Exponential Function:

Activity: Bacterial population

A population of bacterium in laboratory conditions grows every 20 minutes in 10% the number of specimens. At the beginning of the observation, at 8:00 AM, the population had approximately 3,000,000 individuals:

1. Complete the following attached table (table below) as requested by completing each of the blank boxes.

2. What is the approximate population of bacterium at 10:00 AM?

3. Write the function in power form, indicating which is the dependent and independent variable.

4. Using the function found, determine the bacterial population five hours after the start of the observation.

The solution of the expression, \((\frac{2}{3} )^{-4}\) is 81 / 16.

An algebraic expression is an expression which is made up of variables and constants, along with algebraic operations such as multiplication, subtraction, addition etc.

Therefore, lets solve the expression as follows:

\((\frac{2}{3} )^{-4}\)

Using exponential laws,

b⁻¹ = 1 / b

Let's apply the law to the expression as follows:

\((\frac{2}{3} )^{-4} = \frac{1}{(\frac{2}{3})^{4} }\)

Therefore,

1 ÷ (2  / 3)⁴ = 1 × (3 / 2)⁴ = 3⁴ / 2⁴

Finally,

3⁴ / 2⁴ = 81 / 16

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Answer:

Step-by-step explanation:

For step explanation:

1. write the problem

2. distinguishing the neg sign

3. distributing 3

4. moving like terms next to each other through commutative property

5.  Combining like terms

6. getting rid of parentheses

Answer:

-0.5. -0.5 is to the right of -1.5

The probability that more than 2 students will attend is 0.9179.

Part (a) List the values that X may take on.

X may take on the values 0, 1, 2, 3, ..., 13.

Part (b) Give the distribution of X.

The distribution of X can be represented as follows: X-0:0, 1:0.23, 2:0.23, 3:0.23, 4:0.23, 5:0.23, 6:0.23, 7:0.23, 8:0.23, 9:0.23, 10:0.23, 11:0.23, 12:0.23, 13:0.23

Part (c) How many of the 13 students do we expect to attend the festivities? (Round your answer to the nearest whole number.)

We can expect 3 students to attend the festivities.

Part (d) Find the probability that at most 3 students will attend. (Round your answer to four decimal places.)

The probability that at most 3 students will attend is 0.6923.

Part (e) Find the probability that more than 2 students will attend. (Round your answer to four decimal places.)

The probability that more than 2 students will attend is 0.9179.

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Answer:

B, 11000

Step-by-step explanation:

assuming a 365 day year...

\(10500*(1+.15)^{\frac{123}{365}}= 11006.35813\)

which I guess is close enough to 11000

The total repayment amount is $11030.75. Therefore, option C is the correct answer.

Given that, Principal $10,500.00 annual rate of interest 15%, time 123 days.

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.

Simple interest is calculated with the following formula: S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years.

Now, simple interest = (10500 × 15 × 123)/(100 × 365)

= 193725/365

= 530.75

So, amount = 10,500.00+530.75

= 11030.75

The total repayment amount is $11030.75. Therefore, option C is the correct answer.

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The value of the car after 3 years is $79, 000

To determine the value, we have to use the formula;

Value = Initial value × (1 - Depreciation rate)ⁿ

Substitute the values given, we get;

Remaining value after 3 years = $100,000 × (1 - 0.10)³

Expand the bracket, we get;

Value after 3 years = $100,000 × (0.90)³

Find the cube value and substitute, we have;

Value after 3 years = $100,000 × 0.729

Multiply the values, we have;

Value after 3 years = $72,900

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Answer:

\({ \tt{c = \pi d}} \\ { \tt{25 = 2(3.14d)}} \\ { \tt{d = 3.98 \: m}}\)

Answer:

This is a binomial experiment .

Step-by-step explanation:

As the percent is not indicated the success is the amount of percent (if given) say it is 10 % . So p will be equal to = 0.1 and q will be = 1-0.1= 0.9

and n would be five or any number as a binomial experiment is repeated for a fixed number of times.

And x would take any value of n i.e.

X= 0,1,2,3,4,5

If it is 20 % . So p will be equal to = 0.2 and q will be = 1-0.2= 0.8

The probability is the number of the percent indicated. But as it is not indicated we assume it to be 10 % or 20 % .Or suppose any number for it to be a binomial experiment.

The number of trials n would be fixed .

The success remains constant for all trials.

All trials are independent.

Answer:

  (x -14)² +(y -7)² = 1²

Step-by-step explanation:

You want the equation of the circle that represents the border of a logo centered 14 m right and 7 m up from the lower left corner of a soccer field. The logo is 2 m in diameter.

The equation of a circle with center (h, k) and radius r is ...

  (x -h)² +(y -k)² = r²

Since the origin of the coordinate system is the lower left corner of the field, the center is located at (h, k) = (14, 7). The diameter of 2 m means the radius is 1 m. Using these values in the equation, it becomes ...

  (x -14)² +(y -7)² = 1²

Answer:

9 - 4 1/2 = 4 1/2.

To calculate this you can do (9 - 4 - 1) + (1 - 1/2).

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▹ Answer

4 1/2 or 4.5

▹ Step-by-Step Explanation

\(9 - 4\frac{1}{2} \\= 9 - \frac{9}{2} \\Common denominator = 2\\\\\frac{18}{2} - \frac{9}{2} \\= \frac{9}{2} \\\\= 4 \frac{1}{2} or 4.5\)

Hope this helps!

CloutAnswers ❁

Brainliest is greatly appreciated!

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Answer:

(14.88-1.88) divided by 12

Step-by-step explanation:

hope this helps!

Answer:

\(-54\)

Step-by-step explanation:

If the number being halved is x, we can write the expression

\(7-0.5x=34\)

Now, bring like terms and solve!

\(-0.5x=27\)

Multiple both sides by -2 and you get

\(x=-54\)

Wanna check the answer? Well...

\(7-(-54*0.5)=7+27=34\)

Answer:

$35.64

Step-by-step explanation:

9 x 3.96 is 35.64

multiply 9 by 3, then 0.96 and add those answers together.

Answer: 35.64 dollars is your answer

Answer:

the think the answer is A. x ≤ 1 or x 6 >

Maci and 2 appointments and Logan had 3 appointments.

The linear equation that represents the total amount earned by Maci is:

Total amount earned = (amount per appointment x number of appointments)  + tips

$170 = ($60 x a) + $50

$170 = $60a + $50

$170 - $50 = $60a

$120 = $60a

a = $120 / $60

a = 2

The linear equation that represents the total amount earned by Logan is:

Profit = total revenue - total cost

Profit = (fee per appointment  x number of appointments) + amount received in tips - (rental fee x number of appointments)

$235 = ($75 x a) + $40 - ($10 x a)

$235 = $75a + $40 - $10a

$235 = $65a + $40

$235 - $40 = $65a

$195 = $65a

a = $195 / 65

a = 3

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\(\left(3x-1\right)\left(x-3\right)\left(x+2\right)\left(x-2\right)\) is the possible root

What is a root ?

Mathematicians refer to a number as having a root if it can be multiplied by itself to give the original number. The square root of 49, for instance, is 7, as 77=49. 7 is referred to as the square root of 49 in this instance because it takes 49 to multiply 7 by itself twice. Considering that 333=27, the cube root of 27 is 3.

Quadratic equation's roots The roots of a quadratic equation are the values of the variables that fulfill the equation. In other words, if f() = 0, then x = is a root of the quadratic equation f(x). The x-coordinates of the sites where the curve y = f(x) intersects the x-axis are the real roots of an equation f(x) = 0.

3x^4 -10x^3 -9x^2 + 40x - 12

=\(\left(3x-1\right)\frac{3x^4-10x^3-9x^2+40x-12}{3x-1}\)

=\(\left(3x-1\right)\left(x^3-3x^2-4x+12\right)\)

= \(\left(3x-1\right)\left(x-3\right)\left(x+2\right)\left(x-2\right)\)

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Answer:

209

Step-by-step explanation:

now if this is correct or not but i triedi hope this helps but dont trust me i dnt ko

Answer:

99% of all balls she hits with this club will lie between the values in the interval.

Step-by-step explanation:

Edge  2022

For the fractions, the calculation of 3/5 of 2/3 of 3/4 of 560 is equal to 168.

To calculate 3/5 of 2/3 of 3/4 of 560, break it down step by step:

Step 1: Calculate 3/4 of 560:

3/4 × 560 = (3 × 560) / 4 = 1680 / 4 = 420

Step 2: Calculate 2/3 of the result from Step 1:

2/3 × 420 = (2 × 420) / 3 = 840 / 3 = 280

Step 3: Calculate 3/5 of the result from Step 2:

3/5 × 280 = (3 × 280) / 5 = 840 / 5 = 168

Therefore, 3/5 of 2/3 of 3/4 of 560 is equal to 168.

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It is better to apply the 10% off coupon first and then the $2 off coupon.

Let's assume the price of the pizza is P.

If we apply the $2 off coupon first, the price of the pizza would be reduced to $P-2$. Then, if we apply the 10% off coupon, the price would be further reduced by 0.1(P-2). Therefore, the total price paid would be:

\($$P_{total}=P-2-0.1(P-2)=0.9P-1.8$$\)

If we apply the 10% off coupon first, the price of the pizza would be reduced to 0.9P. Then, if we apply the $2 off coupon, the price would be further reduced by 2. Therefore, the total price paid would be:

\($$P_{total}=0.9P-2$$\)

Comparing the two total prices, we can see that:

\($$0.9P-1.8 < 0.9P-2$$\)

Therefore, it is better to apply the 10% off coupon first and then the $2 off coupon.

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Answer:

kjhgfd bjnk

Step-by-step explanation:

hjgfb bnjhgfx

Answer:

-22

Step-by-step explanation:

mark this brainliest and rate 5 stars if it helped :)

Answer: 42\5

               =2.8

               42-2.8

              =39.2

Decimals are multiplied as if they were whole numbers, and then the decimal point is placed in the product.

Answer:

$71.59

Step-by-step explanation:

\(43.25+26.25\)

\(=69.5\)

\(69.5*\frac{103}{100}\)

\(69.5*1.03\)

\(=71.585\)

To express an equation of n in terms of m we can follow these steps:

7m + 2 = 6n - 5

1. add 5 on both sides of the equation:

7m+2+5=6n-5+5

2.Combine like terms

7m+7=6n

3. Divide both sides by 6

(7m+7)/6=6n/6

Then we get:

Then, f(m)=7/6(m+1)

Answer:

88.51

0.085343

67.39

Step-by-step explanation:

Given a normal distribution :

Mean (m) = 73

Standard deviation (s) = 11

Percentage A's = 7.93% = 0.0793

Minimum score needed to receive A :

Using the Z formula

Zscore corresponding to 0.0793 = 1.41

P(x ≥ x) :

Z = (x - m) / s

1.41 = (x - 73) / 11

11* 1.41 = x - 73

15.51 = x - 73

x = 15. 51 + 73

x = 88.51

B. Students who made 57.93 or lower on the exam failedthe course. What percent of students failed the course?

P(x ≤ 57.93)

Z = (x - m) / s

Z = (57.93 - 73) / 11

Z = - 15.07 / 11

Z = - 1.37

P( Z ≤ - 1.37) = 0.085343 ( Z probability calculator)

C.) If 69.5% of the students received grades of C or better, what is the minimum score of those who received C's?

Minimum score of those who received C

Zscore corresponding to 0.695 = -0.51 (Z probability calculator)

Z = (x - m) / s

-0.51 = (x - 73) / 11

11* - 0.51= x - 73

-5.61 = x - 73

x = - 5.61 + 73

x = 67.39

The algebraic rule describes the translation of quadrilateral HIJK to quadrilateral H'I'J'K' is (x, y) => (x+1, y-8)

Translation is defined as the movement on a straight line

Given: quadrilateral HIJK to that translated H'I'J'K'

To determine the algebraic rule, we need to get the coordinates of  HIJK and H'I'J'K' and then subtract them to get the translation:

H => (x, y) = (4, 6)  |  H' => (x, y) = (5, -2)

I =>  (x, y) = (6, 4)   |  I' =>  (x, y) = (7, -4)

J => (x, y) = (4, 2)   |  J' => (x, y) = (5, -6)

K => (x, y) = (4, 2)  |   K' => (x, y) = (3, -6)

Using points H and H' (you can use any point):

The difference in x is 5-4 = +1 => x+1

The difference in y is -2-6 = -8 => y-8

Therefore, the algebraic rule describes the translation is (x, y) => (x+1, y-8). Option C is the answer

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Answer:

(x, y) => (x+1, y-8)

Step-by-step explanation: