Answer:
0.7208 = 72.08% probability that this whole shipment will be accepted.
Step-by-step explanation:
For each tablet, there are only two possible outcomes. Either it meets the required specifications, or it does not. The probability of a tablet meeting the required specifications is independent of any other tablet, which means that the binomial probability distribution is used 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.
4% rate of defects
This means that [tex]p = 0.04[/tex]
26 tablets
This means that [tex]n = 26[/tex]
What is the probability that this whole shipment will be accepted?
Probability that at most one tablet does not meet the specifications, which is:
[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]
Thus
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{26,0}.(0.04)^{0}.(0.96)^{26} = 0.3460[/tex]
[tex]P(X = 1) = C_{26,1}.(0.04)^{1}.(0.96)^{25} = 0.3748[/tex]
Then
[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.3460 + 0.3748 = 0.7208[/tex]
0.7208 = 72.08% probability that this whole shipment will be accepted.
Cos100x+4/3=0.............
answer:
[tex]{ \tt{ \cos(100x) + \frac{4}{3} = 0}} \\ { \tt{ \cos(100x) = - \frac{4}{3} }} \\ { \tt{100x = { \cos }^{ - 1} ( - \frac{4}{3} )}} \\ { \tt{invalid \: answer}}[/tex]
Which of the following is the equation of the line that passes through the point (-7, 12) and is perpendicular to the line whose equation is y=8
a) y=-12
b) y=-7
c) x= -7
d) x=12
Sam and Mary collect marbles. “If you give me 5 marbles I’ll have twice as many as you.” said Sam to Mary.
“But if you give me 4 marbles wwe would have the same number said Mary to Sam.
How many marbles do they have altogether?
Answer:
54 marbles
Step-by-step explanation:
The question is a word problem leading to a simultaneous equation
Let 'x' represent the initial number of marbles with Sam, and let 'y' represent the initial number of marbles with Mary,
If Mary gives Sam 5 marbles, we have;
x + 5 = 2 × (y - 5)...(1)
If Sam gives Mary 4 marbles, we get;
x - 4 = y + 4...(2)
From equation (1), we get;
x + 5 = 2 × (y - 5) = 2·y - 10
x = 2·y - 10 - 5 = 2·y - 15
x = 2·y - 15...(3)
From equation (2), we have;
x - 4 = y + 4
∴ x = y + 4 + 4 = y + 8
x = y + 8...(4)
Equating the two values of 'x' in equation (3), and equation (4), we get;
2·y - 15 = y + 8
2·y - y = 8 + 15 = 23
∴ y = 23
From equation (4), we get;
x = y + 8 = 23 + 8 = 31
x = 31
The total number of marbles they have altogether = x + y
However, x + y = 23 + 31 = 54
Therefore;
The total number of marbles they have altogether = 54 marbles.
What is the length of the line?
Answer:
Step-by-step explanation:
Pretend you see a right triangle here. From the lower end of the line go up 5 and you will be on the same horizontal as the upper end of the line. Go over 6 units and you close your triangle. This is a right triangle with legs 5 and 6 units long. We are looking for the hypotenuse of this triangle. Use Pythagorean's Theorem:
[tex]5^2+6^2=??^2[/tex]
25 + 36 = ??² and
61 = ??² so
?? = √61
-5 3/4 - 3 1/2 = ? Solve please!
Answer:
-9.25
Step-by-step explanation:
-5.75 - 3.5
-9.25
[tex]\implies {\blue {\boxed {\boxed {\pink {\sf { \:- 9 \frac{1}{4} (or) \:- 9.25 }}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex] - 5 \frac{3}{4} - 3 \frac{1}{2} [/tex]
➺[tex] \: \frac{ - 23}{4} - \frac{7}{2} [/tex]
➺[tex] \: \frac{ - 23}{4} - \frac{7 \times 2}{2 \times 2} [/tex]
➺[tex] \: \frac{ - 23 - 14}{4} [/tex]
➺[tex] \frac{ - 37}{4} [/tex]
➺[tex] \: - 9 \frac{1}{4} [/tex]
➺[tex] \: -9.25[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]
one number from 10 to 20 is written on each card select one card randomly what are the probability
Answer:
1
Step-by-step explanation:
S = {,10,11,12,13,14,15,16,17,18,19,}
n(s) = 10
P(a) = n(a) / n(s)
= 10 / 10
= 1 / 1
= 1
hope this helps.....
