Let f(n) = 3n 2 + 5n lg n. a) Give the simplest function g(n) such that f(n) ∈ Θ(g(n)). Justify briefly (just a few words, you do not need a proof). b) As n gets large, the ratio f(2n)/f(n) approaches a constant c: what is the constant? Does it approach this constant from below, from above, or does it oscillate? Justify briefly

Answer:

34 pounds

Step-by-step explanation:

hi again!

so if three students have 10.2 to wash, we can find how many pounds the 3 students have in total by multiplying 10.2*3, because that is the same as doing 10.2+10.2+10.2. this gives us a result of 30.6 points for the three students.

now if the fourth student has 3.4 pounds, we just add that to 30.6

thus we have 30.6+3.4 which equals your answer, 34.

The solution is

a) The total area of the rectangular grass area is 9600 feet²

b) The number of bags required is 9.6 bags

The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle

Area of Rectangle = Length x Width

Given data ,

Let the area of the rectangular grass area be = A

Now , the equation will be

The length of the rectangular grass portion = 120 feet

The width of the rectangular grass portion = 80 feet

The area of the rectangular grass portion = Length x Width

Substituting the values in the equation , we get

The area of the rectangular grass portion A = 80 x 120

The area of the rectangular grass portion A = 9600 feet²

Now , each bag of the grass seed covers 1000 feet²

So , the number of bags required for the entire area = area of the rectangular grass portion A / each bag of the grass seed covers 1000 feet²

On simplifying the equation , we get

The number of bags required for the entire area = 9600 / 1000

The number of bags required for the entire area = 9.6 bags

Therefore , the number of bags required is 9.6 bags

Hence , the total area of the rectangular grass area is 9600 feet²

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Answer:

\(Area = 455.11\ in^2\)

Step-by-step explanation:

Given

\(Patches = 8\ by\ 8\)

\(Length = 2\frac{2}{3}\ in\) each

Required

The area of the quilt

First, calculate the length of the quilt.

\(Length = 8 * 2\frac{2}{3}\)

\(Length = 8 * \frac{8}{3}\)

\(Length = \frac{64}{3}\)

Next, the width

\(Width= 8 * 2\frac{2}{3}\)

\(Width= 8 * \frac{8}{3}\)

\(Width = \frac{64}{3}\)

The area is then calculated using:

\(Area = \frac{64}{3} * \frac{64}{3}\) i.e. Length * Width

\(Area = \frac{4096}{9}in^2\)

\(Area = 455.11\ in^2\) --- approximated

Answer:

3

Step-by-step explanation:

The slope of the given line is \(\frac{2}{3}\).

If a line passes through two points (x₁, y₁) and (x₂, y₂) respectively, then slope of the line is \(m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

Here, the given line passes through points (0, 6) and (-9, 0).

Therefore, the slope of this line is (m)

\(= \frac{0 - 6}{-9 - 0}\\= \frac{6}{9} \\= \frac{2}{3}\)

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Answer:

63a + 6

Step-by-step explanation:

we have to first simplify this

(3a+6)(7a-2)

21a-6+42a+12

63a+6

Answer:

Step-by-step explanation:

Use FOIL method

(3a+ 6)(7a - 2) = 3a* 7a + (3a)*(-2) + 6*7a + 6*(-2)

                       = 21a² - 6a + 42a - 12   {Combine like terms}

                       = 21a² + 36a - 12

Answer:

A translation of 5 units up

and

A translation of 2 units to the right

Step-by-step explanation:

The statistic is 101 out of 152 (66.45%) which  the questionnaires returned from the 800 mailed support the enactment of a statewide smoking ban in all enclosed public places.

To calculate this statistic, I first found the total number of questionnaires returned, which was 152. I then found the number of questionnaires that supported the ban, which was 101. To calculate the percentage, I then divided the number of questionnaires that supported the ban (101) by the total number of questionnaires returned (152), which gave me the answer of 66.45%. This percentage shows that a majority of the voters in the state representative's district support the enactment of a statewide smoking ban in all enclosed public places.

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Answer:

n=5

Step-by-step explanation:

-7-2.1n=-3.5n

 +2.1n    +2.1n

-7   =  -1.4n

/-1.4   /-1.4

n=5

Hope this helps!

If not, I am sorry

Answer:

b = - 1.25

Step-by-step explanation:

-7 - 2.1n = 3.5n

-7 = 3.5n + 2.1n

-7 = (3.5+2.1)n

-7 = 5.6n

-7/5.6 = n

n = -1.25

Check:

-7 -(2.1*-1.25) = 3.5*-1.25

-7 + 2.625 = -4.375

Step-by-step explanation:

fraction of page of photograph is 3/32

(1/2÷4)*3/4

1/2*1/4*3/4

1/8*3/4

=3/32

Answer:

Step-by-step explanation:

To express the confidence interval 0.039 < p < 0.479 in the form p ± E, we need to find the midpoint of the interval and half of the width.

The midpoint of the interval is the average of the lower and upper bounds:

Midpoint = (0.039 + 0.479) / 2 = 0.259

The width of the interval is the difference between the upper and lower bounds:

Width = 0.479 - 0.039 = 0.44

Half of the width is obtained by dividing the width by 2:

Half Width = 0.44 / 2 = 0.22

Therefore, the confidence interval 0.039 < p < 0.479 can be expressed as:

p ± E = 0.259 ± 0.22

So, the correct option is:

D. 0.259 ± 0.22

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Answer:

\(\displaystyle 707\:ft.^2\)

Step-by-step explanation:

Split the diametre in half before proceeding:

\(\displaystyle \pi{r}^2 = A \\ \\ 15^2\pi = A \hookrightarrow 225\pi = A \hookrightarrow 706,85834706... = A \\ \\ \boxed{707 \approx A}\)

I am joyous to assist you at any time.

The given matrix T is one-to-one.

Given matrix is,

\(\left[\begin{array}{ccc}4&2\\12&6\\\end{array}\right]\)

Now, First, find the reduced row-echelon form of A to determine the rank:

\(\left[\begin{array}{ccc}4&2\\12&6\\\end{array}\right]\) -

Apply the operation R₂ = R₂ - 3R₁

\(\left[\begin{array}{ccc}4&2\\0&0\\\end{array}\right]\)

Therefore, the rank of A is 1.

Since the rank of A is 1, the nullity will be zero.

Hence, In this case, since the nullity is zero,

So, T is one-to-one.

For T is onto,

In this case, A has 2 columns.

Since the rank of A is 1, which is less than the number of columns,

Hence, T is not onto.

Therefore, We get;

T is one-to-one.

T is not onto.

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Answer:

(i) The estimated regression equation is;

\(\hat y\) ≈ 1.6896 + 0.0604·X

The coefficient of 'X' indicates that \(\hat y\) increase by a multiple of 0.0604 for each million dollar increase in sales, X

(ii) The estimated earnings for the company is approximately $4.7096 million

(iii) The standard error of estimate is approximately 29.34

The high standard error of estimate indicates that individual mean do not accurately represent the population mean

(iv) The coefficient of determination is approximately 0.57925

The coefficient of determination indicates that the probability of the coordinate of a new point of data to be located on the line is 0.57925

Step-by-step explanation:

The given data is presented as follows;

\(\begin{array}{ccc}Sales \ (\$million)&&Earning \ (\$million) \\89.2&&4.9\\18.6&&4.4\\18.2&&1.3\\71.7&&8\\58.6&&6.6\\46.8&&4.1\\17.5&&2.6\\11.9&&1.7\end{array}\)

(i) From the data, we have;

The regression equation can be presented as follows;

\(\hat y\) = b₀ + b₁·x

Where;

b₁ = The slope given as follows;

\(b_1 = \dfrac{\Sigma(x_i - \overline x) \cdot (y_i - \overline y)}{\Sigma(x_i - \overline x)^2}\)

b₀ = \(\overline y\) - b₁·\(\overline x\)

From the data, we have;

\({\Sigma(x_i - \overline x) \cdot (y_i - \overline y)}\) = 364.05

\(\Sigma(x_i - \overline x)^2}\) = 6,027.259

\(\overline y\) = 4.2

\(\overline x\) = 41.5625

∴ b₁ = 364.05/6,027.259 ≈ 0.06040059005

b₀ = 4.2 - 0.06040059005 × 41.5625 ≈ 1.68960047605 ≈ 1.69

Therefore, we have the regression equation as follows;

\(\hat y\) ≈ 1.6896 + 0.0604·X

The coefficient of 'X' indicates that the earnings increase by a multiple of 0.0604 for each million dollar increase in sales

(ii) For the small company, we have;

X = $50.0 million, therefore, we get;

\(\hat y\) = 1.6896 + 0.0604 × 50 = 4.7096

The estimated earnings for the company, \(\hat y\) = 4.7096 million

(iii) The standard error of estimate, σ, is given by the following formula;

\(\sigma =\sqrt{\dfrac{\sum \left (x_i-\mu \right )^{2} }{n - 1}}\)

Where;

n = The sample size

Therefore, we have;

\(\sigma =\sqrt{\dfrac{6,027.259 }{8 - 1}} \approx 29.34\)

The standard error of estimate, σ ≈ 29.34

The high standard error of estimate indicates that it is very unlikely that a given mean value within the data is a representation of the true population mean

(iv) The coefficient of determination (R Square) is given as follows;

\(R^2 = \dfrac{SSR}{SST}\)

Where;

SSR = The Sum of Squared Regression ≈ 21.9884

SST = The total variation in the sample ≈ 37.96

Therefore, R² ≈ 21.9884/37.96 ≈ 0.57925

The coefficient of determination, R² ≈ 0.57925.

Therefore, by the coefficient of determination, the likelihood of a new introduced data point to located on the line is 0.57925

Answer: The pattern is 800, 400, 200, 100, 50, and 0.

I hope this helped! :)

Answer: Every number in the patten will have a 0 or a 5 in its ones place

Step-by-step explanation:

Answer:

+ -4.3

Step-by-step explanation:

To solve for the missing number, we can use this equation:

7.4 - 3.1 = 4.3

Now, we can insert that into the equation:

7.4 + -4.3 = 3.1

We convert 4.3 into a negative because if it was positive, the number would be getting bigger, not smaller.

Therefore, the calculation completed is 7.4 + -4.3 = 3.1.

Answer:

angle 2 = 75 ; angle 1 = 105

Step-by-step explanation:

a. The missing probability value is 0.4.

b. E(X) = 1.4.

c. Var(X) = 0.56 and σx = 0.75.

d. E(Z) = 2.27, Var(Z) = 2.56, and σz = 1.60.

The given probability distribution of the random variable X shows the probabilities associated with each possible outcome. To find the missing probability value, we know that the sum of all probabilities must equal 1. Therefore, the missing probability can be calculated by subtracting the sum of the probabilities already given from 1. In this case, 0.1 + 0.2 + 0.3 = 0.6, so the missing probability value is 1 - 0.6 = 0.4.

To find the expected value or mean of X (E(X)), we multiply each value of X by its corresponding probability and then sum up the results. In this case, (0 * 0.1) + (1 * 0.2) + (2 * 0.3) + (3 * 0.4) = 0.4 + 0.2 + 0.6 + 1.2 = 1.4.

To calculate the variance (Var(X)) of X, we use the formula: Var(X) = Σ[(X - E(X))^2 * P(X)], where Σ denotes the sum over all values of X. The standard deviation (σx) is the square root of the variance. Using this formula, we find Var(X) = [(0 - 1.4)² * 0.1] + [(1 - 1.4)^2 * 0.2] + [(2 - 1.4)² * 0.3] + [(3 - 1.4)² * 0.4] = 0.56. Taking the square root, we get σx = √(0.56) ≈ 0.75.

Now, let's consider the new random variable Z = 1 + (2/3)X. To find E(Z), we substitute the values of X into the formula and calculate the expected value. E(Z) = 1 + (2/3)E(X) = 1 + (2/3) * 1.4 = 2.27.

To calculate Var(Z), we use the formula Var(Z) = (2/3)² * Var(X). Substituting the known values, Var(Z) = (2/3)² * 0.56 = 2.56.

Finally, the standard deviation of Z (σz) is the square root of Var(Z). Therefore, σz = √(2.56) = 1.60.

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Answer:

I think its D. im not sure.

The appropriate measure of variability for the given data is the IQR, and its value is 16.

Based on the given stem-and-leaf plot, which represents the scores earned in a flower-growing competition, we can determine the appropriate measure of variability for the data.

The stem-and-leaf plot shows the individual scores, and to measure the spread or variability of the data, we have two commonly used measures: the range and the interquartile range (IQR).

The range is calculated by subtracting the smallest value from the largest value in the dataset. In this case, the smallest value is 20, and the largest value is 65. Therefore, the range is 65 - 20 = 45.

The interquartile range (IQR) is a measure of the spread of the middle 50% of the data. It is calculated by subtracting the first quartile (Q1) from the third quartile (Q3). Looking at the stem-and-leaf plot, we can identify the quartiles. The first quartile (Q1) is 25, and the third quartile (Q3) is 41. Therefore, the IQR is 41 - 25 = 16.

In this case, both the range and the IQR are measures of variability, but the IQR is generally preferred when there are potential outliers in the data. It focuses on the central portion of the dataset and is less affected by extreme values. Therefore, the appropriate measure of variability for the given data is the IQR, and its value is 16.

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10.) x-23=-3x+5

x+3=5+23

4x=28

12.) -4ab+5-(-2ab + 3)

-4ab+5+2ab-3

13.) (-3)+(-5)

-3 -5

Answer:

18

Step-by-step explanation:

6+6+3+3=18

Please Brainliest!!!

Answer:

7 3/4 = 775%

Step-by-step explanation:

pls mark meh as brainliest!

The rate of change of h(x) with respect to x when x=2 is -3. To find d/dx, we need to take the derivative of the function h(x) and evaluate it at x=2.

h(2) tells us that when x=2, h(x)=4.

h'(2) tells us that the slope of the tangent line to the graph of h(x) at x=2 is -3.

So, we can use this information to find d/dx as follows:

h(x) = y

dy/dx = h'(x)

We know that when x=2, y=h(2)=4.

We also know that the slope of the tangent line to the graph of h(x) at x=2 is h'(2)=-3.

So, we can write the equation of the tangent line at x=2 as:

y - 4 = (-3)(x - 2)

y = -3x + 10

Now we can take the derivative of y with respect to x to find d/dx:

d/dx (y) = d/dx (-3x + 10)

d/dx (y) = -3

Therefore, d/dx = -3.

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Answer:16 perhaps

Step-by-step explanation:

add 4 and 12. also i am sorry if this is incorrect. if its right mark me as brainliest please.

Answer: Equation: 3x+4=12x-14

x=2

Step-by-step explanation:

3x+4=12x-14

18x=9

x=2

9514 1404 393

9514 1404 393

Answer:

  1) (1 1/2)(7/5) = g

  2) (1 1/2)/(5/7) = g

Step-by-step explanation:

1) Tyler has painted 5/7 of the 7/7 of the fence. So the total amount of the fence is (7/7)/(5/7) = 7/5 as much as what was already painted.

The total amount of paint needed is then 7/5 the amount already used:

  g = (7/5)(1 1/2) . . . . . gallons of paint needed for the whole fence

__

2) If g gallons are required for the whole fence, the amount used so far for 5/7 of the fence is 5/7 of the quantity required:

  (5/7)g = 1 1/2

  g = (1 1/2)/(5/7) . . . . division expression for the paint needed

To find the mass and center of mass of the solid bounded by the paraboloid z = 8x^2 + 8y^2 and the plane z = a, we can use cylindrical coordinates.

In cylindrical coordinates, the paraboloid can be expressed as z = 8r^2, where r is the radial distance and z is the height.

To find the mass of the solid, we need to integrate the density function over the volume of the solid. Since the solid has constant density k, the mass can be expressed as:

M = ∭ k dv

Using cylindrical coordinates, the volume element (dv) is given by dv = r dz dr dθ.

The bounds for the integral are as follows:

r: from 0 to √(a/8) (due to the paraboloid equation z = 8r^2)

θ: from 0 to 2π (to cover the entire azimuthal angle)

z: from 0 to a (due to the plane z = a)

Now, let's evaluate the integral for the mass:

M = ∭ k dv = ∫[z=0 to a] ∫[θ=0 to 2π] ∫[r=0 to √(a/8)] k r dz dr dθ

The integration process will yield the mass M of the solid.

To find the center of mass, we need to evaluate the triple integral:

(x_cm, y_cm, z_cm) = (1/M) ∭ (x, y, z) k dv

Where (x_cm, y_cm, z_cm) represent the coordinates of the center of mass.

The integrals for each coordinate can be set up similarly to the mass integral, using the appropriate expressions for x, y, and z in terms of cylindrical coordinates. Then, divide each integral by the mass M to obtain the coordinates of the center of mass.

Note that the calculations can be quite involved, so it's recommended to use software or a computer algebra system to perform the integrations and simplify the expressions.

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if 1bag is 56.00

x bags= 1344.00

solution

\( \frac{1344.00}{56.00} = 24\)

the trader bought 24 50kg bags of rice

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Answer:

Step-by-step explanation:

a). \(\frac{5\pm\sqrt{-4}}{3}\) = \(\frac{5}{3}\pm \frac{\sqrt{-4}}{3}\)

               = \(\frac{5}{3}\pm\frac{2\sqrt{(-1)} }{3}\)

               = \(\frac{5}{3}\pm\frac{2i}{3}\) [Since, i = \(\sqrt{(-1)}\)]

b). \(\frac{10\pm\sqrt{-16}}{2}\) = \(\frac{10}{2}\pm \frac{\sqrt{-16}}{2}\)

                  = \(5\pm \frac{4\sqrt{-1}}{2}\)

                  = 5 ± 2i [Since, i = \(\sqrt{(-1)}\)]

c). \(\frac{-3\pm \sqrt{-144}}{6}\) = \(-\frac{3}{6}\pm \frac{\sqrt{-144}}{6}\)

                    = \(-\frac{3}{6}\pm \frac{12\sqrt{-1}}{6}\)

                    = \(-\frac{1}{2}\pm 2\sqrt{-1}\)

                    = \(-\frac{1}{2}\pm 2i\) [Since, i = \(\sqrt{(-1)}\)]

Bobby reads more quickly, as he reads 18 pages per day while Billy reads 15 pages per day.

A proportional relationship is modeled as follows:

y = kx.

In which k is the constant of proportionality.

The constant for Billy is given as follows:

k = 180/12 = 105/7 = ... = 30/2 = 15.

Meaning that he reads 15 pages per day.

Bobby reads 18 pages per day, which is a greater amount than the 15 pages per day read by Billy, and thus he reads more quickly.

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