An inequality that can represent the sum of a number and 11.5 is more than −4.5 is b + 11.5 > −4.5 .
What is inequality?
In mathematics, a relationship between two expressions or values that are not equal to each other is called ‘inequality.’ So, a lack of balance results in inequality. For example, if you want to buy a new bicycle that costs 250 but you have 225. It is also an inequality as you are comparing two numbers that aren’t equal.
We use ‘=’ when two quantities are equal and when they are not equal we use the symbol ≠ to denote not equal. If two things are not equal, the first value can be either greater than (>) or lesser than (<) or greater than equal to (≥) or less than equal to (≤) the second value. So, as per the above example, 250 > 225.
Given : the sum of a number and 11.5 is more than −4.5
Let us assume the number be "b"
according to question,
b + 11.5 is more than −4.
Thus, An inequality that can represent the sum of a number and 11.5 is more than −4.5 is b + 11.5 > −4.5 .
Hence , b + 11.5 > −4.5 is the correct answer .
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Answer:
Step-by-step explanation:
thx for the points
Ester writes 6 x 7 = 42 to find
the number of students seated
at tables. Describe what each
factor represents.
Answer:
6 rows to 7 steal in each rows
A simple random sample of n subjects is selected in such a way that every possible sample of the same size n has the same chance of being chosen. (A simple random sample is often called a random sample, but strictly speaking, a random sample has the weaker requirement that all members of the population have the same chance of being selected.) Determine whether each of the following is a simple random sample and a random sample. Complete parts a through c. .. a. In Major League Baseball, there are 30 teams, each with an active roster of 25 players. The names of the teams are printed on 30 separate index cards, the cards are shuffled, and one card is drawn. The sample consists of the 25 players on the active roster of the selected team. This sample a simple random sample. It v a random sample. b. For the same Major League Baseball population described in part (a), the 750 names of the players are printed on 750 separate index cards, and the cards are shuffled. Twenty-five different cards are selected from the top. The sample consists of the 25 selected players. This sample V a simple random sample. It v a random sample c. For the same Major League Baseball population described in part (a), a sample is constructed by selecting the 25 youngest players. This sample a simple random sample. It a random sample.
This sample a simple random sample. It v a random sample.
What is simple random sample?A selection of participants from a population is randomly chosen by the researcher using simple random sampling, a sort of probability sampling. The probability of getting chosen is the same for every person in the population.A simple random sample is a subset of people picked at random from a larger group, all with the same probability. It is the process of choosing a sample at random.Simple random sampling, systematic sampling, stratified sampling, and cluster sampling are the four main types of random (probability) sampling.This sample a simple random sample. It v a random sample.To learn more about simple random sample refer to:
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One hundred offices need to be painted. The workers choose between yellow, blue, or red paint. They decide that 45% of the offices will be painted yellow; 28% will be painted blue, and the remaining offices will be painted red. What amount of offices will be painted red?
Answer:
27 offices will be painted red-------------------------------------------------
Out of 100 offices:
45% of the offices will be painted yellow ⇒ 45 offices28% of the offices will be painted blue ⇒ 28 officesRemaining offices will be painted red:
100 - (45 + 28) = 100 - 73 =27Answer:
27 offices will be painted red.
Step-by-step explanation:
Yellow offices:
= 45% of 100 offices
= 0.45 × 100
= 45 yellow offices
Blue offices:
= 28% of 100 offices
= 0.28 × 100
= 28 blue offices
Red offices:
= Total number of offices - yellow offices - blue offices
= 100 - 45 - 28
= 55 - 28
= 27 red offices
Therefore, 27 offices will be painted red.
A 41-year old woman has $398,100.00 in an IRA account. Due to medical concerns of a family member, she decided to make no additional contributions to the account but expect it to grow at 8% compounded every 4 months. How much does she expect to have in the account when she retires at age 65?
She expects to have $2710591.78 when she retires at age 65 with the principal amount is 398100, the interest rate is 8%, time period is 24 and number of times interest applied is 3 by the concept of compound interest.
What is compound interest?Interest that is paid on the principal and interest at regular periods is known as compound interest. The interest is calculated for the new principal at regular intervals after the interest that has already accumulated has been combined with the existing principal amount. The initial principal plus the interest that has accrued thus far are added together to form the new principal.
Interest on the principal + periodic compound = compound interest.
According to the question the principal amount is 398100, the interest rate is 8%, time period is 24 and number of times interest applied is 3.
Here the interest is compounded every 4 months
So, the formula of compound interest is as follows:
A=p (1+ [tex]\frac{r}{n}[/tex]) ∧ (n× t)
Where P is the principal balance, r is the interest rate, n is the number of times interest is compounded per year and t is the number of years.
Here the interest is compounded every 4 months hence the value of n is 12/4 which is equal too 3.
Insert the values of p, n, t, r in above equation,
A=398100(1+[tex]\frac{8}{300}[/tex]) ∧ (3×24)
A=398100× (1.027) ∧ (72)
A=398100×6.809
A=2710591.78
She expects to have amount $2710591.78 when she retires at age 65.
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Evaluate 8a+3b-10+c^28a+3b−10+c
2
8, a, plus, 3, b, minus, 10, plus, c, squared when a=2a=2a, equals, 2, b=5b=5b, equals, 5, and c=4c=4c, equals, 4.
4
The solution is A = 37
The value of the equation A = 8a + 3b - 10 + c² is A = 37
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is given by
A = 8a + 3b - 10 + c²
When the value of a = 2 , the value of b = 5 and the value of c = 4 ,
The equation A is given as
Substitute the value of a , b and c in the equation , we get
A = 8a + 3b - 10 + c²
A = 8 ( 2 ) + 3 ( 5 ) - 10 + 4²
A = 16 + 15 - 10 + 16
On simplifying the equation , we get
A = 31 + 6
The value of A = 37
Therefore , the value of A is 37
Hence , The value of the equation A = 8a + 3b - 10 + c² is A = 37
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Holly wants to invest $6,800.00 in a savings account.
Determine the simple interest rate required for Holly's investment to grow to $16,500.00 in 14 years.
Round your answer to the nearest tenth of a percent and don't forget to include a percent sign, %, in
your answer.
The interest rate required to grow the investment to $16,500.00 is______
Answer:
Below
Step-by-step explanation:
16500 - 6800 = 9700 interest required to meet this situation in 14 years
6800 * i * 14 = 9700 where i = decimal interest
i = 9700/(6800*14) = .1018 = 10 .2 %
Manuel watered all the flowers at a business park. While watering, he noticed the daisies had been planted in groups of 11 and the lilies had been planted in groups of 12. If Manuel watered the same number of each flower, what is the minimum number of each that he must have watered?
Answer:
The minimum number of daisies and lilies that Manuel must have watered is 11.Step-by-step explanation:
To find the minimum number of daisies and lilies that Manuel must have watered, we need to find the least common multiple (LCM) of 11 and 12. The LCM of two numbers is the smallest positive integer that is a multiple of both numbers.
To find the LCM of 11 and 12, we can list the multiples of each number and find the smallest number that appears in both lists. The multiples of 11 are 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, etc. The multiples of 12 are 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, etc.
We can see that the smallest number that appears in both lists is 11, which is the LCM of 11 and 12. Therefore, the minimum number of daisies and lilies that Manuel must have watered is 11. If he watered the same number of each flower, he must have watered at least 11 daisies and 11 lilies.
Margo sells bracelets for $8 each and necklaces for $12 each. The equation below can be used to calculate E , her total earnings. E=8b+12n If is the number of bracelets, and n is the number of necklaces she sold, which equation can be used to find b , when E and n are known?
The equation that can be used to find b, when E and n are known is: b = (E - 12n) / 8.
This equation can be derived from the original equation of E=8b+12n. To solve for b, we can start by subtracting 12n from both sides of the equation to isolate b. We then divide both sides of the equation by 8 in order to solve for b.
The result is b = (E - 12n) / 8. This equation can be used to find the number of bracelets (b) when the total earnings (E) and the number of necklaces (n) are known.
We can rearrange the equation to solve for b.
E = 8b + 12n
Subtract 12n from both sides:
E - 12n = 8b
Divide both sides by 8:
(E - 12n)/8 = b
Therefore, the equation to find b, when E and n are known, is:
b = (E - 12n)/8
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Please help please and thank you
The list of pairs of triangles are ∠A≅∠N, ∠B≅∠O, ∠C≅∠P for the given similar triangles.
What is meant by triangle?Triangles are polygons because they have three vertices and three edges. This is one of the basic shapes in geometry.
In Euclidean geometry, any three non-collinear points determine a distinct triangle and a distinct plane (i.e. a two-dimensional Euclidean space). To put it another way, every triangle has a plane that it is contained in, and there is only one plane that contains every triangle. If and only if all geometry is the Euclidean plane, all triangles are contained in a single plane; however, this is no longer true in higher-dimensional Euclidean spaces.
Given triangles are,
ΔABC and ΔNOP
And also given that they are similar triangles.
The pairs of the congruent angles are:
∠A≅∠N
∠B≅∠O
∠C≅∠P
Therefore, the list of pairs of triangles are ∠A≅∠N, ∠B≅∠O, ∠C≅∠P for the given similar triangles.
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Use the scale to help you solve the equation and find the value of x. Enter the
value of x below.
x+2=8
X=
Answer: 6
Step-by-step explanation:
x=8-2
x=6
metodo gráfico
y-2x=o
y+x=3
por favor ayúdenme doy coronita
Rick deposits $3 into his bank account. The following week, he deposits 3 times that amount. Each week after that, he deposits 3 times the amount he did the previous week. How much does he deposit in all during the first 3 weeks (THERE ARE 2 PAGES
Rick's deposit in first 3 weeks is $39
What is Rick's weekly deposit ?1. Rick's deposit in the second week = 3 times($3)
= 3(3)
= 9
= [tex]3^{2}[/tex]
The exponential expression for Rick's 2nd week deposit = [tex]3^{2}[/tex]
Where, Base = 3
Exponent = 2
2. Rick's deposit in 1st week = $3
Rick's deposit in 2nd week = 3 (3) = $9
Rick's deposit in 3rd week = 3 (9) = $27
Rick's deposit in first 3 weeks = 3+9+27
= $39
Rick's deposit in all in the first 3 weeks is $39
3. Rick's deposit for 15 weeks = [tex]3^{15}[/tex]
= $1,43,48,907.
We know, no. of weeks in a year = 52
Rick's deposit for 52 weeks ( 1 year ) = 52 times of 3
[tex]=3^{52}\\= 6.4610819e+24[/tex]
Since this is a huge number , Rick cannot keep up this savings plan for a year.
What is an exponential expression?Only a short version of a power can be expressed using an exponential expression. How frequently the base is employed as a factor is shown by the exponent. Any real or complex exponent is acceptable under the notion of exponentiation. For a large number of other algebraic structures, including matrices, exponentiation by integer exponents can also be defined.Compound interest, population expansion, chemical reaction kinetics, wave behaviour, and public-key cryptography are just a few examples of the many domains where exponentiation is widely utilized. It is also used extensively in fields including economics, biology, chemistry, physics, and computer science.To learn more about exponential expression, refer:
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27/22 as a decimal rounded to the nearest hundreth
The expression as a rounded decimal is 1.23
How to evaluate the expression as a rounded decimalFrom the question, we have the following parameters that can be used in our computation:
27/22
To start with, we evaluate the expression using a calculator
So, we have the following representation
27/22 = 1.22727272727
Next, we approximate to the nearest hundredth
So, we have the following representation
27/22 = 1.23
Hence, the approximated expression is 1.23
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Jim has to choose between two gym membership plans. Plan A: $50 monthly membership fee and $10 per visit. Plan B: $25 one time membership fee and $15 per visit. How many visits must Jim make to make Plan A the cheaper option?
How many visits for them to cost the same?
The same cost of both of the plan of the gym will be in 5 visits. And plan B is better than Plan A as B is cheaper than A.
What is an expression?In mathematics, expression is the combining of variables with the application of operations and prescribed rules. It could take the shape of an equation, some numbers, etc.
We have,
plan A consists of :
Amount for monthly membership fee = $50
Cost per visit = $10
The expression of total fees would be:
50+10x,
where x is the number of times Jim visits the gym.
Plan B consists of :
Amount for monthly one time membership fee = $25
Cost per visit = 15
The expression of total fees would be:
25 + 15x,
where x is the number of times Jim visits the gym.
Here, x denotes the number of visits.
Let us suppose x = 1
Then, fees for plan A would be:
50 + 10 x1 = $60
Fees for plan B would be:
25 + 15 x1 = $40
To find the same cost in x number of visits:
We equate both the expressions.
50+10x = 25 + 15x
15x - 10x = 50 - 25
5x = 25
x = 5
That means, if Jim visits 5 times, the gym, then he would have the similar cost for both of the plans.
Hence, Plan B is better than Plan A as B is cheaper than A. The same cost of both of the gym will be in 5 visits.
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Find the equation of the line tangent to the function at the given point. Your answer should be in slope-intercept form. SHOW ALL WORK, LABEL APPROPRIATELY. F(x)= x - 4x² + 7 at x = 1 Find the instantaneous rate of change of the function at the given value. f(x) = 2x² + x +1; -2
On solving the provided question, we can say that - the instantaneous rate of change of the function at the given value, by solving the equation y = 11 - 5x, f'(1) = 3-8 = -5
What is an equation ?A mathematical equation is a formula that uses the equals symbol (=) to link two expressions and represent their equivalence. A mathematical statement that demonstrates the equality of two mathematical expressions is an equation in algebra, in its most basic form. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."
y = f(x) =
[tex]x^3 - 4x^2 + 7 \\at x =1[/tex]
f(x) = 3-4+7
= 6
F'(x) = [tex]3x^2 - 8x[/tex]
f'(1) = 3-8 = -5
equation = y - 6 = -5(x-1)
y = 11 - 5x
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Jeremiah makes \dfrac{4}{5}
5
4
start fraction, 4, divided by, 5, end fraction of the free throw shots he attempts in basketball. Jeremiah likes to shoot free throws until he misses one. Let FFF be the number of shots it takes Jeremiah to miss his first free throw. Assume that the results of each shot are independent.
Find the mean and standard deviation of FFF.
Round your answers to one decimal place.
\mu_F \approxμ
F
≈mu, start subscript, F, end subscript, approximately equals
shots
\sigma_F \approxσ
F
≈sigma, start subscript, F, end subscript, approximately equals
shots
80% is her free throw shooting percentage.
What is Fraction?Fractions are used to represent smaller pieces (or parts) of a whole. The parts might make up one thing, or more than one thing. Either way, altogether, they make up what's called a whole.
Given that, Jeremiah makes 4/5 of the free throw shots he attempts in basketball. Jeremiah likes to shoot free throws until he misses one. Let F be the number of shots it takes Jeremiah to miss his first free throw.
We can construct a fraction in which the numerator is how many shots she makes, and the denominator is how many shots she took overall.
We now have the following fraction:4/5
To convert this to a percentage, we want the denominator to be 20/20
= 4/5×20/20
= 80/100
= 0.8
Now multiply 0.8 with 100
= 0.8×100=80
Hence, 80% is her free throw shooting percentage.
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A card is drawn from a pack of 52 playing cards. Find the probability that the card will be a king, given that it is a face card. (The face cards are the jacks, queens, and kings. Enter your probability as a fraction.)
Answer:
Step-by-step explanation:
There are 4 kings in a deck of playing cards.
There are 52 cards in a deck.
So the probability is 4 out of 52.
Which is 4/52,
Which can be reduced to 1/13.
4 divided by 4 = 1 and 52 divided by 4 =13.
In how many ways can the digits in the number 7,400,000 be arranged?
In a class of students, the following data table summarizes how many students have
cat or a dog. What is the probability that a student chosen randomly from the class
does not have a cat or a dog?
Has a dog
Does not have a dog
Has a cat Does not have a cat
7
4
6
12
Answer:
8/33
p(d'c')
not having a cat=12/18
not a dog =4/11
12/18×4/11=8/33
Ans=8/33
Find an equivalent fraction of 36/48
having denominator 6.
An equivalent fraction of 36/48 having denominator 6 could be 6/6 only.
What is a fraction?A fraction represents a part of a number or any number of equal parts.
we are given a fraction as 36/48.
We can make equivalent fractions by multiplying or dividing both top and bottom by the same amount.
We have to only multiply or divide, never add or subtract, to get an equivalent fraction. Only divide when the top and bottom stay as whole numbers.
In this case we have a clue which is 48,
6 x 8 = 48
Then we would want to take the 6 and times it by the denominator which is 6
So 6 x 6 = 36
An equivalent fraction of 36/48 is 6/6.
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A family compares the cost of renting a truck from two different companies for its 2-day move to another state.The costs are shown in the table.
A. The functions are given as follows:
Company X: X(m) = 245.9 + 0.59m.Company Y: Y(m) = 91.9 + 0.79m.B. The company from which the family should rent the truck is: Company Y.
How to define the functions?There are two costs in the problem, given as follows:
Fixed costs: base, drop-off and insurance.Variable: cost per mile.The fixed costs for Company X are given as follows:
Base: 2 x 29.95 = 59.90.Drop-off: 150.Insurance: 2 x 18 = 36.The variable cost is of 0.59 per mile, hence the function, considering a trip of m miles, is given as follows:
X(m) = 59.90 + 150 + 36 + 0.59m.
X(m) = 245.9 + 0.59m.
The fixed costs for Company Y are given as follows:
Base: 2 x 19.95 = 39.90.Drop-off: included.Insurance: 2 x 26 = 52.The variable cost is of 0.79 per mile, hence the function, considering a trip of m miles, is given as follows:
Y(m) = 39.90 + 52 + 0.79m
Y(m) = 91.9 + 0.79m.
The trip is of 750 miles, hence the costs are given as follows:
X(750) = 245.9 + 0.59 x 750 = $688.4.Y(750) = 91.9 + 0.79 x 750 = $684.4.Due to the lower cost, Company Y should be chosen.
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What is the range of the relation?
{(2, -5), (1, 4), (-3, 0), (6, 2)}
Responses
{-3, 1, 2, 6}
{-3, 0, 2, 6}
{-5, 1, 2, 4}
{-5, 0, 2, 4}
The correct option is (d) i.e. the range of the relation is {-5, 0, 2, 4}.
What is Range ?
A function's range is a collection of all of its potential results, or alternatively, the collection of all conceivable representations of the domain's elements.
Given, {(2, -5), (1, 4), (-3, 0), (6, 2)}
Range is the result of a relation.
let say, X⇒ Y is a relation where X represents the domain and Y represents the range and both can be represented as ( X, Y).
So, all the values at the position of Y are called range of the given relation.
Hence, Range will be {-5, 0, 2, 4}.
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find the solution of the differential equation dr sec21 dt tant 1 which passes through the point (x,5).
The solution of the differential equation is given by r = 5tan(t + c) where c is the constant of integration, determined by the initial condition (x, 5).
The given differential equation is dr sec21dt tant 1. This is a first order linear differential equation which can be solved using an integrating factor. The integrating factor is given by e^(integral(sec^2(t)dt)). The solution of the equation is given by
[tex]r = (integral(sec^2(t))) + c[/tex]
where c is the constant of integration
Let y = sec(2x)
dy/dt = 2tan(2x)sec(2x)
Now, substituting the given point, we get
5 = sec(2x)
⇒ 2x = arccosec(5)
⇒ x = arccosec(5)/2
Now, substituting this in the equation of the differentiable curve, we get
[tex]\int\limits^a_b {x} \, dx dy/dt = 2tan(arccosec(5))sec(arccosec(5))[/tex]
Hence, the solution of the differential equation passing through the given point is y = sec(2x) = sec(arccosec(5))
or r = sec(arccosec(5))
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HELPPP!!!!! I need help with the ASAP PLEASE HELEP ME
The value of x is 7/3 and the value of y is -11/3 for the given equations.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the equations are 2x - 2y = 12 and -8x -y = -15. The value of x and y will be calculated as,
2x - 2y = 12
-8x - y = -15
Solve the above equation,
2x - 2(-8x + 15) = 12
2x + 16x - 30 = 12
18x = 42
x = 42 / 18
x = 7 / 3
The value of y is calculated as,
-8x - y = -15
y = ( -8 x 7 / 3 ) +15
y = (-56 + 45) /3
y = -11 / 3
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The display summarizes grades on a World History exam.
A vertical box plot is titled world history exams, with a minimum of 54, a maximum of 94, a lower quartile of 70, a median of 83, and an upper quartile of 88.
Which of the following describes the data set?
The data is univariate and categorical.
The data is univariate and numerical.
The data is bivariate and categorical.
The data is bivariate and numerical.
The option that best describes the data is The data is band numerical
What is univariate data?This kind of data just has one variable. Since there is only one variable that varies, univariate data analysis is the most straightforward type of analysis.
In this case the one variable is World History scores exam
What are numerical data?Data that is expressed as numbers rather than in any linguistic or descriptive form is referred to as numerical data.
Numerical data, also known as quantitative data, is gathered in number form and differs from all other sorts of number data because it can be calculated mathematically and statistically.
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In right triangle ABC, altitude CD with length h is drawn to its hypotenuse. We also know AD = 12 and DB=3. What is the length of h?
Only sides/angles known are
Base= 12+3,
Angle= Right angle/90°.
No clue how to solve this. I tried many methods. everyone who’s asked this question on here did not get a good answer. Please explain how it is done and what theorem is used.
Answer:
h = 6
Step-by-step explanation:
h is the short leg for AD in ΔADC: AD = 12
h is the long leg for DB in ΔCDB: DB = 3
Hence:
12/h = h/3
3 * 12/h = 3 * h/3 ==> isolate h by multiplying 3 on both sides
36/h = h
h * 36/h = h*h ==> multiply by h on both sides to remove fractions
36 = h^2
h = [tex]\sqrt{36}[/tex]
h = 6
A restaurant wants to make sure that they are serving customers quickly enough. Every day for 10 days, they sample 16 random customers, and measure how long it is until the waiter shows up. Using this sample data, the company calculates the 3-sigma control limits as LCL = 3.5 minutes and UCL = 6.5 minutes.
What would be the LCL and UCL if the company uses 2-sigma control limits instead?
O LCL = 4.5 minutes and UCL = 5.5 minutes
O LCL = 4.5 minutes and UCL = 7.5 minutes
O LCL = 3 minutes and UCL = 7 minutes
O LCL = 4 minutes and UCL = 6 minutes
LCL would be 4 minutes and UCL would be 6 minutes if the company uses 2-sigma control limits instead.
Describe mean.The average of a group of variables is referred to as the mean in mathematics and statistics. There are several methods for calculating the mean, including simple arithmetic means (adding the numbers together and dividing the result by the number of observations), geometric means, and harmonic means. The arithmetic mean, also known as the arithmetic average or simply the mean or average, is the sum of a set of numbers divided by the total number of numbers in the set. The collection frequently consists of a series of findings from a survey, experiment, or observational study.
Given
LCL = 3.5 minutes
UCL = 6.5 minutes
Mean = LCL + UCL/2
Mean = 3.5 + 6.5/2
Mean = 5
Standard deviation = UCL - LCL/6
Standard deviation = 6.5 - 3.5/6
Standard deviation = 0.5
LCL = 5 - 2(0.5)
LCL = 4
UCL = 5 + 2(0.5)
UCL = 6
LCL = 4 minutes and UCL = 6 minutes
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interpret the association. during george bush's presidency there was a strong negative correlation between the stock market performance and his approval ratings. therefore, it can be concluded that: question 14 options: approval ratings tended to rise as stock prices rose. higher approval ratings were the result of a better performing stock market. approval ratings tended to fall as stock prices rose. lower approval ratings were the result of a better performing stock market.
The answer is option 3: approval ratings tended to fall as stock prices rose.
This means that when stock prices rose, the approval ratings of George Bush's presidency decreased. This can be interpreted as an indication that people were not satisfied with the performance of the stock market during the Bush presidency. This could be because the stock market was not performing as well as expected or because the people were not satisfied with the decisions made by the Bush presidency that impacted the stock market.
Whatever the reason, the negative correlation between the stock market performance and Bush's approval ratings shows that when stock prices rose, approval ratings tended to fall.
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Let a, b, c, d, e, f be integers selected from the set {1, 2, . . . , 100}, uniformly and at random with
replacement. Set
M = a + 2b + 4c + 8d + 16e + 32f.
What is the expected value of the remainder when M is divided by 64?
So the expected value of the remainder when M is divided by 64 is approximately 0.2080.
To find the expected value of the remainder when M is divided by 64, we can find the probability that M is congruent to each possible remainder modulo 64 and then sum these probabilities multiplied by the corresponding remainders.
For a positive integer n, let P(n) denote the probability that a positive integer chosen from the set {1, 2, . . . , 100} is congruent to n modulo 64. Then
P(0) = P(64) = P(128) = ... = 1/100
P(1) = P(65) = P(129) = ... = 1/100
P(63) = P(127) = P(191) = ... = 1/100
Since the integers a, b, c, d, e, and f are chosen independently and uniformly at random from the set {1, 2, . . . , 100}, the probability that M is congruent to n modulo 64 is P(n)^6.
Therefore, the expected value of the remainder when M is divided by 64 is
E = 0 * P(0)^6 + 1 * P(1)^6 + 2 * P(2)^6 + ... + 63 * P(63)^6
= (0^6 + 1^6 + 2^6 + ... + 63^6) * P(0)^6
= (0 + 1 + 2 + ... + 63) * P(0)^6
= 2080 * (1/100)^6
= 0.2080
So the expected value of the remainder when M is divided by 64 is approximately 0.2080.
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For a positive integer n, let P(n) denote the probability that a positive integer chosen from the set {1, 2, . . . , 100} is congruent to n modulo 64. Then
P(0) = P(64) = P(128) = ... = 1/100
P(1) = P(65) = P(129) = ... = 1/100
P(63) = P(127) = P(191) = ... = 1/100
Since the integers a, b, c, d, e, and f are chosen independently and uniformly at random from the set {1, 2, . . . , 100}, the probability that M is congruent to n modulo 64 is P(n)^6.
Therefore, the expected value of the remainder when M is divided by 64 is
E = 0 * P(0)^6 + 1 * P(1)^6 + 2 * P(2)^6 + ... + 63 * P(63)^6
= (0^6 + 1^6 + 2^6 + ... + 63^6) * P(0)^6
= (0 + 1 + 2 + ... + 63) * P(0)^6
= 2080 * (1/100)^6
= 0.2080
The serving size for the granola that Ted likes to eat for breakfast is 3/4 cup. How many servings are there in a box that holds 13 cups?