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2 years ago

The table below summarises the number of books in some students' schoolbags.

Mathematics

1 answer:

aliya0001 [1]2 years ago

4 0

Answer:

Total number of students = 50 students.

Step-by-step explanation:

Total number of books = number of books * frequency

1 * 3 = 3

2 * 5 = 10

3 * 12 = 36

4 * 25 = 100

5 * 4 = 20

6 * 1 = 6

Total number of books = 3 + 10 + 36 + 100 + 20 + 6

Total number of books = 175 books.

Now, to find the total number of students;

Total number of students = summation of frequency

Total number of students = 3 + 5 + 12 + 25 + 4 + 1

Total number of students = 50 students.

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Consider the triangle with sides a=1.6, b=2.3 and c=1.2 feet. You can use cosine theorem twice to find two unknown angles:

$b^2=a^2+c^2-2ac\cos \angle B,\\ (2.3)^2=(1.6)^2+(1.2)^2-2\cdot 1.6\cdot 1.2\cos \angle B,\\ 5.29=2.56+1.44-3.84\cos \angle B,\\ 3.84\cos \angle B=4-5.29=-1.29,\\\cos \angle B=-\dfrac{1.29}{3.84} =-0.336$

Then you can conclude that ∠B is obtuse (because $\cos \angle B$ ) and m∠B=110°.

$c^2=a^2+b^2-2ab\cos \angle C,\\ (1.2)^2=(1.6)^2+(2.3)^2-2\cdot 1.6\cdot 2.3\cos \angle C,\\ 1.44=2.56+5.29-7.36\cos \angle C,\\ 7.36\cos \angle C=7.85-1.44=6.41,\\\cos \angle C=\dfrac{6.41}{7.36} =0.871$ .

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3. m∠A+m∠B+m∠C=180°, then m∠A=180°-110°-29°=41°.

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