Using the normal approximation to the binomial, the probabilities are given by:
a) 0.8485 = 84.85%.
b) 0.0244 = 2.44%.
Normal Probability DistributionIn a normal distribution 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]
It 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, which is the percentile of X.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].In this problem, we have that:
There are 600 bulbs, hence n = 600.5% are defective, hence p = 0.05.The mean and the standard deviation of the approximation are given, respectively, by:
[tex]\mu = np = 600(0.05) = 30[/tex]
[tex]\sigma = \sqrt{np(1-p)} = \sqrt{600(0.05)(0.95)} = 5.3385[/tex]
Item a:
Using continuity correction, the probability is P(X > 24.5), which is one subtracted by the p-value of Z when X = 24.5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{24.5 - 30}{5.3385}[/tex]
[tex]Z = -1.03[/tex]
[tex]Z = -1.03[/tex] has a p-value of 0.1515.
1 - 0.1515 = 0.8485.
0.8485 = 84.85% probability.
Item b:
This probability is P(X < 19.5), which is the p-value of Z when X = 19.5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{19.5 - 30}{5.3385}[/tex]
[tex]Z = -1.97[/tex]
[tex]Z = -1.97[/tex] has a p-value of 0.0244.
The probability is of 0.0244 = 2.44%.
More can be learned about the normal distribution at https://brainly.com/question/24663213
A poster is 2 feet wide and 4 feet tall what is the perimeter
Answer:
12
Step-by-step explanation:
P = is you add Length (L) plus Legnth (L) plus Width (W) plus Width (W)
4+4+2+2
)Mrs. Smith bought 6 rolls of foil to use at a bake sale. She used 223 feet of foil and had 77 feet left over. How many feet are on each roll?
Step-by-step explanation:
First you add the number of used and unused feets of foil
223 + 77 = 300
After that you divide the feets of rolls by the total number of foils
that is, 300 / 6 = 50
therefore there are 50 feets in each foil
if this helped pls give brainliest
solve and check the equation 3(5-2x)=2(4x=3)
They got 9/14 as the solution set but I do not know how?
Thank you so much.
Answer:
3(5-2x) = 2(4x=3)
= 15-6x = 8x=6
= 15-6x = 8x-6
= 15-6 = 8x+6x
= 9 = 14x
therefore, x=9/14
Step-by-step explanation:
hope it helps you
Finding congruent angles
1)
First 2 triangles can be proven similar but are not necessarily congruent since you can't from them using the side-angle-side or angle-side-angle or triple side rule.
2)
ONM = QNP since they are vertically opposite angles.
MON = NPQ given equal on the figure
ON=NP given
The two triangles are proven congruent using the angle-side-angle property.
3)
Last 2 pairs cannot be proven congruent as there is not enough info.
. Ferric chloride is used as a flux in some types of extraction metallurgy processes. This material is shipped in containers, and the container weight varies. It is important to obtain an accurate estimate of mean container weight. Suppose that from long experience a reliable value for the standard deviation of flux container weight is determined to be 4 lb. How large a sample would be required to construct a 95% two-sided confidence interval on the mean that has a total width of 1 lb1 lb? (Montgomery, 08/2019, p. E-10) Montgomery, D. C. (2019). Introduction to Statistical Quality Control, Enhanced eText, 8th Edition. [[VitalSource Bookshelf version]]. Retrieved from vbk://9781119399308 Always check citation for accuracy before use.
Answer:
The sample size is [tex]n = 246[/tex]
Step-by-step explanation:
From the question we are told that
The standard deviation is [tex]\sigma = 4\ lb[/tex]
The confidence level is C = 95%
The total width is [tex]w = 1 \ lb[/tex]
Given that the confidence level is 95% then the level of significance is mathematically represented as
[tex]\alpha = (100 -95 )\%[/tex]
=> [tex]\alpha = 0.05[/tex]
From the normal distribution table the critical value for [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the sample size is mathematically represented as
[tex]n = [\frac{Z_{\frac{\alpha }{2}} * \sigma }{E}]^2 [/tex]
Here E is the margin of error which is mathematically represented as
[tex]E = \frac{w}{2}[/tex]
=> [tex]E = \frac{1}{2}[/tex]
=> [tex]E = 0.5 [/tex]
So
[tex]n = [\frac{1.96 * 4 }{0.5}]^2 [/tex]
[tex]n = 246[/tex]
Determine if the two triangular pyramids are similar.
Match up the corresponding parts.
Answer:
no they are not similar
Step-by-step explanation:
8/12 does not reduce to the same amount that 6/8 and 12,16
what is the opposite number of -7
Answer:
+7 will be the opposite or reciprocal of -7
Step-by-step explanation:
Hope it Helps!!!!
The opposite of the number, -7, is its reciprocal, which is: 7.
What is the Opposite of a Number?The opposite of a number is its reciprocal or the value on the number line that would occupy the same distance from zero in the opposite direction.
For example, opposite of b is -b.
The reciprocal of -7 is 7. Therefore, the opposite of the number, -7 is: 7.
Learn more about opposite of a number on:
https://brainly.com/question/2206063
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Which of the following is the prime factorization of 42? Choose the correct answer.
Answer:
2x3x7
Step-by-step explanation:
Because that's what you have to multiply giving you 42
Answer:
7×2×3
Step-by-step explanation:
If 7 books cost Rs. 300 more
than 5 books, find the cost of a
book.
Answer:
150
Step-by-step explanation:
If 7-5=2 books cost 300 and you want to find the cost of 1 book, you would need to divide that 300 by 2.
300÷2=150
Answer:
Step-by-step explanation:
If sin theta = -½ and theta lies in Quadrant IV , find the value of all the other five trigonometric functions.
Given that,
θ € 4th quadrant
3π/2 < θ < 2π
Andsin θ = - 1/2
We know,sin²θ + cos²θ = 1
[ -1/2] ² + cos²θ = 1
1/4 + cos²θ = 1
cos²θ = 1 - 1/4
cos²θ = 4 - 1 / 4
cos²θ = 3/4
cos²θ = + √3/2As,
θ € 4th quadrant = cos θ > 0
cosθ = √3/2
tan θ = sin θ / cos θtan θ = 1/2 ÷ √3/2
tan θ = - 1/√3
Now,cosec θ = 1/sin θ = -2
sec θ = 1/cos θ = 2√3
cot θ = 1/tan θ = - √3what is the mean of the given data -7,-10,-6,-2,8,-2,12
Answer:
-1
Step-by-step explanation:
mean means the average. so, add together all the given data, which you will get -7, then divide by the amount of data given, which is 7, and you will get -1
A hand rail is installed along the stairs OT
house as shown in the figure. The table shows the
distance, in inches, of the top rail f(x) and bottom
rail g(x) from the floor for the middle of each
numbered stęp x. Determine the slope of each rail.
Are the top and bottom rails parallel?
x f(x) g(x)
1 9 43
2
16
50
3
3
23
57
Answer:
Slope of top rail f(x) is 7
Slope of top rail g(x) is 7
Top and bottom rails are parallel.
Step-by-step explanation:
The table shows the distance, in inches, of the top rail f(x) and bottom rail g(x) from the floor for the middle of each numbered stęp x.
x f(x) g(x)
1 9 43
2 16 50
3 23 57
To find the slope of top rail :
x f(x)
1 9
2 16
3 23
[tex](x_1,y_1)=(1,9)\\(x_2,y_2)=(2,16)\\Slope = m = \frac{y_2-y_1}{x_2-x_1}=\frac{16-9}{2-1}=7[/tex]
Slope of top rail f(x) is 7
To Find the slope of bottom rail:
x g(x)
1 43
2 50
3 57
[tex](x_1,y_1)=(1,43)\\(x_2,y_2)=(2,50)\\Slope = m = \frac{y_2-y_1}{x_2-x_1}=\frac{50-43}{2-1}=7[/tex]
Slope of top rail g(x) is 7
We know that if the slopes of two lines are equal then are said to be parallel lines
Since the slopes of both the rail are equal . So, Top and bottom rails are parallel.
Cynthia’s broker charges her a commission of $88 for every $1000 of stock bought or sold. Cynthia bought 2,000 shares of Ombor Medical Supplies at $35.49 apiece. As the price rose and fell, she sold off part of her holdings. When the price rose to $48.57, she sold 600 shares. The price fell somewhat to $46.10, so she sold 1,150 of her shares. When the price climbed to $53.46, she sold off the remainder of her holdings. How much profit did Cynthia make in total?
a.
$9,889.82
b.
$24,542.00
c.
$16,312.06
d.
$74,799.58
Answer:
The answer I got was wrong, but I have a solution process, at least.
Step-by-step explanation:
600*48.57+1150*46.10+250*53.46-2000*35.49
=21942+53015+13365-70980
=17342
Now we need to subtract the commission that Cynthia is paying her broker. $88 per $1000 means Cynthia owes her broker 17*88=$1496. Now we subtract that from 17342 to get $15,846.
Answer:its A. $9,889.82
Step-by-step explanation:
Which of the following statements best describes P on the number line shown? P = -1.5 P > -1 P 0
P > -1
Step-by-step explanation: i have the exact same quiz
How many terms are there in the series 5 + 9 + 13 +.....+ 77 ?
Answer:
19 term
Step-by-step explanation:
you need to know the expression ... these three dots, first
not easy
(77-5)/4+1=19
Answer:
19 terms
Step-by-step explanation:
terms = 5,9,13,17,21,25,29,33,37,41,45,49,53,57,61,65,69,71,73,77
I hope it will be helpfulPlease solve with explanation
Answer:
k=0 or 4
Step-by-step explanation:
[tex]y=x^2+(k+4)x+3k+4\\=x^2+(k+4)x+(\frac{x+4}{2})^2 +3k+4-(\frac{x+4}{2})^2\\=(x+\frac{x+4}{2})^2+3k+4-(\frac{x+4}{2})^2\\[/tex]
so the vertex is at
[tex](-\frac{k + 4}{2}, 3k+4-(\frac{x+4}{2})^2)[/tex]
The vertex lies in the x-axis, so
[tex]3k+4-(\frac{k+4}{2})^2 = 0\\4(3k+4)-(k+4)^2=0\\12k+16-k^2-8k-16=0\\-k^2+4k=0\\-k(k-4)=0\\k-0, 4[/tex]
Bonita deposited $1300 into a bank account that earned 5.75% simple interest each year. She earned $299 in interest before closing the account.
No money was deposited into or withdrawn from the account.
How many years was the money in the account?
Round your answer to the nearest whole year.
Enter your answer in the box.
Answer:
Your answer is 4 Years!
Answer: 4 Years
Step-by-step explanation: Just to confirm the other person it is 4 years!
Carlos provides dog-walking services in his neighborhood. For each walk he charges a flat fee of $5 for clean-up and $6 per dog. Write an equation to represent the relationship between the total charge, c, and the number of dogs he walks, d.
6d + 5 = c
hope that helps :)
Solve this equation. Type your answer in the box below.
12x−7=13(x−12)
x=
Answer: 12*x-7-(13*(x-12)*x)=0
Step by Step Solution
More Icon
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
12*x-7-(13*(x-12)*x)=0
Step by step solution :
STEP
1
:
Equation at the end of step 1
(12x - 7) - (13 • (x - 12) • x) = 0
STEP
2
:
Equation at the end of step 2
(12x - 7) - 13x • (x - 12) = 0
STEP
3
:
STEP
4
:
Pulling out like terms
4.1 Pull out like factors :
-13x2 + 168x - 7 = -1 • (13x2 - 168x + 7)
Trying to factor by splitting the middle term
4.2 Factoring 13x2 - 168x + 7
The first term is, 13x2 its coefficient is 13 .
The middle term is, -168x its coefficient is -168 .
The last term, "the constant", is +7
Step-1 : Multiply the coefficient of the first term by the constant 13 • 7 = 91
Step-2 : Find two factors of 91 whose sum equals the coefficient of the middle term, which is -168 .
-91 + -1 = -92
-13 + -7 = -20
-7 + -13 = -20
-1 + -91 = -92
1 + 91 = 92
7 + 13 = 20
13 + 7 = 20
91 + 1 = 92
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Equation at the end of step
4
:
-13x2 + 168x - 7 = 0
STEP
5
:
Parabola, Finding the Vertex:
5.1 Find the Vertex of y = -13x2+168x-7
Parabolas have a highest or a lowest point called the Vertex . Our parabola opens down and accordingly has a highest point (AKA absolute maximum) . We know this even before plotting "y" because the coefficient of the first term, -13 , is negative (smaller than zero).
Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.
Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.
For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 6.4615
Plugging into the parabola formula 6.4615 for x we can calculate the y -coordinate :
y = -13.0 * 6.46 * 6.46 + 168.0 * 6.46 - 7.0
or y = 535.769
For Exercises 6-9, find the coordinates of each point
described in relation to line segment CD.
