How do you write an exponential growth equation to model a situation?

10^12 in standard number is 1000000000000

The number is given as:

[tex]10^{12[/tex]

Expand the expression

[tex]10^{12} = 10 * 10 * 10 * 10 *10 * 10 * 10 * 10*10 * 10 * 10 * 10[/tex]

Evaluate the product

[tex]10^{12} = 1000000000000[/tex]

Hence, 10^12 in standard number is 1000000000000

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Answer:

2633.88

Step-by-step explanation:

Pe^rt

2200*e^.06*3

The area of the poster is  28.75 feet square.

Note that the area of a rectangle is given as;

Area = length × width

Length = 11. 5 feet

Width = 2. 5 feet

Area = 11. 5 × 2. 5

Area = 28. 75 feet square

Thus, the area of the poster is  28.75 feet square.

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Answer:

The number 23 is prime. Therefore, the cube root of 23 = ∛23 = 2.8439.

Step-by-step explanation:

Answer:

Domain [-4 , +∞)

Range [0 , +∞)

Step-by-step explanation:

the function g such that g(x)=√(x+4) ,is defined

for the values of x that verify :

x + 4 ≥ 0

⇔ x ≥ -4

Then

The domain of g is [-4 , +∞)

………………………………………………

Let  x ∈ [-4 , +∞)  

then x ≥ -4

then x + 4 ≥ 0

then g(x) = √(x+4) ≥ 0

Therefore, we can affirm that the range of g is [0 , +∞)

Answer:

y = 2x + 6

Step-by-step explanation:

We are given the line R, which is y=2x+5, and we want to find the equation of the line that is parallel to this line, and that also passes through the point (-2, 2).

Parallel lines have the same slope, yet different y-intercepts.

So, we should first find the slope of y=2x+5.

The line is written in slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept.

As 2 is in the place of where m (the slope) should be, 2 is the slope of the line.

It is also the slope of the line parallel to it.

We can write the equation of the new line in slope-intercept form as well; here is the equation so far, with what we know:

y = 2x + b

We need to find b.

As the equation passes through the point (-2, 2), we can use its values to help solve for b.

Substitute -2 as x and 2 as y.

2 = 2(-2) + b

Multiply.

2 = -4 + b

Add 4 to both sides.

6 = b

Substitute 6 as b.

y = 2x + 6

Savings after 6 years would be $ 1992.

Savings is the money that remains after expenses and other commitments have been subtracted from income.

Savings are the sum of money that would otherwise be lying about, not being risked on investments or used for consumption.

Savings and investing can be compared because the latter includes putting money at risk in an effort to try to increase wealth.

Indicators of household debt or a negative net worth include negative savings.

According to the question,

Amount contributed(P)= $1200

Rate(R)= 11%

Time(T)= 6 years

Interest(SI)=P*R*T/100

                   = 1200*11*6/100

                   = 792

Savings after 6 years = P+ SI

                                      = 1200 + 792

                                      = $ 1992

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Answer:

11

Step-by-step explanation:

The focal length is 14, and thus the sum of the lengths of the blue and red segments is also 14.

Por restricciones de longitud no es posible resumir las respuestas asociadas a esta pregunta, invitamos cordialmente a leer la explicación para mayores detalles sobre el análisis de secciones cónicas.

Según la geometría analítica, existen cinco tipos de secciones cónicas: (i) Circunferencia, (ii) Parábola, (iii) Elipse, (iv) Hipérbola, (v) Recta. 2) a) La ecuación estándar de la circunferencia se caracteriza con el centro (h, k) y la longitud del radio (r):

(x - h)² + (y - k)² = r²

(x - 2)² + (y + 1)² = 4²

b) La longitud del radio de la circunferencia se obtiene por el teorema de Pitágoras sobre la longitud del segmento CP:

r = √[(4 - 1)² + (6 - 3)²]

r = √(3² + 3²)

r = 3√2

(x - 1)² + (y - 3)² = 18

3) a) El eje focal forma parte del eje de simetría de la parábola. La ecuación estándar de la parábola es:

4 · p · x = y²      

Donde p es la distancia entre el foco y el vértice.

Si tenemos que (x, y) = (2, 4), entonces la ecuación de la parábola es:

4 · p · 2 = 4²

p = 2

8 · x = y²

Las coordenadas del foco de la parábola son de la forma (x, y) = (h + p, k):

F(x, y) = (2, 0)

Ahora se determinan los extremos del lado recto: (x = 2)

8 · 2 = y²

y = ± 4

Los extremos del lado recto son (2, 4) y (2, - 4), cuya longitud de segmento es 8 unidades.

b) El eje focal forma parte del eje de simetría de la parábola. La ecuación estándar de la parábola es:

4 · p · x = y²      

Si tenemos que (x, y) = (6, 3), entonces la ecuación de la parábola es:

4 · p · 6 = 3²

p = 8 / 3

(32 / 3) · x = y²

Las coordenadas del foco son F(x, y) = (8 / 3, 0).

Ahora se determinan los extremos del lado recto: (x = 6)

(32 / 3) · 6 = y²

y = ± 8

Los extremos del lado recto son (6, 8) y (- 6, - 8), cuya longitud de segmento es 16 unidades.

4) a) Tenemos una ecuación estándar de la forma 4 · p · y = x². A continuación, hallamos todas las variables requeridas:

x² = 8 · y

p = 2

Directriz: y = - 2, Foco: F(x, y) = (0, 2), Longitud del lado recto: 4

b) Tenemos una ecuación estándar de la forma 4 · p · x = y². A continuación, hallamos todas las variables requeridas:

y² = - (3 / 2) · x

p = - 3 / 8

Directriz: x = 3 / 2, Foco: F(x, y) = (- 3 / 2, 0), Longitud del lado recto: 3.

5) En esta parte debemos manipular algebraicamente las ecuaciones hasta su forma estándar para determinar los datos requeridos de cada caso. La ecuación estándar de la elipse tiene el siguiente problema:

(x - h)² / a² + (y - k)² / b² = 1      

Donde:

a) 81 · x² + 144 · y² = 11664

x² / 144 + y² / 81 = 1

x² / 12² + y² / 9² = 1

Longitud del semieje mayor: 12

Longitud del semieje menor: 9

c = √(12² - 9²)

c ≈ 7.937

Coordenadas de los focos: F₁ (x, y) = (- 7.937, 0), F₂ (x, y) = (7.937, 0)

Vértices: V₁ (x, y) = (- 12, 0), V₂ (x, y) = (12, 0)

Longitud del lado recto

144 · y² = 11664 - 81 · x²

y² = (11664 - 81 · x²) / 144

y = ± (1 / 12) · √(11664 - 81 · x²)

y = ± (1 / 12) · √(11664 - 81 · 7.937²)

y = ± 6.750

La longitud del lado recto es 13.5.

b) 36 · x² + 25 · y² = 3600

x² / 10² + y² / 12² = 1

Longitud del semieje mayor: 12

Longitud del semieje menor: 10

c = √(12² - 10²)

c ≈ 6.633

Coordenadas de los focos: F₁ (x, y) = (0, - 6.637), F₂ (x, y) = (0, 6.637)

Vértices: V₁ (x, y) = (0, - 12), V₂ (x, y) = (0, 12)

Longitud del lado recto

36 · x² = 3600 - 25 · y²

x² = 100 - (25 / 36) · y²

x = √[100 - (25 / 36) · y²]

x = √[100 - (25 / 36) · 6.637²]

x = ± 8.331

La longitud del lado recto es 16.662.

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Answer:

A. 12

Step-by-step explanation:

If she had 12 quarters, then she would have to have 4 nickels according to the problem.

12 * .25 = $3 (money in quarters)

4 * .05 = $.2 ( money in nickels)

Adding those 2 together, we get $3.2.

She have 12 quarters

It is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.

There are two situation in Unitary method:

There are 5 ice-creams. 5 ice-creams cost $125.

Step 1: Let’s find the cost of 1 ice cream. In order to do that, divide the total cost of ice-creams by the total number of ice-creams. The cost of 1 ice-cream = Total cost of ice-creams/Total number of ice-creams = 125/5 = 25. Therefore, the cost of 1 ice cream is $25.

Step 2: To find the cost of 3 ice-creams, multiply the cost of 1 ice cream by the number of ice-creams. The cost of 3 ice-creams is cost of 1 ice-cream × number of ice-creams = 25 × 3 = $75. Finally, we have the cost of 3 ice-creams i.e. $75.

Given:

If she had 12 quarters, then

12 * .25 = $3 ( quarters)

4 * .05 = $.2 ( in nickels)

Hence, she have 12 quarters.

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The given coordinates are actually a rectangle

The coordinates are given as:

A (3, 1), B (1, 5), C (9, 9), and D (11, 5).

Calculate the distance between the coordinates using:

[tex]d = \sqrt{(x_2 -x_1)^2 +(y_2 -y_1)^2[/tex]

So, we have:

[tex]AB = \sqrt{(3 -1)^2 +(1-5)^2} =\sqrt {20[/tex]

[tex]BC = \sqrt{(1 -9)^2 +(5-9)^2} =\sqrt {80[/tex]

[tex]CD = \sqrt{(9 -11)^2 +(9-5)^2} =\sqrt {20[/tex]

[tex]DA = \sqrt{(11 -3)^2 +(5-1)^2} =\sqrt {80[/tex]

The above shows that the opposite sides are congruent

Next, we calculate the slopes using:

m = (y2- y1)/(x2- x1)

So, we have:

AB = (1- 5)/(3-1) = -2

BC = (5- 9)/(1-9) = 1/2

CD = (9- 5)/(9-11) = -2

DA = (5- 1)/(11-3) = 1/2

The slopes of adjacent sides are opposite reciprocals.

This means that the sides are perpendicular

Hence, the given coordinates are actually a rectangle

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Answer: SQUARE ROOT OF 8

Step-by-step explanation: 2^3^1/2 is SQUARE ROOT OF 8. GOD BLESS

- FRIEND TO DINO

The sample should include 2702 men and 2702 women.

Given that you want to be 99% sure your error doesn't exceed 0.035.

A sample is a group of people selected from a larger population to provide data to researchers. The number of members of the population included in the sample is called the sample size.

The significance level is the probability that the test statistic is in the critical range if the null hypothesis is actually true. The confidence interval is 99% or 0.99.

The level of significance α = 1-0.99 = 0.01

the margin of error, ME = 0.035

The Z-critical value at the 99% confidence level or at the significance level of 0.01 is 2.575 (from standard normal tables).

We will now use the formula:[tex]n=\frac{Z^2_{critical}}{2(ME)^2}[/tex].

Substitute the values ​​in the above formula, we get

n = (2.575) ² / (2 × (0.035) ²)

n = 6.630625 / (2 × 0.001225)

n = 6.630625 / 0.00245

n = 2701.966

Therefore, the sample should include 2702 males and 2702 females with a 99% certainty that the error does not exceed 0.035

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[tex]\textbf{Heya !}[/tex]

✏[tex]\bigstar\textsf{Given:-}[/tex]✏

✏[tex]\bigstar\textsf{To\quad find:-}[/tex]

✏[tex]\bigstar\textsf{Solution \quad steps:-}[/tex] ✏

first use the distributive property

[tex]\sf{\longmapsto{ 5x+5=5x}[/tex]

subtract both sides  by 5x

[tex]\sf{\longmapsto{0x+5=0}[/tex] (strange expression right)

[tex]\sf{\longmapsto 0=-5}[/tex] (whattt ?!)

the above statement's false, so the equation has no solutions

`hope that was helpful to u ~

The expression of v = (2,1,5) as a linear combination of (1,2,1), (1,0,2) and (1,1,0) is [tex](2,1,5)=1(1,2,1)+2(1,0,2)+-1(1,1,0)[/tex]

To express v= (2,1,5) as a linear combination of (1,2,1), (1,0,2) and (1,1,0), it will be written as:

[tex](2,1,5)=x(1,2,1)+y(1,0,2)+z(1,1,0)[/tex]

This will yield the following equations:

x + y + z = 2........(1)

2x + z = 1..........(2)

x + 2y = 5........(3)

The solution to the system of equations above is:

x = 1, y = 2, z = -1

Therefore, the linear combination is:

[tex](2,1,5)=1(1,2,1)+2(1,0,2)+-1(1,1,0)[/tex]

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The type of motion which transforms the letter “p” into a “b” is; Reflection.

It follows that the task content demands that the type of motion which maps p to b be identified. On this note, it follows that the type of motion in discuss is Reflection. More particularly, a reflection over the horizontal axis most definitely causes this transformation.

Therefore, the motion which transforms the letter “p” into a “b” is; Reflection.

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The sum of the given expression is 6b^2+8b-15

Given the following expression

(6b^2+5)+(8b-20)

We are to take the sum. On expansion;

6b^2+5 + 8b-20

Collect the like terms

6b^2+8b +5 - 20

6b^2+8b-15

Hence the sum of the given expression is 6b^2+8b-15

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P-Value becomes 0.8599 when (z < 1.08).

According to the statement

We have given that the Z-stat value is 1.08 and we have to find the P value with the help of Z-stat value.

So,

A Z-score is a numerical measurement that describes a value's relationship to the mean of a group of values.

and we know that

The P-Value is calculated by converting your statistic (such as mean / average) into a Z-Score.

So, If the z-stat is 1.08, the p-value for a left-tail test is the probability that (z < 1.08), which is 0.8599.

So, P-Value becomes 0.8599 when (z < 1.08).

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The time Carlos spend practicing his multiplication facts in fraction is 5/16 hours.

A fraction is a value which has a numerator (upper or top value) divided by a denominator (lower or bottom value).

Time spent practicing his multiplication facts = 1/4 of 1 1/4 hours

= 1/4 × 1 1/4

= 1/4 × 5/4

= (1 × 5) / (4 × 4)

= 5/16 hours

Therefore, the time Carlos spend practicing his multiplication facts is 5/16 hours.

Complete question:

Carlos spent 1 1/4 hours doing his math home work. He spent 1/4 of this time practicing his multiplication facts.

How many hours did Carlos spend practicing his multiplication facts?

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The probability that the diameter of a randomly selected pipe will exceed 0.84 inch is 0.977

Probabilities are used to determine the chances, likelihood, possibilities of an event or collection of events

The given parameters are:

Mean = 0.8

Variance = 0.0004

Calculate Standard deviation using

σ = √σ²

This gives

σ = √0.0004

Evaluate

σ = 0.02

Calculate the z-score at x = 0.84 using

z = (x - [tex]\bar x[/tex])/σ

This gives

z = (0.84 - 0.8)/0.02

Evaluate

z = 2

The probability is then represented as:

P(x > 0.84) = P(z > 2)

Next, we look up the value of the z table of probabilities

From the z table of probabilities, we have:

P(x > 0.84) = 0.977

Hence, the probability that the diameter of a randomly selected pipe will exceed 0.84 inch is 0.977

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Answer:

-2 and -3

Step-by-step explanation:

The minimum of |sin 3x| is 0 and the max is 1 (since the sine function ranges from -1 to 1)

Therefore, the maximum is 1 - 3 = -2 and the minimum is 0 - 3 = -3.

Answer: 5

Step-by-step explanation:

Because there are 35 when you add yourself so u subtract 30 to get 5

There would be 4 people left in the garden.

34 - 30 = 4.

Subtraction is a mathematical operation that involves taking away one number from another to find the difference between them. For the question, At first, there were 34 people in the garden and later 30 people were no longer alive in the garden, so the difference between 30 people and 34 people is 4.

Subtraction is the opposite of addition, and it is used to measure the distance between two values on the number line.

Subtraction is represented by minus Sign (-). For example, subtracting 5 from 10 gives you a difference of 5 (10 - 5 = 5).

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Answer:

222 [ft²].

Step-by-step explanation:

1. the required area can be calculated according to the formula:

A=0.5*b*c*sin(A);

2. after substitution of b=32; c=19 and sin(A)≈0.7313537:

A=0.5*32*19*0.7313537=222.3315248 [ft²].

hi

monthly interest rate is :     [tex]\sqrt[12]{1.05}[/tex]

So in forty month there will be  :  10 000 * ( [tex]\sqrt[12]{1.05}[/tex] )^40  ≈11 776,06

The probability that the mean fill is more than 84.8 ounces is 0.39358

From the question, the given parameters about the distribution are

The z-score of the data value is calculated using the following formula

z = (x - mean value)/standard deviation

Substitute the given parameters in the above equation

z = (84.8 - 84.5)/1.1

Evaluate the difference of 84.8 and 84.5

z = 0.3/1.1

Evaluate the quotient of 0.3 and 1.1

z = 0.27

The probability that the mean fill is more than 84.8 ounces is then calculated as:

P(x > 84.8) = P(z > 0.27)

From the z table of probabilities, we have;

P(x > 84.8) = 0.39358

Hence, the probability that the mean fill is more than 84.8 ounces is 0.39358

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An appropriate numerical summary is descriptive statistics.

It should be noted that a numerical summary means a number used to describe specific characteristics of a data set.

In this case, descriptive statistics can be used. This is used to describe the data set.

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The probability of winning this game is 0.003

Let us name p to be the probability of winning the game.

We have the expected value to be 100

100 = probability of winning + 1-p x loss

win = 100000 - 200

We then input in the formula

100 = p*99800 +(1-p) x -200

100 = 99800p - 200 + 200p

Collect like terms

100 + 200 = 99800 + 200p

300 = 100000p

Divide through by 100000

This give the

Probability of winning =  0.003

The probability of winning the game is very low hence I would not play.

The factors that would influence the decision are:

A game has an expected value to you of ?$100. It costs ?$200 to? play, but if you win you receive? $100,000 (including your ?$200 ?bet), for a net gain of ?$99,800. What is the probability of? winning

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