a certain species of virulent bacteria is being grown in a culture. it is observed that the rate of growth of the bacterial population is proportional to the number present. if there were 4000 bacteria in the initial population and the number doubled after the first 30 minutes, how many bacteria will be present after 3 hours?

Answer:

Improper fraction: -31/30

Mixed number: -1   1/30

Step-by-step explanation:

If x = -5/6 and y = -2/5, we can start by replacing x and y in the equation x + 1/2y.

x+1/2y -> -5/6+1/2(-2/5)

Now we can start solving the equation:

According to the Order of Operations, we have to start with multiplication before addition. So, let's multiply 1/2 and -2/5. We get -2/10, which simplifies to -1/5.

Now we have to do the addition: -5/6+(-1/5)

To add fractions together, we have to find a common denominator. We can do this by finding the LCM of the two denominators(Least common multiple).

6: 6, 12, 18, 24, 30, 36...

5: 5, 10, 15, 20, 25, 30, 35...

The LCM is 30.

-5/6 x 5/5 = -25/30 <-- the equivalent fraction of -5/6

-1/5 x 6/6 = -6/30 <-- the equivalent fraction of -1/5

-25/30 + (-6/30) = -31/30

The answer is -31/30 in improper fraction form, and -1 1/30 in mixed number form.

The solution to this system of equations is (10, 50).

A graph of this system of equations is shown in the image attached below.

Based on the information provided above, one of the plan includes a membership fee of $10 and charges $4 for every DVD borrowed. Therefore, the total cost, y, can be represented by this equation:

y = 4x + 10    .......equation 1.

where:

x represents the number of DVDs borrowed in a month.

For the second plan, it costs $50 per month for unlimited DVD rentals. Therefore, the total cost, y, can be represented by this equation:

y = 50    ....equation 1.

By equating equation 1 and equation 2, we have the following:

4x + 10 = 50

4x = 50 - 10

4x = 40

x = 40/4

x = 10 DVDs.

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Answer:

~ generally is substituted by negation

Hence, option D (Even numbers are not divisible by 2) would be the correct answer.

Answer:

3/8

Step-by-step explanation:

1. If there are three parts green and 5 parts yellow, you can add them to find the total parts

2. 5+3 is 8

3. Then to find the green, which is three, we can divide it

4. 3 green parts/ total which is 8

5. 3/8

Answer:

x^2 +4x +5

Step-by-step explanation:

2x^2 -x^2 will be x^2

3x+x is 4x

-4+9 is 5

slope found by rise over run or m = (y2 - y1) / (x2 - x1)

orientation is important to not mix either values order.

( 9 - 21) / ( -1 - 5) => ( -12 ) / ( - 6 )

negatives cancel and simplify to find

m = 2

Answer:

5894 seconds

Step-by-step explanation:

Convert  1 hour 38 min 14 seconds to seconds​

1 hour = 3600 seconds

1 min = 60 seconds

38 mins = 60 x 38 = 2280 seconds

Now add all numbers together

3600 + 2280 + 14 = 5894 seconds

So, 1 hour 38 minutes 14 seconds is 5894 seconds.

Answer:

f(-3) = 5

Step-by-step explanation:

f(-3) → x = -3

f(x) = -x+2

f(-3) = -(-3)+2

f(-3) = 3+2

f(-3) = 5

Answer:

It would be 3.765 pounds. You have to do 7.53 x 10 to the -10= 0.000000000753. Then do 0.000000000753 x 5 billion to get 3.765.

Step-by-step explanation:

For the equation 3 = (g/-4) - 5, the value of g is g = -32.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The given equation is -

3 = (g/-4) - 5

The equation contains a fractional component.

Simplify the equation to get the value of g.

First collect all the like terms -

g/-4 = 3 + 5

Then use arithmetic operation of addition -

g/-4 = 8

Then move the denominator of the fraction to right hand side of the equation -

g = 8 × -4

Then use arithmetic operation of multiplication -

g = -32

Therefore, the value of g is -32.

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Answer:

369 cans

Step-by-step explanation:

Add the two numbers of cans collected by each:

Alan:   154 cans

Betty:  215 cans

Total:  369 cans

The probability that the sum of the two selected numbers is even is 1/2.

The parity of the two chosen numbers must match for the sum to be even.

Given this information, we can divide the larger problem into smaller ones. First, we may determine the likelihood that the first spinner will land on an even number.

Exists a [tex]$\frac{1}{2}$[/tex] chance that this happens, and a [tex]$\frac{1}{3}[/tex] there is a chance that the second spinner will also land on an even number, hence

[tex]$\frac{1}{2} \cdot \frac{1}{3} = \frac{1}{6}$[/tex]

There is a win if both the first and second spinners land on an odd number.

