I am thinking of a number.
I multiply it by 6 and add 87.
I get the same answer if I multiply
by 11 and subtract 8.
What is my number?

To convert radians to degrees, we need to multiply the radian measure by 180/π. Let's say we have an angle of 3π/4 radians. To convert this to degrees, we would do:

3π/4 * 180/π = 135 degrees

So our angle measures 135 degrees. Now let's determine which quadrant this angle lies in. A positive angle in the second quadrant will have a cosine value that is negative and a sine value that is positive. Using the unit circle, we can see that our angle of 135 degrees is in the second quadrant. Therefore, our cosine value is -cos(135) and our sine value is sin(135).

To find the tangent, we can use the formula tangent = sine/cosine. So our tangent value is:

tan(135) = sin(135)/cos(135) = (-√2/2)/(-√2/2) = 1

So the sine of our angle is √2/2, the cosine is -√2/2, and the tangent is 1.
Hi! To convert radians to degrees, use the formula:

degrees = radians × (180 / π)

First, determine the angle in radians. Let's say the angle is θ radians.

Step 1: Convert radians to degrees
θ degrees = θ × (180 / π)

Step 2: Determine the quadrant
Check the value of θ degrees to see which quadrant it lies in:
- 0° ≤ θ < 90°: Quadrant I
- 90° ≤ θ < 180°: Quadrant II
- 180° ≤ θ < 270°: Quadrant III
- 270° ≤ θ < 360°: Quadrant IV

Step 3: Calculate sine, cosine, and tangent
To find the sine, cosine, and tangent of the angle θ, you can use a calculator or a reference table:
- sin(θ) = sine of the angle
- cos(θ) = cosine of the angle
- tan(θ) = tangent of the angle = sin(θ) / cos(θ)

Make sure to use the angle in radians for these calculations. After finding the sine, cosine, and tangent values, you'll have the complete information about the angle in question.

To know more about how to convert radians to degrees visit :

https://brainly.com/question/22212006

#SPJ11

Answer: $51.48

Step-by-step explanation:

If a $52 item is marked up by 10%, its new price will be:

$52 + 10% of $52 = $52 + $5.20 = $57.20

Then, if this new price is marked down by 10%, the final price will be:

$57.20 - 10% of $57.20 = $57.20 - $5.72 = $51.48

Therefore, the final price of the item after the markup and markdown is $51.48.

Answer:

Step-by-step explanation:

m∠AOB+m∠BOC=180°

m∠AOB=8x+51°

m∠BOC=6x-25°

~

\(\tt 8x+51+6x-25=180\)

\(\tt 14x+26=180\)

\(\tt 14x=180-26\)

\(\tt \cfrac{14x}{14} =\cfrac{154}{14}\)

\(\tt x=11\)

m∠AOB:-

\(\tt 8(11)+51\)

\(\tt =88+51\)

\(\tt =139^{o}\)

Therefore, m∠AOB=139°

Initial size of the culture = 400 , Doubling period = (35 minutes - 10 minutes) / (1900 - 400) = 0.1437 minutes , Population after 60 minutes = 400 * (2^(60/0.1437)) = 10201 and Population will reach 11000 after approx. 74.51 minutes.

The initial size of the culture can be found by substituting t = 0 into the exponential growth formula:

P(t) = P0 * (2^(t/T))

where P(t) is the population at time t, P0 is the initial population, and T is the doubling period. Substituting t = 0, we get:

400 = P0 * (2^(0/T))

Therefore, P0 = 400.

The doubling period can be found by rearranging the exponential growth formula:

T = (t2 - t1) / (ln(P2) - ln(P1))

where t1 and t2 are the time points, and P1 and P2 are the populations at those time points. Substituting t1 = 10, t2 = 35, P1 = 400, and P2 = 1900, we get:

T = (35 - 10) / (ln(1900) - ln(400)) = 0.1437 minutes

The population after 60 minutes can be found by substituting t = 60 into the exponential growth formula:

P(60) = P0 * (2^(60/T))

Substituting P0 = 400 and T = 0.1437, we get:

P(60) = 400 * (2^(60/0.1437)) = 10201

Finally, the population will reach 11000 after approx. 74.51 minutes can be found by setting P(t) = 11000 in the exponential growth formula and solving for t:

11000 = 400 * (2^(t/0.1437))

t/0.1437 = ln(11000/400)

Therefore, t = 0.1437 * ln(11000/400) ≈ 74.51 minutes

Learn more about population here

https://brainly.com/question/19538277

#SPJ4

The bearing of R from P is 019 and the distance |PR| is 8.75

A cyclist set out from a town P on a bearing of 060 to a town Q, 5 km away. He then moves on a bearing of 345 to a town R, 6km from Q.

See attachment

Start by calculating the distance PR using the following cosine ratio

PR² = PQ² + QR² - 2 * PQ * PR cos(Q)

Substitute known values

PR² = 5² + 6² - 2 * 5 * 6 cos(105)

Evaluate

PR² = 76.53

Take the square root of both sides

PR = 8.75

Next, calculate angle R using the following sine ratio

PQ/sin(R) = PR/sin(Q)

Substitute known values

5/sin(R) = 8.75/sin(105)

Evaluate the quotient

5/sin(R) = 9.06

Multiply both sides by sin(R)

9.06 * sin(R) = 5

Divide both sides by 9.06

sin(R) = 0.5519

Take the arc sin of both sides

R = sin⁻¹(0.5519)

Evaluate

R = 34

Calculate angle P using:

P = 180 - 34 - 105

P = 41

The bearing of R from P is then calculated as:

Bearing = 060 - 41

Evaluate

Bearing =  019

Hence, the bearing of R from P is 019

In (b), we have:

PR = 8.75

Hence, the distance |PR| is 8.75

Read more about bearing and distance at:

https://brainly.com/question/15221233

#SPJ1

Answer:

ima need a link and ill answer it

Step-by-step explanation:

answer:

(1/y)^3(1/z)^4

step-by-step explanation:

negative exponents just move the number to the denominator. so all you have to do is move the y & z to the denominator to change the exponents to positive. hope that helps!

It would take Carlos 28.28 years before his salary would reach $106500.

The slope is the rate of change of the y-axis with respect to the x-axis.

The equation of a line in slope-intercept form is y = mx + b, where

slope = m and y-intercept = b.

We know the greater the absolute value of a slope is the more steeper is its graph or the rate of change is large.

As the table represents a linear relation we can write it in the form

S = mn + b

Slope(m) = (92500 - 78500)/(5 - 1).

Slope(m) = 14000/4.

Slope(m) = 3500.

Now, 78500 = 3500(1) + b.

b = 7500.

S = 3500n + 7500.

Therefore, The number of years 'n' required will be,

106500 = 3500x + 7500.

3500n = 99000.

n = 990/35

n = 28.28 years.

learn more about lines and slopes here :

https://brainly.com/question/15874858

#SPJ1

Answer:

\((4x+1)(x-2)\)

Step-by-step explanation:

Factor 4x2−7x−2

4x2−7x−2

=(4x+1)(x−2)

In the given diagram of circle O, we need to find various measurements. Let's consider the following measurements:

Diameter (d): The diameter of a circle is the distance across it, passing through the center. To find the diameter, we can measure the distance between any two points on the circle that pass through the center. Let's say we measure it as 12 units.

Radius (r): The radius of a circle is the distance from the center to any point on the circumference. It is half the length of the diameter. In this case, the radius would be 6 units (12 divided by 2).

Circumference (C): The circumference of a circle is the distance around it. It can be found using the formula C = 2πr, where π is approximately 3.14 and r is the radius. Using the radius of 6 units, we can calculate the circumference as C = 2 * 3.14 * 6 = 37.68 units. Rounding to the nearest whole number, the circumference is approximately 38 units.

Area (A): The area of a circle is the measure of the surface enclosed by it. It can be calculated using the formula A = πr^2. Substituting the radius of 6 units, we can find the area as A = 3.14 * 6^2 = 113.04 square units. Rounding to the nearest whole number, the area is approximately 113 square units.

In summary, for circle O, the diameter is 12 units, the radius is 6 units, the circumference is approximately 38 units, and the area is approximately 113 square units.

For more such questions on various measurements

https://brainly.com/question/27233632

#SPJ8

The probability of having three or more consecutive years with two or fewer compressor failures per year is about 6.16%.

Clark Property Management should expect to experience some consecutive years with higher compressor failure rates.

Let X represent the number of AC compressor failures. Thus, the probability distribution of X is as follows :

Number of Compressor Failures Probability (Relative Frequency)

0 0.061 0.132 0.253 0.284 0.205 0.076 0.01.

We will select two-digit random numbers from a table of random numbers. We will simulate 20 years of compressor failure.

As a result, there will be a total of 20 values of X, each representing a year's worth of data.

We may now determine whether it is typical to have three or more consecutive years with two or fewer compressor failures per year.

The Monte Carlo simulation is used to complete this task. We may use an online random number generator if a table of random numbers is not available.

Monte Carlo simulation is a statistical modeling method that employs random sampling techniques to simulate the output of a complicated system.

It is a stochastic modeling technique that allows for uncertainty and risk evaluation in complex systems where deterministic methods are insufficient.

Monte Carlo simulation generates random input values for a system with a mathematical model, allowing it to calculate possible outcomes.

These results are then used to generate probability distributions of potential results.

In essence, the Monte Carlo simulation is an experiment conducted on a computer that provides insight into the degree of risk related to decision-making.

1. Set up a model: Determine the system and create a mathematical model that will be utilized in the Monte Carlo simulation.

2. Define input values: Identify the variables that will affect the model's output and define input probability distributions for each.

3. Generate random numbers: Using the input probability distributions, generate random numbers for each variable

4. Run simulations: Run a large number of simulations using the random numbers generated in step 3.

5. Analyze the results: Using the outputs of the Monte Carlo simulation, estimate potential outcomes and the likelihood of different results.

6. Make decisions: Use the data and insights obtained from the Monte Carlo simulation to inform your decision-making.

After conducting the Monte Carlo simulation, it was determined that it is unusual to have three or more consecutive years with two or fewer compressor failures per year.

The probability of having three or more consecutive years with two or fewer compressor failures per year is about 6.16%.

Know more about probability, here:

https://brainly.com/question/31828911

#SPJ11

Answer:

h

Step-by-step explanation:

Generalized Information Criterion (GIC) evaluates statistical models based on goodness of fit and complexity.

To reduce bias, increase model complexity, add relevant features, or decrease regularization.

To reduce variance, increase training data, use cross-validation, apply regularization, or employ ensemble methods. Balancing bias and variance improves model performance, as excessive bias leads to underfitting and excessive variance leads to overfitting.

The aim is to find the optimal level of complexity and generalization for accurate predictions.

Read more about statistical models here:

https://brainly.com/question/9509972

#SPJ4

The Complete Question

Explain the statistical model evaluation by generalized information criterion bias and variance reduction techniques

Answer:

(x, y) ≈ (-2.17, ±sqrt(95)) or (x, y) ≈ (-1.03, ±sqrt(21))

Step-by-step explanation:

To solve this system of equations, we can use the method of substitution. We can start by isolating one of the variables in one of the equations and substituting it into the other equation. Let's solve for x in the first equation:

5y² + 24x - 77 = 0

24x = 77 - 5y²

x = (77 - 5y²)/24

Now we can substitute this expression for x into the second equation:

14x² + 5y² + 150x + 119 = 0

14((77-5y²)/24)² + 5y² + 150((77-5y²)/24) + 119 = 0

Simplifying this expression gives:

49y^4 - 5390y² - 108090y - 404271 = 0

We can solve for y using the quadratic formula:

y² = (5390 ± sqrt(5390² - 4(49)(-404271)))/(2(49))

y² = (5390 ± sqrt(16946804))/98

y² = (5390 ± 4118)/98

y² = 95 or y² = 21

Substituting each value of y into the expression we found for x earlier gives:

x = (77 - 5(±sqrt(95))²)/24 ≈ -2.17 or x = (77 - 5(±sqrt(21))²)/24 ≈ -1.03

Therefore, the solution to the system of equations is:

(x, y) ≈ (-2.17, ±sqrt(95)) or (x, y) ≈ (-1.03, ±sqrt(21))

\(f(x)=3x^2-6x+6\\\\f(x)=3(x^2-2x)+6\\\\f(x)=3(\underbrace{x^2-2x+1}-1)+6\\\\ f(x)=3[(x-1)^2-1]+6\\\\f(x)=3(x-1)^2-3+6\\\\f(x)=3(x-1)^2+3\)

Answer:

A sample is a subset of the population.

The missing lengths in the diagram are CU = 18 and UR = 6

From the question, we have the following parameters that can be used in our computation:

QR = ST = 12

Also, we have

CU = 7x - 10

CV = 3x + 6

The length of the chords QR and ST have the same measure

This means that

CU = CV

Substitute the known values in the above equation, so, we have the following representation

7x - 10 = 3x + 6

Evaluate the like terms

So, we have

4x = 16

This gives

x = 4

Next, we have

UR = 1/2 * 12

UR = 6

And, we have

CU = 7(4) - 10

CU = 18

Hence, the missing lengths are CU = 18 and UR = 6

Read more about intersecting secants at

https://brainly.com/question/26340897

#SPJ1

Answer:

Step-by-step explanation:

The graph includes all point to the left from point 2, same point included

Answer:

x <= 2

Step-by-step explanation:

x - (5 - 3x) <= 2x - 1

x - 5 + 3x <= 2x - 1

4x - 5 <= 2x - 1

4x <= 2x + 4

2x <= 4

x <= 2

Best of Luck!

Answer:

42 degrees

Step-by-step explanation:

it’s the same as the other one

Answer:

35 degrees

Step-by-step explanation:

Add 42 and 103

subtract 145 from 180

35 is what you get left

35 is across from angle x (That means they are equal)

There you have your answer.

35 degrees

Total 64900 stamps more is needed to be collected so the group can break the record.

The current record is 150,000.

Friends collected 10,000, 75,000, and 100 stamps

Let the total stamps need to be collected to break the world record be x,

The total stamps collected should be greater than 150000 to break the world record

10000 + 75000 + 100 + x > 150000

85100 + x > 150000

x > 64900

The total stamps need to be collected is greater than 64900 to break the world record.

Therefore, 64900 stamps need to be collected so the group can break the record.

To learn more about inequalities refer here

https://brainly.com/question/25275758

#SPJ1

Answer:

I agree with Hiroko's statement. Dividing 109.2 by 6 is the same as dividing 109.2 by 6/1, which is the same as dividing 109.2 by 60/10, or 1092/60.

In general, when performing division, we can divide by any equivalent fraction instead of the divisor. For example, instead of dividing by 3, we can divide by 6/2, or 9/3, or 15/5, etc. These fractions are all equivalent to 3, since they represent the same value.

Therefore, dividing 109.2 by 6 is the same as dividing 1092 by 60, and the result will be the same in both cases.

Two linear equations in two variables can be solved using the substitution techniques, graphical method or by the elimination method.

Let us consider any two real world linear equations in two variables.

x - y = 0

x + y = 4

Now let us first solve them by substitution method:

equation 1 can be written as : x = y ,

Now we substitute this value of x in the second equation:

x + y = 4

or,  y + y = 4

or, 2y = 4

or, y = 2

At x = 2 , y = 2. Hence the solution is (2,2)

Now let us solve by elimination method:

adding equation 1 and 2 we get:

x - y = 0

x + y = 4

2x = 4

or, x =2

at x=2 , y = 4-2 =2 Hence the solution is (2,2)

Now we will solve the equations graphical method.