Alguien me ayuda Gracias
1) Se lanza un dado la probabilidad de que caiga un número
mayor que 5 es: 26,66%
V o F
2) Se lanza un dado, la probabilidad de que caiga un número mayor que 2 es: 56,66%
V o F
3) En una caja hay 12 pelotas de igual tamaño, de las cuales 7 son azules y 5 blancas.
La probabilidad de que al extraer una esta sea blanca es: 40,66%
V o F
4) Un matrimonio desea tener 3 hijos. La probabilidad de obtener:
Dos varones y una hembra es: 47,5%
V o F
5) Un matrimonio desea tener 3 hijos. La probabilidad de obtener dos varones y dos hembras es: 50%
V o F
Answer:
1) V
2) V
3) V
4) V
5) V
Step-by-step explanation:
Solve for x. Each figure is a parallelogram.
1)
Y
Х
95
8x - 1
V
W
answers
A) 3
C) 11
B) 8
D) 12
what is the value of the expression 2[4(2^3+5)]-4^2
2 [4( 2³ + 5)] - 4²
2 [ 4 (8 + 5)] - 16
2 [ 4 ( 13)] - 16
2 [ 52 ] - 16
104 - 16
88
Good Studies!
x^2-10x=1 Solve by completing the square
Answer:
x = 5±sqrt(26)
Step-by-step explanation:
x^2-10x=1
Take the coefficient of x
-10
Divide by 2
-10/2 = -5
Square it
(-5)^2 = 25
Add this to both side
x^2-10x+25=1+25
(x-5)^2 = 26
Take the square root of each side
sqrt((x-5)^2) = ±sqrt(26)
x-5 = ±sqrt(26)
Add 5 to each side
x = 5±sqrt(26)
Answer:
-0.0990195 and 10.09902
Step-by-step explanation:
To complete the square, the same value needs to be added to both sides
x^2-10x+?=1+?
To complete the square x^2-10x+25=(x-5)^2 add 25 to the expression.
x^2-10x+25=1+?
Since 25 was added to the left-side, you need to add it to the right-side as well.
x^2-10x+25=1+25
use a^2-2ab+b^2=(a-b)^2 to factor this expression.
(x-5)^2=1+25
Then add the numbers together.
(x-5)^2=26
Solve for x.
x1=-squareroot26+5
x2=squareroot26+5
therefore you have 2 solutions
x1=-squareroot26+5
=-0.0990195
and
x2=squareroot26+5
=10.09902
Help me please this is due today and it’s late help help!!
Step-by-step explanation:
I know A is one because positives and negitives are oppisite but i dont know if there are more
Help pls!! this is a presentation I’m doing in class and I NEED this completed rn, ASAP!!! . What I need is just the answers for the picture below and I NEED the explanation to all of them, and if you can pls try to give a similar example to these and solve it or what did u use to solve it. (Only 1 example that is similar) Thank you so much!
15. 70° because a right angle is 90° and we have the angle of ADB which is 20°. So 90°-20°=70°.
16. 70° because angle PSQ is 60° and angle QSR is 10°. So 60°+10°=70°.
17. 55° because it says it in the explanation. I assume this is a typo and they meant to ask the measurement of ADC and in that case it would be 130° because angle ADB is 75° and angle BDC is 55°. 75°+55°=130°.
18. 40° because angle PSQ is a right angle which means it's 90°. So 130°-90°=40°.
19. 140° because angle ADB is 120° and angle BDC is 20° so 120°+20°=140°.
20. 125° because again it's in the explanation. But if it's a typo and they meant what is the measurement of PSQ then it is 50° because PSR is 125° and QSR is 75° so 125°-75°=50°.
Hope this helps! :)
The volume of the triangular prism is 54 cubic units.
A triangular prism with a volume of 54 cubic units is shown. The triangle has a base length of 4 and a height of x. The height of the prism is 3 x.
What is the value of x?
3
5
7
9
Answer:
The answer is 3
Step-by-step explanation:
please i have 15 minutes
Answer:
[tex] x = \dfrac{-\log 7}{\log 7 - \log 2} [/tex]
Step-by-step explanation:
[tex] 2^x = 7^{x + 1} [/tex]
Take the log of both sides.
[tex] \log 2^x = \log 7^{x + 1} [/tex]
Use properties of log.
[tex] x \log 2 = (x + 1) \log 7 [/tex]
[tex] x \log 2 = x \log 7 + \log 7 [/tex]
[tex] x \log 2 - x \log 7 = \log 7 [/tex]
[tex] x(\log 2 - \log 7) = \log 7 [/tex]
[tex] x = \dfrac{\log 7}{\log 2 - \log 7} [/tex]
[tex] x = \dfrac{\log 7}{-(\log 7 - \log 2)} [/tex]
[tex] x = \dfrac{-\log 7}{\log 7 - \log 2} [/tex]
Please help! Will give brainliest! Lucy is going to spin the spinner 85 times. the spinner is divided into equal sections
We can say 85 because we will spin it 85 times and it can happen we will not C
Not sure at all ....
The baker at The Bake Shop makes 24 muffins in 1 hour. How many muffins will the baker make in 5 hours?
97 muffins
100 muffins
101 muffins
120 muffins
120
Step-by-step explanation:
if "1 hour is 24 muffins"
you can either use '+' or '×' to find the ans,
for example,
- 24+24+24+24+24 = 120
[formula 1]
using '+' is the longer way to solve the question
the easier way is by using '×', which will solve the question faster (with this you need to memorise the time table!^^)
- 24 × 5 = 120
[formula 2]
Both gives the same amount of ans, but only has a different way of solving it!
Dr. Johnny Smith is looking up from camp at an angle of elevation of 27
degrees to the top of a Red Wood Tree. The tree is 85 feet tall. What is
the distance from the bottom of the tree to the camp?
Answer:
166.8 feet
Step-by-step explanation:
tan = opp/adj
opp = height of tree
adj = distance
tan27 = 85/distance
distance = 85/tan27
use calculator
distance = 166.821892967937799
166.8 feet
SOMEBODY PLEASE HELP
Answer:
x = 2
Step-by-step explanation:
[tex]\frac{24}{4x} = 3[/tex]
24 = 3*4x
24 = 12x
24 / 12 = x
2 = x
re-write 12% as a common fraction in a simple form
Answer:
[tex]\frac{3}{25}[/tex]
Step-by-step explanation:
[tex]12 \% = \frac{12}{100} = \frac{3}{25}[/tex]
Answer:
3/25
Step-by-step explanation:
12 %
to remove % sign divide 12 by 100
12/100
3/25
A circle has a diameter of 10 centimeters. If a sector with a central angle of 50 degrees is cut out, what is the area of this sector?
What is the value of Y when the value of X is one?
Answer:
….
Step-by-step explanation:
You will need an image for that!
A man bought 2 pounds of coffee and 1 pound of butter for a total of $11.25. A month later, the prices had not changed (this makes it a fictitious problem), and he bought 3 pounds of coffee and 2 pounds of butter for $18.50. Find the price per pound of both the coffee and the butter.
Answer: See explanation
Step-by-step explanation:
Let the price per pound of coffee be c
Let the price ce per pound of butter be b.
We can form an equation based on the information given and this will be:
2c + b = 11.25 ....... i
3c + 2b = 18.50 ....... ii
From equation i, b = 11.25 - 2c ..... iii
Put the value of b into equation ii.
3c + 2b = 18.50
3c + 2(11.25 - 2c) = 18.50
3c + 22.50 - 4c = 18.50
-c = 18.50 - 22.50
c = 4.00
A pound of coffee cost $4.00
Since b = 11.25 - 2c .
b = 11.25 - 2(4.00)
b = 11.25 - 8.00
b = 3.25
A pound of butter costs $3.25
SOMEONE, PLEASE HELP
Use the quadratic model P(x) = 25x² − 24x + 615 to predict P(x) if x equals 8.
Answer:
2,023
Step-by-step explanation:
P(8) = 25(8)²-24(8)+615
= 1600- 192 +615
= 2,023
if I have a 94% in art class and I don’t do one of my assignments and get a 68 what will my grade drop down to?
Answer:
81
Step-by-step explanation:
It depends on how many different grades you have and the values of each one of them.
I don't have those things, so Ill just use average.
You'll have an 81
What is v6/v5 in simplest radical form?
Answer: [tex]\sqrt{30}/5[/tex]
Step-by-step explanation:
You should get this answer because the simpliest form of a radical is that you shouldn't have any radical in the denominator. In order to get rid of the radical sign in the denominator, you have to multiply the numerator and the denominator with the [tex]\sqrt{5}[/tex].
Look at the image below for further explanation
HELP ASAP
Brittany and two of her friends want to join a softball league. The league requires teams to have at least nine players, but teams cannot have more than fifteen players. In interval notation, how many more people can join Brittany's team?
Answer:
The inequality is [tex]9\leq p\leq 15[/tex]
Step-by-step explanation:
The minimum number of players is 9 and the maximum number of players are 15.
let the number of players is p.
The inequality is given by
[tex]9\leq p\leq 15[/tex]
Which of the following ordered pairs represents a solution to the linear inequality y<6x-4?
Answer:
Option D: (0,-5)
Step-by-step explanation:
Comparing the given points to the graph.
So, the point that will lie at the shaded area represent solution to the linear inequality.
So, point (0,-5) is a solution to the linear inequality.
The answer is option D. (0,-5)
Note: the line y = 6x-4 is graphed using the table on the graph.
what is the scale factor from figure a to figure b
Answer:
1/2
Step-by-step explanation:
These two triangles are similar, so there is a scale factor. The heights and the bottom sides of each triangle are similar, figure A has a bottom length of 6, and figure B has a bottom length of 3. To get from A to B, you multiply by 1/2. So the scale factor is 1/2.
I WILL VOTE BRAINLIEST, HELP PLS
Eliminate the x in the following system of equations. What is the result when you add the two equations?
Answer: -7y = 21
explanation:
x+y=2;3x−4y=27
Step: Solve x+y=2 for x:
x+y+−y=2+−y (Add -y to both sides)
x=−y+2
Step: Substitute −y+2 for x in 3x−4y=27:
3x−4y=27
3(−y+2)−4y=27
−7y+6=27 (Simplify both sides of the equation)
−7y+6+−6=27+−6 (Add -6 to both sides)
−7y=21 (answer)
first option
manipulate line 1 to
x = 2 - y
then substitute x in line to for the righthand side above
then solve towards y.
I need help can’t figure this out :/
The table represents Joel's earnings
fordelivering papers. How much does
Joelearnperpaper? Show yourwork. Please help me I’ll give brainliest
Answer:
She earns $0.65 per paper
Step-by-step explanation:
1. She earns $3.90 per 6 papers
2. take $3.90 and divide by 6.
3. you will get the cost per paper.
4. to check the work if you'd like then take 7.80 and divide it by 12 and again you will get $0.65 per paper.
(you don't need to find a special calculator you can use one on your phone since each dollar has 100 cents so you just need to go out to the hundredths place in a decimal or the second decimal place)