Solve the system of equations. 5x−4y=−10 -4x + 5y = 8

The probability of a person being randomly choosing having waiting time greater than 4.25 is 0.2917 or 29.17%.

To answer this question we need to know about-

Probability is the measure of the likelihood of an event to happen. The probability value ranges between 0 and 1.

When the probability value is 0, it means that the event is impossible to happen.

When the probability value is 1, it means that the event is certain to happen.

Uniform distribution is when the values of a probability distribution are spread uniformly across the interval, it is called a Uniform distribution

The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 6 minutes.

The probability that a randomly selected passenger has a waiting time greater than 4.25 minutes is found as follows:

Let X = Waiting time of a randomly selected passenger P(X > 4.25) = ?

Now we have to use the uniform distribution formula to find the probability:

P(C< X >D)=C-D/B-A

where C = lower value of the selected interval

           D= upper value of the selected interval

           B= highest value of the selected interval

           A= lowest value of the selected interval

putting above values in the formula -

P(X > 4.25) = 6 - 4.25/6-0= 0.2917

Hence the probability that a randomly selected passenger has a waiting time greater than 4.25 minutes is 0.2917.

Learn more about variance of uniform distribution : https://brainly.com/question/30639872

#SPJ11

Answer:

34 units

Step-by-step explanation:

Perimeter of ∆ABC is,

2(6+4+7)

= 2×(17)

= 34

Answered by GAUTHMATH

The total income and expenditure of Agri-small business limited in September is R 299596 and expenditure is R 193236.

Given that the expenses on petrol be R4850.00 at the end of September, balance is R 106360.00, usage on income of salaries be 25%, on electricity,rates and taxes be 11%, 42% of the remaining on insurance and investments.

We are required to find the total income and expenditure in September.

Generally the equation for insurance is mathematically given as :

Insurance=42% of the balance

Insurance=0.42*0.64A

Insurance=0.2688A.

Generally the equation for the total after all the other expenditures is mathematically given as:

Total expenditure after all other expenditures=0.64A-0.2688A

Total expenditures after all other expenditures=0.3712A.

Total expenditures after all other expenditures is as 111210 (106360+4850)

Equating both the equation and value:

111210=3712A

A=299596

The total income is 299596.

Therefore the calculation of expense is given as:

Expense=0.25A+0.11A+0.2688A+4850

Expense=0.6288A+4850

=0.6288*299596+4850

=193236

The expense is 193236.

Hence the total income and expenditure in September are "Income is R 299596 and expenditure is R 193236.

Learn more about income at https://brainly.com/question/25745683

#SPJ4

The total income and expenditure of Agri-small business limited in September is R 299596 and expenditure is R 193236.

We have to find the total income and expenditure in September.

The equation for insurance is mathematically given as :

Insurance = 42% of the balance

Insurance=0.42*0.64A

Insurance=0.2688A.

Total expenditure after all other expenditures = 0.64A-0.2688A

Total expenditures after all other expenditures = 0.3712A.

Total expenditures after all other expenditures is as 111210 (106360 +4850)

Equating both the equation and value:

111210 = 3712 A

A = 299596

Thus The total income is 299596.

Therefore the calculation of expense is given as:

Expense=0.25A+0.11A+0.2688A+4850

Expense=0.6288A+4850

=0.6288*299596+4850

=193236

The expense is 193236.

Hence, the total income and expenditure in September are "Income is R 299596 and expenditure is R 193236.

Learn more about income at;

brainly.com/question/25745683

#SPJ1

Part A  - The total cost of the   adjustable-rate mortgage is $483,582.34.

Part B  - The total cost   of the fixed-rate mortgage is  $ 561,486.27.

Part C  -  Advantages and disadvantages are given belwo.

Part A  -  I used a spreadsheet  to calculate the total cost of the adjustable-rate mortgage. The spreadsheet included the following columns  -

I calculated   the total payment   for each year by multiplying the monthly payment by 12.  I then totaled thepayments for each  year to get the total cost of the mortgage.

