prove that every bounded sequence contain a convergent subsequence

Answer:

216.49

Step-by-step explanation:

you have two right triangles, for the left one

[tex]tan(64)=\frac{113}{a}[/tex]

[tex]a=\frac{113}{tan(64)}[/tex]
for the one on the right

[tex]tan(35)=\frac{113}{b}[/tex]

[tex]b=\frac{113}{tan(35)}[/tex]

The total value of X is the sum

[tex]\frac{113}{tan(35)} +\frac{113}{tan(64)}=216.4945073[/tex]

so 216.4945073

Answer:

Please mark as brainliest

Answer:

95,367,431,640,625 (or approximately 9.5 x 10^13)

Step-by-step explanation:

If there are 5 choices for each question in a 20-question multiple-choice test, then there are 5 possible answers for each question. To find the total number of ways to answer the test, we need to multiply the number of choices for each question together.

Therefore, the total number of ways to answer the 20-question multiple-choice test is:

5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5

which is equal to 95,367,431,640,625 (or approximately 9.5 x 10^13) ways to answer the test.

Answer: there you go :)

Step-by-step explanation:

Its D, 90-20=70 ft traveled downwards

The maximum weight occurs when x = 0 and y = 0, and the maximum weight is W = 0.

In calculus, the derivative is a fundamental concept that measures the rate of change of a function with respect to its input variable. The derivative of a function at a particular point gives the instantaneous rate of change of the function at that point.

The derivative of a function f(x) with respect to its input variable x is denoted by f'(x) or df/dx. It is defined as the limit of the difference quotient as the change in x approaches zero:

f'(x) = lim (h → 0) [(f(x+h) - f(x)) / h]

Intuitively, the derivative of a function at a particular point gives the slope of the tangent line to the graph of the function at that point. This slope can be positive, negative, or zero, depending on whether the function is increasing, decreasing, or constant at that point.

To find the maximum weight, we need to find the critical points of the function.

First, we find the partial derivatives of the weight function with respect to x and y:

∂W/∂x = 8y(20 - 2x - 2y)

∂W/∂y = 8x(20 - x - 4y)

Setting these partial derivatives equal to zero, we get:

8y(20 - 2x - 2y) = 0

8x(20 - x - 4y) = 0

Solving for x and y, we get two critical points:

x = 0, y = 0

x = 10, y = 5

To determine which of these critical points correspond to a maximum, we use the second partial derivative test.

The second partial derivatives of W with respect to x and y are:

∂²W/∂x² = -32y

∂²W/∂y² = -32x

At the critical point (0,0), both second partial derivatives are negative, which means that it is a maximum.

At the critical point (10,5), both second partial derivatives are positive, which means that it is a minimum.

Therefore, the maximum weight occurs when x = 0 and y = 0, and the maximum weight is W = 0.

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A) Cube

the two squares will form the top and one side.

Each square right, top and bottom of the square will form the sides

Answer:

Ricky is taller by 11 inches ( a)

Step-by-step explanation:

1 foot = 12 inches

5 feet= 60 inches

Ticky is 68 inches

Ricky is 79 inches

ricky-Ticky=  79- 68= 11 inchesss!

Answer:

83

Step-by-step explanation:

The expression follows the order of operations (PEMDAS): Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction, in that order.

First, simplify what is inside the parentheses: 3 x 9 = 27

Next, multiply 3 by 27: 3 x 27 = 81

Finally, add 2 to 81: 2 + 81 = 83

Therefore, the expression 2+3(3x9) equals 83.

The result of this expression is 83

To solve them we have to start from the inside to out, that is, parentheses, brackets...
And proceed to signal resolution:

[tex]\begin{array}{l}\sf 2+3\tiny\text{$\times$}(3\times9)\\\sf 2+3\tiny\text{$\times$}(27)\\\sf 2+81\\\bf 83\end{array}[/tex]

We get the result 83

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If you have any question about this solution, you can ask me in the comments :)

If ABCD is a rectangle, AD=9, AC=22, and <BCA = 66°, the missing measures are m<ADC = 90°, m<BAC = 24°, m<CDB = 240°, and m<AEB = 132°.

The Pythagorean theorem is a fundamental theorem in geometry that says that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

That is to say mathematically,

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

where a and b are the lengths of the two sides of the triangle (the sides adjacent to the right angle), and c is the length of the hypotenuse.

Thus, substituting our values for this formula,

[tex]x^{2} +9^{2} =22[/tex]

[tex]x^{2} +81= 484[/tex]

[tex]x^{2} = 484-81[/tex]

[tex]x^{2} =403[/tex]

[tex]x=20.1[/tex] = AB

Thus,

BC = 9

AB = 20.1

BD= 22

EC = 11

m<ADC = 90°

m<BAC = 24° (90-66)

m<CDB = 240°

m<AEB = 132° (180-24-24)

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You asked an incomplete question. The complete question reads;

If ABCD is a rectangle, AD=9, AC=22, and <BCA = 66°, find each missing measure. I also attached an image of the question.

The relationship between the diameter of a circle and it's circumference is presented in this problem.

The circumference of a circle of radius r is given by the equation presented as follows:

[tex]C = 2\pi r[/tex]

The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle, while the diameter of the circle is the distance between two points on the circumference of the circle that pass through the center. Hence, the diameter’s length is twice the radius length.

The diameter is twice the radius, hence, for a circle with diameter 35 in, the radius is given as follows:

r = 0.5 x 35

r = 17.5 in.

Then the circumference of the circle is given as follows:

C = 2 x pi x 17.5

C = 109.9 in.

The problem is incomplete, hence the relation between the diameter of a circle and it's circumference is presented.

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Answer:

Therefore, 3 bakers can make 30 loaves of bread in 2 hours.

Therefore, 5 bakers can make 30 loaves of bread in 2 hours.

Therefore, 6 bakers can make 30 loaves of bread in 1.25 hours.

Therefore, 15 bakers can make 30 loaves of bread in 2 hours.

Step-by-step explanation:

In the number of bakers, it would take 2 hours to make 30 loaves of bread.

A proportion is an equation in which two ratios are set equal to each other.

Let h be the number of hours needed for a given number of bakers to make 30 loaves. Then we have:

2 bakers can make 30 loaves in 1 hour, so 1 baker can make 15 loaves in 1 hour.

Therefore:

3 bakers can make 45 loaves in h hours, so 45/3 = 15 loaves can be made in 1 hour. Thus, 3 bakers can make 30 loaves in 2 hours.

5 bakers can make 75 loaves in h hours, so 75/5 = 15 loaves can be made in 1 hour. Thus, 5 bakers can make 30 loaves in 2 hours.

6 bakers can make 90 loaves in h hours, so 90/6 = 15 loaves can be made in 1 hour. Thus, 6 bakers can make 30 loaves in 2 hours.

15 bakers can make 225 loaves in h hours, so 225/15 = 15 loaves can be made in 1 hour. Thus, 15 bakers can make 30 loaves in 2 hours.

Therefore, regardless of the number of bakers, it would take 2 hours to make 30 loaves of bread.

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The surface area of the following solids is:

a.54cm².

b. 43.32cm².

c. 21.2cm².

d. The figures b and c are smaller than a.

In contrast to the lateral surface area, which is used to determine the area occupied by the shape's curved surface, the total surface area takes into account all faces of the 3D shape, including both flat and curved surfaces.

The area around the bases is not included. One 3D shape called a sphere has just one round surface and no flat base.

In the given question,

In the 1st figure,

Total surface area = Total surface area of 6 squares.

= 6 × 3²

= 54cm².

In the 2nd figure,

Total surface area = Total surface area of 2 triangles + Total surface area of 3 squares + Total surface area of larger triangle.

= 2 × 1/2 × 3 × 3 + 3 × 3² + 1/2 × 3.96 × 3.7

= 9 + 27 + 7.32

= 43.32cm².

In the 3rd figure,

Total surface area = Total surface area of 4 triangles

= 1/2 × 3 × 3 + 1/2 × 3 × 3 + 1/2 × 4.2 × 3.7 + 1/2 × 3 × 3

= 9 + 7.77 + 4.5

= 21.2cm².

Hence, the figures b and c are smaller than the figure a.

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The side lengths of given triangle is;

a=5 units

b=18.72 units

c=18.99 units

A triangle is a closed, two-dimensional figure with three straight sides and three angles. It is one of the basic shapes in geometry and is formed when three non-collinear points are connected by straight lines. The sum of the interior angles of a triangle is always 180 degrees, and there are various types of triangles, including equilateral triangles (where all three sides are of equal length and all three angles are 60 degrees), isosceles triangles (where two sides are of equal length), and scalene triangles (where all three sides and angles are different). Triangles are used in many different areas of mathematics and science, including trigonometry, geometry, and physics.

Here,

We can use the trigonometric ratios of sine, cosine, and tangent to find the values of b and c. First, we can use the fact that the sum of the angles in a triangle is 180 degrees to find angle C:

C = 180 - A - B = 180 - 75 - 90 = 15 degrees

Next, we can use the definition of the sine ratio:

sin(A) = opposite/hypotenuse

to find c:

sin(75) = 5/c

c = 5/sin(75) ≈ 18.99

Finally, we can use the Pythagorean theorem:

a² + b² = c²

to find b:

b² = c² - a²

= (18.99)² - 5²

≈ 350.66

b ≈ √350.66 ≈ 18.72

Therefore, a ≈ 5, b ≈ 18.72, and c ≈ 18.99.

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Part A: distance travelled by athlete when she reaches her maximum is 1.3 m.

Part B: her maximum height: 5 m.

Th equation is-

y = -1.2x² + 3.12x +3.

horizontal distance - x

Part A: distance travelled by athlete when she reaches her maximum:

Comparing given equation with standard form of quadratic equation:

x = -b/a

x = -3.12/2(-1.2) = 1.3

Thus, distance travelled by athlete when she traveled horizontally and reaches her maximum of 1.3 m.

Part B: her maximum height:

y = -1.2x² + 3.12x +3.

Put x = 1.3

y = -1.2(1.3)² + 3.12(1.3) +3.

On solving:

y = 5.028

y = 5 m

Thus, her maximum height, round to the nearest tenth of a meter is 5 m.

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Below are some general reasons why a questionnaire might not be suitable:

Poorly constructed questions: If the questions in the questionnaire are not clear, ambiguous, leading, or biased, then the responses obtained may not be accurate or reliable. Poorly constructed questions may also lead to confusion, misunderstandings, and errors.

Lastly Inadequate sampling: If the sampling technique used to select respondents is not representative of the target population, then the results obtained may not be generalizable or applicable to the larger population. The sample size and composition may also affect the validity and reliability of the results.

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The  inferences from the results of the random sample  that are reasonable is: C. The percentage of all bags produced that contain less than 11 ounces is likely to fall between 15% and 25%.

From the sample of 250 bags, we know that 50 of them contain only 10.9 ounces of coffee. Let's calculate the percentage of bags in the sample that contain less than 11 ounces:

50/250 = 0.2 = 20%

Now let's consider each inference:

A. It cannot be inferred that 5% of the bags from a second random sample will contain more than 11 ounces. The sample only provides information about the bags in the sample, not the entire population.

B. It is possible that a second random sample of bags will show a lower percentage of bags with only 10.9 ounces, but it cannot be concluded with certainty based on the given information.

C. It is reasonable to estimate that the percentage of all bags produced that contain less than 11 ounces is likely to fall between 15% and 25%. This is because out of a sample of 250 bags, 50 bags contained 10.9 ounces, which is 20% of the sample.

D. It is not necessarily likely that the company's claim is true because 20% of the bags in the sample contain 10.9 ounces. The sample provides information about the bags in the sample, not the entire population.

E. It is not necessarily unlikely that the company's claim is true because 20% of the bags in the sample contain 10.9 ounces. The sample provides information about the bags in the sample, not the entire population.

Therefore, the correct inferences from the given information are C. The percentage of all bags produced that contain less than 11 ounces is likely to fall between 15% and 25%.

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Answer:

It depends on the equation in question. If Maggie is referring to an equation in the form of x = y, then adding 8 to both sides would still result in the same value of x and y being equal. For example, if the equation is 2x - 5 = 7, then adding 8 to both sides would result in 2x - 5 + 8 = 7 + 8, which simplifies to 2x + 3 = 15. In this case, adding 8 to both sides would not maintain equality.

However, if the equation is in the form of an inequality such as x < y or x > y, adding the same value to both sides may not maintain the inequality. For example, if the inequality is 2x - 5 < 7, then adding 8 to both sides would result in 2x - 5 + 8 < 7 + 8, which simplifies to 2x + 3 < 15. In this case, adding 8 to both sides would still maintain the inequality.

Therefore, whether or not adding 8 to both sides of an equation would still result in equality depends on the equation in question and the mathematical operation being performed.

Yes.  Yes I do.

If you think of an equation as a balance, where both sides have equal weight, then adding the same amount to both sides or taking away the same amount from both sides will still maintain that balanced weight.

We call this the addition property of equality:

    If a = b, then a+c = b+c for any expression c.

Answer:

y = (-1/3)x + 2/3

Step-by-step explanation:

We can use the slope-intercept form of a linear equation to find the equation of the line passing through the points (5, -1) and (2, 2). The slope of a line passing through two points (x1, y1) and (x2, y2) is given by:

slope = (y2 - y1) / (x2 - x1)

Substituting the coordinates of the given points, we have:

slope = (2 - (-1)) / (2 - 5) = -1/3

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. We can use the point-slope form of a linear equation to find the y-intercept.

Using the point (5, -1), we have:

-1 = (-1/3)(5) + b

Solving for b, we get:

b = -1 + 5/3 = 2/3

Therefore, the equation of the line passing through the points (5, -1) and (2, 2) is:

y = (-1/3)x + 2/3

y = $100.00 - $10.00x is the equation for the total amount of money in the savings account after x weeks.

The y-intercept represents the initial deposit of $100.00 and the slope is -10

a. Let's call the amount of money saved each week "s" and

let's call the total amount of money in the savings account after "x" weeks "y".

Since the amount saved each week is the same, we can express the total amount of money in the savings account as:

y = $100.00 + sx

We know that at the end of the 5th week, the total amount in the savings account is $50.00. So we can set up the following equation:

$50.00 = $100.00 + 5s

solving for s:

$50.00 - $100.00 = 5s

-$50.00 = 5s

-10 = s

So the equation for the total amount of money in the savings account after x weeks is:

y = $100.00 - $10.00x

b. In the context of this problem, the slope represents the amount of money that is saved each week.

In this case, the slope is -10, meaning that $10.00 is saved each week. The y-intercept represents the initial deposit of $100.00.

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The linear regression equation is defined as follows:

C. ŷ = 6.5x − 279.1

To find the regression equation, which is also called called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator.

The points for this problem are given on the table as follows:

(58.2, 112), (64.2, 135), (64.3, 138), (66.8, 146), (68.4, 166), (71.6, 180), (72.7, 188), (76.2, 199), (77.8, 220), (82.8, 280).

Inserting these points into a calculator, the line of best fit is given as follows:

ŷ = 6.5x − 279.1

Meaning that the correct statement is given by option C.

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Answer:

Down payment = $3,500 x 0.20 = $700.00So the amount of the loan is:Loan amount = $3,500.00 - $700.00 = $2,800.00Now we can use the formula for the present value of an annuity to find the APR:PV = PMT x [(1 - (1 + r)^-n) / r]where PV is the present value (in this case, $2,800.00), PMT is the monthly payment ($85.18), r is the monthly interest rate, and n is the number of months (36).Solving for r, we get:r = 0.01301 or 1.301%Since the monthly interest rate is 1.301%, the APR is:APR = 12 x 1.301% = 15.61%Therefore, the APR on Jorge Holland's loan is 15.61%.

Joel cannot buy 2 games and 6 puzzles and satisfy the constraints was solved by using inequality.

The total cost of x puzzles and y games must be less than or equal to $96, which gives us the first inequality: 8x + 12y ≤ 96

The second inequality: x + y ≥ 9.

An inequality is a mathematical statement that compares two quantities or expressions and shows the relationship between them using one of the following symbols: <, >, ≤, or ≥. For example, "x > 5" is an inequality that states that x is greater than 5.

In the given question,

Part A:

Let x be the number of puzzles Joel can buy and y be the number of games Joel can buy.

The total cost of x puzzles and y games must be less than or equal to $96, which gives us the first inequality: 8x + 12y ≤ 96

Joel needs to buy at least 9 gifts, which means that the total number of gifts must be greater than or equal to 9. Since x represents the number of puzzles and y represents the number of games, the total number of gifts is x + y. This gives us the second inequality: x + y ≥ 9

We also know that Joel can only buy puzzles or games, not both. Therefore, x and y must be either both integers or both half-integers (such as 1.5 or 2.5), but they cannot be mixed. This gives us the third inequality:

x, y are both integers or both half-integers

Part B:

To see if Joel can buy 2 games and 6 puzzles and satisfy the constraints, we can substitute x = 6 and y = 2 into the inequalities:

8x + 12y ≤ 96

8(6) + 12(2) ≤ 96

72 ≤ 96

This inequality is true, so the first constraint is satisfied.

x + y ≥ 9

6 + 2 ≥ 9

8 ≥ 9

This inequality is not true, so the second constraint is not satisfied. Therefore, Joel cannot buy 2 games and 6 puzzles and satisfy the constraints.

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Answer:

a = 4x with a small 3 at the top ( x with a small 4 at the top + 3x ) with a small 30 + 3

b = B = 6x with a small 17 at the top + 192x with a small 15 at the top + 2520x with a small 13 at the top + 17280x with a small 11 at the top + 64800x with a small 9 at the top + 124416x with a small 7 at the top + 93312 with a small 5 at the top

sorry but I don't know c

Step-by-step explanation:

Answer:

I think

Step-by-step explanation:

We estimate that Jordan will drive a distance of approximately 4668.3 miles during the entire 7-day road trip.

Distance and displacement are two key words in mechanics that, although having similar sounds, have distinct definitions and meanings. How much of an object's path is covered by a moving object is measured in terms of distance. Whereas "How much route is covered by the item in a specific direction" is measured by displacement, The main distinction between distance and displacement is therefore that the former is a scalar quantity while the latter is a vector quantity.

Given that, the distance travelled is  666.9 miles.

The same distance is travelled for 7 days thus,

distance = Distance per day x Number of days

distance = 666.9 miles/day x 7 days

distance = 4668.3 miles

Hence, we estimate that Jordan will drive approximately 4668.3 miles during the entire 7-day road trip.

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Answer:

Step-by-step explanation:

To determine if the job is complete, we need to add up the fractions of the decoration that each person put up:

Anna: 2/5

Manna: 1/4

Hanna: 3/10

Now we can find the total fraction of the decoration that they put up by adding these fractions:

2/5 + 1/4 + 3/10 = 16/40 + 10/40 + 12/40 = 38/40

So they have completed 38/40 of the decoration. To find the fraction of the job that is still left to do, we can subtract this from 1:

1 - 38/40 = 2/40

Therefore, there is still 2/40 of the decoration left to do, or 1/20 of the total job.

The difference between  the Statue of Liberty compared to other outdoor statues is that it is made of copper which is option C.

The Statue of Liberty is a colossal neoclassical sculpture located on Liberty Island in New York Harbor in the United States. It was a gift from the people of France to the people of the United States, dedicated on October 28, 1886, and has since become one of the most recognizable symbols of the United States and its ideals of freedom and democracy.

The statue was designed by French sculptor Frédéric-Auguste Bartholdi, with the help of engineer Gustave Eiffel. The statue depicts a female figure dressed in a flowing robe and holding a torch in one hand and a tablet in the other, upon which is inscribed the date of the American Declaration of Independence (July 4, 1776).

The Statue of Liberty is unique among outdoor statues in that it is made of copper sheets that have oxidized over time to form a green patina. This patina has become an iconic symbol of the statue and is a result of the natural process of copper corrosion. The statue was originally a shiny brown color, but the oxidation of the copper has gradually changed its appearance over time.

Therefore, while the Statue of Liberty is also located in a park and on a pedestal, and it is larger than many outdoor statues, these characteristics are not unique to the statue and can be found in other outdoor statues as well.

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