if two samples a and b had the same mean and sample size, but sample b had a larger standard deviation, which sample would have the wider 95% confidence interval? g

(a) To show that 〈Ax, ty} =〈x, A^T y〉, let's compute both sides:

Left side: 〈Ax, y〉 = (Ax)^T y = x^T A^T y

Right side: 〈x, A^T y〉 = x^T (A^T y)

As you can see, both the left and right sides are equal (x^T A^T y), so the statement is true.

(b) To show that 〈A^T A x, x〉 = ‖A x‖^2, let's compute both sides:

Left side: 〈A^T A x, x〉 = (A^T A x)^T x = x^T A^T A x

Right side: ‖A x‖^2 = (A x)^T (A x) = x^T A^T A x

Again, both the left and right sides are equal (x^T A^T A x), so the statement is true.

To show (a), we start with the definition of the inner product:
<ax,y〉 = (ax)ᵀy

Then we use the properties of matrix multiplication to rewrite this as:〈ax,y〉 = xᵀaᵀy

Now we can take the transpose of both sides and use the fact that aᵀ = a to get:
(〈ax,y〉)ᵀ = (xᵀaᵀy)ᵀ
〈y,ax〉 = yᵀa x

Finally, we can swap the order of x and y on the right-hand side and use the definition of the inner product again:
〈ax,y〉 = 〈x,aty〉

To show (b), we start with the left-hand side:
〈atax,x〉 = (atax)ᵀx

Using the properties of matrix multiplication, we can rewrite this as:
〈atax,x〉 = xᵀ(aᵀa)x

Now we can use the fact that (aᵀa)ᵀ = aᵀa and the definition of the norm to get:
〈atax,x〉 = xᵀ(aᵀa)x = ‖ax‖²


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The 97% confidence interval for a sample of 204 soda cans with a mean of 12.05 ounces and a standard deviation of 0.08 ounces is approximately (12.026, 12.074) ounces.

To find the 97% confidence interval, follow these steps:

1. Identify the sample size (n=204), sample mean (X-bar=12.05), and standard deviation (σ=0.08).
2. Determine the appropriate z-score for a 97% confidence interval, which is 2.17 (from a standard normal distribution table).

3. Calculate the standard error (SE) by dividing the standard deviation by the square root of the sample size: SE = σ/√n = 0.08/√204 ≈ 0.0056.

4. Multiply the z-score by the standard error: 2.17 * 0.0056 ≈ 0.0122.

5. Subtract this product from the sample mean for the lower bound: 12.05 - 0.0122 ≈ 12.026.

6. Add this product to the sample mean for the upper bound: 12.05 + 0.0122 ≈ 12.074.

Thus, the 97% confidence interval is approximately (12.026, 12.074) ounces.

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The probability of a student spending time reading given that the student spends time watching TV is  [tex]P(Reading|Watching\:\:TV)=0.12[/tex]

If any two occurrences in sample space S, A and B, are specified, then the conditional probability of event A given B is:

[tex]P(A|B)=\frac{P(A\:and\:B)}{P(B)}[/tex]

Probability theory is an important branch of mathematics that is used to model and analyze uncertain events in various fields, including science, engineering, finance, and social sciences. The concept of probability is based on the idea of random experiments, where the outcomes are uncertain and can vary each time the experiment is performed.

The probability of an event can be determined by analyzing the possible outcomes of the experiment and assigning a probability to each outcome based on the assumptions of the model. The theory of probability has several applications in real life, such as predicting the outcomes of games of chance, evaluating risks in insurance and finance, and making decisions in scientific research.

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Answer: 55

Step-by-step explanation: 55 - 25 = 30

just subtract all the answers by 25 and try to find something lower then 31

Let's assume that the sum of three consecutive integers is a square, which means we can represent them as n, n+1, and n+2, where n is an integer.

So, the sum of these three consecutive integers can be written as:

n + (n+1) + (n+2) = 3n + 3

Now, we need to prove that this expression cannot be a perfect square.

To do that, let's suppose that the expression is a perfect square, and let's call it x^2, where x is an integer.

So, we have:

3n + 3 = x^2

Rearranging this equation, we get:

3(n+1) = x^2

Now, let's consider two cases:

Case 1: x is even
If x is even, then x^2 is a multiple of 4. So, we can write:

3(n+1) = x^2 = 4k, where k is an integer

Dividing both sides by 3, we get:

n+1 = (4k/3)

However, this is impossible because the right-hand side is not an integer, since 4k is divisible by 3 only if k is divisible by 3. Therefore, x cannot be even.

Case 2: x is odd
If x is odd, then x^2 is an odd integer. So, we can write:

3(n+1) = x^2 = 2m+1, where m is an integer

Dividing both sides by 3, we get:

n+1 = (2m+1)/3

This implies that (2m+1) is a multiple of 3, which means that m is odd. Therefore, we can write:

m = 2k+1, where k is an integer

Substituting this into the equation above, we get:

n+1 = (2(2k+1)+1)/3

n+1 = (4k+3)/3

Multiplying both sides by 3, we get:

3(n+1) = 4k+3

However, this is impossible because the left-hand side is divisible by 3, while the right-hand side leaves a remainder of 1 when divided by 3. Therefore, x cannot be odd either.

Since we have proved that x cannot be even or odd, our initial assumption that the sum of three consecutive integers can be a perfect square is false. Therefore, the sum of three consecutive integers cannot be a square.

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If X has an exponential distribution with parameter λ, the probability density function is f(x) = λe^(-λx) for x ≥ 0. The cumulative distribution function is F(x) = 1 - e^(-λx) for x ≥ 0.

To derive a general expression for the (100p)th percentile of the distribution, we need to find the value x_p such that the probability of X being less than or equal to x_p is equal to p. That is, we need to solve the equation F(x_p) = p. Substituting F(x) into the equation, we get: 1 - e^(-λx_p) = p, e^(-λx_p) = 1 - p.

Taking the natural logarithm of both sides, we get: -λx_p = ln(1 - p) x_p = -ln(1 - p) / λ, This is the general expression for the (100p)th percentile of the exponential distribution with parameter λ. To obtain the median, we need to find the value of p such that x_p is equal to the median. By definition, the median is the value of X such that the probability of X being less than or equal to it is 0.5.

Substituting p = 0.5 into the general expression, we get: x_0.5 = -ln(1 - 0.5) / λ = -ln(0.5) / λ , Simplifying, we get: x_0.5 = ln(2) / λ. Therefore, the median of the exponential distribution with parameter λ is ln(2) / λ.

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The final answer rounded to 1 decimal place is 0.1.

To find the probability P(4 ≤ X ≤ 6) for a normally distributed random variable X with mean μ = 10 and standard deviation σ = 6, you'll need to use the Z-score formula to standardize the values and then look up the probabilities in a standard normal table or use a calculator with a built-in normal distribution function.

The Z-score formula is: Z = (X - μ) / σ

For the lower limit, X = 4:
Z1 = (4 - 10) / 6 = -1

For the upper limit, X = 6:
Z2 = (6 - 10) / 6 = -0.67 (rounded to 2 decimal places)

Now, use a standard normal table or calculator to find the probabilities associated with these Z-scores.

P(Z ≤ -1) = 0.1587
P(Z ≤ -0.67) = 0.2514

To find P(4 ≤ X ≤ 6), subtract the lower probability from the upper probability:

P(4 ≤ X ≤ 6) = P(Z ≤ -0.67) - P(Z ≤ -1) = 0.2514 - 0.1587 = 0.0927

Therefore, rounded to one decimal place, the probability is 0.1.

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Note that the value of x in radical form is √(26² - x²).

Assuming the base is adjacent to the angle of interest, we can use the trigonometric ratio of the tangent function:

tangent of the angle = opposite / adjacent

In this case, we have:

tangent of the angle = x / 26

Since we have a right triangle, one of the angles is 90 degrees. Let's call the other angle of interest theta (θ). Then we have:

tangent of theta = x / 26

We can solve for x by multiplying both sides by 26 and taking the arctangent of both sides:

x = 26 * tangent of theta

x = 26 * tan(θ)

Now, we need to find the value of θ. Since we know the adjacent side (26), we can use the inverse tangent function to find θ:

theta = arctangent (opposite / adjacent)

theta = arctan (x / 26)

Putting it all together, we have:

x = 26 * tangent of arctan (x / 26)

Simplifying using the identity tan(arctan(x)) = x, we get:

x = 26 * x / 26

Simplifying further, we get:

x = √(26² - x²)

So the value of x in radical form is x = √(26² - x²).

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The Ruler Postulate (Axiom M-2) states that for any line l and any two distinct points o and P on l, there exists a bijection c l R such that c(o) = 0 and c(P) ≠ 0. This means that we can assign a unique real number to each point on the line, with point o corresponding to 0 and point P corresponding to some other non-zero real number.

Furthermore, the postulate requires that the distance between any two points A and B on the line is equal to the absolute value of the difference between their assigned real numbers, i.e. d(A,B) = |c(A) - c(B)|. This ensures that the distance function on the line behaves consistently with the usual notion of distance in real numbers.

Overall, the Ruler Postulate provides a way to measure distances and assign coordinates to points on a line in a way that is consistent with the real numbers. The use of a bijection ensures that each point on the line corresponds to a unique real number, which is necessary for the distance function to be well-defined.

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An ordered rooted tree is a tree data structure in which each node has a specific parent-child relationship with its adjacent nodes. Each node in the tree has an address or path that specifies its location in the tree.

Given an ordered rooted tree T with vertex v at address 3.4.5.2.4, we can answer the following questions:

The level of a vertex in a tree is the number of edges on the path from the root to that vertex. In this case, the root is at address 3, and the path from the root to v has four edges: 3->4, 4->5, 5->2, and 2->4. Therefore, v is at level 5.

The parent of a vertex is the node that is immediately above it in the tree. In this case, the parent of v is the node at address 3.4.5.2. Therefore, the address of the parent of v is 3.4.5.2.

The siblings of a vertex are the nodes that have the same parent as the vertex. In this case, we do not have enough information to determine the number of siblings of v. We only know the address of v and its parent, but we do not know the structure of the tree beyond that.

The number of vertices in a tree can be calculated using the formula n = m + 1, where n is the total number of vertices and m is the number of edges. In this case, we know that the path from the root to v has four edges, so there are at least five vertices in the tree (including the root). However, we do not have enough information to determine the exact number of vertices in T, as there may be additional branches and nodes that are not specified.

Based on the address of v, we can determine some of the other addresses that must occur in the tree. For example, the address 3.4.5 must occur in the tree, as this is the parent of v. Additionally, the address 3.4 must occur in the tree, as this is the parent of 3.4.5. However, we cannot determine all of the other addresses that must occur in the tree without additional information about its structure.

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To derive the expression for the differential capacitance of a hyperabrupt p-n junction varactor, we can use the following formula:

Cd = dQ/dV
where Cd is the differential capacitance, Q is the charge stored in the varactor, and V is the applied voltage.
The charge stored in the varactor can be expressed as:
Q = C * V
where C is the capacitance of the varactor.
The capacitance of a varactor is given by:
C = (A / W) * sqrt(2 * e * q * Na * Nd / (Na + Nd))
where A is the area of the varactor, W is the width of the depletion region, e is the permittivity of free space, q is the charge of an electron, Na is the acceptor doping concentration, and Nd is the donor doping concentration.

For a hyperabrupt p-n junction varactor with the n-side doping profile given by n(x) = bx^(-3/2), the doping concentration can be expressed as:
Nd(x) = bx^(-3/2)
The width of the depletion region can be expressed as:
W = sqrt((2 * e * Na * Vbi) / q) * (1 / sqrt(Nd(x)) - 1 / sqrt(Nd(0)))
where Vbi is the built-in potential.
Substituting Nd(x) and W into the expression for capacitance, we get:
C = (A / sqrt(2 * e * q)) * sqrt((Na * Vbi * bx^(-3/2)) / (Na + bx^(-3/2))) * (1 / sqrt(bx^(-3/2)) - 1 / sqrt(b))
Taking the derivative of C with respect to V, we get:
dC/dV = (A / sqrt(2 * e * q)) * sqrt((Na * Vbi * bx^(-3/2)) / (Na + bx^(-3/2))) * (-1 / 2 * sqrt(bx^(-3/2)) / V) * (1 / sqrt(bx^(-3/2)) - 1 / sqrt(b))

Simplifying the expression, we get:
dC/dV = (-A * sqrt(Na * Vbi * b) / (4 * e * q * V)) * (1 / sqrt(x) - 1 / sqrt(b))
Therefore, the expression for the differential capacitance of a hyperabrupt p-n junction varactor with the n-side doping profile given by n(x) = bx^(-3/2) is:
Cd = (-A * sqrt(Na * Vbi * b) / (4 * e * q * V)) * (1 / sqrt(x) - 1 / sqrt(b))
Hi! To derive the expression for the differential capacitance of a hyperabrupt p-n junction varactor with the given n-side doping profile, follow these steps:
1. The n-side doping profile is given by n(x) = b/x^(3/2), where b is a constant and m = -3/2.
2. The charge density in the n-side depletion region can be expressed as qN(x) = qn(x), where q is the elementary charge.
3. The electric field E(x) in the depletion region can be found by integrating the charge density: E(x) = (1/ε) ∫qN(x) dx,where ε is the permittivity of the semiconductor material.
4. Integrate the electric field to obtain the voltage across the depletion region: V(x) = ∫E(x) dx.
5. The capacitance of a varactor is defined as the change in charge per unit change in voltage: C = dQ/dV.
6. The differential capacitance can be found by differentiating the charge Q with respect to the voltage V: C_diff = d²Q/dV².

By following these steps and performing the required integrations and differentiations, you will obtain the expression for the differential capacitance of a hyperabrupt p-n junction varactor with the given n-side doping profile.

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Here are five other iterated integrals that are equal to the given iterated integral:

1. ∫₀¹ ∫₀¹ ∫₀^y f(x, y, z) dz dy dx
2. ∫₀¹ ∫₀^z ∫y^1 f(x, y, z) dx dy dz
3. ∫₀¹ ∫₀^z ∫₀^x f(x, y, z) dy dx dz
4. ∫₀^z ∫₀¹ ∫y^1 f(x, y, z) dx dy dz
5. ∫₀^z ∫₀^x ∫₀¹ f(x, y, z) dy dx dz

Note that in each of these integrals, we have changed the order of integration. This is because the given iterated integral is a triple integral over a region of integration that can be split up into different subregions, each with different limits of integration. By rearranging the order of integration, we can express the same integral as a sum of different iterated integrals, each of which corresponds to a different subregion of the original region of integration. This is the basic idea behind iterated integrals.


These five iterated integrals are equal to the given iterated integral, with the same function f(x, y, z) and appropriate limits of integration.

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166

5x6.5=33

16-6.5=9.5

(9.5x14)/2=133

133+33=166

The total cost function C(x) is found by integrating the marginal cost function MC(x) = 4x + 20, resulting in C(x) = 2x^2 + 20x + C. The constant C is determined by the given information that producing 2 units costs $98, leading to C = 50. Therefore, the total cost function is C(x) = 2x^2 + 20x + 50.

To find the total cost function C(x), we need to integrate the marginal cost function MC(x).

∫MC(x) dx = ∫4x + 20 dx
C(x) = 2x^2 + 20x + C

To find the constant C, we use the given information that the cost of producing 2 units is $98:

C(2) = 2(2)^2 + 20(2) + C = 98
C = 30

Therefore, the total cost function for the product is:

C(x) = 2x^2 + 20x + 30

Option (b) is the correct answer.
To find the total cost function C(x), we need to integrate the marginal cost function MC(x) = 4x + 20.

∫(4x + 20) dx = 2x^2 + 20x + C

Now, we know that the cost of producing 2 units is $98. So, we can plug in x = 2 and C(2) = 98 to solve for the constant C:

98 = 2(2^2) + 20(2) + C
98 = 8 + 40 + C
C = 50

So the total cost function C(x) is:

C(x) = 2x^2 + 20x + 50

The correct answer is a. C(x) = 2x^2 + 20x + 50.

