Finding the factors of a number that are all prime. Finding all the factor of 324?

The probability of getting the number 10 is 0.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes

Given that, a die has six faces numbered 1 to 6.

A) Getting the number 6

Probability of getting the number 6 = 1/6

B) Getting the number 10

Probability of getting the number 10 = 0/6

C) Not getting the number 6

Probability of not getting the number 6 = 1-1/6

(6-1)/6 =5/6

D) Getting one of the numbers 1,2,3,4,5 or 6

Here, P(E) = 5/6 + 1/6

= 6/6

= 1

Therefore, the probability of getting the number 10 is 0.

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The term known as K-value is a constant. The proportionality constant, k, is represented in the direct variation equation y = kx. Similar to this, k is the variational constant in the equation for inverse variation, y = kx.

Which variant of K?

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Answer:

940

Step-by-step explanation:

No. of occupied rooms= (47/100) X 2000

                                     =940

Answer: To simplify the expression, you can first simplify the terms inside the parentheses.

6(3) = 18

(4)n-1(5)/(12)n = (4n-5)/(12n)

Then you can combine the like terms:

18/(4n-5)/(12n) = (18 * 12n)/(4n-5)

This is the simplified form of the original expression.

Step-by-step explanation:

Answers R

Step-by-step explanation:

If k = 0, there is just one distinct solution, sometimes called a double solution.

Depending on the sign of the discriminant, a quadratic equation will always have one of three real solutions: 0, one, or two. Only 2 actual solutions exist if the discriminant is positive.

If you get to the finish with 0=0, it signifies that the left and right sides of the equation are equal to each other regardless of the values of the variables involved. As a result, the solution set for this equation is made up entirely of real numbers for each variable.

There is just one distinct solution, occasionally referred to as a double solution, if k = 0.

The graph shifts upward if k is greater than 0. The graph is moved downward if k is less than 0.

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Following that, the Pythagorean theorem states that the separation between the two points is equal to the square root of the sum of the squares on the horizontal and vertical sides: distance=√(Δx)2+(Δy)2=√(x2−x1)2+(y2−y1) 2.

As per the a sphere, a straight line connects any two points at their closest distance. The earth resembles a spherical in form. The distance between any two places on Earth is calculated using the perpendicular distance or a straight line between the two spots because the radius of the sphere is so large that humans see it as a plane. In the case of in the earth, the arc length and the perpendicular distance are about identical.

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Explicit formula of the sequence: T(n) = 10240(1/4)ⁿ⁻¹.

To get the nth phrase in a series, we can use an explicit formula. Exact or definite is the simplest definition of explicit. The reason the formula is explicit is because it allows for the easy determination of the nth term when used appropriately.

Each sequence in which the ratio of any term to the one before it is constant is said to be geometric. A geometric sequence can be expressed explicitly using the formula a = a₁r⁻¹, where r is the common ratio.

here T₁ = 10240

Explicit formula of the sequence:  T(n+1) = T(n)(0.25)

If a sequence is in the form of ar, ar², ar³,.....,arⁿ terms

Sequence will be the geometric sequence and the explicit formula of the sequence will be: T(n) = arⁿ⁻¹

Here,  

a = First term

r = Common ratio

n = Number of terms

From the table attached,

There is common ratio between the successive term and previous term under the column (height after the bounce) is:

T₂/T₁ = 2560/10240 = 1/4

T₂/T₃ = 064/2560 = 1/4

Therefore, height of the ball after each bounce will represent a geometric sequence.

Explicit formula of a geometric sequence will be given by the expression:

T(n) = 10240(1/4)ⁿ⁻¹

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In the given triangle KLM , measure of k = 4.4 cm , l = 3.1cm , ∠M = 150° then length of m is equal to 7.3 cm ( nearest tenth centimeter ).

As given in the question,

In the triangle KLM,

Length of k = 4.4 cm

Length of l = 3.1cm

Measure of ∠M = 150°

Length of m is calculated using cosine rule

m² = k² + l² - 2kl cos M

⇒ m² = ( 4.4 )² + ( 3.1 )² - 2(4.4)(3.1)cos 150°

⇒ m² = 19.36 + 9.61 - 27.28 (-0.866)

⇒ m² = 52.59

⇒ m = 7.3cm ( nearest tenth in centimeter )

Therefore, in the given triangle KLM the length of m as per the given measurements is equal to 7.3cm ( nearest tenth centimeter ).

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Mikaela would not be able to run for the same distance as she would on her bicycle in one hour. This is because running is a much more strenuous activity than cycling, and humans generally can't maintain the same speed when running as they can when cycling. Therefore, it is not possible to determine how many kilometers Mikaela could run in one hour.

Answer:

  3 -√7

Step-by-step explanation:

You want to rationalize the denominator of 2/(3 +√7).

The denominator of such an expression is turned to an integer by multiplying numerator and denominator by the conjugate of the denominator.

  [tex]\dfrac{2}{3+\sqrt{7}}=\dfrac{2}{3+\sqrt{7}}\cdot\dfrac{3-\sqrt{7}}{3-\sqrt{7}}=\dfrac{2(3-\sqrt{7})}{3^2-7}=\boxed{3-\sqrt{7}}[/tex]

__

Additional comment

This process takes advantage of the factorization of the difference of squares:

  a² -b² = (a +b)(a -b)

If 'b' is a value that can be made a rational real number by squaring it, then this multiplication by the conjugate can achieve that end. The conjugate of a sum is the corresponding difference.

This process is also used with complex numbers, since i² = -1, a real number.

Answer:

Step-by-step explanation:

To calculate the interest rate on Selena's debt, we may utilize the formula for continuous compounding of interest. A = P * e is the formula (rt)

Where:

A = the total amount (including interest)

P denotes the original principal (loan amount)

r denotes the interest rate (as a decimal)

t = time (in years)

We know Selena's total (A) is 8,000 + 2,292.77 = 10,292.77.

8,000 is the initial primary (P).

6 years have passed.

The interest (I) is calculated as A-P = 2,292.77.

We may use the formula for continuous compounding of interest to compute the interest rate on Selena's debt. The formula (rt) is A = P * e.

A denotes the whole sum (including interest)

P stands for the original principle (loan amount)

r represents the interest rate (as a decimal)

t = time (in years)

Selena's total (A) is 8,000 plus 2,292.77 = 10,292.77.

The initial primary is 8,000. (P).

6 years have gone by.

A-P = 2,292.77 is the interest (I) calculation.

The equation for g(x) that matches the graph is g(x) =| -x - 3| +3

There are many tools we can use to find the information of the relation which was used to form the graph.

A graph contains data of which input maps to which output.

Analysis of this leads to the relations which were used to make it.

If we know that the function crosses x-axis at some point, then for some polynomial functions, we have those as roots of the polynomial.

We are given that function, g(x), is shown below. It is a shifted graph of y = |x|.

The vertex of the square root function f(x) = √x is located at (0, 0). In the given graph, it has moved to (2, 4). The vertical and horizontal scale factors remain unchanged.

The equation for g(x)  is g(x) =| -x - 3| +3

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Two line segments are the diagonals. The name of the line segments is KE and JD.

What is the right rectangular prism?

The right rectangular prism has two parallel end faces and four lateral faces, each of which is a rectangle; the faces are perpendicular to the bases of the prism. Parallelograms are the faces of a non-right rectangular prism (oblique prism). A cuboid is another name for a right rectangular prism.

The diagonal length of a right rectangular prism is calculated as √(l² + w² + h²) units. So, the formula for the length of a right rectangular prism's diagonal is √(l²+w²+h²), where l is the length, b is the breadth, and h is the height.

The diagonals are line segments that are in contact with opposite vertices.

The diagonals are KE, JD, IG and HF.

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Step-by-step explanation:

I take it then that all 3 lumbers (the central vertical one, and the 2 left and right slanted ones) have 1 ft in diameter.

the scenario creates 4 large right-angled triangles (left and right inner and outer ones).

and we need a few small ones on the ends of the slanted beams to get the distances there.

let's start on the right side :

inner triangle A

leg1 = 3 ft

leg2 = tbd

Hypotenuse = tbd

angle1 (opposite of leg1) = 30°

angle3 (opposite of Hypotenuse) = 90°

angle2 = 180 - 90 - 30 = 60°

remember the law of sine

a/sin(A) = b/sin(B) = c/sin(C)

with a,b,c being the sides opposite of the corresponding angles A, B, C.

3/sin(30) = Hypotenuse/sin(90) = Hypotenuse

3/0.5 = Hypotenuse

Hypotenuse = 6 ft

Hypotenuse² = leg1² + leg2²

6² = 3² + leg2²

36 = 9 + leg2²

25 = leg2²

leg2 = 5 ft

outer triangle A

the angles are the same as the inner triangle.

the sides increase by the side lengths of small right-angled triangle at the end of the beam.

at both ends of the inner Hypotenuse we draw right-angled heights to the outer edge of the beam.

these heights are 1 ft (remember, 1 ft diameter for each beam).

the bottom right little triangle has also 30°, 60°, 90° angles, the extension of leg2 of the inner triangle A is the Hypotenuse of that small triangle, one leg is the 1 ft diameter of the beam, the other leg is the lower extension of the beam of the outer triangle A.

1/sin(30) = extension of leg2iA = 1/0.5 = 2 ft

leg2oA = 5 + 2 = 7 ft

leg1oA² = 2² - 1² = 3

leg1oA = sqrt(3) = 1.732050808... ft

now for the upper extensions with the upper right little triangle. it had also the angles 30°, 60°, 90°.

1/sin(60) = extension of leg1iA = 1.154700538... ft

leg1oA = 3 + 1.154700538... = 4.154700538... ft

lenghtA² = leg1oA² + leg2oA² =

= 4.154700538...² + 7² =

= 17.26153656... + 49 =

= 66.26153656...

lengthA = 8.140118953... ft

inner triangle B

leg1 = 3 ft

leg2 = 3 ft

(45° angle in right-angled triangle means isoceles triangle)

Hypotenuse² = 3² + 3² = 18

Hypotenuse = sqrt(18) = 4.242640687... ft

since the small triangle at both ends of length B are also isoceles triangles with 1 ft legs

lengthB = Hypotenuse + 1 + 1 = 6.242640687... ft

the extension to the bottom inner leg is

Hypotenuse² = 1² + 1² = 2

Hypotenuse = sqrt(2) = 1.414213562... ft

Dim. X = 15 - 1 - 7 - 1 - 3 - 1.414213562... = 1.585786438... ft

length A ≈ 8.14 ft

length B ≈ 6.24 ft

Dim. X ≈ 1.59 ft

Answer:

the sun because u can't get energy from a bicycle yea kettle or a faucet.

The Pythagorean Theorem can be used to solve for the legs of the right triangle given the sum of their lengths. The equation x2 + y2 = 232 can be rearranged to x2 = 529 - y2 and y2 = 529 - x2.

Let x be the length of one leg and y be the length of the other leg.

x + y = 23 cm

Since this is a right triangle, the Pythagorean Theorem can be used to solve for x and y:

x2 + y2 = 232

x2 + y2 = 529

x2 = 529 - y2

x = √(529 - y2)

y = √(529 - x2)

Therefore, the lengths of the legs of the right triangle are x = √(529 - y2) and y = √(529 - x2).

The lengths of the legs of a right triangle can be determined if the sum of the lengths is known. The Pythagorean Theorem can be used to solve for the lengths. Let x be the length of one leg and y be the length of the other leg. Then x + y = 23 cm and x2 + y2 = 232. This can be rearranged to x2 = 529 - y2 and y2 = 529 - x2. Therefore, the lengths of the legs of the right triangle are x = √(529 - y2) and y = √(529 - x2).

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Plane X contains point C. Plane Y contains points A andB. there are three planes that pass through points A, B, and C.To find these planes, we need to draw a triangle connecting points A, B, and C.

The three planes that pass through A, B, and C are the planes that are parallel to the sides of the triangle and that contain points A, B, and C. These planes divide the space into three sections. Each plane will contain one of the points of the triangle. The three planes together form a three-dimensional space that is bounded by the three planes. This space contains all the points A, B, and C, and all the points in the triangle. Therefore, there are three planes that pass through points A, B, and C.

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Answer:

Step-by-step explanation:

wait a minute

On solving the provided question, we can say that x is an acute angle., cos(x) = 12 => x = cos^{-1}1/2=> x = 60

In Euclidean geometry, an angle is a shape made up of two rays, referred to as the angle's sides, that meet at a point in the middle known as the angle's vertex. Two rays can generate an angle that is in the plane where the rays are located. The meeting of two planes also creates an angle. They are referred to as dihedral angles. An angle is the shape created by two rays or lines that have a shared termination in plane geometry. The Latin word "angulus," which meaning "horn," is the source of the English term "angle." The vertex is the common terminal of the two rays, which are referred to as the sides of the angle.

here,

x is an acute angle.

cos(x) = 12

x = cos^{-1}1/2

x = 60

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The value of expression in the form of fraction is, 13/15.

A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.

We have to given that;

The expression is,

⇒ 7/10 + 1/6

Now, We can solve as;

⇒ 7/10 + 1/6

⇒ (7 × 6 + 1 × 10) /60

⇒ (42 + 10) / 60

⇒ 52/60

⇒ 26/30

⇒ 13/15

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Answer:

Direct Proportion

Step-by-step explanation:

It is linear, meaning that the ratio between the mass and gravity is proportional.

Answer:

[tex]y = \frac{3}{2} x + 2[/tex]

Step-by-step explanation:

from, y=mx+c

2y=3x+4

y=3x/2+4/2

y=3x/2+2

Answer: As x approaches positive infinity, y approaches positive infinity

As x approaches negative infinity, y approaches positive infinity.

Step-by-step explanation:

The key thing to keep in mind is the type of function. This is an absolute value graph that in general has a V shape. This one in specific is a V shape shifted to the right 7 unites from the origin, with positive and negative slopes for each piece-wise line.

4 weeks and 22 weeks after the beginning of the year does the mosquito population equal 200 thousand by solving the given equation.

What is a equation ?

An equation is a statement that shows equality between two expressions. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.

We need to solve the equation [tex]80 cos (\pi t/26) + 130 = 200[/tex]  for t.

First, we can simplify the equation by subtracting 130 from both sides:

[tex]80 cos (\pi t/26) = 70[/tex]

Then, divide both sides by 80:

[tex]cos (\pi t/26) = 7/8[/tex]

To solve for t, we need to take the inverse cosine ([tex]cos^{-1}[/tex]) of both sides.

[tex]cos^{-1} (cos (\pi t/26)) = cos^{-1} (7/8)[/tex]

[tex]\pi t/26 = 0.436[/tex]

[tex]t = 0.436*26/\pi[/tex]

t ≈ 4.19 weeks

So the mosquito population equals 200,000 approximately 4 weeks and 1 day after the beginning of the year.

We can also check the function to see if the mosquito population equals 200,000 more than once during the year.

[tex]A(t) = 80 cos (\pi t/26) + 130[/tex]

When we graph this function, we can see that it oscillates between 50,000 and 210,000.

There are two times during the year when the mosquito population equals 200,000:

Around week 4 (which we already calculated)

Around week 22 (which we can find by solving the equation again, but using [tex]\pi/2[/tex] instead of [tex]cos^{-1}(7/8)[/tex]

Therefore, the correct answers are 4 weeks and 22 weeks.

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When adding two rational numbers with different signs, you can determine the sign of the sum by comparing the magnitudes of the numbers.

•   If the absolute value of the first number is greater than the absolute value of the second number, the sum will have the same sign as the first number.

•   If the absolute value of the second number is greater than the absolute value of the first number, the sum will have the same sign as the second number.

To determine whether the sum will be positive or negative, you can also compare the signs of the numbers:

•   If one number is positive and the other is negative, the sum will be negative if the positive number is smaller than the negative number and positive if it is greater.

•   If the numbers have different signs, the sum will be positive if the numbers have opposite signs and negative if they have the same sign.

•   If the sum of the two rational numbers is zero, it means that the two numbers cancel each other out, which happens when the absolute value of the first number is equal to the absolute value of the second number with opposite signs.

It's important to note that if you are adding two rational numbers with different signs, you also have to keep in mind that the order of the numbers matters and you might get different results depending on the order.

I hope this helps :)

The zero slope means for every unit change in the horizontal distance there is no change of vertical distance.

We know that the slope of a line is nothing but the change in y coordinate with respect to the change in x coordinate.

The slope of the line describes the steepness of a line.

Also,  if a line makes an angle θ with the positive direction of the x-axis, then the slope of the line will be tangent of angle θ

m = tan θ

If the slope is zero, i.e., m = 0 then,

tan θ = 0

θ = arctan(0)

θ = (nπ)                where n = 0, 1, 2, . . .

This means, the line with zero slope must be coincident or parallel to the x-axis.

Sometimes zero slope term is used to describe a line that has a constant rise.

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Cesar's reasoning is incorrect because the degree of a polynomial is determined by the highest exponent of the variable in the polynomial, not the number of terms.

In the example given (2×2 = 3+1 = 4), the degree of the polynomial is not given. Therefore, it is not possible to determine the correct degree without more information about the polynomial in question.

The degree of a polynomial is a measure of the highest power of the variable in the polynomial. For example, the degree of the polynomial 3x2 + 2x - 4 is 2 (the highest power of x is 2), whereas the degree of the polynomial 4x3 + 3x2 - 2x + 1 is 3 (the highest power of x is 3).

Cesar's statement that the degree of the polynomial is 4 because 2×2 = 3+1 = 4 is not a valid way to determine the degree of a polynomial, as it is not related to the powers of the variables in the polynomial. To determine the correct degree of the polynomial, we need more information about the polynomial.

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