Answer:
x = 4√5
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality<u>
</u>
<u>Trigonometry</u>
[Right Triangles Only] Pythagorean Theorem: a² + b² = c²
- a is a leg
- b is another leg
- c is the hypotenuse<u>
</u>
Step-by-step explanation:
<u>Step 1: Define</u>
Leg <em>a</em> = 8
Leg <em>b</em> = 4
Hypotenuse <em>c</em> = <em>x</em>
<em />
<u>Step 2: Solve for </u><em><u>x</u></em>
- Substitute in variables [Pythagorean Theorem]: 8² + 4² = x²
- Evaluate exponents: 64 + 16 = x²
- Add: 80 = x²
- [Equality Property] Square root both sides: √80 = x
- Rewrite: x = √80
- Simplify: x = 4√5
The confidence interval formula is computed by:
Xbar ± Z s/ sqrt (n)
Where:
Xbar is the mean
Z is the z value
S is the standard deviation
N is the number of samples
So our given are:
90% confidence interval with a z value of 1.645
Sample size 40, 45
Mean 180, 179
Standard deviation 2, 4
So plugging that information in the data will give us a
confidence interval:
For 1:
Xbar ± Z s/ sqrt (n)
= 180 ± 1.645 (2 / sqrt (40))
= 180 ± 1.645 (0.316227766)
= 180 ± 0.520194675
= 179.48, 180.52
For 2:
Xbar ± Z s/ sqrt (n)
= 179 ± 1.645 (4 / sqrt (45))
<span>= 179 ± 1.645 (0.596284794)</span>
therefore, the answer is letter b
Answer:
Fn= 174.9 N : Magnitude of the net force the people exert on the donkey.
Step-by-step explanation:
We find the components of the forces in x-y-z
Force of Jack in z =F₁z=90.5 N in direction (+z)
Force of Jill in x = F₂x= -82.3*cos45°= - 58.19 N (-x)
Force of Jill in y =F₂y=-82.3*sin45°= + 58.19 N (+y)
Force of Jane in x =F₃x=125*cos45°= + 88.4 N (+x)
Force of Jane in y =F₃y=125*sin45°= + 88.4 N (+y)
Calculating of the components of the net force the people exert on the donkey.
Fnx= F₂x+F₃x=( - 58.19+ 88.4 )N=30.2N (+x)
Fny= F₂y+F₃y=( 58.19+88.4 ) = 146.59 N (+y)
Fnz =F₁z=90.5 N (+z)
Calculating of the magnitude of the net force the people exert on the donkey.



0.985 is the median.
I hope this helped
-3x - 3/4 = 9
-3x - 3/4 + 3/4 = 9 + 3/4
-3x = 9 3/4
I change 9 3/4 to improper fraction
-3x = 39/4
-3x / -3 = 39/4 / -3
X = 39/4 x -1/3 (change division to multiplication so that you can complete the problem)
X = -39/12
You can convert that if you want to -3 3/12
So x = -3 3/12
Simplify to x = -3 1/4