Complete Question
Problem 7.43
A chemical plant superintendent orders a process readjustment (namely shutdown and setting change) whenever the pH of the final product falls below 6.92 or above 7.08. The sample pH is normally distributed with unknown mu and standard deviation 0.08. Determine the probability:
(a)
of readjusting (that is, the probability that the measurement is not in the acceptable region) when the process is operating as intended and [tex]\mu[/tex] = 7.0 probability
(b)
of readjusting (that is, the probability that the measurement is not in the acceptable region) when the process is slightly off target, namely the mean pH is [tex]\mu[/tex] = 7.02
Answer:
a
The value is [tex]P(X < 6.92 or X > 7.08 ) = 0.26431 [/tex]
b
The value is [tex]P(X < 6.92 or X > 7.08 ) = 0.29344 [/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 7.0[/tex]
The standard deviation is [tex]\sigma = 0.08[/tex]
Considering question a
Generally the probability of readjusting when the process is operating as intended and mu 7.0 is mathematically represented as
[tex]P(X < 6.92 or X > 7.08 ) = P(X < 6.92 ) + P(X > 7.08)[/tex]
=> [tex]P(X < 6.92 or X > 7.08 ) = P(\frac{X - \mu }{\sigma} < \frac{6.9 - 7}{0.08} ) + P(\frac{X - \mu}{\sigma} > \frac{7.08 - 7}{0.08} )[/tex]
Generally
[tex]\frac{X - \mu }{\sigma} = Z(The \ standardized \ value \ of \ X)[/tex]
So
=> [tex]P(X < 6.92 or X > 7.08 ) = P(Z < \frac{6.9 - 7}{0.08} ) + P(Z > \frac{7.08 - 7}{0.08} )[/tex]
=> [tex]P(X < 6.92 or X > 7.08 ) = P(Z < -1.25) + P(Z > 1 )[/tex]
From the z table the probability of (Z < -1.25) and (Z > 1 ) is
[tex]P(Z < -1.25) = 0.10565[/tex]
and
[tex]P(Z > 1 ) = 0.15866[/tex]
So
=> [tex]P(X < 6.92 or X > 7.08 ) = 0.10565 + 0.15866 [/tex]
=> [tex]P(X < 6.92 or X > 7.08 ) = 0.26431 [/tex]
Considering question b
Generally the probability of readjusting when the process is operating as intended and mu 7.02 is mathematically represented as
[tex]P(X < 6.92 or X > 7.08 ) = P(X < 6.92 ) + P(X > 7.08)[/tex]
=> [tex]P(X < 6.92 or X > 7.08 ) = P(\frac{X - \mu }{\sigma} < \frac{6.9 - 7.02}{0.08} ) + P(\frac{X - \mu}{\sigma} > \frac{7.08 - 7.02}{0.08} )[/tex]
Generally
[tex]\frac{X - \mu }{\sigma} = Z(The \ standardized \ value \ of \ X)[/tex]
So
=> [tex]P(X < 6.92 or X > 7.08 ) = P(Z < \frac{6.9 - 7.02}{0.08} ) + P(Z > \frac{7.08 - 7.02}{0.08} )[/tex]
=> [tex]P(X < 6.92 or X > 7.08 ) = P(Z < -1.5) + P(Z > 0.75 )[/tex]
From the z table the probability of (Z < -1.5) and (Z > 0.75 ) is
[tex]P(Z < -1.5) = 0.066807[/tex]
and
[tex]P(Z > 0.75 ) = 0.22663[/tex]
So
=> [tex]P(X < 6.92 or X > 7.08 ) = 0.066807 + 0.22663 [/tex]
=> [tex]P(X < 6.92 or X > 7.08 ) = 0.29344 [/tex]
Two times the reciprocal of a number equals 16 times the reciprocal of 20. Find the number. (1 point)
Let the number be x .
