A nest of ants has been growing exponentially in such a way that its population, P, as a function of w weeks is given by P(w)=24, 000(1.063)^w


Matthew claims that the population of ants is growing at a rate of 0.9% per day. Explain why Matthew’s claim is too high of a rate.

Answer:

The first 5 terms of the sequence are 2, 4, 8, 16 and 32.

Step-by-step explanation:

Given:

[tex]a_{1}[/tex] = 2

[tex]a_{n}[/tex] = 2[tex]a_{n-1}[/tex]   -----------------(i)

To get the first 5 terms of the sequence, substitute in turn, n = 1, 2, 3, 4, 5 into equation (i).

The first term (when n = 1) has been given as:

[tex]a_{1}[/tex] = 2

The second term (when n = 2) is given as:

[tex]a_{2}[/tex] = 2[tex]a_{2-1}[/tex]

[tex]a_{2}[/tex] = 2[tex]a_{1}[/tex]    (but [tex]a_{1}[/tex] = 2 )

=> [tex]a_{2}[/tex] = 2(2)

=> [tex]a_{2}[/tex] = 4

The third term (when n = 3) is given as:

[tex]a_{3}[/tex] = 2[tex]a_{3-1}[/tex]

[tex]a_{3}[/tex] = 2[tex]a_{2}[/tex]    (but [tex]a_{2}[/tex] = 4 )

=> [tex]a_{3}[/tex] = 2(4)

=> [tex]a_{3}[/tex] = 8

The fourth term (when n = 4) is given as:

[tex]a_{4}[/tex] = 2[tex]a_{4-1}[/tex]

[tex]a_{4}[/tex] = 2[tex]a_{3}[/tex]   (but [tex]a_{3}[/tex] = 8 )

=> [tex]a_{4}[/tex] = 2(8)

=> [tex]a_{4}[/tex] = 16

The fifth term (when n = 5) is given as:

[tex]a_{5}[/tex] = 2[tex]a_{5-1}[/tex]

[tex]a_{5}[/tex] = 2[tex]a_{4}[/tex]   (but [tex]a_{4}[/tex] = 16 )

=> [tex]a_{5}[/tex] = 2(16)

=> [tex]a_{5}[/tex] = 32

Therefore, the first 5 terms of the sequence are 2, 4, 8, 16 and 32.

Answer:

$16.32

Step-by-step explanation:

First you need to find how much each thing is going to cost.

So for 32 glue sticks, it will cost $44.80 because you multiply 32 by 1.40.

Next you need to find the cost of thebox of crayons, which is $18.88 because you multiply 32 by 0.59.

Then you add those two totals together and you get 63.68.

Lastly you subtract that from 80 to see how much money Ms. Blankenship has  leftover which is $16.32.

Hope this helps. :)

Answer:

[tex]\sqrt{17.3}[/tex] = 4.159.....  so approx 4.2

Step-by-step explanation:

Answer:

Personal observation.

Step-by-step explanation:

Worthy of note is to say that, it's is practically impossible to have a line of different people retell what they heard, saw or experienced in the same way. Because of the fact that human being differs, there's always a difference in the retelling of the story eventually. Everyone seems to retell the story in a manner they can relate to, in a manner of what they understand, and that's given rise to unreliability in personal observation. Not that they're wrong, nor that one is right than the other, but that they're just not reliable.

Answer:

1/1 or 1

Step-by-step explanation:

Answer:

1 or 1/1

Step-by-step explanation:

Answer:

perimeter = 18.81 units

area = 15 unit²

Answer:

x = 10

Step-by-step explanation:

x = 10

Answer:

The 80 p0und bag will last 128 days.

Step-by-step explanation:

In order to find out how much days the 80 pound bag last we have to divide the 80 pounds by the among that the dog eats each day. And so we get.....

80 / [tex]\frac{5}{8}[/tex] = [tex]\frac{80}{1} / \frac{5}{8}[/tex] = [tex](\frac{80}{1})(\frac{8}{5})[/tex] = [tex]\frac{640}{5}[/tex] = 128

Answer:

For some reason my answer got deleted.

The dog food will last 128 days,

Step-by-step explanation:

80 ÷ 5/8 = 128

Since 5/8 is being used each day, you divide.

I hope this helped and if it did I would appreciate it if you marked me Brainliest. Thank you and have a nice day!

Answer:

it's just asking you to rearrange it into y=mx+c form

2y=2x-2

y=x-1

x+y=9

y = -x+9

Answer:

85.1 g

Step-by-step explanation:

Boris has 91.5 g of pepper

He used 0.4g to make one plate of scrambled egg

If she made 16 plates of scrambled egg then the amount of pepper that will be left can be calculated as follows

= 0.4×16

= 6.4g

= 91.5g - 6.4g

= 85.1g

Hence Boris will have 85.1g of pepper left

Answer:

x = 9

Step-by-step explanation:

2x + 8 = 4x - 10 Given

2x + 8 - 2x = 4x - 10 - 2x Subtraction property of equality

8 = 2x - 10

8 + 10 = 2x - 10 + 10 Addition property of equality

18 = 2x

18 ÷ 2 = 2x ÷ 2 Division property of equality

9 = x Answer

I hope this helped and if it did I would appreciate it if you marked me Brainliest. Thank you and have a nice day!

Solution  of the given equation 2x+8=4x-10 is x=9.

Solution of an equation are the values to the unknown variables that makes the equality in the equation true

Given equation is :

2x+8=4x-10,   consider it as equation (1)

To solve this equation firstly, we isolate the terms which contain x in the LHS and the constant terms in RHS.

Then, the equation will become:

2x-4x = -10-8

Solving the LHS and RHS:

-2x = -18

Divide both the sides by -2, we get:

x = -18/(-2)

x = 9

That means x=9 satisfies the given equation.

Hence, x=9 is the solution of the given equation.

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Answer:

. Negative infinity

. Negative infinity

Answer: D, 1000 m^3.

Step-by-step explanation: We can find the volume by breaking down the surface area.

The formula for the surface area of a cube is 6*x^2 with x being the side length and 6 being the number of sides. Thus we can form the equation as follows:

600 = 6*x^2 - original equation

x^2 = 100 - divide both sides by 6

x = 10 - square root both sides

Thus, the side length is 10.

We can find the volume with the formula l*w*h or, in this case, x^3.

We know that x = 10, so x^3 must be 1000.

Thus, the answer is D, 1000 m^3.

Answer:

give the other guy brainliest please

Step-by-step explanation:

and yes it is 1000

Answer:

15ft

Step-by-step explanation:

Calculation for how tall is the tree

First step Let the proportion be x/10ft = 6ft /4ft

Second step is to cross-multiply by 4x

4x =10ft*6ft

4x = 60

Third step is to divide both sides by 4

4x = 60

4x/4=60/4

x=15 ft

Therefore the tree will be 15ft tall

1. 7.2 x 100 =  720

2. 468.8 ÷ 100 =  4.688

3. 0.12 x 1,000 =  120

4. 86.4 ÷ 100 =  0.864

5. 2.001 x 10 =  20.01

6. 1,200 ÷ 1,000 =  1.2

7. 3.41 x 100 =  341

8. 3.41 ÷ 10 =  0.341

9. 0.0031 x 100 =  0.31

10. 5.7 ÷ 100 =  0.057

11. 1.34 x 1,000 =  1340

12. 10 x 0.57 =  5.7

13. 57 ÷ 100 =  0.57

14. 1.068 x 100 =  106.8

15. 168.1 ÷ 10 =  16.81

16. 0.0341 x 100 = 3.41

Answer:

[tex]\huge\boxed{-8+8i}[/tex]

Step-by-step explanation:

[tex]2(-36-3i)+(5+2i)(12-2i)\\\\\text{use the distributive property and FOIL}\\\\=(2)(-36)+(2)(-3i)+(5)(12)+(5)(-2i)+(2i)(12)+(2i)(-2i)\\\\=-72-6i+60-10i+24i-4i^2\\\\i=\sqrt{-1}\to i^2=-1\\\\=-72-6i+60-10i+24i-4(-1)=-72-6i+60-10i+24i+4\\\\=(-72+60+4)+(-6-10+24)=-8+8i[/tex]

The expression in the form of a + ib is

-88 + 8i

where a = -88 and b = 8.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

2(-36 - 3i) + (5 + 2i)(12 - 2i)

Remove the parenthesis.

-72 - 6i + 60 - 10i + 24i + 4

Add like terms.

-88 + 8i

This is in the form of (a + ib).

Where a = -88 and b = 8

Thus,

-88 + 8i is our final expression.

Learn more about expressions here:

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Answer:

welp umm no one can answer lol

Step-by-step explanation:

Answer:

[tex]\frac{2}{3} * 12.33=8.22[/tex]

Step-by-step explanation:

Given

Two-thirds times 12.33

Required

Solve

Two-thirds means [tex]\frac{2}{3}[/tex]

Mathematically, Two-thirds times 12.33  implies

[tex]\frac{2}{3} * 12.33[/tex]

Solving further

[tex]\frac{2 * 12.33}{3}[/tex]

[tex]\frac{24.66}{3}[/tex]

[tex]8.22[/tex]

Hence:

[tex]\frac{2}{3} * 12.33=8.22[/tex]

Answer:

8.22 is your right answer! The person above me has it down cold! You should mark him brainliest! :)

Step-by-step explanation:

Answer:

29

Step-by-step explanation:

7 1/4 + 9 3/4 = 17

6 1/4 + 5 1/2 = 12

17 + 12 = 29

Answer:

She drank 28,75 liters.

Answer:

Step-by-step explanation:

It expresses that one value will be lesser than the other.

The term 'less than' symbolically represented as '<'.

We can implement certain operations like comparing values, heights, and numbers.

For example, there are 3 pencils in one bag A, and 8 pencils in bag B.

When we compare the two, we can easily observe that bag A has fewer pencils than bag B.

