Long distance phone rate 15 cents per minute. A call cost $1.05. How long was the call

The equation x² + 4x + 9 = 0 are complex numbers: x = -2 + i√5 and x = -2 - i√5.

To find the solutions for the equation x² + 4x + 9 = 0, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

Comparing this equation with the given equation x² + 4x + 9 = 0, we can see that a = 1, b = 4, and c = 9.

Plugging in these values into the quadratic formula, we have:

x = (-4 ± √(4² - 4(1)(9))) / (2(1))

x = (-4 ± √(16 - 36)) / 2

x = (-4 ± √(-20)) / 2

Since the value inside the square root is negative, we know that the solutions will involve complex numbers. Simplifying further, we have:

x = (-4 ± i√20) / 2

x = (-4 ± 2i√5) / 2

Simplifying the expression by dividing both the numerator and denominator by 2, we get:

x = -2 ± i√5

for such more question on quadratic

https://brainly.com/question/17482667

#SPJ8

The system stable with P(1)=1.7 and P(-1)=2.7. The correct answer is b.

To test the stability of a discrete control system with an open loop transfer function, we need to examine the roots of the characteristic equation, which is obtained by setting the denominator of the transfer function equal to zero.

The characteristic equation for the given transfer function G(z) is:

z^2 - 1.2z + 0.2 = 0

We can find the roots of this equation by factoring or using the quadratic formula. In this case, the roots are complex conjugates:

z = 0.6 + 0.4i

z = 0.6 - 0.4i

For a discrete control system, stability is determined by the location of the roots in the complex plane. If the magnitude of all the roots is less than 1, the system is stable. If any root has a magnitude greater than or equal to 1, the system is unstable.

In this case, the magnitude of the roots is less than 1, since:

|0.6 + 0.4i| = sqrt(0.6^2 + 0.4^2) ≈ 0.75

|0.6 - 0.4i| = sqrt(0.6^2 + 0.4^2) ≈ 0.75

Therefore, the system is stable.

The correct answer is:

b. Stable with P(1)=1.7 and P(-1)=2.7

Learn more about open-loop transfer: brainly.com/question/31300185

#SPJ11

The smallest number of minutes that could have passed before the chemical was depleted is 1 minute.

If there are 562mm of the chemical left, we can find out the smallest number of minutes that could have passed by using the formula below;

v = u + at,

where: v = final velocity

u = initial velocity

a = acceleration

t = time

Since we are looking for the smallest number of minutes that could have passed, we will assume that the acceleration of the chemical is 0.

Thus, the formula becomes; v = u + 0 × t = u

Therefore, the velocity is equal to the initial velocity.

Assuming that the initial velocity of the chemical was 562mm of chemical per minute, the smallest number of minutes that could have passed before the chemical was depleted is 1 minute.

If we assume that the rate of depletion is constant, the chemical will be depleted after 1 minute since there is no acceleration.

So, the smallest number of minutes that could have passed before the chemical was depleted is 1 minute.

Learn more about: minutes

https://brainly.com/question/12175640

#SPJ11

When 25 percent of doctors make less than $180k and 25% make more than $320k, a. Approximately 13.14% of physicians earn less than $200,000. and b. Approximately 7.75% of physicians earn between $280,000 and $320,000.

a. The fraction of physicians who earn less than $200,000 can be estimated using the given information as follows:

Let's denote the mean salary of physicians in this specialty by μ and the standard deviation by σ. Since the salaries are approximately normally distributed, we can use the properties of the standard normal distribution to solve this problem.

We know that 25% of the physicians earn less than $180,000, which means that their z-score (number of standard deviations from the mean) is: z = (180,000 - μ) / σ

Using a calculator, we can find the z-score corresponding to the 25th percentile, which is approximately -0.674. Therefore: -0.674 = (180,000 - μ) / σ

Similarly, we know that 75% of the physicians earn more than $180,000, which means that their z-score is: z = (320,000 - μ) / σ

Using the calculator, we can find the z-score corresponding to the 75th percentile, which is approximately 0.674. Therefore: 0.674 = (320,000 - μ) / σ

Solving these two equations simultaneously, we can find μ and σ:

μ = $250,000

σ = $53,333

Now, to find the fraction of physicians who earn less than $200,000, we need to calculate the z-score corresponding to this salary: z = (200,000 - μ) / σ = -1.125

Using the calculator, we can find that the fraction of physicians who earn less than $200,000 is approximately 0.1314.

b. The fraction of physicians who earn between $280,000 and $320,000 can be estimated using the same method as above. We need to calculate the z-scores corresponding to these salaries:

z1 = (280,000 - μ) / σ = 0.596

z2 = (320,000 - μ) / σ = 0.674

Using the calculator, we can find the area between these two z-scores, which represents the fraction of physicians who earn between $280,000 and $320,000. This area is approximately 0.0775.

To know more about percent, refer here:

https://brainly.com/question/29014288#

#SPJ11

Answer:

6.75

Step-by-step explanation:

6 is equivalent to 6

3/4 is equivalent to 0.75

Answer:

It is 6.75

Step-by-step explanation:

Can I have brainliest?

Answer: 26 minutes

Step-by-step explanation:

Assume that the total time spent in the morning which includes getting dressed, eating breakfast, making her bed, and driving to work is x.

Time getting dressed = ¹/₃x

Eating breakfast = 10 mins

Making bed = 5 mins

¹/₃x + 10 + 5 = 35 ½

¹/₃x + 15 = 35 ½

¹/₃x = 35 ½ - 15

¹/₃x = 20 ½

x = 20 ½ / ¹/₃

= 61.5 minutes

Total morning routine is is 61.5 mins

Time taken to drive to work is;

= 61.5 - 35 ½

= 26 minutes

Answer:

120

Step-by-step explanation:

Answer:

\(2m=45\)

Step-by-step explanation:

He earned twice as much washing cars, which is \(2m\). This is given to be equal to 45.

Answer:

B. (3x - 9) (x + 3i)

Step-by-step explanation:

\(\bf 3 {x}^{2} = + 27\)

Therefore, B is your answer!!!!

Answer:

120

Step-by-step explanation:

reduce the fraction from

\(48 \times \frac{250}{100 } \)

to

\(48 \times \frac{5}{2} \)

then multiply and you get 24 × 5 which is 120

The outstanding principal after the 93rd repayment is approximately $532.81.  The correct answer is 1) $532.81.

To calculate the outstanding principal after the 93rd repayment, we need to determine the loan's initial principal and the monthly interest rate.

- Monthly repayment: $180.00

- Number of repayments: 96

- Interest rate: 12 = 8.0730% per annum

First, let's calculate the monthly interest rate by dividing the annual interest rate by 12:

Monthly interest rate = j12 / 12

Monthly interest rate = 8.0730% / 12

Monthly interest rate = 0.67275% or 0.0067275 (as a decimal)

Next, we can use the loan amortization formula to calculate the initial principal (P) of the loan:

Initial principal (P) = Monthly repayment / ((1 + Monthly interest rate)^(Number of repayments) - 1)

P = $180.00 / ((1 + \(0.0067275)^(96) - 1)\)

P ≈ $14,557.91

Now, we can determine the outstanding principal after the 93rd repayment. We need to calculate the remaining principal after 93 repayments using the following formula:

Outstanding principal = Initial principal * ((1 + Monthly interest rate)^(Number of repayments) - (1 + Monthly interest rate)^(Number of repayments made))

Outstanding principal = $14,557.91 * ((1 + 0.0067275)^(96) - (1 + \(0.0067275)^(93))\)

Outstanding principal ≈ $532.81

Therefore, the outstanding principal after the 93rd repayment is approximately $532.81.

The correct answer is 1) $532.81.

Learn more about amortization here:

https://brainly.com/question/32732448

#SPJ11

9514 1404 393

Answer:

  B

Step-by-step explanation:

The associative property just moves parentheses, without changing the values or order of the operands. The only expression for which that is true is ...

  B.  (6·1/3)·7/5

Answer:

Domain: (negative infinite, zero) U (0, infinite)

Range: ( negative infinite, -3) U (-3, infinite)

Step-by-step explanation:

I don't really know how to explain this because I can't use some symbols that are needed. But, yeah.

Answer:

D. 22.5

Step-by-step explanation:

By the property of intersecting tangent and secant outside of the circle, we have:

x° = 1/2[(4x+5)° - 50°]

2x° = [(4x+5)° - 50°]

2x° = (4x-45)°

2x = 4x - 45

45 = 4x - 2x

45 = 2x

x = 45/2

x = 22.5

The measure of the variable x will be 22.5°. Then the correct option is D.

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

We know that half of the difference between the angle (4x + 5)° and 50° will be equal to x°. Then the equation will be

x = [4x + 5 - 50] / 2

Simplify the equation, then we have

2x = 4x - 45

2x = 45

x = 22.5°

The measure of the variable x will be 22.5°.

Then the correct option is D.

More about the circle link is given below.

https://brainly.com/question/11833983

#SPJ5

the wing's lifting force as the aircraft slows down to km per hour is around  \(6,210\) pounds.

Let's begin by writing down the joint variation formula for lifting force, F, area of the wing, A, and the square of the plane's velocity, v:

\(F = k * A * v^2\)

where k is the constant of variation that we need to determine.

We are given that when A  \(= 300\) square feet and \(v = 110\) miles per hour,  \(F = 12,000\) pounds. Let's use this information to solve for k:

\(12,000 = k * 300 * 110^2\)

\(k = 12,000 / (300 *\times 110^2)\)

 \(k \approx 0.00207\)(rounded to at least 5 decimal places)

Now we can use the joint variation formula to find the lifting force on the wing when the plane slows down to  \(100\) miles per hour. We know that A is still  \(300\) square feet, but v is now  \(100\) miles per hour:

\(F = 0.00207 \times 300 \times 100^2\)

\(F \approx6,210\) pounds (rounded to the nearest pound)

Therefore, the lifting force on the wing when the plane slows down to  \(100\) miles per hour is approximately  \(6,210\) pounds.

Learn more about force here:

https://brainly.com/question/31158801

#SPJ1

16,384,000 more people resided in Tokyo

Tokyo population = 34,450,000

Mexico Population = 18,066,000

To find how many more people resided in Tokyo, we subtract =

34,450,000 - 18,066,000 = 16,384,000

What is a good budget for an apartment?

One popular rule of thumb is the 30% rule, which says to spend around 30% of your gross income on rent. So if you earn $2,800 per month before taxes, you should spend about $840 per month on rent.

To learn more about rent visit: https://brainly.com/question/15386402

#SPJ4

F(1) is equal to 0 for the given function F(x).

In order to evaluate a function at a specific value, you simply substitute that value for the input variable in the function and simplify the resulting expression.

If you are given a specific function F(x) and are asked to evaluate it at a specific value, say F(1), then you would substitute x=1 in the function F(x) and simplify the expression.

For example, if \(F(x) = x^2 + 2x - 3\), then to evaluate F(1), we substitute x=1 in the expression:

\(F(1) = (1)^2 + 2(1) - 3\)

Simplifying the expression, we get:

F(1) = 1 + 2 - 3 = 0

Hence, F(1) is equal to 0 for the given function F(x).

A function is a mathematical rule that takes an input value, processes it, and produces an output value. The input value is called the independent variable, and the output value is called the dependent variable, because its value depends on the input.

A function can be represented in various ways, such as an algebraic expression, a graph, a table, or a verbal description. For example, the function f(x) = 2x + 1 is an algebraic expression that represents a linear function, where the independent variable is x and the dependent variable is f(x).

Functions are used to describe and model relationships between variables in various fields of mathematics, science, engineering, economics, and other disciplines. They are important tools for analyzing and solving problems, and they can be used to make predictions, optimize processes, and design systems.

To know more about Functions visit :

https://brainly.com/question/11624077

#SPJ1

Answer:

-4,-1,4,11

Step-by-step explanation:

f(n)=n^2-5

Let n= 1

f(1)=1^2-5 = 1-5 = -4

Let n= 2

f(2)=2^2-5 = 4-5 = -1

Let n= 3

f(3)=3^2-5 = 9-5 = 4

Let n= 4

f(4)=4^2-5 = 16-5 = 11

The correct identification of the dependent variable and the independent variable for the experiment is valid experiment.

Independent variable: The variable that is being changed or manipulated in an experiment is called the independent variable. The experimenter modifies the independent variable to observe its effect on the dependent variable.

Dependent variable: The dependent variable is the variable that is being measured and observed in an experiment. It is dependent on the independent variable because it changes as a result of the manipulation of the independent variable.

Therefore, To carry out a valid experiment, it is crucial to accurately identify the dependent variable and independent variable.

To know more about the "dependent variable" and "independent variable": https://brainly.com/question/25223322

#SPJ11

Answer:

A and D would be the correct answers

Step-by-step explanation:

Since each of the 10 students has 3 choices, there are \(3^{10}\) possible outcomes in the sample space of her experiment.

Using the probability concept, it is found that there is a 70% experimental probability that a shark with red eyes is not picked.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

For an experimental probability, these numbers of outcomes are taken from previous trials.

In this problem, out of 10 students, 3 choose the shark with red eyes, hence 7 did not choose them, thus:

p = 7/10 = 0.7 = 70%.

Hence, there is a 70% experimental probability that a shark with red eyes is not picked.

For the total number of outcomes, there are 10 students, each with 3 choices, hence there are there are \(3 \times 3 \times 3 \cdots \times 3 = 3^{10}\) possible outcomes in the sample space of her experiment.

More can be learned about probabilities at https://brainly.com/question/14398287

Explanation

as we can see in the picture, after drawing the angles, we can observe the common angles is

I hope this helps you

Answer:

C. The results are inconclusive; therefore a generalization cannot be made regarding which option is selected more often.

explanation:

just took the test on plato

Since the study yields the same results for only five of the weeks. So here the generalization could be made like option c.

Since at the closing of the first week the company determined the majority of the employees should prefer the lunch break and also the company repeats the observational study for 10 more weeks.

So here the output is to be inconclusive. Due to this, the generalization cannot be made with respect to the selection of the given options.

hence, the option c is correct.

learn more about study here: https://brainly.com/question/24308401

Answer

The height of the plane at that time is 1.1 miles

The distance of the plane's path is 10.1 miles

Explanation

The situation models a right angle triangle as shown below

Using trigonometric ratio,

tan 6° = opposite / adjacent

The opposite side of the triangle is the height of the plane. The distance traveled horizontally is the adjacent side. Therefore,

The height of the plane at that time ≈ 1.1 miles

The hypotenuse of the triangle formed is the distance of the plane path.

Therefore, this distance can be calculated using Pythagoras rule as follows:

The distance of the plane's path = 10.1 miles

Answer: y= x + 4

Step-by-step explanation:

Answer:

A ray is a a part of a line but a line segment is a line that connects two points

Step-by-step explanation:

A ray has one point at one end and an arrow that goes on forever, Though segments have 2 end points and do not go on forever.

"The angles formed by the lines that meet at each base are 90 degree angles and the distance between each base is the same."

was this your explanation? if so I think that it defines exactly the image shown on the quiz.