Answer:
The answer is below
Step-by-step explanation:
Given that:
mean value (μ) = 12 cm and standard deviation (σ) = 0.04 cm
a) Since a random sample (n) of 16 rings is taken, therefore the mean (μx) ans standard deviation (σx) of the sample mean Xbar is given by:
[tex]\mu_x=\mu=12\ cm\\\sigma_x=\frac{\sigma}{\sqrt{n} }=\frac{0.04}{\sqrt{16} }=0.01[/tex]
The sampling distribution of Xbar is centered about 12 cm and the standard deviation of the Xbar distribution is 0.01 cm
b) Since a random sample (n) of 64 rings is taken, therefore the mean (μx) ans standard deviation (σx) of the sample mean Xbar is given by:
[tex]\mu_x=\mu=12\ cm\\\sigma_x=\frac{\sigma}{\sqrt{n} }=\frac{0.04}{\sqrt{64} }=0.005\ cm[/tex]
The sampling distribution of Xbar is centered about 12 cm and the standard deviation of the Xbar distribution is 0.005 cm
c) n = 16 and the raw score (x) = 11.95 cm
The z score equation is given by:
[tex]z=\frac{x-\mu_x}{\sigma_x} =\frac{x-\mu}{\sigma/\sqrt{n} } \\z=\frac{11.95-12}{0.04/\sqrt{16} }\\ z=-5[/tex]
P(x > 11.95 cm) = P(z > -5) = 1 - P(z < -5) = 1 - 0.000001 ≅ 1 ≅ 100%
d) for n = 64, the standard deviation is 0.01 cm, therefore it is more likely to be within .01cm of 12cm
Using the normal distribution and the central limit theorem, it is found that:
a) The sampling distribution is approximately normal, centered at 12 cm and with a standard deviation of 0.01 cm.
b) The sampling distribution is approximately normal, centered at 12 cm and with a standard deviation of 0.005 cm.
c) 100% probability that the average diameter of piston rings from a sample size 16 is more than 11.95 cm .
d) Due to the lower standard error, the sample of 64 is more likely to be within 0.01 cm of 12 cm.
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.The Central Limit Theorem establishes 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].In this problem:
Mean of 12 cm, thus [tex]\mu = 12[/tex]Standard deviation of 0.04 cm, thus [tex]\sigma = 0.04[/tex].Item a:
Sample of 16, thus [tex]n = 16[/tex] and [tex]s = \frac{0.04}{\sqrt{16}} = 0.01[/tex]
The sampling distribution is approximately normal, centered at 12 cm and with a standard deviation of 0.01 cm.
Item b:
Sample of 64, thus [tex]n = 64[/tex] and [tex]s = \frac{0.04}{\sqrt{64}} = 0.005[/tex]
The sampling distribution is approximately normal, centered at 12 cm and with a standard deviation of 0.005 cm.
Item c:
This probability is 1 subtracted by the p-value of Z when X = 11.95, thus:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{11.95 - 12}{0.01}[/tex]
[tex]Z = -5[/tex]
[tex]Z = -5[/tex] has a p-value of 0.
1 - 0 = 1.
100% probability that the average diameter of piston rings from a sample size 16 is more than 11.95 cm .
Item d:
Due to the lower standard error, the sample of 64 is more likely to be within 0.01 cm of 12 cm.
A similar problem is given at https://brainly.com/question/24663213
Two bond funds pay interest at rates that differ by 4%. Money invested for one year in the first fund earns $550 interest. The same amount invested in the other fund earns $770. Find the lower rate of interest. _________ %
Answer:
10% interest.
Step-by-step explanation:
Interest I = PRT/100
If the rate R = x% we have
550 = P*x *1 / 100
and
770 = P*(x + 4) * 1 / 100
so From first equation
Px = 55000 and from the second
Px + 4P = 77000
So Px = 77000 - 4P
Therefore 77000 - 4P = 55000
4P = 22000
P = 5,500
So x = 55000/5500 = 10%.
And the rate for the other fund is 10 + 4 = 14%.
500
475
450
- ODX Group, Inc
-NAMSEK
-A&D
400
425
Peer Comms Ltd.
