Question 1 of 2
15 Points
A report revealed that the average no. of months that an employee stays in a factory is 36
months. Assuming that the no. of months of an employee tenure in the factory is normally
distributed with a standard deviation of 6 months, find the probability that a certain employee
will stay
a. More than 30 months
b. Less than 24 months
c. Between 24 to 48 months​

Answer: The area of the floor of the hall is approximately 599.2448 square meters.

Step-by-step explanation: Let's assume the breadth of the hall be x meters. Then, the length of the hall will be 2x meters and the height will be 3x meters.

The volume of the hall can be found as follows:

Volume = Length × Breadth × Height

36000 = 2x × x × 3x

36000 = 6x³

x³ = 6000

x = ∛6000 ≈ 17.32 meters

Therefore, the breadth is approximately 17.32 meters, the length is 2 × 17.32 = 34.64 meters, and the height is 3 × 17.32 = 51.96 meters.

The area of the floor can be found by multiplying the length and breadth:

Area = Length × Breadth

Area = 34.64 × 17.32

Area = 599.2448 m²

Therefore, the area of the floor of the hall is approximately 599.2448 square meters.

Answer:

\( c = {10x}^{6} \)

Step-by-step explanation:

\( {40x}^{9} \div {4x}^{3} = {4x}^{3} c \div {4x}^{3} \)

\(therefore ...c = {10x}^{6} \)

Answer:

5,400

Step-by-step explanation:

5% = 270

270 ÷ 5 = 54

54 × 100 = 5400

a) The radius of the sphere is given as follows: 27.13 ft.

b) The surface area can be checked as follows: S = 4 x 3.14 x 27.13² = 9244.

The surface area for a sphere of radius r is given by the equation presented as follows:

S = 4πr².

The surface area for this problem is given as follows:

9244 ft².

Hence the radius is given as follows:

\(r = \sqrt{\frac{9244}{4 \times 3.14}}\)

r = 27.13 ft.

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The value of y in simplest form for the point P = (1/2, y) lying on the unit circle is y = ± √(3)/2.

To find the value of y in simplest form for the point P = (1/2, y) lying on the unit circle, we can use the equation of the unit circle, which states that for any point (x, y) on the unit circle, the following equation holds: x^2 + y^2 = 1.

Plugging in the coordinates of the point P = (1/2, y), we get:

(1/2)^2 + y^2 = 1

1/4 + y^2 = 1

y^2 = 1 - 1/4

y^2 = 3/4.

To simplify y^2 = 3/4, we take the square root of both sides:y = ± √(3/4).

Now, we need to simplify √(3/4). Since 3 and 4 share a common factor of 1, we can simplify further: y = ± √(3/4) = ± √(3)/√(4) = ± √(3)/2.

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The height of the cylinder whose surface area is given would be = 85 yards.

The cylinder is a type of shape that has three sides which consists of two opposite circles that are joined by a curved surface.

To calculate the height of a cylinder, the formula that should be used is given as follows:

Surface area of cylinder = 2πrh + 2πr²

radius = 29 yards

surface area = 20,761.68 square yards

height = ?

That is ;

20,761.68 = 2×3.14× 29×h + 2×3.14× 29×29

20,761.68 =182.12h + 5281.48

182.12h = 20,761.68-5281.48

182.12h = 15480.2

h = 15480.2/182.12

= 85 yards

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The linear combination of the standard unit vectors i and j for the given initial and terminal points is 9i + 20j.

To find the linear combination of the standard unit vectors i and j, we need to determine the components of the vector that connects the initial point to the terminal point.

Given:

Initial Point: (0, -8)

Terminal Point: (9, 12)

To find the linear combination, we subtract the coordinates of the initial point from the coordinates of the terminal point:

So, Terminal Point - Initial Point

= (9, 12) - (0, -8)

= (9 - 0, 12 - (-8))

= (9, 20)

Therefore, the linear combination of the standard unit vectors i and j for the given initial and terminal points is 9i + 20j.