[tex]$\frac{1}{2} \cdot \frac{2}{3} = \frac{2}{6}$[/tex]

chance of this happening. Adding these two probabilities together, we get

[tex]\frac{1}{6} +\frac{2}{6} =\frac{3}{6} =\frac{1}{2}[/tex]

Therefore, The probability that the sum of the two selected numbers is even is 1/2.

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The volume of given triangular prism is 24,000 cubic yards.

Volume is the measure of the capacity that an object holds.

Formula to find the volume of the object is Volume = Area of a base × Height.

Here, the dimensions of base are 30 yards and 20 yards.

Here, area = 1/2×30×20

= 300 yd²

Volume of a triangular prism = Area of base triangle × Length of the prism.

= 300×80

= 24,000 yd³

Therefore, the volume is 24,000 yd³.

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The lower bound for the weight 21.58 g correct to 2 decimal places is 21.57 g. This is because the next smallest value based on the rounding is obtained rounding down the number in second decimal place, which is 5.

To find the lower bound for the weight 21.58 g correct to 2 decimal places, we need to consider the next smallest number that can be represented to 2 decimal places.

Since the second decimal place is 8, the next smallest number is obtained by rounding down the number in the second decimal place, which is 5. Therefore, the lower bound for 21.58 g correct to 2 decimal places is: 21.57g

Note that the weight could be more precise than what we are given, but to represent it to 2 decimal places we have to make an assumption about the last digit.

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Exercise 1: Yes, 1.908 x 10^17 is written in scientific notation.

Exercise 2: Yes, 0.325 x 10^-2 is written in scientific notation.

Exercise 3: No, 7.99 x 10^32 is not written in scientific notation. The decimal d must be between 1 and 10, not between 10 and 100.

Exercise 4: No, 4.0701 + 10 is not written in scientific notation. The correct format is d x 10^n.

Exercise 5: No, 18.432 x 5 is not written in scientific notation. The correct format is d x 10^n.

Exercise 6: No, 8x 10^-11 is not written in scientific notation. The correct format is d x 10^n.

Answer:

113.75

Step-by-step explanation:

13$ x 8.75 h (45 minutes is 3/4 of an hour) = $113.75

keeping in mind that an hour has 60 minutes, so you're really getting paid $13 per 60 minutes, so now, 8 hours and 45 minutes is just 8*60 + 45 = 525 minutes.

[tex]\begin{array}{ccll} \$&minutes\\ \cline{1-2} 13 & 60\\ x& 525 \end{array} \implies \cfrac{13}{x}~~=~~\cfrac{60}{525} \\\\\\ \cfrac{ 13 }{ x } ~~=~~ \cfrac{ 4 }{ 35 }\implies 455=4x\implies \cfrac{455}{4}=x\implies 113.75=x[/tex]

The angle that VSR would correspond to, given that polygon ABCDE is congruent to polygon TVSRK, is 2. Angle C.

When polygons are said to be congruent, then it means that their sides are the same lengths, and they have the same angles which means that they are corresponding.

This therefore means that the angle at A in polygon ABCDE would be congruent to the angle at T in TVSRK.

This therefore means that the angle VSR would correspond to the angle C in ABCDE because S is the third letter in TVSRK and C is the third letter in ABCDE.

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The full question is:

Polygon ABCDE is congruent to polygon TVSRK. what do angle VSR correspond to _____?

1. Angle B

2. Angle C

3. Angle D

4. Angle A

The straight line distance from the front seat to the back is approximately 69.7 feet.

Straight line distance refers to the shortest distance between two points in a straight line, as opposed to the distance that would be traveled along a curved path or following the contours of the terrain.

Let the distance from the front row to the back row be x.

Then, we can use the tangent function to find the height difference between the front and back rows:

tan(12°) = (height difference) / x

Solving for the height difference:

height difference = x * tan(12°)

The problem tells us that the height difference is 15 feet, so we can set up an equation:

15 = x * tan(12°)

Solving for x:

x = 15 / tan(12°) ≈ 69.7 feet

Therefore, the straight line distance from the front seat to the back is approximately 69.7 feet.

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The expression that equals 2D−3C in standard form is -2s² - 11s - 7

Algebraic expressions are defined as expressions that are composed of coefficients, variables, terms,  factors and constants.

From the information given, we have that;

D=1−s^2 −s and C=3+3s,

To determine the expression for 2D - 3C

substitute the values of the expressions, we get;

2(1-s² - s) - 3(3 + 3s)

expand the bracket

2 - 2s² - 2s - 9 -9s

collect the like terms or factors, we get;

-2s² - 2x - 9s - 9 + 2

Add or subtract the values

-2s² - 11s - 7

Hence, the expression is -2s² - 11s - 7

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In a parallelogram, opposite sides are equal. Therefore, AB = CD.

5x * 3 = 15 * x

15x = 15

x = 1

Therefore, the value of x is 1.

To find the area of parallelogram ABCD, we can use the formula A = base x height, where the base is the length of side AB and the height is the perpendicular distance between side AB and the opposite side CD. Since the height of parallelogram ABCD is given as 6, we need to find the length of side AB.

From the given information, we know that AB = 5x * 3, where x = 1. Therefore, AB = 15. Now we can calculate the area of parallelogram ABCD as:

A = base x height

A = 15 x 6

A = 90 square units

Therefore, the area of parallelogram ABCD is 90 square units.

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The number of each type of ticket sold in the following situation:

1. The tickets of $5.00  = 400

2. The tickets of $7.50 =  200

A linear equation is an algebraic equation in which the highest power of the variable is 1. In simple words, a linear equation is an equation in which the variables appear only in the first degree.

Linear equations can be written in the form:

y = mx + b

where y and x are variables, m is the slope (or rate of change), and b is the y-intercept (the point where the line crosses the y-axis).

Let x be the number of tickets sold before the day of the game and y be the number of tickets sold at the game.

Then we have:

x + y = 600 (the total number of tickets sold)

and

5x + 7.5y = 3500 (the total receipts from ticket sales)

To solve for x and y, we can use substitution.

Simplify and solve for y:

3000 - 5y + 7.5y = 3500,

2.5y = 500

y = 200

Substitute y = 200 back into the equation x + y = 600 to find x:

x + 200 = 600,

x = 400.

Therefore, 400 tickets were sold before the day of the game and 200 tickets were sold at the game.

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The complete question:

The number of each type of ticket sold in the following situation: Tickets to a football game cost $5.oo if purchased before the day of the game. They cost $7.50 if purchased at the game. For a particular game, 600 tickets were sold and the receipts were $3500. Find the number of tickets sold before the day of the game and the number of tickets sold at the day of the game?

Answer:

100

Step-by-step explanation:

I hate that I have to use 20 characterz

Option (D) Between 5.1 and 5.3 is the correct answer fore the question where 5.2 on the number line would be located.

On a number line, each number is represented by a point. The location of a number on a number line depends on whether it is greater than or less than other numbers.

In the case of 5.2, it is located between 5.1 and 5.3, as option D states. This is because 5.2 is greater than 5.1 but less than 5.3. Therefore, its location on the number line would be between the points representing 5.1 and 5.3.

A number line is a useful visual tool for understanding the relative position of numbers to each other, as well as for performing basic arithmetic operations. Option (D) Between 5.1 and 5.3 is the correct answer fore the question where 5.2 on the number line would be located.

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Answer:

$8812.50

Step-by-step explanation:

To calculate the simple interest earned on Mia's investment, we can use the formula:

I = Prt

where I is the interest earned, P is the principal amount invested, r is the interest rate as a decimal, and t is the time in years.

Plugging in the values, we have:

I = $7500 * 0.035 * 5

I = $1312.50

The total amount Mia has after 5 years is the sum of her original investment and the interest earned:

$7500 + $1312.50 = $8812.50

Step-by-step explanation:

Equation of ellipse depends on the points

The points that lie on the horizontal axis is (0,8) and (4,8). They have a distance of 4, therefore a radius of 2

The points that lie on the vertical axis is (2,3) and (2,13)

They have a distance of 10, therefore a radius of 5

Since the vertical axis is bigger, we have a vertical ellipse which is the equation of,

[tex] \frac{(y - k) {}^{2} }{ {a}^{2} } + \frac{(x - h) {}^{2} }{ {b}^{2} } = 1[/tex]

Where a is the major radius

b is the minor radius

(h,k) is the center

Step 1: Finding the center

The center should be the midpoint of the horizontal vertices or vertical vertices

Let's use the horizontal vertices

[tex] (\frac{(0 + 4}{2} ) = 2[/tex]

[tex]( \frac{8 + 8}{2} ) = 8[/tex]

So the center is (2,8)

Step 2: Finding the major and minor radius

We already know it , a is 5

b is 2, so we as of now, have this equation

[tex] \frac{(y -8) {}^{2} }{25} + \frac{(x - 2) {}^{2} }{4} = 1[/tex]

This is the equation of the ellisoe

Step 3: Find the foci

The foci for a vertical ellipse should lie on the same line as the same line as the major vertices and center.

The equation for an ellipse foci that is vertical are

(x,y+c) and (x,y-c)

Where C is

[tex]c = \sqrt{ {a}^{2} - {b}^{2} } [/tex]

[tex]c = \sqrt{25 - 4} [/tex]

[tex]c = \sqrt{21} [/tex]

So our foci are

,,,

[tex](2,8 + \sqrt{21} )[/tex]

and

[tex](2,8 - \sqrt{21} )[/tex]

,

Yes, providing additional information affect responses to a survey question. The difference in the proportion of shoppers who admitted to texting and driving in the two groups is 0.2.

To calculate the difference in the proportion of shoppers who admitted to texting and driving in the two groups, we need to first determine the number of shoppers in each group who admitted to texting and driving.

Let's assume that in Group A, 10 shoppers admitted to texting and driving, while in Group B, 5 shoppers admitted to texting and driving.

Then, we can calculate the proportion of shoppers who admitted to texting and driving in each group by dividing the number of shoppers who admitted to texting and driving by the total number of shoppers in each group:

Proportion in Group A = 10/25 = 0.4

Proportion in Group B = 5/25 = 0.2

The difference in proportions is then:

Difference = Proportion in Group A - Proportion in Group B

Difference = 0.4 - 0.2

Difference = 0.2

Therefore, the difference in the proportion of shoppers who admitted to texting and driving in the two groups (A-B) is 0.2 or 20%.

This suggests that providing additional information about the potential consequences of texting and driving may reduce the proportion of people who admit to engaging in this behavior. However, it's important to note that this study has a small sample size and there may be other factors that influence people's responses to survey questions about texting and driving.

Correct Question :

Does providing additional information affect responses to a survey question? Two statistics students decided to investigate by asking different versions of a question about texting and driving. Fifty mall shoppers were divided into two groups of 25 at random. The first group was asked Version A and the other half were asked Version B. Version A: A lot of people text and drive. Are you one of them? Version B: About 6000 deaths occur per year due to texting and driving. Knowing the potential consequences, do you text and drive? Calculate the difference in the proportion of shoppers who admitted to texting and driving in the two groups (A-B).

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The equation will be written as [tex]A = 325[1.004]^{12t}[/tex]. The time taken to reach $200 will be 10 years.

Compound interest is defined as the interest levied upon the interest. The formula to calculate the compound interest will be written as:-

[tex]A = P[1+\dfrac{r}{m}]^{rt}[/tex]

Given that Hassan places $325 into a savings account that offers a monthly compound interest rate of 4.7%.

The equation for the compounding on monthly basis,

[tex]A = 325[1+\dfrac{0.047}{12}]^{12t}[/tex]

[tex]A = 325[1.004]^{12t}[/tex]

The time will be calculated as:-

[tex]A = 325[1.004]^{12t}[/tex]

[tex]200 = 325[ 1.004]^{12t}[/tex]

log(0.615) = 12 x t x log(1.004)

12t = 121.77

t = 10 years

Therefore, the equation will appear as  [tex]A = 325[1.004]^{12t}[/tex]. It will take 10 years for the price to reach $200.

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Completing the equation below by writing an expression equivalent to the length of a, the leg of a right triangle is given below

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry.

According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Hence, the complete equation according to this theorem is given above.

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nonononononononnnono

Answers:

===========================================

Work Shown:

[tex]15 \text{ m} = (15 \text{ m})*\frac{100 \text{ cm}}{1 \text{ m}} = 1500 \text{ cm}\\\\\\1.6 \text{ km} = (1.6 \text{ km})*\frac{1000 \text{ m}}{1 \text{ km}}*\frac{100 \text{ cm}}{1 \text{ m}} = 160,000 \text{ cm}\\\\\\467 \text{ mm} = (467 \text{ mm})*\frac{1 \text{ cm}}{10 \text{ mm}} = 46.7 \text{ cm}[/tex]

Each conversion fraction is set up to cancel out any unit that isn't "centimeters".

Side notes:

The way the altitude changes is  24,600 (0 minutes), 19,475 (5 minutes), 16,400 (8 minutes), 14,350(10 minutes), and 6,150 (30 minutes).

To calculate the change in the altitude, let's use the formula given:

0 minutes:

Y = - 1025 x 0+ 24,600

Y = 24,600

5 minutes:

Y = - 1025 x 5+ 24,600

Y = -5125 + 24, 600

Y = 19,475

8 minutes:

Y = - 1025 x 8+ 24,600

Y = -8200 + 24, 600

Y = 16,400

10 minutes:

Y = - 1025 x 10+ 24,600

Y = -10250 + 24, 600

Y = 14,350

30 minutes:

Y = - 1025 x 30+ 24,600

Y = -30,750 + 24, 600

Y = 6,150

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