You flip a coin 12 times. What is the probability of getting only one tails in all 12 tries?

Answers are in standard notation

Answer:

<

Step-by-step explanation:

1/2 is bigger than 1/4

The equations for circles of a diameter of 12 units and centered on the y-axis are:

For a circle of radius R, centered at the point (a, b), the general equation is:

(x - a)^2 + (y - b)^2 = R^2

so if we want a circle centered on the y-axis, we need to have x = 0, then:

x^2 + (y - b)^2  = R^2

And we also know that the diamter is 12 units, then the radius is half of that:

R = 12/2 = 6 units

Then the circle equation is:

x^2 + (y - b)^2 = 6^2

x^2 + (y - b)^2 = 36

Of the given options the only ones that have this form is the first one:

x^2 + (y - 3)^2 = 36

And the last one:

x^2 + (y + 8)^2 = 36

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Answer:

Gotta be 95

Step-by-step explanation:

The rank of the matrix is 3, since there are three linearly independent rows.

The rank of a matrix is the maximum number of linearly independent rows or columns in the matrix. It is denoted by the symbol "rank(A)" for a matrix A.

To find the rank of the matrix:

[-2, -1, -3, -1] [ 1, 2, -3, -1] [ 1, 0, 1, 1] [ 0, 1, 1, -1]

We can perform row operations to reduce the matrix to row echelon form, which will help us determine the rank.

\(R_2 = R_2 + 2R_1 R_3 = R_3 + 2R_1 R_4 = R_4 + R_2\)

This gives us the following matrix:

[-2, -1, -3, -1] [ 0, 0, -9, -3] [ 0, -1, -1, 1] [ 0, 0, -4, -4]

We can see that the third row is not a linear combination of the first two rows, and the fourth row is not a linear combination of the first three rows. Therefore, the rank of the matrix is 3, since there are three linearly independent rows.

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Answer:

5

Step-by-step explanation:

The expression 5^2.5^0 is equal to 5^(2.5^0), which can be simplified as follows:

2.5^0 = 1 (because any number raised to the power of 0 is equal to 1)

So, 5^2.5^0 = 5^1 = 5

Therefore, the answer is 5.

When the matrices A and B commute, or when they fulfill AB=BA, this is a significant exception.

A matrix is a rectangular array or table of numbers, symbols, or formulae used to represent mathematical objects or qualities of such things. It is often arranged in rows and columns. For instance, a matrix contains two rows and three columns. a group of integers organized in a rectangular array in rows and columns. Matrix elements or entries refer to numbers. In several disciplines of engineering, physics, economics, statistics, and mathematics, matrices have a wide range of applications.

The eigenvalues and eigenvectors of the sum of two matrices are typically not the same as the sums of the eigenvalues and eigenvectors of the individual matrices. In actuality, there is no way to separate the eigenvalues of A and B from one another.

When a vector v is an eigenvector of both A and B, it is also an eigenvector of A+B, with an eigenvalue equal to the sum of its eigenvalues for A and B, respectively. There is, however, no reason to anticipate that two matrices will share an eigenvector in general. There is no method to create an eigenvector of A+B from two random eigenvectors of A and B alone.

When the matrices A and B commute, or when they fulfill AB=BA, this is a significant exception. In this situation, their invariant spaces coincide, and if both of them are diagonalizable, they are concurrently diagonalizable, which means that their eigenvectors do as well. As was already noted, in this specific instance, the eigenvectors of A+B are likewise the same.

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The Propositions are resulting

(a) ∀x∃y(x = y²) is False

(b) ∀x∃y(x² = y) is True.

(c) ∃x∀y(xy = 0) is True.

(d) ∀x∃y(x + y = 1) is True.

(a) ∀x∃y(x = y²)

This proposition states that for every x, there exists a y such that x is equal to y². To determine the truth value, we need to check if this statement holds true for every value of x.

If we take any positive value for x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 4, then y = 2 satisfies the equation since 4 = 2². Similarly, if x = 9, then y = 3 satisfies the equation since 9 = 3².

Therefore, the proposition (a) is false.

(b) ∀x∃y(x² = y)

For any given positive or negative value of x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 4, then y = 2 satisfies the equation since 4² = 2. Similarly, if x = -4, then y = -2 satisfies the equation since (-4)² = -2.

Therefore, the proposition (b) is true.

(c) ∃x∀y(xy = 0)

The equation xy = 0 can only be satisfied if x = 0, regardless of the value of y. Therefore, there exists an x (x = 0) that makes the equation true for every y.

Therefore, the proposition (c) is true.

(d) ∀x∃y(x + y = 1)

To determine the truth value, we need to check if this statement holds true for every value of x.

If we take any value of x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 2, then y = -1 satisfies the equation since 2 + (-1) = 1. Similarly, if x = 0, then y = 1 satisfies the equation since 0 + 1 = 1.

Therefore, the proposition (d) is true.

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Answer:

132 inches

Step-by-step explanation:

33 x 4 = 132 inches

This is the solution, Qxk:

Step 1: Let's review the information provided to us to answer the problem correctly:

Principal = $ 531

Interest rate = 6.1% (0.061) compounded continously

Term = 16 years

Step 2: Let's find the future value of this investment, as follows:

V = Pe^t*r

V

Answer:

They are not.

Step-by-step explanation:

Let's first calculate the vectors joining the first point to the second and the first to the third, they will be useful later.

\(\vec v_1_2 = \vec P_2 -\vec P_1 = <3; -7; -7>\\\vec v_1_3= \vec P_2 -\vec P_1 = <6; -14; -13>\)

At this point we have at least three options:

Write down the line between P1 and P2 in vector form, and then see if we can fit the third point in there.

Calculate the cross product between the two, if it's non-zero the three point are not in a line.

Try to determine the plane passing for the 3 points: if we find one they are not in a line.

Option 1:

The vector form of the lne between the firs two points is \(<6+3t;9-7t;7-7t>\). Let's check the coordinates of the third point:

\(x_3:\ 6+3t= 12 \rightarrow t=2\\y_3:\ 9-7t = -5 \rightarrow t =2\\7z_3:\ 7-7t=-6 \rightarrow t = 13/7\ne 2\)

So the three points are not in a line.

Option 2:

Let's calculate the cross product of the two vectors we found at the beginning.

\(\vec v_1_2 \times \vec v_1_3 = det \left[\begin{array}{ccc}\hat i&\hat j&\hat k\\3&-7&-7\\6&-14&-13\end{array}\right] = \hat i [-7(-13)-(-14)(-7)] - \hat j[3(-13)-6(-7)]+\hat k [3(-14)-6(-7)] = 7\hat i -3 \hat j + 0 \hat k \ne 0\)

Since the result is not the null vector, the three points are not in a line.

Option 3:

Let's write the plane (in the \(z= ax+by+c\) form that contain the three points. If the thre points are in a line, means that we can find only two of these parameters.

\(P1: 7= 6a+9b+c\\P2: 0= 9a+6b+c\\P3: -6= 12a-5b +c\)

Since you can determine a, b and c ( I ended up with \(a=-\frac {10}3; b=-\frac18; c= \frac{123}8\) but I probably messed something in there) the thre points are not in a line

Answer:

6×1+9×1/10+4×1/100+7×1/1000

Step-by-step explanation:

Answer:

below

Step-by-step explanation:

(7p^9)^-4     a negative exponent means move the number up or down in the fraction

=   1 / [ (7 p^9) ^4  ]

           = 1 / ( 7^4 p^36) =   1/(2401 p^36)   <===don't omit the parentheses!

Answer:

(5/2,9)

Step-by-step explanation:

Midpoint Formula: (((x1+x2)/2),((y1+22)/2))= (((-6+11)/2),((13+5)/2))= (5/2,9)

Answer:

58

Bonus :

Odd numbers are numbers that can not be divided by 2 evenly.

e.g. 1; 3; 5; 7; 9

Answer:

We conclude that after 6 drops how much liquid the scientist has added 0.84 mL.

Step-by-step explanation:

Given that the scientist adds drops of liquid to a test tube.

In order to determine the amount of liquid after 6 drops, all we need is to multiply 0.14 mL by 6.

i.e.

The amount of liquid in 6 drops = 0.14 × 6

                                                     = 0.84 mL

Therefore, we conclude that after 6 drops how much liquid the scientist has added 0.84 mL.

The given statement about inequality is true.

The inequality expressions are the mathematical equations related by each other by using the signs of greater than or less than. All the variables and numbers can be used to make the equation of inequality.

The statement is true ''Pick a point on one side of the solid or dashed line and enter its coordinates into the original inequality to determine which side of a linear inequality to colour in for its graph. On that side of the plane, you should shade if the coordinates satisfy the inequality''.

The statement defines how to write an inequality the meaning of inequality is that one part of the inequality will be shaded by some colour indicating that the region is falling under the area of inequality.

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Using translation concepts, function g(x) is given as follows:

g(x) = x² - 3.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

Researching this problem on the internet, g(x) is a shift down of 3 units of f(x) = x², hence:

g(x) = x² - 3.

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Answer:

76 words per minute.

Step-by-step explanation:

49 min = 3724 words

1 min = ?

3724/49 = 76

1 min = 76 words

Hope this helps!!

Answer:

Step-by-step explanation:

Letter B is the correct answer

Initial population is 200, tripled every hour

200 x 3 = 600

First hour 200

Second hour = 600 + 200 = 800

Third hour 800x3 = 2400 + 800 = 3200

and so on.

Answer:

B

Step-by-step explanation:

a function happens when there is exactly one output given for every input

Answer: Y=3/2x+6

Step-by-step explanation:

The slope-intercept form is

y=mx+b, where m is the slope and b is the y-intercept.

Rewrite in slope-intercept form.

Add 3x to both sides of the equation.

2y=12+3x

Divide each term in

2y=12+3x by 2

and simplify.

y=6+3x2

Write in

y=mx+b form.

y=3/2x+6

(ps i like your pfp xd)

Answer:

He needs more bananas. (\(\frac{10}{12}+\frac{9}{12}\))

Step-by-step explanation:

Find the least common multiple for both denominators.

For 6 and 4 in the denominators, their L.C.M is 12.

Cup of mashed bananas:

Multiply both the numerator and denominator by 2.

\(\frac{5}{6} = \frac{10}{12}\)

Cup of mashed strawberries:

Multiply both the numerator and denominator by 3.

\(\frac{3}{4} = \frac{9}{12}\)

Since the denominators are now the same, we can compare them in the same ratio.

\(\frac{10}{12} > \frac{9}{12}\)

Therefore he needs \(\frac{1}{12}\) more mashed bananas than mashed strawberries.

Both g(x) = 5 - x² and h(x) = \(5 - e^(6-^x^)\)have the same range as f(x) = -2√(x) - 3 + 8, which is (-∞, 5].

To determine which function has the same range as f(x) = -2√(x) - 3 + 8, we need to first find the range of f(x).

The square root function √(x) takes non-negative values as input and gives non-negative outputs, so the expression -2√(x) will always be non-positive. Therefore, the range of f(x) will be all real numbers less than or equal to -3 + 8, which is 5.

In other words, the range of f(x) is (-∞, 5].

So, we need to find a function whose range is also (-∞, 5]. One possible function is g(x) = 5 - x². We can see that when x is zero, g(x) is at its maximum value of 5, and as we increase or decrease x, g(x) will decrease, eventually approaching negative infinity.

Another possible function is h(x) = 5 - e^(-x). When x is negative infinity, e^(-x) is approaching positive infinity, so h(x) is approaching 0. As we increase x, e^(-x) is approaching zero, so h(x) is approaching 5.

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Answer:

x < -4

-4 > x

Step-by-step explanation:

⇒ The graph shows that the x-values has to be less than -4 (also not including -4 too)

-This can be written as x < -4

-It also can be written as -4 > x because -4 has to be greater than x (also not including -4 too)

Hope this helps again! :)

The elliptic geometry is a formal geometric system which satisfies the first four Euclidean postulates and considers solely spaces with a constant negative curvature.

The hyperbolic geometry is a formal geometric system which satisfies the first four Euclidean postulates and considers solely spaces with a constant positive curvature.

These formal systems were developed to demonstrate the possibility of the existence of geometries in which the fifth Euclidean postulate is not observed.

The key fact that makes elliptic and hyperbolic geometries different from Euclidean geometry is the consideration of curvature in spaces.

In this case, Euclidean geometry considers only spaces with no curvatures, whereas elliptic geometry considers spaces with a constant negative curvature and hyperbolic geometry makes with spaces with a constant positive curvature.

The elliptic geometry is a formal geometric system which satisfies the first four Euclidean postulates and considers solely spaces with a constant negative curvature.

The hyperbolic geometry is a formal geometric system which satisfies the first four Euclidean postulates and considers solely spaces with a constant positive curvature.

These formal systems were developed to demonstrate the possibility of the existence of geometries in which the fifth Euclidean postulate is not observed.

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Answer:

If you are using a calculator, simply enter 75÷100×780 which will give you 585 as the answer.

Answer:

45/100   IS 45%

Step-by-step explanation:

Answer:

38

Step-by-step explanation: