out of fifteen randomly selected people, how many would you expect to use an online travel website to book their hotel? round down to the nearest whole person

The association between the given lines is that they are 'neither perpendicular nor parallel.'

To prove, let's convert the given equations in their slope-intercept form i.e. 'y = mx + b'

-7x + 2y = 3

2y = 7x + 3

y = 7/2x + 3/2

-6x + 3y = 2

3y = 6x + 2

y = 2x + 2/3

This shows that both the lines have different slopes, as well as, intercepts of y. And,

\(m_{1} * m_{2}\) = 2 * 7/2 ≠ -1

Thus, it is not perpendicular also.

Therefore, option D i.e. 'neither perpendicular nor parallel' is the correct answer.

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Answer:887%

Step-by-step explanation: to write a decimal number as a percentage multiply the number by 100 and then add the percent sign

It is also the same as moving the decimal point two places to the right

Answer

15v^5+4v^3-24v^2

Answer:

Step-by-step explanation:

Answer:

<ABC = 54 degrees

Step-by-step explanation:

Taking the sum of angle on the straight line ABD as 180 degrees

3x+9 + 9x - 9 =180

12x = 180

x = 180/12

x =  15 degrees

Since <ABC = 3x+9 (vertically opposite angles)

<ABC = 3(15)+9

<ABC = 45+9

<ABC = 54 degrees

Answer:

480

Step-by-step explanation:

60% of 800

= \(\frac{60}{100}\) × 800

= 0.6 × 800

= 480 ← number of students who take the bus

The term "average" in statistics refers to a measure that summarizes the central tendency of a data set. Another term that could be used in place of "average" is "mean.  Average plays a crucial role in statistics as it provides a summary measure of central tendency.

The term "average" in statistics refers to a measure that represents the central tendency of a data set. It is commonly used to summarize and describe the typical value or typical level of a particular variable within a population or sample.

The role of the term "average" is to provide a single value that represents the collective information of the data set. It helps in simplifying and summarizing complex data by providing a measure that is representative of the entire distribution. It allows for comparisons, analysis, and inference based on a single value rather than considering each individual data point.

However, it's important to note that depending on the context and the nature of the data, alternative measures of central tendency may be more appropriate than the "average." For example, if the data set contains outliers or is heavily skewed, the median or mode might be better indicators of the typical value.

In summary, the term "average" plays a crucial role in statistics as it provides a summary measure of central tendency. However, it is important to consider the specific characteristics of the data set and potentially use alternative measures when necessary.

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Answer:

(n-2) x 180 degrees where n is the number of sides

Step-by-step explanation:

From one vertex of the polygon you draw triangles inside the polygon.  Multiply the number of triangles by 180 since all triangles interior angles add up to 180 degrees.

example

Pentagon has 5 sides.  (5-2) x 180 = 540 degrees

This is the same as 180n-360

===================================================

Explanation:

Draw any polygon you want. Let's say we draw a hexagon. Split the hexagon into 6 triangles. Check out the diagram below.

The goal is to find what the red angles sum to. Recall that any triangle always has its three angles add to 180 degrees. We have 6 triangles, so all of the angles (red+blue) add to 6*180 = 1080 degrees. However, we don't want to include the blue inner angles. So we'll subtract off 360 since the blue angles add up to this amount (they form a full rotation).

So we have 6*180 - 360 as the expression that represents the sum of the interior angles for this hexagon. The hexagon doesn't have to be a regular polygon.

We can generalize to any polygon and not just hexagons. Simply replace that "6" with n and we get n*180 - 360 which is the same as 180n-360 = 180(n-2)

Answer:

x = 4

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define equation

5x - 7 + 2x = 21

Step 2: Solve for x

Answer:

The answer is 17.

Step-by-step explanation:

Since it's a parallelogram, VY = WX.

Therefore, \(5x + 2 = 6x - 1\).

Solving for x we get: \(x = 3\)

To get the measure of segment WX, substitute \(x = 3\) back into the side \(6x - 1\). Therefore \(6x - 1 = 6(3) - 1 = 17\)

Answer:

in one minute they rake \(\frac{y+x}{xy}\) leaves working together.

Step-by-step explanation:

If Maya rakes the leaves in x minutes, then, in one minute she rakes \(\frac{1}{x}\) leaves.

In the case of Carla, if she rakes the leaves in y minutes, in one minute she rakes \(\frac{1}{y}\) leaves.

Therefore, to know the portion of leaves they can rake in one minute working together, we need to sum up both of the portions each one of them rake in one minute, this gives us: \(\frac{1}{x}+ \frac{1}{y}\)

Now, to simplify this expression:

\(\frac{1}{x}+ \frac{1}{y} =\frac{y+x}{xy}\)

Thus, in one minute they rake \(\frac{y+x}{xy}\) leaves.

Answer:

x=1

Step-by-step explanation:

3x−1+2=4

Add −1 and 2 to get 1.

3x+1=4

Subtract 1 from both sides.

3x=4−1

Subtract 1 from 4 to get 3.

3x=3

Divide both sides by 3.

x=

3

3

​

Divide 3 by 3 to get 1.

x=1

(b) By solving the dual problem graphically, we find that the optimal solution occurs at the vertex (0, 2) with a minimum value of W = 10. The shadow price for resource 1 (x1 + x3 ≤ 3) in the primal problem is 10. This means that an additional unit of resource 1 would increase the objective function value by 10. The shadow price for resource 2 (x2 + 2x3 ≤ 5) in the primal problem is 0. This indicates that the optimal solution is not sensitive to changes in resource 2.

(a) To construct the dual problem, we will assign dual variables y1 and y2 to the constraints of the primal problem and convert the objective function to the dual form. The dual problem has two constraints corresponding to the resources in the primal problem. The objective function in the dual problem represents the costs or prices associated with the resources.

(b) To solve the dual problem graphically, we will plot the feasible region and find the optimal solution.

Constraint 1: y1 + y2 ≥ 2

Rearranging the inequality, we get:

y2 ≥ 2 - y1

Constraint 2: y1 + 2y2 ≥ 6

Rearranging the inequality, we get:

y2 ≥ (6 - y1) / 2

The feasible region is the intersection of the two constraint inequalities, taking into account the non-negativity constraints y1 ≥ 0 and y2 ≥ 0.

Now, let's plot the feasible region on a graph:

Starting with the y-axis, plot points (0, 2) and (0, 3) to represent the non-negativity constraint y2 ≥ 0.

Next, draw a line with a slope of -1 passing through the point (0, 2).

Draw another line with a slope of -0.5 passing through the point (0, 3).

The feasible region is the area bounded by these two lines and the y-axis.

To find the optimal solution, we need to evaluate the objective function at the vertices of the feasible region.

Vertices of the feasible region:

(0, 2)

(0, 3)

Now, substitute these vertices into the objective function:

For (0, 2):

W = 3(0) + 5(2) = 10

For (0, 3):

W = 3(0) + 5(3) = 15

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Using linear function concepts, it is found that the speed of the motorboat is of 22 miles per hour.

A linear function is modeled by:

y = mx + b

In which:

In this problem, each second, the position increased by 22, hence the slope is of 22. Since velocity is the distance divided by the time, which in this problem is the slope, the speed of the motorboat is of 22 miles per hour.

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Answer:

length of the longest pencil that can fit must be less than 13cm

Step-by-step explanation:

To get the longest pencil that fit the case, we will use the pythagoras theorem;

diameter = 10cm

radius = 10/2

radius = 5cm

Height = 12cm

Get the length of the longest side

l² = r²+h²

l² = 5²+12²

l² = 25 + 144

l² = 169

l = √169

l = 13cm

Hence the length of the longest pencil that can fit must be less than 13cm

Answer:

A

Step-by-step explanation:

Radius = 3.25

Base = πr² = π(3.25)²

Height = 12

Volume = Bh = π(3.25)²(12)

Answer:

1 pints or 0.5 quarts each

Step-by-step explanation:

According to the scenario, computation of given data are as follows,

Total orange juice = 2 quarts or  (2 × 2 pints) = 4 pints

Total number of people including Tonya = 4

So we can calculate the quantity of juice each person gets by using following formula,

Each person quantity = (2÷4 quarts )or (4÷4 pints)

= 1 pints or 0.5 quarts each

Answer:

(x + 2) (x + 4) (x^2 + 5 x + 8)

Step-by-step explanation:

Simplify the following:

(x^2 + 4 x + 8)^2 + 3 x (x^2 + 4 x + 8) + 2 x^2

(x^2 + 4 x + 8)^2 + 3 x (x^2 + 4 x + 8) + 2 x^2 = 2 x^2 + 3 x (x^2 + 4 x + 8) + 1 (x^2 + 4 x + 8)^2:

2 x^2 + 3 x (x^2 + 4 x + 8) + (x^2 + 4 x + 8)^2

The factors of 2 that sum to 3 are 2 and 1. So, 2 x^2 + 3 x (x^2 + 4 x + 8) + (x^2 + 4 x + 8)^2 = ((x^2 + 4 x + 8) + 2 x) ((x^2 + 4 x + 8) + 1 x):

(x^2 + 4 x + 2 x + 8) (x^2 + 4 x + x + 8)

Grouping like terms, x^2 + 4 x + x + 8 = x^2 + (4 x + x) + 8:

x^2 + (4 x + x) + 8 (x^2 + 4 x + 2 x + 8)

4 x + x = 5 x:

(x^2 + 5 x + 8) (x^2 + 4 x + 2 x + 8)

Grouping like terms, x^2 + 4 x + 2 x + 8 = x^2 + (4 x + 2 x) + 8:

x^2 + (4 x + 2 x) + 8 (x^2 + 5 x + 8)

4 x + 2 x = 6 x:

(x^2 + 6 x + 8) (x^2 + 5 x + 8)

The factors of 8 that sum to 6 are 4 and 2. So, x^2 + 6 x + 8 = (x + 4) (x + 2):

Answer: (x + 2) (x + 4) (x^2 + 5 x + 8)

Therefore, the missing side of the triangle is 5.

To determine the missing side of a triangle, you can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, if one side of the triangle is 12 and the other side is 13, we can label the missing side as x. Using the Pythagorean theorem, we have:

\(x² = 13² - 12²

x² = 169 - 144

x² = 25\)

Taking the square root of both sides, we find:

\(x = √25

x = 5\)

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The explicit formula for the sequence is aₙ=(-4).(-4)ⁿ⁻¹ and the 8th term is 65536

The given sequence is -4, 16, -64, 256,...

If we observe the sequence it is a geometric sequence

aₙ=a.rⁿ⁻¹

a is the first term and r is the common ratio

From the sequence the first term is -4 and common ratio is -4

aₙ=(-4).(-4)ⁿ⁻¹

Plug in the value n as 8

a₈=(-4).(-4)⁷

The value of minus four power seven is minus sixteen thousand three hundred eighty four

a₈=(-4)(-16384)

When four is multiplied with sixteen thousand three hundred eighty four we get sixty five thousand five hundred thirty six

a₈= 65536

Hence, the explicit formula for the sequence is aₙ=(-4).(-4)ⁿ⁻¹ and the 8th term is 65536

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Answer:

8 days.

Step-by-step explanation:

250 is half of 500

So 4 days takes half of the books.

The total would be 8 days because 4 is half of 8.

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An equation which is parallel to 4x - 6y = -36 passing through points (2, 3) is y = 2x/3 + 5/9.

Parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.

In Geometry, two (2) lines are considered to be parallel if their slopes are the same (equal) and they've different y-intercepts.

This ultimately implies that, two (2) lines are parallel under the following conditions:

m₁ = m₂

Note: m is the slope.

Simplifying the equation, we have:

4x - 6y = -36

6y = 4x + 36

Dividing both sides by 6, we have:

y = 2x/3 + 6

m₁ = m₂ = 2/3.

Mathematically, the standard form of the equation of a straight line is given by;

y - y₁ = m(x - x₁)

At point (2, 3), we have:

y - 3 = 2/3(x - 2)

y - 3 = 2/3(x - 2)

y - 3 = 2x/3 - 4/3

y = 2x/3 - 4/3 + 3

y = 2x/3 + 5/9

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Answer:

24

Step-by-step explanation:

8*3=24

Answer:

24

Step-by-step explanation:

To find the area you have to multiply 3 and 8 together to get 24

3x8=24

Answer:

volume= 1000

total surface area= 600

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Answer:

600 cm² and 1000 cm³

Step-by-step explanation:

The surface area is the area of the 6 square faces of the cube,

area of 1 face = 10 × 10 = 100 cm², then

surface area = 6 × 100 cm² = 600 cm²

The volume (V) is calculated as

V = s³ ( s is the side length )

Here s = 10, then

V = 10³ = 1000 cm³

The probability that the system will function tomorrow is 0.2495 or 24.95%.

To find the probability that the system will function tomorrow, we need to find the probability that at least 4 out of the 6 components will function.

On a rainy day, the probability of 4 components functioning is given by:

P(rainy day and 4 components functioning) = C(6, 4) × (0.5)⁴ × (0.5)² = 15 × 0.0625 × 0.25 = 0.2344

On a non-rainy day, the probability of 4 components functioning is given by:

P(non-rainy day and 4 components functioning) = C(6, 4) × (0.8)⁴ × (0.2)² = 15 × 0.4096 × 0.04 = 0.2534

Now we can find the overall probability of the system functioning tomorrow by using the law of total probability:

P(system functioning tomorrow) = P(rainy day and 4 components functioning) × P(rain) + P(non-rainy day and 4 components functioning) × P(non-rain)

= 0.2344 × 0.20 + 0.2534 × 0.80

= 0.0468 + 0.2027

= 0.2495

Therefore, the probability that the system will function tomorrow is 0.2495 or 24.95%.

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--The given question is incomplete; the complete question is

"A k out of n system is one in which there is a group of n components, and the system will function if at least k of the components function. For a certain 4 out of 6 systems, assume that on a rainy day, each component has a probability of 0.5 of functioning and that on a non-rainy day, each component has a probability of 0.8 of functioning.

Assume that the probability of rain tomorrow is 0.20. What is the probability that the system will function tomorrow?"--

Step-by-step explanation:

11/4 then reduce

2 3/4

because 11/4 is just like saying 11 divided by 4

Answer:

2.75

Step-by-step explanation:

Make a division plane

Step-by-step explanation:

BC = AD (opposite sides in parallelogram is equal)

x + 8 = 2x + 1

8 - 1 = 2x - x

7 = x

x = 7

BC = x + 8 = 7 + 8 = 15