plum island lighthouse, shines a light from a height of 34 feet with a 2 degree angle of depression. how far out can this light reach into the harbor?

By the 46th day, there are 400 water lilies in the pond. the estimate you made: a). close to 46 (or exactly right) because it was estimated well.

We know that the regression equation is: y = 3.915(1.106)ˣ and that the pond can hold 400 water lilies.

y = 3.915(1.106)ˣ

Here, y is equal to the number of water lilies the pond can hold.

So, y = 400

And,  x is the required time taken.

So,

400 = 3.915(1.106)ˣ

⇒ (1.106)ˣ = 400/3.915    

⇒ (1.106)ˣ = 102.17

Taking logarithm on both sides, we get

log (1.106)ˣ = log (102.17)

⇒ x log (1.106) = log (102.17) .............. [log aˣ = x loga]

⇒ x = [log (102.17)/log (1.106)]    

⇒ x = 45.92

x ≅ 46

So, the pond will take 46 days to become full.

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Complete question:

Regression equation: y = 3.915(1.106)ˣ . The pond can hold 400 water lilies. by what day will the pond be full? write and solve an equation. the pond will be full by the end of day.

Answer:

b

Step-by-step explanation:

just did it

Answer:

Step-by-step explanation:

From the parallel lines, we know that corresponding angles are congruent, so:

(2y+78) = X

We also know that vertically opposite angles are equal:

X=5y

Substitute for X:

2y+78=5y

Solve:

2x-5x=-78

-3x=-78

x=26

Therefore, the measure of angle WXZ is 26.

Answer: 22

Step-by-step explanation:

Substitude 1 for i and 19 for H.

19+1(3) = 19+3 = 22

The vοlume οf the cοne is 156π cubic units

A cοne is a three-dimensiοnal geοmetric fοrm with a flat base and a smοοth tapering tip οr end. A cοne is made up οf a cοllectiοn οf line segments, half-lines, οr lines that link the apex—the cοmmοn pοint—tο every pοint οn a base that is in a plane οther than the apex.

Given,

h = 13 units and r = 6 units

We knοw the fοrmula tο determine vοlume οf cοne; that is

(1/3)πr²h

Where r= radius οf the cοne

h=  height οf the cοne

We put the value οf h and r in the fοrmula

(1/3)πr²h

= (1/3)π6² *13

=156π cubic units

The vοlume οf the cοne is 156π cubic units

Hence the cοrrect answer is 156π cubic units

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Answer:

Step-by-step explanation:

In this expression, the number 3 represents the initial group of friends to whom Carol told the joke.

The base number 4 represents the number of people each friend told the joke to on the following day.

The exponent x represents the number of days that have passed since Carol first told the joke, and as a result, the number of "generations" of people who have heard the joke.

Therefore, 4 raised to the power of x represents the total number of people who have heard the joke after x days, including Carol's initial group of friends and all subsequent generations of people who have been told the joke by those who heard it before.

Finally, multiplying 3 and 4 raised to the power of x gives the total number of unique people who have heard the joke after x days, since the initial group of friends is not included in the later generations.

Answer:

27 cubic units

Step-by-step explanation:

Since each small cube is a unit cube, then each small cube has side length 1 unit. Each side of the Rubik's cube has length 3 units.

V = s³ = 3³ = 27

Answer: 27 cubic units

Cinderella would weigh either 187 or 153 pounds this morning.

Unit cοnversiοn is the prοcess οf cοnverting a quantity expressed in οne unit οf measurement tο anοther equivalent quantity expressed in a different unit οf measurement. It invοlves using cοnversiοn factοrs that relate the twο units οf measurement. This is dοne by multiplying οr dividing the οriginal quantity by a cοnversiοn factοr, which is a ratiο οf the twο units οf measurement that is equal tο οne.

Cinderella's weight increased or decreased by 10%, we can find her weight this morning by multiplying her previous weight by 1.10 (to find a 10% increase) or 0.90 (to find a 10% decrease).

For a 10% increase, Cinderella's weight this morning would be:

170 x 1.10 = 187 pounds

For a 10% decrease, Cinderella's weight this morning would be:

170 x 0.90 = 153 pounds

So depending on whether her weight increased or decreased by 10%, Cinderella would weigh either 187 or 153 pounds this morning.

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Using the stars and bars technique, Candice can distribute her 24 pieces of candy among her four siblings in 2,925 different ways. If she must give each sibling at least one of each type of candy, there are 67,200 ways to distribute the candy among the four siblings.

(A) To solve this problem, we can use the technique of stars and bars. We have a total of 24 pieces of candy to share among four children. We can represent this using 24 stars, with 3 bars to separate the stars into four groups, one for each child. For example, the following arrangement represents giving 6 pieces of candy to the first child, 10 pieces to the second child, 3 pieces to the third child, and 5 pieces to the fourth child:

*****|**********|***|****

The number of ways to arrange the stars and bars is equal to the number of ways to choose 3 positions out of the 27 possible positions for the stars and bars. Therefore, the number of different ways that Candice can share her candy with her three younger brothers is:

C(27, 3) = 27! / (3! * 24!) = 2925

(B) Now, we need to ensure that each child receives at least one Tootsie roll and one Twizzler. We can give each child one of each candy to start, and then distribute the remaining 13 Tootsie rolls and 7 Twizzlers using the stars and bars technique. We have 13 Tootsie rolls and 7 Twizzlers to distribute among four children, which can be represented using 13 stars and 3 bars for the Tootsie rolls, and 7 stars and 3 bars for the Twizzlers. The number of ways to arrange the stars and bars for each type of candy is:

C(16, 3) = 560 for the Tootsie rolls

C(10, 3) = 120 for the Twizzlers

To find the total number of ways to distribute the candy, we can multiply the number of ways for each type of candy:

560 * 120 = 67200

Therefore, there are 67,200 different ways for Candice to share her candy with her three younger brothers after her mother asks her to give at least one of each type of candies to each of her brothers.

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Complete question:

After a (not very successful) trick or treating round, Candice has 15 Tootsie rolls and 9 Twizzlers in her pillow case. Her mother asks her to share some of the loot with her three younger brothers.

(A) How many different ways can she do this?

(B) How many different ways can she do this after her Mother asks her to give at least one of each type of candies to each of her brothers?

The steps to find the depth through which the storm submerges the lowest parts of the Pensacola Beach is given below.

As it has been given in the question, Pensacola beach is located 5-10 feet above sea level.

The ocean water rises upto 5.5 feet during a storm

Hence you need to add up the height of the highest tide on 16 September to 5.5 feet.

If the combined height of the highest tide and the storm tide is greater than 10 feet, then the whole Pensacola beach submerges.

You just subtract the combined height of the storm and the highest tide from the height of the beach.

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Portions of Pensacola Beach, a coastal community built on a barrier island, are located at 3 - 10 feet above sea level.

Hurricane Sally, which struck Pensacola on September 16, 2020 and brought a 5.5 foot storm.

Combined with a high tide on September 16,202, by how many feet did that storm surge submerge the lowest parts of Pensacola Beach? (Hint: use the information in question and change the date on the tidal chart to September 16, 2020) Now, compare your answers above, and think about how the type (pattern) and size of the tides differ for these two locations

Answer:

75°

Step-by-step explanation:

The angle in the given figure is 90°.

x + 15 = 90

x = 90 - 15

x = 75°

No, there is not sufficient evidence to substantiate the claim at the 0.10 level. Null Hypothesis (H0): p ≤ 0.69; Alternative Hypothesis (H1): p > 0.69

A newsletter publisher believes that under 69% of their readers own a Rolls Royce.

No, there is not sufficient evidence to substantiate the claim at the 0.10 level. In order to substantiate the claim at the 0.10 level, the publisher would need to collect data from their readers and perform a hypothesis test to compare the observed percentage of readers with the claimed percentage.

Null Hypothesis: The proportion of the newsletter readers that own a Rolls Royce is less than or equal to 69%.

Null Hypothesis (H0): p ≤ 0.69

Alternative Hypothesis: The proportion of the newsletter readers that own a Rolls Royce is greater than 69%.

Alternative Hypothesis (H1): p > 0.69

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Answer:

The term 2x+4y-2 is a binomial equation.

Step-by-step explanation:

Factoring said equation: 2(x+2y-1)

x intercepts: (1,0)

y intercepts: (0, 1/2)

The size of angle DAB in the quadrilateral is 49°.

The sum of the interior angles of a quadrilateral is 360°. We can say:

∠A + ∠B + ∠C + ∠D = 360°

∠A + 34° + ∠C + 228° = 360°

∠A  + ∠C + 262° = 360°

∠A  + ∠C = 360 - 262

∠A  + ∠C = 98

Since angles DAB and BCD are the same size. This implies ∠A  = ∠C. Thus:

∠A  + ∠A = 98

2∠A  = 98

∠A = 98/2

∠A  = 49°

Therefore, the size of angle DAB is 49°.

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Complete Question

Check the attached image

Extrapolation is a useful tool for predicting future values based on past data

Bethany used a method of predicting future values from past values known as extrapolation. Extrapolation is a powerful tool for predicting future values, but it is important to remember that it only works if the underlying trend in the data does not change. In Bethany's case, she is making an assumption that her income over the next 10 years will follow the same trend as it did in the past 5 years.

In extrapolation, the assumption is that the data points that were observed in the past will continue in the same direction and with the same intensity into the future. Therefore, extrapolation can be used to make predictions about future values even when no new data points have been collected. It is important to remember, however, that any predictions made using extrapolation are only estimates and may not be accurate.

Extrapolation is used in many different fields, such as finance, economics, medicine, engineering, and even weather forecasting. For example, stock analysts may use extrapolation to make predictions about future stock prices based on past prices. Similarly, meteorologists may use extrapolation to make predictions about future weather conditions based on historical weather data.

Overall, extrapolation is a useful tool for predicting future values based on past data. However, it is important to remember that it only works when the underlying trend in the data does not change. Additionally, any predictions made using extrapolation are only estimates and may not be accurate.

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The solution of the system 2 -1 5 with -2 -1 in real form is (x, y) = (7/4, 7/2).

To solve the system with the given coefficients, first, let's rewrite it as a linear system of equations:

2x - y = 5
-2x - y = -2

Now, let's solve this system step-by-step:

Step 1: Solve for y in the first equation:
y = 2x - 5

Step 2: Substitute the expression for y from Step 1 into the second equation:
-2x - (2x - 5) = -2

Step 3: Simplify and solve for x:
-2x - 2x + 5 = -2
-4x = -7
x = 7/4

Step 4: Substitute the value of x back into the expression for y:
y = 2(7/4) - 5
y = 7/2

The solution in real form is (x, y) = (7/4, 7/2).

Regarding the ellipse with counterclockwise orientation, the trajectory can be described as a smooth, closed curve in the shape of an ellipse. The ellipse will have a major and minor axis, with the points on the ellipse moving continuously in a counterclockwise direction along the curve.

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We can see here that the figures that have the same area are: A. Figures I and II.

Area is a measure of the size of a two-dimensional surface or shape. It refers to the amount of space inside the boundaries of a flat object, such as a rectangle, triangle, or circle. Area is typically measured in square units, such as square meters, square feet, or square centimeters.

The area of Figure I which is a rectangle is = l × b = 2cm × 5.8cm = 11.6cm².

The area of Figure II which is a parallelogram is = b × h = 4cm × 2.9cm = 11.6cm².

Thus, Figures I and II have the same area.

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The percentage change in the visit of total number of customers in the second week as compare to first week is equal to 16.67%.

Total number of customers visited the store in the first week = 360

Total number of customers visited the store in the second week = 300

Percentage Change = (|First week - second week / First week) x 100%

Substitute the value of the number of customers in different weeks in the formula we get,

Percentage Change

= (|300 - 360| / 360) x 100

= (60 / 360) x 100

=( 100 / 6 )

= 16.66666%

= 16.67%

Therefore, the percentage change in the number of customers that visited the store from the first week to the second week is a decrease of 16.67%.

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The above question is incomplete, the complete question is:

Mr. Davies opened a new retail store. During the first week, 360 customers visited the store. During the second week, 300 customers visited the store.

What is the percentage change of the number of customers that visited the store in the first week to the number of customers that visited the store in the second week?

The zeroes of the factored polynomial as required to be determined in the task content are: x = -6 and x = 8.

It follows from the task content that the zeroes of the completely factorised polynomial are to be determined.

Since the given polynomial is; x² - 2x - 48 which has been factorised completely to; (x + 6) (x - 8).

Ultimately, the zeroes of the Polynomial are as follows;

x + 6 = 0; x = -6.

and

x - 8 = 0; x = 8.

Conclusively, the zeroes of the polynomial are; x = -6 and x = 8.

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Equation:

89.50=2.35c+5.50d

If theres 22 dogs and cats in total you can plug in number less than 22 for c(# of cats) and d(# of dogs).

So we try pats numbers 8 cats and 14 dogs so

89.50=2.35(8)+5.50(14)

89.50=18.8+77

89.50=95.8

So pats numbers were wrong so we try different numbers

So i started pluging in numbers from under 22 so i got c is 10 and d is 12 lets try it with the equation

89.50=2.35(10)+5.50(12)

89.50=23.5+66

89.50=89.50 so it works the answer to how many number of dogs and cats is 12 dogs and 10 cats

Since mXOY = mWOV, we can form the following equations so, m--XZ = m--ZV.

An equation is a mathematical statement that states the equality of two expressions. It usually consists of two terms, with an equals sign between them, representing the relationship between the terms. Equations are often used to describe relationships between variables, such as in physics and chemistry, and can be used to calculate unknown values.

Proof:

Since mXOY = mWOV, we can form the following equations:

m--YZ = m--ZW (Given)

Subtract both sides of the equation by m to get:

YZ = ZW

Then, multiply both sides of the equation by X to get:

XZ = XW

Now, substitute Y for V and W for V in the equation to get:

XZ = ZV

Finally, subtract both sides of the equation by m to get:

m--XZ = m--ZV

Therefore, m--XZ = m--ZV.

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Answer: 1,023 combinations & 4/5 chance

Step-by-step explanation: A bunch of weird math with the first answer, but the 2nd answer is just every clothing article that isn't red over the total amount of articles simplified (8/10 = 4/5).

Hope this helped!

Answer:

The density of the wood is 0.6 g/cm^3

Step-by-step explanation:

The density of an object can be calculated by dividing the mass of the object by its volume. In this case, the mass of the block of wood is 120g and its volume is 200cm^3.

Density = mass / volume

Density = 120g / 200cm^3

Density = 0.6 g/cm^3

Therefore, the density of the wood is 0.6 g/cm^3.

The final result for the money is [tex]172.40[/tex] after you multiply it by a percent.

In essence, percentages are fractions with a 100 as the denominator. We place the percent sign (%) next to the number to indicate that the number is a percentage.

Rather than being stated as a fraction, a percent is a piece of an entire thing expressed as just a number between zero and 100. Nothing is zero percent; everything is 100 percent; half of something is 50 percent; and nothing is zero percent. You divide the part of the total by its entirety and multiply the result by 100 to get the percentage.

[tex]w-[0.15]=146.54[/tex]

so [tex]w-85p=146.54[/tex]

[tex]146.54[/tex] divided by [tex]80=1.724[/tex] so when you make it a percent it turns it into [tex]172.40[/tex] which is the final answer for the money.

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The equation of the circle is with the diameter given is x² + y² = 9.

The standard form of the equation of a circle is (x - h)² + (y - k)² = r², where (h,k) is the center of the circle.

We can quickly determine the circle's centre and radius thanks to this form. We must first square the x and y terms before rearranging the components in order to transform a circular equation into standard form.

The endpoints of the diameter is (-3,0) and (3,0).

Now, using the section formula the coordinates of radius are:

((-3+3)/2, (0+0)/2) = (0,0

The standard form of the equation of a circle is (x - h)² + (y - k)² = r², where (h,k) is the center of the circle.

Substituting the values:

(x - 0)² + (y - 0)² = 3²

Hence, the equation of the circle is x² + y² = 9.

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The recursive formula that represents the given sequence is:

(B) an = -44aₙ₋₁ - 2

Any term of a series can be defined by its preceding term in a recursive formula (s).

For instance: An arithmetic series has the recursive formula a = an-1 + d.

An = An-1r is the recursive formula for a geometric sequence.

Because each phrase, an, goes back to the preceding term, an1, the formula an=2an1+3 is recursive.

According to this equation, any term we want is equal to two times the previous term plus three.

This sequence's first three terms are 4, 11, and 25.

So, we have the sequence:

-44, -46,-48, ...

Now, we have d that is:

= -48 - (-46)

= -48 + 46

= -2

The 1st term would be: a1 = -44

Then, the correct formula would be: an = -44aₙ₋₁ - 2

Therefore, the recursive formula that represents the given sequence is:

(B) an = -44aₙ₋₁ - 2

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A dependent variable that maintains constant measurements throughout an experiment will be depicted by a straight, horizontal line in a graph.

In an experiment, the dependent variable is the variable being measured, and it is expected to change in response to changes in the independent variable. However, if the dependent variable remains constant throughout the experiment, it indicates that it is not affected by the independent variable.

When such a situation arises, the data points for the dependent variable will be located at the same level or value, resulting in a horizontal line in the graph.

This straight, horizontal line represents the constant measurements of the dependent variable, and it can provide valuable insights into the nature of the relationship between the independent variable and the dependent variable.

A dependent variable that maintains constant measurements throughout an experiment may indicate a flaw in the experimental design, such as an incorrect assumption about the nature of the relationship between the independent variable and the dependent variable, or an uncontrolled confounding variable.

Therefore, it is important to carefully analyze the data and the experimental design to identify and address any potential issues.


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The probability of getting 0 toppings when ordering a hamburger with a choice of up to 6 toppings is 0.0154, rounded to four decimal places.

The total number of ways to choose 6 toppings out of a possible 6 is given by the combination formula:

[tex]$${ \choose 6} = \frac{6!}{6!(6-6)!} = 1$$[/tex]

This is the total number of possible outcomes.

To get 0 toppings, we need to choose 0 toppings out of 6. The number of ways to do this is:

[tex]{6_{0} =[/tex] [tex]\frac{6!}{0!(6-0)!} = 1$$[/tex]

So the probability of getting 0 toppings is:

[tex]$$P(\text{0 toppings}) =[/tex]  [tex]\frac{number of ways to get 0 toppings}{total number of possible outcomes} $$[/tex] [tex]\frac{1}{1} = 1$$[/tex]

However, this is assuming that the cashier chooses the toppings randomly and without replacement. If the cashier has some bias or preference towards certain toppings, this probability may be different.

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