two catalysts may be used in a batch chemical process. twelve batches were prepared using catalyst 1, resulting in an average yield of 86 and a sample standard deviation of 3. fifteen batches were prepared using catalyst 2, and they resulted in an average yield of 89 with a stan- dard deviation of 2. assume that yield measurements are approximately normally distributed with the same standard deviation. (a) is there evidence at 1% significance level to support a claim that catalyst 2 produces a higher mean yield than catalyst 1? (b) find a 95% confidence interval on the difference in mean yields.

Answer:

28 and 37

Split 65 into 2 numbers

30 and 35

Then add and subtract till you get your answer

29 and 36

28 and 37

The probability of getting a sample average of 93 or more customers, if the manager had not offered the discount, is zero.

To calculate the probability of obtaining a sample average of 93 or more customers if the manager had not offered the discount, we need to use the concept of sampling distributions and the Central Limit Theorem.

Given that the underlying distribution of the number of customers is normal, with an average of 22 and a standard deviation of 6, we can calculate the standard deviation of the sample mean (also known as the standard error) using the formula:

Standard Error (SE) = Standard Deviation / √(Sample Size)

In this case, the sample size is 5 (for the 5-weekday period), so the standard error is:

SE = 6 / √5 ≈ 2.683

Next, we can calculate the z-score for a sample average of 93 using the formula:

z = (Sample Average - Population Mean) / Standard Error

z = (93 - 22) / 2.683 ≈ 26.359

Finally, we can use the standard normal distribution table or a calculator to find the probability associated with this z-score:

P(Sample Average ≥ 93) = P(z ≥ 26.359)

Since the z-score is extremely large, the probability associated with it is essentially zero.

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Answer:

B

Step-by-step explanation:

i hate math

A number that has all its digits 1/10 of the value compared to the digits in Sid's number 23,459 is 0.2, 0.3, 0.4, 0.5, and 0.9.

Sid wrote the number 23,459. To find a number that has all its digits 1/10 of the value compared to the digits  to the digits in Sid's number, we can follow these steps:

1. Break down Sid's number into its individual digits: 2, 3, 4, 5, and 9.

2. To find a number with digits 1/10 the value, we divide each digit by 10.

  - For the digit 2, 1/10 of its value is 0.2.
  - For the digit 3, 1/10 of its value is 0.3.
  - For the digit 4, 1/10 of its value is 0.4.
  - For the digit 5, 1/10 of its value is 0.5.
  - For the digit 9, 1/10 of its value is 0.9.

3. Combine these digits together to form a new number: 0.2, 0.3, 0.4, 0.5, and 0.9.

4. The new number is 0.2, 0.3, 0.4, 0.5, and 0.9.

Therefore, a number that has all its digits 1/10 of the value compared to the digits in Sid's number 23,459 is 0.2, 0.3, 0.4, 0.5, and 0.9.

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Answer:

The intercept of the line perpendicular to the line \(y = x + 1\) is 5.

Step-by-step explanation:

The line \(y = x + 1\) has a slope 1. By Analytic Geometry, the slope of the line perpendicular to the original line is determine by the following formula:

\(m_{\perp} = -\frac{1}{m}\) (1)

Where:

\(m\) - Slope of the original line.

\(m_{\perp}\) - Slope of the line perpendicular to the original line.

If we know that \(m = 1\), then the new slope is:

\(m_{\perp} = -\frac{1}{1}\)

\(m_{\perp} = -1\)

A line is defined by the following expression:

\(y = m\cdot x + b\) (2)

Where:

\(x\) - Independent variable.

\(y\) - Dependent variable.

\(m\) - Slope.

\(b\) - Intercept.

If we know that \((x,y) = (4,1)\) and \(m = -1\), then the intercept of the line perpendicular to the original line:

\(b = y - m\cdot x\)

\(b = 1+4\)

\(b = 5\)

The intercept of the line perpendicular to the line \(y = x + 1\) is 5.

Answer:

(1, -1)

Step-by-step explanation:

Why not put points on a graph and take a look. Perhaps even without graphing we can notice that the horizontal distance is 15 and the vertical distance is 5. Since the desired ratio is 3:2 we need to divide the segment into fifths. Since the segment is easily divisible into fifths, we can see the point we need on the graph. See image.

Answer:

The process capability index for this system is 0.9103

Step-by-step explanation:

Upper specification = 1.649 inches

Lowe Specification = 1.507 inches

Mean = 1.57 inches

Standard Deviation = 0.026 inches

Process Capability Index = PCI

PCI = (Upper specification - lower specification)/6(standard deviation)

So, we get,

PCI = (1.649 - 1.507)/((6)(0.026))

PCI = 0.142/0.156

PCI = 0.9102564

To four decimal places, we get,

PCI = 0.9103

Answer:

2(x^3-x^2-6)

Step-by-step explanation:

2 out of 2x^3 - 2x^2 - 12

The height ofobject's bounce is the response variable because it depends on many factor.

An independent variable is one which is not affected by any other variable for example, the amount we spend, the time we study ,etc.  

An explanatory variable is a type of independent variable but not fully independent but depends on some factors.

Though explanatory and independent variables are practically used interchangeably the main difference is explanatory variable is not independent but explains the variations in the response varaible.

A response variable, also known as a dependent variable, is a concept, idea, or quantity that someone wants to measure. It depends on an independent variable.

Since, the height of the an object's bounce depends on many factors

like how much energy is lost in the ball during the collision with the floor, the elasticity of the material etc.

Therefore, we can say that height ofobject's bounce is the response variable because it depends on many factor.

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The length and width of the plot that will maximize the area is 60 meters by 120 meters. The largest area that can be enclosed is 7200 square meters.

To maximize the area of the rectangular plot, Farmer Ed must use 9000 meters of fencing to enclose three sides of the plot. The fourth side, which borders the river, does not need to be fenced. To find the length and width of the plot that will maximize the area, the 9000 meters of fencing must be divided into two sides of equal length, with the remaining fencing used for the third side. This results in a length of 120 meters and a width of 60 meters, which maximizes the area of the plot. The largest area that can be enclosed is 7200 square meters.

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Answer:

140 degrees

Step-by-step explanation:

HIF=GFI

Therefore, the total distance Gabe will paddle is 2x + 400 meters. The exact value of x depends on the width of the river, which is not provided in the given information.

To find the total distance Gabe will paddle, we need to consider the distance he will travel from Q to P, then from P to R, and finally from R back to Q.

First, let's consider the distance from Q to P. Since Gabe will paddle in a diagonal line across the river, this distance can be calculated using the Pythagorean theorem.

The length of the bridge (PR) is given as 400 meters, which is the hypotenuse of a right triangle. The width of the river can be considered as the perpendicular side, and the distance Gabe will paddle from Q to P is the other side. Let's call this distance x.

Using the Pythagorean theorem, we have:

x^2 + (width of the river)^2 = PR^2

Since the width of the river is not given, we'll represent it as w. Therefore:

x^2 + w^2 = 400^2

Next, let's consider the distance from P to R. Gabe will paddle along a route beside the bridge, which means he will travel the length of the bridge (PR) again. So, the distance from P to R is also 400 meters.

Finally, Gabe will paddle back from R to Q along the shore. Since he will follow the shoreline, the distance he will paddle is equal to the distance from Q to P, which is x.

To find the total distance, we add up the distances:

Total distance = QP + PR + RQ

= x + 400 + x

= 2x + 400

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The option that is NOT equivalent to 52% is Option B: 5.2.

To determine which option is not equivalent to 52%, we need to compare the given options with the value of 52%. Let's examine each option and determine if it is equivalent to 52%.

Option A: 0.52

Option B: 5.2

Option C: 0.052

Option D: 520

To find the equivalent decimal value of a percentage, we divide the percentage by 100.

Let's calculate the equivalent decimal value for 52%:

52% = 52/100 = 0.52

Now, let's compare this with the given options:

Option A: 0.52

This option is equivalent to 52%, as we calculated earlier.

Option B: 5.2

This option is not equivalent to 52%. It represents 520%, which is ten times greater than 52%.

Option C: 0.052

This option is not equivalent to 52%. It represents 5.2%, which is one-tenth of 52%.

Option D: 520

This option is not equivalent to 52%. It represents the whole number 520, which is a hundred times greater than 52%.

Therefore, the option that is NOT equivalent to 52% is Option B: 5.2.

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Answer

62

5.3

65

5.8

2.5

Step-by-step explanation:

FOr the first one we have the opposite and adjacent side, so we'll use TOA

let x= angle

tan(x)=4.7/2.5

x=61.99 or 62

2.) for this one we can just use pathagoryeous thereom

2.5²+4.7²=c²

28.34=c²

c=5.323

3.) For this one we know that the angles in a traingle must add to 180

let x= missing angle

25+90+x=180

x=65

4.) For this one we have the adjacent side but need the hypotonouse

we will therefore use CAH

cos(25)=5.3/x

5.3/(cos(25))=x

x=5.8

5.) For this one we will just use the pathagoryeous to solve for the missing side

a²+5.3²=5.8²

a²=6.107

a=2.5

The number of each type of flower Eliott will use to design his garden will be =the number of red roses = 5, the number of blue delphiniums = 15

Division is one of the major arithmetic operation that is used to know the number of groups that can be placed under data sets when shared.

The number of flowers that Eliott plans to plant = 20

The types of flower present = 2

The red roses = a

The blue delphiniums = 3a

To find the number of each flower planted, find a.

20 = 3a + a

20 = 4a

a = 20/4

a= 5

Therefore, the number of red roses = 5, The number of blue delphiniums = 3×5 = 15

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a) This hypothesis test is that there is sufficient evidence, at a significance level of 0.01, to suggest that coyotes in the specified region tend to live longer than the average age of 1.75 years.

The level of significance in this hypothesis test is α = 0.1. The null hypothesis (H0) is that the population mean age of coyotes in the region is 1.75 years, while the alternative hypothesis (H1) is that the population mean age is less than 1.75 years.

The sampling distribution to be used in this case is the Student's t-distribution, since the sample size is relatively small (n = 51) and the population standard deviation (σ) is unknown.

The value of the sample test statistic can be calculated by using the formula: t = (x - μ) / (s / √n), where x is the sample mean, μ is the population mean, s is the sample standard deviation, and n is the sample size. The calculated value of the test statistic can then be compared to the critical value(s) from the t-distribution to find the p-value. The p-value represents the probability of observing a test statistic as extreme as the calculated value, assuming that the null hypothesis is true.

Based on the calculated p-value and the chosen level of significance, we can determine whether to reject or fail to reject the null hypothesis. If the p-value is less than α, we reject the null hypothesis and conclude that the data are statistically significant. In this case, the statement "At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant" indicates that the data provide evidence to support the claim that coyotes in the specified region tend to live longer than 1.75 years.

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Answer:

1/9

Step-by-step explanation:

So, we are given the following data or parameters or infomation in the question above;

=>" A container has 14 yellow chips, 10 blue chips, and 12 red chips in it. "

=> "One chip is randomly chosen from the container, then a second chip is randomly chosen after replacing the first chip."

Therefore, the total number of chips in the container = 14 + 10 + 12 = 36 chips.

The probability of drawing a red chip in the first draw = 12/36 = 1/3.

The probability of drawing a red chip in the second draw = 1/3 also.

Thus, the probability that both chips are red => 1/3 × 1/3 = 1/9.

Answer:

DE = 34

AC = 68

Step-by-step explanation:

since DE are midpoints, you can create this equation: 2(8x + 2) = 20x - 12

solve:

16x + 4 = 20x - 12

16x + 16 = 20x

16 = 4x

4 = x

plug this into both equations to find each side:

DE: 8(4) + 2 = 34

AC: 20(4) - 12 = 68

we know our answer is right because AC is twice as long as DE

Josh should mix 1.2 gallons of dark pink paint and 1.8 gallons of light pink paint to achieve the desired medium pink color.

To find out how much of each leftover paint Josh should mix to achieve a medium pink color (50% red), we can set up a system of equations based on the percentages of red in the paints.

Let's assume that Josh needs x gallons of dark pink paint and y gallons of light pink paint to achieve the desired color.

The total amount of paint needed is 3 gallons, so we have the equation:

x + y = 3

The percentage of red in the dark pink paint is 80%, which means 80% of x gallons is red. Similarly, the percentage of red in the light pink paint is 30%, which means 30% of y gallons is red. Since Josh wants a 50% red mixture, we have the equation:

(80/100)x + (30/100)y = (50/100)(x + y)

Simplifying this equation, we get:

0.8x + 0.3y = 0.5(x + y)

Now, we can solve this system of equations to find the values of x and y.

Let's multiply both sides of the first equation by 0.3 to eliminate decimals:

0.3x + 0.3y = 0.3(3)

0.3x + 0.3y = 0.9

Now we can subtract the second equation from this equation:

(0.3x + 0.3y) - (0.8x + 0.3y) = 0.9 - 0.5(x + y)

-0.5x = 0.9 - 0.5x - 0.5y

Simplifying further, we have:

-0.5x = 0.9 - 0.5x - 0.5y

Now, rearrange the equation to isolate y:

0.5x - 0.5y = 0.9 - 0.5x

Next, divide through by -0.5:

x - y = -1.8 + x

Canceling out the x terms, we get:

-y = -1.8

Finally, solve for y:

y = 1.8

Substitute this value of y back into the first equation to solve for x:

x + 1.8 = 3

x = 3 - 1.8

x = 1.2

Therefore, Josh should mix 1.2 gallons of dark pink paint and 1.8 gallons of light pink paint to achieve the desired medium pink color.

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Answer:

that is reading my friend

Step-by-step explanation:

Answer:

Sidney  is shallow but busy. One common boating hazard in this city are the rocks, stingrays, and sharks. Rounf trip fair: $2000 hotel cost: 250 for 1 night and and or 2500 for 10 nights. total travel expense: $4500.

Step-by-step explanation:

Sidney is shallow but busy. One common boating hazard in this city are the rocks, stingrays, and sharks. Rounf trip fair: $2000 hotel cost: 250 for 1 night and and or 2500 for 10 nights. total travel expense: $4500. 

The limit of (e^x - e^(-x) - 2x)/(e^x - x - 1) as x approaches 0 can be found using L'Hôpital's rule.

Using L'Hôpital's rule, we differentiate the numerator and denominator with respect to x:

Numerator: (e^x - (-e^(-x)))' = (e^x + e^(-x))

Denominator: (e^x - x - 1)'

Taking the limit as x approaches 0 of the derivatives, we get:

lim x→0 (e^x + e^(-x))/(e^x - 1)

Now, substituting x = 0 into the expression, we get:

(e^0 + e^(-0))/(e^0 - 1) = (1 + 1)/(1 - 1) = 2/0

The result is an indeterminate form of 2/0, which indicates that L'Hôpital's rule can be applied again.

Differentiating the numerator and denominator once more, we get:

Numerator: (e^x + e^(-x))' = (e^x - e^(-x))

Denominator: (e^x - 1)'

Taking the limit as x approaches 0 of the derivatives, we have:

lim x→0 (e^x - e^(-x))/(e^x) = (1 - 1)/(1) = 0/1 = 0

Therefore, the limit of (e^x - e^(-x) - 2x)/(e^x - x - 1) as x approaches 0 is 0.

In summary, applying L'Hôpital's rule twice, we find that the limit of the given expression as x approaches 0 is 0.

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Answer: x= 6

Step-by-step explanation:

Since the shape is a parallelogram, the angles will either be equal to each other or add up to 180.  

You can see they do not look the same so they add up to equal 180

12x + 3 +105 = 180

12x + 108 = 180

12x = 72

x = 6

Answer:

\(\huge\boxed{\tt{SSS}}\)

Step-by-step explanation:

SSS (Side-Side-Side) Postulate can be used to prove the two triangles congruent.

Here's why:

Whole figure is a parallelogram which means that opposite sides are parallel and equal (or congruent).

So, Two of the sides can be proved congruent by that way.

The third side is common in both of the triangles which means that the third side is also congruent.

Hence, the two triangles are congruent by SSS postulate.

\(\rule[225]{225}{2}\)

Hope this helped!

x=13, no idea what y is.

The riddle mentioned in the question is about a farmer who is traveling along with a sack of rye, a goose, and a mischievous dog.

He comes to a river that he must cross from east to west, and there is a boat available to do so.  Therefore, the farmer takes the goose back to the east side and leaves it there. He then takes the sack of rye across the river, drops it off with the dog, and goes back to the east side to pick up the goose. In this manner, all of the farmer's possessions can be safely transported across the river without any of them being lost to the dog or the goose.This riddle is a classic example of a type of logical puzzle known as a "transport problem."

The goal of a transport problem is to determine how to transport one or more objects from one location to another while satisfying certain constraints, such as the size of the transport vehicle or the safety of the objects being transported.

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Answer:

4 IS THE ANSWER MATE

Step-by-step explanation:

Absolutely, I can do that!

Let's take a look at each statement:

1) f(x) has a y-intercept at (0,2)

To find the y-intercept, we need to set x to 0 and solve for y. Plugging in x = 0 into the equation for f(x), we get:

f(0) = -log(0+4) + 2

f(0) = -log(4) + 2

f(0) = -0.602 + 2

f(0) = 1.398

Since the y-coordinate of the y-intercept is 1.398, not 2, this statement is false.

2) The function -f(x) has a y-intercept at (0,2)

Since the negative sign in front of f(x) reflects the graph of f(x) across the x-axis, we can determine the y-intercept of -f(x) by taking the opposite of the y-intercept of f(x). Since the y-intercept of f(x) is not 2, this statement is also false.

3) As x approaches positive infinity, the function f(x) approaches negative infinity.

The function f(x) is a logarithmic function with a negative coefficient, which means it approaches negative infinity as x approaches positive infinity. Therefore, this statement is true.

4) As x approaches -4 from the right, the function f(x) approaches negative infinity.

As x approaches -4 from the right, the value of f(x) becomes more and more negative without bound, which means that f(x) approaches negative infinity as x approaches -4 from the right. Therefore, this statement is also true.

In summary, statements (1) and (2) are false, while statements (3) and (4) are true.

9514 1404 393

Answer:

  54/(-6) = -9

Step-by-step explanation:

From your knowledge of multiplication tables, you know that ...

  6·9 = 54

From your knowledge of signed arithmetic, you know that ...

  54/(-6) = -(54/6) = -(6·9)/6 = -9

The expression is not undefined. The quotient is -9.

Answer:

y= -20/9

Step-by-step explanation:

4y+5/3=y-5

3y= -(5+5/3)

3y= -20/3

y= -20/9

Answer:

Collect like terms

4y-y=-10/2-5/3

3y=-5-5/3

5-5/3

LCM=3

3/1=3×5=15

3/3=1×5=5

15-5÷3

10/3

3y=10/3÷3

3y=30/3

y=10