Because of an insufficient oxygen supply, the trout population in a lake is dying. The population's rate of change can be modeled by the equation below where t is the time in days. dP dt = = 125e-t/15 = Whent 0, the population is 1875. (a) Write an equation that models the population P in terms of the time t. P= x (b) What is the population after 12 days? fish (c) According to this model, how long will it take for the entire trout population to die? (Round to 1 decimal place.) days

Answer:

$112,710

Step-by-step explanation:

so first we have to find what is 15% of 86700

so 15/100×86700=$13005

so it is written that 86700 is in 2012 means 2010 it will be

2 times more which means 30% that means just have to do is multiply it two times which makes it $26010

so $86700+$26010=$112710

hope it helps you

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No, (−5, −4) is not a solution of the system. The ordered pair (−5, −4) is a point in the Cartesian plane, but it is not necessarily a solution of any system of equations.

To determine whether an ordered pair is a solution of a system of equations, we must substitute the values of the ordered pair into the equations in the system and determine whether the equations are true.

For example, consider the following system of equations:

3x − 5y = 20

2x + 4y = 10

To determine whether (−5, −4) is a solution of this system, we must substitute the values of x and y into the equations and determine whether the equations are true.

For the first equation:

3x − 5y = 20

3(-5) − 5(-4) = 20

15 + 20 = 20

35 ≠ 20

For the second equation:

2x + 4y = 10

2(-5) + 4(-4) = 10

-10 - 16 = 10

-26 ≠ 10

Since neither equation is true when the values of (−5, −4) are substituted into the equations, we can conclude that (−5, −4) is not a solution of the system.

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The symbolic equation A = k\(B^3\) signifies that A is directly proportional to the cube of B. This means that as the value of B increases, the value of A will increase by a factor equal to the cube of B.

The symbolic equation A = k\(B^3\) indicates that A is directly proportional to the cube of B. This means that as the value of B increases, the value of A will increase by a factor equal to the cube of B. Conversely, if the value of B decreases, A will decrease accordingly, following the cube of B.

In other words, if we were to double the value of B, A would increase by a factor of 8 (\(2^3\)), and if we were to triple the value of B, A would increase by a factor of 27 (\(3^3\)). This relationship holds true for any positive real values of B.

To understand this concept better, consider an example where A represents the volume of a cube and B represents the length of its side. If we increase the length of the side (B) by a factor of 2, the volume (A) will increase by a factor of 8 since the volume of a cube is calculated by multiplying the length of the side three times (A = \(B^3\)).

Therefore, option a. A is proportional to the cube of B is the correct interpretation of the symbolic equation A = k\(B^3\).

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The probability can be calculated as given because there are a total of 52 cards.

It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

Total number of card = 52

Number of king of heart = 1

P(getting a king of hearts) = 1/52

P(getting a spade) = 13/52 = 1/4

P (getting a 5 or a club) = (16/52) = 4/13

P(getting a 5 or a 7) = 4/52 + 4/52 = 8/52 = 2/13

P(getting a card which is not a spade) = 1 - 1/4 = 3/4

P(getting 11 of clubs) = 1/52

Thus, the probability can be calculated as given because there are a total of 52 cards.

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Answer:

1. 1

2. 51

3. 7

4. 9

Step-by-step explanation:

hope i helped

Answer:

  B.  6 per hour

Step-by-step explanation:

You want to know the arrival rate if the average time between arrivals is 10 minutes.

The rate is the inverse of the period.

  (1 arrival)/(10 minutes) = (1 arrival)/(1/6 h) = 6 arrivals/h

The arrival rate is 6 per hour.

<95141404393>

Therefore, the arrival rate is 6 per hour. Only option B has the same value as calculated, that is, 6 per hour.

A single-channel queuing system has an average service time of 8 minutes and an average time between arrivals of 10 minutes.

The arrival rate can be determined using the following formula:λ=1/twhere,λ is the arrival rate and t is the average time between arrivals. Substitute t=10 in the above equation, we getλ=1/10=0.1Now, let’s check which of the given options is equal to 0.1.5 per hour is equal to 5/60 per minute=1/12 per minute≠0.1.8 per hour is equal to 8/60 per minute=2/15 per minute≠0.1.6 per hour is equal to 6/60 per minute=1/10 per minute=0.1 (Correct)2 per hour is equal to 2/60 per minute=1/30 per minute≠0.1. Therefore, the correct answer is option B, 6 per hour. Explanation: Arrival rate=λ=1/tWhere t is the average time between arrivals. Given, the average time between arrivals =10 minutes, therefore,λ=1/10=0.1For the given options, only option B has the same value as calculated, that is, 6 per hour.

Therefore, the arrival rate is 6 per hour. Only option B has the same value as calculated, that is, 6 per hour.

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As a result, the two phrases are logically equal. The two formulations are not logically identical, as we can see. The two formulations are not logically identical, as we can see.

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms.

Here,

(a) The first statement can be expressed as:

(~j -> (l v ~r))

The second statement can be expressed as:

((r ^ ~l) -> j)

To determine whether the two expressions are logically equivalent, we can use truth tables. A truth table is a method for checking the validity of logical equivalences by comparing the truth values of the two expressions for all possible combinations of inputs.

Truth table for (~j -> (l v ~r)) and ((r ^ ~l) -> j):

j l r (~j -> (l v ~r)) ((r ^ ~l) -> j)

T T T T T

T T F T T

T F T F F

T F F T T

F T T T T

F T F T T

F F T T T

F F F T T

Since both expressions have the same truth values for all possible combinations of inputs, we can conclude that the two expressions are logically equivalent.

(b) The first statement can be expressed as:

(j -> ~l)

The second statement can be expressed as:

(~j -> l)

Truth table for (j -> ~l) and (~j -> l):

j l (j -> ~l) (~j -> l)

T T T F

T F T T

F T T T

F F T T

Since the expressions have different truth values for some combinations of inputs, we can conclude that the two expressions are not logically equivalent.

(c) The first statement can be expressed as:

((r v ~l) -> j)

The second statement can be expressed as:

(j -> (r ^ ~l))

Truth table for ((r v ~l) -> j) and (j -> (r ^ ~l)):

j l r ((r v ~l) -> j) (j -> (r ^ ~l))

T T T T T

T T F T T

T F T T T

T F F T T

F T T T F

F T F T F

F F T T F

F F F T T

Since the expressions have different truth values for some combinations of inputs, we can conclude that the two expressions are not logically equivalent.

We can conclude that the two expressions are logically equivalent. We can conclude that the two expressions are not logically equivalent. We can conclude that the two expressions are not logically equivalent.

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To show the number of inches the plant grew, the expression will be 8-x.

A finite combination of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression in mathematics.

A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. It is possible to multiply, divide, add, or subtract in math.

Expression is a term used in mathematics to describe a grouping of numbers, variables, and operators that illustrates the value of something. A mathematical statement that has two expressions that are equal is known as an equation. A phrase fragment can be used as an expression to represent a single numerical value.

To show the number of inches the plant grew, it will be 8-x.

As 8 > x.

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RHS stands for Right-Hypotenuse-side rule. If the hypotenuse ans a side of a right-angled triangle is equivalent to the hypotenuse and a side of the second right-angled triangle, then the two right triangles are said to be congruent by RHS rule.

RHS congruence rule states that, in two right-angled triangles, if the length of the hypotenuse and one side of one triangle, is equal to the length of the hypotenuse and corresponding side of the other triangle, then the two triangles are congruent.  Two right triangles are congruent if the hypotenuse and one side of one triangle are equal to the corresponding hypotenuse and one side of the other triangle.  

This rule is only applicable in right-angles triangles. An important point to note here is that when we keep hypotenuse and any one of the other two sides of two right triangles equal, we are automatically getting three similar sides, as all three sides in a right triangle are related to each other and that relation is popularly known as Pythagoras theorem.

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The best description of the passenger's linear and angular velocity while passing point A is option d) Linear Velocity Constant, Angular Velocity Constant.

When the passenger is at point A, which is the highest point of the ride, the seat exerts a normal force with a magnitude of 0.8F, where F represents the person's weight. This normal force provides the necessary centripetal force to keep the person moving in a circular path. At this point, the passenger's linear velocity remains constant, as there is no change in speed.

Since the passenger releases a small rock without hitting anything, there are no external torques acting on the system. Therefore, according to the law of conservation of angular momentum, the passenger's angular velocity remains constant as well. The angular velocity is determined by the rotational motion of the wheel and does not change as the passenger passes point A.

Therefore, the passenger's linear velocity is constant, and their angular velocity is also constant while passing point A, resulting in the most accurate description being d) Linear Velocity Constant, Angular Velocity Constant.

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The final temperature in North Bay is 28° , as calculated using the Newton's model of temperature.

Temperature in north bay = 23°

Temperature falls by 7° , hence new temperature = 23° - 7 ° = 16°

Again temperature rises by 12° , hence final temperature = 16° + 12° = 28°

Therefore the final temperature is 28° .

How hot or cold something is can be expressed numerically using the physical concept of temperature. Temperature is measured with a thermometer.

Different scales of temperature, which normally established a large number of reference points and thermometric materials, are mainly used to calibrate thermometers. The most widely used scales are the Kelvin scale (K), which is mostly used in science, the Fahrenheit scale (°F), and the Celsius scale, also referred to as centigrade and denoted by the unit symbol °C.

Kinetic theory offers a microscopic account of temperature for particular forms of material, especially gases, based on the premise that macroscopic systems are composed of multiple microscopic particles, such as molecules and ions of various species, the particles of a species being all comparable.

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The lines y = 2 and x = 4 are neither parallel nor perpendicular.

The given lines are y = 2 and x = 4.

The line y = 2 is a horizontal line because the value of y remains constant at 2, regardless of the value of x. This means that all points on the line have the same y-coordinate.

On the other hand, the line x = 4 is a vertical line because the value of x remains constant at 4, regardless of the value of y. This means that all points on the line have the same x-coordinate.

Since the slope of a horizontal line is 0 and the slope of a vertical line is undefined, we can determine that the slopes of these lines are not equal. Therefore, the lines y = 2 and x = 4 are neither parallel nor perpendicular.

Parallel lines have the same slope, indicating that they maintain a consistent distance from each other and never intersect. Perpendicular lines have slopes that are negative reciprocals of each other, forming right angles when they intersect.

In this case, the line y = 2 is parallel to the x-axis and the line x = 4 is parallel to the y-axis. Since the x-axis and y-axis are perpendicular to each other, we might intuitively think that these lines are perpendicular. However, perpendicularity is based on the slopes of the lines, and in this case, the slopes are undefined and 0, which are not negative reciprocals.

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The volume of the rectangular prism having a dimensions 12 by 8 by 2 is 192.

A rectangular prism is simply a three-dimensional solid shape which has six faces that are rectangles.

The volume of a rectangular prism is expressed as;

V = w × h × l

Where w is the width, h is height and l is length

From the diagram:

Length l = 12 units

Width w = 8 units

Height h = 2 units

Plug these values into the above formul and solve for the volume:

Volume V = w × h × l

Volume V = 8 × 2 × 12

Volume V = 192 cubic units.

Therefore, the volume is 192.

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Answer:

Joseph recieved a discountwof $85.

Answer:

50/77

Step-by-step explanation:

(1÷2 3/4)+(1÷3 1/2)

2 3/4 is same as 11/44

1/2 is same as 7/2

so to divide fraction you have to flip the second number and multiply

so 1 times 4/11=4/11

and 1 times 2/7=2/7

4/11 +2/7=28/77+22/77=50/77

Answer:

0.333333333333

Step-by-step explanation:

We simplify the equation to the form, which is simple to understand

4(p+2)+8=2(p-1)-7p+15

Reorder the terms in parentheses

+(+4p+8)+8=2*(p-1)-7p+15

Remove unnecessary parentheses

+4p+8+8=+2+*(+p-1+)-7p+15

Reorder the terms in parentheses

+4p+8+8=+(+2p-2)-7p+15

Remove unnecessary parentheses

+4p+8+8=+2p-2-7p+15

We move all terms containing p to the left and all other terms to the right.

+4p-2p+7p=-2+15-8-8

We simplify left and right side of the equation.

+9p=-3

We divide both sides of the equation by 9 to get p.

p=-0.333333333333

Answer:

The answer is p=13

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

−4(p+2)+8=2(p−1)−7p+15

(−4)(p)+(−4)(2)+8=(2)(p)+(2)(−1)+−7p+15(Distribute)

−4p+−8+8=2p+−2+−7p+15

(−4p)+(−8+8)=(2p+−7p)+(−2+15)(Combine Like Terms)

−4p=−5p+13

−4p=−5p+13

Step 2: Add 5p to both sides.

−4p+5p=−5p+13+5p

p=13

Happy Holidays! =)

\(\large\boxed{x = -\frac{5}{2} \text{ and } 1}}\)

4x² + 6x = 10

Move 10 to the other side so we can factor the trinomial:

4x² + 6x - 10 = 0

Factor the GCF, or 2 out of the equation:

2(2x² + 3x - 5) = 0

Factor the terms inside of the parenthesis:

2(2x + 5)(x - 1) = 0

Disregard the coefficient of 2 and set each factor equal to 0:

2x + 5 = 0

2x = -5

x = -5/2

x - 1 = 0

x = 1

The values of x are -5/2 and 1.

Answer:

(x+3/2,y+3/2)=(-6,-16)

Step-by-step explanation:

x+3=-12,y+3=-32

x=-15,y=-35

If the midpoint of a segment is (-6,-16) and one endpoint is (3,3), the other endpoint is, (-15, -35)

Midpoint is a point which is at the equal distance from both the points.

Formula for midpoint,

P(Xₐ, Yₐ) = [ (X₁+X₂)/2 , (Y₁+Y₂)/2 ]

Given that,

Mid-point of segment =   (-6,-16)

one endpoint is (3,3)

other endpoint = ?

-6  = 3+x/2

x = -15

-16 = 3+y/2

y = -35

Hence, the other point is (-15, -35)

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Answer:B

Step-by-step explanation:

The amoeba splits 24 times, meaning that the number of amoebas will be

2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2 or 2^24

Answer:

6seconds

Step-by-step explanation:

Given the height of an object modeled by the expression

h(x)=-5x^2+20x+60

The height of the object on the ground is zero i.e h(x) = 0

On substituting

h(x)=-5x^2+20x+60

0 =-5x^2+20x+60

Multiply through by -1

5x^2-20x- 60 = 0

Divide through by 5

x^2 - 4x - 12 = 0

x^2 - 6x + 2x - 12 = 0

x(x-6)+2(x-6) = 0

(x-6)(x+2) = 0

x - 6 = 0 and x+2  = 0

x = 6 and -2

Since time cannot be negative, hence it takes 6seconds after launch for the object land to on the ground

Answer:

6

Step-by-step explanation:

It was correct on Khan.

By using Python, you will come up with your own challenging algorithm for other students to trace.

If a certain is true, the if/else expression triggers a sequence of instructions to run. Another piece of code may be run if the condition is false.

The if/else statement is a component of Python's "Conditional" Statements, which are used to carry out various operations based on various circumstances.

These conditional statements are available in Python:

If you want a block of code to run only if a certain condition is true, use the if statement.

If the same expression is false, use instead that to provide a set of instructions that should be run.

If the first expression is false, can use else if sentence to establish a comprehensive criterion to test.

To choose which of the several program code should be performed, use the switch.

How to write the code?

num = 100

if num < 20:

print('Less than 20')

if num < 30:

print('Less than 30')

if num < 40:

print('Less than 40')

if num < 50:

print('Less than 50')

if num > 100 or num == 100:

print('More than or equal to 100')

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Answer:

You can use Protector' but dint have use this method:

Acute. Draw a vertical line connecting the 2 rays of the angle. To determine the number of degrees in an acute angle, connect the 2 rays to form a triangle. Line up the short end of your ruler with the bottom ray, then draw a vertical line intersecting the other ray using the long side of your ruler.

Answer:

21

Step-by-step explanation:

-19+26= 7

7+14= 21

Answer:

8.79 % tax rate

Step-by-step explanation:

total paid = tax + price

57.50 = tax +52.85

tax = 4.65

tax rate =( tax ÷ price before the tax) × 100%

= (4.65÷ 52.85) × 100%

= 8.79%

The factorization of 18y - 21 = 3(6y - 7)

Factorization is the simplification of an expression by grouping similar term together into smaller terms.

Since we have the expression 18y - 21, and we desire to factorize it, we proceeds as folows.

Since we have 18y - 21. we write each term out as a product of their common factors.

So,

18y - 21 = 3 × 6 × y - 3 × 7

Factorizing out the common factor 3, we have that

18y - 21 = 3 × 6 × y - 3 × 7

18y - 21 = 3(6 × y - 7)

= 3(6y - 7)

So, we have the expression as 3(6y - 7)

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In the proportional relationship, the value of y when x = 7 is 28.

Direct proportion or direct variation is the relation between two quantities where the ratio of the two is equal to a constant value.

Therefore, the value of y is directly proportional to the value of x. When x = 3.5, the value of y is 14.

Hence,

y ∝ x

y = kx

where

when y = 14 , x = 3.5

14 = 3.5k

k = 14 / 3.5

k = 4

Therefore,  let's find the value of y when x = 7.

y = 4 × 7

y = 28

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Answer:

1 notebook $2.39

Step-by-step explanation:

n=notebook     b= binder

6n +2b =23.52

3n +4b = 25.53

MULTIPLY THE FIRST BY -2 AND ADD BOTH

-12n -4b = -47.04

3n + 4b = 25.53

(b is eliminated since 4b -4b=0)

-9n =  -21.51

9n = 21.51

n = 2.39

Answer:

A), C), E)

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

(f - g )(x)

= f(x) - g(x)

= 3x + 2 - (2x - 2) ← distribute parenthesis by - 1

= 3x + 2 - 2x + 2 ← collect like terms

= x + 4

The value of the function (f-g)(x) is x+4.

A function in math is a rule or expression that defines a relationship between one variable (the input or independent variable) and another variable (the output or dependent variable).

Given are two functions, f(x) = 3x+2 and g(x) = 2x-2, we need to find the value of (f-g)(x)

So,

(f-g)(x) = f(x) - g(x)

= 3x+2 - (2x-2)

= x+4

Hence, the value of the function (f-g)(x) is x+4.

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