Write the equation of the line in slope-intercept form.
The equation of the line in slope-intercept form is ___

Answer:

See below ~

Step-by-step explanation:

⇒ t represents the years after 1992

⇒ So, in 1992, t = 0

⇒ Apply in the formula

⇒ n(0) = 89e^(0.02 × 0)

⇒ n(0) = 89e⁰

⇒ n(0) = 89,000,000

The rat population in 1992 was 89,000,000.

===========================================================

⇒ Number of years after 1992 : 2003 - 1992 = 11

⇒ Substitute for t in the formula

⇒ n(11) = 89e^(0.02 × 11)

⇒ n(11) = 89e^(0.22)

⇒ n(11) = 89 × 1.24607673

⇒ n(11) = 110,900,829 rats

The model predicts that in the year 2003 there will be a rat population of 110,900,829 rats.

Answer:

(a) 89,000,000 rats

(b) 110,900,829 rats

Explanation:

Given equation:

To find the initial population (1992):

insert t = 0

To find the rat population in 2003 (after 11 years):

insert t = 11

A 8 gram sample of a substance that's a by-product of fireworks has a k-value of 0.101. The half-life is 2.98 days.

Exponential decay obeys the equation

[tex]m(t) = m_0 e^{-kt}[/tex]

where t = time, days

Given:

Initial mass, m₀ = 8 g

Decay constant, k = 0.101

For half-life, the mass is m = m₀/2.

Therefore,

[tex]m(t) = m_0 e^{-kt}[/tex]

e^{-0.101t} = 1/2

-0.101t = ln 0.5

t = ln 0.5/-0.101

t = 2.98

Therefore, The half-life is 2.98 days.

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Answer:

1st mechanic:20hours

2ndmechanic:15hours

Step-by-step explanation:

1stmechanic:20hours=20x95

                                   =$1900

2nd mechanic:15hours=15x110

                                     =$1650

total=$1900+$1650

       =$3550

Answer:I think it would be 84 + 0.45m + 108.

Which simplified could be 0.45m + 192.

hope this helps!

Step-by-step explanation:

Any proper CDF [tex]F(x)[/tex] has the properties

• [tex]\displaystyle \lim_{x\to-\infty} F(x) = 0[/tex]

• [tex]\displaystyle \lim_{x\to+\infty} F(x) = 1[/tex]

so we have to have a = 0 and b = 1.

This follows from the definitions of PDFs and CDFs. The PDF must satisfy

[tex]\displaystyle \int_{-\infty}^\infty f(x) \, dx = 1[/tex]

and so

[tex]\displaystyle \lim_{x\to-\infty} F(x) = \int_{-\infty}^{-\infty} f(t) \, dt = 0 \implies a = 0[/tex]

[tex]\displaystyle \lim_{x\to+\infty} F(x) = \int_{-\infty}^\infty f(t) \, dt = 1 \implies b = 1[/tex]

Answer:

4 pints

Step-by-step explanation:

Therefore each can would contain 8/2 =  4 pints

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Please feel free to comment, ask questions, give feedback, or correct me if I am wrong!

Have a great day!

:)

Answer:

See below

Step-by-step explanation:

Interest   3%   in decimal form is  .03

  interest in ONE year    7000 * .03

         interest in SEVEN years   7000 * .07 * 7

           this is added to the original deposit of 7000

              to become   7000 + 7000 * .03 * 7

                                        or  7000 ( 1 + .03*7 )

                                              or   7000 ( 1.21 ) = $ 8470

IF the interest is compounded

   the money in the account will be    7000 ( 1+.03)^7  

I think it's 12 because here it comes out

Answer:

wait I will edit and answer it in a few minutes

The equation which shows the situation are 8g + 6h = 62 and 5g + 10h = 70.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

Given that:-

The equation made by the given situation is:-

For kyle, there are g students attending 8 classes sp total number of students will be 8g similarly for h students there are 6 classes so the total number of h students will be 6h. The total number of students for both g and h students attending kyle's class is 62. So the equation will be given as:-

8g   +  6h  =  62

Now for Lauren, there are g students attending 5 classes so the total number of students will be 5g similarly for h students there are 10 classes so the total number of h students will be 10h. The total number of students for both g and h students attending Lauren's class is 70. So the equation will be given as:-

5g  +  10h  =  70

Therefore the equation which shows the situation are 8g + 6h = 62 and 5g + 10h = 70.

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Answer:

3-x is the inverse of f(x)=x-3

Answer:

a

x

2

+

b

x

+

c

=

0

the two roots of the equation take the form

x

1

,

2

=

−

b

±

√

b

2

−

4

a

c

2

a

So, start by adding

−

5

to both sides of the equation to get

2

x

2

+

x

−

5

=

5

−

5

2

x

2

+

x

−

5

=

0

Notice that you have

a

=

2

,

b

=

1

, and

c

=

−

5

. This means that the two solutions will be

x

1

,

2

=

−

1

±

√

1

2

−

4

⋅

2

⋅

(

−

5

)

2

⋅

2

x

1

,

2

=

−

1

±

√

41

4

You can simplify this if you want to get

x

1

=

−

1

+

√

41

4

≅

1.35078

and

x

2

=

−

1

−

√

41

4

≅

−

1.85078

Answer:

(2x-2)=

     +2 =+2

(2x)=2

----------

    2

x= 1

-----------------------------------------------

(x+5)=

   -5=-5

x= -5

Step-by-step explanation:

You just need to separate the variable from the numbers

Answer: $7.40

Step-by-step explanation:

You can use $177.60 divide by 24 boxed lunches equals $7.40
Since you have to distribute 177.60 in 24 boxes.

A parallelogram is a quadrilateral with four sides and the opposite sides of the parallelogram are equal and parallel.

In the given figure, AB||DC. AD is the transversal, such that:

∠A + ∠D = 180-degrees.

The parallelogram is a quadrilateral with equal such that the interior angles present on the same side of the transversal are supplementary. The sum of supplementary angles is equal to 180-degrees.

From the theorem of same-side interior angles, the supplementary angles present on the parallel lines must be intersected by a transversal.

From the property of transversal, the interior angles on the same side of the transversal are supplementary. Therefore, ∠A and ∠D are supplementary and their sum is equivalent to 180-degrees.

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Answer:

C)

Step-by-step explanation:

f(x)=[tex]8x^{2} -16x-15[/tex]
[tex]8x^{2} -16x-15=0[/tex]
[tex]x=\frac{-b+-\sqrt{b^{2}-4ac } }{2a}[/tex]  ,  a=8, b= - 16, c= - 15

[tex]x=\frac{-(-16)+-\sqrt{(-16)^2-4*8*(-15)} }{2*8} = \frac{16+-\sqrt{736} }{16} =\frac{16+-4\sqrt{46} }{16} = 1 +- \frac{\sqrt{46} }{4} = 1+- \frac{\sqrt{23} \sqrt{2}}{2\sqrt{2} \sqrt{2} } =1+-\frac{\sqrt{23} }{2\sqrt{2} } = 1+-\frac{\sqrt{23} }{\sqrt{8} }[/tex]

Answer: Heyaa!~

                  - Write 63 as the product of prime factors -

              - Write the prime factors in ascending order -

         -   what's the highest common factor of 63 and 105   -

             Hopefully this helps you! ^^^

The probability that the student was NOT a female that got a "C" is 15 / 32.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability that the student was NOT a female that got a "C" = number of males that got a C / total number of people that got a C =  15 / 32.

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To solve the theorem, we will  take the square of the longest side of a right triangle and equate to the sum of the squares of the other two sides

Pythagoras theorem states that the square of the longest side of a right triangle is equal to the sum of the squares of the other two sides

For instance, let;

According to the theorem above, mathematically;

c² = a² + b²

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Answer:

angle M

Step-by-step explanation:

if you are using side angle side the two sides may be

line LK and NK

and angle M

The study benefit from adding a control group as it would help in the correlation

A control group is s used to establish a cause-and-effect relationship by isolating the effect of an independent variable.

The best way to randomly place the bulls into the Therapy A, Therapy B, and control groups is random testing. The best blocking method will be breeding.

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Answer:

the width is 59

Step-by-step explanation:

302/2-92=59

Answer:

A

Step-by-step explanation:

tan60=opp/adj

tan60=15/x

15tan60=x

25.98=x (when you calculate 15 root 3 it is the same number)

Answer:

A

Step-by-step explanation:

Inflation decreases the amount of goods and services that can be purchased with a dollar.

Answer:

Hi! I think you are referring to the Pythagorean Theorem.

Essentially, given a right triangle, the sum of the squares of the shorter sides equals the square of the longer (slant) side or hypotenuse.

The formula is a squared + b squared = c squared

If the triangle has side lengths 3 and 4 (for the shorter sides), the longer side can be solved like this:

3 squared + 4 squared = x squared

(Let x =  the longer side)

3 squared = 9

4 squared = 16

9+16 = x squared

25 = x squared

x =  5

So there you go, that's the Pythagorean theorem.

Let me know if this helped!

Answer:

a theorem attributed to Pythagoras that the square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.

Step-by-step explanation:

A function assigns the values. The graph of the function f(x) and g(x) can be plotted as shown in the below image.

A function assigns the value of each element of one set to the other specific element of another set.

The graph of the function f(x) and g(x) can be plotted as shown in the below image.

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Answer:

55/16 cups or 3.4375 cups

Step-by-step explanation:

there are 5 dozens (12) in 60, so there are 2.5 2 dozens in 60, so you would multiply 1 3/8 by 2.5 to find how many cups are needed in 60 cupcakes because 1 3/8 cups is for 2 dozen cupcakes

[tex]~~~~~~2I_2 - A\\\\\\=2\begin{bmatrix}1&0\\0&1 \end{bmatrix}-\begin{bmatrix}4&2\\3&-3 \end{bmatrix}\\\\\\=\begin{bmatrix}2&0\\0&2 \end{bmatrix}-\begin{bmatrix}4&2\\3&-3 \end{bmatrix}\\\\\\=\begin{bmatrix}2-4&0-2\\0-3&2+3 \end{bmatrix}\\\\\\=\begin{bmatrix}-2&-2\\-3&5 \end{bmatrix}[/tex]

Answer:

16x^6(3x^5)

48x^11

[tex] \textsf{\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let's solve ~

[tex]\qquad \sf  \dashrightarrow \:(2 {}^{ \frac{2}{x} } ) \sdot(2 {}^{ \frac{4}{x} } ) = 2 {}^{12} [/tex]

[tex]\qquad \sf  \dashrightarrow \:(2 {}^{ \frac{2}{x} + \frac{4}{x} } ) = 2 {}^{12} [/tex]

[tex]\qquad \sf  \dashrightarrow \:(2 {}^{ \frac{6}{x} } ) = 2 {}^{12} [/tex]

Now, since the base on both sides are equal, therefore their exponents are equal as well ~

[tex]\qquad \sf  \dashrightarrow \: \dfrac{6}{x} = 12[/tex]

[tex]\qquad \sf  \dashrightarrow \:x = \dfrac{6}{12} [/tex]

[tex]\qquad \sf  \dashrightarrow \:x = \dfrac{1}{2} [/tex]

or

[tex]\qquad \sf  \dashrightarrow \:x = 0.5[/tex]

Hope you got the required Answer ~