a regional director responsible for business development in the state of pennsylvania is concerned about the number of small business failures. if the mean number of small business failures per month is 14, what is the probability that exactly 5 small businesses will fail during a given month? assume that the probability of a failure is the same for any two months and that the occurrence or non occurrence of a failure in any month is independent of failures in any other month. (round your answer to four decimal places.) g

Answer:

Is C.

Step-by-step explanation:

Consider,

2x² = 4x - 7

2x² - 4x + 7 = 0

using Quadratic Formula

Therefore, Option C is correct.

Expected rate of return = 94.3%

Inflation rate is the rate of increase of prices of goods with the time being. It is also called devaluation of money. Risk free rate of return is an investment where possibility of risk is zero.

given, real risk-free rate = 2.5% = 0.025

the future rate of inflation = 2.8% = 0.028

nominal risk-free rate = (1 + real risk-free rate) / (1 + inflation rate)

nominal risk-free rate = (1+ 0.025) / (1 + 0.028) = 0.9971

now, rate of return = [(1 + nominal risk-free rate) / (1 + inflation rate)] - 1

 rate of return expected = [(1 + 0.9971) / (1 + 0.028)] - 1

                                      = 0.943

expected rate of return = 94.3 %

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Answer:

1000.

Step-by-step explanation:

We need 4 weights where 3 of them add up to

900, 1400, 1600 or 1800g.

Not sure of the method for doing this!

Lets assume that the answer is 1000 g.

Then the  3 that make 1800 could be

1000 500 and 300

- then to make 900 we need a 100g tomato giving:

1000 500 300 and 100 grams

So the 1400 will be the 1000, 300 and 100 tomato

and the 1600 will be 1000, 500 and 100.

That seems to fit !!

Answer:

t=2

Step-by-step explanation:

Answer:

t=2

Step-by-step explanation:

t=6-4

t=2

Answer:

Step-by-step explanation:

34.95

Answer:

x = 19.5

Step-by-step explanation:

7x + 5 + 19 + x = 180

or, 8x + 24 = 180

or, 8x = 180 - 24

or, 8x = 156

or, x = 156/8

. x = 19.5 Ans

. .

The equations of the three perpendicular bisectors in the triangle ABC are y = - (1 / 2) · x + 9 / 4, x = 2 and y = - (6 / 7) · x + 24 / 7.

Triangles are polygons with three sides and three perpendicular bisectors, whose equations need the informations of slopes and midpoints of each side. Bisectors are lines that partitions line segments in two parts of equal length.

First, determine the midpoints of each side:

Side AB

M₁(x, y) = 0.5 · (- 3, 0) + 0.5 · (0, 6)

M₁(x, y) = (- 1.5, 0) + (0, 3)

M₁(x, y) = (- 1.5, 3)

Side BC

M₂(x, y) = 0.5 · (0, 6) + 0.5 · (4, 6)

M₂(x, y) = (0, 3) + (2, 3)

M₂(x, y) = (2, 6)

Side AC

M₃(x, y) = 0.5 · (- 3, 0) + 0.5 · (4, 6)

M₃(x, y) = (- 1.5, 0) + (2, 3)

M₃(x, y) = (0.5, 3)

Second, determine the slope of the perpendicular bisectors:

Side AB

m = (6 - 0) / [0 - (- 3)]

m = 2

m' = - 1 / m

m' = - 1 / 2

Side BC

m = (6 - 6) / (4 - 0)

m = 0

m' = - 1 / m

m' = NaN  (Vertical line)

Side AC

m = [4 - (-3)] / (6 - 0)

m = 7 / 6

m' = - 1 / (7 / 6)

m' = - 6 / 7

Third, derive the equations of the bisectors:

Side AB

b = 3 - (- 1 / 2) · (- 1.5)

b = 9 / 4

y = - (1 / 2) · x + 9 / 4

Side BC

x = 2

Side AC

b = 3 - (- 6 / 7) · (0.5)

b = 24 / 7

y = - (6 / 7) · x + 24 / 7

The equations of the three perpendicular bisectors in the triangle ABC are y = - (1 / 2) · x + 9 / 4, x = 2 and y = - (6 / 7) · x + 24 / 7.

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The equation x² - 6x = 8 is equivalent to the equation (x - 3)² = 17. Then the correct option is A.

The equivalent is the expression that is in different forms but is equal to the same value.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The equation is given below.

x² - 6x = 8

Add 9 on both sides, then we have

x² - 6x + 9 = 8 + 9

(x - 3)² = 17

The equation x² - 6x = 8 is equivalent to the equation (x - 3)² = 17. Then the correct option is A.

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Answer:

Step-by-step explanation:

Hey :)

Keep in mind:

y = mx + b

Where m = slope and b = y-intercept

Since we are told:

y = 9x - 3

This means m = 9 and b = -3

Therefore the slope is 9 and y-intercept is at (0,-3)

The equation representing the inequality is 2·x² + 16·x + 32 ≥ 254

The width of the photo on the cake is x.

The dimensional relationship mentioned between the dimensions of the cake & the photo on the cake mentioned in the question are:

Width of cake = Width of photo + 4 inches

i.e., W = x + 4

And, Length of the Cake is twice the Width of the cake

i.e., L = 2*W

Also, It is mentioned that the Area of the Cake is 254 sq inches.

We know Formula to calculate the Area of a rectangle is :

          =>   Area = Length * Width

          =>   254  ≤ 2*W * (x+4)     =>   254 ≤ 2(x+4)*(x +4)

          =>   2·x² + 16·x + 32 ≥ 254

Hence, The inequality representing this case is 2·x² + 16·x + 32 ≥ 254

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Answer:

slope is 0

Step-by-step explanation:

to find slope y2 - y1 / x2 - x1

(6, -2) and (12, -2)

-2 - (-2) / 12 - 6

= -2 + 2/6

= 0/6

= 0

Answer:

slope is 0

Step-by-step explanation:

Answer:

The value of PQ is;

Explanation:

Given the figure in the attached image;

We can see from the figure that the triangle RSQ is similar to the triangle ROP.

So their corresponding sides are proportional;

Substituting the given values;

Therefore, the value of PQ is;

A. To determine if an integral is convergent, we analyze the function's behavior, integrability, apply integration techniques, and examine its limits, ensuring they are finite, leading to a finite result.

B. To determine if an integral is divergent, we look for infinite limits, vertical asymptotes, and erratic behavior within the integration interval, indicating the lack of a finite value for the integral.

A. To determine if an integral is convergent, we need to consider several approaches. First, we check for basic convergence criteria such as infinite limits or vertical asymptotes.

Then, we examine integrability, ensuring the function is continuous or has a finite number of discontinuities. Next, we simplify the integral using integration techniques.

Finally, we analyze the behavior of the function at infinity and apply comparison tests if necessary to establish convergence.

B. To determine if an integral is divergent, we follow a series of steps. First, we check for basic divergence criteria such as infinite limits or vertical asymptotes.

Then, we examine integrability, looking for discontinuities that prevent integration. Next, we simplify the integral using integration techniques. Finally, if the integral does not converge, it is deemed divergent.

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The power ratio of a 30-dB sound is 501.5 times greater than 3-dB sound.

The number of decibels is ten times the logarithm to base 10 of the ratio of the two power quantities.

To find power ratio, we use the following formula: \(Power ratio = 10^{decibels/10}.\)

For a 3-dB sound:

The power ratio is  \(10^{3/10}\) = 1.995.

For a 30-dB sound:

The power ratio is \(10^{30/10}\) = 1000.

The power ratio of a 30-dB sound greater than 3-dB sound in:

= 1000/1.995

= 501.5 times.

Full question:

A sound that is 3 decibels (dB) has a power ratio of 10^((3/10). A sound that is 30 dB has a power ratio of 1000. How many times greater is the power ratio of a 30-dB sound than a 3-dB sound?

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The smallest final thickness that can be obtained for the Cu- 30% Zn brass plate is approximately 2.0944 inches.

To calculate the smallest final thickness that can be obtained for a Cu- 30% Zn brass plate with an elongation greater than 36%, we need to consider the relationship between elongation and thickness.

Elongation is a measure of the material's ability to stretch or deform without breaking. It is typically expressed as a percentage increase in length compared to the original length. In this case, the elongation needs to be greater than 36%.

To calculate the smallest final thickness, we can use the formula:

Final thickness = Original thickness * (1 + Elongation/100)

Let's plug in the given values:

Original thickness = 1.54 inch
Elongation = 36%

Final thickness = 1.54 inch * (1 + 36%/100)
Final thickness = 1.54 inch * (1 + 0.36)
Final thickness = 1.54 inch * 1.36
Final thickness = 2.0944 inch (rounded to four decimal places)

Therefore, the smallest final thickness that can be obtained for the Cu-30% Zn brass plate is approximately 2.0944 inches.

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for A

1. the GCD of 25 and 50 is 25

2.25÷2550÷25

3. Reduced Fraction 12. Therefore, 25/50 simplified to lowest term is 1/2

B

1. The GCD for 200 and 5 is 5

2. Divide the numerator and denominator by the GCD. 200÷5

5÷5

3. Therefore 200/5 simplified to lowest terms is 40/1

a) 1:2

b) 5:2

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The researcher needs to sample 55 more adult Americans to say that the distribution of the sample proportion of adults who respond "yes" is approximately normal, assuming that 22% of all adult Americans support the changes.

To determine the required sample size, we can use the formula for sample size calculation in a proportion estimation problem:

n = (Z^2 * p * q) / E^2

where:

- n is the required sample size,

- Z is the Z-score corresponding to the desired level of confidence (assuming a 95% confidence level, Z ≈ 1.96),

- p is the estimated proportion (22% = 0.22 in this case),

- q is the complement of the estimated proportion (q = 1 - p = 1 - 0.22 = 0.78), and

- E is the desired margin of error (we want the distribution to be approximately normal, so a small margin of error is desirable).

Plugging in the given values, we can calculate the required sample size:

n = (1.96^2 * 0.22 * 0.78) / (0.02^2)

n ≈ 55

Therefore, the researcher needs to sample 55 more adult Americans.

To ensure that the distribution of the sample proportion of adults who respond "yes" is approximately normal when 22% of all adult Americans support the proposed changes, the researcher should sample an additional 55 adult Americans. This larger sample size will provide a more accurate representation of the population and increase the confidence in the estimated proportion.

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Let x represent the number of tickets that he sold at the local theatre.

From the information given, Seth earns $25 a day and $3 for each ticket he sells at the local theatre. The expression representing the amount earned from selling x tickets in a day is

25 + 3x.

To earn at least $115, it means that the amount he would earn is greater than or equal to $115. the symbol for 'greater than or equal to' is '≥'

Therefore, the inequality representing this scenario is

25 + 3x ≥ 115

To solve the inequality, we would subtract 25 from both sides of the inequality. We have

25 - 25 + 3x ≥ 115 - 25

3x ≥ 90

Dividing both sides of the inequality by 3, we have

3x/3 ≥ 90/3

x ≥ 30

He must sell at least 30 tickets to earn at least $115

The probability of at least one is a Samsung in the purchase collection of two independent LED HDTV is equal to 0.376.

Percent of all LED display manufactured by Samsung = 21%

Probability that at least one purchase is Samsung

= 1 - Probability that both purchases are not Samsung

Probability that the first purchase is not Samsung is 1 - 0.21 = 0.79.

The probability that the second purchase is also not Samsung is also 0.79.

Since the purchases are independent,

Multiply these probabilities to get the probability that both purchases are not Samsung,

P(neither is Samsung)

= 0.79 x 0.79

= 0.6241

The probability that at least one purchase is Samsung is,

P(at least one is Samsung)

= 1 - P(neither is Samsung)

= 1 - 0.6241

= 0.3759

Rounding to 3 decimal places, we get,

P(at least one is Samsung) = 0.376

Therefore, the probability that in a collection of two independent LED HDTV purchases, at least one is a Samsung is 0.376.

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Solution

We need to find the volume

From the question, we have

Subtituting the value, we have

To round up, we convert to yard

The answer to four decimal places is

Marcia bought 15 pizzas for her birthday party to accommodate the 30 people, with each person eating 3 slices of pizza that was cut into sixths.

To determine the number of pizzas Marcia bought for her birthday party, let's break down the given information.

We know that there were 30 people at the party, and each person ate 3 slices of pizza.

The pizza was cut into sixths, and there were 12 slices in total.

Since each person ate 3 slices, and each slice is 1/6 of a pizza, we can calculate the total number of pizzas consumed by multiplying the number of people by the number of slices each person ate: 30 people \(\times\) 3 slices/person = 90 slices.

Now, we need to determine how many pizzas Marcia bought. Since there were 12 slices in total, and each slice is 1/6 of a pizza, we can calculate the total number of pizzas using the following formula:

Total pizzas = Total slices / Slices per pizza.

In this case, the total slices are 90, and each pizza has 6 slices.

Thus, the number of pizzas Marcia bought can be calculated as follows: Total pizzas = 90 slices / 6 slices per pizza = 15 pizzas.

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10m

Integer: 7m+3m=X

Answer:0.105

Step-by-step explanation:

84-76=8

8/76=0.105

The denominator in the formula revenue managers use to calculate GOPAR (Gross Operating Profit per Available Room) is D) Total rooms available to be sold.

GOPAR is a key performance indicator used in the hospitality industry to measure the profitability of each available room. It provides insights into the revenue generated from room sales while considering the total rooms available for sale.

The formula to calculate GOPAR is:

GOPAR = Gross Operating Profit / Total rooms available to be sold

Gross Operating Profit refers to the revenue generated from the hotel's operations after deducting operating expenses. It represents the profit generated specifically from the hotel's core operations, excluding non-operating items such as interest, taxes, and non-recurring expenses.

The denominator, "Total rooms available to be sold," represents the number of rooms in the hotel that are available for occupancy and can be sold to guests during a given period. It is an important factor in determining the efficiency and profitability of room sales.

By dividing the Gross Operating Profit by the total rooms available to be sold, revenue managers can assess the profitability of each available room and make informed decisions regarding pricing, occupancy rates, and overall revenue management strategies.

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Answer:

This is true

Step-by-step explanation: