Answer:
Country A = 84
Country B = 28
Country C = 18
Step-by-step explanation:
Country A, Country B, and Country C won a total of 130 medals;
A + B + C = 130 ......1
Country B won 10 more medals than Country C;
B = C + 10 .......2
Country A won 38 more medals than the total amount won by the other two;
A = B + C + 38 ........3
Substituting equation 3 to 1;
(B+C+38) + B+C = 130
2B + 2C + 38 = 130 .......4
Substituting equation 2 into 4;
2(C+10) + 2C + 38 = 130
4C + 58 = 130
4C = 130-58 = 72
C = 72/4 = 18
B = C + 10 = 18 + 10 = 28
A = B + C + 38 = 18 + 28 + 38 = 84
9514 1404 393
3 3/4 cups
The yield from 3/4 cup of sugar is 2 dozen cookies. Multiply that by 5 and you get: the yield from 15/4 cups of sugar is 10 dozen cookies.
As a mixed number 15/4 = 3 3/4.
Ana will need 3 3/4 cups of sugar for 10 dozen cookies.
see explanation
Expand both factors and collect like term
Using Pascal' triangle with n = 6 to obtain the coefficients
1 6 15 20 15 6 1
Decreasing powers of 1 from to
Increasing powers of 3x from to
= 1. + 6. + 15. + 20. + 15.1² + 6. + 1.
= 1 + 18x + 135x² + 540x³ + 1215 + 1458 + 729
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= 1 - 18x + 135x² - 540x³ + 1215 - 1458 + 729
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Collecting like terms from both expressions
+
= 2 + 270x² + 2430 + 1458
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(2)
Using Pascal's triangle with n = 5
1 5 10 10 5 1
Increasing powers of 2x from to
= 1. + 5. + 10. + 10. + 5.+ 1.
= 1 + 10x + 40x² + 80x³ + 80 + 32
option (D) 16.5
Data provided:
Sleep time of , X = 15.9 is at the 10th percentile
Standard deviation, σ = 0.5 hour
also,
10th percentile of normal distribution is
Z = F⁻¹(0.10)
or
Z = - 1.28 (Using Standard Normal distribution)
Now,
X = μ + ( σ × Z )
μ = X - ( σ × Z )
on substituting the respective values, we get
μ = 15.9 - 0.5 × (-1.28)
μ = 16.5
Hence, the correct answer is option (D) 16.5