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An average scanned image occupies 0.5 megabytes of memory with a standard deviation of 0.2 megabytes. If you plan to publish 80 images on your web site, what is the probability that their total size is between 49 megabytes and 53 megabytes?
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Answer:
Approximately [tex]0.012[/tex] (that's approximately [tex]1.2\%[/tex].)
Step-by-step explanation:
The question did not specify the exact distribution of the size of those images. However, the sample size [tex]n = 80[/tex] is a rather large number. Assume that:
the sizes of these [tex]80[/tex] images follow the same distribution, with mean [tex]\mu = 0.5[/tex] megabytes and standard deviation [tex]\sigma = 0.2[/tex] megabytes.the size of each image is independent of one another.If both assumptions are met, the central limit theorem would apply. This theorem would suggest that the sum of the sizes of these [tex]80[/tex] image (a random variable) will approximately follow a normal distribution. The mean of that sum would be approximately [tex]n\cdot \mu= 80 \times 0.5[/tex]. The standard deviation of that sum would be approximately [tex]\sigma\, \sqrt{n} = 0.2\times \sqrt{80}[/tex].
Let [tex]\displaystyle \Sigma X[/tex] denote the sum of these eighty sizes.
Under these assumption, [tex]\displaystyle \Sigma X \stackrel{\text{app.}}{\sim} \mathrm{N}\left(n\, \mu,\, \sigma\,\sqrt{n}\right)[/tex].
That is: [tex]\displaystyle \Sigma X \stackrel{\text{app.}}{\sim} \mathrm{N}\left({80\times 0.5},\, \left(0.2\times \sqrt{80}\right)^2}\right)[/tex].
The question is asking for the probability [tex]P(49 \le \Sigma X \le 53)[/tex]. Therefore, calculate the [tex]z[/tex]-score that corresponding to [tex]\Sigma X = 49[/tex] and [tex]\Sigma X = 53[/tex]:
For [tex]\Sigma X = 49[/tex], the [tex]z[/tex]-score would be [tex]\displaystyle \frac{\sum X - n\, \mu}{\sigma \sqrt{n}} = \frac{49 - 80 \times 0.5}{0.2\times \sqrt{80}} = 2.25[/tex].For [tex]\Sigma X = 53[/tex], the [tex]z[/tex]-score would be [tex]\displaystyle \frac{\sum X - n\, \mu}{\sigma \sqrt{n}} = \frac{53 - 80 \times 0.5}{0.2\times \sqrt{80}} = 3.25[/tex].Make use of a [tex]z[/tex]-table to find these two probabilities:
[tex]P(X \le 49) = P(Z < 2.25) \approx 0.98778[/tex].[tex]P(X \le 53) = P(Z < 3.25) \approx 0.99942[/tex].Calculate the probability that this question is asking for:
[tex]\begin{aligned}& P(49 \le \Sigma X \le 53) \\ &= P(\Sigma X < 53) - P(\Sigma X < 49) \\ & \approx 0.99942 - 0.98778 \approx 0.012 = 1.2\%\end{aligned}[/tex].
Macys is having a sale on all shoes, if I buy a pair of boots that are $125 but are now 30% off what is the sale price of the boots?
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Natalia wants to put a decorative edge around her flower bed. She already has 4 feet of edging, but she needs enough to edge 95 feet. The edging material comes in rolls 7 feet long.
Write and solve an inequality to find the number of rolls Natalia needs?
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Answer:
91 ft ≤ (7 ft)n or n ≤ 13
Step-by-step explanation:
total amount of edging is
e(n) ≤ 4 ft + (7 ft)n
This inequality relates the total length of edging to the number of 7 ft rolls needed.
If Natalia needs 95 ft of edging, we write e(n) ≤ 4 ft + (7 ft)n as
95 ft ≤ 4 ft + (7 ft)n
which simplifies to
91 ft ≤ (7 ft)n or n ≤ 13
Natalia must purchase 13 rolls. This, combined with the initial 4 ft of edging, will be just the right amount of edging to complete the job.
Write the linear equation in slope-intercept form, 3x − y = 7
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add y to both sides
3x = 7 + y
Subtract 7
3x - 7 = y
Solution: y = 3x - 7
Evaluate the following expression, when d=2 and z=6
6z + 3(-7d-5)
Answers
Answer:
-21
Step-by-step explanation:
6(6) + 3(-7(2) -5 )
36 + 3( -14 -5)
36 + 3( -19)
= -21
g(x) = x^2 + 55
What is the minimum value of the given function?
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Answer:
Step-by-step explanation:
55.
The solution is, the function doesn't have a minimum value.
What is derivative?A derivative is described as either the rate of change of a function, or the slope of the tangent line at a particular point on a function.
here, we have,
given that,
the function is,
g(x) = x^2 + 55
now, we have to find the min. value of the function.
so, we have,
g(x) = x^2 + 55
the 1st order derivative is,
g'(x)= 2x
now, we have, critical point, at g'(x)= 0
i.e. at 2x = 0
or, x = 0
so, min. value is at x= 0 of g''(x),
i.e. g''(x) = 2
so, it doesn't have any minimum value.
Hence, The solution is, the function doesn't have a minimum value.
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During a snowstorm, the snow falls at a constant rate of 2 Inches per hour. Before the storm, there were 5 inches of snow on the ground from a previous storm. The total number of inches of snow, y. can be expressed in terms of the number of hours it snowed, ... Which equation represents this situation? y=2x+2 y=2x+5 y=5x+2 y=5x+5
Answers
Answer:
y = 2x + 5
Step-by-step explanation:
y is the amount of snow, and x is the hour. Every our, there is two inches, and the whole equation, you add on 5 because that was at the start
Answer:
y=2x+5
Step-by-step explanation:
This is because the snow falls at two inches PER HOUR. This is why it has an x afte. The +5 is the additional snow the ground had before it started snowing again.
Ellen bought 18 boxes of paper clips. Each box had 150 paper clips. How many paper clips did Ellen buy
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Answer:
Ellen bought 2700 paper clips.
Step-by-step explanation:
Total boxes=18
Paper Clips in 1 box=150
Total paper clips=18×150
=2700
Answer:
ellen bought 2700 paper clips
Step-by-step explanation:
total paper clips in a box = 150
total boxes = 18
multiplication = 150×18=2700
Help Pleasee, Thank You!
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Answer:
A. 354.20 + 50.60w ≥ 1,099.51
Step-by-step explanation:
$354.20 (her savings)
$50.60 (what she can save every week)
she need to get to a total of (at least) $1,099.51
354.20 (she already have) + 50.60 per week it need to be equal or more than 1,099.51
354.20 + 50.60w ≥ 1,099.51
Which number line shows Point A at −4, Point B at 2.5, Point C at −2 and 1 over 2, and point D, which is the opposite of point A?
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Answer:
the answer is D
Step-by-step explanation:
Answer:
Your answer would be D
Step-by-step explanation:
:)
-4x+5y-3-11x-y
Does -3 have a like term?
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Answer:
nope ❎ ❎ ❎ ❎ ❎ ❎ ❎ ❎
Write the equation of the line in fully simplified slope-intercept form.
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Step-by-step explanation:
For every 3 squares across, the line drops by 1 square.
Therefore the slope of the lina is -1/3.
The y-intercept of the line is -8 (when x = 0)
The equation of the line is y = -1/3 x - 8.
A baker orders 162 eggs. Each carton contains 18 eggs. Determine the number c of cartons.
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The speed limit on a highway is 80 miles per hour. How many miles per minute is this?
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Answer:
1.3333
Step-by-step explanation:
1.3333
Conversion Table
miles per hour to miles per minute
mph mi/min
80 1.3333
90 1.5
100 1.6667
The speed of this:
70 miles per hour
1 hour = 60 minutes
70/60 = 7/6
around 1 1/6 mile per minute
hope this helps
What is incorrect About this proof? What needs to be done to correct it?why ?
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True or false: sometimes, a quadratic expression cannot be factored.
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Answer:
true
Step-by-step explanation:
the question is below thanks
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Answer:
[tex]10.02[/tex] units
Step-by-step explanation:
[tex]FH = \frac{82}{360} \times 2 \pi r[/tex] (Multiplying the circumference of the circle by the arc's degree over the total degree of the circle will find the length of the arc [tex]FH[/tex])
[tex]FH = \frac{82}{360}\times 2 \pi (7)[/tex]
[tex]=\frac{82}{360}\times14\pi[/tex]
[tex]=\frac{287\pi}{90}[/tex]
[tex]=10.02[/tex] (to the nearest hundredth)
∴ The length of the arc [tex]FH[/tex] is 10.02 units to the nearest hundredth.
Hope this helps :)
if f = 3, g = -4 and h = -5
[3-h]+13
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write the equation for the line that is parallel to y=2/3x-5 and goes through the point (-12/2)
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Answer:
I put the equation into Point-Slope Form and got:
y - 2 = 2/3(x + (-12))
Distribute the 3 to the numbers on the left:
3y - 6 = 2(x - 12)
Multiply the Parenthesis by 2:
3y - 6 = 2x - 24
Add 6 to the right side:
3y = 2x - 18
Divide both sides by 3:
y = 2/3x - 6 is the answer :)
Do anybody know geometry?
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Answer:
D. 29
Step-by-step explanation:
180 - 151 = 29
A snail can crawl 2/5 of a meter in a minute.
How many minutes will it take the snail to crawl 6 meters?
Please give me an answer A S A P.
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6/0.4= 15
The snail crawls .4 meters per minute and .4*15=6
In the first 1/5 hour of a snowstorm 1/3 inches of snow fell in the snow continues at the same rate how much snow will fall in 4 1/5 hours
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Answer:
70 (I think)
Step-by-step explanation:
1/3 is 3.33 (threes go on forever) but thats only for 1/5 of an hour, so you multiply 3.33 by 5 and get 16.66 (pretty sure the sixes also go on forever) and thats one full hour, so you multiply 16.66 by 4.20 (4 1/5 but in decimal form) and you get 70
Sorry if my answer is incorrect or doesn't make sense because I'm not 100% sure if I'm correct
how do you Graph y = 1/5x+3.
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Answer: If you can see with this Image I created, the Y Intercept (3) is dotted on the line. You move one up, and move five units to the right. You keep on doing this until you can make a line (Which I did).
I hope this helps, and Happy Holidays! :)
Answer:
rise
----
run
Something like these
Step-by-step explanation:
find 3 on the vertical line if the graph
then from that point rise 1 time to should get you to 2 on the horizontal axis, run 5 times to get to 7, and keep doing that. opposing that rise over run but with negatives when going from the other side of the graph
Which statements describe the key features of the graph of ? Check all that apply.
The graph has a y-intercept at –2.
The graph has an x-intercept at –6.
The graph has a vertical asymptote at x = 3.
The graph has a vertical asymptote at x = –3.
The graph has a horizontal asymptote at y = 1.
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Answer:
The answer is A,B,D
Step-by-step explanation:
I got it right on EDGE
The required key features of the given [tex]y\ =\ \frac{\left[18-3x-x^{2}\right]}{x^{2}-9}[/tex] area as follows,
(A) The graph has a y-intercept at –2.
(B) The graph has an x-intercept at –6.
(D) The graph has a vertical asymptote at x = –3.
Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
Given function
[tex]y\ =\ \frac{\left[18-3x-x^{2}\right]}{x^{2}-9}[/tex]
Draw the graph of the above function,
From the graph, we can conclude the points that,
The Y-intercept of the function is y = -2, the X=intercept of the function is x = -6, and the vertical asymptote at x = –3.
Learn more about function here:
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14:56 in simplest form?
Answers
Answer:
4
Step-by-step explanation:
Hope this helps:)
Answer:
No
Step-by-step explanation:
Simplest form is
1:4
14/14 = 1
56/14 = 4
I need help with this question will mark brainliest
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Pls help pls help pls help
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Using only the values given in the table for the function, f(x)=x^3-3x-2,
what is the interval of x-values over which the function is decreasing ?
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The volume of a rectangular prism is represented by the function x
representing the width of the box.
Ox- 4
OX-1
Ox+1
Ox+4
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Answer:
x = 4
Step-by-step explanation:
Hope this helps! Consider Brainiest! <3
In how many ways can the letter of word number taken two at a time
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Answer:
So the number of ways of choosing two distinct letters at a time is (42)=6. We can then add the duplicate pairs which are O,O and N,N to give a total of 8 possible pairs.
Answer:
15
Step-by-step explanation:
There are 6 letters in the word number
This is 6 choose 2
This is a combination
The formula is 6! / ( 2! * (6-2)! )
6! / 2! 4!
(6*5*4*3*2*1) / ( 2*1 * 4*3*2*1)
Canceling like factors
(6*5) / ( 2*1)
30/2
15
There are 15 possible ways to have 6 choose 2