A) 142
B) 146
C) 138
D) 132
E) 144

The process capability index for this lab is 5.14

We know that the formula for the process capability index is:

[tex]C_{p}=min(\frac{X-LS}{3\sigma} , \frac{US-X}{3\sigma} )[/tex]

Here, the average turnaround(X) = 26.2

the standard deviation ( σ) = 1.05 minutes

the nominal value for service = 30 minutes

the upper specification= 50 minutes

and lower specification = 10 minutes

Using above formula the  process capability index would be,

[tex]C_{p}=min(\frac{X-LS}{3\sigma} , \frac{US-X}{3\sigma} )\\\\C_{p}=min(\frac{26.2-10}{3\times 1.05} , \frac{50-26.2}{3.15} )\\\\C_{p}=min(\frac{16.2}{3.15} , \frac{23.8}{3.15} )\\\\C_{p}=min(5.14, 7.56)\\\\C_{p}=5.14[/tex]

Therefore, the  process capability index is 5.14

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Answer: It costs 23.75 for 5 bags of cat food.

Step-by-step explanation: If 3 bags of cat food costs 14.25 to figure out how much it costs. First thing to do is, divide the known number (14.25) or the costs by the amount of bags that made up to this price.

14.25 divided by 3 equals 4.75.

4.75 is the costs of 1 bag of cat foods. Now for the final step, multiply the cost of 1 bag (4.75) by 5 because we’re trying to see how much it costs for 5 bags of cat food.

4.75

x 5

= 23.75!

you’re welcome!!

Answer:

The problem seems to be missing some important information such as the scale factor and the coordinates of the points in the original figure. Without this information, I cannot provide a complete solution to the problem. Please provide me with the missing information so I can help you better.

Step-by-step explanation:

The temperature of the pizza after 20 minutes will be 25 degrees.

the slope refers to the measure of the steepness or inclination of a line.

We can create a linear model to describe the relationship between time and temperature.

So, slope (m) = [tex]\frac{(y_2 - y_1)}{(x_2 - x_1)}[/tex]

Using the temperature and time values from the first and last data points:

m = [tex]\frac{(145 - 450)}{(16 - 0)}[/tex]

m = -305/16

Using the point-slope form of the equation of a line, we can now ascertain the equation of the line:

y - y₁ = m(x - x₁)

Using the first data point (0, 450);

y - 450 = (-305/16)(x - 0)

Simplifying, y = (-305/16)x + 450

To predict the temperature after 20 minutes, we can plug in x = 20 and solve for y:

y = (-305/16)(20) + 450

y = -950/16 + 450

y = 25

Therefore, we can predict that the temperature of the pizza after 20 minutes will be approximately 25 degrees.

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Answer:

x = 2 and x = 1/2.

Step-by-step explanation:

To solve (x-2)(2x-1) = 0, we need to find the values of x that make the left side of the equation equal to 0.

Using the zero product property, we know that if the product of two factors is equal to 0, then at least one of the factors must be equal to 0.

Therefore, we have two possible solutions:

1.x - 2 = 0, which gives us x = 2

2.2x - 1 = 0, which gives us x = 1/2

So, the solutions to the equation (x-2)(2x-1) = 0 are x = 2 and x = 1/2.

Answer:

360 adult tickets and 800 student tickets were sold.

Step-by-step explanation:

Let's use a system of equations to solve this problem.

Let x be the number of adult tickets sold, and y be the number of student tickets sold. We know that a total of 1,160 tickets were sold, so:

x + y = 1160

We also know that the total amount collected was $2,600. The amount collected from adult tickets is $5 times the number of adult tickets sold, and the amount collected from student tickets is $1 times the number of student tickets sold. So:

5x + 1y = 2600

Now we have a system of two equations:

x + y = 1160

5x + y = 2600

We can solve for one of the variables in terms of the other, and substitute into the other equation to solve for the remaining variable. For example, we can solve the first equation for y:

y = 1160 - x

Now substitute this expression for y into the second equation:

5x + (1160 - x) = 2600

Simplifying and solving for x:

4x + 1160 = 2600

4x = 1440

x = 360

So 360 adult tickets were sold. To find the number of student tickets sold, we can use either equation. Let's use the first equation:

x + y = 1160

360 + y = 1160

y = 800

So 800 student tickets were sold.

Therefore, 360 adult tickets and 800 student tickets were sold.

Answer:

28 minutes

Step-by-step explanation:

1/5 × 35 = 7

35 - 7 = 28

After answering the presented question, we can conclude that As a equation result, in 2011, the cost of a residence utilising 0 kWh of power would be zero dollars.

In mathematics, an equation is a proposition that states the equivalence of two expressions. An equation consists of two sides separated by a system of equations (=). For instance, the statement "2x + 3 = 9" states that the word "2x Plus 3" equals the integer "9". The goal of solving equations is to find the value or amounts of the variable in the model) that will permit the calculation to be accurate. Mathematics can be simple or complex, linear or nonlinear, and contain one or more parts. For example, in the equation "x2 + 2x - 3 = 0," the variable x is raised to the power of 2. Lines are used in many areas of mathematics, including algebra, arithmetic, and geometry.

y = x/10 is the provided equation.

If a residence uses 0 kWh of power (x=0), the cost of electricity is as follows:

y = x/10 = 0/10 = $0 per kWh.

As a result, in 2011, the cost of a residence utilising 0 kWh of power would be zero dollars.

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Answer:

Step-by-step explanation:

The Answer is 203 Fahrenheit.

(95 x 9/5) + 32 = 203

The final amount after 2 years of compounding semiannually at 11% is $31,909.52.

First we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where

Plugging in the given values, we get:

P = $24,700

r = 0.11 (11% annual rate as a decimal)

n = 2 (compounded semiannually, or twice per year)

t = 2 (2 years)

A = $24,700(1 + 0.11/2)^(2*2)

= $31,909.52

Therefore, the final amount after 2 years of compounding semiannually at 11% is $31,909.52.

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The slope of the function is 1.

The whole function is simply f(x)=x+3

Answer:

Step-by-step explanation:

h+f

If the hοtel rοοm fοr Karina and her friend cοsts $86 and they park fοr 7 hοurs, then she will pay $119.

The cοst οf anything is the sum οf mοney οr resοurces that must be used up in οrder tο acquire οr manufacture it. It is a measurement οf the cοsts incurred tο attain a specific οbjective οr result.

The expressiοn tο represent the cοst οf Karina's theme park trip wοuld be:

38 + 10 + 4h + (1/2)r

This includes the $38 entry price, the $10 lunch expense, and the $4 per hοur parking expense fοr the 72 hοurs. Given that Karina and her friend are splitting the cοst οf the hοtel rοοm, the final phrase (1/2)r denοtes Karina's pοrtiοn οf the expense.

If the hοtel rοοm fοr Karina and her friend cοsts $86 and they park fοr 7 hοurs, we can change these values intο the fοrmula tο make it simpler:

= 38 + 10 + 4(7) + (1/2)(86)

= 38 + 10 + 28 + 43

= $119

Therefοre, Karina will pay $119 fοr her theme park trip.

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Answer:

.8/10

Because Lisa made 80 out of 100 free throws, and her probability of making a free throw is 0.8, the probability would be .8/10.

Step-by-step explanation: this may be wrong due to lack of detail in the question.

The degree of the polynomial is 2, and the leading coefficient is 3. The polynomial has two terms, so we classify it as a binomial.

What is the polynomial equation?

A polynomial equation is an equation in which the variable(s) are raised to non-negative integer powers and the coefficients are constants. In other words, it is an equation in which the terms involve only addition, subtraction, multiplication, and positive integer exponents.

Assuming that the expression is 7 + 3p²:

To write the polynomial in standard form, we need to arrange the terms in descending order of degree:

3p² + 7

hence, The degree of the polynomial is 2, and the leading coefficient is 3. The polynomial has two terms, so we classify it as a binomial.

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The answer is that the z score is unusual. We can calculate it in the following manner.

To calculate the z-score for a score of 72, we can use the formula:

z = (x - μ) / σ

where x is the individual score, μ is the mean, and σ is the standard deviation.

Substituting the given values, we get:

z = (72 - 77) / 2 = -2.5

Rounding to two decimal places, the z-score is -2.50.

To determine if this z-score is unusual, we need to compare it to a standard normal distribution. In a standard normal distribution, about 95% of the data falls within 2 standard deviations of the mean (i.e., between a z-score of -2 and +2). A z-score beyond this range is generally considered unusual.

Since the z-score for a score of 72 is beyond this range (i.e., it is less than -2), it is considered unusual.

Therefore, the answer is:

Unusual

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For problem (A), subtracting A and B alone cannot solve the problem as the result does not provide the amount of water left in the bowl, and for problem (B), subtracting A and B can solve the problem as it provides the amount of pizza left after James ate.

(A) This problem cannot be solved by subtracting A and B. If we subtract 1/3 from 1/2, we get 1/6, which is the amount of water that was poured out. However, this does not tell us how much water is left in the bowl. To solve the problem, we need to subtract 1/3 from 1/2 and then subtract the result from 1/2. This gives us

1/2 - 1/3 = 1/6

1/2 - 1/6 = 1/3

Therefore, there is 1/3 cup of water left in the bowl.

(B) This problem can be solved by subtracting A and B. If James ate 1/2 of the pizza yesterday and 1/3 of the pizza today, then he ate a total of

1/2 + 1/3 = 5/6

of the pizza. Therefore, the amount of pizza left is:

1 - 5/6 = 1/

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The given question is incomplete, the complete question is:

determine whether the problem can be solved by subtracting A and B . If not, explain why not, and explain how the problem should be solved if there is enough information to do so

A) Zelha pours 1 2 cup of water into an empty bowl and then pours out 1 3. How much water is in the bowl now? Zelha pours 1 2 cup of water into an empty bowl and then pours out 1 3 cup of water. How much water is in the bowl now? (B)  Yesterday James ate 1 2 of a pizza, and today he ate 1 3 of the whole pizza. Nobody else ate any of that pizza. How much pizza is left?

If we roll two die, number of possible outcome is 1 and total number of outcome is 36 therefore the the probability of rolling a one on the first die and a three on the second die is 1/36.

Total number outcome is :

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

Number of possible outcome is 1

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will learn the potential outcomes for a random experiment using this fundamental theorem of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.

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Answer:

If the area of a circle is 2.0096 square miles. The circle's radius is 0.8 .

By the Triangle Sum Theorem, x + y + a = 180° and x + y + b = 180°. By substitution, x + y + a = 180°. Subtract equal quantities from both sides to get a = b.

In Mathematics, a triangle is a two-dimensional geometric shape that comprises three sides, three vertices and three angles only.

Furthermore, the sum of the angles in a triangle is equal to 180. This ultimately implies that, we would sum up all of the angles as follows;

x + y + b = 180°

By substitution, we have the following:

x + y + a = 180°

Next, we would subtract equation 1 from equation 2, we have:

a - b = 0

a = b (Prove).

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After answering the provided question, we can state that As a result, expression rather than a rating of 6, it would be more appropriate to use the median to describe the centre of this data set.

An expression in mathematics is a collection of interpretations, digits, and transnational corporations that resemble a causative link or regimen. A real number, a mutable, or a combination of the two can be used as an expression. Mathematical operators include extension, subtraction, rapid spread, separation, and exponentiation. Expressions are widely used in arithmetic, mathematics, and shape. They are used in the representation of mathematical formulas, the solution of equations, and the simplification of mathematical relationships.

Because the dot plot is not symmetrical and the distribution appears to be skewed towards higher ratings, a rating of 6 may not be a good description of the centre of this data set. The numbers 8, 9, and 10 are more common than the numbers 0-7, indicating that the data set has a right skew.

As a result, the centre of the data set may be better described by a measure of central tendency that accounts for data skewness, such as the median.

As a result, rather than a rating of 6, it would be more appropriate to use the median to describe the centre of this data set.

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The middle οf BC and B′C′ shοuld be crοssed by a line. This line serves as the triangle's reflectiοn line.

A line is a straight, οne-dimensiοnal figure in geοmetry that can gο οn fοrever in bοth directiοns. It is frequently depicted as an infinitely lοng straight line with arrοws at bοth ends. Any twο οf its pοints, referred tο as a line's endpοints, are what characterize a line. Geοmetrical cοncepts like angles, planes, and shapes are defined in terms οf lines, which are fundamental geοmetrical οbjects. These can be depicted using mathematical sοftware οr a straightedge and pencil.

Finding the perpendicular bisectοr οf each pair οf related sides is necessary befοre we can cοnstruct the line οf reflectiοn that reflects triangle ABC οntο triangle A′B′C′. We will find the center οf reflectiοn at the pοint where these three perpendicular bisectοrs cοnnect.

Bypassing the intersectiοn οf AB and A′B′, draw a line. Identify this pοint as M.

The middle οf AC and A′C′ shοuld be crοssed by a line. Identify this pοint as N.

The middle οf BC and B′C′ shοuld be crοssed by a line. Identify this pοint as O.

Lοcate where the MN and MO lines cοnverge. Put a P after this place.

The middle οf BC and B′C′ shοuld be crοssed by a line.  This line serves as the triangle's reflectiοn line.

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Complete Question:

Draw the line of reflection that reflects △ABC onto triangle Δ A'B'C'

The answer is in the picture

The minimum sample size required to ensure that the estimate has an error of at most 0.15 at the 99% level of confidence = 426

Here, the population variance is σ² = 1.44

The mean is [tex]\bar{x}[/tex] = 6

And the margin of error is  E = 0.15

The standard deviation is given by,

⇒ σ = [tex]\sqrt{1.44}[/tex]

⇒ σ = 1.2

Here, the confidence level is 99%

So, the level of signoficance would be,

⇒ α = (100 - 99)%

⇒ α = 0.01

From the normal distribution table the critical value would be,

[tex]z_{\alpha /2}[/tex] = 2.58

Now we find the sample size :

[tex]n=(\frac{z_{\alpha /2}\times \sigma}{E} )^2\\\\n=(\frac{2.58 \times 1.2}{0.15} )^2[/tex]

n = 426

Therefore, the sample size is 426

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The final form of the exponential function is: f(t) = 750(0.8825)raise to the power t

what is exponential function?

An exponential function is a mathematical function of the form f(x) = a to the power x, where "a" is a positive constant (called the base of the exponential function) and "x" is a variable that can take on any real number value.

The key property of an exponential function is that the output value (or "y" value) grows or decays at a constant rate as the input value (or "x" value) increases or decreases. This constant rate of growth or decay is determined by the base "a" of the function.

When the base "a" is greater than 1, the function represents exponential growth, where the output value increases rapidly as the input value increases. When the base "a" is between 0 and 1, the function represents exponential decay, where the output value decreases rapidly as the input value increases.

Exponential functions are commonly used to model natural phenomena such as population growth, radioactive decay, and compound interest. They also have many applications in science, engineering, economics, and finance.

Starting with the given exponential function:

f(t) = 750(0.65)raise to the power (t/35)

We can rewrite 0.65 as 0.65, and 35 as 5 * 7. Then we have:

f(t) = 750(0.65)raise to the power (t/(5*7))

Using the exponent rule that (a to the power b)to the power c = a to the power (bc), we can simplify the expression inside the parentheses:

f(t) = 750(0.65 to the power (t/5))⁷

Letting a = 750 and b = 0.65 to the  power(1/5), we can write the function in the desired form:

f(t) = ab to the power , where a ≈ 750 and b ≈ 0.8825 (rounded to four decimal places)

Therefore, the final form of the exponential function is:

f(t) = 750(0.8825) to the power t

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Therefore, the angle at which the ellipse x² + 3y² = 12 is seen from the point M (0,4) is -30 degrees.

An ellipse is a geometric shape that resembles a stretched or squished circle. It can be defined as the set of all points in a plane, such that the sum of the distances from two fixed points, called the foci, is constant. An ellipse has two axes, a major axis and a minor axis, which intersect at the center of the ellipse. The length of the major axis is twice the distance from the center to one of the foci, while the length of the minor axis is twice the distance from the center to one of the points where the ellipse intersects the major axis. Ellipses have many applications in mathematics, physics, and engineering. They are used to model the orbits of planets and satellites, as well as the paths of objects in electric and magnetic fields. They are also used in optics to describe the shape of lenses and mirrors, and in statistics to model data distributions.

Here,

To determine the angle at which the ellipse x² + 3y² = 12 is seen from the point M (0,4), we first need to find the equation of the tangent line to the ellipse at the point (0,4).

To do this, we take the derivative of the equation of the ellipse with respect to x and evaluate it at the point (0,4):

d/dx (x² + 3y²) = 2x + 6y(dy/dx)

At the point (0,4), we have x = 0 and y = 4, so the equation becomes:

0 + 6(4)(dy/dx) = 0

Solving for dy/dx, we get:

dy/dx = 0

This means that the tangent line to the ellipse at the point (0,4) is a horizontal line passing through the point (0,4).

Now we can find the angle at which the ellipse is seen from the point M (0,4) by finding the angle between the horizontal tangent line and the line connecting the point M to the origin. This angle is given by:

tan θ = (y₂ - y₁)/(x₂ - x₁)

where (x₁, y₁) = (0,4) is the point M and (x₂, y₂) is the point where the tangent line intersects the x-axis.

Since the tangent line is horizontal, it intersects the x-axis at the point (±2√3, 4), which are the x-intercepts of the ellipse. Choosing the positive x-intercept, we have:

x₂ = 2√3

y₂ = 0

Substituting these values into the formula for the tangent, we get:

tan θ = (0 - 4)/(2√3 - 0) = -2/2√3 = -1/√3

Taking the inverse tangent of both sides, we get:

θ = -30 degrees

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Using the empirical rule, the percentage of IQ scores that are greater than 79 is 84%.

The empirical rule, also known as the 68-95-99.7 rule, states that for a normal distribution:

Since we know that the mean is 96 and the standard deviation is 17, we can calculate how many standard deviations away from the mean an IQ score of 79 is:

(79 - 96) / 17 = -1

This means that an IQ score of 79 is one standard deviation below the mean. This also means that approximately 68% of the data falls between 79 and (96 + 17) = 113.

Meanwhile, approximately 32% of the data falls outside of one standard deviation. We can say that half of this 32% are scores less than 79 and the other half are scores greater than 113. So the percentage of IQ scores greater than 79 is:

100 - (1/2 of 32) = 84%

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Therefore, the volume of a cycle that is shaped like a cylinder with a height of 150 feet and a radius of 35 feet is 576975 ft^3.

They are asking us to calculate the volume of a cycle, formed by a cylinder (The cycle is shaped like a cylinder).

To calculate the volume, we apply the formula:

We know that the height you have is 150 feet, and the radius is 35 feet, we solve:

V = 3.14 × (35 ft)² × 150 ft

V = 3.14 × 1225 ft² × 150 ft

V = 576975 ft³

Therefore, the volume of a cycle that is shaped like a cylinder with a height of 150 feet and a radius of 35 feet is 576975 ft^3.

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Answer:

False.

Step-by-step explanation:

Use Pythagorean theorem.

919681+1022121=1067089

1941802≠1067089

so the triangle is acute, not right.