The population of a town increased from 3750 in 2006 to 6150 in 2012. Find the absolute and relative (percent) increase.

The value of tan(t−π) is 4/9.

According to the statement

we have given that  tan(t)=4/9 and we have to find the value of tan(t−π).

So,

tan(t−π)  -(1)

take negative sign common from equation (1) it then

tan(t−π) = -tan(-t+π)

and we know that the according to the mathematics formula it become

tan(-t+π) is -tan t

then

tan(t−π) = -(-tan t)

it becomes

tan(t−π) = tan t

then its value becomes

tan(t−π) = tan(t)=4/9.

because we have given that the value of tan t is tan(t)=4/9.

So, The value of tan(t−π) is 4/9.

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The surface area of the shape is 168 square cm

The surface area of a figure is the area of the faces of the given figure.

For the given figure, the area will be the sum of area of 2 triangles and 3 rectangles.

Area = (6*3) +(10*6)+(6+10) +(10*3)

Surface area = 18 + 120 + 30

Surface area = 168 square cm

Hence the surface area of the shape is 168 square cm

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Answer:

2

Step-by-step explanation:

There are only 2 numbers in the final answer (6.0), so you just need 2 significant figures.

Congruency property relates to two or more triangles with similar dimensions, and internal angles. So that the required statements to complete the proof are:

1. definition of a straight angle.

2. subtraction property of equality

3. corresponding sides of similar triangles are proportional

4. transitive property of equality.

The intersection of two or more lines forms a number of angles which depends on the number of lines involved. These angles formed may have similar or different properties.

When two or more triangles have similar lengths of sides and measure internal angles, it can be said that they are congruent. Thus they have some common properties.

Therefore, the appropriate statements to answer the given question are stated below:

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There are four numbers of 3-coin combinations if we can choose from nickels, dimes, quarters, and half-dollars.

The coins to select from are nickels, dimes, quarters, and half-dollars;

Thus;

Coins (n) = 4

The number of coin to select is:

Coin (r) = 3

The coin combination is then calculated using:

Combination = ⁴C₃

Apply the combination formula, we have;

Combination = 4

Thus, there are four number 3-coin combinations if we can choose from nickels, dimes, quarters, and half-dollars.

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Answer:

12

Step-by-step explanation:

took the exam

The height of the actual house is 26'.26" .

A ratio indicates how many times one number contains another.

Therefore, the heights will form a similar length. Therefore, the corresponding length have the same ratios.

Therefore,

height of Kelly / x = height of Kelly shadows / height of house shadow

Hence,

where

x = actual height of the house

5.4 / x = 8.7 / 42.3

cross multiply

42.3 × 5.4 = 8.7x

Therefore,

228.42 = 8.7x

divide both sides by 8.7

228.42 / 8.7 = 8.7x / 8.7

x = 26.2551724138

Therefore, the height of the actual house is 26'.26"

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3 is the square root of nine.

The square root of a number is the factor that we can multiply by itself to get that number. The symbol for square root is \sqrt{ } ​square root of, end square root . Finding the square root of a number is the opposite of squaring a number.

To find the fraction square root, first, find the square root of the numerator and then find the square root of denominator. After finding the square root values, simplify the fraction. For example, √(4/16), can be written as √4/√16.

(3)^2 = 9

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The equation of parabola becomes y = -2/25(x-3)^2 + 4.

According to the statement

we have given a graph and from this graph we have to find the equation of parabola in the general form.

So,

we know that the equation of parabola in general form is

y = a(x-h)^2 +k - (1)

From the graph we have:

a point on the graph is (x,y) = (-2,2)

the vertex of the graph is (h,k) = (3,4)

Now, substitute these values in the equation number (1)

Then

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

2 = a(-2-3)^2 +4

2 = a(-5)^2 +4

2 = a(25) +4

25a = -2

a = -2/25.

Now put a = -2/25 and (h,k) = (3,4) in the equation(1).

Then

the equation of parabola becomes y = -2/25(x-3)^2 + 4

So, The equation of parabola becomes y = -2/25(x-3)^2 + 4.

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If Andy has 102 coins mixed with dimes and quarters and monetary value of $17.10 then he has 56 dimes and 42 quarters.

Given number of coins Andy has is 102 and montary value of all coins is $17.10.

We have to determine number of dimes and quarters.

1 dime=$0.10

1 quarter=$0.25

Suppose the number of dimes be x and number of quarters be y.

The equations are:

0.10x+0.25y=17.10------------1

x+y=102-------------2

from equation 2, y=102-x

Put the value of y=102-x in equation 1

0.10x+0.25(102-x)=17.10

0.10x+25.5-0.25x=17.10

-0.15x=17.10-25.5

-0.15x=-8.4

x=8.4/0.15

x=56

Put the value of x in y=102-x

y=102-56

y=46

Hence Andy has 56 number of dimes and 46 quarters.

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The system of equation which represent the scenario is;

x + y = 42

x + y = 420.13x + 0.18y = 6.66

let

x + y = 42

x + y = 420.13x + 0.18y = 6.66

Therefore, the equation which represent the problem is;

x + y = 42

0.13x + 0.18y = 6.66

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The limit of f(x) as it approaches -1 is given as 3/2

In mathematics and computation, the limit can be described to be the value that a sequence is going to approach in such a way that the input would approach or tend towards a given value

The unit is used to assign values to numbers at certain points where there are no defined values.

we have 3/x-1

We have to take the value of x here to be three as the equation tends to 1.

Then we apply it in the formula

3/3-1

= 3/2

Hence the limit of f(x) is given as 3/2

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Answer:

Step-by-step explanation:

let x = the number of votes of the first person

winner  = x + 4000

x+ x+4000 = 6000

2x=2000

x=1000

first person = x = 1000

winner  = x+4000 = 5000

The winner got 5000 votes

The length of an edge of a cube is 5 feet.

In Geometry, a Cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges.

Total surface area of a cube = 6[tex]l^{2}[/tex]

Given that,

Total surface area of a cube = 150 square feet

Total surface area of a cube = 6[tex]l^{2}[/tex]

[tex]\Rightarrow[/tex]                                  150 = 6[tex]l^{2}[/tex]

[tex]\Rightarrow[/tex]                                     [tex]l^{2}[/tex] =  [tex]\frac{150}{6}[/tex]

[tex]\Rightarrow[/tex]                                     [tex]l^{2}[/tex] = 25

[tex]\Rightarrow[/tex]                                    l [tex]=\sqrt{25}[/tex]

[tex]\Rightarrow[/tex]                                    l = 5 feet

Hence, the length of an edge of a cube is 5 feet.

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The preferred choice would be a line graph (drawn in the figure attached) for displaying the data.

Why a line graph is the preferred option here?

What is a line graph?

An individual data point is connected by a line in a line graph, sometimes referred to as a line plot or a line chart. A line graph shows numerical values over a predetermined period of time.

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The attached graph represents the scatter plot of the table of values

The table of values is given as:

Variable A 1 4 2 3 5 1 3 7 6 6 2 9 7 5 8

Variable B 6 6 1 6 7 4 4 7 5 3 5 25 21 4 4

Rewrite the table as:

x 1 4 2 3 5 1 3 7 6 6 2 9 7 5 8

y 6 6 1 6 7 4 4 7 5 3 5 25 21 4 4

Next, we plot the values on a graph

See attachment for the scatter plot

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Answer:

(a) $1.98

(b) $6.30

Step-by-step explanation:

(a)

The new value =

1.80 + The value of the percentage increase =

1.80 + (10% × 1.80) =

1.80 + 10% × 1.80 =

(1 + 10%) × 1.80 =

(100% + 10%) × 1.80 =

110% × 1.80 =

110 ÷ 100 × 1.80 =

110 × 1.80 ÷ 100 =

198 ÷ 100 =

1.98

Calculate the actual change (the absolute difference) between the two values

The actual change =

The new value - 1.80 =

1.98 - 1.80 =

0.18

Proof of calculation.

Calculate the percentage increased value...

... and see if we get as a result...

... the actual change (the absolute difference).

Calculate the percentage increased value:

The value of the percentage increase =

10% × 1.80 =

10 ÷ 100 × 1.80 =

10 × 1.80 ÷ 100 =

18 ÷ 100 =

0.18

So we have proven that the calculations are correct.

For positive numbers

The actual change =

The value of the percentage increase

The answer:

1.80 increased by 10% = 1.98

The actual change:

1.98 - 1.80 = 0.18

(b)

Calculate the New value
The new value =

42.0 + The value of the percentage increase =

4.20 + (50% × 4.20) =

4.20 + 50% × 4.20 =

(1 + 50%) × 4.20 =

(100% + 50%) × 4.20 =

150% × 4.20 =

150 ÷ 100 × 4.20 =

150 × 4.20 ÷ 100 =

63,000 ÷ 100 =

630

(but its as a dollar so its 6.30)

Calculate the actual change (the absolute difference) between the two values

The actual change =

The new value - 4.20 =

6.30 - 4.20 =

2.10

Proof of calculation.

Calculate the percentage increased value...

... and see if we get as a result...

... the actual change (the absolute difference).

Calculate the percentage increased value:

The value of the percentage increase =

50% × 4.20 =

50 ÷ 100 × 4.20 =

50 × 4.20 ÷ 100 =

21,000 ÷ 100 =

210

(but its as a dollar so its 2.10)

So we have proven that the calculations are correct.

For positive numbers

The actual change =

The value of the percentage increase

The answer:

4.20 increased by 50% = 6.30

The actual change:

6.30 - 4.20 = 2.10

Answer:

49°

Step-by-step explanation:

Right angled triangle:

This is a type of triangle with one of the angle as 90°

Sum of angles in a Right angled triangle is 90°

Therefore,

y + 41° = 90°

collecting like terms

y = 90 - 41 = 49°

Therefore,

y = 49°

The three stages that have to do with fluency, progression and automaticity are found in the Number Sense and Operations .

This is the part of mathematics that is known to teach the student basic ways to carry out number operations in mathematics. This has to do with representation of numbers as well as solving for the existing relationships in these numbers.

Having a sense of numbers is a very important ability skill that has to be developed early is students to enable them progress in the subject.

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The probability that Rita will need to pick at least five beads before she picks a gray bead from her collection is approximately (C) 0.45.

What is probability?

To find the probability that Rita will need to pick at least five beads before she picks a gray bead from her collection:

Therefore, the probability that Rita will need to pick at least five beads before she picks a gray bead from her collection is approximately (C) 0.45.

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The question you are looking for is given below.

Rita is making a beaded bracelet. She has a collection of 160 blue beads, 80 gray beads, and 240 pink beads. What is the estimated probability that Rita will need to pick at least five beads before she picks a gray bead from her collection?

(A) 0.05

(B) 0.10

(C) 0.45

(D) 0.55

The volume of the box without the lid is 500 cubic inches.

The capacity of an object is measured by its volume. For instance, a cup's capacity is stated to be 100 ml if it can hold 100 ml of water in its brim.

Another way to think of volume is as the amount of space a three-dimensional object takes up.

Calculation for the volume of the box-

The volume of a box without a lid is given by the formula v = 4x(10-x)².

Where,

'x' is a length in inches, and

'v' is the volume in cubic inches.

The volume when x = 5 inches.

Substitute the value of 'x' in the formula of volume;

v = 4×5(10-5)²

  = 20×5²

v  = 500

Therefore, the volume of a box without a lid is 500 cubic inches.

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Answer:

1

Step-by-step explanation:

The factor (x³ - 1) is not repeated.

Using it's concept, the probability that a randomly selected student is in music/drama is: 25%.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

Hence, in this problem, the probability will be found dividing the number of students that are in music or drama by the total number of students.

These data is given in a table, which is not given in this exercise. Researching this problem on the internet, we have that there are 20 + 7 + 3 + 20 + 13 + 2 + 25 + 5 + 5 = 100 students, of which 7 + 13 + 5 = 25 are in music/drama, hence the probability is:

P = 25/100 = 25%.

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The experimental probability of each event is as follows:

The experimental probability of an event is the ratio of the number of outcomes that favored the event to the total number of outcomes in the experiment.

In the question, we are given that Jake tossed a paper cup 50 times and recorded the position how it landed, which is shown in the table:

Open-sided up: 1

Closed side up 5

On the side: 44.

We are asked to determine the experimental probability of each outcome.

The number of outcomes, when the landing is open-sided up is 1.

The number of outcomes, when the landing is closed-sided up is 5.

The number of outcomes, when the landing is on the side up is 44.

The total number of times the experiment took place is 50.

Thus, the experimental probability of each event is as follows:

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Answer:

  (C)  0

Step-by-step explanation:

As always, the first step is to read and understand the question. You are asked to find the smallest number in the set {M₁, M₂, M₃}. Each of these values is defined to be the largest number in the corresponding sets S₁, S₂, S₃.

The numbers in each set are ordered smallest to largest, so the largest number in each set is the one on the right.

The largest number in S₁ is 8, so M₁ = 8.

The largest number in S₂ is 6, so M₂ = 6.

The largest number in S₃ is 0, so M₃ = 0.

This means the set M is ...

  M = {M₁, M₂, M₃} = {8, 6, 0}

The question asks for the smallest number in set M. Clearly, it is 0.

The smallest number in the set is 0.

Answer:

81

Step-by-step explanation:

A perfect square is multiplying a number with the same number in question. 81 is a perfect square because either 9 or -9 will go into it perfectly, like a square's length and height.

[tex]9^{2} = 81[/tex]

Answer: 81

Step-by-step explanation:

81 can be perfectly square rooted into 9. [tex]\sqrt{81}=9[/tex]