Please help me with this

Please Help Me With This

Answers

Answer 1

Answer:

B f(x)=1(8)^x

Step-by-step explanation:

1 is the 0 value, you can see it's exponential by the rapid growth and how it grows by a lot each time


Related Questions

Use the following information to create a two way table that shows the type of music a person likes compared to their gender. 94 males were surveyed. 13 males liked jazz. 27 females liked rock. 90 people total liked rock. 66 females liked country. 200 people total were surveyed

Answers

Here is a two way table that shows the type of music a person likes compared to their gender:

|               | Males | Females | Total |
|---------------|-------|---------|-------|
| Jazz          | 13    | 0       | 13    |
| Rock          | 54    | 27      | 81    |
| Country       | 0     | 66      | 66    |
| Total         | 67    | 93      | 200   |

In this table, we can see that out of the 94 males surveyed, 13 of them liked jazz. Out of the 106 females surveyed, 27 of them liked rock and 66 of them liked country. Overall, out of the 200 people surveyed, 81 of them liked rock, 13 of them liked jazz, and 66 of them liked country.

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Make 20 questions subtraction and addition of fractions only like this

e. G saina ,anika and mercy got some money saina got 1/6 and mercy got 3/4 and anka got the rest

a. Caculate the fraction of saina and mercy

b. What is anika s share in fractions

c. How much was the money

you can use money,fruits or any thing

due 24/04/22

Answers

20 questions subtraction and addition of fractions only like this:

A recipe calls for 2/3 cup of flour and 1/4 cup of sugar. What is the total amount of flour and sugar needed in fraction?

John had 3/4 of a pizza and gave 1/3 of it to his friend. What fraction of the pizza does John have left?If 2/5 of a cake is chocolate and 1/5 is vanilla, what fraction of the cake is another flavor?If Tom can run 5/6 of a mile in 4 minutes, how many minutes will it take him to run 1 mile?If 3/8 of a bag of apples is rotten, what fraction of the bag is not rotten?A store had 5/6 of its shelves stocked with books. If 1/4 of the books were science books, what fraction of the shelves were stocked with science books?If Maria has 3/8 of a tank of gas and she uses 1/4 of it to drive to work, what fraction of the tank is left when she arrives at work?A recipe calls for 1/3 cup of sugar and 1/4 cup of butter. What is the total amount of sugar and butter needed in fraction?If 2/3 of a box of crayons is blue and 1/4 of the box is red, what fraction of the box is another color?If a recipe calls for 3/4 cup of milk and you have only 1/2 cup, what fraction of milk do you need to buy to have enough?If a school has 7/8 of its students enrolled in math and 3/4 of those enrolled in math are also enrolled in science, what fraction of the school is enrolled in both math and science?A store had 1/2 of its apples on sale for 1/4 off. What fraction of the original price did a customer pay for a discounted apple?If a train travels 1/2 of a mile in 2 minutes, how long will it take to travel 1 mile?A recipe calls for 2/3 cup of flour and 1/4 cup of sugar. What is the total amount of flour and sugar needed in fraction?If a recipe calls for 3/4 cup of oil and you have only 1/3 cup, what fraction of oil do you need to buy to have enough?If 3/8 of a class is girls and 2/5 of the girls have brown hair, what fraction of the class is girls with brown hair?If a recipe calls for 1/2 cup of brown sugar and 1/4 cup of white sugar, what is the total amount of sugar needed in fraction?If a store sells 3/4 of a bag of apples and has 2/3 of a bag left, what fraction of the original bag is left?If a car travels 3/4 of a mile in 2 minutes, how long will it take to travel 1 mile?If a recipe calls for 1/3 cup of butter and you have only 1/6 cup, what fraction of butter do you need to buy to have enough?If a recipe calls for 1/4 cup of honey and 1/3 cup of sugar, what is the total amount of honey and sugar needed in fraction?

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A triangular pane of glass has a height of 32 inches and an area of 256 square inches. What is the length of


the base of the pane?


The length of the base of the pane is


inches.

Answers

The length of the base is 16 inches.

To find the length of the base of the triangular pane of glass, we can use the formula for the area of a triangle which is:

Area = (1/2) x base x height

We are given that the height of the pane is 32 inches and the area is 256 square inches. Substituting these values into the formula, we get:

256 = (1/2) x base x 32

To isolate the base, we can divide both sides by (1/2) x 32, which simplifies to 16. This gives us:

256 ÷ 16 = base

Simplifying the left side of the equation, we get:

16 = base

Therefore, the length of the base of the pane is 16 inches.

In summary, the triangular pane of glass has a height of 32 inches and an area of 256 square inches. To find the length of the base, we use the formula for the area of a triangle and solve for the base.

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. let u = <4,8>, v = <-2, 6>. find u + v. (1 point)


how to find find u+v?

