Can someone give me the reason why 2 is congruent to 11

The natural logarithm function is ln(p) = ln(100) - 0.35t

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

The table of values

The function can be represented as

p = ae^kt

Using the points on the table, we have

ae^(k * 0) = 100

So, we have

a = 100

This gives

p = 100e^kt

Using another point, we have

70.5y = 100e^(k * 1)

70.5y = 100e^k

So, we have

e^k = 0.705

Take the natural logarithm of both sides

k = ln(0.705)

k = -0.35

The function becomes

p = 100e^(-0.35t)

Take the natural logarithm of both sides

ln(p) = ln(100) - 0.35t

Hence, the function is ln(p) = ln(100) - 0.35t

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As per the linear equation the system has one solution, which is x = 1 and y = 1.

A linear equation is a mathematical expression that represents a straight line. A linear equation has a set of variables, and the coefficients (numbers in front of the variables) are constant.

The reason why most overdetermined linear systems are inconsistent is that there are more restrictions placed on the variables than what is required to find a solution.

It is possible for an overdetermined linear system to have one solution, but this is a rare occurrence.

When an overdetermined system has infinitely many solutions, this means that there are an infinite number of combinations of values that satisfy all of the equations simultaneously.

For example, consider the following system of linear equations:

2x + 3y = 6

4x + 6y = 12

This system is overdetermined because there are two equations and only one variable (x and y). In this case, the system has one solution, which is x = 1 and y = 1.

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if the bill was $23.60, and the tip was 15%, kim will earn $3.54. the overall total of the meal would be $27.14 :)

Anwser will be $3.54

15% = .15 ( to convert percent to decimal, change the % to . and move the decimal two places to the left)

23.60 * .15 = 3.54

Answer:

yes, yes, yes, no, yes

Step-by-step explanation:

The point on the ellipse x^2 + y^2 = 81, which is formed by the intersection of the cylinder and the plane x + z = 9, that is farthest from the origin can be found by maximizing the distance function from the origin to the ellipse. The point on the ellipse that is farthest from the origin is (-9, 0, 0).

To find the point on the ellipse that is farthest from the origin, we need to maximize the distance between the origin and any point on the ellipse. Since the equation of the ellipse is x^2 + y^2 = 81, we can rewrite it as x^2 + 0^2 + y^2 = 81. This shows that the ellipse lies in the xy-plane.

The plane x + z = 9 intersects the ellipse, which means that we can substitute x + z = 9 into the equation of the ellipse to find the points of intersection. Substituting x = 9 - z into the equation of the ellipse, we get (9 - z)^2 + y^2 = 81. Simplifying this equation, we obtain z^2 - 18z + y^2 = 0.

This is the equation of a circle in the zy-plane centered at (9, 0) with a radius of 9. Since we are interested in the farthest point from the origin, we need to find the point on this circle that is farthest from the origin, which is the point (-9, 0, 0).

Therefore, the point on the ellipse that is farthest from the origin is       (-9, 0, 0).

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False. We do not always evaluate just the specific result obtained in an experiment.

In scientific experiments, we do not just evaluate the specific result obtained in the experiment. Instead, we evaluate the entire experimental design, including the methods used, the sample size, and the statistical analysis.

For example, suppose a researcher conducts an experiment to test a new drug's effectiveness in treating a particular disease. If the result of the experiment shows that the drug is effective, the researcher cannot simply conclude that the drug works based on this one result. Instead, the researcher must evaluate the experimental design to ensure that the result is reliable and valid.

This evaluation includes examining the study's methods to determine if they are appropriate and if the sample size is large enough to produce meaningful results. It also involves statistical analysis to assess the strength of the relationship between the treatment and the outcome and to determine if the result is statistically significant.

Therefore, evaluating just the specific result obtained in an experiment is not sufficient. We must also consider the experimental design, methods used, sample size, and statistical analysis to draw valid and reliable conclusions from the experiment.

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Answer:

x = 14

Step-by-step explanation:

hope this helps! <3

The proportion of defective circulators can be calculated by weighting the defect rates of each company by their respective proportions in the contractor's inventory. Thus, the proportion of defective circulators can be expected to be 0.0065 (0.60*0.005 + 0.40*0.010).Plugging in these values, we get P(B|A) = (0.005*0.60)/0.0065 = 0.046, or approximately 4.6%.

To calculate the probability that a defective circulator came from the first company, we can use Bayes' theorem.

Let A denote the event that a circulator is defective, and let B denote the event that the circulator came from the first company.

We want to find P(B|A), the probability that the circulator came from the first company given that it is defective.

This can be calculated using the formula P(B|A) = P(A|B)*P(B)/P(A), where P(A|B) is the probability of a defective circulator given that it came from the first company (0.005),

P(B) is the probability that a circulator came from the first company (0.60), and P(A) is the overall probability of a defective circulator (0.0065).

Plugging in these values, we get P(B|A) = (0.005*0.60)/0.0065 = 0.046, or approximately 4.6%.

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The reward-to-variability ratio of the best feasible is 0.4221 that is option a.

The proportion of stocks invested in the optimal risky portfolio can be calculated with the use of following formula:

Portfolio Invested in the Stock = [(Expected Return of the Stock - Risk Free Rate)*(Standard Deviation of Bond)^2 - (Expected Return of the Bond - Risk Free Rate)*Covariance between Bond and Stock]/[(Expected Return of the Stock - Risk Free Rate)*(Standard Deviation of Bond)^2 + (Expected Return of the Bond - Risk Free Rate)*(Standard Deviation of Stock)^2 - (Expected Return of Stock - Risk Free Rate + Expected Return of Bond - Risk Free Rate)]*Covariance between Bond and Stock

Portfolio Invested in Bond = 1 - Portfolio Invested in the Stock

Here, Risk Free Rate = 4 and Covariance = 32*24*.1250 = 96

Using these values and other information provided in the question, we get,

Portfolio Invested in the Stock = [(10 - 4)*(24)^2 - (7 - 4)*96]/(10 - 4)*(24)^2 + (7 - 4)*(32)^2 - [(10 - 4 + 7 - 4)]*96 = .5593

Portfolio Invested in Bond = 1-.5593 = .4407

Step 2: Calculate Expected Return and Standard Deviation of the Optimal Risky Portfolio

Expected Return = Portfolio Invested in Stock*Expected Return of Stock Portfolio Invested in Bond*Expected Return of Bond = .5593*10% + .4407*7% = 8.68%

Standard Deviation = [(Portfolio Invested in Stock)^2*(Standard Deviation of Stock)^2 + (Portfolio Invested in Bond)^2*(Standard Deviation of Bond)^2 + 2*(Portfolio Invested in Stock)*(Portfolio Invested in Bond)]^(1/2) = [(.5593)^2*(32)^2 + (.4407)^2*(24)^2 + 2*(.5593)*(.4407)*(96)]^(1/2) = 21.90%

Step 3: Calculate Reward-to-Volatility Ratio

The reward-to-volatility ratio can be calculated with the use of following formula:

Reward-to-Volatility Ratio = (Expected Return of the Portfolio - Risk Free Rate)/Standard Deviation of Portfolio = (8.68 - 4)/21.90 = .4221

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Answer:

\(f(\pi / 2) = 1\)

Step-by-step explanation:

To find the exact output of a function f(x) = sin²x given the input π/2, we can look to the unit circle. Remember that sin²x is an abbreviation for (sin(x))².

We can represent the output of the function for the input π/2 as:

\(f(\pi / 2) = (\sin(\pi / 2))^2\)

First, we need to find the exact value of sin(π/2). We can find this by graphing \(\theta = \pi/2\), finding its intersection with the circumference of the unit circle, then taking the y-coordinate of the point of intersection.

This y-coordinate is 1.

Therefore,

\(f(\pi / 2) = (1)^2\)

\(\boxed{f(\pi / 2) = 1}\)

The Cartesian coordinates of vector A at time t are x(t) = 0, y(t) = 0, and z(t) = 5t.

To find the first derivative of the vector A, we need to differentiate each component of the vector with respect to time.

The spherical coordinates of vector A are given as:

A = 5t * u_r(ϕ(t), θ(t))

where ϕ(t) = 2t and θ(t) = 2π.

a) First, let's differentiate the radial component with respect to time:

dr/dt = d(5t)/dt = 5

Next, we differentiate the azimuthal component ϕ(t) with respect to time:

dϕ/dt = d(2t)/dt = 2

Finally, the derivative of the polar angle θ(t) with respect to time is zero, as it is a constant:

dθ/dt = d(2π)/dt = 0

Therefore, the first derivative of vector A, dA/dt, is:

dA/dt = (dr/dt)u_r + r(dϕ/dt)u_ϕ + r sin(θ)(dθ/dt)u_θ

     = 5u_r + 2tu_ϕ

b) To obtain the Cartesian coordinates x(t), y(t), and z(t) of vector A at time t, we need to convert the spherical coordinates to Cartesian coordinates. The conversion formulas are:

x = r sin(θ) cos(ϕ)

y = r sin(θ) sin(ϕ)

z = r cos(θ)

Using the given spherical coordinates:

r = 5t

θ = 2π

ϕ = 2t

Substituting these values into the conversion formulas, we get:

x(t) = (5t) sin(2π) cos(2t)

    = 0 (sin(2π) = 0)

y(t) = (5t) sin(2π) sin(2t)

    = 0 (sin(2π) = 0)

z(t) = (5t) cos(2π)

    = 5t

Therefore, the Cartesian coordinates of vector A at time t are x(t) = 0, y(t) = 0, and z(t) = 5t.

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Answer:

Step-by-step explanation:

3 weeks is 21 days, so multiply the given quantities by 7. 15? 105

30? 210. 21? 147.

Answer:

63 lbs of dark chocolate

210 lbs of sugar

147 lbs of butter

(that's a lot lol)

Step-by-step explanation:

So basically you do everything divided by three and multiply that by 21

15 lb dark chocolate in one day is: 3 lbs

30lb: 10lbs

21lbs: 7lbs

and now you multiply each of them by 21 because that's how much days there are in three weeks

3 · 21 = 63

10 · 21 = 210

7 · 21 = 147

(answer above)

Therefore , the solution of the given problem of ratio comes out to be

ratio = 500 /(total length of the pool) = laps taken.

The simple formula "a / b" can be used to define a pair of equal variables "a" and "b," where "b" may also be greater than zero. By mixing two ratios, one ratio is produced. If there was only one man and three women, the ratio would be 1:3. The group consists of 3/4 girls and 1/4 boys. A separation among one or more objects, a numeral, or a piece of a component's volume are all examples of parts.

Here,

Given :

500 meters would equal 10 laps in a pool with a length of 50 meters

(long course) (or lengths).

Twenty laps in a 25-meter pool would be 500 meters.

To determine the number of laps necessary to finish the 500 m race, you must know the length of the pool.

You may have to calculate the ratio of to get the total number of laps needed to finish the race by dividing the length of the swimming pool by 500 meters.

Ratio = 500 /(total lenght of the pool) = laps taken.

Therefore , the solution of the given problem of ratio comes out to be

ratio = 500 /(total lenght of the pool) = laps taken.

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Answer: 96

Step-by-step explanation:

A palindrome is a number that is the same when reading in both ways (right to left, and left to right), for example, 121

Then, we have 9 digits, and all the digits need to be even.

the options are: 0, 2, 4, 6, 8.

Now, we can think of a 9-digit number as 9 empty slots, and in each slot, we can put a number.

But because this is a palindrome, the first digit must be equal to the ninth, and the second digit must be equal to the eight, and so on.

So, we can think it as actually only 5 slots, where in each slot, we can put an even number, now let's count the options that we have in each selection.

For the first digit we have 4 options: 2, 4, 6 and 8 (0 is not counted here because if the first digit was a 0, then this would not be a 9-digit number).

for the second digit, we have also 4 options (because we already toked one, but now the 0 can be chosen)

for the third digit, we have 3 options

for the fourth digit, we have 2 options

for the fifth digit, we have only one option.

The total number of combinations is equal to the product of the number of options for each selection:

C = 4*4*3*2*1 = 96

Answer:

x2+8x+15=(x+5)(x+3)

Step-by-step explanation:

Trinomials have the form: ax2+bx+c. When factoring trinomials where a=1

Answer:

x(x - 8)

Step-by-step explanation:

First, factor out an x from both terms:

x² - 8x

x(x - 8)

So, the factored form of the binomial is x(x - 8)

Answer:

Rational

Step-by-step explanation:

This number is rational because it can be expressed as a ratio between two numbers.

Answer: 0%

Step-by-step explanation:

There are 5 colors of jelly beans.

Kaz ate all the green beans, so now only 80% of the jelly beans remain.

Kaz ate half of the orange pieces so now only 70% of the jelly beans remain.

Then Kaz ate half of the remaining pieces, so only 35% of the beans remain.

Current numbers: 0% green, 5% orange, 10% red, yellow, blue

Then he eats red and yellow candies in equal proportions until only 15% of the beans remain.  This means that he ate 20% worth of red and yellow beans.  This means that he ate all of the red and yellow beans.

Thus, there are 0% red beans left.

Answer:

96 km

Step-by-step explanation:

72/3 is 24. When yo add 24 to 72 you get 96km.

Answer:

an obtuse angle is an angle that is wider than 90⁰, 100⁰ for example is an obtuse angle

Answer:

2. x = 3-7y

Step-by-step explanation:

The percentage strength of neomycin in the final compounded product is approximately 2.5%.

To determine the percentage strength of neomycin in the final compounded product, we need to calculate the weight of neomycin in the cream and divide it by the total weight of the cream.

