Answer:
I should use at least 304 students
Step-by-step explanation:
Margin error (E) = t × sd/√n
E = 40
sd = 300
confidence level (C) = 98% = 0.98
significance level = 1 - C = 1 - 0.98 = 0.02 = 2%
t-value corresponding to 2% significance level and infinity degree of freedom is 2.326
n = (t×sd/E)^2 = (2.326×300/40)^2 = 17.445^2 = 304 (to the nearest integer)
The value of the side c will be 5.56 cm and angle C is 32.49° and angle B is 42.51°.
<h3>What is law of cosine?</h3>
Let there is a triangle ABC such that |AB| = a units, |AC| = b units, and |BC| = c units and the internal angle A is of θ degrees, then we have:
a² + b² – 2ab cos C = c²
Given triangle ABC, A = 105°, a = 10 cm, b = 7 cm.
Then we have
7² + c² – (2 · 7 · c) cos 105° = 10²
c² + 3.62c – 51 = 0
On solving, we have
c = 5.56
Then the angle C will be
10² + 7² – 2 · 7 · 10 · cos C = 5.56²
149 – 140 cos C = 30.91
cos C = 0.8435
C = 32.49°
We know that
∠A + ∠B + ∠C = 180°
105° + ∠B + 32.49° = 180°
∠B = 42.51°
Learn more about law of cosines here:
brainly.com/question/17289163
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Answer:
464 feet
Step-by-step explanation:
<em>The Sine of the angle of inclination gives the increase in altitude.</em>
<em>This is because the Sine of an angle is equal to the Opposite side divided by the Hypotenuse side. i.e</em>
Sin Ф = Opposite ÷ Hypotenuse
Sin 5° = O ÷ 5328
0·08716 = O ÷ 5328
<em>Make </em>O<em> the subject and multiply every fraction by </em>5328
(0·08716/1 × 5328)= (O/5328 × 5328)
464·388 = O
∴ The increase in altitude is 464·388 feet
<em>This is supposed to be to the nearest foot so we round off</em>
464·388 becomes 464 feet
Jill will pick up 24 and jack will pick up 25
Answer:
1 7/8 pounds.
Step-by-step explanation:
3/8 * 5
= 15/8
= 1 7/8 pounds.
