Help with question 37-40

Answer: (x + 3)^2 + (y - 4)^2 = 49

Step-by-step explanation:

The equation of a circle given the center and radius: (x - h)^2 + (y - k)^2 = r^2

Given: center (-3,4) ; h = -3 and k = 4

diameter = 14

To find the radius: divide the diameter by 2 = 14/2 = 7 = r

Center: (-3,4) and radius: 7

Equation of a circle: (x - h)^2 + (y - k) ^2 = r^2

Substitute h = -3, k = 4, r = 7

(x - (-3))^2 + (y - 4)^2 = 7^2

Answer:

Equation of the circle: (x + 3)^2 + (y - 4)^2 = 49

We need to know about quadratic equation to solve this problem. The solution for q for the given equation is 1.278 an d-0.978

Quadratic equation is an expression where the highest degree of the variable is two. Quadratic equation can be solved by factorization method or Sridharacharya method. Qudratic equation always has rwo roots. The two roots can be real and unique, real and equal or imaginary. In the question the given equation needs to be expanded to get the quadratic equation. Once expanded we can solve the equation for q, we are supposed to get two values of q.

q=(5q+5)(4q-5)

q=20\(q^{2}\)-25q+20q-25

q=20\(q^{2}\)-5q-25

20\(q^{2}\)-6q-25=0

This is the quadratic equation which we need to solve

q=-(-6)±\(\sqrt{(-6)^{2}+2000 }\)/40=6±\(\sqrt{2036}\)/40=6±45.12/40

q=6+45.12/40=1.278  

or

q=6-45.12/40=-0.978

Therefore the two solutions of q are 1.278 and -0.978.

Learn more about quadratic equation here:

https://brainly.com/question/1214333

#SPJ1

Answer:

The answer is (16.538461(repeated), 26.461538(repeated))

Answer:

x=16.538462 and y=26.461538

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.

To know more about Demand Matrix here

https://brainly.com/question/13012912

#SPJ4

Considering the situation described, it is found that Ashton was born on August 8.

It means that August 31 was on Monday, hence the same is valid for August 24, August 17, August 10 and August 3.

Hence, the first Saturday was August 1, and the second August 8.

A similar problem, involving the interpretation of a situation, is given at https://brainly.com/question/25537936

Answer:

Hourly babysiter money rates. (every hour is $15)

Step-by-step explanation:

Histograms display data using bars of diffrent heights. So on one side you could put the time and on the other side you could put money.

Hope this helps!

The baseballs produced in a day would fill 88 boxes and there would be 8 baseballs leftover.

An equation is an expression that shows the relationship between two or more numbers and variables.

A variable can either be dependent or independent. A dependent variable depend on other variable while an independent variable does not depend on other variables.

The assembly line produces 122 baseballs in a batch, If 8 batches are made in one day hence:

Total baseballs produced = 8 batches * 122 balls per batch = 976 balls

Each box contain 11 baseballs each, hence:

number of boxes = 88 boxes and 8 baseballs remaining

The baseballs produced in a day would fill 88 boxes and there would be 8 baseballs leftover.

Find out more on equation at: https://brainly.com/question/13763238

#SPJ1

Answer:

C: the area is between 0 square unit and 1 square unit.

Step-by-step explanation:

A rectangle is a quadrilateral which has equal and parallel opposite sides. Its area can be determined by;

Area of a rectangle = length x width

In the given question, the length and width of the rectangle are less than 1 unit long. Thus assume that the length is 0.9 cm and width is 0.6 cm, then;

Area = 0.9 x 0.6

        = 0.54

Area = 0.54 \(cm^{2}\)

Thus, since the length and width are both less than 1, then the area of the rectangle is between 0 square units and 1 square unit.

The probability that the sample proportion is greater than 0.24 is 0.9772

Given Data :

population proportion,  p = 0.31

sample size n = 179

μ = p = 0.31

σ = √p(1-p)/n =√( 0.31 (1-0.31 )/179 )= 0.0011

Let p be the sample proportion

p following normal distribution N (μ = 0.31 , σ = 0.0011 )

Here

z = (p - μ) / σ

Now

Now, We Have To Compute P (p > 0.24 )

Therefore,

p (p> 0.15 ) =1 - p( (p-μ )/σ < (0.24 -0.31)/0.0349 )

= 1-p(z < -2.0057) -----from z table

= 1 - 0.0228

=0.9772

Consequently, 0.9772 percent chance exists that the sample proportion will be higher than 0.24.

To learn more about probability click here:

https://brainly.com/question/28045837

#SPJ4

Answer:

$ 11

Step-by-step explanation:

A game costs $ x.

Two games costs 2x.

50 + 2x = 72

2x = 72 - 50

2x = 22

x = 11

A homogeneous system of linear equations is a system where all equations are of the form ax = 0, with no constant terms. It represents a system where the only solution is the trivial solution (all variables equal to zero) or infinitely many solutions.

A homogeneous system of linear equations consists of a set of linear equations with zero constant terms. The general form of a homogeneous system can be represented as:

a₁₁x₁ + a₁₂x₂ + ... + a₁ₙxₙ = 0

a₂₁x₁ + a₂₂x₂ + ... + a₂ₙxₙ = 0

...

aₘ₁x₁ + aₘ₂x₂ + ... + aₘₙxₙ = 0

Here, the variables x₁, x₂, ..., xₙ represent the unknowns, and the coefficients a₁₁, a₁₂, ..., aₘₙ are constants.

A key property of homogeneous systems is that they always have at least one solution, known as the trivial solution, where all variables equal zero. This solution can be easily verified by substituting zero for each variable in the equations. Additionally, if a homogeneous system has nontrivial solutions (solutions other than the trivial solution), it will have infinitely many solutions.

The reason behind the infinite solutions is that if a system has a nontrivial solution (where at least one variable is nonzero), any scalar multiple of that solution will also be a solution. This property is known as the scaling property of homogeneous systems.

Homogeneous systems are extensively studied in linear algebra because they form the basis for concepts such as vector spaces, linear independence, and the null space of a matrix. They also have applications in various fields, including physics, engineering, and computer science.

Learn more about linear equations here:

https://brainly.com/question/32634451

#SPJ11

A homogeneous system of linear equations is a linear system of equations in which there are no constant terms. i.e., a homogeneous linear system is of the form:

a₁₁ x₁ + a₁₂ x₂ + ... + a₁ₙ xₙ = 0

a₂₁ x₁ + a₂₂ x₂ + ... + a₂ₙ xₙ = 0

....

aₘ₁ x₁ + aₘ₂ x₂ + ... + aₘₙ xₙ = 0 Explain.

The value of c guaranteed by the Mean Value Theorem is c = 3.

What is mean value theorem?

The Mean Value Theorem (MVT) is a fundamental theorem in calculus that states that if a function f(x) is continuous on the closed interval [a, b], and differentiable on the interval (a, b), then there exists at least one point c in (a, b) such that:

f'(c) = (f(b) - f(a))/(b - a)

To check if the Mean Value Theorem (MVT) applies to the function f(x) = \(x^3 - 2x\)  on the interval [1, 3], we need to verify two conditions:

Continuity: f(x) must be continuous on the closed interval [1, 3].

Differentiability: f(x) must be differentiable on the open interval (1, 3).

Both of these conditions are met for the given function f(x).

Continuity:

The function f(x) is a polynomial, and all polynomials are continuous for all real numbers. Therefore, f(x) is continuous on the interval [1, 3].

Differentiability:

To show that f(x) is differentiable on the interval (1, 3), we need to show that its derivative exists and is finite at every point in the interval.

\(f(x) = x^3 - 2x\)

\(f'(x) = 3x^2 - 2\)

The derivative f'(x) is a polynomial and exists for all x in the interval (1, 3). Therefore, f(x) is differentiable on the interval (1, 3).

Since both conditions of the MVT are satisfied, there exists a point c in (1, 3) such that:

f'(c) = (f(3) - f(1))/(3 - 1)

We can now find the value of c by solving for it:

f'(c) = (f(3) - f(1))/(3 - 1)

\(3c^2 - 2 = (3^3 - 23) - (1^3 - 21)\)

\(3c^2 - 2 = 25\)

\(3c^2 = 27\)

\(c^2 = 9\)

c = ±3

Since c must be in the interval (1, 3), the only possible value of c is c = 3.

