What is the least four-digit positive integer, with all different digits, that is divisible by each of its digits

Answer:

The correct answer is C.

The probability If no letter can be used twice, 32292000 ways different pass word options are there .

What is probability?

 Mathematical branch known as probability deals with determining the possibility of an event occurring. Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. The possibility of the result of any random event is known as probability. This phrase refers to determining the likelihood that any given event will occur.

Here a password contains 4 letters followed by 2 numbers.

Total number of alphabets = 26

If without repetition the words can be arranged as,

=> 26*25*24*23

Total numbers = 0 to 9 = 10

if without repetition the numbers can be arranged as ,

=> 10 * 9

If no letter can be used twice, number of  different pass word options are,

=> 26*25*24*23*10*9=32292000

Therefore there are 32292000 ways different password options available.

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The following statements are true:

The general least-squares problem is to find an x that makes Ax as close as possible to b.

If b is in the column space of A, then every solution of Ax = b is a least-squares solution.

Any solution of \(A^TAX = A^Tb\) is a least-squares solution of Ax = b.

What is matrix?

In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. Matrices are used in many areas of mathematics, including linear algebra, calculus, and statistics.

The first statement is false. A least-squares solution of Ax = b is a vector x that minimizes the Euclidean norm ||b - Ax||, not necessarily making it smaller than any other norm.

The second statement is true. If b is in the column space of A, then Ax = b has at least one solution, and any solution is also a least-squares solution.

The third statement is true. Any solution of \(A^TAX = A^Tb\) can be written as \(x = (A^TA)^{-1}A^Tb\), and it is a least-squares solution of Ax = b because \((A^TA)^{-1}A^T\) is the left-inverse of A (if A has full column rank), and \((A^TA)^{-1}A^Tb\) is the projection of b onto the column space of A.

The fourth statement is false. A solution of \(A^TAX = A^Tb\) is not necessarily a solution of Ax = b, so it cannot be a least-squares solution of Ax = b.

The fifth statement is false. A least-squares solution of Ax = b is a vector x that satisfies the normal equation \(A^TA x = A^Tb\), not necessarily Ax = b. Moreover, x is the orthogonal projection of b onto Col A only if A has full column rank, in which case the projection matrix is \(A(A^TA)^{-1}A^T.\)

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Complete question : let a be an m x n matrix and b be a vector in rm. which of the following is/are true? (select all that apply)

A least-squares solution of Ax = b is a vector such that ||b - Ax|| ≤ b - Ax|| for all x in Rº.

The general least-squares problem is to find an x that makes Ax as close as possible to b.

If b is in the column space of A, then every solution of Ax = b is a least-squares solution.

Any solution of\(A^TAX = A^Tb\) is a least-squares solution of Ax = b.

A least-squares solution of Ax = b is a vector x that satisfies Ax = b, where is the orthogonal projection of b onto Col A.

Answer:

3.75 cm

Step-by-step explanation:

We know

1.2 cm = 6.4 km

Point A to Point B = 20 km

To find it, we take

20 divided by 6.4 then times 1.2 = 3.75 cm

So, 20 km is 3.75 cm far on the map.

The slope - intercept equation of a line that would pass through (1,-2) and has an undefined slope, is y = -2 x

The slope - intercept equation takes the form:

y = mx + b

m = slope

b = y - intercept

When the slope is undefined, it means that there is no y - intercept as the slope is a vertical line which crosses the x - axis alone. The slope would therefore be :

y = mx

- 2 = 1 x

m = - 2

The slope - intercept form is:

y = -2 x

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Answer:

When you multiply or divide both sides by 2, the result is going to be a negative number.

When you multiply or divide both sides by -2, the results are going to be positive.

Step-by-step explanation:

When you multiply or divide a negative and a negative, it's going to be a positive.

When you multiply or divide a negative and a positive, it's going to be a negative.

Answer: 90 inches

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

(i) Let W be the event that the wind is blowing and H be the event that she hits the target. Using the multiplication rule: Probability of wind and hitting target

= P(W) x P(H|W) = 0.3 x 0.4 = 0.12

(ii) Probability of hitting the target on the first shot:

P(H) = P(not windy) x P(H|not windy) + P(windy) x P(H|windy)

= (1 - 0.3) x 0.7 + 0.3 x 0.4= 0.58

(iii) There are two cases to consider: She hits the target on the first shot and misses on the second, or she misses on the first shot and hits the target on the second.

P(hits target exactly once in two shots)

= P(H1, not H2) + P(not H1, H2)

= [P(not windy) x P(H1, not H2|not windy) + P(windy) x P(H1, not H2|windy)] +[P(not windy) x P(not H1, H2|not windy) + P(windy) x P(not H1, H2|windy)]

= [(1 - 0.3) x 0.7 x 0.6 + 0.3 x 0.4 x 0.6] + [(1 - 0.3) x 0.3 x 0.4 + 0.3 x 0.6 x 0.4]

= 0.282

(iv) Probability of no wind given that she missed:

=P(not W|not H)

= P(not H|not W) x P(not W) / P(not H)

= [P(not windy) x P(not H|not windy) + P(windy) x P(not H|windy)] x [1 - P(H)]

= [(1 - 0.3) x 0.3 + 0.3 x 0.6] x [1 - 0.58]= 0.112

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Answer:

Dimensions of the product matrix = (3 × 3)

Step-by-step explanation:

If matrix P having dimensions (m × n) and matrix Q having dimensions (n × r) are multiplied,

Dimensions of the product matrix PQ will have the dimensions as (m × r).

That means product of the two matrices are defined when columns of first matrix P is equal to the rows of the second matrix Q.

Following this rule,

Dimensions of matrix A = (2 × 3)

[ Rows × Columns]

Dimensions of matrix B = (3 × 3)  [Rows of B = 3, columns of B = 3]

Dimensions of matrix C = (3 × 2) [Rows of C = 3, columns of C = 2]

Since columns of C and rows of A are equal.

Therefore, product of C and A is defined.

Product of the matrices C & A will have the dimensions as (3 × 3).

Answer:

y=9/2x+2

Step-by-step explanation:

Answer:

x=2/9y + -4/9

Step-by-step explanation:

Solve for x:

2y−9x=4

Add -2y to both sides:

−9x+2y+−2y=4+−2y

−9x=−2y+4

Divide both sides by -9:

−9x /−9 =−2y+4 /-9

Then your answer is:

x= 2 /9 y+ −4/ 9

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Hope I helped!

Good luck! :)

Answer:

Step-by-step explanation:

Answer:

the number is 3

Step-by-step explanation:

X= the number

7(x+9) = 84

7x+63 = 84

7x = 21

x=3

     Check:

    7(3+9) =84

      7 x12 = 84

       84=84

By using the rule of 3 we wills ee that the percentage of students who play the trumpet is 20%

We know that there are 150 students in the marching band, that will be our 100% in this case, and we know that 30 of them play the trumpet.

These 30 students represent a percentage X that we want to find, so we can write a little system of equations and use the rule of 3.

30  = X

150 = 100%

Taking the quotient between the two equations we get:

(30/150) = X/100%

Solving for X we get:

(30/150)*100% = X = 20%

So we can say that 20% of the students play the trumpet.

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The result suggests that A) The alternative hypothesis could really be true but because the sample size is small, the power is very low so the researchers are likely to run an experiment whose results lead them to make a type II error.

This result suggests that although the new treatment appears to double survival time, the difference is not statistically significant. This could be due to a type II error, which occurs when the null hypothesis is not rejected even though it is false. In this case, the alternative hypothesis (that the new treatment is effective) could be true, but the small sample size makes it difficult to detect a significant difference. This highlights the importance of statistical power, which is the probability of detecting an effect if it actually exists. In this case, the low statistical power means that the researchers are more likely to make a type II error and fail to detect the effectiveness of the new treatment.

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To find the component form of the velocity of the airplane, we need to break down the velocity vector into its horizontal (x) and vertical (y) components.

Given that the airplane is flying 25 degrees west of north at 800 km/h, we can determine the horizontal and vertical components using trigonometry.

The vertical component (Vy) represents the velocity in the north direction, and the horizontal component (Vx) represents the velocity in the east direction.

To calculate Vy, we use the sine function:

Vy = V * sin(θ)

Vy = 800 * sin(25°)

To calculate Vx, we use the cosine function:

Vx = V * cos(θ)

Vx = 800 * cos(25°)

Therefore, the component form of the velocity vector is:

Velocity = (Vx, Vy) = (800 * cos(25°), 800 * sin(25°))

Calculating the values:

Vx ≈ 722.6 km/h

Vy ≈ 342.0 km/h

Hence, the component form of the velocity vector is approximately (722.6 km/h, 342.0 km/h).

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Therefore, there are 16,807,680 different combinations of pizzas that can be made if each pizza can have any number of toppings, including no toppings, but no two pizzas can have the same set of toppings and the same topping cannot be used more than once.

There are 2^5 = 32 possible combinations of toppings for a single pizza, since each topping can either be included or not. However, since no two pizzas can have the same set of toppings, once a combination is used for one pizza, it cannot be used again.

Therefore, for the first pizza, there are 32 possible combinations of toppings. For the second pizza, there are only 31 possible combinations left, since the combination used for the first pizza cannot be used again. For the third pizza, there are 30 possible combinations left, and so on.

So the total number of different combinations of pizzas that can be made is:

32 x 31 x 30 x 29 x 28 = 16,807,680

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Answer:

There are 2 solutions to square root x = 9

They are 3, and -3

Step-by-step explanation:

The square root of x=9 has 2 solutions,

The square root means, for a given number, (in our case 9) what number times itself equals the given number,

Or, squaring (i.e multiplying with itself) what number would give the given number,

so, we have to find the solutions to \(\sqrt{9}\)

since we know that,

\((3)(3) = 9\\and,\\(-3)(-3) = 9\)

hence if we square either 3 or -3, we get 9

Hence the solutions are 3, and -3

Answer:

x²

Step-by-step explanation:

x³ - 1 ÷ x + 2

the first term of the quotient is x³ ÷ x = x²

Answer:

Yes

Hope that this helps!

Answer:

yes -2 is less then 6

Answer:

i am not sure try 56

Step-by-step explanation:

Hope this helps!:)

The conical surface is the correct answer as it allows for slopes ranging from 20:1 to 50:1. The FAR Part 77 imaginary surface that has slopes that may range from 20:1 to 50:1 is the conical surface.

The conical surface is a three-dimensional surface defined by a combination of horizontal and inclined planes. It extends upward and outward from the end of the primary surface and has varying slope requirements. The slope of the conical surface represents the ratio of the change in elevation to the horizontal distance. A slope of 20:1 indicates that for every 20 units of horizontal distance, there is a 1-unit increase in elevation.

Similarly, a slope of 50:1 means that for every 50 units of horizontal distance, there is a 1-unit increase in elevation. Therefore, the conical surface is the correct answer as it allows for slopes ranging from 20:1 to 50:1.

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An effective sampling method is not cast doubt on the usefulness of the sample

The effective sample is a calculation of the approximate sample size needed to obtain the same degree of accuracy as a simple random sample. It is denoted mathematically by the formula n/D, where n represents the sample size and D denotes the design effect. It is employed as a means of condensing the volume of data.

Effective sample size calculations are mostly used for qualitative analyses of the sample size. The sample size calculates the total number of measurements or observations made during an experiment or survey. The effective sample size—rather than the actual sample size—is utilized in this assessment since it is thought that a sample size of 30 is necessary for an analysis to be valid.

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Answer:

x = 46

Step-by-step explanation:

These 2 angles would add up to 180 degrees.

So 41 + (3x+1) = 180

Let's solve for x.

41 + 3x + 1 = 180

Combine like terms.

42 + 3x = 180

subtract 42 from both sides

3x = 180-42

3x = 138

divide both sides by 3

x = 46

Answer:

77 degrees and 90 degrees

The angle d is shown as 90 by the perfect right angle. The angle e has to equal 180 when added to f. So 180-103=77.

The current age of the artifact is 1600 years

Let's call the current age of the artifact "a" and the current age of the book "b".

The artifact is four times as old as the book, so we have:

a = 4b

In 200 years, the artifact will be a + 200 and the book will be b + 200.

From the problem, we know that in 200 years:

a + 200 = 3 (b + 200)

Expanding the right side:

a + 200 = 3b + 600

Substituting a = 4b:

4b + 200 = 3b + 600

Solving for b:

b = 400

So the current age of the book is 400 years old.

Recall that

a = 4b

So, we have

a = 400 * 4 = 1600

And the current age of the artifact is 4 times that, or 1600 years old.

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Answer:

1/9

Step-by-step explanation:

Answer:

Step-by-step explanation:

Please write this as y = (1/2)x^2 for greater clarity.  (1/2) is the coefficient of x^2 here.  

The applicable form for the equation of this quadratic is 4py = x^2.  

Your y = (1/2)x^2  becomes 2y = x^2.  Therefore, 4p = 2, or p = (1/2).

Thus, the focus is (0, 1/2) (just above the vertex, (0, 0) ), and the equation of the directrix is y = -1/2.

Answer:

A.

Step-by-step explanation:

The volume is LWH

L = 16

W = 9

H = 12

16 * 9 * 12 = 1728

Answer:

The answer should be x=0, hope this helps:)