100 pnts!!!
A scientist is studying the growth of a particular species of plant. He writes the following equation to show the height of the plant f(n), in cm, after n days:

f(n) = 12(1.03)n

Part A: When the scientist concluded his study, the height of the plant was approximately 16.13 cm. What is a reasonable domain to plot the growth function? (4 points)

Part B: What does the y-intercept of the graph of the function f(n) represent? (2 points)

Part C: What is the average rate of change of the function f(n) from n = 3 to n = 10, and what does it represent? (4 points)

The surface area of the triangular prism is 120 sq cm

From the question, we have the following parameters that can be used in our computation:

Dimensions = 10 cm 5 cm 5 cm 5 cm and 4 cm

Using the formula of the surface area of the triangular prism, we have

Surface area = bh + (l1 + l2 + l3) * h

Substitute the known values in the above equation, so, we have the following representation

Surface area = 10 * 5 + (5 + 5 + 4) * 5

Evaluate

Surface area = 120

Hence, the surface area is 120 sq cm

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The value of airplane's climb angle while this is happening is,

⇒ 35.53 degree

We have to given that;

An airplane is climbing 500 feet for every 700 feet it travels.

Hence, We can formulate;

The value of airplane's climb angle while this is happening is,

⇒ tan x = 500 / 700

⇒ tan x = 0.714

⇒  x = 35.53 degree

Thus, The value of airplane's climb angle while this is happening is,

⇒ 35.53 degree

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The value of expression √6 would be,

⇒ √6 = 2.4

We have to given that;

To find the value of number √6.

Now, We get;

⇒ √6 = 2.44

⇒ √6 = 2.4

Thus, The value of expression √6 would be,

⇒ √6 = 2.4

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Answer:

To find the resultant of 4b - 2a, we need to first calculate 4b and -2a separately, and then add them together.

4b = 4(-5, 2) = (-20, 8)

-2a = -2(6, -2) = (-12, 4)

Now, we can add (-20, 8) and (-12, 4) component-wise to find the component form of the resultant:

4b - 2a = (-20, 8) + (-12, 4) = (-20 - 12, 8 + 4) = (-32, 12)

Therefore, the component form of the resultant of 4b - 2a is (-32, 12).

Answer: (-32, 12)

Step-by-step explanation: I took the test.

Given:

a = (6, -2)

b = (-5, 2)

4b = 4( -5, 2) = ( -20, 8)

-2a = -2( 6, -2) = ( -12, 4)

(-20, 8)

( -12, 4)

+______

(-32, 12)

The possible values of a are:

(i) A unique solution: a such that a² ≠ 5

(ii) Infinitely many solutions: a such that a² = 5

(iii) No solution: for all other values of a.

To solve this system of linear equations, use Gaussian elimination to reduce the augmented matrix to row echelon form. Then, examine the resulting matrix to determine the number of solutions.

The augmented matrix for the system is:

[1  2  -3  | 4 ]

[3  -1  5  | 2 ]

[4  1  a²-14 | a+2]

Using row operations, transform the matrix as follows:

[1  2  -3  | 4 ]

[0  -7  14 | -10]

[0  -7  a²-2 | a-6]

The third row is a linear combination of the first two rows, so we can eliminate it. This gives us:

[1  2  -3  | 4 ]

[0  -7  14 | -10]

Further simplify this matrix by dividing the second row by -7:

[1  2  -3  | 4 ]

[0  1  -2  | 10/7]

Use back-substitution to solve for the variables, start with the second row:

y - 2z = 10/7

Rearranging this equation:

y = 2z + 10/7

Substituting this into the first row:

x + 2(2z+10/7) - 3z = 4

Simplifying this equation:

x + (4/7)z = 18/7

So, the solution to the system is:

x = (18/7) - (4/7)z

y = 2z + 10/7

z is free

Now, examine the possible values of a:

(i) A unique solution: If the system has a unique solution, then there can be no free variables. From our solution above, we see that z is a free variable. Therefore, the system can have a unique solution only if a is such that the third row in the original augmented matrix does not reduce to a multiple of the first two rows. This is equivalent to the condition -7 ≠ a² - 2, or a² ≠ 5.

(ii) Infinitely many solutions: If the system has infinitely many solutions, then there must be at least one free variable. From our solution above, we see that z is a free variable. Therefore, the system can have infinitely many solutions for all values of a such that a² = 5.

(iii) No solution: If the system has no solution, then there must be a row in the reduced row echelon form that has all zeros except in the last column. However, our reduced matrix does not have this form. Therefore, the system has no solution for any value of a.

