Solve the system of equations using the elimination method 2x + 9y = -40

Simplify the following expression (3x^2y)^3

kolezko [41]

Answer:

$\large\boxed{\left(3x^2y\right)^3=27x^6y^3}$

Step-by-step explanation:

$\text{Use}\ (ab)^n=a^nb^n\ \text{and}\ (a^n)^m=a^{nm}\\\\\left(3x^2y\right)^3=3^3(x^2)^3y^3=27x^6y^3$

6 0

3 years ago

The sum of the heights of two brothers is 10 feet, 4 inches. The difference between their heights is 10 inches. How tall is the

Leona [35]

Answer:

4.5 ft

Step-by-step explanation:

Let us assume the height of the taller brother be x

And, the height of the shorter brother be y

Now according to the question

x + y = 10.33

x - y = 0.833

Now solve these two equations

2x = 11.666

x = 5.833

y = 10.33 - 5.83

= 4.5 ft

7 0

3 years ago

Suppose that the distribution of typing speed in words per minute (wpm) for experienced typists using a new type of split keyboa

KengaRu [80]

Answer:

a. 0.5 or 50%

b. 0.496 or 49.6%

c. 0.8185 or 81.85%

d. Yes, it would be just 0.0013 or 0.13% of probability to find a typist whose speed exceeds 105 wpm

e. 0.0252 or 2.52%

f. The qualifying speed would be 47.4 wpm.

Step-by-step explanation:

a. Let's find the z-score this way:

μ = 60 σ= 15

z-score = (x - μ)/σ

z-score = (60 - 60)/15

z-score = 0

Now, let's calculate the p value for z-score = 0, using the z-table:

p (z=0) = 0.5 or 50%

b. z-score = (x - μ)/σ

z-score = (59.9 - 60)/15

z-score = -0.01

Now, let's calculate the p value for z-score = -.0.01, using the z-table:

p (z = -0.01) = 0.496 or 49.6%

If the question were less or equal than 60, a and b would have the same answer. But in this case, the question is "less than 60 wpm".

c.

z-score = (x - μ)/σ

z-score = (45 - 60)/15

z-score = - 1

Now, let's calculate the p value for z-score = -1, using the z-table:

p (z = -1) = 0.1587

z-score = (x - μ)/σ

z-score = (90 - 60)/15

z-score = 2

Now, let's calculate the p value for z-score = 2, using the z-table:

p (z = 2) = 0.9772

In consequence,

p (-1 ≤ z ≤ 2) = 0.9772 - 0.1587 = 0.8185 or 81.85%

d. z-score = (x - μ)/σ

z-score = (105 - 60)/15

z-score = 3

Now, let's calculate the p value for z-score = 3, using the z-table:

p (z = 3) = 0.9987

In consequence,

p (z > 3) = 1 - 0.9987 = 0.0013

Yes, it would be just a 0.13% of probability to find a typist whose speed exceeds 105 wpm.

e. z-score = (x - μ)/σ

z-score = (75 - 60)/15

z-score = 1

Now, let's calculate the p value for z-score = 1, using the z-table:

p (z = 1) = 0.8413

In consequence,

p (z > 1) = 1 - 0.8413 = 0.1587

and if the two typists are independently selected, then

p = 0.1587 * 0.1587

p = 0.0252 or 2.52%

f. p = 0.2, using the z-table, the z-score is -0.84, then:

z-score = (x - μ)/σ

-0.84 = (x - 60)/15

-12.6 = x - 60

-x = -60 + 12.6

-x = - 47.4

x = 47.4

The qualifying speed would be 47.4 wpm.

8 0

3 years ago

Combine as indicated by the signs. 8-y/3y + y+2/9y - 2/6y

Taya2010 [7]

Answer:

26 + y

----------

9y

Step-by-step explanation:

Your using parentheses here would remove a great deal of ambiguity. Looking at your 8-y/3y + y+2/9y - 2/6y, I have interpreted it to mean:

(8-y)/3y + (y+2)/9y - (2/6)y. For example, without parentheses, your 8-y/3y might be interpreted differently, as 8 - y/(3y), or 8 - 1/3.

Looking at (8-y)/3y + (y+2)/9y - (2/6)y again, we see three different denominators: 3y, 9y and 6 y. The LCD here is 9y. Multiplying all three terms of (8-y)/3y + (y+2)/9y - (2/6)y by the LCD, we get:

3(8-y) + (y+2) + 3y. We must now divide this by the LCD:

3(8-y) + (y+2) + 3y

--------------------------

9y

Next we need to perform the indicated multiplication:

24 - 3y + y + 2 + 3y

----------------------------

9y

and then to combine like terms:

24 + 2 - 3y + y + 3y, 26 + y

---------------------------- or -----------

9y 9y

7 0

3 years ago

Read 2 more answers

I need help with this math problem please

larisa [96]

Use this graphing app that assists you with problems like these!

5 0

3 years ago