What is the value of "X"?

The function [tex]y=0.3^x[/tex] represents exponential growth with the initial value equal to 1, the decay factor equal to 0.3, and the rate equal to 0.7.

The formula for the Population Growth Equation is:

[tex]P_f=P_o*(1+\frac{R}{100}) ^t[/tex]

Pf= future population

Po=initial population

r=growth rate

t= time (years)

growth or decay factor =  (1 ±r)

When 1+R  > 1, the equation represents growth, while 1+R < 1 the equation represents decay.

The question gives:

[tex]y=0.3^x[/tex], then

Pf=y

Po= 1  

[tex](1+\frac{R}{100}) =0.3[/tex] , thus

[tex](100+R}) =30\\ \\ R=-100+30\\ \\ R=-70[/tex]

r= -70%= -0.7

decay factor= (1-0.7)=0.3

Therefore,

1+R will be = 1+(-0.7)=1 - 0.7 =0.3

When 1+R >1, the function represents exponential growth.

Read more about the exponential function here:

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Step-by-step explanation:

[tex] \tan(2x) = 1.5[/tex]

Take the arc tangent,

[tex] \tan {}^{ - 1} ( \tan(2x) ) = \tan {}^{ - 1} (1.5) [/tex]

[tex]2x = 56.3[/tex]

[tex]x = 28.15[/tex]

b.

[tex](3 \cos(x) + 1)(2 \cos(x) + 3) = - 2[/tex]

[tex]6 \cos {}^{2} (x) + 11 \cos(x) + 3 = - 2[/tex]

[tex]6 \cos {}^{2} (x) + 11 \cos(x) + 5 = 0[/tex]

[tex]6 \cos {}^{2} (x) + 6 \cos(x) + 5 \cos(x) + 5 = 0[/tex]

[tex]6 \cos(x) ( \cos(x) + 1) + 5( \cos(x) + 1) = 0[/tex]

[tex](6 \cos(x) + 5)( \cos(x) + 1) = 0[/tex]

Set each factor equal to zero.

[tex]6 \cos(x) + 5 = 0[/tex]

[tex]6 \cos(x) = - 5[/tex]

[tex] \cos(x) = - \frac{5}{6} [/tex]

[tex]x = \cos {}^{ - 1} ( \frac{5}{6} ) [/tex]

[tex]x = 146.4[/tex]

For the second factor,

[tex] \cos(x) + 1 = 0[/tex]

[tex] \cos(x) = - 1[/tex]

[tex]x = 180[/tex]

So the answer for the second one is

146.4 and 180.

Answer:

How much money did Amy wager on her games?

Step-by-step explanation:

Is she in debt?

Answer:

49

Step-by-step explanation:

So, you can just do 245x1/5.

I got 1/5 from "how many did she LOSE?"

5/5-4/5=1/5.

She lost 49 games.

Answer:

5 inches : 6 inches

Step-by-step explanation:

20 inches : 2 feet

Use Hint: 1 feet = 12 inches

20 inches : 2·12 = 24 inches

Find the simplest form of 20 inches : 24 inches

20 inches : 24 inches , divide both numbers by 2

10 inches : 12 inches, divide both numbers by 2 again

5 inches : 6 inches

Answer:

First find out area of circle and find the A B X angle then substract Total area by ABX

Answer:

68

Step-by-step explanation:

The intercepted arc (AB) is double the inscribed angle (34)

Explanation:

The word "increased" tells us to add a specific number to the addend. Let us take an example to understand the word "increased".

Example: 3 is increased by 4.

⇒ 3 + 4

Notice that the addend (3) is being increased (+) by 4.

Step-by-step explanation:

It is a 5th degree binomial. The highest exponetial power of the polynomial is 5, therefore we are dealing with a 5th degree polynomial. "Polynomial" is a general term. Trinomial and binomial categorize it even more by the number of terms the polynomial has. There are two terms, so we are dealing with a binomial. The prefix bi means "two"

Answer:

Binomial with degree 5

Step-by-step explanation:

The polynomial 3x⁵ + 3 is a binomial with degree 5.

Why?

