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3 years ago

Add this problem 0645 + 0745

Mathematics

1 answer:

Citrus2011 [14]3 years ago

4 0

Answer:1,390

Step-by-step explanation: add the top and bottom

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Use completing the square to determine which of the following gives the solutions to 3x2 - 24x + 40 = 28.

jeka94

Answer:

$x=4+2\sqrt{3}$

$x=4-2\sqrt{3}$

Step-by-step explanation:

Completing the square

when $ax^2+bx+c=0$

Given equation:

$3x^2-24x+40=28$

Subtract 40 from both sides:

$\implies 3x^2-24x=-12$

Divide both sides by 3:

$\implies x^2-8x=-4$

Add the square of half the coefficient of $x$ to both sides:

$(\frac{b}{2})^2=(\frac{-8}{2})^2=16$

$\implies x^2-8x+16=-4+16$

Factor the left side and simplify the right side:

$\implies (x-4)^2=12$

Square root both sides:

$\implies x-4=\pm\sqrt{12}$

Add 4 to both sides and simplify the radical:

$\implies x=4\pm\sqrt{4 \cdot 3}$

$\implies x=4\pm\sqrt{4}\sqrt{3}$

$\implies x=4\pm2\sqrt{3}$

5 0

1 year ago

Simplify. 1/4 (-12+4/3)

matrenka [14]

Add what's in the parentheses first: -12 + 4/3 = -10 2/3

Then multiply -10 2/3 by 1/4: 1/4 x -10 2/3 = - 2 2/3

So your answer is -2 2/3.

Hope this helps! :D

~PutarPotato

3 0

3 years ago

How is arc length calculated? What measurement needs to be used for the angle for the arc length formula? Provide an example.

eimsori [14]

Answer:

i honestly don't know

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

What is 1788.10643 rounded to the nearest hundredth??

wariber [46]

1788.11. Because the 0 will go to 1 because of the 6

3 0

3 years ago

A manufacturer knows that on average 20% of the electric toasters produced require repairs within 1 year after they are sold. Wh

Effectus [21]

Answer:

(a) The value of x is 5.

(b) The value of y is 15.

Step-by-step explanation:

Let the random variable X represent the number of electric toasters produced that require repairs within 1 year.

And the let the random variable Y represent the number of electric toasters produced that does not require repairs within 1 year.

The probability of the random variables are:

P (X) = 0.20

P (Y) = 1 - P (X) = 1 - 0.20 = 0.80

The event that a randomly selected electric toaster requires repair is independent of the other electric toasters.

A random sample of n = 20 toasters are selected.

The random variable X and Y thus, follows binomial distribution.

The probability mass function of X and Y are:

$P(X=x)={20\choose x}(0.20)^{x}(1-0.20)^{20-x}$

$P(Y=y)={20\choose y}(0.20)^{20-y}(1-0.20)^{y}$

(a)

Compute the value of x such that P (X ≥ x) < 0.50:

$P (X \geq x) < 0.50\\\\1-P(X\leq x-1)$

Use the Binomial table for n = 20 and p = 0.20.

$0.411=\sum\limits^{3}_{x=0}[b(x,20,0.20)]$

The least value of x that satisfies the inequality P (X ≥ x) < 0.50 is:

x - 1 = 4

x = 5

Thus, the value of x is 5.

(b)

Compute the value of y such that P (Y ≥ y) > 0.80:

$P (Y \geq y) >0.80\\\\P(Y\leq 20-y)>0.80\\\\P(Y\leq 20-y)>0.80\\\\\sum\limits^{20-y}_{y=0}[{20\choose y}(0.20)^{20-y}(1-0.20)^{y}]>0.80$

Use the Binomial table for n = 20 and p = 0.20.

$0.630=\sum\limits^{4}_{y=0}[b(y,20,0.20)]$

The least value of y that satisfies the inequality P (Y ≥ y) > 0.80 is:

20 - y = 5

y = 15

Thus, the value of y is 15.

3 0

3 years ago