Where do multiplication problems eat?

OverLord2011 [107]

1. We are given:
$a^2 = 64$

The only a which squared gives you 64 is 8. The perimeter of an 8 by 8 square will be 32. Half of that is 16. Now, let's see what we can do. We can set up:
$4a = 16$

Obviously, each side length has to be 4. So, the area of this square will be 16 units².

2. Let n equal her son's age. So, her age right now will be (S = her age):
$S = 18n$
1 year ago it was:
$S-1 = 3n$

We have 2 equations, let's substitute. We can rewrite this as:
$18n-1 = 3n$
Solve for n:
$15n-1=0$
$n= \frac{1}{15}$

We know the value of n, which is her son's age. So, her son is 1/15 of a year old or about 24 days old.

8 0

4 years ago

Relationships between means, standard deviations, X values,and z-scores

Vlada [557]

Answer:

a) The average salary of firefighters in Portugal is $583.

b) The standard deviation of the salary of firefighters in Portugal is $319.8

Step-by-step explanation:

We are given the following in the question:

a) Standard Deviation, σ = $145.80

We are given that the distribution of salary of professor is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

A salary of $510.10 has a z-score of -0.50.

Putting values, we get,

$-0.50 = \displaystyle\frac{510.10-\mu}{145.80}\\\\\mu = 0.50(145.80) + 510.10\\\Rightarrow \mu = 583$

Thus, the average salary of firefighters in Portugal is $583.

b) Mean, μ = $2,132

We are given that the distribution of salary of computer programmers is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

The salary of $2,291.90 has a z-score of +0.50

Putting values, we get,

$0.50 = \displaystyle\frac{2291.90-2132}{\sigma}\\\\\sigma= \frac{2291.90-2132}{0.50}\\\\\sigma = 319.8$

Thus, the standard deviation of the salary of firefighters in Portugal is $319.8

6 0

4 years ago

Rachel is collecting donations for the local animal shelter. So far she has collected $245, which is 70% of what she hopes to co

Nata [24]

Answer:

The money Rachael plan to collect for the shelter is $350.

Step-by-step explanation:

Given:

Rachel is collecting donations for the local animal shelter.

So far she has collected $245, which is 70% of what she hopes to collect.

Now, to find the money Rachael plan to collect for the shelter.

Let the total amount Rachael plan to collect be $x$ .

Amount she collected = $245.

Percentage of amount she collected = 70%.

Now, to get the amount Rachael plan to collect we put an equation:

$70\%\ of\ x=\$245.$

⇒ $\frac{70}{100} \times x=245$

⇒ $0.70\times x=245$

⇒ $0.70x=245$

Dividing both sides by 0.70 we get:

⇒ $x=\$350.$

Therefore, the money Rachael plan to collect for the shelter is $350.

4 0

4 years ago

Please answer these question!! thank you!! :)

Aleks [24]

this made me realize how dumb I am

6 0

3 years ago

Simplify: √(1+x) /√(1+x) - √(1 -x) - 1-x /√(1 -x) + x -1

soldier1979 [14.2K]

Step-by-step explanation:

Given that: [√(1+x)/{√(1+x) - √(1-x)}] - [(1-x)/{√(1-x²) + x -1}]

Here, we see that in first fraction the denominator is √(1+x)-√(1-x) , as we know that the rational factor √(a+b)-√(a-b) is √(a+b)+(a-b). Therefore, the rationalising factor of √(1+x)-√(1-x) is √(1+x)+√(1-x). On rationalising the denominator them.

= [√(1+x)/{√(1+x)-√(1-x)}] * [{√(1+x)+√(1-x)}/{√(1+x)+√(1-x)}] - [(1-x)/{√(1-x²) + x -1}]

= [{√(1+x)(√(1+x)+√(1-x)}/{√(1+x)-√(1-x) - √(1+x)+√(1-x)}] - [(1-x)/{√(1-x²) + x -1}]

Now, comparing the first fraction denominator with (a-b)(a+b), we get

a = √(1+x)
b = √(1-x)
a = √(1+x)
b = √(1-x)

Using identity (a-b)(a+b) = a² - b², we get

= [{√(1+x)(√(1+x)+√(1-x)}/{√(1+x)² - √(1-x)²}] - [(1-x)/{√(1-x²) + x -1}]

= [{√(1+x)(√(1+x)+√(1-x)}/{(1+x) - (1-x)}] - [(1-x)/{√(1-x²) + x -1}]

Now, multiply the numerator on both brackets.

= [{√(1+x) * √(1+x) + √(1+x) * √(1-x)}/{(1+x) - (1-x)}] - [(1-x)/{√(1-x²) + x -1}]

Comparing the first fraction numerator with (a+b)(a+b) , we get

a = √1
b = √x

Using identity (a+b)(a+b) = (a+b)², we get

= [{√(1+x)²+ √(1+x) * √((1+x)(1-x))}/{(1+x) - (1-x)}] - [(1-x)/{√(1-x²) + x -1}]

Cancel out the first fraction denominator numbers 1 and -1 to get 0.

= [{(1+x)+√(1-x²)}/(x+x+0)] - [(1-x)/{√(1-x²) + x -1}]

= [{(1+x)+√(1-x²)}/(x+x)] - [(1-x)/{√(1-x²) + x -1}]

= [{(1+x)+√(1-x²)}/2x] - [(1-x)/{√(1-x²) + x -1}]

= [{1+x+√(1-x²)}{√(1-x²)x-1}-{(1-x)(2x)}]/[2x{√(1-x²)+x-1}]

= [√(1-x²) + x-1 + x√(1-x²) + x² - x + {√(1-x²)}² + x√(1-x²)-√(1-x²) - 2x + 2x²]/[2x{√(1-x²)+x-1}]

= {(√(1-x²) 2x -1 + 3x² + 2x√(1-x²) + 1-x² - √(1-x²)}/[2x{√(1-x²)+x-1}]

Cancel out √(1-x) and -√(1-x) in numerator.

= {-2x - 1 + 2x√(1-x²) + 3x² + 1 - x²}/[2x{√(1-x²)}+x-1}]

Cancel out -1 and 1 in numerator to get 0.

= [2x√(1-x²) - 2x + 2x²}/[2x{√(1-x²)+x-1}]

= {2x{√(1-x²)} + x - 1}]/[2x{√(1-x²)}+x-1}

= 1

Answer: Hence, the simplified form of the expression [√(1+x)/{√(1+x) - √(1-x)}] - [(1-x)/{√(1-x²) + x -1}] is 1.

Please let me know if you have any other questions.

6 0

3 years ago