7+√5/7-√5 + 7-√5/7+√5 = a + 7/11√5b

To calculate the probability that the project will be completed within 75 weeks, we can use the concept of the standard normal distribution.

Given that the mean duration of the critical path is 70.5 weeks and the standard deviation is 3 weeks, we can standardize the value of 75 weeks using the formula:

Z = (X - μ) / σ

where X is the desired value (75 weeks), μ is the mean (70.5 weeks), and σ is the standard deviation (3 weeks).

Plugging in the values:

Z = (75 - 70.5) / 3

Z = 4.5 / 3

Z ≈ 1.5

Now, we need to find the probability of the project being completed within 75 weeks, which corresponds to finding the area under the standard normal curve to the left of Z = 1.5.

Using a standard normal distribution table or a statistical calculator, we can find that the probability corresponding to Z = 1.5 is approximately 0.9332.

Therefore, the probability that the project will be completed within 75 weeks is approximately 0.9332, or 93.32%.

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To find the probabilities for the different events, we need to determine the number of favorable outcomes and the total number of possible outcomes.

In a standard deck of playing cards, there are 52 cards, and each suit (spades, hearts, diamonds, clubs) contains 13 cards (Ace, 2-10, Jack, Queen, King).

1. Probability of drawing a card of spades:

There are 13 cards of spades in the deck, so the probability of drawing a spade is 13/52 = 1/4.

2. Probability of drawing an Ace:

There are 4 Aces in the deck (one for each suit), so the probability of drawing an Ace is 4/52 = 1/13.

3. Probability of drawing a Red King:

There are 2 red Kings in the deck (King of Hearts and King of Diamonds), so the probability of drawing a Red King is 2/52 = 1/26.

4. Probability of neither a King nor a Queen:

There are 4 Kings and 4 Queens in the deck, so the number of cards that are neither a King nor a Queen is 52 - 4 - 4 = 44. Therefore, the probability of drawing a card that is neither a King nor a Queen is 44/52 = 11/13.

5. Probability of either a King or a Queen:

There are 4 Kings and 4 Queens in the deck, but we need to subtract the probability of drawing both a King and a Queen (since they are not mutually exclusive). So the probability of drawing either a King or a Queen is (4 + 4 - 1)/52 = 7/52 = 1/7.

6. Probability of drawing a face card:

There are 12 face cards in the deck (King, Queen, and Jack of each suit), so the probability of drawing a face card is 12/52 = 3/13.

7. Probability of drawing a card that is neither a King nor a red card:

There are 4 Kings and 26 red cards (2 red Kings + 24 red cards), so the number of cards that are neither a King nor a red card is 52 - 4 - 26 = 22. Therefore, the probability of drawing a card that is neither a King nor a red card is 22/52 = 11/26.

Note: The probabilities may change if the deck of playing cards is not a standard 52-card deck or if the cards are not well-shuffled.

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Answer:

umm, i can't read it

Step-by-step explanation:

The difference in length between a 1 1/4-inch bottom and a 3/8-inch bottom is 7/8 inches. To find the difference in length between a 1 1/4-inch bottom and a 3/8-inch bottom, we need to subtract the lengths of the two bottoms.

1 1/4 inches can be written as 1 + 1/4 inches, which is equal to 4/4 + 1/4 inches, resulting in 5/4 inches.

3/8 inch remains as 3/8 inch.

Now we can subtract the lengths:

5/4 inches - 3/8 inch

To subtract fractions, we need a common denominator. The least common denominator (LCD) of 4 and 8 is 8.

Converting both fractions to have a denominator of 8:

5/4 inches = (5/4) * (2/2) = 10/8 inches

3/8 inch remains the same.

Now we can subtract:

10/8 inches - 3/8 inch = (10 - 3)/8 inches = 7/8 inches.

Therefore, the difference in length between a 1 1/4-inch bottom and a 3/8-inch bottom is 7/8 inches.

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Answer: hello your question is incomplete below is the missing part

Based on your simulation, what is the average amount of error you expect to see in the sample proportions in this situation?

answer : 0.0458

Step-by-step explanation:

In 2005 - 2007 : 30% of all current smokers started smoking before the age of 16

n ( sample size ) = 100 smokers

The average amount of error expected can be calculated as

\(\sqrt{pq/n}\)  = \(\sqrt{0.3*0.7/100}\) = 0.0458

where : p = 0.3

             q = 0.7

              n = 100

Answer:

Step-by-step explanation:

(a) The center of the circle is also the circumcenter of the triangle PQR.

