(Q3) Apply the 30º-60º-90º Triangle Theorem to find the length of the longer leg of a triangle if the length of the hypotenuse is 20 cm. Round to the nearest centimeter.

The sequence whose nth term is (2n+1)/(3n-1) converges to the number 2/3.

To use L'Hopital's rule, we need to take the limit of the ratio of the nth term and (n-1)th term as n approaches infinity.

Let a_n be the nth term of the sequence. lim (n->∞) a_n / a_(n-1) = lim (n->∞) (2n+1)/(3n-1) / (2n-1)/(3n-4) = lim (n->∞) [(2n+1)/(3n-1)] * [(3n-4)/(2n-1)] = lim (n->∞) [6n^2 - 5n - 4]/[6n^2 - 7n + 4]

By applying L'Hopital's rule, we can find that the limit of this ratio as n approaches infinity is 1. Thus, the sequence converges to the same limit as the ratio of consecutive terms, which is 2/3.

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Answer: the markup percentage on each shirt is 150%

Step-by-step explanation:

We can start by finding the total revenue generated by selling 200 shirts at $50 each:

Total revenue = 200 * $50 = $10,000

To find the markup percentage, we need to know the cost of producing the shirts. Let's assume the wholesale cost of each shirt is $20 (as given in the previous question).

The total cost of the 200 shirts is:

Total cost = 200 * $20 = $4,000

The profit earned from selling the 200 shirts is:

Profit = Total revenue - Total cost = $10,000 - $4,000 = $6,000

The markup amount per shirt is:

Markup = Selling price - Cost price = $50 - $20 = $30

The markup percentage can be calculated as:

Markup percentage = (Markup / Cost price) x 100%

Markup percentage = ($30 / $20) x 100% = 150%

Therefore, the markup percentage on each shirt is 150%.

Answer: The approximate number of particles of skin a human can shed in five hours can be written in the form a times 10^b, where a is 3 and b is 6 .

Step-by-step explanation:

Given: Humans shed about 3million particles of skin every 5 hours.

Since, 1 million = 1,000,000

Then 3 million = 3 x 1 million

\(= 3 \times1,000,000\)

\(= 3,000,000\)

\(=3\times10^6\)

On comparing to \(a\times 10^{b}\) , we get a = 3 and b=6

So, the approximate number of particles of skin a human can shed in five hours can be written in the form a times 10^b, where a is 3 and b is 6 .

Answer:

6

Step-by-step explanation:

First, write the approximate number of particles of skin a human can shed in five hours in scientific notation. This number is three million which can be written in the form a × 10b, where a is 3 and b is 6.

For triangle DEF,

m∠D = 21°

m∠E = 87°

DF = 16

For triangle RST,

m∠S = 68°

m∠T = 57°

Simple polygons with three sides and three internal angles make up triangles. It is one of the fundamental geometric shapes in which the three vertices are connected to one another.

For ΔDEF, it is given that, m∠F = 72°, DE=15,EF=17.

By the law of cosines,

side DF=(a2+b2﹣2abcosγ)1/2

DF=16

Similarly,

m∠D = 21°

As the sum of angles of triangle is 180,

m∠E = 87°

For ΔRST, it is given that, m∠R = 55°, RS=17,RT=9.

By the law of cosines,

side ST=(a2+b2﹣2abcosγ)1/2

ST=16

Similarly,

m∠S = 68°

As the sum of angles of triangle is 180,

m∠T = 57°

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it A

Step-by-step explanation:

The volume of the solid generated when the region R, bounded by the graph of y = 6sin(x) and the x-axis on the interval [0, π], is revolved about the line y = -6 is _______ cubic units (exact answer in terms of π).

To find the volume of the solid generated by revolving the region R about the line y = -6, we can use the method of cylindrical shells. The volume of each cylindrical shell is given by the formula:

V = 2π * integral[R] (radius * height) dx

In this case, the radius of each cylindrical shell is the distance from the line y = -6 to the curve y = 6sin(x), which is 12 units. The height of each shell is the infinitesimal change in x, dx. We integrate this expression over the interval [0, π] to cover the entire region R.

Therefore, the volume of the solid is given by:

V = 2π * integral[0 to π] (12 * dx)

Integrating this expression will give us the volume of the solid in terms of π. Evaluating the integral will provide the exact volume of the solid generated by revolving the region R.

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From the figures and the properties of the parallelogram was possible to find that: UT=27, ST=18, RV=7 and US=14.

There are different quadrilaterals, for example: square, rectangle, rhombus, trapezoid and parallelogram.  Each type is defined accordingly to its length of sides and angles. For example,  the opposite sides are equal and parallel, for a parallelogram. In a parallelogram is noted too that the opposite angles and the diagonals are equal.

From the properties: the opposite sides are equal and parallel for a parallelogram. It is possible to find:

UT=RS=27

ST=RU=18

Considering that UV=7, then VS= 7 since V is the midpoint of the diagonal US. Therefore, US=14.

From the property: the diagonals are equal for a parallelogram. It is possible to find:

US=RT=14

RV=RT/2=14/2=7

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Answer:

A paralellogram goes in the first one i know

Step-by-step explanation:

Answer:

alternative interior angles

To find the linearization at a certain point, we need to use the formula: \(L(x) = f(a) + f'(a)(x-a)\). We are given that a=1 and f(x)=89. Therefore, f(a)=f(1)=89. Linearization is at point x=1 on the graph of f(x), it will look almost exactly like a horizontal line at y=89, which is  L(x) = 89 + 0(x-1)

To find f'(a), we need to take the derivative of f(x) with respect to x. However, since f(x) is a constant function, its derivative is 0. Thus, f'(a)=0. Plugging these values into the formula, we get: L(x) = 89 + 0(x-1), Simplifying, we get: L(x) = 89, So the linearization of f(x) at a=1 is simply the constant value 89.

In other words, if we zoom in close enough to the point x=1 on the graph of f(x), it will look almost exactly like a horizontal line at y=89.

This linearization can be useful for approximating the value of f(x) near x=1, since it provides a simple, easy-to-use formula that is very close to the true function. However, it is important to keep in mind that this approximation will only be accurate for values of x very close to 1 - as we move further away from x=1, the linearization will become less and less accurate.

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Answer:

Yes

Step-by-step explanation:

To answer this question, all we need to do is find the volume of the full ball, and the volume of the original ball after pumping for 1 minute.

The volume of the full ball is 4/3πr³=4/3π15³=14136.16cm³

The volume of the original ball after 1 minute is

5000cm³+(160×60)=14600cm³.

Since 14600>14136.16, it will take less than a minute to pump the ball full.

Hope this helps!

Answer:

The probability of rolling an odd number or a two on a six-sided die is 1/2 + 1/6 = 2/3. This means that if you roll a six-sided die 300 times, you can expect to roll an odd number or a two approximately 200 times

Step-by-step explanation:

Answer: 400 TIMES

Step-by-step explanation:

1/6 +1/2

4/6

2/3

As range doesn't reveal anything about the distributive property of the data, it is the least helpful measure of variability because it is the most generic.

1. Sort the data either ascendingly or descendingly.

2. Determine how many items are in the data set.

3. The median is the number in the middle of the list if the number of items is odd.

4. The median is the average of the two middle numbers in the list if the number of items is even.

To figure out the range:

1. Sort the data either ascendingly or descendingly.

2. To determine the range, deduct the smallest number from the largest.

As range does not reveal anything about the distribution of the data, it is the least useful measure of variability because it is the most generic. Range does not indicate where the values fall within the range; rather, it measures the difference between the highest and lowest values in a data collection.

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We can conclude that the system experienced an exothermic change

Based on the given information, we know that the system initially had a higher temperature of 97 degrees Celsius, and then it experienced a change to a lower temperature of 86 degrees Celsius.

A decrease in temperature usually indicates that energy is lost from the system to the surroundings, either by heat transfer or some other form of energy transfer. Since the system has lost energy, this implies that the change was exothermic, meaning that heat was released from the system to the surroundings.

Therefore, based on the information given, we can conclude that the system experienced an exothermic change

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Answer:

B

Step-by-step explanation:

Because i took the test

Answer:

B edge2021

Step-by-step explanation:

Answer:

16.8 cm

Step-by-step explanation:

Volume = length x width x height

V = 4 x 3 x 1.4

V = 16.8

Answer:

x will be located in the middle of t&p but in the middle

Step-by-step explanation:

Answer:

x = 12

Step-by-step explanation:

what you do is use 42 plus 90 which you infer fron the intersection add those together which is 48. the you put 11x + 48 = 180 so then you subtract 48 from 180 which equals 132 and then divide by 11x so x = 12

The capacitance of the other cylinders are 2174. 94cm³ and 1208. 30cm³.

Capacity of a cylinder is seen as its volume

Volume of a cylinder = πr²h

The heights of the cylinders are

a. 3cm

b. 9cm

c. 5cm

Let's find the radius

Capacity = 3. 142 × r² × 3

725 = 3. 142 × r² × 3

r² = \(\frac{725}{3. 142 * 3}\)

r² = \(\frac{725}{9. 426}\)

r² = 76. 91

r = √76. 91

r = 8. 77cm

Radius of the cylinders = 8. 77cm

For cylinder with height of 9cm

Capacitance = πr²h

Capacitance = 3. 142 × 8. 77 × 8. 77 × 9

Capacitance = 2174. 94 cm³

For cylinder with height of 5cm

Capacitance = 3. 142 × 8. 77 × 8. 77 × 5

Capacitance = 1208. 30 cm³

Thus, the capacitance of the other cylinders are 2174. 94cm³ and 1208. 30cm³.

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Answer:

Yes thank you

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

It is a 67% percent chance.

Step-by-step explanation:

Please refer to photo for drawing

the solution to the system of equations is x = 2 and y = 1.

To solve the system of equations by substitution, we will solve one equation for one variable and substitute it into the other equation.

Given the system of equations:

1) y = 6x - 11

2) -2x - 3y = -7

Step 1: Solve equation (1) for y.

  y = 6x - 11

Step 2: Substitute the value of y from equation (1) into equation (2).

  -2x - 3(6x - 11) = -7

Step 3: Simplify and solve for x.

  -2x - 18x + 33 = -7

  -20x + 33 = -7

  -20x = -7 - 33

  -20x = -40

  x = (-40)/(-20)

  x = 2

Step 4: Substitute the value of x into equation (1) to find y.

  y = 6(2) - 11

  y = 12 - 11

  y = 1

Therefore, the solution to the system of equations is x = 2 and y = 1.

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The solution to the system of equations y = 6x - 11 and -2x - 3y = -7 is x = 2 and y = 1. This is achieved by substituting y into the second equation, simplifying, and solving for x, then substituting x back into the first equation to solve for y.

To solve the system of equations y = 6x - 11 and -2x - 3y = -7 by substitution, we start by substituting the equation y = 6x - 11 into the second equation in place of y, giving us -2x - 3(6x - 11) = -7. Next, simplify the equation by distributing the -3 inside the parentheses to get -2x - 18x + 33 = -7. Combine like terms to get -20x + 33 = -7. Subtract 33 from both sides to obtain -20x = -40, and finally, divide by -20 to find x = 2.

Once we find the solution for x, we substitute it back into the first equation y = 6x - 11. Substituting 2 in place of x gives y = 6*2 - 11, which simplifies to y = 1.

Therefore, the solution to the system of equations is x = 2 and y = 1.

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Answer:

Step-by-step explanation:

Step one:

we are told that the base salary is $24000

and also earns 8% of the total sale

let the total sales be x

additional earnings= 0.8x

the linear function for this situation is  given as

y=0.8x+c

where y= the expected earning

           x= sales

            c= is the base salary

40000=0.8x+24000

solve for x

40000-24000=0.8x

16000=0.8x

divide both sides by 0.8

x=16000/0.8

x=20000

He needs to make sales of at least $20,000

Answer:

x = -12

Step-by-step explanation:

1. Distribute : 45 - 5x = 105

2. Subtract : -5x = 60

3. Divide : x = -12

Answer:

\(x = - 12\)

Step-by-step explanation:

\( - 5( - 9 + x) = 105 \\ 45 - 5x = 105 \\ - 5x = 105 - 45 \\ - 5x = 60 \\ \frac{ - 5x}{ - 5} = \frac{60}{ - 5} \\ x = -12\)

Answer:  \(2xy^3\\\\\)

===============================================

Work Shown:

\(z = \sqrt[4]{16x^4y^{12}}\\\\z = \sqrt[4]{2^4*x^4*(y^3)^4}\\\\z = \sqrt[4]{(2xy^3)^4}\\\\z = 2xy^3\\\\\)

An alternative method is this

\(z = \sqrt[4]{16x^4y^{12}}\\\\z = \sqrt[4]{16}\sqrt[4]{x^4}\sqrt[4]{y^{12}}\\\\z = \sqrt[4]{2^4}\sqrt[4]{x^4}\sqrt[4]{y^{12}}\\\\z = 2^{4/4}x^{4/4}y^{12/4}\\\\z = 2^{1}x^{1}y^{3}\\\\z = 2xy^{3}\\\\\)

Answer:

-513

Step-by-step explanation:

use gemdas (order of operations) to find your answer!

g- groupings

e- exponents

m- multiplication

d- division

a- addition

s- subraction

3 x 3 = 9

6 x 87 = 522

9 - 522 = -513!

Answer:

261

Step-by-step explanation:

First you have to multiply

\(3 \times 3 = 9\)

Second you you have to multiply again

\(6 \times 87 = 522\)

Finally you have to subtract

\(9 - 522 = - 513\)

Answer: 3/7

Step-by-step explanation:

1. We know that 2/4 + 2/4 is 1.
2. 1 can also be expressed as 7/7, because its easier to subtract 7/7 and 4/7 because they have the same denominator

3. 7/7-4/7=3/7

Answer:

3/7

Step-by-step explanation:

Answer:

i love math 21

Step-by-step explanation:

hehe

A statement that best compares the average values of the number of fish caught at both lakes daily:

There is a significant difference between the sample means.

The average is calculated as the product of all values divided by all possible values. It can also be described as mean. The mean in statistics is the average value for the particular sample or collection of data. It is determined by dividing the sum of the total number of observations by the total number of observations.

The mean number of catfish caught daily at Lake Martin is 85,

with the number of catfish ranging from 75 to 140.

The mean number of catfish caught daily at Smith Lake is 104,

with the number of catfish ranging from 96 to 183.

The difference in all the sample means,

104 - 85 = 19.

Therefore, the difference is 19.

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The length AC of the triangle is 4.47 units.

The diagram on the graph is a triangle. The question wants us to find the length AC of the triangle.

To find the length AC in the triangle, we have to use distance formula as follows:

Therefore,

A = (1, 1)

C = (3, 5)

AC = √(y₂ - y₁)² + (x₂ - x₁)²

AC = √(5 - 1)² + (3 - 1)²

AC = √4² + 2²

AC = √16 + 4

AC = √20

Hence,

AC = 4.472135955

AC = 4.47 units

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