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The correct option regarding the number of bags filled by Nina, using proportions, is given as follows:

Between 20 and 30 bags.

A proportion is a fraction of an amount, and this fraction is combined with the unit rates of the problem and basic arithmetic operations, especially multiplication and division, to find the desired amounts in the context of the problem.

In this problem, a proportion is applied to find the number of bags filled by Nina, which is given by the division presented as follows:

Number of bags = Number of treats / Treats per bag.

The values of these parameters are given as follows:

Hence the numeric value of the expression is:

Number of bags = 78/3 = 26.

Which is a number between 20 and 30.

The problem states that Nina had 78 treats, and each bag has 3 treats, then it asks the correct option regarding the number of bags.

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Answer:

Using that sample, you calculate the corresponding sample characteristic, which is used to summarize information about the unknown population characteristic. The population characteristic of interest is called a parameter and the corresponding sample characteristic is the sample statistic or parameter estimate.

Step-by-step explanation:

If you collect a sample and calculate the mean and standard deviation, these are sample statistics.

Since the graph was obtained by transforming the graph of the square root function, an equation for the function the graph represent is: \(g(x) = -\sqrt{9(x - 1)} + 2\)

In Mathematics and Geometry, a square root function is a type of function that typically has this form f(x) = √x, which basically represent the parent square root function i.e f(x) = √x.

In Mathematics and Geometry, a horizontal translation to the right is modeled by this mathematical equation g(x) = f(x - N) while a vertical translation to the positive y-direction (upward) is modeled by this mathematical equation g(x) = f(x) + N.

Where:

In this context, the required square root function can be obtained by applying a set of transformations to the parent square root function as follows;

f(x) = √x

g(x) = -√9(x - 1) + 2

\(g(x) = -\sqrt{9(x - 1)} + 2\)

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The radius of the cone is=  3.14*160 cm^2.

According to our question-

Total SA of a cone = πr^2+πrl = πr(r+l)

Here r = 8 cm , slant height l=12 cm.

SA of cone =3.14 * 8 * ( 8+12) cm^2

=> 3.14*160 cm^2

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The width of the dog run is 20 feet.

In the given problem, the length of the dog run is given as 30 feet.

The area of the dog run is also given as 240 square feet.

Using the formula for the area of a rectangle (A = lw), we can solve for the width (w).

Rearranging the formula, we have w = A / l.

Plugging in the values, we get w = 240 / 30 = 8 feet.

Since the width is given as (30 minus x) feet, we can set up an equation:

30 - x = 8. Solving for x, we find x = 22.

Therefore, the width of the dog run is 20 feet (30 - 22 = 8).

In this problem, the length and width of the dog run are defined by the dimensions of the fence being built around it.

The area of the dog run is given as 240 square feet.

By using the formula for the area of a rectangle, we can solve for the width. We are also given that the length is 30 feet.

Setting up an equation with the given width (30 minus x) and solving for x, we find that x is equal to 22.

This means that the width of the dog run is 8 feet. The main answer to the problem is that the width of the dog run is 20 feet (30 - 22 = 8).

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Answer : 8$

you have 1$ left

16 is the number which is one-fifth of a number when one-fourth of that same number is 20.

As per the given data:

One-fourth of the number is resulted to 20.

Here we have to determine the result of one-fifth of the same number from the given options.

An expression for a portion of a whole is a fraction.

For any real numbers, the fractional component of x is defined.

Let the number be X.

One-fourth of a number is 20 which means:

Multiply the one-fourth fraction with an unknown number which results in the number 20.

\($\frac{1}{4}\)  (X) = 20

X = 20 × 4

X = 80

Now we have to determine that one-fifth of the same number.

Multiply the one-fifth fraction by 80.

We get:

= \($\frac{1}{5}\) (80)

= \($\frac{1}{5}\)   × 5 × 16

= 16

One-fifth of the number 80 is 16

Therefore Option (D) - 16 is the correct answer.

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The completion of the following table under different depreciation methods is as follows:

Method                           Year 1                     Year 2

Straight line                   $18,000                 $18,000

Units of production      $54,000                 $13,500

Declining balance        $37,600                $22,560

MACRS (5-year class)   $18,800                $30,080

Cost of machine = $94,000

Residual value = $4,000

Depreciable value = $90,000 ($94,000 - $4,000)

Estimated useful life = 5 years

Depreciation expense:

Straight-line method = $18,000 ($90,000/5)

Estimated units of produciton = 100,000

Unit depreciation rate = $0.90

Actual production   Depreciation

Year 1 = 60,000      $54,000 ($0.90 x 60,000)

Year 2 = 15,000      $13,500 ($0.90 x 15,000)

Declining Balance:

Year 1 = $37,600 ($94,000 x 40%)

Year 2 = $22,560 ($94,000 - $37,600) x 40%

MACRS:

Year 1 = $18,800 ($94,000 x 20%)

Year 2 = $30,080 ($94,000 x 32%)

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Answer:

47

Step-by-step explanation:

6x6= 47

Answer:

26

Step-by-step explanation:

ik this is right

For statement 5/3, the reason is the definition of slope. And for statement (5/3)=(15/9), the reason is triangle A is similar to triangle B.

Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line. The slope is also defined as the ratio of the rise to the run.

If the slope of the triangles is equal then triangle A is similar to triangle B.

In the statement  when we simplify

(5/3)=(15/9),

(5/3)=(5/3),

Then the reason for this statement is "If the slope of triangles are equal"

And the definition of slope in general is m = y/x.

Therefore, for statement 5/3, the reason is the definition of slope. And for statement (5/3)=(15/9), the reason is triangle A is similar to triangle B.

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The domain is all real numbers, and the range is (y ≤ -4.855). (option b)

To sketch the graph of a quadratic equation, you can use a graphing calculator, which is a handy tool that can produce a visual representation of the equation. For instance, let's take the quadratic equation y = -0.5x² + 0.7x - 5.1 and sketch its graph using a graphing calculator.

When we enter this equation into the graphing calculator, we can see a U-shaped curve that is symmetric about the vertical line passing through the vertex. The vertex is the point where the parabola changes direction and is given by the formula x = -b/2a, y = f(x), where f(x) is the value of y at the vertex.

Now let's examine the given options and determine their domain and range based on the graph of the quadratic equation.

all real numbers, R: (y ≤ -4.855)

For this option, we can observe that the parabola opens upward, and the vertex is at (0.7, -5.35).

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Answer:

82 points

Step-by-step explanation:

Take 22 and add 20 back to it, and then multiply it by four which gives you 102. You then would subtract 20 and get 82.

Answer:

The answer is letter A.

y<9/4x+2

The meer-kitty survey feedback tab has limitations in its data. The survey results must have at least 120 unique responses to be considered useful and aligned with the business objective. The current data, however, only has 40 total responses, with 11 of them coming from one user. This skews the results and makes it difficult to accurately analyze the feedback.

To address these limitations, it is recommended to remove the duplicates, in this case the 11 responses from one user, and focus on the remaining 29 unique responses. This will provide a clearer picture of the survey results and a more accurate representation of the feedback. By doing so, the analysis of the data will be better aligned with the original business objective and provide more valuable insights.

It is important to consider the limitations of the data when conducting any type of analysis, especially when it comes to surveys and feedback. By taking the necessary steps to ensure the data is as accurate and reliable as possible, the results of the analysis will be more meaningful and relevant to the business.

