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2 years ago

2/9 of the students in a school are in sixth grade.

Mathematics

1 answer:

UNO [17]2 years ago

7 0

20 sixth graders / 6 sixth graders / 216 students

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Use the distributive property to simplify 4^x(2^-6)

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Is it 4 times x or 4 to the power of x, if the first one then, 8x-24x. if the second then 8^-6x

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3 years ago

Total surface area of a cube is 1014cm^2. It's volume will be :

Karolina [17]

Answer:

Option A (2197 cm³)

Step-by-step explanation:

For a cube with length of each side "a" , it's

Total Surface Area = 6a²
Volume = a³

_____________________________________________

According to the question ,

Total Surface Area = 1014 cm²

Let the length of each side of cube be 'a'.

Using the formula ,

$6a^{2} =1014$

$=> a^{2} =\frac{1014}{6} = 169$

$=> a = \sqrt{169} = +13 \: or -13$

But length can't be negative . So , length of each side = 13 cm

∴ Volume of cube = 13³ = 2197 cm³

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3 years ago

Please help me! I really need this!

Paladinen [302]

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3 years ago

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Two parallel lines are crossed by a transversal.<br> What is the value of x? <br> ??!!!??!!!!!????

snow_tiger [21]

The answer for this problem: X = 12.

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3 years ago

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Please help me with the question

mars1129 [50]

(i) The mean is

$\displaystyle E(X) = \sum_x x \, P(X = x) \\\\ E(X) = 1\cdot0.175 + 2\cdot0.315 + 3\cdot0.211 + 4\cdot0.092 + 5\cdot0.207 \\\\ \boxed{E(X) = 2.839}$

The variance is

$V(X) = E((X - E(X))^2) = E(X^2) - E(X)^2$

Compute the second moment $E(X^2)$ :

$\displaystyle E(X^2) = \sum_x x^2 \, P(X = x) \\\\ E(X) = 1^2\cdot0.175 + 2^2\cdot0.315 + 3^2\times0.211 + 4^2\times0.092 + 5^2\times0.207 \\\\ E(X^2) = 9.997$

Then the variance is

$\boxed{V(X) \approx 1.9171}$

(ii) For a random variable $Z=aX+b$ , where $a,b$ are constants, we have

$E(Z) = E(aX+b) = E(aX) + E(b) = a E(X) + b$

and

$V(Z) = E((aX+b)^2) - E(aX+b)^2 \\\\ V(Z) = E(a^2 X^2 + 2ab X + b^2) - (a E(X) + b)^2 \\\\ V(Z) = a^2 (E(X^2) - E(X)^2) \\\\ V(Z) = a^2 V(X)$

Then for $Y=\frac{X+3}2$ , we have

$E(Y) = \dfrac12 E(X) + \dfrac32 \\\\ \boxed{E(Y) = 2.918}$

$E(Y^2) = E\left(\left(\dfrac{X+3}2\right)^2\right) = \dfrac14 E(X^2) + \dfrac32 E(X) + \dfrac94 \\\\ \boxed{E(Y^2) \approx 9.0028}$

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2 years ago