The lengths of two sides of a triangle are 5. 3 and 0. 4. What is the length of the third side if it is an integer?

The probability that on exactly one of these three occasions the voter approves of the mayor's work is given as follows:

0.189 = 18.9%.

The mass probability formula, giving the probability of x successes, is of:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are given by:

The values of these parameters in the context of this problem are given as follows:

n = 3, p = 0.7.

Then the probability of exactly one success is calculated as follows:

P(X = 1) = 3!/(1!2!) x 0.7 x (0.3)² = 0.189 = 18.9%.

The proportion of voters that approve the mayor's work is of 70%.

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I think its like if you got 80% on a quiz and 20% on the exam then your grade would be 60% which is usually a F

The optimal solution is x1 = 4, x2 = 0, x3 = 1, w = 0, and the minimum value of the objective function is 0.

To solve this linear programming problem using the Simplex method, we first need to convert it into standard form by introducing slack variables.

Our problem can be rewritten as follows:

Minimize w = 9x1 + 6x2

Subject to:

x1 + 2x2 + x3 = 5

2x1 + 2x2 + x4 = 8

x1 + 2x2 + 2x3 = 6

where x1, x2, x3, and x4 are all non-negative variables.

Next, we set up the initial simplex tableau:

Basic Variables x1 x2 x3 x4 RHS

x3 1 2 1 0 5

x4 2 2 0 1 8

x5 1 2 2 0 6

z -9 -6 0 0 0

The last row represents the coefficients of the objective function. The negative values in the z-row indicate that we are minimizing the objective function.

To find the pivot column, we look for the most negative coefficient in the z-row. In this case, the most negative coefficient is -9, which corresponds to x1. Therefore, x1 is our entering variable.

To find the pivot row, we calculate the ratios of the RHS values to the coefficients of the entering variable in each row. The smallest positive ratio corresponds to the pivot row. In this case, the ratios are:

Row 1: 5/1 = 5

Row 2: 8/2 = 4

Row 3: 6/1 = 6

The smallest positive ratio is 4, which corresponds to row 2. Therefore, x4 is our exiting variable.

To perform the pivot operation, we divide row 2 by 2 to make the coefficient of x1 equal to 1:

Basic Variables x1 x2 x3 x4 RHS

x3 0 1 1 -1 1

x1 1 1 0 1/2 4

x5 0 1 2 -1 2

z 0 -3 9 9/2 -18

We repeat the process until all coefficients in the z-row are non-negative. In this case, we can stop here because all coefficients in the z-row are non-negative.

Therefore, the optimal solution is x1 = 4, x2 = 0, x3 = 1, w = 0, and the minimum value of the objective function is 0.

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Answer:

Slope = 0.05

General Formulas and Concepts:

Algebra I

Slope-Intercept Form: y = mx + b

Step-by-step explanation:

Step 1: Define

Identify

y = 0.05x + 4.95

Step 2: Identify

Slope m = 0.05

y-intercept b = 4.95

The diagram should help

Answer:

irrational

Step-by-step explanation:

Answer:

rational

Step-by-step explanation:

Total number of men and women wearing sunglasses = 290

According to the question,

Total number of men and women = 2000

half of the adults were women = 1/2 × 2000

Number of women = 1000

Number of men = (Total adults) - (Number of women )

Number of men = 2000 - 1000

= 1000

given,

20% of women were wearing sunglasses = 20/100 × 1000

= 200

9% of men were wearing sunglasses = 9/100 × 1000

= 90

Total number of adults wearing glasses = 200 + 90

= 290

In mathematics, a percentage is a number or ratio that represents a fraction of 100. It is often denoted by the symbol "%" or simply as "percent" or "pct." For example, 35% is equivalent to the decimal 0.35, or the fraction.

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Answer:

There's no A so I'm going to assume you meant X

X = 23

Step-by-step explanation:

X is equal to 23, because 23 - 18 = 5

or 5 + 18 = 23

The statement that the National Vulnerability Database (NVD) is responsible for actively performing vulnerability testing for every company software and hardware infrastructure is false.

The National Vulnerability Database (NVD) is a repository of security vulnerabilities and related information. It serves as a comprehensive database that provides information on known vulnerabilities in various software and hardware products. However, the NVD itself is not responsible for actively performing vulnerability testing for every company's software and hardware infrastructure.

Vulnerability testing is typically conducted by individual companies, organizations, or specialized security firms. Companies and organizations perform their own vulnerability testing or hire external professionals to assess and identify vulnerabilities in their software and hardware systems. They may use a variety of methods, such as penetration testing, code reviews, and vulnerability tools, to uncover potential security weaknesses.

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Step-by-step explanation:

8x + 3y = 7 --------(1)

2x + y = 2 ----------(2)

y = 2 – 2x ---------(3)

just substitute for y in equation (1)

8x + 3(2–2x) = 7

8x + 6 – 6x = 7

8x – 6x + 6 = 7

2x = 7 – 6

2x = 1

x = ½

since x = ½ just substitute for x in equation(3)

y = 2 – 2x

y = 2 – 2(½)

y = 2 – 1

y = 1

so x = ½,y = 1

i hope this helped

Answer:

If y = 290, x = 30

Step-by-step explanation:

y = 200 + 3x   If y = 290

290 = 200 + 3x

290 - 200 = 3x

90 = 3x

90/3 = x

30 = x

A bicycle repair shop that offers two service packages: a tune-up and a complete overhaul.

The shop operates for 60 hours per week and receives an average of 180 bicycles each week. To analyze the capacity and utilization of the process, we need to consider the time taken at each stage and the demand for each service option. We'll break down the problem into multiple parts and provide a detailed explanation using mathematical terms.

a) Creating the Demand Matrix:

To create a demand matrix, we need to determine the number of bicycles going through each stage of the process. Let's denote the demand for tune-up as T and the demand for additional services as A.

Given that the average number of bicycles received per week is 180 and 25% of customers opt for additional services, we can calculate the demands as follows:

Demand for tune-up (T) = Total demand - Demand for additional services

T = 180 - (0.25 * 180)

T = 180 - 45

T = 135

Demand for additional services (A) = 0.25 * Total demand

A = 0.25 * 180

A = 45

Now, we can create a demand matrix based on the demand for each service option:

Demand Matrix:

Tune-up Additional Services Wheel Balancing

Tune-up  [135  0  0]

Additional [0  45  0]

Services

Total [ 135  45  0 ]

The demand matrix shows the number of bicycles flowing through each stage of the process.

b) Daily Capacity at Each Stage:

To calculate the daily capacity at each stage, we need to consider the time taken for each service option. Given that the shop operates for 60 hours per week, we can calculate the daily capacity at each stage:

Tune-up technician time per bicycle (\(T_{tuneup}\)) = 75 minutes

Additional services technician time per bicycle (\(T_{additional}\)) = 72 minutes

Wheel balancing specialist time per bicycle (\(T_{balancing}\)) = 20 minutes

Daily Capacity (C) = (60 hours * 60 minutes) / (\(T_{tuneup}\) + \(T_{additional}\) + \(T_{balancing}\))

Substituting the given values:

C = (60 * 60) / (75 + 72 + 20)

C = 21600 / 167

C ≈ 129.34 bicycles per day

Therefore, the daily capacity at each stage of the process is as follows:

Tune-up: 129 bicycles per day

Additional Services: 129 bicycles per day

Wheel Balancing: 129 bicycles per day

c) Implied Utilizations:

To find the implied utilizations, we need to compare the demand and the capacity at each stage of the process. Utilization can be calculated as the demand divided by the capacity.

Implied Utilization (U) = Demand / Daily Capacity

For the Tune-up stage:

\(U_{tuneup}\) = 135 / 129 ≈ 1.05

For the Additional Services stage:

\(U_{additional}\) = 45 / 129 ≈ 0.35

For the Wheel Balancing stage:

\(U_{balancing}\) = 0 / 129 = 0

The implied utilizations show how efficiently each stage of the process is being utilized. Utilization values greater than 1 indicate that the stage is operating beyond its capacity.

d) Weekly Capacity of the Process:

To calculate the weekly capacity of the process, we multiply the daily capacity by the number of days the shop is open per week:

Weekly Capacity = Daily Capacity * Number of days shop is open per week

Given that the shop is open for 60 hours per week, the number of days the shop is open per week can be calculated as follows:

Number of days shop is open per week = 60 hours / 24 hours per day = 2.5 days

Therefore, the weekly capacity of the process is:

Weekly Capacity = Daily Capacity * Number of days shop is open per week

Weekly Capacity = 129 bicycles per day * 2.5 days

Weekly Capacity = 322.5 bicycles per week

e) Flow Rate and Constraint Analysis:

To determine if the flow rate of the process is capacity-constrained or demand-constrained, we compare the weekly capacity to the demand for each service option.

Demand for Tune-up (\(T_{demand}\)) = 135 bicycles per week

Demand for Additional Services (\(A_{demand}\)) = 45 bicycles per week

Comparing the demands with the weekly capacity:

\(T_{demand}\) < Weekly Capacity (135 < 322.5)

\(A_{demand}\) < Weekly Capacity (45 < 322.5)

Since both the demands for tune-up and additional services are less than the weekly capacity, the flow rate of the process is demand-constrained. This means the shop has the capacity to handle the current demand without operating beyond its limits.

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Below is the Python code to simulate the probability of pulling a gold marble.

Python

import random

def simulate_pulling_gold_marble(num_trials):

 num_gold_marbles = 0

 for _ in range(num_trials):

   marble = random.choice(["gold", "red", "blue", "green"])

   if marble == "gold":

     num_gold_marbles += 1

 return num_gold_marbles / num_trials

def main():

 num_trials = 10000

 probability = simulate_pulling_gold_marble(num_trials)

 print("The probability of pulling a gold marble is", probability)

if __name__ == "__main__":

 main()

This code simulates pulling a gold marble 10,000 times. Each time a marble is pulled, it is put back in the bag so that the probability of pulling a gold marble remains the same each time. The code then calculates the proportion of times a gold marble was pulled and prints the probability.

To run the simulation, you can save the code as a Python file and then run it from the command line.

python simulation.py

The output of the simulation should be something like this:

The probability of pulling a gold marble is 0.2433

This means that the probability of pulling a gold marble is about 24%

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The probability that the proportion of tickets sold in a sample of 865 tickets would differ from the population proportion by greater than 3% would be 0.0456, rounded to four decimal places.

By using the following formula, we can find the standard error in the population:

SE = √(p(1-p)/n),

where p is population proportion and n is sample size.

Since p = 0.2 and n = 865 in this instance, Therefore,

SE = √(0.2 × 0.8 / 865) = 0.015.

The z-score is then determined by dividing (0.03 - 0) by 0.015, which is 2.

We can determine that the likelihood of receiving a z-score larger than 2 or less than -2 is around 0.0456 using a conventional normal distribution table.

So, the likelihood that the proportion of tickets sold in a sample of 865 tickets would deviate from the general proportion by more than 3% is roughly 0.0456, rounded to four decimal places.

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Around 50% to 75% of the daffodils on the south side of the building are not between 46cm and 48cm.

Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty. A probability is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.

Here,

This question asks for the probability that none of the three daffodils selected from the south side of the building are between 46cm and 48cm.

Since the median of the data is 46cm

the third quartile is 48cm,

this means that about 50% to 75% of the daffodils on the south side of the building are between 46cm and 48cm.

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Answer:

1/8 tablespoons

Step-by-step explanation:

Since the child needs to take 1/2 tablespoons off medicine per day in 4 equal doses, you will divide the 1/2 tablespoons into 4 equal doses, so you need to divide by 4.

You can do this by multiplying 1/2 by 1/4.

\(\frac{1}{2} * \frac{1}{4} = \frac{1}{8}\)

Answer:

it would be 1/8

Step-by-step explantion:

simply divide

1/2÷4

=1/8

(that should be right)

Answer:

1.Point form: (5,10) or Equation form: x = 5 , y = 10

2.Point form:(2,0-) or Equation form: x= 2, y=0

Step-by-step explanation:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Hopes this helps!

Answer:

fourth

Step-by-step explanation:

Angle X is the inscribed angle of the two arcs that measure 122 and 64 so

\(x = \frac{1}{2} (122 + 64)\)

\(x = \frac{1}{2} (186) = 93\)

A cyclic quadrilateral states that the opposite angles add up to 180

so

\(y = 18 0 - 83 = 97\)

The correct answer is the fourth option

Answer:

y = mx + b

Step-by-step explanation:

so you first put the points on the graph and connect them with a slanted line.

Next, for your equation start of with y =

then, your going to find your slope, after you find it put it in front of x (slope x) (Ex; if the slope was 3 then it would look like this 3x)

finally you write + and the y intercept (at which point the line goes through the y axis)

the equation together should look like y = slope x + y intercept

The missing values and trigonometric functions are:

a = 25

b = 15

sin(A) = 3/5

cos(A) = 4/5

sec(B) = 5/3

cot(B) = 4/3

Trigonometry is one of the most important branches in mathematics that finds huge application in diverse fields. The branch called “Trigonometry” basically deals with the study of the relationship between the sides and angles of the right-angle triangle.

Given: AB = c = 20, AC = b, BC = a, angle C = 90 degree, tan(B) = 3/4

From the right triangle ABC, we know that:

a² = b² + c² (by the Pythagorean theorem)

tan(B) = opposite/adjacent = b/c

Substituting the given values, we have:

a² = b² + 20²

tan(B) = 3/4 = b/20

Solving the second equation for b, we get:

b = 20(3/4) = 15

Substituting this value into the first equation, we can solve for a:

a² = 15² + 20²

a = √(225 + 400) = √(625) = 25

Therefore, a = 25, b = 15, and c = 20.

To find sin(A) and cos(A), we can use the fact that sin²(A) + cos²(A) = 1:

sin²(A) = 1 - cos²(A)

Using the Pythagorean identity, we have:

sin(A) = b/a = 15/25 = 3/5

cos(A) = c/a = 20/25 = 4/5

To find sec(B) and cot(B), we can use the reciprocal and quotient identities:

sec(B) = 1/cos(B) = 1/(3/5) = 5/3

cot(B) = 1/tan(B) = 4/3

Therefore, the missing values and trigonometric functions are:

a = 25

b = 15

sin(A) = 3/5

cos(A) = 4/5

sec(B) = 5/3

cot(B) = 4/3

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The value of x is -7

These are expressions that are made up of terms, variables, constants, factors and coefficients.

Algebraic expressions are expressions made up of arithmetic operations, such as;

From the information given, we have that;

-3x-5=16

collect the like terms

-3x = 16 + 5

-3x = 21

Divide by the coefficient of x

x = -7

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Answer:

B

Step-by-step explanation:

You substitute the input, 3, for the x. The input is always the x and the output is always the y. So:

y=-4(3)+1

y=-12+1

y=-11

Answer:

27

Step-by-step explanation:

9x3 is 27. Coefficient is the number in the term.

The value of the variables 'x' will be 47° and the value of the variables 'y' will be 27°, respectively.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

Alternate angle - If two lines are parallel then the third line will make z -an angle and z-angles equal angles with the parallel lines.

The equations are given below.

2y = 180° - 126°

2y = 54°

y = 27°

2x + 1 = 180° - 85°

2x + 1 = 95°

2x = 94°

x = 47°

The value of the variables 'x' will be 47° and the value of the variables 'y' will be 27°, respectively.

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The complete question is attached below.

If demand or annual usage increases by 10 percent, the Economic Order Quantity (EOQ) will increase. The EOQ model is used in inventory management to determine the optimal order quantity that minimizes total inventory costs.

The Economic Order Quantity (EOQ) is a model used in inventory management to determine the optimal order quantity that minimizes total inventory costs. It takes into account factors such as demand, holding costs, and ordering costs. When demand or annual usage increases by 10 percent, it means that more units are being consumed or sold within a given time period.

With an increase in demand, the EOQ will also increase. This is because the EOQ formula takes into consideration the trade-off between holding costs and ordering costs. Holding costs are the costs associated with holding inventory, such as warehousing and insurance, while ordering costs are the costs incurred when placing an order, such as administrative and transportation costs.

When demand increases, more units need to be ordered to meet the higher demand. This results in an increase in ordering costs, as more frequent orders will need to be placed. Consequently, the EOQ will increase to find the new optimal order quantity that balances the increased ordering costs with the holding costs.

In summary, if demand or annual usage increases by 10 percent, the EOQ will increase due to the need to order more frequently to meet the higher demand, resulting in increased ordering costs. This adjustment ensures that the inventory management system remains efficient and cost-effective.

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