Answers

The sum of vectors u  = <4,8>,and v = <-2, 6>  i.e. (u+v) is <2, 14>

To find the sum of vectors u and v (u+v), you need to perform the following steps:

1. Identify the components of vectors u and v: u = <4, 8> and v = <-2, 6>.

2. Add the corresponding components of both vectors: To find the sum (u+v), add the x-components (4 and -2) and the y-components (8 and 6) separately.

3. Calculate the sum of the x-components: 4 + (-2) = 2.

4. Calculate the sum of the y-components: 8 + 6 = 14.

5. Combine the results to form the new vector (u+v): <2, 14>.

So, the sum of vectors u and v (u+v) is <2, 14>.

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Explain how to find the measure of angles a and b has a measure of 36 degrees

Answers

The measure of angles a and b is 36 degrees if they are alternate interior angles formed by a transversal intersecting two parallel lines.

How to find the measure of angles a and b with a measure of 36 degrees?

To find the measure of angles a and b when angle b has a measure of 36 degrees, we need additional information.

If we assume that angles a and b are adjacent angles formed by two intersecting lines, then we can use the fact that adjacent angles are supplementary, meaning their measures add up to 180 degrees. Since angle b has a measure of 36 degrees, we subtract it from 180 to find angle a.

Thus, angle a = 180 - 36 = 144 degrees. Therefore, angle a has a measure of 144 degrees when angle b has a measure of 36 degrees.

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Patricia bought 4 apples and 9 bananas for $12. 70 Jose bought 8 apples and I bananas for $17. 70 at the same grocery store What is the cost of one apple?​

Answers

Let's denote the cost of one apple as 'a' and the cost of one banana as 'b'. We can set up a system of two equations to represent the given information:

4a + 9b = 12.70   (equation 1)

8a + b = 17.70    (equation 2)

We can use either substitution or elimination method to solve for 'a' or 'b'. Let's use the elimination method by multiplying equation 2 by 9 and subtracting it from equation 1:

4a + 9b = 12.70

-(72a + 9b = 159.30)   (multiplying equation 2 by 9)

------------------

-68a = -146.60

Dividing both sides by -68, we get:

a ≈ 2.16

Therefore, the cost of one apple is approximately $2.16.

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The current student population of the Brentwood student Center is 2500. The enrollment at center increases at a rate of 6% each year. To the nearest whole number, what will the student population closest to seven years?

Answers

In seven years, the student population at the Brentwood Student Center will be approximately 4,174.

Using the given terms, the current student population at the Brentwood Student Center is 2,500 and the enrollment increases at a rate of 6% each year. To find the student population closest to seven years from now, we'll use the formula for exponential growth:

Future Population = Current Population × (1 + Growth Rate)^Number of Years

In this case, the future population will be:

Future Population = 2,500 × (1 + 0.06)^7

After calculating, we get:

Future Population ≈ 4,174

So, to the nearest whole number, the student population at the Brentwood Student Center will be approximately 4,174  in seven years.

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Rick drew a rhombus. What names might describe the figure based on what you know about quadrilaterals? Explain. ​

Answers

Since it has four sides and four angles, it is also simply called a quadrilateral.

Rick drew a rhombus. Some names that might describe the figure, considering the properties of quadrilaterals, are:
Quadrilateral: A rhombus is a type of quadrilateral, which means it has four sides and four angles.
Parallelogram: A rhombus is also a parallelogram because its opposite sides are parallel to each other.
Square: If the rhombus has four right angles, then it can also be called a square. A square is a specific type of rhombus and a special case of a parallelogram where all angles are right angles.
A rhombus is a type of quadrilateral that has four sides of equal length. It is also classified as a parallelogram because it has two pairs of parallel sides. Additionally, since all angles in a rhombus are equal, it can also be called an equilateral parallelogram. Finally, since it has four sides and four angles, it is also simply called a quadrilateral.
So, Rick's figure can be described as a quadrilateral, parallelogram, and potentially a square depending on its angles.

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find the next three terms in the sequence 3/4, 1/2, 1/4, 0​

Answers

Answer:

[tex]\sf \bf \dfrac{-1}{4} \ ; \ \dfrac{-1}{2} \ ; \ \dfrac{-3}{4}[/tex]

Step-by-step explanation:

Arithmetic sequence:

     Each term in the arithmetic sequence is obtained by adding or subtracting a common number with the previous term.

To find the next three terms, we need to find the common difference.

         Common difference = second term - first term

                                            [tex]\sf = \dfrac{1}{2}-\dfrac{3}{4}\\\\=\dfrac{2-3}{4}\\\\=\dfrac{-1}{4}\\\\\\\text{Each term is obtained by adding $\dfrac{-1}{4} $ with the previous term}[/tex]

Next three terms are,

           [tex]\sf 0 + \left(\dfrac{-1}{4}\right)= 0 - \dfrac{1}{4}=\dfrac{-1}{4}\\\\\\\dfrac{-1}{4}+\left(\dfrac{-1}{4}\right)=\dfrac{-1}{4}-\dfrac{1}{4}=\dfrac{-2}{4}=\dfrac{-1}{2}\\\\\\\dfrac{-1}{2}+\left(\dfrac{-1}{4}\right)=\dfrac{-1}{2}-\dfrac{-1}{4}=\dfrac{-2-1}{4}=\dfrac{-3}{4}[/tex]

PLEASE HELP
A survey was done that asked people to indicate whether they prefer saltwater fishing or freshwater fish in the results of the survey are shown in the two way table
complete a relative frequency table from this data.
enter your answer is rounded to the nearest 10th of a percent in the boxes

Answers

According to the above, the fishing population is divided into 53% prefer fresh water and 47% prefer salt water.

How to find the percentages of each group?

To find the percentage of people that make up each group, we must find the total number of people who were surveyed:

228 + 245 + 242 + 285 = 1,000

Once we find the total number of people who took the survey, we can find the percentage of each value by making rules of three as shown below:

Age 30 and younger and Saltwater fishing:

1,000 = 100%

228 = ?%

228 * 100 / 1,000 = 22.8%

Age 30 and younger and Freshwater fishing:

1,000 = 100%

245 = ?%

245 * 100 / 1,000 = 24.5%

Over 30 years old and Saltwater fishing:

1,000 = 100%

242 = ?%

242 * 100 / 1,000 = 24.2%

Over 30 years old and Freshwater fishing:

1,000 = 100%

285 = ?%

285 * 100 / 1,000 = 28.5%

To find the other percentages we must find the total number of fishermen by age ranges and by fishing preference:

Age ranges

228 + 245 = 473

242 + 285 = 527

1,000 = 100%

473 = ?%

473 * 100 / 1,000 = 47.3%

1,000 = 100%

527 = ?%

527 * 100 / 1,000 = 52.3%

Fishing mode preferences

228 + 242 = 470

245 + 285 = 530

1,000 = 100%

530 = ?%

530 * 100 / 1,000 = 53%

1,000 = 100%

547 = ?%

470 * 100 / 1,000 = 47%

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What are the Actual dimensions of the house(in ft)

Answers

The house's real measurements are 18 feet by 20 feet.

What do we mean by dimensions?

In everyday speech, a dimension is a measurement of an object's length, width, and height, such as a box.

The idea of dimension in mathematics is an expansion of the concepts of one-dimensional lines, two-dimensional planes, and three-dimensional space.

Examples of dimensions include width, depth, and height.

One dimension is that of a line, two dimensions are those of a square, and three dimensions are those of a cube. (3D).

So, scaling is the process of changing a figure's size to produce a picture.

Considering that a scale of 6 cm equals 12 ft.

Hence:

9 cm = 9 cm * (12 ft. per 6 cm) = 18 feet

10 cm = 10 cm * (12 ft. per 6 cm) = 20 feet

Therefore, the house's real measurements are 18 feet by 20 feet.

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Correct question:

A scale drawing of a house shows 9cm x10cm. If 6cm=12 ft, what are the actual dimensions?

Two days after he bought a speedometer for his bicycle; Lance brought it back (0 the Yellow Jersey Bike Shop. FThele problemn with this speedomeler;' Ba Lance complained to the clerk "Yesterday [ cycled the 22-mile Rogadzo Road Trail in 70 minutes and nOt once did the speedometer read above [5 miles per hour"" Yeah?" responded the clerk " What' $ the problem?" To explain Lance's complaint, first compute his average velocity: (Use decimal notation. Give your answer tO two decimal places ) average velocity: DNE mileshcur Incorrecr

Answers

Therefore, Lance's average velocity was 15.43 miles per hour.

What is equation?

An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides, left-hand side (LHS) and right-hand side (RHS), connected by an equal sign (=). The LHS and RHS can contain numbers, variables, operators, and functions, and the equal sign indicates that the value of the expression on the LHS is equal to the value of the expression on the RHS.

Here,

We can compute Lance's average velocity by dividing the total distance he cycled by the time it took him, and then converting the units to miles per hour.

Total distance: 22 miles

Time: 70 minutes = 70/60 hours

= 7/6 hours

Average velocity = Total distance / Time

= 22 / (7/6)

= 15.43 miles per hour (rounded to two decimal places)

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15
Find the first and second derivatives. y = - 5x4+1 dy dx 승 라 ||| dx2

Answers

The first derivative is dy/dx = [tex]-20x^3[/tex], and the second derivative is d^2y/dx^2 = -60x^2.

The function you provided is: y =[tex]-5x^4 + 1[/tex]

To find the first derivative (dy/dx), we'll use the power rule which states that if y = x^n, then dy/dx =[tex]n * x^(n-1)[/tex].

Applying this rule to each term, we get: dy/dx = [tex]d(-5x^4)/dx + d(1)/dx[/tex]dy/dx =[tex]-5(4x^(4-1)) + 0[/tex] (since the derivative of a constant is 0) dy/dx = [tex]-20x^3[/tex]

Now, to find the second derivative [tex](d^2y/dx^2)[/tex], we'll differentiate the first derivative again using the power rule: [tex]d^2y/dx^2 = d(-20x^3)/dx d^2y/dx^2 = -20(3x^(3-1)) d^2y/dx^2 = -60x^2[/tex]

So, the first derivative is dy/dx = [tex]-20x^3[/tex], and the second derivative is [tex]d^2y/dx^2 = -60x^2.[/tex]

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Among 130 pupils, 30 liked both biscuits and chocolates, 10 liked neither and twice as many as liked biscuits liked chocolates.
I) How pupils liked: chocolates, biscuits and exactly one of the two.

Answers

The number of pupils who liked both biscuits and chocolates is 30.

The number of pupils who liked neither biscuits nor chocolates is 10.

Let's assume that the number of pupils who liked only biscuits is x, and the number of pupils who liked only chocolates is y.

According to the problem, twice as many pupils liked chocolates as those who liked biscuits. Mathematically, we can write this as:

y = 2x

Now, let's find the total number of pupils who liked at least one of the two:

Total = P(Biscuits) + P(Chocolates) - P(Biscuits and Chocolates)

Total = x + y + 30

Total = x + 2x + 30

Total = 3x + 30

We know that the total number of pupils is 130, and the number of pupils who liked neither is 10. Therefore,

Total = P(All pupils) - P(Neither)

130 = x + y + 30 + 10

130 = x + y + 40

130 - 40 = x + y

90 = x + y

We can now solve these two equations to get the values of x and y:

3x + 30 = 90

3x = 60

x = 20

y = 2x = 40

Therefore, 20 pupils liked only biscuits, 40 pupils liked only chocolates, and 30 pupils liked both biscuits and chocolates. And, 40 pupils liked exactly one of the two.

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find the distance between each pair of points. (5 1/2, -7 1/2) and (5 1/2, -1 1/2)

Answers

Answer:

6

Step-by-step explanation:

The distance between both those points are 6

Ifj is inversely related to the cube of k, and j = 3 when k is 6, which of the following is another possible value for j and K?
(A) j = 18, k = 2
(B) j=6, k = 3
(C) j=81, k = 2
(D) j = 2, k = 81
(E) j = 3, k=2

Answers

Another possible value for j and K is (A) j = 18, k = 2

How to determine the values

Note that in inverse variation, one of the variables increases while the other decreases.

From the information given, we have that;

j is inversely related to the cube of k,

This is represented as;

j ∝ 1/k³

Now, find the constant of variation

K = jk³

Substitute the vales

K = 3 × 6³

find the cube value

K = 648

Then, we have that;

j = 648 / 2³ = 81

For option B:

j = 648 / 3³ = 24

For option C:

j = 648 / 2³ = 81

For option D:

j = 648 / 81³ = 0.0008

For option E:

j = 648 / 2³ = 81

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gabriela is building wooden box that is 15 in. tall and has a rectangular base that is 18 in by 15 in

Answers

A open box without a top 1260 sq. in. wood will Gabriella use.

Since the top of the box is the same area as the base, calculate the base.

B = length × width

Length of the wooden box = 18 in.

Width of the wooden box = 15 in.

B = 18(15) = 270 in.

Calculate the surface area of the box.

Surface Area = 2(B + wh + hl)

h = 15

w × h = 15(15) = 225

h × l = 15(18) = 270

Surface Area of the wooden box = 2(270 + 225 + 270) = 2(765) = 1,530 sq. inches

Subtract the base from the surface area: 1,530 - 270 = 1,260sq. in.

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The given question is incomplete, complete question is:

Gabriella is beauty a wooden box with a rectangular base that is 18 in by 15 in and is 15 in tall if she wants a open box without a top how much wood will Gabriella use

In a poll of students at the football championship, 90% of the students say that football is better than basketball.

Explain why it is not a valid conclusion to say that football is more popular than basketball at school.

Suggest a better method of determining which sport is more popular.

Answers

Answer:

Part (a):  Because the survey was held at basketball championship.

Part (b): The survey among students should held at school or in any common place.

Step-by-step explanation:

Question 11(Multiple Choice Worth 2 points) (Line of Fit MC) A scatter plot is shown on the coordinate plane. scatter plot with points at 1 comma 2, 2 comma 3, 3 comma 2, 4 comma 5, 5 comma 3, 5 comma 6, 6 comma 4, and 8 comma 4 Which of the following graphs shows a line on the scatter plot that fits the data? scatter plot with points at 1 comma 2, 2 comma 3, 3 comma 2, 4 comma 5, 5 comma 3, 5 comma 6, 6 comma 4, and 8 comma 4, with a line passing through the coordinates 1 comma 2 and 2 comma 3 scatter plot with points at 1 comma 2, 2 comma 3, 3 comma 2, 4 comma 5, 5 comma 3, 5 comma 6, 6 comma 4, and 8 comma 4, with a line passing through the coordinates 1 comma 2 and 8 comma 4 scatter plot with points at 1 comma 2, 2 comma 3, 3 comma 2, 4 comma 5, 5 comma 3, 5 comma 6, 6 comma 4, and 8 comma 4, with a line passing close through the coordinates at about 2 comma 3 and 8 comma 5 scatter plot with points at 1 comma 2, 2 comma 3, 3 comma 2, 4 comma 5, 5 comma 3, 5 comma 6, 6 comma 4, and 8 comma 4, with a line passing through the coordinates 1 comma 3 and a half and 2 comma 3 and a half

Answers

A graph that shows a line on the scatter plot that fits the data include the following: B. scatter plot with points at 1 comma 2, 2 comma 3, 3 comma 2, 4 comma 5, 5 comma 3, 5 comma 6, 6 comma 4, and 8 comma 4, with a line passing through the coordinates 1 comma 2 and 8 comma 4.

What are the characteristics of a line of best fit?

In Mathematics and Geometry, there are different characteristics that are used for determining the line of best fit on a scatter plot and these include the following:

The line should be very close to the data points as much as possible.The number of data points that are above the line should be equal to the number of data points that are below the line.

By critically observing the scatter plot using the aforementioned characteristics, we can reasonably and logically deduce that line B represents the line of best fit because the data points are in a linear pattern.

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Christine has 5 coloured sweets in a bag. 1 of the sweets are red and 4 are green. She removes a sweet at random from the bag, notes the colour, and does not replace the sweet in the bag. She then chooses a second sweet at random. P(double green) P(Red | green) P( ∪) P(Green’)​

Answers

P(double green) = 3/20, P(Red | green) = 1/4, P(∪) = 7/20, P(Green’) = 4/5.

We ought to start by working out the probability of getting two green treats in progression:

P(double green) = P(first green) x P(second green given that the first was green)

The probability of getting a green sweet on the fundamental pick is 4/5, since there are 4 green treats out of 5 total. Beginning from the chief sweet was not superseded, there are by and by only 4 treats left dealt with, with 3 being green. Along these lines, the probability of picking a green sweet on the ensuing pick, taking into account that the first was green, is 3/4. Collecting this, we get:

P(double green) = (4/5) x (3/4) = 0.6

So the probability of getting two green sweets straight is 0.6, or 60%.

Then, we ought to sort out the probability of getting a red sweet on the ensuing pick, it was green to think about that the first:

P(Red | green) = P(Red and green)/P(green)

The probability of getting a red sweet and subsequently a green sweet is (1/5) x (4/4) = 1/5, since there is only a solitary red sweet left and every one of the four green pastries are as yet dealt with. The probability of getting a green sweet on the fundamental pick is 4/5, not entirely set in stone earlier. Collecting this, we get:

P(Red | green) = (1/5)/(4/5) = 0.2

So the probability of getting a red sweet on the resulting pick, taking into account that the first was green, is 0.2, or 20%.

By and by we ought to figure the probability of getting either two green treats in progression or a red sweet followed by a green sweet:

P( ∪) = P(double green) + P(Red and green)

We recently resolved P(double green) to be 0.6. The probability of getting a red sweet and subsequently a green sweet is 1/5, still up in the air earlier. Gathering this, we get:

P( ∪) = 0.6 + (1/5) = 0.8

So the probability of getting either two green treats in progression or a red sweet followed by a green sweet is 0.8, or 80%.

Finally, we ought to resolve the probability of not getting a green sweet on either pick:

P(Green') = P(Red and green') + P(first pick not green and second pick not green)

The probability of getting a red sweet on the principal pick and a non-green sweet on the resulting pick is (1/5) x (1/4) = 1/20, since there is only a solitary red sweet left and simply a solitary non-green sweet left after the essential pick. The probability of not getting a green sweet on the essential pick is 1/5, and the probability of not getting a green sweet on the ensuing pick, taking into account that the first was not green, is 3/4. Collecting this, we get:

P(Green') = (1/5) x (1/4) + (1/5) x (3/4) = 0.2

So the probability of not getting a green sweet on either pick is 0.2, or 20%.

In summation:

P(double green) = 0.6

P(Red | green) = 0.2

P( ∪) = 0.8

P(Green') = 0.2

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What is question asking??? All I need is one example and I get the rest I just don’t understand the assignment

Answers

It's actually asking you to find the angles within the circles and match it with the angles it's supposed to be. For example if angle COE is 90° (im taking a fake angle value), you should put arc CE <——> 90

If you are still confused and need me to do it so that you can understand what I mean, reply and I'll help you!

Answer:

See below

Step-by-step explanation:

The objective of the question has been well explained by user vaishub1101.

I am just adding an additional hint and one answer to get you going

Since you just needed one example, I am providing just that
One thing to note in the figure is that segments DEF, ACD and ABF are all tangents to the circle. This fact is important since at the point of tangency (where the tangent touches the circle), the tangent to a circle is always perpendicular to the radius.

Using this knowledge and the given angles we can compute all the other angles but not the arc length [tex]\frown \atop {CE}[/tex] since to find arc length we need the value of the radius

As an example to help you get going,
[tex]\angle{DFA} \longleftrightarrow 58^\circ[/tex]

You would drag the tile with ∠DFA to the top left box and the tile with 58° to the top right box

I am sure you can figure out the rest or else user vaishub1101 can help you out with the rest

Let f(t) be the outside temperature (°F) 7 hours after 2 A.M. Explain the meaning of f(4) < f(11) .

Answers

The term f(4) < f(11) means that the temperature is lower at 4 A.M. than it is at 11 A.M., and this inequality can be used to make predictions about temperature changes over time.

The function f(t) represents the temperature at a specific time t. In this case, f(t) is the outside temperature (in degrees Fahrenheit) 7 hours after 2 A.M. So, we can think of f(4) as the temperature 4 hours after 2 A.M. and f(11) as the temperature 11 hours after 2 A.M.

Now, the inequality f(4) < f(11) means that the temperature 4 hours after 2 A.M. is less than the temperature 11 hours after 2 A.M. In other words, the temperature is lower at 4 A.M. than it is at 11 A.M. This might seem obvious, as we generally expect temperatures to rise as the day progresses and the sun comes up. However, this inequality is useful for making more specific predictions about temperature changes.

For example, if we know that f(4) < f(11), we can predict that the temperature will increase between 4 A.M. and 11 A.M. This might be important information if you're planning outdoor activities or need to dress appropriately for the day's weather.

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Let E be the smallest region enclosed by the cone Z = - no Ix² + y² and the sphere x2 + y2 + z2 = 32 (note, it is the same region as in Question 8). Then, using spherical coordinates we can compute the volume of E as b d t Vol(E) = = [F(0,0,6) dø do dp, a Cs where F(0,0,0) = a = b = с = d = S = t =

Answers

the volume of the smallest region E enclosed by the cone and sphere is (64/3)π(1 - no⁴/5), where no is the constant in the equation of the cone Z = - no Ix² + y².

To compute the volume of the smallest region E enclosed by the cone and sphere, we will use spherical coordinates. In spherical coordinates, a point in 3D space is represented by three values: radius (r), polar angle (θ), and azimuthal angle (φ).

First, we need to find the intersection of the cone and sphere. Substituting Z = - no Ix² + y² into the equation of the sphere, we get x² + y² + (- no Ix² + y²)² = 32. Simplifying this equation gives us x² + y² + no²x⁴ - 2no²x²y² + y⁴ = 32. We can rewrite this equation in terms of r, θ, and φ as follows:

r²sin²θ + no²r⁴cos⁴θsin²θ - 2no²r⁴cos²θsin²θ + no²r⁴cos²θsin⁴θ = 32

Simplifying this equation gives us:

r = √(32/(sin²θ + no²cos²θsin²θ))

Next, we need to find the limits of integration for r, θ, and φ. Since the region E is enclosed by the sphere x² + y² + z² = 32, we know that the maximum value of r is 4√2. The minimum value of r is zero. The limits of integration for θ are 0 to π/2, since the cone is pointing downwards in the negative z direction. The limits of integration for φ are 0 to 2π, since the region E is symmetric about the z-axis.

The volume of the region E can be computed using the following integral:

Vol(E) = ∫∫∫ r²sinθ dr dθ dφ

Integrating over the limits of integration for r, θ, and φ, we get:

Vol(E) = ∫₀^(2π) ∫₀^(π/2) ∫₀^(4√2) r²sinθ dr dθ dφ

Evaluating this integral gives us:

Vol(E) = (64/3)π(1 - no⁴/5)

Therefore, the volume of the smallest region E enclosed by the cone and sphere is (64/3)π(1 - no⁴/5), where no is the constant in the equation of the cone Z = - no Ix² + y².
Hi! To compute the volume of the region E enclosed by the cone Z = -√(x² + y²) and the sphere x² + y² + z² = 32 using spherical coordinates, we can set up the triple integral as follows:

Vol(E) = ∫∫∫ ρ² sin(φ) dρ dθ dφ

In spherical coordinates, the cone Z = -√(x² + y²) becomes φ = 3π/4, and the sphere x² + y² + z² = 32 becomes ρ = 4.

The limits of integration are:
- ρ: 0 to 4
- θ: 0 to 2π
- φ: π/2 to 3π/4

So, the triple integral can be written as:

Vol(E) = ∫(ρ=0 to 4) ∫(θ=0 to 2π) ∫(φ=π/2 to 3π/4) ρ² sin(φ) dρ dθ dφ

By calculating this triple integral, we can find the volume of the region E.

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Probability and likelihood

a team of scientists is studying the animals at a nature reserve. They capture the animals, mark them so they can identify each animal, and then release them back into the park. The table gives the number of animals they’ve identified. Use this information to complete the two tasks that follow.


animal total in park number marked

elk 5,625 225

wolf 928 232

cougar 865 173

bear 1,940 679

mountain goat 328 164

deer 350 105

moose 215 86

part a

what is the probability of the next elk caught in the park being unmarked? write the probability as a fraction, a decimal number, and a percentage.



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part b

describe the likelihood of the next elk caught being unmarked.



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part c

describe a simulation that you can use to model this situation.



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part d

what is the probability of the next wolf caught in the park being unmarked? write the probability as a fraction, a decimal number, and a percentage.



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part e

describe the likelihood of the next wolf caught being unmarked.



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part f

describe a simulation that you can use to model this situation. The simulation should be different from the one in part c.



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part g

in the unit, you found the probability of a compound event by identifying the sample space. However, it is also possible to find the probability of a compound event without finding the sample space. To do this, multiply the probability of the first event by the probability of the second event. For example, the probability of flipping heads twice on a coin is. Using this idea, what is the probability that the next cougar and bear caught will both be unmarked?



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part h

describe the likelihood that the next cougar and bear caught are both unmarked.



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part i

describe a simulation that you can use to model this event.



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part j

using the method described in part g, what is the probability that the next mountain goat, deer, and moose caught are all unmarked?



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part k

describe the likelihood that the next mountain goat, deer, and moose caught are all unmarked.



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part l

describe a simulation that you can use to model this event. Your simulation should be different from the one in part i.



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Answers

Part g, h, i, j, k, and l:

Since the information for the other parts is not provided, it is not possible to calculate the probabilities, describe the likelihood, or propose simulations for those events.

Part a:

To find the probability of the next elk caught in the park being unmarked, we need to calculate the ratio of unmarked elks to the total number of elks.

Total number of elks: 5,625

Number of marked elks: 225

Number of unmarked elks: Total number of elks - Number of marked elks = 5,625 - 225 = 5,400

Probability = Number of unmarked elks / Total number of elks = 5,400 / 5,625

As a fraction: 5,400/5,625

As a decimal: 0.96

As a percentage: 96%

Part b:

The likelihood of the next elk caught being unmarked is high, as 96% of the elks captured so far have been unmarked.

Part c:

One possible simulation to model this situation is as follows:

Create a sample space consisting of 5,625 elks.

Randomly select an elk from the sample space.

Determine if the elk is marked or unmarked.

Repeat steps 2 and 3 for a desired number of simulations to observe the distribution of marked and unmarked elks.

Part d:

To find the probability of the next wolf caught in the park being unmarked, we need to calculate the ratio of unmarked wolves to the total number of wolves.

Total number of wolves: 928

Number of marked wolves: 232

Number of unmarked wolves: Total number of wolves - Number of marked wolves = 928 - 232 = 696

Probability = Number of unmarked wolves / Total number of wolves = 696 / 928

As a fraction: 696/928

As a decimal: 0.75

As a percentage: 75%

Part e:

The likelihood of the next wolf caught being unmarked is high, as 75% of the wolves captured so far have been unmarked.

Part f:

One possible simulation to model this situation is as follows:

Create a sample space consisting of 928 wolves.

Randomly select a wolf from the sample space.

Determine if the wolf is marked or unmarked.

Repeat steps 2 and 3 for a desired number of simulations to observe the distribution of marked and unmarked wolves.

Part g, h, i, j, k, and l:

Since the information for the other parts is not provided, it is not possible to calculate the probabilities, describe the likelihood, or propose simulations for those events.

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An italian ice shop sells italian ice in four flavors: lime, cherry, blueberry, and
watermelon. the ice can be served plain, mixed with ice cream, or as a drink.
using an organized list or table, what is the sample space of possible
outcomes?

Answers

The possible outcomes of sample space is 12.

To calculate the total number of outcomes in a sample space, multiply the number of serving options with the number of flavors.

There are 4 flavors that are lime, cherry, blueberry, and  watermelon and 3 serving options that are served plain, mixed with ice cream, or as a drink.

Hence, the possible outcomes will be:

4 x 3 = 12

The outcomes can be represented as lime Italian ice mixed with ice cream, cherry Italian ice served as a drink, Watermelon Italian ice mixed with ice cream, Blueberry Italian ice served plain and likewise.

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the radius of the area of a cylinder is 36m and it’s height is 46m. find the surface area of the cylinder in terms of

Answers

Surface area of the cylinder in terms of [tex]$\pi$[/tex] is [tex]$5904\pi m^2$[/tex].

How to find the surface area of the cylinder?

The surface area of a cylinder can be calculated by adding the area of the two bases (which are circles) and the lateral area (which is the area of the curved surface).

The radius of the cylinder is given as 36m and the height as 46m. Therefore, the diameter of the cylinder is 72m (twice the radius). Using the formula for the area of a circle, we can calculate the area of each base:

[tex]$A_{base} = \pi r^2 = \pi (36m)^2 = 1296\pi m^2$[/tex]

The lateral area of the cylinder can be calculated using the formula:

[tex]$A_{lateral} = 2\pi r h$[/tex]

Substituting the given values, we get:

[tex]$A_{lateral} = 2\pi (36m) (46m) = 3312\pi m^2$[/tex]

Therefore, the total surface area of the cylinder is:

[tex]$A_{total} = A_{base} + A_{lateral} + A_{base} = 2A_{base} + A_{lateral}$[/tex]

Substituting the values we calculated, we get:

[tex]$A_{total} = 2(1296\pi m^2) + 3312\pi m^2 = 5904\pi m^2$[/tex]

So the surface area of the cylinder in terms of [tex]$\pi$[/tex] is [tex]$5904\pi m^2$[/tex].

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Luca places $2,000 in an account that earns 2. 5% nominal yearly interest, compounded quarterly. Which of


the following is closest to the amount that the account is worth after 15 years if no additional deposits nor


withdrawals are made?


(1) $2,751. 08


(3) $2,853. 75


(2) $2,812. 19


(4) $2,906. 59

Answers

The closest answer to the amount that the account is worth after 15 years is $2,812.19, Therefore Option 3 is correct

The formulation for calculating the future value (FV) of an investment with compound interest is:

[tex]FV = P * (1 + r/n)^{(n*t)}[/tex]

Wherein P is the primary (the initial amount invested), r is the once a year interest rate, n is the variety of times the interest is compounded per year, and t is the term in years.

In this case, P = $2,000, r = 2.5% = 0.0.5, n = 4 (for the reason that interest is compounded quarterly), and t = 15. Plugging those values into the formulation, we get:

[tex]FV = $2,000 * (1 + 0.1/2/4)^{(4*15)}[/tex]

FV ≈ $2,812.19

Therefore, the closest answer to the amount that the account is worth after 15 years is $2,812.19.

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Angle θ is in standard position and

(



5

,



6

)

(−5,−6) is a point on the terminal side of θ. If

0





θ

<

36

0



0



≤θ<360



, what is the measure of θ, to the nearest tenth of a degree (if necessary)?

Answers

The measure of angle θ, to the nearest tenth of a degree is 233.1°.

To find the measure of angle θ, we need to use trigonometry. We can see that the point (-5,-6) lies in the third quadrant since both x and y coordinates are negative. We can draw a right-angled triangle with the origin (0,0) as the vertex and the given point (-5,-6) as one of the vertices on the x-y plane.

The hypotenuse of this triangle will be the distance between the origin and the point (-5,-6), which can be calculated using the Pythagorean theorem.

Using the Pythagorean theorem, we get:

√(5²+6²) = √(25+36) = √61

Now we can use trigonometry to find the measure of angle θ. We can see that the sine of θ is equal to the opposite side over the hypotenuse and the cosine of θ is equal to the adjacent side over the hypotenuse. So we have:

sin θ = -6/√61 and cos θ = -5/√61

Using a calculator, we can find that θ is approximately 233.1° to the nearest tenth of a degree.

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Three vertices of parallelogram wxyz are w(-5,2), x(2,4), and z(-7, -3). find the coordinates of vertex y.
the coordinates of vertex y are

Answers

Coordinates of vertex y are (-12,-1).

How to find the coordinates of vertex Y?

To find the coordinates of vertex y in parallelogram WXYZ, we can use the fact that opposite sides of a parallelogram are parallel. We can use this property to find the coordinates of y by first finding the vector between points X and Z, and then adding that vector to the coordinates of point W.

The vector between points X and Z is (-7-2,-3-4)=(-9,-7). Adding this vector to the coordinates of point W gives (-5-9, 2-7)=(-14,-5). Therefore, the coordinates of vertex Y are (-14,-5).

Hence, the coordinates of vertex Y in the parallelogram WXYZ are (-14, -5).

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Lines AC←→
and DB←→
intersect at point W. Also, m∠DWC=138°
.

Answers

The measure of the angles are m∠DWC=138°, ∠AWB = 138°, ∠AWD = 42°, ∠BWC = 42°

How do we calculate?

The Vertical angle theorem states that if two lines intersect at a point then vertically opposite angles are congruent.

To find the measure of all the angles:

∠AWB and ∠DWC are vertically opposite angles.

Therefore, ∠AWB = ∠DWC

⇒ ∠AWB = 138°

we know that the Sum of all the angles in a straight line = 180°

⇒ ∠AWD + ∠DWC = 180°

⇒ ∠AWD + 138° = 180°

⇒ ∠AWD = 180° – 138°

⇒ ∠AWD = 42°

Since ∠AWD and ∠BWC are vertically opposite angles.

Therefore, ∠AWD = ∠BWC

⇒ ∠BWC = 42°

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#complete question:

Lines AC←→ and DB←→ intersect at point W. Also, m∠DWC=138° .

Enter the angle measure for the angle shown.

see attached image:

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