The area of a rectangle is 72x^13y^9z^16 square yards. The length of the rectangle is 3x9y4z^5 yards. Find the simplified expression of the width of the rectangle in yards.​

Answers

Answer 1

The expression of the width of the rectangle is 2x¹²y⁸z¹¹/3.

Given that the area of a rectangle is 72x¹³y⁹z¹⁶ sq. yds and the length of the rectangle is 3x9y4z⁵, we need to find the width,

Using these expressions, we have,

Area = length × width

72x¹³y⁹z¹⁶ / 3x9y4z⁵ = width

Width = 72x¹³/3x × y⁹/9y × z¹⁶/4z⁵

Width = 24x¹²y⁸z¹¹/36 = 2x¹²y⁸z¹¹/3

Hence the expression of the width of the rectangle is 2x¹²y⁸z¹¹/3.

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Related Questions

23- Find unit vectors that satisfy the stated conditions (a) Oppositely directed to v = and half the length of v.

Answers

The final answer to this question on vector is : - (v/2)/||v/2|| = -/sqrt((v1/2)^2 + (v2/2)^2 + (v3/2)^2).

To find a unit vector that is oppositely directed to v and half the length of v, we first need to find the length of v. Let's say v = . Then, the length of v, denoted as ||v||, is given by:

||v|| = sqrt(v1^2 + v2^2 + v3^2)

Now, since we want a vector that is half the length of v, we can simply divide v by 2: v/2

However, we also want this vector to be oppositely directed to v, which means we need to change the sign of each component.

Therefore, our final answer is:
- (v/2)/||v/2|| = -/sqrt((v1/2)^2 + (v2/2)^2 + (v3/2)^2)

This is the unit vector that is oppositely directed to v and half the length of v.

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∫76 cos(29 x) cos(34 x) cos(4x) dx=

Answers

after integrating we get ∫76 cos(29 x) cos(34 x) cos(4x) dx= 1/150 [sin(75x) + 2sin(67x) + 2sin(59x)] + C

Using the identity cos(a)cos(b) = 1/2[cos(a+b) + cos(a-b)], we can rewrite the integrand as:

cos(29x)cos(34x)cos(4x) = 1/2[cos((29+34+4)x) + cos((29+34-4)x)]cos(4x)
= 1/2[cos(67x) + cos(59x)]cos(4x)

Now, using the same identity again, we can further simplify:

cos(67x)cos(4x) = 1/2[cos(71x) + cos(63x)]cos(4x)
cos(59x)cos(4x) = 1/2[cos(63x) + cos(55x)]cos(4x)

Substituting these back into the original integral, we get:

∫76 cos(29x)cos(34x)cos(4x) dx = 1/2 ∫76 [cos(71x) + cos(63x) + cos(63x) + cos(55x)]cos(4x) dx
= 1/2 ∫76 [cos(71x)cos(4x) + cos(63x)cos(4x) + cos(63x)cos(4x) + cos(55x)cos(4x)] dx

Now, using the identity ∫ cos(ax) dx = (1/a)sin(ax) + C, we can easily integrate each term:

1/2 [1/75 sin(75x) + 1/67 sin(67x) + 1/67 sin(67x) + 1/59 sin(59x)] + C

Therefore, the final answer is:

∫76 cos(29x)cos(34x)cos(4x) dx = 1/150 [sin(75x) + 2sin(67x) + 2sin(59x)] + C

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40% of a smoothie from Blender Splendor is fruit juice. There are 20 ounces in a smoothie. How many ounces of fruit juice does a smoothie have?

Answers

A 20-ounce smoothie from Blender Splendor contains 8 ounces of fruit juice.

To find out how many ounces of fruit juice are in a 20-ounce smoothie from Blender Splendor, given that 40% of the smoothie is fruit juice, follow these steps:

1. Convert the percentage to a decimal: 40% = 0.40
2. Multiply the total ounces of the smoothie by the decimal: 20 ounces * 0.40 = 8 ounces

Your answer: A 20-ounce smoothie from Blender Splendor contains 8 ounces of fruit juice.

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C C


A student believes that a certain number cube is unfair and is more likely to land with a six facing up. The student rolls


the number cube 45 times and the cube lands with a six facing up 12 times. Assuming the conditions for inference


have been met, what is the 99% confidence interval for the true proportion of times the number cube would land with a


six facing up?


0. 27 2. 58


0. 221-0. 27)


45


0. 7342. 33


0. 731-0. 73)


45


0. 27 2. 33


0. 271 -0. 20)


45


0. 73 +2. 58


0. 73(10. 73)


45


Mix


Save and Exit

Answers

we can say with 99% confidence that the true proportion of times the number cube would land with a six facing up is between 0.05 and 0.49.

Find out the confidence interval for the true proportion of time?

To find the 99% confidence interval for the true proportion of times the number cube would land with a six facing up, we can use the formula:

CI = p ± zsqrt(p(1-p)/n)

where:

CI is the confidence interval

p is the sample proportion (number of times the cube landed with a six facing up divided by the total number of rolls)

z is the z-score corresponding to the desired confidence level (99% in this case)

n is the sample size (45 in this case)

First, let's calculate the sample proportion:

p = 12/45 = 0.27

Next, we need to find the z-score corresponding to a 99% confidence level. Using a standard normal distribution table or calculator, we find that the z-score is 2.58.

Now we can plug in the values and calculate the confidence interval:

CI = 0.27 ± 2.58sqrt(0.27(1-0.27)/45)

CI = 0.27 ± 0.22

CI = (0.05, 0.49)

The number cube would land with a six facing up between 0.05 and 0.49.

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In circle m, secants pamd and pbc are drawn from point p such that mbc = 100 and mcd = 62°. which
of the following is the measure of p?
(1) 19
(2) 22
(3) 34
(4) 40

Answers

In the circle, the measure of p is 34 (option 3).

First, we know that angle MBC is an exterior angle to triangle PBC. Therefore, the measure of angle PBC is equal to the sum of angles MBC and MCB, which is 100 + (1/2)(angle MCP) = 100 + (1/2)(angle MQP).

Similarly, angle MCD is an exterior angle to triangle PCD. Therefore, the measure of angle PDC is equal to the sum of angles MCD and MDC, which is 62 + (1/2)(angle MPQ) = 62 + (1/2)(angle MQP).

Since angle PBC and angle PDC are both subtended by the same arc BC, they are equal. Therefore, we can set the expressions for these angles equal to each other and solve for angle MQP:

100 + (1/2)(angle MQP) = 62 + (1/2)(angle MQP)

38 = (1/2)(angle MQP)

angle MQP = 76 degrees

Finally, we can use the fact that angles MPQ and MQP form a linear pair, so they add up to 180 degrees. Therefore, angle MPQ is 180 - 76 = 104 degrees.

Since angle MPQ is an exterior angle to triangle PAB, we can use the exterior angle theorem to find the measure of angle P, as follows:

angle P = angle MPQ + angle PAB = 104 + 100 = 204 degrees

However, angles in a circle cannot be greater than 180 degrees, so we need to subtract 180 from angle P to get the actual measure of angle P:

angle P = 214 - 180 = 34 degrees

Therefore, the answer is option (3).

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Think about your daily experience how is probability utilized in news papers, television, shows, and radio programs that interest you? What are your general impression of the ways in which probability is used in the print media and entertainment industry

Answers

Probability is frequently used in news reports to convey the possibility of an event occurring.

Generally, in my opinion, probability is used well in the media space.

How Probability is Utilized?

Probability is frequently used in news reporting to demonstrate the likelihood of an event occurring. A news story, for example, might mention that there is a 50% chance of rain tomorrow. Similarly, sports writers may use probability to forecast the outcome of games and goals to be scored.

Overall, I feel probability is utilized fairly responsibly in the media and entertainment industries, with a focus on informing or entertaining audiences rather than misleading them. However, in some cases, such as political polling or advertising, the use of probability may be incorrect or exploited to influence audiences.

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In 2003 the social security tax rate was 6. 2% and the maximum taxable income was $87,000. 0. If Linda earned $54,122, how much did she contribute to social security?

Answers

Linda contributed $3,355.56 to social security in 2003.

The Social Security tax is a payroll tax that is deducted from employees' paychecks to help fund the Social Security program, which provides retirement, disability, and survivor benefits to eligible individuals.

The Social Security tax rate is typically 6.2% for employees and employers, and the maximum amount of taxable earnings is determined each year by the Social Security Administration (SSA).

In 2003, the maximum taxable earnings was $87,000. This means that any earnings above $87,000 were not subject to Social Security taxes.

To calculate Linda's contribution to social security in 2003, we will use the given social security tax rate of 6.2% and her income of $54,122.

Convert the tax rate percentage to a decimal by dividing by 100.
6.2% / 100 = 0.062

Multiply Linda's income by the decimal tax rate.
$54,122 * 0.062 = $3,355.56

Linda contributed $3,355.56 to social security in 2003.

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Mr. Smiths algebra class is inquiring about slopes of lines. The class was asked to graph the total cost, c, of buying h hotdog that cost 75 cent each. The class was asked to describe the slope between any two points on the graph. Which statement below is always a correct answer about the slope between any two points on this graph?

1)the same positive value
2)the same negative value
3) zero
4) a positive value, but the values vary

Answers

The slope of the graph is the same positive value that is 0.75.

Hence the correct option is (1).

We know that the equation of a straight line with slope 'm' and y intercept 'c' is given by,

y = mx + c

Here the model equation

c = 0.75h, where c is the total cost to buy hotdogs

h is the number of hotdogs bought

And 0.75 is the price of one hotdog

Now we can clearly say that c = 0.75h will make a straight line coordinate plane.

Now comparing the equation with slope intercept equation of straight line we get,

m = 0.75 and c = 0

So the slope of the line represented by model equation = 0.75 which is a positive number.

y intercept  = 0.

We know that the slope of one particular straight line on cartesian plane is unique.

So, the slope of the graph is the same positive value.

Hence the correct option is (1).

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What fraction of 2.4 litres is 400 ml?​

Answers


2.4 litres is equal to 2.4 x 1000= 2400 millilitres. (Get it to the same unit.)

400/2400
Simplify: 4/24
Simplify: 1/6

Answer: D, 1/6 (i think)

The fraction is 1/6. Option D

How to determine the fraction

First, we need to know the conversion factor the parameters.

Then, we have that';

1 liter = 1000 milliliter

10 milliliters (ml) = 1 centiliter (cl)

10 centiliters =  1 deciliter (dl) = 100 milliliters

1 liter =  1000 milliliters

1 milliliter =  1 cubic centimeter

1 liter =  1000 cubic centimeters

Then, we can say that;

If 1 liter = 1000ml

Then 2 4/8 = 400ml

2.4 liters is equal to 2.4 x 1000= 2400 milliliters.

400/2400

Simplify the fraction;

4/24

Divide the values, we get;

1/6

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Which functions are not linear? select three such functions.

a. = 2 b. = 5 ―2 c. ―3+ 2= 4

d. = 32 +1 e. = ―5―2 f. = 3

Answers

The three functions that are not linear are b., c., and d. because they include a constant that shifts the graph, both addition and subtraction of constants, and an exponent, respectively.

A linear function is a function where the rate of change between the independent variable (x) and the dependent variable (y) is constant. In other words, if you were to graph a linear function, it would form a straight line.

Looking at the given functions, we can determine which ones are not linear.

Function b. is not linear because it includes a constant (-2) which would cause the graph to shift downwards. The graph of a linear function cannot shift upwards or downwards, it can only shift left or right.

Function c. is not linear because it includes both addition and subtraction of constants. This means that the rate of change is not constant and the graph would not form a straight line.

Function d. is not linear because it includes an exponent (2) which causes the rate of change to increase. Linear functions have a constant rate of change, so the inclusion of an exponent would cause the graph to form a curve, not a straight line.

Functions a., e., and f. are all linear because they have a constant rate of change and do not include any non-linear elements like exponents or constants that would shift the graph.

So, b., c., and d are not linear.

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Morgan takes a train from London to Bewford and then another train to Agon.
The tree diagram shows the probabilities of Morgan's trains being late or not late.
to Bewford
to Agon
Late
0.24
Late
0.35
0.76
Not late
Late
0.24
0.65
Not late
0.76
Not
late
Morgan will not catch the train to Agon if the train to Bewford is late and the train to Agon is not late.
Work out the probability that Morgan will catch the train to Agon.
Give your answer as a decimal.

Answers

The probability that Morgan will catch the train to Agon is 0.578.

To catch the train to Agon, one of the following conditions must be met:

The train to Bewford is not late and the train to Agon is not late.

The train to Bewford is not late and the train to Agon is late.

The probability of the first condition is:

(0.76) x (0.65) = 0.494

The probability of the second condition is:

(0.24) x (0.35) = 0.084

Therefore, the probability that Morgan will catch the train to Agon is:

0.494 + 0.084 = 0.578 (to three decimal places)

So the probability that Morgan will catch the train to Agon is 0.578.

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Need help with these questions!! Person who answers will be marked brainliest

Answers

Answer:

1.5 for both

Step-by-step explanation:

Taking each number and multiplying it by 1.5 will get you the dilated coordinates

From a Word Problem
Jack has $10 in his lunch account. He plans to
spend $2 a week on snacks. How long until
Jack's lunch account reaches zero?

Answers

Answer:

Sure, here's the solution to the word problem:

Jack has $10 in his lunch account and plans to spend $2 a week on snacks. To find out how long it will take his lunch account to reach zero, we can divide the total amount of money in his account by the amount he spends each week.

```

$10 / $2 = 5 weeks

```

Therefore, it will take Jack 5 weeks to spend all of the money in his lunch account.

Here's another way to solve the problem:

We can also set up an equation to represent the situation. Let x be the number of weeks it takes Jack's lunch account to reach zero. We know that Jack starts with $10 and spends $2 each week, so we can write the equation:

```

$10 - $2x = 0

```

Solving for x, we get:

```

x = 5

```

Therefore, it will take Jack 5 weeks to spend all of the money in his lunch account.

Answer:

in 5 weeks he will have 0$ in his account

Step-by-step explanation:

(5)/(6)a+4(1)/(4)a
pls help i need it to finish

Answers

The required answer to the algebraic fraction [ {(5)/(6)}a + 4 {(1)/(4)}a ] is [ {(11)/(6)}a ] .

We can simplify this algebraic fraction problem by simple rule of fraction addition and with application LCM rule as,

{(5)/(6)}a + 4 {(1)/(4)}a

= {(5)/(6)}a + (1)a

= [{ (5)+ (6) }/(6)]a

= {(11)/(6)}a

The LCM (or, Least Common Multiple) rule is used for the two algebraic fraction here as the value that is divisible by the two given numbers in the denominator of the algebraic fractions. Then by rule, the numerators are multiplied by the factor of LCM of the denominator and then the numerators are added.

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In circle P, if mQR = 80 , and m QRT = 39 , find each measure

Answers

In circle P, if m(QR) = 80 , and m(QRT) = 39 , m(QPR) = 39 and m(PT) = 78

Based on the information given, we know that:

- m(QR) = 80 (this is the measure of arc QR)
- m(QRT) = 39 (this is the measure of angle QRT)

To find the other measures, we can use the following formulas:

- The measure of a central angle is equal to the measure of its intercepted arc
- The measure of an inscribed angle is half the measure of its intercepted arc

Using these formulas, we can find the measure of angle QPR and the measure of arc PT as follows:

- m(QPR) = m(QRT) = 39 (since angle QRT and angle QPR intercept the same arc QR)
- m(PT) = 2 * m(QRT) = 78 (since angle QRT and angle PQT intercept the same arc PT, and the measure of an inscribed angle is half the measure of its intercepted arc)

So the final answers are:

- m(QR) = 80
- m(QRT) = 39
- m(QPR) = 39
- m(PT) = 78

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Which of the following statements is correct about the value of: 13 + √50

A. 13 + √50 is an irrational number

B. 13 + √50 is an integer

C. 13 + √50 is a rational number

D. 13 + √50 is neither a rational or irrational number

Answers

The statement that is correct about the value of: 13 + √50 is A. 13 + √50 is an irrational number

The statement that is correct about the value of: 13 + √50

From the question, we have the following parameters that can be used in our computation:

13 + √50

When the above expression is evaluated we have

13 + √50 = 20.0710678119

The above result (20.0710678119) is an irrational number

This is because the number 20.0710678119 cannot be expressed as a ratio of two integers

Hence, the statement that is correct about the value of: 13 + √50 is A. 13 + √50 is an irrational number

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Tyler rides his bike from his house to his cousin's house. He bikes a total of 1.8 kilometers to get there and back. What is the distance, in meters, between Tyler's house and his cousin's house?

Answers

Answer:

Step-by-step explanation:

Total of rides from Tyler's house to Cousin's house and Cousin's house to Tyler's house = 1.8km = 1800m

So, the distance from Tyler's house to his cousin's house is

= 1800m ÷ 2 = 900m

The S&P stock Index fell by an average of 8% each day. Write an equation or function that models the data

Answers

If the S&P stock index fell by an average of 8% each day, we can model the

data using exponential decay. Let P represent the initial value of the S&P

stock index and t represent the number of days. Then, the equation for the

S&P stock index after t days is:

[tex]P(t) = P * (0.92)^t[/tex]

Here, 0.92 represents the daily decay factor, which is derived from

subtracting 8% from 100% (100% - 8% = 92%). As each day passes, the

value of P(t) decreases exponentially by a factor of 0.92.

It's important to note that this equation assumes that the S&P stock index

falls by exactly 8% each day, which may not be a realistic scenario in real

life. Additionally, this equation only models the decay of the S&P stock

index value and does not take into account any external factors that may

affect its value.

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Nora signed up for a streaming music service that costs $5 per month. The service allows Nora to listen to unlimited music, but if she wants to download songs for offline listening, the service charges $0. 75 per song. How much total money would Nora have to pay in a month in which she downloaded 30 songs? How much would she have to pay if she downloaded ss songs?



cost of 30 songs:


cost of s songs:

Answers

Nora would have to pay a total of $5 + $0.75s in a month when she downloaded "s" songs.

The cost for downloading 30 songs would be:

$0.75 per song × 30 songs = $22.50

Therefore, Nora would have to pay a total of $5 + $22.50 = $27.50 in a month when she downloaded 30 songs.

If she downloaded "s" songs, the cost would be:

$0.75 per song × s songs = $0.75s

Therefore, Nora would have to pay a total of $5 + $0.75s in a month when she downloaded "s" songs.

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Build a power series, write the summation notation for the series, find the interval of convergence for,
f(x) = (x^4)/ (1-3x)

Answers

This limit exists and is less than 1 when |x| < 1/3. Therefore, the interval of convergence for the power series is (-1/3, 1/3).

To build a power series for f(x), we can use the geometric series formula:

1 / (1 - r) = ∑(n=0 to infinity) r^n

where r is a constant with |r| < 1. In this case, we have:

f(x) = x^4 / (1 - 3x) = x^4 * 1 / (1 - 3x)

So, we can let r = 3x and use the formula:

1 / (1 - 3x) = ∑(n=0 to infinity) (3x)^n

Multiplying both sides by x^4, we get:

f(x) = x^4 * ∑(n=0 to infinity) (3x)^n

Now we can write the summation notation for the power series as:

f(x) = ∑(n=0 to infinity) (3^n * x^(n+4))

To find the interval of convergence, we can use the ratio test:

lim(n->∞) |(3^(n+1) * x^(n+5)) / (3^n * x^(n+4))| = lim(n->∞) |3x|

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a bank account earns 0.06% annual interest compounded monthly the bank B of the account after T months started with the $250 is given by the equation B =250(1.06)^t. How long will it take to triple the balance of the account?

Answers

It will take about 387.3 months (or about 32.3 years) to triple the balance of the account.

What is Compound Interest ?

Compound interest refers to the process of earning interest on both the initial principal amount as well as any accumulated interest from previous periods. In other words, it is the interest that is earned on the interest that has been accumulated over time.

We can use the formula for compound interest to solve this problem.

Where:

A = the final amount

P = the initial amount

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time (in years)

In this problem, we have:

P = $250

r = 0.06% = 0.0006 (as a decimal)

n = 12 (since the interest is compounded monthly)

A = 3P = $750

Substituting these values into the formula, we get:

750 = 250[tex](1 + 0.0006/12) ^{12t}[/tex]

Dividing both sides by 250, we get:

3 =[tex](1 + 0.0006/12) ^{12t}[/tex]

Taking the natural logarithm of both sides, we get:

㏒(3) = 12t ㏒(1 + 0.0006÷12)

Solving for t, we get:

t = ㏒(3)/(12 ㏒(1 + 0.0006÷12))

Plugging this into a calculator, we get:

t ≈ 387.3 months

Therefore, it will take about 387.3 months (or about 32.3 years) to triple the balance of the account.

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The coach of the soccer team is asked to select 5 students to represent the team in the Homecoming Parade. The coach decides to randomly select 5 students out of the 38 members of the team.


a. What is the population for this problem?


b. What is the sample for this problem?


c. Suggest a method for selecting the random sample of 5 students

Answers

The population is 38, and the sample is 5 students.

find out the population, sample, and method for selection?

. The population for this problem is the entire soccer team, which consists of 38 members.

b. The sample for this problem is the group of 5 students who are selected by the coach to represent the team in the Homecoming Parade.

c. One method for selecting a random sample of 5 students from the team is to use a random number generator to choose 5 numbers between 1 and 38, representing the 38 team members. The coach can then select the students who correspond to the chosen numbers. Another method is to write the names of all 38 team members on identical slips of paper, place the slips in a container, mix them up, and then randomly select 5 slips to determine the students who will participate in the parade. It is important to ensure that the selection method is truly random to avoid any bias or non-representativeness in the sample.

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A shipping company uses baggage tags with 3-letter city codes. The first and third letters of each code are always consonants and the middle letter is always a vowel (CVC). The English language uses 21 consonants and 5 vowels. How many different combinations of tag codes are possible? I will give brainliest to the best



(A) 105


(B)441


(C) 1,638


(D)2,205

Answers

The correct answer is (D) 2,205.

How to calculate the number of different combinations of baggage tag codes for a shipping company?

To calculate the number of different combinations of tag codes, we need to consider the possible options for each position in the code.

For the first and third positions (consonants), we have 21 options for each position since there are 21 consonants in the English language.

For the middle position (vowel), we have 5 options since there are 5 vowels in the English language.

Therefore, the total number of different combinations is calculated by multiplying the number of options for each position:

21 (consonant options) * 5 (vowel options) * 21 (consonant options) = 2,205

Therefore, the correct answer is (D) 2,205.

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21. The population of a small town is 15,000. If the population is growing
by 5% per year, how long will it take for the population to reach 25,000?

Answers

It will take the population 10.5 years to reach 25,000

How long will it take for the population to reach 25,000?

From the question, we have the following parameters that can be used in our computation:

Inital population, a = 15000

Rate of increase, r = 5%

Using the above as a guide, we have the following:

The function of the situation is

f(x) = a * (1 + r)ˣ

So, we have

f(x) = 15000 * (1 + 5%)ˣ

When it reaches 25000, we have

15000 * (1 + 5%)ˣ = 25000

Divide both sides by 15000

(1 + 5%)ˣ = 1.67

Take the logarithm of both sides

x = log(1.67)/log(1 + 5%)

Evaluate

x = 10.5

Hence, the number of years is 10.5

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trains arrive at a specified stop at 15-minute intervals starting at 7am. if a passenger arrives at the stop at a time that is uniformly distributed between 7am and 7:30am, find the probability that she waits a) less than 5 minutes for the train b) more than 10 minutes for the train

Answers

The probability of a passengers waiting at the stop less than 5 minutes and more than 10 minutes is equal to 1/6 and 2/3 respectively.

Probability that the passenger waits less than 5 minutes for the train,

Area under the probability density function (PDF) of the arrival time distribution from 7:00am to 7:05am.

Distribution is uniform,

PDF is a constant function over the interval [7:00am, 7:30am] .

With height 1 / (30 minutes - 0 minutes) = 1/30.

Area under the PDF from 7:00am to 7:05am is,

Probability of waiting less than 5 minutes

= area under PDF from 7:00am to 7:05am

= (1/30) ×(5 - 0) minutes

= 1/6

Probability that the passenger waits less than 5 minutes for the train is 1/6.

Probability that the passenger waits more than 10 minutes for the train is

= Area under the PDF from 7:00am to 7:30am -  area under the PDF from 7:00am to 7:10am.

Area under PDF from 7:00am to 7:30am

= (1/30) × (30 - 0) minutes

= 1

Area under PDF from 7:00am to 7:10am

= (1/30) × (10 - 0) minutes

= 1/3

Area under PDF from 7:10am to 7:30am

= 1 - 1/3

= 2/3

Probability of waiting more than 10 minutes

= area under PDF from 7:10am to 7:30am

= (1/30) × (30 - 10) minutes

= 2/3

Probability that the passenger waits more than 10 minutes for the train is 2/3.

Therefore, the probability of waiting less than 5 minutes and waiting more than 10 minutes is equal to 1/6 and 2/3 respectively.

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If the price of a car is $5,900 and has a down payment of 15%, with a tax rate of 8.5%, how much will the amount of the loan need to be for?

Answers

7361.73 is the amount of the loan needed

Pablo mixed
2
1
2
quarts of fruit juice with
1
gallon of seltzer. If each serving is
8
fluid ounces, how many servings did Pablo make?

A. 20
B. 26
C. 32
D. 36

Answers

The number of servings did Pablo make is (B) 26.

What is Unit conversion:

Unit conversion is the process of converting a value expressed in one unit of measurement to another unit of measurement that represents the same quantity but is expressed in a different unit.

The given quantities are in different units, so we need to convert them to a common unit to determine the number of servings. For this, we need to convert quarts and gallons to fluid ounces.

Here we have

Pablo mixed 2 1/2 quarts of fruit juice with 1 gallon of seltzer.  

Each serving is 8 fluid ounces

Let's first convert the quantities to the same units.

=> 1 gallon = 4 quarts

Total amount of liquid = 2 1/2 + 4 = 6 1/2 quarts

Now, let's find how many 8-ounce servings are in 6 1/2 quarts:

=> 1 quart = 32 fluid ounces

=> 6 1/2 quarts = 6.5 x 32 = 208 fluid ounces

Given that, 1 serving = 8 fluid ounces

Number of servings = 208/8 = 26

Therefore,

The number of servings did Pablo make is (B) 26.

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Complete Question:

Pablo mixed 2 1 /2 quarts of fruit juice with 1 gallon of seltzer. If each serving is 8 fluid ounces, how many servings did Pablo make?

A: 20    B: 26     C: 32    D: 36

The pie chart below shows the favorite hobbies of 120 children.
The number of children who prefer cycling is 12.
Three times as many prefer football than the number who prefer cycling.
How many children prefer swimming?
A. 42
B. 52
C. 58
D. 40
E. 62

Answers

Answer:

72 children prefer cycling

Step-by-step explanation:

Cycling = 12 children

Football = (12×3) = 36 children

120 - (12 + 36) = 72

Answer is A. 42

We are given the following

120 children total
12 Children who like to cycle is given
36 Children who like football = 3 x 12 = 36
30 Children who like reading = 90 degree right angle divided by 360 total degrees of pie chart = 25% of pie chart like reading. We have a total of 120 children x 25% = 30
X unknown children who like swimming.

Total children less the 3 parts of the pie we know = unknown

120 - 12 - 36 - 30 = 42 children who like swimming

Kirk pays an annual premium of $1,075 for automobile insurance, including comprehensive coverage of up to $500,000. He pays this premium for 8 years without needing to file a single claim. Then he gets into an accident during bad weather, for which no one is at fault. Kirk is not injured, but his car valued at $22,500 is totaled. His insurance company pays the claim and Kirk replaces his car. If he did not have automobile insurance, how much more would have Kirk paid for damages than what he had invested in his insurance policy?


$8,600


$13,900


$21,425


$31,100

Answers

Kirk would have paid $13,900 more for damages than what he had invested in his insurance policy if he did not have automobile insurance.

The amount that Kirk would have paid for damages than what he had invested in his insurance policy if he did not have automobile insurance can be determine as follows. Hence,

1. Calculate the total amount Kirk paid in insurance premiums over 8 years:

$1,075 * 8 = $8,600

2. Determine the total value of the car that was totaled:

$22,500

3. Subtract the total amount Kirk paid in insurance premiums from the value of the totaled car:

$22,500 - $8,600 = $13,900

Kirk would have paid $13,900 more for damages.

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5. A ramp is to be built using a 20 foot long board and an 18 foot long board. To make die stable, the builders would like to add a third board to create a right triangle. How longed that board be, to the nearest hundredth of a foot?

Answers

The length of the third board the builders will add to create a right triangle, according to the Pythagorean Theorem is about 8.72 ft

What is the Pythagorean Theorem?

Pythagorean Theorem is the relationship between the lengths of the three sides of a right triangle. The theorem states that the square of the length of the hypotenuse is equivalent to the sum of the square of the other two sides of the right triangle.

The specified dimensions of the ramp are;

Length of one side of the ramp = 20 ft

Length of the other side of the ramp = 18 ft

The shape of the triangle the builders would like to create = A right triangle

Let x represent the length of the third board, and let the 20 ft board represent the hypotenuse side. Pythagorean Theorem indicates that we get;

20² = 18² + x²

20² - 18² = x²

x² = 20² - 18² = 76

x = √(76) = 2·√(19) ≈ 8.72

The length of the third board, x ≈ 8.72 ft

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