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Related Questions
A normal population has a mean of 60 and a standard deviation of 12. You select a random sample of 9. Compute the probability the sample mean is : (a). Greater than 63. (b). Less than 56. (c). Between 56 and 63.
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Using the normal distribution and the central limit theorem, it is found that there is a:
a) 0.2266 = 22.66% probability that the sample mean is greater than 63.
b) 0.1587 = 15.87% probability that the sample mean is less than 56.
c) 0.6147 = 61.47% probability that the sample mean is between 56 and 63.
In a normal distribution 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]
It 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, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem:
Mean of 60, thus [tex]\mu = 60[/tex].Standard deviation of 12, thus [tex]\sigma = 12[/tex].Sample size of 9, thus [tex]n = 9, s = \frac{12}{\sqrt{9}} = 4[/tex].Item a:
This probability is 1 subtracted by the p-value of Z when X = 63, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{63 - 60}{4}[/tex]
[tex]Z = 0.75[/tex]
[tex]Z = 0.75[/tex] has a p-value of 0.7734.
1 - 0.7734 = 0.2266
0.2266 = 22.66% probability that the sample mean is greater than 63.
Item b:
This probability is the p-value of Z when X = 56, so:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{56 - 60}{4}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a p-value of 0.1587.
0.1587 = 15.87% probability that the sample mean is less than 56.
Item c:
This probability is the p-value of Z when X = 63 subtracted by the p-value of Z when X = 56.
These p-values were found in the previous items, so:
0.7734 - 0.1587 = 0.6147
0.6147 = 61.47% probability that the sample mean is between 56 and 63.
A similar problem is given at https://brainly.com/question/24663213
I need help with this question. Please & thank you!
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B
dividing with the same numbers and different exponents is like subtracting the exponents
16-8 = 8
If Kamina can do a job in 43 hours and Simon and Kamina working together can do the same job in 15 hours, find how
long it takes Simon to do the job alone.
hours
Answer:
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Answer:
645/28 hours
Step-by-step explanation:
In 1 hour, Kamina does 1/43 of the job.
Simon takes x hour to do the job alone.
In 1 hour, Simon does 1/x of the job.
Together, they do the job is 15 hours, so in 1 hour, they do 1/15 of the job.
1/43 + 1/x = 1/15
15x/(645x) + 645/(645x) = 43x/(645x)
15x + 645 = 43x
28x = 645
x = 645/28
each big square below represents one whole. What percent is represented by the shaded area
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HELPPPPPPPPPPPPPPPPPPPPPPPPPPP
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I NEED A 100% ACCURATE ANSWER FOR THIS ASAP NO LINKS !!!
Solve for x: 7x = 4x + 27
x =
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Answer:
x = 9
Step-by-step explanation:
Step 1: Subtract 4x from both sides.
[tex]7x - 4x = 4x + 27 - 4x[/tex] [tex]3x = 27[/tex]Step 2: Divide both sides by 3.
[tex]\frac{3x}{3} =\frac{27}{3}[/tex] [tex]x = 9[/tex]Step 3: Check if solution is correct.
[tex]7(9) = 4(9) + 27[/tex] [tex]63 = 36 + 27[/tex] [tex]63 = 63[/tex]Therefore, x = 9.
3x = 27
x = 9
solve the inequality 2x + 3 < 7
A. x < 2
B. x > -2
C. x < -2
D. x > 2
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Answer:
A. x < 2
Step-by-step explanation:
solution:
=2x<7-3
=2x<4
=x<2
Explain why there is not enough information to state that CP is the perpendicular bisector of AB.
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Answer:
First, we need to know if AP is equal to PB. We don't really know that CP passed through the midpoint of AB. We also don't know if CPA is equal to CPB. This is why there is not enough information to state that CP is the perpendicular bisector of AB.
Step-by-step explanation:
A perpendicular bisector is a segment that passes through a midpoint of a segment and is perpendicular to it.
-kiniwih426
Same value as 40% of 84
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Answer:
33.6
you are welcome :)
Step-by-step explanation:
A kennel charges $15 per day board dogs. Upon arrival, each dog must have a flea bath that costs $12.
Part A: Write a function rule for the total cost for n days of boarding plus a bath.
Part B: How much does a 10-day stay cost?
Part C: Does a 5-day stay cost half as much as a 10-day stay? Explain.
What I Think:
I think the function rule is C=15+12n.
10-day stay cost: 135
5-day stay: 75. No, a 5-day stay does not cost half as much as the 10-day stay.
Is this correct???
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Your answer makes sense. Though I would recommend using a different variable for each dog at the kennel. Like D. But other than that you're good!
I need help I don't understand.
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Answer:
x=6
Step-by-step explanation:
True or false
Quotient x Remainder + Dividend - Divisor
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EXPLANATION: s not true that Dividend over Divisor is equal to Quotient plus Remainder. For example if 37 is divided by 8 , then quotient is 4 and remainder is 5 .
c. The number of men in a community is 2,400. If the ratio of women to men in the community is 5:4,
find
i. The total number of people in the community.
ii. The number of women in the community.
iii. How many more women are there than men if 400 men joined the community.
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ii. 3,000
iii. 200
We know that 2,400 relates to the 4 parts of the ratio, so one part is 2,400 : 4 = 600.
i) So, in total, there are 600 (measure for one part) * 9 (total number of parts) = 5400 people in the community
ii) There are 5 parts in the women’s community. So, total number of women: 5 * 600 = 3000
iii) There we’re originally 5400 - 3000 = 2400 men in the community. If 400 more join, there will be 2400+400 = 2800 men.
So, there are still 3000 women and now 2800 men, so the difference between these is 3000-2800= 200.
There are 200 more women than men if 400 men joined the community.
Hope that’s helpful :)
3-3-2-2-2 written as a whole number
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Answer:
I think this would be 33,222 I don't know I feel positive about this.
Step-by-step explanation:
I have 47 questions I posted going to post the second if you answer all the I give you 100 points and brainlist
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Answer:
1. 245
2. Rational Number
3.integers
4. false
5.square root
Step-by-step explanation:
Write an inequality to represent this situation (1 point):
Jake earned more than $49 dollars.
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The inequality that represents the situation is:
[tex]E_J > 49[/tex].
Jake earnings are unknown, so it is going to be represented by a variable, that we are going to call it [tex]E_J[/tex].His earnings are of more than 49 dollars, that is, [tex]E_J[/tex] is greater than $49, which means that the following inequality models this situation:
[tex]E_J > 49[/tex].
A similar problem, also involving an inequality built to represent a situation, is given at https://brainly.com/question/22312773
If x=8, find the value of y in the equation 4x-2y=28
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Answer:
The answer is 2
Step-by-step explanation:
[tex]4x - 2y = 28 \\ 4 \times 8 - 2y = 28 \\ 32 - 2y = 28 \\ 32 - 28 = 2y \\ 4 = 2y \\ devided \: by \: 2 \\ then \\ y = 2[/tex]
if a box holds 24 1/8-in cubes what is the volume
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Answer:
the box volume is 34
Step-by-step explanation:
so you add then multiply 24 by 1/8 and that make 34 and sorry if it's not correct I'm bad at matg
What is James's spendable income this pay period? (use pay stub) *
1 point
$709.74
$1000.00
$797.48
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The path of a baseball is given by the function: f(x)=-0.004x^2 + x + 3
, where f(x) is the height of the baseball (in feet) and x is the horizontal distance from home plate (in feet). Answer the following questions completely. Justify your answers algebraically.
(a) What is the maximum height reached by the baseball?
(b) If the baseball is not caught, how far from home plate does the ball hit the ground? Round your answer to one decimal place.
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Answer:
The initial speed of the ball is 98.22 ft/s
The maximum height of the ball is 75.02 ft.
Step-by-step explanation:
Hi there!
Step-by-step explanation:
The position and velocity vectors of the ball can be calcualted as follows:
r = (x0 + v0 · t · cos α, y0 + v0 · t · sin α + 1/2 · g · t²)
v = (v0 · cos α , v0 · sin α + g · t)
Where:
r = position vector at time t.
x0 = initial horizontal position.
v0 = initial velocity.
t = time.
α = launching angle.
y0 = initial vertical position.
g = acceleration due to gravity (-9.8 m/s² considering the upward direction as positive).
v = velocity vector at time t.
Let´s call r final to the position vector when the ball is caught (see attached figure). The components of r final are:
x = 300 feet
y = 0
Then, r final = (300 feet, 0)
Notice that the origin of the frame of reference is located at the launching point.
