There’s are 12 levels in Kianah’s new video game. If he plays the same number of levels each day, what are all the possibilities for the number of days he could doesn’t playing the game without repeating a level

Answer:

B) 6(x-5) (x+5)

Step-by-step explanation:

Common factor.

6 ( ^2 − 25)

Use the sum-product pattern.

6 ( ^2+5−5−25).

Common factor from the two pairs.

6((+5)−5(+5)).

Rewrite in factored form.

6 ( − 5 ) ( + 5).

Answer:

m=3, n=5

Step-by-step explanation:

(3+√5)² = (3+√5)(3+√5) =

3² + 3√5 + 3√5 + √5·√5 = 9 + 6√5 + 5 = 14+6√5

Answer:

521.25

Step-by-step explanation:

the circle is 78.75 in area and the square is 600 so 600- 78.75 = 521.25

The solutions to the equation -30x² + 9x + 60 = 0 are x = 5/2 and x = -4/5.

To solve the equation, we can start by bringing all the terms to one side to have a quadratic equation equal to zero. Let's go step by step:

-5/3 x² + 3x + 11 = -9 + 25/3 x²

First, let's simplify the equation by multiplying each term by 3 to eliminate the fractions:

-5x² + 9x + 33 = -27 + 25x²

Next, let's combine like terms:

-5x² - 25x² + 9x + 33 = -27

-30x² + 9x + 33 = -27

Now, let's bring all the terms to one side to have a quadratic equation equal to zero:

-30x² + 9x + 33 + 27 = 0

-30x² + 9x + 60 = 0

Finally, we have the quadratic equation in standard form:

-30x² + 9x + 60 = 0

Dividing each term by 3, we get:

-10x² + 3x + 20 = 0

(-2x + 5)(5x + 4) = -10x² + 3x + 20

So, the factored form of the equation -30x² + 9x + 60 = 0 is:

(-2x + 5)(5x + 4) = 0

Now we can set each factor equal to zero and solve for x:

-2x + 5 = 0 --> x = 5/2

5x + 4 = 0 --> x = -4/5

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The ferret tent has six triangular faces and a regular hexagonal base.

The ferret tent shown is a frustum of a regular pyramid, and its faces have unique properties. A frustum is a solid with a flat base and a top portion that has been cut by a plane parallel to the base.

A frustum is the part of a solid that remains after the top portion has been cut by a plane parallel to the base. The term "frustum" is used to describe a cone or pyramid with its top portion removed by a plane parallel to the base.

The shape of the frustum is determined by the height of the plane that intersects the top portion of the solid and the height of the solid itself.

The shape of a frustum is determined by the size and shape of the base, the size and shape of the top surface, and the height of the frustum. The height of the frustum is the distance between the base and the top surface.

Describe the faces of the solid:

The ferret tent shown is a frustum of a regular pyramid. A pyramid is a polyhedron with a base that is a polygon and triangular faces that meet at a common vertex.

The ferret tent has a hexagonal base and six triangular faces. The base is a regular hexagon, meaning that all six sides are the same length, and all six angles are the same size.

The six triangular faces of the ferret tent are also congruent, which means they have the same shape and size. Each of the triangular faces has two sides that are congruent, and the base of each triangle is a side of the regular hexagon base.

In addition, the six triangular faces of the ferret tent have the same angle measures, which means they are similar. This makes the ferret tent a regular pyramid.

Thus, the ferret tent has six triangular faces and a regular hexagonal base. Its faces have unique properties.

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60 different three-digit numbers can be written using digits from the set 1, 2, 3, 4, and 5 without any repeating digits.

To find how many different three-digit numbers can be written using digits from the set 1, 2, 3, 4, and 5 without any repeating digits:

1st Method:

2nd Method:

Therefore, 60 different three-digit numbers can be written using digits from the set 1, 2, 3, 4, and 5 without any repeating digits.

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Answer:

centre = (- 6, - 1 ) , radius = 5

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

Given

x² + y² + 12x + 2y + 12= 0

Collect the x- terms and the y- terms together and subtract 12 from both sides

x² + 12x + y² + 2y = - 12

Using the method of completing the square

add ( half the coefficient of the x / y coefficients )² to both sides

x² + 2(6)x + 36 + y² + 2(1)y + 1 = - 12 + 36 + 1

(x + 6)² + (y + 1)² = 25 ← in standard form

with (h, k ) = - 6, - 1 ) as centre and r = \(\sqrt{25}\) = 5

Mike is 40 years old now.

