A population of protozoa develops with a constant relative growth rate of 0.7944 per member per day. On day zero the population consists of two members. Find the population size after six days

Answer:

By using trigonometric relations, we will see that:

AC = 15.6 in

AB = 8.4 in.

How to get the measures of the other two sides of the right triangle?

Here we have the right triangle where:

B = 90°

C = 40°

BC = 10 in.

Notice that is the adjacent cathetus to the angle C, then we can use the two relations:

sin(a) = (adjacent cathetus)/(hypotenuse).

tan(a) = (opposite cathetus)/(adjacent cathetus).

Where:

hypotenuse = AC

opposite cathetus = AB.

Then we will have:

sin(40°) = 10in/AC.

AC = 10in/sin(40°) = 15.6 in

tan(40°) = AB/10in

tan(40°)*10in = AB = 8.4 in.

So we can conclude that for the given right triangle we have:

AC = 15.6 in

AB = 8.4 in.

If you want to learn more about right triangles:

Step-by-step explanation:

The price of article after 12 percent discount is $4928

Percentage is a part of the whole number. It is denoted by % sign.

1 %= 1/100.

The given amount of article is $5,600.00,

And discount percent is 12%.

The amount of discount = 56,00×12/100

                                        = 672

The price of article after discount = 5600-672 = 4928

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Answer:

a=5

Step-by-step explanation:

Answer:

7                                                                                                   8

Step-by-step explanation:

The expression that shows how much the individual earns everyday if they sell n items would be = $5 × n = $5n.

A salesperson is an individual that helps in the marketing and selling of goods and products for a company and who is equally rewarded with bonus after each sale that is made.

The amount of money that the salesperson makes = $10/day

The amount of money given as bonus for each item sold = $5

Therefore when the number of items sold = n, the amount made = $5 × n = $5n

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Answer:

-12

Step-by-step explanation:

So to start we need to know what makes a line parallel. In an equation we know that for lines to be parallel they must have the same slope(m).

Then, we  need to know the slope-intercept form of an equation. The slope intercept form is \(y=mx+b\) where \(m\) is the slope of the line and \(b\) is the y-intercept. In this problem where can see the second equation is already in this form.

Now that we know we need to find the slope, and we know that the second equation is in slope-intercept form we're going to convert the fist equation into the correct form.

To do this, we know we need to make sure \(y\) is the only thing on the left side of the equal sign. Currently, on the left side of the equal sign we have \(-\frac{1}{2} y\) so we have to divide both sides by \(-\frac{1}{2}\) to get \(y=-12x -20\)

Now that we have it converted to slope-intercept form, we are going to look for what represents the slope or \(m\) in the equation. In this case the slope would be -12, so any line with a slope of -12 will be parallel.

Answer:

$7,362

Step-by-step explanation:

its easy multiplication

$245.40 x 30

Answer:

818

Step-by-step explanation:

you just divide 245.40 by 30 and is gives 8.18 but you take the decimal away Hope that helps

The calculated value of the rate of the graph is 0.8

from the question, we have the following parameters that can be used in our computation:

The graph

Where, we have

(0, -16) and (20, 0)

The rate of the graph is calculated as

Rate = Change in y/x

using the above as a guide, we have the following:

Rate = (0 + 16)/(20 - 0)

Evaluate

Rate = 0.8

Hence, the rate is 0.8

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Answer:

10.5

Step-by-step explanation:

Missing number, 9.8, 9.1

We see that each time it subtracts 0.7

We take

9.8 + 0.7 = 10.5

So, the missing number is 10.5

Answer: 4 pages

Step-by-step explanation:

To solve this problem, we need to use the formula:

Rate = Output/Time

Let's use "p" to represent the number of pages Ethan can type and "t" to represent the time he has before the meeting starts.

Rate = 2 pages/(1/8 hour) = 16 pages/hour

Since the meeting starts 3/4 hour later than the scheduled time, Ethan has t = 1 - 3/4 = 1/4 hour to type pages before the meeting starts.

Output = Rate * Timep = (16 pages/hour) * (1/4 hour) = 4 pages

Therefore, Ethan can type 4 pages before the meeting starts.

Answer: 4 pages

The measure of the complement of a 1-degree angle is 89 degrees.

The complement of an angle is defined as the angle that, when added to the given angle, results in a sum of 90 degrees. To find the measure of the complement of a 1-degree angle, we need to determine the angle that, when added to 1 degree, equals 90 degrees.

Let's denote the measure of the complement as x degrees. According to the definition, we can set up the equation:

1 degree + x degrees = 90 degrees.

To solve for x, we need to isolate it on one side of the equation. By subtracting 1 degree from both sides, we have:

x degrees = 90 degrees - 1 degree.

Simplifying the right side, we get:

x degrees = 89 degrees.

In summary, when an angle measures 1 degree, its complement measures 89 degrees. Complementary angles are pairs of angles that add up to 90 degrees. In this case, since the given angle measures only 1 degree, its complement is significantly larger, nearly forming a right angle. The concept of complementary angles is fundamental in geometry and can be applied to various problems involving angles and their relationships.

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The value of side TS is,

⇒ TS = 28

First, we are going to divide the figure and named new points X and Y as:

Now, we know that TS is the sum of TX and XS.

TS = TX + XS

Additionally, TX has the same length of HJ, so:

TX = HJ = 14

Now, we want to know the length of YK, and we can calculate it using the following equation:

LK = LY + YK

LY = HJ,

so, LY = 14

And, 42 = 14 + YK

42 - 14 = YK

28 = YK

Finally, since T and S are midpoints, the length of XS is the half of the length of YK. It means that XS is:

XS = YK/2

XS = 28/2

XS = 14

Therefore, TS is equal to:

TS = TX + XS

TS = 14 + 14

TS = 28

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Answer:

Graph C represents a cubic function.

Step-by-step explanation:

Only Graph C could represent a cubic function.  

A cubic function is odd, meaning that whatever is in Quadrant I is reflected about the origin into Quadrant I.

The graph C is represent a cubic function.

Option C is true.

What is Cubic polynomial?

A cubic polynomial is a polynomial in which the degree of the highest term is 3.

Given that;

There are four graph is shown in image.

Now, Function of Graph C is;

y = x³

This represents the cubic function.

Thus, The graph C is represent a cubic function.

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Answer:

\( \frac{1}{3} \pi( {3.5}^{2} )(11) = 44.9\pi\)

C is the correct answer.

Answer:

D

Step-by-step explanation:

He goes 66 MPH because 66 times 10= 660 MPH

Hopefully this helps!

Answer: 40mins

Step-by-step explanation: We take each person's time daily and multiply it by 8 days. 30x8=240 and 58x8=280. To find out how much more Jordan rode we subtract them 280-240=40.

Answer:

A) p(24) = 1884

B) Owen has been receiving lawn service for 39 months

Step-by-step explanation:

For A)

"Find p(24)" also means "Find the amount of money Owen pays for lawn service after 24 months" as we're given 24 for t. As such, rewrite the given function as p(24) = 108 + 74(24)

p(24) = 108 + 74(24)

p(24) = 108 + 1776

p(24) = 1884

For B)

If Owen paid a total of $2,994 up to date this means "p(t)" is equal to 2994. Remember p(t) is the total amount of money Owen gains after a certain time, (t)!

So:

p(t) = 108 + 74t

2994 = 108 + 74t

(2994 - 108) = 74t

2886 = 74t

t = 39

Put that into words: "Owen has been receiving lawn service for 39 months"

Answer: 2500

Step-by-step explanation: If you calculate out 5x6 that equals 30 and 5x5-5 equals 20, when you do 30+20 that equals 50 and 50 to the 2nd power is 50x50 and that would equal 2500

A house on the market was valued at $327,000. after several years the value increased by 17% by how much did the house's value increase in dollars? what is the current value of the house?

How much did the house's value increase in dollars?

327,000 x 0.17 (17%) = $55,590

What is the current value of the house?

327,000 + 55,590 = $382,590

Answer:

It is a function.

Step-by-step explanation:

I would suggest use the website Desmos.

Answer:

x = 100

Step-by-step explanation:

1 and 2 are a linear pair and sum to 180° , that is

x + \(\frac{4}{5}\) x = 180 ( multiply through by 5 to clear the fraction )

5x + 4x = 900

9x = 900 ( divide both sides by 9 )

x = 100

Answer:

i really dunonjust need tho points sorry but have a blessed Dayyy

Step-by-step explanation:

The polynomials completely factorized have the following expressions;

50). x³ - 3x² - 26x - 12 = (x - 6)(x + 1)(x + 2)

51). x³ - 12x² + 12x + 80 = (x - 10)(x + 2)(x - 4)

52). x³ - 18x² + 95x + 126 = (x - 9)(x - 2)(x - 7)

53). x³ - x² + 21x + 45 = (x + 5)(x - 3)(x - 3)

For the polynomial x³ - 3x² - 26x - 12 divisible by x - 6;

(x³ - 3x² - 26x - 12)/(x - 6) = x² + 3x + 2

x² + 3x + 2 = (x + 1)(x + 2)

so;

x³ - 3x² - 26x - 12 = (x - 6)(x + 1)(x + 2)

For the polynomial x³ - 12x² + 12x + 80 divisible by x - 10;

(x³ - 12x² + 12x + 80)/(x - 10) = x² - 2x - 8

x² - 2x - 8 = (x + 2)(x - 4)

so;

x³ - 12x² + 12x + 80 = (x - 10)(x + 2)(x - 4)

For the polynomial x³ - 18x² + 95x + 126 divisible by x - 9;

(x³ - 12x² + 12x + 80)/(x - 9) = x² - 9x + 14

x² - 9x + 14 = (x - 2)(x - 7)

so;

x³ - 18x² + 95x + 126 = (x - 9)(x - 2)(x - 7)

For the polynomial x³ - x² + 21x + 45 divisible by x + 5;

(x³ - x² + 21x + 45)/(x + 5) = x² - 6x + 9

x² - 6x + 9 = (x - 3)(x - 3)

so;

x³ - x² + 21x + 45 = (x + 5)(x - 3)(x - 3)

Therefore, by complete factorization the expressions (x - 6)(x + 1)(x + 2), (x - 10)(x + 2)(x - 4), (x - 9)(x - 2)(x - 7), and (x + 5)(x - 3)(x - 3) are the factors of their respective polynomial.

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Probability of students having their own vehicle

= 2/10

= 1/5

Answer:

1). y= -4+ 4x

2). y= 3+ x/2

Step-by-step explanation:

hope this helps !

Answer:

Step-by-step explanation:

Because, if  even , for example x^2,  then the square of a negative and a positive x will always be positive.

For odd x, eg x^3 if x is negative x^3 is negative and if x is positive x^3 is positive.

The person is approximately 8.43 miles from home, and they need to walk in the direction of approximately 26.6 degrees east of north to head directly home.

To determine the distance from home, we can use the concept of vector addition. The person walks 4 miles west, which can be represented as a vector (-4, 0) in a coordinate plane. Then, they walk 5 miles southwest, which can be represented as a vector (-3.54, -3.54) since southwest is a combination of west and south. Adding these two vectors together gives us (-7.54, -3.54).

To find the magnitude or distance from home, we use the Pythagorean theorem. The distance is given by sqrt((-7.54)^2 + (-3.54)^2) = 8.43 miles (approximately).

To determine the direction to head directly home, we need to find the angle between the vector (-7.54, -3.54) and the positive x-axis. We can use trigonometry to find this angle. The tangent of the angle is given by the ratio of the y-coordinate to the x-coordinate, which is -3.54 / -7.54. Taking the inverse tangent of this value gives us approximately 26.6 degrees.

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The problem that would be calculated to find the final answer is 2)  20 x 40; 5 x 40; 20 x 5 ; 5 x 5 = 1125

Given,

When using re-grouping to solve 25 x 45, we have to find the problems that would be calculated to find the final answer;

Here,

25 × 45 = 1125

Now,

This is simply multiplicity;

1. 20 x 40: 20 x 5: 40 x 5

800 ; 100 ; 200

1100

This is not the problem.

2. 20 x 40; 5 x 40; 20 x 5 ; 5 x 5

800 ; 200 ; 100 ; 25

1125

This is the problem

3. 20 x 40 ; 5 x 20 ; 20 x 5 ; 5 x 5

800 ; 100 ; 100 ; 25

1025

This is not the problem

4. 20 x 20 ; 40 x 40 ; 20 x 5 ; 5 x 5

400 ; 1600 ; 100 ; 25

2125

This is not the problem

Therefore,

The problem that would be calculated to find the final answer is 2)  20 x 40; 5 x 40; 20 x 5 ; 5 x 5 = 1125

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To give all possible results, this is the sample space of the distribution ;

Event A, the sum is greater than 8.

The total possible outcomes is 36.

The sum being greater than 8 happens 10 times.

Therefore, the probability that the sum is greater than 8 is;

Event B, The sum is dividible by 4.

In the sample space, there are 9 places where the sum is divisible by 4.

Therefore, the probability that the sum is divisible by 4 is;