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Answer:

The estimated size of the population in 10 days is of 1372 mosquitos.

Step-by-step explanation:

Population after t days:

The population after t days is given by:

[tex]P(t) = P(0)e^{rt}[/tex]

In which P(0) is the initial population and r is the growth rate, as a decimal.

P(0)=574.

So

[tex]P(t) = 574e^{rt}[/tex]

P'(0)=50

[tex]P^{\prime}(t) = 574re^{rt}[/tex]

Since P'(0)=50

[tex]574r = 50[/tex]

[tex]r = \frac{50}{574}[/tex]

[tex]r = 0.0871[/tex]

So

[tex]P(t) = 574e^{0.0871t}[/tex]

Estimate the size of the population in 10 days

This is P(10).

[tex]P(10) = 574e^{0.0871*10} = 1372[/tex]

The estimated size of the population in 10 days is of 1372 mosquitos.

The size of the population of mosquito follows an exponential model.

The size of the population in 10 days is 1370

The given parameters are:

[tex]\mathbf{P(0) = 574}[/tex]

[tex]\mathbf{P'(0) = 50}[/tex]

An exponential function is represented as:

[tex]\mathbf{P(t) = P(0) \times e^r^t}[/tex]

So, we have:

[tex]\mathbf{P(t) = 574 \times e^r^t}[/tex]

Differentiate

[tex]\mathbf{P'(t) = 574r}[/tex]

Substitute 0 for t

[tex]\mathbf{P'(0) = 574r}[/tex]

Substitute [tex]\mathbf{P'(0) = 50}[/tex]

[tex]\mathbf{50 = 574r}[/tex]

Divide both sides by 574

[tex]\mathbf{0.087 = r}[/tex]

So, we have:

[tex]\mathbf{r = 0.087 }[/tex]

The function becomes

[tex]\mathbf{P(t) = 574 \times e^r^t}[/tex]

[tex]\mathbf{P(t) = 574 \times e^{0.087t}}[/tex]

In 10 days, t = 10.

So, we have:

[tex]\mathbf{P(10) = 574 \times e^{0.087 \times 10}}[/tex]

[tex]\mathbf{P(10) = 574 \times e^{0.87}}[/tex]

Solve

[tex]\mathbf{P(10) = 1370}[/tex]

Hence, the size of the population in 10 days is 1370

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Answer:

There are 9 dogs

Step-by-step explanation:

[tex] \frac{10}{x} = \frac{70}{63} \\ x = \frac{630}{70} \\ x = 9[/tex]

Answer:

Reduce the expression, if possible, by eliminating common factors.

Exact form:

1/30

Decimal form:

0.03

Answer:

An equation is y=-3x+7 (I chose slope-intercept form because they already showed us the slope). When y =13 x=-2

Step-by-step explanation:

plugin 13 for y and subtract 7 from both sides, this lets you get 6=-3x then divide 6 by -3 which makes x=-2

Answer:

[tex]\displaystyle \Big(\frac{3\sqrt{5}}{5},\frac{6\sqrt5}{5}+4\Big)[/tex]

Step-by-step explanation:

Recall that the equation for a circle is given by:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Where (h, k) is the center and r is the radius.

Then for a center of (0, 4) and a radius of 3, our equation is:

[tex]x^2+(y-4)^2=9[/tex]

We want to know at what point does the circle intersect with the line:

[tex]y=2x+4[/tex]

Therefore, we can solve for x. To do so, substitute the linear equation into the circle equation:

[tex]x^2+((2x+4)-4)^2=9[/tex]

Simplify:

[tex]x^2+(2x)^2=9[/tex]

Square:

[tex]x^2+4x^2=5x^2=9[/tex]

Divide both sides by 5:

[tex]\displaystyle x^2=\frac{9}{5}[/tex]

Therefore:

[tex]\displaystyle x=\pm\frac{3}{\sqrt{5}}=\pm\frac{3\sqrt{5}}{5}[/tex]

In QI, x is always positive, so we only need to consider the positive case:

[tex]\displaystyle x=\frac{3\sqrt{5}}{5}[/tex]

Using the linear equation again, we can see that:

[tex]\displaystyle y=2\Big(\frac{3\sqrt{5}}{5}\Big)+4=\frac{6\sqrt{5}}{5}+4[/tex]

Therefore, the point in which a circle with center (0, 4) and a radius of 3 intersects the line with equation y = 2x + 4 in the first quadrant is the point:

[tex]\displaystyle \Big(\frac{3\sqrt{5}}{5},\frac{6\sqrt5}{5}+4\Big)[/tex]

Or approximately:

[tex]\approx (1.342, 6.683)[/tex]

And we are finished!

Answer:

x+2 y+1

Step-by-step explanation:

or do u want working out

Answer:

0.86

Step-by-step explanation:

You will get 0.85714.....

Then 0.86 is 2 dp

Answer:

Polynomial Degree:

6

Leading Term:

x⁶

Leading Coefficient:

1

Answer:

Step-by-step explanation:

hello :

here is an solution

Answer:

So

Domain: (-∞,∞)

Range: [[tex]-\frac{105}{8} ,[/tex]∞)

Step-by-step explanation:

Answer:

Domain: (-∞,∞)

Range: [-105/8,∞)

Step-by-step explanation: Hope this helps.

Answer:

x = 28

Step-by-step explanation:

x + 40 + 22 = 90      {Complementary angles}

        x + 62 = 90

              x = 90 - 62

              x = 28

Answer:

12 or 13

Step-by-step explanation:

14 labourers complete the job in 3 days.

The ratio is defined as a relationship between two quantities, it is expressed one divided by the other.

Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.

Given data as :

It takes 6 labourers 7 days to complete a job,

Amount of work completed by 6 labourers over 7 days  = 1

∵ Six labourers completed part of the work in one day = 1/7

∴ one labourers completed part of the work in one day  = (1/6)(1/7) = 1/42

Let x number of labourers complete the job in 3 days.

x × 3 ×(1/42) = 1

x = 42/3

x = 14

Hence, 14 labourers complete the job in 3 days.

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Answer:

i just want the points

Step-by-step explanation:

i just want the points

Step-by-step explanation:

Since the x-intercepts are -20 and 40, the line of symmetry is x = (-20 + 40)/2 = 10.

Now we have y = a(x - 10)² + 30, where a is an unknown constant. We can find a by using an x-intercept point.

=> (0) = a[(40) - 10]² + 30

=> 900a + 30 = 0, a = -1/30.

Hence the rule is y = -(x - 10)²/30 + 30.

Answer:

$700

Step-by-step explanation:

400 x .05=20

20x15=300

300+400=700

Answer:

8 x 17 = 136 give me brainliest

Step-by-step explanation:

Answer:

D. The y-intercept is at (0,2)

Step-by-step explanation:

f(x) = 2^x and g(x)=2f(x) so g(x) = 2(2)^x

In the exponential function ab^x a is the y-intercept (in this case a is 2)

Y-intercept of g(x) at (0,2) which is correct option(D).

A graph can be defined as a pictorial representation or a diagram that represents data or values.

f(x) = 2ˣ

g(x) = 2f(x) = 2(2ˣ)

The y-intercept of g(x) = 2f(x),

Substitute in 0 for x and solve for y

y=2(2⁰)

Anything raised to 0 is 1 .

y=2

Y-intercept in point form.

Hence, y-intercept of g(x) : (0,2)

Learn more about Graph here :

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Answer:

Step-by-step explanation:

He needs 2.5 cm of ribbon left or in easier words 6 cm..-

Answer:

id say just try your best or guess

Step-by-step explanation:

ouu try to put it in a calculator but uhm my answer would be a

Answer:

x = 2

Step-by-step explanation:

We need to write an integer that is 5 more than -3.

Let the integer be x.

So,

x = 5+(-3)

x = 5-3

x = 2

Hence, the required integer be 2.

Answer:

-1 + 2 + 5 + 8 + 11 + 14 + 17 + 20 + 23 + 26

10 terms

sum = 125

Answer:

Each student receives $70 dollars each.

Step-by-step explanation:

Answer:

????

Step-by-step explanation:

Answer:

(-1,-3)

Step-by-step explanation:

Answer: voluntary response sampling

Step-by-step explanation:

Based on the information given in the question, the sampling technique that is being used is the voluntary response sampling.

A voluntary response sampling refers to a sample which is gotten when a researcher tells the members to join a particular sample and then the ones that are interested then joins. Such participants volunteer voluntarily and take part in the research studies and give their opinions on the topic.

Since the student organization at a local college posted a poll on its website and the interested students took part, it is a voluntary response sampling.

Answer:

the ratio would be 9:4 because you just add

Step-by-step explanation:

just add the rstio

Answer:

y = -5x +7

Step-by-step explanation:

You will have to change the equation to equal y.

y = -5x -2

Then find the paralell line which would be be the same slope but different equation so the answer should be: y = -5x + 7 by plugging in the numbers of the point. So -3 = -5(2) + x.

Solve for X,

-3 = -10 + x, add 10 to each side

7 = x