Taxable income Tax on income
$0–$18 200 Nil
$18 201–$37 000 19c for each $1 over $18 200
she was paid a gross salary of $18 700. How much tax should she pay?

$

If the average is 85 minutes, then on the seventh day he skated for 115 minutes.

For a set of N values {x₁, x₂, ..., xₙ} we define the average as:

A = (x₁ + ... + xₙ)/N

Here we know that for four days, he skated for 1hr + 25min = 85 min

Then for 2 days he skated for 1hr + 10min = 70 min

And the seventh day he skated x minutes.

We know that the average is 85 min, then we can write the equation:

(4*85 + 2*70 + x)/7 = 85

x = 85*7 - 2*70 - 4*85

x = 115

He scated for 115 minutes.

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Using arithmetic progression, number of logs in 6th row are 33.

We can use the information that each row has 5 fewer logs than the row below it to create a sequence of the number of logs in each row. Let's call the number of logs in the first row "a" (which we know is 58 logs). Then, the number of logs in the second row will be "a - 5", the number of logs in the third row will be "(a - 5) - 5" or "a - 10", and so on.

So, we have the sequence of the number of logs in each row as:

a, a - 5, a - 10, a - 15, a - 20, ...

To find the number of logs in the 6th row, we need to find the 6th term in this sequence. We can use the formula for the nth term of an arithmetic sequence:

an = a₁ + (n - 1)d

where an is the nth term, a1 is the first term, n is the number of the term we want to find, and d is the common difference between terms (which is -5 in this case, since each row has 5 fewer logs than the row below it).

Substituting the given values, we get:

a₆ = a₁ + (6 - 1)(-5)

= a - 25

So, the number of logs in the 6th row is a - 25. Since we know that a is 58 logs, we can substitute and simplify:

a - 25 = 58 - 25 = 33

Therefore, the answer is (b) 33.

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Answer:

Leg 1 = 13

Leg 2 = 84

Hypotenuse = 85

Step-by-step explanation:

Hello!

The larger of the other two legs would be the hypotenuse, as the hypotenuse is the largest side in a right triangle (as stated in the problem.

The Pythagorean theorem states that the sum of the squares of the legs is equal to the square of the hypotenuse.

Let the smallest of the other legs be x, and the hypotenuse be x + 1.

The equation is: [tex]13^2 + x^2 = (x+1)^2[/tex]

We found the value for x, so we can find the hypotenuse by adding 1, which gives us 85.

Answer:It would be 40•.25=10

Step-by-step explanation: which means 40-10=30 so it’d be .25 and you’d move the decimal over 2 spots so it’d be 25% off

To calculate the probability of Gretchen getting a roast beef sandwich on wheat bread and popcorn in her boxed lunch, we need to know the total number of possible boxed lunch combinations and the number of boxed lunches that contain roast beef on wheat bread and popcorn.

Let's assume there are 4 different types of sandwiches available: roast beef on wheat bread, turkey on white bread, ham on rye bread, and vegetarian on whole wheat bread. Also, let's assume there are 3 different snack options available: popcorn, chips, and fruit.

If each boxed lunch contains one sandwich and one snack, then there are 4 x 3 = 12 possible boxed lunch combinations.

Out of these 12 combinations, we need to determine how many contain roast beef on wheat bread and popcorn. Let's say there are 2 boxed lunches that contain roast beef on wheat bread and popcorn.

Therefore, the probability of Gretchen randomly choosing a boxed lunch with roast beef on wheat bread and popcorn is 2/12, which simplifies to 1/6, or approximately 0.1667.

So, there is a 16.67% chance that Gretchen will get a roast beef sandwich on wheat bread and popcorn in her box.

To create a confidence range for the population standard deviation, we can use the chi-square distribution. Finding the chi-square values that correlate to 10% and 90% in the right tail of the distribution is necessary given that we have 94 samples and want an 80% confidence range.

The chi-square value for the 10th percentile is 71.47, and the chi-square value for the 90th percentile is 112.31, according to a chi-square distribution chart with 93 degrees of freedom (n-1).

The confidence interval's calculation is:

((n-1)*s2)/sqrt(X), (n-1)*s2)/sqrt(Y))

Where:

The group number is n.

The sample's standard variation is s.

X represents the bottom limit of the confidence interval's chi-square value.

Y is the chi-square value for the upper bound of the confidence interval

Substituting the values we have:

(sqrt((94-1)*4.11^2)/sqrt(112.31)) = 5.63

(sqrt((94-1)*4.11^2)/sqrt(71.47)) = 4.81

Therefore, the 80% confidence interval for the population standard deviation of the widths of all doors in this factory is (4.81, 5.63).

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The experimental probability that the card selected was a K or 6 is option B.

What is Probability?

PrοbabiIity is the study οf the chances οf οccurrence οf a resuIt, which are οbtained by the ratiο between favοrabIe cases and pοssibIe cases.

Frοm the tabIe, we can see that the frequency οf drawing a K οr 6 is:

Frequency(K οr 6) = Frequency(K) + Frequency(6) = 4 + 10 = 14

The tοtaI number οf draws is 100.

The experimentaI prοbabiIity οf drawing a K οr 6 can be caIcuIated as:

ExperimentaI PrοbabiIity(K οr 6) = Frequency(K οr 6) / TοtaI number οf draws

ExperimentaI PrοbabiIity(K οr 6) = 14 / 100

ExperimentaI PrοbabiIity(K οr 6) = 0.14

Therefοre, the experimental prοbabiIity that the card seIected was a K οr 6 is 0.14 οr 14%. Optiοn b is the cοrrect answer.

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The solution of the composite function (f. g)(x)  in standard form is x⁵ - 2x³ + 2x² - 8x + 4.

The function (f . g)(x) is a composite function. Composite function is a function that depends on another function. In other words, composite function is a function that is within another function

Therefore, let's solve the composite function as follows:

f(x) = x³ - 4x + 2

g(x) = x² + 2

Hence,

(f. g)(x) = f(x) × g(x)

f(x) × g(x) = (x³ - 4x + 2)(x² + 2)

f(x) × g(x) = x⁵ + 2x³ - 4x³ - 8x + 2x² + 4

f(x) × g(x) = x⁵ - 2x³ + 2x² - 8x + 4

Therefore,

(f. g)(x) = x⁵ - 2x³ + 2x² - 8x + 4

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The weekly median income of a female with an advanced degree is 1,323.

What is a median?

The median, which is the centre value in a sorted, ascending or descending list of numbers, can better describe a data set than the average.

We are given three tables representing different data. The table 1 represents the total data, table 2 represents the data relating to men and the last table represents the data relating to female.

We are asked weekly median income of a female with an advanced degree.

So, from table 3 we get this data wherein the weekly median income of a female with an advanced degree is given as $1,323.

Hence, the  weekly median income of a female with an advanced degree is 1,323.

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Answer:

The volume of a cone is given by the formula V = 1/3πr²h, where r is the radius of the circular base and h is the height of the cone.

Since the diameter of the circular base is 18 inches, the radius is 9 inches. The height of the cone is 3 inches.

Substituting the values in the formula, we get:

V = 1/3π(9²)(3) V = 81π/3 V = 27π

Therefore, the exact volume of the cone is 27π cubic inches.

Answer:

Step-by-step explanation:

The cost increases by $10 for each ton of sugar being transported. This can be seen from the fact that for every 1 ton increase in weight, the cost increases by $10. And the slope of the line is $10/ton.

(a) To calculate the cost increase per ton of sugar being transported, we need to find the change in cost when the weight of sugar increases by 1 ton.

Looking at the graph, we can see that the cost increases from $20 to $30 as the weight of sugar increases from 1 ton to 2 tons. Therefore, the cost increase per ton of sugar is:

$30 - $20 = $10

So the cost increases by $10 for each ton of sugar being transported.

(b) The slope of the line can be calculated using the formula:

slope = (change in y) / (change in x)

where y is the cost and x is the weight of sugar being transported.

Since the line is perfectly horizontal, the change in y is zero for any change in x. Therefore, the slope is:

slope = 0 / (change in x) = 0

So the slope of the line is zero, which means that the cost does not change as the weight of sugar being transported changes.

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Answer:

y=y^2

Step-by-step explanation:

because you have to change X into y

Answer:

the answer is very simple the answer would be, 5 giga horse power every hour, 5/60*360= 30, the answer is 30m/s2

Step-by-step explanation:

according to formula

Answer:

the answer is most certainly 21

Step-by-step explanation:

Answer:

(-6,-3), (3,6), and (3,-3)

Step-by-step explanation:

the triangle has 3 points: (-2,-1), (1,2), and (1,-1)

for (x,y) => (3x,3y)

then

(-2,-1) => (-6,-3)

(1,2) => (3,6)

(1,-1) => (3,-3)

so you should draw the triangle with 3 points: (-6,-3), (3,6), and (3,-3)

Answer:

Step-by-step explanation:

1 quarter = 25 cents

1 dime = 10 cents

Let

q = the number of quarters, q>=0, q is integer

d = the number of dimes, d>=0, d is integ

30 coins totaling $4.80 = 480 cents:

q + d = 30

25q + 10d = 480

q = 12 quarters

d = 18 dimes

12 quarters and 18 dimes.

Answer:

Let x be the number of dimes in the jar.

Then the number of quarters in the jar would be 30 - x.

The total value of the dimes in the jar would be 0.10x, and the total value of the quarters would be 0.25(30 - x) = 7.50 - 0.25x.

We know that the total value of the coins is $4.80, so we can set up the equation:

0.10x + 7.50 - 0.25x = 4.80

Simplifying and solving for x, we get:

0.15x = 2.70

x = 18

Therefore, there are 18 dimes and 30 - 18 = 12 quarters in the jar.

Step-by-step explanation:

The answer of the given question based on the finding the adjoint of M is 16  -4  -33

  -12  -5  -12.

In linear algebra, a cofactor is a scalar value that can be computed for each element of a square matrix. To find the cofactor of a specific element of a matrix, we first remove the row and column containing that element, and then compute the determinant of the remaining matrix. The sign of the cofactor depends on the position of the element within the matrix: it is positive if the sum of the row and column indices is even, and negative if the sum is odd.

The cofactor matrix of a given matrix is obtained by replacing each element of the matrix with its corresponding cofactor. Cofactor matrices are useful in computing the inverse of a matrix and in solving systems of linear equations.

The adjoint of  matrix is  transpose of its co-factor matrix.

First, we need to find the transpose of the co-factor matrix:

16  -12

-4   -5

-33  -12

Therefore, the adjoint of M is:

16  -4  -33

-12  -5  -12

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B. Lin can make 2 batches of blueberry muffins.

C. Lin needs to make 2/3 of a batch of blueberry muffins to use all of the blueberries.

What is mixed fraction?

A mixed number is one that contains both a whole number and a fraction. The fraction is written after the whole number, with a space or plus sign placed between them. The mixed number 2 1/4 serves as an explanation for how the numbers 2 and 1/4 were added. Objects that aren't whole numbers but are close to them, such length or time measurements, are typically represented by mixed numbers.

a) Diagram

   4 cups of blueberries

    __ __ __ __

    |    |     |    |    |

    |__|__|__|__|

Each batch uses 3/2 cups of blueberries

B) To find the number of batches Lin can make, we need to divide the total amount of blueberries by the amount of blueberries per batch:

4 cups of blueberries ÷ (3/2 cups of blueberries per batch)

= (4 cups of blueberries) × (2/3 batches per cup of blueberries)

= 8/3 batches

Therefore, Lin can make 8/3 or approximately 2.67 batches of blueberry muffins using all of the blueberries.

C) To find the fraction of a batch Lin will need to make in order to use all of the blueberries, we need to subtract the number of whole batches from the total number of batches:

8/3 batches - 2 batches = 2/3 of a batch

Therefore, Lin will need to make 2/3 of a batch in order to use all of the blueberries.

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y= 6;

x= 4.

[tex](1)y=6\\ \\(2)-x+y=2[/tex]

[tex](2)-x+(6)=2\\ \\-x+6=2\\ \\[/tex]

[tex]-x+6-6=2-6\\\\-x=-4[/tex]

[tex](-1)-x=-4(-1)\\ \\x=4[/tex]

y= 6;

x= 4.

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

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I hope it's helpful for you

Answer: 1/3 or 33.33%

Step-by-step explanation:

30000000/90000000=1/3 or 33.33%

Answer: (a) John spent 2/5 of the remainder of his money on a toy. Let's first find the remainder of his money after he spent 20% on food. If he spent 20% on food, then he has 80% of his money remaining. So, if he had $x initially, he has $0.8x remaining.

John spent 2/5 of the remainder on a toy, so we can set up the equation:

(2/5)(0.8x) = 12

Simplifying, we get:

0.32x = 12

Dividing both sides by 0.32, we get:

x = 37.5

So, John initially had $37.5.

To find the percentage of his money he spent on the toy, we can use the following formula:

Percentage = (amount spent on toy / initial amount) * 100%

The amount John spent on the toy is $12, and his initial amount is $37.5, so we get:

Percentage = (12 / 37.5) * 100% = 32%

Therefore, John spent 32% of his money on the toy.

(b) John initially had $37.5.

Step-by-step explanation:

Using the distance formula and the converse of the pythagorean theorem to determine whether the points are vertices of a right triangle :

22. The points (1,1), (4,4), and (1,4) form a right triangle.

23. The points (6,0), (6,4), and (2,4) form a right triangle.

24. The points (-2,1), (3,5), and (6,-2) does not form a right triangle.

The points (1,1), (4,4), and (1,4) form a triangle. We can use the distance formula to find the lengths of the three sides, and then use the converse of the Pythagorean theorem to determine whether it is a right triangle. The distance formula is:

d = √((x₂-x₁)² + (y₂-y₁)²)

So the lengths of the three sides are:

d₁ = √((4-1)² + (4-1)²) = √(27)

d₂ = √((1-1)² + (4-1)²) = √(9)

d₃ = √((1-4)² + (4-1)²) = √(18)

To check if it is a right triangle, we need to see if any of the sides squared equals the sum of the squares of the other two sides. If that is the case, then it is a right triangle. Otherwise, it is not. Checking the three possible combinations, we see that:

d₁² = 27

d₂² + d₃² = 9 + 18 = 27

Therefore, the triangle formed by the points (1,1), (4,4), and (1,4) is a right triangle.

Similarly for points (6,0), (6,4), and (2,4), the lengths of the three sides are:

d₁ = √((6-6)² + (4-0)²) = 4

d₂ = √((2-6)² + (4-4)²) = 4

d₃ = √((6-2)² + (0-4)²) = 4√2

To check :

d₁² + d₂² = 16 + 16 = 32

d₃² = 32

Therefore, the triangle formed by the points (6,0), (6,4), and (2,4) is a right triangle.

For points (-2,1), (3,5), and (6,-2) the lengths of the three sides are:

d₁ = √((3-(-2))² + (5-1)²) = √(41)

d₂ = √((6-3)² + (-2-5)²) = √(58)

d₃ = √((6-(-2))² + (-2-1)²) = √(73)

To check :

d₁² + d₂² = 41 + 58 = 99

d₃² = 73

Therefore, the triangle formed by the points (-2, 1), (3,5), and (6, -2) is not a right triangle.

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Answer:

v  = 40 cm

w  = 126

x  = 30

y  =  63 cm

Step-by-step explanation:

So are given that ΔBIG is similar to ΔMOP. This means that their respective angles are the same measurements, but different side lengths. By definition of similar triangles, their respective side lengths are equal in proportion.

∠I corresponds to ∠O, so their measurements are equal. w = 126°.

∠B corresponds to ∠M, so their measurements are also equal. We don't know the angle measurement for x, but we have all the angles for two similar triangles, so we can find the measure of the third angle. The total angle measure for any triangle is 180°.

x = 180 - 24 - 126

x = 30°

Now that we have all the angle measurements, we can proportions to calculate the lengths of the unknown sides. The proportion of ΔBIG to ΔMOP can be calculated using the corresponding side length for each triangle.

Segment BG corresponds to segment MP. The proportion of BG to MP is:

48/72. Proportions are fractions, so this ratio can be simplified to 2/3 (divide by 24 on top and bottom).

Now we know that the ratio of ΔBIG to ΔMOP is 2/3.

Segment BI (aka v) = (2/3) * 60 cm

v = 40 cm

Segment PO (aka y) * (2/3) = 42 cm

y = 42 * 1.5

y = 63 cm

Answer: 8 books

Step-by-step explanation:

y= how much shelf space take up (inches)

x= # of books

y=2x

in this situation 16=y

16=2x

divide both sides by 2

8=x

   The diagram shows two intersecting lines, labeled line m and line n. Line m intersects line n at a point labeled point P. There are several angles labeled in the diagram:

Note that angles 1, 3, 5 are all alternate interior angles formed by the intersection of line m and line n.

Answer:

If the scale factor is -5, it means that the new image will be a reflection across the origin (negative scale factor means reflection) and enlarged by a factor of 5.If the scale factor is 1/2, it means that the new image will be half the size of the original image.If the scale factor is 0.4, it means that the new image will be 40% of the size of the original image.If the scale factor is 3/2, it means that the new image will be enlarged by a factor of 3/2 or 1.5 times the size of the original image.If the scale factor is 1, it means that the new image will be the same size as the original image.II.   The diagram shows two intersecting lines, labeled line m and line n. Line m intersects line n at a point labeled point P. There are several angles labeled in the diagram:Angle 1 is an acute angle that is adjacent to angle 2.Angle 2 is a right angle formed by the intersection of lines m and n.Angle 3 is an obtuse angle that is adjacent to angle 2.Angle 4 is a vertical angle to angle 2 and is congruent to angle 2.Angle 5 is an acute angle that is adjacent to angle 4.Angle 6 is a straight angle formed by the collinear extension of lines m and n.Note that angles 1, 3, 5 are all alternate interior angles formed by the intersection of line m and line n.

Step-by-step explanation:

The point (2, 2) would end up at the point (1, 1) after the transformations.

Functions can be represented in different ways, including graphs, tables, and equations. A graph of a function is a visual representation of the relation between the inputs and outputs, usually plotted on a coordinate plane. A table of values lists the inputs and corresponding outputs of a function. An equation of a function expresses the rule for calculating the output in terms of the input variable.

To sketch the graph of the new function h(x), we can start by considering the effect of each transformation on the original function f(x).

First, we have a horizontal shift of 1 unit to the left, since we are subtracting 1 from the argument of f(x). This means that the graph of f(x+1) will be shifted 1 unit to the left compared to the graph of f(x).

Next, we have a vertical stretch by a factor of 2, since we are multiplying the output of f(x+1) by 2. This means that the graph of 2f(x+1) will be twice as tall as the graph of f(x+1).

Finally, we have a vertical shift downwards by 3 units, since we are subtracting 3 from the output of 2f(x+1). This means that the graph of h(x) will be shifted 3 units downwards compared to the graph of 2f(x+1).

To find where the point (2, 2) ends up after these transformations, we can first apply the horizontal shift of 1 unit to the left, which gives us the point (1, 2). Next, we apply the vertical stretch by a factor of 2, which gives us the point (1, 4). Finally, we apply the vertical shift downwards by 3 units, which gives us the point (1, 1).

Therefore, the point (2, 2) would end up at the point (1, 1) after the transformations.

To sketch the graph of h(x), we can start with the graph of f(x) and shift it 1 unit to the left, stretch it vertically by a factor of 2, and shift it 3 units downwards. The resulting graph will have the same shape as the graph of f(x), but will be shifted and scaled as described above. The point (1, 1) will be on this graph as well.

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A. Regardless of the values of b and c, the point (-2,2) is included in the curve of g(x).

B. On the graph of h(x), the point (2,2) would be changed into the point (2,1).

A graph is a graphical representation of data, functions, or variable connections. It is a method of displaying information that is simple to analyse and comprehend.

Graphs are widely used in a variety of disciplines, including science, economics, business, engineering, and others. They make it simpler for researchers and analysts to visualise data and identify trends or patterns, allowing them to draw conclusions and make educated choices based on the data.

A. To include the spot (-2,2), we must shift the f(x) graph two units to the right and two units up. So far, we have:

g(x) = a f(x - (-2)) + 2

g(x) = a f(x + 2) + 2

We must now determine the worth of "a." Because the point (3,4) on the f(x) graph is transferred to the point (2,2) on the g(x) graph, we have:

g(3) = a f(3 + 2) + 2 = 2

4a + 2 = 2

4a = 0

a = 0

Therefore, the function g(x) is:

g(x) = 0 f(x + 2) + 2

g(x) = 2

As a result, independent of the values of b and c, the point (-2,2) is included in the graph of g(x).

B. The function h(x) has a slope of 2 and a y-intercept of -1. We plug x=2 into h(x) to determine where the point (2,2) would end up after the transformations and get:

h(2) = 2(2+1)-3 = 1

As a result, the point (2,2) on the graph of h(x) would be changed to the point (2,1).

The transformations applied to f(x) to produce h(x) are a one-unit horizontal shift to the left (x+1), a two-unit vertical stretch (2(x+1)), and a three-unit vertical shift downwards (-3).

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Complete question and graph attached below,

Part A:

First, we need to find the dimensions of the print by multiplying the dimensions of the original painting by the scale factor of 3.

The width of the print is 14 inches x 3 = 42 inches

The length of the print is 24 inches x 3 = 72 inches

To convert these dimensions into feet, we need to divide by 12 (since there are 12 inches in a foot):

Width of print = 42 inches / 12 = 3.5 feet

Length of print = 72 inches / 12 = 6 feet

Therefore, the dimensions of the print are 3.5 feet by 6 feet.

Part B:

To find the area of the print, we need to multiply the width by the length:

Area of print = (3.5 feet) x (6 feet) = 21 square feet

Therefore, the area of the print is 21 square feet

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