LAM 1 Mod 6 Question 4b-s2.

Given

To find a solution for the linear equation, the first step is to write the equation in slope-intercept form:

-Pass the x-term to the right side of the equation by applying the opposite operation to both sides of the equal sign:

-Divide both sides by -2:

Once you have expressed the equation of the line in slope-intercept form, replace it with any value for x and calculate the corresponding value of y, for example, x=2

One solution for the linear equation is x=2 and y=-6, you can check the solution by replacing the values on the original equation, with both values the result should be 8:

As you can see the values are a valid solution for the linear equation.

So the solution is:

The probability of winning is 1/42 expressed as a fraction.

Given that the odds on a bet are 41:1 against, we are to find the probability of winning.

We know that odds against = (Number of unfavorable outcomes) : (Number of favorable outcomes).

Thus, odds against = 41:1. This implies that the number of unfavorable outcomes is 41 and the number of favorable outcomes is 1.Probability of winning is given by the formula P(winning) = Number of favorable outcomes / Total number of possible outcomes. In this case, the total number of possible outcomes is the sum of the number of favorable and unfavorable outcomes.

Number of favorable outcomes = 1 and Number of unfavorable outcomes = 41

Therefore, the total number of possible outcomes = 1 + 41 = 42

Thus, P(winning) = Number of favorable outcomes / Total number of possible outcomes

P(winning) = 1 / 42

Therefore, the probability of winning is 1/42 expressed as a fraction.

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Answer:

x = 20

Step-by-step explanation:

the 3 unknown angles form a right angle and sum to 90° , that is

x + 2x + x + 10 = 90

4x + 10 = 90 ( subtract 10 from both sides )

4x = 80 ( divide both sides by 4 )

x = 20

Answer:

Step-by-step explanation:

From the picture we know that x + 2x + x + 10 = 90°

x + 2x + x + 10 = 90

4x = 80

x = 80 : 4

x = 20°

--------------------

check

20 + 2 x 20 + 20 + 10 = 90

90 = 90

the answer is good

Answer:

12

Step-by-step explanation:

32×3/8

.................

Answer:

2$

Step-by-step explanation:

If you buy 8 cans of corn and it cost you 16 dollars for all of the cans Then you can divide

Divide 16 by 8

16 divided by 8 =2

The cost of each can of corn is 2 dollars

Ans. 2

Step-by-step explanation:

Use directly proportional

X1/Y1=X2/Y2

8/16=1/X

and then solve for x

Answer:

linear................

Alessia spent $5,408 on entertainment in 2021.

To determine how much Alessia spent on entertainment in 2021, we need to work backward from the given information about her salary in 2022.

Let's assume Alessia's salary in 2021 was the same as in 2022, which is $26,000 after tax.

Since Alessia spends 35% of her after-tax salary on rent, we can calculate her rent expenditure:

Rent = 35% × $26,000

= $9,100

The remaining amount is split between food, petrol, and entertainment in the ratio 6:11:8.

To determine the ratio's total parts, we sum the individual parts:

Total parts = 6 + 11 + 8 = 25

Next, we calculate the value of one part of the ratio:

One part = ($26,000 - $9,100) / 25

= $16,900 / 25

= $676

Now, we can calculate how much Alessia spent on entertainment in 2021, which is 8 parts of the ratio:

Entertainment expenditure = 8 × $676

= $5,408

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Every rectangle with four congruent sides is a square -> True

Every rhombus is a quadrilateral -> True

Every square is a parallelogram -> True

Every quadrilateral is a square -> False.

A square is a regular quadrilateral, which means that it has four equal sides and four equal angles. It can also be defined as a rectangle with two equal-length adjacent sides.

here, we have,

we know that,

Every rectangle with four congruent sides is a square -> True

Every rhombus is a quadrilateral -> True

Every square is a parallelogram -> True

Every quadrilateral is a square -> False.

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Answer:

122 tickets were sold for adults and the rest is for children.

Step-by-step explanation:

the perimeter of the equilateral triangle with a side length of 12√3 is 36√3 units.

In order to find the perimeter of the given triangle, we have to find the side of the triangle. The altitude of the triangle  = 18 inches. Let us assume the side of the triangle as a. The formula for calculating the altitude of an equilateral triangle is : Altitude  =√3/2×a  (side)

18 =√3/2 × a

a = 18 × 2√3

a = 36√3

a = 36 ×√3 / √3×√3

a =36√3/3

a = 12√3 inches.

If the side of an equilateral triangle is 12√3, then all three sides of the triangle are of equal length, since it is an equilateral triangle. Therefore, the perimeter of the triangle is simply the sum of the lengths of its three sides. Since each side of the triangle has a length of 12√3, the perimeter is: Perimeter = 3 x (12√3) = 36√3.

Therefore, the perimeter of the equilateral triangle with a side length of 12√3 is 36√3 units.

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The average speed of the train can be calculated by dividing the total distance traveled by the total time taken. In this case, the train traveled a total distance of 30 km (10 km from X to Y + 20 km from Y to Z) and took a total time of 36 minutes (11.5 minutes + 0.5 minutes + 24 minutes). Converting the time to hours (36 minutes = 0.6 hours), the average speed of the train is 50 km/hr.

To calculate the average speed of the train, we need to divide the total distance traveled by the total time taken. Let's calculate each component:

1. Total distance: The train traveled 10 km from station X to station Y and then an additional 20 km from station Y to station Z, making a total distance of 30 km.

2. Total time: The train took 11.5 minutes to travel from X to Y, stopped at station Y for 0.5 minutes, and then took another 24.0 minutes to travel from Y to Z, making a total time of 11.5 minutes + 0.5 minutes + 24.0 minutes = 36 minutes.

To convert the total time to hours, we divide it by 60 (since there are 60 minutes in an hour): 36 minutes / 60 = 0.6 hours.

Finally, we can calculate the average speed by dividing the total distance (30 km) by the total time in hours (0.6 hours): 30 km / 0.6 hours = 50 km/hr.

Therefore, the average speed of the train is 50 km/hr.

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Step-by-step explanation:

Proof: equidistance means at an equal distance from two points

so: Take the distance formula and then plug the values in and compare.

Answer:

23

Step-by-step explanation:

a pair is 2 so 2 pairs time 3 2x3=6 so 17+6=23

9514 1404 393

Answer:

  D.  90

Step-by-step explanation:

The radius VG is the same as the radius VO. That radius is ...

  VG = VA +AG = 24 +27 = 51

Then the Pythagorean theorem tells you ...

  VO^2 = VA^2 +AO^2

  AO = √(VO^2 -VA^2)

  AO = √(51^2 -24^2) = √2025 = 45

The desired length is ...

  TO = 2·AO = 2·45

  TO = 90

Answer:

(4^6)*(4^4) = 1,048,576

Step-by-step explanation:

The given expression is \(\dfrac{ r^2-r-6}{(r-2)(r-3)}\). the option C \(\dfrac{ (r+2)}{(r-2)}\)is correct.

Usually, simplification involves proceeding with the pending operations in the expression.

Simplification usually involves making the expression simple and easy to use later.

The given expression is

\(\dfrac{ r^2-r-6}{(r-2)(r-3)}\)

By solving the numerator

\(r^2-r-6\\\\r^2 - (3-2)r- 6\\\\(r-3)(r+2)\)

Put the solution in the above equation

\(\dfrac{ (r+2)(r-3)}{(r-2)(r-3)}\)

\(\dfrac{ (r+2)}{(r-2)}\)

Therefore, the option C is correct.

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Answer:

1.94 ounces are in each bag.

Step-by-step explanation:

The total ounces of nuts in the bag is calculated as:

23 ounces of walnuts + 11.2 ounces of almonds + 14.3 ounces of cashews = 48.5 ounces.

From the question we are told that these amounts make 25 bags.

The number of ounces that are in each bag is calculated as:

25 bags = 48.5 ounces

1 bag = x ounces

Cross Multiply

25 bags × x ounces = 1 bag × 48.5 ounces

x ounces = 1 bag × 48.5 ounces/25 bags

x ounces = 1.94 ounces

Therefore, there are 1.94 ounces in each bag

Answer:

y = 4

Step-by-step explanation:

When given a point and a slope, we use slope-intercept formula:

y - y1 = m (x - x1)

m = slope  point: (-4,4)

y - y1 = m (x - x1)

y - 4 = 0 (x - 1)

y - 4 = 0x + 0

 + 4          + 4

y = 4

The answer can't be written in slope-intercept form, as the 0"s cancel out.

Hope this helps!

Answer:

ill try to answer that has soon has am done with these one

Step-by-step explanation:

Answer :

ill try to answer that has soon has

am done with these one

The option B is correct answer which is ba-r(X) +/- 4.6.

What is Ma-rgin Er-ror?

The ma-rgin of er-ror is a statistic that describes how much ran-dom sa-mpling error there is in survey results. One should have less fa-ith that a p-oll's findings would accurately reflect those of a popu-lation census the higher the ma-rgin of er-ror.

If the ma-rgin of er-ror in an interval esti-mate of μ is 4.6, the interval esti-mates equals to ba-r(X) +/- 4.6.

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Answer:

he dividend number is 80, the number used to divide another number is 10 and the result of the dividing two number is 8.

Step-by-step explanation:

The values of a, b, c, and d, based on the given equation are:

\(a = 10\\b = 3\\c = -6\\d = -5\)

Let's calculate the values of a, b, c, and d based on the given table:

Using the equation \(y = x^2 - 4x - 2\), we can substitute the values of x and find the corresponding values of y:

For x = -3:

\(y = (-3)^2 - 4(-3) - 2 = 9 + 12 - 2 = 19\)

For x = -2:

\(y = (-2)^2 - 4(-2) - 2 = 4 + 8 - 2 = 10\)

For x = -1:

\(y = (-1)^2 - 4(-1) - 2 = 1 + 4 - 2 = 3\)

For x = 0:

\(y = (0)^2 - 4(0) - 2 = 0 - 0 - 2 = -2\)

For x = 1:

\(y = (1)^2 - 4(1) - 2 = 1 - 4 - 2 = -5\)

For x = 2:

\(y = (2)^2 - 4(2) - 2 = 4 - 8 - 2 = -6\)

For x = 3:

\(y = (3)^2 - 4(3) - 2 = 9 - 12 - 2 = -5\)

Now let's match these values with the table:

\(x , y = x^2 - 4x - 2\)

\(\[\begin{align*}(-3, 19) \\(-2, a) \\(-1, b) \\(0, -2) \\(1, -5) \\(2, c) \\(3, d) \\\end{align*}\]\)

From the given table, we have:

\(a = 10\\b = 3\\c = -6\\d = -5\)

Certainly! Here's a 100-word explanation of the given data:

The data provided consists of pairs of values, where the first column represents the x-values and the second column represents the y-values. Each row in the table corresponds to a data point. For instance, when x is \(-3\), the corresponding y-value is \(19\). Similarly, when x is \(-2\), the y-value is denoted as '\(a\)', and when \(x\) is -\(1\), the \(y\)-value is denoted as 'b'.

The pattern continues for the remaining data points, with specific values assigned to \(x \ and \ y\). This data set allows for the representation and analysis of relationships between the variables \(x \ and \ y\).

Therefore, the values of a, b, c, and d are:

\(a = 10\\b = 3\\c = -6\\d = -5\)

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Answer:

The numbers are 0 and 1

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An \(11\)-vertex full graph has around \(19,958,931,200\) Hamiltonian circuits in a complete graph.

At one vertex, the Hamiltonian route begins, and at another, it finishes. Yet, when following a Hamiltonian route, every vertex is encountered. At the same vertex, the Hamiltonian circuit begins and terminates. For instance, if a Hamiltonian circuit's path began at vertex 1, the loop will also conclude at that vertex.

Single circuit is the sole trip a Hamiltonian circuit makes to each vertex. It must begin and terminate at same vertex since it is a circuit. A Hamiltonian route does not start and end in a single location, but it does visit each vertex just once with no repetitions.

We have to divide by \(2(n-2)\)

\(11!/(2(11-2)!) = 11!/2,520\) Hamiltonian circuits we get:

\(11!/2,520 = 19,958,931,200\)

Therefore, there are approximately \(19,958,931,200\) Hamiltonian circuits in a complete graph with \(11\) vertices.

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The equation of the line in point-slope form is y - 5 = -7(x + 1) and in slope-intercept form is y = -7x - 2.

The equation of a line in point-slope form is given by y - y₁ = m(x - x₁), where (x₁, y₁) represents a point on the line and m is the slope of the line.

Given that the slope (m) is -7 and the point (-1, 5) lies on the line, we can substitute these values into the point-slope form equation:

y - 5 = -7(x - (-1))

Simplifying:

y - 5 = -7(x + 1)

y - 5 = -7x - 7

y = -7x - 2

So, the equation of the line in point-slope form is y - 5 = -7(x + 1) and in slope-intercept form is y = -7x - 2.

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The equivalent expression is (2x - 1)(3x - 5)

From the information given, we have the quadratic equation written as;

6x² - 13x + 5

Using factorization, we have that;

Find the product of the coefficient of x squared and the constant.

Then, find the pair factor of the product that add up to -13

We have;

6x² - 10x - 3x + 5

Group the expression in pairs, we get;

2x(3x - 5) - 1(3x - 5)

Then, we have the expression, we have;

(2x - 1)(3x - 5)

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Answer: 1/2

Step-by-step explanation:

:D

Answer:

√(r+n)/5=m

Step-by-step explanation:

r=5m²-n

adding n on both sides

r+n=5m²-n+n

r+n/5=m²

taking square root on both sides

√(r+n)/5=m

The team at Prime Video is developing a method to divide movies into groups based on the number of awards they have won. This method involves the following steps:

1. Collecting data: The team will gather information about movies, including the number of awards they have won. This data can be obtained from reliable sources such as award shows, film festivals, and reputable databases.

2. Grouping movies: Based on the number of awards won, the team will divide movies into different groups. For example, movies with more than 100 awards can be placed in one group, while movies with fewer awards can be placed in another group.

3. Defining criteria: The team will establish specific criteria for each group. These criteria may include the minimum and maximum number of awards required for a movie to be included in a particular group.

By developing this method, the team at Prime Video aims to categorize movies based on their award achievements. This will allow viewers to easily discover and explore movies that have received significant recognition in the industry.

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