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In summary, variables and statistics are essential components of modern probability theory and are used to derive fundamental results that help us understand the behavior of complex systems.

By making the change of variable, we can often simplify complex statistical problems and arrive at fundamental results that are widely used in probability and statistics.

One such fundamental result is the central limit theorem, which states that the sum of a large number of independent and identically distributed random variables tends to a normal distribution.

This result is important because it allows us to make predictions about the behavior of complex systems, even when we do not have a complete understanding of the underlying variables. By using statistical techniques, we can estimate the behavior of these systems based on a few key variables and assumptions.

By making a change of variable, we can transform a given problem into a simpler one, which is a fundamental result for probability and statistics. In the context of probability and statistics, a variable represents an attribute that can take different values. When you change a variable, you are essentially creating a new variable that is a function of the original one.

This change of variable technique is fundamental because it simplifies complex problems, making it easier to analyze data and draw conclusions. It is widely used in probability distributions and hypothesis testing to provide clearer insights into the underlying relationships between variables.

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Answer:

x= 4/3 ; x= -2

Step-by-step explanation:

Your quadratic equation: 3x^2+2x-8 = 0

This is in ax^2+bx+c form which requires you to solve by many methods.

**BEST WAY to solve this is the Quadratic formula. You can factor, but it will take longer.**

Values of r + s and rs are -2/3 and -8/9, respectively.

To find the values of r and s, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

For our equation 3x² + 2x - 8 = 0, we have a = 3, b = 2, and c = -8.

Puting values into the formula, we get:

r, s = (-2 ± √(2² - 4(3)(-8))) / 2(3)
r, s = (-2 ± √100) / 6
r, s = (-2 ± 10) / 6
r = 2/3 or s = -4/3
r + s = (2/3) + (-4/3) = -2/3
rs = (2/3)(-4/3) = -8/9

Therefore, the values of r + s and rs are -2/3 and -8/9, respectively.

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Answer:

no.

Step-by-step explanation:

38.50 divided by 7 = 5.5

30 divided by 6= 5

your sibling gets more than you.

The value of the iterated integral is (-π/4) (cos(64) - 1).

To evaluate the iterated integral by converting to polar coordinates, we need to use the given terms:

- The integral bounds: 0 to 8 (for x), -8 to 8 (for y)
- The integrand: sin(x² + y²)
- The conversion factor for polar coordinates: rdrdθ

First, we convert the integral bounds and integrand to polar coordinates.

In polar coordinates, x = rcos(θ) and y = rsin(θ), so:

x² + y² = r²cos²(θ) + r²sin²(θ) = r²

because sin²(θ) + cos²(θ) = 1.

Now we rewrite the integrand in polar coordinates:
sin(x² + y²) = sin(r²)

The integral bounds in polar coordinates are 0 to 8 (for r), and 0 to π/2 (for θ) as the given bounds cover the first quadrant.

Now we can write the iterated integral:
[tex]\int_{0} ^ {\pi/2} \int_{0} ^{ 8}  sin(r^2) r dr d\theta[/tex]

To evaluate the inner integral with respect to r, we use substitution:
Let u = r², so du = 2r dr

Now the inner integral becomes:

[tex](1/2)\int_{0}^ {64} sin(u) du[/tex] = (-1/2) [cos(64) - cos(0)] = (-1/2) (cos(64) - 1)

Now we evaluate the outer integral with respect to θ:

[tex]\int_{0}^ {\pi/2} ((-1/2)  (cos(64) - 1)) d\theta[/tex] = (-1/2) (cos(64) - 1) [θ] evaluated from 0 to π/2

Finally, substitute the limits of integration:

((-1/2) (cos(64) - 1)) (π/2 - 0) = (-π/4) (cos(64) - 1)

So, the value of the iterated integral is (-π/4) (cos(64) - 1).

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The argument form with premises (p ∧ t) → (r∨s), q→(u∧t), u→p, and ¬s and conclusion q → r is a valid consequence of tautologies and is therefore valid.

Exercise 11 states that an argument form is valid if it is either a tautology or a valid consequence of tautologies. To show that the argument form with premises (p ∧ t) → (r∨s), q→(u∧t), u→p, and ¬s and conclusion q → r is valid, we need to show that it is either a tautology or a valid consequence of tautologies.

1. (p∧t)→(r∨s) Premise

2. q→(u∧t) Premise

3. u→p Premise

4. ¬s Premise

5. q Assumption

6. u∧t (Modus Ponens 2,5)

7. u (Simplification 6)

8. p (Modus Ponens 3,7)

9. p∧t (Conjunction 8,4)

10. r∨s (Modus Ponens 1,9)

11. r (Disjunctive Syllogism 10,4)

12. q→r (Conditional Proof 5-11)

Therefore, the argument form with the given premises and conclusion q→r is valid.

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Answer:

x= 7, -1

Step-by-step explanation:

I hope it helps:)

Answer:7,-1

Step-by-step explanation:

(x-3)^2=16

x^2+9-6x=16

x^2-6x-7=0 .

x^2-7x+1x-7= 0.

x(x-7)+(x-7)=00..

(x+1)(x-7)=0

x= 7,-1 ,

Answer:

8

Step-by-step explanation:

3(y - 2) + 4(2 - 3)          

3(6 - 2) + 4(2 - 3)

18 - 6 + 8 - 12

= 8

The lift force pushing up on the plane is approximately 2,625,992 N.

To determine the lift force pushing up on the plane, we'll use the given terms:

plane's speed (725 m/s),

altitude (4000 m),

air density (0.819 kg/m³),

air velocity above the wing (805 m/s),

air velocity below the wing (711 m/s),

and wing area (45.0 m²).

Calculate the pressure difference above and below the wing using Bernoulli's equation.

ΔP = (0.5 × air density × (velocity below wing² - velocity above wing²))
ΔP = (0.5 × 0.819 kg/m³ × (711 m/s² - 805 m/s²))

Calculate the lift force.
Lift Force = ΔP × Wing Area
Lift Force = (-58355.388) × 45.0

Lift Force = -2625992.46 N

Performing the calculations, we find that the lift force pushing up on the plane is approximately 2,625,992 N.

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The critical values of x² to test the claim that σ = 5.6 with a significance level of 0.10 and 27 degrees of freedom are 38.41 and 16.04.

To find the critical values of the chi-square distribution with 27 degrees of freedom and a significance level of 0.10, we need to use a chi-square table or a statistical software.

Using a chi-square table, we can find that the critical values are 38.41 and 16.04 (rounded to two decimal places).

Alternatively, we can use the inverse chi-square function in a calculator or statistical software to find the critical values. For example, in Excel, we can use the following formula to find the critical values:

=CHISQ.INV.RT(0.10, 27) and =CHISQ.INV(0.10, 27)

The first formula gives the right-tailed critical value of 38.41, and the second formula gives the two-tailed critical values of 16.04 and 43.19.

To express the critical values in terms of x², we can use the formula:

x² = (n - 1) * s² / σ²

where n is the sample size,

s is the sample standard deviation, and

σ is the population standard deviation.

Substituting the given values, we get:

x² = (28 - 1) * 5.6² / 5.6² = 27

Therefore, the critical values of x² are  38.41 and 16.04.

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A. "How many movies did Josh watch last year?" is not a statistical question.

B. "What are the heights of animals at the zoo?" can be a statistical question or not, depending on the context.

C. "How much water do the students at Alex's school drink per day?" is a statistical question.

A statistical question is one that calls for the gathering, examination, and interpretation of data. It aims to comprehend and describe a population's or sample's numerical or categorical characteristics. We can decide whether or not the offered questions are statistical based on this definition.

Question A: "How many movies did Josh watch last year?" is not a statistical question. This is because it is not asking for data from a population or sample, but rather the personal experience of a single individual. There is no data to collect, analyze, or interpret to answer this question.

Question B: "What are the heights of animals at the zoo?" can be a statistical question or not, depending on the context. If the question is asking for a list of specific heights of individual animals at the zoo, then it is not a statistical question because it is not concerned with generalizing the heights to the whole population of animals. However, if the question is asking for a statistical summary of the heights of all the animals at the zoo, such as the mean or range of heights, then it is a statistical question.

Question C: "How much water do the students at Alex's school drink per day?" is a statistical question. This is because the question is asking about a numerical value of interest (amount of water consumed per day) in relation to a specific population (the students at Alex's school). To answer this question, data must be collected from a representative sample of the student population, and statistical analysis must be performed to summarize the data and draw conclusions about the drinking habits of the students at Alex's school.

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The slope of the parametric curve can be obtained using the chain rule of differentiation: dydx=dydt⋅text⋅dt: The point on the curve where the tangent line has a slope of 12 is (1729, 13823).

To find the point(s) on the curve x = 3t^2 + 1, y = t^3 - 1 where the tangent line has a slope of 12, we'll follow these steps:

1. Find the derivatives dx/dt and dy/dt.
2. Compute the slope dy/dx using the formula: dy/dx = (dy/dt) / (dx/dt)
3. Set the slope equal to 12 and solve for t.
4. Find the corresponding x and y coordinates for the obtained t value(s).

Step 1: Find the derivatives dx/dt and dy/dt.
dx/dt = d(3t^2 + 1)/dt = 6t
dy/dt = d(t^3 - 1)/dt = 3t^2

Step 2: Compute the slope dy/dx using the formula.
dy/dx = (dy/dt) / (dx/dt) = (3t^2) / (6t)

Step 3: Set the slope equal to 12 and solve for t.
12 = (3t^2) / (6t)
12 * 6t = 3t^2
72t = 3t^2
t = 24

Step 4: Find the corresponding x and y coordinates for the obtained t value(s).
x = 3t^2 + 1 = 3(24^2) + 1 = 3(576) + 1 = 1729
y = t^3 - 1 = (24^3) - 1 = 13823

The point on the curve where the tangent line has a slope of 12 is (1729, 13823).

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Answer:

A 16.8 is 168 tenths not 168 hundredths.

Indicator variables are used to indicate whether an observation belongs to a discrete category or not. They are important for some statistical models where factor variables must be converted to a set of indicator variables. The general rule is to use one fewer indicator variables than categories.

An indicator variable can also be defined as a random variable that takes the value 1 for some desired outcome and the value 0 for all other outcomes5.

To predict the price of a house based on its location (east, west, or central) and square footage, you would need 2 indicator variables.

One variable would represent the location (with 3 categories: east, west, and central), and the other variable would represent the square footage of the house.

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The number of indicator variables required to predict the price of a house based on location and footage are 3 in count. So, option (b) is right one.

An indicator variable is a random variable that takes the value 1 for some desired outcome or success and the value 0 for all other outcomes like failure. They tell you if a topic is in a category (hence the name). More specifically, it is defined by the variable X, as X = { 1 desired event 0 other event. Logical variables are an example of an indicator variable. Let we want to predict the price of a house based on where the house was located (east, west or central) as well as square footage. Here since total number of levels of indicator =4 ( east, west or central and square footage)

Therefore, number of indicator level needed = 4-1 = 3

Hence, required value is 3.

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The explicit formula for the nth term of the sequence 28, 34, 40, ... is an = 22 + 6n.

What is arithmetic sequence?

An arithmetic sequence is a sequence of numbers where each term is obtained by adding a fixed constant value (called the common difference) to the previous term.

The given sequence 28, 34, 40, ... is an arithmetic sequence with the first term a1 = 28 and common difference d = 6 (each term is obtained by adding 6 to the previous term).

To find the nth term of an arithmetic sequence, we use the formula:

aₙ = a₁ + (n - 1) d

Substituting the given values, we get:

aₙ = 28 + (n - 1) 6

Simplifying this expression, we get:

aₙ = 22 + 6n

Therefore, the explicit formula for the nth term of the sequence 28, 34, 40, ... is an = 22 + 6n.

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Answer:

3

Hope this helps!

Step-by-step explanation:

[tex]\frac{1}{2}[/tex] × 4 × [tex]\frac{3}{2}[/tex]

1 × 2 × [tex]\frac{3}{2}[/tex]  ( Simplify 1/2 and 4 )

2 × [tex]\frac{3}{2}[/tex]

3 ( Simplify 2 and 3/2 )