After a 66% increase your salary is now $75,000. What was your original salary?

I. The correct statement is: m<AOB = m<BOC

The measures of the angles are:

II. m<BOC = 53 degrees.

III. m<AOC = 106 degrees.

When a segment bisects an angle, it forms two equal angles. Therefore, we have following which explains how to find the measure of the given central angle.

I. <AOC is bisected by segment OB into: AOB and BOC, which are equal. Therefore:

m<AOB = m<BOC

II. m<AOB = 53 degrees, therefore,

m<BOC = 53 degrees.

III. m<AOC = 2(53)

m<AOC = 106 degrees.

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Answer:

181

Step-by-step explanation:

To simplify this expression, we need to apply the order of operations (PEMDAS):

First, we evaluate the expression inside the parentheses: 9 ÷ 3 = 3.

Then, we add 6 + 3 = 9.

Finally, we divide 1,629 by 9 to get the answer:

1,629 ÷ 9 = 181.

Therefore, 1,629 ÷ (6 + 9 ÷ 3) simplifies to 181.

For each relation, we would determine whether or not it is a function as follows;

Relation 1 is: B. not a function

Relation 2 is: B. not a function.

Relation 3 is: B. not a function

Relation 4 is: A. a function.

In Mathematics, a function is generally used for uniquely mapping an independent value (domain or input variable) to a dependent value (range or output variable).

This ultimately implies that, an independent value (domain) represents the value on the x-coordinate of a cartesian coordinate while a dependent value (range) represents the value on the y-coordinate of a cartesian coordinate.

Based on relations 1, 2, and 3, we can logically deduce that they do not represent a function because their independent value (domain) has more than one dependent value (range).

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Answer: I am in high school so this may not be the best answer, but I would say that eventually eye sight would simply become useless to the fish because they live in a cave and don’t really need to see, there for I would say that the second answer is correct.

The diagonal distance from the airplane to the runway is approximately 5230.8 ft.

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is used to solve problems related to measurements of angles and distances.

The angle of depression of 18° is the angle between the airplane's line of sight and the horizontal line representing the runway. We can label the altitude of the airplane as 1560 ft:

Now we can use trigonometry to find the diagonal distance from the airplane to the runway. In particular, we can use the tangent function:

tan(18°) = opposite / adjacent

In this case, the opposite side is the altitude of the airplane (1560 ft), and the adjacent side is the diagonal distance we're trying to find (x). Therefore:

tan(18°) = 1560 / x

To solve for x, we can multiply both sides by x and then divide both sides by tan(18°):

x = 1560 / tan(18°)

Using a calculator, we find that:

x ≈ 5230.8 ft

Therefore, the diagonal distance from the airplane to the runway is approximately 5230.8 ft.

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The total price of the sofa is £3000.

To calculate this, multiply the given amount by "0.2", which equals "20%".

[tex]2500*0.2=500[/tex]

[tex]2500+500=3000[/tex]

The total price of the sofa is £3000.

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

So if we want to add 20% of any amount to said amount, we may multiply it by (1+0.2), which equals "1.20", and it'll give us the result immediately:

[tex]2500*(1+0.2)\\ \\2500*1.2=3000[/tex]

Now, working on the opposite way, let's say we want to reduce that same number (2500) by 25%, maybe because there's a discount on the product. In that case, we must multiply by (1-0.25), which equals 0.75:

[tex]2500*(1-0.25)\\ \\2500*(0.75)=1875.[/tex]

Given :-

To Find:-

Solution:-

Here we are given that Ryan purchases a sofa for £2500 . In order to find the cost of sofa after VAT , find 20% of the price of the sofa,

20% of £2500

20/100 * £2500

£500

Now add this to the original price of the sofa,

£2500 + £500

£3000

Hence the cost of the sofa after VAT is £3000 .

Answer:

5 or -2

Step-by-step explanation:

|2x-3| can equal either (2x-3) or -(2x-3) thus

(2x-3) = 7

2x = 10

x = 5

-(2x-3) = 7

-2x = 4

x = -2

Answer: it’s 5 or -2, |2x-3| can equal either (2x-3) or -(2x-3) thus(2x-3) = 72x = 10x = 5-(2x-3) = 7-2x = 4x = -2

Step-by-step explanation: hope this helps0^0

The amount of coverage that you will have on the contents of your home would be = $68,750

The total amount of money that was insured for the house = $125,000

The percentage of insurance that was left for the contents of the house = 55% of insurance.

That is;

= 55/100 × $125,000

= 6875000/100

= $68,750.

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After 2.5 years the price of land and the price of house will be equal.

A quick and easy method of calculating the interest charge on a loan is called a Simple interest.

Given that;

A person purchases a piece of land in Rs.80, 00,000 in 2075 B.S.

And, At the same time of 2075 B.S. a house is constructed on a piece of land in Rs. 2,70,00,000.

Since, The price of land increases at the rate of 20% per annum.

Hence, We get;

A = 80,00,000 (1 + 20/100)ⁿ

And, The price of house depreciates at the rate 20% per annum.

Hence, We get;

A = 2,70,00,000 (1 - 20/100)ⁿ

Let after n years the price of land and the price of house will be equal.

Thus, We get;

80,00,000 (1 + 20/100)ⁿ =  2,70,00,000 (1 - 20/100)ⁿ

8 (120/100)ⁿ = 27 (80/100)ⁿ

8 (6/5)ⁿ = 27 (4/5)ⁿ

Take log both side,

log 8 + n (log 6 - log 5) = log 27 + n (log 4 - log 5)

0.9 + n × 0.8 = 1.4 + n × 0.6

0.9 + 0.8n = 1.4 + 0.6n

0.2n = 0.5

n = 2.5 years

Therefore, After 2.5 years the price of land and the price of house will be equal.

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Graph appears to intersect the X axis in between 20 and 22 and algebraically the estimate of zero is 21.

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

Given a linear function which represents the profit of Bethany, y after x hours of dog walking.

(a) From the graph, we have to estimate the zero.

The graph seems to intersect the X axis in between 20 and 22, approximately 21.

(b) To solve this algebraically, we have the profit function,

y = 23x - 480

When y = 0,

23x - 480 = 0

23x = 480

x = 20.87 ≈ 21

Hence the graphical method gives the same estimate as the algebraic method.

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The length of CF is solved to be 12

In the figure the value of CF is solved using the vertical angle theorem and sum of angles in a triangle

In triangle GBC

angle C = 180 - 90 - 45

angle C = 45

Using vertical angle theorem

angle DCB = angle DCF

Using trigonometry relation we have

cos 45 = CF / 12√2

CF = cos 45 * 12√2

CF = 12

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Answer: it will be square or rhombus

Step-by-step explanation:

I think the radius would be 2

Answer:

Determine Your Budget.

Check Your Credit.

View Multiple Rentals.

Consider Roommates.

Consider a Cosigner.

Gather Your References.

Check Out the Neighborhood.

Check All the Websites.

The probability that $xo$ is shorter than $xp,$ $xq,$ and $xr.$ is,

⇒ 1/3

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

Given that;

Let $pqr$ be an equilateral triangle, centered at $o$ a point $x$ is chosen at random inside the triangle.

Hence, The probability that $xo$ is shorter than $xp,$ $xq,$ and $xr.$ is,

⇒ 1/3

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Answer:

5:1

Step-by-step explanation:

d_a = 20

d_b = 5

Equation for the circumference of a circle:

C = pi*d

C_a = pi * d_a

C_a = pi*20

C_b = pi * d_b

C_b = pi * 5

Ratio of C_a to C_b = C_a/C_b

C_a/C_b = (pi * 20)/(pi * 4) = 5:1

Answer:picture is not clear on my side, please re-upload thx!

Step-by-step explanation:

Therefore, Yellow Trains make up 9.5% of the total modes of transportation in the table.

A percentage that corresponds to one tenth of an amount. One percent, represented by the symbol 1%, is equivalent to one hundredth of something; hence, 100 percent represents the complete object, and 200 percent represents twice the amount given.

According to the table:

The total number of Yellow Trains is 450.

The total number of all modes of transportation is 4730.

To calculate the percentage of the total that Yellow Trains make up, we can use the following formula:

percentage = (part/whole) x 100

Substituting the values we have:

percentage = (450/4730) x 100

percentage = 0.095 x 100

percentage = 9.5%

Therefore, Yellow Trains make up 9.5% of the total modes of transportation in the table.

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Point C is located at -1 3/8

Hope that helps!

Thus, the value of x is 1.

The description that will be used to break this problem is D description of a midpoint.

By description, a midpoint is a point on a line member that divides it into two equal corridor. thus, Y is the midpoint of XZ, which means that XY is equal in length to YZ.

Using the Member Addition hypothetical( A), we can write

XZ = XY YZ

Substituting the values given in the problem, we get

x- 2 = XY 2x 2

Simplifying this equation, we get

x- 2 = XY 2x 2

4x = 4

x = 1

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The current population of Algeria is 38 million

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

P = 38(1 + r)^t

In the initial year, we have

t = 0

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

P = 38(1 + r)^0

Evaluate

P = 38

Hence, the population is 38 million

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Answer:

Step-by-step explanation:

Let's begin by calculating Jim's total cost for creating one painting:

Cost of paint and canvas + Cost of brushes = $44 + $1 = $45

This means that Jim makes a profit of $45 - $45 = $0 per painting sold until he breaks even.

To determine how many paintings Jim needs to sell to break even, we can set up an equation:

Total Cost = Total Revenue

Let's say Jim sells x paintings. Then his total revenue would be:

Total Revenue = $45x

His total cost would be the cost of materials plus the cost of brushes multiplied by the number of paintings:

Total Cost = $45 + $1)x = $46x

Setting these equal, we get:

$46x = $45x

Solving for x, we get:

x = 45

So Jim needs to sell 45 paintings to break even.

Once he has sold 45 paintings, he will have earned:

Total Revenue = $45 x 45 = $2025

So Jim will have earned $2025 after selling 45 paintings.

Answer:

Step-by-step explanation:

To break even, Jim's total revenue from selling his paintings should be equal to his total cost of producing them, including the cost of materials and the cost of the brushes. Let's call the number of paintings he needs to sell to break even as "x".

The cost of producing each painting is $44 + $1 = $45.

The revenue from selling each painting is $45.

So, Jim's total revenue from selling x paintings would be:

Total revenue = Price per painting x Number of paintings sold

Total revenue = $45 x x

Total revenue = $45x

Jim's total cost of producing x paintings would be:

Total cost = Cost per painting x Number of paintings produced + Cost of brushes

Total cost = $45 x x + $1

Total cost = $45x + $1

For Jim to break even, his total revenue must equal his total cost:

Total revenue = Total cost

$45x = $45x + $1

Solving for x:

$45x - $45x = $1

0 = $1

This is a contradiction, meaning that the situation is impossible. It is impossible for Jim to break even by selling his paintings at the given prices. If he sells each painting at $45, which is the same price he paid to produce it, he will not make any profit. In fact, he will lose $1 for every painting he sells due to the cost of the brushes.

If Jim wants to break even or make a profit, he will need to increase the selling price of his paintings or find ways to reduce the cost of producing them.

Step-by-step explanation:

study by the University of London found that participants who multitasked during cognitive tasks, experienced an IQ score decline similar to those who have stayed up all night. Some of the multitasking men had their IQ drop 15 points, leaving them with the average IQ of an 8-year-old chil

The new account balance at the end of 2 years is $517.

Simple interest

5 yearsUsing this formula I= (P+r×t)

Where: I=Interest=?

P=Principal=$400

r=Interest rate=3.5%

t=Time=5 years

Hence: I= ($400×0.035 x 5) which makes I= $70

2 years

I=Interest=?

P=Principal=$470

r=Interest rate=5%

t=Time=2 years

I=($470+0.05×2) which makes I=$47

New balance:

New balance=$400+$70+$47

New balance=$517

Inconclusion the new account balance at the end of 2 years is $517.

Trigonometric functions have some interesting symmetry properties

If tan x= -2.5, then tan (-x)= 2.5 and If sin x= 0.4 then sin (-x)= -0.4

If cos x = 0.9 then cos (-x)= 0.9  If tan x = 1.5 then tan (pi+x)= -1.5

Trigonometric functions are mathematical functions that are widely used in various fields, including mathematics, physics, and engineering. The most commonly used trigonometric functions are sine, cosine, and tangent, which are abbreviated as sin, cos, and tan, respectively.

Trigonometric functions have some interesting symmetry properties. For example, the sine and tangent functions are odd functions, which means that sin(-x) = -sin(x) and tan(-x) = -tan(x). On the other hand, the cosine function is an even function, which means that cos(-x) = cos(x).

These symmetry properties have important implications in many applications of trigonometric functions. For example, if we know the value of sin(x), we can immediately determine the value of sin(-x) by using the odd symmetry property. Similarly, if we know the value of cos(x), we can determine the value of cos(-x) by using the even symmetry property.

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(b) The probability that the call is not for medical assistance = 0.37

(c) The probability that two successive calls will both be for medical assistance = 0.3969

(d) The probability that the first is for medical assistance and the second is not for medical assistance = 0.2331

(e) The probability that exactly one of the next two calls is going to be for medical assistance = 0.4662

The probability of an event is the proportion of favourable outcomes to all other possible outcomes. The symbol x can be used to denote how many successful outcomes there were in an experiment with 'n' outcomes. The formula below can be used to determine a given event's probability:

Probability (Event) = Positive Results/Total Results

                                 = x/n

Given P (call for medical assistance) = 0.63

This means that out of all incoming calls to the fire station, the probability that the call is for medical assistance is 0.63 or 63%. The complement of this event, which is the probability that an incoming call is NOT for medical assistance, is:

P (Not Medical Assistance) = 1 - P (Medical Assistance)

                                            = 1 - 0.63

                                            = 0.37

Now, assuming that successive calls are independent of one another, the probability that two successive calls will both be for medical assistance will be:

P (2 calls for medical assistance)

= 0.63 × 0.63

= 0.3969

The probability that the first is for medical assistance and the second is not for medical assistance will be:

P (1st for medical assistance × 2nd for not medical assistance)

= 0.63 × 0.37

= 0.2331

The probability that exactly one of the next two calls is going to be for medical assistance will be:

P (Exactly 1 call for medical assistance)

= (0.63×0.37) + (0.63×0.37)

= 0.2331 + 0.2331

= 0.4662

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A total of 23800 cubes can fit inside the box of the given dimensions.

The volume of a cube is given by -

Volume = a x a x a = a³

Given is that a box has a length of 10 inches, a width of 8[tex]\frac{3}{4}[/tex] inches, and a height of 4[tex]\frac{1}{4}[/tex] inches.

The volume of the box would be -

V = 10 x 8[tex]\frac{3}{4}[/tex] x 4[tex]\frac{1}{4}[/tex]

V = 10 x 35/4 x 17/4

V = 371.875 inches³

The volume of cube -

v = 1/4 x 1/4 x 1/4

v = 0.015625 inches³

Number of cubes that will fill the box would be -

n = V/v

n = 371.875/0.015625

n = 23800

Therefore, a total of 23800 cubes can fit inside the box of the given dimensions.

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This is consistent with the solutions for the equation [tex]x^{2}[/tex] - 6x + 5 = 0 being x = 1 and x = 5.

An equation is a mathematical statement that expresses the equality of two expressions. It consists of one or more terms, each of which contains one or more variables. The terms are separated by an equal sign (=) and are usually written in a standard form known as an algebraic equation. Equations can be used to model and solve problems in a wide variety of fields, from physics and chemistry to economics and finance.

The graph of the quadratic equation is a parabola that opens upward and intersects the x-axis at two points. The x-intercepts occur when the equation is equal to zero, so the x-intercepts for the equation [tex]x^{2}[/tex] - 6x + 5 = 0 are the solutions for x. These solutions are x = 1 and x = 5.

The graph of the quadratic equation also shows that the two solutions of the equation, x = 1 and x = 5, are the x-intercepts of the parabola. This means that when x equals 1 or 5, the equation is equal to zero, so the x-intercepts are the solutions of the equation. This is consistent with the solutions for the equation [tex]x^{2}[/tex] - 6x + 5 = 0 being x = 1 and x = 5.

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The area of a circle with a diameter of radius 14 inches is given as follows:

A = 153.86 inches².

The area of a circle of radius r is given by π multiplied by the radius squared, as follows:

A = πr².

The radius, representing the distance between the center and a point on the circumference of the circle, has the measure defined as half the diameter, hence it is given as follows:

r = 7 inches.

Hence the area of the circle with radius of 7 inches is given as follows:

A = 3.19 x 7²

A = 153.86 inches².

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The area of the blue-shaded region is 19.95 m²

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

Given that, a rectangle with length 14 m, and diagonal 15.5 m, a parallelogram has been cut out of it, we need to find the area remaining,

Using the Pythagoras theorem,

15.5² = 14²+w² [width]

w² = 240.25-196

w² = 44.25

w = 6.65

Therefore, the width of the rectangle is 6.65 m

That mean, the height of the parallelogram is 6.65 m,

The area of the blue-shaded region, is calculated by subtracting the area of the parallelogram by the area of the rectangle,

Area of the remaining region = 14×6.65-11×6.65

= 6.65(14-11) = 6.65×3

= 19.95 m²

Hence, the area of the blue-shaded region is 19.95 m²

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