A circle with center O has radius 25. Chord AB of length 30 and chord CD of length 14 intersect at point P . The distance between the midpoints of the two chords is 12. The quantity OP^2 can be represented as m/n, where and are relatively prime positive integers. Find the remainder when m+n is divided by 1000.

If the total study sessions for the night class were proportional to the morning class that is 25: 20 then night class have the actual amount 80% students

we can calculate 20/25 *100

and we obtain the actual amount  80%

If the total study sessions for the night class were proportional to the morning class is 25: 20 and 16: 22

What is a proportion simple definition?

the size, number, or amount of one thing or group as compared to the size, number, or amount of another. the proportion of boys to girls in our class is three to one. : a balanced or pleasing arrangement

Initially, the number of lectures is 3 while the number of fieldwork is 12. Furthermore, the class sessions increased to 18 and the number of fieldwork remains the same (i.e. 12). Therefore, the number of lectures will be 18 - 12 = 6. The percentage of the sessions that were  lectures will be:

(6/18)*100% = 33.3%

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The term 5 in 5x is known as the coefficient of the expression.

A coefficient is defined as a term or a number which is multiplied by a variable. This constant terms generally precedes the variable term.

A coefficient is a generally a multiplicative factor in a polynomial series, or in an  equation.

Expressions are mathematical statements which are composed of two terms in which at least one contain variables, numbers, or both. These terms are either numbers or variables or numbers and variables multiplying each other. These expressions are a combination of numbers with mathematical ,operators are used to separate them.

Eg, 2x - 90 =45

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Answer:

3

Step-by-step explanation:

Since [tex]\angle A \cong \angle A[/tex] by the reflexive property and [tex]\angle ABC \cong \angle ADE[/tex] since they are both right angles, [tex]\triangle ABC \sim \triangle ADE[/tex] by AA.

It follows that:

[tex]\frac{x}{9}=\frac{5}{9+6} \implies x=3[/tex]

No, 10 12 15 is not a Pythagorean triple. A Pythagorean triple is a set of three positive integers a, b, and c such that a^2 + b^2 = c^2.

To determine whether 10 12 15 is a Pythagorean triple, we need to calculate a^2 + b^2.

In this case, 10^2 + 12^2 = 100 + 144 = 244. Since 244 ≠ 15^2, 10 12 15 is not a Pythagorean triple. We can also confirm this by plugging 10, 12, and 15 into the Pythagorean Theorem, a^2 + b^2 = c^2.

10^2 + 12^2 = 100 + 144 = 244

244 ≠ 15^2

Therefore, 10 12 15 is not a Pythagorean triple.

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Equation that will determine the amount of last year’s budget

Two or more expressions with an Equal sign is called as Equation.

Given that a school plans to spend twice the amount it did last year on its winter dance , less the cost of the disco ball which was $150 since they have it from last year

A total of $1,500 is being spent this year.

We need to find the equation which determine the amount of last year’s budget

2a-150=1500

When a is the amount of last year’s budget

Hence, 2a-150=1500 is the equation that will determine the amount of last year’s budget

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Customers older than 45 years are 11 in number. This can be solved using stem-and-leaf plot.

A stem and leaf plot, often known as a stem plot, is a method for categorizing discrete or continuous data. Data are organized as they are gathered using a stem and leaf plot. A stem and leaf plot resembles a bar graph in appearance. As each integer throughout the database is divided into a stem and a leaf, thus the name fits.

The last digit of each data point serves as the "leaf" in a stem and leaf plot, which divides the data into numerical points (the leading digit or digits).

The stem and leaf plot represents the age of store patrons. The leaf represents the unit digit, while the stem stands for the tens digit. 45 is not taken into account because the question asks us to determine the percentage of consumers who are over 45.

Customers older than 45 years old include: 48, 50, 50, 51, 55, 56, 62, 64, 65, 65, 73.

So, there are a total of 11 clients.

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The complete question is as follows:

The stem-and-leaf plot shows the ages of customers who were interviewed in a survey by a store. How many customers were older than 45

The positive integers are 14, 15 and 16

An algebraic expression can be defined as an expression that is made up of coefficients, terms, variables, factors and constants.

From the given information, we have that;

Let the consecutive integers be;

x, x+ 1, x+ 2

This can be represented as;

(x+1)(x+2) = 8(x + x+ 2)

Now, expand the bracket

x² + 2x + x + 2 = 8(2x + 2)

x² + 3x + 2 = 16x + 16

collect like terms

x² + 3x - 16x + 2 - 16 = 0

Add or subtract like terms

x² - 13x - 14 = 0

Solve the quadratic equation

x² -14x + x - 14 = 0

factor in pairs

x(x- 14) + 1(x -14) = 0

Then,

x = -1

x = 14

Take 'x' as 14

smallest integer = 14

Median = 14 + 1 = 15

Largest integer = 16

Hence, the values are 14, 15 and 16

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We employ the following equation to get the normal monthly cost:

4m - 8 = 64

Regular monthly expenses amount to $18.

Irma paid for her cats' subscription in advance for a 4-month period.

She saved $8 overall when she utilized a one-time discount.

Irma totaled $64 in payment.

We must identify the equation that can be utilized to calculate m, the average monthly cost.

Let's use m to symbolize the normal monthly expenditure. She signed up for a subscription that would last for four months, thus the full price without the voucher is 4m.

When the coupon is used, the final price is (4m - $8), since she was given a $8 discount.

Irma paid a total of $64 according to the problem, thus we can create the following equation:

4m - $8 = $64

We must now solve for m in order to determine it. Isolating 4m on one side of the equation will be our first step.

4m = $64 + $8

4m = $72

Finally, divide both sides by 4 to solve for m:

m = $72 / 4

m = $18

So, the regular cost per month, m, is $18.

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The triangle of 12 units has a height of 10.39 units by Divide the result by the area (A) after first multiplying the base (b) by 1/2.

what is triangle ?

A triangle, which is a polygon, has three sides and three vertices. One of geometry's basic shapes is it. A triangle with the vertices A, B, and C is referred to as Triangle ABC. A unique plane and triangle are discovered in Euclidean geometry when the three points are not collinear. Having three sides and three corners, a triangle is a polygon. The triangle's corners are defined as where the three sides meet one another end to end. 180 degrees is the sum of the angles in a triangle.

given

Given, side length, a = 12 units.

the height of equilateral triangle, h = (a√3)/2.

Substituting the value of 'a',

h = (12√3)/2 = 6√3 =

10.39 units.

The triangle of 12 units has a height of 10.39 units by Divide the result by the area (A) after first multiplying the base (b) by 1/2.

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In a course of 12 weeks, Perry will be able to play a total of 25 pieces of the piano Leon.

A total of 18 pieces of piano are learnt by Perry in a course of 9 weeks.

By using simple algebra, we can find the number of pieces that will be played by Perry in one week,

So, we can write, The learing speed,

Number of piano pieces learnt = Weeks

19 pieces = 9 weeks

Learning speed = 19/9 Pieces per week

So, the number of pieces learnt in 12 weeks is,

Number of pieces learnt = 19/9 x 12

Number of pieces learnt = 25.22

Number of pieces learnt = 25

So, Perry will be able to play 25 pieces.

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Answer:

3 3/4 or 3 6/8

Step-by-step explanation:

hope this helps <3

For her research, a geneticist has to raise a stock of fruit flies. She presently has 200 fruit flies in stock;

The mathematical function she may use to calculate is given as

f(n)=log1.38(n/200)

Which function could she use to calculate, the number of days required for her stock to grow to n fruit flies?

Generally, the equation for the final value is mathematically given as

A=Ao(1+u)^t

Therefore

n=200(1+0.38)*t

log(1.38^t)=log(n/200)

t=log1.38(n/200)

In conclusion, The function she could use to calculate is

f(n)=log1.38(n/200)

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Answer:

4x-24

Step-by-step explanation:

assume x=Length

perimeter

= x+(x-12)+x+(x-12)

= x+x -12+x+x-12

=4x-24

Donald would need to use 5 levels of cubes, So to make p5 he would need 25-12 = 13 more cubes.

A pyramid is a structure with a square or triangular base and four triangular sides that meet at a point, called the apex. Pyramids were built by ancient civilizations, such as the Egyptians, as tombs for pharaohs and their queens.

In the context of building pyramids with wood cubes, it seems like "pyramid levels" refers to the layers of cubes used to construct the pyramid. Each level is a layer of cubes that sits on top of the previous one, and the number of cubes in each level increases as you move up the pyramid. For example, in the case of p4, the base level would use 1 cube, the next level would use 4 cubes, the next level would use 9 cubes, and so on. The top level, which forms the apex of the pyramid, would use the most cubes. So the pyramid levels refer to the different layers of the pyramid and the number of cubes used in each layer.

To make a pyramid labeled p5, Donald would need to use 5 levels of cubes.

Donald uses 1 cube for the base of p4, 4 cubes for the next layer, 9 cubes for the next, 16 cubes for the next and 25 cubes for the top level.

So to make p5 he would need 25-12 = 13 more cubes.

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It would change to about 9. 960 atmospheres

Following the Boyle's law of gases which states that the product of pressure and volume is exactly a constant for an ideal gas.

This is represented as;

PV = K

then,

P₁V₁ = P₂V₂

From the information given, we have that;

Now, substitute the values

8. 9(4. 7) = P₂(4. 2)

mulitply the values

41. 83 = P₂(4. 2)

Divide both sides by 4.2

P₂ = 9. 960 atmospheres

Hence, the value is 9. 960 atmospheres

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Answer:

45 degree

Step-by-step explanation:

45+45 90 +90 180

All triangles will have 180 degrees angle

A line which is confined between two endpoints is known as a line segment. In other words, we can say that a line segment is a portion of a line that is connected by two points.

The length of the line segment does not vary and the distance between them does not change. The units in which a line can be calculated in centimetres, millimetres, meters, inches, or feet.

The difference between a line segment and a line is that the line segment had two endpoints while the line extends indefinitely. When only one side of the line has an endpoint, it is called a ray or a half-open line segment.

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Answer:

35/4=8.75

Step-by-step explanation:

You and your 3 friends add up to 4 people so you do 35 divided by 4 and get 8.75

Answer:

Step-by-step explanation:

35/3 = p

p = 11.67 per person

Answer:

68

Step-by-step explanation:

25% of a number is 20, where the number is 80 because 25% times 4 is 100% and 20 times 4 is 80.

We can check by doing 60% of 80 to see if it is 48. Instead of 60%, we can do 10% of 80, which is 8. Since we divided by 6, we multiply 8 by 6 which is 48.

Since we know 80 is the number, we have to find 85% of 80. First, let's find 5% of 80, which is 4 since 4 x 20 is 80 and 5% x 20 is 100%. Now, 85 divided by 5 is 17, let's multiply 17 by 4 to get 85% of 80. 17 x 4 is 68 which is 85% of 80.

Answer: solving by forming simple algebra equation

Step-by-step explanation:

8x (x is the cost of 1 volleyball)
6y (y is the cost of 1 basketball)

We know that cost of 8 volleyballs is = cost of 6 basketballs
i.e. 8x = 6y

& total money spent to buy 8 volleyballs and 6 basketballs is $960
so we can write;
8x + 6y = 960
= (6y) + 6y = 960
= 12y = 960
= y or cost of 1 basketball is (960/12) = $80

& if we want to know the value of x (cost of 1 volleyball)
8x = 6y
= 8x = 6(80)
& x = 6(80/8)
      = 6 (10) = 60

so the cost of basketball is $80 & 1 volleyball is $60

Hope it helps :)

p.s. that the equation I formed were made as if I was making an assumption & the conditions were kept uniform from the beginning, this is very applicable in day to day scenario; for e.g. when you go out with you friends to eat and have to split the bill - this assumption and division is called algebra - so value this education!

Monomial, binomial, and trinomial expressions are all categorized by the number of terms they include.

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).

A polynomial with one term is called a monomial. A polynomial having two dissimilar terms is called a binomial. An algebraic expression having three terms is called a trinomial.

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The best estimate for 225% of 50 is (a) greater than O but less than 1. 50

The maximum likelihood method will be used to calculate the point estimate as follows:

T, note the total number of trials.

List the number of accomplishments, S.

MLE = S / T should be used. Your point estimate is the outcome. Prior to explaining a "formal" method of approximation by rounding each number in the calculation to one significant figure, students must first estimate the result of a computation, use a calculator to determine the precise result, then compare the two results. The most accurate estimate is a definite estimate, as it is created by estimating the individual expenses for the various aspects of the project and then combining them into one estimate. Typically, bottom-up estimates are classified under this heading.

The best estimate for 225% of 50 is

= (225*50)/100

= 11250/100

= 112.5

So that, The best estimate for 225% of 50 is (a) greater than O but less than 1. 50

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Therefore, Bob must pay $2530 in income tax for last year if Bob made 15,000 in taxable income last year.

The basis of an income tax system is referred to as taxable income. In other words, the amount of revenue that was subject to taxation.

Revenue is the entire amount of money made through the sale of products and services that are essential to the business's core activities.

The first $8000 of Bob's taxable income is taxed at 15%:

Tax on first $8000 = $8000 * 0.15 = $1200

The remaining $7000 of Bob's taxable income is taxed at 19%:

Tax on remaining income = $7000 * 0.19 = $1330

Total tax = $1200 + $1330 = $2530

So Bob must pay $2530 in income tax for last year.

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Amelie needed 335 cups of flour for the recipe.

Given data :

She is making 2 1/2 or 2.5 times the original recipe.

Cups in original recipe= 134 cups

cups Amelie will need= 2.5 × 134

                                     = 335 cups

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The information in a table shows that f(x) = 3(2)x  exponential function. An exponential function has the formula y = abx, wherein y and x are variables.

An exponential function is a mathematical function with the following formula: f (x) = 1 x. where an is a fixed sum that serves as the function's basis and x is a variable. The most frequent exponential-function base is the transcendent number e, or around 2.71828. Your function must be exponential if it has the equation y = a b x, or where are constant, a Zero and b > 0 and b 1. You always used functions to the power of 2 while solving quadratic equations. An exponential function's exponent is a variable.

Here,

given:

Using the table's (0, 3):

3 = ab° , a = 3

(2) and (12):

=>12 = ab²

=>12 = 3b²

=>b² = 4

=>b = 2

=>f(x) = 3(2)ˣ

The information in a table shows that the exponential function, f(x), equals 3(2)x.

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Elimination is a very easy method when it comes to solving simultaneous equations.

First, the best thing to do is bring the equations down to their lowest form. Try to remove the fractions in the co-efficient and have the equation in the standard form where every variable is expressed as individually as possible.

The next thing to do is to select a variable and manipulate the equations in such a way that the coefficients of that variable across all of the equations are the same. Here select any 2 equations to work on first if more than 2 are given

Now take one of the equations and multiply it by -1.

Add the equations up to eliminate the variable and derive the other variable(s)

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The initial amount is 610 and the growth factor is 7.54.

What is an exponential function?

An exponential function has the form f(x) = a*b^x, where a is the initial amount, also called the y-intercept, and b is the growth factor.

In the function f(X) = 610 • 7.54, the initial amount is a = 610, and the growth factor is b = 7.54.

Hence, the initial amount is 610 and the growth factor is 7.54.

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The initial amount is 610 and the growth factor is 7.54.

An exponential function has the form f(x) = a*b^x, where a is the initial amount, also called the y-intercept, and b is the growth factor.

A growth factor is a naturally occurring substance that stimulates a cell to grow, divide, and differentiate. Growth factors are typically proteins or peptides that bind to specific receptors on the surface of cells, triggering signaling pathways that lead to cell proliferation and survival.

In the function f(X) = 610 • 7.54, the initial amount is a = 610, and the growth factor is b = 7.54.

Hence, the initial amount is 610 and the growth factor is 7.54.

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The total amount of sales he must make should be of $20800.

Given is that a salesperson works 40 hours per week at a job where he has two options for being paid. Option A is an hourly wage of ​$26. Option B is a commission rate of 5​% on weekly sales

Assume that the amount of sales he needs to make is of ${x}. So, for same amount, we can write -

(26 x 40) = 5% of {x}

(26 x 40) = (5/100) x {x}

{x} = (26 x 40 x 100)/5

{x} = (26 x 40 x 20)

{x} = 26 x 800

{x} = 20800

Therefore, the total amount of sales he must make should be of $20800.

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