a soft drink company holds a contest in which a prize may be revealed on the inside of the bottle cap. the probability that each bottle cap reveals a prize is 0.2 and winning is independent from one bottle to the next. what is the probability that a customer loses on their first two bottles and wins on their third bottle?

The dimensions that would guarantee that the garden has the greatest possible area is 190 feet on the shorter side and 380 feet on the longer side to produce an area of 72,200 square feet.

A dimensions of a rectangle is the length of each side.

Let x = length of the shorter side

y = length of the longer side

If one side of the garden is bordered by a river and so it does not need any fencing, and assume that the longer side is this side, then the perimeter that only needs to be fenced by 760 feet of fencing materials is

2x + y = 760

y = 760 - 2x

The area of the rectangular garden is the product of the shorter side and the longer side of the garden. Hence,

A = xy

A = x(760 - 2x)

A = 760x - 2x²

To obtain the largest area possible, the first derivative of the area should be equal to zero.

A(x) = 760x - 2x²

A'(x) = 0

760 - 4x = 0

Solve for x.

760 - 4x = 0

4x = 760

x = 190

length of the shorter side = 190 feet

y = 760 - 2x

y = 760 - 2(190)

y = 380

length of the longer side = 380 feet

Solve for the greatest possible area.

A = xy

A = 190 feet(380 feet)

A = 72,200 square feet

" A gardener has 760 feet of fencing to fence in a rectangular garden. One side of the garden is bordered by a river and so it does not need any fencing. What dimensions would guarantee that the garden has the greatest possible area? "

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Pythagoras's theorem - The two teachers are both seated at a distance of 15 meters from each other.

What is Pythagoras' theorem?

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic Euclidean geometry relationship between a right triangle's three sides. According to this rule, the area of the square with the hypotenuse (the side across from the right angle) is equal to the sum of the areas of the squares with the other two sides. The Pythagorean equation, which generally refers to the relationship between the lengths of the legs a, b, and the hypotenuse c, can be used to represent this theorem.

We are given,
the distance between Krysta and her math teacher to be 12 meters, and the distance between Krysta and her science teacher to be 9 meters

for simplicity, we'll let  
the distance between Krysta and her math teacher to be KM =12 meters
and the distance between krysta and her science teacher to be KS =9 meters we need to find the distance between the maths teacher and the science teacher, i.e. MS.

all three people's sitting arrangement makes a triangle, with them sitting on the vertex of it.

Using Pythagoras' theorem,

(KM)² + (KS)² = (MS)²

(12)² + (9)² = (MS)²

144 + 81 = (MS)²

225 = (MS)²

√225 = (MS)

thus, MS = 15 meters

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Answer:

$400

Step-by-step explanation:

We see that the discount price is (100-40) = 60% of the original price

If 60% corresponds to $240, than 10% corresponds to 240/6 = $40

Since the original price is 100% = 10*10%, the original price is 10* $40 = 400.

I can't make something with scratch paper right now, i hope you will be able yourself to put the above information is a table :-)

Good luck with it!

I will use the law of exponent below

⇒if you re multiplying powers of them same base, keep  one base and add the exponents mathematically we say:

[tex]x^{n} *x^{n} \\=x^{n+n}[/tex]

[tex]=m^{9+(-3)} \\=m^{9-3} \\=m^{6}[/tex]

OPTION D is the solution

1. The given sequence 28, 14 ..... will be either arithmetic or geometric sequence.

2. The common difference of the sequence 28, 14 ..... will be;

d = - 14

And, Next three terms of the arithmetic sequence are;

0, -14, -28

What is Geometric sequence?

An sequence has the ratio of every two successive terms is a constant, is called a Geometric sequence.

Given that;

The first two terms of the sequence,

28, 14 .....

Now,

Let the sequence is in arithmetic sequence, then;

28, 14 ......

The common difference of the sequence is;

d = 14 - 28

d = - 14

And, Let the sequence is in geometric sequence, then;

28, 14 ......

The common difference of the sequence is;

d = 14/28

d = 1/2

Thus, The given sequence 28, 14 ..... will be either arithmetic or geometric sequence.

2. If the given sequence is in arithmetic sequence, then;

28, 14 ......

The common difference of the sequence is;

d = 14 - 28

d = - 14

And, The nth term of the arithmetic sequence is;

⇒ [tex]a_{n} = a + (n - 1)d[/tex]

Where, 'a' is the first term and 'd' is the common difference of the sequence.

So, The 3rd term of the arithmetic sequence is,

⇒ [tex]a_{n} = a + (n - 1)d[/tex]

[tex]a_{3} = 28 + (3-1)(-14)\\ \\a_{3} = 28 - 2 * 14\\\\a_{3} = 28 - 28\\\\a_{3} = 0[/tex]

And, The 4th term of the arithmetic sequence is,

[tex]a_{4} = 28 + (4-1)(-14)\\ \\a_{4} = 28 - 3 * 14\\\\a_{4} = 28 - 42\\\\a_{4} = -14[/tex]

And,  The 5th term of the arithmetic sequence is,

[tex]a_{5} = 28 + (5-1)(-14)\\ \\a_{5} = 28 - 4 * 14\\\\a_{4} = 28 - 56\\\\a_{5} = -28[/tex]

Therefore,  Next three terms of the arithmetic sequence are;

⇒ 0, -14, -28

Thus,

1. The given sequence 28, 14 ..... will be either arithmetic or geometric sequence.

2. The common difference of the sequence 28, 14 ..... will be;

d = - 14

And, Next three terms of the arithmetic sequence are;

0, -14, -28

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The graph of the linear inequality can be seen in the image at the end.

Here we have the linear inequality:

y  ≥ 2x + 1

To graph this, we first need to graph the line.

y = 2x + 1

With a solid line, because we have the symbol ≥, which means that the points on the line are solutions.

Once we graphed that line, we look at our inequality:

y  ≥ 2x + 1

It says that y is larger than or equal to the values on the line, so once the line is graphed we need to shade all the region above that line.

The shaded region (and the line itself) represent all the solutions of the linear inequality.

And the graph can be seen below.

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Answer:

f(x)=(x-4)^2-4

The parent function (x^2) is shifted to the right 4 times (x-4) and down 4 times (-4).

Using proportions, it is found that the number 523 is 523 units from zero.

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the context of the problem using arithmetic operations such as multiplication and division with the unit rates of the measures.

One example of application is for the digit values of a number, as:

And so on...

For the number 523 given in this problem, since each unit is worth one, the number of units that it is away from zero is given by:

523/1 = 523 units.

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Answer:

4_62

Step-by-step explanation:

its is just leave me

Answer:

0.75

Step-by-step explanation:

in the pic

goodluck

The expression shows the product of the number of ladder rungs that Yan climbed is D. (Negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4)

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

We have been given that each time Yan descends 4 rungs on the ladder.

SInce, each time the number of ladder rungs that Yan climbed is negative 4, where negative sign represent descends.

Yan made eight stops with no extra steps.

-4 x 8 = -32

It can also written as; (-4) + (-4)+(-4)+(-4)+(-4)+(-4)+(-4)+(-4)

The correct answer is D. (Negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4)

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Answer:

$19.6

Step-by-step explanation:

B=20.50-0.06.x

B=20.50-0.06*15

B=20.50-0.9

B=19.6

Answer: 30

Step-by-step explanation:

Answer: 8 weeks

Step-by-step explanation:

Given the equation:

Answer:

By using commutative property, if a = b and b = c, then a = c.

Step-by-step explanation:

Answer:

translative property

Step-by-step explanation:

Answer:Tes icahd

Step-by-step explanation:

The load each should get to maximize the profit is $67,500, $78,700 and $90,000

What Is Profit?

In accounting, a profit is an income that is given to the owner throughout a successful market producing process. Profitability, which is the owner's primary interest in the income-formation process of market production, is measured by profit. There are various profit metrics that are frequently used.

Let x represent the total number of laptops and y represent the total number of desktop computers.

A laptop computer occupies 2 cubic feet, hence x laptops each use 2x cubic feet. Desktop computers take up 5 cubic feet of space, hence 5y cubic feet of room is required for 5y desktop computers.

They require 2x + 5y cubic feet in total.

Since the delivery truck's maximum capacity is 800 cubic feet,

2x + 5y <= 800.

They must load at least 300 laptops because of the demand,

hence, x >= 300

They make $225 on each laptop, which translates to $225 times as many computers. They make a profit of $280 on each desktop computer, or $280y on y desktops.

Total profit is:

P=$(225x + 280y)

Draw the inequality system (see attached diagram)

2x + 5y <= 800.

x >= 300

One of the common region's three vertices will have the most profit:

P(300,0) = 225(300) + 280(0) = $67,500

P(300,40) = 225(300) + 280(40) = $78,700

P(400,0) = 225(400) + 280(0) = $90,000

Hence, each should load $67,500, $78,700 and $90,000 on the truck to maximize profit

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The bacterial cell is 6.25 x 10 times smaller than the amoeba cell.

The length of the Bacterial cell is 4 x 10⁻⁶ meters.

The length of the Amoeba cell is 2.5 x 10⁻⁴ meters.

The length L of the bacterial cell can be written as,

L = 0.000004 meters.

Also, the length L' of the amoeba cell can be written as,

L' = 0.00025 meters.

Let us say that the bacterial cell is N times smaller than the amoeba cell.

So. we can write,

Length of bacterial cell x N = length of amoeba cell.

LN = L'

0.000004(N) = 0.00025

N = 0.00025/0.000004

N = 62.5  

So, now we can say that the length of the bacterial cell is 62.5 times smaller than he amoeba cell.

As we have to state our answer in scientific notation,

We can write 62.5 as 6.25 x 10.

Now the number of significant figure is has are three.

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Answer: Yes they do.

Answer:

B

Step-by-step explanation:

it shows that it doesn't go anywhere in the interval of 2 and 5, other ones would be wrong bcs it's either go up or down

Answer:

a) (in order) {-1, 0, 1, 2, 3}
b) {-1, 0, 1, 2, 3}

Step-by-step explanation:

Answer: 56.25 = u

Step-by-step explanation:

1) Multiply 3 on both sides to leave u by itself

18.75 = u/3

18.75*3 = u

56.25 = u

A. A short word problem about a purchase made to illustrate the equation is that John bought six pens and bought books for $18. The total amount is $72. Find the cost of each pen.

B. The cost of each pen is $9

C. The variable is x.

A. The problem is that John bought six pens and bought books for $18. The

B. The equation to illustrate this will be:

6x + 18 = 72

Collect like terms

6x = 72 - 18

6x = 54

Divide

x = 54 / 6.

x = $9

The cost of each pen is $9.

C. The variable is x = 9. This is the cost of the pen.

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The constant of proportionality in the equation:

P = 0.45*n

Is k = 0.45, so we can conclude that Julie is correct.

A proportional relationship between two variables x and y is written as:

y = k*x

Where k is the constant of proportionality.

In this case, we have the variables P and n, and the proportional relationship is:

P = 0.45*n

So we can see that the value of the constant of proportionality is k = 0.45, so yes, Julie is correct.

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The size of the population of mosquito follows an exponential model.

the size of the population in 10 days is 1370

The size of the population in 10 days is 1370

The given parameters are:

p(0) = 574

p'(0)= 50

An exponential function is represented as:

p(t) =p(0) * e^ rt

So, we have:

p(t)=574*e^rt

Differentiate

p'(t)=574*r*e^rt

Substitute 0 for t

50=574 r

Divide both sides by 574

r=0.087

The function becomes

p(t)= 574*e^rt

   = 574*e^0.087 t

In 10 days, t = 10.

So, we have:

p(10)=574*e^0.87

Solve

p(0)=1370

Hence, the size of the population in 10 days is 1370

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The height of an "angry bird" shot into the sky as a function of time (seconds) is h = 8.65 ft.

The height of the bird is given by the following equation

h(t)= -0.25t2 + 1.9t + 17

t= 1

   = -0.25 + 1.9 + 17

   = -8.35 + 17

h   = 8.65 ft.

The following are the three equations:

-First equation of motion: v = u + at

-Second equation of motion: s = u t + 1/2 at2

Third equation of motion: v2 = u2 + 2as

t is the time, in seconds.

h(t) is the height, in feet, which is dependent of the time.

h(t) is height in feet and t is time in seconds

then h = 8.65 ft.

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Answer:

d

Step-by-step explanation:

1 = 1 cup

1/2 can be 2/4

2/4+1/4=3/4

1+3/4 = 1 3/4