A bag contains 10 red marbles, 8 blue marbles and 2 yellow marbles. Find the theoretical probability of getting a yellow marble.

Complete the following exercises by applying polynomial identities to complex numbers. Factor x2 + 64. Check your work. Factor 1

Mumz [18]

$x^2+64=x^2-(8i)^2=(x-8i)(x+8i)$

$16x^2+49=(4x)^2-(7i)^2=(4x-7i)(4x+7i)$

$(x+9i)^2=x^2+2x\cdot9i+(9i)^2=x^2+18xi+81i^2=x^2+18xi-81=x^2-81+18xi$

$(x-2i)^2=x^2-2x\cdot2i+(2i)^2=x^2-4xi+4i^2=x^2-4xi-4=x^2-4-4xi$

$(x+(3+5i))^2=x^2+2x(3+5i)+(3+5i)^2\\\\=x^2+6x+10xi+3^2+2\cdot3\cdot5i+(5i)^2\\\\=x^2+6x+10xi+9+30i+25i^2=x^2+6x+10xi+9+30i-25\\\\=x^2+6x+10xi+30i-16=x^2+6x-16+(10x+30)i$

$Used:\\i^2=-1\\\\a^2-b^2=(a-b)(a+b)\\\\(a+b)^2=a^2+2ab+b^2$

4 0

3 years ago

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where p is the price (in dollars) and x is the number of units (in thousands). Find the average price p on the interval 40 ≤ x ≤

marusya05 [52]

THIS IS THE COMPLETE QUESTION BELOW

The demand equation for a product is p=90000/400+3x where p is the price (in dollars) and x is the number of units (in thousands). Find the average price p on the interval 40 ≤ x ≤ 50.

Answer

$168.27

Step by step Explanation

Given p=90000/400+3x

With the limits of 40 to 50

Then we need the integral in the form below to find the average price

1/(g-d)∫ⁿₐf(x)dx

Where n= 40 and a= 50, then if we substitute p and the limits then we integrate

1/(50-40)∫⁵⁰₄₀(90000/400+3x)

1/10∫⁵⁰₄₀(90000/400+3x)

If we perform some factorization we have

90000/(10)(3)∫3dx/(400+3x)

3000[ln400+3x]₄₀⁵⁰

Then let substitute the upper and lower limits we have

3000[ln400+3(50)]-ln[400+3(40]

30000[ln550-ln520]

3000[6.3099×6.254]

3000[0.056]

=168.27

the average price p on the interval 40 ≤ x ≤ 50 is

=$168.27

8 0

3 years ago

f(x)=5x reflected over the x axis

postnew [5]

Answer:

f(x) = -5x

Step-by-step explanation:

Just add a - sign to reflect it over the x axis

6 0

3 years ago

Please help i dont understand

Greeley [361]

Given:

A quadrilateral inscribed in a circle.

To find:

The value of x and y.

Solution:

If a quadrilateral inscribed in a circle, then it is known as cyclic quadrilateral and the opposite angles of a cyclic quadrilateral are supplementary angles, it means their sum is 180 degrees.

$5x^\circ+110^\circ=180^\circ$ [Supplementary angles]

$5x^\circ=180^\circ -110^\circ$

$x^\circ=\dfrac{70^\circ}{5}$

$x^\circ=14^\circ$

The value of x is 14 degrees.

$2y^\circ+104^\circ=180^\circ$ [Supplementary angles]

$2y^\circ=180^\circ -104^\circ$

$y^\circ=\dfrac{76^\circ}{2}$

$y^\circ=38^\circ$

Therefore, the value of x is 14 degrees and the value of y is 38 degrees.

3 0

3 years ago

What is the value of x in the equation 4x + 8y = 40, when y = 0.8?

storchak [24]

To find your answer you must substitute y for 0.8
4x + (8)(0.8) = 40
Now solve for x
====================================================================
SOLVING...

4x + (8)(0.8) = 40
4x + 6.4 = 40

Subtract 6.4 from each side
4x+ 6.4 − 6.4 = 40 − 6.4
4x = 33.6

Divide each side by 4
4x ÷ 4 = 33.6 ÷ 4
x = 8.4

3 0

3 years ago

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