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vlada-n [284]
3 years ago
13

One number is 20 greater than another. If the lesser number is subtracted from three times the greater number, the difference is

84. Find the numbers. ​
Mathematics
1 answer:
RoseWind [281]3 years ago
6 0

Answer:

<u>The numbers are 12 and 32.</u>

Step-by-step explanation:

x = One number

x - 20 = Another number

3x - (x - 20) = 84 (If the lesser number is subtracted from three times the greater number, the difference is 84)

Let's solve for x, this way:

3x - (x - 20) = 84

3x - x + 20 = 84

2x = 84 - 20 (Subtracting 20 at both sides)

2x = 64

x = 64/2

<u>x = 32 ⇒ x - 20 = 12</u>

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Sindrei [870]

Answer:4.5 cups of sugar

Step-by-step explanation:

Okay so 24 cookies is 2 dozen

1 cup of sugar would be used for every 8 cookies

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5 0
2 years ago
Suppose X, Y, and Z are random variables with the joint density function f(x, y, z) = Ce−(0.5x + 0.2y + 0.1z) if x ≥ 0, y ≥ 0, z
kompoz [17]

a.

f_{X,Y,Z}(x,y,z)=\begin{cases}Ce^{-(0.5x+0.2y+0.1z)}&\text{for }x\ge0,y\ge0,z\ge0\\0&\text{otherwise}\end{cases}

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\displaystyle\int_0^\infty\int_0^\infty\int_0^\infty f_{X,Y,Z}(x,y,z)\,\mathrm dx\,\mathrm dy\,\mathrm dz=100C=1\implies \boxed{C=0.01}

b. Find the marginal joint density of X and Y by integrating the joint density with respect to z:

f_{X,Y}(x,y)=\displaystyle\int_0^\infty f_{X,Y,Z}(x,y,z)\,\mathrm dz=0.01e^{-(0.5x+0.2y)}\int_0^\infty e^{-0.1z}\,\mathrm dz

\implies f_{X,Y}(x,y)=\begin{cases}0.1e^{-(0.5x+0.2y)}&\text{for }x\ge0,y\ge0\\0&\text{otherwise}\end{cases}

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\displaystyle P(X\le1.375,Y\le1.5)=\int_0^{1.5}\int_0^{1.375}f_{X,Y}(x,y)\,\mathrm dx\,\mathrm dy

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\displaystyle P(X\le1.375,Y\le1.5,Z\le1)=\int_0^1\int_0^{1.5}\int_0^{1.375}f_{X,Y,Z}(x,y,z)\,\mathrm dx\,\mathrm dy\,\mathrm dz

\approx\boxed{0.012262}

7 0
3 years ago
Evaluate sec 240Á without using a calculator by using ratios in a reference triangle.
s344n2d4d5 [400]
Sec∅ = 1/cos∅
= 1/cos(240)
= 1/cos(180 + 60)
= 1/-cos(60)
= 1/(-1/2)
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Answer:

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3 years ago
Suppose George wins 34​% of all chess games. ​(a) What is the probability that George wins two chess games in a​ row? ​(b) What
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Answer:

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4 0
3 years ago
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