Answer:
Since both [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], the necessary conditions are satisfied.
0.9945 = 99.45% probability that at most 85 out of 136 DVDs will work correctly.
Step-by-step explanation:
Test if the normal curve can be used as an approximation to the binomial probability by verifying the necessary conditions.
It is needed that:
[tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex]
Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
Assume the probability that a given DVD will work correctly is 52%.
This means that [tex]p = 0.52[/tex]
136 DVDs
This means that [tex]n = 136[/tex]
Test the conditions:
[tex]np = 136*0.52 = 70.72 \geq 10[/tex]
[tex]n(1-p) = 136*0.48 = 65.28 \geq 10[/tex]
Since both [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], the necessary conditions are satisfied.
Mean and standard deviation:
[tex]\mu = E(X) = np = 136*0.52 = 70.72[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{136*0.52*0.48} = 5.83[/tex]
Consider the probability that at most 85 out of 136 DVDs will work correctly.
Using continuity correction, this is [tex]P(X \leq 85 + 0.5) = P(X \leq 85.5)[/tex], which is the p-value of Z when X = 85.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{85.5 - 70.72}{5.83}[/tex]
[tex]Z = 2.54[/tex]
[tex]Z = 2.54[/tex] has a p-value of 0.9945.
0.9945 = 99.45% probability that at most 85 out of 136 DVDs will work correctly.
what is the equation of a line whose slope is -2 and whose y-intercept is 4?
Answer:
y=-2x+4
Step-by-step explanation:
if y is 4..it means x intercept is 0
gradient is -2
and we know gradient is the change in y /change in X
so: we let the second intercepts to be (x,y)
so y-4/x-0=-2
multiply by x-0 both sides then collect like terms together
it will be y= -2x+4
If 20 students have only airpods,
10 students only have beats, and 30
students have beats in total how
many students have both beats and
airpods?
Answer:
There should be 20 students that have both Beats and AirPods.
Step-by-step explanation:
There are 50 students in total.
20 students have only AirPods and 30 students have Beats. Out of the 30 who own Beats, there are 10 students that have ONLY Beats.
30 - 10 = 20.
It's a tricky question, but this is the correct answer!
Hope This Helps!
Evaluate.
10 3/4 plus 8 3/4 subtract 6 1/2
Answer:
13
Step-by-step explanation:
add 3/4 and 3/4 to get 6/4 then get 1/2 times the bottom and the top but 2 to get 2/4 so then do 6/4 - 2/4 to get 4/4 or 1
add 10,8 to get 18 then subtract 6 to get 12 then all the 1 and you get your answer. Hope this helped
Answer:
13
Step-by-step explanation:
Convert 10 3/4
to an improper fraction.
43/4 + 8 3/4 − 6 1/2
Convert 8 3/4
to an improper fraction.
43/4 + 35/4 − 6 1/2
Convert 6 1/2
to an improper fraction.
434 + 354 − 132
Combine fractions.
78/4 + −13/2
Simplify each term.
39/2 − 13/2
Combine fractions.
13
A room has a rectangular floor 5.5 m long and 4.5 m wide. The room is 2.5 m in height.
A. What is the area of wall space in the room?
B. How much paint is required to paint the
walls with two coats if one litre of paint
can cover 11.25 m??
Answer:
Length=8 m,Breadth=6 m,Height=3 m
We know,
LSA=2(l+b)×h
LSA=2×14×3=84 m
2
Therefore, cost of painting = 84×60=Rs.5040.
A machinist must cut 17 strips of metal that are each 2 ft 6 2/8 in long. What is the total length of metal needed in inches? Write as a proper or mixed fraction.
Answer:
Step-by-step explanation:
2/8 inch = ¼ inch
1 ft = 12 inch
17(2(12) + 6¼) = 514¼ inches
provided a shear with zero kerf is used.
How do I find the degree measure?
Answer:
The Degree Measure of the Angle = Radian x (180/)
an expression that is equivalent to 10x - 8 +0.5(2x - 3)?
-
Answer:
......................
As a restaurant, you and four friends divide the bill evenly. Each person pays $7.35. How much is the total bill?
