All categories

2 years ago

In a group of 40 people, 27 can speak English and 25 can speak Spanish. How many can speak

Mathematics

1 answer:

Svetradugi [14.3K]2 years ago

6 0

$\qquad {\: \:\bigstar \: {\underline{\overline{\boxed{\bf{Information \: provided \: with \: us }}}}}\: \bigstar}$

➻ In a group of 40 people, 27 can speak English and 25 can speak Spanish.

$\qquad {\: \:\bigstar \: {\underline{\overline{\boxed{\bf{What \: we \: have \: to \: find ? }}}}}\: \bigstar}$

➻ The required number of people who can speak both English and Spanish .

$\qquad {\: \:\bigstar \: {\underline{\overline{\boxed{\bf{Assumption}}}}}\: \bigstar}$

Consider ,

➻ A → Set of people who speak English.

➻ B → Set of people who speak Spanish

➻ A∩B → Set of people who can speak both English and Spanish

$\qquad {\: \:\bigstar \: {\underline{\overline{\boxed{\bf{Given}}}}}\: \bigstar}$

➻ n (A) = 27

➻ n (B) = 25

➻ n (A∪B) = 40

➻ n(A∩B) = ?

$\qquad {\: \:\bigstar \: {\underline{\overline{\boxed{\bf{Now}}}}}\: \bigstar}$

➻ n(A∪B) = n(A) + n (B) - n(A∩B)

➻ 40 = 27 + 25 - n (A∩B)

➻ 40 = 52 - n (A∩B)

➻ n (A∩B) = 52 - 40

➻ ∴ n (A∩B) = 12

$\qquad {\: \:\bigstar \: {\underline{\overline{\boxed{\bf{Therefore}}}}}\: \bigstar}$

∴ Required Number of persons who can speak both English and Spanish are 12 .

━━━━━━━━━━━━━━━━━━━━━━

$\qquad {\: \:\bigstar \: {\underline{\overline{\boxed{\bf{Verification}}}}}\: \bigstar}$

➻ n(A∪B) = n(A) + n (B) - n(A∩B)

➻ 40 = 27 + 25 - 12

➻ 40 = 52 - 12

➻ 40 = 40

➻ ∴ L.H.S = R.H.S

━━━━━━━━━━━━━━━━━━━━━━

You might be interested in

What is 87 over 62 in simplest form?

lawyer [7]

87/62 = 1 and 25/62 (simplest form)

4 0

3 years ago

Three more than a number is sixty. (Write the equation

Paha777 [63]

Answer:

x + 3 = 60

Step-by-step explanation:

Let the number be x

x + 3 = 60

Hope it helps :)

Please mark my answer as the brainliest

7 0

3 years ago

In a random sample of 1,000 high-school students, 29 percent indicated that they had read the Declaration of Independence at lea

7nadin3 [17]

Answer:

c. Ninety-five percent of the time, the percentage of those questioned who have read the Declaration of Independence would likely be between 25 and 33 percent.

Step-by-step explanation:

Margin of error:

"It means the percentage difference of the result above or below the exact value."

i.e. 4 percent of margin error in the question means that the result will be either 4 percent above the 29 percent or 4 percent below the 29 percent.

OR "the result can vary upto 4 percent above or below the 29 percent."

Let me simplify the answer first in number then convert it percent to understand easily.

29 percent of 1000= (29/100)*1000=290

4 percent of 1000=(4/100)*1000=40

If 290 students had read the declaration of independence at least once with 40 margin of error, then it means the number of students that had read declaration of independence may be 330 or 250

250 is 25% of 1000 and 330 is 33% of 1000, that is why ninety-five percent of the time, the percentage of those questioned who have read the Declaration of Independence would likely be between 25 and 33 percent.

4 0

3 years ago

Find the slope of the line that passes through (-33, -27) and (-32, -25).

Snezhnost [94]

Answer: 2.

Step-by-step explanation:

You can find the slope between two points by using the "rise-over-run" method.

This method essentially calculates the slope as the quotient of the vertical span and horizontal span of the two points.

You can find it through this formula:

$s = \frac{y2 - y1}{x2 - x1}$