Question There are 10 books on a shelf, of which 4 are paperbacks and 6 are hardbacks. How many possible selections of 5 books from the shelf contain at least one paperback and at least one hardback

Yes, the equation C-1(A+X)B-1=In has a solution, X. To find the solution, first use C-1(A+X)B-1=In to simplify to C-1 AB-1=In+X. Next, use matrix multiplication to expand C-1AB-1 to In+X = AC-1B-1-B-1C-1. Subtract In from both sides of the equation to get X=AC-1B-1-B-1C-1-In. This is the solution for X, where A, B, and C are nan invertible matrices.

Given that A, B, and C are invertible nan matrices, we have to check if the equation C-1(A+X)B-1=In has a solution or not, and if there is a solution, we have to find X.

Let's solve it. Let's multiply both sides of the equation by B and C, respectively, we get C-1(A+X)B-1B = IB and C-1(A+X) = B. Now, we have to multiply both sides by C on the left, so we get C*C-1(A+X) = CB, which becomes A+X = CB.

Now we have to multiply both sides by B-1 on the right, so we get A + XBB-1 = CBB-1, which becomes A + XB-1 = CB-1.Now, we have to multiply both sides by C-1 on the left, so we get C-1A + C-1XB-1 = I.

Now, we have to multiply both sides by B and C, respectively, which results in C-1AC-1B + XC-1B = B. Finally, X = B(C-1AC-1B)B-1 - C-1B + I. We know that if A and B are matrices of the same order, then (AB)-1 = B-1A-1. By using this property, we can write the solution as X = B-1(A-1 + C-1)-1B-1 - C-1B + I. So, the solution exists for the given equation.

For more such matrices related questions

https://brainly.com/question/29108022

#SPJ11

Answer:

Mixed number: 1 9/10

Improper fraction: 19/10

The number of cows needed to satisfy the beef appetite would be 5263

With an average yield of 570 pounds (258.1 Kg.) of prepared beef per cow, we need to determine how many people can be fed from this amount. The number of people fed per cow can vary depending on various factors such as portion sizes and individual dietary preferences. Assuming a reasonable estimate, let's consider that one pound (0.45 Kg.) of prepared beef can feed about three people.

To find the number of cows needed to satisfy the beef appetite for New York City's population of approximately 9,000,000 people, we divide the population by the number of people fed by one cow. Thus, the calculation becomes 9,000,000 / (570 pounds x 3 people/pound).

After simplifying the equation, we get 9,000,000 / 1710 people, which equals approximately 5,263 cows. However, it's important to note that this is a rough estimate and does not consider factors such as variations in consumption patterns, distribution logistics, or other sources of meat supply. Additionally, individual dietary choices and preferences may result in different consumption rates. Therefore, this estimate serves as a general indication of the number of cows needed to satisfy the beef appetite for New York City's population.

Learn more about population here;

https://brainly.com/question/30324262

#SPJ11

Answer: $532,000

Step-by-step explanation:

If the company is making $140,000 and they get 20% each year, we just multiply it by 20%, or 0.20, and get $28,000. So, we would multiply that by 14, the years the company operated, and then add it to the original $140,000.

28,000 x 14 = 392,000

392,000 + 140,000 = 532,000

So, over the course of 14 years, the company made a profit of $532,000.

 I am pretty sure it is 782

The database schema mentioned above is for a pizzeria's point-of-sale system. When a customer places an order, the system records the customer's name and contact information, the order date and time, the pizza size and toppings, the quantity, and the order price.

In addition to the Order table, the schema contains a Customers table and a Pizza table.

The Customers table stores the contact information of the pizzeria's customers.

The Pizza table contains a list of available pizza sizes and toppings.

The schema also contains a foreign key constraint, which is a type of data constraint.

It ensures that the values in a column correspond to the values in another column of a different table.

To know more about database schema visit:

https://brainly.com/question/13098366

#SPJ11

The statistics are as follows:

- Test Statistic: The calculated test statistic is approximately 1.02.

- P-value: The P-value associated with the test statistic of 1.02 is approximately 0.154.

- Confidence Interval: The 95% confidence interval for the difference in proportions is approximately -0.0186 to 0.0786.

