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4 years ago

3 times what equals 80

Mathematics

2 answers:

Amanda [17]4 years ago

8 0

Step-by-step explanation:

26.66 repeating is the answer because you divide 80 by 3

Troyanec [42]4 years ago

6 0

Answer:

26.6 repeating?

Step-by-step explanation:

80/3

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Which is the equation of a line that has a slope of 1 and passes through point (5, 3)?

Montano1993 [528]

Answer:

Step-by-step explanation:

6 0

3 years ago

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Find the coordinates of the circumcenter for ∆DEF with coordinates D(1,3) E (8,3) and F(1,-5). Show your work.

luda_lava [24]

Answer: The coordinates of the circumcenter is $(\frac{9}{2}, -1)$ .

Explanation:

The coordinates of triangle DEF are D(1,3) E (8,3) and F(1,-5).

Distance formula,

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$DE=\sqrt{(8-1)^2+(3-3)^2}=7$

$FE=\sqrt{(1-8)^2+(-5-3)^2}=\sqrt{7^2+8^2}$

$DF=\sqrt{(1-1)^2+(-5-3)^2}=8$

Since triangle follows pythagoras theorem,

$(DF)^2+(DE)^2=(FE)^2$

Therefore the given triangle is a right angle triangle.

Or plot these points on a coordinate plane. From the figure we can say that the triangle DEF is a right angle triangle.

The circumcenter of a right angle triangle is the midpoint of the hypotenuse.

The hypotenuse is EF. The midpoint of EF is,

$Midpoint =(\frac{8+1}{2}, \frac{3-5}{2} )=(\frac{9}{2}, -1)$

Therefore, the coordinates of the circumcenter is $(\frac{9}{2}, -1)$ .

5 0

3 years ago

Continue the pattern: 3-6,12,4,20

Brrunno [24]

Answer:

The most likely solution sought is 13:

Beginning with 3: subtract 9, add 18, subtract 8, add 16, subtract 7, add 14, etc. Each time, reduce the number subtracted by one, and double that number to add.

So, beginning with 3: 3-9 = -6, -6+2(9) = 12, 12-8 = 4, 4+2(8) = 20, 20-7 = 13, etc.

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Step-by-step explanation:

4 0

3 years ago

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4(x-5)=10(x-10)<br><br> solve for x

Zina [86]

Answer:

40/3

Step-by-step explanation:

4x -20 = 10x -100 (Distributive Property)

4x -10x = -100 +20 (I swith the numbers so all of them are similar)

-6x= -80 (Divide -6 on both sides)

And you will get 40/3 or 13.3333..

7 0

3 years ago

Exercise 5.2. Suppose that X has moment generating function

soldi70 [24.7K]

Answer:

a) Mean, E(X) = - 0.5

Variance = = 9.25

b) $M_{X}(t)=E(e^{tX})$

⇒ $=\sum e^{tx}p(x)$

⇒ $=\frac{1}{2}+\frac{1}{3}e^{-4t}+\frac{1}{6}e^{5t}$

Step-by-step explanation:

Given:

moment generating function of X as:

MX(t) = $\frac{1}{2} + \frac{1}{3}e^{-4t} + \frac{1}{6} e^{5t}$

a) Now

Mean, E(X) = $M_{X}'(t=0)$

Thus,

$M_{X}'(t)=\frac{1}{3}(-4)e^{-4t}+\frac{1}{6}(5)e^{5t}$

$M_{X}'(t)=\frac{-4}{3}e^{-4t}+\frac{5}{6}e^{5t}$

also,

$E(X^{2})=M_{X}''(t=0)$

Thus,

$M_{X}''(t)=\frac{-4}{3}(-4)e^{-4t}+\frac{5}{6}(5)e^{5t}$

$M_{X}''(t)=\frac{16}{3}e^{-4t}+\frac{25}{6}e^{5t}$

Therefore,

Mean, E(X) = $M_{X}'(t=0)=\frac{-4}{3}e^{-4(0)}+\frac{5}{6}e^{5(0)}$

Mean, E(X) = - 0.5

and

$E(X^{2})=M_{X}''(t=0)=\frac{16}{3}e^{-4(0)}+\frac{25}{6}e^{5(0)}$

$E(X^{2})$ = 9.5

also,

Variance(X) = E(X²) - E(X)²

⇒ 9.5 - (-0.5)²

= 9.25

b) Now,

Let f(x) be the PMF of X

Thus,

$M_{X}(t)=E(e^{tX})$

⇒ $=\sum e^{tx}p(x)$

⇒ $=\frac{1}{2}+\frac{1}{3}e^{-4t}+\frac{1}{6}e^{5t}$

Therefore,

at x = 0, P(x) = $\frac{1}{2}$

at x= - 4 ,P(x) = $\frac{1}{3}$

at x = 5, P(x) = $\frac{1}{6}$

Thus,

E(X) = $\sum xP(x)=0(\frac{1}{2})+(-4)(\frac{1}{3})+5(\frac{1}{6})$

E(X) = - 0.5

also, $E(X^{2})=\sum x^{2}P(x)=0^{2}(\frac{1}{2})+(-4)^{2}(\frac{1}{3})+5^{2}(\frac{1}{6})$

$E(X^{2})$ = 9.5

Hence,

Var(X) = E(X²) - E(X)²

⇒ 9.5 - (-0.5)²

= 9.25

4 0

4 years ago