Let Al's age be x years. According to the problem statement,

Al was 2 years old 8 years ago.

Therefore, Al's present age is:x + 8 years

Now, Mike is 4 times older than Al. That is, the age of Mike is 4(x + 8) years.

Mike is now 4 times older than Al, if Al was 2 years old 8 years ago, then Mike is 36 years old now.

In order to verify the solution, you can use a direct method of substitution.

If Al's present age is x + 8, then his age 8 years ago was x + 8 - 8 = x.

Since Al was 2 years old 8 years ago, we have:x = 2

Therefore, Al's present age is:x + 8 = 2 + 8 = 10 years

Now, Mike is 4 times older than Al.

Therefore, Mike's age is 4 × 10 = 40 years.

This is consistent with the original statement that "Mike is now 4 times older than Al if Al was 2 years old 8 years ago".Therefore, Mike is 40 years old now.

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The distance between points B and C on the graph is equal to: D. √34 units.

In Mathematics, Pythagorean's theorem is represented by the following mathematical expression:

c² = a² + b²

Where:

a, b, and c represent the side length of any right-angled triangle.

In order to determine the distance between points B and C in right-angled triangle ABC, we would have to apply Pythagorean's theorem.

BC² = AB² + AC²

BC² = 5² + 3²

BC² = 25 + 9

BC² = 34

BC = √34 units.

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Answer:

A

Step-by-step explanation:

if you take the dividend and multiply it by 4 you get A

Check the picture below.

Answer:

  i) 3.7 cm

  ii) 3.0 cm

Step-by-step explanation:

When you are given side lengths and angle measures, trig functions will generally be involved in solving the triangle. The mnemonic SOH CAH TOA is intended to remind you of the trig relations pertaining to a right triangle.

__

The sides adjacent to the angle and opposite the angle are given. The relevant relation is ...

  Tan = Opposite/Adjacent

  tan(63°) = k/(1.9 cm)

  k = (1.9 cm)tan(63°) ≈ 3.7 cm

The length k is about 3.7 cm.

__

Again, the tangent function can be used to solve this triangle.

  tan(42°) = (2.7 cm)/p

  p = (2.7 cm)/tan(42°) ≈ 3.0 cm

The length p is about 3.0 cm.

Answer:

5x-7-5+X=5-x-5+X

or,6x-12=0

or,6x=12

or,X=12/6

:.X=2

Answer:

$5,490

Step-by-step explanation:

i = prt

i = ($61,000)(.03)(3)

5,490

Answer:

$5490

Step-by-step explanation:

Using the given formula :

I = P × R × T

I = 61000 × 3/100 × 3

I = $5490

Options A and C are correct for the condition 5 x 4 = 20.

A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.

Factors can be found using either division or multiplication. Rules of divisibility can also be applied.

Given 5 x 4 = 20

factors of 20 are 2*2*5

so 5 is the factor of  20,

A is correct.

now multiples of 20 are 20, 40, 60.......

since all values are greater than 5,

so 5 is not a multiple of 20.

B is not correct.

now multiples of 4 are 4, 8, 12, 16, 20, 24 .......

so 20 is a multiple of 4,

C is correct.

Hence A and C are correct statements.

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We will substitute this value of sin²x in our expression which will give;6 tan²x(1 - sin²x)6 tan²x(1 - (1 - cos²x))6 tan²x cos²x.

We need to simplify the given expression which is given below;

6 tan2 x − 6 tan2 x sin2 x

In order to solve this expression, we will first write it in a factored form which will be;

6 tan²x(1 - sin²x)

We know that the identity for sin²x is;sin²x + cos²x = 1

Which can be rearranged to give;

sin²x = 1 - cos²x

Now we will substitute this value of sin²x in our expression which will give;6 tan²x(1 - sin²x)6 tan²x(1 - (1 - cos²x))6 tan²x cos²x.

