4x^3 - 10 = 2x^3 + 6

After solving : 100!/12^50, we get 1.025513e+104

Here, 100 factorial or 100!

The result of multiplying an integer by each natural number below it is the factorial of that number.

A factorial can be symbolically denoted by the sign "!"

The first n natural integers are added together to form "n factorial," which is represented by the number n.

100! = 100 × 99 × 98 × .... × 3 × 2 × 1 = 9.332621544 E+157.

This product is too big to calculate manually and hence a calculator is used.

Now, 9.332621544 E+157 / 12 ^ 50 = 1.025513e+104

Hence, after solving 100!/12^50, we get 1.025513e+104

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Answer:

a = 3 , b = - 18

Step-by-step explanation:

2 - [tex]\frac{x+1}{x-2}[/tex] - [tex]\frac{x-4}{x+2}[/tex]

express as a fraction with common denominator (x - 2)(x + 2)

= [tex]\frac{2(x-2)(x+2)-(x+1)(x+2)-(x-4)(x-2)}{(x-2)(x+2)}[/tex]

= [tex]\frac{2(x^2-4)-(x^2+3x+2)-(x^2-6x+8)}{x^2-4}[/tex]

= [tex]\frac{2x^2-8-x^2-3x-2-x^2+6x-8}{x^2-4}[/tex]

= [tex]\frac{3x-18}{x^2-4}[/tex]

compare to [tex]\frac{ax+b}{x^2-4}[/tex]

with a = 3 and b = - 18

Answer:

$73

Step-by-step explanation:

Answer:

Step-by-step explanation:

you would cut 99 in half and make your way down until nothing left which gives you 48.985 or

49.99$ rounded

Answer:

A,B,C

Step-by-step explanation:

The variance of the sample mean is 12/35 = 0.3429.. This is a result of uniform distribution.

The uniform distribution is a continuous probability distribution and is concerned with events that are equally likely to occur. When working out problems that have a uniform distribution, be careful to note if the data is inclusive or exclusive.

According to the question, we have

Sample size (n) = 36; uniform continuous distribution has a maximum of 14 and a minimum of 2.

The notation for the uniform distribution is

X U(a,b), where  a=  the lowest value of x  and  b=  the highest value of x. The probability density function is f(x) = 1/(ba ) fo axb .

b = 14 and a = 2.

Variance in uniform distribution = (b-a)² / 12.

Put the value of a and b, 

Variance = ( 14-2)²/12 = 12

Sample variance is used to calculate the variability of sample sets.

The variance of the sample means = variance / (sample size- 1) 9= (b-a)²/ (n-1)

= 12/35= 0.342

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When dividing 4 by 280.8, the answer gotten is 0.014245.

It should be noted that decimal numbers are numbers that have whole numbers as well as fractional parts. One of the number types in algebra that has a whole integer and a fractional portion separated by a decimal point is a decimal. The decimal point is the dot that appears between the parts of a whole number and a fraction. An example of a decimal number is 34.5. Examples are 2.4 and 9.34.

To divide a decimal by a whole number, follow these steps.

In this case, Dividing 4 by 280.8 will give a value of 0.014245.

Therefore the value is 0.014245.

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Dividing 4 by 280.8  gives

given data

4 ÷ 280.8

4 ÷ 280.8 = 4 / 280.8

= 4 / 280.8

= [tex]\frac{4}{\frac{2808}{10} }[/tex]

= 4/1 * 10 /2808

= 40 / 2808

= 20 / 1404

= 10 / 702

= 5 / 351

5//351 is the lowest form of the fraction and in decimal it is solved as

= 5 / 351

= 0.01424501425

= 0.0142 ( to 4 decimal place )

Decimals refers to number types which are displayed using points. The points used here is called decimal points.

Numbers appearing after the decimal point is not a whole number. If the set of number bearing decimal point has zero as the first and only number, then the whole number is not up to a whole number.

This is synonymous to the case of the solved problem. The number 0.0142 does not have a whole number part. Hence the number is less than 1

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The original price of the dishes is $80

The sale price is $72

10% was off from the original price to get the sale price

The original price can be calculated as follows

100-10

= 90%

Let y represent the original price

72 ÷ 90/100

= 72 ÷ 0.9

= 80

Hence the original price of the dishes before 10% was taken off is $80

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From the given function, it is found that:

a. A reasonable domain for the function is of 0 ≤ d ≤ 11.

b. The y-intercept of the graph represents that the initial radius of the algae is of 7 mm.

c. The average rate of change between the 4th and the 11th day of the function means that the radius of the algae grew by an average of 0.64 mm a day.

The function is modeled according to the following rule:

f(d) = 7(1.06)^d

In which:

When the biologist concluded her study, the radius of the algae was approximately 13.29 mm, hence the upper bound of the domain is found as follows:

[tex]13.29 = 7(1.06)^d[/tex]

[tex](1.06)^d = \frac{13.29}{7}[/tex]

[tex]\log{(1.06)^d} = \log{\left(\frac{13.29}{7}\right)}[/tex]

[tex]d\log{1.06} = \log{\left(\frac{13.29}{7}\right)}[/tex]

[tex]d = \frac{\log{\left(\frac{13.29}{7}\right)}}{\log{1.06}}[/tex]

d = 11.

The smallest possible number of days is of 11, hence a reasonable domain for the function is:

0 ≤ d ≤ 11.

The y-intercept of the graph represents that the initial radius of the algae, as it is calculated when d = 0, hence it's value is given by:

[tex]f(0) = 7(1.06)^0 = 7[/tex]

The average rate of change of a function is given by the change in the output divided by change in the input, hence:

r = (13.29 - 8.84)/(11 - 4) = 0.64 mm a day.

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Answer: Here you go

Step-by-step explanation:

The results of the operation of multiplication between two functions are, respectively:

According to function theory, there are five operations between two functions to create resulting functions:

In this problem we must use the operation of multiplication between two functions.

Case 1

(f · g)(x) = (2 · x + 4) · (x² + 4 · x + 4)

(f · g)(x) = (2 · x + 4) · x² + 4 · (2 · x + 4) · x + 4 · (2 · x + 4)

(f · g)(x) = 2 · x³ + 4 · x² + 8 · x² + 16 · x + 8 · x + 16

(f · g)(x) = 2 · x³ + 12 · x² + 24 · x + 16

Case 2

(h · g)(x) = (x² - 4) · (x² + 4 · x + 4)

(h · g)(x) = (x² - 4) · x² + (x² - 4) · (4 · x) + (x² - 4) · 4

(h · g)(x) = x⁴ - 4 · x² + 4 · x³ - 16 · x + 4 · x² - 16

(h · g)(x) = x⁴ + 4 · x³ - 16 · x - 16

Case 3

(f · h)(x) = (2 · x + 4) · (x² - 4)

(f · h)(x) = 2 · x³ - 8 · x + 4 · x² - 16

(f · h)(x) = 2 · x³ - 4 · x² - 8 · x - 16

(f · h)(2) = 2 · 2³ - 4 · 2² - 8 · 2 - 16

(f · h)(2) = - 32

Case 4

(g · f)(x) = (x² + 4 · x + 4) · (2 · x + 4)

(g · f)(x) = 2 · x³ + 12 · x² + 24 · x + 16

Case 5

(g · h)(x) = (x² + 4 · x + 4) · (x² - 4)

(g · h)(x) = x⁴ + 4 · x³ - 16 · x - 16

Case 6

(f · h)(x) = (2 · x + 4) · (x² - 4)

(f · h)(x) = 2 · x³ - 4 · x² - 8 · x - 16

Case 7

(h · g)(x) = (x² - 4) · (x² + 4 · x + 4)

(h · g)(x) = x⁴ + 4 · x³ - 16 · x - 16

(h · g)(1) = 1⁴ + 4 · 1³ - 16 · 1 - 16

(h · g)(1) = - 27

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The bottom is moving at a rate of [tex]4\sqrt{3}[/tex] ft/s along the ground when the botton of the ladder is at a distance of 6 ft from the wall.

Here we have been mentioned that a 12 feet ladder is leaning against the wall which is represened by AC in the below given triangle.

We have AB = y = distance of top of the ladder from the wall

BC = x = distance of bottom of the ladder from the wall

AC = z = height of the ladder = 12 ft (given)

The top of the ladder AB is sliding down at a rate of 4 [tex]ft/s[/tex]

∴ [tex]\frac{dy}{dt}[/tex] = - 4 ft/s (negative sign indicates that the top is sliding downwards)

Let the rate at which the bottom of the ladder is sliding be [tex]\frac{dx}{dt}[/tex]

Now in the right angled triangle [tex]ABC[/tex] by using Pythagoras theorem we have,

[tex]AB^{2} + BC^{2} =[/tex][tex]AC^{2}[/tex]

[tex]y^{2} +x^{2} = z^{2}[/tex]    (equation 1)

When x = 6ft and z = 12 ft,

[tex]y^{2} +6^{2} = 12^{2}[/tex]

⇒ [tex]y^{2} = 144 - 36[/tex]

⇒ [tex]y^{2} = 108[/tex]

⇒ y = √108

⇒ y = 6 √3 ft

Differentiating equation 1 with respect to [tex]time[/tex] we get,

[tex]\frac{d}{dt} (y^{2} +x^{2} ) = \frac{d}{dt} (z^{2})[/tex]

⇒ 2y[tex]\frac{dy}{dt}[/tex] + 2x[tex]\frac{dx}{dt}[/tex] = 2z[tex]\frac{dz}{dt}[/tex]

Putting the values of dz/dt = 0 (as the height is constant) , dy/dt = - 4 ft/s , y = 6 √3 ft, x = 6ft and z = 12ft we have,

∴ 2(6√3) (-4) + 2(6)[tex]\frac{dx}{dt}[/tex] = 2(12)(0)

⇒ -48√3 + 12[tex]\frac{dx}{dt}[/tex] = 0

⇒ 12[tex]\frac{dx}{dt}[/tex] = 48√3

⇒ [tex]\frac{dx}{dt} = \frac{48\sqrt{3} }{12}[/tex]

⇒ [tex]\frac{dx}{dt} = 4\sqrt{3}[/tex] ft/s

Hence the rate at which the bottom of the ladder is sliding is [tex]\frac{dx}{dt} = 4\sqrt{3}[/tex] ft\s

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Lets first look at the cost per round with the 25 round pass

Take the total cost and divide by the number of rounds

$84 / 25 rounds

$ 3.36 per round

OR

They can pay 3.25 per round with the single pay

$3.25 is less than 3.36 so it is cheaper ( less per round) to pay the single round price

Option 2 $3.25 is cheaper

Given:

The length of the rectangle is 50 yards. The perimeter is less than 180 yards.

Required:

Write the solution inequality in terms of width w.

Explanation:

Let the width of the rectangle is w.

The perimeter of the rectangle is given by the formula:

Final Answer:

The first option is the correct answer.

The equation of the parabola, in vertex form, that represents the ball's distance, y, from the hole, x seconds after the ball is hit is

y = (-2m/s²)t² + (-2m/s)t + 6m.

Given:

Let's assume that the hole is at y = 0m, with x seconds as the time.

The vertex of the parabola can be written as (-1s, 8m) where the time variable, x, is supposed to be in seconds, while the distance variable, y, is supposed to be in meters.

The ball reaches the hole at x = 1s, so we have point (1s, 0m)

The vertex of the parabola y = ax² + bx + c is known to be at

x = -b/2a,

So, -1 = -b/2a

We have the following equations,

8m = a(-1s)² + b(-1s) + c

0m = a*(1s)² + b(1s) + c

-1s = -b/2a

b = 2a × 1s

Substituting the value of b in the equations and simplifying them,

8m = a×1s² - 1s×2a×1s + c

⇒ 8m = a( 1s² - 2s²) + c = -a×1s² + c.

0m = a×1s² + 1s×2a×1s + c

⇒ 0m = a(1s² + 2s²) + c = a×3s² + c

Deriving the value of c from the second equation we put it in the first equation,

c = - a×3s²

The first equation is as,

8m = -a×1s² - a×3s² = -a×4s²

a = 8m/-4s² = -2m/s²

From the value of a we can calculate the values of b and c.

c = -a×3s² = -(-2m/s²)×3s²= 6m.

b = 1s×2a = 1s×(-2m/s²) = -2m/s.

Then the equation is:

y = (-2m/s²)t² + (-2m/s)t + 6m

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Answer:

-3 [tex]\frac{5}{7}[/tex]

Step-by-step explanation:

Is this the problem?

1 4/9 (-2 4/7)

[tex]\frac{13}{9}[/tex][tex](\frac{-18}{7})[/tex] = [tex]\frac{-26}{7}[/tex]

-3 [tex]\frac{5}{7}[/tex]

Answer:

Answer down below!

Step-by-step explanation:

Let's write out the equation!

2x + 8 = -4

To solve this, you have to subtract the 8 and bring it over to -4

That would look something like:

2x -(+8) = -4 -8

That leaves you with 2x = -12

Now you divide 2 and -12 which will give you

-6

Answer:X= - 6

Step-by-step explanation:

MOVE +8 to the right which would make it negative so -8-4.You would add both numbers which would be -12 and then u divide -12 with 2 so

-12/2 is -6

Using the area of triangles and rectangles, we know that the area of the shaded region is 255cm².

In the given shaded region there is one rectangle and one triangle.

First, find the area of the shaded rectangle.

Now find the area of the shaded triangle.

So, the Area of the triangle is:

Therefore, the total area of the shaded region is:

Therefore, using the area of triangles and rectangles, we know that the area of the shaded region is 255cm².

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Answer:

0.30 dollar

Step-by-step explanation:

333.33 points == 1 dollar

: 333.33

1 points == 0.003 dollar

* 100

100 points == 0.30 dollar

Given the measurements:

x1 = 10

x2 = 11

x3 = 15

x4 = 6

We're asked to find:

Which is

100+121+225+36

=482

The months will they have same number of miles. is 1.732 months.

Miranda's used car has 5,132 miles on it already, and she drives 525 miles per month. This will be expressed as y = 5132 + 525x

Lily's car has 4,789 miles on it already, and she drives 723 mile per month. This will be:

y = 4789 + 723x

x = number of months

y = miles

The number of months will be gotten by equating the equations. This will be:

5132 + 525x = 4789 + 723x

Collect like terms

198x = 343

Divide

x = 343 / 198

x = 1.732 months.

The number of months is 1.732.

The complete question is written below.

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Miranda and Lily both bought a used car on the same day. Miranda's used car has 5,132 miles on it already, and she drives 525 miles per month. Lily's car has 4,789 miles on it already, and she drives 723 mile per month. How many months will they have same number of miles.

In 12 cups of flour,we are going to have 2 cups of flour in six(6) places.

Thus, for 12 cups of flour, Mrs Smith will use:

Answer:

31 & 32

Step-by-step explanation:

3 x 32 = 96

2 x 31 = 62

62 + 34 = 96

Hello!

The ratio between pig and other animals

 ==> looks like   [tex]\text{number of pigs}: \text{ number of other animals}[/tex]

Since there are 8 pigs and 11 other kind of animals

 ⇒ the ratio is ⇒ 8: 11

Hope that helps!

Answer:

Remember, a positive and a negative while being added is always a negative outcome, so when you add -29.03 + 26.5, you get -2.53

The value of x is −61.5 . option B

An algebraic expression is simply seen as one with terms, factors, variables, coefficients, constants.

These expressions may also consist of arithmetic operations, some of which includes;

Based on the information given, we have;

−0.28x − 15.3 = 1.92

To determine the value of the variable 'x' we need to take the following steps;

collect like terms from the equation

-0. 28x = 1. 92 + 15. 3

Add like terms

-0. 28x = 17.22

Divide both side by the coefficient of x

x = 17. 22/-0.28

x = - 61. 5

Hence, the value is - 61. 5

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It will be a horizontal line