Aria ate the pictured slice of pizza. If the original
pizza was 8 inches in diameter, what is the area
of the slice she ate?

The man needs to pay a total tax of Rs 69780 (3000 for social security and 66780 for yearly tax).

To find the tax, let's find the man's yearly income:

Yearly income = Monthly income x 12

Yearly income = 53000 x 12 = 636000

Next, let's find how much he deposits in civil investment fund and charity:

Amount deposited in civil investment fund = Yearly income x 20%

Amount deposited in civil investment fund = 636000 x 0.2 = 127200

Amount deposited in charity = Yearly income x 10%

Amount deposited in charity = 636000 x 0.1 = 63600

Now, let's calculate the total taxable income:

Total taxable income = Yearly income - Amount deposited in civil investment fund - Amount deposited in charity

Total taxable income = 636000 - 127200 - 63600 = 445200

Since the man's taxable income is above Rs 300000, he needs to pay 1% social security tax on Rs 300000:

Social security tax = 1% of 300000 = 3000

Now, let's calculate the yearly tax imposed at a rate of 15%:

Yearly tax = Total taxable income x 15%

Yearly tax = 445200 x 0.15 = 66780

Therefore, the man needs to pay a total tax of Rs 69780 (3000 for social security and 66780 for yearly tax).

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Answer: -40

Step-by-step explanation:

Rate of change is calculated as the slope. The formula for Slope is:

S = [tex]\frac{x_{1}-x_{2} }{ y_{1}-y_{2}}[/tex]

The two points we have are when x = 3 and 6.

the points are (3, 120) and (6, 0), as we can see.

plugging into the slope formula:

S = [tex]\frac{120-0 }{ 3-6}[/tex]

S = 120/-3

S = -40

Which hopefully makes sense, because the slope is negative, (the graph is falling).

To find the height of the coffee cup, we can use the formula for the volume of a cylinder:

V = πr^2h

where V is the volume, r is the radius, and h is the height.

We are given that the circumference of the coffee cup is 15.1 cm. The formula for the circumference of a cylinder is:

C = 2πr

where C is the circumference and r is the radius.

We can use this formula to find the radius of the coffee cup:

15.1 cm = 2πr

r = 15.1 cm / (2π)

r ≈ 2.4 cm

Now we can use the given volume and radius to find the height of the coffee cup:

161 cm^3 = π(2.4 cm)^2h

h = 161 cm^3 / (π(2.4 cm)^2)

h ≈ 4.0 cm

Therefore, the height of the coffee cup is approximately 4.0 cm.

The cardboard box with the largest volume can hold the greatest number of 1 in x 2 in x 4 in sponges.

To find the box with the largest volume, first determine the volume of each sponge: V_sponge = 1 in x 2 in x 4 in = 8 cubic inches. Next, find the volume of each box by multiplying its length, width, and height (V_box = L x W x H).

To determine how many sponges each box can hold, divide the volume of the box by the volume of the sponge (V_box / V_sponge). The box with the highest resulting quotient can hold the most 1 in x 2 in x 4 in sponges.

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The value of the calculated percent markup of the shirt is 11.1%

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

A department store buys 200 shirts at a cost of ​$ 3600 and sells them at a selling price of ​$ 20 each.

This means that

Cost price = 3600/200

Evaluate

Cost price = 18

The percent markup of the shirt is then calculated as

Percentage = (20 - 18)/18

Evaluate

Percentage = 11.1%

Hence, the percent markup of the shirt is11.1%

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The residual plot can provide valuable insights into the adequacy of the regression model, and whether any modifications or alternative models may be needed to better explain the data.

A residual plot is a visual tool for evaluating a regression model's goodness-of-fit. The residuals—that is, the discrepancies between the observed and expected values—are plotted against the predicted values.

The residuals should be randomly dispersed around zero and the plot should show no clear patterns or trends if the regression equation accurately models the data.

The residuals may show patterns or trends in the plot if the regression equation is a poor model of the data, which would indicate that the model is failing to account for some crucial characteristics of the data.

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a) When the radius is 4 cm, it is changing at a rate of 1/(4π) cm/s.

b) When the circumference is 3 cm, the radius is changing at a rate of 2/3 cm/s.

a. Given that the area of a circle increases at a rate of 2 cm²/s, let's denote this rate as dA/dt.

The formula for the area of a circle is A = πr²,

where A is the area and r is the radius.

We want to find the rate at which the radius is changing, or dr/dt, when the radius is 4 cm.

Using implicit differentiation with respect to time t, we get:

dA/dt = d(πr²)/dt 2 = 2πr(dr/dt)

Now, we'll plug in the radius value of 4 cm:

2 = 2π(4)(dr/dt)

Solving for dr/dt, we get:

dr/dt = 1/(4π) cm/s

b. We are given the circumference, which is 3 cm.

The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius.

First, we need to find the radius when the circumference is 3 cm: 3 = 2πr r = 3/(2π)

Now, we'll plug this value for the radius back into the formula from part a:

2 = 2π(3/(2π))(dr/dt)

Solving for dr/dt, we get:

dr/dt = 2/3 cm/s

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The surface area of the cylinder, rounded to the nearest square meter, is: D. 120 square meters

The surface area of a cylinder can be calculated by using the formula expressed as:

SA = 2πr(h + r), where r is the radius and h is the height.

Given the following:

π = 3.14

radius (r) = 2.2 m

height of the cylinder (h) = 6.5 m

Plug in the values:

SA = 2 * 3.14 * 2.2 * (6.5 + 2.2)

SA ≈ 120 square meters (rounded to the nearest square meter)

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The correct answer is option (a), increase the height of the carton to 7 inches.

How can the volume of a handmade carton be increased by 42 cubic inches?

To increase the volume of the carton by 42 cubic inches, we need to increase either the length, width, or height of the carton or a combination of these dimensions.

Let's first calculate the current volume of the carton:

Volume = length x width x height

Volume = 7 x 6 x 6

Volume = 252 cubic inches

Now, we need to find a new dimension that will increase the volume by 42 cubic inches.

a) If we increase the height to 7 inches, the new volume will be:

New Volume = 7 x 6 x 7

New Volume = 294 cubic inches

The volume has increased by 42 cubic inches, so option (a) is the correct answer.

b) If we increase the height to 8 inches, the new volume will be:

New Volume = 7 x 6 x 8

New Volume = 336 cubic inches

The volume has increased by 84 cubic inches, which is more than required.

c) If we increase the width of the base to 8 inches, the new volume will be:

New Volume = 7 x 8 x 6

New Volume = 336 cubic inches

The volume has increased by 84 cubic inches, which is more than required.

d) If we increase the width of the base to 9 inches, the new volume will be:

New Volume = 7 x 9 x 6

New Volume = 378 cubic inches

The volume has increased by 126 cubic inches, which is more than required.

Therefore, the correct answer is option (a), increase the height of the carton to 7 inches.

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The value of b is 1,500, which means that the author had already written 1,500 words before starting the new plan.

In the equation y = 600x + b, x represents the number of days since the author started the new plan to write 600 words per day, and y represents the total number of words written.

After the fifth day, the author has written 4,500 words. Thus, we can substitute x = 5 and y = 4,500 into the equation and solve for b:

4,500 = 600(5) + b

4,500 = 3,000 + b

b = 4,500 - 3,000

b = 1,500

Therefore, the value of b is 1,500, which means that the author had already written 1,500 words before starting the new plan.

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Answer:

5x^3-25x^2+6x-30

Step-by-step explanation:

Answer:

Step-by-step explanation:

5x2(x − 5) + 6(x − 5)

Using the Distributive Law:

= 5x^3 - 25x^2 + 6x - 30

In factored form it is

(x - 5)(5x^2 + 6)

The equation is (x^2 + y^2 - 38x + 6y = -369).

The center of the lake is 19 miles east and 3 miles south of the town hall, which means the coordinates of the center are (19,-3). The radius of the lake is 0.5 miles.

Using the standard equation of a circle, we have:

(x - h)^2 + (y - k)^2 = r^2

where (h,k) is the center of the circle and r is the radius.

Substituting the given values, we get: (x - 19)^2 + (y + 3)^2 = 0.5^2

Expanding the left side, we get: x^2 - 38x + 361 + y^2 + 6y + 9 = 0.25

Simplifying and rearranging terms, we get:

x^2 + y^2 - 38x + 6y + 369.25 = 0.25

Subtracting 369 from both sides, we get:

x^2 + y^2 - 38x + 6y = -369

Therefore, the equation that represents the lake on the map is:

(x - 19)^2 + (y + 3)^2 = 0.5^2, which can be simplified to (x^2 + y^2 - 38x + 6y = -369).

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The length of the hypotenuse is approximately 7.21 ft.

To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides (legs) is equal to the square of the longest side (hypotenuse). In mathematical terms, it looks like this:

a² + b² = c²

Where "a" and "b" are the lengths of the legs, and "c" is the length of the hypotenuse.

In your case, we can substitute the given values into the equation:

6² + 4² = c²

Simplifying:

36 + 16 = c²

52 = c²

To solve for "c," we need to take the square root of both sides of the equation:

√(52) = c

We can simplify the square root of 52 to be 2 times the square root of 13. Therefore:

c ≈ 7.21 ft

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Complete Question:

Find the value of hypotenuse of the given triangle by using the Pythagoras theorem.

The p-value of 0.416 indicates that there is no significant difference in the proportion of Republicans between the two areas of town. Therefore, we fail to reject the null hypothesis and conclude that there is no evidence of a significant difference in the proportion of Republicans between the two areas of town.

Based on the given information, the p-value is 0.416, which is larger than the conventional level of significance (e.g., 0.05 or 0.01). Therefore, we fail to reject the null hypothesis that there is no significant difference in the proportion of republicans between the two areas of town.

In other words, we cannot conclude that there is a significant difference between the two areas. It is possible that any observed difference could be due to chance.

However, it is important to note that statistical significance does not necessarily mean practical significance, and further investigation may be needed to determine if there are any meaningful differences between the two areas in terms of the proportion of republicans.

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damePor lo tanto, la edad que tienes es de aproximante 14.67 años.

Si al triple de la edad que tengo, se quita mi edad aumentada en 8 años, tendría 36 años. ¿

Podemos plantear este problema como una ecuación algebraica. Si llamamos "x" a la edad que tienes, la ecuación sería:

3x - 8 = 36

Ahora, despejamos la variable "x" para encontrar su valor:

3x = 36 + 8

3x = 44

x = 44/3

.Este resultado nos indica que nuestra edad actual es de aproximadamente 14.67 años. Es importante tener en cuenta que la solución no es un número entero, lo cual puede parecer inusual para una edad, pero es una respuesta matemáticamente correcta según la ecuación planteada en el problema.

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Answer: ∠b = 105°

Step-by-step explanation:

     We know that a straight line is equal to 180 degrees. We will create an equation and solve for ∠b.

180° = ∠b + 75°

∠b = 180° - 75°

∠b = 105°

The statement that is best supported by the data is this: C. The range of data in Mr. Joe’s class is less than the range of data in Ms. Gambino’s class.

The true statement about the data is that the range of data in Mr. Joe's class is less than the range of data in Ms. Gambino's class.

The range of data in Mr. Joe's class spans from 4 to 10 hours while the range of data in Ms. Gambino's class spans from 4 to 12 hours. So, the data range for the latter class is higher than the former.

Complete Question:

The average number of hours of sleep of Ms. Gambino’s and Mr. Joe’s classes is shown below. Which of the following statements is best supported by the data?

The image shows a line graph:

Mr. Gambino's Class: Range 4 - 12

Hours: 4 = 0

5 = 1

6 = 1

7 = 3

8 = 5

9 = 3

10 = 2

11 = 1

12 = 1

Mr. Joe's class: Range 4 -12

4 = 0

5 = 1

6 = 5

7 = 3

8 = 1

9 = 2

10 = 5

11 = 0

12 = 0

The median number of hours slept in Ms. Gambino’s class is less than the median number of hours in Mr. Joe’s class.

The data for Ms. Gambino’s class is symmetrical, while the data for Mr. Joe’s class is skewed right.

The range of data in Mr. Joe’s class is less than the range of data is Ms. Gambino’s class.

The mode of the data in Ms. Gambino’s class was equal to the mode of the data in Mr. Joe’s class.

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The length of the towel bar is 13.5 inches.

Let's use the given information to write and solve an equation for the length of the towel bar.

We know that the door is 29 inches wide and that there is a 7.75-inch distance from each end of the towel bar to the respective end of the door. Let's denote the length of the towel bar as x.

So, the total width of the door can be expressed as the sum of the two distances and the length of the towel bar:
29 = 7.75 + x + 7.75

Now, let's solve for x:
29 = 15.5 + x
x = 29 - 15.5
x = 13.5 inches

Therefore, the length of the towel bar is 13.5 inches.

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Answer: Z=21, Y=9, X=1

Step-by-step explanation:

Z---------

Since 3z and 63 are equal angles, then 3z must equal 63 as well. So 3 times what is 63? 3 times 21. Z=21.

X------1

2 times 1 is 2.

3 times 1 is 3. 3-1 is 2.

x=1

Y----

Same concept as Z. Since the length 13 and Y+4 are equal sides (definition of the kite figure I forget the proper name) then 13-4 is your answer. 9.

The answer to whether it is this a fair game is: No, the game is not fair because Noah does not have equal probabilities of winning or losing. Therefore, the correct option is 1.

The reason why it is not a fair game is as follows.

Since the probabilities of winning and losing are not equal (1/81 vs 64/81), the game is not fair. Therefore, the correct answer is option 1.

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Using  trignometric functions the shorter side AD has length a ≈ 25.75 cm and the longer side AB has length b ≈ 34.25 cm.

In the given scenario, we have a rectangle with sides AD and AB. The length of AD is represented as 'a' and is approximately 25.75 cm, while the length of AB is denoted as 'b' and is approximately 34.25 cm. The diagonal AC of the rectangle has a length of 42.3 cm and forms an angle of 53° with AD.

To find the lengths of sides a and b, we can utilize trigonometric functions, specifically cosine and sine. Since we have the length of the diagonal AC and the angle it forms with AD, we can set up the following equations:

cos(53°) = a/42.3

sin(53°) = b/42.3

By rearranging the equations, we can solve for a and b:

a = 42.3 * cos(53°) ≈ 25.75 cm

b = 42.3 * sin(53°) ≈ 34.25 cm

By substituting the given values into the equations, we can determine that the length of AD (a) is approximately 25.75 cm, and the length of AB (b) is approximately 34.25 cm.

These calculations allow us to find the side lengths of the rectangle based on the given information about the diagonal length and angle. Understanding trigonometric relationships enables us to solve geometric problems involving angles, sides, and diagonals in various shapes and configurations.

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Answer:

i think the answer is 20.25

Step-by-step explanation:

The maximum height reached by the rocket is approximately 504.6 feet.

To find the maximum height reached by the rocket, we need to determine the vertex of the parabola represented by the given quadratic equation: y = -16x^2 + 180x + 63.

The x-coordinate of the vertex can be found using the formula x = -b / 2a, where a = -16 and b = 180.

x = -180 / (2 * -16) = 180 / 32 = 5.625

Now, we'll plug the x-coordinate back into the equation to find the y-coordinate (maximum height).

y = -16(5.625)^2 + 180(5.625) + 63

y ≈ 504.6

The maximum height reached by the rocket is approximately 504.6 feet.

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Answer:

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

Since CD is diameter, therefore the angle CAD opposite to it is a right angle.

We are given the lengths of two legs, AD = 16 and AC = 30.

Use Pythagorean theorem to find the length of the hypotenuse CD:

To determine how many containers of size 3.7 tons are needed to hold all the gravel from one truck, we need to first calculate how many tons of gravel are in one truck.

Since each truck holds 7.5 cubic yards of gravel, and the weight of one cubic yard of gravel is 1.48 tons, we can calculate the total weight of gravel in one truck as follows:

7.5 cubic yards x 1.48 tons per cubic yard = 11.1 tons

Therefore, each truck carries 11.1 tons of gravel.

To determine how many containers of size 3.7 tons are needed to hold all the gravel from one truck, we can divide the total weight of gravel in one truck by the capacity of each container:

11.1 tons ÷ 3.7 tons per container = 3 containers

Therefore, three containers of size 3.7 tons are needed to hold all the gravel from one truck.

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She will need 4 quarts of water.

Given Hannah decided to make finger gelatin for a huge children’s party. She had to make 8 packs of gelatin. Each pack needed 2 cups of water.

Since each pack of gelatin requires 2 cups of water, Hannah will need a total of:

8 packs x 2 cups/pack = 16 cups of water

To convert cups to quarts, we need to divide the number of cups by 4 (since there are 4 cups in a quart):

16 cups ÷ 4 cups/quart = 4 quarts

Therefore, Hannah will need 4 quarts of water to make 8 packs of finger gelatin for the children’s party.

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The equation for the direct variation is y = 2x. This the equation that directly relates y to x. The value of k is 2.

To know that y directly relates to x in a table, we need to check if y increases or decreases proportionally with x. In the given table, we can see that as x increases, y also increases. This indicates a direct relationship between x and y.

The constant of variation, k, can be determined by dividing any y value by its corresponding x value. Let's choose the first row of the table: y=4, x=2. Therefore, k = y/x = 4/2 = 2.

Now, we can write an equation for the direct variation: y = kx. Plugging in the value of k, we get y = 2x. This equation shows that y is directly proportional to x, with a constant of variation, k, equal to 2.

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Answer:

1/169

Step-by-step explanation:

Answer:

Step-by-step explanation:

Unfortunately, I cannot answer this question without additional information about the distances traveled and the time taken by Reiko to travel from point A to point B and back to point A.

The speed at which Reiko traveled is calculated as distance divided by time. Therefore, we need to know both the distance and time for each leg of the journey to determine the speed.

Without this information, it is not possible to determine whether Reiko traveled from A to B at a speed greater than 40 miles per hour.