Answer:
0.0091 = 0.91% probability that their mean time is less than 9.5 minutes.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set 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]
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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The mean is 10.5 minutes and the standard deviation 3 minutes.
This means that [tex]\mu = 10.5, \sigma = 3[/tex]
Sample of 50:
This means that [tex]n = 50, s = \frac{3}{\sqrt{50}}[/tex]
What is the probability that their mean time is less than 9.5 minutes?
This is the pvalue of Z when X = 9.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{9.5 - 10.5}{\frac{3}{\sqrt{50}}}[/tex]
[tex]Z = -2.36[/tex]
[tex]Z = -2.36[/tex] has a pvalue of 0.0091
0.0091 = 0.91% probability that their mean time is less than 9.5 minutes.
Need help with Algebra 2! Thank you! :)
Answer:
Consider the parent logarithm function f(x) = log(x)
Now,
Let us make transformations in the function f(x) to get the function g(x)
•On streching the graph of f(x) = log(x) , vertically by a factor of 3, the graph of y = 3log(x) is obtained.
•Now, shrinking the graph of y = 3log(x) horizontally by a fctor of 2 to get the grpah of y = 3log(x/2) i.e the graph of g(x)
Hence, the function g(x) after the parent function f(x) = log(x) undergoes a vertical stretch by a factor of 3, and a horizontal shrink by a factor of 2 is
g(x) = 3 log(x/2) (Option-B).
Can I have some help
The number of light bulbs produced by a company can be modeled by the expression
15x^3+16x^2–100x+51, where x is the number of years passed since 1980. The number of companies
purchasing the light bulbs is represented by 5x–3. Which is the expression representing the average number
of light bulbs purchased per company?
Answer:
Expression is 3x² + 5x - 17
Step-by-step explanation:
We are told the number of lights produced by a company is;
Number of lights = 15x^3 + 16x^2 – 100x + 51
Also, number of companies that purchased the light bulbs is 5x - 3.
Thus;
The average number of bulbs purchased per company = (15x^3 + 16x^2 – 100x + 51)/(5x - 3)
I have attached the calculation using long division method to get;
3x² + 5x - 17
Which rule describes the x-coordinates in the translation below?.
O x + 0
O x + 6
O x-6
O X+2
if each quadrilateral below is a square, find the missing measures.
please help :(
We want to find the missing measures for the given square.
VU = 15TV = 21.2SU = 21.2SW = 10.6Working with squares.
We know that squares have the same length in all of their 4 sides, with that in mind we can see that:
TS = TU = UV = SV = 15
Then we can already complete:
VU = 15
Now we need the two diagonals, SU and TV.
The diagonal for a square of side length s is:
diagonal = (√2)s
Then the diagonals for our square are:
TV = SU = (√2)*15 = 21.2
And SW is half of the diagonal, so we have:
SW = 21.2/2 = 10.6
If you want to learn more about squares, you can read:
https://brainly.com/question/4916384
Evie buys an energy drink
The can is 12 cm high and the diameter is 5 cm.
Use 1-3
+5 cm
12 cm
SINH
Using the formula V = 12h, work out the volume of the can.
Give the units of your answer.
Select...
ngl I think you'll have to format it clearer, cause I have no clue what's happening
A cone has a height of 7.25 cm and a base with a radius of 4.5 cm.
What is the approximate volume of the cone?
A. 32.63 cm
B. 102.44 cm
C. 146.81 cm3
D. 153.66 cm3
Answer:
v=1\3hπr3
Step-by-step explanation:
1/3×,22/7×4.5×4.5××7.25
=153.66cm3
1. What is the probability that three or more copies will be demanded in a particular day?
a. 0.14
b. 0.20
c. 0.64
d. 1
Answer:
C. 0.64
Step-by-step explanation:
Sana makatulong :-)
Instructions require you to dilute a powder in 3 quarts of water. You only have a container that is marked in liters. How many liters would you use to dilute the powder?
Answer:
1 quart = .947 L
3 Q = 2.841 L
So you should use 2.841 L to dissolve the powder
One quartz is equal to 32 oz, then 2.88 liters of water are used to dilute the powder.
What is a conversion of units?The unit conversion deals with the operation to change one form of the unit to another form of unit.
Instructions require you to dilute a powder in 3 quarts of water. You only have a container that is marked in liters.
We know that
1 quartz = 32 oz
3 quartz = 96 oz
Since 30 milliliters per oz
Then
30 milliliters × 96 oz = 2880 milliliters
Since 1000 milliliters per liter, then we have
[tex]\rm \dfrac{2880}{1000}=2.88\ liters[/tex]
2.88 liters are used to dilute the powder.
More about the conversion of a unit link is given below.
https://brainly.com/question/655411
Kevin can paint a small room in 18 hours. Kevin and Caleb together can paint the same room in 15 hours.
How long would it take for Caleb to paint the room alone?
Answer:
90 hours
Step-by-step explanation:
The computation of the time taken for Caleb to paint the room alone is given below:
Given that
Kevin paint a small room in 18 hours
And, kevin & caleb together paint the same room in 15 hours
So, time taken for Caleb to paint the room alone is
Let us assume the same be x
Kevin time taken + caleb time taken = total time taken
[tex]\frac{1}{18} + \frac{1}{x} = \frac{1}{15}\\\\ \frac{1}{x} = \frac{1}{15} - \frac{1}{18}\\\\ \frac{1}{x} = \frac{6-5}{90} \\\\ \frac{1}{x} = \frac{1}{90}[/tex]
x = 90 hours
If anyone knows this I will give them brainiest
Answer:
x = 12
m(QS) = 52°
m(PD) = 152°
Step-by-step explanation:
Recall: Angle formed by two secants outside a circle = ½(the difference of the intercepted arcs)
Thus:
m<R = ½[m(PD) - m(QS)]
50° = ½[(12x + 8) - (4x + 4)] => substitution
Solve for x
Multiply both sides by 2
2*50 = (12x + 8) - (4x + 4)
100 = (12x + 8) - (4x + 4)
100 = 12x + 8 - 4x - 4 (distributive property)
Add like terms
100 = 8x + 4
100 - 4 = 8x
96 = 8x
96/8 = x
12 = x
x = 12
✔️m(QS) = 4x + 4 = 4(12) + 4 = 52°
✔️m(PD) = 12x + 8 = 12(12) + 8 = 152°
Please help solve, 7th grade work (see image)
Answer:
F) 63
Step-by-step explanation:
Find the original total stories 10 + 8 + 16 + 8 = 42.
Original ratio of Mary's stories to total stories is 8/42 or 4/21.
Then form equation 4/21 = 12/x ; multiply both sides of 4/21 by 3.
4/21 = 12/63
The students need to write 63 stories to keep the ratio of Mary's stories to total stories the same.
17-3/4 17-3/4 just that
Answer: 264.0625
Step-by-step explanation:
let me know if im wrong
What is the product of 2.8 and 2.9? a.) 0.618 b.) 6.18 c.) 9.512 d.) 3.608
Answer:
its a
Step-by-step explanation:
Solve the equation below, remember to check for extraneous solutions.
Answer:
2.66x + 18 = -3
Step-by-step explanation:
X=27?54?61
Hellpppp plz only serious answers
Answer: I’m pretty sure your right
Step-by-step explanation:
sorry if I’m wrong
Answer:
You are right
Step-by-step explanation:
solve 7x+4/3x+2= -4/3
Answer:
7x+4/3x+2= -4/3 don't know
suppose f(×) = 2^×, sketch a graph of f(×) and f^-1(×)
Let f(x) = y
y = 2^x
x = 2^y
Solve for y.
ln x = ln(2^y)
ln x = y ln 2
ln x/ln 2 = y
Replace y with f^(-1) x.
f^(-1) x = ln x/ln 2
We now know f(x) and f^(-1) x.
Use your graphing calculator to graph the function and its inverse on the same xy-plane. If you don't have a graphing calculator, use DESMOS online.
