Answer:
Range:
UCL = 4.73
LCL = 18.08
MEAN :
UCL = 27.115
LCL = 31.219
Step-by-step explanation:
Given the data:
The mean and range of each sample :
Sample __ Thread wear __ xbar __ R
1 ___31 __ 42 ___ 28 ____ 33.67 _14
2___ 26 _ 18 ____35____ 26.33 _17
3___25 __30 ___ 34____29.67 _ 9
4 __ 17 __ 25 ___ 21 _____ 21 ___ 8
5 __ 38 _ 29 ___ 35 _____ 34 __ 9
6 __ 41 __42 ___36 _____39.67_ 6
7 __ 21 __ 17 ___29 _____22.33 _12
8 __ 32 __26___28 ____ 28.67 _ 6
9 __ 41 __ 34 __ 33 ______ 36 __8
10__29___17___30 _____25.33_ 13
11 __26 __ 31 __ 40 _____32.33_ 14
12__23 __ 19 __ 45 _____12.33 __6
13 __17 __ 24 __ 32_____24.33__15
14 __43__ 35___17_____ 31.67 _ 26
15__18 ___25__ 29_____ 24 ___ 11
16__30___42___31 ____34.33__ 12
17__28___36 __ 32____ 32 ____8
18__40 __ 29 __ 31 ____33.33 __ 11
19__18 ___29__ 28____ 25 ____11
20_ 22 __ 34 __ 26 ___ 27.33 __12
Size per sample, sample size, n = 3
Number of samples, k = 20
We calculate the sample mean and range average :
Sample mean, x-- = Σxbar/n = 29.167
Range average, Rbar = ΣR/n = 11.4
The mean control limit :
x-- ± A2Rbar
From the x chart ;
A2 for n = 20 is A2 = 0.180
29.167 ± 0.180(11.40)
LCL = 29.167 - 0.180(11.40) = 27.115
UCL = 29.167 + 0.180(11.40) = 31.219
The Range control limit :
Rbar(1 ± 3(d3/d2))
From the R-chart :
d2 at n = 20 ; d2 = 3.735
d3 at n = 20 ; d3 = 0.729
LCL = 11.40(1 - 3(0.729/3.735)) = 4.725
UCL = 11.40(1 + 3(0.729/3.735)) = 18.075
To determine the organic material in a dried lake bed, the percent carbon by mass is measured at two different locations. To compare the means of the two different locations, it must first be determined whether the standard deviations of the two locations are different. For each location, calculate the standard deviation and report it with two significant figures.
Answer:
[tex]\sigma_1 = 0.08[/tex] --- Location 1
[tex]\sigma_2 = 0.34[/tex] --- Location 2
Step-by-step explanation:
Given
See attachment for the given data
Required
The standard deviation of each location
For location 1
First, calculate the mean
[tex]\bar x_1 =\frac{\sum x}{n}[/tex]
So, we have:
[tex]\bar x_1 =\frac{30.40+30.20+30.30+30.40+30.30}{5}[/tex]
[tex]\bar x_1 =\frac{151.60}{5}[/tex]
[tex]\bar x_1 =30.32[/tex]
The standard deviation is calculated as:
[tex]\sigma_1 = \sqrt{\frac{\sum(x - \bar x_1)^2}{n-1}}[/tex]
[tex]\sigma_1 = \sqrt{\frac{(30.40 - 30.32)^2+(30.20 - 30.32)^2+(30.30 - 30.32)^2+(30.40 - 30.32)^2+(30.30 - 30.32)^2}{5-1}}[/tex]
[tex]\sigma_1 = \sqrt{\frac{0.028}{4}}[/tex]
[tex]\sigma_1 = \sqrt{0.007}[/tex]
[tex]\sigma_1 = 0.08[/tex]
For location 2
First, calculate the mean
[tex]\bar x_2 =\frac{\sum x}{n}[/tex]
So, we have:
[tex]\bar x_2 =\frac{30.10+30.90+30.20+30.70+30.30}{5}[/tex]
[tex]\bar x_2 =\frac{152.2}{5}[/tex]
[tex]\bar x_2 =30.44[/tex]
The standard deviation is calculated as:
[tex]\sigma_2 = \sqrt{\frac{\sum(x - \bar x_2)^2}{n-1}}[/tex]
[tex]\sigma_2 = \sqrt{\frac{(30.10-30.44)^2+(30.90-30.44)^2+(30.20-30.44)^2+(30.70-30.44)^2+(30.30-30.44)^2}{5-1}}[/tex]
[tex]\sigma_2 = \sqrt{\frac{0.472}{4}}[/tex]
[tex]\sigma_2 = \sqrt{0.118}[/tex]
[tex]\sigma_2 = 0.34[/tex]
Which one is a better deal?
a 3 pack of notebooks for $4.50
Or a 12 pack of notebooks for $15.00
Two cities,a and are mapped on the coordinate plane. How far apart are they from each other?
Answer:
[tex]\sqrt{97} \\ \sqrt{9^{2}+4^{2} }[/tex]
Step-by-step explanation:
Gemma recently rode her bicycle to visit her friend who lives 6 miles away. On her way there, her average speed was 16 miles per hour faster than on her way home. If Gemma spent a total of 1 hour bicycle, find the two rates.
first speed --- x mph
return speed -- x+16 mph
6/x + 6/(x+16) = 1
times each term by x(x+16)
6(x+16) + 6x = x(x+16)
x^2 + 4x - 96 = 0
(x-8)(x+12) = 0
x = 8 or x is a negative
her first speed was 8 mph
her return speed was 24 mph
check:
6/8 + 6/24 = 1 , that's good!
Marina spent $13.50 at the grocery store. She bought pears, kiwis, and pineapples. Pears cost $0.50 each, pineapples cost $1.50 each, and kiwis are $0.30 each.How many of each kind did she buy if she bought 9 more pears than pineapples and 2 fewer kiwis than pears? Branliest if correct.
Answer:
Number of pineapples = 10
Number of pears = 10 + 9 = 19
Number of kiwis = 10 - 2 = 8
Step-by-step explanation:
Money = $ 13.5
Cost of a pear = $ 0.5
Cost of a pineapple = $ 1.5
Cost of a kiwi = $ 0.3
let the number of pineapple = p
Number of pears = p + 9
Number of kiwis = p - 2
Cost is
0.5 (p + 9) + 0.15 p + 0.3 (p - 2) = 13.5
0.5 p + 4.5 + 0.15 p + 0.3 p - 0.6 = 13.5
0.95 p = 9.6
p = 10
So, number of pineapples = 10
Number of pears = 10 + 9 = 19
Number of kiwis = 10 - 2 = 8
Answer:
3 pineapples 12 pears 10 kiwis
Joanne's monthly salary is $2400.she spend's ⅒ of it on food and ⅜ of it on leisure activities.How much does she have left?
Answer:
1200$
please mark me as brain liest
Which of the following must be equal to 30% of x?
3x
(A)
1,000
3x
(B)
100
3x
(C)
10
(D) 3x
Answer:
You can go ahead with option D
Step-by-step explanation:
30% of x will be 3xdetermine lcm and HCF of 24 and 26 using prime factors
Answer:
WHAT IS THE FACTOR?
Step-by-step explanation:
I need help with three
Answer:
A and F
Step-by-step explanation:
A and F both represent instances of division of 14/5
B represent multiplication
C represent the reciprocal of the problem, 5/14
D represent addition
There are 16 tablespoons in one cup. Which table correctly relates the number of cups to the number of tablespoons?
Answer:
The first table.
Step-by-step explanation:
1 cup = 1 * 16 = 16 tablespoons
2 = 2 * 16 = 32
3 = 3*16 = 48
4 = 4*16 = 64 and so on....
Create your own proportion problems?
Answer:
See Explanation
Step-by-step explanation:
Required
Proportion problems
An example is:
y is directly proportional to x such that: y=4 when x = 2;
Derive the equation
For direct proportions, we have:
[tex]y\ \alpha\ x[/tex]
This gives:
[tex]y = kx[/tex]
Make k the subject
[tex]k = y/x[/tex]
So:
[tex]k = 4/2 =2[/tex]
So, the equation is:
[tex]y = kx[/tex]
[tex]y = 2x[/tex]
Assume the above question is for inverse proportion
The variation will be:
[tex]y\ \alpha\ \frac{1}{x}[/tex]
This gives:
[tex]y\ = \frac{k}{x}[/tex]
Make k the subject
[tex]k =x*y[/tex]
[tex]k =2* 4 = 8[/tex]
So, the equation is:
[tex]y\ = \frac{k}{x}[/tex]
[tex]y = \frac{8}{x}[/tex]
F(x) = x/2*8 what is f(x), when x=10
Answer
13
Step-by-step explanation:
We are essentially being asked to find f(10), so let's evaluate this function at 10 by plugging this in for x.
f(10)=10/2+8=5+8=13
Answer:
f(x) = 40
Step-by-step explanation:
f(x) = x / 2 * 8
x = 10
f(x) = (10 / 2) * 8
= 5 * 8
= 40
Given: x + 2 < -5.
Choose the solution set.
{x | x R, x < -3}
{x | x R, x < 3}
{x | x R, x < -7}
{x | x R, x < 7}
Answer:
C
Step-by-step explanation:
x + 2 < -5
x < - 5 - 2
x < - 7
Answer:
{x| x R, x<-7}
Step-by-step explanation:
=> x+2<-5
=> x<-5-2
=> x<-7
Find the values of x for which the denominator is equal to zero for y=x^2/x^2+1 .
Answer:
Step-by-step explanation:
I assume that you mean y = x²/(x²+1), not y = x²/x²+1.
x²+1 = 0
x² = -1
x = ±√(-1) = ±i
deleted: deleted by user
Please give me a 100% correct answer
A ship sailed 30 kilometers in 172 hours. What was its rate in kilometers per hour?
(1) 20
(2) 30
(3) 45
(4) 90
(5) Not enough information is given.
Answer:
See edit
A 20 km / hour
Step-by-step explanation:
The exact answer is 30 km / 172 which is less than 1 km / hr. Since that answer isn't offered, I suspect there is something wrong with the question. If there is a decimal after the 1 in 172 you would get 17.44 km / hr. That's roughly A.
If the decimal is not there, I think you should either resubmit the question or answer A.
Edit
The note said (below) that the ship went 30 km in 1 1/2 hours.
Rate = distance / time
distance = 30 km
time = 1 1/2 hours = 1.5 hours
rate = 30 / 1.5 = 20 km / hr
oludonts c) 2x + y = 2
2x + 2y = 0
Answer:
[tex]x = 2[/tex]
[tex]y = -2[/tex]
Step-by-step explanation:
Given
[tex]2x + y = 2[/tex]
[tex]2x + 2y = 0[/tex]
Required
Solfe for x and y
Subtract both equations
[tex]2x- 2x + y - 2y = 2 -0[/tex]
[tex]-y = 2[/tex]
Divide by -1
[tex]y = -2[/tex]
Substitute [tex]y = -2[/tex] in [tex]2x + 2y = 0[/tex]
[tex]2x+2 *-2 = 0[/tex]
[tex]2x-4 = 0[/tex]
[tex]x - 2 = 0[/tex]
Collect like terms
[tex]x = 2[/tex]
Helppp and explain!!!
PLEASE I NEED HELP!!
Answer:
it is (4,120)
hope this helps you
what is the equation of the directx for the following parabola -8(x-5)=(y+1)^2
Answer:
x=7
Step-by-step explanation:
The directrix of a parabola is the vertical line found by subtracting
p from the x-coordinate h
of the vertex if the parabola opens left or right.
x=h-p
Substitute the known values of
p and h
into the formula and simplify.
x=7
A field book is a private notepad used by a surveyor to transcribe notes and is not considered a legal document True False
Answer:
False
Step-by-step explanation:
A field book is a private notepad used by a surveyor to record measurements and notes.
Basically, the size of a field book is 200 millimeters × 120 millimeters (20 centimeters × 12 centimeters) and it's typically opened lengthwise. There are two (2) main types of field book and these includes;
I. Double-line field book.
II. Single-line field book.
As a general rule, it's best that all findings, entries (notes) and observations are recorded or made into a field book after each and every measurement have been taken by a surveyor.
In conclusion, a field book is considered to be a legal document used by surveyors to keep records of accomplished field work or work done in the field. Thus, it's not a private notepad used by a surveyor to transcribe notes.
Answer:
False
Step-by-step explanation:
A field book is a private notepad used by a surveyor to transcribe notes and is not considered a legal document is False.
1). A population of 20 rabbits is released into a wildlife region. The population is growing at a rate of 60% per year.
A) the General Equation from the Video was: P(x) = (blank)
What is the population of rabbits after 5 years?
B) the Evaluated equation I used to get the following answer is (blank)
and After five years there will be(blank)
rabbits.
And What is the population of rabbits after 8 years?
c) the Evaluated equation I used to get the following answer is(blank)
and After eight years there will be(blank)
rabbits.
Answer:
(a) A = 20(1.6)^t
(b) 210 rabbits
Step-by-step explanation:
Initial number of rabbits = 20
rate of growth, R = 60 % annually
(A) The general equation is
[tex]A = P \left ( 1+\frac{R}{100} \right )^t\\\\A = 20\left ( 1+\frac{60}{100} \right )^t\\\\A = 20 (1.6)^t[/tex]
(B) Let the time, t = 5 years
So, the population after 5 years is
[tex]A = 20 (1.6)^5\\\\A = 209.7 = 210 rabbits[/tex]
State the final conclusion in simple nontechnical terms.
Original claim: The proportion of male golfers is less than 0.6.
Initial conclusion: Fail to reject the null hypothesis.
Which of the following is the correct conclusion?
A. There is suffficient evidence to support the claim that the proportion of male golfers is less than 0.6.
B. There is not sufficient evidence to support the claim that the proportion of male golfers is less than 0.6.
Answer:
B. There is not sufficient evidence to support the claim that the proportion of male golfers is less than 0.6.
Step-by-step explanation:
The proportion of male golfers is less than 0.6.
At the null hypothesis, we test if the proportion is of at least 0.6, that is:
[tex]H_0: p \geq 0.6[/tex]
At the alternative hypothesis, we test if the proportion is of less than 0.6, that is:
[tex]H_1: p < 0.6[/tex]
Fail to reject the null hypothesis.
This means that there is not sufficient evidence to conclude that the proportion is less than 0.6, and thus the correct answer is given by option B.
On Monday, Ray had $153.75 in his bank account. On Tuesday, he withdrew $71.00 from his account. After depositing #292.50 on Wednesday, how much money did Ray have in his account
Answer:
$375.25
Step-by-step explanation:
[tex]===========================================[/tex]
Withdrew- taking out money (-)
Deposit- putting in money (+)
[tex]===========================================[/tex]
Ray started off with 153.75. He withdraws (-) 71.
[tex]153.75-71=82.75[/tex]
Then he deposits (+) 292.5.
[tex]82.75+292.5=375.25[/tex]
That's your answer!
I hope this helps ❤
Tell whether the following two triangles can be
proven congruent through SAS.
A.Yes, the two triangles are congruent
because two sides and their included
angle are congruent in both triangles.
B.No, the two triangles don't have
corresponding sides marked congruent.
C. Yes, the two triangles are congruent because they’re both right triangles.
D.No, the two triangles can only be proven congruent through SSA.
Answer:
B. No, the two triangles don't have
corresponding sides marked congruent.
A radioactive material is known to decay at a yearly rate proportional to the amount at each moment. There were 1000 grams of the material 10 years ago. There are 980 grams right now. What will be the amount of the material right after 20 years
Answer:
x = 960.4
Step-by-step explanation:
980 = 1000[tex]e^{kt}[/tex]
.98 = [tex]e^{10 k}[/tex]
ln(.98) = 10k ln(e)
k = ln(.98)/10
k=-0.00202
~~~~~~~~~~~~~~
x = 1000[tex]e^{20 *-.00202}[/tex]
x = 960.4
The amount of the material right after 20 years will be x = 960.4.
What is an exponential expression?Powers can simply be expressed in concise form using exponential expressions. The exponent shows how many times the base has been multiplied. Since 2 is the "base" and 5 is the "exponent," it can be represented as 2x2x2x2=25 for the number 32. This phrase should be understood as "two to the fifth power."
Given that radioactive material is known to decay at a yearly rate proportional to the amount at each moment. There were 1000 grams of the material 10 years ago. There are 980 grams right now.
The amount of the material will be calculated as,
980 = 1000
[tex]0.98 = e^{10k}[/tex]
ln(.98) = 10k ln(e)
k = ln(.98)/10
k=-0.00202
The value after 20 years will be,
[tex]x = 1000e^{20\times 0.00202}[/tex]
x = 960.4
Therefore, the amount of the material right after 20 years will be x = 960.4.
To know more about an exponential expression follow
https://brainly.com/question/2456547
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If there is a 90% chance of rain tomorrow and a 70% chance of wind and rain,
what is the probability that it is windy, given that it is rainy? Round your
answer to the nearest percent.
Answer:
78%
Step-by-step explanation:
the chance of rain
P(R) = 0.9
the chance of wind and rain
P(R∩ W) = 0.7
The probabilities of windy weather is
P(W) = [tex]\frac{P(RW)}{P(R)} =\frac{0.7}{0.9} =0.78[/tex]
The correct answer is B) 78%
Kim ran 9/10 of a mile. Adrian ran 3/5 of a mile Adrian claims that Kim ran 1 3/10 times farther than him Kim says that she actually ran 1/2 times farther than Adrian who is correct
9514 1404 393
Answer:
Kim
Step-by-step explanation:
The ratio of Kim's distance to Adrian's distance is ...
(9/10)/(3/5) = (9/10)/(6/10) = 9/6 = 3/2 = 1.5
__
You need to be very careful with the wording here. Kim ran 1 1/2 times as far as Adrian. That is, she ran Adrian's distance plus 1/2 Adrian's distance.
If we take the wording "1/2 times farther" to mean that 1/2 of Adrian's distance is added to Adrian's distance, then Kim is correct.
_____
In many Algebra problems, you will see the wording "k times farther" to mean the distance is multiplied by k. If that interpretation is used here, neither claim is correct, as Kim's distance is 1 1/2 times farther than Adrian's.
On the other hand, if the value of "k" is expressed as a percentage, the interpretation usually intended is that that percentage of the original distance is added to the original distance. Using this interpretation, Kim's distance is 50% farther than Adrian's. (Note the word "times" is missing here.)
__
Since Adrian ran 1 5/10 the distance Kim ran, Adrian's claim is incorrect regardless of the interpretation. If you require one of the two to be correct, then Kim is.
Which function is the result of translating f(x)=x^2+14 to the right 5 units and down 6 units
The list of ingredients for chocolate brownies given at right will make 16 brownies. Use the list to decide how much of each ingredient is needed to make 6 brownies.
Given: Given that for 16 brownies we need
Butter- [tex]\frac{2}{3}[/tex] cups
unsweetened chocolate-5 ounces
sugar-1-1/2 cup
vanilla-2 teaspoons
eggs-2
flour- 1 cup
To find: The amount of ingredients to make 6 brownies.
Solution: The amount we need to make 6 brownies is,
Butter
[tex](\frac{2}{3}.16)/6\\=0.25125 cups[/tex]
unsweetened chocolate
[tex]\frac{5.6}{16}\\=\frac{30}{16}[/tex]ounces
sugar-0.5625 cup
vanilla-[tex]\frac{12}{16}[/tex]teaspoons
eggs-[tex]\frac{12}{16}[/tex]
flour- [tex]\frac{6}{16}[/tex] cup
37. Two numbers are such that their
difference, their sum and their
product are in the ratio 1:7: 24.
Find the product of the
number.
Answer:
8 and 6
Step-by-step explanation:
Two numbers are such that their difference, their sum, and their product are to
each other as 1:7:24. Their product must equal what number?
:
Two numbers a & b
Let x = the multiplier
:
a - b = 1x
a + b = 7x
a * b = 24x
:
Add the 1st two equations
a - b = x
a + b = 7x
2a = 8x
a = 4x
or
x = .25a
:
a * b = 24x
Replace 24x; a = 4x therefore:
a * b = 6a
b = 6
;
Using the 1st equation
a - b = 1x
Replace b with 6 and x with .25a
a - 6 = .25a
a - .25a = 6
.75a = 6
a =
a = 8
:
Find the multiplier
a - b = x
8 - 6 = 2
:
Check this
a - b = 2 (1*2)
a + b = 14; (7*2)
a * b = 48: (24*2)
:
The numbers are 8 and 6; their products = 48
