-102/119 in standard form

Answer:

you need to upload a pic so we can see what you're talking about

The value of the expression C(6,3) is 20

The expression is given as:

C(6, 3)

This means 6 combination 3.

And it can be written as:

[tex]^6C_3[/tex]

Apply the combination formula

[tex]^6C_3 = \frac{6!}{3!3!}[/tex]

Evaluate the expression

[tex]^6C_3 = 20[/tex]

Hence, the value of the expression C(6,3) is 20

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The half-life of the given exponential function is of 346.57 years.

It is the value of t when A(t) = 0.5A(0).

In this problem, the equation is:

[tex]A(t) = A(0)e^{-0.002t}[/tex].

In which t is measured in years.

Hence the half-life is found as follows:

[tex]0.5A(0) = A(0)e^{-0.002t}[/tex]

[tex]e^{-0.002t} = 0.5[/tex]

[tex]\ln{e^{-0.002t}} = \ln{0.5}[/tex]

[tex]0.002t = -\ln{0.5}[/tex]

[tex]t = -\frac{\ln{0.5}}{0.002}[/tex]

t = 346.57 years.

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Answer: a = -10

Concept:

When an equation has no solution, in most cases, it means that the variables are being canceled out, and left with unequal constants.

For example:

                                             2x + 3 = 2 +2x

The 2x can be canceled out on both sides, which left us with:

                                                     3 = 2

3 does not equal to 2, therefore, it has no solution

Solve:

Given equation

4 (5x + 1) = -2 (ax + 4)

Expand the parenthesis

4 (5x) + 4 (1) = -2 (ax) + (-2) (4)

20x + 4 = -2ax - 8

According to the concept, we need to make the variables equal to cancel them out and left with unequal constants

20x = -2ax

Divide x on both sides

20x / x = -2ax / x

20 = -2a

Divide -2 on both sides

20 / -2 = -2a / -2

[tex]\Large\boxed{a=-10}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

Step-by-step explanation:

The formula for the total of interior angles can be used together with the given angle values to write an equation for the number of sides.

The total of interior angles of an n-sided polygon is 180°×(n -2). In the given n-sided polygon, two angles are 120° and (n -2) angles are 150°. The total of angles is the same either way it is computed:

  2×120 +(n -2)150 = (n -2)180

Subtracting (n-2)150, we have ...

  240 = 30(n -2)

  8 = n -2 . . . . . . . . divide by 30

  10 = n . . . . . . . . add 2

The polygon has 10 sides.

The total of interior angles is ...

  angle sum = 180°×(10 -2) = 1440°

The sum of interior angles is 1440°.

Answer:

10 sides and

1440° total of interior angles.

Step-by-step explanation:

The number of degrees in a polygon (sum of interior angles) is:

(n - 2)×180

This is the total. Here, n is the number of sides (same as the number of angles)

In your question, 2 of the angles are 120° and the remaining angles are 150°.

If n is ALL the angles, then (n-2) is all the 150° angles because the other 2 are 120°

So we can write an equation:

Our polygon:

120°+120°+(n-2)150°

=

(n-2)180°

Combine like terms:

240+(n-2)150=(n-2)180

Use Distributive property.

240+150n-300=180n-360

Again, combine like terms.

300 = 30n

Divide.

10 = n

n is the number of sides (and angles).

Check:

Ten-sided shape:

(10-2)180

= 1440°

Our shape:

120°+120°+ 8(150°)

= 240° + 1200°

= 1440° Check!

Answer:

3.5

Step-by-step explanation:

1 - (-2.5)   =   1 +   2.5   = 3.5

The individual-size box of cereal is a rectangular prism with a volume of 44.625 inches³.

The volume of rectangular prism of length l, width w and height h is given by:

V = lwh.

In this problem, the standard dimensions are:

The individual-size box has a 1/10 of the volume of the original box, hence:

V = 0.1 x 3.5 x 8.5 x 15 = 44.625 inches³.

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Answer:

Step-by-step explanation:

You want to save all the money you earn to buy a guitar that costs $400. You earn $9 per hour and

plan to work 15 hours each week for the next 3 weeks. Will you earn enough money in that time to buy

the guitar? Explain your answer.

