You are the site engineer in charge of the operation of a set micro gas turbines in a factory. The correct operation of the turbines is an important factor in maintaining the energy supply for the machinery. Past experience indicates that there is a 98% chance that a turbine will operate normally in any particular day.
To ensure that a faulty turbine is identified and replaced, you order a test that measures the efficiency of each turbine and use that measure as an indication of possible problems in the turbine.
The test method is not perfect: the probability that a normally operating turbine will pass the test is 0.97 and the probability that a faulty turbine passes the test is 0.01.
The outcomes of the tests are statistically independent.
Suppose that one of the turbines fails the test, what is the probability of that turbine being faulty?

Random sample of size is selected from a population:

The sample statistic that is calculated for the sample values serves as the foundation for the sampling distribution. To estimate the population percentage, the sample proportion, a sample statistic, is computed from the sample values.

In statistics, a simple random sample is a subset of individuals selected at random from a larger population with an equal probability of selection.

Given that we have,

n = 100

p = 0.40

a) The expected value of the sample proportion is defined as:

E(p) = p = 0.40

b) The standard error of the sample proportion is defined as:

[tex]S.E = \sqrt{\frac{p(1-p)}{n} }[/tex]

= [tex]\sqrt{\frac{0.40(1-0.40)}{100} }[/tex]

S.E = 0.0024.

c) The sample proportion's sampling distribution follows a normal distribution, with an expected value of 0.40.

E(p) = 0.40

d) According to the central limit theorem, as the sample size approaches infinity, the sample statistic (sample percentage) tends to the population parameter (population proportion).

so,

p ∼ N ([tex]p, \frac{p(-p)}{n}[/tex]) as n → ∞.

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Complete question:

A random sample of size 100 is selected from a population with p = 0.40 .

a. what is the expected value of p (to decimals)? .

b. what is the standard error of p (to decimals)?

c. show the sampling distribution of p

d. what does the sampling distribution of show?

The equivalent equation to f(x) = 7(x - 60) - 28 is f(x) = 7x - 448 and the y-intercept is -448

Given that

f(x) = 7(x - 60) - 28

To produce an equivalent equation that reveals the y-intercept of the function f(x) = 7(x-60) - 28, we need to simplify the expression by evaluating it when x = 0, since this will give us the y-intercept.

When the brackets are expanded, we have the following

f(x) = 7x - 420 - 28

Evaluate the like terms

So, we have

f(x) = 7x - 448

So, substituting x = 0 into f(x) gives:

f(0) = 7(0) - 448

Evaluate the expression

f(0) = -448

Therefore, the y-intercept is -448.

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The quadratic function to represent the total area of the park and its path is given by: f(x) = 2x² + 18x + 36.

In this problem, we are given that the length of a rectangular park is twice its width, and it is surrounded by a 3-foot wide path.

We are required to write a quadratic function to represent the total area of the park and its path.

The rectangular park can be represented as follows:

Length = 2x (twice the width)

Width = x

Therefore, the total length of the park including the 3-foot wide path can be represented as (2x + 2*3),

and the total width of the park including the 3-foot wide path can be represented as (x + 2*3).

The area of the park is given by the product of its length and width.

Thus, the area of the park can be represented as follows: Area of the park = (2x + 6)(x + 6)

To represent this as a quadratic function,

we can simplify the above expression using the distributive property.

Area of the park = 2x² + 6x + 12x + 36 = 2x² + 18x + 36.

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Answer: 7x - 7y + 21

Step-by-step explanation:

7( x - y + 3) = 7x - 7y + 21

Since the two angles are complementary, their sum is 90 degrees. Let x be the measure of the other angle in degrees. Then:

x + 53 = 90

Subtracting 53 from both sides, we get:

x = 37

Therefore, the measure of the other angle is 37 degrees.

The approximate circumference of this Spaceship is equal to 157 meters.

Mathematically, the volume of a sphere can be calculated by using this mathematical expression:

Volume = 4/3 × πr³

Where:

r represents the radius.

By substituting the given points into the volume of a sphere formula, we have the following;

65,417 = 4/3 × 3.14 × r³

r³ = 65,417/4.1867

Radius, r = ∛15,624.96

Radius, r = 25 meters.

Mathematically, the circumference of a sphere can be calculated by using this mathematical expression:

Circumference of a sphere, C = 2πr

Circumference of a sphere, C = 2 × 3.14 × 25

Circumference of a sphere, C = 157 meters.

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Answer:

A = 196 units²

Step-by-step explanation:

the area (A) of a regular polygon is

A = [tex]\frac{1}{2}[/tex] perimeter × apothem

here perimeter = 56 and apothem = 7 , then

A = [tex]\frac{1}{2}[/tex] × 56 × 7 = 28 × 7 = 196 units²

Answer:

x = 3, y = 4

Step-by-step explanation:

Substitute 4x - 8 in for y and then solve for x:

4x + 2(4x - 8) = 20

Then, 4x + 8x - 16 = 20 --> 12x = 36 --> x = 3.

Once you have x, you can solve for y.

y = 4x - 8 = 4(3) - 8 = 12 - 8 = 4

So, x = 3, y = 4

Therefore, a monthly payment of $168.62 must be made to pay off the $3,500 balance on the credit card in two years.

Percent is a way of expressing a number as a fraction of 100. The symbol for percent is "%". Percentages are used in many different contexts, such as finance, economics, statistics, and everyday life.

Here,

To calculate the monthly payment required to pay off the $3,500 balance on a credit card that charges 16.5% interest, compounded monthly, in two years, we can use the formula for the present value of an annuity:

[tex]PMT = PV * r / (1 - (1 + r)^{-n})[/tex]

where PMT is the monthly payment, PV is the present value of the loan, r is the monthly interest rate, and n is the total number of payments.

First, we need to convert the annual interest rate of 16.5% to a monthly interest rate:

r = 0.165 / 12

= 0.01375

Next, we need to calculate the total number of payments over two years:

n = 2 * 12

= 24

Now we can plug in the values into the formula:

[tex]PMT = 3500 * 0.01375 / (1 - (1 + 0.01375)^{-24}) = $168.62[/tex]

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To calculate your fuel consumption in gallons per hour, divide the speed (in miles per hour) by the fuel efficiency (in miles per gallon). This will give you the gallons per hour (GPH).

For example, if your speed is 50 mph and your fuel efficiency is 30 mpg, your fuel consumption would be 1.67 GPH (50/30). You can then use this result to estimate your fuel costs and overall fuel consumption over a certain period of time.

To understand this concept better, it is important to know that speed (in mph) and fuel efficiency (in mpg) are inversely related. This means that as your speed increases, your fuel efficiency decreases, and as your speed decreases, your fuel efficiency increases.

So, if you want to maximize your fuel efficiency, you need to drive at the lowest possible speed. Additionally, the higher the fuel efficiency, the lower the fuel consumption in GPH.

In short, you can use the readout from your odometer and fuel efficiency meter to calculate your fuel consumption in GPH by dividing the speed (in mph) by the fuel efficiency (in mpg). This result can help you estimate your fuel costs and overall fuel consumption.

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Answer:

20%

Step-by-step explanation:

80 - 64 = 16

16 ÷ 80 = 0.2

0.2 × 100 = 20%

The percent error for Jason's measurement is 7.14%. This means that his measurement was off by 7.14% compared to the actual value.

Percent error is a measure of the difference between an actual value and an estimated or measured value, expressed as a percentage of the actual value. It is used to evaluate the accuracy of measurements or calculations.

To calculate the percent error for Jason's measurement, we first need to find the absolute error, which is the difference between his measurement and the actual value:

Actual value minus measured value equals absolute error.

Absolute error = |14 - 13|

Absolute error = 1 inch

Next, we can use the formula for percent error:

(Absolute error / Actual Value) x 100% equals the percent of error.

Percent error = (1 / 14) x 100%

Percent error = 0.0714 x 100%

Percent error = 7.14%

Therefore, the percent error for Jason's measurement is 7.14%. This means that his measurement was off by 7.14% compared to the actual value.

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The interval is known as a prediction interval when it is created using the estimated regression equation to forecast the mean for all units that satisfy a specific set of supplied criteria.

A prediction Interval is a statistical interval that provides a range of values within which a future observation is likely to fall. It takes into account both the variability of the data and the uncertainty in the estimates of the regression coefficients.

In contrast, a confidence interval is a statistical interval that provides a range of values within which a population parameter is likely to fall. It is used to estimate the true value of a population parameter based on a sample of data.

Therefore, a prediction interval is specific to the individual unit being predicted, while a confidence interval is specific to the population parameter being estimated.

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Answer:

58.3%

Step-by-step explanation:

Since 175 calories out of 300 come from fat, we can just do 175÷300 and multiply by 100 to get the percentage:

[tex] \frac{175}{300} \times 100 = 58.3\% \: (1dp)[/tex]

[tex]\Large\bold{SOLUTION}[/tex]

To find the percentage of calories from fat for one ice cream bar, we need to divide the number of fat calories by the total number of calories, and then multiply by 100 to get the percentage.

First, we know that each ice cream bar contains 300 calories, and 175 of those calories come from fat. So:

[tex]\sf 175\: fat\: calories \div 300\: total\: calories = 0.5833[/tex]

To convert this decimal to a percentage, we multiply by 100:

[tex]\sf 0.5833 \times 100 = 58.33\%[/tex]

Therefore, the percentage of calories from fat for one ice cream bar is 58.33%.

[tex]\rule{200pt}{5pt}[/tex]

Step-by-step explanation:

hope this is correct

The probability of winning the New York State Numbers Lottery is 1 in 1000.

When you pay for a ticket, you pick a number between 000 and 999. If your number is drawn, you win $500, meaning you made a profit of $490. If you don't win, you will lose the $1 that you paid for the ticket.

To calculate the probability of winning the New York State Numbers Lottery, you must first consider the total number of possible outcomes. Since you can pick a number between 000 and 999, there are 1000 possible outcomes. This means that your chance of winning is 1 in 1000, or 0.1%.

It is important to remember that the New York State Numbers Lottery is a game of chance, meaning that there is no guarantee of winning.

However, if your number is drawn, you can win up to $500, which is a profit of $490. The odds of winning are 1 in 1000, and if you lose, you will only lose the amount you paid for the ticket.

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Answer:

31/21

Step-by-step explanation:

First step is to add 17 and 14 = 31

The denominator of the fraction(bottom number stays the same)

so the answer is 31/21

Let me know if it helps

Answer:

EXACT FORM: 31/21

DECIMAL FORM: 1.476190

MIXED NUMBER FORM: 1 10/21

Step-by-step explanation:

The characteristic that best describes 5.1 in the polynomial 5.1xy - 4x + y - 1.5 is that it is the coefficient of the term 5.1xy.

What is polynomial?

A polynomial is a mathematical expression that consists of variables and coefficients, which are combined using arithmetic operations such as addition, subtraction, multiplication, and non-negative integer exponents.

In a polynomial expression, a coefficient is the numerical factor that is multiplied by a variable or variables raised to a certain power. In the expression 5.1xy - 4x + y - 1.5, the coefficient 5.1 is multiplied by the variables x and y, raised to the first power. Therefore, the term 5.1xy consists of the coefficient 5.1 and the variables x and y.

In contrast, the other terms in the polynomial do not have a coefficient that contains a decimal or a fraction. The term -4x has a coefficient of -4, the term y has a coefficient of 1, and the constant term -1.5 has a coefficient of -1.5.

Thus, the characteristic that best describes 5.1 in the polynomial 5.1xy - 4x + y - 1.5 is that it is the coefficient of the term 5.1xy.

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The volume of the cylinder with radius 19 yd and height 21 yd is 23,804.34 cubic yard

Volume refers to the unit of three-dimensional measure of space that comprises a length, a width and a height. It is measured in units of cubic centimeters in metric, cubic inches or cubic feet.

Volume of a cylinder = π × r ²× h

Where,

π = 3.14

Radius, r = 19 yd

Height, h = 21 yd

So,

Volume of a cylinder = π × r² × h

= 3.14 × 19² × 21

= 3.14 × 361 × 21

= 23,804.34 cubic yard

Ultimately, 23,804.34 cubic yard is the volume of the given cylinder.

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Answer: Simplifying this equation, we get the ANSWER 5

Step-by-step explanation: Since g(x) = 3, we can plug this into the given equation 4x-7.

now we rewrite the given equation, which is now 4(3)-7

Now we find 4(3), simplifying/multiplying that, we get 12.

We minus 12 by 7 which is 5

Carter has 13 dimes in his piggy bank

To solve this equation, we need to use the distributive property to simplify the equation:
(x dimes x 10 cents) + (37-x nickels x 5 cents) = $3.10
We can then solve for the number of dimes by isolating the dimes on one side of the equation:
x dimes x 10 cents = $3.10 - (37-x nickels x 5 cents),By dividing both sides of the equation by 10 cents, we can solve for the number of dimes, x:
x dimes = ($3.10 - (37-x nickels x 5 cents)) / 10 cents

Plugging in the value of 37 coins and solving the equation, we get:
x dimes = (3.10 - (37 -x nickels x 5 cents)) / 10 cents
x dimes = (3.10 - 185 + 5x) / 10 centsx dimes = (3.10 - 180) / 10 centsx dimes = 1.30 / 10 centsx dimes = 13 dimes
Therefore, Carter has 13 dimes in his piggy bank.

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The value of x in the given triangle is 1.82 cm using the angle bisector theorem.

A triangle is a polygon with three edges and three vertices. It belongs to the basic geometric shapes. A triangle with the parts A, B, and C is referred to as triangle ABC. Any three points that are not collinear in Euclidean geometry result in a separate triangle and a distinct plane. A triangle is a type of polygon with three sides; the triangle's apex is the point where the two longest sides meet. Two sides are brought together at an angle.

What is angle bisector theorem?

The ratios of the two segments that a line that bisects the opposing angle splits a triangle's side into are the subject of the angle bisector theorem in mathematics. It contrasts their proportionate lengths with the other two triangle sides' proportional lengths.

In the given triangle,

5/6=x/4-x

20-5x=6x

20=11x

x=20/11= 1.82 cm

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Answer:

3

Step-by-step explanation:

Number of people in the choir = 80

Number of women = half of 80 = 40

Number of men in the choir is ¼ of the women = 40/4 = 10

Number of men plus women = 10 +40 = 50

Number of children = 80 - 50 = 30

Ratio of children to men = n:1 = 30:10

Divide both sides by 10

30:10 = 3:1

n = 3

Answer:

If x = 3 and y = 2.3^3, then we can evaluate y using exponents:

y = 2.3^3 = 2.3 × 2.3 × 2.3 = 12.167

So, y = 12.167 when x = 3.

Next, if we want to solve the equation y = 2[?] using order of operations, we need to evaluate what is inside the brackets first. We know that y = 12.167, so we can substitute that value into the equation:

y = 2[?]

12.167 = 2[?]

To solve for the missing value inside the brackets, we need to divide both sides by 2:

12.167 ÷ 2 = ?

6.0835 = ?

Therefore, the solution is y = 2(6.0835), or y = 12.167, which we already found earlier.

Answer:

The value of t is 9.

Step-by-step explanation:

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by:

slope = (y2 - y1) / (x2 - x1)

In this case, we are given two points: (t, 5) and (10, -4), and the slope is given as -9. So we can set up the equation:

-9 = (-4 - 5) / (10 - t)

Simplifying, we get:

-9 = -9 / (10 - t)

Multiplying both sides by (10 - t), we get:

-9(10 - t) = -9

Expanding the left side, we get:

-90 + 9t = -9

Adding 90 to both sides, we get:

9t = 81

Dividing both sides by 9, we get:

t = 9

Therefore, the value of t is 9.

To achieve the maximum output from his electrical system, Steve should set the input to 6, the x-coordinate of the vertex of the parabola described by the equation [tex]y = -x^2 + 12x - 20[/tex].

To find the input that will result in the maximum output of the electrical system, we need to find the vertex of the parabola described by the equation [tex]y = -x^2 + 12x - 20[/tex]. The vertex of a parabola is the point where the curve reaches its highest or lowest point, depending on whether the parabola opens upward or downward. In this case, the coefficient of [tex]x^2[/tex] is negative, which means the parabola opens downward, and the vertex represents the maximum point.

We need to find the vertex of the parabola given by the equation [tex]y = -x^2 + 12x - 20[/tex]. The vertex of a parabola with equation [tex]y = ax^2 + bx + c[/tex] is given by the formula x = -b/2a.

In this case, a = -1, b = 12, and c = -20, so the x-coordinate of the vertex is:

x = -b/2a = -12/(2*(-1)) = 6

Therefore, the input at which Steve will reach his maximum output is x = 6.

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The coordinates of the image after rotating the figure 180 degrees about the origin are T'(4. -3). V'(5, -5), W'(2, -5). X.(1, -3)

Given that

T'(-4, 3). V'(-5, 5), W'(-2, 5). X(-1, 3)

Rotating a figure by 180 degrees is equivalent to flipping it over the horizontal and vertical axes simultaneously.

This means that the x-coordinate of each point will be negated, and the y-coordinate will be negated as well.

Therefore, to find the coordinates of the image of a point after rotating it by 180 degrees, you can use the following formula:

(x', y') = (-x, -y)

Using the above, the image is

T'(4. -3). V'(5, -5), W'(2, -5). X.(1, -3)

Hence, the image is T'(4. -3). V'(5, -5), W'(2, -5). X.(1, -3)

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Complete question

Rotate the figure 180 degrees about the origin

T'(4. -3). V'(5, -5), W'(2, -5). X.(1, -3)

T'(3, 4). V'(5, 5), W'(5, 2), X '(3. 1) (Th

T'(-3, 4) V(-5. 5), W'(-5, 2). X'(-3, 1)

T'(-3, -4), V'(-5, -5). W(-5, -2), X '(-3, -1)

The total number of biscuits the baker should place into each, according to the declaration, is 12.

The mathematical expressions consist of at least a couple of integers or issues, no fewer than one math procedure, and a sentence. It's achievable to multiply, divide, add, or remove with this algebraic method. An expression's form is as follows: Expression: (Math Operator, Number/Variable, Arithmetic Operator)

The total number of cookies in both batches is:

36 + 48 = 84

To divide the cookies into seven equal groups, we need to divide the total number of cookies by 7:

84 / 7 = (12 x 7) / 7 = 12

So the baker should put 12 cookies into each of the seven groups.

A numerical expression that shows how to determine the total number of cookies the baker should put into each group with parentheses is:

(36 + 48) / 7 = (84) / 7 = 12

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Answer:

If the ratio of the number of cats to dogs at the animal shelter is 9 to 5, this means that for every 9 cats at the shelter, there are 5 dogs.

We can express this ratio as:

number of cats : number of dogs = 9 : 5

To find the possible number of cats to dogs, we need to look for pairs of numbers that have a ratio of 9:5. Here are some possible pairs:

   9 cats : 5 dogs

   18 cats : 10 dogs

   27 cats : 15 dogs

   36 cats : 20 dogs

   45 cats : 25 dogs

   54 cats : 30 dogs

   ...

We can see that there are infinitely many possible pairs of numbers that have a ratio of 9:5. To narrow down the possibilities, we need more information such as the total number of animals at the shelter or the number of cats or dogs at the shelter.

In summary, the force required to give the wheel an acceleration of 4.46 rad/s2 when using a 9.00-cm-diameter sprocket is 8,550.54 N, and the force required when using a 5.58-cm-diameter sprocket is 13,764.83 N.

To answer (a) and (b), we need to determine the rotational inertia of the wheel, then calculate the torque and force required to accelerate the wheel with a given angular acceleration.
The rotational inertia of a wheel with all its mass concentrated on the outside radius can be calculated using the formula I = mr^2, where m is the mass of the wheel and r is its radius. In this case, the radius of the wheel is 63.8/2 cm (31.9 cm) and its mass is 1.71 kg, so the rotational inertia is I = [tex]1.71 * (31.9 cm)^2 = 17,214.939 cm^4.[/tex]
To calculate the torque and force required to accelerate the wheel, we use the equation T = I * alpha, where T is the torque, I is the rotational inertia, and alpha is the angular acceleration. Plugging in the values given in the question, we get[tex]T = 17,214.939 cm^4 * 4.46[/tex] rad/[tex]s2 = 76,954.848 Nm.[/tex]
To calculate the force required to accelerate the wheel, we use the equation F = T / r, where F is the force, T is the torque, and r is the radius of the sprocket. For the 9.00-cm-diameter sprocket, the force required is F = 76,954.848 Nm / 9 cm = 8,550.54 N. For the 5.58-cm-diameter sprocket, the force required is F = [tex]76,954.848 Nm / 5.58[/tex] cm = [tex]13,764.83 N.[/tex]

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