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3 years ago

Suppose that of 1400 students, 550 take Spanish, 700 take biology, and 400 take both

Mathematics

1 answer:

jok3333 [9.3K]3 years ago

7 0

Answer:

17/28

Explanation:

1. Call A the event of selecting a student who takes Spanish and P(A) the corresponding probability:

P(A) = number of students who take Spanish / number of students

P(A) = 550 / 1400 = 11/28

2. Call B the event of selecting a student who takes biology and P(B) the corresponding probability:

P(B) = number of students who take biology / number of students

P(B) = 700 / 1,400 = 1/2

3. The joint probability, P(A∩B), is the probability that a student takes Spanish and biology:

P(A∩B) = number of students that take both Spanish and biology / number of students

P(A∩B) = 400/1400 = 2/7

4. By the properties of probabilities, the probability of the event A or B is:

P (A or B) = P (A∪B) = P(A) + P(B) - P(A∩B)

P(A or B) = 11/28 + 1/2 - 2/7 = (11 + 14 - 8) / 28 = 17/28

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Answer:

The quotient of x and 11.

Step-by-step explanation:

Given:

$\frac{x}{11}$

Required:

Write the expression in words

Solution:

In the expression given, we have the numerator which is the dividend (x), and the denominator which is the divisor (8).

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3 years ago

A) Expand and simplify (x + 4)(x-7)

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Answer:

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Step-by-step explanation:

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3 years ago

A rectangle has a length of 12 mm and a width of 15 mm. Which statement best describes the change in the

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Step-by-step explanation:

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3 years ago

Part B

alisha [4.7K]

Question:

Consider ΔABC, whose vertices are A (2, 1), B (3, 3), and C (1, 6); let the line segment AC represent the base of the triangle.

(a) Find the equation of the line passing through B and perpendicular to the line AC

(b) Let the point of intersection of line AC with the line you found in part A be point D. Find the coordinates of point D.

Answer:

$y = \frac{1}{5}x + \frac{12}{5}$

$D = (\frac{43}{26},\frac{71}{26})$

Step-by-step explanation:

Given

$\triangle ABC$

$A = (2,1)$

$B = (3,3)$

$C = (1,6)$

Solving (a): Line that passes through B, perpendicular to AC.

First, calculate the slope of AC

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Where:

$A = (2,1)$ --- $(x_1,y_1)$

$C = (1,6)$ --- $(x_2,y_2)$

The slope is:

$m = \frac{6- 1}{1 - 2}$

$m = \frac{5}{-1}$

$m = -5$

The slope of the line that passes through B is calculated as:

$m_2 = -\frac{1}{m}$ --- because it is perpendicular to AC.

So, we have:

$m_2 = -\frac{1}{-5}$

$m_2 = \frac{1}{5}$

The equation of the line is the calculated using:

$m_2 = \frac{y_2 - y_1}{x_2 - x_1}$

Where:

$m_2 = \frac{1}{5}$

$B = (3,3)$ --- $(x_1,y_1)$

$(x_2,y_2) = (x,y)$

So, we have:

$\frac{1}{5} = \frac{y - 3}{x - 3}$

Cross multiply

$5(y-3) = 1(x - 3)$

$5y - 15 = x - 3$

$5y = x - 3 + 15$

$5y = x +12$

Make y the subject

$y = \frac{1}{5}x + \frac{12}{5}$

Solving (b): Point of intersection between AC and $y = \frac{1}{5}x + \frac{12}{5}$

First, calculate the equation of AC using:

$y = m(x - x_1) + y_1$

Where:

$A = (2,1)$ --- $(x_1,y_1)$

$m = -5$

So:

$y=-5(x - 2) + 1$

$y=-5x + 10 + 1$

$y=-5x + 11$

So, we have:

$y=-5x + 11$ and $y = \frac{1}{5}x + \frac{12}{5}$

Equate both to solve for x

i.e.

$y = y$

$-5x + 11 = \frac{1}{5}x + \frac{12}{5}$

Collect like terms

$-5x -\frac{1}{5}x = \frac{12}{5} - 11$

Multiply through by 5

$-25x-x = 12 - 55$

Collect like terms

$-26x = -43$

Solve for x

$x = \frac{-43}{-26}$

$x = \frac{43}{26}$

Substitute $x = \frac{43}{26}$ in $y=-5x + 11$

$y = -5 * \frac{43}{26} + 11$

$y = \frac{-5 *43}{26} + 11$

Take LCM

$y = \frac{-5 *43+11 * 26}{26}$

$y = \frac{71}{26}$

Hence, the coordinates of D is:

$D = (\frac{43}{26},\frac{71}{26})$

3 0

3 years ago