Answer:
a) 0.0645 = 6.45% probability that the 90 orders can be filled without reordering components.
b) 0.4062 = 40.62% probability that the 100 orders can be filled without reordering components.
c) 0.9034 = 90.34% probability that the 100 orders can be filled without reordering components
Step-by-step explanation:
For each component, there are only two possible outcomes. Either it is defective, or it is not. The components can be assumed to be independent. This means that we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
3% of the components are identified as defective
This means that [tex]p = 0.03[/tex]
a. If the manufacturer stocks 90 components, what is the probability that the 90 orders can be filled without reordering components?
0 defective in a set of 90, which is [tex]P(X = 0)[/tex] when [tex]n = 90[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{90,0}.(0.03)^{0}.(0.97)^{90} = 0.0645[/tex]
0.0645 = 6.45% probability that the 90 orders can be filled without reordering components.
b. If the manufacturer stocks 102 components, what is the probability that the 100 orders can be filled without reordering components?
At most 102 - 100 = 2 defective in a set of 102, so [tex]P(X \leq 2)[/tex] when [tex]n = 102[/tex]
Then
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{102,0}.(0.03)^{0}.(0.97)^{102} = 0.0447[/tex]
[tex]P(X = 1) = C_{102,0}.(0.03)^{1}.(0.97)^{101} = 0.1411[/tex]
[tex]P(X = 2) = C_{102,2}.(0.03)^{2}.(0.97)^{100} = 0.2204[/tex]
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0447 + 0.1411 + 0.2204 = 0.4062[/tex]
0.4062 = 40.62% probability that the 100 orders can be filled without reordering components.
c. If the manufacturer stocks 105 components, what is the probability that the 100 orders can be filled without reordering components?
At most 105 - 100 = 5 defective in a set of 105, so [tex]P(X \leq 5)[/tex] when [tex]n = 105[/tex]
Then
[tex]P(X \leq 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{105,0}.(0.03)^{0}.(0.97)^{105} = 0.0408[/tex]
[tex]P(X = 1) = C_{105,0}.(0.03)^{1}.(0.97)^{104} = 0.1326[/tex]
[tex]P(X = 2) = C_{105,2}.(0.03)^{2}.(0.97)^{103} = 0.2133[/tex]
[tex]P(X = 3) = C_{105,3}.(0.03)^{3}.(0.97)^{102} = 0.2265[/tex]
[tex]P(X = 4) = C_{105,4}.(0.03)^{4}.(0.97)^{101} = 0.1786[/tex]
[tex]P(X = 5) = C_{105,5}.(0.03)^{5}.(0.97)^{100} = 0.1116[/tex]
[tex]P(X \leq 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.0408 + 0.1326 + 0.2133 + 0.2265 + 0.1786 + 0.1116 = 0.9034[/tex]
0.9034 = 90.34% probability that the 100 orders can be filled without reordering components
2 The length of Rectangle A is 7x +11. The
length of Rectangle B is 15x - 9. Given the
two Rectangles are congruent, what is the
value of x?
Answer:
Step-by-step explanation:
If congruent the sides are equal
15x-9=7x+11
8x=20
x=20/8=2.5
ILL GIVE BRAINLIEST AND 50 POINTS PLS help
A cell phone company charges $50 connection fee plus $20 per line. Jake must spend under $140 on his family’s cell phone bill. How many cell phone lines can his family have? Write the linear inequaulity that models this situation then solve the problem
Answer: 2
bc 50+20=70
140 divided by 70 is 2
Step-by-step explanation:
Can anyone help explain this my daughter is 7 does not understand it
Solve the proportion: 9 is to 16 as M is to 32.
(please show working out!)
Answer:
Step-by-step explanation:
9 : 16 :: M : 32
Means of extremes = means of means
= 9 x 32 = 16 x M
= 288 = 16M
288/16 = M
18 = M
what is the slope of (-20,-3), (19,-15)
Answer:
m= - 4/13
Step-by-step explanation:
Answer:
-4/13
Step-by-step explanation:
Hopefully this helps :)
Which expressions are polynomials? Select the two correct answers. (2 points)
ox-3+ ſo
3- +1
0-428
24 + 2y2 + 2 – w?
Answer:
Third and fourth
Step-by-step explanation:
Exponents can't be negative.
Worth 20 points
Please answer these all in a fraction form! :) <3 ily all have a AMAZING day.
1. 1/8 ÷ 3/4 = ?
2. 3/5 ÷ 3/2 = ?
3. 4/1 ÷ 2/3 = ?
4.9/4 ÷ 6/5 = ?
5.22/4 ÷ 2/5 = ?
Answer:
1. 1/8 ÷ 3/4 = 1/6
2. 3/5 ÷ 3/2 = 2/5
3. 4/1 ÷ 2/3 = 6
4.9/4 ÷ 6/5 = 15/8
5.22/4 ÷ 2/5 = 261/80
Step-by-step explanation:
Hope this Helped
A cylinder has a height h, and a radius (3h-2)
The area of the base is pi (3h-2)^2
The volume of the clinder is V= pi(3h-2)^2h
10. Multiply the polynomials to simplify the expression for the volume:
V=pi(3h-2)^2h by
Answer:
[tex]V= 4\pi (9h^2 -12h + 4)[/tex]
Step-by-step explanation:
Given
Shape: Cylinder
[tex]Radius = 3h - 2[/tex]
[tex]Height = h[/tex]
[tex]Base\ Area = \pi (3h - 2)^2[/tex]
Required
Simplify the volume
The volume is calculated as:
[tex]Volume = Base\ Area * Height[/tex]
Substitute values for Base Area and Height
[tex]V= \pi(3h-2)^2*h[/tex]
Expand the bracket
[tex]V= \pi(3h-2)(3h-2)*h[/tex]
Open brackets
[tex]V= \pi (9h^2 -6h - 6h + 4) *h[/tex]
[tex]V= \pi (9h^2 -12h + 4) *h[/tex]
[tex]V= 4\pi (9h^2 -12h + 4)[/tex]
HELP ME PLEASE THIS IS LOCKING ME OUT IN 5 MINUTES
Answer:
Your answer is A
Step-by-step explanation:
The surface covered by a rectangular field is 375 square yards. The width of the field is 10 yards longer than its length. Using factors, determine the length and the width of the field
Answer:
L= 15
W= 25
Step-by-step explanation:
w(w-10) =375
w^2-10w-375=0
w=25 or -15
Length=25-10 =15
The length and width of the rectangle field are 15 yards and 25 yards if the surface covered by a rectangular field is 375 square yards.
What is a rectangle?It is defined as the two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral.
It is defined as the area occupied by the rectangle in two-dimensional planner geometry.
The area of a rectangle can be calculated using the following formula:
Rectangle area = length x width
Let L and W be the length and width of the rectangle.
The area of the rectangular field is 375 square yards
W = 10 + L
As we know,
Area = LW
375 = L(10 + L)
375 = 10L + L²
L²+ 10L - 375 = 0
After solving the above quadratic equation:
L = 15 yards
L = -25 (length cannot be negative)
Plug L in the equation W = 10 + L to get the width of the rectangular field
W = 10 + 15
W = 25 yards
Thus, the length and width of the rectangle field are 15 yards and 25 yards if the surface covered by a rectangular field is 375 square yards.
Learn more about the rectangle here:
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Wilbert needs a student loan to finish school. He needs $4200 and has two options.
Option A: 4 years at 4.5% interest with monthly payments of $95.77 and total payback of $4,596.96
Option B: 3 years at 4.7% interest with monthly payments of $125.31 and total payback of $4, 511.16
Which loan should Wilbert choose and how much will Wilbert save with that loan?
Answer:
85.8
Step-by-step explains
4596.96-4200=396.96
4511.16--4200=
396.96-311.16=85.8
so 85.8 and b
what is :
2x + 10 = ?
Answer:
x = -5
Step-by-step explanation:
2x = -10
x = -10/2
x = -5
Team A scored the following points per game 20,17,25,25,13,25,12,25,25 and 23 team B scored the following points per game 25,25,9,10,25,11,25,15,10 and 25 what is the mean of team A and team B
Answer:
Mean of team A = 21
Mean of team B = 18
Step-by-step explanation:
Formula:
Mean = Sum of values / Number of values
Calculations:
[tex]A = \frac{20+17+25+25+13+25+12+25+25+23}{10} = \frac{210}{10} = 21[/tex]
[tex]B = \frac{25+25+9+10+25+11+25+15+10+25}{10} =\frac{180}{10} =18[/tex]
Mean of team A = 21
Mean of team B = 18
The tape diagram a way to model 5/8x11
Answer:
55/8
Step-by-step explanation:
here u gooo good luck
i really need help!!
Answer:
#8. 2
#9. 7
#10. 2
#11. 2
#12. 0
#13. -4
#14. 17
#15. 1
Answer:#8=2
#9=-11
#10=8
#11=2
#12=0
#14=17
#15=1
Step-by-step explanation: #8-13 (Subtract the numbers using a number line, than add the numbers using a integer chips, after that calculate the sum of the differences) #14-15( normal solving stepping for integers(recommend using a T1-84 Calculator)
Find the equation of the exponential function represented by the table below:
Answer:
[tex]f(x)=5(4)^x[/tex]
Step-by-step explanation:
The exponential function is [tex]f(x)=ab^x[/tex]. [tex]a[/tex] is the initial value of the function, or the y-value when x=0. In this case, [tex]a[/tex]=5. If we enter that into the equation:
[tex]f(x)=5b^x[/tex]
Then we can use another point to solve for [tex]b[/tex].
[tex]20=5b^1[/tex]
Since anything raised to the power of 1 remains the same, we can continue to solve algebraically.
[tex]20=5b\\\frac{20}{5}=\frac{5b}{5}\\b=4[/tex]
Now that we have both the [tex]a[/tex] and [tex]b[/tex] value, we can return to the exponential function and fill in the blanks.
[tex]f(x)=5(4)^x[/tex]
I hope this helps!
Hi, can someone help me?
Answer:
No, no puedo ayudarte aunque te deseo buena suerte
Answer:
the price !!
Step-by-step explanation:
the price of donut holes depends on the number of them!! you cant tell the price without the donuts !!
a way to think of it could be "the price can't exist without the product (the donuts) so, the price dependent on the donuts. its the dependent!"
i really hope this helps!
what are the next 3 terms in this:O,T,T,F,F
Answer:
Step-by-step explanation:
S, S, E.
Come on, do I have to spell it out for you? :)
A person is walking at a rate of 9 feet every 4 seconds.
(a) Find their speed, i.e. the rate the distance
Answer:
v = 2.25 ft/s
Step-by-step explanation:
Given that,
A person is walking at a rate of 9 feet every 4 seconds.
We need to find their speed. We know that, the speed of total distance divided by time taken. So,
[tex]v=\dfrac{d}{t}\\\\v=\dfrac{9\ ft}{4\ s}\\\\v=2.25\ ft/s[/tex]
So, the speed is 2.25 ft/s.
Which inequality is represented by the graph? 3 NI 5 6 4 OA. 21 - 5y 3
Answer:
a
Step-by-step explanation:
Select the smaller of the two given numbers.
-|19|, -|12|
Answer:
-|12|
Step-by-step explanation:
|19| is 19, -|19| is -19
|12| is 12, -|12| is -12
-12>-19
a classroom is 30 feet wide the ceiling is 10 feet above the floor what is the volume
Answer:
300 sqft
Step-by-step explanation:
30 times ten is 300 and the measure is feet squared
Answer:
9000 ft 3
Step-by-step explanation:
solve and recieve brain list I took a better picture
What is the missing side length?
Answer:
the answer is 3 miles
Step-by-step explanation:
1 +2 = 3 so 3
1) : 2x + 5y = 12 a. (1,?) b. (?, 1) C. (0,?) d. (?, 0)
Answer:
A. y = 2
B. x = 7/2
C. y = 12/5
D. x = 6
Step-by-step explanation:
A. Determination of y .
2x + 5y = 12
x = 1
2(1) + 5y = 12
2 + 5y = 12
Collect like terms
5y = 12 – 2
5y = 10
Divide both side by 5
y = 10 / 5
y = 2
B. Determination of x
2x + 5y = 12
y = 1
2x + 5(1) = 12
2x + 5 = 12
Collect like terms
2x = 12 – 5
2x = 7
Divide both side by 2
x = 7/2
C. Determination of y
2x + 5y = 12
x = 0
2(0) + 5y = 12
0 + 5y = 12
5y = 12
Divide both side by 5
y = 12/5
D. Determination of x
2x + 5y = 12
y = 0
2x + 5(0) = 12
2x + 0 = 12
2x = 12
Divide both side by 2
x = 12/2
x = 6
SPEED, DISTANCE AND TIME
please please !!!!!!!!!!!!!!!!!!!!!!!!!!!!!! emergency will give thanks
1) A cyclist travels a distance of 90 miles in 5 hours. What
was her average speed?
2) How far along a motorway would you travel if you drove at
70 mph for 4 hours?
3) I drive to Bude in Cornwall from Sheffield in about 6
hours. The distance from Sheffield to Bude is 315 miles.
What is my average speed?
4) The distance from Leeds to London is 210 miles. The train
travels at an average speed of 90 mph. If I catch the 9.30 am
train in London, at what time should I expect to arrive in
Leeds?
5) How long will an athlete take to run 2000 m at an average
speed of 4 metres per second?
6) The distance between Sheffield and Land’s End is 420
miles.
a) What is the average speed of a journey from Sheffield to
Land’s End that takes 8 hours 45 minutes?
b) If Sam covered the distance at an average speed of 63
mph, how long would it take him?
Answer:
1 --- The cyclist's average speed was 18 miles per hour.
2 --- I would travel 280 miles far.
3 --- Your average speed was 52.5 miles per hour.
4 --- You should expect to arrive in Leeds at 11:50 AM.
5 --- The athlete will run 2000 m in 8 minutes and 20 seconds.
6A --- The average speed of the journey is 48 miles per hour.
6B --- It will take him 6 hours and 40 minutes.
Step-by-step explanation:
1) 90 / 5 = 18
2) 70 x 4 = 280
3) 315 / 6 = 52.5
4) 210 / 90 = 2.3333
0.333 = 0:20
9:30 + 2:20 = 11:50
5) 2000 / 4 = 500
500 / 60 = 8.3333
0.3333 = 0:20
8.3333 = 8:20
6A) 0:45 = 0.75
420 / 8.75 = 48
6B) 420 / 63 = 6.666
6.6666 = 6:40
PLZ ANSWER THESE QUESTIONS IF YOU KNOW ALGEBRA PLZ PLZ PLZ PLZZZZZZZZZZZZ I WILL GIVE BRAINLY AND ALL MY POINTS PLZZ HELP ME
I AM A YOU TUBER I WILL CHEAT IF I HAVE TO
Answer:
Algebra (from Arabic: الجبر al-jabr, meaning "reunion of broken parts"[1] and "bonesetting"[2]) is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols;[3] it is a unifying thread of almost all of mathematics.[4] It includes everything from elementary equation solving to the study of abstractions such as groups, rings, and fields. The more basic parts of algebra are called elementary algebra; the more abstract parts are called abstract algebra or modern algebra. Elementary algebra is generally considered to be essential for any study of mathematics, science, or engineering, as well as such applications as medicine and economics. Abstract algebra is a major area in advanced mathematics, studied primarily by professional mathematicians.
Elementary algebra differs from arithmetic in the use of abstractions, such as using letters to stand for numbers that are either unknown or allowed to take on many values.[5] For example, in {\displaystyle x+2=5}x+2=5 the letter {\displaystyle x}x is an unknown, but applying additive inverses can reveal its value: {\displaystyle x=3}x=3. In E = mc2, the letters {\displaystyle E}E and {\displaystyle m}m are variables, and the letter {\displaystyle c}c is a constant, the speed of light in a vacuum. Algebra gives methods for writing formulas and solving equations that are much clearer and easier than the older method of writing everything out in words.
The word algebra is also used in certain specialized ways. A special kind of mathematical object in abstract algebra is called an "algebra", and the word is used, for example, in the phrases linear algebra and algebraic topology.
A mathematician who does research in algebra is called an algebraist.
Which statement is true if a is the fourth root of 16, Show your work
a x a x a x a = 16
a = 164
4a = 16
a = 16/4
Given:
The statement is " a is the fourth root of 16".
To find:
The true statement for the given statement.
Solution:
The given statement is
a is the fourth root of 16.
Mathematically, it can be written as
[tex]a=\sqrt[4]{16}[/tex]
Taking power 4 on both sides.
[tex]a^4=(\sqrt[4]{16})^4[/tex]
[tex]a\times a\times a\times a=16[/tex]
Therefore, the correct option is A.
A true statement , if a is the fourth root of 16 is
a x a x a x a = 16
Important Information :
'a' is the fourth root of 16'a' is the fourth root of 16 can be written as
[tex]a=\sqrt[4]{16}[/tex]
To remove fourth root, we take exponent 4 on both sides
[tex]a=\sqrt[4]{16}\\(a)^4=(\sqrt[4]{16})^4[/tex]
Exponent 4 and fourth root will get cancelled
[tex]a^4=16\\a \cdot a\cdot a \cdot a=16[/tex]
a x a x a x a = 16
A true statement , if a is the fourth root of 16 is
a x a x a x a = 16
learn more about the radicals here:
brainly.com/question/1799883
3. (07.02 MC) What is the value of y in the equation 3(3y - 12) = 0? (5 points) 4 5 6 9
3(3y-12)=0 divide both sides by 3
3y-12=0 add 12 to both sides
3y=12 divide both sides by 3
y=4
Can some please help 17-19 please
Answer:
Step-by-step explanation:
17. 2(x+6) common factor is 2
18. 8(3+y-2w) common factor is 8
19. 2(7-4m)