Answer:
a. Outcomes of A = { (C,C,C) , (D,D,D), (S,S,S) }
b. Outcomes of B = { (C,D,S),(C,S,D),(D,C,S),(D,S,C),(S,C,D),(S,D,C) }
c. Outcomes of C = { (C,C,C),(C,C,D),(C,C,S),(C,D,C),(C,S,C),(D,C,C),(S,C,C) }
d. Outcomes of A⋂C = { (C,C,C) }
e. Outcomes of Sample space = { (C,C,C), (C,C,D), (C,C,S), (C,D,C), (C,D,D), (C,D,S), (C,S,C), (C,S,D), (C,S,S), (D,C,C), (D,C,D),(D,C,S), (D,D,C), (D,D,D), (D,D,S), (D,S,C), (D,S,D), (D,S,S), (S,C,C), (S,C,D), (S,C,S), (S,D,C), (S,D,D), (S,D,S), (S,S,C), (S,S,D), (S,S,S) }
f. Outcomes of A U B = { (C,C,C) , (D,D,D), (S,S,S), (C,D,S),(C,S,D),(D,C,S),(D,S,C),(S,C,D),(S,D,C) }
g. Outcomes of A⋂[tex]C^{c}[/tex] = { (D,D,D), (S,S,S) }
h. Outcomes of [tex]A^{c}[/tex]⋂C = {(C,C,D),(C,C,S),(C,D,C),(C,S,C),(D,C,C),(S,C,C)}
i. Events A and C are not mutually exclusive
j. Events B and C are mutually exclusive
Step-by-step explanation:
Given - Three times each day, a quality engineer samples a component
from a recently manufactured batch and tests it. Each part is
classified as conforming (suitable for its intended use),
downgraded (unsuitable for the intended purpose but usable for
another purpose), or scrap (not usable). An experiment consists
of recording the categories of the three parts tested in a particular
day.
To find - a. Let A be the event that all the parts fall into the same
category. List the outcomes in A.
b. Let B be the event that there is one part in each category.
List the outcomes in B.
c. Let C be the event that at least two parts are conforming.
List the outcomes in C.
d. List the outcomes in A⋂C
e. List the 27 outcomes in the sample space.
f. List the outcomes in A U B.
g. List the outcomes in A⋂[tex]C^{c}[/tex]
h. List the outcomes in ⋂C.
i. Are events A and C mutually exclusive? Explain.
j. Are events B and C mutually exclusive? Explain.
Proof -
Let
Conforming part = C
Downgraded part = D
Scrap part = S
a.)
Given , Let A be the event that all the parts fall into the same category.
Outcomes of A = { (C,C,C) , (D,D,D), (S,S,S) }
b.)
Given, Let B be the event that there is one part in each category.
Outcomes of B = { (C,D,S),(C,S,D),(D,C,S),(D,S,C),(S,C,D),(S,D,C) }
c.)
Given, Let C be the event that at least two parts are conforming.
Outcomes of C = { (C,C,C),(C,C,D),(C,C,S),(C,D,C),(C,S,C),(D,C,C),(S,C,C) }
d.)
Outcomes of A⋂C = { (C,C,C) }
e.)
Outcomes of Sample space = { (C,C,C), (C,C,D), (C,C,S), (C,D,C), (C,D,D), (C,D,S), (C,S,C), (C,S,D), (C,S,S), (D,C,C), (D,C,D),(D,C,S), (D,D,C), (D,D,D), (D,D,S), (D,S,C), (D,S,D), (D,S,S), (S,C,C), (S,C,D), (S,C,S), (S,D,C), (S,D,D), (S,D,S), (S,S,C), (S,S,D), (S,S,S) }
f.)
Outcomes of A U B = { (C,C,C) , (D,D,D), (S,S,S), (C,D,S),(C,S,D),(D,C,S),(D,S,C),(S,C,D),(S,D,C) }
g.)
Outcomes of [tex]C^{c}[/tex] = { (C,D,D), (C,D,S), (C,S,D), (C,S,S), (D,C,D),(D,C,S), (D,D,C), (D,D,D), (D,D,S), (D,S,C), (D,S,D), (D,S,S), (S,C,D), (S,C,S), (S,D,C), (S,D,D), (S,D,S), (S,S,C), (S,S,D), (S,S,S) }
Outcomes of A⋂[tex]C^{c}[/tex] = { (D,D,D), (S,S,S) }
h.)