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Answer: 6 years

Step-by-step explanation: 32,000 divided by 25% is 24,000. 24,000 divided by 25% is 18,000. 18,000 divided by 25% is 13,500. 13,500 divided by 25% is 10,125. 10,125 divided by 25% is 7,593.75. 7,593.75 divided by 25% is 5,695.3125. so 6

Answer:

To write the number 0.000089 in scientific notation, we need to move the decimal point to the right until there is only one non-zero digit to the left of the decimal point, and count the number of places we moved the decimal point. In this case, we need to move the decimal point 5 places to the right:

0.000089 = 8.9 × 10^(-5)

Therefore, the number 0.000089 in scientific notation is 8.9 × 10^(-5).

The polynomial  (2m + 2n)6 = 12m + 12n.

For the long division, the quotient is x - 2, the remainder is 6, and the dividend can be written as (x - 2)(x² - 4x + 3) + 6.

To expand the expression (2m + 2n)6, using the distributive property of multiplication over addition:

(2m + 2n)6 = 2m(6) + 2n(6)

Simplifying further, evaluate the products:

= 12m + 12n

Therefore, (2m + 2n)6 = 12m + 12n.

Using long division to divide the polynomial x³ - 6x² + 11x - 6 by the polynomial x² - 4x + 3. The steps are as follows:

      x - 2

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

x² - 4x + 3 | x³ - 6x² + 11x - 6

- (x³ - 4x² + 3x)

      - 2x² + 8x

      - 2x² + 8x - 6

                + 6

Therefore, x³ - 6x² + 11x - 6 = (x - 2)(x² - 4x + 3) + 6.

So the quotient is x - 2, the remainder is 6, and the dividend can be written as (x - 2)(x² - 4x + 3) + 6.

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The radius of the circle is 6 inches and the circumference is 30.84 in

For a circle of radius R, the circumference is given by:

C = (pi*R + 2*R)

Where pi = 3.14

For the given semicircle, we can see that the diameter is 12 inches. Then the radius is half of that, we will get.

R = D/2 = 12in/2 = 6 inches.

Now we can replace that in the circumference formula to get.

C = (3.14*6in + 2*6in)

C = 30.84 in

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The calculatd value of the model width is 11.4 m

From the question, we have the following parameters that can be used in our computation:

Scale factor = 1/3

Actual apartment building will be 39 m wide

Using the above as a guide, we have the following:

Model width = Scale factor *Actual apartment building

Substitute the known values in the above equation, so, we have the following representation

Model width = 1/3.4 * 39

Evaluate

Model width = 11.4

Hence, the model width is 11.4 m

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The concentration (C) in ounces of sugar per ounce of milk will be C = 10/(10/t + 1) + 1

The domain is all real numbers except t = 0.

The concentration (C) in ounces of sugar per ounce of milk will be

C = S/M

C = (10 + 10t)/(10 + t)

C = 10/(10/t + 1) + 1

The concentration after five minutes, will be:

C = 10/(10/5 + 1) + 1

C = 10/3

C ≈ 3.33 ounces of sugar per ounce of milk

The time it takes to reach a concentration of 8 ounces of sugar per ounce of milk, will be:

8 = 10/(10/t + 1) + 1

7 = 10/(10/t)

70/t = 10

t = 7 minutes

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well, we know is a square, so that means all sides are equal, so if we just find one side and multiply it by 4, that's our perimeter, hmmmm let's use the points of K(-2 , 0) and J(3 , 5)

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ K(\stackrel{x_1}{-2}~,~\stackrel{y_1}{0})\qquad J(\stackrel{x_2}{3}~,~\stackrel{y_2}{5})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ KJ=\sqrt{(~~3 - (-2)~~)^2 + (~~5 - 0~~)^2} \implies KJ=\sqrt{(3 +2)^2 + (5 -0)^2} \\\\\\ KJ=\sqrt{( 5 )^2 + ( 5 )^2} \implies KJ=\sqrt{ 25 + 25 } \implies KJ=\sqrt{ 50 } \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{\LARGE perimeter} }{4\sqrt{50} ~~ \approx ~~ }\text{\LARGE 28.3}[/tex]

The population of the town in 2018 will be 5,040.

To predict the population in 2018, we need to use the following formula:

Population in 2018 = Population in 1993 × (1 - rate of decrease)[tex].^n[/tex]

Here, the population in 1993 is 10,500, the rate of decrease is 5.2% or 0.052 (in decimal form), and the number of years from 1993 to 2018 is 25.

Substituting these values, we get:

Population in 2018 = 10,500 × (1 - 0.052)^25

= 10,500 × 0.480

= 5,040

Rounding this answer to the nearest integer, we get a predicted population of 5,040 in 2018.

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The shape generated by the cross-section is a rectangle. So the correct option is D.

Notice that the cross-section goes through two opposite sides of the cube.

Then the shape that we will get will also be a quadrilateral of parallel sides. Notice that if the plane was parallel to the square, the cross-section would be also a cube, but because it is slanted, one of the sides will be larger, then we will get a rectangle, thus, the correct option is the last one.

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The rule of dilation is a dilation by a scale factor of 2

From the question, we have the following parameters that can be used in our computation:

The scale factor is calculated as

Scale factor  = A'/A

Substitute the known values in the above equation, so, we have the following representation

Scale factor  = (2, 2)/(1, 1)

Evaluate

Scale factor  = 2

Hence, the rule of dilation is (2x, 2y)

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Answer: 55/60

Step-by-step explanation:

The statement which is true about the end behaviour of the given quadratic function is;

As evident from the task content; the answer choice which correctly describes the end behaviour of the given quadratic function is to be determined.

By observation, the given quadratic graph opens upwards and on this note, its end behaviour is such that; As x approaches -∞, f(x) approaches ∞, and as x approaches ∞, f (x) approaches ∞.

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Therefore, after 4 weeks, Liz will have $275 in her savings account and Fareed will have $300 in his savings account.

After 1 week

Liz will have saved $75 + $50 = $125, and

Fareed will have saved $100 + $50 = $150.

After 2 weeks,

Liz will have saved a total of $125 + $50 = $175, and

Fareed will have saved a total of $150 + $50 = $200.

After 3 weeks,

Liz will have saved a total of $175 + $50 = $225, and

Fareed will have saved a total of $200 + $50 = $250.

After 4 weeks,

Liz will have saved a total of $225 + $50 = $275, and

Fareed will have saved a total of $250 + $50 = $300.

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The graph of the inverse of the function is shown below.

In Mathematics, an inverse function simply refers to a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).

From the information provided, we can logically deduce the following ordered pairs from the graph of the parent function:

x, f(x) = {(-2, 5), (-1, 1), (1, 2), (2, 3)}

In order to determine the inverse of this function f(x), we would interchange (swap) both the input value (x) and output value (y) as follows:

Inverse of f(x) = {(5, -2) (1, -1), (2, 1), (2, 3)}

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Answer:1/25

Step-by-step explanation:100/25=4. So 1/25 of the box.

The requried probability that a randomly selected adult has an IQ between 85 and 115 is also 0.6827.

Standardize 85 and 115 using the formula:

z = (x - μ) / σ

where x is the value we want to standardize, μ is the mean, and σ is the standard deviation.

For 85:

z = (85 - 100) / 15 = -1

For 115:

z = (115 - 100) / 15 = 1

So we want to find the probability that a standard normal random variable Z is between -1 and 1. Using a standard normal distribution table or a calculator, we can find that this probability is 0.6827.

Since IQ scores are normally distributed with a mean of 100 and a standard deviation of 15, the probability that a randomly selected adult has an IQ between 85 and 115 is also 0.6827.

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The total area of the table runner is 858 square inches

Given that Table Runner has an overall length of 72" and a width of 13",

Area = length ×width

=60×13

=780 sq in

Area of triangle = 1/2×base ×height

=1/2×13×6

=39

There are two triangles so area is 2(39) = 78

Total area is 936+78

=858 square inches

Hence, the total area of the table runner is 858 square inches

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The type of transformation shown is vertical translation. That is option D.

Transformation of geometrical figures or points is the manipulation of a given figure to take the same shape but with different direction of its original angles.

Different types of transformations are Rotation, Reflection, Glide reflection, Translation and Dilation.

Given a polygon ABDC.

It is transformed to another polygon with the same size A'B'D'C'.

Here the polygon ABDC is just moved downwards as it is and mark is as A'B'D'C'.

In rotation or reflection transformation, the points will change it's correspondent place.

Translation is a type of transformation where the original figure is shifted from a place to another place without affecting it's size.

Since the shifting is done vertically, it is vertical translation.

Hence the transformation is vertical translation.

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The slope of f(x) is less than the slope of g(x).

A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If we know two points on a line, then the slope is equal to the quotient between the difference of the y-values and the difference of the x-values.

So the slope of f(x) is:

a = (3 - 0)/(0 + 2) = 3/2

And g(x) = (4/5)*x - 2

So here the slope is 4/5

We can see that clearly the slope of g(x) is larger.

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Answer:18 wings

Step-by-step explanation: 28.50 divided by 15 is 1.9 so if you do 1.9 x 18 you get 34.2

Answer:

18 wings

Step-by-step explanation:

Use a proportion.

15/$28.5 = x/$34.2

28.5x = 15 × 34.2

28.5x = 513

x = 18

Answer: 18 wings

Answer:

  8

Step-by-step explanation:

Brenda sold 2 brass signs of the 10 signs she sold this week. You want an estimate of the number of brass signs she will sell out of the next 40.

We expect the proportion of brass signs to remain the same, so the number (x) of brass signs in the next 40 signs is expected to be ...

  x/40 = 2/10

  x = 40(2/10) = 8

We estimate Brenda will sell 8 brass signs out of the next 40 signs she sells.

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