There are three containers: a 10 liter container, a 7 liter container, and a 4 liter container. The 7 and 4 liter containers are initially full of water, while the 10 liter container is empty. There is only one operation: pour the contents of one container into the other stopping only when the pouring container is empty or the receiving container is full. • Is there a sequence of pourings that leaves exactly 2 liters in the 4 liter container? • Model this as a graph problem: Define the graph. What is the problem that needs to be solved? What algorithm can be used to solve this problem?

a) The sum of the measures of the interior angles of the regular nonagon is given by S₉ = 1260°

b) The measure of each interior angle of the regular nonagon is a = 140°

c) The measure of each exterior angle of the regular nonagon​ is b = 40°

Given data ,

Sum of the measures of the interior angles of a regular nonagon:

The Polygon Interior Angle Sum Theorem states that the sum of the measures of the interior angles of a polygon with n sides is given by the formula:

Sum of interior angles = (n - 2) * 180°

For a nonagon, which has 9 sides, we can plug in n = 9 into the formula:

Sum of interior angles = (9 - 2) * 180

Sum of interior angles = 7 * 180

Sum of interior angles = 1260°

So, the sum of the measures of the interior angles of a regular nonagon is 1260°

Measure of each interior angle of a regular nonagon:

Since a regular nonagon has 9 sides, we can divide the sum of the interior angles (which we calculated as 1260 degrees) by the number of sides to find the measure of each interior angle:

Measure of each interior angle = Sum of interior angles / Number of sides

Measure of each interior angle = 1260 / 9

Measure of each interior angle = 140°

So, the measure of each interior angle of a regular nonagon is 140°

Measure of each exterior angle of a regular nonagon:

The Polygon Exterior Angle Sum Theorem states that the sum of the measures of the exterior angles of a polygon with n sides is always 360°

Since a regular nonagon has 9 sides, we can divide 360 degrees by the number of sides to find the measure of each exterior angle:

Measure of each exterior angle = 360 / Number of sides

Measure of each exterior angle = 360 / 9

Measure of each exterior angle = 40°

Hence , the measure of each exterior angle of a regular nonagon is 40°

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Using the normal distribution, it is found that there is a 0.2798 = 27.98% probability that he’ll use all the toothpaste in the tube.

In a normal distribution with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

In this problem:

The probability that he’ll use all the toothpaste in the tube is 1 subtracted by the p-value of Z when X = 0.85, hence:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{0.85 - 0.78}{0.12}\)

\(Z = 0.583\)

\(Z = 0.583\) has a p-value of 0.7202.

1 - 0.7202 = 0.2798

0.2798 = 27.98% probability that he’ll use all the toothpaste in the tube.

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To determine the area of the remaining piece of cardboard expressed in terms of x when a square of side length x inches is cut out from a rectangular piece of cardboard having a length of 6x+2 inches and a width of 2x-4 inches, use the following steps.

Draw and label a diagram of the problem. The rectangle should be labeled as 6x+2 inches by 2x-4 inches, and the square cut out should be labeled as x inches by x inches. This is how the diagram looks like: Determine the area of the rectangle, Arect.

The area of the rectangle is given by the product of its length and width. Thus, Arect = (6x + 2)(2x - 4) Determine the area of the square, Asq. The area of the square is given by the square of its side length. Thus, Asq = x²Step 4: Determine the area of the remaining cardboard after the square is cut out, Ar.

This is the difference between the area of the rectangle and the area of the square. Thus, Ar = Arect - Asq= (6x + 2)(2x - 4) - x²= 12x² - 20x - 16

Simplify the expression. The final answer is given in terms of x. Thus, Ar = 12x² - 20x - 16.The area of the remaining piece of cardboard is expressed in terms of x as 12x² - 20x - 16.

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Answer:

0 degrees

120 degrees

240 degrees

Step-by-step explanation:

The solutions to the equation √3sin(x/2) + cos(x) = 1, for 0º < x < 360°, are x = 0°, 120°, and 240°.

The given equation is √3sin(x/2) + cos(x) = 1.

Rearrange the equation to isolate the term with sin(x/2):

√3sin(x/2) = 1 - cos(x)

Square both sides of the equation to eliminate the square root:

3sin²(x/2) = (1 - cos(x))²

Apply the trigonometric identity sin²(x/2) = (1 - cos(x))/2:

3(1 - cos(x))/2 = (1 - cos(x))²

Multiply both sides by 2 to remove the fraction:

3(1 - cos(x)) = 2(1 - cos(x))²

Expand the square on the right side:

3 - 3cos(x) = 2(1 - 2cos(x) + cos²(x))

Simplify and rearrange the equation:

3 - 3cos(x) = 2 - 4cos(x) + 2cos²(x)

Combine like terms:

2cos²(x) - cos(x) - 1 = 0

Factor the quadratic equation:

(2cos(x) + 1)(cos(x) - 1) = 0

we can solve for x by setting each factor equal to zero:

2cos(x) + 1 = 0:

cos(x) = -1/2

x = 120°, 240° (in the range 0° < x < 360°)

cos(x) - 1 = 0:

cos(x) = 1

x = 0° (in the range 0° < x < 360°)

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Denis's and Dasha's methods use different operations to simplify the expressions in different orders.

Denis's method uses addition, subtraction, and multiplication operations, but Dasha's method does not.

Multiplication operations are described as using mathematical operation that indicates how many times a number is added to itself.

Denis's Assignment

2* 6+2w-54

12+2w = 54

12-12+2w= 54-12

2w=42

w= 21  

Dasha's Assignment

54-2* 6

54-12= 42

The two widths add to 42 cm

42/ 2-21

We can see that Dasha's method also uses addition and subtraction operations, but she simplifies the expression by performing the operations in a different order.

She subtracts the product of 2 and 6 from 54.

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Answer:

a. 15 ft

b. cos(53.13) = 0.6

Step-by-step explanation:

a. use pythagorean theorem to find hypotenuse.

9^2 + 12^2 = x^2

225 = x^2

15 = x

b. find the angle that the ladder makes with the ground first.

sin^-1(12/15) = 53.13 degrees

find the cosine of that angle

cos(53.13) = 0.6

Answer: wow that's crazy cause I need help with the same answer

Step-by-step explanation:

Answer:

a₅ = -3125

Step-by-step explanation:

Given that,

a₁ = -5, r = 5 and n = 5

The geometric sequence is given by :

\(a_n=a_1\cdot r^{n-1}\)

Put all the values,

\(a_5=-5\times 5^{5-1}\\\\=-5\times 5^4\\\\=-3125\)

So, the fifth term is equal to -3125.

Answer:

Leading Coefficient: - 1

Degree: 6

Step-by-step explanation:

Hope this helps! :)

Answer:

Step-by-step explanation:

We know that:

Work:

Hence, the length of the side of the regular pentagon is x + 3.

Hoped this helped.

\(BrainiacUser1357\)

The statement which is true about the quadrilateral is D. Some rhombuses have four right angles.

Quadrilaterals are four sided polygons which also have four vertices and four angles.

Sum of all the interior angles of a quadrilateral is 360 degrees.

Rectangles, squares, trapezium, parallelogram, rhombus are all quadrilaterals.

A. All squares are rectangles but all rectangles are not squares, since for squares, all sides need to be equal.

But for a rectangle, opposite sides only need to be equal.

B. A rhombus has all the sides equal and opposite sides are parallel.

So there are 2 pairs of parallel sides.

C. A trapezoid can have only one pair of sides parallel.

D. Some rhombuses have four right angles.

This is true since square is a rhombus and it has 4 right angles.

Hence the true option is D.

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Answer:

the probability you lose one or more friends is 0.9836

Step-by-step explanation:

 Given the data in the question;

P( you lose one or more friend ) = 1 - P( keeping all friends )

Now, keeping all friends is possible only when each friend receives red candy.

As there are only 9 red candies and 9 friends, 1 red candy needs to be given to each friend out of 9 candies

Thus, total candies given = 63

and each friend will get 8 non red and 1 red candy

Thus, P( keeping all friends )

= [ ⁹C₁ × ⁹C₁ × ⁹C₁ × ⁹C₁ × ⁹C₁ × ⁹C₁ × ⁹C₁ × ⁹C₁ × ⁹C₁ ] / × ⁶³C₉

SO

⁹C₁  = 9!/(1!(9-1)!) = 9 and ⁴⁹C₇ = 63!/(9!(63-9)!)  = 23,667,689,815

so

P( keeping all friends ) = [ 9 × 9 × 9 × 9 × 9 × 9 × 9 × 9 × 9 ] / 23,667,689,815

P( keeping all friends ) = 387,420,489 / 23,667,689,815 = 0.016369

P( you lose one or more friend ) = 1 - P( keeping all friends )

P( you lose one or more friend ) = 1 - 0.016369

P( you lose one or more friend ) = 0.9836

Therefore, the probability you lose one or more friends is 0.9836

The inequality that represents p, the number of people the theater can seat is p ≤ 25

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

A movie theater can seat a maximum of 25 people

This means that

Maximum =  25 people

In other words, the movie theatre can allow 25 or less people to attend a movie

In inequality, 25 or less means less than or equal to 25

When represented as an inequality expression, we have

≤ 25

Using the variable p, we have

p ≤ 25

Hence, the inequality is p ≤ 25

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Points located at each ordered pairs are:

The ordered pair for each given point.

Points to plot on the coordinate grid

Single quadrant ordered pairs are coordinates that lie in only one quadrant of the coordinate plane. To find single quadrant ordered pairs, follow these steps:

Identify the quadrant you want the ordered pairs to be in. For example, if you want the ordered pairs to be in the first quadrant, then the x-coordinate and y-coordinate must both be positive.

Choose a value for the x-coordinate that satisfies the condition for the quadrant you want. For example, if you want the ordered pairs to be in the first quadrant, choose a positive number for the x-coordinate.

Choose a value for the y-coordinate that satisfies the condition for the quadrant you want. For example, if you want the ordered pairs to be in the first quadrant, choose a positive number for the y-coordinate.

Write the ordered pair in the form (x, y), where x is the value you chose for the x-coordinate and y is the value you chose for the y-coordinate.

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Image transcribed:

Single Quadrant Ordered Pairs

Tell what point is located at each ordered pair.

1) (7,1)_

2) (3,0)

3) (1,6)

4) (3,8)

5) (1,5)

6) (8,0)

7) (4,1)

8) (0,4).

9) (8,9)

10) (1,1)_

Write the ordered pair for each given point.

11) B

14) Q

17) F

12) E

15) Y

18) S

13) T

16) R

19) C

Plot the following points on the coordinate grid.

20) K (7,0)

22) D (8,5)

24) V (7,2)

21) Z (2,1)

23) P (2,2)

25) L (2,4)

Answer:

s = 13.6

m∠T = 35.7°

m∠U = 61.3°

Step-by-step explanation:

• Solving for side s:

To find the length of side s, we have to use the cosine rule:

\(\boxed{a^2 = b^2 + c^2 - 2bc \ cosA}\),

where:

In this case, the unknown side is s, and the sides adjacent to it have lengths of 8 and 2. The angle opposite to s is ∠S = 83°. Therefore,

\(s^2 = 8^2 + 12^2 -2(8)(12) \cdot cos(83^{\circ})\)

⇒ \(s = \sqrt{8^2 + 12^2 -2(8)(12)\cdot cos(83^{\circ})}\)

⇒ \(s = \bf 13.6\)

• Solving for m∠T:

In order to find m∠T, we can use the sine rule:

\(\boxed{\frac{sinA}{a}= \frac{sinB}{b} =\frac{sinC}{c}}\),

which means that the ratios of the sines of angles and their opposite sides are equal for a triangle.

The side opposite to ∠T is US = 8. Therefore:

\({\frac{sinT}{8} = \frac{sin(83^{\circ})}{13.6}}\)

⇒ \(sinT= \frac{sin(83^{\circ})}{13.6} \times 8\)

⇒ \(T = sin^{-1}( \frac{sin(83^{\circ})}{13.6} \times 8)\)

⇒ \(T = \bf 35.7^{\circ}\)

• Solving for m∠U:

Now that we know the values of two angles of the triangle, we can calculate the third angle using the fact that the angles in a triangle add up to 180°:

∠U + ∠S ∠T = 180°

⇒ ∠U + 83° + 35.7° = 180°

⇒ ∠U = 180° - 83° - 35.7°

⇒ ∠U = 61.3°

24/35.................

Answer:

A trapezoid prism from the looks of it.

Step-by-step explanation:

Hope this helps!

The resulting conditional mean squared error of the LMS estimator, given N=3 is 0.0383746

In general, the conditional distribution of X given Y does not equal the conditional distribution of Y given X, i.e., pX|Y(x|y)≠pY|X(y|x). If X and Y are independent, discrete random variables, then the following are true: pX|Y(x|y)=pX(x)pY|X(y|x)=pY(y)

The full conditional for a given node (parameter) is simply the product of the probability model (likelihood or prior) for that node and its parent node (at least up to a constant of proportionality).

1) fY|N(y∣N=3)=84 y^6 (1-y)^3

2)0.0636363

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 ( -4)¹⁹  =  -  274877906944 is standard form of 4 to power -19.

What are power and exponent?

a)  ( -8 )⁰   =   1               ( positive )

b)  ( -4 )⁶    = - 4× -4 × -4 × -4 × -4 × -4 = 4096  ( Positive )

c)  ( -5 )¹²  =  244,1406,25           ( positive )

d)  ( -4)¹⁹  =  -  274877906944   ( Negative)

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The constant of proportionality in the box to match the table will be 2/3. Then the last option is correct.

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

The table is given below.

x      y

0     0

3      2

6      4

9      6

The variable 'y' is directly proportional to the variable 'x'. Then we have

y ∝ x

y = k x

At (9, 6), the value of the constant 'k' is given as,

6 = 9k

k = 6 / 9

k = 2/3

The proportionality is given as,

y = (2/3) x

The constant of proportionality in the box to match the table will be 2/3. Then the last option is correct.

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Answer

2

Step-by-step explanation:

6+2=8     15/5*2=6       8-6=2

Answer:

y = - 5x - 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - 5 , then

y = - 5x + c ← is the partial equation

To find c substitute (- 2, 6 ) into the partial equation

6 = 10 + c ⇒ c = 6 - 10 = - 4

y = - 5x - 4 ← equation of line

Answer:

8400

Step-by-step explanation:

Round it 5 and above go up 4 and below go down

Answer:

8,400

Step-by-step explanation:

it says round to the nearest hundred to find the answer look at the number behind the place value you want to round.

5 and up you round the number higher

4 and down you round it lower.

example:

35 rounded to the nearest ten is 40

34 rounded to the nearest ten is 30

Answer:

Step-by-step explanation:

a) To prove that PQ || AB, we can use the fact that in any parallelogram, the opposite sides are parallel and equal. Therefore, since AD is parallel to AB, the line PQ which connects the midpoint of AD to the opposite corner A will also be parallel to AB.

b) To prove that PO = 1/2 CD, we can use the fact that in any parallelogram, the diagonals bisect each other. Therefore, since AC and BD intersect at O, PO must be equal to 1/2 of its length. Since the length of CD is twice that of PO, it follows that PO = 1/2 CD.

Answer:

9 bags

Step-by-step explanation:

2 1/4 ÷ 1/4

9/4 ÷ 1/4

9/4 x 4/1 = 9

Answer: 4

Step-by-step explanation: because he needs to divided by 2

The equation of the line of best fit is y = x + 16 and the money spent on entertainment for a student who works 8 hours is $24

Drawing the line of best fit, we have the following points

(0, 6) and (16, 22)

The equation is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx + 6

Using the points, we have

16m + 6 = 22

So, we have

m =1

So, the equation is

y = x + 6

This means that

x = 8

So, we have

y = 8 + 16

y = 24

Hence, the amount is $24

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