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boyakko [2]
3 years ago
8

A population of beetles is modeled by the equation b(t) = 3,000 (2)t where t represents the number of weeks since the population

was first measured?
Mathematics
1 answer:
Liula [17]3 years ago
8 0

Answer:

See Explanation

Step-by-step explanation:

Given

b(t) = 3000 * 2^t

The question is incomplete;

A possible question could be to calculate the initial amount of beetle

An exponential function is represented as:

f(x) = ab^x

Where

a \to Initial\ amount

By comparison:

a = 3000 --- The initial number of beetles

Another question could be to solve for f(t), after a certain number of weeks (say 3)

Substitute 3 for t in: b(t) = 3000 * 2^t

b(3) = 3000 * 2^3

b(3) = 3000 * 8

b(3) = 24000

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Find an explicit rule for the nth term of the sequence.The second and fifth terms of a geometric sequence are 18 and 144, respec
vova2212 [387]

Given:

second term = 18

fifth term = 144

The nth term of a geometric sequence is:

\begin{gathered} a_n\text{ = ar}^{n-1} \\ Where\text{ a is the first term} \\ r\text{ is the common ratio} \end{gathered}

Hence, we have:

\begin{gathered} \text{ar}^{2-1}\text{ = 18} \\ ar\text{ = 18} \\  \\ ar^{5-1}=\text{ 144} \\ ar^4\text{ =144} \end{gathered}

Divide the expression for the fifth term by the expression for the second term:

\begin{gathered} \frac{ar^4}{ar}\text{ = }\frac{144}{18} \\ r^3\text{ = }\frac{144}{18} \\ r\text{ = 2} \end{gathered}

Substituting the value of r into any of the expression:

\begin{gathered} ar\text{ =  18} \\ a\text{ }\times\text{ 2 =  18} \\ Divide\text{ both sides by 2} \\ \frac{2a}{2}\text{ =}\frac{18}{2} \\ a\text{ = 9} \end{gathered}

Hence, the explicit rule for the sequence is:

a_n\text{ = 9\lparen2\rparen}^{n-1}

5 0
1 year ago
64% of 25 students in the class have a phone. How many students have a phone?​
Damm [24]

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Step-by-step explanation: looked it up on Google

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HURRY PLEASE!! I’ll mark you as brainliest!!<br><br> Solve the system: 3x + y = 10 and -4x - 2y = 2
BaLLatris [955]

Answer:

uld you like to ask?

10th

Maths

Pair of Linear Equations in Two Variables

Algebraic Solution of a Pair of Linear Equations

Solve: 3x + 4y = 10,2x - 2y...

MATHS

Asked on December 27, 2019 byShweta Rudravaram

Solve: 3x+4y=10,2x−2y=2 by the method of elimination.

EASY

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Study later

ANSWER

3x+4y=10 …………..(1)

2x−2y=2 (or) x−y=1 …………(2)

(1) ⇒(3x+4y=10)1

(2) ⇒(x−y=1)3

                     _____________________

                                3x+4y=10

                                3x−3y=3

                      _____________________

                                    7y=7

∴y=1

Put y=1 in (1) we get 3x+4×1=10

3x=10−4=6

∴x=36=2

Hence x=2,y=1.

7 0
3 years ago
Solve 2|3x-4|+4=12 show your work
slamgirl [31]

Answer:

0.6

Step-by-step explanation:

2×3x+4+4=12

6X+8=12

6x=12-8

6x=4

Divide by 6

X=0.6

5 0
3 years ago
Plz help asap......................................
ziro4ka [17]

Option B:

Law of cosine, two sides and the included angle are known.

Solution:

Let us first know the law of cosines and law of sines.

Law of cosine:

If we know the sides a, b and the included angle θ, then we can find the third side c. This is known as the law of cosine.

c^2=a^2+b^2-2abcos\theta

Law of sine:

The sides of a triangle are to one another  in the same ratio as the sines of their opposite angles.

$\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}

Given ∠P and the sides r, q are known.

<u>To find the value of p:</u>

Option A: Law of cosines, all sides are known.

It is false by the above definition of law of cosine.

Option B: Law of cosine, two sides and the included angle are known.

It is true by the above definition of law of cosine.

Option C: Law of sines, all sides are known.

It is false, because one angle is given in question.

Option D: Law of sines, two angles and the included side are known.

It is false, because two angles are not given.

Option B is the correct answer.

Hence the answer is "Law of cosine, two sides and the included angle are known".

7 0
3 years ago
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