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3 years ago

Please help! A clear explanation on how to simplify the exponents and a detailed step by step solution is greatly appreciated.

Mathematics

1 answer:

Amanda [17]3 years ago

8 0

Answer:

0.125 or 1/8

Step-by-step explanation:

2^3 +2^-3= (2*2*2) + (1/(2*2*2))= 8 + 1/8= 8 + 0.125= 8.125

4^3 +1= (4*4*4) + 1= 64 + 1= 65

8.125/65= 0.125 or 1/8

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The equation of a circle is x2 + y2 + 6x + 4y + 10 = 1. What is this equation written in its standard form?

Over [174]

You need to complete the square in x and in y,

$x^{2} + y^{2} + 6x + 4y + 10 = 1$

First, group the x-terms and the y-terms separately.

$x^{2} + 6x + y^{2} + 4y + 10 = 1$

Move the 10 to the right side by subtracting 10 from both sides.

$x^{2} + 6x + y^{2} + 4y = -9$

Now complete the square in x and in y.
The constant you need to add to complete each square is the square of half of the coefficient of the x or y term. Make sure to add the constants to both sides of the equation.

$x^{2} + 6x + 9 + y^{2} + 4y + 4= -9 + 9 + 4$

$(x + 3)^{2} + (y + 2)^{2} = 4$

8 0

3 years ago

If a certain machine makes electrical resistors having a mean resistance of 40 ohms and a standard deviation of 2 ohms, what is

V125BC [204]

Answer:

The probability is $P(\= X < 40.4) = 0.84134$

Step-by-step explanation:

From the question we are told that

The mean is $\mu =40 \ \Omega$

The standard deviation is $\sigma = 2 \ \Omega$

The sample size is n = 25

The combined resistance is $\sum x_i = 1010 \ \Omega$

Generally the sample mean is mathematically represented as

$\= x = \frac{\sum x_i }{n}$

=> $\= x = \frac{1010 }{25}$

=> $\= x = 40.4 \ \Omega$

Generally the standard error of the mean is mathematically represented as

$\sigma_{x} = \frac{\sigma }{\sqrt{n} }$

=> $\sigma_{x} = \frac{ 2 }{\sqrt{25} }$

=> $\sigma_{x} = 0.4$

Generally the probability that a random sample of 25 of these resistors will have a combined resistance of less than 1010 ohms is mathematically represented as

$P(\= X < 40.4) = P( \frac{\= X - \mu }{\sigma_{x }} < \frac{ 40.4 - 40 }{0.4} )$

$\frac{\= X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ \= X )$

$P(\= X < 40.4) = P( Z < 1 )$

From the z table the area under the normal curve to the left corresponding to 1 is

$P(\= X < 40.4) = P( Z < 1 ) = 0.84134$

$P(\= X < 40.4) = 0.84134$

3 0

3 years ago

If an object is projected upward with an initial velocity of 126ft per? sec, its height h after t seconds is h=?16t^2+126t. Find

Archy [21]

Answer:

=760 ft

Step-by-step explanation:

h=16t^2+126t

Let t=4

h = 16 (4)^2 +126(4)

h = 16*16 +126(4)

=256+504

=760 ft

5 0

4 years ago

How do you solve this equation ( ASAP PLS )

makvit [3.9K]

Solve this by substitution:

Solve 5x - 4y = -13 for x:5x − 4y + 4y = -13 + 4y (Add 4y to both sides)
5x = 4y - 13 (Divide both sides by 5)
5 5

x = 4 y + -13
 5 5
You can use https://www.mathpapa.com/algebra-calculator.html
5x - 4y = -13, 8x +10y = 12 (enter both equations with a comma between them and it will solve for you and show you step by step.

8 0

4 years ago

Can u guys help me with this assignment

n200080 [17]

Answer:

1: ratio

2: decimal

3: fraction

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers