Answer:
the range is from 105 to 234
Step-by-step explanation:
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?
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].
need an answer showing work thax!
Answer:
Option (a) [tex]\sum_{k=1}^{\infty} \dfrac{3}{k(k+1)}[/tex]
Step-by-step explanation:
The given expression is :
[tex]\dfrac{3}{1{\cdot} 2}+\dfrac{3}{2{\cdot} 3}+\dfrac{3}{3{\cdot} 4}+\dfrac{3}{4{\cdot} 5}+....[/tex]
We need to rewrite the sum using sigma notation.
The numerator is 3 in all terms.
At denominator, in first term (1)(2), in second term (2)(3) and so on.
A general term for the denominator is k(k+1).
Sigma notation is :
[tex]\sum_{k=1}^{\infty} \dfrac{3}{k(k+1)}[/tex]
Hence, the correct option is (A).
A bakery needs to make 7 batches of muffins before opening in 4 hours. Each batch of muffins takes 2/3 hour to bake.
HELPP PLEASE FAST!! a store has televisions on sale for 20% off the original price. The original price of a television is 150 before the sale what will be the sale price of the television set
Method 1: A pure algebraic approach
The unknown in this problem is the percent of decrease. A percent of decrease is the percentage of the original price that was deducted from the original price to obtain the sale price. We could write a "word equation" for this process like this:
original price - (percent of decrease)(original price) = sale price
Since the percent of decrease is the unknown in this problem, we'll call the percent of decrease x%.
Here's what we know so far:
The original price was $200
The sale price was $170
The percent of increase was x%
Putting this information in our word equation gives us an algebraic equation:
200 - (x%)(200) = 170
What do we do with the percent sign in this equation? "Percent" means "out of 100", so x% means x out of 100, or . Now we have this:
200 - (200) = 170
Now we'll solve our equation:
200 - (200) = 170
200 - 2x = 170
-2x = -30
x = 15
So the percent of decrease is 15%
Method 2: A method involving pure arithmetic.
If we know the original price and the sale price, we can find the percent of decrease in two steps:
Find the amount of decrease
Divide the amount of decrease by the original amount
This will give us the percent of decrease (written as a decimal number). We can then write the decimal as an equivalent percent to find our final answer.
Let's use method 2 on the same problem:
Frank bought a new television set on sale. If the TV's original price was $200 and Frank paid $170 for the TV, what was the percent of decrease?
First, let's find the amount of decrease:
Amount of decrease = 200 - 170 = 30
So the price decreased by $30.
Next, we'll find the percent of decrease, and rewrite the decimal answer as a percent:
Percent of decrease = = = .15 = 15%
So the percent of decrease is 15%
Before we leave the problem, let's check our answer:
Original price = $200
Price reduced by 15% of original price = 200(.15) = $30
Sale price would then be = $200 - $30 = $170
Our answer checks. We're done! Me not know if correct.
what is the answer for this
Answer:
4
Step-by-step explanation:
Evaluate: 12/y+9d if y = 5 and d = 7
here's the answer.....I hope it would work
Answer:
3/17
Step-by-step explanation:
Substitute the given values for the variables.
[tex]\frac{12}{5+9(7)}[/tex]
Simplify
[tex]\frac{12}{5+63}[/tex]
[tex]\frac{12}{68}[/tex]
[tex]\frac{3}{17}[/tex]
which is bigger 1.7m or 0.9m
The explains why a x b = b x a and a + b = b + a.
Question 15 (1 point)
The surface area of a sphere varies directly with the square of its radius. A soap bubble with a
0.75 in. radius has a surface area of approximately 7.07 square inches. Find the value of k, and
then find the radius of a seventeenth-century cannonball that has a surface area of 113.1
square inches.
Answer:
The value of k is 12.57Radius of a seventeenth-century cannonball is 2.999 inches which can be rounded off to 3Step-by-step explanation:
Let s be the surface area and r be the radius
Then according to given statement
s∝r²
Removing the proportionality symbol introduces k, the constant of proportionality
[tex]s = kr^2[/tex]
Now
A soap bubble with a 0.75 in. radius has a surface area of approximately 7.07 square inches.
Putting in the equation
[tex]7.07 = k (0.75)^2\\7.07 = k * 0.5625\\k = \frac{7.07}{0.5625}\\k = 12.5688..\\k = 12.57[/tex]
The euqation beomes
[tex]s = 12.57r^2[/tex]
Putting s = 113.1 in the equation
[tex]113.1 = 12.57r^2\\r^2 = \frac{113.1}{12.57}\\r^2 = 8.99761...\\\sqrt{r^2} = \sqrt{8.9976..}\\r = 2.9996..[/tex]
Hence,
The value of k is 12.57Radius of a seventeenth-century cannonball is 2.999 inches which can be rounded off to 3What is the equation of the line that passes through the points (-1, 3) and (1, 11)? (5 points)
4x - y = 1
x - 4y = -13
4x - y = -7
4x + y = 1
Answer:
4
Step-by-step explanation:
I am pretty sure its that one
I will give brainliest
Find x and y, there is no given info, and the line that is 8 units long is not a midsegment, but it is parallel to the line that is ten units long
Answer:
x = 1.25
y = 1.75
Step-by-step explanation:
Since, the line that is 8 units long is parallel to the line that is ten units long.
Therefore, both the triangles are similar by AA postulate.
Corresponding sides of of the similar triangles are in proportion.
Therefore,
[tex] \frac{5}{x + 5} = \frac{7}{y + 7} = \frac{8}{10} \\ \\ \implies \frac{5}{x + 5} = \frac{8}{10} \\ \\ 5 \times 10 = 8(x + 5) \\ \\ 50 = 8x + 40 \\ \\ 50 - 40 = 8x \\ \\ 10 = 8x \\ \\ \frac{10}{8} = x \\ \\ x = 1.25 \\ \\ \\ \frac{7}{y + 7} = \frac{8}{10} \\ \\ 7 \times 10 = 8(y + 7) \\ \\ 70 = 8y + 56 \\ \\ 70 - 56 = 8y \\ \\ 14 = 8y \\ \\ \frac{14}{8} = y \\ \\ y = 1.75[/tex]
What is the difference between twice twenty-five and twice five and twenty?
Compute $\sqrt{25^2-7^2}$.
Answer:
24
Step-by-step explanation:
[tex]\sqrt{25^2-7^2}\\\\=\sqrt{(25-7)(25+7)}\\\\=\sqrt{18(32)}\\\\=\sqrt{9*2*2^5}\\\\=\sqrt{3^2\cdot 2^6}\\\\=\sqrt{(3\cdot2^3)^2}\\\\=3\cdot2^3\\\\=3\cdot8\\\\=24[/tex]
Answer:
24
Step-by-step explanation:
First we compute the number under the radical.
We have 25² = 625 and 7² = 49, so 25² - 7² = 625 - 49 = 576.
Thus, √25² - 7² = √576 = √24², which is 24.
If f(x)=6x-2, what is the value of f(4)?
Please explain I don’t understand these questions.
Answer:
I think it might be 16 or 24.
Step-by-step explanation:
Pardon if I'm wrong.
Please help and explain how you got the answer. Im giving out brainliest. || Q4
Answer: 32
Step-by-step explanation:
Answer:
32
Step-by-step explanation:
Inside the parentheses, we see 5+3, which equals 8. Now, do 8x4, which equals 32!
true or false all states have a sale tax
Answer:
False
Step-by-step explanation:
As of 2017, 5 states (Alaska, Delaware, Montana, New Hampshire and Oregon) do not levy a statewide sales tax. California has the highest base sales tax rate, 7.25%. Including county and city sales taxes, the highest total sales tax is in Arab, Alabama, 13.50%.
Please, I give 20 score. Find the volume
Answer:
2388.16 in³
Step-by-step explanation:
1) find volume of cylinder
formula: πr²h
given:
π = 3.14
r = 8/2 = 4 in
h = 9 in
[tex]\pi \: r {}^{2} h[/tex]
[tex](3.14) \times (4 {}^{2} ) \times 9[/tex]
[tex]3.14 \times 16 \times 9[/tex]
[tex]452.16 \: {in}^{3} [/tex]
2) find volume of cuboid
formula: length × width × height
given:
length = 16 in
width = 11 in
height = 11 in
[tex]l \: \times w \: \times h[/tex]
[tex]16 \times 11 \times 11[/tex]
[tex]1936 \: in {}^{3} [/tex]
total volume of figure
= volume of cylinder + volume of cuboid
= 452.16 in³ + 1936 in³
= 2388.16 in³
Which of the following represents an inequality statement with a solution of
Please help out I’ll give you brainliest
Answer:
the second to last one
Step-by-step explanation:
Sorry if it is incorrect!
An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 5.6 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 160 engines and the mean pressure was 5.7 pounds/square inch. Assume the variance is known to be 0.25. A level of significance of 0.01 will be used. Make a decision to reject or fail to reject the null hypothesis.
Answer:
The decision rule is
Reject the null hypothesis
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 5.6 \ pounds/inch^2[/tex]
The sample size is n = 160
The sample mean is [tex]\= x = 5.7 \ pounds/ inch^2[/tex]
The variance is [tex]\sigma ^2 = 0.25[/tex]
The level of significance is [tex]\alpha = 0.01[/tex]
The null hypothesis is [tex]H_o : \mu = 5.6[/tex]
The alternative hypothesis is [tex]H_a : \mu > 5.6[/tex]
Generally the standard deviation is mathematically represented as
[tex]\sigma = \sqrt{\sigma ^2 }[/tex]
=> [tex]\sigma = \sqrt{0.25 }[/tex]
=> [tex]\sigma = 0.5[/tex]
Generally the test statistics is mathematically represented as
[tex]z = \frac{\= x - \mu }{ \frac{\sigma}{\sqrt{n} } }[/tex]
=> [tex]z = \frac{5.7 - 5.6 }{ \frac{0.5 }{\sqrt{ 160 } } }[/tex]
=> [tex]z = 2.53[/tex]
From the z table the area under the normal curve to the left corresponding to 2.53 is
[tex]p-value = P(Z > 2.53 ) =0.0057[/tex]
From the value obtained we see that the [tex]p-value < \alpha[/tex] hence
The decision rule is
Reject the null hypothesis
The conclusion is
There is sufficient evidence to conclude that the believe that the valve performs above the specifications is true
9 multiplied by 21 equals what
Answer:
189
Step-by-step explanation:
Also can you make me brainliest please
Which expressions are equivalent to 4• (7 • y)?
Drag and drop the equivalent expressions into the box.
(7• y)• 4
4 • 7 + 4 • Y
(4 7 • y
28 y
4•7•4• y
PLEASE HELP ASAP!!!
50 POINTS AND BRAINLY!!
Answer:
Step-by-step explanation:
4• (7 • y) is equivalent to all of the following:
28 • y
4 · 7y or (4 · 7) · y
(7 · 4) · y
Note that 4 • 7 + 4 • Y is absolutely wrong, since the original expression has no " + " sign
how do you spell 20k?
twenty thousandddd
20k
Answer:
twenty thousand
Step-by-step explanation:
Because you just have to spell it out spell twenty and then thousand.
Find the slope and the y-intercept of the line.
5x - 4y= -16
Write your answers in simplest form.
Step-by-step explanation:
Use the slope-intercept form
y=mx+b
to find the slope m and y-intercept b
Slope: 5/4
y-intercept: (0,-4)
2x^2-20x+100 quadratic formula
Answer:10
Step-by-step explanation:
5/6 - (-2/3)
Steps please
Answer:
9/6
Steps:
5/6 - (-2 x 2)
____. = 9/6
3 x 2
Based on the graph, what does the point (0, 0) represent
Answer:
you didn't post the graph but (0,0) is the origin
Answer:
ok
Step-by-step explanation:
X = 3/4. Y = -1/2.
What is x + y?
Can you please help me with the question.
Answer:
Step-by-step explanation:
A. 40:80
B: 80/40
C; 40: 120
D: 80:120 ;)
WHAT IS THE ANSWER PLZ HELP ME??? I WILL MARK BRAINLIEST!!!
Answer:
- 5/6
Step-by-step explanation:
turn it into an improper fraction.
1 and 2/3 = 5/3
2 and 1/2 = 5/2
5/3 - 5/2 = 10/6 - 15/6
= -5/6
Answer:
First you have to change both of the mixed numbers to improper fractions. To do this you would multiply the denominator and the whole number then add the numerator.
1 2/3 = 5/3
-2 1/2 = -5/2
Find the least common denominator (LCM). Add the numerator, and keep the denominator the same.
The LCM for these two fractions would be 6 so to get to six you would multiply 5/3 by 2/2 and -5/2 by 3/3.
5/3 = 10/6
-5/2 = -15/6
Add the numerators (10 + -15 = -5), and keep the denominator the same (6). Therefore, the answer would be -5/6.
An auto-parts store offers a fuel additive that claims to increase a vehicle’s gas mileage. The additive is poured into a vehicle’s gasoline tank after the tank is filled. To measure the claim, 30 taxi drivers receive a bottle of the additive to use the next time they fill their gas tank. The drivers then compare their gas mileage with the additive to their gas mileage before the additive was used.
What is the response variable in this scenario?
the age of the car
the 30 cars used in the study
the use of the additive
the gas mileage after the additive is used
Answer:
The answer is D. the gas mileage after the additive is used
Step-by-step explanation:
I got 100% on edg!
Answer:
d
Step-by-step explanation:
edge2o2o