6. of the way from C to D
7. of the way from D to C
8. of the way from C to D
9. of the way from D to C
10. What is the distance formula?
Answer:
we need the coordinates really. I can tell you that for any 2 coordinates the distance between them can be found using the Distance formula D=sq. rt (x1-x2)^2 + (y1-y2)^2
The lunch special at Scott's Restaurant is a sandwich, a drink and a dessert. There are 3 sandwiches, 1 drink, and 2 desserts to choose from. How many lunch specials are possible?
Answer:
24 for being able to not have one, 6 for having one of each
Step-by-step explanation:
multiplication
with the option of none
4*2*3=24
without the option of none
3*1*2=6
Suppose 59% of the students in a university are baseball players. If a sample of 632 students is selected, what is the probability that the sample proportion of baseball players will be greater than 63%
Using the normal probability distribution and the central limit theorem, it is found that there is a 0.0207 = 2.07% probability that the sample proportion of baseball players will be greater than 63%.
Normal Probability DistributionIn a normal distribution 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]
It 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, which is the percentile of X.By the Central Limit Theorem, for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].In this problem, we have that:
59% of the students in a university are baseball players, hence p = 0.59.A sample of 632 students is selected, hence n = 632.The mean and the standard error are given by:
[tex]\mu = p = 0.59[/tex]
[tex]s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.59(0.41)}{632}} = 0.0196[/tex]
The probability that the sample proportion of baseball players will be greater than 63% is one subtracted by the p-value of Z when X = 0.63, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.63 - 0.59}{0.0196}[/tex]
[tex]Z = 2.04[/tex]
[tex]Z = 2.04[/tex] has a p-value of 0.9793.
1 - 0.9793 = 0.0207.
0.0207 = 2.07% probability that the sample proportion of baseball players will be greater than 63%.
To learn more about the normal probability distribution and the central limit theorem, you can check https://brainly.com/question/24663213
7 - (- __ ) = 12
what is the missing number
Answer:
7 - - 5 = 12
Step-by-step explanation:
Answer:
7+5=12
Step-by-step explanation:
even numbers of negatives alwasy equal positive
anyone helpp me.....
25 pnts.
Domain is the x-intercept(first number) for example if I were told to find the domain in (1,3)(4,7)(8,9) the domain would be 1,4, and 8 because they're the x-factors and then plotting a point, the x-factors come first.
Range is the y-factors(second number) and given an example above, the ranges would be 3,7, and 9 because when plotting, they are the second number.
You can tell if it is a function or not if the X-factors repeat. For example, the first one is NOT a function because the 2 repeats for the x-factor. Number 2 IS a function because the x-factor doesn't repeat.
Sorry if this doesn't make sense, that's the best way I can explain!
Someone plz help me out
write the expressions using exponents b*b*b
Answer:
[tex]b^{3}[/tex]
Step-by-step explanation:
b × b × b = [tex]b^{3}[/tex]I hope this helps!
What is the measure of 21? 100° 90° 80° 85° 95%
Answer:
A quadrilateral's interior angles have a sum of 360°.
Given that we have 85°, 100°, and 90°(the right angle), and an unknown angle.
We can add these angles plus the unknown angle to equal a total of 360°.
85 + 100 + 90 + x(our unknown missing angle) = 360
simplify
275 + x = 360
Isolate x by subtract 275 from both sides;
-275 -275
x = 85, ∠1 = 85°
We can also double check:-
85 + 100 + 90 + 85 = 360
360 = 360 which is correct.
Which Choice is equivalent to the product below when x is greater than or equal to zero
PLEASE HURRY 100 POINTS!
Marques made a mistake when solving this problem. On what line did he make the error?
A) Line 1
B) Line 2
C) Line 3
D) Line 4
E) Line 5
Answer:
B) Line 2
using the formula:
[tex]\sf c^2 = a^2 + b^2 -2abcos(C)[/tex]
[tex]\sf c^2 = 14^2 + 8^2 -2(14)(8)cos(80)[/tex]
[tex]\sf c^2 = 196 + 64 -244 *0.173[/tex]
[tex]\sf c^2 = 221.1[/tex]
[tex]\sf \sqrt{c} = \sqrt{221.1}[/tex]
[tex]\sf c = 14.87[/tex]
Use law of cosines
c²=a²+b²-2abcosCc²=14²+8²-2(14)(8)cos80c²=196+64-244(0.173)c²=221.1c=14.87Error at line 2
If
[tex] \frac{1}{x} + \frac{1}{y} + \frac{1}{z} = 0[/tex]
and
[tex] {x}^{2} + {y}^{2} + {z}^{2} = 25[/tex]
, then x + y + z will be? Z
Answer:
5
Step-by-step explanation:
We would like to find out the value of [tex] x + y + z [/tex] from the given equations , which are ;
[tex]\longrightarrow \dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z}=0[/tex]
[tex]\longrightarrow \\ x^2+y^2+z^2=25[/tex]
Now consider ,
[tex]\longrightarrow \dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z}=0\\[/tex]
[tex]\longrightarrow \dfrac{xy + yz + zx }{xyz }=0\\[/tex]
[tex]\longrightarrow xy + yz + zx = 0(xyz)\\ [/tex]
[tex]\longrightarrow xy + yz + zx = 0\\ [/tex]
[tex]\longrightarrow 2(xy + yz + zx)=0(2)\\[/tex]
[tex]\longrightarrow 2(xy + yz + zx)=0[/tex]
Now recall the identity ,
[tex]\longrightarrow (a + b + c)^2=a^2+b^2+c^2+2(ab + bc + ca)[/tex]
Plug in the values ,
[tex]\longrightarrow (x+y+z)^2= 25 + 0\\ [/tex]
[tex]\longrightarrow (x + y + z )^2=25\\[/tex]
[tex]\longrightarrow (x + y + z)=\sqrt{25}\\[/tex]
[tex]\longrightarrow \underline{\underline{\boldsymbol{ x + y + z = 5}}}{} [/tex]
And we are done !
Answer :
5⠀
Step-by-step explanation:
Given,
⠀
[tex]{ \longrightarrow \qquad{ { \sf{ \dfrac{1}{x} + \dfrac{1}{y} + \dfrac{1}{z} = 0}}}}[/tex]
⠀
[tex]{ \longrightarrow \qquad{ { \sf{ {x}^{2} + {y}^{2} + {z}^{2} = 25 }}}}[/tex]
⠀
To Find :
[tex]{ \longrightarrow \qquad{ { \sf{ x + y + z }}}}[/tex]
⠀
Solution :
[tex]{ \longrightarrow \qquad{ { \sf{ \dfrac{1}{x} + \dfrac{1}{y} + \dfrac{1}{z} = 0}}}}[/tex]
⠀
[tex]{ \longrightarrow \qquad{ { \sf{ \dfrac{yz + zx + xy}{xyz} = 0}}}}[/tex]
⠀
[tex]{ \longrightarrow \qquad{ { \sf{ {yz + zx + xy} = 0}}}}[/tex]
⠀
Multiplying both sides by 2 :
⠀
[tex]{ \longrightarrow \qquad{ { \sf{ 2( {yz + zx + xy} )= 0.2}}}}[/tex]
⠀
[tex]{ \longrightarrow \qquad{ { \sf{ 2( {yz + zx + xy} )= 0}}}}[/tex]
⠀
We know,
⠀
[tex]{ \longrightarrow \qquad{ { \sf{ {(x + y + z)}^{2} = {x}^{2} + {y}^{2} + {z}^{2} + 2(xy + yz + zx) }}}}[/tex]
⠀
As, It is given that,
⠀
[tex]{ \longrightarrow \qquad{ { \sf{ {x}^{2} + {y}^{2} + {z}^{2} = 25 }}}}[/tex]
⠀
and as we get,
⠀
[tex]{ \longrightarrow \qquad{ { \sf{ 2( {yz + zx + xy} )= 0}}}} \\ \\{ \longrightarrow \qquad{ { \sf{ 2( {xy + yz + zx} )= 0}}}}[/tex]
⠀
Now, We'll substitute it in the formula :
[tex]{ \longrightarrow \qquad{ { \sf{ {(x + y + z)}^{2} = 25 + 0 }}}}[/tex]
⠀
[tex]{ \longrightarrow \qquad{ { \sf{ {(x + y + z)}^{2} = {25} }}}}[/tex]
⠀
[tex]{ \longrightarrow \qquad{ { \sf{ {x + y + z}^{} = \sqrt{25} }}}}[/tex]
⠀
[tex]{ \longrightarrow \qquad{ { \bf{ \pmb {x + y + z}^{} = {5} }}}}[/tex]
⠀
Therefore,
The value of x + y + z is 5 .