The population of a city (in millions) at time t (in years) is P(t)=2.6 e 0.005t , where t=0 is the year 2000. When will the population double from its size at t=0 ?

Answer:

0.10

Step-by-step explanation:

The experimental likelihood of getting a 50% coupon is thus 2/20, or 0.1 to the decimal place.

The likelihood of rolling any one of the number cube's 6 equally likely results is 1/6. We must roll the number cube 20 times and tally how many times we receive a 50% discount in order to determine the experimental chance of doing so.

Assume that rolling a 1, 2, or 3 means you won't receive a coupon, a 4 means you'll receive a 25% coupon, a 5 means you'll receive a 50% coupon, and a 6 means you'll receive a 75% coupon.

The following outcomes are possible after 20 rolls of the number cube:

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Answer:

-9

Step-by-step explanation:

Plug in 15 for x in the equation

you should get (1/5*15) -12

multiply 1/5 and 15 to get 3

then 3-12=-9

therefore the answer is -9

Answer:

EX=-$1

Step-by-step explanation:

Expected Value of Probability Distribution

Assume a discrete probability distribution is

[tex]P=\{p1,p2,p3,...pn\}[/tex]

For

[tex]X=\{x1,x2,x3,...xn\}[/tex]

The expected value is

[tex]EX=\sum x_i.p_i[/tex]

We have two possible outcomes from our random experience: The sum of the die is 7 or different from 7. If it sums 7, the player wins $9, otherwise, they lose $3. Thus

[tex]x=\{9,-3\}[/tex]

We must find the probability of having a 7. Each dice can be a 1, 2, 3 ,4 , 5, or 6. The combinations to sum 7 are 1+6, 2+5, 3+4, 4+4, 5+2, and 6+1. That is 6 possibilities out of 36 in total. The probability of having a 7 is

[tex]\displaystyle p_1=\frac{6}{36}=\frac{1}{6}[/tex]

The probability of not getting 7 is the negation of the previous event

[tex]\displaystyle p_2=1-\frac{1}{6}=\frac{5}{6}[/tex]

The probability set is:

[tex]\displaystyle P=\left\{\frac{1}{6},\frac{5}{6}\right\}[/tex]

The expected value is:

[tex]\displaystyle EX=9\cdot \frac{1}{6}-3\cdot \frac{5}{6}[/tex]

[tex]\displaystyle EX=\frac{3}{2}-\frac{5}{2}=-1[/tex]

Therefore, the player can expect to lose $1

The expected value of the game "Under-or-Over-Seven" is a loss of $1, computed by considering the probabilities of winning $9 or losing $3 based on dice sums.

To compute the expected value of the game, we need to consider all possible outcomes and their associated probabilities.

1. The sum of two fair dice can range from 2 to 12.

2. The probability of each sum can be calculated by considering all possible combinations of the dice.

Here's the breakdown of the sums and their probabilities:

- Sum of 2: Probability = 1/36

- Sum of 3: Probability = 2/36

- Sum of 4: Probability = 3/36

- Sum of 5: Probability = 4/36

- Sum of 6: Probability = 5/36

- Sum of 7: Probability = 6/36

- Sum of 8: Probability = 5/36

- Sum of 9: Probability = 4/36

- Sum of 10: Probability = 3/36

- Sum of 11: Probability = 2/36

- Sum of 12: Probability = 1/36

Now, let's calculate the expected value:

[tex]\[ E(X) = (P(X=7) \times \$9) + (P(X\neq7) \times (-\$3)) \][/tex]

[tex]\[ E(X) = (\frac{6}{36} \times \$9) + (\frac{30}{36} \times (-\$3)) \][/tex]

[tex]\[ E(X) = (\frac{6}{36} \times \$9) - (\frac{30}{36} \times \$3) \][/tex]

[tex]\[ E(X) = \frac{54}{36} - \frac{90}{36} \][/tex]

[tex]\[ E(X) = \frac{-36}{36} \][/tex]

E(X) = -$1

So, the expected value of the game is a loss of $1.

Answer:

16 apples.

Step-by-step explanation:

[tex]U(x, y) = x^2y^8[/tex]

[tex]MU_x =\frac{\partial U}{\partial x} = 2xy^8\\MU_y = \frac{\partial U}{\partial x} = 8x^2y^7\\[/tex]

Price of apples, Px=$4

Price of tomatoes,  Py=$3

Ratio of their Marginal Utilities

[tex]\frac{MU_x}{MU_y} = \frac{Px}{Py}[/tex]

[tex]\frac{y}{4x} = \frac{4}{3}[/tex]

[tex]y=\frac{16x}{3}[/tex]

Since Natalie’s income is $320

320 = xPx+yPy

[tex]320=4x + 3*\frac{16x}{3} \\320= 4x+16x = 20x\\x=\frac{320}{20} = 16\\Also\\y=\frac{16x}{3}=\frac{16X16}{3}=\$85.33[/tex]

Since x=16, Natalie will consume 16 apples.

Given Natalie's budget and the prices of apples and tomatoes, plus the fact that her utility function indicates she consumes two as many tomatoes as apples, we determined that Natalie will consume up to 32 apples under these conditions.

To determine how many apples Natalie will consume, we first need to solve the utility maximization problem where she chooses 'x' and 'y' to maximize her utility subject to her budget constraint. This problem is typically solved using calculus, but here is a simplified way of solving it:

Firstly, let's consider Natalie's budget constraint. With $320, the prices of apples and tomatoes being $4 and $3 respectively, her budget constraint is $4x + $3y ≤ $320.

Due to the nature of Natalie's utility function U(x, y) = x 2y 8, it's clear that for every apple she buys, she consumes twice as many tomatoes (since y=2x). Replacing 'y' in the budget constraint yields to $4x + $3(2x) ≤ $320, or $10x ≤ $320.

x ≤ 32, that is, Natalie will consume up to 32 apples.

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Answer:

Both of them are D

Step-by-step explanation:

1ST QUESTION

D. 18

2ND QUESTION

D. Any number greater than or equal to 55

brainliest?

The plane would travel approximately 4533.33 miles in 6 hours.

To find the distance the plane would travel in 6 hours, we can use the formula:

Distance = Speed × Time

Given that the plane travels at 3400 miles in 8 hours, we can substitute the values into the formula:

Distance = 3400 × 8/6

Simplifying the expression:

Distance = 4533.33 miles

Therefore, the plane would travel approximately 4533.33 miles in 6 hours.

Answer:

THE ANSWER IS (6,-9)

Step-by-step explanation:

The solution to the equation is ( 6 , -9 )

The value of x = 6

The value of y = -9

What is an Equation?

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 first equation be represented as A

Now , the value of A is

y = x - 15   be equation (1)

Let the second equation be represented as B

Now , the value of B is

y = -2x + 3   be equation (2)

Substituting the value of equation (1) in equation (2) , we get

x - 15 = -2x + 3

On simplifying the equation , we get

Adding 2x on both sides of the equation , we get

x + 2x - 15 = 3

Adding 15 on both sides of the equation , we get

3x = 18

Divide by 3 on both sides of the equation , we get

x = 6

Therefore , the value of x is 6

Substitute the value of x in equation (1) , we get

y = x - 15

y = 6 - 15

y = -9

Therefore , the value of y is -9

Hence , the values of x and y of the equation is ( 6 , -9 )

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Answer:

0.00198

Step-by-step explanation:

The number of total ways that 5 cards can be selected from a deck of 52 cards is given as

⁵²C₅ = 2,598,960 ways.

Number of ways a flush, including straight and royal flushes, that is, five cards of the same suit can happen is given by

⁴C₁ × ¹³C₅ = 4 × 1287 = 5148

Note that of the 52 cards, each suit has 13 cards, So, ⁴C₁ represents selecting a suit out of 4 different suits and ¹³C₅ represents selecting 5 cards out of 13 cards thay a suit contains.

So, the probability of a flush

= 5148 ÷ 2,598,960 = 0.0019807923 = 0.00198 to 5 d.p

Hope this Helps!!!

The probability of  five cards of the same suit is 0.00198

Probability of any event happen is calculated by, divide favourable number of outcomes by total number of outcomes.

The number of total ways that 5 cards can be selected from a deck of 52 cards is given as

                    Total outcomes =     ⁵²C₅ = 2598960  

Number of ways a flush, including straight and royal flushes, that is, five cards of the same suit can happen is given by

         Number of favourable outcomes =       ⁴C₁ × ¹³C₅ = 4 × 1287 = 5148

 ⁴C₁ represents selecting a suit out of 4 different suits .

¹³C₅ represents selecting 5 cards out of 13 cards that a suit contains.

Therefore, the probability that a five-card poker hand contains a flush,

                              =[tex]\frac{5148}{2598960}=0.00198[/tex]

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Answer: The weekly demand equation would  be

[tex]p=-0.2m+84.8[/tex]

Step-by-step explanation:

Since we have given that

Number of units of their portable media player = 109 units per week

Cost per unit = $63.00

At unit price of $12.80, consumer are buying 360 units per week.

So, here, p = $63.00 and x = 109 units

Here, price and quantity are linearly related by

[tex]p=mx+b\\\\63=109m+b\\\\63-109m=b-----------------(1)[/tex]

If p = $12.80, x= 360

So, the equation of price would be

[tex]12.80=360m+b\\\\12.80-360m=b-------------(2)[/tex]

From eq(1) and (2), we get that

[tex]63-109m=12.80-360m\\\\63-12.80=-360m+109m\\\\50.20=-251m\\\\\dfrac{50.2}{251}=-m\\\\-0.2=m[/tex]

So, the value of b would be

[tex]63=109m+b\\\\63-109(-0.2)=b\\\\63+21.8=b\\\\84.8=b[/tex]

So, the weekly demand equation would  be

[tex]p=-0.2m+84.8[/tex]

Answer:

n= - 11/3

Step-by-step explanation:

3(n+8)=13

3n+24=13

3n=13-24

3n-11

n= - 11/3

Final answer:

To simplify √72 by removing all perfect squares, you factor 72 into 2³ × 3², then take out the square root of 4 and 9 to get 6√(2) as the simplified result.

Explanation:

To simplify the square root of 72 and remove all perfect squares from inside the square root, you first need to factor 72 into its prime factors. The prime factorization of 72 is 2³ × 3². This can be rewritten as (2² × 3²) × 2, which simplifies to (4 × 9) × 2.

Since the square root of 4 and 9 are perfect squares, you can take them out of the square root, resulting in √(4) × √(9) × √(2) = 2 × 3 × √(2) = 6√(2).

Therefore, the simplified form of √72 is 6√(2), which removes all perfect squares from inside the square root.

The question is incomplete. The complete question is as follows.

Juan, Carlos and Maria went to the museum. The entrance ticket cost $5 per person, but, as they are students, there is a discount of $1 per ticket. After, they bought: 3 combos of chicken and fries costing $4 each; 3 bottles of water costing $1 each; 3 vanilla cookies costing $1 each; How much money each student paid if they divided the costs in equal amount?

Answer: $10

Step-by-step explanation: As each students split the bill in equal parts, to find how much they spent, we can calculate how much one of the three spent.

For ticket: 5 - 1 (because of the students discount) = $4

Each combo of chicken and fries cost $4, so: combo = $4

Each bottle of water costs $1, so: water = $1

and each vanilla cookie costs $1: cookie = $1

Total spent is:

T = 4+4+1+1

T = 10

Each student spent a total of $10 for this outing.

Answer:

$2,520

Step-by-step explanation:

The simple Interest earned on an deposit, P at a rate of r% for a period of t years is calculated using the formula:

[tex]\text{ Simple Interest}=\dfrac{Principal*Time*Rate}{100}[/tex]

P=$10,500

R=6%

T=4 years

Therefore:

[tex]\text{ Simple Interest}=\dfrac{10500*4*6}{100}\\=\$2,520[/tex]

Sally will earn $2520 interest after 4 years.

Answer:

70%

Step-by-step explanation:

Answer:

Type of investigation = Experimental

Dependent variable = The reaction time of the controllers

Independent variable =  Controlled breaks

Step-by-step explanation:

A researcher is examining the effects of controlled breaks on reaction times of Air Traffic Controllers.

The controllers are randomly assigned to two groups.

Group 1 and Group 2

Group 1 has 20 controllers who spend 45 minutes on a break in a quiet room, with no talking, TV, or other electronics.

Group 2 has 20 controllers who spend their 45 minutes on a break in a common area break room where people are allowed to talk, watch TV, or use electronic devices.

After the breaks, the reaction times of controllers in the two groups were measured.

Type of investigation?

This is clearly an experimental type of investigation where the researcher performs an experiment and after that measures the results.

Type of variables involved?

In this experimental investigation, we have both dependent as well as independent variable.

The controlled break is the independent variable since it can be manipulated by the researcher.

The reaction time of the controllers is the dependent variable since it is being measured and is expected to get affected when the independent variable is manipulated that is controlled breaks.

Final answer:

This is an experimental investigation where the effects of controlled breaks on reaction times of Air Traffic Controllers are examined. The independent variable is the type of break, and the dependent variable is the reaction times of the controllers.

Explanation:

The type of investigation used in this study is an experimental investigation. The independent variable in this study is the type of break given to the Air Traffic Controllers, with two levels: controlled breaks in a quiet room and breaks in a common area with allowed talking, TV, and electronic devices. The dependent variable is the reaction times of the controllers after their breaks. There are no extraneous variables mentioned in the given information.

The correct answer is 96 degrees for the circle.

Equation

Since angles KJL and KML are opposite angles of a cyclic quadrilateral, their sum is 180 degrees.

(7x - 8) + (3x + 8) = 180° is the equation.

10x = 172

x = 17.2

Therefore, angle KJL measures 7(17.2) - 8 = 115.4 degrees, and angle KML measures 3(17.2) + 8 = 52.6 degrees.

The measure of arc KL is equal to the sum of the measures of angles KJL and KML:

115.4 + 52.6 = 168

So the measure of arc KL is 168 degrees.

Therefore, the correct answer is 96 degrees, which matches one of the answer choices.

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Answer:

473 milliliters in 1 pint

Step-by-step explanation:

divide 946 by 2

Answer:

There are 473 milliliters in 1 pint so 5 pints would be 2,365

Step-by-step explanation:

Answer:

9x - 3y = -12

-9x +5y = -1

2y = -13

y = -13/2

-3x - 13/2 = 8/2

-3x = 21/2

-6x = 21

x = -21/6 = -7/2

(-7/2, -13/2)

Answer: Obviously chose Pizza Hut, as no other pizza place can out pizza the hut.

Answer:

I devour the souls of the innocent

Step-by-step explanation:

XD what question is this???

Final answer:

The expected value of the sample mean weight of watermelons, given a population mean of 21.3 pounds, is also 21.3 pounds.

Explanation:

Expected Value of the Sample Mean Weight of Watermelons

If we have a population in which the average watermelon weighs 21.3 pounds with a standard deviation of 1.07 pounds, and we consider the sample mean weight of 90 watermelons, we can calculate the expected value of this sample mean. In statistics, the expected value of the sample mean is the same as the population mean when the samples are drawn from the population independently. Thus, the expected value of the sample mean weight for the watermelons is 21.3 pounds.

Answer:

0.0498 = 4.98%

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given time interval.

Inquiries arrive at a record message device according to a Poisson process of rate 15 inquiries per minute.

Each minute has 60 seconds.

So a rate of 1 inquire each 4 seconds.

The probability that it takes more than 12 seconds for the first inquiry to arrive is approximately

Mean of 1 inquire each 4 seconds, so for 12 seconds [tex]\mu = \frac{12}{4} = 3[/tex]

This probability is P(X = 0).

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-3}*3^{0}}{(0)!} = 0.0498[/tex]

The probability that it takes more than 12 seconds for the first inquiry to arrive in a Poisson process at a rate of 15 inquiries per minute is calculated using the exponential distribution formula: e^{-15*0.2}.

The student is asking for the probability that it takes more than 12 seconds for the first inquiry to arrive at a record message device, with inquiries arriving according to a Poisson process with a rate of 15 inquiries per minute. Since the time between arrivals in a Poisson process follows an exponential distribution, we can calculate this probability using the exponential distribution's formula.

The mean interval between inquiries is the inverse of the rate, which for 15 inquiries per minute is 1/15 minute per inquiry, or 4 seconds per inquiry. To convert minutes to seconds, multiply by 60. Therefore, the average interval is 4 seconds.

The exponential distribution gives us the probability that the time until the first event (inquiry) exceeds a certain amount, t, which is P(T > t) = e-λ*t, where λ is the rate and T is the time. In this case, t is 12 seconds or 0.2 minutes. Therefore, the probability (P) that the time is more than 12 seconds is: P(T > 0.2) = e-15*0.2.

Answer:

The ratio is 2:1

Step-by-step explanation:

This is since there are 2 times the amount of hands as there are phones

Answer: the volume is: 280.8

Step-by-step explanation:

volume= length x width x height

Answer:

140.4 cm^3

Step-by-step explanation:

The formula for calculating volume of a triangular prism : 1/2 × h × l × b

1/2 × 4 × 9 × 7.2 = 140.4 cm^3

Answer:

(1,1) is a solution of the system.

Step-by-step explanation:

Let's solve the system.

y = 2x - 1

5x - 4y = 1

In the first equation, y is already separated as a function of x. So we replace in the second equation;

5x - 4(2x - 1) = 1

5x - 8x + 4 = 1

4 - 1 = 8x - 5x

x = 1

y = 2x - 1 = 2(1) - 1 = 1

(1,1) is a solution of the system.

Answer:

Radius = 6.5cm

Diameter = 13cm (given)

Step-by-step explanation:

The diameter is the length of one side of a circle to the other. It's already given in the diagram as 13cm.

The radius is half of the diameter. 13 divided by 2 is 6.5cm.

The correct answer are as follows

Radius = 6.5 cm

Diameter = 13 cm

So , The diameter is 13cm

and The radius is 1/2 x diameter = 1/2 x13 = 6.5cm

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Step-by-step explanation:

The Length ,

L

=

284

f

t

.

Explanation:

Given:

Rectangle

Area,

A

=

8804

f

t

2

let W bet he width of the rectangle

L be the length of the rectangle

L

=

10

W

−

26

E

q

u

a

t

i

o

n

1

substitute to

e

q

u

a

t

i

o

n

2

A

=

(

L

)

(

W

)

e

q

u

a

t

i

o

n

2

A

=

(

10

W

−

26

)

(

W

)

8804

=

(

10

W

−

26

)

(

W

)

factor

8804

=

2

(

5

W

−

13

)

(

W

)

divide both sides by 2

4402

=

(

5

W

−

13

)

(

W

)

4402

=

5

W

2

−

13

W

transposing 4402 to the right side of the equation

0

=

5

W

2

−

13

W

−

4402

by quadratic formula

W

=

−

(

−

13

)

+

√

(

−

13

)

2

−

4

(

5

)

(

−

4402

)

2

(

5

)

W

=

[

13

+

√

169

+

88040

]

10

W

=

13

+

(

√

88209

)

10

W

=

13

+

297

10

W

=

310

10

W

=

31

ft

Thus ,

L

=

10

W

−

26

=

10

(

31

)

−

26

L

=

284

f

t

.

answer

W

=

−

(

−

13

)

−

√

−

(

−

13

2

)

−

4

(

5

)

(

−

4402

)

2

(

5

)

this is discarded since this will yield a negative

To find the length of the rectangle, set up an equation using the given information. Solve the quadratic equation to find the width and substitute it back to find the length.

To find the length of the rectangle, we can set up an equation using the given information. Let's assume the width of the rectangle is 'w' meters. According to the problem, the length of the rectangle is 10 times its width minus 11 meters, so it can be represented as 10w - 11 meters. The area of the rectangle is given as 9888 square meters. We know that the formula for the area of a rectangle is length times width, so we can write the equation as:

w (10w - 11) = 9888

Expanding the equation and rearranging terms, we get:

10w^2 - 11w - 9888 = 0

Now, we can solve this quadratic equation for 'w' and find the width of the rectangle. Once we have the width, we can substitute it back into the expression for the length (10w - 11) to find the length of the rectangle.

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Answer:

68% of the diameters are between 7.06 cm and 7.78 cm

Step-by-step explanation:

Mean diameter = μ = 7.42

Standard Deviation = σ = 0.36

We have to find what percentage of diameters will be between 7.06 cm and 7.78 cm. According to the empirical rule, for a bell-shaped data:

So, we first need to find how many standard deviations away are the given two data points. This can be done by converting them to z-score. A z score tells us that how far is a data value from the mean. The formula to calculate the z-score is:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

x = 7.06 converted to z score will be:

[tex]z=\frac{7.06-7.42}{0.36}=-1[/tex]

x = 7.78 converted to z score will be:

[tex]z=\frac{7.78-7.42}{0.36}=1[/tex]

This means the two given values are 1 standard deviation away from the mean and we have to find what percentage of values are within 1 standard deviation of the mean.

From the first listed point of empirical formula, we can say that 68% of the data values lie within 1 standard deviation of the mean. Therefore, 68% of the diameters are between 7.06 cm and 7.78 cm

Approximately 68% of the apples have diameters between 7.06cm and 7.78cm.

To determine the percentage of apples with diameters between 7.06cm and 7.78cm, we can use the empirical rule which is based on the standard deviation. According to the empirical rule, approximately 68% of the apples will fall within one standard deviation of the mean, which in this case is between 7.42 - 0.36 and 7.42 + 0.36. In other words, between 7.06cm and 7.78cm. Therefore, approximately 68% of the apples have diameters between 7.06cm and 7.78cm.

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Approximately 215 samples are needed for a 95% confidence interval estimating the mean breakdown voltage with a 2 kV width and a 1 kV margin of error, assuming the range is 40 to 70 kV.

To determine the required sample size for estimating the mean breakdown voltage with a 95% confidence interval (CI) width of 2 kV and an estimated margin of error (m) of 1 kV, you can use the formula:

[tex]\[ n = \left(\frac{{Z^2 \cdot \sigma^2}}{{m^2}}\right) \][/tex]

Where:

- n is the required sample size,

- Z is the Z-score corresponding to the desired confidence level (for 95%, it's approximately 1.96),

- [tex]\( \sigma \)[/tex] is the estimated standard deviation of the population.

Since you mentioned the investigator believes breakdown voltage is between 40 and 70, assuming a uniform distribution, you might consider using [tex]\( \sigma = \frac{{\text{{range}}}}{4} \)[/tex] as an approximation. Therefore,

[tex]\[ \sigma = \frac{{70 - 40}}{4} = 7.5 \][/tex]

Now plug these values into the formula:

[tex]\[ n = \left(\frac{{1.96^2 \cdot 7.5^2}}{{1^2}}\right) \][/tex]

Let's calculate the required sample size n:

[tex]\[ n = \frac{{(1.96)^2 \cdot (7.5)^2}}{{1^2}} \]\[ n = \frac{{3.841 \cdot 56.25}}{{1}} \]\[ n \approx \frac{{214.6}}{{1}} \]\[ n \approx 214.6 \][/tex]

So, the required sample size for the 95% confidence interval to have a width of 2 kV (with a margin of error of 1 kV) is approximately 215.

Therefore, the investigator would need a sample size of about 215 to estimate the mean breakdown voltage with the desired level of confidence and precision.

Using a system of equations, it was determined there were 336 bottles worth 5 cents each and 82 bottles worth 10 cents each, summing up to a total of $25.

The local organization collected 418 returnable bottles and cans, some worth 5 cents each and the rest worth 10 cents each. The total value was $25.00. We need to find out how many bottles were worth 5 cents and how many were worth 10 cents.

We can set up two equations to solve this problem using algebra. Let's assume that the number of 5-cent bottles is x and the number of 10-cent bottles is y.

The first equation will represent the total number of bottles: x + y = 418.

The second equation will represent the total value of these bottles: 0.05x + 0.10y = 25.

To solve this system of equations, we can multiply the second equation by 100 to eliminate the decimals and then apply the method of substitution or elimination to find the values of x and y.

Rewrite the second equation without decimals: 5x + 10y = 2500.

Multiply the first equation by 5: 5x + 5y = 2090.

Subtract the modified first equation from the second equation: 5y = 410.

Divide both sides by 5 to find y: y = 82.

Substitute y = 82 into the first equation and solve for x: x = 418 - 82 = 336.

Therefore, there were 336 bottles or cans worth 5 cents each and 82 bottles or cans worth 10 cents each.