David wants to build a rectangular fencing with the 5 identical parts for his animals. He has 780 feet of fencing to make it. What dimensions of each part will maximize the total enclosed area?

Answer:

132860 to nearest whole number.

Step-by-step explanation:

Sum of n terms = a1 .(r^n - 1) / (r - 1).

S25 = 177,147 ((-1/3)^25 - 1) / (-1/3 - 1)

= 177,147 * -1 /    -4/3

= 132860.

The given task involves finding the sum of the first 25 terms of a geometric sequence with a specific first term and common ratio. This is done using the sum formula for a finite geometric sequence, with the terms alternating in sign due to a negative common ratio.

The subject question deals with the concept of a geometric sequence, specifically finding the sum of the first 25 terms. A key formula to solve this question is the sum of a finite geometric sequence: Sₙ = a₁(1 - rⁿ)/(1 - r), where a1 is the first term, r is the common ratio, and n is the number of terms.

In this case, a₁ is 177,147, r is -1/3 and n is 25. Substituting these values into the formula, the sum, S25 = 177,147 × (1 - (-1/3)25) / (1 - -1/3).

By solving this equation, we get the sum of the first 25 terms of the given geometric sequence. Note that due to the negative common ratio, the terms alternate in sign in this particular geometric sequence.

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Answer:

Step-by-step explanation:

The slope is  1.5 miles / day

Final answer:

The slope of the equation that represents Ashley's walking distance over the number of trips is 1.5, which indicates that she walks 1.5 miles for each trip to school.

Explanation:

Ashley has already walked 0.5 miles this week and plans to walk 1.5 miles each trip to school for a total of 3 trips. To find the slope of the equation that represents her walking distance as a function of the number of trips, we use the slope formula, which is rise over run, or in this context, the change in distance over the number of trips.

Let's calculate her total planned distance. Since she plans on walking 1.5 miles for each trip and takes 3 trips, that's 1.5 miles/trip × 3 trips = 4.5 miles. Including the 0.5 miles she has already walked, her total distance for the week would be 0.5 miles + 4.5 miles = 5 miles, which matches with her goal.

Now, the slope is the distance she covers per trip, which is consistent and equal to 1.5 miles per trip. Therefore, the slope of the line that represents her distance over the week as a function of each trip is 1.5.

Answer:

if its division then: 17.89

Step-by-step explanation:

The result of the division 1449.09 divided by 81 equals approximately  17.89 .

To find the result of 1449.09 divided by 81, we simply divide the numerator by the denominator.

The division can be calculated as follows :

1449.09 ÷ 81 = 17.892654321.

Rounded to two decimal places , the result is approximately 17.89.

The result of the division 1449.09 divided by 81 equals approximately  17.89. This means that 1449.09 can be divided evenly by 81 a total of 17 times with a remainder of 0.

The quotient, 17.89, represents the value obtained when equally distributing 1449.09 among 81 parts.

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Below is a labeled rectangle:

length = w + 20

we know length is 36 so we plug that in:

36 = w + 20

We need to isolate w and to do that we must subtract 20 from both sides:

(36 - 20) = w + (20 - 20)

16 = w + 0

w = 16

width is 16 feet

Hope this helped!

Answer:

ones good ones bad

Step-by-step explanation:

Answer:

Pros means Advantages

Cons means Disadvantages.

Step-by-step explanation:

Pros and Cons are often used where advantages and disadvantages of certain things need to be explained. Pros and Cons are the terms derived from Latin Language which means 'for or against'.

In simple words, when we describe the advantages of certain topic, theory or concept, we are actually defining the pros of that certain thing. Similarly, when we are talking about the disadvantages of something, we are actually defining the cons of that particular thing.

Answer:

by multiplying all numbers seperatly by each other and adding those

Step-by-step explanation:

we called it the rainbow method :)

The answer is A.

-9 • -2x = 18x

-9 • -3 = 27

Therefore, it is 18x+27

Answer:

mean =median, so the data is symmetrical

Step-by-step explanation:

Given

Data set= {10,5,8,10,12,6,8,10,15,6,12,18}

Mean= Sum of data points/number of data points

        = (10+5+8+10+12+6+8+10+15+6+12+18)/12

        =10

Median= mid value

           ={5,6,6,8,8,10,10,10,12,12,15,18}

Middle values are 10 and 10

Median = 10+10/2

             = 20/2

              = 10

Mean= median so there will be no skewness and the distribution is equal !

Answer:

5.3 miles

Step-by-step explanation:

tan(62) = x / 2.8 where x = the height of the mountain

tan(62) * 2.8 = x = 5.3 miles

Using the law of tangents.

Tan(angle) = Opposite Leg / adjacent leg

Tan(68) = x / 2.8 miles

x = 2.8 x tan(68)

x = 6.93

The mountain is about 6.9 miles high.

Answer:

The percent increase of the population of chipmunks was 29%

Step-by-step explanation:

we know that

The population of 300,000 chipmunks represent the 100%

The increase of population is equal to

(387,000-300,000)=87,000 chipmunks

Using proportion find the percent increase

Let

x-----> the percent increase

300,000/100%=87,000/x

x=100*87,000/300,000

x=29%

Answer:

Step-by-step explanation:

Look at the picture.

Answer:

Step-by-step explanation:

Warning:

. You just wrote - and +, adding them both would result in a 0; (positive + negative = 0). If you haven't checked twice before asking, it is your problem. I'm going to solve for:

x(100-15x) when x = 5.

Answer:

Step By Step Explanation:

You'll need to substitute (that word is hard, it means replace though) the x, and get a proper equation (because they already gave you the x).

Look at how ugly and hard this is: x(100-15x) When x = 5.

Now it's better when replacing the x: 5(100-15×5)

Put it in a calculator if you wanted to avoid step by step work, but I'll show you how to do it step by step if you wanted.

5(100-15×5)

(5)×(100)+(5)(-75)

500-375

=125.

So, write this for your answer:

x(100-15x) = 125 Because 5(100-15×5)=125. And x = 5.

Answer:

∠4 = 50°

Step-by-step explanation:

∠1 + ∠5 = 100°, but ∠1 = ∠5 ( corresponding angles ), hence

∠1 = ∠5 = 50°

∠4 = ∠1 = 50° ( vertical angles )

Answer:

X=60% Chance

Step-by-step explanation:

This is because if you take 1 whole (100%), imagine it is at the value of 1, 4x.10=.40. 1-.40=.60 which is equal to 60%

12-5x= 7x+3

12-7x-5x= 7x-7x+3

12-12x= 3

12-12-12x= 3-12

-12x= -9

Divide by -12 for -12x and -9

-12x/-12= -9/-12

x= 9/12

Divide by 3 for 9/12

x= 3/4

Answer is x= 3/4

Step-by-step explanation:

12 - 5x = 7x + 3

Add 5x on the both sides so there would only be 12 on the right side.

So...... 12 = 12x + 3

Then minus 3 from both sides

9 = 12x

0.75 = x

:0 ITS MAGIC

:)))

Answer:

x-intercept: 4  This means that only 4 adults can come under the budjet of $20

y-intercept: 10 This means that only 10 children can come under the budjet of $20

Step-by-step explanation:

for y:

5(0) + 2y = 20

2y = 20

2y/2 = 20/2

y = 10

for x:

5x + 2(0) = 20

5x = 20

5x/5 = 20/5

x = 4

- Since lines BC, CD, and DE are all congruent, then we know that every time a line reaches either a point or an orange line, we can consider that to have a value of 1, for instance.  BD and CE, in this case, both have a value of 6, and therefore the correct answer is BD=CE.

The option third BD ≅ CE is correct because BD and CE are equal in length, so they are congruent.

Congruent geometry are those that are exactly the same size and shape. Congruent is represented by the symbol ≅

We have a line segment shown in the figure:

From the figure:

BD = 2BC

BE = 3BC

BC ≅ BD (as the BC and BD are unequal in length, so they cannot be congruent)​

BD ≅ CE (as the BD and CE are equal in length, so they are congruent)​

Thus, the option third BD ≅ CE is correct because BD and CE are equal in length, so they are congruent.

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Answer:

The value of x is [tex]24\sqrt{3}\ in[/tex]

Step-by-step explanation:

we know that

An equilateral triangle has three equal sides and three equal internal angles (each internal angle measure 60 degrees)

In this problem

see the attached figure to better understand the problem

In the right triangle ABD

[tex]sin(60\°)=BD/AB[/tex]

Solve for AB

[tex]AB=BD/sin(60\°)[/tex]

we have

[tex]BD=36\ in[/tex]

[tex]sin(60\°)=\frac{\sqrt{3}}{2}[/tex]

substitute

[tex]AB=36/(\frac{\sqrt{3}}{2})=24\sqrt{3}\ in[/tex]

Using the sine ratio, the value of x in the equilateral triangle is: 24√3 inches.

The sine ratio used to solve a right triangle is given as, sin ∅ = opposite side/hypotenuse.

Given the following:

Apply the sine ratio:

sin 60 = 36/x

√3/2 = 36/x

x = 36/√3/2

x = (36 × 2)/√3

x = 72/√3

Rationalize

x = (72)(√3) / (√3)(√3)

x = 72√3 / 3

x = 24√3

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Answer:

3.2

Step-by-step explanation:

Calculate the length using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (A(2,2) and (x₂, y₂ ) = B(5, 1)

d = [tex]\sqrt{(5-2)^2+(1-2)^2}[/tex]

  = [tex]\sqrt{3^2+(-1)^2}[/tex]

  = [tex]\sqrt{9+1}[/tex] = [tex]\sqrt{10}[/tex] ≈ 3.2 ( nearest tenth )

Answer:

3.2

Step-by-step explanation:

Distance formula = √ (x₂ - x₁ )² + (y₂ - y₁ )²

Distance = [tex]\sqrt{(5-2)}^{2}  + (1-2)^{2}[/tex]

Distance = [tex]\sqrt{ {3}^{2}  + ( - 1 )^{2}[/tex]

Distance = 3.16227766

Answer:

15.597 mm^2

Step-by-step explanation:

The formula for circumference of a circle 2πr, in which r is the circle's radius.

The formula for area of a circle π[tex]r^{2}[/tex]. This means that we can find the radius from the circle's circumference and use it to find the area.

First we have to equal 14 to 2πr because both are representations of circumference and we need to find r.

14 = 2πr

Solve:

14/2 = 2πr/2

7 = πr

7/π = πr/π

2.23 = r

Plug 2.23 into the formula for area as r and solve:

π(2.23)^2

π4.96

15.597

Answer:

The volume of the pill is [tex]V=452\ mm^{3}[/tex]

Step-by-step explanation:

Find the volume of the pill in cubic millimeters

we know that

The volume of the pill is equal to the volume of the cylinder plus the volume of a sphere (two hemisphere is equal to one sphere)

so

we have

[tex]V=\frac{4}{3}\pi r^{3}+\pi r^{2}h[/tex]

[tex]r= (18-12)/2=3\ mm\\ h=12\ mm[/tex]

assume

[tex]\pi =3.14[/tex]

substitute

[tex]V=\frac{4}{3}(3.14)(3)^{3}+(3.14)(3)^{2}(12)\\V=452\ mm^{3}[/tex]

Volume is a three-dimensional scalar quantity. The volume of the pill is 452.3893mm³.

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

The height of the cylindrical portion is 12mm and the overall height is 18mm. Therefore, the radius of the hemisphere at any one end will be half the difference between the cylindrical portion and the overall height. Thus,

The radius of the sphere, R = (18mm - 12mm)/2 = 3mm

The volume of the capsule

= Volume of cylinder +2(Volume of the hemisphere)

= (πR²h) + 2[(4/6)πR³]

= (π×3²×12) + 2[(4/6)×π×3³]

= 339.292mm³ + 113.0973mm³

= 452.3893 mm³

Hence, the volume of the pill is 452.3893mm³.

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Answer:

go on symbolab type the equation in and it gives u anwsers and work

Step-by-step explanation:

=\frac{4}{\left(x+2\right)\left(x+4\right)}

your answer is b) 3.88

Answer:

a) i) No

ii) Probability of drawing a diamond and then spade without replacement is 0.0637.

b) i) Yes

ii) Probability of drawing a diamond and then spade with replacement is 0.0625

Step-by-step explanation:

Part a) Without replacement:

i) Are these events independent?

No, because the both events are dependent. because a card taken out of the deck is not replaced back before taking out the other card so the chances of event occur change.

ii) Determine the probability of drawing a diamond and then a spade without replacement.

Probability of drawing a diamond and then spade = (Probability of drawing a diamond) * (Probability of drawing a spade)

Probability of drawing a diamond :

Total cards in deck = 52

Diamonds = 13

Probability of drawing a diamond  = 13/52

Probability of drawing a spade:

Total cards in deck after taking diamond = 52 -1 =51

Spades = 13

Probability of drawing a spade  = 13/51

Probability of drawing a diamond and then spade = 13/52 * 13/51

= 169/2652

=0.0637

So, Probability of drawing a diamond and then spade without replacement  is 0.0637

Part b) With replacements

i) Are these events independent?

Input Yes or No:

Yes, these events are independent because a card taken out of the deck is replaced back before taking out the other card so the chances of event occur doesn't change.

ii) Determine the probability of drawing a diamond and then a spade with replacement.

Probability of drawing a diamond and then spade = (Probability of drawing a diamond) * (Probability of drawing a spade)

Probability of drawing a diamond :

Total cards in deck = 52

Diamonds = 13

Probability of drawing a diamond  = 13/52

Probability of drawing a spade:

Total cards in deck after replacing diamond = 52

Spades = 13

Probability of drawing a spade  = 13/52

Probability of drawing a diamond and then spade = 13/52 * 13/52

= 169/2704

=0.0625

So, Probability of drawing a diamond and then spade with replacement is 0.0625

The first two events are not independent, with a probability P = 0.0637

The second pair of events is independent, and the probability is P = 0.0625

First, all the cards on the deck have the same probability of being randomly drawn, which will be p = 1/52.

A) Now, if Lacy first draws a diamond card, now the number of cards in the deck are less (now there are 51 cards on the deck). So the probability of drawing now a spade is larger than before. Then the first two events are not independent.

The probability of drawing a diamond card at first is:

P = 13/52 (because there are 13 diamonds and a total of 52 cards).

The probability of drawing a spade after is:

Q = (13/51)

The joint probability is the product of the individual probabilities, this will give:p = P*Q = (13/52)*(13/51) = 0.0637

B) Now we replace the first card, then the events are now independent, as the probability of drawing a spade after the first draw is not changed (because the total number of cards will be 52).

The probability of drawing a diamond is:

P = 13/52

Now we replace the diamond card drawn.

The probability of drawing a spade will be:

Q = 13/52

The joint probability is:

p = P*Q = (13/52)^2 = 0.0625

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Answer:

222- 50+1=0? 225 - 50 = 175 175+1 = 176 176+0 = 176

Answer: 49°

Step-by-step explanation:

I'm guessing you meant complement?  Complementary angles add up to 90°.  90° - 41° = 49°

Answer:

m = 1

b = -4

Step-by-step explanation:

The "slope-intercept form" of the equation for a line is often written ...

y = mx + b

The x-coefficient, m, is the slope of the line. The constant, b, is the y-intercept.

Comparing the slope-intercept form to your equation, we see that ...

m = 1

b = -4

_____

The slope is the ratio of "rise" to "run" for the graph. Here, that means the line goes through the point (0, -4), the y-intercept, and rises 1 unit for each 1 unit to the right of that point. For example, the point (4, 0) will also be on the line. (It is right 4 units and up 4 units from the y-intercept.)

The equation can be graphed by entering it into a graphing tool, or by plotting two points on the line and drawing a line through them.

X will equal 8 and y would equal 3

The solution to the system of equations -2x + 9y = 11 and -5x + 2y = -34 is found using the elimination method. The solution is x = 8 and y = 3.

The system of equations provided appears to be:

To solve this system, we can use the method of substitution or elimination. In this case, we'll use the elimination method. First, we want to manipulate the equations so that when we add them together, one of the variables gets eliminated.

Let's multiply the first equation by 5 and the second equation by 2:

Now, we subtract the second equation from the first:

-10x + 45y - (-10x + 4y) = 55 - (-68)

Which simplifies to:

41y = 123

Divide both sides by 41 to find the value of y:

y = 123 / 41 = 3

Now, substitute y = 3 into one of the original equations to solve for x. We'll use the first equation:

-2x + 9(3) = 11

-2x + 27 = 11

-2x = 11 - 27

-2x = -16

Divide both sides by -2:

x = -16 / -2 = 8

The solutions to the system of equations are x = 8 and y = 3.

Answer:

The Answer is A

Step-by-step explanation:

The mean or average is highly sensitive to outliers - and is one reason why the median is a more reliable statistic.

Answer:

see explanation

Step-by-step explanation:

The n th term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 10 and d = - 3, hence

[tex]a_{n}[/tex] = 10 - 3(n - 1) = 10 - 3n + 3 = - 3n + 13, so

[tex]a_{n}[/tex] = - 3n + 13 ← n th term formula