Help and explain too (using elimination to solve systems of equations ) !!!!!

Answer:

a) P(0) = 80

b) [tex]P(t) = 80(2.2361)^t[/tex]

c) 22,363 cells.

d) The rate of growth after 7 hours is of 18,000 bacteria per hour.

e) 9.7 hours.

Step-by-step explanation:

A bacteria culture grows with a constant relative growth rate.

This means that the population is given by:

[tex]P(t) = P(0)(1+r)^t[/tex]

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

After 2 hours there are 400 bacteria and after 8 hours the count is 50,000.

This means that in 6 hours, the population went from 400 bacteria to 50,000 bacteria. We use this to find r. So

[tex]50000 = 400(1+r)^6[/tex]

[tex](1+r)^6 = \frac{50000}{400}[/tex]

[tex](1+r)^6 = 125[/tex]

[tex]\sqrt[6]{(1+r)^6} = \sqrt[6]{125}[/tex]

[tex]1 + r = 125^{\frac{1}{6}}[/tex]

[tex]1 + r = 2.2361[/tex]

So

[tex]P(t) = P(0)(2.2361)^t[/tex]

(a) Find the initial population. P(0)

We have that P(2) = 400. We use this to find P(0). So

[tex]P(t) = P(0)(2.2361)^t[/tex]

[tex]400 = P(0)(2.2361)^2[/tex]

[tex]P(0) = \frac{400}{(2.2361)^2}[/tex]

[tex]P(0) = 80[/tex]

So

[tex]P(t) = 80(2.2361)^t[/tex]

(b) Find an expression for the population after t hours.

[tex]P(t) = 80(2.2361)^t[/tex]

(c) Find the number of cells after 7 hours.

This is P(7). So

[tex]P(7) = 80(2.2361)^7 = 22363[/tex]

22,363 cells.

(d) Find the rate of growth after 7 hours.

We have to find the derivative when t = 7. So

[tex]P(t) = 80(2.2361)^t[/tex]

[tex]P^{\prime}(t) = 80\ln{2.2361}(2.2361)^t[/tex]

[tex]P^{\prime}(7) = 80\ln{2.2361}(2.2361)^7 = 18000[/tex]

The rate of growth after 7 hours is of 18,000 bacteria per hour.

(e) When will the population reach 200,000?

This is t for which [tex]P(t) = 200000[/tex]. So

[tex]P(t) = 80(2.2361)^t[/tex]

[tex]200000 = 80(2.2361)^t[/tex]

[tex](2.2361)^t = \frac{200000}{80}[/tex]

[tex](2.2361)^t = 2500[/tex]

[tex]\log{(2.2361)^t} = \log{2500}[/tex]

[tex]t\log{2.2361} = \log{2500}[/tex]

[tex]t = \frac{\log{2500}}{\log{2.2361}}[/tex]

[tex]t = 9.7[/tex]

So 9.7 hours.

Answer:

-85

Step-by-step explanation:

You can use calculator for this question

Answer:

9/49

Step-by-step explanation:

that is the procedure above

Answer:

d). Any Integer.

Step-by-step explanation:

Regression analysis is characterized as the statistical method that is employed to determine the association between a dependent, as well as, the independent variable(one or more). It

As per the question, the probable values for the arrangement of a polynomial would be 'any integer' in order to determine the relationship among the different variables(the two physical quantities). Since a regression analysis helps in knowing the factors that influence the other and the factors that do not affect much in order to reach a reliable conclusion. Thus, any of the values can be examined to examine the association among them. Hence, option d is the correct answer.

Ellen makes $20 per hour in her job as a kiental assistant. She works 8 hours per day and 40 hours per week. How much does Ellen make in a day before taxes?

Money earned by Ellen per hour = $20.

Number of hours she works per day = 8 hours.

Money she'll make per day = 20×8 = 160

Hence, the answer is $160.

Step-by-step explanation:

70 + 45 = 115

180 - 115 = 65

angle c = 65

use sohcahtoa

cos angle = adjacent

hypotenuse

cos 65 = 2.5

b

b cos 65 = 2.5

use the calc for further answers

hope that helped

Answer:

we will then have to also multiply the y with three so the answer is B and that's ( ×3)

Answer:

26m^2

Step-by-step explanation:

Area of triangle=1/2b*h

We have,

b=6.5

h=8m

Now,

Area=1/2b*h=1/2*6.5*8=26m^2

Answer:

hello mateee ;)

Step-by-step explanation:

lets go step by step...

216 cub root = 6

x^3 cube root = 3/3 = power 1 = x

y^6 cube root = 6/3 = power 2 = y^2

z^12 cube root = 12/3 = power 4 = z^4

final ans becomes 6x y^2 z^4 hence option a is correct

glad for brainliest <3

Answer:

Step-by-step explanation:

There are two possible equations, but neither matches the the choices you listed. The choices seem to have several typographical errors.

Point-slope form of an equation of the line through the points (-4, 7) and (5,-3) is y - 7 =(-10/9)(x + 4).

Slope

[tex]$= \frac{y_{2} -y_{1}}{x_{2} -x_{1}}[/tex]

= (-3 - 7) / (5 - (-4))

= -10/9

The point-slope equation for the line of slope -(10/9) that passes through the point (5, -3).

y + 3 = (-10/9)(x - 5)

Point slope equation for the line of slope -(10/9) that passes through the point (-4, 7)

Point-slope form of an equation of the line through the points (-4, 7) and (5,-3) is y - 7 = (-10/9)(x + 4).

Therefore, the correct answer is y - 7 = (-10/9)(x + 4).

To learn more about the equation of a line refer to:

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Answer:

120

Step-by-step explanation:

5x4x3x2x1=120

Answer:

87.5

Step-by-step explanation:

Let the missing side be x.

28 / 35 = x / 50

4 / 7 = x / 50

4 ( x ) = 7 ( 50 )

4x = 350

x = 350 / 4

x = 87.5

Answer: 85 i think

Step-by-step explanation:

Answer:

x^2 + x - 42

Step-by-step explanation:

use the distributive property:

(x+7)(x-6) = x^2 + x - 42

Answer: x^2 + x - 42

Step-by-step explanation:

Answer:

Converting into metre (1m=100cm)= 5/100=0.05m.. Converting into km. (1km=100000cm). so 5 cm=5/100000=0.00005km.

Answer:

5cm in meters = 0.05 metre

5cm in kilometres = 0.00005km

Answer:

Hello,

Very bad written!!!

Step-by-step explanation:

[tex]e^{1-3x}=e^{4x-3}\\\\1-3x=4x-3\\\\7x=4\\\\\boxed{x=\dfrac{4}{7} }\\[/tex]

[tex]\\ \sf\longmapsto XY+YZ=XZ[/tex]

[tex]\\ \sf\longmapsto 7a+5a=6a+24[/tex]

[tex]\\ \sf\longmapsto 12a=6a+24[/tex]

[tex]\\ \sf\longmapsto 12a-6a=24[/tex]

[tex]\\ \sf\longmapsto 6a=24[/tex]

[tex]\\ \sf\longmapsto a=\dfrac{24}{6}[/tex]

[tex]\\ \sf\longmapsto a=5[/tex]

Value of a is 4 and value of YZ is 20 units

Step-by-step explanation:

Given:

Y is between point X and Z

Value of line XY = 7a

Value of line YZ = 5a

Value of line XZ = 6a + 24

Find:

Value of "a" and line YZ

Computation:

We know that

XY + YZ = XZ

So,

7a + 5a = 6a + 24

12a = 6a + 24

6a = 24

a = 4

Value of a = 4

So,

Value of line YZ = 5a

By putting value of a

Value of line YZ = 5(4)

Value of line YZ = 20 units

Learn more;

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Answer:

1107.

You are rounding up because the number in the tenths slot is over 5.

Answer:

2/52=1/26

Step-by-step explanation:

Answer:

where are u from bro?

Step-by-step explanation:

I didn't understand your language.

Answer:

What is a linear inequality ? A linear inequality has the same condition as a linear equality, but instead of the equal sign, we have for example this one ≤ wish means less than or equal to.

But what are the condition of a linear equality ? There are many ways of writing linear equations but they usually have constants (like "2" or "c") and must have simple variables (like "x" or "y") BUT the variables (x and y) on a linear equation do NOT have Exponents (like the 2 in x²) and square roots,

1. y < 3

Yes, this is a linear inequation. Frequently, the term linear equation refers implicitly to the case of just one variable (here y).

2. x ≥ 6

Yes.

3. x² > - 3

No, remember the rule the variable (here x) must not have exponents.

4. x - 3 > 1/2

Yes.

5. xy + 5 ≤ 7

This one is nice. If both x and y are variables then the answer is no, it's not a linear inequation. Why ?The linear equation is a sum of terms like "Ax" where x is a variable, and A is a number or a constant. On the other hand if x or y was a constant (like e or π), it could be treated as a number and the whole expression would become linear.

You can also have fun and write :

xy ≤ 2

for y > 0 we write:

x ≤ 2/y

x ≤ 2[tex]y^{-1}[/tex]

and then simply say exponents are not allowed so not a linear inequation.

Answer:

3166.7

Step-by-step explanation:

V = πr²h

V = π * (12 km)² * 7 km

V ≈ 3166.7 km³

Hey there!

First, let's review the formula for finding a cylinder's volume.

Formula: [tex]\pi r^2h[/tex]

Our new equation would look like this: [tex]\pi[/tex] x [tex]12^{2}[/tex] x 7.

The original answer would be 3166.72539482, but the question states that it want it rounded to the nearest tenth. So, your answer would be 3166.7.

Hope this helps! Have a great day!

Is this question complete?

Answer:

the answer will be 3.........

[tex]\\ \sf\longmapsto 10x=\dfrac{1}{0.001}[/tex]

[tex]\\ \sf\longmapsto 10x=\dfrac{1}{\dfrac{1}{1000}}[/tex]

[tex]\\ \sf\longmapsto 10x=1000[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{1000}{10}[/tex]

[tex]\\ \sf\longmapsto x=100[/tex]

Answer:

A. 200 square inches

Step-by-step explanation:

First, use Pythagorean Theorem to find the base of each triangle.

[tex]a^2+b^2=c^2\\20^2+b^2=(28\frac{1}{4})^2\\400+b^2=798.0625\\b^2=398.0625\\b=\sqrt{398.0625}\\b=19.9515037[/tex]

Finally, use the area of a triangle formula to find the area of each triangle.

[tex]A=\frac{1}{2}bh\\A=\frac{1}{2}(19.9515037)(20)\\A=199.515037[/tex]

Therefore, the area of each triangle is approximately 200 in².

The area of each triangle in square inches is 200 square inches.

The area of triangle is defined as the region enclosed by its perimeter or the three sides of triangle.

Mathematically,

Area of triangle = 1/2(base*height)

Now given that,

Base of the triangle, B = 20''

Hypotenuse of the triangle, H = 28(1/4)'' = 28.25''

So, Height of the triangle, P = [tex]\sqrt{H^2 - B^2}[/tex]

or,  Height of the triangle, P = [tex]\sqrt{28.25^2 - 20^2}[/tex]

or,  Height of the triangle, P = [tex]\sqrt{398.0625} }[/tex]

or,  Height of the triangle, P = 19.95 inches

Finally, use the area of a triangle formula to find the area of each triangle.

Area of triangle = 1/2*(BasexHeight)

⇒Area of triangle = 1/2*(20x19.95)

⇒Area of triangle = 1/2*399

⇒Area of triangle = 199.5 square inches

or, Area of triangle ≈ 200 square inches.

Hence, The area of each triangle in square inches is 200 square inches.

More about triangle :

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Using the concept of probability, it is found that there is a 0.0592 = 5.92% probability that you get a total of 17 given on the first spin you spin a 2.

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

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In each trial, there are 13 possible outcomes(pockets numbered from 0 to 12), so the total number of outcomes is:

[tex]T = 13^2 = 169[/tex]

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The desired outcomes are those who result in a sum of 15. Thus, they are:

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

Thus, the probability is:

[tex]p = \frac{D}{T} = \frac{10}{169} = 0.0592[/tex]

0.0592 = 5.92% probability that you get a total of 17 given on the first spin you spin a 2.

A similar problem is given at https://brainly.com/question/21444373

Answer:

its the 1st one

Step-by-step explanation:

they need to know what the Total

Answer:

English; 12

French; 9

Both; 7

Step-by-step explanation:

28 - 19 = 9, therefore there are only 9 students who can only speak French

28 - 16 = 12, therefore there are only 12 students who can only speak English

12 + 9 = 21, then subtract 21 from the 28 total students

28 - 21 = 7, therefore there are only 7 students who can speak both