This option is correct because:

[tex]\rule{150pt}{2pt}[/tex]

[tex] \sf :\implies \quad {\pmb{x = - 4}}[/tex]

Let's solve the given equation step by step ;

[tex] \sf :\implies \quad 6(x + 4) + 1 = x + 5[/tex]

The first step is to distribute the equation:

[tex] \sf :\implies \quad (6 \times x ) + (6 \times 4) + 1 = x + 5[/tex]

[tex] \sf :\implies \quad 6x + 24 + 1 = x + 5[/tex]

[tex] \sf :\implies \quad 6x + 25 = x + 5[/tex]

Second step is to combine the like terms:

[tex] \sf :\implies \quad 6x + 25 - x = 5[/tex]

[tex] \sf :\implies \quad( 6x - x) + 25 = 5[/tex]

[tex] \sf :\implies \quad 5x + 25 = 5[/tex]

Now, subtract 25 from both sides :

[tex] \sf :\implies \quad 5x + 25 - 25 = 5 - 25[/tex]

[tex] \sf :\implies \quad 5x = - 20[/tex]

Divide both sides by 5:

[tex] \sf :\implies \quad \dfrac{5x}{5} = - \dfrac{20}{5} [/tex]

[tex] \sf :\implies \quad \boxed{ \pmb{\sf x = - 4}}[/tex]

Hence, your answer is ; x = -4

Answer:

2.60

Step-by-step explanation:

This is a strange way to solve the problem, but it works for me.

1. Convert to decimals

         -3/20 = -.15

         2- 9/20 = 49/20 = 2.45

2. Solve

     2.45 - (-.15)

     2.45 + .15 = 2.60

Answer:

1 1/8 cups of vanilla for a cup of milk.

Step-by-step explanation:

v-3/8  m-1/3

v-6/8  m-2/3

v-1 1/8 m-1

Answer:

a>=-5

Step-by-step explanation:

when a+5>/=0

a>/=-5 because the if the contents of the absolute value are equal to the same expression in the absolute value if the expression is non negative. So we find the values of a when the expression is nonnegative.

Answer:

*** "and" means multiply

2/9

Step-by-step explanation:

*** "and" means multiply

spinning a vowel is 1/3

not spinning a 1 is 2/3

1/3 times 2/3 is 2/9

Answer:

$4.5

Step-by-step explanation:

Hot dogs=h

Cheese burgers=c

2h+3c=20

2h+5c=29

There are two ways to solve-

1. Elimination- multiply the bottom by -1.

2h+3c=20

-2h-5c=-29

-2c=-9

c=4.5

2. Just move 2h, and you get 2c=9, 4.5

Answer:

Step-by-step explanation:

The maximum is achieved at vertex of parabola.

The x- coordinate of the vertex is determined by x = - b/(2a).

The maximum height is the corresponding y- coordinate

Find vertex

x coordinate

Y coordinate (Max height)

Answer:

Less Likely

Step-by-step explanation:

A 2/7 probability means that it will happen less than half the time.

The eliminates equally likely, more likely, and certain as those are 50% or greater.

The probability is also greater than 0%, so it's not "impossible"

Therefore, the answer must be B, Less Likely.

It happens less than half the time, but can at times happen.

Hope this helps!

The solution is, Less Likely, best describe the likelihood of this event.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

here, we have,

given that,

An event has a probability of 2/7.

now, we get,

A 2/7 probability means that it will happen less than half the time.

The eliminates equally likely, more likely, and certain as those are 50% or greater.

The probability is also greater than 0%, so it's not "impossible"

It happens less than half the time, but can at times happen.

Therefore, the answer must be B, Less Likely.

To learn more on probability click:

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Answer:

95,013

Step-by-step explanation:

If you use the formula A=L*W You multiply the width, 24 3/4, by how long it is, 39, 1/2. And you should get a rounded answer of 95,013!

Answer:

Step-by-step explanation:

Hi!

To find the inverse, first we express your function as:

y = 3x - 8

Then, we interchange x and y variables:

x = 3y - 8

From there, we isolate y:

x + 8 = 3y

x/3 + 8/3 = y

Then, the inverse, g(x) = (x+8)/3.

We can check this by getting g(f(x)):

(f(x) + 8)/3 = (3x - 8 + 8)/3 = 3x /3 = x.

This is correct by the definition of the inverse function.

You can also think about the inverse as a "reverse function", so for example, in f(x) = 3x-8, x is multiplied by 3, then 8 is subtracted from it.

If we are to go from f(x) to x, we first add 8 (to reverse the subtraction), then divide by 3 (to reverse the multiplication).

This means g(y) = (y+8)/3, the same answer.

Hope this helps!

Answer:

70 degrees

Step-by-step explanation:

rectange angle total = 360

1 corner = 90

90-20 = 70

b is a answer

Step-by-step explanation:

formula

=a+b/2×h

Answer: 126 mm^2.

Step-by-step explanation: When finding the area of a trapezoid, you need to add two bases, multiply the height, and divide it all in half.  The steps are done below:

Have a great day! :)

Answer:

The answer is

→ 18:32

Step-by-step explanation:

The total number of students in the class is 32 students. 3 boys and 5 girls. But wait! Were not done yet.

Boys:

3 x 4 = 12

or

3 + 3 + 3 + 3 = 12

Girls:

4 + 4 + 4 + 4 + 4 = 20

or

4 x 5 = 20

20 + 12 = 32

Hope this helped! :^)

- ✨7272033Alt✨

Answer:

Variables

Let m = number of movies rented

Let g = number of video games rented

Given:

System of equations

m + g = 5

2m + 3g = 13

Solution

Rewrite  m + g = 5  to make m the subject:

⇒ m = 5 - g

Substitute this equation into  2m + 3g = 13 and solve for g:

⇒ 2(5 - g) + 3g = 13

⇒ 10 - 2g + 3g = 13

⇒ 10 + g = 13

⇒ g = 3

Substitute found value of g into  m = 5 - g  and solve for m:

⇒ m = 5 - 3

⇒ m = 2

Therefore, 2 movies and 3 video games were rented.

Answer:

A. 5.0 * 10⁻⁹ J

Step-by-step explanation:

Q is charge.

ΔV is electric potential energy.

All we have to do is plug both values in.

PE = (1/2)(1.0 * 10⁻¹⁰)(100) = (1/2)(1.0* 10⁻⁸) = 5.0 * 10⁻⁹ J

Answer:

A.

Step-by-step explanation:

Plug the values in and there is your answer.

I hope it helps! Have a great day!

Anygays-

Answer:

5280 ft/1 mi, 1848 ft

Step-by-step explanation:

Whatever unit is given on the top (miles), you will write it on the bottom of the second fraction. Since we are solving for length in feet, we know that the numerator will be in feet. The only answer choice that has this option is 5280 ft/ 1 mi. You can check this math by taking 0.35 of 5280 feet, or 1 mile = 1848 ft.

[tex]\frac{0.35 mi}{1} *\frac{?ft}{?mi}[/tex]

[tex]\frac{0.35 mi}{1} *\frac{5280 ft}{1mi}[/tex]        (miles cancels out, left with feet)

[tex]\frac{1848ft}{1}[/tex]

1848 feet

I hope this helps!

Answer:

0.29

Step-by-step explanation:

greatest numberrr

Answer:  Choice C

The fraction 1/16

In other words the "StartFraction 1 Over 16 EndFraction"

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Work Shown:

[tex]\displaystyle L = \lim_{x \to -2}4^x\cos(\pi x)\\\\\\L = 4^{-2}\cos(\pi (-2))\\\\\\L = \frac{1}{4^2}\cos(-2\pi)\\\\\\L = \frac{1}{16}\cos(2\pi)\\\\\\L = \frac{1}{16}(1)\\\\\\L = \frac{1}{16}\\\\\\[/tex]

The limit of the function f(x)=[tex]4^{x}[/tex]cos(πx) is 1/16 which is start fraction 1 over 16 end fraction.

The limit is the extent to which the value of function exists.

The function which is given is f(x)=[tex]4^{x}[/tex]cos(πx) and we have to find the limit of f(x).

L.H.L of f(x)

[tex]\lim_{x \to \-2} 4^{x}cos([/tex]πx)

Put x=-2-h

[tex]\lim_{h \to \0} 4^{-2-h}cos([/tex]π(-2-h)

put h=0

=[tex]4^{-2} cos(2[/tex]π)

=[tex]4^{-2}*1[/tex]  {cos(2π)=1}

=1/16

R.H.L of f(x)

[tex]\lim_{x \to \-2} 4^{x}[/tex] cos(πx)

Put the value of x=-2+h

=[tex]\lim_{h \to \0}4^{-2+h}[/tex] cos{π(-2+h)}

Put the value of h=0

=[tex]4^{-2}*cos(2[/tex]π)

=1/16

L.H.L=R.H.L

Hence the limit of the function [tex]4^{x}cos([/tex]πx) is 1/16.

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Answer:

4x+8 =5

Step-by-step explanation:

sum = +

times = Multiply

is = =

4*x +8 = 5

Answer:

4x+8=5

Step-by-step explanation:

Let's assume the number is x

Four times x plus 8 is 5

4x+8=5

***Optional

If you need to solve it...

4x+8=5

4x=-3

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

Hope this helps! :D

Answer:

yes ur on track

Step-by-step explanation: