Answer:
a) 10.73%
b) 45.60%
c) 0.0094%
d) 54.4%
Step-by-step explanation:
The probability of one transistor being defective is equal the number of defective transistors over the total number of transistors
a)
The probability of the first one being defective is 4/24, and then the probability of the second one being defective is 3/23, because we have one less defective transistor. The probability of the third one being not defective is 20/22, and the fourth one not being defective is 19/21. We also multiply the final probability by a combination of 4 choose 2, because the defective transistors can be any 2 of the group of 4:
C(4,2) = 4! / (2! * 2!) = 6
P = 6 * (4/24) * (3/23) * (20/22) * (19/21) = 0.1073 = 10.73%
b)
Similar to the letter a), we have:
First one not defective: P = 20/24
Second one not defective: P = 19/23
Third one not defective: P = 18/22
Fourth one not defective: P = 17/21
P = (20/24) * (19/23) * (18/22) * (17/21) = 0.4560 = 45.60%
c)
First one defective: P = 4/24
Second one defective: P = 3/23
Third one defective: P = 2/22
Fourth one defective: P = 1/21
P = (4/24) * (3/23) * (2/22) * (1/21) = 0.000094 = 0.0094%
d)
If we want at least 1 defective, we just need to subtract 100% from the case where all 4 are not defective:
P = 1 - 0.4560 = 0.5440 = 54.4%
In this exercise we have to use the knowledge of probability to calculate each of the requested probabilities, so we can say that:
a) [tex]10.73\%[/tex]
b) [tex]45.60\%[/tex]
c) [tex]0.0094\%[/tex]
d) [tex]54.4\%[/tex]
a)The probability of the first one being defective is 4/24, and then the probability of the second one being defective is 3/23, because we have one less defective transistor. So the combination will be:
[tex]C(4,2) = 4! / (2! * 2!) = 6\\P = 6 * (4/24) * (3/23) * (20/22) * (19/21) = 0.1073 = 10.73%[/tex]
b)So find the not defective, we have:
First one: P = 20/24 Second one: P = 19/23 Third one: P = 18/22 Fourth one: P = 17/21
[tex]P = (20/24) * (19/23) * (18/22) * (17/21) = 0.4560 = 45.60%[/tex]
c)So find the defective, we have:
First one: P = 4/24 Second one: P = 3/23 Third one: P = 2/22 Fourth one: P = 1/21
[tex]P = (4/24) * (3/23) * (2/22) * (1/21) = 0.000094 = 0.0094%[/tex]
d)We just need to subtract 100% from the case where all 4 are not defective:
[tex]P = 1 - 0.4560 = 0.5440 = 54.4%[/tex]
See more about probability at brainly.com/question/743546
The total population of students was 380. Based on the data, what is the best approximation for the total number of students who have a cell phone plan with company Y?
Answer:
114
Step-by-step explanation:
PLEASE HELP Three subtracted from x is less than 20
Answer:
x < 23 (x is less than 23)
Step-by-step explanation:
x - 3 < 20
x < 20 + 3
x < 23 (x is less than 23)
A sector of a circle whose radius is 4 centimeters, has a central angle of 30 Which of the following. which of following represents the area of this sector in square centimeters?
(1). 12π/5
(2). 8π/15
(3). 4π/3
(4). 6π/5
Answer:
area of the sector =4π/3 cm²
Step-by-step explanation:
To find the area of the sector, we will follow the steps below;
first write the formula for finding area of a sector
area of a sector = Ф/360 × πr²
where r is the radius
from the question given
Ф= 30 and radius = 4 centimeters
we can proceed to insert the values into he formula above
area of a sector = Ф/360 × πr²
=30/360 ×π×4²
=1/12 ×π×16
=16π /12
=8π/6
=4π/3
area of the sector =4π/3 cm²
Solve these simultaneous equations.
3 pillows and 5 quilts cost £49
5 pillows and 5 quilts cost £55
Find the cost of one of each.
Answer:
pillow cost 3, quilt costs 5
Step-by-step explanation:
let p represent pillow and q represent quilt
rest is in pic attached
How many 6 packs of soda do jace and jake need to buy if each person has one soda?
Answer:
3 6 pks are required
Step-by-step explanation:
There are 14 people at the party
14 = 6x where x is the number of 6 pks
Divide each side by 6
14/6 = 6x/6
2 1/3 = x
Since we cannot buy part of a 6 pk, we round up
3 6 pks are required
3
gathered at
There were 632
animals
the river. A herd of
187 elephants and
266 zebras left the
river area. How
many animals were
still at the river?
Answer:
179
Step-by-step explanation:
The total number of animals in the river was 632.
A herd of 187 elephants and 266 zebras left the river area.
Adding them up, the total number of animals that left the river area is:
187 + 266 = 453
Therefore, the total number of animals left at the river area is the subtraction for the animals that left the river area from the number of animals that were there initially:
632 - 453 = 179
HELP FOR BRAINLIEST ANSWER Ben bowled 126 and 220 in his first two games. What must he bowl in his third game to have an average of at least 190?
Answer:
224
Step-by-step explanation:
I used an average calculator and tried every possibility, adding 224 in results in an anverage of exactly 190.
Answer:
224
Step-by-step explanation:
190x3=570
570-126-220=224
So ben must bowl a 224
Solve the equation using the Quadratic Formula:
x2 + 6x + 3 = 0
Answer:
x = -2[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
First we have to distinguish the numbers with x from the "normal" numbers.
2x and 6x are numbers with x.
3 and 0 are "normal" numbers.
Now we have to seperate them on different sides of the equal sign.
To do this, we can subtract 3 from the left side and then add it to 0 on the left side.
Therefore, the equation will now be 2x + 6x = -3.
Now we can add 2x and 6x together, making it 8x.
The equation will now be 8x = -3.
To find the product of x, we need to divide both sides together.
So 8 divided by -3 will make -2[tex]\frac{2}{3}[/tex].
Therefore, x is -2[tex]\frac{2}{3}[/tex].
Hope my explination makes sense :)
a certain Forest covers an area of 2000 square kilometers. Suppose that each year this area, decreases by 6%. What is the equation that best represents the area of the forest each year?
Using substitution to alive equation with two variables
Answer:
X=27
Step-by-step explanation:
-4•4= -16
Move -16 to the other side
3x=81
x=27
Solve this inequality.
-5x + 7 > 42
A. x> 245
B. x < -175
C. x > 7
D. x < -7
Answer:
x < -7
Step-by-step explanation:
-5x + 7 > 42
Subtract 7 from each side
-5x + 7-7 > 42-7
-5x > 35
Divide each side by -5, remembering to flip the inequality
-5x/-5 <35/-5
x < -7
Find the next three terms of the arithmetic sequence 5, 9, 13, 17, … .
Question 9 options:
a)
21, 23, 25
b)
41, 45, 49
c)
21, 41, 61
d)
21, 25, 29
The next three terms of the arithmetic sequence 5, 9, 13, 17 is 21, 25, 29.
Given that,
The given arithmetic sequence is 5, 9, 13, 17.We need to find the next three terms.Based on the above information, we can see that
There is the addition of 4 in each next number i.e.
5 + 4 = 9
9 + 4 = 13
13 + 4 = 17
17 + 4 = 21
21 + 4 = 25
25 + 4 = 29
Therefore, the option d is correct
Hence, the other options are incorrect.
Therefore we can conclude that the next three terms of the arithmetic sequence 5, 9, 13, 17 is 21, 25, 29.
Learn more: brainly.com/question/14069515
A thousand dollars is left in a credit union drawing 7% compounded monthly.
What is the balance at the end of 10 years?
Please show the work to answer compound interest work
Answer: $2009.66
Step-by-step explanation:
A = P(1 + r/n)^nt
The balance at the end of 10 years in account after the credit union drawing 7% compounded monthly is $2009.66
What is compound interest?Compound interest is the amount charged on the principal amount and the accumulated interest with a fixed rate of interest for a time period.
The formula for the final amount with the compound interest formula can be given as,
[tex]A=P\times\left(1+\dfrac{r}{n\times100}\right)^{nt}\\[/tex]
Here, A is the final amount (principal plus interest amount) on the principal amount P of with the rate r of in the time period of t.
A thousand dollars is left in a credit union drawing 7% compounded monthly. The balance at the end of 10 years has to be find out.
Here the data given are,
Principal amount $1000.The rate of interest is 7%.Time period is 10 years.The number of month in a year is 12.Put these values in the above formula as,
[tex]A=1000\times\left(1+\dfrac{7}{12\times100}\right)^{12\times10}\\A=2009.66[/tex]
Thus, the balance at the end of 10 years in account after the credit union drawing 7% compounded monthly is $2009.66
Learn more about the compound interest here;
https://brainly.com/question/24274034
945/7 i dont know it is confused
Answer:
135
Step-by-step explanation:
We have been given the equation 945 ÷ 7. Seven goes into 9 one time. 9 minus 7 equals 2. Now drag down the four, 7 goes into 24, three times. 24 minus 21 equals 3. Drag down the five. 7 goes into 35 perfectly 5 times. Please mark me as brainliest. :)
If a line has a slope of 2 and contains the point (-2,1), what is its equation in point-slope form?
A. y+ 2 = -2(x-1)
B. y-1 = 2(x-2)
C. y-2 = -2(x-1)
D. y- 1 = 2(x+2)
What is the problem with this statement?
If you taking geometry, then you are in the 9th grade
A. It does not assume that all students take geometry
B. It does not assume that all students are in the 9th grade
C. It assumes that no students taking geometry are in the 9th grade
D. It assumes that all students taking geometry are in the 9th grade
Please I need help with this
Answer:
D. It assumes that all students taking geometry are in the 9th grade
Step-by-step explanation:
Find the equation of the line. Use exact numbers. y=y=y, equals x+x+x, plus 5
Answer:
y=3x+5
Step-by-step explanation:
y=y=y=x+x+x+5 is what I think you were saying. In that case:
y=x+x+x+5
y=3x+5
The equation of the line is y=3x+5
The equation of the given line is y = 2/3 x - 2
The standard form of the equation of a line is expressed as y = mx + b
m is the slope of the line
b is the y-intercept
from the diagram attached, we can use the coordinate (0, -2) and (3, 0)
Get the slope
Slope "m" = 0-(-2)/3-0
m = 2/3
Since the line cuts the y-axis at y = -2, hence the y-intercept is b = -2
Substitute the given parameters into the equation:
y = mx + b
y = 2/3 x + (-2)
y = 2/3 x - 2
Hence the equation of the given line is y = 2/3 x - 2
Learn more here: https://brainly.com/question/17003809
In what ways are the sine and cosine graphs different?
Answer: A cosine graph is the darker curve on a graph. It shifts to the left of the sine curve. A sine graph is the lighter curve on the graph.
Given a line segment that contains the points A,B, & C in order, and given B is the midpoint of AC, if AB = 7x - 2, and BC = 4x + 7, find x. Select one: a. 9 b. - 2 c. 3 d. 7
Answer: the answer is c. 3
Step-by-step explanation:
Subtract 4x from 7x
3x-2=7
Then add 2 to 7
3x=9
Then divide 3 by 3x and 9 by 3
X=3
c. The value of x is 3
What is line segment ?
A line segment is a part of straight line measured between two points.
A line segment always have a definite length.
What is the value of x ?Given, a line segment contains points A, B, C in order.
Also the point B is the middle point of AC.
Hence, we can say that, AB = BC ......(1)
Here, AB = 7x-2 & BC = 4x+7
Therefore, from (1) we get,
7x-2 = 4x+7
⇒ 7x-4x = 7+2
⇒ 3x = 9
⇒ x = 3
The value of x = 3
Learn more about Line segment here :
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Please help I really need this answer since I am preparing for my nationals
Will give branliest if it is correct.
Answer: [tex]\bold{a)\ \overline{CD}=6\qquad b)\ \overline{AD}=\dfrac{32}{3}\qquad c)\ \overline{AC}=\dfrac{50}{3}\qquad d)\ \overline{OB}=\dfrac{25}{3}}[/tex]
Step-by-step explanation:
a) First, use the Pythagorean Theorem to find CD:
8² + (CD)² = 10² → CD = 6
d) Next, find OB. Notice that both OB and OC are the radius of the circle.
Using the Segment Addition postulate, we know the radius (r) = CD + DO → DO = r - 6
Use the Pythagorean Theorem for ΔOBD to find OB:
(DO)² + (BD)² = (OB)²
(r - 6)² + 8² = r²
r² - 12r + 36 + 64 = r²
-12r + 100 = 0
100 = 12r
[tex]\dfrac{25}{3}\quad = r[/tex]
c) Now, find AC. Notice that AC is the diameter.
Diameter = 2r
= 2(OB)
[tex]=2\bigg(\dfrac{25}{3}\bigg)\qquad =\dfrac{50}{3}[/tex]
b) Lastly, find AD. Using the Segment Addition Postulate, we know that
AD + CD = AC → AD = AC - CD
[tex]= \dfrac{50}{3}-6\qquad \rightarrow \quad \dfrac{50}{3}-\dfrac{18}{3}\qquad =\dfrac{32}{3}[/tex]
Can someone help me??
Answer:
67.5 degrees
Step-by-step explanation:
The piece that isn't marked with xs is 90 degrees marked by the square symbol representing a right angle.
Full circle = 360 degrees
360 degrees - 90 degrees = 270 degrees
Now, if we add all the like terms we have 4 x's in total. This is becauswe 3x + another x = 4x.
So, we need to divide 270 by 4. We get 67.5 degrees.
Hope this helps!
treviglaslibrary
Answer:
67.5 degrees
Step-by-step explanation:
Hope that helps
a) write in simplified form the value of the area of the trapesoid.
Answer:
[tex]A=\frac{x^4y^9+3x^4y^9}{2}4x^2y^5=2x^4y^9(4x^2y^5)=8x^6y^{14}[/tex]
someone help please, summer school is annoying
Answer:
6
Step-by-step explanation:
2y/3 + 1/3 = y/2 + 1/6
We want to eliminate the fractions
The least common multiple of 3,2 and 6 is 6
Multiply each side by 6 to get rid of the fractions
6(2y/3 + 1/3) = 6(y/2 + 1/6)
4y +2 = 3y +1
Help please.....anyone
Answer:
200 dollars
Step-by-step explanation:
Find the area of parallelogram BDKJ.
Answer:
6 x 4 = 24
Step-by-step explanation:
JC = 4
BD = 6
The quadratic equation 2x^2+4x-30=0 has two solutions. one of the solutions is x=3 the other solution is?
Answer:
2x^2+4x-30=0
Step-by-step explanation:
2x^2+10x-6x-30=0
2x(x+5)-6(x+5)=0
(2x-6)(x+5)=0
2x-6=0 x+5=0
x=6/2 x=-5
x=3
Answer:
Step-by-step explanation:
[tex]2x^2+4x-30=0\\<=> x^2+2x-15=0[/tex]
so we know that the sum of the two solutions is -2 and the multiplication -15
so we are looking for x so that
x+3=-2 and 3x=-15
it gives x = -5
another way to do it is to put (x-3) in factor as we know that 3 is one of the solutions it gives
[tex]2x^2+4x-30 = 2(x-3)(x+5)[/tex]
and then the second solution is -5
Plz help ASAP will give brainliest if answered correctly!!
Answer:
C
Step-by-step explanation:
Multiply 5/8 by 4 in which you get 2.5 which is 5/2 and simplify, then you get answer C
Conner has $25,000 in his bank account. Every month he spends
$1,500. He does not add money to the account. Which equation could
be used to figure out when Conner will run out of money?
Answer: The answer is the last variant.[tex]\boxed{\boxed{25000-1500*x=0}} \\\\\\ \b{For x=16 months} \ \ \ \to \to \to \ \ \ 25000-1500*16= 25000-24000 = \boxed { 1000 < 1500}[/tex]
Step-by-step explanation:
Simplify the expression below and show each step. Justify the order of your steps in a brief explanation. 5-6x8diviededby8+3
Answer:
2
Step-by-step explanation:
First we have to figure out which order to solve this equation.
Following the rules of PEMDAS, we know it would be 5 - [6 x 8 ( ÷ 8 ) ] + 3.
Please tell me if you need a larger explanation on PEMDAS, or what the brackets and parenthesis mean.
Next we simplify the equation, bringing us to the answer, 2.
Once again, please tell me if you need to know how I simplified the equation.
Hope this helped :)
which is lighter 900000g or 9 tonnes
900000g coz 9 tonnes is like 9000000g
Answer:
900000gm is lighter than 9 tonnes
Step-by-step explanation:
907185 = 1 ton
907185 x 9 = 8164665
You underline how many digits = 7 and see that 900000gm has only 6 digits.
