Answer:
a) P[ Z < 45 ] = 0,14 %
b) P[ Z > 65 ] = 16%
c) z = 71,65 minutes
Step-by-step explanation:
Normal Distribution
Mean (μ₀) 1 hour or 60 minutes
Standard Deviation σ = 5 (minutes)
a) The probability that a cell divides in less than 45 minutes is:
Let´s call Z standard normal random with distribution function Φ then:
P[ Z < 45 ] = ( Z - μ₀ ) / σ
P[ Z < 45 ] = ( 45 - 60 ) / 5
P[ Z < 45 ] = - 3
With this value we look in Z table and find the value 0,00135
P[ Z < 45 ] = 0,00135 or
P[ Z < 45 ] = 0,14 %
b)The probability of Z > 65 minutes is:
P[ Z > 65 ] = 1 - P[ Z ≤ 65 ]
P[ Z ≤ 65 ] = ( Z - μ₀ )/ σ
P[ Z ≤ 65 ] = ( 65 - 60 ) / 5
P[ Z ≤ 65 ] = 1
From Z table we find the reciprocate value of 0,84134 then
P[ Z ≤ 65 ] = 0,84134 and
P[ Z > 65 ] = 1 - 0,84134
P[ Z > 65 ] = 0,15866
P[ Z > 65 ] = 0,16 or P[ Z > 65 ] = 16%
c) The time to get 99% of all cell completed the process is:
P [ Z ≤ z ] = ( z - 60 ) / σ
In Z table the value of 0,99010 which is a good aproximation of 0,99 (or 99%) reciprocate with the value 2,33 then
P [ Z ≤ z ] = 2,33 = ( z - 60 ) / σ
2,33 * 5 = z - 60
11,65 + 60 = z
z = 71,65 minutes
As a matter of fact checking this value, we can see according to the empirical rule that 99,7 % of all values will occur
mean + 3σ or 60 + 15 = 75
In this exercise we have to use statistical knowledge to calculate the probability of cells dividing, so we can say that:
a) [tex]P[ Z < 45 ] = 0,14 \%[/tex]
b) [tex]P[ Z > 65 ] = 16\%[/tex]
c) [tex]Z = 71,65 minutes[/tex]
With the knowledge and information given about probability we have:
a) The probability that a cell divides in less than 45 minutes, so let´s call Z standard normal random with distribution function then:
[tex]P[ Z < 45 ] = ( Z - \mu_0 ) / \sigma\\P[ Z < 45 ] = ( 45 - 60 ) / 5\\P[ Z < 45 ] = - 3\\P[ Z < 45 ] = 0,00135 \ or \ P[ Z < 45 ] = 0,14 \%[/tex]
b)The probability of Z > 65 minutes is:
[tex]P[ Z > 65 ] = 1 - P[ Z \leq 65 ]\\P[ Z \leq 65 ] = ( Z - \mu_0 )/ \sigma\\P[ Z \leq 65 ] = ( 65 - 60 ) / 5\\P[ Z \leq 65 ] = 1\\P[ Z \leq 65 ] = 0,84134 \ and \ P[ Z > 65 ] = 1 - 0,84134\\P[ Z > 65 ] = 0,15866\\P[ Z > 65 ] = 0,16 \ or \ P[ Z > 65 ] = 16\%[/tex]
c) The time to get 99% of all cell completed the process is:
[tex]P [ Z\leq z ] = ( z - 60 ) / \sigma\\P [ Z \leq z ] = 2,33 = ( z - 60 ) / \sigma\\2,33 * 5 = z - 60\\11,65 + 60 = z\\z = 71,65 minutes[/tex]
See more about stattistics at brainly.com/question/10951564
A. No, because it fails the vertical line test.
B. Yes, because it passes the vertical line test.
C. Yes, because it passes the horizontal line test.
D. No, because it is not a straight line.
Answer:
B. Yes, because it passes the vertical line test.
Step-by-step explanation:
The is a function. It has a one to one correspondence
It will pass the vertical line test
Help pls urgent!!!!!!!!!!
Answer:
d
Step-by-step explanation:
The following values of (x) and f(y) are given. Find the best value of (dy/dx) at
(x=6) using center difference method?
x
F(y)
5
3.2188
5.5
3.4096
6.5
3.7436
7
3.8918
7.5
4.0298
3.7436
4.1588
Answer:
dy/dx at x=6 is 0.334
Step-by-step explanation:
The center difference method requires that the values of the function are given in equal intervals which is the case, and allows one to find the value for x = 6 using those of the function for x = 5.5 and for x = 6.5 as follows:
[tex]\frac{dy}{dx} =\frac{3.7436-3.4096}{6.5-5.5} =0.334[/tex]
7. Look at the figure below.
Which theorem can be used to show that triangles QSN and LEJ are congruent?
A. HL
B. ASA
C. SAS
D. SSA
I'm pretty sure that ' HL ' stands for "hypotenuse and leg". That's the one.
-- We see the little boxes in the lower left corners, so we know that these are right triangles, and we can use the rules we know about for right triangles.
-- The hypotenuses of both triangles are marked with the same length.
-- The base legs of both triangles are marked with the same length.
-- So we have (the hypotenuse and one leg of one right triangle) equal to (the hypotenuse and corresponding leg of another right triangle). That's exactly the description of the HL conguence theorem, so we know that these two triangles are congruent.
Answer the following True or False:
If the p-value is 0.13 and the level of significance , a , is 0.05 in a hypothesis test for a mean, then we
accept the null hypothesis.
O false
O true
Answer:
false.
I think .???
a null hypothesis doesn't matter regardless
Perform the indicated operation and simplify the result.
Answer:
7/ (3a-1)
Step-by-step explanation:
3a^2 -13a +4 28+7a
------------------ * --------------------
9a^2 -6a+1 a^2 -16
Factor
(3a-1)(a-4) 7(4+a)
------------------ * --------------------
(3a-1) (3a-1) (a-4)(a+4)
Cancel like terms
1 7
------------------ * --------------------
(3a-1) 1
Leaving
7/ (3a-1)
if you make $2710.00 a month and must spend 89% of that on recurring and variable expenses, how much money can you potentially save in one year?
Answer:
$3577.20
Step-by-step explanation:
You can save 11% of your income each month, so in 12 months, you can save ...
12×0.11×$2710 = $3577.20
What is 15 x minus 3 y = 0 written in slope-intercept form?
Answer:
y= 5x
Step-by-step explanation:
15x - 3y =0
3y= 15x
y= 5x - slope- intercept form
Answer:
a
Step-by-step explanation:
y=5x
What statement is true? Use the number line to help
Answer:
-2 is greater than -2 1/2
Step-by-step explanation:
All the other questions are false and only answer a is correct because -2 is closer to 0 than -2 1/2.
Answer:
-2 is greater than -2.5Step-by-step explanation:
B is wrong. This is because when you look on the number like you can see that the option for 1.5 is greater than one is false. This is because 1.5 is ahead of the 1 on the number line.
C is wrong. This is because the number 1 is greater than -1.5. The number one is ahead of the number -1.5.
D is wrong. D is wrong because when a smaller number is negative then it is bigger than a larger number that is negative. So -1.5 is smaller than -0.5.
So the answer is A. -2 is greater than -2.5. It can be proved because of the rule written that a smaller number is negative then it is bigger than a larger number that is negative. So -2.5 is smaller than -2. And the reciprocal is true. -2 is larger than -2.5.
Hope this helped,
Kavitha
The U.S. Department of Agriculture (USDA) uses sample surveys to obtain important economic estimates. One USDA pilot study estimated the price received by farmers for corn sold in January from a sample of 20 farms. The mean price was reported as $3.64 per bushel with a standard deviation of $0.0835 per bushel. Give a 95% confidence interval for the mean price received by farmers for corn sold in January.
Answer:
{$3.60; $3.68}
Step-by-step explanation:
The confidence interval for a sample of size 'n', with mean price 'X' and standard deviation 's' is determined by:
[tex]X\pm z*\frac{s}{\sqrt n}[/tex]
The z-score for a 95% confidence interval is 1.96.
Applying the given data, the lower and upper bounds of the confidence interval are:
[tex]3.64\pm 1.96*\frac{0.0835}{\sqrt 20} \\L=\$3.60\\U=\$3.68[/tex]
The confidence interval for the mean price received by farmers for corn sold in January is:
CI : {$3.60; $3.68}
Find the slope through each pair of two points. Report answers in simplest form.