Therefore, by the MVT, there exists a point c in (1, 3) such that:

f'(c) = (f(3) - f(1))/(3 - 1)

\(3c^2 - 2 = (3^3 - 23) - (1^3 - 21)\)

\(3c^2 - 2 = 25\)

\(3c^2 = 27\)

\(c^2 = 9\)

c = 3

Hence, the value of c guaranteed by the Mean Value Theorem is c = 3.

To learn more about mean value theorem, visit the link:

https://brainly.com/question/19052862

#SPJ4

Answer: 8575/2

Step-by-step explanation:

Answer:

The answer is c.

a. Pair 2 is selected.

b. Respiratory system, its function is to breathe. Digestive system, its function is to break down food into nutrients.

c. The two systems work together by sharing the region of the mouth and upper throat.

First picture in Pair 2 is Respiratory system, which its function is to breathe. Second picture in Pair 2 is Digestive system, which its function is to break down food into nutrients such as carbohydrates, fats and proteins. The respiratory system takes in oxygen from the air, and also gets rid of carbon dioxide. The digestive system absorbs water and nutrients from the food we consume.

The respiratory system is mainly used to transport air, whilst the digestive system is used to transport fluids and solids, from water and food we eat. The respiratory and the digestive systems share the area of the mouth and upper throat, in which air, fluids, and solids can be mixed.

The digestive system does homeostasis by ensuring that the stomach area has the right pH balance. The body uses both positive and negative mechanisms to perform homeostasis. If the body detects an imbalance, the other systems work together to counterbalance and restore the right equilibrium.

Learn more about homeostasis at: https://brainly.com/question/3888340

#SPJ4

The number of cupcakes that Chad are is 8 cupcakes.

A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

Let the number of cupcakes that Chad can buy be x.

The number of cupcakes Chad can eat is 2 times the amount his sister can eat. This will be 2x.

Therefore, the appropriate equation will be:

2x + x = 12

3x = 12

Divide

x = 12/3

x = 4

Chad = 2x = 2 × 4 = 8 cupcakes

Learn more about equations on:

brainly.com/question/2972832

#SPJ1

2/3  is the probability that the product of the two spinners' numbers is even.

How does probability explain work?

The simple definition of probability is the likelihood that something will occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out.

                       Statistics is the study of events that follow a probability distribution. There are four primary categories of probability: axiomatic, classical, empirical, and subjective.

An even number comes from multiplying an even and even, even and odd, or odd and even. Since an odd number only comes from multiplying an odd and odd, there are less cases and it would be easier to find the probability of spinning two odd numbers from 1.

            =  1 - 2/4 . 2/3

             =  1 - 1/3

            =  2/3

Learn more about probability

brainly.com/question/30034780

#SPJ4

There are \(\frac{60!}{57!}\) ways we can do it.

Since organization has 60 members from which we haveto pick one person at random to be the president, another person to be the vice president and a third person to be the transformer,

the president can be select in 60c1 = \(\frac{60!}{1! 59!}\)

                                                           = \(\frac{60 *59!}{1*59!}\)

                                                           = 60 ways

After this for vice president we have 59 members from which vice president can be select in 59c1 = 59 ways.

and for treasure we have 58 members from which treasure can be select in 58c1 = 58 ways.

∴ No. of ways in which we can select president, vice president and treasure = 60 × 59 × 58

              =  \(\frac{60 * 59 * 58 * 57!}{57!}\)

              =  \(\frac{60!}{57!}\)

Learn more about probability here;

https://brainly.com/question/13604758

#SPJ4

To find the probability that the student will be from Kenilworth, we need to divide the number of students from Kenilworth by the total number of students in the class.

The number of students from Kenilworth is 4 girls + 5 boys = 9 students. The total number of students in the class is 11 boys from Wilmette + 4 girls from Kenilworth + 10 girls from Wilmette + 4 boys from Glencoe + 5 boys from Kenilworth + 8 girls from Glencoe = 42 students.

Therefore, the probability that the student called upon will be from Kenilworth is 9/42 or approximately 0.214 or 21.4%.
In this class, there are 4 girls from Kenilworth and 5 boys from Kenilworth, totaling 9 students from Kenilworth.

The total number of students in the class is 11 boys from Wilmette + 4 girls from Kenilworth + 10 girls from Wilmette + 4 boys from Glencoe + 5 boys from Kenilworth + 8 girls from Glencoe = 42 students.

