The gravitational attraction between two bodies varies inversely as the square of the distance between them: If the force of attraction is 64 pounds when the distance between the bodies is 9 feet, what is the distance between them when the force is 36 pounds?

The sequence of the angles from lower to bigger will be ∠WXY < ∠YXZ < ∠WYX < ∠XZY < ∠XYZ.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

In a triangle, if the angle is small then the opposite side will be short, and if the angle increases then the side also increases.

The sides of the triangle are in ascending order, then we have

WY < YZ < WX < XY < XZ

Then the sequence of the angles is given as,

∠WXY < ∠YXZ < ∠WYX < ∠XZY < ∠XYZ

The sequence of the angles from least to biggest is ∠WXY < ∠YXZ < ∠WYX < ∠XZY < ∠XYZ.

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The 32th term of the arithmetic sequence AP is estimated to be 0.3.

In math, an arithmetic progression (AP) is a list or sequence of numbers in which each term is obtained by adding a finite number to the term before it.

Now for the answer to the question;

The numbers in the given sequence are-

-9,-8.7,-8.4, ...........

There are 32 terms with in series for that we need to find the 32nd number.

Let's say the first term is 'a₁' = -9.

Let 'a₂' = -8.7 be the second term.

Let 'a₃' = -8.4 be the third term.

The common difference between two consecutive terms that are equal of an AP is 'd.'

d = a₂ - a₁  

Substitute the values in the preceding equation; the 32nd term is

d = -8.7 - (-9)

d = -8.7 + 9

d = 0.3

Now calculated using the nth term formula.

Substitute all of the values in the formula now.

a₃₂ = a + (n - 1) d

a₃₂ = -9 + (32 - 1)(0.3)

a₃₂ = -9 + 9.6 - 0.3

a₃₂ = 0.3

As a result, the arithmetic sequence's 32nd term is estimated to be 0.3.

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He will break even on the 25th month.

The cost to start the business is $20,000 and the monthly costs are $8,000.

He has been earning $8,800 every month in revenue.

Profit = Selling Price - Cost Price

Therefore,

let

x = number of month

Hence,

selling price = 8800x

cost price = 20000 + 8000(x) = 20,000 + 8000x

Therefore,

profit =  8800x - (20,000 + 8000x)

profit = 8800x - 20000 - 8000x

profit = 8800x - 8000x - 20000

profit = 800x - 20000

Hence,

The month when they will break even is as follows:

8800x = 20,000 + 8000x

20000 = 8800x - 8000x

20000 = 800x

x = 20000 / 800

x = 25

Therefore, he will break even on the 25th month.

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The coordinates of the midpoint M of the segment AB is (-4,6).

The midpoint formula is expressed as;

M = ( (x₁+x₂)/2, (y₁+y₂)/2 )

Given the data in the question;

Point A (-8, 5)

Point B (0,7)

To determine the midpoint, plug the given points into the formula above and simplify.

M = ( (x₁+x₂)/2, (y₁+y₂)/2 )

M = ( ((-8)+0)/2, (5+7)/2 )

M = ( ( -8+0 )/2, (5+7)/2 )

M = ( ( -8 )/2, (12)/2 )

M = (-4,6)

Therefore, the coordinates of the midpoint M of the segment AB is (-4,6).

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Answer:

hi

Step-by-step explanation:

Answer:

FITNESS Laura wants to go to a fitness class

tomorrow. She can choose a 5:00 or a 7:30 class and

spin or water aerobics. Represent the sample space

for the situation by making an organized list, a table,

and a tree diagram.

Step-by-step explanation:

The company catches 1,237,275.5 fishes over 10 years.

Given that, a company catches 175000 fishes in a year, the population decreases, the number of fish the company was able to catch decreased by 8% each year.

So, the population in 10 year =

The second year = 175000 × 0.92 = 161000

The third year = 161000 × 0.92 = 148120

The fourth year = 148120 × 0.92 = 136,270.4

The fifth year = 136270.4 × 0.92 = 125368.8

The sixth year = 125268.8 × 0.92 = 115339.3

The seventh year = 115339.3 × 0.92 = 106112.2

The eighth year = 106112.2 × 0.92 = 97623.2

The ninth year = 97623.2 × 0.92 = 89813.3

The tenth year = 89813.3 × 0.92 = 82628.3

The total = 175,000+161000+148120+136,270.4+125368.8+115339.3+106112.2+97623.2+89813.3+82628.3 = 1,237,275.5

Hence, the company catches 1,237,275.5 fishes over 10 years.

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The set of items that exist as part of both sets A and B exists at the intersection of the two sets.

If p(a|b) =0.40, p(b) = 0.74, and p(a) = 0.42, then P(A∩B) is 0.46.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

It exists given that the Probability of two independent event A and B exists given by P(A)  and P(B).

The intersection of event A and B is given by P( A∩B).

The group of items that are part of both sets A and B is the intersection of the two sets. A ∩ B represent the intersection. The symbol "∩" can be used to represent the intersection of sets.

The collection of all outcomes that are components of both sets A and B is known as the intersection of events A and B (abbreviated AB).

Given: P(a|b) = 0.40

P(A) = 1 - 0.40 = 0.6

P(B) = 1 - 0.74 = 0.26

P(A∪B) = P(A) + P(B) − P(A∩B)

substitute the values in the above equation, we get

0.40 = 0.6 + 0.26 - P(A∩B)

- P(A∩B) = 0.40 -  0.6 - 0.26

P(A∩B) = 0.46

Therefore, the independent events of A and B exists 0.46.

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Answer:

Hello,

x=-4, y=3

Step-by-step explanation:

14*x+19*y=1 since gcd(182,247)=13

Here is a automatic calculus (using Bezout 's method)

All you have to do is to put in B1 and B2 the right numbers

The values of x and y given that 182x + 247 y = gcd(182, 247) would be x=-4 and y=3.

An equation represents equality of two or more mathematical expression.

To solve an equation, then the values of the unknowns for which that equation would be true (the equality between expressions should hold true for those values).

And Solutions to an equation are values of the variables involved in that equation for which the equation is true.

We have given the equation as;

182x + 247 y = gcd(182, 247)

Then we get

14*x+19*y=1

Thus, x=-4 and y=3.

since we have given gcd(182,247)

=13

Hence, The values of x and y given that 182x + 247 y = gcd(182, 247) would be x=-4 and y=3.

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The slope of a line perpendicular to the line of x + 4y = 16 is 4.

Given the equation of line;

x + 4y = 16

First, rearrange in slope intercept form ( y = mx + b ) by solving for y

x + 4y = 16

Subtract x from both sides

x - x + 4y = 16 - x

4y = -x + 16

Divide each term by 4 and simplify

4y/4 = -x/4 + 16/4

y = -(1/4)x + 4

Using the slope intercept form ( y = mx + b ) to compare.

y = -(1/4)x + 4

Slope m = -(1/4)

Now, the equation of a perpendicular line to y = -(1/4)x + 4 must have a slope that is the negative reciprocal of the original slope.

Hence, m_perpendicular will be;

m_perpendicular = -( 1 / original slope )

m_perpendicular = -( 1 / -(1/4) )

m_perpendicular = -( -4 )

m_perpendicular = 4

Therefore, the slope of a line perpendicular to the line of x + 4y = 16 is 4.

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The probability of the event P(A is on [tex]\bar{CE}[/tex]) is 21/26.

Probability:

Probability defines the possibility of the event across the total event.

Given,

Point A is chosen at random on [tex]\bar{BE}[/tex].

Here we need to find the the probability of the following event.

P(A is on [tex]\bar{CE}[/tex]).

Let us consider the following image, in order to solve this.

Based on the image we have identified that the probability of the event  P(A is on [tex]\bar{CE}[/tex]) is calculated by dividing the length of CE by the length of BE.

So, the probability of the event P(A is on [tex]\bar{CE}[/tex]) is,

P(A is on [tex]\bar{CE}[/tex]) =  (length of CE) / (length of BE)

Then, length of CE is calculated by adding the distance,

=> CD + DE

=> 12 + 9

=> 21

Now,

Apply the values then we get,

P(A is on [tex]\bar{CE}[/tex]) = 21 / ( 5 + 12 + 9)

P(A is on [tex]\bar{CE}[/tex]) = 21 / 26

Therefore, the probability of the event P(A is on [tex]\bar{CE}[/tex]) is 21/26.

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Answer:

A. s+7726>=12,600

Step-by-step explanation:

s is the number of steps left to reach her goal of at least 12,600 steps.

7726 is the number of steps already taken.

12,600 is her goal.

s+7726>=12,600

Hope this helps!

Please mark as brainliest if correct!

If two trains leave towns 978 miles apart at the same time and travel toward each other and one train travels 21 miles per hour faster than the other and if they meet in 6 hours, then the rate of the faster and slower train will be 92mph and 71 mph respectively.

To determine the rate or speed of each train, an algebraic expression can be used.

As one train travels 21 miles per hour faster than the other, consider x to be the speed of the train that travels slower. In this case, an algebraic expression can be given as,

6x + 6(x + 21) = 978

Here, (x + 21) represents the speed of the faster train

6x + 6x + 126 = 978

12x = 978 - 126

12x = 852

x = 852 ÷ 12

x = 71

x + 21 = 71 + 21 = 92

Hence, the rate of the faster train is 92 miles per hour and the rate of the slower train is 71 miles per hour.

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Answer:

5 degres

Step-by-step explanation:

0-10 is -10

-10+15 is 5

Answer:

Option 2

Step-by-step explanation:

2.2 x 1.25 = 2.7510-2.75=7.25

Answer: DB=6.5 units

Step-by-step explanation:

DB=BD

AB+BD=AD

AB=BD ==> Bisectors divide a segment into two equal parts

BD+BD=13

2*BD=13

BD=13/2

BD=

DB=6.5 units

Step-by-step explanation:

222-6=216

216÷4=54

so 54 students per bus

Answer:

54 students

Step-by-step explanation:

222 - 6 (students that had to travel in cars) = 216

216 / 4 (4 buses) = x

x = number of students on each bus

216 / 4 = 54

x = 54

54 students on each bus

216 students rode the bus, 6 students rode in cars

The second term of the given geometric sequence is: 6.

Given:

To find: Second term of the GP (a₂).

Finding:

Since the given sequence is a GP, the nth term will be given by: [tex]a_n=a_1(r^{n-1})[/tex], where r = common ratio of the GP.

Now, for n  = 3, [tex]a_3=3(r^{3-1})[/tex]

=> 12 = 3 (r²)

=> 4 = r²

=> r = ±2

Since the given sequence is increasing and positive, r = 2.

Thus, a₂ = a₁ (r¹)

=> a₂ = 3 (2) = 6

Hence, The second term of the given geometric sequence is: 6.

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Answer:

195.86

Step-by-step explanation:

Answer: 195.86. Yw.

Step-by-step explanation: Pls add me Brainliest >3

Answer:

The graph of g(x) shows exponential decay, while the graph of f(x) shows exponential growth. What you need in your answer: The graphs are reflections of each other over the y-axis. The g(x) function represents exponential decay.

Answer:

2 times as much

Step-by-step explanation:

1 hour 2/3 = 60 + (2/3) 40 mins = 100 minutes

3 hours 1/3 = (60 ×3 ) + 20 mins = 200 mins

200 is twice as much as 100

The situation can be solved by determining the probability of the selecting a certain color marble.

Probability is the ratio of a favorable outcome x to the total number of outcomes n of an event. In the give case, if the prediction is correct, you get a dollar.

Probability=x/n

On the first draw, the chance that predicted color is drawn is:

Probability=2/4=1/2

Amount you may get is ½*1=1/2

On the second draw, the chance the color with two left balls is predicted and come out:

Probability=2/3

Amount you may get is 2/3*1=2/3

On the third draw, you predicted a color with no same color balls left:

Probability=1/3

Amount you may get is 1/3*1=1/3

Or you predicted a color with two different color balls left

Probability=2/3*1/2=2/6=1/3

Amount you may get is 1/3*1=1/3

On the fourth draw, the probability of correct predicted ball is 1

Amount you may get is 1=1

If you played the game optimally, summing up the amount=1/2+2/3+1/3+1/3+1=17/6≈2.88

Hence, by playing the game optimally, the expected value of the game is $2.88.

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It is proved that ΔLMN is an isosceles triangle.

So,

Given:

To prove congruency:

Therefore,  ΔM LO ≅ ΔMNO under SSA congruency.

Therefore, it is proved that ΔLMN is an isosceles triangle.

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Answer:

The method for appearing with numbers for the 2x2 matrix whose determinant is 13 is clarified.

Step-by-step explanation:

Determinant of 2×2 matrix

If we have a 2×2 matrix A of the form;

A =

\binom{a \: \: \: b}{c \: \: \: d}(

cd

ab

)

The determinant of the matrix is;

|A| = (a.d) - (b.c)

Therefore, to appear with numbers for a, b, c, and d, we must ensure; (a.d) - (b.cdeterminantse, if a = 3, d = 15, b = 2, and v = 1.

Ultimately, |A| = (3×5) - (2×1) = 13

Hello,

[tex]f(x) = - {x}^{2} + 8[/tex]

[tex]h(x) = - {x}^{2} + 8 - 3 = - { {x}^{2} } + 5[/tex]

The number of minutes it will take the marshal to catch up to the robber in discuss is; 210.

Let 30minutes = 0.5 hours.

Let x represent the time for which the marshal has ran.

On this note, the robber must have galloped at; (x +0.5) hours.

Hence, it follows from the task content that if they are at the same distance from the bank; we have;

14(x+0.5) = 16(x)

14x + 7 = 16x

7 = 2x

x = 7/2 = 3.5 hours.

= 3.5 × 60minutes = 210minutes.

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The equation of the line 4x + 6y = 12 expressed in slope-intercept form is y = -2/3 x + 2 with a slope equal to -2/3.

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The slope-intercept form of the equation of a line is given by the formula:

y = mx + b

where m is the slope of the line

b is the y- intercept

Given the equation of the line 4x + 6y = 12, which is in standard form, transform it into slope-intercept form by isolating the variable y in one side.

4x + 6y = 12

6y = -4x + 12

Dividing both sides by 6,

y = -4/6 x + 2

y = -2/3 x + 2

Hence, the equation of the line in slope-intercept form is y = -2/3 x + 2 where the slope, m, is equal to -2/3.

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If AC = 4x - 3, DC = 2x + 9, m ∠ ECA = 15x + 2, and EC is a median of ΔAED then EC is not an altitude of ΔAED because of m ∠ ECA = 92.

In geometry, an altitude is a line that passes through two very specific points on a triangle: a triangle's vertex, or corner, and its opposite side at a right, or 90-degree, angle. The base is the opposite side. Triangles have three vertices and three opposite sides in common.

Given: AC = DC

4x - 3 = 2x + 9

4x - 2x - 3 = 2x - 2x + 9

simplifying the above equation, we get

2x - 3 = 9

2x - 3 + 3 = 9+3

2 x = 12

x = 6

Substitute the value of x in m ∠ ECA, then we get

m ∠ ECA = 15x + 2

= 15(6) + 2

m ∠ ECA = 92

EC is not an altitude of ΔAED because of m ∠ ECA = 92.

Therefore, EC is not an altitude of ΔAED.

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Answer:

a

Step-by-step explanation: codigo binario