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Rewrite each square root using the imaginary unit i.

Square root -54

The percentage of the fire fighters have moderate to severe risk for alcohol problems is 28%  

From the sample, we can get that number of fire fighters who participated in rescue of 9/11 attack and are under moderate to severe risk for alcohol problems is =309.

Total number of fire fighters participated in 9/11 attack is =1102

So, percentage of fire fighters have moderate to severe risk for alcohol problems are =(309/1102)×100

    percentage from the sample= 0.28×100=28%

Hence, 28% fire fighters are in  severe risk for alcohol problems

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(Complete question) is:

what percentage of the fire fighters in the sample have moderate to severe risk for alcohol problems?

The y- intercept of line is (0, -1).

The equation of line in slope intercept form is,

                         \(y=mx+c\)

Where m is slope and c is y intercept.

y-intercept is a point on y axis where line is crosses y- axis.

Given that A line passes through the y-axis at -1 .

So that y- intercept of line is (0, -1).

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Answer:

Yes, it is. Functions can only have one output (y) for each input (x). Furthermore, this means each x value will only have one y passing through it. Thus if we plot it on a graph and it passes through a horizontal line more than once, it is not a function. This is called the vertical line test.

Angle between hour hand and minutes hand is 60 degrees.

What is angle ?

An angle is a shape created by two rays or lines that have a shared termination.

Main Body:

As a clock is complete circle , total angle created by it is 360 degrees.

Numbers of hours in a clock = 12

Angle created by 1 hour = total angle / total no. of hours

                                        = 360/12

                                        = 30 degrees.

Now according to the question total hours = 2

multiplying 2 with degrees between 1 hour hand and minute hand.

Hence total angle created by hour and minute hand id 60 degrees.

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Answer:

13:  312yd squared

14: 907.5 rounded up but not rounded is 907.46

Step-by-step explanation:

this is because the formula is pi*r^2  so you'd

Step by step:

1. 20yd/2= 10 to get the radius for 13

2. substitute r in the formula pi*r^2 for 10 making it pi*10^2

3. multiply 10 by itself, 10*10=100

4. multiply pi by 100, 3.14*100= 314

314yd^2 is the answer for 13

14:

1. 34ft/2=17 to get the radius for 14

2. substitute r on the formula pi*r^2 for 17 making it pi*17^2

3. multiply 17 by itself, 17*17=289

4. multiply pi by 289, 3.14*289=907.46

5. round 907.46 to the nearest tenth, 907.5

907.5ft^2 is your answer

hope this helps :)

Answer:

375 = 40x + 100

Step-by-step explanation:

Answer:

151°

Step-by-step explanation:

angle m_3 and m_4 must add up to 180 because they both lie on a straight line. Thus, we can do 180-29 to get m_4.

Answer:

\(44,826.72\ \text{pounds}\)

Step-by-step explanation:

Given that,

The diameter of a hemispherical tank= 14 feet

Radius, r = 7 feet

water

Water weighs 62.4 pounds per cubic foot.

We need to find the total weight of the water in a full tank to the nearest pound.

The volume of the hemisphere is given by :

\(V=\dfrac{2}{3}\pi r^3\\\\V=\dfrac{2}{3}\pi \times (7)^3\\\\V=718.377\ \text{feet}^3\)

If water weighs 62.4 pounds per cubic foot, it means

\(V=718.377\times 62.4\\\\V=44,826.72\ \text{pounds}\)

So, the total weight of the water is \(44,826.72\ \text{pounds}\).

Answer:

The answer is below

Step-by-step explanation:

A triangle is a polygon with three sides and three angles. Types of triangles are acute, obtuse, isosceles, equilateral, scalene and right angled triangle.

A right angled triangle is a triangle in which one of the angles is 90°. In a right angled triangle, the longest side is known as the hypotenuse and the side is opposite to the right angle.

Pythagoras theorem states that the square of the hypotenuse is equal to the sum of the square of the other two sides.

Given the question attached, using Pythagoras theorem:

18² = x² + 12²

324 = x² + 144

x² = 180

x = 13.42

Answer: 1.8 L/h

Step-by-step explanation:

To convert the rate of water dripping from a tap from millilitres per second (ml/sec) to litres per hour (L/h), we need to use conversion factors.

Step 1:

First, let's convert the rate from millilitres per second to litres per second.

There are 1000 millilitres in a litre, so we can divide the rate in millilitres per second by 1000 to get the rate in litres per second:

\(\LARGE \boxed{\textsf{0.5 ml/sec $\div$ 1000 = 0.0005 L/sec}}\)

Step 2:

We can convert the rate from litres per second to litres per hour. There are 3600 seconds in an hour, so we can multiply the rate in litres per second by 3600 to get the rate in litres per hour:

\(\LARGE \boxed{\textsf{0.0005 L/sec $\times$ 3600 = 1.8 L/h}}\)

Therefore, the rate of water dripping from the tap is 1.8 L/h.

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The rule that show the relationship between the input (x) and the output (y) is y = 4x - 2

An equation is an expression that shows the relationship between two or more numbers and variables.

Independent variables represent function inputs that do not depend on other values, while dependent variables represent function outputs that depends on other values.

Let x represent the input and y represent the output, hence using the point (8, 30) and (10, 38):

y - 30 = [(38 - 30)/(10 - 8)](x - 8)

y = 4x - 2

The rule that show the relationship between the input (x) and the output (y) is y = 4x - 2

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By definite integrals and area formula of a rectangle, we find that the area of the region in the first quadrant is 147 / 4 square units.

Integrals can be used to determine the area of regions bounded by curves set on Cartesian plane. The upper limit of the integral of the question is initially found:

(2 / 3) · x = 7

x = 21 / 2

The area can be defined as an rectangle in the first quadrant minus the area below the linear equation:

\(A = \left(\frac{21}{2} \right) \cdot (7) - \frac{2}{3} \int\limits^{\frac{21}{2} }_{0} {x} \, dx\)

\(A = \frac{147}{2} - \frac{1}{3} \cdot \left[\left(\frac{21}{2} \right)^{2}-0^{2}\right]\)

A = 147/4

By definite integrals and area formula of a rectangle, we find that the area of the region in the first quadrant is 147 / 4 square units.

The statement is poorly formatted and incomplete. Correct form is shown below:

A region in the first quadrant is bounded by the line y = (2/3) · x, the y-axis and the horizontal line y = 7. Determine the area of the region.

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Answer:

28

Step-by-step explanation:

71.12 divided by 2.54 = 28

Answer:

Using dimensional analysis:

71.12 cm / 2.54 cm/inch = 28 inches

Therefore, 71.12 centimeters is equal to 28 inches.

An eigenvalue of a matrix is a scalar value that satisfies the equation ax = λx for some vector x. If a is an n × n matrix, then if ax = λx for some vector x, λ is an eigenvalue of a

An eigenvalue of a matrix is a scalar value that satisfies the equation ax = λx for some vector x. If a matrix a is an n × n matrix, then the equation ax = λx can be used to find the eigenvalues associated with the matrix. By taking the equation ax = λx and rearranging it, we can isolate the eigenvalue λ on the left side of the equation, leaving the vector x on the right side. λ is then the eigenvalue of the matrix a. For example, if we have a 2 x 2 matrix a, and we have an equation of the form ax = λx, where x is a 2-dimensional vector, then by rearranging the equation we can find the eigenvalue λ associated with the matrix a. In summary, if a is an n × n matrix and ax = λx for some vector x, then λ is an eigenvalue of a.

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Answer:

The length of the ladder  = 6.5077 ft

Step-by-step explanation:

Given A ladder leans against the side of a house

Given the angle of elevation of the ladder is 68° when the bottom of the ladder is 16 ft from the side of the house

Let 'C' be the point of observation.

Given CA= 16 ft

 From right angle triangle

     x = 16 × cos 68°

    x = 16 × 0.4067

    x = 6.5077

  x = 6.5 ft

The length of the ladder = 6.5 ft

Answer:

  -7/8 gallons

Step-by-step explanation:

You want to know the change in the amount if 1/6 of 5 1/4 gallons evaporated.

The word "of" in this context means "times."

  1/6 of 5 1/4 gallons = (1/6)·(21/4) = 21/24 = 7/8

The decrease of 7/8 gallons can be represented by the value -7/8.

__

Additional comment

The wording of the problem is unclear as to whether you need the minus sign.

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The triangle DEF's section EF measures 24 units in length.

As per the data given in the above question are as bellow,

The provided details are as follow,

Procedure: Calculating the length that results from distorting a triangle by a scale factor

The triangle mentioned in the previous sentence is summarised in the diagram below. Using a trigonometric relationship, we discover that the following formula best describes the length of the section EF:

\($\sin a^{\circ}=\frac{E F}{D E}$\)

If we know that DE=30 and \($\sin a^{\circ}=\frac{4}{5}$\), then the length of the segment EF is:

\(E F=D E \cdot \sin a^{\circ} \\& E F=30 \cdot\left(\frac{4}{5}\right) \\\)

EF=24

Sine (sin), cosine (cos), and tangent (tan), which are defined in terms of the ratios of the sides of a right triangle, are the fundamental trigonometric functions.

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Note: The correct question would be as bellow,

A triangle was dilated by a scale factor of 6. If sin a° = four fifths and segment DE measures 30 units, how long is segment EF?triangle DEF in which angle F is a right angle, angle D measures a degrees, and angle E measures b degrees

15.5 units

24 units

30 units

37.5 units

Answer:

.

Step-by-step explanation:

The probability density function for a normal distribution N(68, 5) reaches its maximum height at x = 68, which is the mean of the distribution. The function does not touch the x-axis at μ±30.

The probability density function (PDF) for a normal distribution is bell-shaped and symmetrical around its mean. In this case, the mean (μ) is 68, and the standard deviation (σ) is 5.

(a) To find the x value at which the PDF reaches a maximum, we look at the mean of the distribution, which is 68. The PDF is highest at the mean, and as we move away from the mean in either direction, the height of the PDF decreases. Therefore, the x value at which f(x) reaches a maximum is x = 68.

(b) The PDF of a normal distribution does not touch the x-axis at μ±30. The x-axis represents the values of x, and the PDF represents the likelihood of those values occurring. In a normal distribution, the PDF is continuous and never touches the x-axis. However, the PDF becomes close to zero as the values move further away from the mean. Therefore, the probability of obtaining values μ±30, which are 38 and 98 in this case, is very low but not zero. So, the PDF does not touch the x-axis at μ±30, but the probability of obtaining values in that range is extremely small.

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It is not always true that if two fractions have the same numerator, then the fraction with the greater denominator is the greater fraction.

The statement that if two fractions have the same numerator, then the fraction with the greater denominator is the greater fraction is not always correct. This is because the value of a fraction is determined by both its numerator and denominator, and if the denominators of two fractions with the same numerator are different, then the fractions are not directly comparable.

Consider the fractions 3/4 and 3/5. Both have a numerator of 3, but the denominator of the first fraction is greater than the denominator of the second fraction. However, 3/5 is actually the greater fraction because it represents a larger portion of the whole.Consider the fractions 5/7 and 5/9. Both have a numerator of 5, but the denominator of the second fraction is smaller than the denominator of the first fraction. Therefore, 5/7 is the greater fraction because it represents a larger portion of the whole.

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Probability according to question a = 3/40 and question b = 37.2/50

Probability is the possibility of occurring a particular event. It is expressed as the ratio of favorable outcome to the total possible outcome.

A retailer randomly bought 200 packs of eraser

the probability for at least 15 packs, the average weight of the eraser is at least 31.95 g

the required probability = 15/200 = 3/40

Each day quality control unit examines the eraser produced by factory and choose an eraser randomly for checking the weight and this process repeated 50 times.

hence, total 50 eraser is chosen each day for weighing.

The unit works total 42 days in the factory.

now, the probability that, on average to find at least 37.2 "good" eraser per day = 37.2/50

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The distribution it represents is positively skewed.

The correct answer is option D.

A density curve is a graph that shows probability. The area under the curve (AUC) is 100% for all probabilities. Alternatively, as probabilities are usually given as decimals, you might say that the area is equal to 1.

The density curve is provided along with the following response. Its distribution is positively skewed, whichever one that may be.

As a result, it reflects a favourably skewed distribution.

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Answer: The cost of a small box is $4. The cost of a large box is $7.

Step-by-step explanation:

Let s = cost of a small box and L = cost of a large box

3s + 5L = 47

11s + 10L = 114

Multiply the top equation by -2 to combine with the second equation

-6s - 10L = -94

+11s +10L = 114

L cancels out, now solve for s

5s = 20

s = 4

Now, plug the value of s back into an equation to find the value of L

3(4) + 5L =47

12 + 5L = 47

5L = 35

L = 7

The percentage increase per year in the winner's check over the given period. If the winner's prize increases at the same rate, it will be $1,454,735,139.69 in 2040.

To calculate the percentage increase per year in the winner's check over the period from 1895 to 2007, we can use the following formula:

Percentage Increase = (Final Value - Initial Value) / Initial Value * 100

a. Calculating the percentage increase:

Initial Value = $140

Final Value = $1,171,000

Percentage Increase = (1,171,000 - 140) / 140 * 100 ≈ 835,714.29%

b. To estimate the winner's prize in 2040, we can assume the same annual percentage increase will continue. We need to calculate the number of years from 2007 to 2040 and apply the percentage increase to the 2007 prize.

Number of years = 2040 - 2007 = 33 years

Estimated prize in 2040 = 1,171,000 * (1 + (Percentage Increase / 100))^33

Estimated prize in 2040 = 1,171,000 * (1 + (835,714.29 / 100))^33 ≈ $1,454,735,139.69

Therefore, if the winner's prize increases at the same rate, it is estimated to be approximately $1,454,735,139.69 in 2040.

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Allocable costs are assigned based on the ratio of a segment's income before allocable costs to total income before allocable costs. This is an appropriate method of allocation. Segment B's profit for 20X2 is $ 60,000.

Allocable costs are indirect costs that can be charged to a specific cost object. Such as, job or product based on a logical relationship between the item and the cost. If a cost object has the potential to be affected by certain indirect costs, these indirect costs can be allocated to it. These costs are called assignable or allocable costs.

Sales:

Segment A = $400,000

Segment B = $300,000

Segment C = $200,000

Total Sales = $900,000

Traceable Costs:

Segment A = $225,000

Segment B = $240,000

Segment C = $135,000

Total Traceable Costs = $600,000

Allocable Costs:

Total Allocable Costs = $150,000

Ratio of Segment B income before allocable costs to total income before allocable costs = (300,000-240,000) / (900,000-600,000) = 0.20

The amount of allocable costs assigned to Segment B = 150,000 × 0.20 = $30,000

Segment B's total costs = $240,000 + $30,000 = $270,000

Segment B's profit for 20X2 = $300,000 - $270,000 = $ 60,000

Therefore, Segment B's profit for 20X2 is $ 60,000.

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Answer:3x+5

Step-by-step explanation:

Answer:

In(3xe^4 - e^4)

Step-by-step explanation:

In(3x-1)+4

convert the constant to a log with base e:

In(3x-1) + In(e^4)

Simplify the expression:

In((3x-1)e^4)

Remove the parentheses:

In(3xe^4 - e^4)

Hope it help !

We can write the product (y - x)(y - x) as -

x² + y² - 2xy.

Normal distribution is a function that represents the distribution of many random variables as a symmetrical bell-shaped graph. Mathematically -
\($f(x)= {\frac{1}{\sigma\sqrt{2\pi}}}e^{- {\frac {1}{2}} (\frac {x-\mu}{\sigma})^2}\)

Given is to find the product of -

(y - x)(y - x)

We can write the product as -

(y - x)(y - x)

y(y - x) - x(y - x)

y² - xy - xy + x²

x² + y² - 2xy

Therefore, we can write the product (y - x)(y - x) as -

x² + y² - 2xy.

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Answer:

Step-by-step explanation:

Here we see regrouping of the multiplied numbers.

Relevant property is given below

Answer:

Your answer is C

Step-by-step explanation: