a new security system needs to be evaluated in the airport. the probability of a person being a security hazard is 0.023. at the checkpoint, the security system denied a person without security problems 1.5% of the time. also the security system passed a person with security problems 1% of the time. what is the probability that a person who passed through the system is without any security problems? report answer to 4 decimal places.

The mean, median, and mode for my set of test scores turned out to be the same: 83 · The range of my scores is 42 therefore the five test scores are 58, 83, 83, 90, 100.

This is referred to as the difference between the largest and smallest values, the result of subtracting the sample maximum and minimum.

Range = maximum - minimum

      42  = 100 - x

      x = 100 - 42 = 58

Since the mode and mean is 83 then the set of values = 58, 83, 83, 91, 100/5 = 83

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Answer:

"In

In a 30-60-90 triangle, the sides are in a ratio of 1:√3:2.

So, the hypotenuse of the triangle is 62 = 12 ft long.

The longer leg of the triangle is 6√3 = 10.8 ft long (to the nearest tenth of a foot)

(x,y)⇒(x+5,y+10) is the translation rule for A'B, which is a translation of AB.

A translation is a geometric transformation in Euclidean geometry that moves every point in a figure, shape, or space by the same distance in the same direction. A translation may alternatively be thought of as adding a constant vector to each point or changing the coordinate system's origin. A translation is a sort of transformation that involves sliding each point in a figure the same distance in the same direction. A translation in mathematics moves a form left, right, up, or down but does not turn it. The translated (or picture) shapes appear to have the same size as the original shape, showing that they are congruent. They've just moved in one or more directions.

Here,

A translation is a sort of transformation in which every point in a figure moves the same distance in the same direction. Slides are another term for translations. A translation can be described with words like "moved up 3 and over 5 to the left" or using notation.

The translation rule for A'B is a translation of AB is (x,y)⇒(x+5,y+10).

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The graph of g(x) = -f(x + 4) is the reflection of the graph of f(x) = |x| about the x-axis, translated 4 units to the left.

The graph of f(x) = |x| is a V-shape with the vertex at the origin. The graph of g(x) will have the same V-shape, but with the vertex located 4 units to the left of the origin and reflected about the x-axis.

Therefore, g(x) = -f(x + 4) is the reflection of the graph of f(x) = |x| about the x-axis, translated 4 units to the left. It could be concluded that the correct answer is as given above.

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Sample average: To calculate the sample average, add up all the measurements and divide by the number of measurements.

42.4 + 65.7 + 29.8 + 58.7 + 52.1 + 55.8 + 57.0 + 68.7 + 67.3 + 67.3 + 54.3 + 54.0 = 751.4

Sample average = 751.4 / 12 = 62.62

Sample standard deviation steps:

Subtract the sample average from each measurement to find the deviations.

Square each deviation.

Add up the squared deviations.

Divide the sum by the number of measurements minus one (n-1).

Take the square root of the result.

Sample standard deviation = sqrt(sum of squared deviations / (n-1))

Dot diagram: A dot diagram, also known as a dot plot, is a simple graphical representation of a set of data where each data point is represented by a dot on a number line. To create a dot diagram, plot each measurement as a dot on a number line with the corresponding value.

This is a useful tool to visualize the distribution of the data and to see the general pattern, such as the presence of outliers, skewness, or clusters.

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Answer: 45,60

Step-by-step explanation:

OK

Answer:

The angle marked x can be calculated using the angle sum property of a triangle. Since ∠CBE = 48° and ∠DBC + ∠BCE = 180°, then x = 180° - 48° = 132°.

Answer:Since lines AB and DE are parallel, corresponding angles are congruent. This means that angle x (which is formed by lines AB and DE) is congruent to angle CBE (which is formed by lines DE and BC). Therefore, angle x is also equal to 48 degrees.

x = 48°

The rectangular block has a perimeter of 10 units. The triangle's perimeter is 7.5 units.

The size of a region on a surface is measured in area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina. The total space occupied by a flat (2-D) surface or the form of an item is defined as its area. Draw a square on a sheet of paper using a pencil. It is a two-dimensional figure. The area of the form on the paper is referred to as its Area.

Here,

area=6 units

length on scale=5-2

=3 units

3*w=6

w=2 units

perimeter=2*(3+2)

=10 units

length of side of triangle=2.5 units

perimeter=2.5+2.5+2.5

=7.5 units

The perimeter of rectangle block is 10 units. The perimeter of triangle is 7.5 units.

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The line y = ax + b is parallel to the line y = 2x - 6 and passes through the point (1, -7), the value of a and b is 2 and -9 respectively.

The equation of line:

y = 2x - 6

We firstly find the slope of the equation by comparing the equation by y = mx + c.

On comparing m = 2

The point is (1, -7).

So x(1) = 1 and y(1) = -7

The formula of slope intercept form is:

y - y(1) = m(x - x(1))

Now putting the value:

y - (-7) = 2(x - 1)

y + 7 = 2x - 2

Subtract 7 on both side, we get

y = 2x - 9

On comparing the equation from y = ax + b, we get

a = 2 and b = -9

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The complete question is:

The line y = ax + b is parallel to the line y = 2x - 6 and passes through the point (1, -7). Find the value of a and b.

The solution of the system of equation is (1, 0). Therefore, the answer is b.

System of equation can be solved using different method such as elimination method, substitution method and graphical method.

We are asked to solve the system of equation by substitution method.

Hence,

y = x - 1

3x + 2y = 3

Using substitution method, let's substitute the value of y in equation(ii)

3x + 2(x - 1) = 3

3x + 2x - 2 = 3

5x  = 3 + 2

5x = 5

x = 5 / 5

x = 1

Let's find the value of y in the equation.

y = 1 - 1

y = 0

Therefore,

x = 1 and y = 0

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The stated margin of error account for this possible bias is random error.

The term margin of error is defied as a statistic expressing the amount of random sampling error in the results of a survey

Here we know that the bias due to nonresponse is not accounted for by the margin of error.

And the people who have longer travel times to work might have less time to respond to a survey.

And the calculated estimate from the sample to be less than the true mean travel time to work.

Where as the bias due to nonresponse is not accounted for by the margin of error.

Here we have also know that the the margin of error doesn't account for any mistakes that we've made.

So now we have to look at longer travel times might have less time to respond for a survey right.

Then we get that  it only accounts for random error.

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The first equation into the second to eliminate [tex]y[/tex] and solve for [tex]x[/tex]

[tex]$$\begin{gathered}-x+4\left(\frac{1}{4} x-3\right)=-4 \\\Rightarrow \\-x+x-12=-4 \\\Rightarrow \\-12=-4 \\\Rightarrow \\x=3\end{gathered}$$[/tex]

At infinite solutions, both sides are equal. For example, 6x + 2y - 8 = 12x +4y - 16. Simplifying an equation with an infinite-solution formula or method results in an infinite solution, because both sides are the same. Infinity represents infinity or infinity. It is usually represented by the “∞” symbol.

Some equations have infinitely many solutions. In these equations any value of the variables makes the equation true. When you try to solve an equation to get a variable or number equal to itself, you find that the equation has infinitely many solutions. 

This system of linear equations can be graphed on a [tex]$x-y$[/tex] plane. The first equation represents a line with slope [tex]\frac{1}{4}[/tex] and [tex]$y$[/tex]-intercept [tex]-3[/tex]. The second equation represents another line with slope [tex]-1[/tex] and [tex]$y$[/tex]-intercept [tex]-4[/tex]. The intersection point of the two lines is the solution to the system of linear equations.

To find the solution, we can substitute the first equation into the second to eliminate [tex]y[/tex] and solve for [tex]x[/tex]

[tex]$$\begin{gathered}-x+4\left(\frac{1}{4} x-3\right)=-4 \\\Rightarrow \\-x+x-12=-4 \\\Rightarrow \\-12=-4 \\\Rightarrow \\x=3\end{gathered}$$[/tex]

We can then use either equation to find the value of [tex]y[/tex]

[tex]$$\begin{gathered}y=\frac{1}{4} x-3 \\\Rightarrow \\y=\frac{1}{4} \cdot 3-3 \\= \\y=-2\end{gathered}$$[/tex]

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The product of two numbers whose sum is 10 and whose product is 24 is 4 and 6. 10x can be written as (4x6)x3 and factored by grouping as (4x3)+(6x3).

a. The product of two numbers is 24, and the sum is 10. This means that 4 and 6 must be the numbers, because 4x6=24 and 4+6=10.

b. 10x can be written as (4x6)x3, since 4x6=24 and 24x3=10x.

c. 10x can be factored by grouping as (4x3)+(6x3). This is because 4x3=12 and 6x3=18, and 12+18=30, which is the same as 10x.

The product of two numbers whose sum is 10 and whose product is 24 is 4 and 6. 10x can be written as (4x6)x3 and factored by grouping as (4x3)+(6x3).

The complete question is :

Find two numbers whose product is 8•3=24 and whose sum is 10, write 10x using the factors from part (a), and factor by grouping. The answer is that the two numbers are 4 and 6, 10x can be written as (4x6)x3, and factored by grouping as (4x3)+(6x3).

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Buyers get a percentage off on any purchase above the Minimum Basket Price. It will also be capped at the Maximum Discount Price if you choose to set a limit. E.g. "10% OFF with Min.

Answer: The one in the middle

Step-by-step explanation:

The one in the middle because of the huge downhill

Answer:

Choice C    (1/3b)/7 = 25.50

Step-by-step explanation:

1/3 of budget b =(1/3)b

7 bills at $25.50 per bill = 7 x 25.50

Setting both equation to each other we get
(1/3)b = 7 x 25.50

Dividing by 7:
(1/3b)/7 = 25.50

(a) Confidence interval of 4547 to 8473 steps means the average number of steps taken by employees falls in that range with 95% confidence.

(b) The point estimate was 6510 and  the margin error is 1963

(c) Yes, there  is convincing evidence that the employees of this company are not meeting the guideline, on average

If we take many samples of size 50 and calculate many intervals, about 95% of the interval will capture the true average of steps for an employee in a day.

We are 95% confident that the interval from 4547 to 8473 steps contains the true average steps for employees/day.

Since all plausible values in our interval are under 10,000, there is convincing evidence that the employees are not meeting this guideline, on average.

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The values of F(4; 5) (the incomplete gamma function) and F(5; 4) are 4.41 and 8.904

The value of the incomplete gamma function can be obtained as:

F(4; 5) = ₀∫⁵ t⁴⁻¹ . e^(-t) dt

          = г(4)  ₀∫⁵ (t⁴⁻¹ . e^(-t)) г(4) dt

          = г(4)  [P(T < 5)]    ( the integral is the density function of T ∼ Gamma(4, 1) )

          = (3!) [P(2(1)T < 5(2) (1) )]

          = 6 [P( X²₈ < 10 )]

          = 6 [0.735]

          = 4.41

F(5; 4) = ₀∫⁴ t⁵⁻¹ . e^(-t) dt

          = г(5)  ₀∫⁴ (t⁵⁻¹ . e^(-t)) г(5) dt

          = г(5)  [P(T < 4)]    ( the integral is the density function of T ∼ Gamma(4, 1) )

          = (4!) [P(2(1)T < 4(2) (1) )]

          = 24 [P( X²₁₀ < 8 )]

          = 24 [0.371]

          = 8.904

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The probability that at least 3 of them will be carrying a reusable water bottle is 74.6%

Here it is given that probability of people who carry at least 1 reusable water bottle is p = 0.58.

A random sample of n = 5 people is selected.

This data follows a binomial distribution, with success denoted by a person carrying t least 1 reusable water bottle. The probability mass function of the binomial distribution is,

[tex]P(X=x)=(^n_x)P^x(1-P)^n^-^x; x=0,1,2,...0 < P < 1[/tex]

Compute the probability that at least 3 of them will be carrying a reusable water bottle as follows:

P (X ≥ 3) =P(X=3)+P(X=4)+P(X=5)

[tex]P(X\geq 3)=(^5_3)0.58^3(1-058)^5^-^3+(^5_4)0.58^4(1-058)^5^-^4+(^5_5)0.58^5(1-058)^5^-^5[/tex]        

P(X≥3)=0.449538048+0.237646416+0.0656356768

P(X≥3)=0.746821224

The percentage is,0.746821224 × 100 = 74.6%.

Thus, the probability that at least 4 of them will be carrying a reusable water bottle is 74.6%.

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Answer:

below

Step-by-step explanation:

We need to eliminate oneof the variables....I'll choose 'y'

x+ y = 60      <======multiply this equation - 22 to get

-22x -22y = -1320

44x  =22y = 2024        Now add the two equations together to eliminaty 'y'

22x = 704     then x = 32     x+y = 60   so y = 28

The value for $\frac{0.\overline{72}}{0.\overline{27}}$ as a common fraction in lowest terms is 2.666

To convert repeating decimals to fractions, we can use the following method:

Let's call the repeating decimal 0.72... = x, and the repeating decimal 0.27... = y.

Then 10x = 7.2... and 10y = 2.7...

Subtracting the original expressions from the above:

10x - x = 7.2... - 0.72...

=> 9x = 7

=> x = 7/9

And similarly,

10y - y = 2.7... - 0.27...

=> 9y = 2

=> y = 2/9

Therefore,

0.72... / 0.27... = x / y = (7/9) / (2/9) = 7/2 = 3.5

A repeating decimal is a decimal that has a repeating pattern of digits after the decimal point. To convert a repeating decimal to a fraction, we need to identify the repeating pattern and convert it to a fraction. This is done by multiplying both the numerator and denominator by a power of 10 that makes the repeating part an integer.

Then, the resulting fraction can be simplified to its lowest terms. In this case, the repeating decimals 0.72... and 0.27... can be converted to the fractions 7/9 and 2/9 respectively, and dividing the two results in a fraction of 7/2 can be simplified to 3.5.

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The results for systems under rotational motion are listed below:

First section:

Part A - The angular speed of the large gear is 90π radians per minute.

Part B - The linear velocity of the large gear is 27π centimeters per minute.

Part C - The linear velocity of the smaller gear is 27π centimeters per minutes.

Part D - The angular speed of the smaller gear is 27π / 8 radians per minute.

Part E - The angular speed of the smaller gear is 27 / 16 revolutions per minute.

Second section:

Part A - The angular speed of the LP is 200π / 3 radians per minute.

Part B - The angular velocity of the LP is 200π / 3 radians per minute.

In the first part of this question we find the case of rigid transmission system under rotational motion, two gears that transmits power and whose angular speed ratio is shown below:

ωL / ωS = rS / rL

Where:

And the linear velocity (v), in centimeters per minute, is calculated by this formula:

v = rL · ωL = rS · ωS

Part A - How many radians per minute is the large gear turning?

R/ The angular speed is:

ωL = 45 rev / min × 2π rad / rev

ωL = 90π rad / min

Part B - What is the linear velocity of the teeth on the large gear?

v = (0.3 cm) · (90π rad / min)

v = 27π cm / min

Part C - What is the linear velocity of the teeth on the smaller gear?

v = 27π cm / min

Part D - How many radians per minute is the smaller gear turning?

ωS = v / rS

ωS = (27π cm / min) / (8 cm)

ωS = 27π / 8 rad / min

Part E - How many revolutions per minute is the smaller gear turning?

nS = 27π / 8 rad / min × (1 / 2π rev / rad)

nS = 27 / 16 rev / min

The second part uses the same kinematic equation used in the previous part:

Part A - How many radians per minute is this:

ω = (33 + 1 / 3 rev / min) × (2π rad / rev)

ω = 200π / 3 rad / min

Part B - Find the angular velocity:

The angular velocity is independent from radius of rotation, thus:

ω = 200π / 3 rad / min

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Answer:

[tex]c^6 -7[/tex]

Step-by-step explanation:

c to the sixth power is [tex]c^6[/tex], and this minus 7 is [tex]c^6 -7[/tex].

Answer:

7 - c^6

Step-by-step explanation:

First, calculate the value of c raised to the 6th power: c^6

Then, subtract the result from 7: 7 - c^6. The expression represents the calculation of raising c to the 6th power, and then subtracting the result from 7.

For the given matrix, Cartesian products to elements is verified,

(a) (1,2)

A X A: This set contains all possible ordered pairs where x is a member of set A and y is also a member of set A. The element (1,2) does not belong to this set because 1 is a member of set A, but 2 is not.

B X A: This set contains all possible ordered pairs where x is a member of set B and y is a member of set A. The element (1,2) does not belong to this set because 2 is a member of set B, but 1 is not.

A X B: This set contains all possible ordered pairs where x is a member of set A and y is a member of set B. The element (1,2) belongs to this set because 1 is a member of set A and 2 is a member of set B.

B X B: This set contains all possible ordered pairs where x is a member of set B and y is also a member of set B. The element (1,2) does not belong to this set because 1 is not a member of set B.

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By using the Angle Sum Property, we can find that m angle a = 180 - (3(x - 5) + x 25) = 180 - 4x + 25

We can use the Angle Sum Property to solve this problem. The Angle Sum Property states that the sum of the measures of the angles in a triangle is equal to 180°. We can use this to write the equation 180 = m angle bdc + m arc bc + m angle a. Since we have the values for m angle bdc and m arc bc, we can plug them in and rearrange the equation so that m angle a is the only unknown. We get 180 = 3(x - 5) + x 25 + m angle a. Subtracting 3(x - 5) + x 25 from both sides, we get m angle a = 180 - (3(x - 5) + x 25). Simplifying, we get m angle a = 180 - 4x + 25, which is the final answer.

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Answer:

3570

Step-by-step explanation:

Find the prime factorization of 105

105 = 3 × 5 × 7

Find the prime factorization of 170

170 = 2 × 5 × 17

Multiply each factor the greater number of times it occurs in steps 1 or 2 above to find the LCM:

LCM = 2 × 3 × 5 × 7 × 17

LCM = 3570

The value of the cross product of two given vectors is = 6i-7j.

We only want to think about a portion of the rod. We first wish to think about a narrow slice of the rod. We can solve a straightforward equation if the thermal energy density is constant across the volume.

A *B stands for the vector product or cross product of two vectors A and B, and the resulting vector is perpendicular to the original two. While the dot product is used to identify the length of a vector or the angle between two vectors, the cross product is typically employed to determine the vector that is perpendicular to the plane surface spanned by two vectors. In three dimensions, the cross product of two vectors, such as A B, equals a vector at right angles to both.

we have a = i - 6k and b= j + k then find a×b

[tex]a*b=\left[\begin{array}{ccc}i&j&k\\1&0&-6\\1&0&1\end{array}\right] \\\\a*b=(6)i-(1+6)j+(0k)\\\\a*b=6i-7j[/tex]

The value of the cross product of two given vectors is = 6i-7j.

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