What is the answer for y?

What Is The Answer For Y?

Answers

Answer 1

The linear function that models the data is y=3/5x - 2/5 which has the form y=mx+b, where m is the slope and b is the y-intercept.

What is linear function?

This can be written in the form y = mx + b where m and b are constants and x is a variable. The graph of a linear function is a straight line that goes through the origin.

To calculate the linear function, we must first calculate the slope. The slope is the numerical change in y (rise) divided by the numerical change in x (run).

Subtracting the y-values for x=-9 and x=-8, we get

-29/5 - (-26/5) = -3/5.

Similarly, subtracting the x-values for x=-9 and x=-8, we get

-9 - (-8) = -1.

Now, -3/5 / -1, we get the slope, m, of 3/5.

Next, we must calculate the y-intercept, b.

To do this, we can use either of the points given.

Using the points (x=-9, y=-29/5), we can substitute the x and y values into the linear equation, y=mx+b.

-29/5 = 3/5(-9) + b, which can be simplified to

-29/5 = -27/5 + b.

Adding 27/5 to both sides, we get b = -2/5.

Therefore, the linear function that models the data is y=3/5x - 2/5.

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Related Questions

The standard deviation of the weights of elephants is known to be approximately 15 pounds. We wish to construct a 95% confidence interval for the mean weight of newborn elephant calves. Fifty newborn elephants are weighed. The sample mean is 244 pounds. The sample standard deviation is 11 pounds Construct a 95% confidence interval for the population mean weight of newborn elephants. State the confidence interval (Round your answers to two decimal places.) Sketch the graph. (Round your answers to two decimal places.) CL - 0.95 X Calculate the error bound (Round your answer to two decimal places)

Answers

The error bound for the 95% confidence interval is (1.96 x Standard Deviation/√n), which in this case is (1.96 x 11/√50) = 2.56. This means that the true mean weight of newborn elephant calves lies within +/-2.56 pounds of the interval range.

The 95% confidence interval for the population mean weight of newborn elephants can be calculated using the sample mean of 244 pounds and the sample standard deviation of 11 pounds. The confidence interval is calculated using the following formula:
Confidence Interval = (Mean - (1.96 x Standard Deviation/√n)), (Mean + (1.96 x Standard Deviation/√n))
Where n is the sample size.
Therefore, the 95% confidence interval for the population mean weight of newborn elephants is (231.14, 256.86).
This can also be represented in a graph. The graph would have the x-axis representing the confidence interval, with a range from 231.14 to 256.86, and the y-axis representing the probability, which would be 0.95.

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Ted is five times as old as Rosie was when Ted was Rosie's age. When Rosie

reaches Ted's current age, the sum of their ages will be 72. Find Ted's current age.

Answers

Answer:

45 yo

Step-by-step explanation:

Let's start by defining some variables to represent the ages of Ted and Rosie:

- Let's call Ted's current age "T"

- Let's call Rosie's current age "R"

From the problem statement, we know that:

- Ted is five times as old as Rosie was when Ted was Rosie's age. Written as an equation, this becomes:

T = 5(R - (T - R))

Simplifying this equation, we get:

T = 5(R - T + R)

T = 10R - 5T

- When Rosie reaches Ted's current age, the sum of their ages will be 72. Written as an equation, this becomes:

R + T = 72 - T

We now have two equations with two variables. We can use substitution to solve for T.

Substitute the second equation into the first equation to eliminate R:

T = 10R - 5T

T = 10(72 - T) - 5T

T = 720 - 15T

16T = 720

T = 45

Therefore, Ted's current age is 45.

Tanya is making a scale drawing of her house. She is using a 6 inch line on her drawing to represent the 30 foot width of her house. Tanya's room is 12 feet by 12 feet. What will be the length of the lines she uses to represent her room on the scale drawing?

Answers

Answer:2.4 inches

Step-by-step explanation:

if 6 is for 30 feet, we can use a proportional statement to find what the length of the line will be for a room that is 12 feet.

Suppose we create a box model for the outcome of a game of darts. The player has a 1/3 chance of throwing a dart in the inner ring, and a 2/3 chance of the dart landing in the outer ring. In our model, we have two unique tickets marked "inner" and "outer." We put in 1 ticket marked "inner." How many tickets do we put in that are marked "outer?"
a. 0
b. 1
c. 2
d. 3

Answers

As per the combination method, the number of tickets that we put in that are marked "outer" is 3 (option d).

In this case, we want to choose the number of tickets marked "outer." Let's call this number k. We know that we already put one ticket marked "inner" in the box, so the total number of tickets in the box is 2. Therefore, n = 2.

Now we need to determine k. We want to know how many tickets we need to put in that are marked "outer." We can represent this as a. So we have:

ᵃC₁ = a! / ((1!)(a-1)!) = a

We want to find the value of a that satisfies the condition that the probability of choosing an "inner" ticket is 1/3 and the probability of choosing an "outer" ticket is 3/2.

Since we already put in 1 ticket marked "inner," the probability of choosing an "inner" ticket is 1/2, which means the probability of choosing an "outer" ticket is also 1/2.

We know that the probability of choosing an "outer" ticket is 3/2, so we can set up the following equation:

ᵃC₁ / 2 = 3/2

Solving for a, we get:

a = 3

In conclusion, the answer is (d) 3.

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WHAT IS THE CENTRAL ATOM OF NITRIC OXIDE (NO)

Answers

Answer:

The answer is Nitrogen

Hope this helps :)

A bag contains 8 green cubes, 12 black cubes and 16 white cubes. What is the ratio of green to black to white cubes in its simplest form?​

Answers

Answer:

Total number bags is 36

green cubes is 8white cubes is 16Black cubes is 12

1:2:3 the answer

This is the answer, hope it helps

josh borrowed $250 from his mother to buy an electric scooter. josh will pay her back in 1 year with 3% simple annual interest. how much interest will josh pay?

Answers

The interest which josh will pay on the electric scooter with a simple annual interest of 3% is 7.50.

What is interest rate?

Interest rate can be defined as the amount of interest which is due per period, as a proportion of the amount lent, deposited, or borrowed by someone.

The interest rate formula is:

Interest Rate = {(Simple Interest × 100)}/{ (Principal × Time)}

Here,

Josh borrowed 250 from his mother to buy an electric scooter and will pay her back in one year with three simple annual interest.

The amount of interest that Josh will pay is calculated as:

Interest = Principal Amount × Rate of Interest × Time

Interest = 250 × 3

Therefore, Josh will pay his mother $7.50 in interest for the loan.


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To be honest I don’t know what I’m doing with this question

Answers

Answer:

[tex]\sqrt{231}[/tex] cm

Step-by-step explanation:

The Pythagorean theorem is a mathematical principle that relates to the three sides of a right triangle. The formula for this is:

[tex]a^2 + b^2 = c^2[/tex]

In this case, the hypotenuse (c) is 16 cm, and one of the legs (a) is 5 cm. We can plug in the values and solve for the missing value.

[tex]5^2+b^2=16^2[/tex]

[tex]25+b^2=256[/tex]

[tex]b^2=256-25[/tex]

[tex]b^2=231[/tex]

[tex]b = \sqrt{231}[/tex] cm

Please help me I am stuck on this question

Answers

Answer:

9

Step-by-step explanation:

-5 + (-18) +32

-23 + 32

32 -23

Each of these measures is rounded to nearest whole: a=5cm and b=3cm Calculate the upper bound of a +b

Answers

The upper bound of a + b can be found by adding the upper bounds of a and b.

For a = 5cm, the nearest whole number is 5. The upper bound would be the midpoint between 5 and 6, which is 5.5.

For b = 3cm, the nearest whole number is 3. The upper bound would be the midpoint between 3 and 4, which is 3.5.

So the upper bound of a + b is:

5.5 + 3.5 = 9

Therefore, the upper bound of a + b is 9cm.

The following set of scores was obtained from a quiz: 4, 5, 8,9, 11, 13, 15, 18, 18, 18, 20. The teacher computes the usual descriptive measures of central tendency and spread for these data and then discovers that an error was made. One of the 18s should have been a 16. Which of the following measures will NOT need to be changed from the original computations? (There may be more than one correct answer.) Mean 73 Median Standard deviation 1 IQR They all will need to be changed.

Answers

All of the measures of central tendency and spread for these data will need to be changed from the original computations in order to reflect the correct values.



In this case, the initial set of scores was 4, 5, 8, 9, 11, 13, 15, 18, 18, 18, and 20. The teacher initially computed the mean, median, standard deviation, and IQR and then discovered that one of the 18s should have been a 16.The mean is affected by any change in the data, so this measure will need to be changed to reflect the correct values. The new mean is 73.The median is also affected by any change in the data, so this measure must be recalculated to reflect the correct values.

The new median is 15.5.The standard deviation measures the spread of data from the mean, so this measure must also be changed to reflect the correct values. The new standard deviation is 1.4.Finally, the IQR measures the spread of the middle 50% of the data, so this measure must also be changed to reflect the correct values. The new IQR is 6. All of the measures of central tendency will need to be changed.

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D. A population of rabbits is doubling every 3 months. If there were 2 rabbits to begin
with, how many will there be after 5 years?

Answers

There will be a population of 2,097,152 rabbits after 5 years.

What is exponential growth?

A form of growth known as exponential growth occurs when a quantity's rate of expansion is proportionate to its present value. In other words, a quantity expands more quickly the greater it is. A prime example of exponential expansion is the rabbit population, which doubles in size every three months.

Given that, population of rabbits is doubling every 3 months.

That is,

5 years = 5 x 12 = 60 months

Number of doublings = 60 / 3 = 20

For every doubling, the population will be twice as large.

Thus,

P = 2 x 2²⁰ = 2 x 1,048,576 = 2,097,152 rabbits

Therefore, there will be approximately 2,097,152 rabbits after 5 years.

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#1 Brainlist!
Answer and show steps and I will make you brainlist.

Answers

Answer:

Multiplying the second equation by 5, we get:

15x + 20y = 180

Now, we can add this equation to the first equation:

26x = 208

x = 8

Substituting x = 8 in the second equation:

3(8) + 4y = 36

4y = 12

y = 3

Therefore, the solution to the system is (8, 3).

Solve each equation and verify the solution.​Please heeelp

Answers

We have established that the answer to the equation,  [tex]x = 24/7[/tex] , is that the left side equals the right side.

What is the equation in algebra?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation [tex]3x + 5 = 14[/tex]  consists of the two equations  [tex]3x + 5[/tex] and 14, which are separated by the 'equal' sign.

The equation is as follows:

[tex]\frac{1}{2}\times (x-2)+ 1+2/3x-3[/tex]

This equation can be made simpler by first merging like terms:

[tex]\frac{1}{2}\times (x-2)+ 1+2/3x-3[/tex]

[tex]= 1/2x + 2/3x - 4[/tex]

[tex]= 7/6*x - 4[/tex]

As a result, the equation becomes [tex]7/6*x - 4 = 0.[/tex]

We can now get the value of x by multiplying both sides by 6/7 after adding 4 on both sides: [tex]7/6*x = 4 x = 24/7.[/tex]

We rewrite the original equation with x = 24/7 to confirm the solution:

[tex]1/2*(24/7-2)+1+2/3(24/7)-3[/tex]

[tex]= 1/2*(10/7)+1+16/21-3[/tex]

[tex]= 5/7+1-2/3[/tex]

[tex]= 6/7[/tex]

Therefore, 6/7 demonstrates the equality.

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Use the following points to find the slope.
(1, -1)
(4, 8)



Use the slope and one of the points to find the y-intercept.



Write the final formula.

*

Answers

Answer:

the formula is -xcomma y because I there is y intercept then there x will be negative. not y

how do i work this out i dont understand it

Answers

Answer:

37

Step-by-step explanation:

we know that:

C=?

c=17

b=26

a=14

using the law of cosine:

[tex]a^{2} +b^{2} -2ab Cosc=c^{2}[/tex]

[tex]14^{2} +26^{2} -2(14)(26)Cosc=17^{2} \\872-728Cosc=289\\-728Cosc=-583\\Cosc=\frac{-583}{-728} \\C=36.791\\C=37[/tex]

Jessie is considering a purchase of a $135,000 home at 5. 5%. Under this rate,
her mortgage payment would be $766. 51. If she purchases a point, her new
mortgage payment is $755. 96. How many months would it take her to break-
even on the points purchase?

Answers

As per unitary method, the number of months would take her to break - even on the points purchase is 128

To break even on the points purchase, Jessie needs to recoup the cost of the point through the savings in her monthly mortgage payments. In this case, the cost of the point is 1% of the loan amount, which is $1,350.

To calculate the break-even point, we can use the following formula:

Break-even point = Cost of point / Monthly savings

In this case, the monthly savings is the difference between the original mortgage payment ($766.51) and the new mortgage payment with the point ($755.96), which is $10.55 per month.

Substituting the values, we get:

Break-even point = $1,350 / $10.55

Break-even point = 128 months

Therefore, it would take Jessie 128 months, or just over 10 years, to break even on the points purchase.

