the ratio of boys to girls in your class is 3:4 there are 20 girls in the class how many boys are there ?

The correct equation is P(B|A) = P(A and B) / P(A), which demonstrates that the conditional probability depends on the order of events and the individual probabilities of A and B.

The confusion of the inverse occurs when we mistakenly believe that P(B|A) is equal to P(A and B), disregarding the individual probabilities of events A and B. However, the correct formula for conditional probability is P(B|A) = P(A and B) / P(A), which takes into account the probability of A and the joint probability of A and B.

The equation P(at least one) = 1 - P(none) represents the complement rule of probability, stating that the probability of at least one occurrence of an event A is equal to 1 minus the probability of none of the occurrences of A.

Furthermore, the equation P(A) + P(Ā) = 1 represents the total probability rule, indicating that the sum of the probability of event A and the probability of the complement of A (not A) is equal to 1.

To avoid confusion, it is crucial to understand and correctly apply the formulas for conditional probability, the complement rule, and the total probability rule.

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The correct question is : Confusion of the inverse occurs when we incorrectly believe Confusion of the inverse occurs when we incorrectly believe P(BIA) = P(AB). P(at least one) = 1 - P(none). P(A)+PĀ) = 1. P(A and B) P(BIA) = P(A)

Because Hermite interpolation can result in oscillatory behavior close to the boundary points, we avoid using it to estimate the derivative of a function using difference methods.

Hermite interpolation utilizes both the values of the function and its derivatives at the specified places. While this might produce closer approximations that are more accurate, it might also cause oscillations in the approximation close to the boundary points.

Lagrange interpolation, on the other hand, uses only function values and can result in smoother approximations. Lagrange interpolation is therefore favored over Hermite interpolation when estimating the derivative of a function using difference methods in order to prevent oscillatory behavior close to the boundary points.

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Alex has $15.78 and Rick has $12.15 money.

According to the question,

We have the following information:

Alex had $3.63 more than Rick. Together they had $27.93.

Let's take the money Rick has to be $x.

Now, we have the following expression for the money Alex has:

3.63+x

Now, we have:

x+3.63+x = 27.93

2x+3.63 = 27.93

Subtracting 3.63 from both the sides:

2x = 27.93-3.63

2x = 24.3

Dividing by 2 on both the sides:

x = 24.3/2

x = $12.15

So, Rick has $12.15.

Now, the money Alex has:

3.63+12.15

$15.78

Hence, Alex has $15.78 and Rick has $12.15 money.

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Answer:

45

Step-by-step explanation:I had that question on my test.

Answer:

Given -

Now, we'll calculate the work done by both the taps -

\( \\ \sf \: \frac{1}{4} + \frac{1}{6} \\ \\ \\ \bf \: lcm \: \: of \: \: 4 \: \: \& \: \: 6 = 12 \\ \\ \\ \implies \sf \: \frac{3 + 2}{12} \\ \\ \\ \implies \sf \frac{5}{12} \\ \\ \)

Now, reciprocal it -

\( \\ \implies \sf \frac{12}{5} = 2 \frac{2}{5} \\ \)

Therefore, time taken by both the taps will be 2 2/5 hours.

Answer:

5:7

Step-by-step explanation:

The limit of (x^4 - 1) / (x^2 - 1) as x approaches 1 is 1. To find the limit of the expression (x^4 - 1) / (x^2 - 1) as x approaches 1, we can simplify the expression and then evaluate the limit. The limit exists and is equal to 2.

To find the limit of (x^4 - 1) / (x^2 - 1) as x approaches 1, we can first simplify the expression. Notice that both the numerator and the denominator are differences of squares.

(x^4 - 1) = (x^2 + 1)(x^2 - 1)

(x^2 - 1) = (x + 1)(x - 1)

We can now rewrite the expression as:

[(x^2 + 1)(x^2 - 1)] / [(x + 1)(x - 1)]

We can then cancel out the common factors:

(x^2 + 1)/(x + 1)

Now we can evaluate the limit as x approaches 1 by substituting x = 1 into the simplified expression:

lim(x→1) [(x^2 + 1)/(x + 1)]

= (1^2 + 1)/(1 + 1)

= (1 + 1)/(1 + 1)

= 2/2

= 1

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The best way to remedy Ask customers throughout the day on both weekdays and weekends.

The cause of the bias in the survey is likely sampling bias. This means that the sample of 110 customers may not be representative of the entire population of food court shoppers. The bias can arise if the sample is not selected randomly or if certain groups of shoppers are overrepresented or underrepresented in the sample.

To remedy the sampling bias, the best way would be to  Ask customers throughout the day on both weekdays and weekends.

