Which aquatic ecosystem is the deepest?

estuary
open ocean
lake
coral reef

\((\stackrel{x_1}{-2}~,~\stackrel{y_1}{4})\qquad \qquad \stackrel{slope}{m}\implies 5 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{5}(x-\stackrel{x_1}{(-2)})\implies y-4=5(x+2)\)

The function P(x) for the total profit from the production and sale of x toilets is P(x) = 90x - 16600

The given parameters are

Fixed cost = 16600

Variable cost = 67 per toilet

Cost of toilet = 157 per toilet

Let the number of toilets be x

So, the cost function is

C(x) = Fixed cost + Variable cost * Number of toilets

This gives

C(x) = 16600 + 67x

Also, we have the revenue function to be

R(x) = Cost of toilet  * Number of toilets

This gives

R(x) = 157x

The function P(x) for the total profit from the production and sale of x toilets is

P(x) = R(x) - C(x)

So, we have

P(x) = 157x - 16600 - 67x

Evaluate

P(x) = 90x - 16600

Hence, the function P(x) for the total profit from the production and sale of x toilets is P(x) = 90x - 16600

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Answer:

FE→

Step-by-step explanation:

You start with the endpoint and go in the direction of the arrow

FE

It will have an arrow on top with an endpoint on the left and an arrow going in the same direction to indicate it is a ray→

Answer:

the minimum possible time for Emma to reach the island is approximately 2.9583 hours, when she starts swimming at a point 5/6 km east of the cottage.

Step-by-step explanation:

We can use the concept of minimum distance to find the minimum possible time for Emma to reach the island. Let's assume that Emma walks to some point P along the shoreline and then swims to the island. We want to find the point P that minimizes the total distance that Emma has to cover.

Let the distance from the cottage to point P be x km. Then the distance from point P to the island is (3 - x) km. Using the Pythagorean theorem, we can find the distance from the cottage to the island as follows:

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

distance^2 = 10x - 6x^2 + 13

To minimize the distance, we can take the derivative of the distance equation with respect to x and set it equal to zero:

d(distance^2)/dx = 10 - 12x = 0

x = 5/6 km

Substituting x = 5/6 km into the distance equation, we get:

distance^2 = 25/3 km^2

distance = 5/sqrt(3) km

Therefore, the minimum possible time for Emma to reach the island is the time it takes her to walk to point P (distance x) plus the time it takes her to swim to the island (distance 3 - x), divided by her swimming speed:

time = x/4 + (3 - x)/3

time = (3x + 12 - 4x)/12

time = (12 - x)/4

time = (12 - 5/6)/4

time = 2.9583 hours (rounded to 4 decimal places)

Therefore, the minimum possible time for Emma to reach the island is approximately 2.9583 hours, when she starts swimming at a point 5/6 km east of the cottage.

Let's call the point where Emma starts swimming P. We can draw a diagram to visualize the situation:

Cottage ---------- Q ---------------- Island

x km 3 km 2 km

The distance from the cottage to Q is x km, and the distance from Q to the island is 2 km. The total distance Emma will have to travel can be expressed as:

d = √(x^2 + 2^2)

The time it will take Emma to walk the distance from the cottage to point P is:

t1 = x / 4

The time it will take Emma to swim from point P to the island is:

t2 = √((d - x)^2 + 2^2) / 3

The total time it will take Emma to reach the island can be expressed as:

T = t1 + t2

To find the minimum possible value of T, we can take the derivative of T with respect to x and set it equal to zero:

dT/dx = (1/4) - (d-x)/3√((d-x)^2+4) = 0

Solving for x, we get:

x = (3/5)d

Substituting this value of x back into the expression for T, we get:

T = (3/20)d + (2/5)√(5)

Rounding to the nearest hundredth, we get:

T ≈ 0.96 hours

Therefore, the minimum possible time it will take Emma to reach the island is approximately 0.96 hours.

Answer:

\(\sf 22\dfrac{1}{2}\; years\)

Step-by-step explanation:

\(\textsf{First convert all mixed fractions to improper fractions: }\\\\3\dfrac{2}{3} = \dfrac{3 \times 3 + 2}{3}= \dfrac{11}{3}\\\\18\dfrac{5}{6 } = \dfrac{18 \times 6 + 5}{6} = \dfrac{113}{6}\)

Let Carlo's age be C

Carlo's age = sister's age + 11/3

\(\sf == > C = \dfrac{113}{6} +\dfrac {11}{3}\\\\\textsf{Multiply both sides by 6 to eliminate the denominator}\\\\\sf 6C = 6\cdot\dfrac{113}{6} + 6\cdot\dfrac {11}{3}\\\\\)

\(\sf == > C = \dfrac{113}{6} +\dfrac {11}{3}\\\\\textsf{Multiply both sides by 6 to eliminate the denominator}\\\\\sf 6C = 6\cdot\dfrac{113}{6} + 6\cdot\dfrac {11}{3}\\\\\sf 6C = 113 + 22 = 135\\\)

\(\textsf {Divide both sides by 6}\\\\\sf C = \dfrac{135}{6} \\\\\textsf {Reduce $\dfrac{135}{6}$ by dividing numerator and denominator by 3}\\\\== > C = \dfrac{135 \div 3}{6\div3} = \dfrac{45}{2}\)

\(\textsf{So Carlo's age is $\dfrac{45}{2}$ or $22\dfrac{1}{2}$ years}\)

The graph of f(x) is shifted 16 units down

The equation of the functions are given as

f(x) = 1/x

g(x) = 1/x - 16

The transformed function is the function f(x)

i.e. from function f(x) to g(x)

By comparing the functions' equation, we can see that the function f(x) is translated to get to function g(x)

In this case, the function is f(x) is translated down by 16 units to get to function g(x)

So, the graph of g(x) is gotten by translating the function f(x) = 1/x down by 16 units to get to function g(x)

Hence, the graph of f(x) is shifted 16 units down

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Answer:

12345 < 54321

21435 > 12534

:

Step-by-step explanation:

Given the digits:

1, 2, 3, 4 and 5

We have to use every digit only once and have to make two different five digit numbers.

Using these 5 numbers only once without repetition, we have many numbers possible.

Let us have a look at a few sets and let us compare them.

Set 1: 12345 and 54321

We can see that 12345 is lesser than 54321.

Therefore, we can write (using lesser than sign):

12345 < 54321

Set 2: 21435 and 12534

We can see that 21435 is greater than  12534.

Therefore, we can write (using greater than sign):

21435 > 12534

Answer:

Option (2) and Option (4)

Step-by-step explanation:

From the picture attached,

Length of ladder AC = 20 feet

Height of the highest point of the ladder from ground AB = 16 ft

By Pythagoras theorem,

AC² = BC² + AB²

BC² = AC² - AB²

BC = \(\sqrt{(20)^2-(16)^2}\)

     = \(\sqrt{400-256}\)

     = \(\sqrt{144}\)

     = 12

Now, Sinθ = \(\frac{\text{Opposite side}}{\text{Hypotenuse}}=\frac{\text{AB}}{\text{AC}}\)

                 = \(\frac{16}{20}\)

Cosθ = \(\frac{\text{Adjacent side}}{\text{Hypotenuse}}=\frac{\text{BC}}{\text{AC}}\)

         = \(\frac{12}{20}\)

tanθ = \(\frac{\text{Opposite side}}{\text{Adjacent side}}=\frac{\text{AB}}{\text{BC}}\)

        = \(\frac{16}{12}\)

Therefore, Option (2) and Option (4) are the correct options.

The equation that should be used is option 2 and option 4.

Since

Length of ladder AC = 20 feet

Height of the highest point of the ladder from ground AB = 16 ft

So here we apply the Pythagoras theorem,

AC² = BC² + AB²

BC² = AC² - AB²

So,

\(BC = \sqrt{(20)^2 - (16)^22}\\\\ = \sqrt{400 - 256}\\\\ = \sqrt{144}\)

= 12

Now

Sin θ = 16\20

Cos θ = 12\20

tan θ = 16 \12

hence, The equation that should be used is option 2 and option 4.

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Answer:

2

Step-by-step explanation:

Leah uses 1/4 cup of chocolate chips for 2/3 cups of batter, so if Leah uses 3/4 cup of chocolate chips, she should use 2 cups of batter.

The percentage of children with cancer who enter remission after five years is the variable being measured. This proportion is typical of all the youngsters who have been given a cancer diagnosis.

Calculating the chance that an event will occur or a statement will be true is the subject of probability theory, a branch of mathematics. A risk is a number between 0 and 1, where 1 denotes certainty and a probability of about 0 denotes the likelihood that an event will occur. The likelihood that an event will take place is mathematically expressed as probability. Probabilities can also be expressed as percentages ranging from 0% to 100% or as integers between 0 and 1. the proportion of equally plausible possibilities that actually happen in relation to all possible outcomes when a certain event occurs.

B) In 2001, 78% of children with cancer were in remission after five years, and this percentage is rising. This analysis employs a population parameter. The percentage of children with cancer who enter remission after five years is the variable being measured. This proportion is typical of all the youngsters who have been given a cancer diagnosis.

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Answer:

74

Step-by-step explanation:

plug the numbers in: 10(2) + 6(9)

multiply it out: 20 + 54

add: 74

The cost of each pound of grass seed is $6.

A graph of the solution for the cost of each pound of grass seed is shown below.

In order to determine the cost of each pound of grass seed, we would assign a variable to the cost of each pound of grass seed and then translate the word problem into an algebraic linear equation.

Let the variable x represent the cost of each pound of grass seed.

Since Lori bought 3.6 pounds of grass seed and she was charged $22.90, including a tax of $1.30, an algebraic linear equation that best represent this situation is given by;

3.6x + 1.30 = 22.90

3.6x = 22.90 - 1.30

3.6x = 21.60

x = 21.60/3.6

x = $6.

In conclusion, we would sue an online graphing calculator to plot the solution for the cost of each pound of grass seed as shown in the image attached below.

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Answer:

\(\sqrt{11}\)

Step-by-step explanation:

well first you have to plug in a and c in the Pythagorean theorem.

\(a^2+b^2=c^2\\(2\sqrt{2})^2+b^2 =(\sqrt{15})^2\)

then squaring the square roots cancels them out sooo it becomes

\(4 +b^2=15\)

and then isolate b

\(b^2 = -4 +15\\\\\\b=\sqrt{-4+15} \\b=\sqrt{11}\)

and there you have it. b is \(\sqrt{11}\)

Juliet will earn the same amount of money whether she chooses a monthly salary of ​$1900 from the company or a base salary of ​$1800 plus a ​5% commission on furniture sales if her sales amount to $2000.

To find the amount of sales for which the two salary choices are equal, we set the equation for the base salary plus commission equal to the equation for the flat monthly salary. The equation can be written as:

1800 + 0.05x = 1900

where x is the amount of furniture sales in dollars.

Simplifying and solving for x, we get:

0.05x = 100

x = 2000

If she sells less than $2000 of furniture, she will earn more with the flat monthly salary of $1900. If she sells more than $2000 of furniture, she will earn more with the base salary plus commission. This calculation provides an important decision-making tool for Juliet, as she can tailor her salary choice based on her expected sales for the month.

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Answer:

Step-by-step explanation:

We are given that the probability of a millennial being an active user of social media is 0.904. Let X be the number of millennials in a group of 54 who are active users of social media. Then X follows a binomial distribution with n = 54 and p = 0.904.

(a) To find the probability that more than 48 are active on social media, we can use the cumulative distribution function (CDF) of the binomial distribution:

P(X > 48) = 1 - P(X ≤ 48)

Using a binomial distribution table or a calculator with a binomial CDF function, we find:

P(X > 48) = 1 - 0.991 = 0.009

Therefore, the probability that more than 48 out of 54 millennials are active users of social media is 0.009.

(b) To find the probability that at most 45 are active on social media, we can use the binomial CDF:

P(X ≤ 45) = 0.077

Therefore, the probability that at most 45 out of 54 millennials are active users of social media is 0.077.

(c) To find the probability that between 42 and 47 (including 42 and 47) are active on social media, we can use the binomial CDF:

P(42 ≤ X ≤ 47) = P(X ≤ 47) - P(X < 42)

Using a binomial distribution table or a calculator with a binomial CDF function, we find:

P(42 ≤ X ≤ 47) = 0.996 - 0.126 = 0.870

Therefore, the probability that between 42 and 47 out of 54 millennials are active users of social media is 0.870.

(d) To find the probability that exactly 48 are active on social media, we can use the probability mass function (PMF) of the binomial distribution:

P(X = 48) = (54 choose 48) * (0.904)^48 * (0.096)^6

Using a binomial distribution table or a calculator with a binomial PMF function, we find:

P(X = 48) = 0.135

Therefore, the probability that exactly 48 out of 54 millennials are active users of social media is 0.135.

Answer:

Domain: All real numbers, except for x=4

Range: All real numbers

Step-by-step explanation:

There is no limit to how far either of the graphs go, so it will be infinite.

Answer:

C) y = -1/3x + 3

Step-by-step explanation:

y - 3x = 2

  + 3x   + 3x

y = 3x + 2

find the reciprocal of the slope (3) which is -1/3 so -1/3 will be the slope for the perpendicular line

y = (-1/3)x + b

now find the y-intercept (b)

(6,1) x = 6   y = 1

y = (-1/3)x + b

1 = (-1/3)6 + b

1 = -2 + b

+2  +2

3 = b

y = (-1/3)x + 3

Answer:

7.) The coordinates of point K are (10,8)

8.) The length of the radius, to the nearest hundreth, is of 4.24 units.

Step-by-step explanation:

P is the center of a circle with diameter KR:

This means that P is the midpoint between K and R.

I will see that the points are:

Since P is the midpoint:

P(7,-5) and R(4,-2)

This means that:

7. If P(7,-5) and R(4,-2), find the coordinates of point K

Substituting:

Now we do the same for y:

Replacing with what we have

The coordinates of point K are (10,8)

8. What is the length of the radius to the nearest hundredth?

The radius is half the diameter(distance between KR divided by 2). It can also be the distance between an endpoint of the circle and the centre(Distance between P and K, or between P and R).

I am going to calculate the distance between P and R.

P(7,-5) and R(4,-2). So

The length of the radius, to the nearest hundreth, is of 4.24 units.

Answer:

A

Step-by-step explanation:

Answer:

$5.02

Step-by-step explanation:

Answer:

5.02

Step-by-step explanation:

If water flows into the container at a constant rate of 6 cubic feet per minute, the rate at which the water level rising when the height of the water is 5 feet is; 0.688 ft/min

When we are given an equation that gives the relationship between two or more variables, then by differentiating the equation with respect to time would give us a new equation that involves the rate of change of each of the given variables.

We are given the dimensions of the tank as;

Radius; r = 4 feet

Height; h = 12 feet.

The water in the tank will also have a conical shape.

By similar triangles, we know that;

r/h = 4/12

r = h/3

Now the volume of the water is;

V = ¹/₃πr²h

Put h/3 for r in this volume equation to get;

V = ¹/₃π(h/3)²h

V = (1/27)πh³

Differentiating with respect to time gives;

dV/dt = (3/27)πh²(dh/dt)

We are given;

dV/dt = 6 cubic feet per minute

h = 5

Thus;

6 = (3/27)π(5²)(dh/dt)

dh/dt = 0.688 ft/min

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Answer: 72

Because the picture shows that there's a 90 degree angle in the bottom. We know that the bottom triangle is a 45-45-90 triangle. So the length of one side   is 18 because a 45 45 90 triangle has two sides that are equivalent (x) and one side that is x\(\sqrt{2} \\). So now that we know the length of one side is 18, we know the lengths of all 4 sides. Adding them up ( 18 + 18 + 18 + 18) gives 72, which is the perimeter.

Answer:

=)

Step-by-step explanation:

False, that is if the number of data observations is even, the median is generally considered to be the average of middle values not the first and last values.

The median is a simple measure of central tendency. To find the median, we arrange the observations in order from smallest to largest value. If there is an odd number of observations, the median is the middle value. If there is an even number of observations, the median is the average of the two middle values.

At least half of the observations are equal to or smaller than the median, and at least half of the measurements are equal to or greater than the median. The median divides the bottom half of observations from the upper half.

Even Number of Observations :

Suppose we have the monthly wages of 4 employees of a company. How would you find the median wage?

wages are 120,240,500,400

we have arranged their wages above from lowest to highest. This ranking will help us to determine the median. Using the method introduced earlier, the median is computed by taking the simple average of the (n/2)ᵗʰ = (4/2)ᵗʰ = 2ⁿᵈ and

(n/2 + 1)ᵗʰ = (2+1)ᵗʰ = 3ʳᵈ observations.

Therefore, the median is 240+500/2

= 370.

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Complete question

True/false

if the number of data observations is even, the median is generally considered to be the average of the first and last values

Answer:

e

Step-by-step explanation:

Answer: green cube=48% chance, blue=36% chance, white =16% chance.

Step-by-step explanation: 1. You want to add up all the cubes. There are 25 cubes in total (9+4+12=25)

2. For the green cube, we know there are 12 cubes, so there would be a 12/25 chance which is a 48% chance

3. The same thing applies to the blue cube. There are 9 of them so it would be a 9/25 chance (36%)

4. There are 4 white cubes. 4/25 is a 16% chance.

The number of 100 dollar bills in one billion dollars  is 10 million hundreds or 70,900 hundred dollar bills.

To find the number of 100 dollar bills in one billion dollars, we can use the following steps:

First, we need to find the value of one billion dollars in terms of hundreds. Since each hundred dollar bill has a value of $100,

we can divide one billion by 100 to get the number of hundreds

\(:$$\frac{1\text{ billion}}{100}=10\text{ million}$$\)

So one billion dollars is equal to 10 million hundreds.

Now we need to find the volume of one hundred dollar bill. To do this, we multiply its length, width, and thickness:\($$6.14 \text{ in} \times 2.61 \text{ in} \times 0.00043 \text{ in}=0.00709 \text{ in}^3$$\)

The volume of one hundred dollar bill is approximately 0.00709 cubic inches.

Finally, we need to find the total volume of 10 million hundreds:\($$0.00709 \text{ in}^3 \times 10,000,000=70,900 \text{ in}^3$$\)

Therefore, the total volume of 10 million hundred dollar bills is approximately 70,900 cubic inches.10 million hundreds or 70,900 hundred dollar bills.

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