If 6 cards are drawn at random from a standard deck of 52 cards, what is the probability that exactly 2 of the cards are spades? A. 0. 038 B. 0. 200 C. 0. 315 D. 0. 465 E. 0. 747.

The correct formula that defines an arithmetic sequence is option d) tn = 5n + 14.

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms remains constant. In other words, each term can be obtained by adding a fixed value (the common difference) to the previous term.

In option a) tn = 5 + 14, the term does not depend on the value of n and does not exhibit a constant difference between terms. Therefore, it does not represent an arithmetic sequence.

Option b) tn = 5n² + 14 represents a quadratic sequence, where the difference between consecutive terms increases with each term. It does not represent an arithmetic sequence.

Option c) tn = 5n(n+14) represents a sequence with a varying difference, as it depends on the value of n. It does not represent an arithmetic sequence.

Option d) tn = 5n + 14 represents an arithmetic sequence, where each term is obtained by adding a constant value of 5 to the previous term. The common difference between consecutive terms is 5, making it the correct formula for an arithmetic sequence.

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The probability of event A given event B, denoted as P(A | B), is 0.750. The probability of event B given event A, denoted as P(B | A), is 0.900. A and B are not independent events because the conditional probabilities P(A | B) and P(B | A) are not equal to the marginal probabilities P(A) and P(B), respectively.

To find P(A | B), we use the formula:

P(A | B) = P(A ∩ B) / P(B)

In this case, P(A ∩ B) = 0.45 and P(B) = 0.60.

Plugging these values into the formula, we get

P(A | B) = 0.45 / 0.60 = 0.750.

To find P(B | A), we use the formula:

P(B | A) = P(A ∩ B) / P(A)

Here, P(A ∩ B) = 0.45 and P(A) = 0.50.

Substituting the values, we find

P(B | A) = 0.45 / 0.50 = 0.900.

A and B are not independent because the probabilities of A and B are affected by each other. If A and B were independent, then P(A | B) would be equal to P(A), and P(B | A) would be equal to P(B). However, in this case, both P(A | B) and P(B | A) differ from their respective marginal probabilities. Therefore, A and B are dependent events.

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Answer:

Yes it will form a triangle

Step-by-step explanation:

The sum of any two side lengths of the triangle must be greater than the third one.

18+12>10

18+10>12

10+12>18

Hope you have a good day :)

Answer:

  r = 0.073/12 ≈ 0.0060833...

Step-by-step explanation:

In the given amortization formula, the interest rate (r) is the rate for one payment period.

The given 7.3% interest rate is presumed to be a nominal annual interest rate. Since there are 12 months in a year, the corresponding monthly interest rate is ...

  7.3%/12 = 0.073/12 ≈ 0.00608333...(repeating)

The value of r that goes in this formula is 0.0608333...(repeating).

Answer:

0.61

Step-by-step explanation:

1. (1³ + 2³ + 3³)\(^{\frac{1}{2}\) , the expression is simplified as 6.

2. \(\left[ (625^{- \frac{1}{2} })^{- \frac{1}{4} } \right]^2\), the expression is simplified as 5.

3. \(\frac{9^{\frac{1}{2}}\ \times \ \ 27^{- \frac{1}{3}} }{3^{\frac{1}{2} }\ \times \ 3^{- \frac{2}{3}} } }\), the expression is simplified as  \(3^{\frac{1}{6} }\).

4. \(64^{- \frac{1}{3} }\left [ 64^{\frac{1}{3}} \ - \ 64^{\frac{2}{3} }\right ]\), the expression is simplified as -3.

The given expression is simplified as follows;

1. (1³ + 2³ + 3³)\(^{\frac{1}{2}\)

We simplify this expression by expanding the numbers in the bracket.

= (1 + 8 + 27)\(^{\frac{1}{2}\)

= (36)\(^{\frac{1}{2}\)

= √36

= 6

2. \(\left[ (625^{- \frac{1}{2} })^{- \frac{1}{4} } \right]^2\)

We will simplify the term in the bracket as follows;

\(\left[ (625^{- \frac{1}{2} })^{- \frac{1}{4} } \right]^2\\\\= \left[ (\frac{1}{625^ \frac{1}{2} }} )^{- \frac{1}{4} } \right]^2\\\\= \left[ (\frac{1}{(5^4)^ \frac{1}{2} }} )^{- \frac{1}{4} } \right]^2\\\\= \left[ (\frac{1}{5^2} )^{- \frac{1}{4} } \right]^2\\\\= \left[ (5^2 )^{ \frac{1}{4} } \right]^2\\\\= \left[ 5^{ \frac{1}{2} } \right]^2\\\\= 5^{\frac{1}{2} \times 2 }\\\\= 5\)

3. \(\frac{9^{\frac{1}{2}}\ \times \ \ 27^{- \frac{1}{3}} }{3^{\frac{1}{2} }\ \times \ 3^{- \frac{2}{3}} } }\)

This expression is simplified by applying rules of exponent as follows;

\(\frac{9^{\frac{1}{2}}\ \times \ \ 27^{- \frac{1}{3}} }{3^{\frac{1}{2} }\ \times \ 3^{- \frac{2}{3}} } }\\\\= \frac{3^2^{(\frac{1}{2}) }\ \times \ \ 3^{3}^{(- \frac{1}{3})} }{3^{\frac{1}{2} }\ \times \ 3^{- \frac{2}{3}} } }\\\\= \frac{3 \ \times \ 3^{-1} }{3^{\frac{1}{2} }\ \times \ 3^{- \frac{2}{3}} } } \\\\= \frac{3^{(1 - 1)}}{3^{(\frac{1}{2} - \frac{2}{3} )} } \\\\= \frac{3^0}{3^{-\frac{1}{6}} } \\\\= 3 ^{(0 + \frac{1}{6})}\\\\= 3^{\frac{1}{6} }\)

4. \(64^{- \frac{1}{3} }\left [ 64^{\frac{1}{3}} \ - \ 64^{\frac{2}{3} }\right ]\)

This expression is simplified by multiplying out the bracket as follows;

\(64^{- \frac{1}{3} }\left [ 64^{\frac{1}{3}} \ - \ 64^{\frac{2}{3} }\right ]\\\\= 64^{- \frac{1}{3} } (64^{\frac{1}{3}}) - 64^{- \frac{1}{3} } (64^{\frac{2}{3}})\\\\= 64^{(- \frac{1}{3} + \frac{1}{3} )} - 64^{(- \frac{1}{3} + \frac{2}{3} )}\\\\= 64^0 \ - \ 64^{ \frac{1}{3} }\\\\= 1 - 4^{(3)\times \frac{1}{3} }\\\\= 1 - 4^1\\\\= 1 - 4\\\\=-3\)

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Given:

\(\Delta ABC\sim \Delta QRS\)

To find:

The missing value of m.

Solution:

We have,

\(\Delta ABC\sim \Delta QRS\)

Corresponding parts of similar triangles are proportional.

\(\dfrac{AB}{QR}=\dfrac{AC}{QS}\)

Putting the given values, we get

\(\dfrac{m}{10}=\dfrac{2}{4}\)

\(\dfrac{m}{10}=\dfrac{1}{2}\)

Multiply both sides by 10.

\(\dfrac{m}{10}\times 10=\dfrac{1}{2}\times 10\)

\(m=5\)

Therefore, the value of m is 5.

Answer:

Explanation:

24 ÷ 6 = 4

24 · 4 = 96

[1] 6

· 4

[2] 24

· 4

[3] 96

· 4

[4] 384

· 4

[5] 1536

· 4

[6] 6144

· 4

[7] 24576

· 4

[8] 98304

· 4

The completed statement based on two-dimensional motion in the x-y plane can be presented as follows;

The two-dimensional motion in the x-y plane, the x part of the motion and the y part of the motion are independent, whether or not there is an acceleration in any direction. The correct option is therefore;

D) Whether or not there is an acceleration in any direction

Two-dimensional motion in the x-y plane can be analyzed by separating them into its horizontal (x) and vertical (y) components, and analyze each component using the one dimensional equations of motion.

The meaning of the motion on the x-y plane is that the x-direction motion of an object exclusive or excludes the effect of the motion of the object in the y-direction, vis a vis, the y-direction motion.

The horizontal and vertical components of the motion can be analyzes individually or by themselves, by making use of the equations of motion for a one-dimensional motion, whether or not there is an acceleration in any direction as the acceleration are also evaluated using one dimensional equations.

The possible options in the question from a similar question on the internet are;

A) When there is no acceleration in any direction

B) When there is no acceleration in one direction

C) Only when an acceleration is present in both directions

D) Whether or not there is an acceleration in either direction

E) Only when the acceleration is in the y-direction

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Answer:

8feet high

Step-by-step explanation:

To get the height of the pole, we will use the pythagoras theorem. Let H be the height

H²  = 10² -6²

H² = 100 - 36

H² = 64

H = √64

H = 8feet

Hence the pole is 8feet high

lets remember the formula for the area of a triangle

A= 1/2 * b* h

A=35.7 h=8.9 we replace what we know with the values

35.7= 1/2 *8.9*b

b= (35.7*2)/8.9=8.02

b=8.02

Answer:

See Below.

Step-by-step explanation:

Statements:                                                        Reasons:

\(1)\text{ }\angle AOD=180\)                                                  Straight Angle Theorem

\(2)\text{ } \angle AOB+\angle BOC+\angle COD=\angle AOD\)              Angle Addition    

\(3)\text{ } \angle AOB+\angle BOC+\angle COD=180\)                   Substitution

\(\displaystyle 4)\text{ } \angle AOB=\frac{1}{2}\angle BOC\)                                          Given

\(\displaystyle 5)\text{ } \angle BOC=\frac{2}{3}\angle COD\)                                          Given

\(\displaystyle 6)\text{ } \frac{1}{2}\angle BOC+\frac{2}{3}\angle COD+\angle COD=180\)              Substitution

\(\displaystyle 7)\text{ } \frac{1}{2}\Big(\frac{2}{3}\angle COD\Big)+\frac{2}{3}\angle COD+\angle COD=180\)       Substitution

\(\displaystyle 8)\text{ } \frac{1}{3}\angle COD+\frac{2}{3}\angle COD+\angle COD=180\)              Multiplication

\(\displaystyle 9)\text{ } 2\angle COD=180\)                                                 Addition

\(10)\text{ } \angle COD=90\)                                                   Division Property of Equality

\(\displaystyle 11)\text{ } \frac{1}{2}\angle AOD=90\)                                                Division Property of Equality

\(\displaystyle 12)\text{ } \angle COD=\frac{1}{2}\angle AOD\)                                        Substitution

Answer:

this is your answer. good luck.

Answer: acute

Step-by-step explanation:

Any angle less then 90 degrees is acute

Answer:Idek

Step-by-step explanation:

Answer:

120

Step-by-step explanation:

Find how many were there before the adoption event by dividing 84 by 0.7

84/0.7

= 120

So, there were 120 animals before the adoption event

If the columns of matrix B are linearly dependent, then the columns of AB are also linearly dependent.

Suppose the columns of matrix B are linearly dependent, which means there exist constants c₁, c₂, ..., cₙ (not all zero) such that c₁b₁ + c₂b₂ + ... + cₙbₙ = 0, where b₁, b₂, ..., bₙ are the columns of B.

Now, let's consider the product AB. Suppose A is an m × n matrix.

The jth column of AB is given by the product AB(:, j) = A(b₁j) + A(b₂j) + ... + A(bₙj), where b₁j, b₂j, ..., bₙj are the jth columns of B.

Substituting the linear dependence relation for the columns of B into the expression for AB(:, j), we get:

AB(:, j) = A(c₁b₁ + c₂b₂ + ... + cₙbₙ)

         = c₁A(b₁) + c₂A(b₂) + ... + cₙA(bₙ)

Since matrix multiplication distributes over column vectors, we have:

AB(:, j) = c₁A(b₁) + c₂A(b₂) + ... + cₙA(bₙ)

This shows that the jth column of AB can be expressed as a linear combination of the columns of A, multiplied by the corresponding coefficients c₁, c₂, ..., cₙ. Therefore, if the columns of B are linearly dependent, the columns of AB are also linearly dependent.

In conclusion, if the columns of matrix B are linearly dependent, then so are the columns of the product AB.

Complete Question:

Show that if the columns of B are linearly dependent, then so are the columns of AB.

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The phrase "number of values for which a certain condition holds" is referred to as multiplicity. The phrase, for instance, can be used to describe the magnitude of the totient valence function or the frequency with which a given polynomial equation has a root at a specific location.

Let z_0 be a root of a function f, and let n be the least positive integer n such that f^((n))(z_0)!=0. Then the power series of f about z_0 begins with the nth term,

f(z)=sum_(j=n)^infty1/(j!)(partial^jf)/(partialz^j)|_(z=z_0)(z-z_0)^j,

and f is said to have a root of multiplicity (or "order") n. If n=1, the root is called a simple root '

The multiplicity of a member of a multiset in mathematics is the number of times the member appears in the multiset. The multiplicity of a root, for instance, is how many times a given polynomial has a root at a particular point.

It's crucial to understand the concept of multiplicity in order to correctly count without mentioning exceptions (for example, double roots counted twice). Thus, "counted with multiplicity" is used.

This can be highlighted by counting the number of different elements, as in "the number of separate roots," if multiplicity is disregarded. However, multiplicity is always taken into account when a set (as opposed to a multiset) is established, therefore the word "different" is not necessary.

Hence ,Multiplicity means the quality or state of being multiple or various. and

the number of components in a system (such as a multiplet or a group of energy levels)

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Let z_0 be a root of a function f, and let n be the least positive integer n such that f^((n))(z_0)!=0. Then the power series of f about z_0 begins with the nth term,

f(z)=sum_(j=n)^infty1/(j!)(partial^jf)/(partialz^j)|_(z=z_0)(z-z_0)^j,

and f is said to have a root of multiplicity (or "order") n. If n=1, the root is called a simple root '

The multiplicity of a member of a multiset in mathematics is the number of times the member appears in the multiset. The multiplicity of a root, for instance, is how many times a given polynomial has a root at a particular point.

Answer:

  (a)  10x^2−x−21

Step-by-step explanation:

The area of a rectangle is given by the formula ...

  A = LW . . . . . where L is the length, and W is the width

__

The area of the given rectangle will be ...

  A = (2x -3)(5x +7)

This product is simplified using the distributive property to eliminate parentheses. Then like terms are combined.

  A = 2x(5x +7) -3(5x +7)

  = (2x)(5x) +(2x)(7) -3(5x) -3(7)

  = 10x^2 +14x -15x -21

  A = 10x^2 -x -21

The expression 10x^2 -x -21 represents the area of the rectangle in square inches.

Answer:

Step-by-step explanation:

Write in slope-intercept form,

y=mx + b. − mowing, week, 20, 450

Answer:

The original selling price is $520.632

Explanation:

Consider the initial selling price be $x

After marking down 10%,

Final Selling price  = Selling price(1-10%)

Selling price = x – 10% of x = x – 0.1x = 0.9x

After marking 30%

Final Selling price  = Selling price(1-10%)

Selling price = 0.9x – 0.3*0.9x = 0.9x – 0.27x = 0.63x

According to the question,

0.63x = 328

Therefore, the original selling price is $520.632

Hope It helps!!❤

Answer:

Present Day:

Bob:Rob:Difference

 3   :  4  :        1

 6   : 12  :       2

4 years ago:

Bob:Rob:Difference

    5 : 7 : 2

Step-by-step explanation:

Scale factor=1/3

one side of spuare=9 (being reduced)

=9÷3=3

perimeter =(3)4

Answer: 4/15

Step-by-step explanation:

Answer:

\(\frac{4}{15}\)

Step-by-step explanation:

Number sentence: \(30x^{2}\) = \(8x\)

You can start by applying algebra to the left side of the equation by dividing each side by x. This should be how it looks now: 30x = 8

Now divide each side by 30 to keep reducing it: \(x = \frac{8}{30}\)

Now that we have \(\frac{8}{30}\), we can reduce that by dividing the top and bottom by 2:

\(\frac{8}{30} = \frac{4}{15}\).

Therefore, the number is \(\frac{4}{15}\).

magnetic field at (i) is B = (μ₀/4π) * (I * (0, 0, dz) x (1, 2, 5)) / r³ (ii)B = (μ₀/4π) * (I * (0, 0, dz) x (2, 7/3, 10)) / r³ (iii)B = (μ₀/4π) * (I * (0, 0, dz) x (10, π/3, π/2)) / r³.

To find the magnetic field at different points in space due to a wire aligned with the z-axis, we can use the Biot-Savart Law.

Given that the wire is aligned with the z-axis and symmetrically placed at the origin, we can assume that the current is flowing in the positive z-direction.

(i) At point (1, 2, 5):

To find the magnetic field at this point, we can use the formula:

B = (μ₀/4π) * (I * dl x r) / r³

Since the wire is aligned with the z-axis, the current direction is also in the positive z-direction.

Therefore, dl (infinitesimal length element) will have components (0, 0, dz) and r (position vector) will be (1, 2, 5).

Substituting the values into the formula, we get:

B = (μ₀/4π) * (I * (0, 0, dz) x (1, 2, 5)) / r³

(ii) At point (2, 7/3, 10):

Similarly, using the same formula, we substitute the position vector r as (2, 7/3, 10):

B = (μ₀/4π) * (I * (0, 0, dz) x (2, 7/3, 10)) / r³

(iii) At point (10, π/3, π/2):

Again, using the same formula, we substitute the position vector r as (10, π/3, π/2):

B = (μ₀/4π) * (I * (0, 0, dz) x (10, π/3, π/2)) / r³

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Step-by-step explanation:

Add them all up and subtract from 360.

Answer: 71

I think this is right

hope this helps :)

The centroid of a triangle is the point where the three medians of the triangle intersect. In this case, the triangle has vertices at (0, 0), (5, 0), and (0, 7).

First, let's calculate the average x-coordinate:
¯x = (0 + 5 + 0) / 3 = 5/3 ≈ 1.67

Next, let's calculate the average y-coordinate:
¯y = (0 + 0 + 7) / 3 = 7/3 ≈ 2.33, the centroid of the triangle with vertices at (0, 0), (5, 0), and (0, 7) is approximately (1.67, 2.33).
In summary, the centroid of the triangle with verticesvertices at (0, 0), (5, 0), and (0, 7) is located at approximately (1.67, 2.33). This point represents the average position of the three vertices and is the intersection point of the medians of the triangle.

The centroid coordinates are found by taking the average of the x-coordinates and the average of the y-coordinates of the three vertices. In this case, we add up the x-coordinates (0 + 5 + 0 = 5) and divide by 3 to get an average of 5/3, which is approximately 1.67. Similarly, we add up the y-coordinates (0 + 0 + 7 = 7) and divide by 3 to get an average of 7/3, which is approximately 2.33. These values represent the x-coordinate (¯x) and the y-coordinate (¯y) of the centroid, respectively. Therefore, the centroid of the triangle is located at approximately (1.67, 2.33).

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Answer:

B) n = 12

Step-by-step explanation:

To find the unknown variable of an equation, you have to follow these steps.

n x 25 = 5 x 60

n x 25 = 300

Now that the variables on one side of the equation have been simplified, you can solve for n.

We know that n times 25 is equal to 300.

To find the value of n you can divide 300 by 25.

300/25 = 12

n = 12

Now, use substitution to check the answer:

n x 25 = 5 x 60

n x 25 = 300

12 x 25 = 300

300 = 300

So, n = 12.

The unknown number is 12. Answer: B. 12.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

We can solve for the unknown number, denoted by n, by dividing both sides of the equation by 25:

n x 25 = 5 x 60

n = (5 x 60) / 25

n = 12

Therefore, the unknown number is 12. Answer: B. 12.

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Answer:

b

Step-by-step explanation:

Answer: 3:2

Step-by-step explanation:

AB / BC = AB:BC

therefore,  6:4  

6:4 simplified -> 3:2

Alessia spent $5,408 on entertainment in 2021.

To determine how much Alessia spent on entertainment in 2021, we need to work backward from the given information about her salary in 2022.

Let's assume Alessia's salary in 2021 was the same as in 2022, which is $26,000 after tax.

Since Alessia spends 35% of her after-tax salary on rent, we can calculate her rent expenditure:

Rent = 35% × $26,000

= $9,100

The remaining amount is split between food, petrol, and entertainment in the ratio 6:11:8.

To determine the ratio's total parts, we sum the individual parts:

Total parts = 6 + 11 + 8 = 25

Next, we calculate the value of one part of the ratio:

One part = ($26,000 - $9,100) / 25

= $16,900 / 25

= $676

Now, we can calculate how much Alessia spent on entertainment in 2021, which is 8 parts of the ratio:

Entertainment expenditure = 8 × $676

= $5,408

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21

Step-by-step explanation:

4×5=20

Means greater than 20

5×5=25 and less than 25

So you can check it by dividing all the 4 numbers 21,22,23,and 24 with 5 the correct answer will be which has 1 as reminder.

Answer:

38

Step-by-step explanation:

:) hope this helps