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].
The life span of a domestic cat is normally distributed with a mean of 15.7 years and a standard deviation of 1.6 years. a. Find the probability that a cat will live to be older than 14 years. b. Find the probability that a cat will live between 14 and 18 years. c. If a cat lives to be over 18 years, would that be unusual? Why or why not? d. How old would a cat have to be to be older than 90% of other cats?
Answer
a. 0.856
b. 0.78071
c. It is not unusual
d. 13.65 years old
Step-by-step explanation:
The life span of a domestic cat is normally distributed with a mean of 15.7 years and a standard deviation of 1.6 years.
We solve this question using z score formula:
z = (x-μ)/σ, where
x is the raw score
μ is the population mean
σ is the population standard deviation.
a. Find the probability that a cat will live to be older than 14 years.
For x > 14 years
z = 14 - 15.7/1.6
z = -1.0625
Probability value from Z-Table:
P(x<14) = 0.144
P(x>14) = 1 - P(x<14) = 0.856
b. Find the probability that a cat will live between 14 and 18 years.
For x = 14 years
z = 14 - 15.7/1.6
z = -1.0625
Probability value from Z-Table:
P(x = 14) = 0.144
For x = 18 years
z = 18 - 15.7/1.6
z= 1.4375
Probability value from Z-Table:
P(x = 18) = 0.92471
The probability that a cat will live between 14 and 18 years is calculated as:
P(x = 18) - P(x = 14)
0.92471 - 0.144
= 0.78071
c. If a cat lives to be over 18 years, would that be unusual? Why or why not?
For x > 18 years
z = 18 - 15.7/1.6
z= 1.4375
Probability value from Z-Table:
P(x<18) = 0.92471
P(x>18) = 1 - P(x<18) = 0.075288
Converting this to percentage:
0.075288 × 100 = 7.5288%
Hence, 7.5288% of the cats live to be over 18 years. Hence, it is not unusual.
d. How old would a cat have to be to be older than 90% of other cats?
From the question above, 10% of the cats would be older than 90% of other cats.
Hence, we find the z score of the 10th percentile
= -1.282
Hence,
-1.282 = x - 15.7/1.6
Cross Multiply
-1.282 × 1.6 = x - 15.7
- 2.0512 = x - 15.7
x = 15.7 -2.0512
x = 13.6488 years old
Approximately = 13.65 years old
Write the following in standard form: eight and twelve thousandths.
Answer:
8.012
Step-by-step explanation:
standard : 8.012
written: eight and twelve thousandths.
4. -5x-15=-3x+23
29. -107-7x=73-13x
EXPLAIN STEPS AND SHOW WORK
THANKS BROTHA
`•••~Low_Millenial~•••`
°°°°°°Tutor and pal°°°°°°°
Answer:
x=-19 x=30
Step-by-step explanation:
-5x-15=-3x+23
-23 -23
-5x-38=-3x
+5x +5x
-38=2x
/2 /2
-19=x
-107-7x=73-13x
-73 -73
-180-7x=-13x
+7x +7x
-180=-6x
30=x
Which of the following statements about photocopier A1 is correct compared to the other photocopiers?
Answer:
Option 2
Step-by-step explanation:
Number of breakdowns of the photocopiers in year 2011,
A1 = 15
A2 = 21
B1 = 34
B2 = 32
B3 = 23
Option (1)
A1 had just under a half the number of breakdowns compared to photocopier B3.
Half of B3 = 12
And A1 = 15
Therefore, A1 > B3
So the statement is False.
Option (2)
A1 had just under 50% of the breakdowns compared to photocopier B2
50% of the breakdowns of B2 = 16
A1 = 15
So, A1 < 50% of B2
Statement (2) is True.
Option (3)
A1 had more than 25 extra breakdowns compared to B1.
A1= 15
B1 = 34
A1 < B1
Therefore, statement is False.
Option (4)
A1 had 6% less breakdowns than photocopier A2.
A1 = 15
A2 = 21
A2 - A1 = 21 - 15 = 6
Percentage less breakdowns = [tex]\frac{6}{21}\times 100[/tex] = 28.6%
So this Option is False.
Therefore, Option (2) is the correct option.
Factorise 3x to the power of 2 + xy
Answer:
x • (3x + y)
Step-by-step explanation:
Answer:
Step-by-step explanation:
3x to the power of to +xy= x (3x+y)
please help!Thank you so much
Answer:
An equation is a math sentence that DOES contain an equals sign (=).
The inverse of addition is subtraction.
The inverse of subtraction is addition.
The inverse of multiplication is division.
The inverse of division is multiplication.
Step-by-step explanation:
I'm sorry if I got the first one incorrect.
4. Write as a fraction in simplest form: 38 minutes to 12 minutes
Answer:
3 ⅙
Step-by-step explanation:
38 and 12’s common factor would be 2. Now the fraction is 19/6.
How many 6’s can fit into 19? 3. With a remainder of 1 we have:
3 ⅙
Help I on my have 10 minutes!!!PLZZZZZX
Helpppp pleaseeeeeeee
Answer:
x= 6.85 or 89/13
Step-by-step explanation:
perimeter is sum of all sides added, so add them all and set them equal to 84
4(x-3) + 3x - 1 + 6x + 8 = 84
distribute
4x + 12 + 3x - 1 + 6x + 8 = 84
combine like terms
13x - 5 = 84
solve for x
x = 89/13 = 6.85
2. Which of the following is the correct value of (0.22) - (0.4)? Show your reasoning. c. 0.088 d. 0.0088 w
Answer:
C
Step-by-step explanation:
there would have to be one more zero between 0 and 8 for both of them
what the answer?please tell me
12 points
Step-by-step explanation:
[7 + (-2)] * (-3)
= 7(-3) + (-2)(-3)
= -21 + 6
= -15. (C)
Answer:
C. -15
Step-by-step explanation:
Hope this helped have an amazing day!
You run 6 miles in one hour and 24 miles in four hours.
a. 6 miles
per hour
c. 4 hours
b. 4 miles per hour
d. 6 miles
Answer:b
Step-by-step explanation:
What if it is asking you to divide and not multiply?
Answer:
Then you divide :)
<3 Enjoy,
Dea
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
Help thank you to who ever does I will mark brainliest.
Answer:
V = 200.96 units ^3
Step-by-step explanation:
The volume of a cone is given by
V = 1/3 pi r^2 h
The radius is 4 and the height is 12
V = 1/3 ( 3.14 ) ( 4)^2 * 12
V = 200.96 units ^3
ANSWER: 200.96 units
help plz very very confused
Answer:
x=-2
Step-by-step explanation:
In the parallelogram below,
z = [ ? ]°
Find the unit rate. Round to the nearest hundredth, if necessary.
$5.99 for 12 lb
what does the dot (.) stand for in math
Answer:
The dot is called a decimal. Its what separates the whole number and the fraction of the number.
Step-by-step explanation:
For example, 0.5 is saying half, or 50 out of 100.
HELP ASAP PLEASE!!! senora need 300 grams of a spice mix to put in her pasta dish. The store sells the spice mix by the ounce. there are approximately 28.35 grams in 1 ounce how many ounces of spice mix does senora need, rounded to the nearest hundredth?
Answer: 3,969
Step-by-step explanation:
multiply 140x28.35
True or False. A triangle can be made with side lengths 4, 4 and 8.
Answer:
False
Step-by-step explanation:
5. What are the dimensions of this matrix?
Please help meeeeeeeeeee
Answer:
4 x 1
Step-by-step explanation:
The matrix shown in the illustration has 4 rows and 1 column, and thus we give the dimensions as 4 x 1.
Perform the indicated operation.
1 1/7x 2 4/5
DATE
PERIOD
Unit 3, Lesson 7: Cool-down
M
7.5: Cheetah Speed
(2 4
A cheetah can run at its top speed for about 25 seconds. Complete the table to represent a cheetah
running at a constant speed. Explain or show your reasoning.
time (seconds) distance (meters) speed (meters per second)
4
120
25
270
Answer:
ok this was a good one so here
Step-by-step explanation:
time (seconds)
distance (meters)
speed (meters per second)
4 120 30
25 750 30
9 270 30
The required values are in the completed table which has been attached below.
What is the distance?Distance is defined as the product of speed and time.
Since the Cheetah's speed is constant, the speed must be consistent throughout the table.
To calculate the unknown time and distance, use the following formula:
Speed = Distance/Time = c
When distance = 120m, time = 4 secs
Speed = 120/4 = c
Speed = 30m/s = c
We are to get the distance when the time is 25 secs
Speed = Distance/Time
30 = d₂/25
d₂ = 30 × 25
d₂ = 750 m
To get the time in the third column
Time = Distance/Speed
t₃ = 270/30
t₃ = 9seconds
Therefore, the required values are in the completed table which has been attached below.
Learn more about the distance here:
brainly.com/question/13269893
#SPJ2
Determine whether the functions f(x) = -7/5x +4/5 and g(x) = x – 4 intersect at x = 2.
A.No, because f (2) #g(2) when r =
B. No, because f (0) = 9(2) when I = 2.
C. Yes, because f(x) + 9(2) when r = 2.
D. Yes, because f(x) = 9(2) when I = 2.
Answer:
D. Yes, because f(x) = g(x) when x = 2.Step-by-step explanation:
Given the functions f(x) = -7/5x +4/5 and g(x) = x – 4, for the functions to intersect, f(x) must be equal to g(x) i.e f(x) = g(x) at x = 2
-7/5x +4/5= x- 4
If x = 2
f(2) = -7/5 (2)+ 4/5
f(2) = -14/5 + 4/5
f(2) = -10/5
f(2) = -2
g(x) = x - 4
g(2) = 2-4
g(2) = -2
Since f(2) = g(2), hence the lines intersects at x = 2
Answer: abidemiokin is ritgh
Step-by-step explanation:
Plz help with question
Answer:
I believe it's B
Step-by-step explanation:
Isosceles triangles have congruent base angles, so base angle A and B should both be the same number. (25)
Added up, 25+25+130 is 180 degrees.
Find the Lateral Area
A triangular prism and its dimensions are shown in the diagram.
5 cm
5 cm
8 cm
6 cm
What is the lateral surface area of this triangular prism in square centimeters?
Answer:
? please explain
Step-by-step explanation:
Answer:128 I think is the answer
Step-by-step explanation:
1) What is the constant of proportionality that relates y to x
х
Y
8
6
20
15
28
21
a. 1.33
6,48
0.0.75
b. 14
f
Answer: The Answer Is A Because if u just add the numbers then divide them
HELP FASTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTT
Answer:
Step-by-step explanation:
U bot. Nub
Evaluate p + 2 for p = -8.
Answer:
-6
Step-by-step explanation: