the distance between the two points (-6, 1) and (-4, 5). Round to the nearest tenth.

The probability of having 2 trucks with no violations, 2 with 1 violation, and 3 with 2 or more violations when 7 trucks are inspected are approximately 0.041 (rounded to three decimal places).

To find the probability of this specific situation, we can use the multinomial probability formula:
P(X) = (n! / (x1! × x2! × ... × xn!)) × (p1^x1) × (p2^x2) × ... × (pn^xn)
In this case:
- n = 7 (total number of trailer trucks)
- x1 = 2 (trucks with no violations)
- x2 = 2 (trucks with 1 violation)
- x3 = 3 (trucks with 2 or more violations)
- p1 = 0.1 (probability of no violations)
- p2 = 0.3 (probability of 1 violation)
- p3 = 0.6 (probability of 2 or more violations)
Now we plug in the values:
P(X) = (7! / (2! × 2! × 3!)) × (0.1^2) × (0.3²) × (0.6³)
P(X) = (5040 / (2 × 2 × 6)) × (0.01) × (0.09) × (0.216)
P(X) = (210) × (0.01) × (0.09) × (0.216)
P(X) ≈ 0.040788

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Transformation doesn't depend on the shape of the figure if it has an overlap or not

The transformation \(8d\) can be applied to a figure with overlap or not with overlap.

Transformations are operations on a plane that change the position, shape, and size of geometric figures.

When a geometric figure is transformed,

its new image has the same shape as the original figure.

However,

it is in a new position and may have a different size.

Let's talk about different types of transformations.

Rotation:

It occurs when a shape is turned around a point, which is the rotation center.

Translation:

It moves the shape from one point to another on a plane.

Reflection:

It is an operation that results in the mirror image of the original shape.

Scaling:

The shape is transformed by changing the size without changing its orientation.

Transformation on \(8d\):

In the given problem, the transformation of \(8d\) can be applied to the figure with or without overlap.

This means that \(8d\) transformation doesn't depend on the shape of the figure if it has an overlap or not.

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Answer:

$137.82

Step-by-step explanation:

The volume of a hemisphere stone is given by the volume of a half-sphere:

Volume = (2/3) * pi * radius^3

If the diameter is 16 inches, the radius is 16/2 = 8 inches, so the volume is:

Volume = (2/3) * pi * 8^3 = 1072.33 in3

We need a total of 8 stones, so the total volume is:

Total Volume = 8 * 1072.33 = 8578.64 in3

The density of clay is 0.0035 pounds per cubic inch, so the total weight of the 8 stones is:

Weight = Total Volume * density = 8578.63 * 0.0035 = 30.0252 pounds

Finally, if the price of each pound of clay if $4,59, the final price is:

Price = 30.0252 * 4.59 = $137.82

The rockready battery is most likely to last all day at the beach.

When you're headed to the beach and you have to choose between two batteries that are marketed to owners of personal music players, you would want to know which battery is most likely to last all day. Duratunes claims a mean battery life of 11 hours with a standard deviation of 2 hours, while Rockready advertises 12 hours with a standard deviation of 1.5 hours. The answer to the question is Rockready battery. The explanation is given below:Let's assume that the distribution of battery lives is normal for both batteries. Thus, for the Duratunes battery, the mean (μ) and standard deviation (σ) are 11 hours and 2 hours, respectively. The mean and standard deviation for the Rockready battery are 12 hours and 1.5 hours, respectively. We must compute the probabilities that each battery will last at least 8 hours.Below is the formula to calculate the probabilities for both batteries: z = (x - μ) / σHere, x represents the number of hours the battery lasts. We get the following values of z:Duratunes battery: z = (8 - 11) / 2 = -1.5Rockready battery: z = (8 - 12) / 1.5 = -2.67We will use the normal distribution table to determine the probabilities associated with these z-values. We will find the area to the left of each z-value in the table. Because we want to find the probability that each battery lasts at least 8 hours, we will subtract this probability from 1. In other words:P(Duratunes battery lasts at least 8 hours) = 1 - P(z < -1.5) = 1 - 0.0668 = 0.9332P(Rockready battery lasts at least 8 hours) = 1 - P(z < -2.67) = 1 - 0.0038 = 0.9962Therefore, the Rockready battery is most likely to last all day at the beach.

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The conversion factor we used is (1 meter / 100 centimeters), which allowed us to convert 600 centimeters to 6 meters.

To convert 600 centimeters to meters, we can use this conversion factor as a fraction and set up the equation as follows:

600 centimeters x (1 meter / 100 centimeters) = meters

In this equation, the units of centimeters cancel out, leaving us with the unit of meters, which is what we want to find. The fraction (1 meter / 100 centimeters) represents the conversion factor we're using, and it allows us to convert from centimeters to meters.

Now, we can simplify the equation by multiplying 600 by the fraction (1 meter / 100 centimeters):

600 centimeters x (1 meter / 100 centimeters) = (600 x 1) meters / 100

This gives us:

600 centimeters = 6 meters

Therefore, the conversion factor we used is (1 meter / 100 centimeters), which allowed us to convert 600 centimeters to 6 meters.

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The length of the rectangle is 7 cm and the width is 5 cm.

The whole distance covered by the rectangle's borders or its sides is known as its perimeter. As we know the rectangle will have 4 sides then the perimeter of the rectangle will be equal to the total of its four sides. And the unit will be in meters, centimeters, inches, feet, etc.        

The formula for the Perimeter of the rectangle is given by

Here we have

The length of a rectangle is 2cm greater than the width of the rectangle

And perimeter of the rectangle = 24 cm

Let x be the width of the rectangle

From the given data,

Length of the rectangle = (x + 2) cm  

As we know Perimeter of rectangle = 2(Length+width)

=> Perimeter of rectangle = 2(x+2 + x) = 2(2x +2)

From the given data,

Perimeter of rectangle =  24cm

=> 2(2x +2) = 24 cm

=> (2x +2) = 12     [ Divided by 2 into both sides ]

=>  2x = 12 - 2

=>  2x = 10

=>   x = 5         [ divided by 2 into both sides ]  

Length of rectangle, (x+2) = 5 + 2 = 7 cm

Therefore,

The length of the rectangle is 7 cm and the width is 5 cm.

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Answer:

Step-by-step explanation:

1/2x + 3 = 6

1/2x = 3

x = 6

Answer:

2cos(3x)

Step-by-step explanation:

If the function were just cos(x), then the second peak would happen at 2π.  Instead though, it happen 2π / 3.   That means that the coefficient of x must be 3.

At zero, we see a peak of the curve, so we're dealing with a cos function, that peak happens at (0, 2), so the coefficient of the function is 2.

That tells us that the function graphed here must be 2cos(3x).

The correct answer is option A which is the equation of the given graph is y = 2cos(3x)

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

If the function were just cos(x), then the second peak would happen at 2π.  Instead, though, it happens 2π / 3.   That means that the coefficient of x must be 3.

At zero, we see a peak of the curve, so we're dealing with a cos function, that peak happens at (0, 2), so the coefficient of the function is 2.

Therefore the correct answer is option A which is the equation of the given graph is y = 2cos(3x)

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Answer:

32 words per minute

Answer:

I think it's -1, 4. But i'm not a 100% sure.

Step-by-step explanation:

Answer:

To find the range, first order the data from least to greatest. Then subtract the smallest value from the largest value in the set.

Step-by-step explanation:

This is how you solve for Range; I can't view the image on my chromebook.

For given triangle, the length of BX is 10 cm.

What is triangle?

A triangle is a geometric shape that consists of three sides and three angles. It is one of the most fundamental and commonly studied shapes in geometry.

To find the length of BX, we can use the formula for the area of a triangle:

Area = (base * height) / 2.

We are given the areas of triangles ADX and BCX, as well as the lengths of AX and DX.

Area of triangle ADX = \(36 cm^2\)
Area of triangle BCX = \(65.61 cm^2\)
AX = 8.6 cm
DX = 7.2 cm

Let's start by finding the height of triangle ADX. We can use the formula:

\(36 cm^2\) = (BX * 7.2 cm) / 2

Simplifying the equation:

\(36 cm^2\) = (BX * 3.6 cm)

Dividing both sides by 3.6 cm:

BX = \(36 cm^2\) / 3.6 cm
BX = 10 cm

Therefore, the length of BX is 10 cm.

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Step-by-step explanation:

A no

n + 7 = 16

n + 7 - 7 = 16 - 7

n = 9

that is not n = 15

B yes

(2/3)v = 8

3×(2/3)v = 3×8

2v = 24

2v/2 = 24/2

v = 12

C no

6z = 84

6z/6 = 84/6

z = 14

that is not z = 8

The probability that a college student selected at random has cheated on an exam is 0.3328 or 33.28% .

The given problem requires us to find the probability that a student has cheated on an exam given that the number of college students who have cheated on an exam is 855 and the number of students who have not cheated on an exam is 1717.

The total number of students is the sum of those who have cheated and those who have not cheated.

Total number of possible outcomes = Number of students who have cheated on an exam + Number of students who have not cheated on an exam

= 855 + 1717

= 2572

Therefore, the probability that a college student selected at random has cheated on an exam is:

P(C) = Number of outcomes favorable to event C / Total number of possible outcomes

= 855 / 2572

= 0.3328 or 33.28% (approx.)

Hence, the probability that the student has cheated on an exam is 0.3328 or 33.28% (approx.).

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Answer:

Part A: (C) 16 square inches

Part B: (C) 36 square inches

Answer:

because they all have 3 corners

Answer:

x=31

Step-by-step explanation:

Hello there!

the shown angles are supplementary meaning that the sum of the two is 180

so we create an equation

180=3x+25+2x

step 1 combine like terms

3x+2x

now we have

180=25+5x

step 2 subtract 25 from each side

180-25=155

now we have

155=5x

step 3 divide each side by 5

155/5=31

5x/5=x

we're left with x=31

~TheMathWiz

The connection between linear equations and geometry lies in the fact that a single linear equation corresponds to a plane, while the solution of multiple linear equations corresponds to the intersection of these planes, resulting in geometric shapes such as lines, points, or empty sets.

A single linear equation in two variables represents a line on a Cartesian plane. The equation can be rearranged into slope-intercept form (y = mx + b), where 'm' represents the slope of the line and 'b' represents the y-intercept. Each point (x, y) on the line satisfies the equation. In three dimensions, a single linear equation with three variables represents a plane. The equation can be expressed as Ax + By + Cz + D = 0, where A, B, C, and D are constants. Every point (x, y, z) that satisfies the equation lies on the plane.

When multiple linear equations are considered, each equation corresponds to a plane in three-dimensional space. The solution to the system of equations corresponds to the points where these planes intersect. Depending on the configuration of the planes, the solution may result in geometric shapes such as lines, points, or an empty set. For example, if two planes intersect in a single line, the solution represents the coordinates of points along that line. If the planes do not intersect, the system has no solution, indicating an empty set. The relationship between linear equations and geometry allows us to understand and analyze geometric configurations through the language of algebraic equations.

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Answer:

f(2)= -2

g(2)= 12

Step-by-step explanation:

To solve this we use the substitution method. Since f(2) is your variable, we will plug the x-value of 2 into each equation

f(2)= 2(2)^2-5(2)

f(2)=8-10

f(2)= -2

If the same variable is used for both equations then g(x) would be g(2) as well leaving you with

g(x) = 3x^2

g(2)= 3(2)^2

g(2)=12

Answer:

x=26°, y=26°, z=26°

Step-by-step explanation:

x+74=100 (the sum of linear pair)

x=100-74

x=26

x=y=26 (alternate angle)

y=z=26 (vertically opposite angle V.O.A)

82 students attended the dance.

In algebra, an equation can be expressed as a mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value.

An equation is defined as two expressions, connected by an equals sign ("="). The expressions on the two sides of the equals sign are said the "left-hand side" and "right-hand side" of the equation. Assuming this does not reduce the generality, this can be realized by subtracting the right-hand side from both sides.

According to the given problem,

Let the number of students be x,

2.50x + 120 = 325

⇒ 2.5x = 325 - 120

⇒ 2.5x =   205

⇒ x = 82

Hence, 82 students attended the dance.

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Answer:

B

Step-by-step explanation:

Red goes first then blue

5:3

Answer:

5

3

; 5 to 3; 5:3

Step-by-step explanation:

Answer:

9.2

Step-by-step explanation:

divide percentages by 100 if you're converting it to a decimal

;)

Answer:

9.2

920%

900-20

9.00

+

0.20

_____

9.20 or 9.2

The absolute value of x minus one is equal to two. Therefore, x must be either one greater than two (x = 3) or one less than two (x = 1).

One less than x results in a value of two in absolute terms. As a result, x minus 1 has an absolute value of 2, which is a positive number. The separation of an integer from zero is its absolute value. As a result, x minus 1 is two units from zero in absolute terms. As x minus one has an absolute value of two, its real value must either be two or a negative two. That is to say, x must either be one more than two (x = 3) or one less than two (x = 1).In order to confirm this, let's look at a few examples. If x = 3, then |x - 1| = |2 - 1| = |1| = 1 which is not equal to two. Therefore, x = 3 is not the answer we are looking for. On the other hand, if x = 1, then |x - 1| = |1 - 1| = |0| = 0 which is not equal to two. Therefore, x = 1 is also not the answer we are looking for. The only two possible solutions for the equation |x - 1| = 2 are x = 3 and x = 1. Therefore, the result of |x - 1| = 2 is that x must be either one greater than two (x = 3) or one less than two (x = 1)

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Answer:

Step-by-step explanation:

-1+(-2)

Answer:

distance = 10,000 feet  rate = 500 feet / minute

distanced traveled in 20 minutes = 500 * 20 = 10,000 feet

I'm guessing you need these minute by minute

minutes         distance

0 0

1 500

2 1,000

3 1,500

4 2,000

5 2,500

6 3,000

7 3,500

8 4,000

9 4,500

10 5,000

11 5,500

12 6,000

13 6,500

14 7,000

15 7,500

16 8,000

17 8,500

18 9,000

19 9,500

20 10,000

Hope that helps

Step-by-step explanation:

Answer:  a) increases

               b) decreases

               c) remains the same

Step-by-step explanation:

a) As time increases, the distance traveled increases because you are traveling from home to work at a rate of 500 ft/min

b) As time increases, the distance remaining decreases because you are getting closer to your goal of 10,000 ft

c) As time increases, the distance from home to work remains the same because the distance from point A (home) to point B (work) hasn't changed - only YOUR distance between them has changed.

Step-by-step explanation:

slope interception formula is

y-y1=m(x-x1)

where m is m=y-y1/x-x1 in this case m=-2 because the line we are trying to find is parallel to the given one y=-2x-6 where slope k=-2

so the final equation would be

y-1=-2(x-(-4))

y-1=-2x-2*4

y=-2x-8+1=-2x-7

Answer:

1 in

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

you are looking for perfect square factors of the numbers under the radical sign. both numbers and the sum are irrational because they contain √5

125 = 5×25

80 = 5×16

3√125 = 3√(25×5) = 3×5√5 = 15√5

√80 = √(16×5) = 4√5

1)  15√5 + 4√5 = 19√5      the √5 is the same square root so you add the coefficients

perfect square factors are bold

4×√(25×2)×√(9×2) =

4×5×3×√(2×2) =

60×√4 =

2)  60 × 2 = 120

the numbers are both irrational but the answer is rational because √2 ×√2 = √4 = 2