By surveying customers at different times, including both weekdays and weekends, a more diverse and representative sample can be obtained. This will help to capture the preferences of a wider range of food court shoppers and reduce the bias introduced by sampling only weekday mornings.

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The manager of a shopping mall wishes to expand the number of shops available in the food court. He has a market researcher survey the first 110 customers who come into the food court during weekday mamings in distin what types of food the shoppers would like to see added to the food court,

Which of the following is the best way to remedy this problem?

OA cisne the sample size so that more people respond to the question OB Ask customers throughout the day on both weekdays and hands

OC Reward the question so that it is balanced

Answer:

14+14 + 4pi= 28 + 4pi

\(\pi\)

Answer:

The point of intersection between 2x+3y=12 and 2x-y=4 is (3,2)

Step-by-step explanation:

Answer:

i think its the 3 one

Step-by-step explanation:

sorry if im wrong

Answer:

x=3y-29/y-8

Step-by-step explanation:

3(y-10)+1=x(y-8)

xy-8x=3y-29

x(y-8)=3y-29

/y-8        /y-8

x=3y-29/y-8

Answer: f (x) = 9(2) ^2

Step-by-step explanation:

this is the correct answer :)

Answer:Here you go

Step-by-step explanation:

Change everything into terms of sine and cosine.

Use the identities when you can.

Start with simplifying the left-hand side of the equation, then, once you get stuck, simplify the right-hand side. As long as the two sides end up with the same final expression, the identity is true.

Answer:

Jacob got 18 votes.

Hope this helps :)

Answer:

Josephine

Step-by-step explanation:

2 criteria was given to pass an exam:

1. At least, a mean mark of 40% must be achieved in the exam consisting of 4 papers

2. Score at least, 33% in each paper.

From the table given, and considering these two criteria, James definitely didn't pass the examination. He scored below 33% in one of the 4 papers. James scored 30% in Maths

Calculated the mean score for John and Josephine to determine if they meet the first criteria of having at least a mean score of 40%.

Mean score of John = (35 + 36 + 42 + 44) ÷ 4 = 39.25%

Mean score for Josephine = (60 + 55 + 38 + 75) ÷ 4 = 57%

Josephine passed the examination because she had a mean score of 57%, and also scored 33% and above in each test.

Answer:

Perimeter: 56 cm

Area: 196 cm²

Answer:

Step-by-step explanation:

1. m/-8 = -2.5

*-8 = *-8

m = -2.5*-8

m = 2.5*8

m = 20

2. 7/8a = 42

*8            *8

7a = 336

/7       /7

a = 336/7

a = 48

Hope this helped,

Kavitha

We can calculate the product of 5/8 and 4 to be 5/2 using multiplication.

Multiplication is one of the four basic mathematical operations, along with addition, subtraction, and division.

The result of a multiplication operation is a product.

There are four different methods for multiplying: addition, long multiplication, grid multiplication, and drawing lines.

So, we have:
5/8 and 4

5/8 is in the form p/q which represents the fraction that must be multiplied by 4.

Now, calculate the product as follows:

5/8 * 4

5/2

Therefore, we can calculate the product of 5/8 and 4 to be 5/2 using multiplication.

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Answer: B

Step-by-step explanation:t+4+3−2.2t

Add 4 and 3 to get 7.

t+7−2.2t

Combine t and −2.2t to get −1.2t.

−1.2t+7

In exercise 10(b) of Chapter 10, Section 5, the question asks whether it is possible to cross all the bridges shown in a given map exactly once and return to the starting point.

This problem is known as the "Seven Bridges of Königsberg" puzzle, famously solved by Leonhard Euler in the 18th century. The solution involves applying graph theory principles to analyze the connectivity and degree of the bridges. The Seven Bridges of Königsberg problem is a well-known mathematical puzzle that involves a network of bridges and islands. The goal is to determine whether it is possible to cross each bridge exactly once and return to the starting point. This problem was originally posed by the Swiss mathematician Leonhard Euler in 1736 and played a significant role in the development of graph theory.

To solve this problem, we can represent the bridges and islands as a graph. Each island is represented as a vertex, and each bridge is represented as an edge connecting two vertices. By analyzing the connectivity and degree of the vertices in the graph, we can determine whether a solution exists.

In the given map, we would analyze the graph formed by the bridges and islands. If each island has an even degree (an even number of bridges connected to it), then it is possible to find a path that crosses each bridge exactly once and returns to the starting point. This can be proved using Euler's theorem, which states that in a connected graph, if the number of vertices with an odd degree is either 0 or 2, then there exists an Eulerian path or an Eulerian circuit respectively. However, if any island has an odd degree, it is not possible to find a path that satisfies the conditions of crossing each bridge exactly once and returning to the starting point.

Without further information or a specific map, it is not possible to determine the exact solution to exercise 10(b) in Chapter 10, Section 5. The solution would require analyzing the connectivity and degree of the bridges and islands in the given map and applying graph theory principles to determine the possibility of crossing all the bridges exactly once and returning to the starting point.

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Answer:

x < -7

Step-by-step explanation:

The circle is open meaning -7 is not included in the answer

Answer:

  24.1 billion

Step-by-step explanation:

One way to write the logistic function is ...

  P(t) = AB/(A +(B-A)e^(-kt))

where A is initial value (P(0)), and B is the carrying capacity (P(∞)). We are told to use relative population growth in the 1990s as the value for k.

In billions, we have ...

  A = 5.3

  B = 100

  k = 0.02/5.3 ≈ 0.003774 . . . . . relative growth rate at 20 M per year

  t = 2450 -1990 = 460

  \(P(t)=\dfrac{530}{5.3+94.7e^{-0.003774t}}\\\\P(460)=\dfrac{530}{5.3+94.7e^{-1.73604}}\approx \boxed{24.1\quad\text{billion}}\)

Answer:

b= -16/3

Step-by-step explanation:

The total surface area of the cylinder is equal to 117.8 in^2

The total surface area of a cylinder can be calculated using the formula

\(TSA = 2\pi rh + 2\pi r^2\)

Let's substitute the values and proceed to solve.

\(TSA = 2\pi rh + 2\pi r^2\\TSA = 2\pi * 2.5 * 5 + 2\pi * 2.5^2\\TSA = 117.8in^2\)

The total surface area of the cylinder is 117.8 squared inch.

The area of each circle is

\(A = \pi r^2 \\A = 19.6in^2\)

And there are two identical circle in the diagram and this will have a total area of

\(A = 2 * 19.6\\A = 39.2in^2\)

The area of the sum of the two circles is 39.2in^2 and the total surface area of the cylinder is 117.8in^2

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The area being measured will not match the Riemann sum. By employing ever smaller forms to divide the area more precisely, this mistake can be minimized. The sum approaches the area as the shapes become ever-smaller.

A specific type of approximation of an integral by a finite sum in mathematics is known as a Riemann sum. It bears the name of the German mathematician Bernhard Riemann from the nineteenth century. Approximating the area of functions or lines on a graph, as well as the length of curves and other approximations, is a highly typical use.

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Answer:

Step-by-step explanation:

The probability of getting three tails in three tosses When Mickey tosses a coin 50 times and records 27 heads is 12,167:125,000.

It is the ratio in an event of the number of favorable outcome to the total number of outcome of that event.

As the probability of an event can not be more than the number 1. Thus, he probability of failure of a event is equal to the difference of the 1 to the success of the event.

Mickey tosses a coin 50 times and records 27 heads. Thus, the probability of getting a head is,

\(P=\dfrac{27}{50}\\\)

The probability of not getting a head or getting a tail is,

\(P^{-1}=1-\dfrac{27}{50}\\P^{-1}=\dfrac{50-27}{50}\\P^{-1}=\dfrac{23}{50}\)

Now, Mickey tosses the same coin three more times. The probability of getting three tails in these tosses are,

\(P_{3t}=\dfrac{23}{50}\times\dfrac{23}{50}\times\dfrac{23}{50}\\P_{3t}=\dfrac{12167}{125000}\)

Thus, the probability of getting three tails in three tosses When Mickey tosses a coin 50 times and records 27 heads is 12,167:125,000.

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The expression that is equivalent to 0.40a, where a is the original attendance at a play, is 0.40 times a or 40% of a.

In this context, Stella is using the expression 0.40a to calculate the reduced attendance at the next performance. The variable "a" represents the original attendance at a play. When Stella multiplies 0.40 by "a," she is essentially finding 40% of the original attendance. This means that the expression 0.40a is equivalent to multiplying the original attendance by 0.40 or finding 40% of the original value. By using this expression, Stella can determine the reduced attendance for the next performance based on a certain percentage of the original attendance.

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The statement "x^2 - y^2 = (x - y)(x + y)" is always true. Since this holds true for any values of x and y, the statement is always true.

The statement "x^2 - y^2 = (x - y)(x + y)" is always true. We can prove this by expanding the right-hand side of the equation using the distributive property.

Expanding (x - y)(x + y) gives us:

(x - y)(x + y) = x(x + y) - y(x + y)

Using the distributive property, we can multiply each term:

x(x + y) - y(x + y) = x^2 + xy - xy - y^2

The middle terms, xy and -xy, cancel each other out, leaving us with:

x^2 - y^2

Thus, we have shown that x^2 - y^2 is equal to (x - y)(x + y).

Since this holds true for any values of x and y, the statement is always true.

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