The Transportation Security Administration (TSA) is responsible for airport security. On some flights, TSA officers randomly select passengers for an extra security check before boarding. One such flight has 76 passengers (12 in first class and 64 in coach). TSA officers selected an SRS of 10 passengers for screening. Let p-hat be the proportion of first class passengers in this sample. So, assuming that you are checking for the probability of choosing a first class passenger out of all passengers on the flight. Is the 10% condition met in this case? Justify your answer. (POS 447#31)


- Yes, 10 passengers out of 76 is less than 10% of the population of the flight.

- yes, 10 passengers out of all passengers on all flights is less than 10% of the population

- No, 10 passengers is the population being studied and is not less than 10% of the 10 total

- No, 10 passengers out of 76 is more than 10% of the population of the flight.

The volume of the prism is

The volume of the prism is solved by the formula

= area of triangle * depth

Area of the triangle

= 1/2 base * height

base = p = cos 51.34 * √41 = 4

height = q = sin 51.34 * √41 = 5

= 1/2 * 4 * 5

= 10

volume of the prism

= area of triangle * depth

= 10 * 7

= 70 cm³

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1.a, the center of the circle is (6, 3) and the radius is 6√2. For 1.b, the equation of the circle is (x - 5)^2 + (y + 4)^2 = 36. For 2.a, the slope of the line passing through the given points is 2. For 2.b, the linear equation passing through the given points is y = 2x - 1.

1.a. The equation of the given circle is (2 - 6)^2 + (y - 3)^2 = 72. To find the center and radius of the circle, we can compare the equation to the standard form of a circle, which is (x - h)^2 + (y - k)^2 = r^2. By comparing the equations, we can determine that the center of the circle is (6, 3) and the radius is √72 or 6√2.

b. Given the center of the circle as (5, -4) and the radius as 6, we can write the equation of the circle using the standard form. Substituting the values into the equation, we have (x - 5)^2 + (y + 4)^2 = 6^2. Simplifying this equation gives us (x - 5)^2 + (y + 4)^2 = 36.

2.a. To find the slope of the line passing through the points (3, 5) and (5, 9), we can use the slope formula: m = (y2 - y1) / (x2 - x1). Substituting the coordinates into the formula, we get m = (9 - 5) / (5 - 3) = 4 / 2 = 2.

b. To find the linear equation passing through the points (3, 5) and (5, 9), we can use the point-slope form of a linear equation: y - y1 = m(x - x1). Substituting the values into the equation with the slope we found in part (a), we have y - 5 = 2(x - 3). Simplifying this equation gives us y - 5 = 2x - 6. Rearranging the terms, we get y = 2x - 1.

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The tax consequences to Lucy associated with the collection of the account receivable is $7,000.

What is the cost price?

The cost price in retail systems represents the particular value that represents the unit price purchased. This value is utilized as a crucial aspect in calculating profitability, and it is employed in various stock market theories to determine the value of stock holdings.

Here, we have

Given: Lucy purchased a $100,000 account receivable for $90,000. During the current year, Lucy collected $97,000 from the account.

We have to find the tax consequences to Lucy associated with the collection of the account receivable.

Collected = $97,000

Purchase cost = $90,000

The amount collected more than Lucy’s basis in the receivable:

= $97,000 -  $90,000

= $7,000

Hence, the tax consequences to Lucy associated with the collection of the account receivable is $7,000.

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Answer:

Step-by-step explanation:

(a + b)(a - b) = a² - b²

\((7 + 4\sqrt{3}) (7 - 4\sqrt{3}) = 7^{2}-(4\sqrt{3} )^{2}\\\\ = 49 - 4^{2}*(\sqrt{3})^{2}\\\\= 49 - 16 * 3\\\\= 49 - 48\\\\= 1\)

\(\boxed{1}\) ✅

\(\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}\)

\((7 + 4 \sqrt{3} ) \: (7 - 4 \sqrt{3} ) \\ \\ = 7 \: (7 - 4 \sqrt{3} ) + 4 \sqrt{3} (7 - 4 \sqrt{3} ) \\ \\ = 49 - 28 \sqrt{3} + 28 \sqrt{3} - 48 \: (since \: \sqrt{3} \times \sqrt{3} = 3)\\ \\ = 49 - 48 \\ \\ = 1\)

You can also use the identity:

( a + b ) ( a - b ) = \( {a}^{2} - {b}^{2}\)

\(\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{!}}}}}\)

The relationship the ratios of sin x° and cos y° share is 12/13.

The value of sin (x) and Cos (y) is calculated by applying trig ratio as follows;

The trig ratio is simplified as;

SOH CAH TOA;

SOH ----> sin θ = opposite side / hypothenuse side

CAH -----> cos θ = adjacent side / hypothenuse side

TOA ------> tan θ = opposite side / adjacent side

The value of sin (x) is calculated as follows;

sin x = 12/13

The value of cos (y) is calculated as follows;

cos y = 12 / 13

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Answer:

A

Step-by-step explanation:

The radian measure of the angle at the center of the circle is approximately 1.6623 radians.

We are given that the radius of the circle is 77.0 cm and the length of the intercepted arc is 128 cm. We need to find the radian measure of the angle at the center of the circle.

To solve this problem, we use the formula relating the angle at the center of a circle, the radius of the circle, and the arc length intercepted by the angle.

The formula is given byθ = s/rwhereθ = angle at the center of the circle in radians s = arc length intercepted by the angle r = radius of the circle Substituting the given values, we getθ = 128/77.0 = 1.6623 radians (rounded to four decimal places)

Therefore, the radian measure of the angle at the center of the circle is approximately 1.6623 radians.

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The only point that could be on the line parallel to line GH and passes through point J is (3, 3).

To identify the points that could be on the line parallel to line GH and passes through point J, we need to apply the concept of slope of a line and parallel lines. Two lines are parallel if they have the same slope.Let's first find the slope of line GH using the slope formula m = (y2 - y1) / (x2 - x1)The points on line GH are (–4, 1) and (2, –2)m = (–2 – 1) / (2 – (–4)) = –3 / 6 = –1 / 2Therefore, the slope of line GH is –1 / 2.Let's now find the equation of the line that is parallel to line GH and passes through point J. We know that the slope of this line is also –1 / 2 since it is parallel to line GH.Using the point-slope form of a linear equation, the equation of the line isy - y1 = m(x - x1)where (x1, y1) = (1, 3) and m = –1 / 2So, the equation of the line isy - 3 = –1 / 2 (x - 1)Multiplying by 2 on both sides to remove the fraction, we get:2y - 6 = –x + 1x + 2y = 7This is the equation of the line parallel to line GH and passes through point J.Let's now check the options to see which points lie on this line.(0, 7): This point does not lie on the line since 0 + 2(7) ≠ 7.(-4, 2): This point does not lie on the line since –4 + 2(2) ≠ 7.(1, 5): This point does not lie on the line since 1 + 2(5) ≠ 7.(2, 4): This point does not lie on the line since 2 + 2(4) ≠ 7.(3, 3): This point lies on the line since 3 + 2(3) = 7.

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Answer:

$2.50

Step-by-step explanation:

The formula predicts that the triangle's perimeter will be 12f+9g+3.

What is a triangle?

The sides of a triangle are (10f +6) centimetres, (2f-4) centimetres, and (9g+1) centimetres long, respectively.

The expression for the triangle's perimeter will be

P = (10f+6) + (2f- 4) + (9g+1)

P = 12f+9g+3

The formula predicts that the triangle's perimeter will be 12f+9g+3.

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The new exchange rate is 12.5 SEK: $1.

The Swedish krona trades at 10 SEK: $1. If the kroner weakens by 20% vs. the USD, the new exchange rate will be 12.5 SEK : $1.

Since we are looking for the exchange rate between Swedish krona and the dollar, let us find how many dollars we can buy with one Swedish krona initially.

10 SEK: $1 is the exchange rate. One can buy 1 dollar for every 10 SEK.

20% weakening of SEK would imply that one needs to spend more SEK to purchase the same amount of USD.

Since we have 20% depreciation, 1 dollar should now cost more than 10 SEK.

20% of 10 is 2, which means 2 SEK is now lost.

10 SEK - 2 SEK = 8 SEK

Now, 1 dollar is worth 8 SEK. Now we will reverse the ratio for the new exchange rate: 1/8 = 0.125, which means that 1 USD is worth 0.125 SEK.

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Fractography can distinguish interlaminar and intralaminar failure modes in composites by analyzing characteristic features on the fractured surfaces.

In composites, interlaminar and intralaminar failure modes refer to different types of failure mechanisms that can occur between or within the layers of the composite material.

Interlaminar failure modes:

Intralaminar failure modes:

Fractography, the study of fractured surfaces, can be used to distinguish between these failure modes in composites. By analyzing the fracture surface, characteristic features associated with each failure mode can be observed:

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Answer:

A. The shape has perpendicular but not parallel lines.

Step-by-step explanation:

The shape is a right triangle, which has a 90 degree angle. This means that two of the sides are perpendicular because they meet each other at a right angle. None of the lines are parallel because if any of the sides were to never meet, there would not be a closed shape.