Outcomes of [tex]A^{c}[/tex] = {(C,C,D), (C,C,S), (C,D,C), (C,D,D), (C,D,S), (C,S,C), (C,S,D), (C,S,S), (D,C,C), (D,C,D),(D,C,S), (D,D,C), (D,D,S), (D,S,C), (D,S,D), (D,S,S), (S,C,C), (S,C,D), (S,C,S), (S,D,C), (S,D,D), (S,D,S), (S,S,C), (S,S,D), }
Outcomes of [tex]A^{c}[/tex]⋂C = {(C,C,D),(C,C,S),(C,D,C),(C,S,C),(D,C,C),(S,C,C) }
i.)
As we two that Two events A and C are mutually exclusive iff A ∩ C = ∅
Now,
A ∩ C = { (C,C,C) }
⇒Events A and C are not mutually exclusive.
j.)
As we two that Two events B and C are mutually exclusive iff B ∩ C = ∅
Now,
B ∩ C = ∅
⇒Events B and C are mutually exclusive.
The profit for a company this year was $100,000. Each year the profit increases at a rate of 1.2% per
year. Which function shows the company's profit as a function of time in years?
a. f(t) = 100,000 0.012^t
b. f(t) = 100,000(1 + 1.2)^t
c. f(t) = 100,000(1 + 0.012)^t
d. f(t) = 100,000 - 1.2^t
Given:
Initial profit = $100,000
Increasing rate of profit = 1.2%
To find:
The function that shows the company's profit as a function of time in years.
Solution:
The exponential growth model is defined as:
[tex]f(t)=a(1+r)^t[/tex]
Where, a is the initial value, b is the growth rate and t is the time period.
Putting a=100,000 and r=0.012, we get
[tex]f(t)=100,000(1+0.012)^t[/tex]
Where, t is the number of years.
Therefore, the correct option is c.
An archer releases an arrow with an initial velocity of 20 feet per second at a height of 12 feet. The path the arrow takes can be modeled using the function f(x)=−16x2+20x+12, where f(x) represents the height, in feet, of the arrow and x represents the time the arrow travels in seconds. What is the maximum height, in feet, reached by the arrow? Round your answer to the nearest hundredth if necessary. Do not include units in your answer
Answer: 18.25
Step-by-step explanation:
The arrow reaches its highest point at the y-value of the turning point. Thus, we need to find the maximum quadratic function.
-16x^2+20x+12
We know that the maximum( or minimum) of a parabola is reached at x= -b/(2a)= -20/ 2(-16)= 18.25
Showing that the object will reach a maximum height of 18.25 feet
what is the value of the 1 in 56.123
Answer:
The value of 1 is tens =) i hope i help u
Enter the pair of fractions 6/7 and 13/14 with the smallest common denominator between the two fractions
Answer:
25/14
Step-by-step explanation:
solve for x. x+53=99 A.36 B.46 C.47 D.152
Answer:
Hii, the answer B. 46
Step-by-step explanation:
x+ 53 = 99
So to find what x equals we just do simple subtraction
99 - 53 = 46
so x = 46
Hope this helps!
PLEASE HELP
determine the intercepts of the line
x intercept (__ , __)
y intercept (__ , __)
Answer:
i think y=2 and x=-7
Step-by-step explanation:
Select all expressions that are equal to 3⋅3⋅3⋅3⋅3.
3^5
3^4 ⋅ 3
5 ⋅ 3
5^3
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{3\times3\times3\times3\times3}\\\\\mathsf{3\times3=\bf9}\\\\\mathsf{9\times9\times3}\\\\\mathsf{9\times9=\bf81}\\\\\mathsf{81\times3=\bf result}\\\\\mathsf{= \bf \underline{243}}\large\checkmark[/tex]
[tex]\text{Option A. }\downarrow\\\mathsf{3^5}\\\\\mathsf{3^5= 3\times3\times3\times3\times3}\\\\\mathsf{3\times3\times3\times3\times3}\\\\\mathsf{3\times3 = 9}\\\\\mathsf{9\times9\times3}\\\\\mathsf{9\times9 = 81}\\\\\mathsf{81\times3= 243}\\\\\large\text{\bold{Option A.} could possibly be your \bf ANSWER}\huge\checkmark[/tex]
[tex]\text{Option B. }\downarrow\\\mathsf{3^4\times5}\\\mathsf{3^4 = 3\times3\times3\times3}\\\\\mathsf{3\times3\times3\times3}\\\\\mathsf{3\times3=9}\\\\\mathsf{9\times9= 81}\\\\\mathsf{81\times3=243}\\\\\large\text{Option B. could possibly be your \bf ANSWER}\huge\checkmark[/tex]
[tex]\text{Option C. }\downarrow\\\mathsf{3\times5}\\\\\maths{3+3+3+3+3}\\\\\mathsf{3+3=6}\\\\\mathsf{6+6+3}\\\\\mathsf{6+6=12}\\\\\mathsf{12+3=15}\\\\\mathsf{15\neq243}\\\\\large\text{Option C is NOT your ANSWER}[/tex]
[tex]\text{Option D.}\downarrow\\\mathsf{5^3}\\\\\mathsf{5^3=5\times5\times5}\\\\\mathsf{5\times5\times5}\\\\\mathsf{5\times5=25}\\\\\mathsf{25\times5 = 125}\\\\\mathsf{125\neq243}\\\\\large\text{Option D. is NOT your ANSWER}[/tex]
[tex]\boxed{\boxed{\large\text{Answers: \boxed{\boxed{\mathsf{\bf{Option\ A.)\ 3^5 \ \& \ Option\ B.)\ 3^4 \times 3}}}}}}}}\huge\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Answer:
A) 3^5 B) 3^4*3
Step-by-step explanation:
which of the following is correct statement about this relation?
Given:
The relation is:
(-3,1),(-2,3),(-1,5),(0,7),(1,9),(2,11)
To find:
The slope and y-intercept for the given relation.
Solution:
Consider any two points from the given relation.
Let the two points are (0,7) and (1,9). So, the slope of the given relation is:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\dfrac{9-7}{1-0}[/tex]
[tex]m=\dfrac{2}{1}[/tex]
[tex]m=2[/tex]
The slope of the given relation is 2.
A point of relation is (0,7). It means the value of relation is 7 at x=0.
So, the y-intercept is 7.
Therefore, the correct option is D.
y=3x-4 slope intercept form
Answer:the slope is 3 and the y intercept is -4
Step-by-step explanation:
Please help me I wanna go to sleep
What is true about this sequence?
8000, 4000, 2000, 1000, ...
Answer:
B
Step-by-step explanation:
each consecutive term is divided by 2
If a point on a coordinate plane is placed 5 lines to the right and 3 lines up, what would the ordered pair be?
Answer:
(5,3)
Step-by-step explanation:
HEY can You help me with this work pls i need help don't put random. if u don't know it pls guys.
1️⃣Remove parentheses
6a+6+3x-2+2a+4
2️⃣Collect like terms
(6a+2a)+(6-2+4)+3x
3️⃣Simplify
8a+8+3x
Answer: 8a+8+3x
QUESTION 21️⃣Remove parentheses.
-2z-3+4c+6y+y+3c
2️⃣Collect like terms.
-2z-3+(4c+3c)+(6y+y)
3️⃣Simplify
-2z-3+7c+7y
Answer: -2z-3+7c+7y
QUESTION 31️⃣Subtracting (7.8 - 5.1t) from (2.8 - 3.2t)
(2.8 - 3.2t) - (7.8 - 5.1t)
2️⃣Remove the parentheses.
2.8 - 3.2t - 7.8 + 5.1t
= 5.1t - 3.2t + 2.8 - 7.8 (we have now shown the difference in another way)
3️⃣Subtracting the like terms, will give:
1.9t - 5
4️⃣Recall
(2.8 - 3.2t) - (7.8 - 5.1t).
(-3.2t + 2.8) - (-5.1t + 7.8)
Answer:
a. (-3.2t + 2.8) - (-5.1t + 7.8)
b. 1.9t - 5
c. (-3.2t + 2.8) - (-5.1t + 7.8)
QUESTION 41️⃣Simplify
1/2p-(1/4p-4)
2️⃣Simplify
p2-(p/4-4)
3️⃣Simplify
p2-p/4+4
4️⃣Combine Terms
(p/2-p/4)+4
5️⃣Combine Terms
p/4+4
Answer: p/4+4
Done ✔
12(-5z - 4)
please help me
Answer:
-60z - 48
Step-by-step explanation:
Is your expression.
A company offers broadband for a one-off charge of £60 for every 3 months, then £28 per month after that. How much will 12 months' broadband cost?
Step-by-step explanation:
12 months with $60 every 3 months is $240
then add $28 "per month after that"
Definition the value of a number regardless of its sign Definition
Highlight all of the Like Terms on questions 1-2 please!! (any color) (due in 5 minutes)
Answer:
1. 8,13,8,3,g
2. 8,13,3,g (Like term pair 1) and 8 (Like term pair 2)
Step-by-step explanation:
I need help with this one.
9514 1404 393
Answer:
1,563.5 in³904.8 yd³2,144.7 mm³1,288.2 cm³434.9 in³Step-by-step explanation:
The formula for the volume of a sphere is ...
V = (4/3)πr³
When you have several of these calculations to do, it is convenient to let a graphing calculator or spreadsheet do them. A spreadsheet can do the rounding for you, too. The results are attached. The units are the cube of the units of the radius.
Example calculation:
(4) Radius = diameter/2 = 13.5 cm/2 = 6.75 cm
V = (4/3)π(6.75 cm)³ = 4.18879 × 307.547 cm³ = 1288.2 cm³
Note that the constant (4/3)π ≈ 4.18879 remains the same for each calculation. All you need to do is multiply that by the cube of the radius.
What is the value of x?
K
х
X-6
Q
P
5
ال)
L
J
Answer:
C
Step-by-step explanation:
The value of x is equal to 9
Multiple Choice
Use the diagram below to answer questions 1–3.
Which angle is congruent to angle 1?
A. angle2
B. angle5
C. angle6
D. angle7
If f(x) = 5x2 – 6x + 13 and g(x) = 6 – 4(x – 1) which is an equivalent form of f(x) + g(x)?
Answer:
61-4-2. (3t-a)(at+1) f. 6x2 - 17x+10. 16x-5X(x-2) e x-2x*-*+2 x2{x-2)-1(x-2). (x-2)(x2_1). (x-2)x+1)(x-) hi ** +5x2 +6 ... Leave your answers in simplest radical form if needed. ... 4. Let 'n(x)=x2-Ox and g(x)=2x-7. Find all values of x, for which h(x) = g(x) ... p=2 4p=8. (x+6*=8(y+3) x+6X+36=8Y+24. X*+6x +12= By gx+x+1=Y. 13.
Step-by-step explanation:
3-gallon container of disinfectant costs $52.80. What is the price per cup?
What type of number is v5?
Choose all answers that apply:
1. Whole number
2. Integer
3. Rational
4. Irrational
PLEASE HELP ME ILL GIVE 10 POINTS
The revenue from selling x bracelets is f(x) = 8x.
The cost of buying x bracelets is c(x) = 3x + 12.
The profit from selling x bracelets is p(x) = (x) - c(x).
Write a function for p(x), the profit from selling x bracelets.
O A. p(x) = 11x - 12
B. p(x) = 11x + 12
C. p(x) = 5x - 12
O D. p(x) = 5x + 12
We are given r(x) and c(x).
p(x) = 8x - (3x + 12)
p(x) = 8x - 3x - 12
p(x) = 5x - 12
Done.
What is the distance between - 10
and 2 on the number line?
12 units
-8 units
5 units
8 units
Answer:
12 units
Step-by-step explanation:
Draw a number line and mark x = -10 and x = 2. You can readily see that the distance from -10 to the origin is 10 units, and from the origin to 2 is 2 units, in both cases measured from left to right. Adding these two positive quantities together, we get 10 + 2, or 12.
The distance from -10 to 2 on the number line is 12 units.
At an Auto Repair shop, 4 of the 16 cars received oil changes. What percent of the cars received oil changes?
Answer:
its 25 percent
Step-by-step explanation:
want an explanation cuz im happy to give you 1
Factorise 3x⁴-4y⁴ completely
Answer:
Step-by-step explanation:
[tex]3x^4-4y^4\\=(\sqrt{3}x^2)^2-(2y^2)^2)\\=(\sqrt{3}x^2+2y^2)(\sqrt{3}x^2-2y^2)\\=(\sqrt{3} x^{2} +2y^{2} )((3^{\frac{1}{4} } x)^2-(\sqrt{2} y)^{2} )\\=(\sqrt{3} x^{2} +2y^{2} )(3^{\frac{1}{4} } x+\sqrt{2} y)(3^{\frac{1}{4} } x-\sqrt{2} y)[/tex]
What is the average rate of change for f(x) = 2 ^ x + 10 over the interval 2 <= x <= 4
PLEASE HELP ITS DONE IN 16 HOURSSS!!!
question: A substance with 12 negatively charged atoms combined with a substance that has 10 positively charge atoms. What is the total charge of the substance when the atoms are combined?
answer options:
+22
-22
+2
-2
Hey guys can someone help me out?
Answer: yes with what
Step-by-step explanation:
Consider a graph of the equation y = x + 6. What is the y-intercept? (5 points) 6 −1 1 −6
D I am not 100% sure, If I am wrong sorry