Answer:
29.4
Step-by-step explanation:
Write an equation in point-slope form for the line that passes through the given points (1,-3),(4,-15)
Answer: b=7
Step-by-step explanation:
Over the summer, Paulo opens a dog-washing business and begins with $32. The table shows how much he earns and spends each week. He works for 8 weeks washing dogs. When he starts back at school, he budgets $60 to spend each week. How many weeks pass before he needs to wash more dogs?
Two mechanics worked on a car. The first mechanic worked for 20 hours, and the second mechanic worked for 5 hours. Together they charged a total of $2750.
What was the rate charged per hour by each mechanic if the sum of the two rates was $205 per hour?
-Whats the First mechanic: $ -----per hour
-Whats the Second mechanic: $ ---- per hour
Need help with question please!
Answer:
You got this just keep trying i know you can do it even if it is really hard
Step-by-step explanation:
A video game is on sale for 30% off the
regular price of $50. What is the sale
price of the video game
A.$20
B.$30
C.$33
D.$35
Answer:
d! 35 ......!!!!!!!!!!!!
solve the inequality 2x+2-6x<32
x>−15/2
15/2 is a fraction
A jet travels 1198 miles against the wind in 2 hours and 1438 miles with the wind in the same amount of time. What is the rate of the jet in still air and what is the rate of the jet wind?
Rate of the jet still in the air: x mi/h
Rate of the wind: x mi/h
Answer: tbh jets arent really a good way to travel man. you better start walking ur lazy butt and get movin.
Step-by-step explanation:
what is the sum of 2/3,1/2and1/4=
Answer:
17/12
Step-by-step explanation:
In order to add fractions, you have to have a common denominator. The denominators in these fractions are 3, 2, and 4 (the bottom numbers). To get a common denominator, figure out what number all three of them can go into. Their common factor would be 12 because all three numbers go into 12.
Multiply each numerator in the fraction (the top number) by how much it takes to get from our current denominators (3,2,4) to our final denominator (12).
For example, in 2/3 we know that 3 times 4 equals 12. Multiply the top number by 4 to get 8/12.
In 1/2 we know that 2 times 6 equals 12. Multiply by 6 to get 6/12.
In 1/4 we know that 4 times 3 equals 12. Multiply by 3 to get 3/12.
Add the fractions to get 17/12.
Y=3x-1 i need help now right now.
If 18 is subtracted from twice the square of an integer, the result is equal to nine times the integer. What is the value of the integer?
Answer:
6 or -1.5
Step-by-step explanation:
We can let this integer be x.
Therefore, according to the question we have:
[tex]2x^2-18=9x[/tex]
Subtracting 9x, we have a quadratic:
[tex]2x^2-9x-18=0[/tex]
Plugging into the quadratic equation:
[tex]\frac{9+\sqrt{81+144}}{4}, \frac{9-\sqrt{81+144}}{4},[/tex]
the square root of 81+144 is 15, so the answer is either 6 or -1.5
How many solutions does the system of equation have?
2x + 3y = 9 and y = 2/3x - 2
A.
One solution
B.
Two solutions
C.
Infinitely many solutions
D.
No solutions
Answer:
A. One solution
Step-by-step explanation:
y = 2/3x - 2 has slope of 2/3
2x + 3y = 9
3y = -2x + 9
y = (-2/3)x + 3 has slope of -2/3
lines with different slopes have only ONE intersection
PLEASE ANSWER ILL GIVE 5 STARS AND A HEART!!!
Answer:
120
Step-by-step explanation:
5x6 = 30
30x4= 120
If 90° < θ < 180° and cscθ = 3, then cotθ = _____.
[tex]\text{Given that,}\\\\\csc \theta = 3\\\\\implies \csc^2 \theta = 9\\\\\implies 1+ \cot^2 \theta = 9\\\\\implies \cot^2 \theta = 8\\\\\implies \cot \theta = \pm \sqrt 8 = \pm 2\sqrt 2\\\\\text{Since,}~90^{\circ}< \theta < 180^{\circ},\\\\\cot \theta = -2\sqrt 2[/tex]
1/3(6-9j)
PLEASE HELP!!!
Answer:
2-3j
Step-by-step explanation:
Distribute 1/3 to the rest of the equation and you'll get 2-3j
I hope this helps!
can retainers still fit w a small gap?
Answer:
Retainers have been designed to be used as an end of treatment to help retain your teeth in their new position. ... These are removable and fixed retainers. The reason why retainers can't be used to close a gap is because they are fitted at the end of treatment and are made to fit the straight teeth mould.
hope it help u
itz by Riddhi
Answer:
yes
Step-by-step explanation:
What are the first five terms of the arithmetic progression with the first term 8 and common difference 7 , then find the 17th?.
Step-by-step explanation:
a1 = 8
a2 = 8 + 7 = 15
a3 = 15 + 7 = 22
a4 = 22 + 7 = 29
a5 = 29 + 7 = 36
an = an-1 + 7 = a1 + 7×(n-1)
a17 = 8 + 7×16 = 8 + 112 = 120
The quotient of 2 numbers, p and q
Answer:
2p/q
2q/p
q/p=2
p/q =2
Step-by-step explanation:
Here are some possible answers. The way your statement is formated in does not ask a question nor does it provide enough information for one to deduce what the question was.
Derivative of tan^2 x
Answer:
[tex]2sec^2xtanx[/tex]
Step-by-step explanation:
[tex]\frac{d}{dx} tan^2x[/tex]
[tex]\frac{d}{dx} tanxtanx[/tex]
[tex](\frac{d}{dx}tanx)(tanx)+(tanx)(\frac{d}{dx}tanx)[/tex]
[tex]\frac{d}{dx}tanx=\frac{d}{dx}\frac{sinx}{cosx}=\frac{(cosx)(cosx)-(sinx)(-sinx)}{(cosx)^2}=\frac{cos^2x+sin^2x}{cos^2x}=\frac{1}{cos^2x}=sec^2x[/tex]
[tex](sec^2x)(tanx)+(tanx)(sec^2x)[/tex]
[tex]2sec^2xtanx[/tex]
Helpful tips:
Product Rule: [tex]\frac{d}{dx}f(x)g(x)=f'(x)g(x)+f(x)g'(x)=\frac{d}{dx}f(x)*g(x)+f(x)*\frac{d}{dx}g(x)[/tex]
Quotient Rule: [tex]\frac{d}{dx}\frac{f(x)}{g(x)}=\frac{g(x)f'(x)-f(x)g'(x)}{(g(x))^2}=\frac{g(x)\frac{d}{dx}f(x)-f(x)\frac{d}{dx}g(x)}{(g(x))^2}[/tex]
Pythagorean Identity: [tex]cos^2x+sin^2x=1[/tex]
How many days are in 52 weeks?
Answer:
A year but -1.
Step-by-step explanation:
52x7=364.
Hope this helps!
Answer:
there are 364 days in 52 weeks.
Step-by-step explanation:
To find out how many days are in 52 weeks you have to multiply the amount of days there are in a week by 52, there are 7 days in a week and 7 times 52 is 364 so the answer is 364
please help! ASAP I need help fast!!
Answer: 4.8
Explanation: divide total needed of blue paint (3) by 1/2 to find the ratio, which is 6. then multiply that by 4/5 to get the total of yellow paint, which is 4.8
Estimate. Then divide. check for reasonableness 25,600 divided by 25.
Answer:
Step-by-step explanation:
Jason stands in the corner of a very large field. He walks, on a bearing of 030°,
a distance of d metres. Jason then changes direction and walks twice as far on a new
bearing of 120°. At the end of the walk Jason calculates both the distance he must
walk and the bearing required to return to his original position. Given that the total
distance walked is 120 metres, what answers will Jason get if he is correct?
Answer:
Step-by-step explanation:
d + 2d = 120
3d = 120
d = 40 m
east distance was 40cos30 + 80cos120 = -5.35898 m
north distance was 40sin30 + 80sin120 = 89.282032
as 30° and 120° bearings are 90° apart, Jason needs to walk
D = √(d² + (2d)²) = d√5 or 40√5 meters or about 89.44 m to return to his original position.
we could also use √(-5.35898² + 89.282032²) = 89.44 m
direction will be
θ = arctan -89.28/5.359 = -86.565° or a bearing of 273.4°