In the graph attached below we can clearly see that the straight line representation of the two equations intersect at the point (2,2)

Hence the solution is (2,2) .

Therefore any linear equation in 2 variables can be solved by substitution , elimination and graphically.

To learn more about linear equations visit:

https://brainly.com/question/21835898

#SPJ4

Therefore, 6 minutes and 40 seconds are needed to test possibilities.

Combinations are sometimes known as selections. Combinations are the results of selecting elements from a set assortment. Nothing specific is being organized here. We are choosing them. To denote the number of unique r-selections or combinations among a set of n items, we write n C r. Combinations are distinct from arrangements or permutations.

Here,

The first two numbers in this three-term series are 17 and 24, and the third one remains a mystery.

Given that there are 40 options for the third number and that each try takes 10 seconds, we have 40 x 10 seconds, or 400 seconds, to try every possible combination.

Thus,

=> 400 seconds  is equals to 6 minutes and 40 seconds

Therefore, 6 minutes and 40 seconds are needed to test every scenario.

To know more about combination , visit

brainly.com/question/28042664

#SPJ4

Answer to -1/3x-1+x2 in standard form:

x²-1/3x-1

Answer:

The answer is 13%

Step-by-step explanation:

The approximate percent increase is 13%.

Percentage increase is the difference between the final value and the initial value, expressed in the form of a percentage. To calculate the percentage we need to have the initial value and the increased (new) value. In other words, we can say that percentage increase is a measure of percent change which gives the extent to which a quantity gains magnitude, intensity, or value. If the percentage increase is a negative value, then we can say that there is a percentage decrease of the same magnitude.

Following the concept of percentage increase, the percentage increase formula is derived and expressed as: Percentage Increase = [(Final Value - Initial Value)/Initial Value] × 100. It should be noted that since the percentage has to be a positive quantity, we take the absolute value of the initial value. If the percentage increase is a negative value, then it is a percentage decrease. The percentage increase is the relative change in the quantity with respect to its initial value. If the percentage change is positive, then it is the percentage increase and if the percentage change is negative, it is a percentage decrease.

Given:

initial =$900,000

Final = $900,000

% increase = $900,000- $800,000/ $800,000 * 100

% increase = 100, 000/8000

% increase = 12.5 %

Learn more about percentage increase here:

https://brainly.com/question/27992848

#SPJ6

A matrix structure is an adaptation of the divisional structure whereby various divisions or parts of divisions are grouped together based on some common strategic elements, usually linked to distinct product/market differences.

In a matrix structure, organizations create a dual reporting system where employees report to both functional managers and project or product managers. This structure allows for greater flexibility and collaboration across departments, as individuals from different functional areas come together to work on specific projects or initiatives. The matrix structure is often employed in complex organizations that operate in multiple markets or industries, as it enables efficient resource allocation and coordination. By grouping divisions or parts of divisions based on common strategic elements, organizations can streamline decision-making processes and enhance cross-functional communication and cooperation.

To learn more about matrix structure : brainly.com/question/30403441

#SPJ11

To find the expected number of sixes appearing on three die rolls, we can calculate the probability of rolling a six on each individual roll and then multiply it by the number of rolls.

The probability of rolling a six on a single roll of a fair die is 1/6, since there are six equally likely outcomes (numbers 1 to 6) and only one of them is a six.

Since the rolls are independent events, we can multiply the probabilities together to find the probability of rolling a six on all three rolls:

(1/6) * (1/6) * (1/6) = 1/216

Therefore, the probability of rolling a six on all three rolls is 1/216.

To find the expected number of sixes, we multiply the probability by the number of rolls:

Expected number of sixes = (1/216) * 3 = 1/72

So, the expected number of sixes appearing on three die rolls is 1/72.

To know more about probability click here: brainly.com/question/31828911

#SPJ11

We get the Laplace transform Y(s) of the solution y(t) to the initial value problem:y′′+5y=t⁴ , y(0)=0 , y′(0)=0 as:Y(s) = { 4! / s² } / [ s⁵ + 5s³ ] + [ 10 / (2s³) ] [ 5! / (s + √5)³ + 5! / (s - √5)³ ].

The solution y(t) to the initial value problem is:

y′′+5y=t⁴ ,

y(0)=0 ,

y′(0)=0

We are required to find the Laplace transform of the solution y(t) using the table of Laplace transforms and the table of properties of Laplace transforms. To begin with, we take the Laplace transform of both sides of the differential equation using the linearity property of the Laplace transform. We obtain:

L{y′′} + 5L{y} = L{t⁴}

Taking Laplace transform of y′′ and t⁴ using the table of Laplace transforms, we get:

L{y′′} = s²Y(s) - sy(0) - y′(0)

= s²Y(s)

and,

L{t⁴} = 4! / s⁵

Thus,

L{y′′} + 5L{y} = L{t⁴} gives us:

s²Y(s) + 5Y(s) = 4! / s⁵

Simplifying this expression, we get:

Y(s) = [ 4! / s⁵ ] / [ s² + 5 ]

Multiplying the numerator and the denominator of the right-hand side by s³, we obtain:Y(s) = [ 4! / s² ] / [ s⁵ + 5s³ ]

Using partial fraction decomposition, we can write the right-hand side as:Y(s) = [ A / s² ] + [ Bs + C / s³ ] + [ D / (s + √5) ] + [ E / (s - √5) ]

Multiplying both sides by s³, we get:

s³Y(s) = A(s⁵ + 5s³) + (Bs + C)s⁴ + Ds³(s - √5) + Es³(s + √5)

For s = 0, we have:

s³Y(0) = 5! A

From the initial condition y(0) = 0, we have:

sY(s) = A + C

For the derivative initial condition y′(0) = 0, we have:

s²Y(s) = 2sA + B

From the last two equations, we can find A and C, and substituting these values in the last equation, we get the Laplace transform Y(s) of the solution y(t).

Using partial fraction decomposition, the right-hand side can be written as:Y(s) = [ A / s² ] + [ Bs + C / s³ ] + [ D / (s + √5) ] + [ E / (s - √5) ]

Multiplying both sides by s³, we get:s³Y(s) = A(s⁵ + 5s³) + (Bs + C)s⁴ + Ds³(s - √5) + Es³(s + √5)

For s = 0, we have:

s³Y(0) = 5! A

From the initial condition y(0) = 0, we have:

sY(s) = A + C

For the derivative initial condition y′(0) = 0, we have:

s²Y(s) = 2sA + B

Substituting s = √5 in the first equation, we get:

s³Y(√5) = [ A(5√5 + 5) + C(5 + 2√5) ] / 2 + D(5 - √5)³ + E(5 + √5)³

Substituting s = -√5 in the first equation, we get:

s³Y(-√5) = [ A(-5√5 + 5) - C(5 - 2√5) ] / 2 + D(5 + √5)³ + E(5 - √5)³

Adding the last two equations, we get:

2s³Y(√5) = 10A + 2D(5 - √5)³ + 2E(5 + √5)³.

To know more about Laplace transforms visit :

https://brainly.com/question/33315896

#SPJ11

Prime factorization of 10 x 4  is 2 x 5 x 2 x 2.

Finding the prime numbers that are multiplied together to produce the original number is the process of prime factorization. The prime factors of 16, for instance, are 2 x 2 x 2 x 2.

Any number can be represented as a sum of prime numbers by prime factorization. A number with exactly two factors, 1 and the number itself, is said to be a prime number. As an illustration, the prime factorization of 18 is 2 x 3 x 3. Here, the two main factors of 18 are 2 and 3. For instance, 72 = 2 x 3 x 3  x 2 can be written as a product of prime factors. The prime factorization of 72 is said to be the expression 2 x 3 x 3  x 2.

Learn more about prime factorization here

https://brainly.com/question/18187355

#SPJ9

Answer:

Step-by-step explanation:

if it's talking about between the numbers 75 to 97, then it's 22.