The ratio would be 14:6
If you reduce it it would be 7:3
Answer to part A: If the sun produces 3.9 * (10^33) ergs or radiant energy for every second, then how much energy does the sun produce in 3.25 * (10^3) seconds? Just multiply (3.25 * [10^3]) * (3.9[10^33]) = <span>1.2675 * 10^37 of ergs of radiation.
Answer to part B: 1.435 * 10^3 mm is a reasonable answer because it is much smaller than </span>1.435 * 10^3.
<span>
Answer to BONUS:
</span>(2^8 * 5^-5 * 19^0) ^-2 (5^-2 / 2^3) * 2^28 <-- Start
(256 * 0.00032 * 1) ^-2 (0.04 / 8) * <span>268435456 <-- Simplify
</span>0.08192^-2 * 0.005 * 268435456 <-- Simplify the terms in parentheses.
<span>
Final Answer: </span><span>200000000
Whew! That was hard!</span>
Answer:
Two diameters that separate the top 4% and the bottom 4% are 5.77 and 5.53 respectively.
Step-by-step explanation:
We are given that the diameters of bolts produced in a machine shop are normally distributed with a mean of 5.65 millimeters and a standard deviation of 0.07 millimeters.
<em>Let X = diameters of bolts produced in a machine shop</em>
So, X ~ N()
The z score probability distribution is given by;
Z = ~ N(0,1)
where, = population mean
= standard deviation
<u>Now, we have to find the two diameters that separate the top 4% and the bottom 4%.</u>
- Firstly, Probability that the diameter separate the top 4% is given by;
P(X > x) = 0.04
P( > ) = 0.04
P(Z > ) = 0.04
<em>So, the critical value of x in z table which separate the top 4% is given as 1.7507, which means;</em>
= 1.7507
= 5.65 + 0.122549 = 5.77
- Secondly, Probability that the diameter separate the bottom 4% is given by;
P(X < x) = 0.04
P( < ) = 0.04
P(Z < ) = 0.04
<em>So, the critical value of x in z table which separate the bottom 4% is given as -1.7507, which means;</em>
= -1.7507
= 5.65 - 0.122549 = 5.53
Therefore, the two diameters that separate the top 4% and the bottom 4% are 5.77 and 5.53 respectively.
Answer:
(-15, 3)
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
<u>Algebra I</u>
- Solving systems of equations using substitution/elimination
Step-by-step explanation:
<u>Step 1: Define Systems</u>
x + 5y = 0
3y + 2x = -21
<u>Step 2: Rewrite Systems</u>
x + 5y = 0
- Subtract 5y on both sides: x = -5y
<u>Step 3: Redefine Systems</u>
x = -5y
3y + 2x = -21
<u>Step 4: Solve for </u><em><u>y</u></em>
<em>Substitution</em>
- Substitute in <em>x</em>: 3y + 2(-5y) = -21
- Multiply: 3y - 10y = -21
- Combine like terms: -7y = -21
- Isolate <em>y</em>: y = 3
<u>Step 5: Solve for </u><em><u>x</u></em>
- Define equation: x + 5y = 0
- Substitute in <em>y</em>: x + 5(3) = 0
- Multiply: x + 15 = 0
- Isolate <em>x</em>: x = -15