1. The sum of two numbers is 2000. If 25% of the smaller number is one-sixth of the larger, find
the numbers.​

Answer:

i can only help for the second question

Sum of the sequence is -22407

An arithmetic sequence is a sequence where the common difference between two consecutive terms are always same.

If a be the first term and d be the common difference of a arithmetic sequence, then n th term of it = \(a_{n}\) = a+(n-1)d

Sum of n terms = \(S_{n}\) = \(\frac{n}{2}\)(2a+(n-1)d)

GIven sequence is 9+4+(-1)+.......+(-471)

First we arrange the sequence in right sequence.

(-471)+................(-1)+4+9

Now, we have to find the value n,

Here a = -471

So, nth term 9, common difference = 5

So,  \(a_{n}\) = \(a\\\)+(n-1)d

   ⇒  \(a_{n}\)-\(a\)=(n-1)5

   ⇒ 9+(-471)=5(n-1)

   ⇒ 480=5n-5

   ⇒  5n = 485

   ⇒  n = 97

So, sum of terms =  \(S_{n}\) = \(\frac{n}{2}\)(2a+(n-1)d)

                                     =  \(\frac{97}{2}\)(-942+(96×5))

                                     =  \(\frac{97}{2}\)(-942+480)

                                     =  \(\frac{97}{2}\)×(-462)

                                     = -22407

Hence, The sum is -22407.

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The error made in subtracting the two rational expressions 1/(x - 2) - 1/x is that the common denominator is not correctly identified and applied.

To subtract rational expressions, we need to find a common denominator and then subtract the numerators. In this case, the common denominator should be (x - 2) * x. However, the error lies in neglecting the parentheses in the first expression, leading to a miscalculation of the common denominator.

The correct subtraction of the given expressions should be: (x - 2)/(x - 2) - 1/(x * (x - 2)). Simplifying this expression further would result in (x - 2 - 1)/(x * (x - 2)), which can be simplified as (x - 3)/(x * (x - 2)).

Therefore, the error made in the subtraction lies in incorrectly identifying and applying the common denominator, which resulted in an inaccurate calculation of the expression.

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The inferential statistics would employ the probability to predict how many miles one should be able to drive a 2000 Toyota Celica during its lifetime.

The inferential statistics are calculated by using analytical tools such as test-statistic values, degree of freedom, sample size, and the rejection criteria(assumption or hypothesis).

Thus, the given information is about predicting the miles. So, according to the probability theory, it needs a sample of data about 2000 Toyota Celica.

Hence, it falls under the inferential branch of statistics. So, option C is correct.

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Disclaimer: The given question on the portal was incomplete. Here is the complete question.

Question: Which branch of statistics would employ probability to predict how many miles one should be able to drive a 2000 Toyota Celica during its lifetime?

A. Predictive statistics

B. Descriptive statistics

C. Inferential statistics

D. Differential statistics

Answer:

1)     ( \(-\frac{5}{2}\), \(\frac{5}{2}\))

2)    5

3)    ( 2, \(\frac{1}{2}\))

4)    (17, 2)

5)    (8, 7)

Step-by-step explanation:

No. 1

You can use the midpoint formula: \(\frac{ChangeInX}{2} ,\frac{ChangeInY}{2}\)

So, the Change In X is: -1 - 4 = -5

And the Change in Y is: 6 - 1 = 5

Once you divide both of the changes by 2, you get

X: \(-\frac{5}{2}\)

Y:  \(\frac{5}{2}\)

So the midpoint is: ( \(-\frac{5}{2}\), \(\frac{5}{2}\))

_________________________________________________________

No. 2

You can just find the middle of the two numbers. You could honestly just count it on your fingers if you wanted.

8 - 3 = 5

__________________________________________________________

No. 3

You can use the midpoint formula: \(\frac{ChangeInX}{2} ,\frac{ChangeInY}{2}\)

So, the Change In X is: -3 - (-9) = 6

And the Change in Y is: 4 - 3 = 1

Once you divide both of the changes by 2, you get

X: 2

Y:  \(\frac{1}{2}\)

 So the midpoint is: ( 2, \(\frac{1}{2}\))

__________________________________________________________

No. 4

You can use the midpoint formula: \(\frac{ChangeInX}{2} ,\frac{ChangeInY}{2}\)

So, the Change in X is: -1 - X

And the Change in Y is: -12 - Y

Once you divide both of the changes by 2, you get

X:  \(\frac{-1-X}{2} = -9\)

    -1 - X = -18

    -X = -17

     X = 17

Y:  \(\frac{-12-Y}{2} = -7\)

     -12 - Y = -14

     -Y = -2

      Y = 2

So the endpoint is: (17, 2)

__________________________________________________________

No. 5

You can use the midpoint formula: \(\frac{ChangeInX}{2} ,\frac{ChangeInY}{2}\)

So, the Change in X is: -14 - X

And the Change in Y is: -13 - Y

Once you divide both of the changes by 2, you get

X:  \(\frac{-14-X}{2}=-11\)

    -14 - X = -22

    -X = -8

     X = 8

Y:  \(\frac{-13-Y}{2} =-10\)

     -13 - Y = -20

     -Y = -7

      Y = 7

So the endpoint is: (8, 7)

To calculate the magnetic force pulling on the proton, we can use the formula for the magnetic force on a charged particle moving in a magnetic field:

F = q * v * B * sin(theta)

The magnetic force pulling on the proton is approximately 1.92 x 10^-12 N

F = q * v * B * sin(theta)

F is the magnetic force,

q is the charge of the particle,

v is the velocity of the particle,

B is the magnetic field strength, and

theta is the angle between the velocity vector and the magnetic field vector.

In this case, the proton has a positive charge (q = +e), a velocity of 3.0 x 10^7 m/s, and experiences a magnetic field of 4 T at a right angle to its motion (theta = 90 degrees).

Plugging in the values into the formula:

F = (+e) * (3.0 x 10^7 m/s) * (4 T) * sin(90 degrees)

The sin(90 degrees) is equal to 1, so we can simplify the equation to:

F = (+e) * (3.0 x 10^7 m/s) * (4 T) * 1

Now, we can substitute the charge of the proton (q = +1.6 x 10^-19 C) into the equation:

F = (+1.6 x 10^-19 C) * (3.0 x 10^7 m/s) * (4 T) * 1

Calculating the expression:

F = 1.92 x 10^-12 N

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The exact numbers listed in this problem are given by:

Exact numbers are numbers that are not rounded. Volumes and lengths, for example, are usually rounded, hence they cannot be called exact.

Thus, the exact numbers listed in this problem are given by:

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A relation R on Z is an equivalence relation if and only if it is reflexive, symmetric, and transitive. Specifically, in this case, xRy if and only if x^2+y^2 is even.

Reflexive: for any x in Z, x^2+x^2 is even, thus xRx. So, R is reflexive.

Symmetric: for any x,y in Z, if xRy, then x^2+y^2 is even, which implies y^2+x^2 is even, thus yRx. So, R is symmetric.

Transitive: for any x,y,z in Z, if xRy and yRz, then x^2+y^2 and y^2+z^2 are both even, thus x^2+z^2 is even, thus xRz. So, R is transitive.

Therefore, R is an equivalence relation.

To describe the equivalence classes, we need to find all the integers that are related to a given integer x under the relation R.

Let [x] denote the equivalence class of x.

For any integer x, we can observe that xR0 if and only if x^2 is even, which occurs when x is even.

Therefore, every even integer is related to 0 under R, and we have:[x] = {y in Z: xRy} = {x + 2k: k in Z}, for any even integer x.

Similarly, for any odd integer x, we can observe that xR1 if and only if x^2 is odd, which occurs when x is odd. Therefore, every odd integer is related to 1 under R, and we have:[x] = {y in Z: xRy} = {x + 2k: k in Z}, for any odd integer x.

In summary, the equivalence classes of R are of the form {x + 2k: k in Z}, where x is an integer and the parity of x determines whether the class contains all even or odd integers.

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Answer:

I'm not exactly sure, but I'm gonna say a reflection across line y = x because if you draw a diagonal line between the y and the x axis going through the top right and bottom left quadrants, it would be a reflection across that line.

pls vote brainliest

Answer:

it has one solution

Step-by-step explanation:

Answer:

$3

Step-by-step explanation:

19-4= 15

15 divided by 5= 3

The value of x is in the solution set of 4x - 12 ≤ 16+8x is x ≥ -7.

Given inequality:

⇒ 4x - 12 ≤ 16+8x

rearranging the like terms

4x - 8x - 12 ≤ 16

4x - 8x ≤ 16+12

-4x ≤ 16+12

-4x ≤ 28

divide by 4 on both sides

-4x/4 ≤ 28/4

-x ≤ 28/4

-x ≤ 7

x ≥ -7.

Therefore the value of x is in the solution set of 4x - 12 ≤ 16+8x is x ≥ -7.

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The time she will be done with her breakfast is by = 10:48 am

The time Megan started her breakfast = 9:54 AM.

In terms of hours = 9

In terms of minutes = 54

If she takes the given number of minutes to eat which is = 54 mins .

Therefore, the time she will be done with her breakfast is = 9:54 + 54

= 10: 48 am

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The statement that is most likely to be true is "The present value factor is always less than 1, given that r < 0."

The future value factor is a multiplier that represents the growth or accumulation of a present value to a future value based on an interest rate (r) and time period. However, the future value factor is not always greater than 1, given that r > 0. The future value factor can be greater than 1 or less than 1, depending on the combination of interest rate and time.

Similarly, the present value factor represents the discounting of future cash flows to their present value. When the interest rate (r) is negative (r < 0), the present value factor will be less than 1. This is because negative interest rates imply a discounting effect, reducing the value of future cash flows to a lower present value.

Therefore, the statement that the present value factor is always less than 1, given that r < 0, is the most likely to be true, as it aligns with the concept of present value and the discounting effect of negative interest rates.

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Events, of randomly drawing a King OR a card with an even number describe by a) Mutually Exclusive.

The events of randomly drawing a King and drawing a card with an even number are mutually exclusive. This means that the two events cannot occur at the same time.

In a standard deck of 52 playing cards, there are no Kings that have an even number.

Therefore, if you draw a King, you cannot draw a card with an even number, and vice versa.

The occurrence of one event excludes the possibility of the other event happening.

It is important to note that mutually exclusive events cannot be both independent and conditional. If two events are mutually exclusive, they cannot occur together, making them dependent on each other in terms of their outcomes.

The correct option is (a) Mutually Exclusive.

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It has 816 ways to 3-element subsets, such that no two consecutive integers are in the subset.

You need three digits from 1 to 20, but you don't want any consecutive ones. You should call them a, b, and c.

Without loss of generality, a < b < c.

We use combinations,

Remember that we can write a + 1 b if a b and they're not sequential. With the aid of this insight, we can see the number of desired the number of methods for choosing a, b, and c from among the integers so that,

(1 ≤ a) & (a + 1 < b) & (b + 1 < c) & (c ≤ 20)

In other words, you want to know how many possibilities there are to choose the three numbers a, b, and c so that;

1 ≤ a < b − 1 < c − 2 ≤ 18

As a result, the question is equal to asking how many ways there are to select three integers (a, b - 1, and c - 2) from a range of 1 to 18. In other words, we are interested in how many ways we can select three items from a total of 18 options.

So, the response is:

\((^1^8_3)\) = 816 ways

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Answer:

Per pretty much means 1. So for example if I say I'm going 12 miles PER hour it means 12 miles every 1 hour.

x=-4 if you are in a hurry

The solution of the equation are; x = -16 or x = -4. so option A is correct.

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

Given equation;

x²+ 20 x + 100 = 36.

x²+ 20 x + 100 - 36 = 0

x²+ 20 x + 64 = 0.

x²+ (16 + 4)x + 64 = 0.

x²+ 16x + 4x + 64 = 0.

x(x + 16) +4 (x + 16) = 0.

(x+ 4) (x + 16) = 0

Thus, the solution of the equation are; x = -16 or x = -4.

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The size of the crowd is 12,000

This is the portion covered by the shape.

Analysis:

Area of field = 100 x 300 = 30000 square feet

If 1 person covers 2.5 square feet of the file then 30000/2.5 = 12,000 persons will cover the whole field.

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The correct option is c) Easier interpretation. One of the main advantages of simple models is their ease of interpretation. Simple models tend to have fewer parameters and less complex mathematical equations, making it easier to understand and interpret how the model is making predictions.

This interpretability can be valuable in various domains, such as medicine, finance, or legal systems, where it is important to have transparent and understandable decision-making processes.

Complex models, on the other hand, often involve intricate relationships and numerous parameters, which can make it challenging to comprehend the underlying reasoning behind their predictions. While complex models can sometimes offer higher accuracy or make more detailed predictions, they often sacrifice interpretability in the process.

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Answer:

attachment?

Step-by-step explanation:

Answer:

x = 144°

Step-by-step explanation:

In the figure given , two regular polygons are given to us. Since the polygon has five sides , it is a regular Pentagon. We know that each angle of a regular Pentagon is 108° .

So , here as per figure two regular Pentagons are attached base to base . Now , we know that,

According to Question ,

⇒ 108° + 108° + x = 360°

⇒ 216° + x = 360°

⇒ x = 360° - 216°

⇒ x = 144°

Answer:

The answer is D

Step-by-step explanation:

To be a function, you cannot have the same x values.

Answer:

258cm

it is the vertex's hieght as well as the length of the sides to multiply together and also divide since there is 5 sides

Answer:

17.28

Explanation:

We know that the total cost is given by

If Lindy orders 4 drinks and a medium pizza with 3 toppings. then d = 4 and t = 3. Putting these values into the expression gives

which we evaluate to get

Hence, the total cost of 4 drinks and a medium pizza with 3 toppings is $17.28.

1. Minimize w = -2y₁ - 5y₂

2. Maximize w = 2y₁ + 5y₂

3. Minimize w = 5y₁

1. Dual of primal LP:
a) The primal LP is:
Maximize z = -5x₁ + 2x₂
Subject to:
-1x₁ + 1x₂ ≤ -2
2x₁ + 3x₂ ≤ 5
x₁, x₂ ≥ 0

To write the dual LP, we need to change the objective function and constraints. The objective function of the dual LP is to minimize the sum of the products of the dual variables and the primal constraint coefficients.

The constraints of the dual LP correspond to the primal LP's objective coefficients.

The dual LP for the given primal LP is:
Minimize w = -2y₁ - 5y₂
Subject to:
-y₁ + 2y₂ ≥ -5
y₁ + 3y₂ ≥ 2
y₁, y₂ ≥ 0

b) The primal LP is:
Minimize z = 6x₁ + 3x₂
Subject to:
6x₁ - 3x₂ + x₃ ≥ 2
3x₁ + 4x₂ + x₃ ≥ 5
x₁, x₂, x₃ ≥ 0

The dual LP for the given primal LP is:
Maximize w = 2y₁ + 5y₂
Subject to:
6y₁ + 3y₂ ≤ 6
-3y₁ + 4y₂ ≤ 3
y₁ + y₂ ≥ 1
y₁, y₂ ≥ 0

c) The primal LP is:
Maximize z = x₁ + x₂
Subject to:
2x₁ + x₂ = 5
3x₁ - x₂ unrestricted

The dual LP for the given primal LP is:
Minimize w = 5y₁
Subject to:
2y₁ + 3y₂ ≥ 1
y₁ - y₂ unrestricted
y₁, y₂ ≥ 0

These are the dual LPs for the given primal LPs.

The dual LPs are obtained by changing the objective function and constraints of the primal LPs.

The objective function of the dual LP is the opposite of the primal LP's objective function, and the constraints of the dual LP correspond to the primal LP's objective coefficients.

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Answer: 11!

Step-by-step explanation:

The base, lateral area and surface area is B = 96 cm², L = 499.2 cm²,S = 691.2 cm²

The lateral area for the triangular prism is the sum of all three areas. Thus, the formula for lateral area of triangular prism, Lateral surface area of triangular prism (LSA) = ah + bh + ch (or) (a + b + c) h.

To find the lateral area (L) of this solid, we need to calculate the area of the four rectangles that make up the sides of the solid. Since each rectangle has a height of 10.4 cm and a width of 12 cm, the area of one rectangle is:

A = 10.4 cm * 12 cm = 124.8 cm²

Since there are four rectangles, the total lateral area is:

L = 4 * A = 4 * 124.8 cm² = 499.2 cm²

To find the surface area (S) of the solid, we need to add the lateral area to the area of the two circular bases. The base area is given as 96 cm², so the area of both bases is:

A = 2 * 96 cm² = 192 cm²

Therefore, the total surface area is:

S = L + A = 499.2 cm² + 192 cm² = 691.2 cm²

Rounding to the nearest tenth, we have:

B = 96 cm²

L = 499.2 cm²

S = 691.2 cm²

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The given categories of variables that are mutually exclusive and exhaustive are weekdays and weekend and vowels and consonants.

Mutually exclusive and exhaustive variables: A variable is mutually exclusive and exhaustive if it includes all possible outcomes and each outcome can only be assigned to one variable category.a. Days: Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, and Sunday - Mutually exclusive and exhaustiveb. Days: Weekday and Weekend - Mutually exclusive and exhaustive c. Letters: Vowels and Consonants - Mutually exclusive and exhaustive. Letters: Alphabets and Consonants - Not mutually exclusive and exhaustiveThe given categories of variables that are mutually exclusive and exhaustive are weekdays and weekend and vowels and consonants. Hence, the options a and c are correct.

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