The initial population of a town is 3500, and it grows with a doubling time of 10 years. What will the population be in 8 years?

Answer:

y = -2x + 1

Step-by-step explanation:

Substitute  the slope and the given point into y = mx + b and solve for "b".

y = mx + b

7 = -2(-3) + b

7 = 6 + b

1 = b       the y-intercept is 1

The equation of the line is y = -2x + 1

Answer:

C. 9x=18

Step-by-step explanation:

3x+2(3x)=18

3x+6x=18

9x=18

Using the logarithmic function, it is found that:

a) The initial score is of 92.

b) After 6 months, the score is of 88.6.

c) After 18 months, the score is of 86.9.

The average score after t months is modeled by:

[tex]f(t) = 92 - 4\log{(t + 1)}[/tex]

Item a:

The initial score is of f(0), hence:

[tex]f(0) = 92 - 4\log{1} = 92 - 0 = 92[/tex]

The initial score is of 92.

Item b:

After 6 months, the score is of f(6), hence:

[tex]f(6) = 92 - 4\log{7} = 88.6[/tex]

After 6 months, the score is of 88.6.

Item c:

After 18 months, the score is of f(18), hence:

[tex]f(6) = 92 - 4\log{19} = 86.9[/tex]

After 18 months, the score is of 86.9.

A similar problem is given at https://brainly.com/question/24286043

Answer:

y=2x-2

You use rise/run in this problem

A projectile is an object launched into space, and moving under the influence of gravity and momentum. The stone here is an example. Thus, the time taken for the stone to reach the ground is 10 seconds.

On launching of the stone into space, it behaves as a projectile. Thus moving under the influence of gravity and its momentum. Its momentum is the product of its mass and velocity.

The height h, is given as:

h = 16[tex]t^{2}[/tex] + 32t + 240

Differentiating the expression with respect to t, we have;

32t + 32 = 0

t = -1 seconds

Substitute the value of time, t, in the equation for the height;

h = 16 - 32 + 240

  = 224

h = 224 m

Total height, S = 240 + 224

                         = 464

S = 464 m

The total height covered by the stone is 464 m.

From the second equation of free fall,

S = Ut + [tex]\frac{1}{2}[/tex]g[tex]t^{2}[/tex]

S = [tex]\frac{1}{2}[/tex]g[tex]t^{2}[/tex]

464 = [tex]\frac{1}{2}[/tex]*9.8*[tex]t^{2}[/tex]

[tex]t^{2}[/tex] = [tex]\frac{928}{9.8}[/tex]

  = 94.694

t = [tex]\sqrt{94.694}[/tex]

 = 9.7311

t ≅ 10 seconds

The time taken for the stone to hit the ground is 10 seconds.

Thus option A is the required answer.

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Answer:

The traditional scale consists of two plates or bowls suspended at equal distances from a fulcrum. One plate holds an object of unknown mass (or weight), while known masses are added to the other plate until static equilibrium is achieved and the plates level off, which happens when the masses on the two plates are equal. The perfect scale rests at neutral. A

Answer:

240oz.

Step-by-step explanation:

15oz=1batch

She needs 16 batches.

15oz. x 16batches = 240oz.

Hope this helps :)

Answer:

62

Step-by-step explanation:

SA=2(5x2)+2(5x3)+2(3x2)

SA=20+30+12

SA=62

[tex]\begin{array}{ccll} Juice&OJ\\ \cline{1-2} \frac{2}{3}&\frac{1}{3}\\[1em] x&1 \end{array}\implies \cfrac{~~ \frac{2}{3}~~}{x}=\cfrac{~~\frac{1}{3} ~~}{1}\implies \cfrac{~~ \frac{2}{3}~~}{x}=\cfrac{1}{3}\implies \cfrac{~~ \frac{2}{3}~~}{\frac{x}{1}}=\cfrac{1}{3} \\\\\\ \cfrac{2}{3x}=\cfrac{1}{3}\implies 6=3x\implies \cfrac{6}{3}=x\implies 2=x[/tex]

Answer:

Wouldn’t negative 9 be the inequality because its less than 2.25

Step-by-step explanation:

Hey budddy if i got this wrong im soooooo, sorry

Answer:

yes, the triangle are congruent by SAS

•ω• Hewo fren!

☆☆●◉✿ Answer:✿◉●☆☆

3•1 1/4•1.8= 6 3/4

☆☆●◉✿Step-by-step explanation:✿◉●☆☆

Let’s start of with 3•1 1/4~

3 times 1 and 1/4 is 3 3/4

Now let’s multiply 3 3/4 • 1.8

1.8 is also 1 8/10, simplified: 1 4/5.

3 3/4 • 1 4/5 = 6 3/4

THERE IS YOUR ANSWER! >o<

HOPE I HELPED!  ∧∧

→⇒brainliest please? ∑(OΔO )♥♥︎

Answer

1. ΔABC ≅ ΔEFG

2. ΔMKL ≅ ΔVKU

3. ΔMLN ≅ ΔNCD (With this one I couldn't fully read the letter in the middle. I couldn't tell if it was an N or a B so just swap it for the right letter. <3)

4. ΔFGH ≅ ΔRHQ

5. ΔUVL ≅ ΔMNL

6. ΔQRS ≅ ΔVUT

Step-by-step explanation:

hope this helps. . .<3

good luck! UwU

Step-by-step explanation:

use SOHCAHTOA as shown above in the picture

Answer:

QTR is 36

PTR is 62

Step-by-step explanation:

P+R+T=180

Answer:

x = 6

Step-by-step explanation:

Because we have parallel lines, we can use alternate angles are equal. Therefore, we know that 11x-6 = 10x.

Minus 11 from both sides, and we get -6 = -x, so x = 6

Answer:

Well, 30+23+23 = 76 which means there are only a total of 76 bags that are accounted for. 110-76 = 34 bags which we do not know if they have zips or not. If we assume they have zips, that would be 34+23 bags with zips which is 57 bags.

Answer:

7 and 9

Step-by-step explanation:

4/3÷1/6 = 4/3 × 6/1

= 8

So the value of p falls between the range of 7 and 9

Answer:

60

Step-by-step explanation:

1 dozen=12 eggs. 12 ×5=60

Answer:

60

Step-by-step explanation:

dozen=12

5x12=60

Answer:

  x = -2

Step-by-step explanation:

The expression f(x) = 1 corresponds to the point on the graph that is 1 unit above the x-axis. You can locate that horizontal line and see where it intersects the graph. That point of intersection  is 2 grid squares to the left of the y-axis, where x = -2.

  f(-2) = 1

  x = -2

Answer:

2 parks

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

There would be 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20

Answer: 125

Step-by-step explanation: ∠4 and 55 are supplementary angles. This means that ∠4 and 55 add up to 180. We can use this to solve for ∠4.

180 - 55 = ∠4

125 = ∠4

So, ∠4 is equal to 125 degrees.

Would appreciate brainly <3

Let

[tex]\displaystyle y(x) = \sum_{n=0}^\infty a_nx^n = a_0 + a_1x + a_2x^2 + \cdots[/tex]

Differentiating twice gives

[tex]\displaystyle y'(x) = \sum_{n=1}^\infty na_nx^{n-1} = \sum_{n=0}^\infty (n+1) a_{n+1} x^n = a_1 + 2a_2x + 3a_3x^2 + \cdots[/tex]

[tex]\displaystyle y''(x) = \sum_{n=2}^\infty n (n-1) a_nx^{n-2} = \sum_{n=0}^\infty (n+2) (n+1) a_{n+2} x^n[/tex]

When x = 0, we observe that y(0) = a₀ and y'(0) = a₁ can act as initial conditions.

Substitute these into the given differential equation:

[tex]\displaystyle \sum_{n=0}^\infty (n+2)(n+1) a_{n+2} x^n - \sum_{n=0}^\infty a_nx^n = 0[/tex]

[tex]\displaystyle \sum_{n=0}^\infty \bigg((n+2)(n+1) a_{n+2} - a_n\bigg) x^n = 0[/tex]

Then the coefficients in the power series solution are governed by the recurrence relation,

[tex]\begin{cases}a_0 = y(0) \\ a_1 = y'(0) \\\\ a_{n+2} = \dfrac{a_n}{(n+2)(n+1)} & \text{for }n\ge0\end{cases}[/tex]

Since the n-th coefficient depends on the (n - 2)-th coefficient, we split n into two cases.

• If n is even, then n = 2k for some integer k ≥ 0. Then

[tex]k=0 \implies n=0 \implies a_0 = a_0[/tex]

[tex]k=1 \implies n=2 \implies a_2 = \dfrac{a_0}{2\cdot1}[/tex]

[tex]k=2 \implies n=4 \implies a_4 = \dfrac{a_2}{4\cdot3} = \dfrac{a_0}{4\cdot3\cdot2\cdot1}[/tex]

[tex]k=3 \implies n=6 \implies a_6 = \dfrac{a_4}{6\cdot5} = \dfrac{a_0}{6\cdot5\cdot4\cdot3\cdot2\cdot1}[/tex]

It should be easy enough to see that

[tex]a_{n=2k} = \dfrac{a_0}{(2k)!}[/tex]

• If n is odd, then n = 2k + 1 for some k ≥ 0. Then

[tex]k = 0 \implies n=1 \implies a_1 = a_1[/tex]

[tex]k = 1 \implies n=3 \implies a_3 = \dfrac{a_1}{3\cdot2}[/tex]

[tex]k = 2 \implies n=5 \implies a_5 = \dfrac{a_3}{5\cdot4} = \dfrac{a_1}{5\cdot4\cdot3\cdot2}[/tex]

[tex]k=3 \implies n=7 \implies a_7=\dfrac{a_5}{7\cdot6} = \dfrac{a_1}{7\cdot6\cdot5\cdot4\cdot3\cdot2}[/tex]

so that

[tex]a_{n=2k+1} = \dfrac{a_1}{(2k+1)!}[/tex]

So, the overall series solution is

[tex]\displaystyle y(x) = \sum_{n=0}^\infty a_nx^n = \sum_{k=0}^\infty \left(a_{2k}x^{2k} + a_{2k+1}x^{2k+1}\right)[/tex]

[tex]\boxed{\displaystyle y(x) = a_0 \sum_{k=0}^\infty \frac{x^{2k}}{(2k)!} + a_1 \sum_{k=0}^\infty \frac{x^{2k+1}}{(2k+1)!}}[/tex]

Answer:

33

Step-by-step explanation:

Answer:

5/4 and 7/4 are the two solutions.

Hello!

-5(x+2)=35

-5x-10=35

-5x=35+10

-5x=45

x=-9

Hope it helps!

~Just a determined gal

#CarryOnGainingKnowledge

[tex]MysteriousNature[/tex]

Answer:

x = -9

Step-by-step explanation:

-5(x + 2) = 35

~Distribute

(-5 * x) + (-5 * 2) = 35

~Simplify

-5x - 10 = 35

~Add 10 to both sides

-5x = 45

~Divide -5 to both sides

x = -9

Best of Luck!

Answer:

x = about 2.705

Step-by-step explanation:

Does this help? Are you supposed to find x? That's what I did but you don't state what exactly you need.... So.....?

Answer: Probability is 4/12, or 1/3