Find the value of the linear correlation coefficient r. Round your answer to 3 decimal places if necessary.

(1 , 6) , (3 , 4) , (5 , 2)

The future value of $8904.56 compounded semi annually is $13,468.95 The interest earned is approximately $4,564.39

The future value of $8904.56 compounded continuously is $66,185.90.

The interest earned is approximately $57,281.34.

When an investment is compounded semi annually, it means that both the amount that was invested and the interest that has already been earned increases in value twice in a year.

The formula for calculating future value:

FV = P (1 + r)^nm

Where:

FV = 8904.56 x 1.03^(7 x 2) = $13,468.95

Interest = future value - amount invested

$13,468.95 -  $8904.56 = $4,564.39

When an amount is compounded continusoly, it increases in value infinitely over the investment time horizon.

The formula for calculating future value when there is continuous compounding is : A x e^r x N

Where:

FV = 8904.56 x e^0.06 x 7 = $66,185.90

Interest = future value - amount invested

$66,185.90 - 8904.56 = $57,281.34

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Because the graph only intercepts the x-axis only once, the equation has only one solution. The correct option is the second one.

Here we want to see, based on a graph, how many solutions does the cubic equation:

x³ + 6x² + 12x +8 = 0

The graph of the function:

g(x) = x³ + 6x² + 12x +8

Can be seen below, the number of real solutions that the equation:

x³ + 6x² + 12x +8 = 0

has, will depend on how many times the graph intercepts the x-axis.

We can see that there is only one intercept, so there is one real solution.

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β=-α is the solution for alpha beta square +alpha square beta quadratic equation​

A quadratic equation is a second-order polynomial equation in a single variable x , ax2+bx+c=0. with a ≠ 0 .

alpha beta square +alpha square beta quadratic equation​

αβ²+βα²

αβ(β+α)

αβ=0

and

β+α=0

β=-α

Hence β=-α is the solution for alpha beta square +alpha square beta quadratic equation​

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Answer:

slice it in the middle in the top and bottom or do it corner to corner.

Step-by-step explanation:

1. have 2 braincells

2. put them toghether and think.

Answer:

x      y

1      0

2     10

5     40

10   90

Step-by-step explanation:

In a linear function, every time x is increased by 1, y is increased by a set amount. The only two complete rows in the table are when x = 1 and x = 5. x is increased four times in that interval while y has increased by 40(40 - 0). This means that every time x increases by 1, y increases by 10(40/4).

Therefore, when x is 2, y will be 10.

To get to ninety, 10 will needed to be added to 0(when x=1) 9 times. 1 + 9 is 10, so x = 10 when y = 90.

Answer:

Step-by-step explanation:

(1,0)   (5,40)

Using these coordinates we find the line equation y=mx+b:

[tex]\displaystyle\\m=\frac{y_2-y_1}{x_2-x_1} \\\\x_1=1\ \ \ \ \ x_2=5\ \ \ \ \ y_1=0\ \ \ \ y_2=40\\\\m=\frac{40-0}{5-1} \\\\m=\frac{40}{4} \\\\m=10\\\\Thus,\ y=10x+b \ \ \ \ (1)\\[/tex]

We substitute the value of coordinate (1,0) into equation (1):

[tex]0=10(1)+b\\\\0=10+b\\\\-10=b\\\\Thus, \ b=-10\\\\Hence,\\\\ y=10x-10\\\\x=2\\\\y=10(2)-10\\\\y=20-10\\\\y=10\\\\Thus,(2,10)\\\\y=90\\\\90=10x-10\\\\100=10x[/tex]

Divide both parts of the equation by 10:

[tex]10=x\\\\Thus, (10,90)[/tex]

   x   |    y

-----------------

   1    |   0    

------------------

   2   |   10

------------------

   5   |   40

------------------

  10   |  90

Answer:

16x+4

Step-by-step explanation:

Perimeter= side+side+side+side or 4(side)

Plug in side length

Perimeter= 4(4x+1)

Perimeter=16x+4

It can't be further simplified

Answer:

x= 12/5

Step-by-step explanation:

Distribute the fraction and solve for x.

Answer:

we can't give an answer if there's not explanation of which "t" is

The unit rate which correctly corresponds to.the given rate; 6 eggs in 7 months is; 0.86 eggs per month.

A unit rate as the name implies is one in which case a given quantity is expressed in terms of one unit of the other quantity.

Such units are expressed as; a per b.

On this note, since the given rate is; 6 eggs in 7 months.

It follows that the rate can be expressed as;

6 eggs / 7 months

= 6/7 eggs per month.

= 0.85714 eggs per month.

And ultimately, when rounded to the nearest hundredth; we have; 0.86 eggs per month.

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If annual fundraising goal of a is​ $100,000 and so far ​$46,088 has been raised, then they have to raise $53912 to reach the goal

The goal of the annual fund raising = $100000

The raised amount = $46088

The amount of money needed to reach the goal = The goal of the annual fund raising - The raised amount

Here we have to use the subtraction

Substitute the values in the equation

The amount of money needed to reach the goal  = 100000 - 46088

= $53912

Hence, if annual fundraising goal of a is​ $100,000 and so far ​$46,088 has been raised, then they have to raise $53912 to reach the goal

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The value of n is given by either 4/5 or 16/25.

Given that the positive number is n which is n<1.

Reciprocal of the number is = 1/n

Addition of the number and the reciprocal is 2.05.

So the suitable equation for this,

n + 1/n = 2.05

[tex]n^2+1=\frac{41}{20}n\\20n^2-41n+20=0\\n=\frac{41\pm\sqrt{1681-1600}}{40}=\frac{41\pm9}{40}=\frac{50}{40},\frac{32}{50}=\frac{4}{5},\frac{16}{25}[/tex]

So the number can be either 4/5 or 16/25.

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The answer is tom will give 440 cards to Bala, using arithmetic operation.

What is the arithmetic operation?

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.

The total number of cards is 780+240 = 1020.

If in the end Bala will have twice as many cards as Tom then I would divide the 1020 by 3 which equals 340.

So Bala will have 2*340 = 680 cards

Tom will have 340 cards.

Now Bala will need (680-240) = 440 more cards.

Hence Tom will give 440 cards to Bala.

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Answer:

x = 1

y = 7

Step-by-step explanation:

y = -x + 8

-y= -2x - 5 (Switch the signs of y = 2x + 5)

0= - 3x + 3 (Subtract both equations)

3x = 3 (Add 3x on both sides)

x = 1 (Divide by 3 on both sides)

y = -1 + 8 (Plug x as 1 in the equation y = -x + 8)

y = 7 (Simplify)

Leading to the answer

x = 1

y = 7

The inequality y > x+1 graphed is false.

Given,

In the question:

When the inequality y > x +1 is graphed,

The shade is below the line and the line is dashed.

Check the above information is true or false.

Now, According to the question:

The inequality is given as:

y > x +1

The graph is:

∴The shade is below the line and the line is dashed

The answer is false.

Hence, The inequality y > x+1 graphed is false.

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8. The value of x is 9.

9. The value of x is 6.

Two triangles are congruent if all the corresponding sides and corresponding angle are equal.

8.

In the given triangle ∠A=(3x-4)°, ∠B=(13x+2)° and ∠C=(5x-7)°

The sum of all three angles of a triangle is 180°,

Implies that,

∠A+∠B+∠C=180°

3x-4+13x+2+5x-7=180

21x-9=180

21x=189

x=9

9.

In the given triangle, ∠A=(7x+1)°, ∠B=(19x-18)° and ∠C=(10x-9)°

The sum of all three angles of a triangle is 180°,

Implies that,

∠A+∠B+∠C=180°

7x+1+19x-18+10x-9=180

36x-26=180

36x=216

x=6

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The correct number line that shows the solution to the compound inequality is given by:

Number Line A.

A compound inequality is an inequality that is composed by multiple conditions.

Then these conditions are related with one of two operations, listed as follows:

In this problem, the compound inequality is given as follows:

3x - 5 > 1 or -2x ≤ -10.

The solutions to the first condition are given as follows:

3x > 6

x > 2.

The solutions to the second condition are given as follows:

2x ≥ 10

x ≥ 5.

The interval of values that is the union of these solutions is given by:

x > 2.

Hence number line A is the solution to the inequality.

The complete problem is given by the image shown at the end of the answer.

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Answer:

b=4

Step-by-step explanation:

b-14 =-10

b-14+14=-10+14

b=4

u raised to the 10th power, then the result doubled gives  2u¹⁰

An algebraic expression is an expression that is made up of variables and constants, along with algebraic operations like addition, subtraction, multiplication, exponent, etc.

Given: raise u to the 10th power, then double the result

Step 1: Raising u to the 10th power implies: u¹⁰

Step 2: Doubling the result means multiplying what you obtained in step 1 by 2, that is, 2 × u¹⁰ = 2u¹⁰

Therefore, raising u to the 10th power and then doubling the result gives 2u¹⁰

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The value of a when the value of 5-a is 20 greater than the vaule of 6a-1 is -2.

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

Since the value of 5-a is 20 greater than the vaule of 6a-1. This will be:

5 - a > 6a - 1 + 20

Collect like terms

-a - 6a > - 1 + 20 - 5

-7a > 14

Divide

a > 14 / -7

a > -2

Therefore, a is greater than -2.

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The probability that your would get an odd number twice when the rolling is 1-8 is 12.5%

Probability is the chance of occurrence of an even (E) Over a period of time. That is, it is the extent to which an event is likely to occur, measured by the ratio of the favorable cases to the whole number of cases possible.

How to get the probability of the spinning?

From the analysis, the spinning is done twice from numbers 1-8

this means that in ever row, each number appears double.

The sample size is 8x8=64

1,1     1,2     1,3    1,4     1,5    1,6    1,7    1,8

2,1    2,2    2,3    2,4    2,5   2,6   2,7   2,8  

3,1     3,2    3,3   3,4     3,5   3,6   3,7   3,8

4,1    4,2    4,3   4,4    4,5   4,6    4,7   4,8

5,1      5,2   5,3   5,4     5,5    5,6    5,7  5,8

6,1      6,2    6,3  6,4     6,5    6,6   6,7   6,8

7,1      7,2     7,3   7,4    7,5    7,6   7,7  , 7,8

8,1     8,2     8,3  ,,8,4 ,,, 8,5 ,,8,6  8,7,,, 8,8

The required outcome is 8

These outcomes are

1,1  2,2   3,3   4,4   5,5   6,6  7,7  8,8=8 outcomes

Probability of and event is

P=[tex]\frac{number of required outcome}{number of possible outcome}[/tex]

P(E)=[tex]\frac{8}{64}[/tex]

P(E)=[tex]\frac{1}{8}[/tex]

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Answer: 25%

Step-by-step explanation:

You have 4/8 chances of getting an odd number on the spinner, which equals 1/2, or 50%. Now if you are going to get another odd number, you have an additional 1/2 (half your chances) or 50% of a chance of getting it after you get the first odd number. This means you must mutliply these chances. 1/2x1/2 which is 1/4 = 25%

Answer:

(2a + 3b)(2a - b)

Step-by-step explanation:

4a² + 4ab - 3b²

consider the factors of the product of the coefficient of a² and b² which sum to give the coefficient of the ab- term.

product = 4 × - 3 = - 12 and sum = 4

the factors are + 6 and - 2

use these factors to split the ab- term

= 4a² + 6ab - 2ab - 3b² ( factor the first/second and third/fourth terms )

= 2a(2a + 3b) - b(2a + 3b) ← factor out (2a + 3b) from each term

= (2a + 3b)(2a - b)

The solution set. for the given inequality : x-5> -10. is (-5, ∞]

An inequality is a relationship that shows a non-equal comparison between two numbers or mathematical expressions.

We need to find the solution set for  x-5> -10.

x - 5 > - 10

x > -10 + 5

x > -5

The solution set = (-5, ∞]

Therefore, the  solution set. for the given inequality : x-5> -10. is (-5, ∞]

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[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{"y" varies inversely to }x^2}{y=\cfrac{k}{x^2}}\hspace{5em}\textit{we also know that} \begin{cases} y=5\\ x=3 \end{cases} \\\\\\ 5=\cfrac{k}{(3)^2}\implies 5=\cfrac{k}{9}\implies 45=k\hspace{5em}\boxed{y=\cfrac{45}{x^2}} \\\\\\ when~y=1\frac{4}{5}\textit{ what is "x"?}\implies 1\frac{4}{5}=\cfrac{45}{x^2}\implies \cfrac{9}{5}=\cfrac{45}{x^2} \implies 9x^2=(5)(45) \\\\\\ x^2=\cfrac{(5)(45)}{9}\implies x^2=25\implies x=\sqrt{25}\implies {\Large \begin{array}{llll} x=5 \end{array}}[/tex]

Answer:

this should help

Step-by-step explanation:

it is step by step on screenshots I have above

The population of the country in 2003 is 302.5 million

From the question, we have the following parameters that can be used in our computation:

Exponential model, A = 302.5e^0.0211t

Where i is the number of years after 2003

In the year 2003, the value of t is 0

i.e. 0 years after 2003

So, we have

A = 302.5e^(0.0211 * 0)

Evaluate the products

A = 302.5 * 1

So, we have the following result

A = 302.5

Hence, the population is 302.5 million

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a) The linear function is:

y = 2 + 0.25x.

b) The amount of snow on the ground after 4 hours will be of 3 inches.

c) The time that he has to complete the hike is of 16 hours, which is enough to finish the hike, as they don't take this long.

The slope-intercept representation of a linear function is presented by the rule as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

In this problem, the values of these coefficients are given as follows:

Hence the equation is:

y = 2 + 0.25x.

After four hours, the amount of snow on the ground will be of:

y = 2 + 0.25(4) = 2 + 1 = 3 inches.

The time until the amount reaches 6 inches is of:

2 + 0.25x = 6

0.25x = 4

x/4 = 4

x = 16 hours.

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This calls for applying rates:

18 minutes = 36 rows

1 minute = 36/18 = 2 rows

25 minutes = 2 x 25 = 50 rows

The answer is 50 rows in 25 minutes. I hope this helps!

Answer:

(x-5),(y+2)

Step-by-step explanation:

The fraction of strawberry and chocolate flavored candies that Aurora has in her box is 5/4

From the information illustrated, 30 of the candies are strawberry flavored and 24 are chocolate flavored.

Therefore, to get the fraction, we have to divide them. This will be illustrated as:

= Number of strawberry candies / Number of chocolate candies

= 30 / 24

= 5/4

The fraction is 5/4.

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Complete question

In Aurora’s candy box, 30 of the candies are strawberry flavored and 24 are chocolate flavored. What is the fraction of strawberry and chocolate flavored candies that Aurora has in her box?