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3 years ago

13

Fill in missing information to make the equality true: (... +2a)2 = … +12ab2+4a2.

1 answer:

DIA [1.3K]3 years ago

6 0

${ (3b + 2a)}^{2} = 9 {b}^{2} + 12ab + 4 {a}^{2}$

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You buy a lottery ticket to a lottery that costs $10 per ticket. There are only 100 tickets available to be sold in this lottery

riadik2000 [5.3K]

Answer:

Loss of $1.20

Step-by-step explanation:

The possible outcomes for this lottery and their probabilities are:

- a 1 in 100 chance of winning $450

- a 2 in 100 chance of winning $120

- a 4 in 100 chance of winning $30

- a 93 in 100 chance of losing $10

Therefore, the expected value of this lottery when buying one ticket is:

$E(X) = \frac{1}{100}*\$450+ \frac{2}{100}*\$120+ \frac{4}{100}*\$30-\frac{93}{100}*\$10 \\E(X) = -\$1.2$

Therefore, you are expected to lose $1.2 per ticket.

3 0

3 years ago

a line whose perpendicular distance from the origin is 4 units and the slope of perpendicular is 2÷3. Find the equation of the l

GrogVix [38]

Answer:

$\huge\boxed{y=\dfrac{2}{3}x-\dfrac{4\sqrt{13}}{3}\ \vee\ y=\dfrac{2}{3}x+\dfrac{4\sqrt{13}}{3}}$

Step-by-step explanation:

The equation of a line:

$y=mx+b$

We have

$m=\dfrac{2}{3}$

substitute:

$y=\dfrac{2}{3}x+b$

The formula of a distance between a point and a line:

General form of a line:

$Ax+By+C=0$

Point:

$(x_0,\ y_0)$

Distance:

$d=\dfrac{|Ax_0+By_0+C|}{\sqrt{A^2+b^2}}$

Convert the equation:

$y=\dfrac{2}{3}x+b$ |<em>subtract $y$ from both sides</em>

$\dfrac{2}{3}x-y+b=0$ |<em>multiply both sides by 3</em>

$2x-3y+3b=0\to A=2,\ B=-3,\ C=3b$

Coordinates of the point:

$(0,\ 0)\to x_0=0,\ y_0=0$

substitute:

$d=4$

$4=\dfrac{|2\cdot0+(-3)\cdot0+3b|}{\sqrt{2^2+(-3)^2}}\\\\4=\dfrac{|3b|}{\sqrt{4+9}}$

$4=\dfrac{|3b|}{\sqrt{13}}\qquad|$ |<em>multiply both sides by $\sqrt{13}$ </em>

$4\sqrt{13}=|3b|\iff3b=-4\sqrt{13}\ \vee\ 3b=4\sqrt{13}$ |<em>divide both sides by 3</em>

$b=-\dfrac{4\sqrt{13}}{3}\ \vee\ b=\dfrac{4\sqrt{13}}{3}$

Finally:

$y=\dfrac{2}{3}x-\dfrac{4\sqrt{13}}{3}\ \vee\ y=\dfrac{4\sqrt{13}}{3}$

4 0

2 years ago

Is the result of Double 5 and add 1 the same as the result of Add 1 to 5; then double the result?

just olya [345]

B. Double 5 plus 1 equals 11 and add 1 to 5 doubled equals 12.

7 0

3 years ago

Read 2 more answers

Can somebody help me with this math problem?

skad [1K]

Answer:

B) Rational, not an integer.

Step-by-step explanation:

The number is a decimal continuing forever; it is predictable. This means that it is Rational. If the number was not repeating then it would be irrational.

The number is not an integer because it is not a whole number; it is a decimal.

7 0

3 years ago

Gnesinka [82]

Answer: $x^2=8y$

Step-by-step explanation:

Let the given parabolic mirror opens upwards and vertex=(0,0)

Focus point of the parabolic mirror is located 2 inches from the vertex of the mirror. ∴ p=2

Since, the parabola opens upward, then the equation of the parabola is of the form $x^2=4py$

Substitute the value of p=2 in this, we get the equation of the parabolic mirror

$x^2=4(2)y\\\Rightarrow\ x^2=8y$

Hence, the equation of the parabola that models the cross section of the mirror is $x^2=8y$

7 0

2 years ago

Read 2 more answers