To solve the problem completely, let's go through each step in detail:

1. Test Statistic:

The test statistic can be calculated using the formula:

z = (p1 - p2) / √[(p_cap1 * (1 - p-cap1) / n1) + (p_cap2 * (1 - p_cap2) / n2)]

We have:

p1 = 0.55 (proportion in the first poll)

p2 = 0.53 (proportion in the second poll)

n1 = 630 (sample size of the first poll)

n2 = 1010 (sample size of the second poll)

Substituting these values into the formula, we get:

z = (0.55 - 0.53) / √[(0.55 * (1 - 0.55) / 630) + (0.53 * (1 - 0.53) / 1010)]

z = 0.02 / √[(0.55 * 0.45 / 630) + (0.53 * 0.47 / 1010)]

z ≈ 0.02 / √(0.0001386 + 0.0002493)

z ≈ 0.02 / √0.0003879

z ≈ 0.02 / 0.0197

z ≈ 1.02 (rounded to two decimal places)

Therefore, the test statistic is approximately 1.02.

2. P-value:

To find the P-value, we need to determine the probability of observing a test statistic as extreme as 1.02 or more extreme under the null hypothesis. We can consult a standard normal distribution table or use statistical software.

The P-value associated with a test statistic of 1.02 is approximately 0.154, which means there is a 15.4% chance of observing a difference in proportions as extreme as 1.02 or greater under the null hypothesis.

3. Confidence Interval:

To estimate the difference in proportions with a 95% confidence interval, we can use the formula:

(p1 - p2) ± z * √[(p_cap1 * (1 - p_cap1) / n1) + (p_cap2 * (1 - p_cap2) / n2)]

We have:

p1 = 0.55 (proportion in the first poll)

p2 = 0.53 (proportion in the second poll)

n1 = 630 (sample size of the first poll)

n2 = 1010 (sample size of the second poll)

z = 1.96 (for a 95% confidence interval)

Substituting these values into the formula, we get:

(0.55 - 0.53) ± 1.96 * √[(0.55 * (1 - 0.55) / 630) + (0.53 * (1 - 0.53) / 1010)]

0.02 ± 1.96 * √[(0.55 * 0.45 / 630) + (0.53 * 0.47 / 1010)]

0.02 ± 1.96 * √(0.0001386 + 0.0002493)

0.02 ± 1.96 * √0.0003879

0.02 ± 1.96 * 0.0197

0.02 ± 0.0386

The 95% confidence interval for the difference in proportions is approximately (0.02 - 0.0386) to (0.02 + 0.0386), which simplifies to (-0.0186 to 0.0786).

To know more about confidence intervals, refer here:

https://brainly.com/question/32546207#

#SPJ11

If you wanted to measure satisfaction with this course on a scale from 1, not very satisfied, to 7, very satisfied, you would use an ordinal scale.

An ordinal scale is a type of scale used to measure variables that have an inherent order or ranking, such as the level of satisfaction in this case. However, the differences between the categories are not necessarily equal or measurable, which rules out the use of an interval or ratio scale. A nominal scale is used for variables that are categorical and cannot be ranked or ordered, which is not appropriate for this scenario.

To know more about measurement,

https://brainly.com/question/17940519

#SPJ11

Answer:

see explanation

Step-by-step explanation:

To find her earnings multiply hourly rate by number of hours worked, then

n → 8n is the algebraic expression

15 → 8 × 15 → $120

20 → 8 × 20 → $160

25 → 8 × 25 → $200

30 → 8 × 30 → $240

Answer:

15 feet

Step-by-step explanation:

\(a^{2} +b^{2} =c^{2} \\a^{2} +(20)^{2} =(25)^{2} \\a^{2} +400=625\\a^{2} =225\\a=15\)

Answer:

15 feet

Step-by-step explanation:

We can imagine the structure as a right triangle: the right angle is formed where the ground meets the wall.

Based on the question:

We can solve using the Pythagorean theorem: a² + b² = c²

Solve:

The distance from the base of the ladder to the wall is 15 feet.

-Chetan K

a = -14

-14+28= 14

14 x 2 = 28

1/2 of -28 --> -14

This means a equals -14.

Esto significa A=-14

(sorry my spanish is not good, hope this helps)

Answer:

brainliest please?

:)   <3

Step-by-step explanation:

3 goes to A

1 goes to B

6 goes to C

5 goes to D

and 8 goes to E

The line that passes through the points (-2, 6) and (r,-4) has a slope of -5, then the value of r = 0

The points through which the equation passes are ​(–2, ​6), (r, -4), with slope​ m ​ = -5

Slope is the steepness of a line as it moves from left to right. Slope is the ratio of the rise, the vertical change, to the run, the horizontal change of a line. The slope of a line is always constant (it never changes) no matter what 2 points on the line you choose.

Whenever the equation of a line is written in the form y = mx + b, it is called the slope-intercept form of the equation. The m is the slope of the line. And b is the b in the point that is the y-intercept (0, b).

m = rise/run

m = \(\frac{y_{2} -y_{1} }{x_{2}-x_{1} }\)          (Equation-1)

Where,

m = slope

\((x_{1} ,y_{1} )\) = coordinates of first point in the line

\((x_{2} ,y_{2} )\) = coordinates of second point in the line

From the given expression,

slope m = -5         (Equation-2)

Slope, m = (change in y) / (change in x)

m = \(\frac{y_{2} -y_{1} }{x_{2}-x_{1} }\)

From the points, ​(–2, ​6​), (r, -4)

\(x_{1}\) = -2

\(y_{1}\) = 6

\(x_{2}\) = r

\(y_{2}\) = -4

We can substitute values in equation-1,

m = \(\frac{-4-6}{r-(-2)}\)

m = \(\frac{-10}{r+2}\)      

So,

We can write,

\(\frac{-10}{r+2}\)  = -5

-10 = -5(r+2)

-10 = -5r - 10

-10 + 10 = -5r

-5r = 0

r = 0/-5

r = 0  

Therefore,

The line that passes through the points (-2, 6) and (r,-4) has a slope of -5, then the value of r = 0.

To learn more about information visit Slope :

brainly.com/question/13683246

#SPJ1

The line that connects the coordinates (-2, 6) and (r, -4) has a slope of 5, hence r = 0.

The equation travels through the locations (-2, 6), (r, -4), with a slope of m = -5.

The steepness of a line as it goes from left to right is what is known as a slope. The slope of a line is determined by dividing its rise, or vertical change, by its run, or horizontal change. No matter which two locations on the line you choose, the slope of a line is always constant (it never varies).

The slope-intercept form of an equation is used whenever the equation of a line is expressed in the form y = mx + b. M represents the line's slope. B is the b in the location where the y-intercept is located (0, b).

m = rise/run

m = \(\frac{y_{2}-y_{1} }{x_{2} -x_{1} }\)         (Equation-1)

Where,

m = slope

(\(x_{1} ,y_{1}\)) = coordinates of first point in the line

(\(x_{2} ,y_{2}\)) = coordinates of second point in the line

From the given expression,

slope m = -5         (Equation-2)

Slope, m = (change in y) / (change in x)

m = \(\frac{y_{2}-y_{1} }{x_{2} -x_{1} }\)    

From the points, ​(–2, ​6​), (r, -4)

We can substitute values in equation-1,

m = \(\frac{-4-6}{r-(-2)}\)

m =  \(\frac{-10}{r+2}\)     

So,

We can write,

 \(\frac{-10}{r+2}\)  = -5

-10 = -5(r+2)

-10 = -5r - 10

-10 + 10 = -5r

-5r = 0

r = 0/-5

r = 0  

Therefore,

The line that passes through the points (-2, 6) and (r,-4) has a slope of -5, then the value of r = 0.

The probability of seeing a shooting star during the first 15 minutes of the hour is approximately 19.95%

To solve this problem, we need to use conditional probability. We want to find the probability of seeing a shooting star during the first 15 minutes of the hour given that the chances of seeing a shooting star in any given hour are 80%.

First, we need to determine the probability of seeing a shooting star in the first 15 minutes of the hour. Since the probability is uniform for the entire hour, we can assume that the probability of seeing a shooting star in any given minute is 80% divided by 60 (the number of minutes in an hour), which is approximately 1.33%.

To find the probability of seeing a shooting star during the first 15 minutes of the hour, we need to add up the probabilities of seeing a shooting star in each of the 15 minutes. This can be calculated as follows:

P(seeing a shooting star in the first 15 minutes) = P(seeing a shooting star in minute 1) + P(seeing a shooting star in minute 2) + ... + P(seeing a shooting star in minute 15)
= 15 x 1.33%
= 19.95%

Therefore, the probability of seeing a shooting star during the first 15 minutes of the hour is approximately 19.95%. This means that if you go out star gazing again and the chances of seeing a shooting star are 80%, there is a 19.95% chance that you will see one during the first 15 minutes of the hour you are out.

Know more about   shooting star  here:

https://brainly.com/question/31451954

#SPJ11

`

Answer:

$17.04

Step-by-step explanation:

After a stock split, the number of shares a shareholder owns is increased, while the value of each share is decreased. In this case, Lea's shares were increased by a factor of 5/2 = 2.5 times. Therefore, Lea's number of shares after the split was 800 * 2.5 = 2000 shares.

The value of each share after the split is decreased by a factor of 2/5 = 0.4 times. Therefore, the post-split price per share was $42.60 * 0.4 = $17.04.

Therefore, after the stock split, Lea had 2000 shares worth $17.04 each.

If the original quantity is 8 and the new quantity is 2, then the correct answer is 75%.

For this question we need to subtract and multiply the numbers. We know that 2 = 25% of 8 so:

\(\boxed{8-2=6}\\\boxed{6/2=3}\)

We are going to take that 25% and multiply it with 3 to get are final answer.

\(\boxed{25*3=75}\\\boxed{So,2=75}\)

Therefore, If the original quantity is 8 and the new quantity is 2, then the correct answer is 75%.

Answer:

12%

Step-by-step explanation:

based on the simulation info, if there is both

1. A "1"

2. An "A" or "B",

then it will rain on both days. This occurs 3 times out of 25, or 3/25 = 0.12 = 12%

1. 2nd row 1st column

2. 3rd row 4th column

3. 5th row 2nd column

When the alpha level is changed from α = 0.05 to α = 0.01, the boundaries for the critical region become narrower, making it more difficult to reject the null hypothesis and increasing the level of confidence required for statistical significance.

When the alpha level is changed from α = 0.05 to α = 0.01, the boundaries for the critical region in hypothesis testing become more stringent or strict.

The critical region represents the range of values for the test statistic that would lead to rejecting the null hypothesis.

It is determined based on the chosen level of significance (alpha), which represents the maximum probability of making a Type I error (rejecting the null hypothesis when it is actually true).

By lowering the alpha level from 0.05 to 0.01, the critical region becomes smaller.

This means that the range of values for the test statistic that would lead to rejecting the null hypothesis becomes more restricted.

As a result, it becomes harder to reject the null hypothesis and more evidence is required to claim statistical significance.

Changing the alpha level to a smaller value indicates a higher level of confidence required to reject the null hypothesis.

This decision is made to reduce the likelihood of Type I errors, which occur when the null hypothesis is wrongly rejected.

For similar question on critical region.

https://brainly.com/question/15970126  

#SPJ11

Answer: There are no values that make the equation true  .  No solution

Between 48% and 54% believe that their health is extremely important.

According to the statement

Given that a random sample of 1001 Americans aged 18-24 years showed that 51% believe their health is extremely important.

Here

Sample size n =1001

sample proportion p = 0.51

By these values we calculate the Standard error of proportion.

So, Standard error of proportion = 0.0158.

Since sample size is sufficiently large we can take Z critical value for confidence interval

Z critical value for 95% = 1.96

Margin of error = ±1.96*std error

= ±0.0310

confidence interval = 0.51 ±0.0310

= (0.48, 0.54)

So, Between 48% and 54% believe that their health is extremely important.

Learn more about PROPORTION here https://brainly.com/question/870035

#SPJ4

For the given percentage less the current average is $936.

The average or  mean is defined as the mean  equal to the ratio of the sum of the numbers of a given set of values ​​to the total number of values ​​present in the set.

What is percentage?

In mathematics,  percentage is a number or ratio which can be expressed as a fraction of 100. If we need to calculate the percentage of a number, we divide the number by the whole number and multiply by 100. So , percent means one hundredth and the  word percent means every 100th. The symbol of percentage is  "%".

Last spring, the average amount of rent paid for apartments in Vindale was $1040.

This spring the less percentage is 10.

current average = 1040(1-10%)

                           =1040(1-10/100)

                           =1040(1-1/10)

                           = 1040 × 9/10

                           = 104×9

                           =936

Hence, the current average becomes $936.

To know more about average and percentage

https://brainly.com/question/1136789

#SPJ1

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.

SOLUTIONS

Using the Pythagoras theorem

opposite = x

hypotenuse = 10

Final answer = 6

Linear systems have no solution.

What are the solutions to the linear system?

The solution to a system of linear equations is the point that lies on both lines. In other words, the solution is the point where the two lines intersect

A system of linear equations usually has a single solution, but sometimes it can have no solution (parallel lines) or infinite solutions (same line).

How do you determine a linear system?

Simplify the equation as closely as possible to the form of y = mx + b. Check to see if your equation has exponents. If it has exponents, it is nonlinear. If your equation has no exponents, it is linear

Linear means something related to a line. All the linear equations are used to construct a line. A non-linear equation is such that it does not form a straight line. It looks like a curve in a graph and has a variable slope value.

Hence, the linear systems have no solution.

To learn more about the linear system, visit:

https://brainly.com/question/2226590

#SPJ4

Suppose that if you arrive at a bus stop at 8:00, the number of minutes that you will have to wait for the next bus is uniformly distributed on the interval [0, 20].

A uniformly distributed variable has a range of potential values that are distributed evenly across the range. This implies that each potential value has an equal chance of being chosen. If we have a uniformly distributed variable between 0 and 20, for example, and a sample of 200 potential values is chosen, then each value between 0 and 20 will be represented about 10 times.

The formula for calculating the expected value for a uniformly distributed variable is:

(minimum value + maximum value) / 2

In this scenario, the minimum value is 0 and the maximum value is 20,

So the expected value is:(0 + 20) / 2 = 10

Therefore, on average, you should expect to wait for about 10 minutes for the next bus.

To know more about minutes visit:-

https://brainly.com/question/13387533

#SPJ11

Answer:20x+6/3

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The x value is a positive one since it has nothing in front of the x variable and x -3 represents y value of negative 3

Hope this helps plz mark brainliest!

Answer: B. y = -3x

Step-by-step explanation:

By plugging in the given point into each answer choice for the x and y values for which ever equation is true that is the correct answer.

For the purpose of speeding things up the correct answer is B y = -3x

If we plug in the point give, (1, -3) for (x, y) then we get the equation:

-3 = -3 * 1

This equation when solved: -3 = -3 which is true so this is the correct answer.

Answer:

The data that we have is:

Total time  = 40min

Rate at which ascends or descends = 900ft/min

Maximum height = 18,000 ft.

We can assume that at t = 0 minutes, the plane is on the ground.

Now we can write the height of the plane as a piecewise function of time.

This means that the dependent quantity is the height, and the independent quantity is the time,

The first piece is.

h(t) = (900ft/min)*t   for 0min ≤ t ≤ 20min

We know that the total flight lasts 40 min, so 20 mins represent half of the flight, and we also know that at half the flight the plane reaches the maximum height of 18,000 ft, that checks our equation:

h(20min) = 900ft/min*20min = 18,000ft

And after that points, the plane starts descending at a rate of 900ft/min (now the initial position is 18,000ft), then we can write:

h(t) = 18,000ft - 900ft/min*(t - 20 min) for 20min ≤ t ≤ 40min

Then the function is:

h(t) =  (900ft/min)*t   for 0min ≤ t ≤ 20min

h(t) = 18,000ft - 900ft/min*(t - 20 min) for 20min ≤ t ≤ 40min

Notice that t = 20mins is a value allowed in the two pieces, and gives the same value of h(t) in the two pieces.