12 pounds.

⇒ (2,9)

⇒ (8,12)

Equation of line will be = y - yo = m (x - xo)

= y - 9 = 1/2 (x - 2)

= 2y - 18 = x - 2

= x - 2y = -16

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[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{3}-\stackrel{y1}{1}}}{\underset{\textit{\large run}} {\underset{x_2}{3}-\underset{x_1}{1}}} \implies \cfrac{ 2 }{ 2 } \implies 1[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{ 1}(x-\stackrel{x_1}{1})\implies y-1=x-1\implies \boxed{y=x}[/tex]

Answer: y=x+2

Step-by-step explanation: to find the slope use the formula y2-y1/x2-x1 which will get 3-1/3-1= 2/2= 1 so the slope is one. then take formula (y-y1)=m(x-x1) m is slope so you will get (y-3)=1(x-1) distribute the one y-3=x-1 add three to both sides to get y=x+2

Step-by-step explanation:

Elaine spent 6.30 + px dollars on her purchase and Elena spent 4.15 + 4p dollars on her purchase. To find how much more Elaine spent, we can subtract Elena's total cost from Elaine's total cost: (6.30 + px) - (4.15 + 4p) = (6.30 - 4.15) + (px - 4p) = 2.15 + (px - 4p) = 2.15 + p*x - 4p. This is the simplified expression for how much more Elaine spent than Elena.

Answer:

36-30:[26-100:(10-12:b)]=6 - 10417845.

Answer:

Table C

Step-by-step explanation:

This is a problem that is just process of elimination. The first step here is to organize all the x values (in each table) by value (lowest to highest). Luckily this has already been done for us. The next step is to establish slope. We can do this from any two points in the table. You find the difference between the y-values (y2-y1), then the x values (x2-x1) (where the points are (x1,y1) (x2,y2)). Now we just need to make sure the rest of the points obey that same slope.

For Example, take table A. The first two points are (1,-1) and (3,1) so using what was said before, the change in the x values is +2, and the change in the y values is +2 as well. Now applying that to the last two points, (5,3) and (8,5) we can see the slope is not the same. The change is x is +3 and the change in y is +2. Therefore we know that Table A does not represent a linear function.

The only table that has a constant slope is Table C with a change in x of +3, and a change in y of +2.

A Closed Question is a type of question which has fixed choices for answers, whereas an Open Question is a free response question.

The Open Questions are questions that allow for a free-flowing response, they often starting with "what," "how," "why," etc. They encourage the  elaboration and provide deeper insights about topic .

The Closed Questions are questions which can be answered with a simple "yes" or "no" or a specific piece of information. They are good for quickly gathering specific information.

For Open Questions :

⇒ Advantages : Encourages elaboration and deeper insights , Builds rapport and relationship , Promotes active listening and understanding .

⇒ Disadvantages  : Can be time-consuming and harder to analyze , May lead to vague or irrelevant responses

For Closed Questions :

⇒ Advantages : Quick and easy to answer , Facilitates efficient information gathering , Good for verifying information

⇒ Disadvantages : May limit information obtained , Can come across as rigid and uninterested .

The given question is incomplete  , the complete question is

What is an Open and Closed Question ; discuss the advantages and disadvantages of each type of question .

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Answer:

The expression for the truck's position in terms of t would be xtruck = t × vtruck, where vtruck is the truck's velocity. The expression for the car's position in terms of t would be xcar = t × vcar + x0, where vcar is the car's velocity and x0 is the car's initial position. For the vehicles to eventually meet, these two equations must be equal, so vtruck = vcar + (x_0/t).

Same amount of money can buy 95 dinners after 12 years.

Inflation is a decrease in the purchasing power of money, reflected in a general increase in the prices of goods and services in an economy.

Given,

Purchasing power of a fixed quantity of money decreases by 5% every year

It can buy 175 frozen dinners today,

Principal value P = 175 frozen dinners

Rate of decrease R = 5% = 0.05

Time n = 12 years

Equation for the future value

A = P (1- R)ⁿ

Frozen dinners that can be bought in 12 years with same amount

A = 175 ( 1 - 0.05 )¹²

A = 175 (0.95)¹²

A = 175 × 0.540360088

A = 94.5630154 ≈ 95

Hence, 95 frozen dinners can be bought after 12 years with same amount of money.

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Answer:

3+[tex]\frac{1}{4}w[/tex]  represents the distance ran on week w

Answer:

16/2

Step-by-step explanation:

2 2/7  = 16/2

2 times 7 = 14 + 2 = 16/2

So, the answer is 16/2

Answer:

2 2/7 = 17/7

Step-by-step explanation:

The way I learnt it is that when you take 2 2/7 we just have to multply the denominator (7) by the whole number (2) which gives us 14 and then we have to add the numerator (2) which gives us our numerator which is 16 and the denominator stays the same meaning our answer would be 17/7. (It is the simplest form)