What are the values for SS and variance for the following sample of n = 4 scores? What is the sample standard deviation?​ Sample: 1, 1, 0, 4, 2​ Show all work, use correct notations, by hand. Create a frequency table.

To solve the problem we must know about the formula of the length of the Arc.

\(\rm{ Length\ of\ Arc = \dfrac{2\pi r \theta}{360^o}\)

The angle made by the arc in the center is 2.7 radians.

Given to us

Let the angle be θ.

Substituting the values in the formula of Length of Arc,

\(\rm{ Length\ of\ Arc = \dfrac{2\pi r \theta}{360^o}\\\\ \)

\(8\ in. = \dfrac{2\pi \times 3 \times \theta}{360^o}\)

\(\theta = \dfrac{360^o\times 8\ in.}{2\pi \times 3 }\\\\ \theta = 152.788^o \approx 152.79^o\)

\(\theta = 152.79^o\\\\ \)

   \(=\dfrac{\theta \times \pi}{180^o}\)

   \(\rm{=2.6666667 \approx 2.7\ radians\)

Hence, the angle made by the arc in the center is 2.7 radians.

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Answer:

A regular polygon is a polygon with sides of equal length. Some examples include, a equilateral triangle, square, regular pentagon, regular hexagon, regular heptagon, regular octagon, regular nonagon, regular decagon...

Answer:

96 squared meters

Step-by-step explanation:

Area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.

To solve this, we need to first find out how big the area is with the path. To do this, we need to add the 2m on to the length and width of the lawn.

Now, we have the numbers we need to solve for the total area. If we know that the area can be solved using length × width, we can use this equation:

So, the lawn's area including the fence is 576 square meters.

To find out the area of just the fence, we can take the area of the lawn with the fence and subtract the area of the lawn from it. The equation can look like this:

Therefore, the area of the path is 96 squared meters.

Answer:

The area of the path is 200 m².

Step-by-step explanation:

To find the area of the path, subtract the area of the lawn from the area of the path and lawn.

If a lawn that is 30 m long and 16 m wide is surrounded by a path that is 2 m wide, then the length and width of the area of the path and lawn is 34 m long and 20 m wide.  

Given the area of a rectangle is the product of the measures of its length and width:

Therefore, the area of the path is:

Compound amount = $8867.39

compound interest = $1867.39

EXPLANATION

Given:

Principal(p) = $7000 Rate(r) = 0.12 Time(t) = 2 n= 4

We can calculate the compound amount(A) using the formula below:

Substitute the values and evaluate.

Hence, the compound amount = $8867.39

We proceed to find the compound interest.

A = P + I

⇒ I = A - P

= 8867.39 - 7000

=1867. 39

Therefore, the compound interest = $1867.39

Answer:

  a.  $110,700

Step-by-step explanation:

You want to know the value of a $141,000 house after 15 years, if it declines in value 1.6% each year.

The value multiplier each year is ...

  1 - 1.6% = 1 -0.016 = 0.984

When the house value is multiplied by this factor 15 times, it becomes ...

  $141,000×0.984^15 ≈ $110,700

Russell's house is worth about $110,700.

Answer:

=2.524

Step-by-step explanation:

6.31

Divided by

2.5

6 divided by 2.5

= 2.4

Divide them up.

Convert the fraction to a decimal by dividing the numerator by the denominator.

= 2.524  

Hope this helps.

Have a good night ma'am/sir.

Be safe!

Answer:

y = -4 - 1/3x

Step-by-step explanation:

x + 3y = -12

-x              -x

3y = -12 - x

divide all by 3, to isolate the y

y = -4 - 1/3x

Answer:

A) 255 meters; B) 172

Answer:

A: 145m

B: 172 m

Step-by-step explanation:

Answer:

D. All the terms are odd.

Step-by-step explanation:

\(\text{According to the image description provided:}\\\text{Term one starts with one dot. One is an odd number.}\\\text{If you add two to an odd number, the sum would be another odd number.}\\\text{This is what's happening with the pattern.}\\\text{For example:}\\3+2=5\\\text{Three is an odd number. If you add two to it, you would get five, which is}\\\text{another odd number.}\\\text{Term two has 3 dots, term three has 5 dots, term four has 7 dots.}\\\text{So, all terms should be odd.}\)

If f: Z₅→Z₅ be a random permutation function , then the Probability , Pr[f(2)=2| f(0)=0 and f(1)=1] is 1/60  .

Let f: Z₅→Z₅ be a random permutation function ;

There are n! permutations functions defined on set of n elements ;

So , the total number of permutations defined on Z₅ is 5! = 120 ;

Now , if f(2) = 2 , f(0) = 0 and f(1) = 1 , then the remaining elements of Z₅ are 3 and 4 .

So , the possible images of 3 and 4 are f(3) = 3 ⇒ f(4) = 4 ;

or f(3) = 4 ⇒ f(4) = 3 .

So , there are only 2 such permutations ,

⇒ Pr[f(2)=2| f(0)=0 and f(1)=1] = 2/120 = 1/60 .

Therefore , the probability Pr[f(2)=2| f(0)=0 and f(1)=1] is = 1/60 .

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The given question is incomplete , the complete question is

Let f : Z₅→Z₅ be a random permutation function. what is Pr[ f(2)=2| f(0)=0 and f(1) = 1 ]? Express your answer as a reduced fraction without any spaces (e.g., 1/10 and not 2/20 or 0.1), or as 0 or 1, if appropriate.

The fractions to show the value of each 9 in the decima 0.999 are 9/10, 9/100, 9/1000.

To write the fraction that shows the value of each 9 in the decimal 0.999, we can use the following method

The digit 9 in the tenths place represents 9/10 or 0.9.

The digit 9 in the hundredths place represents 9/100 or 0.09.

The digit 9 in the thousandths place represents 9/1000 or 0.009.

Thus, the fractions are

0.9 = 9/10

0.09 = 9/100

0.009 = 9/1000

The value of the 9 on the left is related to the value of the 9 in the middle by a factor of 10.

The value of the 9 on the right is related to the value of the 9 in the middle by a factor of 10, so the 9 on the right is one-tenth the value of the 9 in the middle.

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The statement is true, An orthogonal set with the same dimension as the initial collection of vectors is created by the Gram-Schmidt process.

Given that,

From a linearly independent collection of {x₁, x₂,..., xp}, the gram-Schmidt process creates an orthogonal set of {v₁, v₂,..., vp} with the feature that for each k, the vectors v₁...vk span the same subspace as that spanned by x₁...xk.

The statement is true.

An orthogonal set with the same dimension as the initial collection of vectors is created by the Gram-Schmidt process. An orthogonal set is further linearly independent. The orthogonal set produced by the Gram-Schmidt process and the original set will cover the same subspace if their dimensions are the same.

Therefore, An orthogonal set with the same dimension as the initial collection of vectors is created by the Gram-Schmidt process.

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Disclaimer

The given question is incomplete, a question based on the same concept has been solved here.

The question is

From a linearly independent collection of {x₁, x₂,..., xp}, the gram-Schmidt process creates an orthogonal set of {v₁, v₂,..., vp} with the feature that for each k, the vectors v₁...vk span the same subspace as that spanned by x₁...xk.

Whether the statement is true or false.

The closest correlation of rates of return between stocks a and b is approximately -0.487 (negative), indicating opposite movements.

The relationship coefficient between two stocks an and b can be determined utilizing the equation:

relationship coefficient = covariance/(standard deviation of stock a * standard deviation of stock b)

Considering that the covariance between the profits of stocks an and b is - 0.073, and the standard deviation of the paces of return is 0.5 for stock an and 0.3 for stock b, we can substitute these qualities into the recipe to track down the connection coefficient.

relationship coefficient = - 0.073/(0.5 * 0.3) ≈ - 0.487

Consequently, the nearest worth of the connection of the paces of return between stock an and b is - 0.487. This negative relationship coefficient demonstrates that the profits of the two stocks will generally move in inverse bearings. At the point when one stock's return is high, the other stock's return is probably going to be low, as well as the other way around.

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Answer:

Skyla looks for the x-value at which the graph of the function \(2^x\) intersects the horizontal line defined by the constant function: \(f(x)=128\)

Step-by-step explanation:

Look for an answer that involves something like:

By looking for the point where both functions intersect, Skyla can find for which x value the following equation is verified: \(2^x=128\)

She must read at which x-value the intersection occurs, and that is the answer.

Answer: Intersect at (7,128) and x=7

Step-by-step explanation:

Delila is correct as she multiplying three negative numbers and determines that the solution will be negative.

As given in the question,

Let the three negative numbers be -x , -y , and -z.

Delia is multiplying three negative numbers

Multiply First two numbers

(-x) (-y) = + x y  as (-)(-) = +

Multiply by third numbers

(+x y) (-z) = -x y z   as ( +)(-) = -

Therefore, Delila is correct as she multiplies three negative numbers and determines that the solution will be negative.

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Answer:

Yes, she is correct.

Answer:

B because it's a fraction I just divided them and got b

Step-by-step explanation:

Expression given,

\( \\ \longrightarrow \qquad \sf 5x+3x+2y+4y \\ \\ \)

Here, in the expression we have to find the like terms.

So from the expression we that, 5x and 3x are like terms and 2y and 4y are like terms too, so now we have to combine them and then we will get a new expression so.

\(\\ \longrightarrow \qquad \sf 8x + 6y \\ \\ \)

So, 8x + 6y is the new expression.

Quantrell bought a television set on sale for his apartment for $1,500, but he will spread the payments over two years. The store charges 18 percent interest for financing, and his payments will be $74.89. Hence, he will pay $1650.22 in interest over the life of the loan.

How much will he pay in interest over the life of the loan?He bought a television set on sale for $1500 that he will spread the payments over two years.The total amount he will pay in two years for the TV is obtained by adding up the cost of the TV set and the interest over the life of the loan. To compute the interest, we will first find the total payment he will make in two years.

To find the total payment, multiply the number of payments by the amount of each payment. Then,Total payment = Number of payments × Amount of each paymentSubstituting the values of number of payments and amount of each payment, we get:Total payment = 2 × $74.89Total payment = $149.78Now, let's calculate the interest on the loan,Interest = Total payment − Cost of the TV setInterest = $149.78 − $1500Interest = $1650.22

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The relation between logarithmic function and exponential function is they both are inverse of each other.

As given in the question,

Relation between logarithmic function and exponential function is given by:

Therefore, relation between the logarithmic function and the exponential function is  that both are inverse of each other.

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After conversion into exponential equation :

Given

The statement is "three times three".

To find:

The value of given statement.

Solution:

We know that the multiplication sign "×" is used for "times".

The given statement is "three times three".

So, the mathematical expression for the given statement is:

three times three = 3 × 3

                             = 9

Therefore, the value of three times three is 9.

Answer:

1/16

Step-by-step explanation:

This is abt completing the square, so the missing space is half of b (1/2) squared. (1/4)^2= 1/16.

Answer:

Step-by-step explanation:

Completing the square:

>Divide the x term by 2 which also means multiplying by 1/2 and then square it:

\([\frac{1}{2} (\frac{1}{2} )]^{2}\)

=\((\frac{1}{4} )^{2}\)

=\(\frac{1}{16}\)       >This is the completed square number

x² + (1/2)x +  1/16 = 2 + 1/16

The solution to the given differential equation is: x⁷ cos y = y + C

where C is the constant of integration

To solve the given differential equation:

\(\[7x^6\cos y dx - dy = 0\]\)

We can separate the variables and integrate both sides.

Separating variables, we can write the equation as:

\(\[7x^6\cos y dx = dy\]\)

Now, we can integrate both sides with respect to their respective variables:

\(\[\int 7x^6\cos y dx = \int dy\]\)

Integrating the left side:

\(\[\int 7x^6\cos y dx = 7 \int x^6 \cos y dx\]\)

To integrate \(\(x^6 \cos y\)\)with respect to x, we can use integration by parts.

Let's take u = x⁶ and \(\(dv = \cos y dx\)\).

Differentiating u with respect to \(\(x\) gives \(du = 6x^5 dx\).\)

Integrating dv with respect to x gives \(\(v = \int \cos y dx = \cos y \cdot x\).\)

Applying the integration by parts formula:

\(\[\int x^6 \cos y dx = u \cdot v - \int v \cdot du\]\)

Substituting the values:

\(\[\int x^6 \cos y dx = x^6 \cdot \cos y \cdot x - \int (\cos y \cdot x) \cdot (6x^5 dx)\]\)

Simplifying:

\(\[\int x^6 \cos y dx = x^7 \cos y - 6 \int x^6 \cos y dx\]\)

Moving the integral term to the left side:

\(\[7 \int x^6 \cos y dx = x^7 \cos y\]\)

Dividing both sides by 7:

\(\[\int x^6 \cos y dx = \frac{x^7 \cos y}{7}\]\)

Now, substituting this result back into our original equation:

\(\[7 \int x^6 \cos y dx = dy\]\)

\(\[\frac{7x^7 \cos y}{7} = dy\)

Simplifying:

x⁷ cos y = dy

Finally, the solution to the given differential equation is:

x⁷ cos y = y + C

where C is the constant of integration.

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Answer:

Congruent triangles are exact same triangles, but they might be placed at different positions. The corresponding congruent part for each segment or angle can be arranged as shown below.

What are congruent triangles?

Suppose it is given that two triangles ΔABC ≅ ΔDEF

Then that means ΔABC and ΔDEF are congruent. Congruent triangles are exact same triangles, but they might be placed at different positions.

The order in which the congruency is written matters.

For ΔABC ≅ ΔDEF, we have all of their corresponding elements like angle and sides congruent.

Thus, we get:

(|AB| denotes the length of line segment AB, and so on for others).

Given the two triangles, ΔDFC and △SNP are congruent to each other, DFC≅△SNP. Therefore, we can write,

Step-by-step explanation:

The volume V of solid S is e - 1 cubic unit.

What is Volume?

Volume refers to the measure of three-dimensional space occupied by an object or a region. It quantifies the amount of space enclosed by the boundaries of an object or contained within a given region. In mathematical terms, volume is often calculated by integrating the cross-sectional areas of the object or region along a particular axis. Volume is typically expressed in cubic units, such as cubic meters (m^3) or cubic centimeters (cm^3). It is an essential concept in geometry, physics, engineering, and other scientific fields where the measurement of three-dimensional space is involved.

To find the volume of solid S, we need to integrate the areas of the cross sections perpendicular to the x-axis along the interval \([e, \infty).\)

The area of each square cross-section is equal to the square of the side length, which in this case is \(y = \sqrt{\ln(x)}.\)

Therefore, the volume V of solid S can be calculated as:

\(V = \int_{e}^{\infty} (\sqrt{\ln(x)})^2 dx\)

To evaluate this integral, we can simplify the expression:

\(V = \int_{e}^{\infty} \ln(x) dx\)

Using integration by parts, we let \(u = \ln(x)\)and dv = dx:

\(du = \frac{1}{x} dx\\v = x\)

Applying the integration by parts formula:

\(V = [uv] - \int v du= [x \ln(x)] - \int x \left(\frac{1}{x}\right) dx= x \ln(x) - \int dx= x \ln(x) - x + C\)

Evaluating the definite integral:

\(V = [x \ln(x) - x]_{e}^{\infty}= (\infty \cdot \ln(\infty) - \infty) - (e \cdot \ln(e) - e)= \infty - 0 - (1 - e)= e - 1\)

Therefore, the volume V of solid S is e - 1 cubic unit.

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Answer: 13,900

Step-by-step explanation:

To round numbers to the nearest hundred, you always look at the place one down which is the tens place. The tens place is 5.

The options for 856 to round to is either 800 or 900.

The rule is that 0-4 rounds down, 5-9 rounds up. Since the tens place is 5, it will round up to 900.

Therefore, the answer would be 13,900.

a. If 4 - 5i and -√3 are roots of the polynomial, the other two roots are

b. If polynomial P(x) is divided by x - a, the remainder is zero, then a.  x - a is a factor of the polynomial P(x)

A polynomial is a mathematical function in which the least power of the variable is 2.

a. Suppose that a polynomial function has four roots and two of its roots are 4 - 5i and -√3. We desire the other two roots. We proceed as follows.

We know that know that complex roots and irrational roots of a polynomial occur in conjugate pairs.

So, since 4 - 5i and -√3 are roots of the polynomial, then their conjugate pairs are also roots.

So, the conjugate pairs are

So, the other two roots are

b. A polynomial P(x) is divided by x - a, the remainder is zero. What can we conclude?

Using the factor theorem, if p(x) is a polynomial and x - a is a linear factor, then if x - a is a factor of p(x), then the remainder when p(x) is divided by x - a is zero.

So, from the above since the remainder when P(x) is divided by x - a is zero, then x - a is a factor of P(x)

So, the answer is a.  x - a is a factor of the polynomial P(x)

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Answer:

Step-by-step explanation:

\( \frac{9}{3} = 3 \\ \\ \frac{36}{x} = 3 \\ x = \frac{36}{3} \\ x = 12\)

I hope that is useful for you :)