An experiment involves rolling two dice simultaneously. The following table shows the possible outcomes using the format of (die 1,die 2).


1 2 3 4 5 6

1 (1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

2 (2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

3 (3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

4 (4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

5 (5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

6 (6,1) (6,2) (6,3) (6,4) (6,5) (6,6)


What is the probability of rolling two numbers with a sum that is less than 7?

Answer:

The answer is actually 31.6 m (3 s.f.). The correct process will be use the sine rule to find out BC and CD. Then find out the length of AC by adding AB (which is 5.8 m) and BC (16.9 m after working out). Then work out the angle of CAD, which will be 46 degrees. Then use the cosine rule on triangle ACD to dine out AD.

Step-by-step explanation:

pls subs to my yt

For any integer m, m² is always congruent to either 0, 1, or 4 modulo 5. Therefore, m² is always of the form 5k, 5k+1, or 5k+4 for some integer k.

The statement is true, and it is known as the Law of Quadratic Reciprocity.

For any integer m, m² is always congruent to either 0, 1, or 4 modulo 5.

That is, m² is always of the form 5k, 5k+1, or 5k+4 for some integer k.

This can be proven using the fact that every integer can be written in one of the forms 5k, 5k+1, 5k+2, 5k+3, or 5k+4 for some integer k.

Squaring each of these forms modulo 5 yields:

(5k)² = 25k² ≡ 0 (mod 5)

(5k+1)² = 25k² + 10k + 1 ≡ 1 (mod 5)

(5k+2)² = 25k² + 20k + 4 ≡ 4 (mod 5)

(5k+3)² = 25k² + 30k + 9 ≡ 4 (mod 5)

(5k+4)² = 25k² + 40k + 16 ≡ 1 (mod 5)

m² is always 0, 1, or 4 modulo 5. So, m² is always of the form 5k, 5k+1, or 5k+4.

To practice more questions about integers:

https://brainly.com/question/929808

#SPJ11

The zeros of the polynomial 54x³ + 99x² + 15x - 18 are -3/2, 2/3 and 1/3 while the factorization is 3(3x - 1)(x + 2)(2x + 3)

Zeros of a polynomial can be defined as the points where the polynomial becomes zero as a whole. A polynomial having value zero (0) is called zero polynomial. The degree of a polynomial is the highest power of the variable x.

For a polynomial, there could be some values of the variable for which the polynomial will be zero. These values are called zeros of a polynomial. Sometimes, they are also referred to as roots of the polynomials. In general, we find the zeros of quadratic equations, to get the solutions for the given equation.

The zeros of the polynomial f(x) = 54x³ + 99x² +15x - 18 are -3/2, 2/3 and 1/3 respectively.

b.

Factorization of the polynomial 54x³ + 99x² + 15x - 18 is 3(3x - 1)(x + 2)(2x + 3)

Learn more on zeros of a polynomial here;

https://brainly.com/question/29415775

#SPJ1

Option C is correct

The given logarithmic equation is:

f(x) = log(x + 1) - 4

For a logarithmic equation of the form:

f(x) = log(a + b) - c

the y-intercept = -c

Comparing the two equations above:

The y-intercept = -4

Taking note of the point above, the logarithmic function f(x) = log(x + 1) - 4 is plotted below

Based on the information given, we can assume that "x" represents the price of sandwiches, and "demand" refers to the quantity of sandwiches that consumers are willing and able to buy at that particular price. The term "market" refers to the overall demand for sandwiches in the entire market, rather than just one individual consumer.

If x = 1, we can look at the table to see that the quantity demanded is 6 sandwiches. We can use this information to calculate the slope of the market demand curve, which represents the relationship between the price of sandwiches and the quantity demanded by all consumers in the market.

To calculate the slope, we need to find two points on the demand curve. Let's use the points (1,6) and (2,4), since they are the closest to x=1. We can use the slope formula:

slope = (y2 - y1) / (x2 - x1)

slope = (4 - 6) / (2 - 1)

slope = -2

So the slope of the market demand curve when the price is on the vertical axis is -2. However, none of the answer choices given match this result.

The closest answer is (b) -1/3, but this is not correct based on the calculations we just did.

Therefore, the correct answer cannot be determined with the information given.

To learn more about “demand” refer to the https://brainly.com/question/1245771

#SPJ11

Answer:

g(t - 1) = t² - 3t + 2

Step-by-step explanation:

substitute x = t - 1 into g(x) , that is

g(t - 1)

= (t - 1)² - (t - 1) ← expand squared factor using FOIL

= t² - 2t + 1 - t + 1 ← collect like terms

= t² - 3t + 2

Pythagoras was an ancient Greek mathematician who founded the Pythagorean school of thought. The Pythagorean theorem is a fundamental concept in mathematics that is attributed to Pythagoras and his followers.

It states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. While this theorem is considered a cornerstone of mathematics today, it is important to understand that Pythagoras did not have access to the advanced mathematical tools and methods that we have today.

He had to rely on geometric constructions and reasoning to prove his theorem. Furthermore, Pythagoras believed that all numbers could be expressed as ratios of whole numbers, which is not always true in reality. Despite these limitations, the Pythagorean theorem has stood the test of time and continues to be a crucial tool in mathematics and other fields.

Learn more about theorem here:

brainly.com/question/343682

#SPJ11

Answer:

2/7  ?

Step-by-step explanation:

Because 1/4 divided by 7/8th is 1/4. Hope this works

The ratio of the weight of a bag of cat food to the weight of a bag of dog food is 5:1, or simply 5.

Let's assume the weight of a bag of cat food is represented by x pounds, and the weight of a bag of dog food is represented by y pounds.

From the given information, we have the following equations:

5x + y = 85 (equation 1)

7x + y = 105 (equation 2)

To find the ratio of the weight of a bag of cat food to the weight of a bag of dog food, we can eliminate the variable y by subtracting equation 1 from equation 2:

(7x + y) - (5x + y) = 105 - 85

2x = 20

x = 10

Substituting the value of x into equation 1, we can solve for y:

5(10) + y = 85

50 + y = 85

y = 35

Therefore, the weight of a bag of cat food is 10 pounds, and the weight of a bag of dog food is 35 pounds. The ratio of cat food to dog food is 10:35, which simplifies to 2:7.

To learn more about variable click here:

brainly.com/question/15078630

#SPJ11

The correct answer to the question is option d) 75 PCF.

To calculate the expected vertical load, we need to consider the weight of the concrete slab and the additional load due to the concrete's temperature and pouring rate. The weight of the slab can be calculated by multiplying the density of the concrete (150 PCF) by the depth (6 inches) and the area (1 square foot). This gives us a weight of 75 pounds per square foot (PSF).

The temperature and pouring rate do not directly affect the vertical load. The temperature and pouring rate are factors that may affect the structural integrity of the slab or the time it takes for the concrete to fully cure. However, they do not contribute to the actual load borne by the slab itself. Therefore, the correct answer is 75 PCF, as it represents the weight of the concrete slab alone.

For more information on PCF visit: brainly.com/question/21579391

#SPJ11

The dog drinks 112 ounces, or 14 cups, or 7 pints, or 3.5 quarts of water per week.

The dog drinks 16 oz of water every day, so in a week (7 days), the dog will drink:

16 oz/day × 7 days/week = 112 oz/week

To convert ounces to cups, we divide by 8 (since there are 8 fluid ounces in a cup):

112 oz/week ÷ 8 oz/cup = 14 cups/week

To convert ounces to pints, we divide by 16 (since there are 16 fluid ounces in a pint):

112 oz/week ÷ 16 oz/pint = 7 pints/week

To convert ounces to quarts, we divide by 32 (since there are 32 fluid ounces in a quart):

112 oz/week ÷ 32 oz/quart = 3.5 quarts/week

Therefore, the dog drinks 112 ounces, or 14 cups, or 7 pints, or 3.5 quarts of water per week.

Learn more about ounces

https://brainly.com/question/29374025

#SPJ1

Answer:

I'd be happy to help you find the area of the figure! However, I need more information about the figure you're referring to. Can you please describe the figure or provide an image of it?

Step-by-step explanation:

please follow me for more if you need any help

Answer:

12

Step-by-step explanation:

Probability = Expected outcome/Total outcome

GIven

Total outcome = 28marbles

probability of randomly drawing a  blue marble = 3/7

Substitute

3/7 = number of blue marbles/28

Cross multiply

7N = 3* 28

N = 3*4

N= 12

Hence there 12 blue marbles in the bag

Answer:

10.1

Step-by-step explanation:

Step-by-step explanation:

it goes by this formula

\(a = \frac{1}{2} bh \\ \\ \\ a = \frac{1}{2} 6 \times 4.1 = 12.3\)

Answer:

9\(\sqrt{2}\) inches

or

12.728 inches

Step-by-step explanation:

Use Phytagorean Theorem

\(a^{2} +b^{2} =c^{2}\)

Since both all sides of a square are equal, this means that \(a^{2}\) and \(b^{2}\) are equal.

So that leaves us with:

\(a^{2} +a^{2} = 18^{2}\)

Simplify

\(2a^{2} = 324\)

Divide both sides by 2

\(\frac{2a^{2} }{2} =\frac{324}{2}\)

Simplify

\(a^{2} = 162\)

Find the square root of both sides

\(\sqrt{a^{2} } =\sqrt{162}\)

a = 9\(\sqrt{2}\)

(or if you want the decimal, rounded to the 3rd decimal place: 12.728)

Answer:

11/6 I think

Step-by-step explanation:

Welp that's all that came when I get the answer

Based on the average total cost to the monopolistically competitive firm and the revenue, the loss they are expecting is -$400

The losses that the monopolistically competitive firm would be the difference between their revenue from the 20 units and their average total cost.

Solving for the loss to the monopolistically competitive firm gives:

= (Average total cost - Price) x number of units

= (70 - 50) x 20

= -$400

Find out more on monopolistically competitive firms at https://brainly.com/question/25717627

#SPJ4

The problem of unit root in standard regression and time-series models arises when a variable exhibits a non-stationary behavior, meaning it has a trend or follows a random walk. Unit root tests, such as the Dickey-Fuller and augmented Dickey-Fuller tests, are used to detect the presence of a unit root in a time series. These tests examine whether the coefficient on the lagged value of the variable is significantly different from one, indicating the presence of a unit root.

In standard regression analysis, it is typically assumed that the variables are stationary, meaning they have a constant mean and variance over time. However, many economic and financial variables exhibit non-stationary behavior, where their values are not centered around a fixed mean but instead follow a trend or random walk. This presents a problem because standard regression techniques may produce unreliable results when applied to non-stationary variables.

Time-series models, such as autoregressive integrated moving average (ARIMA) models, are specifically designed to handle non-stationary data. They incorporate differencing techniques to transform the data into a stationary form, allowing for reliable estimation and inference. Differencing involves computing the difference between consecutive observations to remove the trend or random walk component.

The Dickey-Fuller test and augmented Dickey-Fuller test are commonly used to detect the presence of a unit root in a time series. These tests examine the coefficient on the lagged value of the variable in a regression framework. The null hypothesis of the tests is that the variable has a unit root, indicating non-stationarity, while the alternative hypothesis is that the variable is stationary.

The Dickey-Fuller test is a simple version of the test that includes only a single lagged difference of the variable in the regression. The augmented Dickey-Fuller test extends this by including multiple lagged differences to account for potential serial correlation in the data. Both tests provide critical values that can be compared to the test statistic to determine whether the null hypothesis of a unit root can be rejected.

To learn more about regression click here: brainly.com/question/32505018

#SPJ11

Together, it will take the two machines 102 minutes to produce 5100 cans.

To solve this problem, we will use the work formula,

which is Work = Rate × Time.

1. First, let's find the rate of each machine.

New machine rate: 5100 cans / 170 minutes = 30 cans/minute

Old machine rate: 5100 cans / 255 minutes = 20 cans/minute

2. Now, let's find the combined rate of both machines. Combined rate: New machine rate + Old machine rate = 30 cans/minute + 20 cans/minute = 50 cans/minute

3. Finally, we will use the combined rate to find the time it takes for both machines to produce 5100 cans together.

Time = Work / Combined rate = 5100 cans / 50 cans/minute = 102 minutes

Together, it will take the two machines 102 minutes to produce 5100 cans.

Learn more about Work, rate and time,

https://brainly.com/question/14464103

#SPJ11

Answer:

c=39

Step-by-step explanation:

4+2=6

To remove square root you have to square everything making the 6 a 36 and then add 3. At the end it is a 39.

The employee's yearly salary is calculated as $37,440 using the arithmetic operations.  

The employee earns $18 per hour and works 40 hours per week. To calculate the weekly salary, we multiply the hourly wage by the number of hours worked:

Weekly salary = Hourly wage × Hours worked per week

Weekly salary = $18/hour × 40 hours/week = $720

Next, to calculate the yearly salary, we use the multiplication operation the weekly salary by the number of weeks in a year:

Yearly salary = Weekly salary × Weeks in a year

Yearly salary = $720/week × 52 weeks/year = $37,440

Therefore, the employee's yearly salary is $37,440. This calculation assumes a 40-hour work week and 52 weeks in a year. It's important to note that this calculation does not account for overtime pay or any other additional benefits or deductions that may affect the employee's total annual income.

Learn more about arithmetic operations here:

https://brainly.com/question/30553381

#SPJ11

To calculate the probabilities in this scenario, we need to consider the possible combinations of children's genders. The probability of having at least two boys is determined by calculating the probability of having two boys, three boys, or four boys. The probability of all children being of the same sex can be calculated by considering the probabilities of having all boys or all girls.

(a) To find the probability of having at least two boys, we need to consider the combinations of children's genders that satisfy this condition. There are four possibilities: BBGG, BGBG, GBGB, and GGBB. Each of these combinations has a probability of (1/2) * (1/2) * (1/2) * (1/2) = 1/16. Therefore, the total probability of having at least two boys is 4 * (1/16) = 1/4.

(b) To find the probability of all the children being of the same sex, we need to consider the combinations of all boys or all girls. There are two possibilities: BBBB and GGGG. Each of these combinations has a probability of (1/2) * (1/2) * (1/2) * (1/2) = 1/16. Therefore, the total probability of all children being of the same sex is 2 * (1/16) = 1/8.

To know more about probability here: brainly.com/question/32117953

#SPJ11

Answer:

y = 2x + 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = A (1, 7 ) and (x₂, y₂ ) = B (- 3, - 1 )

m = \(\frac{-1-7}{-3-1}\) = \(\frac{-8}{-4}\) = 2 , then

y = 2x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (1, 7 )

7 = 2(1) + c = 2 + c ( subtract 2 from both sides )

5 = c

y = 2x + 5 ← equation of line

Answer: $80

Step-by-step explanation:

Let the original price of the refrigerator be represented by y.

We are told that an appliance store reduced the price of a refrigerator by 20%. This will be:

= y - (20% of y)

= y - (20/100 × y)

= y - (0.2 × y)

= y - 0.2y

= 0.8y

We are then told that the store then raised the prices by 10% from the lower price. This will be:

= 0.8y + (10% of 0.8y)

= 0.8y + (0.1 × 0.8y)

= 0.8y + 0.08y

= 0.88y

Since we told that now the price was $70.49, this means that we have to find the value of y using the above expression. This will be:

0.88y = $70.49

y = $70.49/0.88

y = $80.10

y = $80 approximately

The original price of the refrigerator is $80.

Answer:

If a rectangle

77ft

Step-by-step explanation:

Answer:17in

Step-by-step explanation:

In the case above, Jaime claim is true.

1. Note that radian measure:

=   \(\frac{60° }{360°}\) x 2π  x 3

= 1/6 x 6π  

= π  

2. Note that radian measure:

=  \(\frac{60° }{360°}\) x 2π  x 6

= 1/6  x 2π  x 6

=2π  

So we can write it as:

π/3  x 180°/π    = 60°

Therefore, via the solution above, Jaime claim is true.

3. Note that: Radian measures: the percentage of arc measures x  2π  x radius and so one can say that The explanation to agree with Jaime’s statement or not is that the longer the length of the radius, the longer the length of the arc.

Learn more about radius from

https://brainly.com/question/358744

#SPJ1

Thus, the test for homogeneity follows the same procedures as the test for independence because the assumptions for performing the chi-square test for independence and chi-square test for homogeneity are the same.

The procedures for the chi-square test of homogeneity are the same as for the chi-square test of independence. The data is different for both tests. Tests of independence are used to determine whether there is a significant relationship between two categorical variables from the same population. One population is segmented based on the value of two variables. So there will be a column variable and a row variable.

The chi-square test of homogeneity of proportions can be used to compare population proportions from two or more independent samples, determining whether the frequency counts are distributed identically among different populations.

For more information about chi-square test,visit

https://brainly.com/question/17142834

#SPJ4

Answer:

3

Step-by-step explanation: