Rewrite each expression in its equivalent form.

8pq - 3pq


ASAP PLZ HELPPP

The probability of drawing a face card followed by condition of drawing non face card is equal to 18% ( approximately).

In a standard deck of cards,

There are 12 face cards 4 jacks, 4 queens, and 4 kings

And 40 non-face cards 10 numbered cards each for the 4 suits.

The probability of drawing a face card on the first draw is

=  12/52

= 3/13.

Assuming a face card was drawn on the first draw,

There are now 51 cards remaining in the deck.

Of which 40 are non-face cards.

Probability of drawing a non-face card on the second draw is

= 40/51.

Probability of both events happening drawing a face card followed by a non-face card

= Multiply the probabilities of the individual events

= (3/13) x (40/51)

= 120/663

=  0.181approximately  

= 18% (rounded to the nearest whole number).

Therefore,  the probability of drawing a face card followed by drawing a non-face card in a standard deck of cards is approximately 18%.

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Answer:

-5<x<-3

Step-by-step explanation:

Hope this helps! ;-)

Answer:

D) 21,14

Step-by-step explanation:

Answer:

35 degrees.

Step-by-step explanation:

m < TSK = 180 - 22 - 123

= 180 - 145

= 35.

Answer:

Can you add a screenshot of the equations? It's hard to figure it out in this format and I don't want to give you the wrong answer.

Step-by-step explanation:

Answer:

9/20 or 45%

Step-by-step explanation:

If we make common denominators (for this example, we will make each denominator 20), this would make 7/10 = 14/20 and 1/4 = 5/20. From there, we subtract the numerators from each other (14-5) and leave the denominators alone. The difference comes out to 9/20 and there is no way to simplify it further, making it the final answer.

The next step would be to factor the left-hand side of the equation as (x - 3)^2 - 8 = 0, which can be solved using the square root method or by adding 8 to both sides and then taking the square root.

The first step when solving the equation x^2 - 6x - 40 = 0 by completing the square is to add the square of half the coefficient of x (which is (-6)/2 = -3) to both sides of the equation:

x^2 - 6x - 40 + (-3)^2 = (-3)^2

This simplifies to:

x^2 - 6x + 1 = 0

what is equation?

In mathematics, an equation is a statement that two expressions are equal. It contains one or more variables and may involve mathematical operations such as addition, subtraction, multiplication, division, exponents, and roots. The goal of solving an equation is to determine the value or values of the variables that make the equation true. Equations are used to model real-world situations and to solve problems in various fields, such as science, engineering, economics, and physics.

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The rectangular form of the provided complex number is Z = -20√3 - 20i option (C) is correct.

It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.

We have a complex numbers in the trigonometric form:

Z = 40[cos(7π/6) + i sin(7π/6)]

As we know,

7π/6 = 7(180)/6

= 1260/6

= 210 degrees

From the trigonometric table:

cos210 = -√3/2

sin210 = -1/2

Plug the above values in the complex number:

Z = 40[-√3/2 + i (-1/2)]

Z = (40/2)[-√3 - i]

Z = 20[-√3 - i]

Z = -20√3 - 20i

Thus, the rectangular form of the provided complex number is Z = -20√3 - 20i option (C) is correct.

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The expression that equals 24 is (4 x 2)(3).

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a complete sentence. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.

(The options are given twice, consider once)

Consider option C.

(4 x 2)(3)

=8 (3)

=8 x 3

=24

So, the expression that equals 24 is  (4 x 2)(3).

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Answer:

21

Step-by-step explanation:

Because h(3) times h(7) is equal to 21.

Hope it helps!

Therefore, the compass heading of the plane is 200 degrees.

To determine the compass heading, we need to consider the reference direction of north as 0 degrees on the compass.

Since the plane is traveling 20 degrees east of south, we can calculate the compass heading as follows:

Compass heading = 180 degrees (south) + 20 degrees (east)

= 200 degrees

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If the subset of R^2 consisting of vectors of the form [a b], where a + b = 1 is a subspace. The statement: This set is closed under scalar multiplications This set is a subspace .This set is closed under vector addition The set contains the zero vector is False.

A vector is a quantity or phenomenon that has two independent properties: magnitude and direction. The term also denotes the mathematical or geometrical representation of such a quantity.

Examples of vectors in nature are velocity, momentum, force, electromagnetic fields, and weight. A quantity or phenomenon that exhibits magnitude only, with no specific direction, is called a Scalar . Examples of scalars include speed, mass, electrical resistance, and hard-drive storage capacity.

Scalar multiplication is the multiplication of a vector by a scalar (where the product is a vector), and is to be distinguished from inner product of two vectors (where the product is a scalar).

For quaternion scalars and matrices:

λ = 2     A = \(\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right]\)

2A = 2\(\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right]\)

     = \(\left[\begin{array}{ccc}2a&2b\\2c&2d\\\end{array}\right]\)  = \(\left[\begin{array}{ccc}a.2&b.2\\c.2&d.2\\\end{array}\right]\)

     = \(\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right]\) × 2 = A2

In mathematics, and more specifically in linear algebra, a linear subspace, also known as a vector subspace is a vector space that is a subset of some larger vector space. A linear subspace is usually simply called a subspace when the context serves to distinguish it from other types of subspaces.

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Answer:

A = 6.4

Step-by-step explanation:

A - 5.36 = 1.04

    +5.36   +5.36

A = 6.4

The solution to the equations are;

a. x = 3

b. x = 2

c. x = 4

d. x = 1

It is important to note that index forms are mathematical forms used to represent numbers that are too large or too small in more convenient forms.

From the information given, we have that;

a. 7 + x² = 16

collect like terms, we have;

x² = 9

Find the square root

x = 3

b. 5 - x² = 1

collect the like terms

-x² = -4

x= √4

x = 2

c. 2 × 2³ = 2ˣ

1 + 3 = x

add the like terms, we get;

x = 4

d. 3⁴/3ˣ = 27

Convert the same base

3⁴⁻ˣ = 3³

4-x = 3

collect the like terms

x = 1

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Answer:

b, 5=3

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Because ∠5 = ∠2    {Vertically opposite angles}

               ∠3 = ∠6      {Vertically opposite angles}

∠5 ≠ ∠3

Answer:

the answer is

-17-1/17-2=-18/15=Slope

When both groups are shifted to a situation in which they earn an alternative reward after being trained to navigate a runway for food, the group that received three food pellets will continue to perform the task at a high level while the group that received one food pellet will experience difficulty.

It is known that rats have a natural preference for higher rewards. As a result, the group that received three pellets will be more motivated to complete the task since they have already tasted a higher reward. Therefore, they will continue to perform at a high level in the new environment.

On the other hand, the group that received only one pellet may find it challenging to adapt to the new situation since they are now receiving a lower reward. As a result, they may struggle to complete the task, and their performance may decrease.

In conclusion, the group that received three pellets will perform better than the group that received one pellet when both groups are shifted to a situation in which they earn an alternative reward. This is because the rats have a natural preference for higher rewards.

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Answer:

He had to have walked 5 dogs and done one survey

Step-by-step explanation:

The standard matrix of the linear transformation T is [1/2 0 ; √3/2 0].

The transformation T: R2 => R2 rotates points clockwise through π/3 radians and then projects each point onto the x1 axis. Here, we are supposed to find the standard matrix of the linear transformation T.To find the standard matrix of the linear transformation T, we need to find out the standard matrix of each step involved in the transformation.

Then the standard matrix of the transformation T can be found out by taking the product of the standard matrices of each step. Let A be the standard matrix of the linear transformation that rotates points clockwise through π/3 radians, and B be the standard matrix of the linear transformation that projects each point onto the x1 axis.

The standard matrix of the linear transformation that rotates points clockwise through π/3 radians can be found out by using the formula that is given below.cosθ  −sinθsinθcosθHere, θ = π/3 cos (π/3) = 1/2, sin (π/3) = √3/2The standard matrix of the linear transformation that rotates points clockwise through π/3 radians is A.

A = (1/2)  −√3/2√3/2 1/2= [1/2  -√3/2 ; √3/2 1/2]The standard matrix of the linear transformation that projects each point onto the x1 axis is B.B = [1 0 ; 0 0]The standard matrix of the linear transformation T can be found out by taking the product of the standard matrices A and B.T = AB= [1/2  -√3/2 ; √3/2 1/2][1 0 ; 0 0]= [1/2 0 ; √3/2 0]

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Answer:

a. 14

b. 10

c. 11

Step-by-step explanation:

You need to use the distance formula.

\(\sqrt{(x_{2}-x_{1})^{2} +(y_{2}-y_{1})^{2}}\)

Ex: (1,2) and (1,16)

You will need to lable each

1st Point: 1 will be \(x_{1}\) and 2 will be \(y_{1}\)

2nd Point: 1 will be \(x_{2}\) and 16 will be \(y_{2}\)

Then you will need to plug it in

\(\sqrt{(1-1)^{2} +(16-2)^{2}}\)

The retail price of the video game is $56 if the store pays $32.00 for each video game. The store’s percentage of markup is 75%.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

It is given that:

A store pays $32.00 for each video game. The store’s percentage of markup is 75%.

Let x be the retail price of the video game:

The value of x can be found as follows:

x = (75% of 32) + 32

x = (75/100)32 + 32

x = 24 + 32

x = $56

Thus, the retail price of the video game is $56 if the store pays $32.00 for each video game. The store’s percentage of markup is 75%.

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If one of the longer sides of the Isosceles triangle is 6.3 centimeters, the length of the base is 3.1 centimeters.

Let's solve the problem step by step:

1. Identify the given information:

  - The triangle is isosceles, meaning it has two equal sides.

  - The two equal sides, labeled "a," are longer than the base, labeled "b."

  - The perimeter of the triangle is 15.7 centimeters.

  - One of the longer sides is 6.3 centimeters.

2. Set up the equation based on the given information:

  Since the triangle is isosceles, the sum of the lengths of the two equal sides is twice the length of the base. Therefore, we can write the equation:

  2a + b = 15.7

3. Substitute the known value into the equation:

  One of the longer sides is given as 6.3 centimeters, so we can substitute it into the equation:

  2(6.3) + b = 15.7

4. Simplify and solve the equation:

  12.6 + b = 15.7

  Subtract 12.6 from both sides:

  b = 15.7 - 12.6

  b = 3.1

5. Interpret the result:

  The length of the base, labeled "b," is found to be 3.1 centimeters.

Therefore, if one of the longer sides of the isosceles triangle is 6.3 centimeters, the length of the base is 3.1 centimeters.

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The median of the following set of numbers  (18, 26, 29, 18, 44) is 26. The correct option to this question is option A

To find median of the following sequence (18, 26, 29, 18, 44) we will arrange them in ascending order

                            18 , 18 , 26 , 29 , 44   . . . . . .  . . . .(1)

Since the number of terms is odd we will apply the formula

                     Median  = \(\frac{(n+1)}{2} th\) term . . . . . . .(2)

       Here n = number of terms

As per question the n = 5

Therefore putting in equation 2 we get

                      Median = \(\frac{(5+1)}{2} th\) term

                      Median = \(\frac{6}{2} th \\\)  term

                      Median = 3 term

Hence the third term from the sequence ( shown in 1 ) we get the median that is 26

Hence the median of the following set of numbers (18, 26, 29, 18, 44) is 26 .

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The median is:

26

Explanation:

First, we will arrange the numbers from least to greatest.

18, 26, 29, 18, 44

Rearrange

18, 18, 26, 29, 44.

Now, the median is the number in the middle, which is 26.

Answer:

in six hours it would be $34.25

Step-by-step explanation:

The computation of the total cost for 6 hours is shown below:

For one hour it would be $8.50

For two hours

= $13.65 - $8.50

= $5.15

For three hours

= $18.80 - $13.65

= $5.15

For four hours

= $23.95 - $18.80

= $5.15

For five hours

= $23.95 + $5.15

= $29.10

For six hours

= $29.10 + $5.15

= $34.25

Hence, in six hours it would be $34.25

The equation to relate the flow of water from the 8-inch pipe (1600) to the flow of water from the 4-inch pipe (2400) is 2400.

To relate the flow of water from the 8-inch pipe to the flow of water from the 4-inch pipe, we can use the equation of continuity, which states that the product of the cross-sectional area of a pipe and the velocity of the fluid is constant.

Let's assume that the velocity of water flowing through the 8-inch pipe is V1 and the velocity of water flowing through the 4-inch pipe is V2. The cross-sectional area of the 8-inch pipe is A1 = π\((8/2)^2\) = 64π square inches, and the cross-sectional area of the 4-inch pipe is A2 = π\((4/2)^2\) = 4π square inches.

According to the equation of continuity, A1 * V1 = A2 * V2.

Substituting the given values, we have:

64π * V1 = 4π * V2

Simplifying, we get:

16V1 = V2

So, the equation to relate the flow of water from the 8-inch pipe (1600) to the flow of water from the 4-inch pipe (2400) is:

1600 * 16 = 2400

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Answer:

Does NOT support

Step-by-step explanation:

While the absolute value is greater, when it comes to negative, bigger numbers aren't always better. In fact, two out of three of these equations go AGAINST his claim. For example, -15(x)<14(y), and -0.9(x)<-0.8(y).

The equation of the ellipse with foci at ​(39​,0) and ​(-39​,0) and a constant difference of 30 is given as follows:

x²/39² + y²/9² = 1.

The equation of an ellipse of center (h,k) is given by the rule presented as follows:

(x - h)²/a² + (y - k)²/b² = 1.

In which:

The coordinates of the foci are given as follows:

​(39​,0) and ​(-39​,0).

The center is the midpoint of these two coordinates, hence:

The coefficient a is given as follows:

a = |39 - 0| = |0 - 39| = 0.

Considering the constant difference of 30, the constant b is given as follows:

b = a - 30 = 39 - 30 = 9.

Thus the equation of the ellipse is given as follows:

x²/39² + y²/9² = 1.

The problem asks for the equation of the ellipse with the given features.

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Answer:

1) D

2) A

3) C

I thinkkkkkk... tell me if it's correct;?)