Reciprocal of x :-
[tex] = \frac{1}{x} [/tex]
An equation to find x :-
[tex]2 \times \frac{1}{x} = 16 \times \frac{1}{20} [/tex]
[tex] \frac{2}{x} = \frac{16}{20} [/tex]
[tex]16 \times x = 20 \times 2[/tex]
[tex]16x = 40[/tex]
[tex]x = \frac{16}{40} [/tex]
[tex]x = \frac{4}{10} [/tex]
[tex]x= \frac{4 \div 2}{10 \div 2} [/tex]
[tex]x = \frac{2}{5} [/tex]
Reciprocal of x :-
[tex] = \frac{5}{2} [/tex]
Which means the number :-
[tex] = \frac{5}{2} [/tex]
We can check it by :-
[tex]2 \times \frac{2}{5} = \frac{16}{20} [/tex]
[tex] \frac{4}{5} = \frac{16}{20} [/tex]
[tex] \frac{4}{5} = \frac{16 \div 4}{20 \div 4} [/tex]
[tex] \frac{4}{5} = \frac{4}{5} [/tex]
LHS = RHS
Which means we have found the correct number .
Therefore , the value of the number , whose reciprocal multiplied by 2 gives 16 times the reciprocal of 20 is :-
[tex] = \frac{5}{2} [/tex]
Helppppppp plzzzzzzzzzxzxzmfyfdtidt
Answer:
y=7
Step-by-step explanation:
Distribute: 9y-4y-4=31
Add like terms: 5y-4=31
Isolate: 5y=35
Divide each side by 5: y=7
ANSWER: y=7
Hope this helps
1
2
How did Buddhism change as it spread throughout Asia?
Buddhism became less focused on seeking enlightenment.
Buddhism combined with Hinduism to create a new religion.
Buddhism split into three groups based on the places where it spread.
Buddhism adopted Christian and Islamic teachings to reach a wider audience.
Answer:
Buddhism split into three groups based on the places where it spread.
Step-by-step explanation:
Answer:
Buddhism split into three groups based on the places where it spread.
Step-by-step explanation:
Jason inherited a piece of land from his great-uncle. Owners in the area claim that there is a 45% chance that the land has oil. Jason decides to test the land for oil. He buys a kit that claims to have an 80% accuracy rate of indicating oil in the soil. What is the probability that the land has oil and the test predicts it?
A.
0.09
B.
0.11
C.
0.36
D.
0.44
Answer:
0.36
Step-by-step explanation:
0.45 x 0.80
= 0.36
if the crab 5ft below sea level and the cliff is 3ft above the sea level what is the distance between them?
8ft is the dstance between them.
5+3 = 8
Sharon wants to open a checking account from which to pay bills. She wants online services, and a debit card, which both banks provide for free. Based upon past experience, she expects to accidentally overdraft the account 1 time per year, due to unexpected charges and miscommunications. She expects no 2nd copies of statements, and to use network ATMs 4 times per month with either bank. She has $3300 in an emergency savings account at First State Bank, and thinks that the balance will be enough to cover overdrafts in the future if automatic transfers are made when needed.
Answer:
a.No, Common Bank will save Sharon more money.
Step-by-step explanation:
There are two banks i.e. first state bank and the common bank that should be compared in the table depend upon the prices of both the banks
On seeing it we get to know that the first state bank would charged a fee on a monthly basis i.e. $4 while on the other hand the common bank has no fee on the monthly basis
Also the unsufficient bonds are more cheaper in the common bank if we compared with the first state bank
Moreover, the $7 is charged in the first state bank and $3 charged in the common bank.
Therefore the common bank would become cheaper
Hence, the correct option is a.
Answer:
Sharon wants to open a checking account from which to pay bills. She wants online services, and a debit card, which both banks provide for free. Based upon past experience, she expects to accidentally overdraft the account 1 time per year, due to unexpected charges and miscommunications. She expects no 2nd copies of statements, and to use network ATMs 4 times per month with either bank. She has $3300 in an emergency savings account at First State Bank, and thinks that the balance will be enough to cover overdrafts in the future if automatic transfers are made when needed.
A 4-column table with 5 rows. Column 1 is labeled First State Bank with entries monthly fee, non-sufficient funds fee, second copy of statement, network A T M usage, non-sufficient funds protection from a First State Bank savings account. Column 2 is labeled Description with entries 4 dollars, 36 dollars, 7 dollars, 3 dollars each transaction, 4 dollars on each day that a transfer occurs to cover an overdraft. Column 3 is labeled Common Bank with entries monthly fee, non-sufficient funds, second copy of statement, network A T M usage, non-sufficient funds protection from a Common Bank savings account. Column 4 is labeled Description with entries 0 dollars, 24 dollars, 4 dollars, 2 dollars each transaction, not offered with this account.
Based on the tables of fees, above, if Sharon chooses First State Bank, will it save her money over choosing Common Bank?
a. No, Common Bank will save Sharon more money. <<<---Correct b. Yes, First State Bank will save Sharon money. c. No, First State Bank and Common Bank would have the same costs for Sharon. d. No, costs cannot be estimated in advance, so this information cannot be used.Step-by-step explanation:
Edge 2021
If the two remote interior angles of a triangle measure 60 degrees and 38 degrees , what is the measure of the exterior angle.
Answer:x + y + z = 180
Step-by-step explanation:
How many solutions does this equation have?
7a+5(a+3) = 8a+4(a+2)
Answer:
There is no solution
Step-by-step explanation:
The football team has a total of 20 jerseys there are 10 medium sized jerseys what percent of the jerseys are medium sized jerseys
Answer:
50% of the jerseys are medium
Answer:
50% of the jerseys are medium sized.
Step-by-step explanation:
20 is 100% and half of them are medium so half of 100 is 50%
Find M<1 in the figure below. PQ and RS are parallel
Answer:
m∠1= 105°
Step-by-step explanation:
The m∠1 and 75° are supplementary angles that sum up to 180°.
The equation here would be: m∠1+75= 180.
Step 1- Subtract 75 to both sides of the equation.
m∠1+75= 180
-75 -75
m∠1= 105
Hope this helps! :)
Answer: The answer would be 105.
Step-by-step explanation:
If you look at the angle's corresponding angle, then you will see that it is right next to angle one. So the angle next to angle one is also 75 degrees because it is the same angle or the corresponding angle to the other one that is 75 degrees. So, together, angle one and the angle next to it should equal 180 degrees. So you subtract 180-75=105. And angle one equals 105.
Of 1000 randomly selected cases of lung cancer, 838 resulted in death within 10 years. Construct a 95% two-sided confidence interval on the death rate from lung cancer. (a) Construct a 95% two-sided confidence interval on the death rate from lung cancer. Round your answers to 3 decimal places. (b) Using the point estimate of p obtained from the preliminary sample, what sample size is needed to be 95% confident that the error in estimating the true value of p is less than 0.03
Answer:
0.8152 ≤ p ≤ 0.8608
579
Step-by-step explanation:
Given the following :
Samples size n = 1000
Deaths within 10 years, p = 838
α = 95%
Construction a two way confidence interval:
p ± Zα/2 * √p(1-p) / n
point estimate p = 838/n = 838/1000 = 0.838
Z0.05/2 = Z0.025 = 1.96
0.838 - 1.96√0.838(1-0.838) / 1000
0.838 - 1.96*0.0116514 = 0.8152
0.838 + 1.96√0.838(1-0.838) / 1000
0.838 + 1.96*0.0116514 = 0.8608
0.8152 ≤ p ≤ 0.8608
b) Using the point estimate of p obtained from the preliminary sample, what sample size is needed to be 95% confident that the error in estimating the true value of p is less than 0.03
Error (E) = 0.03
To find the samome size, use the relation:
n = (Zα/2 / E)² * p(1-p)
n = (1.96/0.03)² * 0.838(1-0.838)
n = (1.96/0.03)² * 0.838 * 0.162
n = 4268.4444 * 0.838 * 0.162
n = 579.46
n = 579
The square below represents one whole.
What percent is represented by the shaded area?
No. of total boxes=100
No. of total shaded boxes=85
percentage of the shaded area=85/100×100=85%
If It rained for 9.5 hours, how many inches of rain would have fallen?
Answer:
I believe the answer is 6.5 inches of rain
Step-by-step explanation:
6.33 (with 3 repeating forever) OR 6 [tex]\frac{1}{3}[/tex]
If it was 4 inches after 6 hours lets make an equation. h being the number of hours and i being the inches of rain.
[tex]\frac{4}{6}[/tex]xh = i
Now fill it in with what we know
[tex]\frac{4}{6}[/tex]x9.5 = i
Now solve it.
You get:
6.33 (with 3 repeating forever) OR 6 [tex]\frac{1}{3}[/tex]
This is a lot of questions AND WHOEVER ANSWERES THESE BY THURSDAY 10/22/2020 WILL BE HONORED BY ME. I WILL MARK THE BRANLIEST.
