Devils Lake, North Dakota, has a layer of sedimentation at the bottom of the lake that increases every year. The depth of the sediment layer is modeled by the function

D(x) = 20+ 0.24x

where x is the number of years since 1980 and D(x) is measured in centimeters.

(a) Sketch a graph of D.
(b) What is the slope of the graph?
(c) At what rate (in cm) is the sediment layer increasing per
year?

The length of BC rounded to 3 significant figures is 6.98.

Since ∠cab = 90°, we can use the Pythagorean Theorem to find the length of AB.

Let's call BC = x, then we have:

sin(65°) = AB/BC

AB = sin(65°) * BC

In right triangle ABC, we have:

AB^2 + BC^2 = AC^2

(sin(65°) * BC)^2 + BC^2 = 8.9^2

Solving for BC, we get:

BC = 8.9 / sqrt(sin^2(65°) + 1)

BC ≈ 6.98

Therefore, the length of BC rounded to 3 significant figures is 6.98.

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Answer: So the second model is 0.2667 feet longer than the first.

Step-by-step explanation: 8 inches * (1/12 feet per inch) * (1/2.5) = 0.1333 feet

So the length of the first model is 0.1333 feet.

The length of the second model is also at a scale of 1/2.5 feet, so its length can be found directly by multiplying the length of the actual building by the scale factor:

Length of second model = 1/2.5 * 1 foot = 0.4 feet

to make next step we can use difference between these numbers by their lengths: Length of second model - Length of first model = 0.4 feet - 0.1333 feet = 0.2667 feet

With all of the edges 6 feet long, the total surface area of the greenhouse including the floor is approximately 98.39 ft².

To find the total surface area of Reina's greenhouse, we'll need to calculate the area of the equilateral triangular sides and the square base.

1. Equilateral triangular sides:
There are four congruent equilateral triangles with edges of 6 feet each. To find the area of one triangle, we can use the formula A = (s² * √3) / 4, where A is the area and s is the side length.

A = (6² * √3) / 4 = (36 * √3) / 4 = 9√3 square feet

Since there are four triangles, the total area of the triangular sides is 4 * 9√3 = 36√3 square feet.

2. Square base:
The base is a square with side lengths of 6 feet. To find the area, we can use the formula A = s².

A = 6² = 36 square feet

Now, let's add the area of the triangular sides and the square base

Total surface area = 36√3 + 36 ≈ 98.39 ft² (rounded to the nearest hundredth)

So, the total surface area of the greenhouse including the floor is approximately 98.39 ft².

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Answer:

(1, 1.5)

Step-by-step explanation:

If x = 1, plug it into the other equation, y = 1/2x + 1, and y = 1.5.

The area of the sprinkled lawn is approximately 19.625 square meters.

The formula for the area of a circle is:

A = πr²

Where A is the area and r is the radius and π is constant pi ( 3.14 ).

If the sprinkler as a circle with a radius of 2.5 meters. The area that the sprinkler can cover is the area of this circle.

Here, the radius is 2.5 meters, so we can substitute that into the formula:

A = πr²

A = 3.14 × 2.5²

Area = 3.14 × 6.25

Area = 19.625 m²

Therefore, the area is 19.625 m²

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The solutions for the value of k for the polynomial k²x³ - 6kx + 9 divided by x - 1 is derived to be k = 4 or k = 2 .

A polynomial is a mathematical expression which have a sum of powers in one or more variables with coefficients. The highest power of the variable in a polynomial is called its degree.

The remainder theorem states that if a polynomial say f(x) is divided by x - a, then the remainder is f(a)

For the polynomial; k²x³ - 6kx + 9 divided by x - 1, we shall evaluate for f(1) to solve k as follows:

k²(1)³ - 6k(1) + 9 = 1

k² - 6k + 9 - 1 = 0

k² - 6k + 8 = 0

by factorization;

(k - 4)(k - 2) = 0

k = 4 or k = 2

Therefore, solutions for the value of k for the polynomial k²x³ - 6kx + 9 divided by x - 1 is derived to be k = 4 or k = 2 .

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The total number of outcomes for the compound event is m*n

option B.

The Fundamental Counting Principle states that if there are m ways to do one thing and n ways to do another thing, then there are m*n ways to do both things together.

This applies to compound events that consist of two or more independent events.

For example, suppose you have two dice and you want to know how many possible outcomes there are when you roll them. Each die has 6 possible outcomes, so by the Fundamental Counting Principle, the total number of outcomes for the compound event is 6*6 = 36.

So, for any two independent events with m and n outcomes, respectively, the total number of outcomes for the compound event is m*n.

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Plan C has the lower expected cost, so, this is best to minimize costs for safety glass coverage.

In order to compare expected cost of Plan C and D, we must calculate expected payout for each plan and add to the premium.

For Plan C, expected payout is:

= 0.5*(0) + 0.3*(50) + 0.2*(300)

= 15 + 60

= 75

The total expected cost of Plan C is:

= 75 + 50 + 20

= 145

For Plan D, expected payout is:

= 0.5*(0) + 0.3*(50) + 0.2*(300)

= 15 + 60

= 75

The total expected cost of Plan D is:

= 75 + 100 + 0

= 175

Therefore, the Plan C has the lower expected cost.

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Answer:

Sure, I can help you with that.

To find the area of the gazebo floor, we can think of the decagon as being composed of ten congruent triangles. Each triangle has a base of 10 feet and a height of 192 feet. The area of a triangle is equal to (1/2)bh, so the area of each triangle is (1/2)(10)(192) = 960 square feet. The area of the decagon is equal to 10 times the area of each triangle, or 960*10 = 9600 square feet.

Therefore, the area of the gazebo floor is 9600 square feet.

Here is a diagram of the decagon, with the ten congruent triangles labeled:

[Image of a decagon with ten congruent triangles labeled]

I hope this helps! Let me know if you have any other questions.

Step-by-step explanation:

I'm so grateful for your help. I would be honored if you would give me a Brainlyness award."

(a) Since the character occurs with a frequency higher than 2=5, it is guaranteed to be merged with another character with the same frequency or a lower frequency. Therefore, there is guaranteed to be a codeword of length 1 for this character. (b) Since all symbols occur with a frequency less than 1=3, the root of the tree will have a frequency less than 1=3. Therefore, there is guaranteed to be no codeword of length 1 for any symbol in this case.

(a) Let's assume that some character occurs with frequency more than 2=5.

The two nodes with the lowest frequency are merged into a single node, with the sum of their frequencies as the frequency of the new node.

This process is repeated until all the nodes are merged into a single node, which becomes the root of the tree.

Since the character occurs with a frequency higher than 2=5, it is guaranteed to be merged with another character with the same frequency or a lower frequency.

Therefore, there is guaranteed to be a codeword of length 1 for this character.

(b) Let's assume that all characters occur with frequency less than 1=3.

Consider the binary tree created by the Huffman algorithm. The root of the tree corresponds to the least frequent symbol, which will be assigned the longest codeword.

Since all symbols occur with a frequency less than 1=3, the root of the tree will have a frequency less than 1=3.

This means that the corresponding codeword for the root will be longer than 1 bit. Therefore, there is guaranteed to be no codeword of length 1 for any symbol in this case.

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the answer is Q1 = 27.5

Answer:  In bold

Step-by-step explanation:

The formula they gave is a rate

Let's solve for the rate first.

This equation is done for 3 years 2018-2021  that's why ^3

3.55 =  2.90(1+x)³                 >divide both sides by 2.90

1.224 = (1+x)³                         > take cube root of both sides

1.0697 =  1+x

x= .0697

so let's make our generic formula

[tex]y = 2.90(1+.0697)^{t}[/tex]        let t be years and let y=  price  

Let's calculate 2018, so this would be year 0

[tex]y = 2.90(1+.0697)^{0}[/tex]

y=$2.90   this is for 2018

They already gave you 2021 price

y=$3.55   this is for 2021

Rate of increase is .0697 

In 2025

That's 7 years=t

[tex]y = 2.90(1+.0697)^{7}[/tex]

y=$4.65    for 2025

Diego selling raffle tickets for $1.75 per ticket and she earned for 50 tickets is $87.50.

When a purchase, appropriation, requisition, or direct engagement with the customer occurs at the point of sale, the seller or supplier of the products or services completes a transaction. Title (property or ownership) of the object is transferred, and a price is settled, meaning a price is agreed upon for which the ownership of the item will transfer.

We can calculate how much money Diego would make if he sold each quantity of raffle tickets for $1.75 each using Excel's multiplication function. It is possible to create a table with the number of tickets sold in one column and the money taken in the other.

Diego would receive $17.50, for instance, if he sold 10 tickets (10 x $1.75). If he sold 20 tickets, he would earn $35 (20 x $1.75), and so on. Using Excel's fill handle, you can quickly fill the table with the totals for each sold ticket.

The table would look like this:

Number of Tickets Sold | Amount of Money Earned

•----------------------------------|---------------------------------------•

   10                                |    $17.50

   20                               |    $35.00

   30                               |    $52.50

   40                               |    $70.00

   50                               |    $87.50

By using the multiplication function in Excel, we can quickly calculate the amount of money Diego would earn for any number of raffle tickets sold at $1.75 per ticket.

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Answer:

w ≈ 68,3

Step-by-step explanation:

Use trigonometry:

[tex] \sin(42) = \frac{w}{102} [/tex]

Cross-multiply to find w:

[tex]w = 102 \times \sin(42°) ≈68.3[/tex]

If Sin F = 3/5 , then the value of Cos D is 4/5 (option a)

Let us consider the triangle in the given question. Since we are given that Sin F = 3/5, we know that the side opposite angle F is 3 and the hypotenuse is 5. Using Pythagoras theorem, we can find the length of the adjacent side as follows:

Opposite² + Adjacent² = Hypotenuse²

3² + Adjacent² = 5²

9 + Adjacent² = 25

Adjacent² = 16

Adjacent = 4

So we have found that the length of the adjacent side is 4. Now we can use the definition of cosine to find Cos D.

Cosine is defined as the ratio of the adjacent side to the hypotenuse. Therefore,

Cos D = Adjacent/Hypotenuse = 4/5

Hence, the answer is option A) 4/5.

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To find the car's average velocity between t=4 and t=10, we need to use the formula:

average velocity = (change in displacement) / (change in time)

Since we are only given the velocity function, we need to first find the displacement function by integrating the velocity function:

displacement = ∫(1t^(1/2) + 4) dt

displacement = (2/3)t^(3/2) + 4t + C

where C is the constant of integration.

Since we are only interested in the change in displacement between t=4 and t=10, we can ignore the constant of integration.

change in displacement = [(2/3)10^(3/2) + 4(10)] - [(2/3)4^(3/2) + 4(4)]

change in displacement = 28.147 - 14.265

change in displacement = 13.882

Now we can use the formula for average velocity:

average velocity = (change in displacement) / (change in time)

average velocity = 13.882 / (10 - 4)

average velocity = 1.98 m/s

Therefore, the car's average velocity between t=4 and t=10 is 1.98 m/s.

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Base on the word problem, Bernard is currently 21.25 years old. When Hector turns 18, he will be (18 - 17) = 1 year older than his current age. At that time, Bernard will be (21.25 + 1) = 22.25 years old.

Let's start by assigning variables to represent the current ages of Bernard and Hector. Let B be Bernard's current age and H be Hector's current age. Then we can write two equations based on the given information:

"When Bernard was as old as Hector is now, Bernard's age was 4 times Hector's age then." This means that Bernard is currently (B - H) years older than Hector, and that the age difference between them has remained constant over time. So, we can write: B - (B - H) = 4(H - (B - H)).

Simplifying this equation, we get: B - B + H = 4(2H - B)

Simplifying further, we get: 5H - 4B = 0, or B = (5/4)H.

"When Hector will be as old as Bernard is now, the sum of their ages will be 51." This means that when Hector is (B - H) years older than his current age, their sum of ages will be 51. So, we can write: B + (B - H + (B - H)) = 51.

Simplifying this equation, we get: 3B - 2H = 51.

Now we have two equations with two variables. We can substitute the expression for B from the first equation into the second equation, and solve for H:

3B - 2H = 51

3(5/4)H - 2H = 51

(15/4)H = 51

H = 17

So, Hector is currently 17 years old. To find out how old Bernard will be when Hector turns 18, we can use the expression we found earlier for B in terms of H:

B = (5/4)H

B = (5/4)(17)

B = 21.25

So, Bernard is currently 21.25 years old. When Hector turns 18, he will be (18 - 17) = 1 year older than his current age. At that time, Bernard will be (21.25 + 1) = 22.25 years old.

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The equation of the circle with center at the origin and radius 16 is x^2 + y^2 = 256.

To find the equation of a circle with center at the origin and radius 16, we can use the general equation of a circle:

x^2 + y^2 = r^2

where (x, y) are the coordinates of any point on the circle, and r is the radius.

In this case, the center is at the origin, so the coordinates (x, y) are both 0. The radius is given as 16. Plugging these values into the equation, we have:

0^2 + 0^2 = 16^2

0 + 0 = 256

Thus, the equation of the circle is:

x^2 + y^2 = 256

So, the equation of the circle with center at the origin and radius 16 is x^2 + y^2 = 256.

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The sets of side lengths that could form a right triangle are 36-48-60 (option b) and 14-48-50 (option d).

To determine which of these sets of side lengths could form a right triangle, we will use the Pythagorean theorem (a² + b² = c²), where a and b are the shorter sides and c is the hypotenuse. Let's evaluate each option:

a) 4-7-10
Applying the Pythagorean theorem: 4² + 7² = 16 + 49 = 65, which is not equal to 10² (100). So, this set does not form a right triangle.

b) 36-48-60
Applying the Pythagorean theorem: 36² + 48² = 1296 + 2304 = 3600, which is equal to 60² (3600). So, this set does form a right triangle.

c) 6-10-14
Applying the Pythagorean theorem: 6² + 10² = 36 + 100 = 136, which is not equal to 14² (196). So, this set does not form a right triangle.

d) 14-48-50
Applying the Pythagorean theorem: 14² + 48² = 196 + 2304 = 2500, which is equal to 50² (2500). So, this set does form a right triangle.

In conclusion, the sets of side lengths that could form a right triangle are 36-48-60 (option b) and 14-48-50 (option d).

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The constant of proportionality is 1.75.

What is proportion?

A percentage is created when two ratios are equal to one another. We write proportions to construct equivalent ratios and to resolve unclear values. a comparison of two integers and their proportions. According to the law of proportion, two sets of given numbers are said to be directly proportional to one another if they grow or shrink in the same ratio.

Given two variables x and y, y is directly proportional to x (x and y vary directly, or x and y are in direct variation) if there is a non-zero constant k such that

=> y=kx

The relation is often denoted, using the ∝ or ~ symbol, as

=> y ∝ x

and the constant ratio

=> k =y/x

In this equation y=1.75 x.

Hence the constant of proportionality is 1.75.

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p and q both are equal and p=q=20.

Given are an equation show equivalent fractions 2p/5q = 40/100

We need to find the p and q,

So

2p/5q = 40/100

2p/5q = 2×20/2×20

p/q = 20/20

p/q = 1

p = q

Therefore p and q both are equal and p=q=20.

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The problem represents a linear equation.

What is linear equation?

A linear equation is a particular type of equation in which the highest power of the variable is always 1(linear). This type of equation is also known as a one-degree equation.

Larry is paid $10 per hour he receives a $1 per hour raise each year.

Let he works for x hours.

In 1 hour he receives $10 so for x hours he will receive $10x

$1 per hour raise.

So there will be a linear equation

The linear equation will be if we take total income as $y then,

y= 10x+1

which is of the linear equation form y=m x+ b where m is the slope.

Hence, the problem represents a linear equation.

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The hypothesis to be tested here is that the number of cars arriving for service is the same for each day of the week.

The null hypothesis, denoted as H0, is that the observed frequency distribution of cars is the same as the expected frequency distribution.

The alternative hypothesis, denoted as H1, is that the observed frequency distribution of cars is not the same as the expected frequency distribution.

To test this hypothesis, we use a goodness-of-fit test with the chi-square distribution. The critical value for a chi-square distribution with 6 - 1 = 5 degrees of freedom (one for each day of the week) and alpha level of 0.10 is 9.2363.

If the computed chi-square statistic is greater than 9.2363, then we reject the null hypothesis and conclude that the observed frequency distribution is significantly different from the expected frequency distribution.

Thus, if the computed chi-square statistic is greater than 9.2363, we can conclude that the number of cars arriving for service is not the same for each day of the week, and there is evidence to support the alternative hypothesis.

If the computed chi-square statistic is less than or equal to 9.2363, then we fail to reject the null hypothesis, and there is not enough evidence to suggest that the observed frequency distribution is different from the expected frequency distribution.

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The constant of proportionality between y and x in the graph is 3

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

The graph

On the graph, we have the following readings

(x, y) = (1, 3)

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

The constant of proportionality between y and x in the graph is

k = y/x

substitute the known values in the above equation, so, we have the following representation

k = 3/1

Evaluate

k = 3

Hence, the constant of proportionality between y and x in the graph is 3

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Answer:

C is the right answer I think

To find the cost of the house in 1980, divide the cost of the house in 1990 by the rate of increase. The house would have cost approximately $62,200 in 1980 when the CPI was 82.4.

To find the cost of the house in 1980, we need to use the concept of inflation. In this case, we can use the consumer price index (CPI) to compare the prices of the house in 1990 and 1980.

First, we need to determine the rate of increase from 1980 to 1990. The rate of increase is calculated by dividing the CPI in 1990 by the CPI in 1980:

Rate of increase = CPI in 1990 / CPI in 1980 = 130.7 / 82.4 = 1.585

Next, we can use the rate of increase to find the cost of the house in 1980. We divide the cost of the house in 1990 by the rate of increase:

Cost in 1980 = Cost in 1990 / Rate of increase = $98,700 / 1.585 = $62,200.

Therefore, the house would have cost approximately $62,200 in 1980 when the CPI was 82.4.

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If Ron were to borrow $4,500 at a simple interest rate of 7% per year, he would be charged $315 in interest each year.

Ron is seeking a loan with a simple interest rate of 7% per year, which means that he will be charged 7% of the loan amount as interest each year. Ron wants to borrow $4,500, so to calculate the amount of interest he will be charged each year, we can use the following formula:

Interest = Principal x Rate x Time

In this formula, "Principal" refers to the loan amount, "Rate" refers to the interest rate as a decimal (so 7% would be 0.07), and "Time" refers to the length of time the loan will be outstanding, typically measured in years.

Since Ron is seeking a loan with a simple interest rate, we can assume that the interest will be calculated on an annual basis. So if Ron wants to borrow $4,500 at a simple interest rate of 7% per year, the amount of interest he will be charged each year would be:

Interest = $4,500 x 0.07 x 1

Interest = $315

Therefore, if Ron were to borrow $4,500 at a simple interest rate of 7% per year, he would be charged $315 in interest each year. It's important to note that this calculation assumes that Ron will not be making any payments on the loan during the year, and that the interest will be added to the principal amount at the end of the year. In practice, many loans are structured differently and may involve monthly payments or other terms.

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The nearest tenth how many miles is alshleys house from Bridget house is  AB = √[(xB-xA)² + (yB-yA)²]

The nearest tenth how many miles is Ashley’s house from carlys house is AC = √[(xC-xA)² + (yC-yA)²]

The distances from Ashley's house to both Bridget's house and Carly's house, we can compare them and see which one is shorter.

To find the distance between Ashley's house and Bridget's house, we need to know the coordinates of both locations. Let's say Ashley's house is located at point A, and Bridget's house is located at point B. We can use the distance formula to find the distance between A and B:

distance AB = √[(xB-xA)² + (yB-yA)²]

Here, xA and yA represent the coordinates of Ashley's house, and xB and yB represent the coordinates of Bridget's house. The formula calculates the square root of the sum of the squares of the differences between the x-coordinates and y-coordinates of the two points.

To find the distance between Ashley's house and Carly's house, we again need to know the coordinates of both locations. Let's say Ashley's house is located at point A, and Carly's house is located at point C. We can use the same distance formula as before:

distance AC = √[(xC-xA)² + (yC-yA)²]

Here, xC and yC represent the coordinates of Carly's house. Plug in the values and calculate the distance to the nearest tenth of a mile.

To determine whose house Ashley lives closest to, we need to calculate the distances from Ashley's house to both Bridget's house and Carly's house. Whichever house has the shorter distance will be the closer one.

To find the difference between the two distances, we can subtract the smaller distance from the larger distance.

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It will take the rock 1.5 seconds  to hit the ground

Since the situation is modeled by the equation h = -16t² + 16t + 12

The rock will hit the ground when height is zero i.e. h = 0. Thus, we have:

-16t² + 16t + 12 = 0 and we can then solve for the time (t) .

-16t² + 16t + 12 = 0  (divide through by -16)

t² - t - 3/4 = 0

Using factorization method:

(t + 1/2) (t - 3/2) = 0

t = -1/2 or 3/2

Since t cannot be negative. Thus, t = 3/2 = 1.5.

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