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Standard error of the mean is 0.05267 in (a). The actual mean degradation rate has a 90% probability of being between 0.978 and 1.174 micromoles/minute/gram, according to (b).

The group mean's likelihood to vary from a sampling distribution is indicated by the standard deviation of a mean, or merely standard error. It reveals how much is the sample imply would change if a research were to be repeated with fresh samples drawn from a particular population.

(a)

Sample size, n = 9

Sample standard deviation, S = 0.158

Standard error of the mean,

\(\sigma_{\bar{x}}=\frac{S}{\sqrt{n}}=\frac{0.158}{\sqrt{9}}=0.05267\)

(b)

Since we do not know the distribution of the parent population or the population standard deviation, and further the sample size, n = 8 < 30,

Therefore we will use the t-distribution to construct the confidence interval for the true population mean α

Sample size, n = 9

Sample mean, r  = 1.076

Sample standard deviation, S = 0.158

Standard error of the mean,

\(\sigma_{\bar{x}}=\frac{S}{\sqrt{n}}=\frac{0.158}{\sqrt{9}}=0.05267\)

Level of confidence, c (in percentage) = 90

α = (1-(c/100) = 0.1

Degrees of freedom, df = n-1 = 9 - 1 = 8

The critical t-score, \(\mathrm{t}_{\mathrm{c}}\) is the

t-score corresponds to the given level of confidence and degrees of freedom :

\(\begin{aligned}& P\left(x > t_{d f}\right)=\Rightarrow / 2 \\& \Rightarrow \\& P\left(x > t_8\right)=0.1 / 2=0.05 \\& \Rightarrow t_c=1.86\end{aligned}\)

The confidence interval is calculated as:

\(\mathrm{Cl}=\bar{x} \pm\left(\mathrm{t}_{\mathrm{c}}\right)^*\left(\sigma_{\bar{x}}\right)\)

= 1.076 ± (1.86)*(0.05267)

= 1.076±  0.098

= (1.076 - 0.098, 1.076 + 0.098)

= (0.978, 1.174)

The actual mean degradation rate has a 90% probability of being between 0.978 and 1.174 micromoles/minute/gram, according to this information.

The mean degradation rate must be higher than 1 for the process to be cost-effective.

However, because the 90% confidence interval does not completely fall above 1, the experts cannot be certain that the process will be cost-effective.

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Answer:

27/35 points

Step-by-step explanation:

The probability of getting one double;

P(getting one double) = 5/36

Probability of getting two doubles is;

P(getting two doubles) = 1/36

Probability of getting no doubles is;

P(getting no doubles) = 1/36

For us to find the Number of points that the player should lose for not rolling doubles, we have;

(12/36) + (5(3 - x)/36) - (5x/6) = 0

(12/36) + (15 - 5x)/36 - 5x/6 = 0

Multiply through by 36 to get;

12 + 15 - 5x - 30x = 0

35x = 27

x = 27/35

the standard deviation of the random variable x, which is uniformly distributed between 3.19 and 9.58, is 1.845.

To compute the standard deviation of a uniformly distributed random variable x between 3.19 and 9.58, follow these steps:

Step 1: Determine the range of the random variable x. In this case, it is given as 3.19 to 9.58.

Step 2: Calculate the difference between the upper limit (b) and the lower limit (a).
b = 9.58
a = 3.19
Difference = b - a = 9.58 - 3.19 = 6.39

Step 3: Use the formula for the standard deviation of a uniformly distributed random variable, which is:
Standard Deviation (σ) = √((b - a) ²/ 12)

Step 4: Plug in the values from step 2 into the formula:
σ = √((6.39)/ 12)

Step 5: Calculate the result:
σ = √((40.8321) / 12) = √(3.402675) = 1.845

So, the standard deviation of the random variable x, which is uniformly distributed between 3.19 and 9.58, is 1.845.

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Answer:

c

Step-by-step explanation:

Answer:

the answer is C

Step-by-step explanation:

On solving the provided question, we can say that by trigonometry so sin 90 = p/h => z = 11

The area of mathematics known as trigonometry examines the correlation between triangle side lengths and angles. The area first appeared in the Hellenistic era, around the third century BC. from the use of geometry in astronomical study. The area of mathematics known as exact methods deals with specific trigonometric functions and how they might be used in calculations. There are six popular trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their respective names and acronyms (csc). Studying the characteristics of triangles, particularly right triangles, is called trigonometry. The study of geometry, however, is the characteristics of all geometric figures.

here,

it is a right angled triangle

by trigonometry

so sin 90 = p/h

1 = 11/z

z = 11

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The length of CD is 6.32 units.