The probability that the teacher calls upon a student from Kenilworth is the number of Kenilworth students divided by the total number of students, which is 9/42. Simplified, this probability is 3/14, or approximately 0.214.

To know more about probability click here

brainly.com/question/15124899

#SPJ11

For a process to be considered in control, the output sample means should be within the control limits and ideally, the distribution of the means should be normally distributed.

However, the process can still be considered in control if the means are uniformly distributed or increasing over time, as long as they are within the control limits. The key is consistency and stability, and if the means are consistently within the control limits, it indicates that the process is predictable and reliable.

Therefore, options (b) and (d), which suggest that the output is increasing or decreasing over time, respectively, are incorrect.

Option (c), which suggests that the output is normally distributed, is not necessarily required for a process to be considered in control. The distribution of the output may vary depending on the process, and as long as the output is within the control limits and stable over time, it can be considered in control.

Option (a), which suggests that the output is uniformly distributed, is not a requirement for a process to be considered in control.

Option (e), which suggests that the output is uniformly distributed and increasing over time, is not a valid option. The output cannot be uniformly distributed and increasing over time at the same time.

Thus, for a process to be considered in control, the output sample means should be within the control limits and ideally, the distribution of the means should be normally distributed.

Learn more about "normally distributed":

https://brainly.com/question/4079902

#SPJ11

Answer:

Renee would have to sell 750 food processors for both companies to pay her the same amount. Also, if Renee expects to sell less than 750 food processors she should accept Puree Processors offer but if she expects to sell more than 750 food processors, she should accept Pro Process Processors offer.

Step-by-step explanation:

In order to determine the number of food processors Renee would have to sell for both companies to pay her the same amount, you can write an expression in which the salary at  Pro Process Processors is equal to the salary at Puree Processors, which can be expressed as:

15,000+25x=18,000+21x

Now, you can solve for x that represents the number of food processors:

15,000+25x=18,000+21x

25x-21x=18,000-15,000

4x=3,000

x=3,000/4

x=750

According to this, Renee would have to sell 750 food processors for both companies to pay her the same amount. Also, if Renee expects to sell less than 750 food processors she should accept Puree Processors offer but if she expects to sell more than 750 food processors, she should accept Pro Process Processors offer.

Answer:

2=3408493-=2=9

Step-by-step explanation:

Quantum numbers describe the states of electrons in their respective orbitals in an atom.

Quantum numbers are mathematical descriptions that show the possible states of an electron.

There are four types of quantum number

principal quantum number (n)

angular momentum quantum number (l)

magnetic quantum number (ml)

spin quantum number (ms)

The values for the principal quantum number (n) are integers greater than zero.

The values for the angular momentum quantum number (l) are integers from 0 to n - 1.

The values for the magnetic quantum number (ml) are integers from -l to l.

The values for the spin quantum number (ms) are -1/2 and 1/2.

Learn more about quantum numbers:

brainly.com/question/18835321

#SPJ4

A statistically significant finding indicates that it is unlikely to just be explained purely by chance or random influences.

The notion that a set given observed data is not the result of random but can instead be linked to a specific cause is referred to as statistical significance.

Statistical significance indicates that a result is unlikely to be attributed purely by chance and random causes.

Thus, in other words, if there is no genuine effect in a research study, a statistically significant conclusion has an extremely low likelihood of occuring.

To know more about the statistically significant, here

https://brainly.com/question/15848236

#SPJ4

Answer:

6 cubic meters

Step-by-step explanation:

To calculate the cash balance at the end of the period, we need to consider the cash inflows and outflows.

Starting cash balance: $4,520

Cash inflows: $1,654 (receivables collected)

Cash outflows: $1,961 (payments to suppliers) + $500 (cash expenses)

Total cash inflows: $1,654

Total cash outflows: $1,961 + $500 = $2,461

To calculate the cash balance at the end of the period, we subtract the total cash outflows from the starting cash balance and add the total cash inflows:

Cash balance at the end of the period = Starting cash balance + Total cash inflows - Total cash outflows

Cash balance at the end of the period = $4,520 + $1,654 - $2,461

Cash balance at the end of the period = $4,520 - $807

Cash balance at the end of the period = $3,713

Therefore, the cash balance at the end of the period is $3,713.

To learn more about cash : brainly.com/question/31754110

#SPJ11

Answer:

Ummm where is the options ?????

Step-by-step explanation: