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A collection of paired data consists of the number of years that students have studied Spanish and their scores on a Spanish language proficiency test. A computer program was used to obtain the least squares linear regression line and the computer output is shown below. Along with the paired sample data, the program was also given an x value of 2 (years of study) to be used for predicting test score.

Equation: y = mx + b

Statistics:

r2 = 0.83
r = 0.91
Parameters:

m = 10.90
b = 31.55
Answer the following questions based on the information given above.

Use the information in the display to find the value of the linear correlation coefficient r. Determine whether there is significant linear correlation between years of study and test scores. Use a significance level of 0.05. There are 10 pairs of data.

A. r = 0.91; There is significant linear correlation.

B. r = 0.83; There is significant linear correlation.

C. r = 0.91; There is no significant linear correlation

D. r = 0.83; There is no significant linear correlation.

The percentage of money Indrani receives is 43.75%.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given,  Indrani and Jagad share some money in the ratio,

Indrani : Jagad = 7 : 9.

We know the percentage of money for both a and b in the form of a : b can be obtained as, [a/(a + b)]×100.

Therefore, the percentage of money Indrani gets is,

= [7/(7 + 9)]×100.

= (7/16)×100.

= 43.75%.

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Answer:

43.75%

Step-by-step explanation:

The mean deviation of the data 8,9,12,15,16,20,24,30,32,34​ is 8

Given data: 8,9,12,15,16,20,24,30,32,34

The formula for the mean (x bar) =  sum of observations /no. of observations

Mean (x bar) = 8+9+12+15+16+20+24+30+32+34/ 10

Mean = 200/10

∴ Mean = 20

Now, we find the mean deviation using mean

Mean deviation using mean = 1/n Σ|x- x bar|

where n= number of observations = 10

x= each observation in the data

x bar= mean of the data= 20

Mean deviation using mean

= 1/10 x [(20-8)+(20-9)+(20-12)+(20-15)+(20-16)+(20-20)+(24-20)+(30-20)+           (32-20)+(34-20)]

= 1/10 x [12+11+8+5+4+0+4+10+12+14]

= 1/10 x (80)

= 80/10

Mean deviation = 8

Thus the mean deviation is 8.

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Answer:

A. M1+ M2 + M3

Step-by-step explanation:

M1 is the money supply that makes it easy to convert assets/items into currency.

M2 is the deposits and money market funds.

Add M1, M2, and M3 to calculate the entire money supply of all the money in the economy.

Answer:

A. M1+ M2 + M3

M3 consists of all currency notes held by the public, all demand deposits with the bank, deposits of all the banks with the RBI and the net Time Deposits of all the banks in the country. So M3 = M1 + time deposits of banks.

Step-by-step explanation:

The price of the two pencils is Rs.100 (expensive) and Rs.60 (cheaper).

Let the price of the expensive pencil be = x

And the price of the cheaper one be = y.

According to the question:

The difference between the price of 2 = 40

Therefore,

x- y =40

Total amount = 1800.

The number of Expensive pencils that can be bought = 1800/x.

The number of Expensive pencils that can be bought = 1800/y.

According to the question,

1800/y -1800/x = 15 (the number of extra pencils)

= (1800x -1800y)/xy = 15

= 1800x -1800y =15xy

= 1800 (x-y) =15xy

Substituting x-y as 40

1800 x 40 =15xy

xy = 4800.

We know that x-y =40

Therefore, x = y+ 40

xy = 4800

(y+40) y = 4800

[tex]y^{2}[/tex] + 40 y = 4800

Using the quadratic equation formula,

y = 52.111 or y = -92.111

Thus, the cost of the cheaper pencil (y)= Rs. 52.111

The cost of the expensive pencil (x) = 52.111 + 40 = Rs 92.111

Therefore the cost of two pencils is =   Rs. 52.111 and Rs 92.111.

Therefore , the 4 year old children can able to count to 1 to 100 counting by making them learn.

Mathematicians can add numbers using the counting-on technique. When using this method, a learner begins by adding the larger number, then "counts on" with the other addends to get the sum. The student will recognize 4 as the higher number and add three more numbers, such as integers "4... 5, 6, 7," if the number sentence is 4 + 3.

Here,

Children develop and learn on an individual basis, however many

4 year old are able to learn their numbers between 1 and 100 and can count over 10.

They could be prepared to practice counting by fives or other skip counting techniques (5, 10, 15, 20, and so on).

Start working on number recognition with your kid as soon as you can.

Therefore , the 4 year old children can able to count to 1 to 100 counting by making them learn.

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The equations of the asymptotes are y = 2 and x = -1, respectively

The equation of the function is given as

f(x) = 2x² + 7x - 4/x² + 5x + 4

Introduce bracket, to differentiate the numerator and the denominator

So, we have

f(x) = (2x² + 7x - 4)/(x² + 5x + 4)

Next, we plot the graph of the function (see attachment)

The asymptotes are the points on the graph is a line that acts as the limit of another line or curve

From the graph, we have the asymptotes to be

x = -1 and y = 2

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Complete question

What is the equation of the asymptote?

f(x) = 2x² + 7x - 4/x² + 5x + 4

The sum of the geometric sequence is 88,573.

The formula for the sum of a geometric sequence is

S = a₁(1 - rⁿ)/(1-r),

where a₁ is the first term of the sequence, r is the common ratio between terms, and n is the number of terms in the sequence. In this case, the first term is a₁ = 1, the common ratio between terms is r = 3, and the number of terms is n = 10. Inserting these values into the formula,

we get S = 1(1 - 3⁹)/(1-3) = 1(1 - 19,683)/(-2) = -9,841.5.

Therefore, the sum of the geometric sequence is 88,573.

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Answer:

Step-by-step explanation:

The y-intercept of g(x) is 3 * 2 = 6.

To find the x-intercepts of g(x), we need to find the values of x that make g(x) equal to 0. Since g(x) = 2f(2x + 3), this means we need to find the values of x that make f(2x + 3) equal to 0. Therefore, we can find the x-intercepts of g(x) by solving the equation f(2x + 3) = 0 for x.

Since the x-intercepts of f(x) are at 2 and -4, this means that the equation f(x) = 0 has solutions at x = 2 and x = -4. Substituting these values into the equation f(2x + 3) = 0, we get:

f(2(2) + 3) = 0

f(4 + 3) = 0

f(7) = 0

and

f(2(-4) + 3) = 0

f(-8 + 3) = 0

f(-5) = 0

Therefore, the x-intercepts of g(x) are at x = 7/2 and x = -5/2. These are the only intercepts of g(x) that we can determine for certain.

Overall, you required 12 to 14 gallons, or 45 to 53 liters, of paint to paint the exterior of your 2000 square foot home.

It might be challenging to calculate or estimate the precise amount of paint that you will need when painting your home. When calculating how much paint you will need, there are many factors to take into account. Every paint has a varied coverage, which determines how many square feet may be painted with each gallon of paint.

According to a rule of thumb and general recommendations, you will require 10 to 12 gallons, or 38 to 45 litres, of exterior paint for a G+0/1 storey house with a 2000 square foot area, as well as 2 gallons of paint for exterior trim for approximately two coats, which includes painting for sliding, overhangs, and soffits, as well as exterior trim for painting the gutters, fascia, and window trims. Overall, you required 12 to 14 gallons, or 45 to 53 liters, of paint to paint the exterior of your 2000 square foot home.

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Answer: an=2(-2)ⁿ⁻¹    a₉=512     a₆=-64

Step-by-step explanation:

Since we have an alternating minus sign in this sequence, therefore the first multiplier of the following sequence will be (-1)ⁿ.

And since the first term of the following sequence is positive, the first multiplier of the following sequence is (-1)ⁿ⁻¹.

The second multiplier of the following sequence is 2ⁿ because the sequence has the form: 2, 4, 8, 16, ..., 2ⁿ .

[tex]Thus,\ a_n=(-1)^{n-1}(2^n)\\\\ a_n=2(-2)^{n-1}\ \ \ (1)[/tex]

Find the 9th and 6th terms of the sequence by formula (1):

a₉=2(-2)⁹⁻¹

а₉=2(-2)⁸

a₉=2(256)

a₉=512

a₆=2(-2)⁶⁻¹

а₆=2(-2)⁵

a₆=2(-32)

a₆=-64

"It's pouring if the grass is wet." Our inverse sentence would be, "If it is NOT raining, then it is NOT wet on the grass."

Given,

Inverse Sentence;

Each of the original statements is presupposed to be false in an inverted statement. "If it is not snowing" would be the polar opposite of "If it is snowing." "Then it is not chilly" would be the polar opposite of "then it is cold."

Example of inverse sentence;

Now, we can construct the three other statements using the concepts we established before. If anything, we would say the opposite: "If the grass is wet, it's pouring." "If it is NOT raining, then the grass is NOT wet," would be our inverse claim.

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Answer:

3

Step-by-step explanation:

She's got 315 total pictures. if she uses one page for 6 pictures then she will fix 52 and a half pages. if only half the page is filled you have 3 photos left

The number of pictures leftover in the scrapbooks is A = 3

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

The total number of pictures = 315

The number of pictures in each page = 6

Since Anne can only fill complete pages, she will use 52 pages. The remaining pictures will be:

The remaining pictures = total pictures - (pictures per page x pages used)

On simplifying the equation , we get

The remaining pictures A = 315 - (6 * 52)

The remaining pictures A = 315 - 312

The remaining pictures A = 3

Hence , Anne will have 3 pictures left over.

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The sum of the interior angle of a regular nonagon will be 1,260°.

The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.

The interior angle of the polygon is given as,

Interior angle = 180° - 360° / n

And the sum of the interior angle is given as,

Sum of the interior angle = n x (Interior angle)

The number of sides of the regular nonagon is 9. Then the interior angle is given as,

Interior angle = 180° - 360° / 9

Interior angle = 180° - 40°

Interior angle = 140°

Then the sum of the interior angle of a regular nonagon will be given as,

Sum of the interior angle = 9 x 140°

Sum of the interior angle = 1,260°

The sum of the interior angle of a regular nonagon will be 1,260°.

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The equation describes a line that contains the point (4, -3) is y = ( -1/25 )x - 71/25 .

Given :

The point (4, -3) and is perpendicular to the line represented by the equation y = 25x +3 .

Here slope m = 25

Perpendicular slope = -1 / m

= -1 / 25

The line equation is y = mx + c

Substitute m and ( 4 , -3 ) we get

-3 = -1/25 * 4 + c

-75 = -4 + 25c

-71 = 25c

c = -71/25

y = mx + c

y = ( -1/25 )x - 71/25

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The time t at which the population is 500 is 45 hours.

The equation gives the rate of change of the population at time t:

dP/dt = kP

where P is the population at time t and k is the constant of proportionality.

We can use this equation to find the value of k by substituting the known values of P and t at time t=24 hours:

dP/dt = kP

1000 = k*300

k = 1000/300

k = 10/3

Now that we know the value of k, we can use the equation to find the time t at which the population is 500:

dP/dt = kP

500 = (10/3)P

P = 500*3/10

P = 150

Since the population at time t=0 hours is 300, the population has decreased by 150 over the 24 hours, so t = -150/(-10/3) = 45 hours.

Therefore, the time t at which the population is 500 is 45 hours.

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dP/dt = kP

We can use this equation to find the value of k by substituting the known values of P and t at time t=24 hours:

dP/dt = kP

1000 = k*300

k = 1000/300

k = 10/3

dP/dt = kP

500 = (10/3)P

P = 500*3/10

P = 150

Since the population at time t=0 hours is 300, the population has decreased by 150 over the 24 hours, so t = -150/(-10/3) = 45 hours.

Therefore, the time t at which the population is 500 is 45 hours.

The basic approach to solve this problem is to first sort array and then traverse through all the the elements and check for missing value and repeating value.

Approach:

c++ implementation

#include <bits/stdc++.h>

using namespace std;

void printTwoElements(int arr[], int size)

{

   int i;

   cout << "The repeating element is ";

   for (i = 0; i < size; i++) {

       if (arr[abs(arr[i]) - 1] > 0)

           arr[abs(arr[i]) - 1] = -arr[abs(arr[i]) - 1];

       else

           cout << abs(arr[i]) << "\n";

   }

   cout << "and the missing element is ";

   for (i = 0; i < size; i++) {

       if (arr[i] > 0)

           cout << (i + 1);

   }

}

int main()

{

   int arr[] = { 8, 3, 4, 5, 5, 6, 1 };

   int n = sizeof(arr) / sizeof(arr[0]);

   printTwoElements(arr, n);

}

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The graph of f(x) = [tex]x^{5}-8x^{4}-16x^{3}[/tex] has the following end behavior : as x decreases, x5 increases; as x increases, x5 decreases; and the graph crosses the x-axis at x = 0 instead of at x = 4.

Given, f(x) =  [tex]x^{5}-8x^{4}-16x^{3}[/tex]

                   f(x) =  [tex]x^{5}-8x^{4}-16x^{3}[/tex]

                         = [tex]x^{3}[/tex](x - 4)(x - 4) = 0

                    [tex]x^{3}[/tex] = 0

                     x = 0

                   x - 4 = 0

                        x = 4

         Thus, x = 0 and x = 4 are the roots.

As a result, the graph will touch the x-axis but not the repeated root of x = 4, indicating that the graph has a repeated root.

Correct question :

What is the end behavior of the graph of f(x)= [tex]x^{5}-8x^{4}-16x^{3}[/tex]   ?

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Answer:

B • r = s - 2

Step-by-step explanation:

Rachel will always be two year younger than Sean. if we substitute the letters with their ages...

[rachel's age] 2 = [ sean's age] 4 - 2

2 = 4 - 2

it can't be A

2 = 4 (two does not equals four)

it can't be C

2 = 4 + 2 (the correct answer is 6, Rachel is not 6 years old)

it can't be D

4 = 2 - 2 (the correct answer is 0. Rachel's not 0 years old as well.

[ also s is the subject in this case. but we are looking for r ]

Answer: B

Step-by-step explanation:

The two-column proof is given below:

Mathematics' earliest branch is geometry, along with arithmetic. The distance, size, shape, and relative position of objects in relation to one another are all aspects of space that are addressed. The term "geometer" refers to a mathematician who specializes in geometry.

Before the 19th century, Euclidean geometry which incorporates the concepts of point, line, plane, distance, angle, surface, and curve as fundamental concepts—was nearly entirely the focus of geometry.

Geometry's use was greatly expanded during the 19th century by a number of discoveries. One of the first of these discoveries is Gauss Theorema Egregium, which roughly states that the Gaussian curvature of a surface is independent of any particular embedding in a Euclidean space.

Statements                                                         Reasons

4.7(2f-0.5)=-6(1.6f-8.3f)                                      Given

4.7(2f-0.5)=-6(-6.7f)                                           Combine like terms

9.4f-2.35= -40.2f                                               Get all the terms to the one  

                                                                           side of an equation

49.6f=23.5                                                           Addition property

f=47/992                                                              Division property                  

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Answer:

The graph of given function is shown below.

Step-by-step explanation:

The absolute parent function is g(x)=|x|. The graph of parent function is a V-shape d and vertex of the function is origin.

The given function is

             .... (1)

The vertex from of an absolute function is

         .... (2)

where, a is a constant and (h,k) is vertex of the function.

From (1) and (2) we get

The value of a is -1. The value of a is negative it means the graph of parent function reflect across x-axis.

The vertex of the function is (0,-2). It means the graph of parent function shifts 2 units down.

A one-dimensional array is the simplest type of array in which the elements are stored linearly and can be accessed individually by determining the index value of each element stored in the array.

A one-dimensional array is the simplest type of array in which the elements are stored linearly and can be accessed individually by determining the index value of each element stored in the array.

One Dimensional Arrays are used to implement other data structures such as stacks, queues, heaps, graphs.

A typical advantage of one Dimensional Arrays is that they help in accessing elements easily using the index number.

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The square root of some number 'X' is a number which, when you multiply it by itself, the answer is 'X'.

The square root of a number is the factor that we can multiply by itself to get that number. The symbol for square root is [tex]\sqrt{x}[/tex] . Finding the square root of a number is the opposite of squaring a number.

In mathematics, a square root of a number x is a number y such that y² = x; in other words, a number y whose square (the result of multiplying the number by itself, or y ⋅ y) is x.[1] For example, 4 and −4 are square roots of 16, because 4² = (−4)² = 16.

Thus , the square root of some number 'X' is a number which, when you multiply it by itself, the answer is 'X'.

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The true statement about the interval is that:

The given interval is -7 ≤ x < -4, the numbers in the interval are

-7, -6, -5,

The numbers are all negative and the number starts from -7 but did not get to -4

since the interval starts from -7 which is a lesser number than -6 and a lesser when compared with -5 we say the interval is increasing

In negative numbers, the larger the number the lesser it has value and and lesser the number the closer it is to zero and the higher the number

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Answer:

False

Step-by-step explanation:

Vertical angles are always congruent regardless of if the lines are parallel.

The joint relative frequency of students using mobile devices in traditional classes, is

The joint relative frequency of students that use mobile devices in the setting of a traditional class is :
= Number of students using mobile devices in traditional class / Number of total students accessing courses

Number of students using mobile devices in traditional class =  46 students

Number of total students accessing courses = 200

The  joint relative frequency of students using mobile devices in traditional classes :

= 46 / 200

= 23 %

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Answer:

A. It is an increase in assets.

Step-by-step explanation:

The Debit section shows what the business purchased which is $12,000 worth of equipment. Hence, the business gained equipment worth $12,000 which is an increase in assets.

Answer:

A. It is an increase in assets.

Step-by-step explanation:

The entry "Equipment 12,000" is listed as a debit in the T-account because it is an increase in assets.

A T-account is a visual representation used in accounting to track and display the balances of a specific account, with the "debit" side showing increases and the "credit" side showing decreases.

When office equipment is purchased, it represents an increase in the company's assets. An increase in assets (or a decrease in liabilities) is recorded as a debit on a company's balance sheet.

In this case, the business is acquiring equipment, which is considered an asset, and therefore, it is debited to reflect the increase in the asset account.

TRUE: The ratio of 6 and 8 is equivalent to 3/4.

Remember that the ratio is the same when you multiply both sides of a fraction by a number.

= 3/4

= 3*2 / 4*2

= 6/8

= 6:8

Thus, the ratio of 6 and 8 is equivalent to 3/4.

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Is 6:8 equals 3/4 ? Is it true or false and why?

Inspect the graph to see if any vertical line drawn would intersect the curve more than once.

What is graph?

A graph is a structure that resembles a set of items in discrete mathematics, more especially in graph theory, in which certain pairs of the objects are conceptually "connected." The items are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.

If there is any such line, the graph does not represent a function. If no vertical line can intersect the curve more than once, the graph does represent a function.

f(x)=log(2x)

g(x)=log1/10(x-3)  the base of log is 1/10

Domain is x>3

Range is all real numbers

g(x) is decrease on the interval x>3

asymtote is x=3

x intercept is x=4

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Answer:

A = 5 + 3t

B = 7 + 2t

2 hours

Step-by-step explanation:

7 + 2t > 5 +3t

                      (subtract 2t from both sides)

7         > 5 + t

                      (subtract 5 from both sides)

2         > t

therefore in 2 hours, the parking would be cheaper in Garage A than B

The weight of container will be 20 kg

Let x be the number of car toys packed into container. Toy cars weigh 3 kilogram apiece and are shipped in a container that weighs 5 kilograms when empty, then the total weight of container with toy cars is

x.3 + 5 = 3x + 5

The number of toy trucks is also x. Toy trucks, which weigh 2 kilograms apiece, are shipped in a container weighing 10 kilograms, then the total weight of container with toy trucks is

x.2 + 10 = 2x +10

When packed with toys and ready for shipment, both kinds of containers have the same weight. Thus,

3x + 5 = 2x + 10

x = 15

The weight of container = x + 5

= 15 + 5

= 20 kg

Hence, the weight of container will be 20 kg

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