How to solve this equation? Combinatorics

Answer: X= 5

Step-by-step explanation:

The equilibrium point for James T-shirt business is (P, Q) = (7, 24).

To find the equilibrium point (P, Q) for James T-shirt business

we need to set the demand function equal to the supply function and solve for the values of P and Q.

Demand function: P = -Q + 31

Supply function: P = Q - 17

Setting them equal:

-Q + 31 = Q - 17

Adding Q to both sides and subtracting 31 from both sides:

2Q = 48

Dividing both sides by 2:

Q = 24

Now, we can substitute this value of Q into either the demand or supply function to find the corresponding value of P.

P = Q - 17

P = 24 - 17

P = 7

Therefore, the equilibrium point for James T-shirt business is (P, Q) = (7, 24).

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Answer: 11 1/2 laps

Step-by-step explanation:

18-7=11

1/4-3/4=1/2

Answer:

3x^2 and 9x^2, 3x and 4x

Step-by-step explanation:

Answer:

800,000=8,00,000 in Indian system.

Eight Hundred Thousands(800,000)=Eight Lakh(8,00,000)

in Indian system.

Answer:

C is the answer

Step-by-step explanation:

Because he have most tresures.

Answer: deep diving dan

Step-by-step explanation: he dived 26 times and found 104 treasure boxes

The area of the shaded region is,

(3) 100.28 sq. unit

(4) 72 sq.m

(5) 49.09  sq.m

What is the area?

The area of an object is the amount of room it occupies in two dimensions. It is the calculation of how many unit squares entirely encircle the area of a closed figure.

The accepted measure of area is the square unit, which is frequently expressed as square inches, square feet, etc. Most shapes and objects have edges and angles.

(3)

To calculate the area of the semi-circle having a radius of 3 cm,

\(A_1=\frac{1}{2} \pi r^2\\A_1=\frac{1}{2} \pi(3)^2\\A_1=14.14 \ \ sq. \ cm\)

To calculate the area of the rectangle having a width of 12 cm and a height of 6 cm,

\(A_2=l*w\\A_2=12*6\\A_2=72 \ sq.cm\)

To calculate the area of the semi-circle having a radius of 3 cm,

\(A_3=\frac{1}{2} \pi (3)^2\\A_3=14.14\)

The shaded region's size was calculated using

\(A=A_1+A_2+A_3\\A=14.14+72+14.14\\A=100.28 \ \ sq.cm\)

(4)

To calculate the area of the rectangle having a width of 13 m and a height of 8 m,

\(A_1=l*w\\A_1=13*8\\A_1=104 \ sq.m\)

To calculate the area of an unshaded triangle,

\(A_2=\frac{1}{2} *b*h\\A_2=\frac{1}{2} *8*8\\\\A_2=32 \ sq.m\)

The shaded region's size is thus,

\(A=A_1-A_2\\A=104-32\\A=72 \ sq.m\)

(5)

The shaded region's size was calculated using

\(A=Area \ of \ circle-Area \ of \ square\\A=\pi (6)^2-(8)^2\\A=36\pi -64\\A=49.09 \ sq.m\)

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Answer:

Option (1)

Step-by-step explanation:

Since the length of arc YZ = 12 units

m∠YXZ = one third of the full circle = \(\frac{360}{3}\) = 120°

From the formula of arc length,

Length of arc = \(\frac{\theta}{360}(2\pi r)\)

Where θ = Central angle subtended by the arc

r = radius of the circle

By substituting these values in the formula,

12 = \(\frac{120}{360}(2\pi r)\)

12 = \(\frac{2}{3}\pi r\)

\(18=\pi r\)

r = \(\frac{18}{\pi }\)

r = 5.73

r ≈ 6 units

Therefore, Option (1) will be the answer.

If the archaeologist found a fossil whose length is 489.44 inches, using the conversion table, the length in feet, to the nearest tenth, is 40.8 feet.

The conversion table refers to the tabulated standard units of measurement, showing temperature, length, area, volume, weight, and metric conversions

For instance, the conversion table shows that 12 inches equal 1 foot.

The length of the fossil = 489.44 inches

12 inches = 1 foot

489.44 inches = 40.8 feet (489.44 ÷ 12)

Thus, using the conversion table, which relies on multiplication or division operations using the conversion factors, the length in feet of the fossil is 40.8 feet.

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Answer:

a)

Step-by-step explanation:

a) The probability of drawing a green ball on any given draw is 30/50 (since there are 30 green balls out of a total of 50 balls). Since the ball is replace....

The measure of angle DCE in this problem is given as follows:

m < DCE = 22.5º.

The triangles in this problem are right triangles, meaning that the trigonometric ratios are used to find the measures.

The three trigonometric ratios are given as follows:

The segment DB is adjacent to angle of 38º, while the hypotenuse is of 12.2 cm, hence the length of segment DB is calculated as follows:

cos(38º) = DB/12.2

DB = 12.2 x cosine of 38 degrees

DB = 9.6 cm.

BE:ED = 3:1, means that segment DE is one-fourth of segment DB, and thus it's length is given as follows:

DE = 1/4 x 9.6

DE = 2.4 cm.

Then for the angle DCE, we have that the opposite side is of 2.4 cm while the adjacent side is of 5.8 cm, hence the tangent is used to find it's measure, as follows:

tan(x) = 2.4/5.8

x = arctan(2.4/5.8)

x = 22.5º

m < DCE = 22.5º.

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Answer:

x = 22.5°

Step-by-step explanation:

Answer:

Length of third side = 9

Step-by-step explanation:

Because this is a right triangle, we can find the length of the third side using the Pythagorean theorem, which uses the equation a^2 + b^2 = c^2, where

Thus, we can plug in 5 for a and √106 for c to find b, the length of the third side:

Step 1:  Plug in 5 for a and √106 for for c.  Then simplify:

5^2 + b^2 = (√106)^2

25 + b^2 = 106

Step 2:  Subtract 25 from both sides:

(25 + b^2 = 106) - 25

b^2 = 81

Step 3:  Take the square root of both sides to find b, the length of the third side:

√(b^2) = √81

b = ± 9

However, we can't have a negative side length so the third side is 9 units.

Answer:

Radius = 25.5 units

Diameter = 51 units

Step-by-step explanation:

r = radius of circle

d = Diameter of circle

  = \(2r\)

Circumference of circle = \(2\pi r\)

Substitute the provided value of the circumference:

                               \(51\pi = 2\pi r\)

r is to be isolated and made the subject of the formula:

                                 \(r = \frac{51\pi}{2\pi}\)

\(\pi\) in the numerator and denominator cancel each other outcompletely:

                                 \(r = \frac{51}{2}\)

                          ∴r = radius of circle = 25.5 units

This also means that:

\(d = 2r\)

\(d = 2(25.5)\)

∴d = Diameter of the circle = 51 units

The zeros with each multiplicity are given as follows:

The factor theorem is used to define the functions, which states that the function is defined as a product of it's linear factors, if x = a is a root, then x - a is a linear factor of the function.

Considering the linear factors of the function in this problem, the zeros are given as follows:

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Answer:

e-5=2f

take '-5' to the other side where '2f' is

e=2f+5

Answer:

1.833, 3.3052, 3.35, 3.5

Step-by-step explanation:

Hope this helps! :)

Answer:

I'm going to help you figure this out because I am actually on the same assignment. If you do not understand what it is asking, it is not asking you to break down the function notation, it is simply asking you to substitute (X) with 2,3,4,5,and 6 and then to solve it on each line

The domain of the question is expressed as; 0 ≤ x ≤ 4

The range of the question is expressed as; 100 ≤ f(x) ≤ 207.36

The domain of a graph is defined as the set of all possible input values that makes the function possible while the range is defined as the set of all possible output values that can result from the possible input values.

Now, we are told that the insect population increases by 20% each month from May 1 to September 1.

The function that represents the insect population after x months is;

f(x) = 100(1.2)ˣ

Thus, the domain is from x = 0 to 4 months inclusive. 0 ≤ x ≤ 4

f(0) = 100(1.2)⁰

f(0) = 100

f(4) = 100(1.2)⁴

f(4) = 207.36

100 ≤ f(x) ≤ 207.36

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Answer:

(3m - 2) + (2m + 7) + (5m - 3)

Step-by-step explanation:

Perimeter is found by combining all side measurements together to find the total measurement. In this case, combine the sides:

(3m - 2) + (2m + 7) + (5m - 3) is your answer.

If you need a simplified expression, simply combine all the like terms together. Like terms are terms with the same as well as same amount of variables:

(3m + 2m + 5m) + (7 - 2 - 3)

(10m) + (2)

10m + 2 is your answer.

~

The rule of (x, y) → (-x, y), which is reflection over y-axis.

Given that, ΔABC maps to triangle ΔA'B'C'.

When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).

The coordinate points of ΔABC are A(-4, 3), B(-3, -3) and C(1, 2) and the coordinate points of ΔA'B'C' are A'(4, 3), B'(3, -3) and C'(-1, 2).

Here, A(-4, 3) → A'(4, 3), x-coordinate is negated and y-coordinate remains same.

Similarly, B(-3, -3) → B'(3, -3) and C(1, 2) → C'(-1, 2) follows the same pattern.

From this, it is clear that the coordinates of triangle ABC is reflected on y-axis.

Therefore, the rule of (x, y) → (-x, y), which is reflection over y-axis.

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Answer:

15,000 feet cubed

Step-by-step explanation:

15 x 15 = 225

10 x 15 = 150

150 / 2 = 75

225 = 75 = 300

300 x 50 = 15,000 feet cubed

Answer:

15000 ft^3

Step-by-step explanation:

You said you just wanted the answer so I won't explain in depth but let me know if you want an in depth explanation.

15*15=225

225*50= 11250

10*15=150

150/2=75

75*50=3750

11250+3750= 15000

Answer: 15000ft^3

Answer:

Change the mixed numbers into an improper fraction:

\(2\frac16 \div 2\frac12=\dfrac{2 \times 6+1}{6}\div \dfrac{2 \times 2+1}{2}=\dfrac{13}{6}\div \dfrac{5}{2}\)

Dividing two fractions is the same as multiplying the first fraction by the reciprocal of the second fraction. (Reciprocal is when you swap the numerator and denominator).  Therefore,

\(\dfrac{13}{6}\div \dfrac{5}{2}=\dfrac{13}{6}\times\dfrac{2}{5}\)

Now we simply multiply the numerators and the denominators:

\(\dfrac{13}{6}\times\dfrac{2}{5}=\dfrac{13 \times 2}{6\times 5}=\dfrac{26}{30}\)

We can now reduce the fraction to its simplest form by dividing the numerator and denominator by 2:

\(\dfrac{26}{30}=\dfrac{26\div 2}{30 \div 2}=\dfrac{13}{15}\)

Answer:

\(\frac{1}{3}\)

Step-by-step explanation:

I'll assume it is \(\frac{21}{6}\)÷\(\frac{21}{2}\)

Not so sure if it is that or in mixed form

The division sign will become multiplication sign when two becomes the numerator and 21 becomes the denominator

\(\frac{21}{6}\)×\(\frac{2}{21}\)

21 will cancel out leaving \(\frac{2}{6}\)

=\(\frac{1}{3}\)

Step-by-step explanation:

the answer is in the above image

The number of kilograms of the weight of the boy will be 21.32 kg.

Conversion means to convert the same thing into different units.

A boy weighs 47 pounds.

Then the number of kilograms of the weight of boy will be

We know the conversion

1 pound = 0.45359237 kg

Then we have

47 pound = 47 x 0.45359237 kg

47 pound = 21.31884139 kg

47 pound = 21.32 kg

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A. The distance moved by the effort is 100 m

B. The workdone by the effort in lifting the load is 8000 J

C. The losses in energy involve the operating in machine 1800 J

Velocity ratio = Effort distance / Load distance

5 = Effort distance / 20

Cross multiply

Effort distance = 5 × 20

Effort distance = 100 m

Workdone = force × distance

Workdone by effort = 80 × 100

Workdone by effort = 8000 J

We'll begin by calculating the workdone in lifting the load. This is illustrated below:

Workdone = mgh

Workdone = 50 × 9.8 × 20

Workdone = 9800 J

Now, we can determine the energy lost as follow:

Energy lost = 9800 - 8000

Energy lost = 1800 J

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Answer:

7000

Step-by-step explanation:

plz mark brainliest

Answer:

7,000

Step-by-step explanation:

First, round the numbers:

Next, add:

I hope this helps!

Answer:

h > 2

Step-by-step explanation:

It may look hard, but it is not really.

1. Solve

Here we have the equation 5+h>7.

All we have to do to find h is to subtract 5 from both sides.

5+h>7

-5     -5

When you subtract 5 from both sides, you get

5 - 5 = 0

7 - 5 = 2

All is left is 0+h>2, or h > 2.

2. Substitute

To make sure, (I do this but you can if you want to) I will substitute.

The values of h have to be greater than 2. So, Let's substitute 3.

5 + h > 7 --> 5 + 3 > 7

It's simple math.

5+3=8

8>7

Now, also to confirm, let's try a value less than 2, 1.

5 + h > 7

5 + 1 > 7

6 > 7 is not true, so it is confirmed that anything less than 2 is not true and anything greater is true.

Hence, h > 2

Hope this helps :)

-jp524

(a) We want to find a scalar function \(f(x,y,z)\) such that \(\mathbf F = \nabla f\). This means

\(\dfrac{\partial f}{\partial x} = 2xy + 24\)

\(\dfrac{\partial f}{\partial y} = x^2 + 16\)

Looking at the first equation, integrating both sides with respect to \(x\) gives

\(f(x,y) = x^2y + 24x + g(y)\)

Differentiating both sides of this with respect to \(y\) gives

\(\dfrac{\partial f}{\partial y} = x^2 + 16 = x^2 + \dfrac{dg}{dy} \implies \dfrac{dg}{dy} = 16 \implies g(y) = 16y + C\)

Then the potential function is

\(f(x,y) = \boxed{x^2y + 24x + 16y + C}\)

(b) By the FTCoLI, we have

\(\displaystyle \int_{(1,1)}^{(-1,2)} \mathbf F \cdot d\mathbf r = f(-1,2) - f(1,1) = 10-41 = \boxed{-31}\)

\(\displaystyle \int_{(-1,2)}^{(0,4)} \mathbf F \cdot d\mathbf r = f(0,4) - f(-1,2) = 64 - 41 = \boxed{23}\)

\(\displaystyle \int_{(0,4)}^{(2,3)} \mathbf F \cdot d\mathbf r = f(2,3) - f(0,4) = 108 - 64 = \boxed{44}\)