Ivan and Tanya share £150 in the ratio 4:1 how much more Ivan has then tanya

Answer:

Step-by-step explanation:

Hello!

To determine whether boys excel in math classes compared to girls, two random samples were collected:

Sample 1

X₁: score achieved by a boy in calculus

n₁= 15

X[bar]₁= 82.3%

S₁= 5.6%

Sample 2

X₂: score obtained by a girl in calculus

n₂= 12

X[bar]₂= 81.2%

S₂= 6.7%

To estimate a confidence interval for the difference between the average percentages of boys and girls in calculus, it's essential that both variables come from normally distributed populations.

For utilizing a pooled variance t-test, it is also required that the population variances, though unknown, are assumed to be equal.

The confidence interval can then be calculated with:

[(X[bar]_1 - X[bar]₂) ± * ]

[(82.3 - 81.2) ± 1.708 * (6.11 * ]

[-2.94; 5.14]

Using a 90% confidence level, the interval [-2.94; 5.14] is expected to encompass the true difference between the average percentages achieved by boys and girls in calculus.

I hope this is of assistance!

We can summarize that

By applying the law of cosines: 

c² = a² + b² - 2abcos(C) 

where: 

a,b, and c represent the triangle's sides and C denotes the angle opposing side c.

Let us assign:

a=170 miles

b=200 miles

c=160 miles

Thus, we establish: 

160² = 170² + 200² - 2(170)(200)cos(C).

We now aim to solve for C.

25,600 = 28,900 + 40,000 - 68,000cos(C).

25,600 - 28,900 - 40,000 = -68,000cos(C).

-43,300=-68,000cos(C).

Thus, cos(C)=0.6367.

C=arc cos(0.6367)--------> C=50.45°.

Consequently, the captain should adjust toward island B by

180 - 50.45 = 129.55 degrees.

The final answer is

129.55 degrees