From the question, we have

CB / AB = DB / CB

CB / 14 = 10 / CB

CB² = 14 × 10

CB = √140

using the Pythagorean theorem,

AB² = CB² + AC²

14² = (√140)² + AC²

196 - 140 = AC²

AC = √56

Using the ratio of the similar triangle,

CD / AC = DB / CB

CD / √56 = 10 / √140

CD = (√56 × 10)/√140

CD = 6.32 units

the length of CD is 6.32 units.

Divide:

Repetitive subtraction is the process of division. It is the multiplication operation's opposite. It is described as the process of creating equitable groups. When dividing numbers, we divide a larger number down into smaller ones such that the larger number obtained will be equal to the multiplication of the smaller numbers. One of the four fundamental mathematical operations, along with addition, subtraction, and multiplication, is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things. It is a mathematical operation used for equal distribution and equal grouping.

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#2

Reflexive sides

#3

Already given in question

#4

Given in the question

#5

By bisector definition

#6

Third angle therom

#7

Angle-Side-Angle

Done

Step-by-step explanation:

Missing reasons:

The value of θ for the given trigonometric equation are 37° and -63°.

Given trigonometric equation is,

4tan²θ + 5tanθ = 6

We have to find the value of θ.

The value of θ is in the range [0, 360).

This is in the form of a quadratic equation.

4tan²θ + 5tanθ - 6 = 0

Discriminant = 25 - (4 × 4 × -6) = 121

tan θ = (-5 ± √121) / 8

tan θ = (-5 ± 11) / 8

tan θ = 6/8 = 3/4 and tan θ = -16/8 = -2

The value of θ are tan⁻¹ (3/4) and tan⁻¹(-2).

The value of θ are approximately 37° and -63°.

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we can write an equation with the condition so:

and we can solve for x so:

So the unknow number is 7

Answer: I think it's 30 degrees. Sorry if I'm wrong.

Step-by-step explanation:

Answer:

3 pieces

I hope this helps

Step-by-step explanation:

X(1/3) = 1

x/3 = 1

X= 1×3 = 3

Answer:

Value of theta Ф = 1.33 radians

Step-by-step explanation:

We are given :

S= 8

r = 6

We need to find angle Ф

The formula used is: S=rФ

Finding theta Ф by putting values in formula:

\(S=r\theta\\\theta=\frac{S}{r}\\ \theta=\frac{8}{6}\\\theta=1.33\)

So, value of theta Ф = 1.33 radians

The formula for the circumference of a circle (or a sphere) is \(2\pi r\\\).
The formula the volume of a sphere is \(\frac{4}{3}\pi r^3\).
Assuming 43.4 includes the pi, we can do the equation \(43.4=2\pi r\)
Solving the equation, we get \(\frac{43.4}{2\pi } =r\)

Substituting r into the formua for the volume of a sphere, we get \(\frac{4}{3} *\pi *(\frac{43.4}{2\pi } )^3\)
Solving the cube (probably with a calculator), we get \(\frac{4}{3} *\pi *\frac{81746.504}{8\pi ^3}\)

It is a bit messy, but we can simplify further by cancelling out the pi's, which leaves us with \(\frac{4}{3} *\frac{81746.504}{8\pi ^2}\).
With the butterfly method (or whatever you may call it), we can cancel out the 4 in the numerator and the 8 in the denominator, and multiply the 3 in the denominators.
Which gets us this: \(\frac{81746.504}{6\pi ^2}\)
Using a calculator, we get our final answer of (about) 1380.44cm^3

This was very messy, I apologize if I did make any mistakes.

Answer:

The first option (the uppermost) is correct.

Step-by-step explanation:

When you multiply 1/2 by 3/4, you obtain the result of (1x3) / (2x4).

Simplifying, this gives us the result: 3/8, which is represented by the first choice.

Let me know if this helps!

Answer: y=-25

Step-by-step explanation:

Plug in -8 for x

3(-8)-1

-24-1

-25

Answer:

x= -25

Step-by-step explanation:

-8(3)-1=

-24-1=

-25

The inputs that are solutions for the inequality are:

x = 2

x= 1

Here we have the following inequality:

-5x < 2

We want to see which of the given inputs is a solution for this.

First we can isolate the variable in our inequality, so we get:

-5x < 2

-2 < 5x

-2/5 < x

-0.4 < x

So any value larger than -0.4 is a solution, from the given options, the two that are solutions are:

x = 1

x = 2.

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The system with impulse response g(t, t) = e^(-2|t|^-|t|) is not BIBO stable, while the system with impulse response g(t, t) = sin(t)e^(-(-t^2)) is BIBO stable.

To determine if a system is BIBO (Bounded-Input Bounded-Output) stable, we need to analyze the impulse response of the system.

For the first system with impulse response g(t, t) = e^(-2|t|^-|t|), let's examine its behavior. The function e^(-2|t|^-|t|) decays rapidly as |t| increases. However, it does not decay fast enough to satisfy the condition for BIBO stability, which requires the integral of |g(t, t)| over the entire time axis to be finite. Since the integral of e^(-2|t|^-|t|) diverges, the first system is not BIBO stable.

For the second system with impulse response g(t, t) = sin(t)e^(-(-t^2)), the term e^(-(-t^2)) represents a Gaussian function that decays exponentially. The sinusoidal term sin(t) can oscillate, but it is bounded between -1 and 1. As the exponential decay ensures that the impulse response is bounded, the second system is BIBO stable.

In summary, the system with impulse response g(t, t) = e^(-2|t|^-|t|) is not BIBO stable, while the system with impulse response g(t, t) = sin(t)e^(-(-t^2)) is BIBO stable.

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If the triangle has sides with lengths of 49 cm, 68 cm, and 92 cm , then the triangle is not a Right Triangle .

If the Triangle is a right triangle , then the sides of the triangle should satisfy the Pythagoras Theorem which states that the sum of the square of two smaller sides is equal to square of longest side(hypotnuse) .

that means ⇒ (Hypotnuse)² = (Perpendicular)² + (Base)² ;

Substituting the longest value as 92 and other values as 49 and 68 ,

we get ;

⇒ 92² = 49² + 68² ;

⇒ 8464 = 2401 + 4624 ;

⇒ 8464 ≠ 7025 .

the sides 49 cm, 68 cm, and 92 cm do not satisfy Pythagoras theorem ,

Therefore , the side lengths do not form a Right Triangle .

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Answer:

5.49

Step-by-step explanation:

5.489, the number 9 that is underlined is 5 or more so you put that at 0 then it would be 5.48, but since the 8 is also 5 or more and is the hundreths place you round that to 9 giving you 5.49

In the ratio of 2:6 , Lacey will get 6 cards and Martha will get 18 cards

Total number of cards = 24

Let Lacey gets "x" numbers of cards and Martha gets "y" numbers of cards

Ratio of cards given to Lacey to Martha = 2:6

x:y = 2:6

and we also know that total cards are 24

x + y = 24

x = 24 - y

putting value of x in the ratio,

\(\frac{24 - y}{y} = \frac{2}{6}\\\)

cross multiplication,

6(24 - y) = 2y

144 - 6y = 2y

8y = 144

y = 18

Substituting value of y ,

x = 24 - 18

x = 6

Hence , Lacey will get 6 cards and Martha will get 18 cards.

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Answer:

It's the second graph.

Step-by-step explanation:

\(\huge\text{Hey there!}\)

\(\large\text{If x = 3, y = 2, and z = 4 then substitute it in the given equation!}\)

\(\large\text{Equation: 3 (2) (4)}\\\large\text{3 (2) (4)}\\\large\text{3(2) = 6}\\\large\text{(6)(4) = \bf{ANSWER}}\\\large\text{= \bf{\underline{24}}}\)

\(\boxed{\boxed{\large\text{Answer: \bf{24}}}}\huge\checkmark\)

\(\text{Good luck on your assignment and enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

Answer:

2/7th

Step-by-step explanation:

The equation of a line is 3y + x - 15 = 0.

What is the equation of a line?

The set of points that make up a line in a coordinate system is represented algebraically by a line's equation. An equation of a line is an algebraic expression that represents the many points that together make up a line in the coordinate axis as a set of variables, x, and y. We may determine whether a given point lies on a line using the equation of any line.

Here, we have

Given: A(0,0), B(1,3)

The slope of AB = (3-0)/(1-0) = 3

The slope of a line perpendicular to AB = -1/3

y-intercept is 5

Equation of a line:

y - 5 = (-1/3)(x-0)

3y - 15 = -x

3y + x - 15 = 0

Hence, the equation of a line is 3y + x - 15 = 0.

Question: Given A(0,0) and B(1,3), find the equation of the line perpendicular to the y-intercept of 5

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