The sum of two numbers is 50. the greater number is four less than five times the lesser number. Find the numbers

Answer:

Step-by-step explanation:

In 12 hours, the train will travel 487.5 miles

8/325=40.625

40.625 x 12 = 487.5

The third side of the triangle can be found out by using the Pythagoras theorem or the Heron's formula.

When there is a right angle triangle (A triangle whose on angle is of 90 degrees) then we use the Pythagoras theorem to find the third side.

The relation says that the sum of the square of the base and perpendicular is equal to the square of the hypotenuse.

In case of the scalene triangle the heron's formula is used to find out the value of the third side of the triangle.

There are several methods also present to find the value of the third side of the triangle.

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Answer:

Step-by-step explanation:

you have studied this in grade 8 grade 9 and grade 10 if you are studying under CBSE, so, better call textbook

The combined gas law for a gas is discussed below.

Given is the combined gas law.

The ideal combined gas law is given by →

PV = nRT

Where -

{P} = pressure     {T} = temperature     {V} = volume    

{n} = number of moles   {R} = gas constant

Non ideal gases are often modelled by the Van der Waals equation as →

(p + n²a/V²)(V - nb) = nRT

Where -

{a} and {b} = constants for a particular gas

{p} = pressure       {v} = volume    

{n} = number of moles       {t} = temperature  

{R} = gas constant

Therefore, the combined gas law for a gas is discussed above.

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Answer:

7.5 which rounds to 8

Step-by-step explanation:

2,722 divided by 360 equals 7.56

check if needed <3

The coefficient of expression 5x^2 in 5x^2 5x is 5.

The coefficient of 5x^2 in 5x^2 5x is the number that is multiplied with 5x^2. In this expression, the number multiplied with 5x^2 is 5, so the coefficient of 5x^2 is 5.

The expanded expression is 5x^2 5x = 5x^3 + 5x^2. The coefficient of 5x^2 in this expression is still 5.

The coefficient of 5x^2 in 5x^2 5x is the number that is multiplied with 5x^2. When we expand the expression 5x^2 5x, it becomes 5x^3 + 5x^2. The number that is multiplied with 5x^2 in this expression is still 5, so the coefficient of 5x^2 is 5.

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The value of P(X<Y) could be p(1−q) / p+q−pq if  X ∼ Geom(p) and Y ∼ Geom(r) are independent

What is probability ?

Probability could be defined as the ratio of number of favourable outcomes and total number of outcomes.

Given ,

X ∼ Geom(p) and Y ∼ Geom(r) are independent.

P(X<Y)=P(⋃1≤k<n,n∈N{X=k,Y=n})

=∑1≤k<n,n∈NP(X=k,Y=n)

=∑n=1∞∑k=1n−1P(X=k)P(Y=n)

=∑n=1∞∑k=1n−1p(1−p)k−1q(1−q)n−1

=pq∑n=1∞(1−q)n−11−(1−p)n−1p

=q∑n=1∞(1−q)n−1(1−(1−p)n−1)

=1−q / ∑n=1∞[(1−q)(1−p)]n−1

=1−q / 1−(1−p)(1−q)

=1−(1−p)(1−q)−q / 1−(1−p)(1−q)

=p(1−q) / p+q−pq.

Hence, The value of P(X<Y) could be p(1−q) / p+q−pq if  X ∼ Geom(p) and Y ∼ Geom(r) are independent.

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A traditional yearbook should have a few pages for the school's administrators, faculty, and other staff members, class or student portraits, several pages for clubs, teams, or other group photos, a section for special awards & superlatives, event pages typically with a collage of school events, and graduating class.

Despite possible differences in size and appearance, school yearbooks all have a similar structure and content makeup. A school yearbook is essentially a "memory book" that emphasizes the pupils, teachers, and activities that took place during the academic year.

Additionally, yearbooks give kids the chance to request the autographs of their friends and professors and give them a place to write personal notes, "inside jokes," and other remarks. Overall, a yearbook gives students a tangible memento of the academic year.

The only thing we are doing is dividing if we require that all of the rows be equal.

20/1= 20

20/2= 10

20/4=5

20/5=4

20/10=2

20/20=1.

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On solving the provided question, we can say that - the radicals are as follows be = 3x^2|y| sqrt(7x)  

The square root or nth root symbol is called a radical. Expressions with square roots are referred to as root expressions. A radical's radicand is a number or phrase that appears there. The radicals 7, 2y+1, and so on are examples. The following phrases can also be used to describe radicals: Radical equations are equations contained within of radicals. The term "root expression" refers to the expression found inside the square root. Examples of radical representations are the numbers 2, 372, 2x+7, and 41p.

here,

the radicals will be - 7xy ∛(xy^2)

and   3x^2|y| sqrt(7x)  

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We know that the derivative means the rate of change of the function. Graphically, this means that the derivative is the slope of the graph of that function.

The derivative of a function is the slope of the curve for the specified function. Physically speaking, the derivative of a function is the instantaneous rate of change of a function with respect to the variable at a location.

A securities with a price that is based on or derived from one or more underlying assets is referred to as a derivative. A contract between two or more parties based on the asset or assets constitutes the derivative itself. Changes in the underlying asset's value affect its value.

The instantaneous pace at which a function changes with regard to one of its variables is known as the derivative. Finding the slope of the tangent line to the function at a certain location is equal to doing this.

lim/h→0f(x+h)−f(x)h=f'(x).

lim/h→06−6/h=0.

f'(x)=limΔx→0

f'(x)=limΔx→0

f(x+Δx)−f(x)Δx=

f'(x)=limΔx→06−6Δx=0

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A graph of quadrilateral ABCD whose vertices are A (0, 0) B(5, 0), C(3, 2) and D (0, 2) is shown in the image attached below.

In Geometry, there are different types of quadrilateral and these include the following:

Next, we would use an online graphing calculator to construct (plot) quadrilateral ABCD on a cartesian coordinate based on the given vertices. Also, you should enter the value for each vertices of quadrilateral ABCD on the x-coordinate and y-coordinate respectively as shown in the table.

By critically observing the graph of quadrilateral ABCD, we can reasonably infer and logically deduce that it represents a trapezium.

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Answer: To convert 20% profit into a profit amount, you would multiply 20% by the revenue or cost of the item or service.

Let's say,

You have revenue of $1000

So,

20/100 * 1000 = $200

So the 20% profit on the revenue of $1000 is $200.

It's important to note that profit is the amount of money you make after you subtract your costs from your revenue. It's the amount you have left after all the expenses, taxes and other deductions are made.

Step-by-step explanation:

For the described situation, y  = 6sin ( (π / 10) x )  -  10 is the sine function.

The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths.

They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.

Asin(Bx)+C is the usual sine function formula.

A buoy bobs 6 meters up and down.

That is, the amplitude of the buoy shifts by 6 meters both vertically and horizontally.

A=6 Amplitude

The x-axis distance that constitutes one complete oscillation is known as the period.

We are aware that it takes a buoy 10 seconds to go from its greatest position to its lowest point (half oscillation).

20 seconds make up the complete oscillation period.

⇒ 20 (B) = 2π

B=2π /20

= π/ 10

Given that the buoy is 10 meters under the ocean's surface, C equals –10.

Using the formula's whole range of values:

⇒y  = 6sin ( (π/ 10) x )  -  10

The midline is the initial point.

x=0 is the first point.

⇒y=6sin(0)-10

y= -10

The line is drawn from the origin at y = -10.

Either the highest or smallest value is at the second point.

Therefore, (5,-4) and (15, -16.)

Therefore, for the described situation, y  = 6sin ( (π / 10) x )  -  10 is the sine function.

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Complete question:
At an ocean depth of 10 meters, a buoy bobs up and then down 6 meters from the ocean's depth. Ten seconds pass from the time the buoy is at its highest point to when it is at its lowest point. Assume at x = 0 the buoy is at normal ocean depth. Use the sine tool to graph the function. The first point must be on the midline and the second point must be a maximum or minimum value on the graph closest to the first point.

The most accurate value for AB is 37.699111843077516 (approximately)

The measure of an arc is directly related to the measure of the central angle that intercepts it. The measure of an arc is equal to the measure of its central angle, multiplied by the radius and divided by the degree of the circle.

Since, radius is not given let's assume it 20.

In this case, the central angle AOB has a measure of 110 degrees, and the radius of the circle is 20. Therefore, the measure of the arc AB is:

AB = (110/360) * 20 * 2 * π

or

AB = (110/360) * 20 * π

where π is the mathematical constant (approximately equal to 3.14).

So, the measure of the arc AB is (110/360) times the circumference of the circle, or (110/360) of the total length of the circumference.

The most accurate value for AB is 37.699111843077516 (approximately)

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The average rate of change of the function h(x) = -x² + 8x over the interval 0 ≤ x ≤ 5 is 3.

What is the average rate of change?

The Average Rate of Change function is defined as the average rate at which one quantity is changing with respect to something else changing. In simple terms, an average rate of change function is a process that calculates the amount of change in one item divided by the corresponding amount of change in another.

To find the average rate of change of a function over an interval, we need to find the difference in the function values at the endpoints of the interval, divided by the difference in the x-values of the endpoints.

In this case, the function is h(x) = -x² + 8x, the interval is 0 ≤ x ≤ 5, and we want to find the average rate of change over that interval.

So, we can use the following formula:

Average rate of change = (h(5) - h(0)) / (5 - 0)

Now we have to substitute the values into the equation:

h(5) = -5^2 + 85 = -25 + 40 = 15

h(0) = -0^2 + 80 = 0

Average rate of change = (15 - 0) / 5 = 3

Hence, The average rate of change of the function h(x) = -x² + 8x over the interval 0 ≤ x ≤ 5 is 3.

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Answer:

Step-by-step explanation:

3x=24

x=8

A polynomial of degree 4 is called bi-quadratic polynomial.

Bi-quadratic polynomial

A biquadratic equation is a polynomial equation with degree 4, and it strictly does not consist of any term with degrees 3 and 1.

Polynomial

A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division

Degree of polynomial

The degree of a polynomial is defined as the highest exponent of a monomial within a polynomial. Thus, a polynomial equation having one variable which has the largest exponent is called a degree of the polynomial.

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Sandra needs to score at least 87.67% to get an average score of 85%.

Let's look at the average formula in more detail in this part and use some examples to illustrate how it may be used. The following is an example of the average formula for a specific set of data or observations: Average = (Sum of Observations) ÷ (Total Numbers of Observations).

Given, Sandra has taken 3 Test this Quarter. She has scored an 78%, 76%, and a 93%.

Now as per the question she needs 85%.

The average of the 1st three tests is 78+76+93/3 = 247/3 = 82.33

Now to get 85%, we have to average out as 82.33+x/2 = 85

x+82.33 = 85*2 = 170

x = 170-82.33 = 87.67

Hence, Sandra needs to score at least 87.67% to get an average score of 85%.

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To prove a number is irrational we divide the integer by another integer is the decimal is non terminating and non repeating then it will be a irrational number .

What are Irrational Numbers ?

The Irrational numbers can be defined  a number that cannot be expressed as a fraction [tex]\frac{p}{q}[/tex] for any integers p and q.

The Irrational numbers have decimal expansions that do not terminate nor repeat (periodic) . Every transcendental number is an irrational number .

(i) To prove a number irrational  when we divide an integer by another integer, and  if decimal expansion does not terminate and do not  repeat then it is an irrational .

(ii) if the number cannot be expressed in the form of [tex]\frac{p}{q}[/tex] , then also the number will be called as irrational numbers .

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The maximum possible width of the box will be equivalent to

w = (V/302.4).

The volume of cuboid is given by -

V{C} = Length x Breadth x Height

Given is a piece of luggage has a height of 20.5 inches and a length of 14.75 inches.

We can write the volume of the box as -

V{b} = L x B x H

Assume the volume of the box is {V} cubic inches and its width be {w} inches. So, we can write the inequality as -

(20.5 x 14.75 x w) = V

w = (V/302.4)

Therefore, the maximum possible width of the box will be equivalent to

w = (V/302.4).

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Step-by-step explanation: To solve this equation, you'll need to use the order of operations to determine the correct sequence of steps to follow. The order of operations is a set of rules that specifies the order in which calculations should be performed in a math problem. It helps to prevent ambiguity and ensures that all calculations are performed consistently.Here is the order of operations:Perform any calculations inside parentheses or brackets first.Perform all multiplications and divisions, working from left to right.Perform all additions and subtractions, working from left to right.Using this order, we can solve the equation as follows:3.5 x 4 + 11 x 2.2 = 14 + 11 x 2.2

3.5 x 4 + 11 x 2.2 = 14 + 24.2

3.5 x 4 + 11 x 2.2 = 38.2Therefore, the solution to the equation is 38.2.

Using BODMAS,

B-Bracket

O-Of

D-Division

M-Multiplication

A-Addition

S-Subtraction

Multiplication comes first before addition, so

3.5×4=17

+

11×2.2=24.2

17+24.2=41.2

An equation for the number of points y, and the correct answers x  is y = 10x.

One mathematical expression makes up a term. It could be a single variable (a letter), a single number (negatively or positively), or a number of variables multiplied but just never added as well as subtracted.

For the stated question-

Consequently, the total points earned equal the total points earned for each question. number of questions with accurate responses.

Consequently, points earned = 10x

y = 10x.

First geography test: x = 3

y = 10*3 = 30

Second geography test: x = 7

y = 10*7 = 70

Thus, the graph for the enrique's first and second geography test is plotted.

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The correct question is-

Enrique earns 10 points for each question that he answers correctly on a geography test. Write an equation for the number of points, y Enrique scores on the test when he answers x questions correctly.

On his first geography test, Enrique answered 3 questions correctly. On his second test, Enrique answered 7 questions correctly.

Place points on the graph to show Enrique's first and second geography test.

Answer:

64?

Step-by-step explanation:

Basically the idea is we suppose the number she thinks of is "x"

She says that if she cube roots the number and then quadruples it (means multiply by 4 I think) she gets 16. We set this up as equation below:

[tex]4\sqrt[3]{x} = 16\\\sqrt[3]{x} = 4\\x = 4^{3}\\ x= 64[/tex]

This is my best guess, not totally sure sorry

The statistical model is not good, and this is true for a negatively skewed curve.

It is a statistical term implies that a curve is skewed at the left side.

In a statistical data for a certain distribution, we can get a negatively skewed curve when most of the data values are located on the right side of the distribution graph. The high concentration of values on the right side of distribution curve forms a long tail in the negative direction.

In general, negatively skewed curve is not good because it expresses the tendency of left tail events. Negatively skewed curves indicate a poor return from an investment. That means a person might be earn lower or no profit from his business. In case of an exam scores, negative skewed data value implies the question was too easy to perform better than usual.

In a word, left skewed or negatively skewed curve or data values inform us to be aware about the current statistical model and inspire us to take proper steps for wellbeing.

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The correct graph which represents the equation y = 1/2x - 1 is,

⇒ Graph of a line passing through the points negative 2 comma negative 2 and 0 comma negative 1.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The equation is,

⇒ y = 1/2x - 1

Now, After draw the equation we get;

Graph of a line passing through the points (-2, - 2) and (0, - 1).

Thus, The correct statement is,

⇒ Graph of a line passing through the points negative 2 comma negative 2 and 0 comma negative 1.

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She can knit total 8 pairs of identical mittens with a ball of yarn twelve inches in diameter

In the given question, Mrs. Read can knit one pair of children's mittens with a ball of yarn six inches in diameter.

We have to find how many pairs of identical mittens she can knit with a ball of yarn twelve inches in diameter.

The radius of a ball of yarn six inches in diameter is

r = 6/2 = 3 inches

The radius of a ball of yarn twelve inches in diameter is

r = 12/2 = 6 inches

Now, the volume of the six inches yarn = [tex]\frac{4}{3} \pi r^3[/tex]

The volume of the six inches yarn = [tex]\frac{4}{3} \pi (3)^3[/tex]

The volume of the six inches yarn = 36π

Now, the volume of the twelve inches yarn = [tex]\frac{4}{3} \pi r^3[/tex]

The volume of the twelve inches yarn = [tex]\frac{4}{3} \pi (6)^3[/tex]

The volume of the twelve inches yarn = 288π

Now we finding the numbers of pairs of identical mittens she can knit with a ball of yarn twelve inches in diameter

= 288π/36π

= 8

Hence, she can knit total 8 pairs of identical mittens with a ball of yarn twelve inches in diameter.

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The required function that gives [tex]f(g(x))[/tex] that represents the total amount of money Raul earned is

                [tex]f(g(x)) = 10x^{3}+16[/tex]

What is a function?

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

Mostly functions are written as f(x) where x is the input of the function.

Given,

[tex]f(x) = 2x^{2}+16[/tex]

[tex]g(x)[/tex] = [tex]\sqrt{5x^{3} }[/tex]

If [tex]f(x)[/tex] represents amount of money Raul earns per ticket and [tex]g(x)[/tex] represents number of tickets Raul sells per hour, where x is the number of hours he works, then,

[tex]f(g(x))[/tex] represents the total amount of money Raul earned in a day.

To find [tex]f(g(x))[/tex], substitute value of [tex]g(x)[/tex] in the place of x in function [tex]f(x)[/tex] .

[tex]f(g(x))[/tex] = [tex]f[/tex]([tex]\sqrt{5x^{3} }[/tex])

          = 2(    [tex]\sqrt{5x^{3} }[/tex])² +16

          = 10x³ + 16

Therefore the required function is [tex]f(g(x)) = 10x^{3}+16[/tex].

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The equation that is modeled to the situation is x - 2y + 2 = 0 and the slope of the line is 1/2.

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in determining if the lines are parallel, perpendicular, or none at all.      

The slope intercept form of a line is y = mx + c              

Where, c - y-intercept and m - the slope of the line

Given that

The cost of using the internet at an internet cafe is equal to a fee plus a certain rate per minute.

4 minutes of internet costs $ 3

8 minutes of internet costs $ 4  

[ We can represent the given situation as given below ]      

And the coordinates formed are (4, 3) and (8, 4)

The slope of the line formed = (4 - 3)/(8 - 4) = 1/4

Let y = mx + c be the equation to the model situation

=> y = (1/2)x + c

=> 2y = x + c ---- (1)

As we know (1) will pass through (4, 3)

=> 2(3) = 4 + c

=> 6 = 4 + c

=> c = 6 - 4

=> c = 2

=> 2y = x + 2

=> x - 2y + 2 = 0

Therefore,

The equation that is modeled to the situation is x - 2y + 2 = 0 and the slope of the line is 1/2.

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