Suppose that a stable process has upper and lower specifications at USL = 51 and LSL = 31. A sample of size n = 20 from this process reveals that the process mean is centered approximately at the midpoint of the specification interval and that the sample standard deviation s = 2. 1. Find a point estimate of C, the potential capability of the process. 2. Find a 95% confidence interval on C, Note that: xổ.975, 19 = 8.71 and xã.02s, 19 = 32.85. X2 X4 B 四四四

Answer:

For 1 cup of  pineapple 1 .5  cups of strawberries are used.

Step-by-step explanation:

This question can be solved by using ratios

Strawberry       :      Pineapple

1     cup              :          2/3 cup

x cup                  ;            1 cup

Using the cross product rule

2/3 * x= 1*1

x= 1*1 ÷ 2/3

x= 1*3/2= 1 1/2= 1.5

For 2 cups of pineapple 3 cups of strawberries are used.

For 1 cup of  pineapple 1 .5  cups of strawberries are used.

For 3 cups of pineapple 4.5 cups of strawberries are used.

The​ chi-squared statistic measures which of the "goods of fit". Therefore option B is correct.

The chi-squared statistic is a statistical measure that is used to test the goodness of fit between an observed frequency distribution and an expected frequency distribution. It measures how well the observed values fit the expected values and quantifies the differences between them.

The calculation of the chi-squared statistic involves comparing the observed and expected frequencies for each category and computing a sum of squared differences between them, divided by the expected frequency. The resulting value indicates the degree to which the observed frequencies differ from the expected frequencies.

In summary, it can be sais that the chi-squared statistic is used to assess whether the observed frequencies are consistent with the expected frequencies or not , and it is commonly used in hypothesis testing, particularly in testing for independence in contingency tables or testing the fit of a model to observed data.

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Lorie should deposit $6,986.05 today at 5.25% to have enough money to pay off the loan in 7 months.

To determine the amount that Lorie should deposit today to have enough money to pay off the loan.

We use the simple interest formula for accrued amount.

A = P( 1 + rt )

Where A is total amount, P is initial amount, r is interest rate and t is elapsed time.

Given that;

First, converting R percent to r a decimal

r = R/100

r = 5.25/100

r = 0.0525

Next, we put time into years for simplicity,

t = 7 months / 12 months

t = 7/12 year

Plug the values into the above formula.

A = P( 1 + rt )

P = A / ( 1 + rt )

P = $7,200 / ( 1 + ( 0.0525 × 7/12 ) )

P = $7,200 / ( 1 + 0.030625 )

P = $7,200 /  1.030625

P = $6,986.05

Therefore, the principal or initial amount is $6,986.05.

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The amount she should deposit today to have enough money to pay off the loan would be = $1,060

The cost of the small car that Lorie Reilly needs to buy for college = $7,200.(P)

The number of months that she plans to repay the money = 7 months = 0.58 yr.(T)

The rate at which the money needs to be deposited = 5.25%. (R)

The simple interest = Principal× Time × Rate /100

Simple interest = 7200× 0.58 × 5.25/100

= 21924/100

= $219.24

The amount she is expected to pay after 7 months = 7200+219.24 = 7419.24

The amount she should deposit today to have enough money to pay off the loan = 7419.24/7 = $1,060( approximately)

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The 8 painters will take 12 hours and 9.6 minutes to paint the office. The result is obtained by comparing the two variables, worker and time duration.

If the they work at the same rate, find the time needed for the 8 painters to finish their job!

Let's say

We convert the unit of time in hours.

t₁ = 7 h 36 min

t₁ = (7 + 36/60) h

t₁ = (7 + 0.6) h

t₁ = 7.6 hours

If they work at the same rate, the number of workers and time durations of each day are directly proportional. So,

w₁/w₂ = t₁/t₂

5/8 = 7.6/t₂

t₂ = 8/5 × 7.6

t₂ = 12.16 hours

In hours and minutes,

t₂ = 12 h + (0.16 × 60) min

t₂ = 12 h 9.6 min

Hence, to paint the office, the 8 painters will take 12 hours and 9.6 minutes.

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The Cartesian coordinates of the point (10, π) in polar coordinates are (-10, 0). To convert a point from polar coordinates to Cartesian coordinates, we use the formulas x = r * cos(θ) and y = r * sin(θ). In this case, the radius is 10 and the angle is π.

Substituting these values into the formulas, we get x = 10 * cos(π) = 10 * (-1) = -10, and y = 10 * sin(π) = 10 * 0 = 0.

Therefore, the Cartesian coordinates of the point (10, π) in polar coordinates are (-10, 0). The point lies on the negative x-axis, as the x-coordinate is negative, while the y-coordinate is 0, indicating that it does not extend in the vertical direction.

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Answer: −

1

7

−

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Graph it and you will see it is a function and since you are adding them it is also a relation. Good luck.

Answer:

it represents both a relation and a function.

Step-by-step explanation:

Answer:

7.92%

Step-by-step explanation:

Given the following

Weight of package at home = 20.2 ounces.

Weight of the package at the office = 18.6ounces

Decrement = 20.2 - 18.6

percentage error = decrement/wt at home * 100

percentage error = 1.6/20.2* 100

percentage error = 160/20.2

percentage error = 7.92

HEnce  the percent error in the weight of the package is 7.92%

Based on the analysis of the given functions and the given differential equation, the following conclusions can be drawn:

The function y(t) = t + 1 + 2e^t is a solution to the differential equation dy/dt = y - t.

The function y(t) = t + 1 is also a solution to the differential equation dy/dt = y - t.

The function y(t) = t + 2 is not a solution to the differential equation dy/dt = y - t.

Step-by-Step Explanation:

To determine if a given function is a solution to a differential equation, we need to perform the following steps:

Find the derivative of the given function with respect to t. This gives us the value of dy/dt.

Substitute the given function and the value of dy/dt into the differential equation and simplify the expression.

Check if the simplified expression is equal to the value of dy/dt. If they are equal, then the given function is a solution to the differential equation.

Applying this process to the three given functions, we obtain the following:

For y(t) = t + 1 + 2e^t:

Step 1: Find the derivative of y(t) with respect to t:

dy/dt = 1 + 2e^t

Step 2: Plug the function y(t) into the given equation and compare it to the found dy/dt:

y - t = (t + 1 + 2e^t) - t = 1 + 2e^t

Since dy/dt = y - t, y(t) = t + 1 + 2e^t is a solution to the differential equation.

For y(t) = t + 1:

Step 1: Find the derivative of y(t) with respect to t:

dy/dt = 1

Step 2: Plug the function y(t) into the given equation and compare it to the found dy/dt:

y - t = (t + 1) - t = 1

Since dy/dt = y - t, y(t) = t + 1 is also a solution to the differential equation.

For y(t) = t + 2:

Step 1: Find the derivative of y(t) with respect to t:

dy/dt = 1

Step 2: Plug the function y(t) into the given equation and compare it to the found dy/dt:

y - t = (t + 2) - t = 2

In this case, dy/dt ≠ y - t, so y(t) = t + 2 is not a solution to the differential equation.

Therefore, we can conclude that the first two functions are solutions to the given differential equation, while the third function is not.

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The probability that a person arriving to use the machine will find it idle is 1/3 or 0.3333. Option a is correct.

Use the concept of an M/M/1 queue to calculate the probability, which models a single-server queue with exponential interarrival times and exponential service times.

In this case, the interarrival time follows an exponential distribution with a rate parameter of λ = 5 persons per hour (or 1/12 persons per minute). The service time (copying time) also follows an exponential distribution with a rate parameter of μ = 1/8 persons per minute (since each person uses the machine for an average of 8 minutes).

In an M/M/1 queue, the probability that the system is idle (no person is being served) can be calculated as:

P_idle = ρ⁰ × (1 - ρ), where ρ is the traffic intensity, defined as the ratio of the arrival rate to the service rate. In this case, ρ = λ/μ.

Plugging in the values, we have:

ρ = (1/12) / (1/8) = 2/3

P_idle = (2/3)⁰ × (1 - 2/3) = 1/3

Therefore, the probability is 1/3 or approximately 0.3333.

Thus, option (A) is the correct answer.

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Answer:

The domain is all real number:

i.e.