Thus,

Pencils in Bag A       <         Pencils in Bag A

           3                     <                    8

Answer:

k = +10 or -10

Step-by-step explanation:

It's given in the question that the roots of the eqn. are real and equal. So , the discriminant of the eqn. should be equal to 0.

[tex] = > {b}^{2} - 4ac = 0[/tex]

[tex] = > {( - 2k)}^{2} - 4 \times 5 \times 20 = 0[/tex]

[tex] = > 4 {k}^{2} - 400 = 0[/tex]

[tex] = > 4( {k}^{2} - 100) = 0[/tex]

[tex] = > {k}^{2} - 100 = 0[/tex]

[tex] = > k = \sqrt{100} = + 10 \: or \: - 10[/tex]

Step-by-step explanation:

Given Equation

5x-2kx+20=0

[tex]\boxed{\sf \longrightarrow D=0 }[/tex]

[tex]\\\qquad\quad\displaystyle\sf {:}\longrightarrow b^2-4ac=0 [/tex]

[tex]\\\qquad\quad\displaystyle\sf {:}\longrightarrow (-2k)^2-4\times 5\times 20=0 [/tex]

[tex]\\\qquad\quad\displaystyle\sf {:}\longrightarrow 4k^2-20\times 20=0 [/tex]

[tex]\\\qquad\quad\displaystyle\sf {:}\longrightarrow 4k^2-400=0[/tex]

[tex]\\\qquad\quad\displaystyle\sf {:}\longrightarrow 4k^2=400 [/tex]

[tex]\\\qquad\quad\displaystyle\sf {:}\longrightarrow k^2=\dfrac {400}{4}[/tex]

[tex]\\\qquad\quad\displaystyle\sf {:}\longrightarrow k^2=100 [/tex]

[tex]\\\qquad\quad\displaystyle\sf {:}\longrightarrow k=\sqrt{100}[/tex]

[tex]\\\qquad\quad\displaystyle\sf {:}\longrightarrow k=10 [/tex]

[tex]\therefore\sf k=10 [/tex]

Answer:

1, -2

Step-by-step explanation:

The x axis is 1 to the right, and the y axis is 2 down.

Răspuns:

318 de participanți

Explicație pas cu pas:

Dat fiind:

Număr în parc = 106

Numărul din parc reprezintă 1/3 din numărul elevilor care participă la activitatea de curățenie.

Pentru a obține numărul total de studenți care participă la activitate; fie numărul total = x

Prin urmare;

1/3 din x = 106

x / 3 = 106

Înmulțiți ambele părți cu 3

x = 318

Prin urmare, numărul total de studenți implicați în activitatea de curățenie = 318 stuaen

Answer:

1/3

Step-by-step explanation:

To make it shorter.

Answer:

6.25 or 6 1/4

Step-by-step explanation:

Jodie sold 6.25 candy altogether.

A fraction is defined as a numerical representation of a part of a whole that represents a rational number.

Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.

The operator that perform the arithmetic operations are called arithmetic operators.

Operators which let do basic mathematical calculation

+ Addition operation : Adds values on either side of the operator.

For example 4 + 2 = 6

- Subtraction operation : Subtracts right hand operand from left hand operand.

For example 4 -2 = 2

* Multiplication operation : Multiplies values on either side of the operator

For example 4*2 = 8

Given that

Jodie sells 2½ pounds of gumdrops,

3 pounds of orange slices, and ¾ pounds of gummi bears.

Convert the fractions into decimals

Number of pounds of gumdrops = 2½ = 5/2 = 2.5

Number of pounds of gummi bears = ¾ = 0.75

So the total amount of candy Jodie sold :

⇒ 2.5 + 3 + 0.75

⇒ 6.25

Hence, Jodie sold 6.25 candy altogether.

Learn more about the fraction here:

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Answer:

64 child tickets

Step-by-step explanation:

Let's set this up a system of equations. Number child tickets is c and adults are a.

5.1c+8.8a=1144.8

c+a=157

We can now solve by elimination. Let's multiply the second equation by -8.8 so that we are left with the child tickets.

-8.8c-8.8a= -1,381.6

We combine the two equations.

-3.7c=-236.8

Divide both sides by -3.7

c=64

Have a wonderful day! :D

Answer:

x=3

y=8

Step-by-step explanation:

the given equations are y=3x-1 --------(1)

and y=2x+2---------(2)

Using substitution method,

and solving y=3x-1

y+1=3x

or y+1/3 =x ------(3)

Putting the value of x= y + 1 / 3 in equation 2

y= 2x+2

or, y = 2 ( y + 1/3) +2

or, y= 2y + 2 / 3 +2

or, y = 2y + 2 + 6 // 3 ( Taking LCM)

Or, 3 y = 2y + 2 + 6 ( the denominator gets multiplied to y)

OR, 3 Y - 2Y =6 PLUS 2

or y = 8

therefore, y=8

now substituting the value of y=8 in equation (3)

y + 1 /3 = x

or ,,, 8 plus 1 by 3 =x

or,,,,, 9 by 3 =x

Therefore, x is 3