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Answer:

These kind of problems  are super difficult Anna, don't feel bad for not getting this. there is a bunch of "implied" ideas here... i'll go over them below, maybe it will seem a bit easier.  if not, ask some more questions in the comments of this problem , I'll see the comments and answer your question

Step-by-step explanation:

the 1st implied idea is that there is 360 ° in a circle

next you have to know, that the angle x   is also matched on the interior of the circle where the line of the angle x, first touches the circle.  if that is confusing , don't worry i'll make a rough drawing to show you.  

so we can know that the arc from the point where the angle x makes the tanget.. or just touches the circle to where it's other leg crosses the circle the 1st time,  that's angle is equal to the arc that is left over from the total circle.  see this is very "implied"  nobody said.. by the way... it's 360 ° minus the other arcs.. well.. I just did.. but  you had to come up with that on your own, before I said that.

x =  left over arc

360 = 200 + 40 + x

120 = x

Answer:

The vertex of the function is at (–3,–16)

The graph is increasing on the interval x > –3

The graph is positive only on the intervals where x < –7 and where

x > 1.

Step-by-step explanation:

The graph of \(f(x)=(x-1)(x+7)\) has clear zeroes at \(x=1\) and \(x=-7\), showing that \(f(x) > 0\) when \(x < -7\) and \(x > 1\). To determine where the vertex is, we can complete the square:

\(f(x)=(x-1)(x+7)\\y=x^2+6x-7\\y+16=x^2+6x-7+16\\y+16=x^2+6x+9\\y+16=(x+3)^2\\y=(x+3)^2-16\)

So, we can see the vertex is (-3,-16), meaning that where \(x > -3\), the function will be increasing on that interval

In this case, the coefficent 1.5 represents the cost of each topping! the more toppings we want, the more money it will cost!

Answer:

1f, 2b, 3a, 4c, 5d, 6e

see image

Step-by-step explanation:

Solve the equations by getting x all by itself on one side. Then, square root to get rid of the exponent.

Any problem where you square root a negative will give you an i in the answer. This is because sqrt(-1) is i. Because i^2 = -1

Also, when you are simplifying square roots for your final answer, look for a perfect square number inside of the radical. Like Sqrt45 can be broken down to

Sqrt9•sqrt5

And because 9 is a perfect square, sqrt9 simplifies to just 3. See image.

Answer:

0.53 x 10^ -8

Step-by-step explanation:

Just move the decimal over to the right and add 1 to the exponent.

The simplified form of √([2m5z6]/[xy]) is (√2m√5z√6) / (√x√y).

To simplify the expression √([2m5z6]/[xy]), we can break it down step by step:

Simplify the numerator:

√(2m5z6) = √(2) * √(m) * √(5) * √(z) * √(6)

= √2m√5z√6

Simplify the denominator:

√(xy) = √(x) * √(y)

Combine the numerator and denominator:

√([2m5z6]/[xy]) = (√2m√5z√6) / (√x√y)

Thus, the simplified form of √([2m5z6]/[xy]) is (√2m√5z√6) / (√x√y).

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Answer:

B only

Step-by-step explanation:

Triangles A and C are similar, but not congruent to each other. Similar triangles have proportional sides and congruent angles, while congruent triangles have congruent sides and congruent angles.

Therefore, only B is correct

The question is asking for pairs of congruent triangles but lacks key information needed to accurately answer this, such as lengths or angles. Congruent triangles are identified in geometry based on either side-lengths or angles.

The question is about congruent triangles, which in mathematics means triangles that have the same size and shape. But to accurately answer which pairs show two congruent triangles, we need more information. The options provided include 'A', 'B', and 'C' but without knowing more about these elements (for example their lengths or angles), it is impossible to determine which are congruent. Congruent triangles are identified in geometry based on either side lengths (SSS: Side-Side-Side, SAS: Side-Angle-Side, ASA: Angle-Side-Angle) or angles (AAS: Angle-Angle-Side, HL: Hypotenuse-Leg for right triangles). Without this vital information, we cannot definitively answer the question. Be sure to verify all the properties required to prove two triangles congruent.

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Answer:

4.5 hours

Step-by-step explanation:

fbdjdbercyTxxivdu

Answer:

Basically You are asking how many hours we need to reach 7:00, if we are at 2:30, so: we need 4hours, to reach 6:30, and and extra 30minutes to reach 7:00pm. The answer is 4hours and 30minutes.