Then, when the ball is caught:
300 feet = x0 + v0 · t · cos α
0 = y0 + v0 · t · sin α + 1/2 · g · t²
We have a system of two equations with two unknowns (t and v0), so, let´s solve it.
Let´s solve the first eqation for v0:
300 feet = x0 + v0 · t · cos α
Since the frame of reference is located at the launching point (x0 = 0). Then:
300 feet = v0 · t · cos 45°
300 feet /( t · cos 45°) = v0
Now, let´s replace v0 in the secod equation of the system:
0 = y0 + v0 · t · sin α + 1/2 · g · t² (y0 = 0)
0 = 300 feet/(t · cos 45°) · t · sin 45° - 1/2 · 9.8 m/s² · t²
0 = 300 feet · sin 45°/cos45° - 4.9 m/s² · t² (sin45°/cos45° = 1)
0 = 300 feet - 4.9 m/s² · t²
-300 feet = -4.9 m/s² · t²
-300 feet / -16.08 ft/s² = t²
t = 4.32 s
Now, we can calculate the initial velocity:
300 feet /( t · cos 45°) = v0
300 feet /( 4.32 s · cos 45°) = v0
v0 = 98.22 ft/s
The initial speed of the ball is 98.22 ft/s
To obtain the maximum height of the ball, we have to find at which time the ball is at its maximum height. We can do this in several ways, but we will use the equation of velocity. See in the figure that when the ball is at its maximum height, the y-component of the velocity is zero (because the vector is horizontal). Then, using the equation of the y-component of the velocity:
vy = v0 · sin α + g · t
0 = 98.22 · sin 45° - 32.15 ft/s² · t
(-98.22 · sin 45°) / - 32.15 ft/s² = t
t = 2.16 s
(Notice that this time is half the total time of flight calculated above (4.32 s). This is also the time at which the horizontal distance traveled by the ball is half the total horizontal traveled distance. This is so because the trajectory of the ball is a parabola).
Now that we have the time, we can calculate the y-component of the position vector (r1y in the figure).
r1y = v0 · t · sin α + 1/2 · g · t²
r1y = 98.22 ft/s · 2.16 s · sin 45° - 1/2 · 32.15 ft/s² · (2.16 s)²
r1y = 75.02 ft
The maximum height of the ball is 75.02 ft.
A farmer sold did he sell? of his sheep. His original flock was 300 sheep. How many sheep did he sell?
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all of his sheep
Hope that helps :)
PLEASE ANSWER ASAP
i can't figure out the answer
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I will give Brainliest :)
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Answer:
Step-by-step explanation:
Solve the problems. Write the complete proof in your homework and for online (only) respond to questions or statements (if any) that are parts of your proof or related to it.
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Step-by-step explanation:
Well we know that ZACB=LABC because
AABC is isosceles, so base angles theorem applies.
m<ACB=70°
So mzDCE=m/DEC-35° because of base angles theorem, and because mzDCE=m/ACB-m<ECB=70°-35°
Finally, DE || CB because the alternate interior angles ECB=<DEC
A supermarket advertises a new product by offering samples to customers. The table shows the number of samples distributed each hour. At what rate does the supermarket distributes samples?
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Answer:
38 samples an hour, next time taken the first two numbers in the table and divide the one on the right by the one on the left
Which angles are alternate interior angles?
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Answer:
<SRU and <TUW
Step-by-step explanation:
They are on opposite ends which makes them alternate interior angles
What do you already know about credit cards?
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Answer:
A credit card is a payment card issued to users to enable the cardholder to pay a merchant for goods and services based on the cardholder's accrued debt.
Step-by-step explanation:
can anyone heelp me pls pls
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Answer: liquid= lotion capsule= solid suspension=semisolid
Step-by-step explanation:
What is the equation of the following line be sure to scroll down first to see all answer options
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Answer:
b
Step-by-step explanation:
mark me as brainliest have a great day
Correct answer gets brainiest
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Answer:
[tex]x + 2x + a + 90 \degree = 360\degree \\ x + 2x + 132\degree + 90 \degree = 360\degree \\ 3x + 222\degree = 360\degree \\ 3x = 360\degree - 222\degree \\ 3x = 138\degree \\ x = \frac{138\degree}{3} \\ \boxed{ x = 46\degree}[/tex]