15 hours × 3 weeks × $9 per hour

15 × 3 × 9 =

45 × 9 = 405$

The answer is YES

The equation in point slope form is given as y+3 = -5/8(x-4)

The formula for calculating the equation of a line in point-slope form is expressed as:

y-y1= m(x-x1)

Given the coordinate point

Slope = 2-(-3)/-2-4
Slope = 5/-8

Determine the equation

y-(-3) =-5/8(x-4)

y+3 = -5/8(x-4)

Hence the equation in point slope form is given as y+3 = -5/8(x-4)

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a) The exponential function that models the number of cells is: [tex]A(t) = 200(1.75)^{\frac{t}{3}}[/tex]

b) There will be 1292 cells after 10 hours.

An increasing exponential function is modeled by:

[tex]A(t) = A(0)(1 + r)^{\frac{t}{n}}[/tex]

In which:

For this problem, the parameters are:

A(0) = 200, r = 0.75, n = 3.

Hence the equation is:

[tex]A(t) = A(0)(1 + r)^{\frac{t}{n}}[/tex]

[tex]A(t) = 200(1 + 0.75)^{\frac{t}{3}}[/tex]

[tex]A(t) = 200(1.75)^{\frac{t}{3}}[/tex]

The number of cells after 10 hours is:

[tex]A(t) = 200(1.75)^{\frac{t}{3}}[/tex]

[tex]A(10) = 200(1.75)^{\frac{10}{3}}[/tex]

A(10) = 1292.

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Answer:

20 x 20 x 20 = 8000

Using the least common factor, they need to wait 14 days until they next get to work together.

To find the time that passes between the events happening at the same time, we need to find the least common multiple of the periods.

In this problem, the periods are of 2 days and 7 days, which already are prime numbers, hence:

lcm(2,7) = 2 x 7 = 14.

They need to wait 14 days until they next get to work together.

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There are no real solutions to solve Z. If there may be a typo or something, there are no solutions.

Answer:

x=5

Step-by-step explanation:

Resolvamos tu ecuación paso a paso.

4+x=9

Paso 1: simplifica ambos lados de la ecuación.

x+4=9

Paso 2: Resta 4 de ambos lados.

x+4−4=9−4

x=5

Answer:

4+x=9

or, x=9-4

or, x=5

the value of x is 5

Answer: [tex]g(x) \ge f(x)[/tex] for all x such that [tex]x\le-2[/tex] or [tex]x\ge0[/tex]

Step-by-step explanation:

This question is essentially asking at what x values would the graph of g(x) be greater than (higher than) or equal to f(x).

In the graph, we can see that g(x) is greater than (or higher than) f(x) at all x's before (to the left of) point E and after (to the right of) point A. An easy way to find the points E and A is by setting f(x) = g(x).

[tex]f(x)=g(x)\\1-x^2=2x+1\\1=x^2+2x+1\\0=x^2+2x\\0=x(x+2)\\x=0\hspace{0.1cm}or\hspace{0.1cm}x=-2[/tex]

Since any value with x=-2 is left of the y-axis, we know that point E would have its x-coordinate as -2. Similarly, any point on the y-axis would have x=0; therefore, we can tell that point A would have its x-coordinate at 0.

If we remember that g(x) is greater than f(x) to the left of E and to the right of A, we can say that

[tex]g(x) \ge f(x)[/tex] for all x such that [tex]x\le-2[/tex] or [tex]x\ge0[/tex]

Answer: for the factor one: The expression isn't factorable with rational numbers

Step-by-step explanation: Since the polynomial can be factored it isn't prime (i don't know if that is what you meant or not but I hope this helps and I got all of them correct )

Answer:3522

Step-by-step explanation:222

2

Answer:

The set can be defined by listing all its elements, separated by commas and enclosed within braces. This is called the roster method.

Step-by-step explanation:

Mark me as Brainy.

Based on the given situation, Max final number if his starting number is 7 is -4.5

n + 8

2(n + 8)

So,

2(n + 8) = 7

2n + 16 = 7

2b = 7 - 16

2n = -9

n = -9/2

n = -4.5

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The given polynomial is a Quartic trinomial

From the question, we are to determine the type of the given polynomial

The given polynomial is

3x⁴−2x³−2

The highest degree of the polynomial is 4. Thus, it is a Quartic Polynomial.

Also, the expression contains exactly 3 terms. Thus, it is a trinomial.

Hence, the given polynomial is a Quartic trinomial

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The value of To from the t table will be 2.131

The following can be deduced from the information:

P(-t0 < t < t0) = 0.95

2*P(t < t0) - 1 = 0.95

P(t < t0) = 0.975

df = 15

From t-table (column 1-0.975 = 0.025) in the row 15. Therefore, t0 = 2.131.

In conclusion, the answer is 2.131.

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A quadratic equation that models something from one's daily life is when calculating areas, and determining a product's profit.

It should be noted that a quadratic equation means an algebraic equation of the second degree in x.

The quadratic equation in its standard form is ax² + bx + c = 0. Here, a and b are the coefficients, x is the variable, while c is the constant term.

Quadratic equations are used in everyday life, as when calculating areas, and the determination of a product's profit and formulating the speed of an object.

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The transformation that occurred after the dilation of the parallelogram is a translation of 9 units to the right.

A unique variety of quadrilateral made up of parallel lines is called a parallelogram. A parallelogram can have any angle between its neighboring sides, but it must have opposite sides that are parallel for it to be a parallelogram. If the opposite sides of a quadrilateral are parallel and congruent, it will be a parallelogram. Consequently, a quadrilateral in which both pairs of opposite sides are parallel and equal is referred to as a parallelogram.

The initial parallelogram was dilated by a scale factor of 2 about point P.

The points of the initial parallelogram are: (-4, 0), (-2, 0), (-3, -3), (-5, -3).

The parallelogram obtained on dilation will have the points: (-6, 0), (-2, 0), (-4, -6), (-8, -6).

The points of the final parallelogram are: (3, 0), (7, 0), (5, -6), (1, -6).  

(-6,0) →(3,0)  ⇒ (x,y)→(x+h , y+k)

x = -6 , x+h = 3 ⇒ h=3-x = 3-(-6) = 9

y = 0 , y+k = 0 ⇒ k = 0

The transformation rule is (x,y)→( x+9 , y )

That is, a translation of 9 units to the right.

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Answer:

A. a translation of 9 units to the right

Step-by-step explanation:

Edge 2023

Answer:Principal P = 2000

Amount= A

years=n 10.00

compounded 12 times a year t

Rate = 2.00 0.02

Amount = P*((n+r)/n)^n*t

Amount = = 2000 *( 1 + 0.02 /t)^ 10 * 12

Amount = 2000 *( 1 + 0 )^ 120

2000 *( 1 )^ 120

Amount = 2442.4

Step-by-step explanation:

Total amount of money in the savings account after 11 weeks is $1310.

Total money in the account =

 Initial Money + Money added per week x Number of weeks

Given:

Initial Money = $650

Money added per week = $60

Total money in the account = S

Number of weeks = W

Substituting it in the above equation we get,

S = $650 + $60xW                                          (General Equation)

Total amount of money in the savings account after 11 weeks

S = $650 + $60x11

S = $650 + $660

S = $1310

Thus total amount of money in the savings account after 11 weeks is $1310.

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Answer:

a.

2 / 3 + 5 / 6 - 1 / 2a.

2 / 3 + 5 / 6 - 1 / 2

= 0,66... + 0,833... - 0,5

= 1,5 - 0,5

= 1

Step-by-step explanation:

sorry I only know the letter A hope I helped anyway

Answer:  Point B

Reason:

This point is the highest point in the neighborhood or interval. Yes point D is higher up, but points immediately adjacent to point D are higher. This means D is not a relative max. We need a hill shape like where B is located.  In contrast, point C is a relative minimum since it is at the bottom of the valley.

Answer:

0

Step-by-step explanation:

sin²t + cos²t = 1, so since cos²t = 1, sin²t = 0, and thus sint = y = 0.

we conclude that 900 cubes enter in the given box.

We need to find the volumes of both figures.

The blocks are cubes of 2cm by 2cm by 2cm, then the volume of each block is:

[tex]V = (2cm)^3 = 8cm^3[/tex]

The box has dimensions of 10cm by 12cm by 60cm, then the volume is:

[tex]V = 10cm*12cm*60cm = 7,200 cm^3[/tex]

The number of cubes that enter in the box is N such that:

[tex]N*8cm^3 = 7,200cm^3[/tex]

Solving for N, we get:

[tex]N = 7200cm^3/8cm^3 = 900[/tex]

In this way, we conclude that 900 cubes enter in the given box.

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Answer:

429/7 kg or 61 2/7 kg

Step-by-step explanation:

I'll answer according to how I understand this problem, but I'm not sure this is correct.

"39 kg of rice is taken out of bag of rice. If 8/22 of the rice is left, what was the original weight of the rice in the bag?"

8/22 is a strange number to work with because it could have been given as 4/11. This is another reason I'm not too sure about this problem.

8/22 = 4/11

If 4/11 is left, then since 11/11 - 4/11 = 7/11, 7/11 of the rice remains.

7/11 x = 39

x = 39 × 11/7

x = 429/7

x = 61 2/7