Answer:

6

Step-by-step explanation:

(8/3) / (-4/9)

when dividing fractions you use the acronym k.c.f (keep change flip)

keep the first fraction

change the operation (divide to multiply)

flip the other fraction

(8/-3) x (9/4)

after re-writing your expression, you want to solve

do this by multiplying both numerators by each other and same with the denominators

(-8x9) / (3x-4)

then you get a new fraction,

-72/-12

simplify,

-72/-12 = 6 (multiplying/dividing 2 negatives will always give you a positive)

Answer:

6

Step-by-step explanation:

6

Did on test hope it helps

Answer:

-3+(-8)=-11

Step-by-step explanation:

your answer u want more ex. ican

The expression is y + (-3) = -8 results to y=-5.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

given:

The sum of a number y and −3 is −8.

Now, writing the mathematical expression as

y + (-3) = -8

y -3 = -8

y= -8+ 3

y= -5

Hence, the resultant value is -5.

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Answer:

a = -2

Step-by-step explanation:

15 = 3(a+7)

15 = 3a + 21

-6 = 3a

a = -2

Answer:

12 is A, 13 is C

Step-by-step explanation:

I took the test. MARK AS BRAINLIST!

Answer:

needed what??????????

The solution to the given inequality as represented in the task content are; z < - 1.00485413 OR z > 1.00485413.

It follows from the task content that the solution of the given inequality; ( 29 / 289z ) < ( 16 / 161 ) z is to be determined.

Since the given inequality is;

( 29 / 289z ) < ( 16 / 161 ) z

By cross multiplication; we have;

161 × 29 < ( 16z × 289z )

( 161 × 29 ) / ( 16 × 289 ) < z²

1.00973183 < z²

Therefore;

1.00485413 < z. OR. -1.00485413 > z.

Ultimately, z < - 1.00485413 OR z > 1.00485413.

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Answer:

Yield per share = 7.68% (Approx.)

Step-by-step explanation:

Given:

Dividend paid = $4.15

Price per dividend = $54

Find:

Yield per share

Computation:

Yield per share = [Dividend paid / Price per dividend]100

Yield per share = [4.15 / 54]100

Yield per share = [0.0768]100

Yield per share = 7.68% (Approx.)

Answer:

\(3k = 36\)

\(k = 12\)

Answer:

12

Step-by-step explanation:

If y = 36 and X = 3 then K would = (y divided by x) so it would be 36 divide 3

that being 12 so, therefore, the answer is 12.

K= 12

The area of the stop sign is 124 square units.

To find the area of the stop sign, we need to separate it into 8 triangles. The height of each triangle would be the apothem of the octagon, which is the distance from the center of the octagon to the midpoint of one of its sides.

Using the Pythagorean theorem, we can find the apothem of the octagon:

apothem = sqrt(4^2 - 2^2) = sqrt(12) = 3.46 (rounded to two decimal places)

Now, we can find the area of one of the triangles:

area = (1/2) x base x height

Since the stop sign is a regular octagon, all 8 triangles have the same base and height. The base is the length of one of the sides of the octagon, which we can find using the fact that the octagon is inscribed in a circle with radius 4.

The length of one of the sides is:

side = 2 x sqrt(2) x radius = 2 x sqrt(2) x 4 = 8.94 (rounded to two decimal places)

Therefore, the area of one of the triangles is:

area = (1/2) x 8.94 x 3.46 = 15.47 (rounded to two decimal places)

Since there are 8 triangles, the total area of the stop sign is:

area of stop sign = 8 x 15.47 = 123.76

Rounded to the nearest integer, the area of the stop sign is 124 square units.

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Answer:

1: 5/2 = 2.5 eggs

2: 25 1/3 bags of gravel

Step-by-step explanation:

Based on the calculations, the height of this ravine is equal to 143.95 feet.

Given the following data:

First of all, we would assign a variable to the height of the ravine, which is 100 feet tall.

Let the height of ravine be h.

Note: We would choose 46° as a measure for angle A.

From the image attached, we would determine the length of the hypotenuse by using Cosine trigonometric:

\(Cos A=\frac{Adj}{Hyp} \\\\Cos 46=\frac{100}{h} \\\\0.6947=\frac{100}{h}\\\\h=\frac{100}{0.6947}\)

h = 143.95 feet.

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The main difference between the reciprocal and inverse of a function is their definition and properties. The reciprocal of a function f(x) is defined as 1/f(x), while the inverse of a function f(x) is a function f^(-1)(x) such that \(f(f^(-1)(x))=x and f^(-1)(f(x))=x\) for all x in their respective domains.

The domains of sine, cosine, and tangent functions need to be restricted to define their inverse functions because they are not one-to-one functions. In order to have an inverse, a function must be both one-to-one (each output has only one input) and onto (each output value is mapped by at least one input value).

For example:
- sine: restricted domain to [-π/2, π/2] to define its inverse, arcsin (sin^(-1))
- cosine: restricted domain to [0, π] to define its inverse, arccos (cos^(-1))
- tangent: restricted domain to (-π/2, π/2) to define its inverse, arctan (tan^(-1))

These restrictions ensure that the functions become one-to-one and onto, making it possible to define their inverses uniquely.

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The graph has y-intercept (0,5) and increases with a constant ratio of 3.

A function in mathematics is a connection between a set of inputs (sometimes referred to as the domain) and a set of outputs (also referred to as the range). Each input value is given a different output value.

The y-intercept lies at (0, 5) because the value of the function at x=0 is 530 = 5. The 'constant ratio' is 3, meaning that any increment of 1 in x causes the function value to grow by a factor of 3. (That serves as the exponential term's foundation.)

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Missing parts;

Which of the following statements is true for a function with equation f(x) = 5(3)*?

The graph has y-intercept (0,5) and increases with a constant ratio of 3.

The graph has y-intercept (0, 3) and decreases with a constant ratio of 3.

The graph has y-intercept (0, 3) and increases with a constant ratio of 5.

The graph has y-intercept (0,5) and decreases with a constant ratio of 3.

Answer:

B!

Step-by-step explanation:

Hope this helps :))

Answer:

B) 60 square inches

Step-by-step explanation:

They are asking for the area of the triangle. The formula for area is (length × width) ÷ by 2 = area

so, (8 × 15) ÷ 2 = 60 square inches

With a frame length of 1, the expectation is 5 seconds and the         standard deviation is approximately 3.464 seconds for the number of seconds between two consecutive connections.

(a) To determine the frame length Δ that gives a probability of 0.15 of an arrival during any given frame, we need to consider the Binomial counting process and its probability distribution.

In a Binomial distribution, the probability of success (an arrival) is given by p, and the probability of failure (no arrival) is given by q = 1 - p. In this case, p = 12 connections per minute.

We can use the cumulative distribution function (CDF) of the Binomial distribution to find the frame length Δ. The CDF gives the probability of having k or fewer arrivals in a given number of frames.

Using a binomial probability table or a calculator, we find that when p = 0.15, the corresponding value of k is 1. Therefore, the frame length Δ that gives a probability of 0.15 of an arrival during any given frame is 1 frame.

(b) With a frame length Δ of 1, we can compute the expectation (mean) and standard deviation for the number of seconds between two consecutive connections.

The average rate of connections is 12 per minute. To find the average time between two consecutive connections, we take the reciprocal of the rate: 1/12 minutes per connection.

To convert minutes to seconds, we multiply by 60: (1/12) * 60 = 5 seconds.

Therefore, the expectation (mean) for the number of seconds between two consecutive connections is 5 seconds.

The standard deviation can be calculated using the formula for the standard deviation of a Poisson process, which is the limit of the Binomial distribution as the number of trials becomes large. For a Poisson process, the standard deviation is equal to the square root of the average rate: √(12) ≈ 3.464 seconds.

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Answer:

58

Step-by-step explanation:

Given :-

To solve :-

Solving :-

Answer:

58

is the final answer

Step-by-step explanation:

8(7)- (-2)=

56 +2= 58

Answer:

(f-g)(x)=-x^(2)+2x+8

the solutions are:

x=4 or x=-2

Step-by-step explanation:

(f-g)(x)=2x+1-(x^(2)-7)

(f-g)(x)=-x^(2)+2x+1+7

(f-g)(x)=-x^(2)+2x+8

does this help or should I solve for the zeros/solutions of this quadratic equation?

then:

-x^(2)+2x+8=0

-(x^(2)-2x-8)=0

x^(2)-2x-8=0

(x-4)(x+2)=0

x=4 or x=-2

Answer:

The required answer is: -x^2+2x+8

Step-by-step explanation:

We have been given the two function:

f(x)=2x+1

And g(x)=x^2-7

We have to find (f-g)(x):

(f-g)(x)=f(x)-g(x)

(2x+1)-(x^2-7)

2x+1-x^2+7

-x^2+2x+8

Hence, the required answer is: -x^2+2x+8