A(b c) = a • b a • c, where a, b, and c are real numbers use the distributive property to simplify the expression. 8(3 4) = 24

If we chosen the one year subscription we have to pay  7.49 per each month.

What is Linear Equation ?

Linear Equation can be defined as the equation in which the highest degree of the variable is one.

Given,

The cost of an online newspaper is 7.99

And if we bought the one year subscription the cost is 89.88

Let the the cost of the each month if we bought the one year subscription be x .

for one year the cost is 89.88

for one month could be

that is, x = 89.88/12

x = 7.49

Hence , If we chosen the one year subscription we have to pay  7.49 per each month.

To learn more about the Linear Equation from the given link.

https://brainly.com/question/12788590

#SPJ4

Vito finds his way out of the maze in 8.5 minutes starting from the center.

Let the expected time it takes for Vito to find his way out of the maze starting from the center as E.

Case 1: Vito chooses Path 1 with probability 1/6

In this case, Vito finds his way out of the maze in 2 minutes.

Case 2: Vito chooses Path 2 with probability 2/6

In this case, Vito goes back to the center of the maze and starts again. Since Vito has already spent 2 minutes, the total expected time in this case is E + 2.

Case 3: Vito chooses Path 3 with probability 3/6

Vito goes back to the center and starts again. Since Vito has already spent 3 minutes, the total expected time in this case is E + 3.

Now, let's use the Law of Total Expectation to find E

E = (1/6) x 2 + (2/6) x (E + 2) + (3/6) x (E + 3)

E = 1/3 + (2/6)E + 1 + (3/6)E + 3/2

6E = 2 + 4E + 6 + 9

6E - 4E = 17

2E = 17

E = 8.5

Therefore, on average, Vito finds his way out of the maze in 8.5 minutes starting from the center.

Learn more about Law of Total Expectation here:

https://brainly.com/question/27811090

#SPJ4

Answer:

23.32 Miles

Step-by-step explanation:

According to the Question,

(For Diagram Please Find in Attachment)

In Triangle ABC , Apply Pythagoras Theorem, We get

AC²=AB² + BC²

AC² = 12² + 20²

AC² = 544 ⇒ √544 ⇔ 23.32 miles

Answer:

1.33

Step-by-step explanation:

a.  If we let u = (3 - 2x), then the derivative du/dx would be -2, which is not equal to zero. This indicates that the substitution does not satisfy the requirement for u to be differentiable.

b. Michael's substitution satisfies the requirement for u to be differentiable.

(a) i. Kayla's proposed substitution of u as (3 - 2x) will not work in this case. The reason is that when using the u-substitution method, it is necessary for the chosen u to be differentiable, meaning that its derivative du/dx should exist and be non-zero. However, if we let u = (3 - 2x), then the derivative du/dx would be -2, which is not equal to zero. This indicates that the substitution does not satisfy the requirement for u to be differentiable.

ii. Kayla's idea of always picking the most inside factor as u does not work for all u-substitutions. There can be cases where choosing the most inside factor may not lead to a valid substitution that simplifies the problem or makes integration easier. It is important to consider the properties of the function and choose a suitable substitution accordingly.

(b) i. Michael's proposed substitution of u as 3√3 - 2x will work in this case. If we let u = 3√3 - 2x, then the derivative du/dx would be -2, which is non-zero. Therefore, Michael's substitution satisfies the requirement for u to be differentiable.

ii. Michael's idea of always picking the most complicated factor as u also does not hold true for all u-substitutions. The choice of u depends on various factors, including the structure of the function, simplification possibilities, and making the integration process more manageable. It is not necessarily the case that the most complex factor will always result in a successful substitution.

It is important to consider the specific characteristics of the function and apply appropriate judgment in choosing the substitution u to simplify the problem effectively.

Learn more about  derivative  from

https://brainly.com/question/23819325

#SPJ11

The probability that a student learns more than 11 years is approximately 0.0548 or 5.48%.

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence.

To find the probability that a student learns more than 11 years, we need to standardize the variable using the standard normal distribution. We can do this by calculating the z-score for 11 years as follows:

z = (x - μ) / σ

z = (11 - 7) / 2.5

z = 1.6

Here, μ is the mean of the distribution (7 years) and σ is the standard deviation (2.5 years). We have calculated the z-score as 1.6.

We can now use a standard normal distribution table or a calculator to find the probability that a z-score is greater than 1.6. The probability of a z-score being greater than 1.6 is approximately 0.0548.

Therefore, the probability that a student learns more than 11 years is approximately 0.0548 or 5.48%.

Learn more about probability on:

https://brainly.com/question/13604758

#SPJ4

Answer:its the graph of f(x) =( x/ was shifted to the right 2 units, down 5 units.

Step-by-step explanation:

(i)  The expression for l in terms of T and g is: \(l = g(T/(2\pi ))^{2}\)

(ii) the length of the pendulum is approximately 0.362 meters

The formula for the time taken for a pendulum to complete one oscillation is given by:

\(T = 2\pi \sqrt{ (l/g)}\)

where l is the length of the pendulum and g is the acceleration due to gravity.

(i) Expressing l in terms of T and g:

We can rearrange the above formula to solve for l:

\(T = 2\pi \sqrt{(l/g)}\)

\(T/(2\pi ) = \sqrt{(l/g)}\)

\((T/(2\pi ))^{2} = l/g\)

\(l = g(T/(2\pi ))^{2}\)

So, the expression for l in terms of T and g is:

\(l = g(T/(2\pi ))^{2}\)

(ii) Finding the length of the pendulum:

We are given that T = 12 seconds for 20 oscillations. So, the time taken for one oscillation is:

T/20 = 12/20 = 0.6 seconds

Substituting this value of T into the formula for l that we obtained in part (i), we get:

\(l = g(T/(2\pi ))^{2}\)

\(l = 10(0.6/(2\pi ))^{2}\)

l = 0.362 m (rounded to 3 decimal places)

Therefore, the length of the pendulum is approximately 0.362 meters if it takes 12 seconds to complete 20 oscillations

To know more about Pendulum refer the following link:

https://brainly.com/question/26449711

The surface area of the white mug would be 125 cm² since the surface area of the blue mug is 80 cm²

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

Independent variables represent function inputs that do not depend on other values, while dependent variables represent function outputs that depends on other values.

Since the coffee mugs are similar, hence ratio of their sizes are similar

Ratio of volume = scale factor³

Scale factor³ = 125 ml / 64 ml = 1.95

Scale factor = 1.25

Surface area of white mug = scale factor² * surface area of the blue

mug = 1.25² * 80 cm² = 125 cm²

The surface area of the white mug would be 125 cm² since the surface area of the blue mug is 80 cm²

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Answer: y = -3/5x - 6

Step-by-step explanation:

There are a few equations that can be used for this, but the simplest one would be y = mx + b

We are given:

y = -3

m = -3/5 (slope)

x = -5

b = ?

Our equation is this, we are solving for b

==> -3 = -3/5 ( -5) + b

==> -3 = -3/5 ( -5) + b ( multiply the brackets)

==> -3 = 3 + b ( subtract 3 to both sides)

==> -6 = b

Now we can make the desired equation in slope intercept form;

y = -3/5x - 6

Hope this helped! Have a great day :D

Answer:

solution

x-3x= -2-1

-2x= -3

x= -3 by -2

and then cut the minus sign and then again write x= 3 by 2

The substitution method is used in elimination to find the solution to the equation.

A set of two linear equations with two variables is called a system of linear equations. They create a system of linear equations when evaluated collectively.

The given equation in the problem is;

Equation P: a - b = 9

Equation Q: a+b=5

The value obtained from the equation P is;

a - b = 9

a=b+9

Substitute the value in the equation Q;

a+b=5

b+9+b=5

2b=9-5

b=2

The value of a is;

a-b=9

a-2=9

a=9+2

a=11

Hence the value of a and b will be 11 and 2.

To learn more about the system of two equations, refer to the link;

https://brainly.com/question/21620502

#SPJ1

Answer:

34.0522° N, 118.2437° W

Step-by-step explanation:

Answer:

14+28i

Step-by-step explanation:

Answer:

180

Step-by-step explanation:

we are increasing by 20 for every increasing spot

Answer:

y = 55

Step-by-step explanation:

(4x - 12) and (2x + 8) are alternate angles and are congruent , so

4x - 12 = 2x + 8 ( subtract 2x from both sides )

2x - 12 = 8 ( add 12 to both sides )

2x = 20 ( divide both sides by 2 )

x = 10

then

4x - 12 = 4(10) - 12 = 40 - 12 = 28

(3y - 13) and (4x - 12) are same- side interior angles and sum to 180° , so

3y - 13 + 28 = 180

3y + 15 = 180 ( subtract 15 from both sides )

3y = 165 ( divide both sides by 3 )

y = 55

Answer:

y = x + 1

Step-by-step explanation:

The slope of the line shown in the graph is __2/3__

and the y-intercept of the line is __6___

The general linear equation is written as follows:

y = ax + b

Where a is the slope and b is the y-intercept.

On the graph we can see that the y-intercept is y = 6, then we can write the line as:

y = ax + 6

The line also passes through the point (-9, 0), replacing these values in the line we will get:

0 = a*-9 + 6

9a = 6

a = 6/9

a = 2/3

That is the slope.

Learn more about linear equations at:

https://brainly.com/question/1884491

#SPJ1

Answer:

1.6

Step-by-step explanation:

Answer:

1.6% hope this helps a little

Step-by-step explanation:

Answer:

1.8

Step-by-step explanation:

The key that minimizes the Euclidean distance between the probability distributions is: A → C, B → A, C → D, and D → B

To find the key that minimizes the Euclidean distance between the probability distribution in the message space and the ciphertext, we need to compare the probabilities of each letter in both distributions.

Let's consider the four letters in the message space: A, B, C, and D.

In the message space, the probability distribution is given by P[A] = 0.1, P[B] = 0.2, P[C] = 0.3, and P[D] = 0.4.

In the ciphertext, the relative frequencies are given by P[A] = 0.35, P[B] = 0.45, P[C] = 0.05, and P[D] = 0.15.

To find the key, we need to match the letters in the message space with their corresponding letters in the ciphertext based on the highest probability.

Comparing the probabilities, we can see that the letter with the highest probability in the message space is D (0.4), and in the ciphertext, it is B (0.45). Therefore, we can deduce that D in the message space corresponds to B in the ciphertext.

Similarly, we can match A in the message space to C in the ciphertext, B in the message space to A in the ciphertext, and C in the message space to D in the ciphertext.

Thus, the key that minimizes the Euclidean distance between the probability distributions is: A → C, B → A, C → D, and D → B.

This key represents the mapping of letters from the message space to the ciphertext that best aligns the probabilities of the two distributions.

Learn more about: Euclidean distance

https://brainly.com/question/30930235

#SPJ11

Answer:

(3, \(\frac{1}{8}\) )

Step-by-step explanation:

Hi there,

To find the answer to this question, you can simply use a graphing calculator to graph this function. When looking at the values of points along the function, we find that (3, \(\frac{1}{8}\) ) is one of the answer choices.

Hope this answer helps.

Cheers.

The units of measure for the rate of increase would be frogs per unit of time

(The largest rate of increase in the number of frogs in the pond would be when the growth rate is at its maximum. This can be determined by finding the derivative of the growth function and setting it equal to zero to find the maximum point.

Since we are not given a specific growth function, we cannot accurately determine the largest rate of increase. However, we can say that the largest rate of increase would occur at the point where the derivative of the growth function is at its maximum. The units of measure for the rate of increase would be frogs per unit of time (e.g. frogs per day or frogs per week).

Learn more about Units

brainly.com/question/10433377

#SPJ11

Answer:

A. 150

Step-by-step explanation:

Calculate the probability of landing on an odd number: 1/2.

Multiply the probability by the number of trials: (1/2) * 300.

Simplify the expression: 150.

Therefore, a reasonable prediction is that the event of landing on an odd number will occur 150 times out of the 300 rolls of the fair 6-sided die.

Answer:

-28

Step-by-step explanation:

Answer:

-28

Step-by-step explanation:

Scatter plots are employed to demonstrate data points on a vertical and horizontal axis in an effort to illustrate how much one variable influences another. The position of the marker that symbolises each row in the data table is determined by the values of the sections plotted on the X and Y axes. Using a scatter plot, ascertain the relationship or correlation among two variables.

The scatterplot reveals a significant link between the variables.

There is an exponential curve in the scatterplot.

y = 6.7e⁰³³ˣ is the equation for the line or curve of best fit.

The R-squared value of 0.9995 shows that this equation is an excellent predictor of the data. The R-squared number shows that the model

accounts for 99.95% of the variation in the data. This demonstrates that the model accurately predicts the data.

In conclusion, the scatterplot displays an exponential curve and the data are highly connected. y = 6.7e⁰³³ˣ is the equation for the line or curve that best fits the data, and the R-squared value indicates how well it predicts the data.

To know more about Scatter plots, visit:

https://brainly.com/question/6592115

#SPJ1

Graph attached below,

There are 9 members in the math club

What is frequency distribution?

The gathered data is arranged in tables based on frequency distribution. The information could consist of test results, local weather information, volleyball match results, student grades, etc. Data must be presented meaningfully for understanding after data gathering. A frequency distribution graph is a different approach to displaying data that has been represented graphically.

The following frequency distribution is derived from the dot plots:

Age 9 = 2

Age 10 = 0

Age 11 = 1

Age 12 = 2

Age 13 = 4

So, the total membership of the math club is: Total 9

Hence, there are 9 members in the math club.

Learn more about frequency distribution, by the following link

https://brainly.com/question/16698786

#SPJ4

To answer this question, we need to know the median and upper quartile of the data set. Once we have these values, we can determine what percentage of the data falls to the right of the median and to the left of the upper quartile.
Let's say the median of the data set is 50 and the upper quartile is 75. To find the percentage of measurements to the right of the median, we need to look at the data values that are greater than 50 and divide that number by the total number of measurements. Let's say there are 40 data values greater than 50 and a total of 100 measurements.

Then, the percentage of measurements to the right of the median would be:

(40/100) x 100% = 40%

To find the percentage of measurements to the left of the upper quartile, we need to look at the data values that are less than or equal to 75 and divide that number by the total number of measurements. Let's say there are 60 data values less than or equal to 75 and a total of 100 measurements. Then, the percentage of measurements to the left of the upper quartile would be:

(60/100) x 100% = 60%


Your answer:
1. 40% of the measurements lie to the right of the median.
2. 60% of the measurements lie to the left of the upper quartile (Q3).

To learn more about quartile : brainly.com/question/17198478

#SPJ11

The volume of the cube is 27\(z^{15}\)

A cube is a three dimensional shape having 6 square faces , all the faces are of equal length , breadth and height.

Here we have to find the volume of a cube

The length of the side is 3\(z^{5}\).

The formula for the volume of the cube = a³

where a is the length of the side.

Substituting the value of a we get,

The volume of the cube = (3\(z^{5}\))³

                                        = 27\(z^{15}\)

Therefore the volume of a cube is 27\(z^{15}\).

To know more about the volume of a cube refer to the link given below:

https://brainly.com/question/19891526

#SPJ1