Answer:
12
Step-by-step explanation:
16 x 12 = 192
Suppose that 50% of the watches produced by a certain factory are defective. A store buys a box with 400 watches produced by this factory. Assume That this is a random sample.(a) Write an expression for the exact probability that at least 215 watches out ofthe 400 are defective. You do not need to numerically evaluate it.(b) Argue whether the normal or the Poisson approximation is appropriate to es-timate the above probability and then estimate it.
Answer:
[tex](a)\ P(x \ge 215)[/tex]
[tex](b)\ P(x \ge 214.5) = 0.07353[/tex]
Step-by-step explanation:
Given
[tex]p = 0.50[/tex] ---- proportion of watches with defects
[tex]n = 400[/tex] --- Number of watches
Solving (a): Represent at least 215 of 400 are defective
In inequalities, at least means: [tex]\ge[/tex]
So, the probability is represented as: [tex]P(x \ge 215)[/tex]
Solving (b): Calculate [tex]P(x \ge 215)[/tex]
Normal or Poisson: Normal distribution is characterized by 2 parameters [tex]\mu[/tex] and [tex]\sigma[/tex].
These two parameters can be easily calculated from the given parameters in the question. So, we solve using normal distribution
Start by calculating the mean
[tex]\mu =np[/tex]
[tex]\mu = 0.50 * 400[/tex]
[tex]\mu = 200[/tex]
Calculate standard deviation
[tex]\sigma = \sqrt{\mu (1 - p)[/tex]
[tex]\sigma = \sqrt{200 * (1 - 0.50)[/tex]
[tex]\sigma = \sqrt{200 * 0.50[/tex]
[tex]\sigma = \sqrt{100[/tex]
[tex]\sigma = 10[/tex]
By continuity correction, we have:
[tex]x \to x - 0.5[/tex]
[tex]x \to 215 - 0.5[/tex]
[tex]x \to 214.5[/tex]
So, we have:
[tex]P(x \ge 215) = P(x \ge 214.5)[/tex]
Calculating [tex]P(x \ge 214.5)[/tex], we have:
[tex]P(x \ge 214.5) = 1 - P(x < z)[/tex]
Calculate z score
[tex]z = \frac{x - \mu}{\sigma}[/tex]
[tex]z = \frac{214.5 - 200}{10}[/tex]
[tex]z = \frac{14.5}{10}[/tex]
[tex]z = 1.45[/tex]
So, we have:
[tex]P(x \ge 214.5) = 1 - P(x < 1.45)[/tex]
Using the z score probability table, we have:
[tex]P(x < 1.45) = 0.92647[/tex]
So, we have:
[tex]P(x \ge 214.5) = 1 - 0.92647[/tex]
[tex]P(x \ge 214.5) = 0.07353[/tex]
what is the slope of the line that passes through the pair of points (-1, 4), (3,12)
Answer:
[tex]\displaystyle m = 2[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinates (x, y)Slope Formula: [tex]\displaystyle m = \frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Identify
Point (-1, 4)
Point (3, 12)
Step 2: Find slope m
Simply plug in the 2 coordinates into the slope formula to find slope m
Substitute in points [Slope Formula]: [tex]\displaystyle m = \frac{12-4}{3--1}[/tex][Fraction] Subtract: [tex]\displaystyle m = \frac{8}{4}[/tex][Fraction] Divide: [tex]\displaystyle m = 2[/tex]What is the least common multiple of 4, 5, and 12 ?
Answer:
60
Step-by-step explanation:
which expression is equivalent to (4^-5 * 4^4) + (2^6/ 2^3)
Answer:
A
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
Can Someone Please Help Asap!!
Answer:
y = 54
x = 36
Step-by-step explanation:
Using tan x or y = opp/adj
Which choice is equivalent to the product below when x > 0
Answer:
c
Step-by-step explanation:
[tex] \sqrt{ \frac{1}{ {x}^{2} } } \times \sqrt{ \frac{ {x}^{2} }{81} } = \frac{1}{x} \times \frac{x}{9 } = \frac{1}{9} [/tex]
The value of the expression [√(1 / x²)] · [√(x² / 81)] will be 1/9. Then the correct option is C.
What is the value of the expression?When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The expression is given below,
⇒ [√(1 / x²)] · [√(x² / 81)]
Simplify the equation, then we have
⇒ [√(1 / x²)] · [√(x² / 81)]
⇒ [1/x] · [x/9]
⇒ 1/9
The value of the expression [√(1 / x²)] · [√(x² / 81)] will be 1/9. Then the correct option is C.
More about the value of the expression link is given below.
https://brainly.com/question/23671908
#SPJ7
Not sure how to do this.
Answer:
200π
Step-by-step explanation:
Surface area is abbreviated to SA
TOTAL SA of cone = Base area + πrl
Base area = πr² = π x 8² = 64π
Curved SA = πrl = π x 8 x l
to work out l, use pythagoras theorem: √(15)² + (8)² = 17
so, curved SA = π x 8 x 17 = 136π
Total SA of cone = 64π + 136π = 200π
3. Solve the following problem using PEMDAS, 3x +3 (9x
2) – 4 =?
a. 48
b. 125
c. 2
Answer:
a
Step-by-step explanatio
Which of the following pairs of coordinates represents the same point in polar coordinates? Check all that apply.
(r,theta) and (r,theta+2pi)
(r,theta) and (-r,theta)
(r,theta) and (-r,theta+ 2pi)
(r,theta) and (-r,theta+pi)
A point that has the polar coordinate [tex](r,\theta)[/tex] can also be represented by [tex](r, \theta+2n\pi)[/tex] and [tex](-r, \theta+(2n+1)\pi)[/tex].
From the list of given options, [tex](r,\theta)[/tex] and [tex](-r, \theta+\pi)[/tex] are represents the same point
Recall that:
[tex](r, \theta+2n\pi)[/tex] and [tex](-r, \theta+(2n+1)\pi)[/tex] represents the same point
Where n is an integer
Assume [tex]n = 0[/tex]
[tex](r, \theta+2n\pi)[/tex] becomes
[tex](r, \theta+2n\pi) = (r, \theta+2\times 0 \times \pi)[/tex]
[tex](r, \theta+2n\pi) = (r, \theta+0)[/tex]
[tex](r, \theta+2n\pi) = (r, \theta)[/tex]
Similarly,
[tex](-r, \theta+(2n+1)\pi)[/tex] becomes
[tex](-r, \theta+(2n+1)\pi)=(-r, \theta+(2\times 0+1)\pi)[/tex]
[tex](-r, \theta+(2n+1)\pi)=(-r, \theta+(0+1)\pi)[/tex]
[tex](-r, \theta+(2n+1)\pi)=(-r, \theta+(1)\pi)[/tex]
[tex](-r, \theta+(2n+1)\pi)=(-r, \theta+\pi)[/tex]
This means that: [tex](r,\theta)[/tex] and [tex](-r, \theta+\pi)[/tex] represent the same point.
Hence, (d) is correct.
Read more about polar coordinates at:
https://brainly.com/question/13206882
Find the quotient: 2 2/3 ÷ 3 1/4
Answer:
2/9
Step-by-step explanation:
convert mixed number to improper fraction
8/3÷3 1/4
dividing is equivalent to multiplying by the reciprocal
8/3×1/3×1/4
reduce the numbers with the greatest common factor 4
2/3×1/3
multiply the fraction
2/3×1/3=2/9
2/9 is your answer
Ten divided by the quantity of y increased by 5.
Answer: what I need to know is what is y
Step-by-step explanation: I cant solve the problem if I dont know what y is, so can you plz tell me what y is!
Answer:
10
------
y + 5
Hope this helped!
What is the volume of a sphere with a radius of 3.1 cm, rounded to the nearest tenth
of a cubic centimeter?
3360832553 ____ pass___ wZE2XQ
Answer:nice
Step-by-step explanation:
Answer:was this
Step-by-step explanation:
Please help soon- The weight of oranges growing in an orchard is normally distributed with a mean
weight of 6 oz. and a standard deviation of 1 oz. From a batch of 2500 oranges, how
many would be expected to weight less than 4 oz., to the nearest whole number?
image below look at it and please help
Answer:
AB = 5.6 cm
Step-by-step explanation:
From the question given above, the following data were obtained:
Angle θ = 62°
Hypothenus = BC = 12 cm
Adjacent = AB =?
The lenght of side AB can be obtained by using Cos θ ratio. This is illustrated:
Cos θ = Adjacent / Hypothenus
Cos 62 = AB / 12
0.4695 = AB / 12
Cross multiply
AB = 0.4695 × 12
AB = 5.6 cm
Thus, length AB is 5.6 cm
pls help me loves :((
Answer:
609 m²
Step-by-step explanation:
Area of unshaded:
(6 x 18) + ((13-6) x 7) = 157
Area of overall rectangle:
36 x 28 = 1008
Area of the chunck of rectangle not included:
11 x 22 = 242
Area of shaded:
1008 - 157 - 242 = 609
What formula could you use to calculate 0.9m circumference of the circle
Answer:
The formula for circumference of a circle is 2πr
Mark me brainliest teehee :)
Which statement tells how to graph the point (3, 2) on a coordinate plane? A. LIVE From the origin, move 2 units up and 3 units to the left. B. LIVE From the origin, move 3 units to the right and 2 units up. C. LIVE From the origin, move 3 units up and 2 units to the right. D. LIVE From the origin, move 2 units to the right and 3 units down
Answer:
Step-by-step explanation:
²³
0.125,0.25,0.5,1 sequence
Answer:
1,2,4,8,16,32
Step-by-step explanation:
power of two sequence
2. Maya Nakai deposited $3,250 at 5.5% interest compounded daily for 120 days.
Answer:
$2005296.14
Step-by-step explanation:
(3250)(1+.055)^120=2005296.1362 rounded to the nearest penny =$2005296.14
A curve passes through a point P(0, 3) and has the property that slope of curve at every point P is twice the y-coordinate of point P. Use the concept of exponential growth function to find the equation of curve.