\(-\infty \:<x<\infty \:\)

Therefore,

\(\mathrm{Domain\:of\:}\:10^x\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:<x<\infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}\)

Step-by-step explanation:

Given the function

y = 10ˣ

Determining the domain of the function y = 10ˣ :

We know that the domain of the function is the set of input or arguments for which the function is real and defined.  

In other words,

From the graph, it is clear that the function has no undefine points nor domain constraints.

Thus, the domain is all real number:

i.e.

\(-\infty \:<x<\infty \:\)

Therefore,

\(\mathrm{Domain\:of\:}\:10^x\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:<x<\infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}\)

Answer:

The domain is all real numbers

Step-by-step explanation:

The sales price on an item that is $50 with a 54% markdown is $23

The given parameters are

Item price = $50

Markdown = 54%

The sales price on an item that is $50 with a 54% markdown is calculated as

Sales price = Item price * (1 - Markdown)

So, we have

Sales price = 50 * (1 - 54%)

Evaluate

Sales price = 23

Hence, the sales price on an item that is $50 with a 54% markdown is $23

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Therefore, the equation \(+3 + 5(2n - 1)^2 + n^2 + D(n + 2)\) is true for every positive integer n.

To verify the equation for every positive integer n using induction, we'll follow the steps of mathematical induction.

Step 1: Base Case

Let's check if the equation holds true for n = 1.

For n = 1:

\(3 + 5(2(1) - 1)^2 + 1(1) + D(1 + 2)\)

\(3 + 5(1)^2 + 1 + D(3)\)

3 + 5 + 1 + D(3)

9 + D(3)

At this point, we don't have enough information to determine the value of D. However, as long as the equation holds for any arbitrary value of D, we can proceed with the induction.

Step 2: Inductive Hypothesis

Assume that the equation holds true for an arbitrary positive integer k. That is:

\(3 + 5(2k - 1)^2 + k^2 + D(k + 2)\)

Step 3: Inductive Step

We need to prove that the equation also holds true for n = k + 1, based on the assumption in the previous step.

For n = k + 1:

=\(3 + 5(2(k + 1) - 1)^2 + (k + 1)^2 + D((k + 1) + 2)\\3 + 5(2k + 1)^2 + (k + 1)^2 + D(k + 3)\)

Expanding and simplifying:

=\(3 + 5(4k^2 + 4k + 1) + (k^2 + 2k + 1) + D(k + 3)\\3 + 20k^2 + 20k + 5 + k^2 + 2k + 1 + Dk + 3D\)

Combining like terms:

=\(21k^2 + 22k + 9 + Dk + 3D\)

Now, we compare this expression with the equation for n = k + 1:

=\(3 + 5(2(k + 1) - 1)^2 + (k + 1)^2 + D((k + 1) + 2)\)

We can see that the expression obtained in the inductive step matches the equation for n = k + 1, except for the constant terms 9 and 3D.

As long as we choose D in a way that makes 9 + 3D equal to zero, the equation will hold true for n = k + 1 as well. For example, if we set D = -3, then 9 + 3D = 9 - 9 = 0.

Step 4: Conclusion

Since the equation is true for the base case (n = 1) and we have shown that if it holds for an arbitrary positive integer k, it also holds for k + 1, we can conclude that the equation is true for every positive integer n.

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We can use the pythagorean theorem to answer this question.

We know that \(l\) is the hypotenuse, and the 2 sides are 7 and 7.

So, we can build the equation:

\(7^2+7^2 = l^2\)

\(98 = l^2\)

\(\sqrt{98} = l\)

Answer: its a half a percent or 50%

Step-by-step explanation:

Answer:

50%

Step-by-step explanation:

First, to find a percentage, you divide the part out of the whole (numerator out of the denominator in a fraction);

4 ÷ 8 = 0.5

Once you have your decimal number, you need to move the decimal point 2 spaces to the left to turn it into a percentage;

0.5 = 50

Therefore, the percent decrease is 50%.

The probability that the artist chosen will be a painter or a photographer is 3/4

Probability is the function that measures the chances that an outcome of a random event will be as expected. In this way you can measure how likely it is that an event will happen.

