Answer:
a) 38.74% probability that the main printer is operating properly for exactly 9 inspections.
b) Approximately 100% probability that the main printer is operating properly for at least 3 inspections.
c) The expected number of inspections in which the main printer is operating properly is 9.
Step-by-step explanation:
For each inspection, there are only two possible outcomes. Either it is operating correctly, or it is not. The probability of the printer operating correctly for an inspection is independent of any other inspection, 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.
Based on past experience, the main printer in a university computer centre is operating properly 90% of the time.
This means that [tex]p = 0.9[/tex]
Suppose inspections are made at 10 randomly selected times.
This means that [tex]n = 10[/tex]
A) What is the probability that the main printer is operating properly for exactly 9 inspections.
This is [tex]P(X = 9)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 9) = C_{10,9}.(0.9)^{9}.(0.1)^{1} = 0.3874[/tex]
38.74% probability that the main printer is operating properly for exactly 9 inspections.
B) What is the probability that the main printer is operating properly for at least 3 inspections?
This is:
[tex]P(X \geq 3) = 1 - P(X < 3)[/tex]
In which
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{10,0}.(0.9)^{0}.(0.1)^{10} \approx 0[/tex]
[tex]P(X = 1) = C_{10,1}.(0.9)^{1}.(0.1)^{9} \approx 0[/tex]
[tex]P(X = 2) = C_{10,2}.(0.9)^{2}.(0.1)^{8} \approx 0[/tex]
Thus:
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0 + 0 + 0 = 0[/tex]
Then:
[tex]P(X \geq 3) = 1 - P(X < 3) = 1 - 0 = 1[/tex]
Approximately 100% probability that the main printer is operating properly for at least 3 inspections.
C) What is the expected number of inspections in which the main printer is operating properly?
The expected value for the binomial distribution is given by:
[tex]E(X) = np[/tex]
In this question:
[tex]E(X) = 10(0.9) = 9[/tex]
find the length of arc RS. Use 3.14 for pie. Round to the nearest tenth.
3.10
Step-by-step explanation:
If you round 3.14 to the nearest tenth 4 is nearer to 10 than 20. Therefore, the answer is 3.10
Chen can jump rope 60 times a minute. At that rate, how many jumps can he make in 9 minutes?
Answer:
540 jumps in 9 minutes.
Step-by-step explanation:
60 jumps a minute. Chen is fast, but we need to find how many jumps in 9 minutes.
Let's say one minute is m
m = 60
9m = 60x9
We do x9 because from m to 9m you need to multiply by 9, so lets do that on both sides.
9m = 540
9 minutes = 540 jumps
Hope this helps!
--Applepi101
Problema de Ecuación de la demanda La demanda semanal para un CD es de 26 mil unidades cuando el precio es de $12 cada una, y de 10 mil cuando el precio unitario es de $18. Encuentra una ecuación de la demanda para el CD suponiendo que es lineal.
Answer:
d(x) = - 2666.67*a + 42000
Step-by-step explanation:
Vamos a llamar a d(x) la ecuación de la demanda de CD, entonces como la relación entre las dos variables es lineal la ecuación de la demanda es del tipo:
d(x) = a*x + b (1)
en esa relación a es la pendiente de la recta y b es el intercepto con el eje y que en este cas es el eje de valores de d(x).
Tenemos dos condiciones que cumplir y dos incógnitas que determinar ( a y b).
Cuando el precio ( x = 18 $ ) el monto de d(x) es de 10000 entonces por sustitución en la ecuación general (1)
10000 = 18*a + b (2)
Y cuando ( x = 12 $) d(x) = 26000
26000 = 12*a +b (3)
Resolviendo para a y b el sistema de dos ecuacions con dos incógnitas tenemos:
restando ec 3 - ec 2
16000 = - 6*a
de donde a = - 16000/6
a = - 2666.67
Llevando ese valor a ec 2
10000 = 12 *(- 2666.67) + b
10000 + 32000 = b
b = 42000
Finalmente la ecuación buscada es:
d(x) = - 2666.67*a + 42000
Como la pendiente es negativa significa que d(x) va decreciendo cuando x va en aumento
HELPPP PLEASEEEE
Identify the transformations you would apply to f(x) = sin x to graph f(x) = 0.5 sin (x - 30%)
HELP ASAP NEED HELP. WILL GIVE BRAINIEST AND 100 POINTS.
