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The quadratic equation x² + 2 - 4x = -4 in standard form is  x² - 4x + 6 = 0

A quadratic equation in standard form is given by ax² + bx + c = 0

Now, given the equation x² + 2 - 4x = -4, we desire to write it in standard form, we proceed as follows.

Since we have the quadratic equation x² + 2 - 4x = -4 writing it in standard form, we have

x² + 2 - 4x = -4

Adding 4 to both sides of the equation, we have that

x² + 2 - 4x + 4 = -4 + 4

x² + 2 + 4 - 4x = 0

x² + 6 - 4x = 0

Re-arranging, we have that

x² - 4x + 6 = 0

So, in equation in standard form is  x² - 4x + 6 = 0

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Compared to smaller firms, larger companies tend to option (B) systematically scan foreign markets to see where export opportunities lie.

Larger companies tend to systematically scan foreign markets to identify potential export opportunities due to their greater resources, including financial and human capital. This allows them to invest in researching and analyzing foreign markets, and to create effective exporting strategies. Furthermore, larger companies often have established distribution networks and greater brand recognition, which can make exporting a more viable option.

In contrast, smaller firms may lack the necessary resources and expertise to effectively navigate the complexities of exporting to foreign countries, and may therefore be more hesitant to seek out export opportunities.

Therefore, the correct option is (B) systematically scan foreign markets to see where export opportunities lie.

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The given question is incomplete, the complete question is:

Compared to smaller firms, larger companies tend to

Multiple Choice

A) delay exporting until after their domestic market is fully saturated.

B) systematically scan foreign markets to see where export opportunities lie.

C) be intimidated by the complexities and mechanics of exporting to foreign countries.

D) hesitate to seek export opportunities because they do not know how big the opportunities actually are

E) be reactive about seeking opportunities for profitable exporting.

To simulate the minutes between customer arrivals in Excel, one would use the Exponential distribution function in Excel.

This function is part of the Statistical functions category and can be found under the "Statistical" tab in Excel.

An exponential distribution is a probability distribution that describes the time between events in a Poisson process, where events occur continuously and independently at a constant average rate.

The Exponential distribution function in Excel takes two arguments: Lambda and x.

Lambda is the rate parameter, which describes the average number of events per unit of time.

In this case, the rate is 6 customers per hour, so Lambda would be equal to 6.

X is the time interval, and in this case, it would be the time between customer arrivals in minutes.

Therefore, to simulate the minutes between customer arrivals, one would use the following formula in Excel: =EXPON.DIST(x/60,1/6,TRUE)

The "x/60" part of the formula is used to convert the time interval from minutes to hours, as the rate is given in customers per hour.

The "1/6" part of the formula is used to set the Lambda value to 6.

The "TRUE" part of the formula is used to specify that we want the cumulative distribution function (CDF), which gives the probability that the time between events is less than or equal to x.

To simulate the minutes between customer arrivals in Excel, we would use the Exponential distribution function with Lambda = 6 and x being the time interval between customer arrivals in minutes.

The formula would be = EXPON.DIST(x/60,1/6,TRUE).

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Answer: 12 cups

Step-by-step explanation:

Answer:

12 cups

Step-by-step explanation:

1 pint = 2 cups

6 pints = 6 × 2 cups = 12 cups

Answer:

Step-by-step explanation:

The answer is 23/40

To simplify this expression, we need to find a common denominator for each pair of fractions that are being added or subtracted.

 
The common denominator for 1/4 and 1/5 is 20, so we can rewrite 1/4 as 5/20 and 1/5 as 4/20. Then, we can subtract these fractions to get 1/20.

 
The common denominator for -3/4 and 1/8 is 8, so we can rewrite -3/4 as -6/8. Then, we can add these fractions to get -5/8.

 
Now, we can combine the two simplified fractions by finding a common denominator of 40. We can do this by multiplying 20 and 8, which gives us 160.

Then, we can rewrite 1/20 as 2/40 and -5/8 as -25/40. Adding these fractions together gives us:

2/40 - 25/40 = -23/40.

The absolute value of any number is always positive so it becomes 23/40.

The simplified version of (1/4 - 1/5) + (-3/4 + 1/8) is 23/40.

Answer:

Step-by-step explanation:

All you have to do is subtract 6 from 14. The answer is 8. If the question is something like this one, always take the remainder and subtract it from how many you had in the beginning to get the answer.

Good luck

Peyton

Theprobability of the employee arriving between 8:30 a.m. and 8:35 a.m. is 0.5 or 1/2.

The probability that the employee will arrive between 8:30 a.m. and 8:35 a.m. has to be determined. The given data is that the particular employee arrives at work sometime between 8:00 a.m. and 8:50 a.m.

Based on past experience the company has determined that the employee is equally likely to arrive at any time between 8:00 a.m. and 8:50 a.m.To find the probability that the employee will arrive between 8:30 a.m. and 8:35 a.m.

Using the above data, the probability that the employee will arrive between 8:00 a.m. and 8:50 a.m. is one. Therefore, the probability that the employee will arrive between 8:00 a.m. and 8:30 a.m. is 0.5, and the probability that the employee will arrive between 8:35 a.m. and 8:50 a.m. is 0.5.

The probability that the employee will arrive between 8:30 a.m. and 8:35 a.m. is also equally likely, so its probability is 0.5.

Therefore, the probability that the employee will arrive between 8:30 a.m. and 8:35 a.m. is 0.5 or 0.5 or 1/2.

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(a) The area of the triangle is 16 square units.

(b) The area of the triangle is 54 square units.

(c) the area of the quadrilateral is 20 square units.

(d) The area of the triangle is 12.5 square units.

(a) To find the area of the triangle with vertices (0,0), (3,7), and (5,1), we can use the formula:

A = 1/2 | x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2) |

Plugging in the values, we get:

A = 1/2 | 0(7 - 1) + 3(1 - 0) + 5(0 - 7) |

= 1/2 | 0 + 3 - 35 |

= 1/2 |-32|

= 16

(b) To find the area of the triangle with vertices (-4,2), (0,-8), and (5,11), we can again use the same formula:

A = 1/2 | x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2) |

Plugging in the values, we get:

A = 1/2 | (-4)(-8 - 11) + (0)(11 - 2) + (5)(2 - (-8)) |

= 1/2 | 108 |

= 54

(c) To find the area of the quadrilateral with vertices (-2,-4), (3,1), (-1,5), and (6,-3), we can divide it into two triangles and find the area of each triangle.

We can use the formula for the area of a triangle:

A = 1/2 | x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2) |

For the triangle with vertices (-2,-4), (3,1), and (-1,5), we get:

A1 = 1/2 | (-2)(1 - 5) + (3)(5 + 4) + (-1)(-4 - 1) |

= 1/2 | (-8 + 35 + 5) |

= 16

For the triangle with vertices (3,1), (-1,5), and (6,-3), we get:

A2 = 1/2 | (3)(5 + 3) + (-1)(-3 - 1) + (6)(1 - 5) |

= 1/2 | (24 + 4 - 20) |

= 4

Therefore, the area of the quadrilateral is:

A = A1 + A2

= 16 + 4

= 20 square units

(d) To find the area of the triangle with vertices (-1,-2), (-2,3), and (4,-4), we can use the same formula:

A = 1/2 | x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2) |

Plugging in the values, we get:

A = 1/2 | (-1)(3 + 4) + (-2)(-4 + 2) + (4)(-2 - 3) |

= 1/2 | (-7 - 4 - 14) |

= 12.5

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Answer:

To calculate the slope of the line that passes through the points (1, 2) and (-3, 5), we use the slope formula:

m = (Y2 - Y1) / (X2 - X1)

where (X1, Y1) = (1, 2) and (X2, Y2) = (-3, 5).

Substituting the values into the formula, we get:

m = (5 - 2) / (-3 - 1)

m = 3 / (-4)

Simplifying the fraction by dividing both the numerator and denominator by their greatest common factor of 1, we get:

m = -3/4

Therefore, the slope of the line in simplest form is -3/4.

We select H1: μ ≠ 10, we will estimate the true mean of the target population 10 outside of the confidence interval.

p-value = 0.025

Confidence interval = 95% = 0.95

Level of significance (α) = 1 - Confidence interval

Level of significance (α) = 1- 0.95

Level of significance (α) = 0.05

However we are aware that the null hypothesis is rejected if the p-value is less than 0.05.

Due to the fact that our p-value (0.025) is below the α, we may thus reject our null hypothesis with α level of significance.

We choose H1: μ ≠ 10, the true mean of the target population 10 will be estimated outside of the confidence interval using the same data.

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The complete question is:

Suppose we do the below hypothesis test for the mean and obtained a p value 0.025.

H(0): μ = 10 Vs. H1: μ ≠ 10

If 95% confidence interval for the true mean of the target population is calculated using the same data, will 10 be inside or outside the confidence interval? Explain.

Karla paid 57.1% of the original price for an item that was originally priced at $350.

The explanation is that we can find the percentage that Karla paid by dividing the amount she paid by the original price and then multiplying by 100.

Percentage is a fraction out of 100. The formula for finding the percentage is as follows:  (part / whole) × 100.

So, if Karla paid $200 for an item that was originally priced at $350, we can find the percentage she paid as follows: (200/350) × 100 = 57.1%.

Therefore, Karla paid 57.1% of the original price. To round it to the nearest tenth of a percent, we can simply round the answer to one decimal place, which is 57.1%.

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Answer: 60%

Step-by-step explanation:

As mentioned earlier, we need to know the number of senior nutrition majors and sophomore non-nutrition majors to calculate the exact probability. Without this information, we cannot provide a specific answer to the question.

However, we can provide a general formula for computing the probability, assuming that the selections are made without replacement and the population of students is large enough to assume independence:

Probability of selecting a senior nutrition major and then a sophomore non-nutrition major = (Number of senior nutrition majors / Total number of students) × (Number of sophomore non-nutrition majors / (Total number of students - 1))

Once we have the values for the number of senior nutrition majors and sophomore non-nutrition majors, we can substitute them into this formula to obtain the probability, which will be a decimal number rounded to four decimal places.

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Answer:

y- intercept = 18

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 3x + 8 ← is in slope- intercept form

with slope m = - 3

• Parallel lines have equal slopes , then

y = - 3x + c ← is the partial equation

to find c substitute (5, 3 ) into the partial equation

3 = - 3(5) + c = - 15 + c ( add 15 to both sides )

18 = c

y = - 3x + 18 ← equation of parallel line

with y- intercept c = 18

The correlation between the ages of men and women in this situation would be +1. This means that for every one-year increase in the age of the man, the age of the woman would increase by one year as well. The correlation coefficient of +1 signifies a perfect positive linear correlation between the two variables.

In other words, if a man is 40 years old, the woman he is married to would be 37. If the man was 50, then the woman would be 47, and so on. This would remain true for any age, regardless of the difference in their ages. Therefore, the correlation between their ages would always remain +1.

It is important to note that this correlation coefficient is not necessarily reflective of  traditional or even natural social or biological behavior. Rather, it is simply a mathematical relationship that would exist in this specific situation. In reality, the age gap between married couples can vary widely depending on various social and cultural factors.

To summarize, the correlation between the ages of men and women in this scenario would be +1, signifying a perfect positive linear correlation. This means that for any given age of the man, the age of the woman would be exactly three years younger.

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ARMY DISBANDED MEANS SOLDIERS WERE RELEASED FROM SERVICE

When George Washington became president in 1789, the army he had

commanded in the American Revolution had disbanded. This means that

the soldiers were released from service and the military units were

dissolved after the end of the war.He pursued two intertwined interests:

military arts and western expansion. At 16 he helped survey Shenandoah

lands for Thomas, Lord Fairfax. Commissioned a lieutenant colonel in 1754,

he fought the first skirmishes of what grew into the French and Indian War.

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The Airbus A320 Sullenberger was piloting typically cruises at about 550 miles, or 807 ft per minute. His greatest horizontal range would have been between 4.4 and 6.0 nautical miles.

In certain circumstances, you may trade your miles for items like cash back and gift cards in addition to using them to pay for flights. Most of the time, redeeming airline points is straightforward. By entering into your account while making your reservation with most flights, you may use your points to get a free ticket.

You may also determine distance in miles unless you already know your speed and how long it takes to go a particular distance. Just double the time by the speed.

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The option that would result in the smallest margin of error in estimating the mean salt content, u, is 95% confidence, n = 50. The correct answer is Option D.

The margin of error is the amount by which a statistic is expected to differ from the true value of the population parameter. The interval estimate is calculated with the help of a margin of error. The margin of error and the interval estimate are inversely related to each other. If we want a small margin of error, we must increase the sample size.

The confidence level is the likelihood that a population parameter will fall within a specified range of values. The confidence level is determined by the sample size and margin of error. The sample size and margin of error are directly related to each other. When the sample size is smaller, the margin of error is larger. When the sample size is larger, the margin of error is smaller.

The margin of error is the highest at a confidence level of 50%. In general, as the confidence level increases, the margin of error decreases, and vice versa. As the sample size increases, the margin of error decreases. It follows that a 95% confidence level, n = 50 would yield the smallest margin of error in estimating the mean salt content, u. Hence, option D) 95% confidence, n = 50 would result in the smallest margin of error in estimating the mean salt content, u.

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The mode of this data set is 3 inches.

In the given data set, the values of rainfall in inches for each week are as follows:

Week 1: 2 inches

Week 2: 3 inches

Week 3: 1 inch

Week 4: 3 inches

Week 5: 5 inches

Week 6: 4 inches

The mode is the value that appears most frequently, which in this case is 3 inches. Therefore, the mode of this data set is 3 inches.

Note that a data set can have more than one mode if there are two or more values that appear with the same frequency and are more frequent than any other value in the data set.

However, in this data set, there is only one mode, which is 3 inches.

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the test statistic (1.58) is greater than the critical value for a right-tailed test with α = 0.05.

To test the hypothesis H0: μ ≤ 50 vs Ha: μ > 50 at a significance level of α = 0.05, we can use a one-tailed z-test.

a) For the sample result x = 52.7, the test statistic is given by:

z = (x - μ) / (σ / [tex]\sqrt{n}[/tex]) = (52.7 - 50) / (8 / [tex]\sqrt{60}[/tex] ) = 2.38

To find the critical values for the rejection rule, we need to determine the z-value that corresponds to a right-tail probability of 0.05. Since we are using a one-tailed test, we can look up the z-value in the standard normal distribution table. The critical value for a right-tailed test with α = 0.05 is:

zα = 1.645

Since the test statistic (2.38) is greater than the critical value (1.645), we reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis at a significance level of α = 0.05.

b) For the sample result x = 51, the test statistic is given by:

z = (x - μ) / (σ /[tex]\sqrt{n}[/tex] ) = (51 - 50) / (8 / [tex]\sqrt{60}[/tex] ) = 0.53

Since the test statistic (0.53) is less than the critical value for a right-tailed test with α = 0.05, we fail to reject the null hypothesis and conclude that there is insufficient evidence to support the alternative hypothesis at a significance level of α = 0.05.

c) For the sample result x = 51.8, the test statistic is given by:

z = (x - μ) / (σ / [tex]\sqrt{n}[/tex] ) = (51.8 - 50) / (8 / [tex]\sqrt{60}[/tex]) = 1.58

Since the test statistic (1.58) is greater than the critical value for a right-tailed test with α = 0.05, we reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis at a significance level of α = 0.05.

In summary, the test statistic represents the number of standard deviations between the sample mean and the hypothesized population mean, and the critical values represent the cutoff points for rejecting the null hypothesis. The decision to reject or fail to reject the null hypothesis depends on whether the test statistic falls within or outside the critical values for the given level of significance.

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The probability of winning is 1/42 expressed as a fraction.

Given that the odds on a bet are 41:1 against, we are to find the probability of winning.

We know that odds against = (Number of unfavorable outcomes) : (Number of favorable outcomes).

Thus, odds against = 41:1. This implies that the number of unfavorable outcomes is 41 and the number of favorable outcomes is 1.Probability of winning is given by the formula P(winning) = Number of favorable outcomes / Total number of possible outcomes. In this case, the total number of possible outcomes is the sum of the number of favorable and unfavorable outcomes.

Number of favorable outcomes = 1 and Number of unfavorable outcomes = 41

Therefore, the total number of possible outcomes = 1 + 41 = 42

Thus, P(winning) = Number of favorable outcomes / Total number of possible outcomes

P(winning) = 1 / 42

Therefore, the probability of winning is 1/42 expressed as a fraction.

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Answer:

The correct answer is 21 km.

Step-by-step explanation:

Because

A = (1/2) · (p + q) · h

Where p is 9 and q is 5 (the bases)

and h is the height (3)

Then:

A = (1/2) · (p + q) · h

A = (1/2) · (9 + 5) · 3

A = (1/2) · (14) · 3

A = (1/2) · 42

A= 21

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answer: 21

7 times 3 = 21

The measure of the missing angles of the right triangle are 57 degree and 33 degrees.

The sum of the interior angles of a triangle equals 180 degrees.

From the diagram:

Angle A =  (4x - 7) degrees

Angle B = (3x - 15) degrees

Angle C = 90 degrees

In a right triangle, the sum of the two acute angles is 90 degrees.

So, we have:

angle A + angle B + 90 = 180 (sum of angles in a triangle)

(4x - 7) + (3x - 15) + 90 = 180

Solve for x

4x - 7 + 3x - 15 + 90 = 180

4x + 3x - 15 - 7 + 90 = 180

7x - 15 - 7 + 90 = 180

7x + 68 = 180

7x = 180 - 68

7x = 112

x = 112/7

x = 16

Therefore, the missing angles will be:

angle A = (4x - 7) =  4(16) - 7 = 57 degrees

angle B = (3x - 15) = 3(16) - 15 =  33 degrees.

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Answer:

The measure of the missing angles of the right triangle are 57 degree and 33 degrees.

Step-by-step explanation:

The probability that the student will finish her trip in 60 minutes or less is 0.4

To find the probability that the student will finish her trip in 60 minutes or less, we need to find the proportion of the total area under the uniform distribution curve that lies to the left of 60 minutes.

Since the travel time is uniformly distributed between 40 and 90 minutes, the probability density function is

f(x) = 1/(90-40) = 1/50, for 40 ≤ x ≤ 90

The probability of finishing the trip in 60 minutes or less is therefore

P(X ≤ 60) = ∫[40, 60] f(x) dx

= (60-40)/50

Do the arithmetic operations

= 0.4

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Answer: 81 ham subs

Step-by-step explanation:

4 times 9 is 36. That means you have to multiply 9 by 9, to get 81 ham subs. The ratio is 81:36. :)

When n > 30, the sampling distribution of the mean will have a shape of symmetric, the mean will be equal to the population mean (μ), and the standard error will be equal to σ/√n.

The shape of a sampling distribution of the mean is always symmetric when n > 30. This is because the Central Limit Theorem (CLT) states that the sampling distribution of the mean is approximately normal when the sample size is greater than 30. Therefore, when n > 30, the shape of the sampling distribution of the mean will be symmetric.

The mean of the sampling distribution of the mean is equal to the population mean, μ. This is because the sampling distribution of the mean is a probability distribution of all the possible sample means, and it is centered around the population mean. Therefore, the mean of the sampling distribution of the mean is equal to μ.

The standard error (SE) of the sampling distribution of the mean is equal to the population standard deviation (σ) divided by the square root of the sample size (n). This is because the standard error is a measure of how accurately the sample mean estimates the population mean. Since the sample size is greater than 30, the sample mean will accurately estimate the population mean and the standard error will be equal to σ/√n.

In summary, when n > 30, the sampling distribution of the mean will have a shape of symmetric, the mean will be equal to the population mean (μ), and the standard error will be equal to σ/√n.

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