The total cost of the adjustable  rate mortgage is $483,582.34.

Part B  -  I also utilized a spreadsheet to compute the total cost of the fixed-rate mortgage. The spreadsheet included the following columns  -

Note that I calculated the  monthly payment for the fixed-rate mortgage by using the following formula  -

monthly payment = principal x  interest rate/ (1 - (1 + interest rate) ^ -term)

Thetotal cost of the fixed-rate mortgage is   $561,486.27.

Part C  -  The adjustable-rate mortgage has a lower initial monthly payment than the fixed-rate mortgage.

However, the adjustable  rate mortgage has the potential to become more expensive over time if the interest rates go up.

The advantages of the adjustable-rate mortgage are  -

Note that the disadvantages of the adjustable-rate mortgage are  -

The advantages of the fixed-rate mortgage are  -

The disadvantages of the fixed-rate mortgage are  -

Conclusievely, the best loan type for you will depend on your individual circumstances and risk tolerance.

Learn more about fixed mortgage at:

https://brainly.com/question/29351798

#SPJ4

Let's denote the ages of the two remaining men as x and x + 3 (since one is 3 years older than the other).

We know that the average age of 6 men is 35 years. So, the sum of their ages is 6 * 35 = 210 years.

We also know that the average age of four of them is 32 years. So, the sum of their ages is 4 * 32 = 128 years.

To find the sum of the ages of the two remaining men, we subtract the sum of the ages of the four men from the sum of the ages of all six men:

210 - 128 = 82 years.

Now, we can set up an equation to solve for the ages of the remaining two men:

x + (x + 3) = 82.

Combining like terms, we get:

2x + 3 = 82.

Subtracting 3 from both sides:

2x = 79.

Dividing both sides by 2:

x = 39.5.

So, one of the remaining men is 39.5 years old, and the other is 39.5 + 3 = 42.5 years old.

The score which is needed on the fourth test so that as average score of 90 is earned as required in the task content is; 93.

According to the task content, it follows that the score needed so that an average score of 90 is earned on all four tests is to be determined.

Since, The average is the ratio of the sum of all scores to the number of scores; we have;

90 = (88 + 92 + 87 + x)/4

Multiply both sides by 4 so that we have;

360 = 88 + 92 +87 + x

Isolate x on one side of the equation;

x = 360 -88 -92 - 87

x = 93.

Ultimately, The score which is needed on the fourth test so that as average score of 90 is earned as required in the task content is; 93.

Read more on average;

https://brainly.com/question/20118982

#SPJ1

Answer:

x=15

Step-by-step explanation:

\(\angle A+\angle B+\angle C=180^\circ\\(5x-27)^\circ+(7x-26)^\circ+[180^\circ-(10x-23)^\circ]=180^\circ\\12x-53+180-10x+23=180\\2x-30+180=180\\2x-30=0\\2x=30\\x=15\)

Answer:

x = 15.

Step-by-step explanation:

By the External angle of a triangle theorem:-

The external angle = the sum of the 2 opposite internal angles.

So:

10x - 23 = 7x - 26 + 5x - 27

10x - 7x - 5x = -27 - 26 + 23

-2x = -30

x = 15.

Answer:

Step-by-step explanation:

5p+10 equals big 5

Answer:

p = 0.8; q = 0,6

Step-by-step explanation:

5p + 10q = 10

2p - q = 1

5p + 10q = 10

q = 2p - 1

5p + 10 ( 2p - 1 ) = 10

5p + 20p - 10 = 10

25p = 20

p = 0,8

q = 2 x 0,8 - 1

q = 0,6

Answer: y = 5x + 26

Step-by-step explanation:

To find the equation of a line that is perpendicular to the given line y = -1/5x + 1 and passes through the point (-5, 1), we need to determine the slope of the perpendicular line. The given line has a slope of -1/5. Perpendicular lines have slopes that are negative reciprocals of each other. So, the slope of the perpendicular line will be the negative reciprocal of -1/5, which is 5/1 or simply 5. Now, we have the slope (m = 5) and a point (-5, 1) that the perpendicular line passes through.

We can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Substituting the values, we get:

y - 1 = 5(x - (-5))

Simplifying further:

y - 1 = 5(x + 5)

Expanding the brackets:

y - 1 = 5x + 25

Rearranging the equation to the slope-intercept form (y = mx + b):

y = 5x + 26

Therefore, the equation of the perpendicular line that passes through the point (-5, 1) is y = 5x + 26.

Answer:

Slope: -3/4

y-intercept: (0,-5)

Step-by-step explanation:

Hope it helps!

The dimensions of the rectangle are, length is 20 cm and the width is 12 cm.

What is an area?

Area is a mathematical concept that expresses the size of a region on a planar or curved surface. The area of an open surface or the boundary of a three-dimensional object is referred to as the surface area, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

Let

The width of the rectangle is x.

As length is 8km longer than than width.

So length = x + 8

The area of the rectangle is 240 sq - km

Since,

   Area of rectangle = length x width

                        240   = (x + 8) x x

                          240 = x^2 + 8x

         x^2 + 8x - 240 = 0

x^2 + 20x - 12x -240 = 0

x(x + 20) - 12(x + 20) = 0

          (x + 20)(x 2 12) = 0

⇒ (x + 20) = 0,     (x - 12) = 0

⇒   x = -20,           x = 12

Since, length is not negative.

So, x = 12

Hence, the width of the rectangle is 12 cm and the length of the rectangle is 12 + 8 = 20 cm.

To know more about the area, click on the link

https://brainly.com/question/25292087

#SPJ4

If r = 2 then substitute it for where r is in your given equation

New equation:

\(\dfrac{7(2)}{2}\)

\(\bf{7(2) = 14}\)

\(\dfrac{14}{2} = 7\)

\(\bf{Answer: 7}\) ☑️

Good luck on your assignment and enjoy your day!

\(\frak{LoveYourselfFirst:)}\)

Answer:

65

Step-by-step explanation:

The inside of a triangle is 180 degrees and the other two angles are the same so 50+65+65 =180. The answer is 65

If the area and width of the rectangle are 45x² − 42x − 48 and (5x − 8) then the length of the rectangle will be (3x + 2).

It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a rectangle, opposite sides are parallel and equal and each angle is 90 degrees. And its diagonals are also equal and intersect at the mid-point.

A rectangle has an area of 45x² − 42x − 48 and a width of 5x − 8.

Then the length of the rectangle will be

area = length × width

Then we have

Area = 45x² − 42x − 48

Then the factor of the polynomial will be

Area = (5x − 8)(3x + 2)

Then the length of the rectangle will be (3x + 2).

More about the rectangle link is given below.

https://brainly.com/question/10046743

Answer:

First blank is Dividend.
Second blank is Divisor
INCLUDED WHOLE PAGE!!
☆
EDGE2022; Good Luck :3!!!

The limit of \(L_n\) as n approaches infinity is 1/2, and it can be expressed as the definite integral of x from 0 to 1.

To express the limit of \(L_n\) as n approaches infinity as a definite integral, we can use the fact that the limit of a Riemann sum is equal to the corresponding definite integral. Thus, we can rewrite \(L_n\) as:

\(L_n\) = 1/n * (0 + 1 + 2 + ... + (n-1))

This is a Riemann sum for the integral:

\(\int\limits^1_0 {x} \, dx\)

with n subintervals of width 1/n. Therefore, we can write:

\(\lim_{n \to \infty} L_n = \lim_{n \to \infty} 1/n * (0 + 1 + 2 + ... + (n-1)) = \int\limits^1_0 {x} \, dx = [x^2/2] \ from \ 0 \ to \ 1 = 1/2\)

So, the limit of Ln as n approaches infinity is 1/2, and it can be expressed as the definite integral of x from 0 to 1.

To know more about definite integral refer here:

https://brainly.com/question/29974649

#SPJ11

A formula for calculating the area of a triangle is A=1/2(b*h), where b is the length of the base and h is the height  of or length of the altitude, of the triangle.

Identify the base and sketch in the height on each type of triangle.

right triangle - One of the sides that touches the 90-degree angle constitutes the foundation of a right triangle.

The height of a triangle is measured from its base to its highest point, and in a right triangle, that height can be determined from the side that forms a right angle to the base.

acute triangle - Three sides and three vertices make up the fundamental polygon known as the triangle. It has three sides, which results in three interior angles. An acute angle is one that is between 0° and 90° in length. When all three of the triangle's internal angles are acute, the triangle is said to be acute.

obtuse triangle - In an obtuse triangle, the height or altitude from the acute angles is outside the triangle. To find the height of the obtuse triangle, we extend the base as illustrated.

what is a triangle?

Three edges and three vertices make up a triangle, which is a polygon. It is among the fundamental shapes in geometry. Triangle ABC refers to a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear identify a distinct triangle and a distinct plane at the same time.

To learn more about triangles visit:

https://brainly.com/question/1058720

#SPJ13

Answer:

x = 16

Step-by-step explanation:

7x-15=97  ==> 7x-15 and 97 are congruent since they are both made from

                    both sides of a transversal(diagonal line) and are on opposite

                    sides of the straight line

7x-15+15=97+15  ==> add 15 on both sides to isolate x

7x = 112

x = 112/7  ==> simplify

x = 16

Answer:a= 3b/2 b =2a/3

Step-by-step explanation:

Answer:

The statement "(a) all whole numbers are rational numbers" is true.

Step-by-step explanation:

A rational number is the number which can be expressed in the from  of  \(\frac p q\), where p, q are integers and q\neq0.

(a.) As all the whole numbers (0,1,2,3...) can be expressed in the form of p/q having q=1.

Hence,  the statement "(a) all whole numbers are rational numbers" is true.

(b). As the rational numbers can have the fractional value but any integers don't have fractional value, so all the rational numbers are not integers.

Hence, the statement "(b). All rational numbers are integers" is not true.

(c). As the rational numbers can have the fractional value but any whole numbers don't have fractional value, so all the rational numbers are not whole numbers.

Hence, the statement "(c). All rational numbers are whole numbers." is not true.

(d). Integers( ...,-2,-1,0,1,2,...) can be negative, but the whole numbers (0,1,2,...) can't be negative. So, all integers can't be whole numbers.

Hence, the statement "(d). All integers are whole numbers" is not true.

Answer:

A

Step-by-step explanation:

Answer:

-4x^3 +x^2+4x-3

Step-by-step explanation:

Answer:

-4x³ + x² + 4x - 3

The percentage of the students who wore a silly hat is 64 %.

The percentage is defined as a ratio expressed as a fraction of 100.

We have been given that Last Tuesday was a silly hat day at Aaron's school. 64 students wore a silly hats and 36 students did not.

We have to determine the percentage of the students who wore a silly hat

The total number of students = 64 students wore silly hats and 36 students did not.

The total number of students = 64 + 36 = 100

We have to determine the percentage of the students who wore a silly hat

The percentage of the students wore a silly hat = (64/ 100) × 100

The percentage of the students wore a silly hat = 0.64 × 100

The percentage of the students wore a silly hat = 64 %

Thus, the percentage of students who wore silly hats is 64 %.

Learn more about percentage here:

brainly.com/question/24159063

#SPJ1

The volume of the cylinder with radius r = x - 3 and height h = 2x + 7 is given by the expression V = π ( 2x³ - 5x² - 24x + 63 )

A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder. The volume of a cylinder is

Volume of Cylinder = πr²h

Surface area of cylinder = 2πr ( r + h )

where r is the radius of the cylinder

h is the height of the cylinder

Given data ,

Let the volume of the cylinder be represented as V

Now , the radius of the cylinder r = ( x - 3 ) units

Let the height of the cylinder be h = ( 2x + 7 ) units

And , Volume of Cylinder = πr²h

On simplifying the equation , we get

Volume of Cylinder = π ( x - 3 )² ( 2x + 7 )

Volume of Cylinder = π ( x² - 6x + 9 ) ( 2x + 7 )

On further simplification , we get

Volume of Cylinder = π ( 2x³ - 5x² - 24x + 63 )

Hence , the expression for the cylinder is V = π ( 2x³ - 5x² - 24x + 63 )

To learn more about cylinder click :

https://brainly.com/question/16134180

#SPJ7

Answer:

D

since 45027/3 is is 15009 and 804597/3 is 268199

Answer: 80 dollars

Step-by-step explanation:

You can find a percentage with one of two ways.

For hundreds like this, oftentimes it's quicker and more simple to think of it as just 100. The proportion from 100 to 500 is just 5.  16% of 100 is 16. So, multiply 16 * 5. You would get 80.

The second method is you can use 0.16 * 500. It's the more conventional method, and you get 80, like the last method.

Answer:

√87 and √200

Step-by-step explanation: If a square root is not a perfect square, then it is considered an irrational number. These numbers cannot be written as a fraction because the decimal does not end (non-terminating) and does not repeat a pattern (non-repeating).

The keyword used to indicate that a field belongs to a class, and not an instance, is C) Static.

In object-oriented programming, the keyword "static" is used to define class-level variables or methods. When a field is declared as static, it means that it is shared among all instances of the class and belongs to the class itself, rather than to individual instances of the class.

By using the static keyword, the field or method can be accessed directly through the class without needing to create an instance of the class. This is useful when you want to have a variable or method that is common to all instances of the class and does not need to be replicated for each instance.

Static fields are often used for constants, counters, or shared data that needs to be accessed and modified by different instances of the class. They can be accessed using the class name followed by the dot operator, without creating an object of the class.

In summary, the static keyword is used to indicate that a field belongs to a class, not an instance, and can be accessed directly through the class name

Learn more about object-oriented programming here:

https://brainly.com/question/31741790

#SPJ11

Answer:

See below ~

Step-by-step explanation:

Question 1

The missing angles

⇒ The sides are equal

⇒ Angles are not 90°

⇒ It is a rhombus

Question 2

From the class of 28 students, 8 students are in the band and 20 students are not in the band.

Here, the total number of students in Mr Moffit's class = 28

Let us assume that t be the total number of students in the class,

n number of students are in the band,

and m number of students are not in the band.

2/7 of the students are in the band.

So, we get an equation:

n = 2/7 × t

n = 2/7 × 28

n = 2 × 4

n = 8

so, the number of students not in tha band:

m = t - n

m = 28 - 8

m = 20

Therefore, the number of students in the band = 8 and 20 students are not in the band.

Learn more about an equation here:

https://brainly.com/question/28243079

#SPJ4

The greatest ingredient by weight in juice B is sugar. As it is listed first, sugar is the major ingredient in juice B.

Juice B also has additional artificial colors and hydrogenated vegetable oil, which are not included in Juice A.The healthier choice between Juice A and Juice B is Juice A. This is due to the fact that Juice A has no sugar and no artificial colors or flavors, making it a more natural option.

Juice A only contains grape juice, grape juice concentrate, and ascorbic acid (vitamin C). Additionally, the vitamin C in Juice A, which is not present in Juice B, can help support the immune system and is a valuable nutrient for overall health.

Learn more about ingredients list at

https://brainly.com/question/14552098

#SPJ11

Answer:

1.31 meters

Step-by-step explanation:

Answer:

converting 1.4 m to cm = 140 cm. Since she grew 9 cm in the past therefore 140 - 9 = 131 cm. converting it back to m: 131 cm = 1.31 m.

Step-by-step explanation: