Which of these ordered triples indicates where the plane cuts the x-axis for this equation? 7x +2y +3z =42 A. (14,0,0) B. (7,0,0) C. (21,0,0) or D. (6,0,0)

The point on the line [tex]y=3x+2[/tex] that is closest to the origin is [tex](-0.6, 0.2)[/tex].

Given,  [tex]y=3x+2[/tex], whose slope is [tex]3[/tex].

Let [tex]m[/tex] is the slope of the line perpendicular to the above line.

So,

[tex]3\times m=-1\\m=-1/3[/tex]

Then, the general equation of a line perpendicular line will be [tex]y=-1/3x+k[/tex].

So the equation line passing through the origin [tex](0,0)[/tex] and perpendicular to the line [tex]y=3x+2[/tex] is [tex]y=-1/3x[/tex] , [tex](k=0)[/tex].

Then the closest point will be the intersection point of these two lines, i.e.

[tex]3x+2=-1/3x\\9x+6=-x\\10x+6=0\\x=-0.6[/tex]

and

[tex]y=\dfrac{-0.6}{3} \\y=0.2[/tex]

Therefore, the point on the line [tex]y=3x+2[/tex] that is closest to the origin is [tex](-0.6, 0.2)[/tex].

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5  7/32 = 167/32

5/32 + 5/32 (2 wall thicknesses of the pipe) =10/32

167/32 - 10/32 = 157/32

= 4 29/32

Answer:

The missing coordinate is 5

Step-by-step explanation:

To find the probability of the union of two independent events, use the formula P(A U B) = P(A) + P(B). In this case, P(A U B) = 0.4 + 0.1 = 0.5.

To find the probability of the union of two independent events, we can use the formula:

P(A U B) = P(A) + P(B) - P(A ∩ B)

Since the two events, A and B, are independent, the probability of their intersection, P(A ∩ B), is 0. This is because the occurrence of one event does not affect the occurrence of the other event. Therefore, we have:

P(A U B) = P(A) + P(B)

Substituting the given values, we get:

P(A U B) = 0.4 + 0.1

= 0.5

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To solve this problem, let us first define what a median is. A median is a line segment that connects a vertex and the midpoint of the side opposite to that vertex.

In this case, the vertex is point A while the opposing side is side CB. Since it connects to the midpoint of CB, therefore this means that the median AD equally divides side CB into 2 parts.  Since the length side CB is the sum of the lengths side CD and side BD. Therefore this means that:

length of CD = length of BD

length of CD = 24

Answer:

 24

To avoid distortion of extreme values, a good indicator would be the

B. median.

A continuous random variable can assume any value within one or more intervals and result from measurements, providing an uncountable range of possibilities. Continuous random variables are commonly used in many fields, including reliability engineering and standardized testing, to assess continuous data.

A continuous random variable is a type of random variable that can assume any value within one or more intervals. Unlike discrete random variables, which take on countable values, continuous random variables result from measurements rather than counts. For instance, the temperature of a day measured by a thermometer or the height of students measured by a ruler are examples of continuous random variables. The values are uncountable as they lie on a continuum, like the speed of an automobile or the duration of a telephone call.

Two main characteristics of a discrete probability distribution function include the fact that each probability must be between zero and one, inclusive, and the sum of the probabilities should equal one. These rules do not apply to continuous random variables, which instead use probability density functions to describe their distributions.

Continuous random variables play significant roles in numerous applications such as assessing baseball batting averages, calculating IQ scores, and evaluating SAT scores. In the field of reliability engineering, a variety of continuous random variables are essential for analyzing the life expectancy of components.

Due to the lack of numerical details, a precise ratio of men to all members at the swim club cannot be determined. The ratio would be based on the exact number of men verses total members. Ratios offer a method to compare quantities.

Unfortunately, without more information, it's impossible to definitively say what the precise ratio of men to all members at the swim club is. To determine the correct ratio, we would need to know the total number of members at the club, and the number of those members who are men. A ratio is a way to compare quantities or numbers, and in this case, the quantity of men compared to the quantity of all members.

For example, if there were 20 members total in the club, and 10 of those members were men, the ratio would be 1:2 (choice C), because for every one man, there are two total members. However, if there were 4 members and 3 of them were men, then the ratio would be 3:4 (choice B). Without the specific numbers, we cannot determine the correct answer from choices A, B, C, or D.

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The probability of getting either a sum of 5 or at least one 5 in the roll of a pair of dice will be 5/12.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the probability is given as,

P = (Favorable event) / (Total event)

The total number of probability is given as,

Total event = 6 x 6

Total event = 36

The samples are given as,

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

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

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

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

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

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

Then the probability of getting either a sum of 5 or at least one 5 in the roll of a pair of dice will be given as,

P = (4/36) + (11/36)

P = 15/36

P = 5/12

The probability of getting either a sum of 5 or at least one 5 in the roll of a pair of dice will be 5/12.

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Answer:

y axis and

Step-by-step explanation:

The point P(a, b) where the value of a is 0, hence point P is located on the y axis.

The coordinate plane is a two-dimensional surface formed by two lines known as the horizontal axis (x axis) and the vertical axis (y axis). The origin is the point of intersection of both axis and it serves as a reference point.

A point on the coordinate plane is located using the x and y coordinates.

Given the point P(a, b) where the value of a is 0, hence point P is located on the y axis.

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To solve this problem, let us first calculate the probability of designing one shoe out of all the combinations.

Probability of designing one shoe = (probability of choosing 1 color for the base) * (probability of choosing 1 color for the accent) * (probability of choosing 1 font for the embroidery)

We know that probability is:

Probability = number of chosen event / number of total events

Therefore:

Probability of designing one shoe = (1 / 4) * (1 / 6) * (1 / 2)

Probability of designing one shoe = 1 / 48

This means that either Ray or Lilli has this probability of designing a specific shoe. Since we are asked for the probability that they will both design this specific shoe, so we multiply:

Probability they will design the same shoe = (1 / 48) * (1 / 48)

Probability they will design the same shoe = 1 / 2304 = 4.34 * 10^-4

The probability is around 0.043% that they will design the same shoe.

volume = l x w x h

51 x 44 x 8 = 17952 cubic feet

1 cubic foot = 0.0283168 cubic meters

17952 x 0.0283168 = 508.343 cubic meters

1 cubic meter = 1,000,000 cubic centimeters

508.343 x 1000000 = 508,343,000 cubic centimeters

The polygon which has an interior angle sum of 1080° is an Octagon

From the question, we are to determine which polygon has an interior angle sum of 1080°

To find that, we will determine the number of sides the polygon has.

From the formula for sum of the interior angles in a polygon

Sum of interior angles = (n-2)180°

Where n is the number of sides

Then,

1080° = (n-2) 180°

1080° ÷ 180° = n-2

6 = n-2

n = 6 + 2

n = 8

A polygon with 8 sides is called an Octagon

Hence, the polygon which has an interior angle sum of 1080° is an Octagon

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Answer:

3181 yards.

Step-by-step explanation:

All the given information can be used to draw a simple diagram. The diagram shows a triangle which is formed by the ships. There are two angles given and one side is given. Therefore, the sine rule must be used to solve the question. The sine rule can be written as:

sin V / v = sin G / g.

It can be observed that the angle V is unknown, however, it can be calculated very easily. Simply use the law of triangle in which all the 3 angles sum up to 180 degrees. So V = 180 degrees - 44 degrees - 36 degrees = 100 degrees. So plugging in v = 4510 yards, V = 100 degrees, G = 44 degrees, and g = x yards into the sine rule gives:

sin 100 / 4510 = sin 44 / x.

Cross multiplying gives:

x*sin 100 = 4510*sin 44

Making x the subject gives:

x = (4510*sin 44)/sin 100.

x = 3181 yards (to the nearest yard).

Therefore, Norman and Voyager are 3181 yards apart from each other!!!

The required distance between the Norman and the Voyager is 3181 yards.

Given that,
A ship at sea, the Gladstone, spots two other ships, the Norman and the Voyager, and measures the angle between them to be 44°. The distance between the Gladstone and the Norman is 4510 yards. The Norman measures an angle of 36° between the Gladstone and the Voyager. To the nearest yard, what is the distance between the Norman and the Voyager is to be determined.

These are the equation which contains trigonometric operators such as sin, cos.. etc.. In algebraic operation.

Here,
The measure of the angle between Gladstone and the norman,
= 180 - 44 + 36
= 100°

sin(100) / 4510 = sin(44) / x.

x = 3181.12

x ≈ 3181 yards

Thus, the required distance between the Norman and the Voyager is 3181 yards.

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Answer:

The missing term is x=32.

Step-by-step explanation:

Given :  The median for the given set of six ordered data values is 26.5.

To find : What is the missing value?

Solution :

The data set is 7 12 21 ?41 50

let the missing term or 4th term be x.

We know, The median of an even number is sum of nth term by 2 and nth+1 term by 2.

So, Applying median formula for even terms is

Term, [tex](\frac{n}{2},\frac{n}{2}+1)[/tex]

[tex](\frac{6}{2},\frac{6}{2}+1)=3^{rd},4^{th}[/tex]

The median is sum of 3rd and 4th term.

[tex]26.5=\frac{21+x}{2}[/tex]

[tex]53=21+x[/tex]

[tex]53-21=x[/tex]

[tex]32=x[/tex]

Therefore, The missing term is x=32.

If the median for the given set of six ordered data values is 26.5 then the missing value is 32.

The ordered set of data values is:

7, 12, 21,x, 41, 50

Given that the median is 26.5, it represents the middle value of the data set.

Since the set has six values, the median should be the average of the two middle values.

Let's assume the missing value is 'x':

7, 12, 21, x, 41, 50

We can see that 'x' should be the fourth value to maintain the ascending order.

Now, we need to find the value of 'x' that makes the median equal to 26.5.

To calculate 'x', we can set up the equation:

(21 + x) / 2 = 26.5

Multiply both sides by 2:

21 + x = 53

Subtract 21 from both sides:

x = 32

Therefore, the missing value in the set is 32.

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The solution is, The greatest angle measure is angle F which is 119°

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

here, we have,

The sum of all the angles of a quadrilateral is 360°

(15x-10)°+(15x+14)°+(9x-4)°+(11x+10)° = 360°

Open up the brackets and rearrange the expression

15x-10°+15x+14°+9x-4°+11x+10°=360°

15x+15x+9x+11x-10°+14°-4°+10° = 360°

50x+10°=360°

Collect like terms

50x=360°-10°

50x=350°

Divide by the coefficient of x

x= 350/50

X=7°

Substitute the value of x into the various angles

15x-10°=(15×7)-10= 105-10=95°

15x+14°=(15×7)+14=105+14=119°

9x-4°=(9×7)-4=63-4=59°

11x+10°=(11×7)+10=77+10=87°

The greatest angle measure is angle F which is 119°

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