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2 years ago

What is the value of x in the equation. 8 x - 2 y= 48 when y =4

Mathematics

2 answers:

goldfiish [28.3K]2 years ago

4 0

$\qquad$ ❄️ $\boxed{\bf x = 7}\\\\$

We are given –

$\qquad$ $\twoheadrightarrow\bf 8x -2 y =48$

And also value of y's given. So, just put the value of y in the given equation.

___________________________________

$\qquad$ $\purple{\twoheadrightarrow\bf 8x -2 y =48}$

$\qquad$ $\twoheadrightarrow\sf 8x - \underbrace{2 \times 4} =48$

$\qquad$ $\twoheadrightarrow\sf 8x - 8 =48$

$\qquad$ $\twoheadrightarrow\sf 8x = 48 +8$

$\qquad$ $\twoheadrightarrow\sf 8x = 56$

$\qquad$ $\twoheadrightarrow\sf x =\cancel{\dfrac{56}{8}}$

$\qquad$ $\purple{\twoheadrightarrow\bf x= 7}$

Henceforth, value of x is 7.

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denis-greek [22]2 years ago

4 0

Hey there!

8x - 2y = 48

8x - 2(4) = 48

8x - 8 = 48

ADD 8 to BOTH SIDES

8x - 8 + 8 = 48 + 8

CANCEL out: -8 + 8 because it give you 1

KEEP: 48 + 8 because it help solve for the x-value

NEW EQUATION: 8x = 48 + 8

SIMPLIFY IT!

8x = 56

DIVIDE 8 to BOTH SIDES

8x/8 = 56/8

CANCEL out: 8/8 because it give you 1

KEEP: 56/8 because it help solve for the x-value

NEW EQUATION: x = 56/8

SIMPLIFY IT!

x = 7

Therefore, your answer is: x = 7

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

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olga_2 [115]

Question:

The amount of cereal that can be poured into a small bowl varies with a mean of 1.5 ounces and a standard deviation of 0.3 ounces. A large bowl holds a mean of 2.5 ounces with a standard deviation of 0.4 ounces. You open a new box of cereal and pour one large and one small bowl.

Answer:

a) The expected amount of cereal left in the box is 12.2 ounces

b) The standard deviation $\sigma_{x+y+z}$ , is 0.5099

c) In a Normal model, the probability that the box still contains more than 13 ounces is P(Z-(X+Y) > 13) = 5.821 %.

Step-by-step explanation:

Let X represent the amount of cereal that can be poured into a small bowl and Y represent the amount of cereal that can be poured into a large bowl and Z represent the amount of cereal that the manufacturer puts in the box, then the expected amount of cereal left in the box is given by

Z - (X + Y)

(a) The expected amount of cereal left in the box is given as

P(Z - (X + Y)) = μ = μ $_Z$ - μ $_X$ - μ $_Y$ = 16.2 - 1.5 - 2.5 = 12.2 ounces

The expected amount of cereal left in the box = 12.2 ounces

b) The standard deviation is given by the root of the sum of the variance

That is

$\sigma_{x+y+z} ^2 = \sigma_x^2 + \sigma_y^2 +\sigma_z^2$ and

$\sqrt{\sigma_{x+y+z} ^2} = \sqrt{\sigma_x^2 + \sigma_y^2 +\sigma_z^2} =\sqrt{0.1^2+0.4^2+0.3^2}$ = 0.5099

The standard deviation, $\sigma_{x+y+z}$ , = 0.5099

c) The probability that the box still contains more than 13 ounces is given by

P(Z-(X+Y) > 13)

Where z-score is

$z=\frac{x-\mu}{\sigma} = \frac{13-12.2}{0.5099}= 1.5689$ ≈ 1.57

From the z-score table P(Z = 1.57) = 0.94179

Therefore the probability of the box containing ≤ 13 is 0.94179, that is

P(Z-(X+Y) ≤ 13) = 0.94179 and

P(Z-(X+Y) > 13) = 1 - 0.94179 = 0.05821 = 5.821 %.

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Step-by-step explanation:

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For synthetic division:

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