Good luck.
Need help on this please still lost on this
Step-by-step explanation:
Area of Circle =
[tex]\pi {r}^{2} \\ = \pi {(4)}^{2} \\ = 16\pi {km}^{2} [/tex]
answer..................
If Jeffrey invested $2,000 (principal) for 5 years at 5% interest rate compounded annually how much Interest would he earn over 5 years?
Answer:
Total = principal * (1+ rate/100)^ years
Total = 2,000 * 1.05^5
Total = 2,000 * 1.2762815625
Total = 2,552.36
Source: http://www.1728.org/compint2.htm
Step-by-step explanation:
Please help I’ll mark you as brainliest if correct!
Answer:
the anwer is C.
Step-by-step explanation:
Answer:
190.50
Step-by-step explanation: 6 ft. 3in divided by 2.54
Hi help pls and ty no link pls
Answer:
3.141
Step-by-step explanation:
just find area of full circle which is 12.566 then divide by 4 (its pi)
Answer:
3.14x2
Step-by-step explanation:
Can someone please help me sorry it’s kinda hard to see
Answer:
C.
Step-by-step explanation:
each edge/vertex was taken 2 units to the right and 8 units down to make the figure M'
I traced it to make sure
hope this helps <3
Answer:
C.
Step-by-step explanation:
each edge/vertex was taken 2 units to the right and 8 units down to make the figure M'
I traced it to make sure
hope this helps <3
a builder has built 1/6 of the floors of a new skyscraper. If the builder has built 13 floors, how many floors will the skyscraper have when it is finished? Write and solve an equation to find the answer.
Answer: 78 floors total
Step-by-step explanation:
if 13=1/6
6 x 13=78
Answer:
13*6=78
Step-by-step explanation:
If one part of something is equal to 13, then 6 parts are equal to 13*6. Let us denote that "something" by x, and we get
[tex]x = 6 \times \frac{1}{6} x = 6 \times 13[/tex]
Which is obviously an identity
What is 468,839 rounded to the nearest hundred thousand?
Answer:
500,000
Step-by-step explanation:
Answer:
500,000
hope this is right
What is the right answer?? Please tell meeee
Answer:
2\sqrt{x}+\frac{1}{2\sqrt{x}}\left(2x+3\right)
Step-by-step explanation:
which is D on your phone
10 POINT PLEASE HELP ME
Answer:
9.0
Step-by-step explanation:
A box contains 16 chocolates, of which
3 are known to contain nuts.
Two chocolates are selected at random.
a. Find the probability that
a exactly one chocolate contains
nuts
b at least one chocolate contains
nuts.
Answer:
3/16??? and 1/16???
Step-by-step explanation:
im so sorry this might be wrong
The probability that a exactly one chocolate contains nuts is 3/16 and probability that at least one chocolate contains nuts is 0.339.
How to calculate probability ?Probability is calculated by dividing the number of possible outcomes by the total number of possible outcomes. Probability and odds are two distinct concepts. Odds are calculated by dividing the probability of something happening by the probability of it not happening.
When you calculate probability, you are estimating the likelihood of something occurring and representing it with a precise number.
The probability that a exactly one chocolate contains nuts
No of total chocolates = 16 chocolates
No of chocolates contain nuts = 3
The probability that a exactly one chocolate contains nuts = 3/16
Probability that at least one chocolate contains nuts is
P(at least one contains nut) = 1 – P(given contains no nuts )^n
P(at least one contains nut) = 1 – (0.8125)^2
P(at least one contains nut) = 0.339
Probability that at least one chocolate contains nuts = 0.339
To learn more about Probability refer :
https://brainly.com/question/251701
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50 POINTS
NO LINKS
WILL MARK BRAINLYEST
My mother is 43 years old.I am w years old. Write an expression as to how old we will both be in h year's time.
Answer:
W+h= 43+h=
Step-by-step explanation:
THis shows your age plus h the amount of years time. the second expression represents your mothers age plus h.