Cost ($)
Rocko paid $12.50 for 25 game tickets.
Louisa paid $17.50 for 35 game tickets. What
is the constant of proportionality?

As per the concept of combination method, there are 19,600 different ways in which the prizes can be awarded.

To solve this problem, we can use a combination formula. A combination is a selection of objects without regard to order. In other words, it doesn't matter which order the winning tickets are selected in - we just want to know how many different combinations of three tickets can be selected from fifty.

The combination formula is ⁿCₓ, where n is the total number of objects to choose from, and x is the number of objects to be chosen. In this case, n = 50 (the total number of tickets), and r = 3 (the number of winning tickets).

So, we can calculate the number of ways the prizes can be awarded using the following formula:

⁵⁰C₃ = 50! / (3! * (50-3)!)

Simplifying this equation, we get:

⁵⁰C₃ = (504948) / (321)

⁵⁰C₃ = 19,600

To know more about combination here

https://brainly.com/question/28998705

#SPJ4

We can write {x} as follows -

{x} = (4/3) - (c/3)

An function in mathematics defines a relationship between one variable (the independent variable, x)  and another variable (the dependent variable, y). Example -

y = f{x} = ax + b

Given is a equation as -

3x + c = 4

The given equation is -

3x + c = 4

3x = 4 - c

x = (4 - c)/3

x = (4/3) - (c/3)

Therefore, we can write {x} as follows -

{x} = (4/3) - (c/3).

To solve more questions on functions, visit the link below -

brainly.com/question/26182329

#SPJ1

The correct option H0: µD ≥ 0,HA: µD < 0, is used to determine whether the first population's mean is lower than the second population's mean, a set of hypotheses.

Paired testing, commonly referred to as auditing, is a practical and easy technique to determine whether and how discrimination is present.

Thus, µD ≥ 0,HA: µD < 0, is used to determine whether the first population's mean is lower than the second population's mean, a set of hypotheses.

To know more about the matched-paired sampling, here

https://brainly.com/question/13777653

#SPJ4

The water gauge pressure at the house will be 9.63×10⁵ N/m².

Firstly we will be calculating the total height which will comprise of height from tank to house and elevated height. The formula for total height will be -

Total height = 5 + 110 sin 58°

Keep the value of sin 58° in formula and performing multiplication followed by addition

Total height = 5 + 110×0.848

Total height = 5 + 93.28

Total height = 98.28 meters

Now, calculating the water gauge pressure at house. The formula to be used is -

P = ρ×g×h, where P is pressure, ρ is density of water, g refers to acceleration due to gravity and h represents total height. We are aware that density of water is 1000 kg/m³ and accelerate due to gravity is 9.8 m/s².

Keep the values in formula to find the gauge pressure.

P = 1000 × 9.8 × 98.28

Performing multiplication

P = 963,144 N/m² or 9.63×10⁵ N/m²

Hence, the water gauge pressure at the house will be 9.63×10⁵ N/m².

The complete question is -

A house at the bottom of a hill is fed by a full tank of water 5m deep and connected to the house by a pipe that is 110m long at an angle of 58 degrees from the horizontal. Determine the water gauge pressure at the house.

Learn more about gauge pressure calculations -

https://brainly.com/question/17003910

#SPJ4

Answer:

The sum of the first 47 terms of the given series = 6016

Step-by-step explanation:

Given the sequence

13, 18, 23, ...

An arithmetic sequence has a constant difference 'd' and is defined by

\(a_n=a_1+\left(n-1\right)d\)

\(18-13=5,\:\quad \:23-18=5\)

As the difference between all the adjacent terms is the same.

so

\(d=5\)

\(a_1=13\)

Arithmetic sequence sum formula

\(n\left(a_1+\frac{d\left(n-1\right)}{2}\right)\)

Put the values

\(d=5\)

\(a_1=13\)

\(n=47\)

\(=47\left(13+\frac{5\left(47-1\right)}{2}\right)\)

\(=47\left(13+\frac{5\left(47-1\right)}{2}\right)\)

\(=47\left(13+115\right)\)

\(=47\cdot \:128\)

\(=6016\)

Thus, the sum of the first 47 terms of the given series = 6016

m∠C > m∠A > m∠B is correct regarding the angles of the triangle ABC.

What is the angle of the triangle?

While the exterior angles of a triangle are equal to the sum of the two interior angles that are not adjacent to it, the interior angles of a triangle always add up to 180°.

Here, we have

In Δ ABC, the side lengths of triangle ABC are written in terms of the variable p, where p ≥ 3.

AB=4p-1 , AC=p+4 , BC=3p

where p+4 < 3p        [as p≥3]

3p < 4p-1          [as p≥3]

⇒  4p-1> 3p > p+4

⇒AB > BC > AC

Angle opposite to AB, BC, and AC is m∠C,m∠A, and m∠B.

m∠C > m∠B > m∠A    [∵Angle opposite to greater side is greater]

Hence, mC > mA > m∠B is correct regarding the angles of the triangle ABC.

To learn more about the angles of the triangle from the given link

https://brainly.com/question/20126678

#SPJ13

Answer:

i think 28cm is the answer.

The correct function that gives the right syntax for the given data analysis is; =RIGHT(B3,5)

Data cleaning is defined as the process of fixing or removing data that are incorrect,  incorrectly formatted, duplicate, corrupted, or even incomplete data that exists within a dataset.

Now, when we combine multiple data sources, what it means is that there could be many opportunities for the data to be duplicated or mislabeled.

Now, from the question, we can see the given data of the spreadsheet with customer names and address and as such, we can easily say that the correct syntax is =RIGHT(B3,5). This is because the RIGHT Function usually returns a set number of characters from the right side of a text string.

Read more about Data Analysis at; https://brainly.com/question/14724376

#SPJ1

Answer:

2(50)+5

"twice a number" means to multiply the number by 2 giving: 2×n or 2⋅n or 2n. Then, "five more than" means to add 5 to what follows or: 2n+5.

So if "n" is 50 it would be 2(50)+5

The inequalities that can represent this situation if m is the number of songs he can buy are:

The above given  inequality accounts for the cost of each song ($1.50) plus the $1.00 activation fee, and it need to be less than or equal to the total amount of $25 on the gift card.

So: 1.5m ≤ 25

Note that this inequality stands for the cost of each song ($1.50) multiplied by the number of songs (m), and it has to  be less than or equal to the total amount of $25 on the gift card.

Hence the options given below are correct.:

Learn more about inequalities  from

https://brainly.com/question/25275758

#SPJ1

Answer:

11,550.

Step-by-step explanation:

Since we are trying to find the number of people in the stadium, we just need to find 75% of 15,400.(The reason is because each seat is for each person)

To calculate this, you have to:

0.75 x 15,400(The percentage is converting a whole number into decimal)

11,550. (And after you solve it, here is the answer)

Hope you have a nice day!!

Answer:

11,550 people are in the stadium when 75% of the seats are occupied.

Step-by-step explanation:

To solve this, we first need to set up our equation to solve the percent.

Our equation is: \(\frac{75}{100} = \frac{x}{15400}\)

To solve, we do cross multiplication.

75*15,400=100x

Now, multiply

1,155,000=100x

Now, divide both sides by 100 to get x by itself.

1,155,000/100=100/100x

11,550= x

As such, 11,550 people are in the stadium when 75% of the seats are occupied.

6 × 3,725 is equivalent to the value of 22,350.

We have,

To find the value of 6 × 3,725, we multiply the number 6 by the number 3,725.

This can be done by adding 3,725 to itself 6 times or by adding 6 to itself 3,725 times.

However, it is more efficient to use the multiplication operation, which is a shorthand way of adding a number to itself multiple times.

Using the multiplication operation, we can write 6 × 3,725 as:

6 × 3,725 = 6 × (3,000 + 700 + 20 + 5)

= (6 × 3,000) + (6 × 700) + (6 × 20) + (6 × 5)

= 18,000 + 4,200 + 120 + 30

= 22,350

Therefore,

6 × 3,725 is equivalent to the value of 22,350.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ1

Answer:

y = 75 - 9d

Step-by-step explanation:

y = amount of $ left

An algebraic expression to represent the amount of money left over is y = 75 - 9d

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

The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol can also be used to indicate the logical syntax's order of operations and other features.

Given that You have $75 and need to buy 9 books at the bookstore and each book costs d dollars.

Let y be the amount of $ left

Therefore, the expression would be;

y = 75 - 9d

To know more about an expression follow;

brainly.com/question/19876186

#SPJ2

Answer:

1) 48

2)44

Step-by-step explanation:

Answer:  48 44 Are The Correct Answers

Step-by-step explanation:Hope This Helps

f(x) = x is a simple linear function with a slope of 1, f(x) = 3 5 6 is a constant function, f(x) = 3-x is a linear function with a negative slope of -1,  f(x) = 1 is a constant function, f(x) = 2 is a constant function

A constant function is a mathematical function whose output value is the same for every input value

From the given parameters, f(x) = x is a simple linear function with a slope of 1, this implies  that for every unit increase in x, the value of y increases by 1.

Also,  f(x) = 3 5 6 is a constant function, where the value of y is always 3 5 6, regardless of the value of x.

In the same way,  f(x) = 3-x is a linear function with a negative slope of -1, which means that for every unit increase in x, the value of y decreases by 1. The fourth function f(x) = 1 is a constant function, where the value of y is always 1, regardless of the value of x.

The domain of the fifth function is 3 0, which means that x can take any value between 3 and 0.

The sixth function f(x) = 2 is a constant function, where the value of y is always 2, regardless of the value of x.

Learn more about domain of a function on https://brainly.com/question/28599653

#SPJ1

A. The solution to the congruence 3x - 107 ≡ 0 (mod 12) is x ≡ 1 (mod 12).

B. The solution to the congruence 5x + 3 - 102 ≡ 0 (mod 7) is x ≡ 6 (mod 7).

C. The solution to the congruence 66 + 9 ≡ 0 (mod 11) is x ≡ 4 (mod 11).

To solve modulo equations or congruences, we need to find values of x that satisfy the given congruence.

A. For the congruence 3x - 107 ≡ 0 (mod 12), we want to find an x such that when 107 is subtracted from 3x, the result is divisible by 12. Adding 107 to both sides of the congruence, we get 3x ≡ 107 (mod 12). By observing the remainders of 107 when divided by 12, we see that 107 ≡ 11 (mod 12). Therefore, we can rewrite the congruence as 3x ≡ 11 (mod 12). To solve for x, we need to find a number that, when multiplied by 3, gives a remainder of 11 when divided by 12. It turns out that x ≡ 1 (mod 12) satisfies this condition.

B. In the congruence 5x + 3 - 102 ≡ 0 (mod 7), we want to find an x such that when 102 is subtracted from 5x + 3, the result is divisible by 7. Subtracting 3 from both sides of the congruence, we get 5x ≡ 99 (mod 7). Simplifying further, 99 ≡ 1 (mod 7). Hence, the congruence becomes 5x ≡ 1 (mod 7). To find x, we need to find a number that, when multiplied by 5, gives a remainder of 1 when divided by 7. It can be seen that x ≡ 6 (mod 7) satisfies this condition.

C. The congruence 66 + 9 ≡ 0 (mod 11) states that we need to find a value of x for which 66 + 9 is divisible by 11. Evaluating 66 + 9, we find that 66 + 9 ≡ 3 (mod 11). Hence, x ≡ 4 (mod 11) satisfies the given congruence.

Modulo arithmetic or congruences involve working with remainders when dividing numbers. In a congruence of the form a ≡ b (mod m), it means that a and b have the same remainder when divided by m. To solve modulo equations, we manipulate the equation to isolate x and determine the values of x that satisfy the congruence. By observing the patterns in remainders and using properties of modular arithmetic, we can find solutions to these equations.

Learn more about modulo

brainly.com/question/27976134

#SPJ11

Answer:

1.6kg

explanation:

2.4kg = 12 boxes of the soap

0.8kg = 4 boxes of the soap

1.6kg = 8 boxes of the soap

In the given scenario, we have to determine the value of c that minimizes f(c). The data points are x1, x2,....xn which are fixed and c is the only variable.Let's assume that f(c) = g(x1, x2,...,xn, c) is a function of one variable. In this case, we can find the minimum or maximum of the function by differentiating it with respect to c and equating it to zero.

Let's differentiate the function f(c) with respect to c: $f'(c) = \frac{df}{dc} = \frac{\partial g}{\partial c}$ (partial derivative of g with respect to c)Since we are interested in finding the minimum value of f(c), we have to check whether this critical point is a minimum or a maximum by analyzing the second derivative of f(c). So let's differentiate f'(c) with respect to c: $f''(c) = \frac{d^2f}{dc^2} = \frac{\partial^2g}{\partial c^2}$If $f''(c)>0$, then the critical point is a minimum, and if $f''(c)<0$, it is a maximum. If $f''(c) = 0$, then we can't say anything about the nature of the critical point.

If we are interested in finding the global minimum, we also have to check the endpoints of the interval on which c is defined.I hope that helps!

To know more about global minimum

https://brainly.com/question/31403072

#SPJ11

Answer:

3/7 (simplified)

Step-by-step explanation:

The original answer would be 6/14 because 6 out of 14 people said tennis. However, you divide both by 2 to get 3/7. The percent would be 42% if that is needed.

The probability is 7/72 that each of the final three rolls is at least as large as the roll preceding it.

Let \(N_{i}\) represent the number appearing on die when die is rolled ith time,

i=1,2,3,4

Given that \(N_{1}\)≤\(N_{2}\)≤\(N_{3}\)≤\(N_{4}\)

Each time when a die is rolled, six options are there.

Let we have four equal sets

{1,2,3,4,5,6}, now we have to select four numbers such that, exactly one number is selected from each set

Case 1: All four are same

Number of ways:⁶C₁ =6

Case 2: Three are same but one is different

Number of ways: ⁶C₁ ⁵C₁ =30

Case 3: Two are same of one kind and two are same of second kind

Number of ways: \(\frac{1}{2}\) ⁶C₁ ⁵C₁=15

Case 4: Two are same and two are different

Number of ways: ⁶C₁ ⁵C₂=60

Case 5: All four are different

Number of ways: ⁶C₄=15

Required probability:

=\(\frac{6+30+5+60+15}{6*6*6*6}\)

=\(\frac{126}{36*36}\)

=\(\frac{72}{7}\)

For further information regarding die probability, click the link below:

brainly.com/question/4407739

#SPJ4

The estimated probability that of the next 100 speeding summonses issued, there will be at least 90 convictions is about 0.9997 or 99.97%.

The conviction rate for speeding in the county is 85%, it means that out of every 100 speeding summonses issued, 85 are likely to result in convictions. Therefore, we can assume that the probability of a conviction in any given case is 0.85 or 85%.

To estimate the probability that of the next 100 speeding summonses issued, there will be at least 90 convictions, we can use the binomial distribution formula. Let X be the number of convictions out of the 100 summonses. Then,

P(X ≥ 90) = 1 - P(X < 90)
           = 1 - Σ P(X = i) for i = 0 to 89

where Σ denotes the sum from i = 0 to 89.

Using the binomial distribution formula, we can calculate the probability of getting exactly i convictions out of 100 summonses as:

P(X = i) = (100 choose i) * 0.85^i * 0.15^(100-i)

where (100 choose i) denotes the binomial coefficient, which represents the number of ways to choose i items out of 100.

Plugging this formula into the above equation and using a calculator or statistical software, we get:

P(X ≥ 90) = 1 - Σ P(X = i) for i = 0 to 89
           = 1 - 0.0003 (approx.)
           = 0.9997 (approx.)

Therefore, the estimated probability that of the next 100 speeding summonses issued, there will be at least 90 convictions is about 0.9997 or 99.97%. This suggests that it is highly likely that at least 90 out of 100 speeding summonses will result in convictions, given the high conviction rate of 85% in the county.

To estimate the probability that of the next 100 speeding summonses issued, there will be at least 90 convictions, we'll use the binomial probability formula:

P(X ≥ 90) = Σ [C(n, k) * p^k * (1-p)^(n-k)]

Here, n = 100 (number of summonses), p = 0.85 (conviction rate for speeding), and k represents the number of successful convictions (90 to 100).

Step 1: Calculate the individual probabilities for k = 90 to 100:
For each value of k from 90 to 100, compute the binomial probability using the formula. C(n, k) represents the number of combinations of choosing k convictions from n summonses.

Step 2: Sum the individual probabilities:
Add up the probabilities calculated in Step 1 to find the total probability of having at least 90 convictions out of 100 speeding summonses.

By following these steps, you can estimate the probability that of the next 100 speeding summonses issued, there will be at least 90 convictions.

Learn more about binomial at: brainly.com/question/13870395

#SPJ11

In the context of your experiment comparing the effectiveness of two treatments using a randomized block design, the following must be true:

1. The subjects are divided into two blocks based on their age: under 40 years and 40 years or older.
2. Randomization is used within each block to assign subjects to one of the two treatments. This ensures that each treatment group within a block has a random mix of subjects, reducing potential biases.
3. The purpose of blocking by age is to control for any confounding variables or potential effects that age might have on the treatment outcomes. By blocking, researchers can more accurately measure the differences between the two treatments.
4. The experiment is well-designed, which means it should minimize potential sources of error, include sufficient sample size, and ensure proper randomization and data collection.
5. To analyze the results, researchers will compare the treatment outcomes within each age block and then combine the results to get an overall measure of the effectiveness of the two treatments.

By using a randomized block design in this experiment, researchers can control for age-related factors and obtain a more accurate comparison of the treatment effectiveness.

Learn more about Random Design here:

https://brainly.com/question/17128981

#SPJ11

Step-by-step explanation:

y=5(x+1/5)² -36/5

y=5(x+1/5)² -36/5

The total number of third-class people was 709, and 402 of them survived.

In order to create a table and an appropriate graph for each question,

we need data first.

Assuming the data is about the Titanic, let's proceed with the questions.

Percentage of people survived :

To answer this question, we need to have the total number of people who were aboard the Titanic, and how many of them survived.

Let's say the total number of people was 2224, and 722 of them survived.

Using this data, we can create a table as follows:

|                       |   Survived  |   Not Survived  |   Total  ||-------------------|-------------------|----------------------|-----------||   Number of People |   722            |   1502                |   2224  ||   Percentage        |   32.46%       |   67.54%              |            ||-------------------|-------------------|----------------------|-----------|

To create an appropriate graph, we can use a pie chart as follows:

Did women have a better survival rate than men:

To answer this question, we need to have the total number of men and women who were aboard the Titanic, and how many of them survived.

Let's say the total number of women was 887, and 342 of them survived.

Also, the total number of men was 1337, and 380 of them survived.

Using this data, we can create a table as follows:

|                      |   Survived  |   Not Survived  |   Total  ||------------------|-------------------|---------------------|-----------||   Women           |   342             |   545                 |   887   ||   Men               |   380              |   957                 |   1337  ||------------------|-------------------|---------------------|-----------|

To create an appropriate graph, we can use a stacked bar plot as follows:

How does class affect the survival rate.

To answer this question, we need to have the total number of people who were aboard the Titanic, how many of them survived, and their class (first, second, or third).

Let's say the total number of first-class people was 324, and 202 of them survived.

Also, the total number of second-class people was 277, and 118 of them survived.

Finally, the total number of third-class people was 709, and 402 of them survived.

Using this data, we can create a table as follows:|                       |   Survived  |   Not Survived  |   Total  ||-------------------|-------------------|---------------------|-----------||   First-Class         |   202             |   122                  |   324   ||   Second-Class  |   118             |   159                  |   277   ||   Third-Class         |   402             |   307                  |   709   ||-------------------|-------------------|---------------------|-----------|

To create an appropriate graph, we can use a stacked bar plot, facet wrapped by class, as follows:

For similar question on total.

https://brainly.com/question/29509552

#SPJ11

Answer:

the answer is 10

Step-by-step explanation:

*please give me brainliest, i only need four more*

Answer:

-10

I did the math

(-4)-6

Answer:

AB = 11.287

sorry i probably explained it poorly but hope this helps :)

nice profile pic btw :D

Answer:

h = -8

Step-by-step explanation:

-2(3 + 7h) + 2 = 108

-2 * 3 + -2 * 7h + 2 = 108

combine like terms

-6 - 14h + 2 = 108

-4 - 14h = 108

add 4 to both sides of the equation

-4 + 4 - 14h = 108 + 4

-14h = 108 + 4

-14h = 112

divide both sides of the equation by -14

-14h/-14 = 112/-14

h = 112/-14

h = -8

Answer:

7

Step-by-step explanation:

total cost/total yards=cost per yard. $24.50/3.5=7

In order to determine the cost of 1 T-shirt, divide $12.75 by 3. The value gotten is $4.25. This is equal to the unit rate of the T-shirt.

In order to determine the cost of one T-shirt, divide the total cost of the T-shirts by the number of t-shirts.

Division is the mathematical operation that is used to determine the quotient of two or more numbers. It entails grouping a number into equal parts using another number.

Cost of one T-shirt = total cost / number of T-shirts

$12.75 / 3 = $4.25

To learn more about division, please check: https://brainly.com/question/194007

#SPJ1

The percentage of 37.5% when converted to fraction, the denominator will be 1000.

The percentage is 37.5% , to convert it to fraction we have to divide the number that is in percentage by 100.

Hence, 37.5% = 37.5 / 100

Again When we remove the decimal we get that we will divide the number again by 10.

Hence the number becomes 375 / 1000.

Therefore we have to divide it by 1000 .

By employing an unlimited series of digits following the decimal separator, the decimal system has been expanded to represent any real number in an infinite number of decimals (see decimal representation).

The decimal numerals in this context are frequently referred to as terminating decimals since they have a limited amount of non-zero digits after the decimal separator. A repeating decimal is an infinite decimal that, after a certain point, repeats the same set of digits indefinitely.

To learn more about percentage visit:

https://brainly.com/question/15272068

#SPJ4