which represents the solution(s) of the system of equations, y=x^2-2x-15 and y=8x-40? determine the solution set algebraically

There are 210210210 students in a twelfth grade high school class. 909090 of these students have at least one sister and 1051051

BlackZzzverrR [31]

Answer:

(1) The value of P (A) is 0.4286.

(2) The value of P (B) is 0.50.

(3) The value of P (A ∩ B) is 0.2143.

(4) The the value of P (B|A) is 0.50.

(5) The events A and B are independent.

Step-by-step explanation:

The events are defined as follows:

A = a student in the class has a sister

B = a student has a brother

The information provided is:

N = 210

n (A) = 90

n (B) = 105

n (A ∩ B) = 45

The probability of an event E is the ratio of the favorable number of outcomes to the total number of outcomes.

$P(E)=\frac{n(E)}{N}$

The conditional probability of an event X provided that another event Y has already occurred is:

$P(X|Y)=\frac{P(A\cap Y)}{P(Y)}$

If the events X and Y are independent then,

$P(X|Y)=P(X)$

(1)

Compute the probability of event A as follows:

$P(A)=\frac{n(A)}{N}\\\\=\frac{90}{210}\\\\=0.4286$

The value of P (A) is 0.4286.

(2)

Compute the probability of event B as follows:

$P(B)=\frac{n(B)}{N}\\\\=\frac{105}{210}\\\\=0.50$

The value of P (B) is 0.50.

(3)

Compute the probability of event A and B as follows:

$P(A\cap B)=\frac{n(A\cap B)}{N}\\\\=\frac{45}{210}\\\\=0.2143$

The value of P (A ∩ B) is 0.2143.

(4)

Compute the probability of B given A as follows:

$P(B|A)=\frac{P(A\cap B)}{P(A)}\\\\=\frac{0.2143}{0.4286}\\\\=0.50$

The the value of P (B|A) is 0.50.

(5)

The value of P (B|A) = 0.50 = P (B).

Thus, the events A and B are independent.

6 0

2 years ago

Three less than the difference of 16p and 15p is equal to the difference of 3 and 1/2

Paraphin [41]

3 less: -3

difference of 16p and 15p: 16p - 15p = p

is equal to: =

the difference of 3 and 1/2: 3 - 1/2 = 2.5

p - 3 = 2.5

Isolate the p. Note the equal sign. What you do to one side, you do to the other. Add 3 to both sides

p - 3 (+3) = 2.5 (+3)

p = 2.5 + 3

p = 5.5

5.5 is your answer for p

hope this helps

5 0

2 years ago

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A news organization previously stated that three of four people believed that the state of the economy was the country's most si

gizmo_the_mogwai [7]

Answer:

Option d)

$H_{0}: p = 0.75\\H_A: p \neq 0.75$

Step-by-step explanation:

We are given the following in the question:

Three of four people believed that the state of the economy was the country's most significant concern.

They would like to test the new data against this prior belief.

The null hypothesis will state that the three of four people believed that the state of the economy was the country's most significant concern.

The alternate hypothesis will state that this is not true. It states that people believed that the state of the economy was the country's most significant concern is not the same.

$p =\dfrac{3}{4} = 0.75$

We design the null and the alternate hypothesis

$H_{0}: p = 0.75\\H_A: p \neq 0.75$

4 0

2 years ago

Simplify the function f (x) = one-half (27) Superscript StartFraction 2x Over 3 EndFraction. Then determine the key aspects of t

AleksandrR [38]

Answer:

(See explanation)

Step-by-step explanation:

The function is:

$f(x) = \frac{1}{2}\cdot 27 \cdot \frac{2\cdot x}{3}$

Its simplified form is presented hereafter:

$f(x) = 9\cdot x$

The resultant expression is a linear function, first-order polynomial, whose domain and range are the set of the real numbers.

6 0

2 years ago

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Which best describes the transformation that occurs from the graph of f(x) = x2 to g(x) = (x – 2)2 + 3?

Andrei [34K]

Answer:

A. right 2, up 3

Step-by-step explanation:

We have that,

The function $f(x) = x^2$ is transformed to $g(x) =(x- 2)^2+3$ .

We see that,

The function f(x) is translated 2 units to the right and 3 units upwards to obtain the function g(x).

So, the correct transformation is 'right 2, up 3'.

Hence, option A is correct.

5 0

2 years ago

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