A.X'3+3x2 -10x = 24<br> x + 4

Simplify the expression 13+(x+8)

Fudgin [204]

Answer:x+21

Step-by-step explanation:

7 0

3 years ago

What is the solution to he equation (y/y-4)-(4/y+4)=3^2/y^2-16

kicyunya [14]

Answer:

$y=\pm i \sqrt{7}$

Step-by-step explanation:

Given equation is $\frac{y}{\left(y-4\right)}-\frac{4}{\left(y+4\right)}=\frac{3^2}{(y^2-16)}$

Factor denominators then solve by making denominators equal

$\frac{y}{\left(y-4\right)}-\frac{4}{\left(y+4\right)}=\frac{3^2}{(y^2-16)}$

$\frac{y}{\left(y-4\right)}-\frac{4}{\left(y+4\right)}=\frac{9}{(y+4)\left(y-4\right)}$

$\frac{y\left(y+4\right)-4\left(y-4\right)}{\left(y-4\right)\left(y+4\right)}=\frac{9}{(y+4)\left(y-4\right)}$

$y\left(y+4\right)-4\left(y-4\right)=9$

$y^2+4y-4y+16=9$

$y^2=9-16$

$y^2=-7$

take squar root of both sides

$y=\pm \sqrt{-7}$

$y=\pm i \sqrt{7}$

Hence final answer is $y=\pm i \sqrt{7}$ .

7 0

3 years ago

Quadratic equation solve using formula

kiruha [24]

Answer:

2 , 1\2

Step-by-step explanation:

b² - 4ac = (-5)² - 4*2*2

= 25 - 16

= 9

$\sqrt{b^{2}-4ac} = \sqrt{9} = \sqrt{3*3}=3$

$x= \dfrac{-[-5] + 3}{2*2} ; x = \dfrac{-[-5]-3}{2*2}\\\\x =\dfrac{5+3}{4} ; x = \dfrac{5-3}{4}\\\\x=\dfrac{8}{4} ;x = \dfrac{2}{4}\\x = 2 ; x = \dfrac{1}{2}$

8 0

3 years ago

2.A production process manufactures items with weights that are normally distributed with mean 10 pounds and standard deviation

Vesna [10]

Answer:

Step-by-step explanation:

Given that:

population mean = 10

standard deviation = 0.1

sample mean = 9.8 < x > 10.2

The z score can be computed as:

$z = \dfrac{\bar x - \mu}{\sigma}$

if x > 10.2

$z = \dfrac{10.2- 10}{0.1}$

$z = \dfrac{0.2}{0.1}$

z = 2

If x < 9.8

$z = \dfrac{9.8- 10}{0.1}$

$z = \dfrac{-0.2}{0.1}$

z = -2

The p-value = P (z ≤ 2) + P (z ≥ 2)

The p-value = P (z ≤ 2) + ( 1 - P (z ≥ 2)

p-value = 0.022750 +(1 - 0.97725)

p-value = 0.022750 + 0.022750

p-value = 0.0455

Therefore; the probability of defectives = 4.55%

the probability of acceptable = 1 - the probability of defectives

the probability of acceptable = 1 - 0.0455

the probability of acceptable = 0.9545

the probability of acceptable = 95.45%

4.55% are defective or 95.45% is acceptable.

sampling distribution of proportions:

sample size n=1000

p = 0.0455

The z - score for this distribution at most 5% of the items is;

$z = \dfrac{0.05 - 0.0455}{\sqrt{\dfrac{0.0455\times 0.9545}{1000}}}$

$z = \dfrac{0.0045}{\sqrt{\dfrac{0.04342975}{1000}}}$

$z = \dfrac{0.0045}{\sqrt{4.342975 \times 10^{-5}}}$

z = 0.6828

The p-value = P(z ≤ 0.6828)

From the z tables

p-value = 0.7526

Thus, the probability that at most 5% of the items in a given batch will be defective = 0.7526

The z - score for this distribution for at least 85% of the items is;

$z = \dfrac{0.85 - 0.9545}{\sqrt{\dfrac{0.0455\times 0.9545}{1000}}}$

$z = \dfrac{-0.1045}{\sqrt{\dfrac{0.04342975}{1000}}}$

z = −15.86

p-value = P(z ≥ -15.86)

p-value = 1 - P(z < -15.86)

p-value = 1 - 0

p-value = 1

Thus, the probability that at least 85% of these items in a given batch will be acceptable = 1

6 0

3 years ago

In accounting, a company's gross profit rate measures how well the company controls cost of goods sold to maximize gross profit.

postnew [5]

Answer:

Step-by-step explanation:

The gross profit rate of the company is expressed as $P = \dfrac{S - C}{S}$ where C is the cost of goods sold and S is the net sales. If the net sales S = $1,200,000, and gross profit ratio is 0.20, the cost of goods sold will be expressed as shown;

Making C the subject of the formula from the expression given.

$P = \dfrac{S - C}{S}\\\\cross \ multiply\\\\SP = S-C\\\-C = SP-S\\\\C = S -SP\\$

Substituting P = 0.20 and S = $1,200,000 into the resulting equation, we will have;

$C = $1,2000,000 - 0.2($1,2000,000)\\C = $1,2000,000- 240,000\\ C = 960,000$

<em>Hence the cost of goods sold is $960,000</em>

6 0

3 years ago

A.X'3+3x2 -10x = 24 x + 4