Give me a list of integers

Answer:

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Let the cost of a 1 kg of apples be x.

Then pear costs x - 1.12 and banana costs x + 2.35.

The total cost is 25.02:

The coordinate pair of the given solution of the system would be= (g, h) (1,-8).

Substitution equation is defined as the equation that can be solved when a value is being solved and substituted for the other missing value to be gotten.

4g + h = -4 ---->. eq 1

12g + 2h = -4 ----> eq 2

Make h the subject of formula;

h = -4 - 4g -----> eq 3

Substitute equation 3 into equation 2;

12g + 2( -4 - 4g) = -4

12g - 8 -8g = -4

4g -8 = -4

4g = -4 +8

4g = 4

g = 4/4= 1

Solve for g = 1 in equation 1;

4(1) + h = -4

4 + h = -4

h = -4-4

h = -8

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Answer:

To find out how much money is allotted for each of these items, we can multiply the percentage of the income allocated to each item by the total income.

Food: 20% of $25,000 = $25,000 x 0.20 = $5000

Shelter: 25% of $25,000 = $25,000 x 0.25 = $6250

Clothing: 15% of $25,000 = $25,000 x 0.15 = $3750

So the family has $5000 for food, $6250 for shelter and $3750 for clothing.

(a) Mean of given sample = 75

(b) Mean (60, 80) = 70

(c) All possible samples of size two are 6 (60,70), (60,80), (60,90), (70, 80), (70,90), (80,90) and means are 65, 70, 75, 75, 80, and 85 respectively.

The given sample is (60, 70, 80, 90)

(a) Mean of sample = (60+70+80+90)/4 = 300/4 = 75

(b) Mean of any 2 of scores

let's take (60,80)

mean(60,80) = (60+80)/2 = 70

(c) All possible samples of size 2 are

(60,70), mean(60,70) = 65

(60,80), mean(60,80) = 70

(60,90), mean(60,90) = 75

(70,80), mean(70,80) = 75

(70,90), mean(70,90) = 80

(80,90), mean(80,90) = 85

Therefore, for the given sample (a) Mean of the sample = 75, (b) Mean (60, 80) = 70, (c) All possible samples of size two are 6 (60,70), (60,80), (60,90), (70, 80), (70,90), (80,90) and means are 65, 70, 75, 75, 80, and 85 respectively.

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The complete question is:

How did the Chapter 6 test go? Today, we will be taking a sample from a population. We will use the average from the sample to estimate the average for the population. Let's start with a very simple example. My 5th period is very small. There were only 4 students who took the chapter 6 test. Their scores were: 60, 70, 80, and 90. Answer the following questions:

(a) Find the mean of the sample

(b) Take a sample of any 2 of the scores. Find the mean of your sample.

(c) Figure out all of the possible samples of size two. Calculate a sample mean for each sample of 2.

Allocating the congressional seats among the states in a fair manner would mean that the seats per state would be:

The fairest way to allocate the seats in a fair manner would be by proportional representation where the population of a state determines the seats it gets in Congress.

State A seats :

= Population / Total population x Number of seats available

= 258 / 1, 858 x 90

= 13 seats

State B seats :

= 377 / 1, 858 x 90

= 18 seats

State C seats :

= 456 / 1, 858 x 90

= 22 seats

State D seats :

= 767 / 1, 858 x 90

= 37 seats

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The coordinates of the points C and D are:

C = (1, -2), D = (-1, -2).

What is cartesian coordinate system?

A Cartesian coordinate system in a plane is a system of coordinates that uniquely identifies each point by a pair of numerical coordinates. These numerical coordinates are the signed distances from two fixed perpendicular oriented lines to the point, measured in the same unit of length.

Given:

The coordinates of A and B are A(1, 3) and b(-1, 3).

We have to find the coordinates of point C and D.

We know that C and D are directly below A and B respectively. So the x-values must coincide.

Then we can say that:

C = (1, y)

D = (-1, y)

Now, remember that for a rectangle of length L and width W the area is:

A = W*L

In this case, the length is AB, then:

L = 1 - (-1) = 2

And the area is 10 square units, so:

10 = W*2

10/2 = W = 5

This means that:

AC = BD = 5

So the difference between the y-component of A and the y-component of C is 5 units

3 - y = 5

3 - 5 = y = -2

Hence,  the coordinates of the points C and D are:

C = (1, -2), D = (-1, -2)

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Answer:

0.0021645

Step-by-step explanation:

The potential energy of a 50kg boulder at the ledge of a cliff 250m high is 122500 J.

Potential energy is the energy carried by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors.

The PE energy of a boulder 250 m from the ground is given by the formula

PE = h x m x g    where h is the height above the ground, m is the mass, and g is the acceleration of gravity.

Putting the given values in the equation

PE = 250m x 50 kg x 9.8 m/s²  =  122500 J

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Answer:

L^2 = area of square = As

As = 14 L H / 2      where L H /2 = area of triangle

L^2 = 14 L H / 2

H = L / 7    or L = 7 H

Let the length of one side of square = 7 in

As = 7^2 = 49 in^2        area of square

H = 7     height of one side of triangle (other side = 1)

Area of triangle = 7 * 1 / 2 = 7/2 in^2

14 * At = 49

Area of square 7 * 7 = 49 in^2      Seems to checkout

Answer:

The standard form of the equation of a line is:

y = mx + b

Where m is the slope of the line and (x,y) is a point on the line. We know that the line passes through the point (4, -11) and has a slope of 3/4.

We can use the point-slope form to find the equation of the line:

y - y1 = m(x - x1)

Where (x1, y1) is the point on the line and m is the slope.

Substituting in the given information we get:

y - (-11) = (3/4)(x - 4)

Simplifying the equation we get

y = (3/4)x + (33/4)

This is the equation of the line in standard form.

The length in order for the quadrilateral JKLM to be a parallelogram are:

i. JK = 10

ii. JL = 7

A quadrilateral is a family of shapes or figures which has four straight sides, and four measures of internal angles. Examples are: trapezium, rhombus, kite, square, parallelogram etc.

To determine the length of each sides, we have;

opposite sides of a parallelogram are equal, so that;

3x - 2 = x - 6

collect like terms

3x - x =  2 + 6

2x = 8

x = 4

Thus,

i. JK = 3x - 2

       = 3(4) - 2

       = 12 - 2

JK = 10

ii. JL = 2x - 1

         = 2(4) - 1

         = 8 - 1

JL = 7

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The value of x is equal to 0.660441.

In mathematics, the logarithmic function is an inverse function to exponentiation. The logarithmic function is defined as For x > 0, a > 0, and a ≠1, y= logₐ x if and only if x = a^y Then the function is given by f(x) = logₐ x The base of the logarithm is a. This can be read it as log base a of x.

Given here: The exponential function 2(3e)ˣ=8

Simplifying further we get, (3e)ˣ=4

Taking log both sides we get x (ln3+1)=ln4

                                              x×2.0986=1.386

                                                       x=0.660441

Hence, The value of x is equal to 0.660441.

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Answer:

The last option:

Minnesota, Pennsylvania, Michigan, Florida

Step-by-step explanation:

Coldest to warmest:

-20°C, -10°C, 0°C, 16°C

Then the order is:

Minnesota, Pennsylvania, Michigan; Florida

The sides of the triangle based on the information will be 5 unit, 5 units and 6 units.

From the information, we are given that the isosceles triangle and a square have the same perimeter and we want to find the side lengths of the triangle.

It should be noted that a isosceles triangle has two sides that are equal. In this case, the perimeter of the square and Triangle is the same. The perimeter will be:

= 4 + 4 + 4 + 4

= 16 units.

Therefore, the sides of the triangle will be calculated thus:

3x + 2x + 1 + 2x + 1 = 16

7x + 2 = 16

7x = 16 - 2

7x = 14

Divide

x = 14 / 7

x = 2

The sides will be:

3x = 3 × 2 = 6

2x + 1 = 2(2) + 1 = 5

2x + 1 = 2(2) + 1 = 5

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Answer:

84

Step-by-step explanation:

this is an isosceles triangle so the base angles are equal meaning <BAC= <BCA =48°

48° +48° =96°

180°- 96° = 84°

<ABC = 84°

The percent error of Alex's measurement is 5.714%.

Percent error is a measure of how accurate a measurement is compared to the true value. It is calculated by taking the absolute value of the difference between the measured value and the true value, divided by the true value, and then multiplying by 100%.

In this case, the measured value is 3.7 cm and the true value is 3.5 cm.

To calculate the percent error, we can use the following formula:

Percent error = |(measured value - true value) / true value| x 100%

Plugging in the given values, we get:

Percent error = |(3.7 - 3.5) / 3.5| x 100%

= |0.2 / 3.5| x 100%

= 0.05714 x 100%

= 5.714%

This means that Alex's measurement is off by 5.714% from the true value, indicating that the measurement has a low accuracy.

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Answer: x=5

Step-by-step explanation:

[tex]\displaystyle(\frac{125}{27} )*(\frac{125}{27} )^x=(\frac{5}{3})^{18} \\\\(\frac{5^3}{3^3})*(\frac{5^3}{3^3})^x=(\frac{5}{3})^{18}\\\\(\frac{5}{3} )^3*((\frac{5}{3})^3)^x =(\frac{5}{3})^{18}\\\\(\frac{5}{3} )^3*(\frac{5}{3})^{3*x}= (\frac{5}{3} )^{18}\\\\(\frac{5}{3} )^3*(\frac{5}{3})^{3x}= (\frac{5}{3} )^{18}\\\\(\frac{5}{3})^{3x+3}= (\frac{5}{3} )^{18}\\\\Hence,\ \\\\3x+3=18\\\\3x+3-3=18-3\\\\3x=15\\\\[/tex]

Divide both parts of the equation by 3:

[tex]x=5[/tex]

There are 37,837,800 ways to distribute 15 distinguishable objects into five distinguishable boxes so that the boxes have one, two, three, four, and five objects in them, respectively.

We are trying to find the number of ways to distribute 15 distinguishable objects into five distinguishable boxes so that each box has 1, 2, 3, 4, and 5 objects in them, respectively.

We can use the formula for combination to solve this problem. The number of ways to distribute n distinct objects into r distinct boxes where the first box has k1 objects, the second box has k2 objects, ..., and the last box has kr objects is:

n! / (k1! * k2! * ... * kr!)

Where n! is the factorial of n, k1! is the factorial of k1 and so on.

In this case, we have 15 distinct objects and 5 distinct boxes where the first box has 1 object, the second box has 2 objects, the third box has 3 objects, the fourth box has 4 objects, and the fifth box has 5 objects.

So, the number of ways to distribute 15 distinguishable objects into five distinguishable boxes so that the boxes have one, two, three, four, and five objects in them, respectively is:

15! / (1! * 2! * 3! * 4! * 5!) = 15! / (1×2×6×24×120)

= 37,837,800

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Yes, it makes sense that the number of cats falling from 5th floor would be greater since the terminal velocity of the cat would be greater at higher altitudes.

The pace at which an object's location changes in relation to a frame of reference and time is what is meant by velocity. Although it may appear sophisticated, velocity is just the act of moving quickly in one direction. Since it is a vector quantity, the definition of velocity requires both magnitude (speed) and direction.

A distance measurement between a reference datum and a point or object, typically in the vertical or "up" direction, is known as altitude, height, or depth.

The terminal velocity of the cat would be greater at higher altitudes; hence cats have higher risk of falling from heights.

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A good sampling method for this scenario would be a probability-based method called Simple Random Sampling.

In Simple Random Sampling, each individual from the population of individuals who have high cholesterol has an equal chance of being selected for the sample. This ensures that the sample is representative of the population and that each individual in the population has a known non-zero probability of being selected.

This method can be supported by the fact that it is easy to implement, and it does not require any prior knowledge of the population characteristics. It also ensures that the sample is unbiased and has a good chance of being representative of the population.

Additionally, Simple Random Sampling is also a cost-effective sampling method as it is less expensive and time-consuming than other sampling methods such as stratified random sampling or cluster sampling.

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Answer:

  CD = 3/√2 in

Step-by-step explanation:

You want the measure of altitude CD in isosceles right triangle ACB with the right angle at C.

All of the isosceles right triangles in this figure are similar, and all have sides in the ratio 1 : 1 : √2.

In ∆BCD, side BC is the longest, given as 3 in. That means the other two sides of that triangle are ...

  CD = BD = CB/√2

  CD = 3/√2 in

__

Additional comment

Often, we like to rationalize the denominator of expressions involving roots. That would make the expression for CD be ...

  CD = 3/√2 = (3/2)√2 = 1.5√2

<95141404393>

1 is a factor of every whole number. Every whole number can be evenly divided by 1, so 1 is a factor of every whole number.

1 is the factor of every number as one divides every number exactly, without leaving any remainder behind, and gives the quotient as the number itself.

1 is the greatest factor of itself and the smallest factor of any other number.

There are some properties of factors one:

Every whole number is the product of 1 and itself so, each number is a factor of itself.

Every number is a factor of zero and 1 is the smallest factor of every number, and multiple and the greatest factor of a multiple is the multiple itself.

Every number other than 1 has at least two factors, namely the number itself and 1.

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The general solution of the given higher-order differential equation is y(x) = e2x + x2 + c4e3x + c5e-3x.

A general solution is an answer that can be applied to a wide range of problems. It is a broad-based approach that can be used to solve any problem, regardless of its complexity or specific details. General solutions take into account the overall goal of a problem, rather than its individual elements, and look for a way to achieve the desired result. Additionally, they are often easy to implement and can be applied to a variety of scenarios.

The general solution of the given higher-order differential equation, y(4) + y''' + y'' = 0, is given by

y(x) = c1e2x + c2e-2x + c3x2 + c4e3x + c5e-3x + c6x3.

Here, c1, c2, c3, c4, c5 and c6 are constants of integration.

To determine the values of these constants, we must use initial conditions. Suppose we are given y(0)=1 and y'(0)=2, then we can solve for the constants using this information.

Substituting y(0)=1 and y'(0)=2 into the equation, we get

1 = c1 + c2 + c3(0)2 + c4 + c5 + c6(0)3
2 = 2c3 + 3c6(0)2

Solving these equations, we get c1 = 1, c2 = 0, c3 = 1 and c6 = 0.

Therefore, the general solution of the given higher-order differential equation is

y(x) = e2x + x2 + c4e3x + c5e-3x.

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The expression that represents the statements are

1. R = 114+P

2. M = 10+2B

3. H = 1/2M -29

Linear expressions are those statements that each term is either a constant or a variable raised to the first power.

In linear expressions, the highest power of the variable is 1.

In the first statement 'Rhona got 114 more votes Tham Petro'. Let's represent the votes for Rhona by R and for Pedro by P

therefore R = 114+ P

In the second statement 'Matt took 10 minutes longer than twice as long as Bryce took to do his assignment'

Let's represent the time it took Matt to do his assignment' by M and time it took Bryce by B.

then,

M = 10+2B

In the third statement 'A hamburger costs 29 cents less than half as much as a full meal'.

Let's represent the cost of hamburger by H and the cost of full meal' by M, then,

H = 1/2M -29

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The 2x2x2 cube has 6 fully white faces.

A cube is a solid shape with six square faces. Each square face has the same side length and thus all the faces have the same size. A cube has 12 edges and 8 vertices. Each vertex refers to a corner where three edges of a cube meet.

from given conditions, a 2x2x2 cube is made of 8 small cubes of which 4 are blue and 4 are white. the surface of the cube is formed from 6 2x2 squares.

and have to arranged in such a a way that the surface has as many fully white faces (faces white no black color anywhere) as possible.

So, A 2x2x2 cube has a total of 6 faces, and since the goal is to have as many fully white faces as possible, there must be at least 1 fully white face on each of the 6 sides. hence, the 2x2x2 cube has 6 fully white faces.

Therefore, the 2x2x2 cube has 6 fully white faces.

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The greatest number of police officers needed is 28.

In a scenario where there are n straight lines in a city, and none of the lines are parallel to each other, the maximum number of police officers needed at the intersections can be determined by using the summation formula. The summation formula for the series of numbers from 1 to n-1 is (n-1) * n / 2.

Thus, if there are 8 straight lines in a city, the maximum number of police officers needed at the intersections is (8-1) * 8 / 2 = 28. This is because there will be 8-1 = 7 intersection points in total, and at each intersection point, one police officer is needed.

It's important to note that this is the maximum number of officers needed and it assumes that all lines are intersecting at different points. In case of any parallel lines this number would be less.

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The probability that a randomly selected family owns a dog or a cat is 0.61 and family owns a dog or doesn't own a cat is 0.39

AS we all know the rule of the probability is defined as the amalgamation of set theory and the probability theory yields some rules which form a part of the basic probability theory

Here we have listed down the rules as Multiplication Rule, Addition Rule and Complement Rule

Here we have given Information the following that is written as

=> Probability that a family can own a dog = 0.38.

=> Probability that a family can own a cat = 0.23.

Then the probability that a randomly selected family owns a dog or a cat is calculated as follows,

=> (0.38 + 0.23)

=> 0.61

And the the probability that a randomly selected family owns a dog or doesn't own a cat.

=> 1 - (0.38 + 0.23)

=> 1 - 0.61

=> 0.39

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You can get a number between two numbers by adding the two numbers together and then dividing by two.

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The price of an adult ticket is $20

The price of a child's ticket is $19

Let x represent the price of a child ticket

Let y represent the price of an adult ticket

Three adults and four children must pay 136

3y + 4x= 136.........equation 1

Two adults and three children must pay $97

2y + 3x= 97.........equation 2

From equation13 1

3y+4x= 136

3y= 136-4x

y= 136-4x/3

Substitute 136-4x/3 for y in equation 2

2(136-4x) + 3x= 97

272-8x/3 + 3x/1= 97

272-8x+9x/3= 97

cross multiply

272-8x+9x=291

collect the like terms

-8x+9x= 291-272

x= 19

Substitute 19 for x in equation 1

3y+4x= 136

3y + 4(19)= 136

3y+ 76= 136

3y= 136-76

3y=60

y= 60/3

y= 20

Hence children tickets cost $19 and adult tickets cost $20

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