The Income-tax for the state of Kalamazoo is as follows:

An annual salary up to and including $45,000 is charged an income tax of 2%. From $45,000 - $80,000 is charged 2% for the first $45,000 and 3% for the salary over $45,000. For salaries above $80,000 it is 2% for the first $45,000, 3% for $45,000-80,000 plus 4% for anything over $80,000.

Write a piecewise function representing this situation:

and

Evaluate f(15,435) What would the income tax be for this amount?

Answer:

N/a^3/2

Step-by-step explanation:

loga(N/X)=3/2

N/X= a^3/2

X= N/a^3/2

Step-by-step explanation:

When subtracting logarithms with the same base, it is equivalent to combining them into one logarithm, then dividing the arguments inside:

\( log_{a}(n) - log_{a}(x) = log_{a}( \frac{n}{x} ) \)

Then use the formula:

\( log_{a}( \frac{n}{x} ) = \frac{3}{2} \)

\({a}^{ \frac{3}{2} } = \frac{n}{x} \)

\(x = n {a}^{ - \frac{3}{2} } \)

Answer:

Therefore x is either 6 or 5.

The category in the Excel Options dialog box that contains the option to change the user name is "General".

In the Excel Options dialog box, the category that contains the option to change the user name is the General category.

Excel graphing methods, Go to Insert > Line after selecting the data. The type of line chart you want may be chosen from a dropdown menu that appears when you click the icon.

We'll use the fourth 2-D line graph (Line with Markers) for this illustration. Your line graph for the chosen data series will be added by Excel.

What are the primary three graphs?

How to Use Graphs in Science

Bar, circle, and line graphs are the three most often utilized graph kinds. Each form of graph may be used to display a certain kind of data.

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Porosity calculated as ratio of pore to total vol. Plot of porosity vs averaging length scale (edge of square used for averaging). Rep. elemental vol = vol of square used for averaging.

The porosity as a function of the averaging length scale can be calculated as follows:

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The marble will roll 180cm distance in fifth second.

Distance travelled by an object in rectilinear motion is always in arithmetic Progression. Arithmetic Progression is collection of number in increasing or decreasing order with a common difference.

The marble rolls 20cm, 60cm, 100cm, 140cm in 1st, 2nd, 3rd, 4rth second respectively

As the ball travels in rectilinear motion on floor, so the distance covered by it in successive seconds will be in Arithmetic Progression

so, 5th term of the AP 20,60,100,140..... will be the distance travelled by it 5th second

Since A=20 and common difference(d)=40

then, 5th term= A + (5-1)d

or, 20+ (4×40) = 180cm

Final answer, the marble will roll 180cm in 5th second.

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Answer:the cycle repeats every 2pi radians

Step-by-step explanation:

Answer:

The statement which does not describe the tangent function is A. The cycle repeats every 2pi radians.

Step-by-step explanation:

The tangent function is the ratio of the length of the opposite side to that of the adjacent side. It is also described  as the ratio of sine and cos .

If we analyses the tan function graph we will happened to find that it repeats itself after every π radian .

So, its cycle cannot repeat every 2pi radians.

Therefore,  The statement which says that The cycle repeats every 2pi radians does not describe the tangent function.

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Answer:

-5.2

Step-by-step explanation:

15.6/-3= - 15.6/3= -5.2

The dependent variable is the "height the ball bounces". The dependent variable is an essential component of the scientific experiment. It is the variable that you control to determine how the changes will impact the subject being investigated.

Height the ball bounces is your dependent variable, which varies based on the other variables.The term dependent variable refers to a variable whose value is determined by the presence of one or more variables (i.e., the independent variables) being evaluated. The dependent variable is commonly represented on the vertical or y-axis of a graph, while the independent variable is frequently shown on the horizontal or x-axis of the same graph.

The term dependent variable refers to a variable whose value is determined by the presence of one or more variables (i.e., the independent variables) being evaluated. The dependent variable is commonly represented on the vertical or y-axis of a graph, while the independent variable is frequently shown on the horizontal or x-axis of the same graph. The dependent variable is the "height the ball bounces". The dependent variable is an essential component of the scientific experiment.

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Answer:

Answer

= -7×5-2

= -35-2

=-37

Answer:

i got -37

Step-by-step explanation:

=-7x5+-2

=-35-2

=-37

Answer:

Yes, C is a scaled copy of B.

Step-by-step explanation:

The scale factor of C from B is 1/9th.

C is also a scaled copy of R. The scale factor is 1/36th.

The scale factor of B to R is 1/4th.

Answer:

first you need to set up the equation which is 20+2x=44 then isolate 2x by doing the inverse operation for 20 which is -20 and add them to both sides which would now give you 2x=24 so divde 24 by 2 which is 12, x=12 answer 12ml

Step-by-step explanation:

The volume of the solid generated by revolving the triangle about the -axis is (8π/3).

The region enclosed by the -axis, the line y = 2, and the curve y = -x is a triangle with base 2 and height 2.

To find the volume of the solid generated by revolving this triangle about the -axis, we can use the method of cylindrical shells.

The volume of each shell is given by the formula:

V = 2πr * h * δr

where r is the distance from the -axis to the shell, h is the height of the shell, and δr is the thickness of the shell.

We can express r as a function of y, since each shell corresponds to a vertical slice of the triangle:

r = y

The height of each shell is given by the difference between the -axis and the curve y = -x:

h = 2 - (-x) = 2 + x

Finally, the thickness of each shell is δr = dy.

Therefore, the volume of the solid is:

V = ∫[0,2] 2πy * (2 + y) dy

= 2π ∫[0,2] (2y + y^2) dy

= 2π [y^2 + (1/3)y^3] |[0,2]

= (8π/3)

Therefore, the volume of the solid generated by revolving the triangle about the -axis is (8π/3).

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The probability that Omar randomly selects a sugar cookie from the bag eats it, then randomly selects an oatmeal cookie is 0.06.

Omar buys a bag of cookies that contains,

5 chocolate chip cookies,9 peanut butter cookies, 6 sugar cookies, and 7 oatmeal cookies,

We have to find the probability that Omar randomly selects a sugar cookie from the bag, eats it, then randomly selects an oatmeal cookie

Total number of cookies in bag = 27

the probability that Omar randomly selects a sugar cookie from the bag, eats it, then randomly selects an oatmeal cookie

\(=\frac{6}{27}.\frac{7}{26}\\\\=0.0598 =0.06\)

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At year-end, White Paw Co. will record an unrealized gain on its investment in Crown, Inc. The journal entry will include a debit to "Fair Value Adjustment" for $21,000 and a credit to "Unrealized Gain on Investment" for $21,000. This entry reflects the increase in market value from $211,000 to $232,000.

The journal entry will have two parts. Firstly, White Paw Co. will record an increase in the value of the investment by $21,000 ($232,000 - $211,000) in the balance sheet. This will be recorded as a debit to the investment account and a credit to the unrealized gain account. Secondly, White Paw Co. will record an increase in the equity method income by the portion of Crown, Inc.'s earnings attributable to the investment.

This will be recorded as a debit to the equity method income account and a credit to the investment account. The portion of Crown, Inc.'s earnings attributable to the investment can be calculated as 11% of the net income of Crown, Inc. for the year.

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Answer:

Step-by-step explanation:

you get 5000 and divide 21and it equals 238 people

The probability of selecting an 8 and landing on tails is 1/13

First, we need to get the two individual probabilities.

The probability of selecting an 8 is given by the quotient between the number of eights in the deck, and the total number of cards in the deck.

P = 4/52.

For the case of the coin the probability of landing on tails is just 1/2 (the coin has two possible outputs, tails and head, both with the same probability).

Finally, the joint probability (getting the 8 and landing on tails) is given by the product between the individual probabilities, this is:

p = (4/52)*(1/2) = 2/26 = 1/13

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Given the measures of the angle, the measure of angle A is 109 degrees

A supplementary angles are angles that add up to 180 degrees. For example 100 and 80 degrees are supplementary angles.

The first step is to determine the value of x:

(4x + 3) + (8x - 27) = 180

12x - 24 = 180

12x = 180 + 24

12x = 204

x = 17

A = 8(17) - 27 = 109 degrees

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Answer: x = 50\(\sqrt{2}\)

side lengths = 300\(\sqrt{2}\) ft

side lengths = 100\(\sqrt{2}\) ft

Step-by-step explanation:

Pythagoras theorem:

\((6x)^{2}\) - \((2x)^{2}\) = \(400^{2}\)

36\(x^{2}\) - 4\(x^{2}\) = \(400^{2}\)

32\(x^{2}\) = \(400^{2}\)

\(x^{2}\) = 5000

x = \(\sqrt{5000\\\)

x = 50\(\sqrt{2}\)

side lengths = 6 × 50\(\sqrt{2}\) = 300\(\sqrt{2}\) ft

side lengths = 2 × 50\(\sqrt{2}\) = 100\(\sqrt{2}\) ft

Step-by-step explanation:

You can remember the commutative property by thinking of the numbers "commuting," or changing places. The example shows us that "negative two plus positive four" is the same as "positive four plus negative two."

Answer:

proportional bc all of them are 1 shirt = 12.95

The dual linear program is as follows:

y1 + 4y2 - w1 = 1

2y1 + 3y2 + w2 = -2

-y1 + 4y2 + 2y3 >= 1

y1 - 2y3 <= 0

y2, y3 >= 0

The primal linear program is:

x1 + 2x2 - x3 + x4 >= 0

4x1 + 3x2 + 4x3 - 2x4 <= 3

-x1 - x2 + 2x3 + x4 = 1

x2, x3 >= 0

To find the dual, we introduce dual variables y1, y2, and y3 for the primal's three constraints, and w1 and w2 for the primal's two non-negativity constraints on x2 and x3, respectively.

The dual linear program is:

maximize 0y1 + 3y2 + y3

subject to:

y1 + 4y2 - w1 = 1

2y1 + 3y2 + w2 = -2

-y1 + 4y2 + 2y3 >= 1

y1 - 2y3 <= 0

y2, y3 >= 0

The objective function of the dual is the sum of the products of the primal's objective coefficients and the dual variables, which gives 0y1 + 3y2 + y3. The new objective is to maximize this expression subject to the dual constraints.

Note that the dual program is also written in standard form, with all inequality constraints replaced by equality constraints and non-negativity constraints.

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Answer:

34.8°

Step-by-step explanation:

90-55.2=34.8

Hope this helps:)

Answer:

4 ft higher

Step-by-step explanation:

Since the ladder is 10 ft long and its top is 6 feet high(above the ground), we find the distance of its base from the wall since these three (the ladder, wall and ground) form a right angled triangle. Let d be the distance from the wall to the ladder.

So, by Pythagoras' theorem,

10² = 6² + d²  (the length of the ladder is the hypotenuse side)

d² = 10² - 6²

d² = 100 - 36

d² = 64

d = √64

d = 8 ft

Since the ladder is moved so that the base of the ladder travels toward the wall twice the distance that the top of the ladder moves up.

Now, let x be the distance the top of the ladder is moved, the new height of top of the ladder is 6 + x. Since the base moves twice the distance the top of the ladder moves up, the new distance for our base is 8 - 2x(It reduces since it gets closer to the wall).

Now, applying Pythagoras' theorem to the ladder with these new lengths, we have

10² = (6 + x)² + (8 - 2x)²

Expanding the brackets, we have

100 = 36 + 12x + x² + 64 - 32x + 4x²

collecting like terms, we have

100 = 4x² + x² + 12x - 32x + 64 + 36

100 = 5x² - 20x + 100

Subtracting 100 from both sides, we have

100 - 100 = 5x² - 20x + 100 - 100

5x² - 20x = 0

Factorizing, we have

5x(x - 4) = 0

5x = 0 or x - 4 = 0

x = 0 or x = 4

The top of the ladder is thus 4 ft higher

The point (9, -7) is the only solution to the system of linear inequalities given.

To determine which point would be a solution to the system of linear inequalities, let's substitute the given points into the inequalities and see which point satisfies both inequalities.

The system of linear inequalities is:

y > -4x + 6

y > (1/3)x - 7

Let's test each given point:

For the point (9, -7):

Substituting the values into the inequalities:

-7 > -4(9) + 6

-7 > -36 + 6

-7 > -30 (True)

-7 > (1/3)(9) - 7

-7 > 3 - 7

-7 > -4 (True)

Since both inequalities are true for the point (9, -7), it is a solution to the system of linear inequalities.

For the point (-12, -2):

Substituting the values into the inequalities:

-2 > -4(-12) + 6

-2 > 48 + 6

-2 > 54 (False)

-2 > (1/3)(-12) - 7

-2 > -4 - 7

-2 > -11 (False)

Since both inequalities are false for the point (-12, -2), it is not a solution to the system of linear inequalities.

For the point (12, 1):

Substituting the values into the inequalities:

1 > -4(12) + 6

1 > -48 + 6

1 > -42 (True)

1 > (1/3)(12) - 7

1 > 4 - 7

1 > -3 (True)

Since both inequalities are true for the point (12, 1), it is a solution to the system of linear inequalities.

For the point (-12, -7):

Substituting the values into the inequalities:

-7 > -4(-12) + 6

-7 > 48 + 6

-7 > 54 (False)

-7 > (1/3)(-12) - 7

-7 > -4 - 7

-7 > -11 (True)

Since one inequality is true and the other is false for the point (-12, -7), it is not a solution to the system of linear inequalities.

In conclusion, the point (9, -7) is the only solution to the system of linear inequalities given.

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Lines that are greater than 12 feet in real life are AB, CE, GH, IJ, KL, MN, OR, QS, TU, VW, and Y.

The given scale drawing tells us that every 3 cm on the scale drawing is equal to 4 feet in real life.

To determine which lines on the drawing would be greater than 12 feet in real life, we have to find the length of the line in centimeters and then convert it into feet.

We can use the proportion 3 cm/4 ft to convert the length of the line on the scale drawing into feet. Lines that are greater than 12 feet in real life are those that have a length of more than 9 cm on the scale drawing.

The lines that are greater than 12 feet in real life are as follows: ABCEGHIJJKLMNORQSTUVWY

The above lines have a length of more than 9 cm on the scale drawing, and using the proportion 3 cm/4 ft we can see that their length in real life is greater than 12 feet.

Hence, the lines that are greater than 12 feet in real life are AB, CE, GH, IJ, KL, MN, OR, QS, TU, VW, and Y.

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(a) The graph of the linear functions is as attached.

(b) The equation of the linear function in slope-intercept form is; y = x

(c) The equation of the transformed function in slope-intercept form is;

y = x + 2 and y = x - 3

Functions are defined as the relationship between sets of values. For example, in the function; y = f(x), for every value of x there exists a set of y values.

x is the independent variable.

y is the dependent variable.

If the linear function is; y = x,

The equation of the transformation in slope-intercept form is given as;

For translation of 2 units up, we have;

y = x + 2

For a translation of 3 units down, we have;

y = x - 3

Thus, the required graph has been attached and the solution is determined.

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We need to find the he probability of drawing a red or green marble

8 blue marbles

5 green marbles

8 red marbles

8 + 5 +8 = 21 total of marbles

To find probability of drawing a red or green marble

use the formula of probability: P = favorable outcome / total outcome

The P of get a blue marble is P(B) = 8 / 21

The P of get a red marble is P(G) = 8 / 21

The probability of get blue or red is the sum of the two P(B) and P(G)

P(B) + P(G) = 8/21 + 8/21 = 16/21

So the probability of drawing a red or green marble is 16/21

Answer:

e and c

Step-by-step explanation:

both are the exact same size, which would allow them to be placed on top of each other without any overlap

Answer:

A, B and E are the correct answers

Step-by-step explanation:

I had that same question on the test too.

Answer:

Step-by-step explanation:

Compare the relevant values of functions. They are given in the table for function g(x) and on the graph for function f(x).

Answer:

g(1) > f(1)

Step-by-step explanation:

Based on the graph :

The statement is :