Answer:
The equation of curve is [tex]y = 3\cdot 7.389^{x}[/tex].
Step-by-step explanation:
The exponential growth function is represented by the expression described below:
[tex]y = a\cdot b^{x}[/tex] (1)
Where:
[tex]x[/tex] - Independent variable.
[tex]y[/tex] - Dependent variable.
[tex]a[/tex] - Initial value of [tex]y[/tex].
[tex]b[/tex] - Base.
By deriving (1), we obtain an expression for the slope of the curve:
[tex]y' = a\cdot b^{x} \cdot \ln b[/tex] (2)
If we know that [tex]x = 0[/tex], [tex]y = 3[/tex] and [tex]y' = 6[/tex], then we have the following system of equations:
[tex]a = 3[/tex] (3)
[tex]a\cdot \ln b = 6[/tex] (4)
By (3) in (4):
[tex]3\cdot \ln b = 6[/tex]
[tex]\ln b = 2[/tex]
[tex]b = e^{2}[/tex]
[tex]b = 7.389[/tex]
Therefore, the equation of curve is [tex]y = 3\cdot 7.389^{x}[/tex].
What is the expanded form of 8,609?
A 8,000+600+ 90
8,000+60+9
8,000 +900+ 6
8,000+600 +9
The last one 8,000 + 600 + 9
The sum of two integers is 2. Their difference is 10.
What are the two integers?
-14 and -4
B
4 and 14
-2 and 4
D
-4 and 6
Find the area of the shape shown below.
Answer:
8 units²
Step-by-step explanation:
What you have is a square with two triangles. We will break them apart, calculate the area and then add them together.
Square: A = l · w
2 · 2 = 4 un²
Triangle: A = (b · h) ÷ 2
(2 · 2) ÷ 2 = 2 un²
4 un² + 2 un² + 2 un²
8 un²
I need this please help me
Answer:
A. Right 6, Down 5
Step-by-step explanation:
I don't know how to explain this
Calculate the volume of this can of baked beans:
Choices:
120.95cm3
38.5cm3
77cm3
423.32cm3
Answer:
423.32cm³
Step-by-step explanation:
Volume of a cylinder = [tex]V=\pi r^2h[/tex]
where r = radius and h = height
Given height = 11 cm
Given radius = 3.5 cm
* plug in these values into the formula *
[tex]V=\pi 3.5^211\\3.5^2=12.25 \\12.25\pi =38.48\\34.48*11=423.32\\V=423.32[/tex]
So we can conclude that the answer would be D
Identify a second of transformations that maps triangle ABC onto triangle A"B"C in the image below.
Answer: The answer is B because the triangle rotated a 90 degrees counterclockwise then got a reduction.
Step-by-step explanation:
PLSSSSSSSSSSS ASAP!!!!! Find the area of the figure shown below.
Answer:
54 square ft
Step-by-step explanation:
Find missing sides:
8+6 = 14
9-6 = 3
Find area of full rectangle:
9×8 = 72
Find the area of the missing part of the full rectangle
3×6 = 18
Find the area of the actual shape:
72-18 = 54
Area = 54 square ft
21. A Figure is shown below.
What is the area of the figure, in square inches?
Answer:
[tex]36+27\pi\:\mathrm{in^2}[/tex]
Step-by-step explanation:
The figure consists of a square and a sector. We can add the areas of the square and sector to get the total area of the figure.
The area of a sector with measure [tex]\theta[/tex] in a circle of radius [tex]r[/tex] is equal to [tex]\frac{\theta}{360}\cdot r^2\pi[/tex]. Since there are 360 degrees in a circle and 90 degrees in each corner of a square, the measure of the sector is [tex]270^{\circ}[/tex].
Thus, its area is:
[tex]\frac{270}{360}\cdot6^2\cdot pi=\frac{3}{4}\cdot 6^2\cdot \pi=27\pi[/tex].
The area of a square with side length [tex]s[/tex] is given by [tex]s^2[/tex]. Therefore, the area of the circle is [tex]6^2=36[/tex] and the total area of the figure is [tex]\boxed{36+27\pi\:\mathrm{in^2}}[/tex]
Answer: 36+27in2
Step-by-step explanation:
1+1 why does my dog not love me?
Answer:
2
Step-by-step explanation:
your dog doesn't love you because it saw what you did. it knows. be cautious around your dog from now on. it knows more than you think and sees all. I'm warning you