Answer:
<u>The correct answer is 61,650 Yens</u>
Step-by-step explanation:
US$ in cash that Ben has = 500
Exchange rate (US$/Yen) = 1 : 123.3
For calculating the total amount in Yens that Ben has, we use this formula:
Yens in Cash = US$ in Cash * Exchange rate given
Yens in Cash = 500 * 123.3
Yens in Cash = 61,650
<u>After converting the US$ 500 Ben has, he will receive Yens 61,650</u>
Answer:
- 5.8206 cm
- 10.528 cm
- 23.056 cm^2
Step-by-step explanation:
(a) The Law of Sines can be used to find BD.
BD/sin(48°) = BD/sin(50°)
BD = (6 cm)(sin(48°)/sin(60°)) ≈ 5.82064 cm
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(b) We can use the Law of Cosines to find AD.
AD^2 = AB^2 +BD^2 -2·AB·BD·cos(98°) . . . . . angle ABD = 48°+50°
AD^2 ≈ 110.841
AD ≈ √110.841 ≈ 10.5281 . . . cm
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(c) The area of ∆ABD can be found using the formula ...
A = ab·sin(θ)/2 . . . . . where a=AB, b=BD, θ = 98°
A = (8 cm)(5.82064 cm)sin(98°)/2 ≈ 23.0560 cm^2
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Angle ABD is the external angle of ∆BCD that is the sum of the remote interior angles BCD and BDC. Hence ∠ABD = 48° +50° = 98°.
Answer:
The absolute brightness of the Cepheid star after a period of 45 days is -5.95
Step-by-step explanation:
Since the absolute magnitude or brightness of a Cepheid star is related to its period or length of its pulse by
M = –2.78(log P) – 1.35 where M = absolute magnitude and P = period or length of pulse.
From our question, it is given that P = 45 days.
So, M = –2.78(log P) – 1.35
M = –2.78(log 45) – 1.35
M = –2.78(1.6532) – 1.35
M = -4.60 - 1.35
M = -5.95
So, the absolute magnitude or brightness M of a Cepheid star after a period P of 45 days is -5.95
The volume of a prism is the product of the area of a the base and its height. Given the volume of the prism as 15x2 + x + 2 and the height as x2, the base can be expressed using this expressions. Volume = base x height. By substitution, <span>15x2 + x + 2 = (base) x (x2). Thus the answer is, base = (15x2 + x + 2)/x2 or base = 15 + (1/x) + (2/x2).</span>
multiply the price by the discount then subtract the answer from the price
4 * 0.20 = 0.80
4-0.80 = 3.20
sale price is $3.20