1. What’s a better buy? 16 ounces of crackers for $4.00 or 20 ounces of crackers for $5.00?
2. What’s a better buy? 3 bagels for $2.85 or 5 bagels for $4.00?
3. What's a better buy? 3 pounds of apples for $1.89 or 1 pound of apples for $.79?
4. What's a better buy? 80 marbles for $4.99 or 90 marbles for $5.99?
5.Which rate is better? Sam runs 10 miles in 1 and 1/9 of an hour. Rina runs 8 miles in 7/8 of an hour.
6. Which rate is better? Emily bikes 18 miles in 2 hours. Ella bikes 22 miles in 2.5 hours.
7.Which rate is better? Dan types 100 words in 5 minutes. Dora types 118 words in 6 minutes.
8.Which rate is better? Fran reads 60 pages in 2 hours. Fanny reads 100 pages in 3 hours.
9.Which rate is better? Mona earns $44.55 in 9 hours. Mina earns $51 in 12 hours.
10.Which rate is better? Todd scored 132 points in 12 games. Terry scored 81 points in 8 games.
I KNOW IT'S A LOT BUT IF YOU KNOW THE ANSWERS TO SOME, THEN PLEASE SAY SO. AGAIN, I WILL MARK BRAINLIEST!!
Answer:
1. both are the same
2. 20 ounces
3. 3 pounds
Step-by-step explanation:
If SSR=30 and SSE=20, determine SST, then compute the coefficient of determination, r2, and interpret its meaning. SST=nothing r2=nothing (Type an integer or a decimal. Do not round.) Interpret the meaning of r2. Choose the correct answer below. A. It means that 1−r2 of the variation in the dependent variable cannot be explained by the variation in the independent variable. B. It means that r2•100% of the variation in the dependent variable can be explained by the variation in the independent variable. C. It means that 1−r2•100% of the variation in the independent variable cannot be explained by the variation in the dependent variable. D. It means that r2 of the variation in the independent variable can be explained by the variation in the dependent variable.
Answer:
R² value implies that 60% of the variation in the dependent variable can be explained by the variation in the independent variable.
Step-by-step explanation:
The information provided is:
SSR = 30
SSE = 20
Compute the total sum of squares as follows:
SST = SSR + SSE
= 30 + 20
= 50
The coefficient of determination R² specifies the percentage of the variance in the dependent-variable (Y) that is forecasted or explained by linear regression and the forecaster variable (X, also recognized as the independent-variable).
The coefficient of determination R² can be computed as follows:
[tex]R^{2}=\frac{SSR}{SST}[/tex]
[tex]=\frac{30}{50}\\\\=0.60[/tex]
The coefficient of determination value is 0.60 or 60%.
This value implies that 60% of the variation in the dependent variable can be explained by the variation in the independent variable.
a drawer contained 49 pencils and erasers. William removed p pencils from the drawer. the remaining pencils and erasers were in the ratio of 2:5. write an algebraic expression for the number of pencils left in the drawer.
Answer:
hey
Step-by-step explanation:
Can someone help me please I’ll mark brainliest !!
Answer:
56
Step-by-step explanation:
because a bisector splits in the middle, meaning that whatever the value is for the one side, it's the same on the other. So we multiply by 2.
What is the slope-intercept form of 3x + 5y = -15?
3x+5y=1 in slope-intercept form is y=−35x+15 .
How would you write 2 × 2 × 2 using exponents?
Answer:
2³
Step-by-step explanation:
2×2×2...there are 3 2s which is 2³
The recipe for 1 pie calls for 2 cups of flour. Which statement is true?
A 12 cups of flour are needed for 6 pies.
B. O 8 cups of flour are needed for 4 pies.
C.
1 cup of flour are needed for 2 pies.
D.
9
cups of flour are needed for 8 pies.
Hi!
Lets use a ratio. the recipe calls for 2 cups, for every pie, which is one pie.
So the ratio is 2:1
Now, lets look at the possible answers.
A, has the ratio 12:6. We need to use the ratio 2:1 to make sure this is correct. 2 x 6 = 12, and 12 ÷ 6 = 2, so A is a possibility.
B, has the ratio 8:4. Again, we check with the first ratio 2:1. 2 x 8 = 16, and 16 ÷ 4 = 4, so because the first equation did NOT equal 4, B is not a possibility.
C, has the ratio of 1:2. Because its TWO cups for ONE pie, it wouldn't be correct, so C is not a possibility as well.
D, has the ratio of 9:8. Again, we need to check if its correct using the original ratio of 2:1. 2 x 9 = 18, and 18 ÷ 2 = 2. The ratios do not match, therefore D is not a possibility at all as well.
So, Your Answer Is: A, 12 cups of flour are needed for 6 pies. Also know as the ratio, 12:6
(Here's a tip. When using ratios, use the original ratio to help you out. If when you multiply it doesn't equal the 2nd ratio (as in, 0:6 ⇇⇇ that one right there), and then you divide and it equals the first ratio (as in, this one right here ⇉⇉0:6), it still incorrect.... if all of that made sense)
Hope this helps!
~~~PicklePoppers~~~hello I need help on it
Tom drove 504 miles in 8 hours. At the same rate, how many miles would he drive in 12 hours
Answer:
756 miles in 12 hours
Step-by-step explanation:
504÷8=63
63 miles per hour
63×12=756
9514 1404 393
Answer:
756
Step-by-step explanation:
If you recognize that 12 (=8 +8/2) is half-again as much as 8, then you would know that Tom would drive half-again as much as 504 miles. That is, he would drive 504 +504/2 = 504+252 = 756 miles in 12 hours.
__
Since the rate is constant, you can write a proportion:
d/12 = 504/8 = distance/time
d = (12/8)(504) 1.5×504 = 756
Tom would drive 756 miles in 12 hours at that rate.
HELP ME PLZZZZZZZZZZZZZZ
Answer: 1
Step-by-step explanation: HELP ME PLS TOO
7 days left until launch of products with $668 left in budget. Need to spend $85 on last day. How many dollars do we spend on remaining days?
Answer:
In total, you have $668.00.
To reserve enough for the last day, you need to subtract the last day's budget:
This means that, for the remaining 6 days in the week, you have $583.00.
Assuming an equal amount is being spent each day, you can calculate the daily budget by dividing the remaining total by the number of days left.
To avoid going over budget, you can spend $97.16 per day for the other six days.
Hope this helps!
Step-by-step explanation:
Which is a member of the solution set of -5 < x ≤ -1?
Answer:
-1
Step-by-step explanation:
Put these two numbers on a number line with the correct circles. Now choose from any of the between numbers.
The amount the price of an item is increased above the price the store paid for the item?
Answer:
Markup
Step-by-step explanation:
Charlene and Gary want to make confetti. In order to get the right balance of ingredients for their tastes they bought 3 pounds of paper hearts at $2.46 per pound, 5 pounds of sparkling stars for $3.05 per pound, and 3 pounds of shiny coils for $2.33 per pound. Determine the cost per pound of the coffeti.
Answer:
0.712 cents per pound
Step-by-step explanation:
Since we are given the exact amount of each ingredient as well as the price for that amount then we simply need to calculate how much each pound of the confetti actually costs. We do this by adding together all of the pound of all of the ingredients and then adding together all of the costs. Lastly, we divide the cost by the total amount of pounds to find the cost per pound of the confetti like so...
3lbs. + 5lbs. + 3lbs. = 11 lbs.
$2.46 + $3.05 + $2.33 = $7.84
$7.84 / 11 lbs. = 0.712 cents per pound
Therefore, the cost per pound of the confetti is 0.712 cents per pound
Helpppp I have 5 minutes left
The expression on the left side of an equation is shown below.
Negative 4 (x minus 2) + 5 x = box
If the equation has no solution, which expression can be written in the box on the other side of the equation?
2(x + 4) – x
x + 8
4(x + 2) – 5x
x
Answer:
The correct answer is B.) x + 8
Step-by-step explanation:
I just did the test on edge 2020 and got it right
Answer:
B: x + 8
Step-by-step explanation:
A dog-washing salon is filling up the tub to was a dog. When the employee got to the tub,
there were already 2 gallons of water in the tub. She will fill the tub at a rate of 3 gallons a
minute.
Answer:
If there was 2 gallons in the tub at the moment, it must mean that it has been 2/3 of a minute or 40 seconds.
The two rates would be 3:60 and 2:40 and so on 1:20
Step-by-step explanation:
Good luck! Hope this helps! <3
is 3/4 less than,greater than,or equal to -1/2 ?
Answer: Greater than
3/4 greater than -1/2
3/4 > -1/2
Any positive number is always larger than any negative number
On a number line, stuff on the right side is always larger than stuff on the left side.
Answer:
it"s greater then
