Find the value of B, Please.

\(\frac{-5x^3+2x+3}{x+2} = A+\frac{B}{x+2}\)

A. -13
B. 39
C. -21
D. -33

Answer:

$15,500

Step-by-step explanation:

It would help if you put the actual question in place

    10³ CDs = 1000 at $12 each    = $12000

+ 10² Players = 100 at $35 each = $  3500

Total                                                 $15500

103(12) + 102(35) = $4806

The angle of the water slide is 60 degrees.

The equation that models his work is 3 × 20 = 60 degrees.

He wants to measure the angle of a water slide at the lake.

He used a sheet of folded paper that formed 20 degrees to measure the angle of the the water slide at the lake.

He noticed three folded paper angle fits in the angle made by the slide and the ground.

Since each angle is equals to 20 degrees, and the three fits into the angle made by the slide and the ground, the angle of the water slide is as follows:

20 × 3 = 60 degrees

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Using the Pythagorean Theorem, it is found that the lot has an area of about 35 acres.

The Pythagorean Theorem relates the length of the legs \(l_1\) and \(l_2\) of a right triangle with the length of the hypotenuse h, according to the following equation:

\(h^2 = l_1^2 + l_2^2\)

Researching the problem on the internet, the lot has one leg of 800 feet and the hypotenuse is of 3900 feet, hence the other leg is found as follows:

\(800^2 + l^2 = 3900^2\)

\(l = \sqrt{3900^2 - 800^2}\)

l = 3817 feet.

The area of a right triangle is given by half the multiplication of it's legs. Hence, the area of the lot, in square feet, is given by:

A = 0.5 x 800 x 3817 = 1,526,800 square feet.

Each square feet is equivalent to 0.000029568 acres, hence the area in acres is given by:

Aa = 0.000029568 x 1,526,800 = 35 acres.

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The amount of work done is Option A) 12 N/m

Work done is simply defined as the product of the magnitude of displacement, (d) and the component of the force that in the direction of displacement.

It measures energy transfer that occurs when an object is moved to a distance by an external force which is applied in the direction of the displacement.

Work done on a body is equivalent  to the increase in the energy of the body, because it transfers energy to the body.

The formula for work done is;

W = fd

Where, 'f' is the applied force and d is the distance

Substitute the values

Work done = 6(2)

Work done = 12 N/m

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Probability of randomly selecting two members who currently hold positions of chairman and ranking member and reassigning them to their current positions from a committee of 14 members is (1 /182).

As given,

Total members in the committee=14

Number of members serve as chairman and ranking member=2

Total number of ways to assigned new position

=¹⁴P₂

=(14!) / (14-2)!

=(14 × 13 × 12!) / 12!

=14 ×13

=182

Each member is equally likely to serve in any of positions.

Each position there is only one way to reassign position.

Probability of randomly selecting two members = 1 /182

Therefore, probability of randomly selecting two members who currently hold positions of chairman and ranking member and reassigning them to their current positions from a committee of 14 members is (1 /182).

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Answer:

The correct answer is $1233

Step-by-step explanation:

You need to invest $260,045 each month to reach a savings goal of $550,000 at the end of 25 years.

It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.

We can calculate the compound interest using the below formula:

\(\rm A = P(1+\dfrac{r}{n})^{nt}\)

Where A = Final amount

          P = Principal amount

          r  = annual rate of interest

          n = how many times interest is compounded per year

          t = How long the money is deposited or borrowed (in years)

From the data given in the question:

A = $550,000

r = 3% = 0.03

t = 25 years

n = 12

Plug all the values in the formula:

\(\rm 550000 = P(1+\dfrac{0.03}{12})^{12\times25}\)

After solving:

P = $260,044.88 ≈ $260,045

Thus, you need to invest $260,045 each month to reach a savings goal of $550,000 at the end of 25 years.

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The revised Doubtful Debts Provision should be, $4,555.

Now, Using a net debtors value of $91,100 and a provision rate of 5%, use the calculation to get the adjusted Provision for Doubtful Debts (PDD):

Net Debts x Provision Rate equals Adjusted PDD.

The computation would then be:

= $91,100 x 0.05

= $4,555 is the adjusted PDD.

Because of the additional $550 in bad debt and the revised net debtors value of $91,100, the Provision for Doubtful Debts must be raised by ,

= $4,555 - $3,500

= $1,055

Hence, The revised Doubtful Debts Provision should be $4,555.

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The last expression finally simplifies to cot β + tan α using quotient identity in trigonometric identities.

We want to verify the trigonometric  identity;

cos (α - β)/(cos α sin β) = cot β + tan α

Now, according to trigonometric identities in mathematics, we know that;

cos (α - β) = (cos α cos β) + (sin α sin β)

Thus, plugging that back into our left hand side of the main question gives;

[(cos α cos β) + (sin α sin β)]/(cos α sin β)

Rewriting this expression by separating the denominator gives;

[(cos α cos β)/(cos α sin β)] + [(sin α sin β)]/(cos α sin β)

Using quotient identities, this can be simplified to;

cot β + tan α

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Answer:

Area of ΔQRS = 2.3 square inches

Step-by-step explanation:

From the given information,

<S + <Q + <R = \(180^{o}\)

51 + 44 + <R = \(180^{o}\)

95 + <R = \(180^{o}\)

<R = \(180^{o}\) - 95

    = \(85^{o}\)

<R = \(85^{o}\)

Applying the Sine rule, we have;

\(\frac{q}{SinQ}\) = \(\frac{r}{SinR}\) = \(\frac{s}{SinS}\)

Using \(\frac{r}{SinR}\) = \(\frac{s}{SinS}\)

\(\frac{r}{Sin 85}\) = \(\frac{2.3}{Sin51}\)

r = \(\frac{2.3*Sin85}{sin51}\)

  = 2.9483

r = 2.9 inches

Also, \(\frac{q}{SinQ}\) = \(\frac{s}{SinS}\)

\(\frac{q}{Sin44}\) = \(\frac{2.3}{Sin51}\)

q = \(\frac{2.3*Sin44}{Sin51}\)

  = 2.0559

q = 2.0 inches

From Herons formula,

Area of a triangle = \(\sqrt{s(s-q)(s-r)(s-s)}\)

s = \(\frac{2.3 + 2.0 + 2.9}{2}\)

  = 3.6

Area of ΔQRS = \(\sqrt{3.6(3.6-2.0(3.6-2.9)(3.6-2.3)}\)

                        = 2.2895

Area of ΔQRS = 2.3 square inches

Answer:

2.4

Step-by-step explanation:

Step-by-step explanation:

The floor of a round hut has a diameter of 4 yards. What is the floor's area?

Answer:

12.56637 or 4 pi hope this helps

If the nex day, the biologist retums to the lake and takes a sample of 7 fish. Of those fish, 2 of them have tags. The estimated number of fish in the lake is 35 fish.

Let x represent the estimated number of fish in the lake

Hence,

x /10 = 7/2

Cross multiply

2x = 10 × 7

2x = 70

Divide both side by 2x

x =70/2

x = 35 fish

Therefore 35 is the number of fish.

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By using trigonometric functions, the value of \(\sin \text{x}^\circ\) is \(\frac{\text{a}}{\text{b}}\).

Trigonometric functions are also known as Circular Functions can be simply defined as the functions of an angle of a triangle. It means that the relationship between the angles and sides of a triangle are given by these trig functions. The basic trigonometric functions are sine, cosine, tangent, cotangent, secant and cosecant.

Given

\(\sin \text{x}^\circ= \ ?\)

\(\tan \text{x}^\circ=\dfrac{\text{a}}{4}\)

\(\cos \text{x}^\circ=\dfrac{4}{\text{b}}\)

Formula to find \(\sin \text{x}^\circ\)

\(\sin \text{x}^\circ=\dfrac{\text{Opposite}}{\text{Hypotenuse}}\)

\(\rightarrow\sin \text{x}^\circ=\bold{\dfrac{a}{b}}\)

Therefore, by using trigonometric functions, the value of \(\sin \text{x}^\circ\) is \(\frac{\text{a}}{\text{b}}\).

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Based on the 3 x 3 grid given, the number of ways that three points can be chosen to form triangles is 28 ways.

Given that there are 9 points on the grod, a triangle could be formed using 3 grids, 4 grids, and 6 grids.

When these triangles are drawn - as shown in the attached picture - 28 triangles are formed.

In conclusion, there are 28 ways to form a triangle from the 3 x 3 grid.

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Answer:

he can walk directily to the fire pit

Step-by-step explanation:

Answer:

Its would be A -11/31

Step-by-step explanation:

To prove that there are only these five regular polyhedra, we can consider Euler's polyhedron formula, which states that for any convex polyhedron, the number of vertices (V), edges (E), and faces (F) satisfy the equation V - E + F = 2.

The five regular polyhedra, also known as the Platonic solids, are the only convex polyhedra where all faces are congruent regular polygons, and the same number of polygons meet at each vertex.

The five regular polyhedra are:

1. Tetrahedron: It has four triangular faces, and three triangles meet at each vertex.

2. Cube: It has six square faces, and three squares meet at each vertex.

3. Octahedron: It has eight triangular faces, and four triangles meet at each vertex.

4. Dodecahedron: It has twelve pentagonal faces, and three pentagons meet at each vertex.

5. Icosahedron: It has twenty triangular faces, and five triangles meet at each vertex.

To prove that there are only these five regular polyhedra, we can consider Euler's polyhedron formula, which states that:

"for any convex polyhedron, the number of vertices (V), edges (E), and faces (F) satisfy the equation V - E + F = 2".

For regular polyhedra, each face has the same number of sides (n) and each vertex is the meeting point of the same number of edges (k). Therefore, we can rewrite Euler's formula for regular polyhedra as:

V - E + F = 2  

=>  kV/2 - kE/2 + F = 2  

=>  k(V/2 - E/2) + F = 2

Since each face has n sides, the total number of edges can be calculated as E = (nF)/2, as each edge is shared by two faces. Substituting this into the equation:

k(V/2 - (nF)/2) + F = 2  

=>  (kV - knF + 2F)/2 = 2  

=>  kV - knF + 2F = 4

Now, we need to consider the conditions for a valid polyhedron:

1. The number of faces (F), edges (E), and vertices (V) must be positive integers.

2. The number of sides on each face (n) and the number of edges meeting at each vertex (k) must be positive integers.

Given these conditions, we can analyze the possibilities for different values of n and k. By exploring various combinations, it can be proven that the only valid solutions satisfying the conditions are:

(n, k) pairs:

(3, 3) - Tetrahedron

(4, 3) - Cube

(3, 4) - Octahedron

(5, 3) - Dodecahedron

(3, 5) - Icosahedron

Therefore, there exist only five regular polyhedra.

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Answer:

(-5,-5)

Step-by-step explanation:

The similar triangles for this problem are given as follows:

RST and VUT.

Then the measure VT is given as follows:

VT = 5.4 units.

Similar triangles are triangles that share these two features listed as follows:

Hence the similar triangles for this problem are given as follows:

RST and VUT.

The proportional relationship for the side lengths is given as follows:

6/14 = (x + 2)/(4x - 1).

Applying cross multiplication, the value of x is obtained as follows:

14(x + 2) = 6(4x - 1)

14x + 28 = 24x - 6

10x = 3.4

x = 3.4.

Then the length VT is given as follows:

VT = 3.4 + 2

VT = 5.4 units.

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Answer:

51

Step-by-step explanation:

Itsssssssssssss 51 ezyyy

Answer:

51 is correct Answer. Please mark me as brainlist answer.

If there are 4 boys and 4 girls , then the number of ways in which

(i) there is no restriction is 40320 ways  ,

(ii) not all girls sit together is 37440 ways  ,

(iii) no two girls sit together is 2880 ways  .

the number of boys in the class is =  4 boys ;

the number of girls in the class is = 4 girls ;

Part(i) ,

we have to find number of ways in which they can sit in a row where there is no restriction .

there are total of 8 persons ,

So ,the number of ways in which 8 persons can be arranged without any restrictions is = 8! ways.

= 40320 ways

Part(ii) ,

we have to find number of ways in which they can sit in a row where not all girls sit together.

the cases where all gets sit together is written as :

= B₁ , B₂ , B₃ , B₄ , G ⇒ 5! ways ;

= B: G₁ , G₂ , G₃ , G₄ ⇒ 4! ways ;

the number of ways all girls are together is = 5! × 4! ;

So , the number of ways not all girls are together is = 8! - 5!×4!  ;

= 37440 ways

Part(iii) ,

we have to find number of ways in which they can sit in a row where no two girls sit together.

this case can be denoted as : G , B₁ , G , B₂ , G , B₃ , G , B₄ .

So , the boys can be arranged in 4! ways ;

and there will be 5 places for 4 girls , which can be arranged in ⁵P₄ ways ;

total number of ways is = 5!×4! =  2880 ways .

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1. The x - intercepts of the parabola are

2. The meaning of the x-intercepts are the plane takes of at x = 2.5 s and lands at x = 7.5 s

3. The vertex of the parabola is at (5, 80).

A parabola is a curved shape

1. Given the parabola above, to find the x - intercepts, we proceed as follows.

The x-intercepts are the points at which the graph cuts the x-axis.

They are

2. The meaning of the x-intercepts in this problem are the points where the plane takes off and lands on the ground.

The plane takes of at x = 2.5 s and lands at x = 7.5 s

3. The vertex is the maximum point on the graph.

So, we see that the vertex is at x = 5 s and y = 80 ft

So, the vertex is at (5, 80).

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1. Bank 1 is the best option for opening a savings account for one year, as it offers the highest total amount after one year.

2. Bank 1 is the best option for opening a savings account for one year, as it offers the highest total amount after one year.

We will use the formula A = P(1 + r/n)^(nt).

Bank 1:

= 3675(1 + 0.0236/4)^(4*1)

= 3762.50058402

= $3762.50

Bank 2:

= 3675(1 + 0.0236/1)^(1*1)

= 3696.6825

= $3696.68

Bank 3:

= 3675(1 + 0.0236/2)^(2*1)

= 3718.49292675

= $3718.49

To calculate which bank is the best option to open a savings account for twelve years, we can use the same formula and plug in t = 12:

Bank 1:

= 3675(1 + 0.0236/4)^(4*12)

= 4874.02928821

= $4874.03

Bank 2:

= 3675(1 + 0.0236/1)^(1*12)

= 4862.06398635

= $4862.06.

Bank 3:

= 3675(1 + 0.0236/2)^(2*12)

= 4870.00654814

= $4870.00

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By using Euclidean geometry, the set of side lengths  2.5 cm, 1.8 cm, 4 cm can form a triangle.

The sum of the lengths of any two sides must be greater than the length of the third side.

a + b ≥ c

A triangle is a three-sided polygon with three straight sides. It is a basic geometric shape that is found in many areas of mathematics and geometry.

Using this rule, we can determine which of the given sets of side lengths can form a triangle:

(a) 3 cm, 4 cm, 7 cm: It is not possible to form a triangle with these side lengths, because the sum of the lengths of the first two sides (3 cm + 4 cm = 7 cm) is equal to the length of the third side.

(b) 2 cm, 3 cm, 7 cm: It is not possible to form a triangle with these side lengths, because the sum of the lengths of the first two sides (2 cm + 3 cm = 5 cm) is less than the length of the third side.

(c) 2.5 cm, 1.8 cm, 4 cm: It is possible to form a triangle with these side lengths, because the sum of the lengths of the first two sides (2.5 cm + 1.8 cm = 4.3 cm) is greater than the length of the third side.

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One option is to use the distance formula.

In this case, this is what Julie would be working with:

\(d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\\\\d = \sqrt{(x-w)^2+(y-z)^2}\\\\\)

If Julie knew the values of x, y, w, and z, then she could find a numeric result for the distance (d).

Probabilities are used to determine the chances of an event.

Let P represents the event that a student passes the course, and C represents the event that a student completes the assignment

(a) The probability a student passed the course given that they completed their homework?

From the table, we have:

\(\mathbf{n(P\ n\ C) = 25}\)

\(\mathbf{n(C) = 30}\)

So, the required probability is:

\(\mathbf{Pr = \frac{n(P\ n\ C)}{n(C)}}\)

This gives

\(\mathbf{Pr = \frac{25}{30}}\)

\(\mathbf{Pr = 0.8333}\)

Express as percentage

\(\mathbf{Pr = 83.33\%}\)

Hence, the probability a student passed the course given that they completed their homework is 83.33%

(b) The probability a student passed the course given that they didn't complete their homework

From the table, we have:

\(\mathbf{n(P\ n\ C'= 7}\)

\(\mathbf{n(C') = 25}\)

So, the required probability is:

\(\mathbf{Pr = \frac{n(P\ n\ C')}{n(C')}}\)

This gives

\(\mathbf{Pr = \frac{7}{25}}\)

\(\mathbf{Pr = 0.28}\)

Express as percentage

\(\mathbf{Pr = 28\%}\)

Hence, the probability a student passed the course given that they didn't complete their homework is 28%

(c) The probability a student completed their homework given that passed the course?

From the table, we have:

\(\mathbf{n(P\ n\ C) = 25}\)

\(\mathbf{n(P) = 32}\)

So, the required probability is:

\(\mathbf{Pr = \frac{n(P\ n\ C)}{n(P)}}\)

This gives

\(\mathbf{Pr = \frac{25}{32}}\)

\(\mathbf{Pr = 0.78125}\)

Express as percentage

\(\mathbf{Pr = 78.125\%}\)

Approximate

\(\mathbf{Pr = 78.13\%}\)

Hence, the probability a student completed their homework given that they passed the course is 78.13%

(d) The probability a student didn't complete their homework given that they didn't pass the course

From the table, we have:

\(\mathbf{n(P'\ n\ C'= 18}\)

\(\mathbf{n(P) = 23}\)

So, the required probability is:

\(\mathbf{Pr = \frac{n(P'\ n\ C')}{n(P')}}\)

This gives

\(\mathbf{Pr = \frac{18}{23}}\)

\(\mathbf{Pr = 0.7826}\)

Express as percentage

\(\mathbf{Pr = 78.26\%}\)

Hence, the probability a student didn't complete their homework given that they didn't pass the course is 78.26%

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The area of the square with a side length of 3.1 meters is 9.61 square meters.

To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.

Area of a square = side length × side length

Substituting the given side length into the formula:

Area = 3.1 m × 3.1 m

To perform the calculation:

Area = 9.61 m²

It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.

Remember, to find the area of any square, you simply need to multiply the length of one side by itself.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

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Answer:

10:35 is the ratio

Step-by-step explanation:

2 x 5 = 10

7 x 5 = 35

Let the president's salary be x

Let the vice president's salary be y

The first statement of total salaries can be represented thus:

The president making more than the vice-president can be represented thus:

So we will substitute the x value above into the initial expression to get what their salaries will be:

Answer:

i think it 32214

Step-by-step explanation:

59 x 42 = 2478 x 26 = 66428. And divided by 1/2 (I'm sorry if im wrong)

Answer:

1) soln,

or,2x+6=x

or,2x-x= -6

or,x= -6

•°•x= -6 Ans#