Factor 147a^2b-675b^3

Mike has coffee worth $4 per pound that he wishes to mix with 20 pounds of coffee worth $7 per pound to get a mixture that can b

Alinara [238K]

$\bf \begin{array}{lccclll}
&\stackrel{lbs}{amount}&\stackrel{per~lb}{price}&\stackrel{amount}{price}\\
&------&------&------\\
\textit{\$4/lb coffee}&x&4&4x\\
\textit{\$7/lb coffee}&20&7&140\\
------&------&------&------\\
mixture&y&5&5y
\end{array}$

so, we know the mixture is the sum of both types of coffee, thus x + 20 = y, and 4x + 140 = 5y.

$\bf \begin{cases}
x+20=\boxed{y}\\
4x+140=5y\\
----------\\
4x+140=5\left( \boxed{x+20} \right)
\end{cases}
\\\\\\
4x+140=5x+100\implies 140-100=5x-4x\implies 40=x$

5 0

2 years ago

A certain firm has plants a, b, and c producing respectively 35\%, 15\%, and 50\% of the total output. The probabilities of a no

TEA [102]

The proportion of production that is defective and from plant A is

... 0.35·0.25 = 0.0875

The proportion of production that is defective and from plant B is

... 0.15·0.05 = 0.0075

The proportion of production that is defective and from plant C is

... 0.50·0.15 = 0.075

Thus, the proportion of defective product that is from plant C is

... 0.075/(0.0875 +0.0075 +0.075) = 75/170 = 15/34 ≈ 44.12%

_____

P(C | defective) = P(C&defective)/P(defective)

8 0

2 years ago

Which shows one way to determine the factors of 12x3 – 2x2 + 18x – 3 by grouping?

Debora [2.8K]

Option A

$2x^2(6x-1) + 3(6x-1)$ is one way to determine the factors of $12x^3-2x^2+18x-3$ by grouping

Solution:

Factoring by grouping means that you will group terms with common factors before factoring

Given expression is:

$12x^3-2x^2+18x-3$

Group the first two terms together and then the last two terms together.

$(12x^3-2x^2)+(18x-3)$

We can see that $2x^2$ is common in first two terms

And 3 is common in last two terms

Factor them out

$(12x^3-2x^2)+(18x-3) = 2x^2(6x-1) + 3(6x-1)$

$2x^2(6x-1) + 3(6x-1)$

Thus option A is correct

6 0

2 years ago

Read 2 more answers

How would u find 4 1\5 divided by 2 1\3

Over [174]

Remmber
(a/b)/(c/d)=(a/b)(d/c)=(ad)/(bc)
conver to improper

4 and 1/5=20/5+1/5=21/5
2 and 1/3=6/3+1/3=7/3

(21/5)/(7/3)=(21/5)(3/7)=63/35=9/5=1 and 4/5

3 0

2 years ago

Read 2 more answers

Given circle X with radius 10 units and chord AB with length 12 units, what is the length of segment CX, which bisects the chord

andrew-mc [135]

Consider the circle with center X, as shown in the figure.

Draw the diameter of the circle which is parallel to cherd AB, as shown in the figure.

Since the diameter and AB are parallel, then the line segment XC which bisects AB at C, will be perpendicular to AB.

SO triangle XCB is a right triangle. Thus the length of CX, by the Pythagorean theorem is

$\sqrt{ XB^{2}- CB^{2}} = \sqrt{ 10^{2}- CB^{6}}= \sqrt{100-36}= \sqrt{64}=8$ units.

Answer: 8 units

7 0

2 years ago