3-(+4) as an a addition

Based on the size of the pool that Mr. DelGrande wants to build, the ratio of the Olympic pool to the smaller pool is 2.5:1 and the area of an Olympic pool is 1,250 m².

The ratio of the pools is:

Olympic pool length : Mr. DelGrande pool

             50                 :              20

Simplest terms give:

50 / 20 : 20 / 20

2.5 : 1

Given the area of Mr. DelGrande's pool, the area of an Olympic pool is:

= Ratio ² x Area of Mr. DelGrande pool

= 2.5² x 200

= 1,250 m²

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The objects that have not been found in the Galactic halo is emission nebulae. The correct option is E. emission nebulae.

Objects such as globular clusters (A), RR Lyrae variables (B), planetary nebulae (C), and Population II stars (D) have been observed and found in the Galactic halo.

Globular clusters are dense, spherical clusters of stars that are commonly found in the halo of galaxies, including the Milky Way.

RR Lyrae variables are pulsating stars used as standard candles to measure distances. They are commonly found in globular clusters and the halo of galaxies.

Planetary nebulae are glowing shells of gas and dust ejected by certain types of stars during their late stages of evolution. They are found in various regions of the galaxy, including the halo.

Population II stars are generally older, metal-poor stars that belong to the older stellar population. They are commonly found in the halo and globular clusters.

On the other hand, emission nebulae (E) are regions of interstellar gas that emit light due to the excitation of hydrogen gas by nearby hot stars. They are primarily found in the disk of the galaxy and are associated with star formation regions, such as H II regions. They are not typically observed in the Galactic halo.

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Answer:

21x - 18y = 30

Step-by-step explanation:

7x - 6y = 10

multiple both sides by 3

3(7x - 6y) = 3(10)

21x - 18y = 30

The area of the rectangle whose length is twice its width, having a perimeter of 24√3 - 6√2 is 100 - 16√6.

The perimeter and area of a rectangle are expressed as;

Perimeter = 2( length + Width )

Area = Length × Width

Let the width be represented by 'x'.

Plug the given values in the formula above and solve for x.

Perimeter = 2( length + Width )

24√3 - 6√2 = 2( 2x + x)

24√3 - 6√2 = 2( 3x )

24√3 - 6√2 = 6x

6x = 24√3 - 6√2

x = ( 24√3 - 6√2 ) / 6

x = 4√3 - √2

Hence;

Width = x = 4√3 - √2

Length = 2x = 2(4√3 - √2) = 8√3 - 2√2

Now, we determine the area;

Area = Length × Width

Area = (8√3 - 2√2) × (4√3 - √2)

Expand using FOIL Method

Area = 8√3(4√3) + 8√3(-√2) - 2√2(4√3) - 2√2(-√2)

Area = 100 - 16√6

Therefore, the area is 100 - 16√6.

Option A) 100 - 16√6 is the correct answer.

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Answer:

63^3

Step-by-step explanation:

Index is an element's numeric position within an array. The correct answer is B.

When an array is created, each element is assigned an index or position, starting from zero for the first element and incrementing by one for each subsequent element.

The index allows for easy access to specific elements within the array, by specifying the index value as an argument when referencing or manipulating elements. The index of an element is an important concept in computer programming and is used extensively in array-based data structures and algorithms.

Therefore the correct option is b

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Wronskian of y1 = e^{5x} and y2 = e^{−2x} is -7e^{3x}. General solution to differential equation (d²y/dx²) -10(dy/dx) + 25y = 0 is y(x) = c1e^{5x} + c2e^{-2x} on interval of (-∞, ∞).

To compute the Wronskian of the functions y1 = e^{5x} and y2 = e^{−2x}, we use the formula:

W(y1,y2) = y1*y2' - y1'*y2

where y1' and y2' denote the derivatives of y1 and y2 with respect to x, respectively.

Taking the derivatives, we have:

y1' = 5e^{5x}

y2' = -2e^{-2x}

Substituting these values into the formula, we get:

W(y1,y2) = e^{5x}*(-2e^{-2x}) - (5e^{5x})*e^{-2x}

W(y1,y2) = -2e^{3x}- 5e^{3x}

W(y1,y2) = -7e^{3x}

Therefore, the Wronskian of y1 = e^{5x }and y2 = e^{−2x} is -7e^{3x}.

To find the general solution to the differential equation (d² y)/(dx²) - 10(dy/dx) + 25y = 0, we use the fact that y1 and y2 are linearly independent solutions, and thus the general solution has the form:

y(x) = c1y1(x) + c2y2(x)

Substituting y1 and y2, we get:

y(x) = c1e^{5x} + c2e^{-2x}

This is the general solution on the entire real line (-∞, ∞).

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Answer:

A

Step-by-step explanation:

Simply guess and check, meaning the boys category must be divisible by 2 and the girls category must be divisible by 3

A: 24 boys ÷ 2 = 12 (equals a whole number so it is divisible; not a decimal)

36 girls ÷ 3 = 12 (both of the boys and girls are divisible by their corresponding numbers)

Yes

Now make sure the boys are a lower count than the girls as the ratio says it should be 2 to 3, meaning there are more girls than boys

B: 20 ÷ 2 = 10 (divisible)

35 ÷ 3 = 11.666 (this is a decimal answer so it is not divisible)

No

C: 36 ÷ 2 = 18

24 ÷ 3 = 8

Yes, they are divisible

Now lets check if boys have a lower count than girls

36 boys > 24 girls

This is not the solution as it doesn't reflect the correct ratio of less boys than girls

D: 35 ÷ 2 = 17.5 (not divisible)

20 ÷ 3 = 6.66 (not divisible)

Answer:

B) This student performed better than 78% of the other test-takers in the verbal part and better than 34% in the quantitative part.

Step-by-step explanation:

In Statistics, Percentile refers to how specific variables can be divided according to the distribution of values in a population of 100 equal groups.

The data value of a given percentile can be determined  as 100 times the cumulative relative frequency of that value.

From the given question.

Suppose a test-taker scored at the 78th percentile for their verbal sent to test-takers, the percentiles associated grade and at the 34th percentile for their quantitative grade.  

This implies that ;

The student score shows the relation between a particular score of :

78% and the scores of the rest of a group for the verbal test takers   &

34% and the scores of the rest of a group for the quantitative test takers.

Therefore; we can conclude that ;

This student performed better than 78% of the other test-takers in the verbal part and better than 34% in the quantitative part.

From options a) and e) are uncountable, b) and c) are countable, and d) is countable.

a) The set of all real numbers in the interval (0,1) is uncountable. This can be proved using the Cantor Diagonal Argument. Assume that the set is countable, and list the numbers in the set as a sequence. Now, construct a new number by taking the first digit after the decimal point of the first number, the second digit after the decimal point of the second number, and so on. This new number will be different from every number in the original list, showing that the set is uncountable.

b) The set of all rational numbers in the interval (0,1) is countable. This can be proved by establishing a bijection with the set of all positive integers (N). We can list the rational numbers in the interval (0,1) as a sequence, and assign each rational number a unique positive integer. This shows that the set is countable.

c) The set of all points in the plane with rational coordinates is countable. We can establish a bijection between this set and the set of all ordered pairs of positive integers (N x N). We can list the rational points in the plane as a sequence and assign each point an ordered pair of positive integers. This shows that the set is countable.

d) The set of all functions f:{0,1}→N is countable. We can establish a bijection between this set and the set of all binary sequences. Each function can be represented by a binary sequence, where each digit represents the value of the function for a given input. Since the set of all binary sequences is countable, the set of all functions is countable as well.

e) The set of all functions f:N→{0,1} is uncountable. This can be proved using the Cantor Diagonal Argument. Assume that the set is countable, and list the functions in the set as a sequence. Now, construct a new function by taking the opposite value of the diagonal element for each function in the original list. This new function will be different from every function in the original list, showing that the set is uncountable.

In conclusion, a) and e) are uncountable, b) and c) are countable, and d) is countable.

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The number of pieces per stack after 3 cuts represented by a power expression can be written as \( 3^{3} \)

Using a power expression :

Therefore, the Number of pieces present in stack after 3 cuts is \( 3^{3} \)

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1110.5 is the answer and your welcome

The origin in rectangular coordinates coincides with the pole (or origin) in polar coordinates.The positive x-axis in rectangular coordinates coincides with the polar axis (also known as the polar ray or polar axis of rotation) in polar coordinates.

In polar coordinates, a point is defined by its distance from the pole (called the radius or r) and its angle from the positive x-axis (called the azimuthal angle or theta).

The polar axis is a reference line in polar coordinates that extends from the pole in the direction of the positive x-axis in rectangular coordinates.

The relationship between rectangular and polar coordinates allows for the conversion of points between these two systems. To convert a point from rectangular to polar coordinates, the distance from the origin (r) can be calculated using the Pythagorean theorem, where r = sqrt(x^2 + y^2), and the angle (theta) can be found using trigonometric functions such as atan2(y, x).

Conversely, to convert a point from polar to rectangular coordinates, the x-coordinate can be obtained by multiplying the radius (r) by the cosine of the angle (theta), and the y-coordinate can be found by multiplying the radius (r) by the sine of the angle (theta).

It is important to understand the relationship between rectangular and polar coordinates as they provide alternative ways of representing points in a two-dimensional space, each with its own advantages and applications.

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Answer:

D

Step-by-step explanation:

The relative rate of population change after seven years from now is a) 1.7 % (rounded off to 1 decimal place) b) Yes, the relative rate of population change will reach 2.3% in 19.21 years

The function for population t years from now is P(t)= 2+ 1.2e^(0.04t)

a) relative rate of change of population

= P'(t) / P(t)

= (0+1.2e^(0.04t) * 0.04 )/ ( 2+ 1.2e^(.04t) )

= 0.048 e ^(0.04t) / (2 + 1.2e^(0.04t) )

Relative rate of change of population 7 years from now

= 0.048 e ^(0.04 * 7) / (2+ 1.2e^(0.04*7))

=0.0177 = 0.177 * 100 = 1.7 % per year (rounded off to one decimal place

b) For the relative rate of change to reach 2.3 %

P'(t) / P(t) = 2.3 % = 0.023

⇒(0+1.2e^(0.04t) * 0.04 )/ ( 2+ 1.2e^(0.04t) ) = 0.023

⇒0.048e ^(0.04t) = 0.046 + 0.0267e^(0.04t)

⇒e ^(0.04t) = 0.958 + 0.556e ^(0.04t)

⇒e ^(0.04t) ( 1 - 0.556) = 0.958

⇒e ^(0.04t) ( 0.444) = 0.958

⇒e ^(0.04t) = 2.157

⇒0.04t = ln(2.157)           (applying ln on both sides)

⇒t = 19.21 years

The relative rate of population change is 2.3% in 19.21 years

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Answer:

Domain of the given function is all real numbers i.e. R.

Step-by-step explanation:

It is given that the given graph is a V shaped graph.

It is crossing x - axis at \((-2,0)\)

then y-axis at \((0,-2)\) and

then again x - axis at \((2,0)\).

If we try to plot the graph, the graph will be like it comes down from the negative x axis side and then intersect x axis at \((-2,0)\), then intersects y axis at \((0,-2)\)  and then rises towards the right side (i.e. positive x axis) intersecting the positive x axis at \((2,0)\).

Please find attached graph for the same.

This graph denotes the following function:

\(y=f(x)=|x|-2\)

Domain of a function \(y =f(x)\) is the values of \(x\) that can be provided to the function.

Here function is a modulus function and from graph we can easily infer that it can have any Real Number, R as its input.

Modulus function has R as its domain.

So, the answer is:

Domain of given function is all Real Numbers, R

Answer:

A on edg. all real numbers

Step-by-step explanation:

The order in which the numbers are drawn is not important will be 1287.

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter. In combinations, you can select the items in any order.

When order of selecting things does not matter, then the combination odd n things taking r at a time is given by :-

\(nC_r=\dfrac{n!}{r!(n-r)!}\)

Given : The total numbers in lottery = 13

The total numbers to choose to win the lottery =- 5

Then the combination of 13 numbers taken 5 at a time is given by

\(13C_r=\dfrac{13!}{5!(13-5)!}=1287\)

Hence the order in which the numbers are drawn is not important will be 1287.

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I'll help.

A student needs 15 minutes to solve an algebra problem. How many minutes does the student need to solve 5 problems?

it's easy, you only need to divide 15 by 5.

Like this :

15÷5= 3

• because 5×3 = 15 , so you just need to flip it over

so, the student need 3 minutes to solve 5 problems

Answer: k = √27-i

Step-by-step explanation:

Given:

The function is:

\(y=2x^2+3x\)

Domain is the set {-2, -1, 0).

To find:

The range of the given relation.

Solution:

We have,

\(y=2x^2+3x\)

Substituting \(x=-2\), we get

\(y=2(-2)^2+3(-2)\)

\(y=2(4)+(-6)\)

\(y=8-6\)

\(y=2\)

Substituting \(x=-1\), we get

\(y=2(-1)^2+3(-1)\)

\(y=2(1)+(-3)\)

\(y=2-3\)

\(y=-1\)

Substituting \(x=0\), we get

\(y=2(0)^2+3(0)\)

\(y=0+0\)

\(y=0\)

The range for the given relation is {2, -1,0}. Therefore, the correct option is (c).

Answer:

GCF = 5x^3

Step-by-step explanation:

25x^3/5x^3 = 5

10x^4/5x^3 = 2x

Answer:

push the x on the top left corner of the tab

Step-by-step explanation:

Results would you expected to see at testing is one group of participants who is told to try to understand the structure of the geometry problem to solve it will be able to get good marks in the test.

One group of participants is who told to try to understand the structure of the problem will be able solve the problem by analyzing and geometry problem.

The other group who is asked to try to memorize the problem may not be able to solve the test because they will not be able to understand the  problem as the question will be different and will not get good marks in the test.

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Answer:

ftyjbnkdxfcgvhbjn

Step-by-step explanation:

Answer:

896

Step-by-step explanation:

HEY SISTERS!!!

Using the law of cosines, it is found that the length of side AB is of AB = 13.

The law of cosines states that we can find the angle C of a triangle as follows:

\(c^2 = a^2 + b^2 - 2ab\cos{C}\)

in which:

For this problem, the parameters are:

C = 120, a = 8, b = 7.

Hence:

\(c^2 = a^2 + b^2 - 2ab\cos{C}\)

\(c^2 = 8^2 + 7^2 - 2(8)(7)\cos{120^\circ}\)

\(c^2 = 169\)

\(c = \sqrt{169}\)

c = 13.

Hence AB = 13.

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Answer:

Ok, so. You can think of the mean being acually mean because you have to do more work. When solving for the mean you add all the answers together then divide by the amount of numbers you have. For example,  you have the numers (1, 2, 3) add them together (1+2+3) to get 6 then divide by 3 (6/3) to get a mean of two. The median is also fairly easy to remember. You line your numbers up least to greatest, left to right. and mark one off of each side at a time. If you have a even amount of numbers and reach the center, you add the two centers together then divide by to to get the median. If you have an odd amount of numbers, there should be one in the exact center left over.

Step-by-step explanation:

Mean) 3+8+10+15=36, 36/4=9 ANSWER=9

Median) 8+10=18, 18/2=9 ANSWER=9

In the case, the mean and median are the same and depending on context you could choose either method. It also helps that there is no outlyer. If there were on I would recomend finding the median.

Answer:

i think the answer is 110

The ratio shows how many times one value is contained in another value.

The fraction of the bracelets from the total items is 6/13.

The ratio shows how many times one value is contained in another value.

Example:

There are 3 apples and 2 oranges in a basket.

The ratio of apples to oranges is 3:2 or 3/2.

We have,

The ratio of earrings, bracelets, and necklace is 13:24:15.

This means,

Earrings = 13x

Bracelets = 24x

Necklace = 15x

The fraction of the bracelets from the total items.

= 24x / (13x + 24x + 15x)

= 24x / 52x

= 24/52

= 12/26

= 6/13

Thus,

The fraction of the bracelets from the total items is 6/13.

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Answer:popular sovereignty

Step-by-step explanation: this is because when the bill is passed sovereignty is within

Answer: This will be A .

Step-by-step explanation: