A set of sides that creates a right triangle has sides in a ratio of 5 : 12 :13. Find two different sets of sides in feet that would create a right triangle using this ratio.

The amount James have left after paying his debt in his profit is $32.50.

Blake, James and Staunton invested $9,000, $7,000, and $6,000, respectively. Their profits were to be divided according to the ratio of their investments.

James uses his share of the firm's profit of $825 to pay a personal debt of $230. The amount of money James have left can be calculated as follows;

The ratio of the investment is 9000: 7000 : 6000(9:7:6)

Hence,

James share of profit = 7 / 22 × 825

James share of profit = 5775 / 22

James share of profit = 262.5 dollars

Therefore,

amount he has left after paying his debt = 262.5 - 230

amount he has left after paying his debt = 32.50 dollars

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The given model predicts a relative minimum value for the depth in 2021 year.

The curve of a function has peaks and troughs called maxima and minima. A function may have any number of maxima and minima. Calculus allows us to determine any function's maximum and lowest values without ever consulting the function's graph.

The given equation is shown models the average depth y, in feet, of a lake, x years after 2016, where 0 < x < 6

y = x⁴- 9x³ + 24x²-31x + 66

From the attached graph it is noticed that the lowest point of the function is (4.441, 2.357), therefore the local minima is (4.441, 2.357).

So, x is years after 2016 is 4.441 which means this model predicts a relative minimum value for the depth in the 2021 year.

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The straight-line distance and the shortest distance between point X and point Y will be 2,260 m and 2,361.78, respectively.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

The distance between streets is around 80 m and the distance between avenues is around 260 m, as shown below.

The straight-line distance between point X and point Y will be given as,

⇒ (24 - 15) x 260 + (9 - 5) x 80

⇒ 2,340 + 320

⇒ 2,260 m

The shortest distance along the roads to get from point X to point Y will be given as,

D² = (2,340)² + (320)²

D² = 5,475,600 + 102,400

D² = 5,578,000

D = 2,361.78 meters

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The complete question is attached below.

Answer:

18°

Step-by-step explanation:

We know that, sum of the angles in a straight line are added up to 180°.

Accordingly,

[tex]x - 6 + 8x + 24 = 180[/tex]

Combine like terms.

[tex]9x + 18 =180[/tex]

Subtract 18 from both sides.

[tex]9x = 180 - 18 \\ 9x = 162[/tex]

Divide both sides by 9.

[tex]x = 18 \degree[/tex]

Answer:

x = 18

Step-by-step explanation:

The given angles are,

→ x - 6

→ 8x + 24

We generally know that,

→ Sum of angles in straight line is 180°.

Forming the equation,

→ (8x + 24) + (x - 6) = 180

Now required value of x will be,

→ (8x + 24) + (x - 6) = 180

→ 8x + 24 + x - 6 = 180

→ (8x + x) + (24 - 6) = 180

→ 9x + 18 = 180

→ 9x = 180 - 18

→ 9x = 162

→ x = 162 ÷ 9

→ [ x = 18 ]

Therefore, the value of x is 18.

The price of an adult ticket is $8.

An algebraic expression is the combination of numbers and variables in expressing and solving a particular mathematical question.

Let x = price of an adult ticket

If an adult ticket costs $2 more than a child ticket, then

price of a child ticket = x - 2

If fair tickets for 2 adults and 3 children cost $34, then

2x + 3(x - 2) = 34

Simplify the equation and solve for the value of x.

2x + 3(x - 2) = 34

2x + 3x - 6 = 34

5x = 40

x = 8

price of an adult ticket = $8

price of a child ticket = x - 2 = $6

Hence, the price of each ticket is $8 and $6 for adult and child, respectively.

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These two perpendicular bisectors will meet at (1, 5, 1). These are the coordinates of the triangle's circumcenter.

the triangle's circle's center. It is the point where the "perpendicular bisectors," or lines parallel to the centre of both sides, cross.

The intersection of any two perpendicular bisectors of any two triangle sides is known as the circumcenter of a triangle ABC.

The equation y=1 is the perpendicular bisector of sides B(3,0) and C(3,2). Because AB's midpoint is at 3,1 and its slope is unknown. The perpendicular bisector has zero slope. The equation for such a line is y=y1.

The equation for the perpendicular bisector of A(0,0) and B is also x=1.5 (3,0). The reason is that AB has a midpoint of zero slope and (1.5,0). The perpendicular bisector's slope won't be clearly defined. The equation for such a line is x=x1.

These two perpendicular bisectors will meet at (1, 5, 1). These are the coordinates of the triangle's circumcenter.

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It is proved that f(g(x)) = g(f(x)) =  x , So f(x) and g(x) are inverses of one other

Function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.

We are given the function as;

f(x) = 5x + 2

g(x) = (x -2)/ 5

If two functions f(x)  and g(x) are inverses of each other, their compositions will equal

f(g(x)) = 5[ (x -2)/ 5] + 2

f(g(x)) = x - 2 + 2

f(g(x)) = x

Now,

g(f(x)) =  ((5x + 2) -2)/ 5

g(f(x)) =  (5x + 2 -2)/ 5

g(f(x)) =  x

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Answer:

4x = 20

Divide.

x = 20 / 4

x = 5

John has 5 cars

Answer: A.

Step-by-step explanation: Roberto has 4 times as many toy cars as John and Roberto has 20 toy cars so it is 4 x 20 = a

Answer:

To solve this problem, we can use the formula for the slope of a line: slope = (y2 - y1)/(x2 - x1).

Plugging in the given values, we get: slope = (9 - v)/(-4 - (-7)).

We can simplify this to: slope = (9 - v)/3.

Since the slope is given as 6, we can set this expression equal to 6 and solve for v:

6 = (9 - v)/3

Multiplying both sides by 3 gives us: 18 = 9 - v

Adding v to both sides gives us: 18 + v = 9

Subtracting 9 from both sides gives us: v = 9 - 18

Finally, we can simplify this to: v = -9

So the value of v is -9.

Answer:

-9

Step-by-step explanation:

(9 - v)/(-4+7)= 6

9 - v = 18

-v = 9

v = -9

Answer:

5x

Step-by-step explanation:

The word "product" is used for multiplication.

The sum of the given expression is [tex]\dfrac{(-7x - 45)}{(x - 3)(x + 3)(x - 2)}[/tex].

To find the sum of the given expression, we can simplify and combine the fractions with the same denominator. Let's break it down step by step:

When used to indicate a mathematical computation or connection, numbers, variables, operators, and mathematical symbols are called expressions. It might include variables, constants, addition, subtraction, multiplication, division, exponentiation, and other mathematical operations.

The expression is:

[tex]\dfrac{3}{(x^2 - 9)} + \dfrac{5}{(x + 3)} - \dfrac{8}{(x^2 + x - 6)} - \dfrac{(5x - 12)}{(x - 3)} - \dfrac{5x}{(x + 3)(x - 3)}[/tex]

First, let's simplify the denominators:

[tex]x^2 - 9 = (x - 3)(x + 3)\\x^2 + x - 6 = (x - 2)(x + 3)[/tex]

Rewrite the expression with the simplified denominators:

[tex]\dfrac{3}{(x - 3)(x + 3)} + \dfrac{5}{(x + 3)} - \dfrac{8}{(x - 2)(x + 3)} - \dfrac{(5x - 12)}{(x - 3)} - \dfrac{5x}{(x + 3)(x - 3)}[/tex]

Combine the fractions with the same denominator:

[tex]\dfrac{((3x - 6) + (5x - 15) - (8x - 24) - (5x^2 - 12x + 15x - 36) - (5x^2 - 10x))}{((x - 3)(x + 3)(x - 2))}[/tex]

Simplifying further,

[tex]\dfrac{(-7x - 45)}{(x - 3)(x + 3)(x - 2)}[/tex]

Therefore, the sum of the given expression is [tex]\dfrac{(-7x - 45)}{(x - 3)(x + 3)(x - 2)}[/tex].

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For y = the number of kings drawn,  y a binomial variable

In this question we have been given that in a game involving a standard deck of 52 playing cards, an individual randomly draws 7 cards without replacement.

Also, y represents the number of kings drawn

We need to determine whether y a binomial variable or not.

y = "number of kings drawn"

We know that in the standard deck of 52 playing cards there are 4  King cards(each from the 4 suits:; Diamonds, Clubs, Hearts, Spades)

If we draw 7 cards from a standard deck of 52 playing cards, there would be 5 possible values of y.

y = 0     (there would be no king card)

y = 1      (there would be 1 king card)

y = 2     (there would be 2 king cards)

y = 3     (there would be 3 king cards)

y = 4     (there would be 4 king cards)

We know that a binomial variable is a variable that represents two outcomes.

Assume that x = "drawing a king" 7 times, then x is a binomial variable, because it has two outcomes, or you draw a king, or you don't.

Also, as we know a binomial variable can also represent the number of outcomes of each type for several events.

Hence, y is a binomial variable.

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No, yyy is not a binomial variable. A binomial variable is a discrete random variable that follows a binomial distribution and has two possible outcomes - success and failure.

In this case, yyy is not a binary outcome, since it can take on any number from 0 to 777.

To calculate the probability of yyy, we can use the formula P(y) = (n! / ((n-y)!*y!)) * (p^y * (1-p)^(n-y)), where n is the total number of trials (in this case, 777), y is the number of successes (in this case, number of kings), and p is the probability of success (in this case, 4/52). Therefore, the probability of drawing yyy kings from 777 cards is:

P(y) = (777! / ((777-y)!*y!)) * ((4/52)^y * ((48/52)^(777-y))

For example, if y=3, then the probability of yyy is:

P(3) = (777! / (774!*3!)) * ((4/52)^3 * ((48/52)^(774))

= 0.00307%

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Answer:

34

Step-by-step explanation:

Each number is added to by a doubling sequence

4, 4+2=6, 6+4=10, 10+8=18, 18+16=34, 34+32=66

Answer: If the measure of interior angle of a regular polygon is 108°,then the number of sides are 5.

Step-by-step explanation:

Given:

108° equals one internal angle of a regular polygon.

The sum of an regular polygon's internal angles = (n - 2) 180°.

The interior angle of a regular polygon equals [(n - 2) 180°] divided by n.

By equating them, we obtain

108 = [(n - 2) × 180°]/n

By additional simplification

108n = 180n - 360

180n - 108n = 360

So we get

72n = 360

n = 5

Therefore, it is a pentagon, a polygon with five sides.

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Life expectancy in the U.S. is steadily increasing due to medical advancements and the increased awareness of maintaining a healthy lifestyle.  0.126 x + 76.74 less-than-or-equal-to 85.  Option A

Generally,  Based on an organism's birth year, present age, and other demographic parameters like sex, life expectancy is a statistical assessment of the typical amount of time that it is predicted to live. Life expectancy at birth, which has two definitions, is the most often used metric.

This inequality states that the life expectancy of women, modeled by the function W(x), is at least 85.

The less-than-or-equal-to symbol is used because the inequality is asking for the minimum birth year required to achieve a life expectancy of at least 85, which means that the value of the function can be equal to 85 as well as greater than 85.

The correct answer is A: 0.126 x + 76.74 less-than-or-equal-to 85.

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On solving the provide question we can say that - the equation, 40 = 10t - 5t^2 = > t^2 - 2t - 8 = 0

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

u+ 10m/s , a = -10 and s = -40m

-40 = 10t - 5t^2

t^2 - 2t - 8 = 0

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The required percentages are

There is no association between passing the exam and completing the exam review

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

The table of values

The required percentage can be calculated as

Percentage = (Pass the exam and complete the review)/Complete the review)

Using the table of values, we have

Percentage = 55%/65%

Evaluate

Percentage = 85%

Here, the required percentage can be calculated as

Percentage = (Pass the exam and did not complete the review)/Did not complete the review)

Using the table of values, we have

Percentage = 20%/35%

Evaluate

Percentage = 57%

From (a) and (b), we can see that

These percentages are above 50% and they represent opposite entities

This means that there is no association

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16) Yes because each probability is between 0 and 1 and sum of all probability equals 1 so option A . 17) (D)= 0.44  18)(C)=1.7            
    
A) yes because each probability is between 0 and 1 and sum of all probability equals 1.            

:   ( σ <p(x)<1 and  Σ p(x)=1)

17)  probability that random selected passenger car an highway contain 2 or more people is 0.44

(P(x≥ 2)=p(x=2)+p(x=3)+p(x=4)+p(x=5)
P(x≥ 2=0.44
OR P(x≥ 2)=1-p(x≥ 2)=1-p(x=1)=1-0.56
p(x≥ 2)=0.44

18) Mean number of people in passenger cars are

E(X)=Σxp(x)=(1*0.56)+(2*0.28)+(3*0.08)+(4*0.06)+(5*0.02)
E(X)=1.7                        


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The array depicted displays the division represented by the equation

20 ÷ 5 = 4

Division is one of the four basic mathematical operators other include

addition

subtraction and

multiplication

Multiplication is the inverse or opposite of division, this means that when reverting the process of division we et to multiplication

In the array the number to be divided is the counting the whole small boxes which is 20.

Division is used to group the numbers in groups of 4 showing 5 divisions in group of four

This may also be 4 divisions in group of 5

Mathematically this written as

20 / 5 = 4

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The unknown multiplier is 6, and the new values for the ingredients are: Flour: 6 cups, Sugar: 4 cups and Baking Soda: 6 teaspoons.

Ingredients are the components used in the production of food or other products.

To find the unknown multiplier in #2, we need to set up an equation with the original recipe and the new recipe.
Original Recipe: Flour: 3 cups, Sugar: 2 cups, Baking Soda: 1 teaspoon

New Recipe: Flour: 6 cups, Sugar: 4 cups, Baking Soda: x teaspoons

We can set up the equation 3/6 = 2/4 = 1/x.
To solve this equation, we can multiply each side of the equation by 6.
3 = 2 × 6 = 4 × 6 = x
Therefore, the unknown multiplier is 6, and the new values for the ingredients are: Flour: 6 cups, Sugar: 4 cups and Baking Soda: 6 teaspoons.

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Significant differences are NOT the result of chance but rather some systematic impact.

Significant difference means that the difference between two results is due to some systematic influence rather than chance. In this case, the difference between the two results is not due to randomness, but instead, due to an influence that is causing the difference between the two results. This influence could be a factor such as someone's age, gender, lifestyle, or other circumstances. In any case, the difference between the two results is not due to chance, but instead, due to a systematic influence. This is why it is important to consider the potential influences when conducting research, as these influences can impact the results of the study and should be taken into account when making conclusions.

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The cost of 1kg of carrot is $3.1 and 1kg radish is 1.6.

A set of two or more first-degree equations with two or more connected unknowns is known as a system of linear equations.

A system of equations is solved by determining the value of each unknown until the system's equations are all satisfied. That is, it is necessary to find the values of the unknowns so that, when substituted, they will produce the suggested solution in both equations.

Let x=cost of carrot

y= cost of radishes

1.5x+4y=14.80

2x+3y=12.50

Simultaneously solving gives

x=3.1

y=1.6

The cost of 1kg of carrot is $3.1 and 1kg radish is 1.6.

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The probability that a student is chosen randomly from the class plays basketball or baseball

10/13= 0.769.

Generally, The probability that a student chosen randomly from the class plays basketball is 16/26.

The probability that a student is chosen randomly from the class plays baseball is 9/26.

There are 5 students who play both basketball and baseball, so we need to subtract the probability that a student chosen randomly from the class plays both sports.

The probability that a student plays both sports is 5/26. The total probability that a student chosen randomly from the class plays either basketball or baseball is

16/26 + 9/26 - 5/26

= 20/26

= 10/13.

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The slope of the line that passes through the points (0, 3) and (5, 13) as required is; 2.

As evident in the task content, it follows that the slope of the line which passes through the points (0, 3) and (5, 13) is to be determined.

Since the slope of a line is given by the formula;

Slope, m = ( y₂ - y₁ ) / ( x₂ - x₁ ).

The slope of the line in discuss is therefore;

Slope, m = ( 13 - 3 ) / ( 5 - 0 )

m = 10 / 5

m = 2.

Ultimately, the slope of the line in discuss is; 2.

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The measure of each base angle of an isosceles triangle is is 65 degree.

In an isosceles triangle, the two base angles are congruent, or equal in measure. To find the measure of one of the base angles, we can use the fact that the measures of the angles in a triangle always add up to 180 degrees. This means that if we know the measure of the vertex angle, we can use this information to find the measures of the base angles.

we have an isosceles triangle with a vertex angle that measures 50 degrees. To find the measure of a base angle, we can use the following formula:

(180 - measure of vertex angle)/2 = measure of base angle

Plugging in the given value of 50 degrees for the measure of the vertex angle, we get:

(180 - 50)/2 = measure of base angle

Solving this equation, we find that the measure of a base angle is 65 degrees. Therefore, if the vertex angle of an isosceles triangle measures 50 degrees, the measure of a base angle is 65 degrees.

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Complete question:

What is the measure of one of the base angles in an isosceles triangle if the measure of the vertex angle is 50 degrees?

The base angle of an isosceles triangle measures 54°. 72 is the measure of its vertex angle

We know that the sum of all the angles of any triangle is 180

We have to use the above property in order to find the measurement of the vertex angle.

Now our triangle is isosceles , that is the two equal sides will be containing equal angle. One of them is given as 54

And hence the other will also be 54.

Let the vertex angle be x

180=54+54+×

180=108+×

x=180-108

x=72

Hence the vertex angle is 72

complete question is

The base angle of an isosceles triangle measures 54°. What is the measure of its vertex angle?

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The volume of the pool, if The depth of the pool is 10 feet, is 1040 cubic feet.

The capacity occupied by a three-dimensional solid shape is known as volume. It is difficult to visualize in any shape, yet it may be compared among shapes. For instance, a compass box has a larger volume than an eraser placed inside of it.

Given:

The depth of the pool is 10 feet,

Calculate the volume of the pool as shown below,

The volume of the pool = the Volume of a rectangular prism with dimensions 20ft. × 10ft. × 4ft. + volume of a rectangular prism has dimensions: 6ft. × 4ft. × 10ft.

The volume of the pool =  20 × 10 × 4 +  6 × 4 × 10

The volume of the pool = 200 × 4 + 24 × 10

The volume of the pool = 800 + 240

The volume of the pool = 1040

Thus, the volume of the pool is 1040 ft³.

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Answer:

9

Step-by-step explanation:

if you search it up you get the answer your looking for

The probability of rolling a number less than 2 and flipping tails as required is; 1/12.

It follows from the task content that one rolls a die and flips a coin.

It is noteworthy to know that the probability of rolling a number less than 2 from a six-sided die is; 1 / 6. since, only 1 is less than 2 on the face of the die.

Also, the probability of flipping a tail is; 1/2.

On this note, the combined probability of rolling a number less than 2 and a flipping tail is; 1/6 × 1/2 = 1 / 12.

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The evaluation of the equations in the questions are as follows;

10. The equation 18·y - 10 = 2 + 18·y has no solutions

11. x = 0

12. x = 20

13. The consecutive integers are -46 and -45

An equation is a statement which indicates the equivalence between two expressions.

10. 18·y - 10 = 2 + 18·y

18·y - 18·y - 10 + 10 = 2 + 18·y - 18·y + 10

0 = 12

The equation 18·y - 10 = 2 + 18·y is a contradiction with no solution.

11. 2·(6·x - 4) - 16x = 4·(3·x - 2)

2·(6·x - 4) - 16x = 12·x - 8 - 16·x = -8 - 4·x

4·(3·x - 2) = 12·x - 8

2·(6·x - 4) - 16x = -8 - 4·x = 4·(3·x - 2) = 12·x - 8 therefore

-8 - 4·x = 12·x - 8

16·x = 0

x = 0 ÷ 16 = 0

x = 0

12. (3/4)·x + 2 = (3/5)·x + 5

(3/4)·x + 2 - (3/5)·x  - 2 = (3/5)·x + 5 - (3/5)·x - 2

(3/4)·x - (3/5)·x = 5 - 2 = 3

(3/20)·x = 3

x = 3 × 20 ÷ 3 = 20

x = 20

13. The sum of the two integers = -91

Let a represent one of the integers, therefore, based on the details;

The other integer = a + 1

a + a + 1 = -91

2·a = -91 - 1 = -92

a = -92 ÷ 2 = -46

One of the integers, a = -46

The other integer, a + 1 = -46 + 1 = -45

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