To solve this exercise the formula and the procedure that we have to use for probability is:

probability= (achieving success / possible outcomes)

Achieving success = 7 painters + 5 photographer = 12

Possible outcomes = 7 painters + 5 photographer + 4 sculptors = 16

Applying the formula to calculate the probability we get:

probability= (achieving success / possible outcomes)

probability= 12/16

Simplifying:

probability= 3/4

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Answer:

Follows are the solution to this question:

Step-by-step explanation:

Given:

\(s_1 = 21 \ \ t_1 = 1\\\\s_2 = 59 \ \ t_2 = 2\\\\s_3 = 141 \ \ t_3 = 4\)

All points are on the graph including its quadratic function, in order to install their coordinates to values of x and y with the following values:

\(y= ax^2 + bx + c\\\\21=a+b+c\)      Inserting the coordinates of the first point

\(y= ax^2 + bx + c\\\\59 =4a+2b+c\)              Inserting the coordinates of the second point

\(y= ax^2 + bx + c\\\\141=16a+4b+c\)       Inserting the coordinates of the third point

If the variable attractiveness increases while the variable weight remains constant, the correlation is said to be a positive correlation. A positive correlation means that as one variable increases, the other variable also tends to increase.

For example, let's consider a study examining the relationship between the attractiveness of a person and their weight. If the study finds that as attractiveness increases, weight also tends to increase while keeping other factors constant, then we can say there is a positive correlation between attractiveness and weight.

In this case, the variable attractiveness is increasing while the variable weight remains constant. This means that as attractiveness increases, weight also tends to increase, indicating a positive correlation.

It's important to note that correlation does not imply causation. Just because two variables are correlated does not necessarily mean that one variable causes the other to change. Correlation simply measures the strength and direction of the relationship between two variables.

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Answer:

x=10

Step-by-step explanation:

The area of a rectangle is two times the area of the triangle if the rectangle is divided into two triangles.

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

It is defined as two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral.

As we know, the triangle is two-dimensional geometry and has three sides.

The rectangle can be divided in two triangles with the same area

The area of the rectangle = 2(area of each triangle)

Thus, the area of a rectangle is two times the area of the triangle if the rectangle is divided into two triangles.

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Answer:

1

Step-by-step explanation:

this is because the number is not getting multiplied by anything.

Answer:

1

Step-by-step explanation:

(8/9) ^0

Any number( besides 0) raised to the power of 0 is 1

The total cost before the sales tax was 19.828 pounds.

For a party, Jordan purchased 3.8 pounds of turkey, 2.2 pounds of cheese, and 3.6 pounds of egg salad.

We have to determine the total cost before sales tax.

As per the question, we have prices as:

cost of turkey = 3.95 per pound

cost of egg cheese = 1.3 per pound

cost of egg salad = 0.89 per pound

The total cost of turkey = 3.8 × 3.95  = 15.01 pounds

The total cost of cheese = 2.2 × 1.3 = 2.86 pounds

The total cost of egg salad = 2.2 × 0.89 = 1.958 pounds

The total cost before sales tax = 15.01 + 1.958 +2.86

Apply the addition operation, and we get

The total cost before sales tax = 19.828 pounds

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The question seems to be incomplete the correct question would be:

Jordan bought 3.8 pounds of turkey, 2.2 pounds of cheese, and 3.6 pounds of egg salad for a party. If prices are 3.95 per pound turkey, 1.3 per pound cheese and 0.89 per pound egg salad What was the total cost before sales tax?

Using the properties of parallelograms and the given information, we proved that BAEC is equal to FABC. We utilized angle-angle similarity and the proportional relationships of corresponding sides in similar triangles to establish the equality.

To prove that BAEC = FABC, we will use the properties of parallelograms and the given information.

Given:

ABCD is a parallelogram.

BE is parallel to CD.

BF is parallel to AD.

To prove:

BAEC = FABC

Proof:

Since ABCD is a parallelogram, we know that opposite sides are parallel and equal in length. Let's denote the length of AB as a, BC as b, AD as c, and CD as d.

Since BE is parallel to CD and AD is parallel to BF, we have angle ABE = angle CDF and angle ADB = angle BFD.

By alternate interior angles, angle CDF = angle FAB.

Now, we have two pairs of congruent angles: angle ABE = angle CDF and angle ADB = angle BFD.

Using angle-angle similarity, we can conclude that triangle ABE is similar to triangle CDF and triangle ADB is similar to triangle BFD.

As the corresponding sides of similar triangles are proportional, we have the following ratios:

AB/CD = AE/CF (from triangle ABE and triangle CDF similarity)

AD/BC = BD/CF (from triangle ADB and triangle BFD similarity)

Cross-multiplying the ratios, we get:

AB * CF = CD * AE (equation 1)

AD * CF = BC * BD (equation 2)

Adding equation 1 and equation 2, we have:

AB * CF + AD * CF = CD * AE + BC * BD

Factoring out CF, we get:

CF * (AB + AD) = CD * AE + BC * BD

Since AB + AD = CD (opposite sides of a parallelogram are equal), we have:

CF * CD = CD * AE + BC * BD

Simplifying, we get:

CF = AE + BC

Therefore, we have shown that BAEC = FABC.

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Take the difference between Tiffany's score and the average:

53 - 67 = -14

Divide this difference by the standard deviation to get the z-score:

(53 - 67)/5.5 = -14/5.5 ≈ -2.55

Jason will be charged $188.55 if he buys 5 football jerseys with a 6% discount.

The original price of each football jersey is $39.90 before the discount. To calculate the total cost after the discount, we need to apply the 6% discount to each jersey and then multiply it by the number of jerseys Jason wants to buy.

Discount per jersey = 6% of $39.90 = $2.39

Total discount for 5 jerseys = $2.39 * 5 = $11.95

Total cost after discount = Total cost before discount - Total discount

Total cost after discount = ($39.90 * 5) - $11.95 = $199.50 - $11.95 = $188.55

Therefore, Jason will be charged $188.55 if he buys 5 football jerseys with a 6% discount.

If Jason buys 5 football jerseys with a 6% discount, the total amount he will be charged is $188.55. This is calculated by applying the discount to each jersey's original price and then multiplying it by the number of jerseys.

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The probability of Jack taking 2 red candies is 3/28.

What do you mean by a union in probability?
The letter "U" (union) stands for "or." Specifically, P(AB) represents the probability of that event A or event B occurring. The sample points that are present in both event A and event B must be counted in order to determine P(AUB).

The new probability set made up of all the elements from both sets is created when two sets are joined. When two sets intersect, a new set is created that includes every element from both sets.

Solution Explained:

Given in the question,

A bag contains 3 red and 5 green candies.

Total possibilities is 3 + 5 = 8  

Jack takes a candy at random and eats it  

A/Q there are 3 red candies out of 8, the probability is given by,

P(R) = 3/8

Now there are 2 red candies out of 7, so the probability is given by,

P(R') = 2/7

The probability of both events is given by,

P(2R) = P(R) × P (R') = 3/8 × 2/7 = 3/28

Therefore, the probability of Tim taking 2 red candies is P(2R) = 3/28

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The lengths a and b in the right triangle are given as follows:

The three trigonometric ratios are defined as follows:

The side length opposite to the angle of 30º has a length of 6, hence the hypotenuse a is obtained as follows:

sin(30º) = 6/a

1/2 = 6/a

a = 6 x 2

a = 12.

The side length b is obtained applying the cosine of 60º, as follows:

cos(60º) = b/12.

\(\sqrt{3}{2} = \frac{b}{12}\)

\(b = 6\sqrt{3}\)

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Given:

In the given figure \(m\parallel n\parallel p\).

\(m\angle 10=2x+70\)

\(m\angle 7=5x-20\)

To find:

The \(m\angle 3\).

Solution:

If a transversal line intersect two parallel lines, then the alternate exterior angles are equal.

\(m\angle 7=m\angle 10\)          (Alternate exterior angle)

\(2x+70=5x-20\)

\(70+20=5x-2x\)

\(90=3x\)

Divide both sides by 3.

\(\dfrac{90}{3}=\dfrac{3x}{3}\)

\(30=x\)

Now,

\(m\angle 3=m\angle 7\)               (Corresponding angles)

\(m\angle 3=5x-20\)

\(m\angle 3=5(30)-20\)

\(m\angle 3=150-20\)

\(m\angle 3=130\)

Therefore, the measure of angle 3 is 130 degrees.