Suppose you are a quality controller in a manufacturing company and want to determine whether there is any difference in the mean measurements of shaft ...

To find the probability that the mean salary of a person selected at random from Acme Corporation is less than 61,000, we can use the Z-score formula.

First, we need to calculate the Z-score, which measures the number of standard deviations a value is away from the mean. The formula for the Z-score is:

Z = (X - μ) / (σ / √n)

Where:
- X is the value we are interested in (in this case, $61,000)
- μ is the population mean annual salary for Acme Corporation ($63,500)
- σ is the population standard deviation (unknown in this case)
- n is the sample size (unknown in this case)

Since we don't have the population standard deviation or sample size, we cannot calculate the exact Z-score. Therefore, we cannot find the exact probability.

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Based on the assumption of a sample standard deviation of $5,000, the probability that the mean salary of a person selected at random will be less than $61,000 is approximately 30.85%.

The probability of a person selected at random having a salary less than $61,000 can be determined using the z-score and the standard normal distribution.

To calculate the z-score, we need to know the population standard deviation. Since it is not provided, we cannot calculate the exact probability. However, we can use the assumption that the population standard deviation is the same as the sample standard deviation.

Let's assume the sample standard deviation is $5,000.

First, we calculate the z-score:
    \(z = (x - \mu) / (\sigma / \sqrt n)\)
=> z = (61000 - 63500) / (5000 / √1)
=> z = -2500 / 5000
=> z = -0.5

Next, we find the corresponding area under the standard normal curve using a z-table or a calculator. The area to the left of -0.5 is approximately 0.3085.

Therefore, the probability that a person selected at random will have a salary less than $61,000 is approximately 0.3085 or 30.85%.

In conclusion, based on the assumption of a sample standard deviation of $5,000, the probability that the mean salary of a person selected at random will be less than $61,000 is approximately 30.85%.

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Answer:

Q/ Draw a line ; Ans;

\( \frac{9}{5} —>1 \frac{4}{5} \)

*explain ; We put the 5 in the denominator and 5 multiply 1 + 4 so equal 9 so the choice 9/5 .

Ans; 7/3—> 2 1/3

*explain ; We put the 3 in the denominator and 3 multiply 2 + 1 so equal 7 so the choice 7/3 .

Ans; 12/10 —> 1 1/5

*explain; simple (12 and 10) ÷ 2 so equal 6/5

We put the 5 in the denominator and 5 multiply 1 + 1 so equal 6 so the choice 6/5 =12/10 .

\( \frac{12 \div 2}{10 \div 2} = \frac{6}{5} = 1 \frac{1}{5} \)

Q/ Compare the fractions;Ans;

\( \frac{2}{3} < \frac{14}{6} \)

* explain; 2/3 = 0.66 and 14/6=2.33 so 2.33 greater from 0.66 so 14/6 greater from 2/3 .

\( \frac{3}{8} < \frac{8}{3} \)

* explain; 3/8 = 0.375 and 8/3=2.666 so 2.666 greater from 0.375 so 8/3 greater from 3/8 .

\(2 \frac{1}{6} > \frac{5}{9} \)

* explain; 2 1/6 —> We put the 6 in the denominator and 6 multiply 2 + 1 so equal 13 so equal 13/6

13/6 = 2.16 and 5/9=0.55 so 2.16 greater from 0.55 so 13/6 = 2 1/6 greater from 5/9 .

Q/Add; Ans;

\( \frac{7}{8} + \frac{5}{8} = \frac{7 + 5}{8} = \frac{12}{8} = \frac{3}{2}

\)

\( \frac{1}{9} + \frac{2}{3} \\ \\ \frac{1}{9} + \frac{6}{9} = \frac{ 1+6 }{9} = \frac{7}{9} \)

Q/Subtract; Ans;

\( \frac{6}{7} - \frac{4}{7} = \frac{6 - 4}{7} = \frac{2}{7} \)

\( \frac{7}{3} - \frac{2}{9} \\ \\ \frac{21}{9} - \frac{2}{9} = \frac{21 - 2}{9} = \frac{19}{9} \)

Q/ Multiply;Ans;

\( \frac{1}{5} \times \frac{1}{2} = \frac{1}{10} \)

\( \frac{2}{3} \times \frac{3}{8} = \frac{6}{24} = \frac{1}{4} \)

Q/Divide;Ans;

\( \frac{3}{4} \div \frac{2}{5} \\ \\ \frac{3}{4} \times \frac{5}{2} = \frac{15}{8} \)

\( \frac{8}{9} \div \frac{1}{3} \\ \\ \frac{8}{9} \times \frac{3}{1} = \frac{24}{9} = \frac{8}{3} \)

I hope I helped you^_^

The surface given by the equation \(4x^2 - 16y^2 + z^2 = 16\) is a hyperboloid of two sheets. It consists of two distinct surfaces that intersect along the z-axis and open upwards and downwards.

To identify the surface defined by the equation \(4x^2 - 16y^2 + z^2 = 16,\) we can analyze the equation and determine its geometric properties.

First, let's rewrite the equation in a standard form:

\(4x^2 - 16y^2 + z^2 = 16\)

By rearranging terms, we have:

\((x^2/4) - (y^2/1) + (z^2/16) = 1\)

Comparing this equation to the standard form of a hyperboloid, we can see that the x and z terms have positive coefficients, while the y term has a negative coefficient. This indicates that the surface is a hyperboloid of two sheets.

The trace of the surface can be obtained by setting one variable constant and examining the resulting equation. Let's consider the traces in the xz-plane (setting y = 0) and the xy-plane (setting z = 0).

When y = 0, the equation becomes:

\(4x^2 + z^2 = 16\)

This represents an ellipse in the xz-plane centered at the origin, with the major axis along the x-axis and the minor axis along the z-axis.

When z = 0, the equation becomes:

\(4x^2 - 16y^2 = 16\)

This represents a hyperbola in the xy-plane centered at the origin, with the branches opening along the x-axis and the y-axis.

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identify the surface from the following equation \(4x^2-16y^2 z^2=16\)

Answer:

D

Step-by-step explanation:

\( \frac{3}{10} = 0.3\)

\( \frac{1}{3} = 0.333333333\)

\(0.333 = 0.333\)

\(33\% = 0.33\)

\(0.3 < 0.33 < 0.333 < 0.333333333\)

Answer:

y = 12x

Step-by-step explanation:

From the question, we are told that a person consumes 12 gallons of water each day

Now, we want to complete an equation

From the question, x is the number of days and y is the amount of water consumed

Thus, mathematically, we have the equation as;

y = 12x

since in the first day, 12 gallons is consumed, the second will be 12 * 2 and so on

So the amount of water depends on rate number of days

Answer:

12

Step-by-step explanation:

I got it correct.

Answer:

MEOW MEOW MEOW MEOW MEOW

It is false that when using a least squares regression line, we should not predict a value of y unless the given value of x is in the experimental region

A least square regression line equation is represented as

y = mx + c

From the question, we have the statement:

When using a least squares regression line, we should not predict a value of y unless the given value of x is in the experimental region

The above statement is false

This is because whether the x values is in the experimental region or not, the y value can be predicted

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The area of the shaded region will be equal to the (area of the hexagon - area of pentagon) + (area of a square - area of equilateral triangle).

From the complete question, the area of the shaded region 1 will be:

= Area of regular hexagon - Area of regular pentagon

The shaded region 2 will be:

= Area of a square - Area of equilateral triangle

Therefore, the area of the shaded region will be equal to the (area of the hexagon - area of pentagon) + (area of a square - area of equilateral triangle).

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Answer:

4.074 hours

Step-by-step explanation:

r =

The formula for speed = Distance × Time

Hence,

Let the outbound speed = r

return trip speed = r + 25x/100 = 125r/100 = 1.25r

Note that: 9 hours and 20 minutes = 9.167

Let t1 and t2 be the time taken to travel on way and return journey.

t1 + t2 = 9 hr 10 min = 9.167 hrs

Hence:

2688/r + 2688/1.25r = 9.167

LCM(1.25r)

(2688 × 1.25) + 2688 /1.25r= 9.167

3360 + 2688 = 9.167 × 1.25r

6048 = 11.45875r

r = 6048/11.45875

Outbound trip rl = 527.8062615904876mph

Return trip speed = r + 25x/100 = 125r/100 = 1.25r

= 1.25 ×

659.75782699mph

Time for return trip = Distance/Speed

= 2,688 miles/659.75782699mph/

= 4.0742222222 hours

Approximately = 4.074 hours

Answer:

n = 10

Step-by-step explanation:

(10 * 3) + 7 = 37

Answer: 6

Step-by-step explanation:

With these type of problems, it is best to work backwards.

1. Because of the seven more, you subtract 7 from 25. This gives you 18.

2. Then it says three times, this means to divide by 3. 18/3 is 6

3. Your final answer is 6

Proving the answer is 6:

1.   3 \(*\\\) 6 = 18

2. 18 + 7 = 25

Answer: Intersection of A and B = 2

Step-by-step explanation:

Total cards = 52

Let A is the event of drawing a 6 from the deck, and B is the event of drawing a black playing card from the deck.

Total cards having 6 on them = 4

[There are 4 suits of two different colors red and black.]

Total  black playing card =26

Intersection of A and B = Black cards having 6 = 2

hence, Intersection of A and B = 2

Answer:

3a. 7.2

3b. 0.9

4a. 7.2

4b. 2.4

5a. 104

5b. 260

hope this helps, everything in bold is the correct answer,

have an awesome day, -TJ

Answer:

3.a. 36

b. 4.5

4.a. 7.2

b. 2.4

5.a. 104

b. 260

Step-by-step explanation:

100/20 = 5

18 x 5 = 90 (100%)

18 x 2 = 36

18/4 = 4.5

14.4/2 = 7.2

7.2/3 = 2.4

52 x 2 = 104 (100%)

(195/3) 4 = 65 x 4

65 x 4 = 260 (100%)

Answer:  False, True, False

Step-by-step explanation:

1.  to find the y-intercept x=0  so

for f(x)=-5 but

g(x) the intercept is between -4 and 14,

which is bigger than -5   So the first one is false

2.   this is when y=0 what is x.  

  For f(x), when y=0   x=5/2

  For g(x)   it looks like when y is 0, x is going to be closer to -1 and will be a negative fraction

So f(x) is greater for x-int. and answer is true

3.  The slope for f(x) is 2

The slope for g(x)=(32-14)/(3-1) = 9  

g(x) slope is bigger

So this is false

Answer:

12-x²

Step-by-step explanation:

I hope this helps you, please give me brainliest

Answer:

1

Step-by-step explanation:

Substitute the values for their respective variables.

\(\frac{ac}{b^2+1}\\\\\frac{(2)(5)}{(3)^2+1}\\\\\frac{10}{9+1}\\\\\frac{10}{10}\\\\1\)

Step-by-step explanation:

Q. the sum of the zeroes of polynomail ax² + bx + 4c is.

\(\mathbb\red{ \tiny A \scriptsize \: N \small \:S \large \: W \Large \:E \huge \: R}\)

\( \\ \pmb{\boxed{\rm \leadsto\ b) \: \: \frac{ - b}{a} }}\)

Adjacent angles are two angles that lie in the same plane and have a common vertex and a common side but have no common interior points.

The terms adjacent, neighboring, contiguous, and juxtaposed all denote being close by. Although adjacent might indicate a touch or not, it is usually assumed that there is nothing of the same sort in between. a home with a garage close by. Adjoining clearly means coming together and touching at a certain location or line.

When two angles have a similar vertex and side, they are referred to as neighboring angles. The vertex of an angle is the point at which the rays that make up its sides come to a stop. When adjacent angles have the same vertex and side, they might be a complimentary angle or supplemental angle.

Thus, adjacent angles are two angles that lie in the same plane and have a common vertex and a common side but have no common interior points.

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The volume of the helium-filled balloon at 0.855 atm and 10.0 °C will be approximately 42.81 L, calculated using the ideal gas law equation.

To compute this problem, we can use the ideal gas law, which states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.

First, we need to convert the initial temperature of 25 °C to Kelvin:

T1 = 25 + 273.15 = 298.15 K

Next, we can rearrange the ideal gas law equation to solve for V2:

V2 = (P1 * V1 * T2) / (P2 * T1)

We have:

P1 = 1.08 atm (initial pressure)

V1 = 50.0 L (initial volume)

P2 = 0.855 atm (final pressure)

T2 = 10.0 °C (final temperature)

Converting the final temperature to Kelvin:

T2 = 10 + 273.15 = 283.15 K

Substituting the values into the equation:

V2 = (1.08 * 50.0 * 283.15) / (0.855 * 298.15)

V2 ≈ 42.81 L

Therefore, the volume of the helium-filled balloon at 0.855 atm and 10.0 °C will be approximately 42.81 L.

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In mathematics, the place value chart is a tool that helps students understand the value of digits in a number. It is a visual representation of how digits are grouped and arranged to represent numbers. The place value chart is arranged in columns, with each column representing a different place value.

The place value chart starts with the ones place, also called units place. This is the rightmost column and it represents the ones digit in a number. The next column is the tens place, which represents the tens digit in a number. The hundredth place represents the hundreds digit and so on. Each column is ten times larger than the previous one.

A place value chart can be used to understand the value of a digit in a number.

Place value chart also helps to understand decimal numbers, which are numbers that have a decimal point. The decimal point separates the whole numbers from the fractional numbers. Each place to the right of the decimal point represents a smaller value.

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Answer: -5/3

Step-by-step explanation:

Answer: m = -4/3

Step-by-step explanation:

If you're given two different coordinates, and you want to find the slope, the general rule is that you subtract the first coordinates from the first. The formula for these kinds of problems is \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\) .

Answer:

Area = 36 cm^2

Explanation:

The area of a parallelogram is the product of width and height

Now in our case w = 9 cm and h = 4cm; therefore, the area is

which is our answer!

The equation to determine the length and width of the rug is

28 = w² + 12w

Since, the shape of the rug is rectangle, therefore area of rectangle has been used to obtain the solution.

What is a rectangle?

Rectangle is a flat, two-dimensional shape, having four sides and vertices with opposite sides being equal and parallel. We may easily represent a rectangle in an XY plane by using its length and breadth as the arms of the x and y axes, respectively.

Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.

We are given a rectangular rug with an area of 28 square feet.

Also, the rug is 12 feet longer than it is wide.

So,

Let 'l' be the length of the rug and 'w' be the width of the rug

As given, Length is 12 feet longer than its width

Therefore, l = w + 12

We know Area of rectangle = Length * Width and area is given to be 28 square feet.

So,

⇒28 = (w + 12)w

⇒28 = w² + 12w

Hence, the equation to determine the length and width of the rug is

28 = w² + 12w.

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Question: Tammy has a rectangular rug with an area of 28 square feet. The rug is 12 feet longer than it is wide.

Create an equation to determine the length and the width of the rug.

The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

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Answer:

Common Ratio = 5

Step-by-step explanation:

See picture below :)

A group of two or more equations containing the same variables but with at least one non-linear equation is a non-linear system of equations.

What is a non-linear equation?

What is a nonlinear equation example?

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If \(x^(3/3) = y^(2/2)\), then \(x^3\) can be determined by simplifying the exponents.

To solve the given equation, we need to simplify the exponents on both sides.

Using the property of exponentiation, when we raise a power to another power, we multiply the exponents.

In this case, x^(3/3) can be simplified as x^(1), since 3/3 equals 1. Similarly, y^(2/2) simplifies to \(y^(1).\)

Therefore, the given equation \(x^(3/3) = y^(2/2)\) simplifies to \(x^1 = y^1.\)

Since any number raised to the power of 1 is equal to the number itself, we have x^1 = x and y^1 = y.

Hence, x^3 can be written as \(x^1 x^1 x^1 = x x x = x^3.\)

Therefore, x^3 is the answer to be filled in the space provided.

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1. The volume of water in the tank before the valve is opened is 9362 cubic meters. 2. It takes 151 hours for the tank to fully empty.

Modeling is the process of representing and analyzing real-world events using mathematical ideas and methods. It is a crucial component of mathematics because it enables systematic, quantitative prediction, problem-solving, and understanding of complicated processes.

We may learn about the behavior of systems, test hypotheses, and arrive at wise conclusions by using mathematical models. We may use models to enhance processes, forecast results, and discover key factors.

The equation of the volume is given as V = 62(151 - t).

At t= 0 we have the volume as:

V = 62(151 - 0) = 9362 cubic meters

To empty the tank we take V = 0:

0 = 62(151 - t)

151 - t = 0

t = 151

Hence, the volume of water in the tank before the valve is opened is 9362 cubic meters and it takes 151 hours for the tank to fully empty.

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