Use the function f(x) = 4x^2 - 7x - 15 to answer the questions.
Part a: completely factor f(x).
Part b: what are the x-intercepts of the graph of f(x)? Show your work.
Part C: describe the end behavior of the graph of f(x). Explain.
Part D: what are the steps you would use to graph f(x)? Justify that you can use the answers obtained in part B and part C to draw the graph.
9514 1404 393
Answer:
a. f(x) = (4x +5)(x -3)
b. x-intercepts: {-1.25, +3}
c. f(x) goes to +infinity as x goes to ±infinity
d. plot the x-intercepts, the vertex, and a few other points; draw a smooth curve through them
Step-by-step explanation:
a. Here, you're looking for factors of (4)(-15) = -60 that have a sum of -7. Those factors will be -12 and +5, so we can factor the function as ...
f(x) = (4x -12)(4x +5)/4
f(x) = (x -3)(4x +5)
__
b. The x-intercepts are the values of x that make the factors zero:
x -3 = 0 ⇒ x = 3 . . . . (add 3)
4x +5 = 0 ⇒ x = -5/4 . . . . (add -5, divide by 4)
__
c. As with all even-degree polynomials with positive leading coefficients, the end behavior of f(x) matches that of |x|:
as x → ∞, f(x) → ∞
as x → -∞, f(x) → ∞
__
d. The vertex of the function will be located halfway between the x-intercepts, at x = (3-5/4)/2 = (7/4)/2 = 7/8. The value of f(x) there is ...
f(7/8) = (4(7/8) +5)(7/8 -3) = -289/16 = -18.0625
Since the leading coefficient is 4, the normal x^2 function behavior is stretched vertically by a factor of 4. So, additional points would be
x = 7/8 ±1, f(x) = -18.0625 +4·1 = -14.0625
x = 7/8 ±2, f(x) = -18.0625 +4·2^2 = -2.0625
The answers of part B locate two points on the graph, and help find the vertex. The answer of part C confirms the graph as opening upward.
__
Additional comment
I find a graphing calculator to be very helpful finding the roots and making the graph.
A bag contains balls of five different colors. Two are red, three are blue, ten are white, four are green and three are black. Balls are taken from the bag without looking, and not returned. What is the smallest number of balls that should be taken from the bag to be sure that two balls of the same color have been taken? please explain with the answer
Answer:
6
Step-by-step explanation:
The worst scenario is that of a slight possibility, the first 5 balls you took are completely different color. The chance of this happening is tiny, but if you want to be sure, then you should consider about it.
But, after taking out the sixth ball, you can be sure that the ball, now right on your hand, must share a same color with at least one of the balls you took out, since there are only five colors.
Help me please i will give brainliest.
Answer:
1) 13 Students were surveyed
2) 3 students
3) 7 Students
4) 10 Books
Pls mark brainliest
Answer:
13 students were surveyed
3 students read 5 fiction books
7 students read more than 5 fiction books
The maximum number was 10
Step-by-step explanation:
Hope this helps
-Unbrand-
Sadly even though I answered first I didn't get any credit. Quite sickening.
please tell me answers
Answer:
×=50,×+09+673-23
×=(33)+(2×)
Can someone please help me!!!
Answer:
Option C
Step-by-step explanation:
same logic as in 2D problems. if C wasn't true, then the two planes couldn't be parallel
Its a quadratic equation I Dont know exactly how to solve it help please
Answer:
Step-by-step explanation:
(x - 2)(x + 4)
=x(x + 4) -2(x + 4)
=x^2 + 4x - 2x - 8
=x^2 + 2x - 8
(x + 1)(x + 6)
=x(x + 6) +1(x + 6)
=x^2 + 6x + x + 6
=x^2 + 7x + 6
(x - 4)(x + 2)
=x(x + 2) -4(x + 2)
=x^2 + 2x - 4x - 8
=x^2 - 2x - 8
(x + 5)(x - 3)
=x(x - 3) +5(x - 3)
=x^2 - 3x + 5x - 15
=x^2 + 2x - 15
(x - 6)(x - 2)
=x(x - 2) -6(x - 2)
=x^2 - 2x - 6x + 12
=x^2 - 8x + 12
(Please help!) What is the value of x?
B
(x + 5) ft 910
8 ft
more
91°
А
38°
P.
38°
13 ft
13 ft
R
X=
Answer:
x = 5.1
Step-by-step explanation.
Our first step is to find all the angles. If b = 91 degree and c is 38, a. has to be 51 because all triangles add up to 180 degree. Because we have both B and b, we can use sine law.
a/A 13/sin91 c/38
we can use b in this situation.
The legnth of a is 10.1.
So, x-5 would be 5.1
Square ABCD has an area of 1600. E is the midpoint of AC and F is the midpoint of AB.
What is the area of the trapezoid BCEF?
O 300 square units
O 1,200 square units
600 square units
O 109 square units
What is the solution to the inequality
|2n + 5| > 1?
Answer:
The solution to the inequality would be n < -3 or n > -2 . Isolate the variable be diving each side by the factors that don’t contain the variable.
Step-by-step explanation:
A ABC is isosceles. Find AC.
B
3x + 3
20 + 8
A
A
C
Ansfdfgh gggghjtyuhjrswzargfyf
Step-by-step explanation:
can you help me do this Q please :)
Answer:
i didnt get it
Step-by-step explanation:
can you explain
Which one of the following phrases best describes the line that passes through the
points (5, -7) and (a, -4), where a < 0?
o Rises from left to right
Falls from left to right
o Horizontal
o Vertical
The phrases best describes the line that passes through the points (5, -7) and (a, -4) is rise from left to right.
What are coordinates?Coordinates are two numbers (Cartesian coordinates), or sometimes a letter and a number, that locate a specific point on a grid, known as a coordinate plane. A coordinate plane has four quadrants and two axes: the x axis (horizontal) and y axis
As, we locate this coordinate in graph we can see the line will either rise from left to right or falls from right to left.
Hence, line that passes through the points (5, -7) and (a, -4) will rise from left to right.
Learn more about coordinates here:
https://brainly.com/question/12149933
#SPJ2
what is the measure of x
Answer:
56.25°
Step-by-step explanation:
cos x° = b/h = 15/27 = 5/9
x° = cos^(-1) (5/9) = 56.25°
the sum of 25 and x is 48 find x. . Solve.
Answer:
x = 23
Step-by-step explanation:
Sum of 25 and x = 48
25 + x = 48
Subtract 25 from both sides
25 - 25 cancels out
48 - 25 = 23
We would be left with x = 23
Answer:
[tex]x =23[/tex]
Step-by-step explanation:
Sum of 25 and x
[tex]25 + x[/tex]
Sum of 25 and x is 48
[tex]25 + x = 48[/tex]
Now lets simply Solve the equation
[tex]25 + x = 48 \\ x = 48 - 25 \\ x =23[/tex]
Hope this helps you.
Have a nice day!
Can someone help me with this question please
Answer:
the anwser is d
Step-by-step explanation:
Here we are given that C is between A and B.
So using the midpoint rule, sum of whole length AB will be addition of lengths AC and BC
Hope that helps
Answer:
AC Or CA
Step-by-step explanation:
So, this is what a b and c would look like on a number line:
A----C----B
However, we dont know exactly what these variables are. THey could be somerthing like this:
A------------------C-B
But this doesnt matter.
If we look at the first numberline, A and C make up the first half of the numberline.
C to B make up the later half.
AB is the total numberline.
SO tecnically, A to C+ C to B = AB
Or:
AC + CB = AB
This can also be seen in the second numberline.
A to C make up almost all of the numberline.
C to B make up a smll amount.
But in the end, AC + CB will still make AB.
Hope this helps you! :D
The number line diagram shows the distance between each number in a set of ata and the data's mean of 12. Which is the mean absolute deviation? 5 6 H HHH 6 7 8 9 10 11 12 13 14 15 16 17 18 mean
Answer:4
Step-by-step explanation:
The Mean Absolute Deviation is 4 from the data given
Some one please help me at this point I am so tireddd thankyou
Answer:
4b+8 is 12b I'm pre sure
dont know about the rest sorry
Please please help me
Answer:
22is the answer cuz it is
Answer:
Step-by-step explanation:
using pythagoras theorem
a^2 + b^2 = c^2
here 4 and 9 are the legs of the right angled triangle so let them be a and b respectively . third side is the hypotenuse because it is opposite to 90 degree so let it be c.
4^2 + 9^2 = c^2
16 + 81 = c^2
97 = c^2
[tex]\sqrt{97} = c[/tex]
help please i beg for help please
What is the standard form for the quadratic function?
f(x)=(x−3)2+5
f(x)=x2+14
f(x)=x2+6x−4
f(x)=x2−4
f(x)=x2−6x+14
Answer:
f(x)= x2 -4
Step-by-step explanation:
it is because it has no complex roots
7th grade math help me pleaseeee
Answer:
4x + 5y = 20
Step-by-step explanation:
4x + 5y = 20
5y = -4x + 20 (Subtract 4x to isolate 5y. Put the 4x in front of the 20)
y = [tex]-\frac{4}{5}x[/tex] + 4 (Divide all by 5 to isolate y)
And then it's done and in slope-intercept form
[tex]-1< -\frac{4}{5} < 0[/tex] or [tex]-\frac{4}{5}[/tex] is greater than -1 but less than 0
I hope this helped :)
How do I solve for this?
Answer:
don't
Step-by-step explanation:
i don't know
HELP!!
BONUS!!!
PLS ANSWER A B C OR D
Answer:
About 1 1/2 :)
Step-by-step explanation:
The answer is 1.46 which is close to 1.5
If line a has a slope of -3 and is perpendicular to line b, what would is the slope of line b?
Answer:
Slope of line B: 1/3
Step-by-step explanation:
To find a slope perpendicular to another slope, you take its negative reciprocal.
Therefore, line B will have a slope of 1/3 because -3 -> -1/3 -> 1/3
Latoya has b decks of cards . Each deck has 52 cards in it , what is the expression for the total numbers of cards latoya has
Answer:
52b
Step-by-step explanation:
She has 52 cards per deck, and b decks.
This means she has 52b cards.
How this works:
For 1 deck, she has 52 cards, or 52×1 cards.
For 2 decks, she has 104 cards, or 52×1 cards.
For 5 decks, she has 260 cards, or 52×5 cards.
For 10 decks, she has 520 cards, or 52×10 cards.
Therefore, for b decks, she has 52×b, or 52b cards.
**This content involves writing algebraic expressions, which you may wish to revise. I'm always happy to help!
What is the quotient?
-4/5 divided by 2
Answer:
-0.4
fraction form: -4/10 or -2/5
A silo in the shape of a cylinder is partially filled with corn to feed cows. The corn fills 25% of the height of the silo. What is the approximate volume of the part of the silo that is filled with corn if the silo is 12 feet in diameter and 60 feet high?
- PLEASE HELP im in the middle of an exam
Answer:
1695.6 cubic feet
Step-by-step explanation:
Given that,
The corn fills 25% of the height of the silo.
The diameter of silo, d = 12 feet
Radius, r = 6 feet
Height, h = 60 feet
The volume of the part of the silo that is filled with corn is given by :
[tex]V=25\%\ of\ \pi r^2 h\\\\=\dfrac{25}{100}\times 3.14\times 6^2\times 60\\\\V= $$1695.6\ feet^3[/tex]
So, the required volume is equal to 1695.6 cubic feet.