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I need help with these two graphs. I'll give brainliest if I can.

Answers

Answer:

13) F(-5, 0), so F' will be at (1, 2)

G(-1, -1), so G' will be at (5, 1)

H(-2, 3), soH' will be at (4, 5)

14) G(-2, 1), so G' will be at (-1, 3)

H(-1, 3), so H' will be at (0, 5)

I(3, 1), so I' will be at (4, 3)

J(2, -1), so J' will be at (3, 1)

Step-by-step explanation:

13) Add 6 to each original x-coordinate and add 1 to each original y-coordinate.

14) Add 1 to each original x-coordinate and add 2 to each original y-coordinate.

You may plot the new points to confirm my answer.

Find the mean, median, mode, and range for the data set given.

112, 122, 132, 142, 152

Answers

mean - 112+122+132+142+152=660/5 =132
median - [middle number] = 132
range - 152-112=40
mode - 152

what proportion of values for a standard normal distribution are less than 2.98?

Answers

Regardless of the appearance of the normal distribution or the size of the standard deviation, approximately less than 2.98% of observations consistently fall within two deviations types (one high and one low).

The normal distribution, also known as the Gaussian distribution, is a probability distribution symmetrical about the mean, indicating that data near the mean occurs more frequently than data far from the mean. In graphical form, the normal distribution is represented by a "bell curve".

The normal distribution is important in statistics and is often used in the natural and social sciences to represent real-valued random variables whose distribution is unknown. Their importance is partly due to the central limit theorem. It states that in some cases the mean of many samples (observations) of a random variable with finite mean and variance is itself a random variable - whose distribution converges to a normal distribution as the size of the l sample increases. Therefore, physical quantities assumed to be the sum of many independent processes, such as measurement errors, tend to have a near-normal distribution.

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Please urgent need the work and answer
X=3.2
Y=6.1
Z=0.2

XZ +Y2

Answers

Answer: 12.84

Step-by-step explanation:

if x = 3.2 and y = 6.1  and Z = 0.2

then plug in the numbers

(3.2)(0.2) + (6.1)(2)

0.64 + 12.2 = 12.84

Any variable next to a number means multiplication.

if I was wrong lmk

Suppose that 30 students take a quiz worth 30 points. The SD of the scores is 1 point. Which of the following gives the most reasonable description of the distribution of quiz scores?
A) All of the individual scores are one point apart.
B) The difference between the highest and lowest score is 1.
C) The difference between the 1st and 3rd quartile marks is 1.
D) A typical score is within 1 point of the mean.

Answers

The statement that gives the most reasonable description of the distribution of quiz scores is "A typical score is within 1 point of the mean." The correct answer is Option D.

What is Standard deviation?

The standard deviation (SD) is a measure of the variability of data in a population. Standard deviation is a measure of how much each value differs from the mean (average) value of the data set.

What is the range?

The difference between the highest and lowest values in a dataset is known as the range. It's a quick way to see the data's spread. If the range is big, it implies that the data is more diverse, while if it's small, it implies that the data is more consistent.

What is the first quartile?

The first quartile (Q1) is the value that splits the lowest 25% of a data set from the rest of the data set. If we order the dataset from smallest to largest, the first quartile is the value at the 25th percentile.

What is the third quartile?

The third quartile (Q3) is the value that splits the highest 25% of a data set from the rest of the data set. If we order the dataset from smallest to largest, the third quartile is the value at the 75th percentile.

What is the mean?

The sum of all values in a dataset divided by the total number of values in the dataset is known as the mean. The mean, often known as the arithmetic mean, is one of the most basic measures of central tendency in statistics.

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You have five student groups to present in class one group cannot go first because they need additional set up time and how many orders can they present

Answers

They can present in 96 different orders. Given, there are five student groups to present in class and one group cannot go first because they need additional set-up time.

Permutation is to select an object then arrange it and it cares about the orders while Combination is about only selecting an object without caring the orders.

We have 5 positions to fill here.

First position: 4 ways (one of the rest 4 groups will present first)

Second position: 4 ways (one of the rest 3 groups and the group which could not present first, will present second)

Third position: 3 ways (one of the rest 3 groups will present third)

Fourth position: 2 ways (one of the rest 2 groups will present fourth)

Fifth position: 1 way (rest group will present last)

Total ways in which they can present = 4*4*3*2*1 = 96

Hence, the answer is 96.

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I need the answer for number 3 step by step, please help!

Answers

Answer:

[tex]\frac{-1}{3}[/tex]

Step-by-step explanation:

Look at the red slope triangle that is drawn. If you start at the point on the left, you go down 1 unit and then to the right 3 units.  This would be represented by -1/3.  Down would be negative and going right would be positive.  The slope is the rise over the run.

Helping in the name of Jesus.

You have a circular loop of wire in the plane of the page with an initial radius of 0.40 m which expands to a radius of 1.00 m. It sits in a constant magnetic field B = 24 mT pointing into the page. Assume the transformation occurs over 1.0 second and no part of the wire exits the field. Also assume an internal resistance of 30 Ω. What average current is produced within the loop and in which direction? Express your answer with the appropriate units. Enter positive value if the current is clockwise and negative value if the current is counterclockwise. My INCORRECT work: emf = -BAcos(theta)/dt emf = -B*1*(dA/dt) emf = -B*pi*(2*(expansion rate/1)^2*t+2*r0*(expansion rate/1) Then V=IR so emf=IR so I=emf/R I = -[B*pi*(2*(expansion rate/1)^2*t+2*r0*(expansion rate/1)]/R I = -[24x10^-3*pi*(2*.6^2*1+2*.4*.6)]/30 I ~ -3.015928947x10^-3 I ~ -3.0x10^-3 Which is wrong.

Answers

In the given scenario, the average current produced within the loop is approximately 2.13 A.

We can begin by computing the change in magnetic flux across the loop as it expands to determine the average current generated within the loop.

The following equation provides the magnetic flux across a loop:

Φ = B * A * cos(θ)

ΔΦ = B * ΔA

ΔA = A₂ - A₁ = π * (1.00 m)² - π * (0.40 m)² = π * (1.00² - 0.40²) = π * (1.00 + 0.40)(1.00 - 0.40) = π * (1.40)(0.60) = 0.84π m²

So,

ΔΦ = B * ΔA = (24 mT) * (0.84π m²) = 20.25π m²·T

emf = ΔΦ / Δt = (20.25π m²·T) / (1.0 s) = 20.25π V

As:

emf = I * R

So, again

I = emf / R = (20.25π V) / (30 Ω) ≈ 2.13 A

Thus, the average current produced within the loop is approximately 2.13 A.

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An electric dipole with its center located at the origin of a Cartesian coordinate system oscillates along the z axis, creating an electromagnetic wave. At a position on the y axis far from the origin, what is the polarization of the wave and which axis are the magnetic (a) The wave is polarized parallel to the a axis and the magnetic field lines are parallel to b The wave is polarized parallel to the z axis and the magnetic field lines are parallel to (c) The wave is polarized parallel to the y axis and the magnetic field lines are parallel to (d) The wave is polarized parallel to the y axis and the magnetic field lines are parallel to (e) The wave is polarized parallel to the z axis and the magnetic field lines are parallel to field lines parallel to? the y axis the axis the r axis the z axis the z axis

Answers

The wave is polarized parallel to the y-axis, and the magnetic field lines are parallel to the x-axis. Here option D is the correct answer.

The oscillating electric dipole along the z-axis creates an electromagnetic wave with electric and magnetic fields perpendicular to each other and to the direction of wave propagation. At a position on the y-axis far from the origin, the electric field will be parallel to the y-axis.

The polarization of the wave refers to the orientation of the electric field vector. Since the electric field is parallel to the y-axis, the wave is polarized parallel to the y-axis.

According to the right-hand rule, the direction of the magnetic field lines will be perpendicular to both the electric field and the direction of wave propagation, which is along the z-axis. Therefore, the magnetic field lines will be parallel to the x-axis.

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Will a 12.5-inch x 17-inch rectangular tray fit in
the box shown? Explain.
Please help!!!

Answers

Therefore, the correct response is OB: No, the box is a rectangle, and the tray's 12.5-inch length is greater than the box's 11-inch breadth.

what is rectangle ?

A rectangle is a geometric shape with four edges and four angles that exists in two dimensions. Because it is a sort of quadrilateral, it has four sides that are parallel to one another. Rectangles are a form of parallelogram because they have opposite sides that are the same length and opposite angles that are the same size. A rectangle's two adjacent sides make right angles, so all four of the angles, which each measure 90 degrees, are right angles.

given

The tray has a breadth of 17 inches and a length of 12.5, according to the measurements given. The package is 13 inches by 11 inches by 11 inches in size.

The platter can fit inside the box because its length is less than the box's length, which is 13 inches. But we also need to think about the box's breadth and height.

The tray cannot fit inside the box in that dimension because its width, which is 17 inches, is larger than the box's, which is 11 inches. The tray cannot fit inside the box because the height of the box is also 11 inches, which is shorter than the length of the tray neither in that realm.

Therefore, the correct response is OB: No, the box is a rectangle, and the tray's 12.5-inch length is greater than the box's 11-inch breadth.

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13. The diagonals of a trapezium ABCD intersect at O. AB is parallel to DC, AB = 3 cm and DC = 6 cm. If CO = 4 cm and OB = 3 cm, find AO and DO.​

Answers

Answer:

AO = 2 cmDO = 6 cm

Step-by-step explanation:

You want the measures of AO and DO in a trapezium in which AB║CD, the diagonals intersect at O, and AB = 3 cm, CD = 6 cm, CO = 4 cm, OB = 3 cm.

Similar triangles

Diagonal AC is a transversal to parallel lines AB and CD, so alternate interior angles BAO and DCO are congruent. Vertical angles AOB and COD are also congruent, so ∆ABO ~ ∆CDO by the AA similarity postulate.

This means the side lengths are proportional, so ...

  AB/CD = AO/CO = BO/DO

  3/6 = AO/4 = 3/DO   ⇒   AO = 2, DO = 6

The measures of AO and DO are 2 cm and 6 cm, respectively.

__

Additional comment

It can help to draw a diagram.

What are the exact lengths of BC and CF?

The length, in feet, of BC is the square root of.

The length, in feet, of CF is the square root of

Answers

The length, in feet, of BC is the square root of  √242 and, The length, in feet, of CF is the square root of √363

Cube:

In geometry, a cube is a three-dimensional solid object bounded by six faces, facets, or square sides, with three points of intersection at each vertex. Seen from a certain angle, it is a hexagon and its canvas is often represented by a cross.

Cube is the only regular hexahedron and one of the five Platonic solids. It has 6 faces, 12 edges and 8 vertices. Cube is also a cube, an equilateral cuboid, a rhombus and a 3-sonohedron.

Three orientations are square prisms and four orientations are triangular trapezoids. A cube is twice as large as an octahedron. It has cubic or octahedral symmetry. Cube is the only convex polyhedron whose faces are square.

Then the length CB is given by the Pythagorean theorem as:

CB = √(AC² +AB²)

     = √{(2 cm)² + (√2 cm)²}

     = √(4 +2) cm

CB = √6 cm

Now,

The length, in feet, of BC is the square root of  

√242

And,

The length, in feet, of CF is the square root of  

√363

Complete Question:

A cube. The top face has points C, A, B, D and the bottom face has points G, E, F, H. Diagonals are drawn from B to C and from C to F. Side B F is 11 feet.

What are the exact lengths of BC and CF?

The length, in feet, of BC is the square root of

The length, in feet, of CF is the square root of

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Answer:

The length, in feet, of BC is the square root of

✔ 242

The length, in feet, of CF is the square root of

✔ 363

Step-by-step explanation:

Elmer is on a Ferris wheel which has a diameter of 180 ft and whose center is 120 ft off the ground. Find all of the angles θ such that 0≤θ≤3π and such that Elmer's carriage is at a height of 165 ft when it makes an angle of θ with the horizontal. Leave your answers in exact form

Answers

The angles θ at which Elmer's carriage is at a height of 165 ft are θ = π/6, 13π/6 and 25π/6

The center of the Ferris wheel is represented by the point at the top of the triangle, and Elmer's carriage is represented by the lower point on the right-hand side of the triangle. We are given that the diameter of the Ferris wheel is 180 ft and that its center is 120 ft off the ground. This means that the radius of the Ferris wheel is 90 ft (half of the diameter), and that the distance from the center of the Ferris wheel to Elmer's carriage is also 90 ft.

We are also given that Elmer's carriage is at a height of 165 ft when it makes an angle of θ with the horizontal. Using trigonometry function , we can find the sine of θ as follows:

sin(θ) = (165 - 120) / 90

= 45 / 90

= 1/2

Therefore, we have:

θ = sin^(-1)(1/2)

= π/6

Since we are looking for all angles θ such that 0≤θ≤3π, we need to add multiples of 2π to our answer. The multiples of 2π that satisfy this inequality are 0, 2π, and 4π. Therefore, the solutions to the problem are:

θ = π/6, 13π/6, 25π/6

Learn more about trigonometric functions here

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