(0,0) and (0.5,0.25)
m =
Answer: m=0.5 or m=1/2
Step-by-step explanation:
To find the slope, you use the formula [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]. Since we are given the coordinate points, we can directly plug them in.
[tex]m=\frac{0.25-0}{0.5-0} =\frac{0.25}{0.5} =0.5[/tex]
Jaleel and Lisa are simplifying the expression 2 (x minus 2) + 2 as shown. Jaleel’s Method 2 (x minus 2) + 2 = 2 x minus 4 + 2 = 2 x minus 2 Lisa’s Method 2 (x minus 2) + 2 = 2 x minus 2 + 2 = 2 x Whose method is correct and why? Lisa’s method is correct because 2 (x minus 2) equals 2 x minus 2. Lisa’s method is correct because 2 (x minus 2) equals 2 x. Jaleel is correct because 2 (x minus 2) equals 2 x minus 2. Jaleel is correct because 2 (x minus 2) equals 2 x minus 4.
Answer:
(D)Jaleel's method is correct because 2(x-2)=2x-4.
Step-by-step explanation:
Jaleel and Lisa are simplifying the expression 2(x-2)+2 as shown.
[tex]J$aleel's Method: \left\{\begin{array}{ccc}2 (x -2) + 2 \\= 2 x - 4 + 2 \\= 2 x - 2\end{array}\right[/tex]
[tex]L$isa's Method: \left\{\begin{array}{ccc}2 (x-2) + 2 \\= 2 x -2 + 2 \\= 2 x\end{array}\right[/tex]
We can see that Jaleel's method is correct because:
2(x-2)=2x-4.
When you expand, you must multiply the term outside by all the terms inside the bracket.
The correct option is D.
Answer:
Jaleel is correct because 2 (x minus 2) equals 2 x minus 4.
D is correct
Step-by-step explanation:
i just took the quiz.
What is the discriminant of the quadratic equation 0 = –x2 + 4x – 2?
Answer:
Discriminant=8
Step-by-step explanation:
-x²+4x-2=0
here a=-1,b=4 and c=-2
Discriminant=b²-4ac
Discriminant=(4)²-4(-1)(-2)
Discriminant=16-8
Discriminant=8
i hope this will help you :)
Find the slope through each pair of two points. Report answers in simplest form.
(0,0) and (0.5,0.25)
m =
Answer:
m = 0.5
Step-by-step explanation:
m = (y2 - y1) / (x2 - x1)
= (0.25 - 0) / (0.5 - 0)
= 0.25/0.5
= 0.5
Which best compares the volumes of the two cylinders? Geometry
Answer:
The correct answer would be C
Step-by-step explanation:
please mark brainliest
The choice which best compares the volume of the cylinders is; Choice B; The volume of cylinder B is the same as that of cylinder A.
Which best compares the volumes of the two cylinders?From geometry, It can be concluded that the volume of a solid shape is the product of its cross sectional area and the height over which the area spans. On this note, since the volume of a cylinder is dependent on the radius and height of the cylinder, both cylinders have equal volumes.
Read more on cylinders;
https://brainly.com/question/9554871
#SPJ2
what is the slope of a line of duty hat is parallel to the line whose equation is 5y+2x=12
Answer:
-2/5
Step-by-step explanation:
The slope of two parallel lines will be the same.
Here, our equation is 5y + 2x = 12. Let's find the slope by isolating y:
5y + 2x = 12
5y = -2x + 12
y = (-2/5)x + 12/5
So, the slope is -2/5.
Thus, the slope of the line parallel to the given one will be -2/5.
~ an aesthetics lover
Answer:
-2/5
Step-by-step explanation:
5y+2x=12
Solve for y
Subtract 2x
5y = -2x+12
Divide by 5
5y/5 = -2/5 x +12/5
y = -2/5x +12/5
The slope is -2/5
Parallel lines have the same slope
Find the length of ST to the nearest meter.
Answer:
42 m
Step-by-step explanation:
First, find <S
<S = 180 - (41+113) [ sum of angles in a triangle)
<S = 180 - 154 = 26°
Next is to find length of ST, using the law of sines: a/sin A = b/sinc B = c/sin C
Let a = RT = 28m
A = <S = 26°
b = ST
B = <R = 41°
Thus, we have:
28/sin(26°) = b/sin(41°)
Cross multiply
28*sin(41°) = b*sin(26°)
28*0.6561 = b*0.4384
18.3708 = b*0.4384
Divide both sides by 0.4384 to make b the subject of formula
18.3708/0.4384 = b
41.9041971 = b
b ≈ 42m (rounded to nearest meter)
Length of ST to nearest meter = 42 meters
An arhaeologist, exploring the pyramids
of Africa, discovers a mummy. He finds
that it contains 53 % of original amount
of C-14. Find age of the mummy.
Answer:
5249 years
Step-by-step explanation:
Half-Life of Carbon-14 is approximately 5730 years.
When we want to determine the age of a fossil using carbon dating, we use the formula:
[tex]t=\dfrac{\ln(N/N_0)}{-0.693} \cdot t_{1/2}[/tex]
Where:
[tex]t_{1/2}[/tex] is the half-life of the isotope carbon 14, t = age of the fossil (or the date of death) and ln() is the natural logarithm functionIn this case:
N(t)=100
[tex]N_o=53\\t_{1/2}\approx 5730$ years[/tex]
Therefore, the age of the mummy
[tex]t=\dfrac{\ln(53/100)}{-0.693} \cdot 5730\\=5249.43$ years\\t \approx 5249$ years[/tex]
Answer:
the answer is 6349 :)
Step-by-step explanation:
Someone put the correct answer in the comments so I figured I would put it here so you wouldn't miss it :) (It is correct I have tested it)
write down 3 numbers that have a range of 5 and a mode of 8
Answer:
8, 8, 13
Step-by-step explanation:
The three numbers 8, 8, 13 have a range of 5.
13 - 8 = 5
The mode is 8, the repeated number.
Answer:
need pls
Step-by-step explanation:
The Foot Locker is having a 60% off sale on shorts. John paid $18 for a pair of shorts. What was the original price of the shorts?
Answer:
$30 is the price of the original pair of sneakers.
Step-by-step explanation:
You wanna cross multiply so you put :
18. 60
_ = _
x. 100
You multiply 18 the cost of the sneakers by 100 and then divide the product (1800) by 60 and you get $30.
MARK ME AS BRAINLIEST!
Recall the equation that modeled the volume of the raised flower bed, y, in terms of the width of the box, y = x3 + 11x2 − 312x. Now, open the graphing tool and graph the equation. Remember, this equation represents the volume of a flower box, so neither the width nor the volume can be negative. Using the pointer, determine the x-intercept where the width is positive and the volume will change to positive as x increases.
Answer:
x = 17.349
Step-by-step explanation:
The right-most x-intercept is 17.349, where the curve continues upward to the right.
What is the value of p?
Answer:
Step-by-step explanation:
The angle next to 90 degrees is also 90 degrees and it's supplementary
the angle next to 133 degrees is 47 degrees and it's also supplementary
p + 90 + 47 = 180
p + 137 = 180
p = 43 degrees
the solution is d
Find the area of the regular polygon. Round your answer to the nearest hundredth.
(4 , 3.3)
The area is about __
square units.
Answer:
total area = 39.6 square units
Step-by-step explanation:
determine the inside angle
360 / 5 = 72°
half of the triangle = 36°
given:
adj = 3.3
Ф = 36°
length of the opp of a small triangle is = adj. tan Ф
opp = 3.3 * tan 36 = 2.4
area of a triangle = 1/2 b * h x 2 tringles
area =( 1/2 * 2.4 * 3.3 ) * 2
area = 7.92 multiplied by 5 equal shapes
total area = 7.92 * 5
total area = 39.6 square units
hope this helps
If the volume of a full sphere is 4/3x πr^3 what is the volume of a half sphere, also called a hemisphere?
Answer:
Rebekah, the height of a hemisphere is its radius. The volume of a sphere is 4/3 π r3. So the volume of a hemisphere is half of that: V = (2 / 3) π r3.
Answer:
V = (2 / 3) π r3.
Step-by-step explanation:
1/2 x 4/3 x π r3 = 2/3π r3
Plz solve this question, it's very urgent.
i think it is ur required ans..
The decay constant for 14C is 0.00012. A 4050-year-old wooden chest is found by archaeologists. What percentage of the original 14C would you expect to find in the wooden chest? (Express your answer as a percentage rounded to one decimal place.)
Answer:
The radioactive decay constant or k = ln (.5) / Half-Life
Half-Life = -.693147 / .00012
Half-Life = -5,776.225 years
We'll call beginning amount as 100%
Ending Amount = Beginning Amount / 2^n (where n = # of half-lives)
n = 4,050 / 5,776.225 = 0.7011499725
Ending Amount = 100% / 2^0.7011499725
Ending Amount = 100% / 1.625800202
Ending Amount = 61.5081729452%
Ending Amount = 61.5 % (rounded)
Step-by-step explanation:
Eruptions of the Old Faithful geyser have duration times with a mean of 245.0 sec and a standard deviation of 36.4 sec (based on sample data). One eruption had a duration time of 110 sec.Eruptions of the Old Faithful geyser have duration times with a mean of 245.0 sec and a standard deviation of 36.4 sec (based on sample data). One eruption had a duration time of 110 sec.
a. What is the difference between a duration time of 110 sec and the mean? Answer
135
b. How many standard deviations is that (the difference found in part (a))? Answer
c. Convert the duration time of 110 sec to a z score. Answer
d. If we consider "usual" duration times to be those that convert to z scores between -2 and 2, is a duration time of 110 sec usual or unusual?
Answer:
a) 135 seconds
b) 3.71 standard deviations below the mean
c) Z = -3.71
d) Unusual
Step-by-step explanation:
Z-score:
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
In this question:
[tex]\mu = 245, \sigma = 36.4[/tex]
a. What is the difference between a duration time of 110 sec and the mean?
Duration of 110 seconds.
Mean of 245
245 - 110 = 135 seconds
b. How many standard deviations is that (the difference found in part (a))?
This is |Z|
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{110 - 245}{36.4}[/tex]
[tex]Z = -3.71[/tex]
[tex]|Z| = 3.71[/tex]
3.71 standard deviations below the mean
c. Convert the duration time of 110 sec to a z score
From b, Z = -3.71
d. If we consider "usual" duration times to be those that convert to z scores between -2 and 2, is a duration time of 110 sec usual or unusual?
Z is not in the interval of -2 and 2, so a duration time of 110 sec is unusual
Please answer this correctly
There are 6 total cards. There is one 5 and one 7
You have a 1/6 probability of picking each number.
The probability of picking the 5 then the 7 would be 1/6 x 1/6 = 1/36
A population of monkeys' tail lengths is normally distributed with a mean of 25 cm with a standard deviation of 8 cm. I am preparing to take a sample of size 256 from this population, and record the tail length of each monkey in my sample. What is the probability that the mean of my sample will be between 24 and 25 cm?
Answer:
The probability that the mean of my sample will be between 24 and 25 cm
P(24 ≤X⁻≤25) = 0.4772
Step-by-step explanation:
Step(i):-
Given mean of the Population 'μ'= 25c.m
Given standard deviation of the Population 'σ' = 8c.m
Given sample size 'n' = 256
Let X₁ = 24
[tex]Z_{1} = \frac{x_{1}-mean }{\frac{S.D}{\sqrt{n} } } = \frac{24-25}{\frac{8}{\sqrt{256} } } = -2[/tex]
Let X₂ = 25
[tex]Z_{2} = \frac{x_{2}-mean }{\frac{S.D}{\sqrt{n} } } = \frac{25-25}{\frac{8}{\sqrt{256} } } = 0[/tex]
Step(ii):-
The probability that the mean of my sample will be between 24 and 25 cm
P(24 ≤X⁻≤25) = P(-2≤ Z ≤0)
= P( Z≤0) - P(Z≤-2)
= 0.5 + A(0) - (0.5- A(-2))
= A(0) + A(2) ( ∵A(-2) =A(2)
= 0.000+ 0.4772
= 0.4772
Final answer:-
The probability that the mean of my sample will be between 24 and 25 cm
P(24 ≤X⁻≤25) = 0.4772
Please answer this question now in two minutes
Answer:
the slope equation is y2 - y1 divided by x2 - x1
Step-by-step explanation:
so the answer would be 3 over 2 because of this method
Answer:
3/2
Step-by-step explanation:
Use the easy rise over run method.
start at the point (50,20) then go up 3 units and 2 units to the right to get the next point.
3/2 should be the slope.
Hope I helped you!