1. Billy's mother started a college fund on Billy's 8th birthday. She
deposited $8,200 into a savings account that yields an interest rate of
0.21% compounded annually. How much money will the savings account
be worth when Billy turns 18 years old?

9/10 mile = 5 min

9/10 ÷ 5 mile = 1 min

9/10 × 1/5 mile = 1 min

9/50 mile = 1 min

(a) The expected length of the queue, not including the vehicle being served, is 0.625 vehicles.

(b) The probability that there are no more than 5 cars at the gate, including the vehicle being served, is approximately 0.0176.

(c) The average waiting time of a vehicle at the ticket gate is 1.5 minutes or 0.025 hours.

(a) To find the expected length of the queue at the ticket gate, we need to calculate the expected number of vehicles waiting in the queue at any given time. This can be found by using the Little's Law, which states that the expected number of customers in a stable system is equal to the arrival rate multiplied by the average time spent in the system.

In this case, the arrival rate is 25 vehicles per hour, and the average time spent in the system is the time it takes to buy the tickets, which is 1.5 minutes or 0.025 hours. Therefore, the expected number of vehicles waiting in the queue is

E[N] = λW = 25 x 0.025 = 0.625 vehicles

So the expected length of the queue, not including the vehicle being served, is 0.625 vehicles.

(b) To find the probability that there are no more than 5 cars at the gate, including the vehicle being served, we need to use the Poisson distribution with a mean of 25 vehicles per hour. Let X be the number of vehicles arriving in an hour, then X Poisson(25).

P(X ≤ 5) = ∑ P(X = k) for k = 0 to 5

= ∑ (e^(-λ) × λ^k / k!) for k = 0 to 5

= e^(-25) × (25^0 / 0!) + e^(-25) × (25^1 / 1!) + ... + e^(-25) × (25^5 / 5!)

Using a calculator or software, this probability is found to be approximately 0.0176.

(c) The average waiting time of a vehicle can be found by dividing the expected number of vehicles waiting in the queue by the arrival rate. From part (a), we know that the expected number of vehicles waiting in the queue is 0.625 vehicles. The arrival rate is 25 vehicles per hour. Therefore, the average waiting time of a vehicle is

W = E[N] / λ = 0.625 / 25 = 0.025 hours or 1.5 minutes

So the average waiting time for a vehicle at the ticket gate is 1.5 minutes.

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Answer:

1. x=1

2. x=-1

3. No solution

4. x=2

5. x= -6

Step-by-step explanation:

Answer:

88 i think so

Step-by-step explanation:

Answer:

n= 250

Step-by-step explanation:

simplify both sides of the equation then isolate the variable

Answer:

n=250

Step-by-step explanation:

Answer:

The answer is 4/3 or 1.33 square units.

Step-by-step explanation:

Length = 1 + 7/9 = 16/9 units.

Width = 3/4 units.

Since area of rectangle = Length * Width

Area = 16/9 * 3/4 = 4/3 square units.

Answer:

  a)  an = 12 -2(n -1)

  b)  an = 25 -5(n -1)

Step-by-step explanation:

The n-th term of an arithmetic sequence is given by ...

  an = a1 +d(n -1) . . . . . first term a1, common difference d

__

The first term is a1 = 12; the common difference is d = 10 -12 = -2.

The n-th term is ...

  an = 12 -2(n -1)

__

The first term is a1 = 25; the common difference is d = 20 -25 = -5. The n-th term is ...

  an = 25 -5(n -1)

Answer:

c must be more than -5

Step-by-step explanation:

-4 x -5 =20

20-1=19

Answer:

1325

Step-by-step explanation:

6 percent sales tax is 6 cents for every dollar. you do 1250 times 0.06 is 75. it is $75 is tax.

A 99% confidence interval for the average number of free throws in practice is; CI = (211.25, 238.75)

A confidence interval is defined as the mean of your estimate plus and minus the variation in that estimate. Thus, the formula for confidence interval is;

CI = x' ± z(s/√n)

where;

x' is sample mean

s is standard deviation

n is sample size

z is z-score at confidence level

Now, z-score at confidence level of 99% is; z = 2.576

We are given;

x' = 225

Sample size; n = 43

Standard deviation; s = 35

Thus;

CI = 225 ± 2.576(35/√43)

CI = 225 ± 13.75

CI = (225 - 13.75), (225 + 13.75)

CI = (211.25, 238.75)

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The answer is x = 12.

The probability of one microbial spore surviving in 10x containers processed is given by the formula:1/10x. The question below asks for a process that reduces cell numbers by 12 decimal reductions (a 12d process) applied to a raw material that contains 1,000,000 spores per container would reduce microbial numbers to 10-x per container. x is then found by solving the equation `10-x = 1/10¹²`.Here's how to solve the equation:First, the fraction 1/10¹² is simplified.10¹²=10x10x=10¹²log(10x)=log(10¹²)x=log(10¹²)/log(10)x=12

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The student covers a total distance of 22.05 kilometers in a week's time, walking between the park and the house each day.

To find the total distance covered by the student in a week's time, we need to calculate the distance covered in one round trip (from the house to the park and back) and then multiply it by the number of round trips in a week.

Given that the difference between the park and house is 1 kilometer and 575 meters, we can convert it to a total distance of 1.575 kilometers.

In a round trip, the student covers twice the distance between the park and the house, which is 1.575 kilometers * 2 = 3.15 kilometers.

Now, we need to determine how many round trips the student makes in a week. Let's assume the student makes one round trip each day.

Since there are 7 days in a week, the total distance covered by the student in a week's time is 3.15 kilometers * 7 = 22.05 kilometers.

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The sum of the two digits of Joey's age the next time his age is a multiple of Zoe's age is of 11, and this measure was found using a system of equations.

The variables for the system of equations in this problem are given as follows:

Joey is one year older than Chloe, hence:

x = y + 1.

Zoe is exactly one year old, hence:

z = 1.

The difference between the ages of Chloe's and Zoe's have 9 factors. Numbers with nine factors have the following format:

x² x y² , with different x and y.

These numbers have to be different of 1, due to Zoe's age, hence the smallest number is given as follows:

2² x 3² = 4 x 9 = 36.

Since the difference is of 36 years old, so the ages are as follows:

The next time this will happen is in 36 years, hence Joey's age will be of:

36 + 38 = 74 years old.

The sum of the digits will be of:

7 + 4 = 11.

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Heyyyyyyyy how u doing I. Doing good how abt yo self

Range of a function are the output values of the function:

since the domain is (-3, 0, 4), then we have to substite x with this values:

f(x)=2(-3)-4

f(x)=-6-4

f(x)=-10

f(x)=2(0)-4

f(x)=-4

f(x)=2(4)-4

f(x)=4

Range of the function is (-10, -4, 4)

Answer:

There are 2,500 misquitos after 3 days and it takes 158 days to reach 80,000 mosquitos.

Answer:

20 miles $80

Step-by-step explanation:

20 miles

P%5Bc%5D%2820%29=20%2B3%2820%29=20%2B60=80

$80

Answer:

M=Main buses

C=Country buses

Step-by-step explanation:

so the charges from Main are $40 fee, then additional $2 for every mile you drive it for, so M = 40 + 2m

if your mileage is 20miles, when 2*20 is the charge

if your mileage is 50miles, when 2*50 is the charge

if your mileage is 1000miles, when 2*1000 is the charge

if your mileage is "m" miles, when 2*m is the charge

and County charges are $20 fee, then additional $3 for every mile... .so then C = 20 + 3m

if your mileage is 20miles, when 3*20 is the charge

if your mileage is 50miles, when 3*50 is the charge

if your mileage is 1000miles, when 3*1000 is the charge

if your mileage is "m" miles, when 3*m is the charge

so, their total charge is M and C respectively

when are the charges equal? well, when M = C

or

40 + 2m = 20 + 3m

solve for "m", to see at how many miles that happens

what will the charge be? plug that value for "m" on either, to get the charge

The smaller the p-value, the stronger the evidence against the Null Hypothesis is because a small p-value suggests that the null hypothesis should be rejected.

The p-value is the probability that the observed data occurred purely by chance if the null hypothesis is true, and it is a measure of the strength of the evidence against the null hypothesis.

When p is small, it implies that the possibility of obtaining data as extreme or more extreme than that observed if the null hypothesis is true is very low. This low probability indicates that the null hypothesis is unlikely to be true, and hence, the alternative hypothesis is more likely to be true.

So, when we have a small p-value, we reject the null hypothesis and accept the alternative hypothesis. On the other hand, if the p-value is large, the data do not provide sufficient evidence to reject the null hypothesis.

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Answer:

Step-by-step explanation:

Given the explicit function as

f(n) = 15n+4

The first term of the sequence is at when n= 1

f(1) = 15(1)+4

f(1) = 19

a = 19

Common difference d = f(2)-f(1)

f(2) = 15(2)+4

f(2) = 34

d = 34-19

d = 15

Sum of nth term of an AP = n/2{2a+(n-1)d}

S20 = 20/2{2(19)+(20-1)15)

S20 = 10(38+19(15))

S20 = 10(38+285)

S20 = 10(323)

S20 = 3230.

Sum of the 20th term is 3230

For the explicit function

f(n) = 4n+15

f(1) = 4(1)+15

f(1) = 19

a = 19

Common difference d = f(2)-f(1)

f(2) = 4(2)+15

f(2) = 23

d = 23-19

d = 4

Sum of nth term of an AP = n/2{2a+(n-1)d}

S20 = 20/2{2(19)+(20-1)4)

S20 = 10(38+19(4))

S20 = 10(38+76)

S20 = 10(114)

S20 = 1140

Sum of the 20th terms is 1140

the probability of randomly selecting the correct unscrambling would be 1/n!. As the length of the word increases, the probability of randomly selecting the correct unscrambling becomes increasingly small due to the exponential growth of possible arrangements.

The probability of coming up with the correct unscrambling through random letter selection depends on the specific word being unscrambled and the number of possible permutations. In general, the probability can be quite low due to the large number of possible combinations.

To calculate the probability, you would need to know the total number of possible letter arrangements and the number of arrangements that result in the correct unscrambling. Let's assume we have a word with n letters. The total number of possible arrangements is n!, which represents n factorial (the product of all positive integers from 1 to n).

The number of arrangements that result in the correct unscrambling depends on the specific word and the length of the word. For example, if the word has 4 letters, there are 24 possible arrangements (4!). However, only one of those arrangements is the correct unscrambling.

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A trinomial is a polynomial with three terms that has a leading coefficient of 3 and a constant term of -5 is

3m²+m-5

Here the degree of the trinomial is 2, so the leading coefficient is the coefficient of the term with m², which is 3.

The constant term is the term without a variable, which is -5

To find the coefficient of middle term of the trinomial, formula is:

coefficient of middle term =

(sum of the coefficients of the first and last terms)

                                    2

The sum of the coefficients of the first and last terms is 3 - 5 = -2.

Dividing by 2, we get -1 as the coefficient of the middle term.

Putting all of this together, we can write the trinomial as:                     3m² +m - 5

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Answer:

This should help.

Step-by-step explanation:

The attached image will help.

Rounding up to the nearest unit, it would take Calvin approximately 27 months to pay off his credit card with a monthly payment of $165.

To determine how long it would take Calvin to pay off his credit card, we need to consider the monthly payment amount and the interest rate. Let's calculate the time it would take for two different monthly payment amounts: $220 and $165.

a. Monthly payment of $220:

Let's assume the initial balance on Calvin's credit card is $3,000, and the annual interest rate is 4 percent. To calculate the monthly interest rate, we divide the annual interest rate by 12 (number of months in a year):

Monthly interest rate = 4% / 12 = 0.3333%

Now, we can calculate the time it would take to pay off the credit card using the monthly payment of $220 and the monthly interest rate. We'll use a formula for the number of months required to pay off a loan with fixed monthly payments:

n = -(log(1 - (r * P) / A) / log(1 + r))

Where:

n = number of months

r = monthly interest rate (as a decimal)

P = initial balance

A = monthly payment

Plugging in the values:

n = -(log(1 - (0.003333 * 3000) / 220) / log(1 + 0.003333))

Using a calculator, we can find:

n ≈ 15.34

Rounding up to the nearest unit, it would take Calvin approximately 16 months to pay off his credit card with a monthly payment of $220.

b. Monthly payment of $165:

We can repeat the same calculation using a monthly payment of $165:

n = -(log(1 - (0.003333 * 3000) / 165) / log(1 + 0.003333))

Using a calculator, we find:

n ≈ 26.39

Please note that these calculations assume that Calvin does not make any additional charges on his credit card during the repayment period. Additionally, the interest rate and the balance are assumed to remain constant. In practice, these factors may vary and could affect the actual time required to pay off the credit card balance.

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The problem requires merging two binary trees by summing up the values of overlapping nodes. A recursive solution is used to traverse the trees and merge them.

rees.

Here's a Python implementation of the solution:

```
class TreeNode:
   def __init__(self, val=0, left=None, right=None):
       self.val = val
       self.left = left
       self.right = right

def mergeTrees(root1, root2):
   if not root1:
       return root2
   if not root2:
       return root1
   merged_node = TreeNode(root1.val + root2.val)
   merged_node.left = mergeTrees(root1.left, root2.left)
   merged_node.right = mergeTrees(root1.right, root2.right)
   return merged_node
```

The solution uses a recursive approach to merge the two trees. At each recursive call, we check if either of the roots is null. If one of them is null, we return the other root as it is.

If both roots are not null, we create a new node with the sum of their values. We then recursively call the function to merge the left subtrees and right subtrees of both roots. We set the left and right children of the merged node to the result of the recursive calls.

Finally, we return the merged node.

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Answer:

230,300 different selections.

Step-by-step explanation:

If the order does not matter, the number of possible different selections is determined as the combination of choosing four numbers out of 50:

\(n=\frac{50!}{(50-4)!4!}\\\\n=\frac{50*49*48*47}{4*3*2*1} \\\\n=230,300\ combinations\)

There are 230,300 possible different selections.

Answer:

1000

Step-by-step explanation:

The volume of the rectangular building is 2,731,050 feet³ depending on the given height, base and width.

The volume of the building will be calculated by the formula -

Volume = length × breadth × height

Thus, keeping the value of each component of building in the formula to find the volume of the building.

Volume of building = 255 × 255 × 42

Performing multiplication on Right Hand Side of the equation to find the value of volume

Volume of building = 2,731,050 feet³

Therefore, the volume of the building is 2,731,050 feet³.

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