which statement is not a step used when constructing an inscribed equilateral triangle ?

To increase the speed of the response in the given system, we need to identify the parameters that influence the time constant (T) of the system. The time constant is a measure of how quickly the system responds to changes.

In the given equation, y(s) = 1/(sT + 1)[C*A - C*/q* . qAmax/Cmax d(s) + C*b - c*/q* . q Bmax/Cmax u(s)], the time constant (T) is present in the denominator term sT + 1. To increase the speed of the response, we need to decrease the value of T.

The time constant T is determined by the product of the capacitance (C) and the resistance (R), where T = RC. In this case, we can observe that T is directly proportional to the capacitance C.

To increase the speed of the response, we can decrease the capacitance value (C). This can be achieved by decreasing the values of C*A and Cmax in the equation. By reducing the capacitance, we reduce the time constant T, resulting in a faster response.

Mathematically, the time constant T can be expressed as T = (V/q*) * C. By reducing the value of C, the time constant T decreases, leading to a faster response.

To justify the reasoning, we can analyze the step response plots. The step response shows how the system output responds to a sudden change in the input. By decreasing the capacitance (C), we reduce the time constant and observe a steeper rise in the step response, indicating a faster response time. Conversely, increasing the capacitance would result in a slower response characterized by a more gradual rise in the step response.

Therefore, to increase the speed of the response, we need to decrease the capacitance values C*A and Cmax in the equation by adjusting the corresponding parameters.

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Determined by various factors such as sample size, statistical significance, and the chosen level of confidence. the probability that the test will fail to decide that the true value is 72.5 when it is indeed 72.5.  

In order to calculate the probability of a Type II error, one would need to know the specific details of the test being used, such as the sample size, the statistical power of the test, and the chosen level of significance.

In general, the probability of a Type II error increases as the sample size decreases and the level of significance decreases. This means that if the test being used is not sufficiently powered or if the level of confidence is too low, there is a higher probability of failing to detect a true effect.

If the test is not able to accurately determine if the statement is true or not when the actual value is 72.5, then there is a possibility that a Type II error has occurred. The probability of this error depends on the specific details of the test being used and cannot be determined without further information.

The probability of a test failing to decide a certain hypothesis is true, when it is actually true, can be determined using the concept of Type II error or false negative rate. In statistical hypothesis testing, Type II error (β) refers to the probability of failing to reject a false null hypothesis. These factors influence the power of the test, which is the probability of correctly rejecting the null hypothesis when it is false. The power of the test (1 - β) is complementary to the probability of making a Type II error.

In this case, the null hypothesis (H0) could be that the value is not equal to 72.5,

while the alternative hypothesis (H1) states that the value is equal to 72.5.

The probability you are looking for is the Type II error rate when the true value is 72.5.

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The volume of water in Tank 1 can be modeled by the equation V₁(m) = 1540 - 6m, where m represents the number of minutes. The volume of water in Tank 2 can be modeled by the equation V₂(m) = 246 + 6m. The two tanks will have the same number of gallons when V₁(m) = V₂(m). It will take 219 minutes for the tanks to have the same volume of water.

1. Let's start by setting up the equation for the volume of water in Tank 1. Since water is draining out of Tank 1 at a rate of 6 gallons per minute, we can subtract 6m from the initial volume of 1540 gallons. Thus, the equation for Tank 1 becomes V₁(m) = 1540 - 6m.

2. Similarly, since water is flowing into Tank 2 at a rate of 6 gallons per minute, we can add 6m to the initial volume of 246 gallons in Tank 2. Therefore, the equation for Tank 2 becomes V₂(m) = 246 + 6m.

3. To find the time it takes for the two tanks to have the same volume of water, we need to find the value of m when V₁(m) = V₂(m). Setting the two equations equal, we have:

1540 - 6m = 246 + 6m

4. Now, let's solve this equation for m:

1540 - 246 = 6m + 6m

1294 = 12m

m = 1294 / 12

m ≈ 107.83

5. Since we are looking for the time to the nearest minute, we round m to the nearest whole number, which is 108 minutes.

6. Therefore, it will take approximately 108 minutes (or 1 hour and 48 minutes) for the two tanks to have the same number of gallons.

7. Comparing this time to 2 hours, we can see that it will take shorter than 2 hours for the tanks to reach the same volume. Two hours would be equal to 120 minutes, which is longer than the 108 minutes it actually takes. This is because the rate of flow in and out of the tanks is the same, causing the volumes to equalize at a faster rate.

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Actually Welcome to the Concept of the Straight lines.

equation of the line perpendicular to the given line is

\(y = \frac{1}{4} x + 3\)

Answer: 16+d>20

d>4

Step-by-step explanation:

d=digs

16+d>20

16-16+d>20-16

d>4

Answer:

Cost of 12 pencils = 37 4/5 = 189/5

Cost of 1 pencil = 189/5 ÷ 12

= 189/5 x 1/12 = 189/60 = 63/20 = 3 3/20

So required answer is 3 3/20

Hope This Helps You!

The forecast for week 6 if Y is forecast for demand of chips sale and X is the week 18. The correct answer is 1) 18 KD.

This forecast assumes a linear relationship between the demand for chips sale and time. To use the equation Y=2X+6 for forecasting the demand of chips sale, we need to plug in the value of X, which is the week for which we want to create the forecast. Here, we want to forecast for week 6, so X=6.

Substituting the value of X=6 in the equation, we get:

Y=2(6)+6

Y=12+6

Y=18

Therefore, the forecast for week 6 using the given equation is 18.

Hence, option 1) 18 KD is the correct answer.

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Answer:

y=2

Step-by-step explanation:

probably

Answer:

y = -2

Step-by-step explanation:

-10 = y - 12

For the correct form, we have to get y by itself.

So, to get rid of ten, we'll add it to both sides.

-10 = y - 12

+10       +10

y = 10 - 12

Now, we'll simplify the answer.

y = -2

Answer:

x=0, - 9

Step-by-step explanation:

x^2+9x=0

x(x+9)=0

x=0 or x=-9

Answer:

x =0  x= -9

Step-by-step explanation:

x^2 + 9x = 0

Factor out x

x(x+9) =0

Using the zero product property

x =0 x+9 =0

x =0  x= -9

Answer:

x=1 y=

-3

Step-by-step explanation:

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Answer:

Step-by-step explanation:

Simplifying                                                Simplifying

                                                                      5x + 4y = -7

-5x + -2y = 1

Simplifying

                                                                  Simplifying   x = -0.2 + -0.4y

x = -1.4 + -0.8y

Answer:

(24y^3x-20y^5x^2)/(-3y^5x^2)

= y^3x(24-20y^2x))/(-3y^5x^2)

=(24-20y^2x)/(-3y^2x)

=(24/(-3y^2x))-((20y^2x)/(-3y^2x))

=(-8/y^2x)-(-20/3)

=-8/y^2x + 20/3

The greatest common divisor of each of these pairs of integers are

a) 1    b)  1    c) 12   d)  1     e)  3   g)  1     h)  2    i) 1  

f) 0 is not a positive integer, so it doesn't have a prime factorization.

The greatest common divisor (GCD), also known as the highest common factor (HCF), of two or more integers is the largest positive integer that divides each of the integers without a remainder.

To find the GCD we need to write each number as a product of prime factorization and then we need to find out the common factors which is greatest among them.

a) 10 = 2 × 5,

11 is prime

GCD(10, 11) = 1 (no common factors)

b) 21 = 3 × 7,

44 = 2 × 2 × 11

GCD(21, 44) = 1 (no common factors)

c) 36 = 2 × 2× 3 × 3

48 = 2 × 2 × 2 × 2 × 3

GCD(36, 48) = 2 × 2 × 3 = 12

d) 34 = 2  × 17,

55 = 5 × 11

GCD(34, 55) = 1 (no common factors)

e) 117 = 3 × 3 × 13,

213 = 3 × 71

GCD(117, 213) = 3

f) 0 is not a positive integer, so it doesn't have a prime factorization.

g) 123 = 3 × 41, 2347 is prime

GCD(123, 2347) = 1 (no common factors)

h) 3454 = 2 × 1727,

4666 = 2 × 2333

GCD(3454, 4666) = 2

i) 9999 = 3 × 3 × 11 × 101,

11111 = 41 × 271

GCD(9999, 11111) = 1 (no common factors)

Therefore,

The greatest common divisor of each of these pairs of integers are

a) 1    b)  1    c) 12   d)  1     e)  3   g)  1     h)  2    i) 1  

f) 0 is not a positive integer, so it doesn't have a prime factorization.

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The amount of each quarterly payment, rounded, for a $30,000 loan with a 6% annual interest rate to be paid off in 10 equal quarterly payments is $2,803 (option B).


To calculate the amount of each quarterly payment, we need to use the formula for calculating the equal payments on an installment loan. In this case, the loan amount is $30,000, the annual interest rate is 6%, and the loan term is 10 quarters.

Using the formula, we can determine that the amount of each quarterly payment is approximately $2,803. This amount is rounded to the nearest whole number, as specified in the question. Therefore, option B, $2,803, is the correct answer. The other options (A, C, and D) are not applicable to the calculation based on the given information.

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Let's evaluate :

Hey there!

2x³ + 5x² - 10

It's given that the value of x is -2. So substitute it in the place of x in the equation.

2(-2)³ + 5(-2)² - 10

= 2 × -8 + 5 × 4 - 10

= -16 + 20 - 10

= 4 - 10

= - 6

Hope it helps ya!

The 99% confidence interval for the true mean length of the manufactured bolt is (2.9177, 3.0823)

Here, we need to construct a 99% confidence interval for population mean (μ) is given by

μ = x + Zα/2 * σ/√n   or    μ = x - Zα/2 * σ/√n

where, μ = population mean

x = sample mean

  = 3 inches

σ = population standard deviation

  = 0.3 inches

Zα/2= z score for a two tailed test at level of significance α = 2.576( for a 99% confidence level)

So, the upper limit would be,

μ = 3 + 1.645 * (0.3/√36)

μ = 3 + 1.646 * (0.3/6)

μ = 3.0823

And the lower limit would be,

μ = 3 - 1.645 * (0.3/√36)

μ = 3 - 1.646 * (0.3/6)

μ = 2.9177

Hence, the 99% confidence interval is (2.9177, 3.0823)

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True, all three parts of a whole, parts of a set, and division meanings of fractions involve the idea of partitioning.

Partitioning is a method of splitting numbers into smaller parts to make work easy. An example of Partitioning is when the child is taught to recognize that the number 54 represents 5 tens and 4 ones, which shows how the number can be partitioned into 50 and 4.

A fraction is defined as a part of the whole thing in mathematics, for example, when we say "1/2 of the pizza", we are partitioning the whole pizza into two equal parts and taking one of those parts. Types of Fractions are Proper Fractions, Improper Fractions, Mixed fractions, Like fractions, Unlike fractions, and Equivalent fractions

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Answer

well first u put it as 2/2 which is 2 then you have to times it by 69 which is 138 then divide that by 6.5 which is 21

Step-by-step explanation:

actual answer is 4 if you were serious about this

Answer: 4

Step-by-step explanation:

Use your hands:

2 on one hand

2 on the other hand

Put them together which is 4

The fractions in the simplest form is: = -73/24.

Given the expression involving fractions, -7/8 + (-2⅙), we would solve as shown below:

-7/8 + (-2⅙)

Convert the mixed fraction to improper fraction

= -7/8 + (-13/6)

Distribute to eliminate the parentheses

= -7/8 - 13/6

= (-21 - 52)/24

= -73/24

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The table of values is a linear equation which is given as y = -7/2x + 2

A linear function is a mathematical function that represents a straight line when graphed on a coordinate plane. It is a type of function where the independent variable (usually denoted as x) has a constant rate of change with respect to the dependent variable (usually denoted as y).

The slope-intercept form of a linear equation is given as;

y = mx + c

From the table of value given;

f(x) = mx + c

Let's calculate the slope of the equation;

m = y₂ - y₁ / x₂ - x₁

m = 2 - 9 / 0 - (-2)

m = -7 / 2

The slope is -7/2

Taking the slope to find the linear equation;

y = mx + c

Taking any point;

9 = -7/2(-2) + c

9 = 7 + c

c = 2

The equation is y = -7/2 + 2

Taking another point to confirm our answer;

2 = -7/2(0) + c

c = 2

This shows the values is a linear equation;

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The mathematical proof is given below. Then the claims are correct.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

The triangle ΔABC is a right-angle triangle. And line CD is perpendicular to line AB.

In triangles ΔABC, ΔACD, and ΔCDB, we have

∠ACB = ∠ADC = ∠BDC                     (Right angle)

∠ABC = ∠ACD = ∠CBD                     (Corresponding angles)

Then the triangles ΔABC, ΔACD, and ΔCDB will be similar to each other. And in triangle ΔABC by the Pythagoras theorem is written as,

AB² = AC² + BC²

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When a data value is converted to a standardized scale representing the number of standard deviations the data value lies from the mean, we call the new value a Z-Score.

In statistics, each mathematical formula and each element has an internationally recognised name. This is to ensure that everyone in the world understands what every researcher has to say in every letter. A statistic that tells the number of standard deviations a data value is above or below the mean is called a z-score. And its formula is, Z = (X − μ)/σ

where, μ--> population mean,

σ --> population standard deviation and

x --> the raw-score.

Hence, when a data value is converted to a standardized scale, new value, Z-Score is representing the number of standard deviations the data value lies from the mean.

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A. The probability that one selected subcomponent is longer than 122 cm can be found by calculating the area under the normal distribution curve to the right of 122 cm. We can use the z-score formula to standardize the value and then look up the corresponding probability in the standard normal distribution table.

z = (122 - μ) / σ = (122 - 100) / 5.6 = 3.93 (approx.)

Looking up the corresponding probability for a z-score of 3.93 in the standard normal distribution table, we find that it is approximately 0.9999. Therefore, the probability that one selected subcomponent is longer than 122 cm is approximately 0.9999 or 99.99%.

B. To find the probability that the mean length of three randomly selected subcomponents exceeds 122 cm, we need to consider the distribution of the sample mean. Since the sample size is 3 and the subcomponent lengths are normally distributed, the distribution of the sample mean will also be normal.

The mean of the sample mean will still be the same as the population mean, which is 100 cm. However, the standard deviation of the sample mean (also known as the standard error) will be the population standard deviation divided by the square root of the sample size.

Standard error = σ / √n = 5.6 / √3 ≈ 3.24 cm

Now we can calculate the z-score for a mean length of 122 cm:

z = (122 - μ) / standard error = (122 - 100) / 3.24 ≈ 6.79 (approx.)

Again, looking up the corresponding probability for a z-score of 6.79 in the standard normal distribution table, we find that it is extremely close to 1. Therefore, the probability that the mean length of three randomly selected subcomponents exceeds 122 cm is very close to 1 or 100%.

C. If we want to find the probability that all three randomly selected subcomponents have lengths exceeding 122 cm, we can use the probability from Part A and raise it to the power of the sample size since we need all three subcomponents to satisfy the condition.

Probability = (0.9999)^3 ≈ 0.9997

Therefore, the probability that if three subcomponents are randomly selected, all three of them have lengths that exceed 122 cm is approximately 0.9997 or 99.97%.

Based on the given information about the normal distribution of subcomponent lengths, we calculated the probabilities for different scenarios. We found that the probability of selecting a subcomponent longer than 122 cm is very high at 99.99%. Similarly, the probability of the mean length of three subcomponents exceeding 122 cm is also very high at 100%. Finally, the probability that all three randomly selected subcomponents have lengths exceeding 122 cm is approximately 99.97%. These probabilities provide insights into the performance of the automatic machine in terms of producing longer subcomponents.

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Answer:

#1 is a cereal box  

#2 is a water bottle

#3 is the amount of space a 3 dimensional object takes up

Hope this helps :)

Answer:

1.D

2.B

Step-by-step explanation:

Explanation:

The order of the runners from fastest to slowest is:

Math friend

Red Sox pair (first member)

Golden State Warrior pair

Red Sox pair (second member)

Math friend

Patriot pair (first member)

Patriot pair (second member)

Last runner wearing a Patriots shirt

Based on the given information, we can deduce the order of the runners from fastest to slowest.

Since the last runner wore a Patriots shirt, we know that the Patriot pair is not the first pair to finish. This eliminates the possibility of the Patriots pair finishing in the first and second positions.

From the clues given:

(a) 1 runner between the Math friends

(b) 2 runners between the Red Sox pair

(c) 3 runners between the Golden State Warrior pair

(d) 4 runners between the Patriot pair

We can determine the following order:

Math friends (M)

Red Sox pair (R)

Golden State Warrior pair (G)

Patriot pair (P)

To satisfy the given conditions:

(a) There is 1 runner between the Math friends, which means one runner (M) must be between the two members of the Math friends.

(b) There are 2 runners between the Red Sox pair, which implies that one member of the Red Sox pair (R) must finish before the other member, with two runners (M and G) between them.

(c) There are 3 runners between the Golden State Warrior pair, indicating that the two members of the Golden State Warrior pair (G) must finish before the third member, with three runners (M, R, and P) between them.

(d) There are 4 runners between the Patriot pair, so both members of the Patriot pair (P) must finish after the other pairs, with four runners (M, R, G, and the last runner) between them.

Therefore, the order of the runners from fastest to slowest is:

Math friend

Red Sox pair (first member)

Golden State Warrior pair

Red Sox pair (second member)

Math friend

Patriot pair (first member)

Patriot pair (second member)

Last runner wearing a Patriots shirt

This order satisfies the given conditions and ensures that the last runner wore a Patriots shirt.

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Answer:

1 2/25

Step-by-step explanation:

Answer:

1 2/25

Step-by-step explanation:

there's one 25 in 27 and two left over

1 2/25

Answer:150%

Step-by-step explanation:because 50% increases

The number of houses sold this month are -

y = 3x/2.

In mathematics →

Given is that compared to last month, there was a 50% increase in the number of houses sold this month.

Assume that the number of houses sold of previous moth were [x]. Then, we can write -

y = {x} + 50% of {x}

y = {x} + (50/100) × {x}

y = {x} + {x/2}

y = 3x/2

Therefore, the number of houses sold this month are -

y = 3x/2.

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Answer:

69

Step-by-step explanation:

150*(0.46) = 69 blueberry muffins

The equation of the line for the given point (-2,-5) and slope m=1/2

as y = (1/2)x - 4.

Given, the point = (-2,-5)

m = 1/2

we know that the equation of a line passing through the point and slope is:

y - y₁ = m(x-x₁)

y - (-5) = 1/2 (x-(-2))

y + 5 = 1/2 (x+2)

2y + 10 = x + 2

arrange the constants and variables on one side.

2y - x = 2 - 10

2y - x = -8

2y = x - 8

hence slope intercept form:

y = mx + c

y = x/2 - 8/2

y = (1/2)x - 4

hence m = 1/2 and c = 4

Hence we get the equation of the line as y = (1/2)x - 4.

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