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Producing rDNA involves isolating and cleaving DNA, inserting fragments into a vector, and transforming host cells. rDNA can be introduced via transformation, transfection, or viral vectors. Clinical applications include protein production, gene therapy, vaccines, and diagnostics.

Producing a recombinant DNA (rDNA) vector involves several general steps. Here are the three main steps involved in the process:

Isolation and Cleavage of DNA:

The first step is to isolate the desired DNA fragments from the source organism. This can be done using various techniques such as PCR (Polymerase Chain Reaction) or restriction enzyme digestion. Restriction enzymes are enzymes that cut DNA at specific recognition sites. By using the appropriate restriction enzymes, the desired DNA fragment and a vector DNA can be cut at specific sites. The vector is usually a plasmid, which is a small circular DNA molecule.

Insertion of DNA Fragments into the Vector:

Once the DNA fragments and vector have been cut, they are mixed together and joined through a process called ligation. DNA ligase is used to catalyze the formation of covalent bonds between the ends of the DNA fragments and the vector. This creates a recombinant DNA molecule containing the desired DNA fragment within the vector. The recombinant DNA molecule is then introduced into host cells for replication.

Transformation of Host Cells:

The recombinant DNA molecules need to be introduced into host cells to produce multiple copies of the recombinant DNA. This is typically done using a process called transformation. Host cells, such as bacteria or yeast, are treated in a way that makes them more receptive to taking up the recombinant DNA. Methods for transformation include heat shock, electroporation, or using chemical agents. Once the host cells have taken up the recombinant DNA, they can be grown in culture to produce large quantities of the desired DNA fragment.

Introduction of rDNA into Cells:

Recombinant DNA can be introduced into cells using various methods, depending on the type of cells being targeted. Some common techniques include:

Transformation: As mentioned earlier, host cells, such as bacteria or yeast, can be treated to make them receptive to taking up the recombinant DNA. This can be achieved by exposing the cells to heat shock, electroporation, or using chemical agents.

Transfection: This method is used for introducing rDNA into eukaryotic cells, including animal cells. It involves the use of techniques such as calcium phosphate precipitation, liposome-mediated transfection, or electroporation.

Viral Vectors: Certain viruses, such as retroviruses, adenoviruses, or lentiviruses, can be modified to carry the recombinant DNA. These viral vectors can then infect target cells and deliver the rDNA into the host genome.

Clinical Applications of rDNA:

Recombinant DNA technology has revolutionized biomedical research and has led to numerous clinical applications. Some important applications include:

Production of Therapeutic Proteins: rDNA technology allows for the production of large quantities of therapeutic proteins, such as insulin, growth factors, clotting factors, and monoclonal antibodies. These proteins can be used to treat various diseases, including diabetes, cancer, and genetic disorders.

Gene Therapy: rDNA vectors can be used to deliver functional copies of genes into target cells to correct genetic defects. This holds promise for the treatment of inherited diseases caused by single gene mutations, such as cystic fibrosis and muscular dystrophy.

Vaccine Development: Recombinant DNA technology has been instrumental in the development of vaccines. By expressing specific antigens from pathogens, recombinant vaccines can be created to stimulate an immune response without causing disease.

Diagnostic Tools: Recombinant DNA techniques are used to produce specific DNA or RNA probes for diagnostic purposes. These probes can detect the presence of specific genes or mutations associated with diseases, aiding in early detection and personalized medicine.

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Answer:

B: 4^1

Step-by-step explanation:

The function is decreasing in the interval (-∞,-3/2) and (3/2, ∞) and increasing in the interval (-3/2, 3/2).

What is a function?

A function is a mathematical relation between a set of inputs (often called independent variables, or the domain) and a set of outputs (often called dependent variables, or the range). A function assigns exactly one output for each input. It can be represented by an equation, such as y = f(x), where x is the input and y is the output.

To find the interval(s) in which the function is increasing and decreasing, we can first find the critical points of the function by setting the derivative equal to 0 and solving for x.

The derivative of y = |2x² + x - 6| is not a defined function, it is not differentiable, it is a piece-wise defined function, it has a break at x = -3/2

Hence, the function is decreasing in the interval (-∞,-3/2) and (3/2, ∞) and increasing in the interval (-3/2, 3/2).

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The area to the right of x in the normal distribution is 0.229, or 22.9% when expressed as a percentage. This means that the probability of observing a value greater than x is 0.229.

In a normal distribution, the total area under the curve represents the probability of all possible outcomes occurring, and it is equal to 1. When we refer to the area to the left or right of a specific value, we are essentially calculating the cumulative probability up to that value.

Given that the area to the left of a certain value, x, is 0.771, we want to determine the area to the right of x. This can be done by subtracting the area to the left of x from 1.

To explain this further, let's consider the standard normal distribution, which has a mean of 0 and a standard deviation of 1. The cumulative distribution function (CDF) of the standard normal distribution gives us the probability of observing a value less than or equal to a given value.

In this case, the area to the left of x represents the cumulative probability up to x. So, if the area to the left of x is 0.771, it means that the probability of observing a value less than or equal to x is 0.771.

Now, to find the area to the right of x, we can subtract the area to the left from 1. This is because the total area under the curve is equal to 1, so the remaining area to the right of x can be calculated by taking the complement of the area to the left.

Area to the right of x = 1 - Area to the left of x

Area to the right of x = 1 - 0.771

Area to the right of x = 0.229

Therefore, the area to the right of x in the normal distribution is 0.229, or 22.9% when expressed as a percentage. This means that the probability of observing a value greater than x is 0.229.

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Answer:

width = 20 in

length = 24 in

Step-by-step explanation:

A = 480

L = 4 + w

w

A = L x w

A = (4 + w)w

A = 4w + \(w^{2}\)

480 = 4w + \(w^{2}\)

\(w^{2}\) + 4w - 480 = 0

(w + 24)(w - 20) = 0

w = -24 or w = 20

length can't be negative, so w = 20

if w = 20,

L = 4 + w

L = 4 + 20

L = 24

Check:

A = L x w

A = 24 x 20

A = 480

Expressing the solution of the inequality in interval notation

To solve the inequality algebraically, we solve as follows

(x - 7)/2 < 29/7.

clear the fractions

multiply both sides by 2

2 * (x - 7)/2 < 2 * (29/7).

x - 7 < 58/7.

Add 7 to both sides of the inequality

x - 7 + 7 < 58/7 + 7.

x < 58/7 + 49/7.

x < 107/7.

A number line is used to show the solution and attached

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Answer:

(5,1)

Step-by-step explanation:

if macs house if it’s 1/2 of the distance from Nate house to the park then half the distance of 10,2 is 5,1

The required coordinate of the max location is (4, 3).

Given that,
Nate wants to visit his friend max before going to the park. Nate's house is located at (-2,4), while the park is located at (10,2).
To find the location of macs house if it’s 1/2 of the distance from Nate's house to the park.

The midpoint is that point the line whose distance from both the ends of the line is equal.

Here,
Max lies 1/2 the distance of Nate and Park,
Location of max is given by,
= 10 - 2 / 2 and 4 + 2 / 2
= 8 / 2 and 6 / 2
= 4 and 3
Location of max is (4, 3)

Thus, the required coordinate of the max location is (4, 3).

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Answer:

6 out of 12

Step-by-step explanation: there was 12 before but now there are 6 because probally somebody ate them

The functions y = 2 (1/5)^(x) - 5 and y = 2^x are compared as follows

                                 y = 2 (1/5)^x - 5                y = 2^x

Starting value:               2                                    1

base function:        decay function = 1/5         growth function = 2

Transformation:     translation: 5 units down  no transformation

A decay function is a mathematical function that models the decrease or diminution of a value over time and is used in many disciplines including physics, engineering, economics, and machine learning.

It is a sort of function that, as time goes on, approaches zero at a pace proportionate to its current value.

The base function for decay functions is an exponential function, is

0 < k < 1

The growth function, which has values greater than 1, is the reverse of the decay function.

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Answer: x=3

Step-by-step explanation: Hope this help :D

Answer:

x=3

Step-by-step explanation:

4(2x+3)=36

8x+12=36

8x=24

x=3

Answer:

Step-by-step explanation:

The table shows the rainfall for 12 months.

The median value takes account of the value in the middle after arranging in order from least to greatest. Hence we now have,

From the data set above, the middle values are 1.11 and 1.89 (since the data set is an even number) and that means the median is

The Median monthly rainfall is 1.50 inches