Since ΔPQR is equilateral, all sides are equal, therefore opposite angles are also congruent:

Sum of the three angles is 360° as cover the full circle.

Each angle measure is:

(b) Each side is 16 cm and the radius is 12 cm.

The distance of the midpoint M of PQ from the center O is perpendicular bisector of ΔPOQ.

The segment MO is:

ΔXYZ is isosceles with:

(a) The altitude of ΔXYZ is a perpendicular bisector of YZ. h = XM is the altitude

Find h:

(b) Note the ∠ZXM is half of the ∠ZOM as both the angles intercept half of the arc ZY and ∠ZOM is a central angle.

Find ∠ZXM:

Find ∠ZOM:

Find the measure of the radius:

Find the measure of the diameter:

Answer:

-27

Step-by-step explanation:

Answer:

49.6 liters

Step-by-step explanation:

Let the number of water that the smaller chest be x liters. If the smaller chest can hold 4/5 of the water that the large chest can hold, then:

The amount of water held by small chest (x) = 4/5 × amount of water that can be held by large chest

x = 4/5 × 62 liters = 49.6 liters

This means that the small chest can hold up to 49.6 liters of water

Smaller chest can hold 49.6 liters.

The smaller chest holds 4/5 the amount of water that the larger chest can hold which is 62 liters.

The amount the smaller chest can hold is therefore:

= Amount of water large chest can hold x proportion of large chest that small chest can hold

= 62 x 4/5

= 248/5

= 49.6 liters

The smaller chest can therefore hold 49.6 liters.

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Given:

The variable y varies directly as x and inversely as z. When x = 4 and z= 14, y=2.

To find:

The combined variation equation and find y when x = 6 and z= 3.

Solution:

The variable y varies directly as x and inversely as z.

\(y\propto \dfrac{x}{z}\)

\(y=k\dfrac{x}{z}\)           ...(i)

Where, k is the constant of proportionality.

Putting x=4, y=2 and z=14, we get

\(2=k\dfrac{4}{14}\)

\(2=k\dfrac{2}{7}\)

\(2\times \dfrac{7}{2}=k\dfrac{2}{7}\times \dfrac{7}{2}\)

\(7=k\)

Putting k=7 in (i), we get

\(y=7\dfrac{x}{z}\)

Putting x=6 and z=3, we get

\(y=7\times \dfrac{6}{3}\)

\(y=7\times 2\)

\(y=14\)

Therefore, the required equation is \(y=7\dfrac{x}{z}\) and the value of y is 14 when x = 6 and z= 3.

we will use the formula of tan(A+B)= (tanA+tanB)/(1-tanAtanB)

and tan(A-B)= (tanA-tanB)/(1+tanAtanB)

tan[(pie/4)+(x/2)]= [1+tan(x/2)]/[1-tan(x/2)] ......(1)

tan[(pie/4)-(x/2)]= [1-tan(x/2)]/[1+tan(x/2)]......(2)

now add the equation (1) and (2) which is LHS of question. So we get:

{[1+tan(x/2)]^2 + [1- tan(x/2)]^2}/1-tan^2(x/2)=2[1+tan^2(x/2)]/1-tan^2(x/2)= 2/cosx = 2secx =RHS

Hence proved.

The assumptions of a normal population distribution and a randomly selected sample are required in order to make valid statistical inferences.

To explain further, the assumption of a normal population distribution means that the values in the population follow a bell-shaped curve. This assumption is important because many statistical tests and procedures are based on the assumption of normality. It allows us to make accurate predictions and draw conclusions about the population based on the sample data.

The assumption of a randomly selected sample means that every individual in the population has an equal chance of being included in the sample. This is important because it helps to ensure that the sample is representative of the entire population. Random sampling helps to minimize bias and increase the generalizability of the findings to the population as a whole.In summary, the assumptions of a normal population distribution and a randomly selected sample are both required and must be satisfied in order to make valid statistical inferences.

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Answer:

9/4

Step-by-step explanation:

Answer:

9/4

Step-by-step explanation:

First we simplify 4.5 into a fraction.

4.5 is in decimal format, and to make it a fraction, we put it into a tenths format, which is 45/10. we can then simplify to get 9/2

Then, we do (9/2) divided by 2. Fraction division goes like this:

(9/2) x (1/2) = 9/4

The correct answer is 9/4

Answer:

8 pounds

Step-by-step explanation:

x represents the starting amount

5 = 3x/8 + x/4

40 = 3x + 2x     multiply both sides by LCD, 8

40 = 5x

x=8

The EOQ for Sam's optimal order quantity is 28 bags, and the average time between orders is 0.3 weeks. The reorder point should be set at 400 bags.

a. The Economic Order Quantity (EOQ) is the optimal order quantity that minimizes the total cost of inventory. In this case, the EOQ can be calculated using the given information, such as demand, order cost, and annual holding cost. The EOQ is rounded to the nearest whole number. The average time between orders can be calculated by dividing the EOQ by the weekly demand and rounding it to one decimal place.

b.The reorder point (R) represents the inventory level at which a new order should be placed to avoid stockouts. It is calculated by multiplying the lead time (in weeks) by the average weekly demand and rounding to the nearest whole number.

a. To calculate the Economic Order Quantity (EOQ), we use the formula:

EOQ = √((2 * Demand * Order cost) / Annual holding cost)

Substituting the given values:

Demand = 100 bags/week

Order cost = $55/order

Annual holding cost = 25% of cost (25% * $55 = $13.75)

EOQ = √((2 * 100 * $55) / $13.75) ≈ √(11000 / 13.75) ≈ √800 ≈ 28.3

Rounding the EOQ to the nearest whole number gives us 28 bags.

To calculate the average time between orders, we divide the EOQ by the weekly demand:

Average time between orders = EOQ / Demand = 28 / 100 ≈ 0.28 weeks

Rounding the average time between orders to one decimal place gives us 0.3 weeks.

b. The reorder point (R) is calculated by multiplying the lead time (in weeks) by the average weekly demand:

R = Lead time * Demand = 4 weeks * 100 bags/week = 400 bags

Therefore, the reorder point is 400 bags.

In summary, the EOQ for Sam's optimal order quantity is 28 bags, and the average time between orders is 0.3 weeks. The reorder point should be set at 400 bags. These calculations help Sam determine the appropriate inventory management strategy to maintain an optimal level of inventory and avoid stockouts.

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Answer:

572557486637778886367828766664728274747447378328288273

Answer: $11.52 left for each student

Step-by-step explanation:

First, divide the total amount of money spent by the total amount of students. 170.64/18. You will get $9.48. So, that means that so far Mr. Chang has spent $9.48 on each student. Then, just subtract $9.48 from $21 (which is the total amount he is willing to spend on each student. You should get $11.52. So, Mr. Chang has $11.52 left to spend on each student. Hope this helps!

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:

y = -2/3 + 6

Step-by-step explanation:

Slope = -2/3

Point (- 3, 8)

b = 8 - (-2/3)(-3)

= 8 - 2

= 6

The probability that this baseball team will win the World Series, based on the provided odds, is 1/26 or approximately 0.0385 (rounded to four decimal places).

To determine the probability of the baseball team winning the World Series based on the odds given by the sportsbook, we can use the formula:

Probability = (Number of ways the event can occur) / (Total number of possible outcomes)

In this case, the "event" is the baseball team winning the World Series, and the "total number of possible outcomes" is the number of teams participating in the World Series. Assuming there are 30 teams in the Major League Baseball, the total number of possible outcomes is 30.

To calculate the number of ways the event can occur, we can use the odds provided by the sportsbook. The odds of 1:25 mean that for every 25 times the event does not occur (i.e. the baseball team does not win the World Series), it occurs once (i.e. the baseball team wins the World Series). Therefore, the number of ways the event can occur is 1.

Using the formula above, we can now calculate the probability:

Probability = 1 / 30

Therefore, the probability of the baseball team winning the World Series based on the odds of 1:25 is approximately 0.04 or 4%.
Hi! You've asked about the probability of a certain baseball team winning the World Series, given that the sportsbook at the High Roller Casino has set the odds at 1:25.

To find the probability, you'll need to use the odds provided. In this case, the odds are 1 to 25, meaning there's 1 chance of winning for every 25 chances of losing. To calculate the probability, you can use the following formula:

Probability = Number of winning outcomes / (Number of winning outcomes + Number of losing outcomes)

In this case, the number of winning outcomes is 1, and the number of losing outcomes is 25. Plugging these numbers into the formula, you get:

Probability = 1 / (1 + 25)

Probability = 1 / 26

So the probability that this baseball team will win the World Series, based on the provided odds, is 1/26 or approximately 0.0385 (rounded to four decimal places).

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To calculate the probability of a baseball team winning the World Series based on odds of 1:25, we need to convert the odds to a probability. The formula for converting odds to probability is:

Probability = 1 / (odds + 1)

Using this formula, we can calculate the probability of the baseball team winning the World Series as follows:

Probability = 1 / (1 + 25) = 0.038

Therefore, the probability of the baseball team winning the World Series based on the odds of 1:25 is 0.038 or 3.8%.

it is important to understand that odds and probability are two different ways of expressing the likelihood of an event occurring. Odds are typically expressed as a ratio of the number of ways an event can happen to the number of ways it cannot happen. Probability, on the other hand, is expressed as a number between 0 and 1 that represents the likelihood of an event occurring.
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Answer:

10.1

Step-by-step explanation:

Step-by-step explanation:

it goes by this formula

\(a = \frac{1}{2} bh \\ \\ \\ a = \frac{1}{2} 6 \times 4.1 = 12.3\)

x/9>12

x>12×9

x>108

This is your answer

Option (D), the last option is the correct statement, If heights in inches of 200 graduating seniors were summarized in the frequency table;

The median height is greater than or equal to 60 inches but less than 66 inches.

The median is the number value that separates the lower and upper values to halves. The median height is determined by arranging all the given heights in order either from the smallest to highest or from highest to smallest without skipping any measurement of the heights.

After arranging all the heights in order, the median height is usually at the middle.

The reason as to why the median height is greater than or equal to 60 inches but less than 66 inches is because the middle height should not be same as the largest height of 66 inches. It is possible to have multiple 60 inch heights from the 200 seniors. It is also possible to have multiple 66 inch of heights from the 200 seniors.

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Solving for the rate, you make $15 per hour as a tutor.

Rate is defined as the ratio between two quantities of different units.

Let x = rate

n = total amount you've earned = $195.00

t = time you've worked = 8 hours

If in one week, you earned $75.00 at your afterschool tutoring job, and after working 8 more hours the following week, you had a total of $195.00, then we can express this as

n = xt + $75.00

Substitute the values to solve the rate, x.

n = xt + $75.00

$195.00 = x(8 hours) + $75.00

8hours (x) = $195.00 - $75.00

8hours (x) = $120.00

x = $15/hr

rate = $15 per hour

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Answer:

2nd and 3rd

Step-by-step explanation:

Answer:

-If the resistance decreases, then the current increases. Assume voltage is constant.

-If the voltage increases, then the current increases. Assume resistance is constant.

Step-by-step explanation:

I took this test.

Hope this helps!

1. speed = 36 km/h

   Distance = 210 km

Time = Distance/speed

    T= 210/36 = 5.8 hour

2. T= 4 hr

   D= 340km

  Speed = Distance / time

              = 340/4 = 85km/hr.

3. Distance= 300km

    Time = 6 hour

   Speed = 300/6   = 50 km/hr

4.  Distance = 7200

    Time = 9 hour

    Speed = 7200/9

                =  80 km/hr

5. Speed= 50km/hr

    Time = 14hour

   Distance = 50*14

                 = 700km

6.  Speed = 16000 km/hr

       Time = 66 hr

       Distance = 16000* 66

                    = 1056000 km

7. Distance = 60 km

   Time = 2 km/hour

  Speed = 60/2  = 30km/hr

8.  distance = 26mile

    Speed = 0.001 mile/hr

  time =  26/0.001  =  26000 mile /hr.

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Using the relation speed = distance / time, the different values of time , speed and distance are given below -  

So, speed equals distance times time. The time can also be calculated by dividing the distance travelled by the speed. If you are aware of two of the inputs, you can determine the third one. For instance, we may get the speed as 120 x 2 = 60 miles per hour if a car travels 120 miles in two hours.

The total movement of an object, independent of direction, is its distance. The amount of space that an object has travelled, regardless of where it started or ended, is referred to as distance. How quickly or slowly an object is travelling is determined by its speed.

1. speed = 36 km/h

  Distance = 210 km

Time = Distance/speed

  T= 210/36 = 5.8 hour

2. T= 4 hr

  D= 340km

 Speed = Distance / time

             = 340/4 = 85km/hr.

3. Distance= 300km

   Time = 6 hour

  Speed = 300/6   = 50 km/hr

4.  Distance = 7200

   Time = 9 hour

   Speed = 7200/9

              =  80 km/hr

5. Speed= 50km/hr

   Time = 14hour

  Distance = 50*14

                = 700km

6.  Speed = 16000 km/hr

      Time = 66 hr

      Distance = 16000* 66

                  = 1056000 km

7. Distance = 60 km

  Time = 2 km/hour

 Speed = 60/2  = 30km/hr

8.  distance = 26mile

   Speed = 0.001 mile/hr

 time =  26/0.001 =  26000 mile /hr.

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Answer:

The type of number that represents -4/2 is:

Choice B) Integer

Choice C) Rational

Step-by-step explanation:

The number -4/2 is an integer because it represents a whole number (-2) and it is also a rational number because it can be expressed as a fraction of two integers.

-4/2 is an :

Solution:

Before we make any decisions about the type of number -4/2 is, let's simplify it first.

It's the same as -2. Now, let's familiarize ourselves with the sets of numbers out there. Where does -2 fit in?

______________

This set incorporates only positive numbers and zero. So -2 doesn't belong here.

This set incorporates whole numbers and negative numbers. So -2 belongs here.

This set has integers, fractions, and decimals. So -2 does belong here too.

This is a set for numbers that cannot be written in fraction form (a/b, where b ≠ 0). So -2 doesn't belong here.

-4/2 belongs in the integer and rationals set.

Answer:

The dimensions of the box is 2 units.

Step-by-step explanation:

Volume of cube, V = 8 cubic units

Let the length of the side is a.

So,

The volume of the cube is

\(V = a^3\\\\8 = a^3\\\\a = 2 units\)

So, the dimensions of the box is 2 units.  

The tree diagram with probabilities that  shows all possible outcomes for Yusuke's situation is mentioned below .

A tree diagram is a visual tool used to represent hierarchical structures or relationships.

It consists of a branching structure where each branch represents a different category or possibility, allowing for easy visualization of complex systems or decision-making processes.

                   LB (+)                                   LB (-)

Test (+)     0.045 (true)                         0.055 (false positive)

Test (-)      0.005 (false negative)        0.895 (true negative)

The probabilities are as follows:

0.05 (5%) of the students have LB, and therefore the probability of Yusuke having LB is 0.05.

The blood test detects LB accurately 90% of the time, meaning that the probability of a correct positive test result (i.e., Yusuke has LB and the test detects it) is 0.05 * 0.9 = 0.045.

The probability of a false positive test result (i.e., Yusuke does not have LB but the test detects it) is 0.95 * 0.1 = 0.055.

The probability of a true negative test result (i.e., Yusuke does not have LB and the test does not detect it) is 0.95 * 0.9 = 0.855.

The probability of a false negative test result (i.e., Yusuke has LB but the test does not detect it) is 0.05 * 0.1 = 0.005.

Note that the sum of the probabilities for each possible outcome (i.e., correct positive, false positive, true negative, false negative) should add up to 1.

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Yusuke having LB is 0.05. Yusuke has LB, the test detects it is 0.05 * 0.9 = 0.045. Yusuke does not have LB, the test detects it is 0.95*0.1 = 0.055. Yusuke does not have LB , the test does not detect it is 0.95 0.9 =0.855.

A tree diagram is a visual tool used to represent hierarchical structures or relationships.

It consists of a branching structure where each branch represents a different category or possibility, allowing for easy visualization of complex systems or decision-making processes.

                  LB (+)                                   LB (-)

Test (+)     0.045 (true)                         0.055 (false positive)

Test (-)      0.005 (false negative)        0.895 (true negative)

The probabilities are as follows:

0.05 (5%) of the students have LB, and therefore the probability of Yusuke having LB is 0.05.

The blood test detects LB accurately 90% of the time, meaning that the probability of a correct positive test result (i.e., Yusuke has LB and the test detects it) is 0.05 * 0.9 = 0.045.

The probability of a false positive test result (i.e., Yusuke does not have LB but the test detects it) is 0.95 * 0.1 = 0.055.

The probability of a true negative test result (i.e., Yusuke does not have LB and the test does not detect it) is 0.95 * 0.9 = 0.855.

The probability of a false negative test result (i.e., Yusuke has LB but the test does not detect it) is 0.05 * 0.1 = 0.005.

Note that the sum of the probabilities for each possible outcome (i.e., correct positive, false positive, true negative, false negative) should add up to 1.

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Answer:

Step-by-step explanation:

Its because 1.5x number of dried × x =? So we determine that its 18 but no otsnot 18, 12 not the point rather its 12,15.