.
Solve: 108/9 this is hard for me can anyone help me.

Answer:H = 3 + 0.5x

Step-by-step explanation:

This would be H = 3 + 0.5x

Answer:

The first one to your left

Step-by-step explanation:

Answer:

Diameter: Circumference

Step-by-step explanation:

Because this is Pi, which is the same for any circle.

The slope and y intercept of the graph of function h is2 and 9.5, respectively.

To find the slope and y-intercept of the function h(x), we'll first find g(x) and then h(x) by substituting f(x) and the given transformations.

1. g(x) = f(x - 3): Substitute (x - 3) for x in f(x)
g(x) = -1/2(x - 3) + 8

2. h(x) = g(-4x): Substitute (-4x) for x in g(x)
h(x) = -1/2(-4x - 3) + 8

Now we have the function h(x), and we can identify the slope and y-intercept:

h(x) = -1/2(-4x - 3) + 8
h(x) = 2x - 1/2(-3) + 8

The slope is the coefficient of x, which is 2, and the y-intercept is the constant term, which is 1.5 + 8 = 9.5. So, the slope is 2, and the y-intercept is 6.5.

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The correct interpretation of this result is that the researcher is 94% certain that the average amount of time spent by commuters who use the public transit system is between 17.86 to 27.45 minutes.

The confidence interval is the average estimate, plus and minus the values obtained from the research. The two values obtained from the research represent the expected range within which the values can fall between.

In the question above, the range is between 17.86 to 27.45 minutes. The research is sure that the average about of time spent by commuters must fall within these values. The degree of certainty is 94%.

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To find the maximum vertical distance between the line y = x + 42 and the parabola y = x², we need to determine the points where the line and the parabola intersect.

Setting the equations equal to each other, we have:

x + 42 = x²

Rearranging the equation:

x² - x - 42 = 0

Now we can solve this quadratic equation. Factoring it or using the quadratic formula, we find the solutions:

x = -6 and x = 7

These are the x-coordinates of the points where the line and the parabola intersect.

Next, we substitute these values of x back into either equation to find the corresponding y-coordinates.

For x = -6:

y = (-6) + 42 = 36

For x = 7:

y = 7 + 42 = 49

So the points of intersection are (-6, 36) and (7, 49).

Now, we calculate the vertical distance between the line and the parabola at each of these points.

For (-6, 36):

Vertical distance = y-coordinate of the parabola - y-coordinate of the line

Vertical distance = 36 - (-6 + 42) = 36 - 36 = 0

For (7, 49):

Vertical distance = y-coordinate of the parabola - y-coordinate of the line

Vertical distance = 49 - (7 + 42) = 49 - 49 = 0

From these calculations, we see that the maximum vertical distance between the line y = x + 42 and the parabola y = x² is 0.

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Yes, they can use the walkie-talkies to talk to each other.

The distance between them is given as 28.2 meters.

The horizontal and vertical distances should be considered when calculating the distance between their apartments using the three-dimensional form of the Pythagorean theorem.

This comes out as \(\sqrt((18^2 + 19^2 + 7^2))\), which equals \(\sqrt(798)\) square root meters, or, to the nearest tenth, 28.2 meters.

Since this distance is less than the 35-meter range of the walkie-talkies, communication should be possible between the two apartments.

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Answer:

\( \sf \: 3x + 12 \)

Step-by-step explanation:

Now we have to,

→ Simplify the given expression.

The property we use,

→ Distributive property.

The expression is,

→ 3(x + 4)

Let's simplify the expression,

→ 3(x + 4)

→ 3(x) + 3(4)

→ (3 × x) + (3 × 4)

→ 3x + 12

Hence, the answer is 3x + 12.

\(2\sqrt{3}\)

------------------------

Steps:

1st write out equation

\(\frac{\sqrt{60}}{\sqrt{5}} \\\)

Second write the conjugant and multiply it.

\(\frac{\sqrt{60}}{\sqrt{5}} * \frac{\sqrt{5} }{\sqrt{5} }\)

After multiplying you should get,

\(\frac{10\sqrt{3}}{5}\)

now after simplifying you should get

\(2\sqrt{3}\)

Given

He bought 5/6 pound for $5

The price per pound can be calculated using the formula:

Hence, the price per pound is:

Answer:

price per pound : $6/ pound

The chart showing the results of data collection for frequency of fast food consumption by each of three head of household age groups is an example of a frequency distribution chart.

A frequency distribution or frequency table is a way of organizing and presenting data by categorizing it into different groups or intervals and indicating the number of occurrences or frequency within each group. In this case, the data collected pertains to the frequency of fast food consumption for three different age groups of household heads.

The chart would typically have three columns representing the age groups (e.g., 18-30, 31-45, 46-60), and another column indicating the frequency or number of households within each age group that reported a specific frequency of fast food consumption (e.g., daily, weekly, monthly). The frequencies can be represented in numbers or percentages.

This type of chart helps visualize the distribution of fast food consumption habits across different age groups, allowing for comparisons and analysis of patterns or trends. It provides a concise summary of the collected data and facilitates easy interpretation and understanding of the frequency distribution within each age group.

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The relation n² ≡ 1 (mod 8) for any odd positive integer n.

To prove that if n is an odd positive integer, then n² ≡ 1 (mod 8), we can use direct proof.

Let's consider an odd positive integer n. We can express n as n = 2k + 1, where k is a non-negative integer.

Now let's square both sides of the equation:

n² = (2k + 1)²

n² = 4k² + 4k + 1

n² = 4k(k + 1) + 1

Now we need to consider two cases:

Case 1: k is even.

If k is even, we can write k = 2m, where m is a non-negative integer. Substituting this into the equation, we get:

n² = 4(2m)(2m + 1) + 1

n² = 8m(2m + 1) + 1

In this case, 8m(2m + 1) is clearly divisible by 8, so we can write it as 8p, where p is an integer. Therefore, we have:

n² = 8p + 1

Case 2: k is odd.

If k is odd, we can write k = 2m + 1, where m is a non-negative integer. Substituting this into the equation, we get:

\(n² = 4(2m + 1)(2m + 2) + 1 \\ n² = 4(2m + 1)(m + 1) + 1 \\ n² = 8(m + 1)(2m + 1) - 8(m + 1) + 1 \\ n² = 8(m + 1)(2m + 1) - 8m - 7

\)

In this case, we can see that 8(m + 1)(2m + 1) is clearly divisible by 8, so we can write it as 8p, where p is an integer. Therefore, we have:

n² = 8p - 8m - 7

n² = 8(p - m) - 7

Now, we need to consider two subcases:

Subcase 2.1: p - m is even.

If p - m is even, we can write p - m = 2q, where q is an integer. Substituting this into the equation, we get:

n² = 8(2q) - 7

n² = 16q - 7

Subcase 2.2: p - m is odd.

If p - m is odd, we can write p - m = 2q + 1, where q is an integer. Substituting this into the equation, we get:

n² = 8(2q + 1) - 7

n² = 16q + 1

In both subcases, we can see that n² ≡ 1 (mod 8).

Therefore, regardless of whether k is even or odd, we have shown that n² ≡ 1 (mod 8) for any odd positive integer n.

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The sequence whose nth term is (2n+1)/(3n-1) converges to the number 2/3.

To use L'Hopital's rule, we need to take the limit of the ratio of the nth term and (n-1)th term as n approaches infinity.

Let a_n be the nth term of the sequence. lim (n->∞) a_n / a_(n-1) = lim (n->∞) (2n+1)/(3n-1) / (2n-1)/(3n-4) = lim (n->∞) [(2n+1)/(3n-1)] * [(3n-4)/(2n-1)] = lim (n->∞) [6n^2 - 5n - 4]/[6n^2 - 7n + 4]

By applying L'Hopital's rule, we can find that the limit of this ratio as n approaches infinity is 1. Thus, the sequence converges to the same limit as the ratio of consecutive terms, which is 2/3.

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Answer:

\( \frac{1}{6} \)

Step-by-step explanation:

let constant = k, then the proportional equation must be

y=kx

as the graph we get random point through (12, 2) so x=12 and y=2, substitute to y=kx we get

2=k.12

2/12=k

1/6 = k

Given:

\(f(1)=3,f(n)=2\times f(n-1)\)         ...(i)

For \(n\geq 2\).

To find:

The nth term for the given recursive formula.

Solution:

The given recursive formula is of the form of

\(f(n)=r\times f(n-1)\)            ...(ii)

It is the recursive formula of a GP, where r is common ratio.

On comparing (i) and (ii), we get

\(r=2\)

Now,

First term: \(a=f(1)=3\)

Common difference: \(r=2\)

nth term of a GP is

\(f(n)=ar^{n-1}\)

Putting a=3 and r=2, we get

\(f(n)=3(2)^{n-1}\)

Therefore, the equation for the nth term is \(f(n)=3(2)^{n-1}\).

Answer:

se llama agudo el ángulo de 80 grados

a. From fastest to slowest, the speeds of the balls at the right ends of the tracks will depend on the curvature of the tracks.

If the tracks are of equal length but have different curvatures, the ball on the track with the least curvature will have the highest speed, followed by the ball on the track with the next least curvature, followed by the ball on the track with the most curvature.

b. From longest to shortest, the tracks in terms of the times for the balls to reach the ends will depend on the curvature of the tracks. If the tracks are of equal length but have different curvatures, the track with the most curvature will have the longest time for the ball to reach the end, followed by the track with the next most curvature, followed by the track with the least curvature.

c. From greatest to least, the tracks in terms of the average speeds of the balls will depend on the curvature of the tracks. If the tracks are of equal length but have different curvatures, the track with the least curvature will have the highest average speed, followed by the track with the next least curvature, followed by the track with the most curvature.

All the balls will have the same average speed on all three tracks if the track lengths are equal, but will have different speeds at the end of each track due to the different curvatures.

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A 2x3x2 factorial design has three independent variables. What is a factorial design? A factorial design is an experimental design that studies the impact of two or more independent variables on a dependent variable.

The notation of a factorial design specifies how many independent variables are used and how many levels each independent variable has. In a 2x3x2 factorial design, there are three independent variables, with the first variable having two levels, the second variable having three levels, and the third variable having two levels.

The number of treatments or conditions required to create all feasible combinations of the independent variables is equal to the total number of cells in the design matrix, which can be computed as the product of the levels for each factor.

In this case, the number of cells would be 2x3x2=12.Therefore, a 2x3x2 factorial design has three independent variables and 12 treatment groups..

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Answer:

\(AB = 8\)

Step-by-step explanation:

Given

\(x = 60\)

\(BC = 4\)

See attachment

Required

Find AB

From the attachment, using cosine rule:

We have:

\(cos\ x = \frac{BC}{AB}\)

Make AB the subject

\(AB = \frac{BC}{cos\ x}\)

Substitute values for BC and x

\(AB = \frac{4}{cos\ 60}\)

\(AB = \frac{4}{0.5}\)

\(AB = 8\)

Answer:

If he taped the edges of the photograph, then the width is 5 inches.

Step-by-step explanation:

The perimeter of a rectangular photo is composed of 2 lengths and 2 widths

2l + 2w = 24in

l = 7in

2*7in + 2w = 24in

14in + 2w = 24in

2w = 10in

w = 5in

Answer:

The correct answer is c.) 3/36.There are three favorable outcomes (2, 11, and 12) out of a total of 36 possible outcomes (assuming a fair six-sided number cube). Therefore, the probability of X being a 2, 11, or 12 is 3/36, which can be simplified to 1/12.

Step-by-step explanation:

Answer:

21/2 so 10.5.

Step-by-step explanation:

7÷2/3=21/2=10.5

hope this helps you

Answer:

21/2 (10 1/2) or 10.5

Step-by-step explanation:

7 ÷ 2/3 = 7 ⋅ 3/2

7 ⋅ 3/2 = 21/2

21 ÷ 2 = 10.5

A curvilinear term in mathematics is "Consisting of, bounded by, or characterized by a curved line." However, the definition of a quadratic is a second-order polynomial equation in a single variable \(0= ax^{2}+bx+c\) with

\(a\neq 0\). A quadratic is a curvilinear term according to my definition, but a function like \($x^{4}$\) would also fit the definition of curvilinear. So, your answer is

False, a quadratic and a curvilinear term are not the same.

False, a curvilinear term is more broad, but quadratics have specific restrictions.

The first five terms of the sequence in which each number is 4 less than 3 times the previous number is 10, 26, 74, 218 and 650.

An equation is an expression that shows the relationship between two or more numbers and variables. An independent variable is a variable that does not depend on other variables while a dependent variable is a variable that depends on other variables.

Let x represent the second term, since the first term is 10, hence:

x = 3(10) - 4 = 26

Third term = 3(26) - 4 = 74

Fourth term = 3(74) - 4 = 218

Fifth term = 3(218) - 4 = 650

The first five terms of the sequence in which each number is 4 less than 3 times the previous number is 10, 26, 74, 218 and 650.

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The value of VW which is the missing length of the given triangle VWZ would be = 43.2

To calculate the missing part of the triangle, the formula that should be used is given as follows;

XW/VX = YZ/YV

Where;

XW = 72

YZ = 55

VX = 72+VW

YV = 88

That is;

= 72/72+VW = 55/88

6,336 = 3960+55VW

55VW = 6336-3960

55VW = 2376

VW = 2376/55

= 43.2

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Answer:

15÷4÷1/6.

first of all change ÷ to ×.

which will be 15×1/4×6/1.

which will be 15×1/2×3.

which is 15×3=45/2.

the answer is 22.5 or 22 whole number 1/2.

15 divided by 4 and 1/6 is equal to 18/5 or 3 and 3/5.

To divide 15 by 4 and 1/6, we can convert the mixed number 4 and 1/6 into an improper fraction.

4 and 1/6 can be written as (4 x 6 + 1) / 6 = 25/6.

Now, we can divide 15 by 25/6:

15 ÷ (25/6) = 15 x (6/25)

= (15 x 6) / 25

= 90/25.

Now, the fraction 90/25 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 5:

= 90/25

= (90 ÷ 5) / (25 ÷ 5)

= 18/5.

Therefore, 15 divided by 4 and 1/6 is equal to 18/5 or 3 and 3/5.

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(a) To compute the eigenvalues and eigenvectors of A, we solve the characteristic equation:

det(A - λI) = 0

where I is the identity matrix and λ is the eigenvalue. Substituting the given matrix A and simplifying, we have:

|1-λ 1 4|

|2 3-λ 2|

|3 4 2-λ| = 0

Expanding along the first row, we get:

(1-λ)[(3-λ)(2-λ) - 4(4)] - (1)[(2)(2-λ) - 4(4)] + (4)[(2)(4) - (3)(3)] = 0

Simplifying and rearranging, we obtain:

λ^3 - 6λ^2 - 5λ + 60 = 0

We can factor this polynomial as (λ-5)(λ-4)(λ+3) = 0, so the eigenvalues of A are λ₁ = 5, λ₂ = 4, and λ₃ = -3.

To find the eigenvectors corresponding to each eigenvalue, we substitute back into the equation (A - λI)x = 0 and solve for x.

For λ₁ = 5, we have:

|1-5 1 4|   |-4 1 4|

|2 3-5 2| x =| 2-2|

|3 4 2-5|   | 3 4-3|

Reducing this to row echelon form, we get:

|1 0 -4/5|   | 4/5|

|0 1 -2/5| x =|-1/5|

|0 0 0   |   |  0 |

So the eigenvector corresponding to λ₁ is x₁ = (4/5, -1/5, 1).

Similarly, for λ₂ = 4, we have:

|-3 1 4|   | 1|

| 2 -1 2| x =|-1|

| 3 4 -2|   | 0|

Reducing to row echelon form, we get:

|1 0 -2|   |2/3|

|0 1 -2| x =|-1/3|

|0 0 0 |   |  0 |

So the eigenvector corresponding to λ₂ is x₂ = (2/3, 1/3, 1).

Finally, for λ₃ = -3, we have:

|4 1 4|   |-1|

|2 6 2| x =| 0|

|3 4 5|   |-1|

Reducing to row echelon form, we get:

|1 0 -2/5|   | 1/5|

|0 1 1/5 | x =|-1/5|

|0 0 0   |   |  0 |

So the eigenvector corresponding to λ₃ is x₃ = (2/5, -1/5, 1).

Next, we compute the eigenvalues and eigenvectors of I + A. Since I is the identity matrix, the characteristic equation is:

det(I + A - λI) = det(A + (I - I) - λI) = det(A + (1-λ)I) = 0

Substituting the given matrix A and simplifying, we have:

|2-λ 1 4|

|2 4-λ

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