Neomycin (5%) cream: 30g

The neomycin content is 5% of the total cream weight. To find the weight of neomycin in the cream, we multiply the cream weight by the neomycin percentage:

Weight of neomycin = 30g × 0.05 = 1.5g

Now, to calculate the percentage strength of neomycin in the final compounded product, we divide the weight of neomycin by the total weight of the cream and multiply by 100:

Percentage strength of neomycin = (Weight of neomycin / Total weight of cream) × 100

Percentage strength of neomycin = (1.5g / 60g) × 100 ≈ 2.5

Therefore, the percentage strength of neomycin in the final compounded product is approximately 2.5%.

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It is true that the binomial x + 1 is a factor of the polynomial P(x) = 5x^2 + 11x + 6

From the question, the given parameters are

Start by setting the binomial to 0

So, we have

x + 1 = 0

Solve for x in the above equation

x = -1

Substitute -1 for x in the polynomial equation P(x) = 5x^2 + 11x + 6

P(-1) = 5(-1)^2 + 11(-1) + 6

Evaluate

P(-1) = 0

Because P(-1) equals 0, then the binomial is a factor of the polynomial

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The z-score for a raw score of 6 is 0.5.A z-score indicates how many standard deviations a raw score is away from the mean.

To calculate the z-score for a raw score of 6 given a mean of 4 and a standard deviation of 4, we can use the formula:

z = (raw score - mean) / standard deviation

Substituting the values into the formula, we get:

z = (6 - 4) / 4

z = 0.5

Therefore, the z-score for a raw score of 6 is 0.5.

In this case, a z-score of 0.5 indicates that the raw score of 6 is half a standard deviation above the mean of 4.

Z-scores are useful because they allow us to compare scores from different distributions. For example, if we have two sets of data with different means and standard deviations, we can convert them into z-scores to compare them directly. A positive z-score means that the raw score is above the mean, while a negative z-score means that the raw score is below the mean. The magnitude of the z-score indicates how far the raw score is from the mean in terms of standard deviations.

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The number of yards, as a mixed number, will you drive until you reach this exit is 333 1/3 yards

The complete question is added as an attachment

From the attached figure, we have:

Exit = 1000 feet

From the question, we have

3 feet = 1 yard

So, the number of yards is

Number of yard =Exit/3 yards

This gives

Number of yard = 1000/3 yards

Evaluate the quotient

Number of yard = 333 1/3 yards

Hence, the number of yards, as a mixed number, will you drive until you reach this exit is 333 1/3 yards

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In order to use the sum theorem to find the measure of angle a, we need to know the measures of the other angles in the triangle. Let's assume that angle b measures 70 degrees and angle c measures 45 degrees.

According to the sum theorem, the sum of the measures of the angles in a triangle is always 180 degrees. So we can write an equation:

a + b + c = 180

Plugging in the known values, we get:

a + 70 + 45 = 180

a + 115 = 180

a = 65

Therefore, angle a measures 65 degrees.

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Angle a measures 65 degrees. In order to use the sum theorem to find the measure of angle a, we need to know the measures of the other angles in the triangle. Let's assume that angle b measures 70 degrees and angle c measures 45 degrees.

According to the sum theorem, the sum of the measures of the angles in a triangle is always 180 degrees. So we can write an equation:

a + b + c = 180

a + 70 + 45 = 180

a + 115 = 180

a = 65

Therefore, angle a measures 65 degrees.

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Step 1. The following table represents the cost per hour of the repair service:

Required: Find the equation that relates the number of hours and the cost.

Step 2. Let h be the number of hours and c be the cost of the service.

As we can see in the table each hour that goes by, the cost increases by 30:

That means that the cost per hour is 30.

Step 3. Now that we know that the cost per hour is $30, we can find the additional fee using the first row of the table.

If the cost for 1 hour is $70, and only $30 of those $70 is the cost per hour, the additional $40 is the fee.

Step 4. All of this is represented by the equation:

Because it is charged 30 per hour h plus an additional fee of 40.

Answer:

The inequality to describe the situation is

xy + (6 - x)y < 18

Given, Corinne's cookies sells gourmet cookies in boxes of 6.

Depending on the type of cookie, a box can cost at most $18.

Let the cookies of type A be, x

then the cookies of type B be, (6 - x)

and the cost of the cookie be, y

So, the inequality be

xy + (6 - x)y < 18

Hence, the inequality to describe the situation is

xy + (6 - x)y < 18

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Assume a stick of length 1 is randomly broken into two portions. The smaller piece's estimated length is 0.25.

The random variable L (the length for the shorter stick) has a uniform distribution.

Thus the probability density function for L is as follows:

This means 2 for all length in the range 0 - 0.5

Now, we calculate the expected value for random variable L as seen on the attachment. Based on the calculation, 0.25 is the smaller piece's estimated length for the randomly broken stick.

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Answer:235

Step-by-step explanation:i got it right on test