some friends decided to equally split the cost of gas on their trip. the expression 3g4 represents how much money each person had to pay in dollars for g gallons of gas. what does the expression 3g in the numerator represent?

There are 1078 different combinational methods to choose five baseball players and four basketball players from a pool of twelve baseball players and thirteen basketball players.

5 baseball players and 4 basketball players are chosen from a pool of 12 baseball players and 13 basketball players.

This is an issue of combination.

The combination is a way of estimating an event's total outcome when the sequence of the outcomes is irrelevant.

The formula is as follows: \({}^{n}C_{r}\) = n! ÷ (r! × (n - r)!)

Where n is the total number of things and r is the number of items picked at one time.

Let us first compute 5 baseball players from a total of 12 baseball players.

In this case, n = 12 and r = 5.

\({}^{12}C_{5}\) = 12! ÷ (5! × (12 - 5)!)

\({}^{12}C_{5}\) = 12! ÷ (5! × 7!)

The factorial of n for a number n is expressed as:

n! = n × (n-1) × (n-2) × (n-3) × .... × 2 × 1

Therefore,

\({}^{12}C_{5}\) = 12! ÷ (5! × 7!)

\({}^{12}C_{5}\) = 792

Similarly, 3 basketball players are chosen from a pool of 13 basketball players (n = 13 and r = 3).

\({}^{13}C_{3}\) = 13! ÷ (3! × (13 - 3)!)

\({}^{13}C_{3}\) = 13! ÷ (3! × 10!)

The factorial of n for a number n is expressed as:

n! = n × (n-1) × (n-2) × (n-3) × .... × 2 × 1

Therefore,

 \({}^{13}C_{3}\) = 13! ÷ (3! × 10!)

 \({}^{13}C_{3}\) = 286

As a result, the total number of methods is as follows:

\({}^{12}C_{5}\) + \({}^{13}C_{3}\) = 792 + 286

\({}^{12}C_{5}\) + \({}^{13}C_{3}\) = 1078

As a result, there are 1078 distinct methods.

Learn more about the permutation and combination at

https://brainly.com/question/14645584?referrer=searchResults

#SPJ4

The mean number of students with 20-20 vision in the class is 5.7 and the standard deviation is 2.027.

To get mean and standard deviation, we will model the number of students with 20-20 vision in the class as a binomial distribution.

Let us denote X as the number of students with 20-20 vision in the class.

The probability of an individual having 20-20 vision is given as p = 0.19. The number of trials is n = 30 (the number of students in the class).

The mean (μ) of the binomial distribution is given by:

μ = np = 30 * 0.19

μ = 5.7

The standard deviation (σ) of the binomial distribution is given by:

\(= \sqrt{(np(1-p)}\\= \sqrt{30 * 0.19 * (1 - 0.19)} \\= 2.027\)

Read more about mean

brainly.com/question/1136789

#SPJ4

Answer:

When you multiply both sides by a negative value you make the side that is greater have a "bigger" negative number, which actually means it is now less than the other side! This is why you must flip the sign whenever you multiply by a negative number.

Step-by-step explanation:

The number of driving lessons you need to take with a professional instructor before your parents can teach you varies depending on the regulations in your area. In some regions, a specific number of driving lessons is required by law before you can apply for your driver's license. As a result, you should check with your local Department of Motor Vehicles (DMV) or other regulatory agency to learn more about the specific requirements in your area.

In general, however, it is usually beneficial to take as many driving lessons as possible with a professional instructor. Professional driving instructors have been educated in how to teach driving skills safely and effectively. They have also assisted many other people in learning how to drive, and as a result, they have a wealth of knowledge and expertise to draw on.

The more driving lessons you take with a professional instructor, the more chances you'll have to learn and improve your driving abilities. You may be able to practice with your parents after only a few lessons, but it's generally a good idea to take as many as possible with an instructor before doing so. This will give you the best chance of success while you learn to drive safely and confidently.

To learn more about driving :

https://brainly.com/question/2619161

#SPJ11

The resulting amount after three years, starting with an initial amount of $6 that triples in value every six months, is $1,458.

If an amount of money triples in value every six months, the resulting amount after three years can be calculated by compounding the initial amount over the given time period.

Since the amount triples every six months, we can divide the three-year period into six-month intervals. Each interval will result in a tripling of the amount. Therefore, there are a total of six intervals in three years.

Let's assume the initial amount is $6. After the first six months, the amount triples to $6 x 3 = $18. After the second six months, the amount triples again to $18 x 3 = $54. This process continues for the remaining intervals.

After three years, there are a total of six intervals, and the amount at the end of each interval is three times the previous amount. Thus, the resulting amount after three years is $6 x 3 x 3 x 3 x 3 x 3 = $6 x 3^5 = $6 x 243 = $1,458.

Learn more about tripling in value here:

https://brainly.com/question/24413549

#SPJ11

for this question your answer is D

Answer:

Step-by-step explanation:

Take two points on the line:

The slope-intercept form:

Find the slope:

The y- intercept is b = 3 according to the first point.

The line is:

The minimum score needed to be in the top 5% on this standardized aptitude test is 7. The distribution of scores on a standardized aptitude test is approximately normal with a mean of and a standard deviation of. What is the minimum score needed to be in the top on this test?

In statistics, we assume that the distribution of scores on a standardized aptitude test is approximately normal with a mean of µ and a standard deviation of σ, where µ and σ are the parameters of the normal distribution. To calculate the minimum score needed to be in the top 5%, we must first determine the z-score corresponding to the top 5%.It is known that the area to the left of z is 0.95, which corresponds to the top 5%.

To find the z-score that corresponds to the 95th percentile, we can use a standard normal distribution table, such as the one found in most statistics textbooks or online. The table gives the z-score that corresponds to the given area to the left of the mean.Using the standard normal distribution table, we find that the z-score corresponding to the top 5% is approximately 1.645. This means that the score needed to be in the top 5% is 1.645 standard deviations above the mean. We can calculate this score using the formula:X = µ + zσwhere X is the score we are trying to find, µ is the mean, z is the z-score corresponding to the top 5%, and σ is the standard deviation. Substituting the values we know into this formula:X = + 1.645 × = + 6.58. Rounding to the nearest integer, we get X = 7.

To know more about standard deviation click here

brainly.com/question/29088233

#SPJ11

Answer:

y < 106

Step-by-step explanation:

In this equation, we simply add 21 to both sides, so we get y < 106.

Answer:

53 degrees

Step-by-step explanation:

because its at a right angle and measure 1 is 37 so 90-37 would equal 53

Step-by-step explanation:

because it is on a corner the hole corner = 90

1 + 2 = corner so

1+ 2 = 90

1 is 37

37 + 2 = 90

rearrange

90 - 37 = 2

so 2 = ???

U and V are continuous random variables, the probability \(p_1\) that train X arrives before train Y is \(p_1=P(U < V)=\frac{1}{2}\)

Two trains, X and Y, arrive at a station at random between 8:00 am and 8:20 am. The times of their arrival are independent.

Let U denotes the time (in minutes) train X takes to arrive at station after 8:00 am, V denotes the time (in minutes) train Y takes to arrive at station after 8:00 am.

So, U, V ~ U(0, 20) . Therefore \(\frac{U}{20},\frac{V}{20}\) ~ U (0, 1)

Since U and V are continuous random variables, the probability \(p_1\) that train X arrives before train Y is \(p_1=P(U < V)=\frac{1}{2}\)

Learn more about Random variables at:

https://brainly.com/question/17238189

#SPJ4

The given question is incomplete, complete question is:

Two trains, X and Y, arrive at a station at random between 8:00 am and 8:20 am. The times of their arrival are independent. Train X stops for 4 minutes, and train Y stops for 5 minutes.

a) Find the probability p1 that train X arrives before train Y.

Answer:

1 2/3 hours Levon studied.

Step-by-step explanation:

2/3 as long = multiply by 2 1/2 of the time.

2.5 x 2/3 = 1.66666667

Simplify:

1.66666667 = 1 2/3

Answer:

Corine= 2 1/2 hours

Levon= 1 2/3 hours

For n = 3, x = 9, and x = 2i, we can say that one of the factors is (x - 9) as well as (x - 2i).

(x - 2i) is derived from x² = -4 which is equal to (x² + 4). Therefore, the two factors are (x - 9) and (x² + 4). To get the polynomial function, let's multiply the two factors using FOIL Method.

The polynomial function of the first bullet is f(x) = x³ - 9x² + 4x - 36.

For n = 3, x = -1, and x = 4 + i, we can say that the factors are:

(x + 1) , (x - (4 + i)), and (x - (4 - i))

Note: Always remember those complex zeros like x = 4 + i come in conjugate pairs.

To solve the polynomial function, let's multiply the three factors.

The polynomial function of the second bullet is f(x) = x³ - 7x² + 9x + 17.

Because the temperature is greater, the relative humidity of the atmosphere is higher.

Water vapor is also measured by relative humidity (RH), which is stated as a percentage but RELATIVE to the air's temperature. In plenty of other terms, it is a comparison between the quantity of water vapor that is really present in the air and the maximum amount water vapor that is possible for the air at the current temperature.

By deducting the temperature just on wet-bulb thermometer from of the temperature just on dry-bulb thermometers and utilizing a relative humidity chart, one may determine the relative humidity.

To know more about relative humidity visit:

https://brainly.com/question/29654889

#SPJ4

Single Sampling Plan: AQL = 0, LTPD = 3.41, AOQ = 1.79 Double Sampling Plan: AQL = 0, LTPD = 2.72, AOQ = 1.48

The values for the ASN (Average Sample Number) curves for the given single sampling plan and double sampling plan are:

Single Sampling Plan (n=80, c=3):

ASN curve values: AQL = 0, LTPD = 3.41, AOQ = 1.79

Double Sampling Plan (n1=50, c1=1, r1=4, n2=50, c2=4, r2):

ASN curve values: AQL = 0, LTPD = 2.72, AOQ = 1.48

The ASN curves provide information about the performance of a sampling plan by plotting the average sample number (ASN) against various acceptance quality levels (AQL). The AQL represents the maximum acceptable defect rate, while the LTPD (Lot Tolerance Percent Defective) represents the maximum defect rate that the consumer is willing to tolerate.

For the single sampling plan, the values n=80 (sample size) and c=3 (acceptance number) are used to calculate the ASN curve. The AQL is 0, meaning no defects are allowed, while the LTPD is 3.41. The Average Outgoing Quality (AOQ) is 1.79, representing the average quality level of outgoing lots.

For the equally effective double sampling plan, the values n1=50, c1=1, r1=4, n2=50, c2=4, and r2 are used. The AQL and LTPD values are the same as in the single sampling plan. The AOQ is 1.48, indicating the average quality level of outgoing lots in this double sampling plan.

These ASN curve values provide insights into the expected performance of the sampling plans in terms of lot acceptance and outgoing quality.

To learn more about average  click here

brainly.com/question/30873037

#SPJ11

The average speeds are 78 km/h and 84 km/h respectively

An equation is an expression that shows the relationship between numbers and variables using mathematical operations like exponents, addition, subtraction, multiplication and division.

The equation for speed is:

Speed = distance / time

a) James drove for 1.5 hours at an average speed of x km/h and then 2.5 hours at an average speed of y km/h.

For distance 1:

x = distance 1 / 1.5

distance 1 = 1.5x

For distance 2:

y = distance 2 / 2.5

distance 2 = 2.5y

Total distance = distance 1 + distance 2

1.5x + 2.5y = 327

multiply through by 2:

3x + 5y = 654    (1)

b) Ryan drove for 4 hours at an average speed of x km/h and then 6 hours at an average speed of y km/h. He drove a total distance of 816 km

For distance 1:

x = distance 1 / 4

distance 1 = 4x

For distance 2:

y = distance 2 / 6

distance 2 = 6y

Total distance = distance 1 + distance 2

4x + 6y = 816     (2)

c) Solving equations 1 and 2 simultaneously:

x = 78; y = 84

The value of x and y are 78 and 84 respectively

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

The confidence interval and critical value methods are equivalent in providing an interval estimate, the p-value method is used for hypothesis testing and evaluates the strength of evidence against the null hypothesis.

What is the confidence interval?

A confidence interval is a range of values that is likely to contain the true value of an unknown population parameter, such as the population mean or population proportion. It is based on a sample from the population and the level of confidence chosen by the researcher.

In general, when dealing with inferences for two population proportions, the confidence interval method and the critical value method are equivalent. These two methods provide a range of plausible values (confidence interval) for the difference between two population proportions and involve the calculation of critical values to determine the margin of error.

On the other hand, the p-value method is not equivalent to the confidence interval and critical value methods. The p-value method involves calculating the probability of observing a test statistic as extreme as, or more extreme than, the one obtained from the sample data, assuming the null hypothesis is true. It is used in hypothesis testing to determine the statistical significance of the difference between two population proportions.

To summarize:

- Confidence interval method: Provides a range of plausible values for the difference between two population proportions.

- Critical value method: Uses critical values to determine the margin of error in estimating the difference between two population proportions.

- P-value method: Determines the statistical significance of the observed difference between two population proportions based on the calculated p-value.

Hence, the confidence interval and critical value methods are equivalent in providing an interval estimate, the p-value method is used for hypothesis testing and evaluates the strength of evidence against the null hypothesis.

Learn more about the confidence interval here:

https://brainly.com/question/20309162

#SPJ4

Given:

Principal (p) =$3,000

Time (T) = 48 months = 4 years

Interest rate = 4.5%

Required :

Ending balance = ?

The simple interest :

Ending balance :

Ending balance = $ 3540

The total amount to be paid at the end of the 10-year period is $24,465. The correct answer is option d. To calculate the total amount to be paid, we need to consider the compounded interest on the borrowed amount.

The nominal interest rate of 12% compounded quarterly means that interest is added to the principal four times a year. Using the formula for compound interest, we can calculate the future value of the loan. The formula is given as:

Future Value = Principal * (1 + (Nominal Interest Rate / Number of Compounding Periods))^Number of Compounding Periods * Number of Years

In this case, the principal is $7,500, the nominal interest rate is 12% (or 0.12), the number of compounding periods per year is 4 (quarterly), and the number of years is 10.

Plugging in these values into the formula, we get:

Future Value = $7,500 * (1 + (0.12 / 4))^(4 * 10) = $24,465

Therefore, the total amount to be paid at the end of the 10-year period is $24,465. The correct answer is option d.

Learn more about principal here: brainly.com/question/27870032

#SPJ11

Answer:

the graph of g(x) will be the same shape as the graph of f(x), but shifted downward by 3 units.

Step-by-step explanation:

The functions g(x) = 4(0.5)^x - 3 and f(x) = 4(0.5)^x are both exponential functions with the same base of 0.5 and the same coefficient of 4.

However, the graph of g(x) will be shifted downward by 3 units compared to the graph of f(x), because of the constant subtraction of 3 at the end of the function. This shift will occur for all values of x, meaning that the distance between the two graphs will remain constant as x changes.

In other words, the graph of g(x) will be the same shape as the graph of f(x), but shifted downward by 3 units.

\( \frac{a}{8 \sqrt{2} } = \cos(45) \)

\(a = \cos(45) \times 8 \sqrt{2} \)

\(a = \frac{1}{ \sqrt{2} } \times 8 \sqrt{2} \)

\(a = 8\)

Answer: C

Step-by-step explanation:

The latter integral is a p-series with p=2, and it is known to converge. Therefore, by comparison, the former integral must also converge.

The given integral is ∫₀¹ 6/(x+1)² dx. To determine whether it is convergent or divergent, we can use the comparison test.

First, note that for x ≥ 1, we have (x+1)^2 ≥ x^2. Hence,

6/(x+1)^2 ≤ 6/x^2.

Now, consider the integral

∫₀¹ 6/(x+1)^2 dx.

Using the comparison test, we can compare this integral with the integral

∫₀¹ 6/x^2 dx.

The latter integral is a p-series with p=2, and it is known to converge. Therefore, by comparison, the former integral must also converge.

Hence, the given integral is convergent. This means that the area under the curve of the function f(x) = 6/(x+1)² from x=0 to x=1 is finite and well-defined. Geometrically, this means that the region bounded by the x-axis, the vertical line x=0, the vertical line x=1, and the curve y=6/(x+1)² has a finite area.

Learn more about integral here:

 https://brainly.com/question/31109342

#SPJ11

The water pipe sometimes bursts in winter because of the flowing water getting transformed into freezing water due to drop in temperature and the volume increases creating more pressure on the wall pipes.

Bursting of Water Pipes During a Very Cold Winter

The straightforward explanation is that during very cold winters, as water freezes into ice, it expands, causing solid ice to fill a larger volume than the liquid that was previously flowing through the pipes.

As we know that, the pressure P increases with increase in volume, V, the increased volume of frozen water leads to increase in the pressure inside the pipe.

The pressure that the ice builds up inside the pipes could rupture the pipe walls.

Learn more about pressure here:

https://brainly.com/question/356585

#SPJ4

Answer:

55degrees

Step-by-step explanation:

Let the other angles of the triangle are x, x degrees. Since the sum of angles in a  triangle is 180degrees, hence;

<A + <B+ <C = 180

x + 70 + x = 180

2x+70 = 180

2x = 180 - 70

2x = 110

x = 110/2

x = 55

SInce <A is equal to x, hence <A is 55degrees

C)The greatest number is 8.2 × 10-3. It is 2,000 times greater than the smallest number.

In scientific notation, a number is written as the product of a number between 1 and 10 and a power of 10. The power of 10 tells us how many places to move the decimal point to the right (if the exponent is positive) or to the left (if the exponent is negative).

In this case, 8.2 × 10-3 means 8.2 × (10^-3) = 0.0082, 5.2 × 10-6 means 5.2 × (10^-6) = 0.0000052 and 4.1 × 10-6 means 4.1 × (10^-6) = 0.0000041.

To compare the numbers, we can compare the coefficient or the number in front of the 10 power. We can see that 8.2 is greater than 5.2 and 4.1. To check how many times greater the smallest number is, we can use the following formula: (greatest number / smallest number) = (8.2 / 0.0000041) = 2,000

Therefore, the greatest number is 8.2 × 10-3 and it is 2,000 times greater than the smallest number.

For more questions like Scientific notation click the link below:

https://brainly.com/question/21289208

#SPJ4

]

Answer:

13 months

Step-by-step explanation:

Total spent: $440

Sign-up fee: $50 (a one-time fee)

Membership fee: $30/month

\((440 - 50) \div 30 = 13 \: months\)

Dilation and rotation transformation produces shapes that are not congruent.

Rotations, reflections and translations are known as rigid transformations; this means they do not change the size or shape of a figure, they simply move it. These rigid transformations preserve congruence.

Dilation, however, are not rigid transformations, since they change the size of a shape. Dilation would not change the shape, just the size; the angle measures would be the same, and the ratio of corresponding sides would be equal to the scale factor used in the dilation. This would give us a similar, but not congruent, figure.

Learn more about Transformations at :

https://brainly.com/question/4289712

#SPJ4

Answer:

x= -5

Step-by-step explanation:

-4 (x +3) = 8

-4x - 12 = 8

-4x = 20

x= -5