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Wittaler [7]
3 years ago
6

Four friends were born in consecutive years. The sum of their ages is 62.

Mathematics
1 answer:
Bas_tet [7]3 years ago
3 0

Answer:

4+62=66

Step-by-step explanation:

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I need help with these three problems please​
Liono4ka [1.6K]

Answer:

Q7. 11.3 inches (3 s.f.)

Q8. 96.2 ft

Q9. 36.4cm

Step-by-step explanation:

Q7. Please see attached picture for full solution.

Q8. Let the length of a side of the square be x ft.

Applying Pythagoras' Theorem,

34^{2}  =  {x}^{2}  +  {x}^{2}  \\ 2 {x}^{2}  = 1156 \\  {x}^{2}  = 1156 \div 2 \\  {x}^{2}  = 578 \\ x =  \sqrt{578}  \\

Thus, the perimeter of the square is

= 4( \sqrt{578} ) \\  = 96.2 ft\:  \:  \: (3 \: s.f.)

Q9. Equilateral triangles have 3 equal sides and each interior angle is 60°.

Since the perimeter of the equilateral triangle is 126cm,

length of each side= 126÷3 = 42 cm

The green line drawn in picture 3 is the altitude of the triangle.

Let the altitude of the triangle be x cm.

sin 60°= \frac{x}{42}

\frac{ \sqrt{3} }{2}  =  \frac{x}{42}  \\ x =  \frac{ \sqrt{3} }{2}  \times 42 \\ x = 21 \sqrt{3}  \\ x = 36.4

(to 3 s.f.)

Therefore, the length of the altitude of the triangle is 36.4cm.

4 0
3 years ago
Read 2 more answers
What is the final amount if 1548 is increased by 5% followed by a further 6% increase?
stiv31 [10]

Answer:

1,718.28

Step-by-step explanation:

1,548, percentage increased by 11% (percent) of its value = 1,718.28

3 0
3 years ago
In a clinical test with 2161 subjects, 1214 showed improvement from the treatment. Find the margin of error for the 95% confiden
Vlad [161]

Answer:

The margin of error for the 95% confidence interval used to estimate the population proportion is of 0.0209.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the z-score that has a p-value of 1 - \frac{\alpha}{2}.

The margin of error is of:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

In a clinical test with 2161 subjects, 1214 showed improvement from the treatment.

This means that n = 2161, \pi = \frac{1214}{2161} = 0.5618

95% confidence level

So \alpha = 0.05, z is the value of Z that has a p-value of 1 - \frac{0.05}{2} = 0.975, so Z = 1.96.

Margin of error:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

M = 1.96\sqrt{\frac{0.5618*0.4382}{2161}}

M = 0.0209

The margin of error for the 95% confidence interval used to estimate the population proportion is of 0.0209.

4 0
3 years ago
The first term of a geometric sequence is equal to a and the common ratio of the sequence is r.
ololo11 [35]

Answer: (a)  {a, ar, ar², ar³, ar⁴, ar⁵...}, (b)  arⁿ⁻¹

For part (a), the question gives us the first term a, and then asks us to apply the common ratio r six times.

In order for ar = a, the nth term of r will have to equal 0 (this implies that n is an exponent; thus giving us the first term a, as r = 1).

Since we use this method on the first term, we must use it for the next five, in which r gains an additional exponent for every consecutive value (nth term) thereafter.  

Ultimately getting: {a, ar, ar², ar³, ar⁴, ar⁵...}

For part (b), we first have to understand that the sequence does not start at 0, but at 1 for n. In order for ar = a, with n = 1, there needs to be subtraction of -1 within the exponent. So that arⁿ⁻¹

If we check and apply this, we can see that:

{ar¹⁻¹, ar²⁻¹, ar³⁻¹, ar⁴⁻¹, ar⁵⁻¹, ar⁶⁻¹...} = {a, ar, ar², ar³, ar⁴, ar⁵...} = arⁿ⁻¹ = Tn

4 0
3 years ago
Qué capital prestó Carlos a Miguel. Si realizó el préstamo a un tiempo de 200 días, al 15 % y el beneficio que obtuvo Carlos del
MrRa [10]

Answer:

I do not know how to read Spanish sorry........

Step-by-step explanation:

8 0
2 years ago
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