350
350
300
300
250
275
Value of 100 shares in $
250
200
200
175
175
150
150
175
150
125
100
150
-100
100
100
125
125
50
25
0
Year 1
Year 2
Year 3
Year 4
Year 5
How much would it cost to buy 100 shares in ODX Group, Inc. and 300 shares in
Peer Comms Ltd, in Year 5?
Options
(A)350 (B)375 (C)725 (D)750 (E)775
Answer:
(E)775
Step-by-step explanation:
From the attached graph
In Year 5
100 shares in ODX Group, Inc. was worth $175100 shares in Peer Comms Ltd was worth $200Therefore the Cost of 100 shares in ODX Group, Inc. and 300 shares in Peer Comms Ltd, in Year 5
=175+3(200)
=175+600
=$775
The correct option is E.
David and Tina share their profit in a ratio of 5:7. Tina gets £70 more than David. How much money did David receive?
Answer:
Amount of money David received = £ 175
Step-by-step explanation:
Both of them share their profit in a ratio of 5:7 . Tina got £70 more than David. Let
the amount David received = a
amount Tina received = 70 + a
the total profit = 70 + 2a
Amount David received = 5/12 × 70 + 2a = a
Therefore,
5/12 × 70 + 2a = a
350 + 10a/12 = a
cross multiply
350 + 10a = 12a
collect like terms
350 = 12a - 10a
350 = 2a
divide both sides by 2
a = 350/2
a = 175
Amount of money David received = £ 175
Please answer this correctly
Answer:
12.5%
Step-by-step explanation:
There is only 1 seven card from the 8 total cards.
1 out of 8.
1/8 = 0.125
P(7) = 12.5%
Answer:
12.5%
Step-by-step explanation:
Total Cards = 8
Number 7 = 1
P(7) = 1/8
In %age:
=> 12.5%
Basic kinematics. Please help! Will give brainliest! Show all work!
Answer: 3.5 m/s
Step-by-step explanation:
[tex]v=\frac{vf+vi}{2}[/tex]
[tex]v=\frac{5+2}{2}[/tex]
5+2=7
7/2= 3.5
PLEASE HELP ME!!!!!!!!!! What polygon is tesellated to form this image?
Answer:
Pentagon
Step-by-step explanation:
the head is the closest I see
I NEED HELP PLEASE, THANKS! :) Write the augmented matrix for the system of linear equations. –9w + x + 8y + 2z = –6 –5x + 9y – 7z = 6 –3w – 6x + 4y + 9z = 4 –3w – 8x + y = –2
Answer:
3rd Matrix
Step-by-step explanation:
When you start putting the coefficients in as the matrix, you see that -9 has to be the 1st number, so that eliminates choice B and choice D as answers. You are left with choices A and C. C is the correct choice because when you plug in the second equation, your coefficient is -5, not 0.
Answer:
First Matrix
Step-by-step explanation:
Looking at the first equation, we see that the leading coefficient is -9. This gets rid of choice B and D because the first number in these matrices are not -9. You are left with choices A and C. Looking at the second equation, we see that there is no "w" variable, so we need to add one. The coefficient of this "w" is going to be 0. This means that A is the correct choice. Just to be sure though, evaluate all other coefficients to see if they line up with the matrix. Hope this helps.
PLEASE 36 POINTS!!! I WILL ALSO GIVE BRAINLIEST A system of linear equations includes the line that is created by the equation y = 0.5 x minus 1 and the line through the points (3, 1) and (–5, –7), shown below. On a coordinate plane, points are at (negative 5, negative 7) and (3, 1). What is the solution to the system of equations? (–6, –4) (0, –1) (0, –2) (2, 0)
Answer: D: (2, 0)
Step-by-step explanation:right on Edge 2020
Answer:
yes its d
Step-by-step explanation:
did on edge
Of the last 100 customers entering a computer shop, 25 have purchased a computer. If the relative frequency method for computing probability is used, the probability that the next customer will purchase a computer is
Answer: 0.25
Step-by-step explanation:
The relative frequency of the customers that buy computers is equal to the number of customers that bought a computer divided the total number of customers that entered the shop.
p = 25/100 = 0.25
If we take this as the probability, then the probability that the next customer that enters the shop buys a computer is 0.25 or 25%
Find the value of
5x when x = 6
Answer:
30solution,
X=6
[tex]5x \\ = 5 \times x \\ = 5 \times 6 \\ = 30[/tex]
Hope this helps...
Good luck on your assignment
Answer:
Step-by-step explanation:
x = 6
5x = 5 *6 = 30
Consider the two savings plans below. Compare the balances in each plan after 14 years. Which person deposited more money in the plan? Which of the two investment strategies is better? Yolanda deposits $100 per month in an account with an APR of 5%, while Zach deposits $1200 at the end of each year in an account with an APR of 5%.
Step-by-step explanation:
It is not specified the compounding period, which in general is a month these days. So we will assume money is compounded each month, otherwise there is no point depositing monthly.
1. Yolanda:
APR=5% is equivalent to
Monthly interest = 5%/12 = 5/12% = 5/1200 = 1/240 = i
Monthly deposit = 100 = A
Future value after 14 years = 14*12 months = 168 months = n
FV1 = A((1+i)^n-1)/i
=100*((1+1/240)^168-1)/(1/240)
= $24259.83
2. Zach
He deposits 1200 at the end of the year. The last payment does not benefit from interest.
Since it is a yearly payment, each amount earns interest over a year, giving an annual interest of
(1+i)^12 -1 = 1.051161897881733 -1 =0.051161897881733 = j
Thus for 13 annual payments with annual interest j gives a compounded amount after 14 years, plus the last payment which does not earn interest
FV2 = A((1+j)^n-1)/j
= 1200((1.051161897881733)^13-1)/(0.051161897881733)+1200
= 22613.34
Summary
Total investments:
Yolanda = 12*100*14 = 16800
Zach = 1200 * 14 = 16800
So both investors have invested $16800 over the 14 year period.
Since Yolanda achieves a higher future value after 14 years ($24259.83) over that of Zach ($22613.34), financially Yolanda has a better strategy.
Note:
If zach had invested annually at the beginning of the year, he would have obtained:
A((1+j)^n-1)/j
= 1200((1.051161897881733)^14-1)/(0.051161897881733)
= 24908.88
which is superior over Yolanda's return.
John is going for a walk. He walks for 6.4 miles at a speed of 2 miles per hour. For how many hours does he walk?
Answer:
t = d/s
t = 6.4 / 2 miles
t = 3.2 miles
Step-by-step explanation:
follow me plzzz
Help pls any kind soul pls help
Answer:
3x
Step-by-step explanation:
If Dan is x years old and Olly is 3 times as old, that means that Olly's age is 3 * x or 3x for short.
Answer:
3x
Step-by-step explanation:
If Dan is x years old and Olly is 3 times old as Dan, then the expression is 3x.
26.355 rounded to the nearest hundredth tell anser
Answer:
26.36
Step-by-step explanation:
Hundredths are the second decimal place from the decimal. You would round up to 26.36 because the number before that is up to 5. If it was below 5 you would round down to 26.35.
Find the value of X.
Answer:
x = 4√5
Step-by-step explanation:
The triangles are all similar, so corresponding lengths are proportional.
hypotenuse/short side = x/5 = (11+5)/x
x^2 = 80 . . . . cross multiply
x = 4√5 ≈ 8.94427
Can you please help me solve thanks step by step
Answer:
40 degrees
Step-by-step explanation:
We know the entire angle of ABD is 70 and CBD and ABC are in it.
Since we know one of them (CBD) is 30, we can subtract 30 from 70 to find ABC. This is because the angle of ABC and CBD equal ABD.
30 + x = 70
-30 from both sides
x = 40
Triangle L M N is shown. Angle L M N is a right angle. Angles N L M and L M N are 45 degrees. The length of L N is x. Which statements are true regarding triangle LMN? Check all that apply. NM = x NM = LM = x StartRoot 2 EndRoot tan(45°) = StartFraction StartRoot 2 EndRoot Over 2 EndFraction tan(45°) = 1
Answer:
A.) NM= x
C.) LM = x√2
E.) tan (45°) = 1
Step-by-step explanation:
If the legs are both x, then the hypotenuse is equal to [tex]x\sqrt{2[/tex]
Therefore, LM= [tex]x\sqrt{2[/tex] is correct and MN= x
Disclaimer: The sum is done according to the picture attached as the question given is wrong.
The true statements regarding the given isosceles right triangle ΔLMN are:
NM = xLM = x√2tan 45° = 1.What are isosceles right triangles?An isosceles triangle is a triangle where two sides and their corresponding angles are equal.
A right triangle is a triangle with one angle = 90°.
An isosceles right triangle is a right-angled triangle with two legs including the right angle are equal. Their corresponding angles are equal and each of them = 45°. So, the three angles of an isosceles right triangle are 45°, 45°, and 90°, always.
How do we solve the given question?In the figure, we can see that we have a ΔLMN, with ∠L = 45°, ∠M = 45°, and ∠N = 90°. Also, we can see that LN = x.
The given angles of ΔLMN determine that it is an isosceles right triangle with a right angle at N.
Since, the two legs involving the right angle, that is N, are equal, we can say that, NM = LN = x.
The hypotenuse of the ΔLMN, that is the side opposite to ∠N, that is LM, can be found using the Pythagoras theorem, by which in a right-angled triangle,
Hypotenuse² = Base² + Perpendicular².
∴ LM² = LN² + NM² = x² + x² = 2x².
or, LM = √(2x²) = x√2.
The tangent of an angle ∅, that is, tan ∅ is computed using the formula,
tan ∅ = Perpendicular/Base.
To calculate tan 45°, that is, tangent to ∠L, we take Perpendicular = NM and Base = LN.
∴ tan 45° = NM/LN = x/x = 1.
Now, we check all the given options:
NM = x. TRUE (computed)NM = x√2. FALSE (∵ NM = x)LM = x√2. TRUE (computed)tan 45° = √2/2. FALSE (∵ tan 45° = 1)tan 45° = 1. TRUE (computed)∴ The true statements regarding the given isosceles right triangle ΔLMN are:
NM = xLM = x√2tan 45° = 1.Learn more about isosceles right triangle at
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Any help would be greatly appreciated
Answer: (-3, -2)
Step-by-step explanation:
Plug in -2 for y to find x
x - 5(-2) = 7
Multiply -5 and -2
x + 10 = 7
Subtract 10 from both sides
x = -3
The first ordered pair is (-3, -2)
Which expression is not requivalent to
3x - 2?
Answer:
anything that is not -2+3x or x=2/3 is wrong
Step-by-step explanation:
6th grade math , help me please :D
Answer:
a) 6t
b) 6q
c) 8a
d) 2r + 22y
Step-by-step explanation:
a) 6t = 2t +4t
b) 6q = 7q + q-2q
c) 8a = 6-6+8a
d) 2r + 22y = 12r + 10y - 10r +12y
good luck!!
A right rectangular prism is packed with cubes of side length 1 inch. If the prism is packed with 16 cubes along the length, 8 cubes along the width and 6 cubes
8
along the height, what is the volume of the prism?
Answer: 768 cubic inches.
Step-by-step explanation:
V= L * W *H
V = 16 * 8 * 6
V= 768
You want to order carpet for an area in your house. The room measures 12 feet by 10 feet. Remember, Area = Length × Width. If each square yard of carpet costs $30.25, how much will the carpet cost you? Use your answer from the previous question to answer this question.
Answer:
402.9 $
Step-by-step explanation:
first you must turn foot into yards "every 3 foot = 1 yard"
3.33 , 4
then we will use the area=length x width formula
3.33 x 4 = 13.32 square yards
the cost of the carpet is
13.32 x 30.25 = 402.9$
Please help me I will mark BRAINLIEST THANK YOUUUUU
Answer:
33%
Step-by-step explanation:
The multiples of 3 are 3,6,9,12
Sum is 6+14+12+1 = 33
The total is 3+6+8+11+14+16+15+12+9+5+1=100
The experimental probability is number of multiples of 3 over the total
33/100 = 33%
Chris placed $7,400 in a savings account which compounds interest annually at a rate of 5.7%. How much will he have in the account after 4 years?
Answer:$9237.02
Step-by-step explanation:
A = p(1+r/n)^nt
A = 7400 (1 + 0.057)^4
A = 7400(1.057)^4
A = 9237.02
Do not add the .02 at the end of this answer
ial
What should be her first step?
isolating the constant 1
adding 4 to both sides of the equation
O isolating the second term, -4x
O adding 1 to both sides of the equation
Answer:
Fiona is completing the square to solve the polynomial equation.
x2 – 4x + 1 = 0
What should be her first step?
CORRECT--->>> 1) isolating the constant 1
2) adding 4 to both sides of the equation
3) isolating the second term, –4x
4) adding 1 to both sides of the equation
Step-by-step explanation:
EDGE 2021
The correct first step is to add 7 on both sides of the equation.
Option B is the correct answer.
We have,
To solve the equation 3x - 7 = 8, the first step is to add 7 on both sides of the equation.
We can also solve the equation as:
3x - 7 = 8
Adding 7 on both sides.
3x - 7 + 7 = 8 + 7
3x = 15
Dividing 3 on both sides.
x = 15/3
x = 5
Therefore,
The correct first step is to add 7 on both sides of the equation.
Learn more about equations here:
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The complete question:
Solve the equation 3x - 7 = 8.
What should be your first step?
O Isolating the constant term, -7
O Adding 7 to both sides of the equation.
O Isolating the second term, 3x.
O Subtracting 8 from both sides of the equation.
Which expression is equivalent to x + y + x + y + 3(y + 5)?
Answer:
2x + 5y + 15
Step-by-step explanation:
Step 1: Combine like terms
2x + 2y + 3(y + 5)
Step 2: Distribute
2x + 2y + 3y + 15
Step 3: Combine like terms
2x + 5y + 15
Answer: 2x + 5y + 15
Step-by-step explanation:
Which expression is equivalent to x + y + x + y + 3(y + 5)?
3) The fastest train on Earth, the TGV from France, can travel at faster speeds than trains in the
United States. During a speed test, the train traveled 8.0 x 10^2 miles in 2.5 hours. Compute the
speed of the train. (Try solving this problem using scientific notation.)
Answer:
[tex]3.2*10^2=320[/tex] mph
Step-by-step explanation:
hello,
it travels [tex]8.0*10^2[/tex] miles in 2.5 hours
So in 1 hours it travels
[tex]\dfrac{8.0*10^2}{2.5}=3.2*10^2[/tex]
miles
hope this helps
2. Ricardo descended to a depth of 24 feet
below sea level. His friend Martin
descended 3 times as far. Write the
depth of Martin's descent as an integer.
Answer:
-72
Step-by-step explanation:
3*24=72
So he is 72 foot below see level or -72
Martin descended to a depth of 72 feet below sea level.
How to calculate the integerRicardo descended to a depth of 24 feet below sea level. His friend Martin descended 3 times as far.
If Ricardo descended to a depth of 24 feet below sea level, and Martin descended three times as far, we can calculate Martin's descent by multiplying Ricardo's depth by 3.
Martin's depth = Ricardo's depth * 3
Martin's depth = 24 feet * 3
Martin's depth = 72 feet
Therefore, Martin descended to a depth of 72 feet below sea level.
Learn more about integer
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Convert 58% to a decimal
Answer: 0.58
Step-by-step explanation: To write a percent as a decimal, first remember that a percent is a ratio that compares a number to 100.
So we can think of 58% as the ratio 58 to 100 or 58/100.
Dividing by 100 moves the decimal point 2 places to the left so 58/100 would move the decimal point 2 places to the left which would give us .58 or 0.58. So 58% can be written as the decimal 0.58.
I NEED HELP PLEASE, THANKS!
As we are not being asked to draw this component form, it makes things a bit more simple. Take the following points that we are given, ( 8, - 2 ) and ( - 2, - 2 ) and consider them in the form ( P1, P2 ) and ( Q1, Q2 ). To determine this component form, you would have to subtract P1 and Q1, P2 and Q2 - or vice versa -
[tex]( 8 - ( - 2 ) ), ( - 2 - ( - 2 ) \\( 10, 0 )\\< 10, 0 >[/tex]
Solution = Option A