how is evaluating an expression with fractions like evaluating an expression with whole numbers? how is it different?

If the caffeine in the body drops by 15% each hour then the equation for this problem is [tex]f(t) = 150\times (0.85)^{t}[/tex]  and the equation represents a exponential decay problem .

the amount of caffeine present in the cup of coffee (a) = 150 mg  ;

the percent drop in caffeine in body each hour (r) = 15% = 0.15  ;

Since the percent of caffeine is dropping in the body , the exponential decay function will be used to represent this situation ;

the exponential decay equation is written as : [tex]f(t) = a\times (1-r)^{t}[/tex] ;

substituting the given values of "a" and "r" in the equation ,

we get ;

⇒ [tex]f(t) = 150\times (1-0.15)^{t}[/tex]

⇒ [tex]f(t) = 150\times (0.85)^{t}[/tex]

Therefore , the exponential decay equation is [tex]f(t) = 150\times (0.85)^{t}[/tex] .

Learn more about Exponential Decay here

https://brainly.com/question/29239811

#SPJ4

There are 1001 different committees can be chosen.

The problem is asking how many different committees can be chosen or the number of ways to select 4 students out of a group of 14 without regard to order. This is a combinatorics problem, and it can be solved using the combination formula:

nCr = n!/(r!(n-r)!)

Where n is the total number of items to choose from (14 students in this case) and r is the number of items to choose (4 students).

Plug in the values and solve.

14C4 = 14!/(4!(14-4)!)

14C4 = 14!/(4!10!)

14C4 = 1001

Therefore, the number of different committees that can be chosen is 1001.

Learn more about combinations here: https://brainly.com/question/12725706

#SPJ4

Answer:

1/2x-10

Step-by-step explanation:

[tex]\frac{1}{5} x+\frac{1}{2} (\frac{3}{5}) +\frac{1}{2}(-20)\\\frac{1}{5} x+\frac{3}{10} x-10\\\frac{1}{2} x-10\\[/tex]

Hope this helped! :)

Hey there!

1/5x + 1/2(3/5x - 20)

DISTRIBUTE 1/2 within the PARENTHESES:
= 1/5x + 1/2(3/5x) + 1/2(-20)

= 1/5x + 3/10x - 10

COMBINE the TERMS

= (1/5x + 3/10x) - (10)

= 1/5x + 3/10x - 10

= 1/2x - 10

Therefore, your should be:

1/2x - 10

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

The solutions to the given quadratic equation are 1/4 and -1.

The correct options are Options E and F.

          [tex]x = \frac{-b + \sqrt{b^{2} -4ac} }{2a}[/tex]  and [tex]x = \frac{-b - \sqrt{b^{2} -4ac} }{2a}[/tex]

Given equation :

4x² + 3x -1 = 0

Here,a = 4, b = 3, and c = -1.

[tex]x = \frac{-b + \sqrt{b^{2} -4ac} }{2a}[/tex]

The roots of the equation are:

[tex]x = \frac{-3 + \sqrt{3^{2} -4(4)(-1)} }{2(4)}[/tex] and  [tex]x = \frac{-3 - \sqrt{3^{2} -4(4)(-1)} }{2(4)}[/tex]

[tex]x = \frac{-3 + \sqrt{25} }{2(4)}[/tex]  and  [tex]x = \frac{-3 - \sqrt{25} }{2(4)}[/tex]

[tex]x = \frac{2}{8} = \frac{1}{4}[/tex]   and  [tex]x = \frac{-8}{8} = -1[/tex]

Hence the roots of the equation are 1/4 and -1.

To learn more about Quadratic Formula visit:

https://brainly.com/question/9300679

#SPJ1

To find the distance between two places, we can apply the distance formula d=((x2 - x1)² + (y2 - y1)²).

The distance of an object is its overall motion, regardless of direction.

Distance is the amount of space that an object has covered, regardless of where it began or concluded.

By understanding how far an object is from us, we may calculate its actual size.

It is possible to calculate the area that an object takes up in the sky.

The actual size of an object can then be determined by taking into account its distance.

The further away something is, the smaller it appears.

The distance between two locations on a plane is the length of the line segment connecting them.

The formula d=((x2 - x1)² + (y2 - y1)²) is frequently used to calculate the separation between two points.

Therefore, to find the distance between two places, we can apply the distance formula d=((x2 - x1)² + (y2 - y1)²).

Know more about the distance here:

brainly.com/question/26550516

#SPJ4

The total distance cover by Sagar is, 15 km 385 m.

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

We have to given that;

To reach the Powai lake picnic spot from star apartments,

Sagar went 13 km 665m by bus ,1 km220 m by autorickshaw and 500 m by foot.

Now, Total distance cover by Sagar is,

⇒ 13 km 665 m + 1 km 220 m + 500 m

We know that;

1 km = 1000m

Hence, We get;

⇒ 13665 m + 1220 m + 500 m

⇒ 15,385 m

⇒ 15 km 385 m

Thus, The total distance cover by Sagar = 15 km 385 m.

Learn more about the addition visit:

https://brainly.com/question/25421984

#SPJ1

The area of triangle OPQ is 44 square units.

How to find the area of tringle?

There are different ways to find the area of a triangle, depending on the information given. Here are a few common methods:

There are different methods to find the area of a triangle, but one common method is to use the coordinates of its vertices and the distance formula. The distance formula is

d = √((x2-x1)^2 + (y2-y1)^2)

We can use the distance formula to find the lengths of the sides of the triangle OPQ, which are:

OP = √((8-3)^2 + (3-4)^2) = √((5)^2 + (-1)^2) = √(25+1) = √26

OQ = √((4-3)^2 + (8-4)^2) = √((1)^2 + (4)^2) = √(1+16) = √17

PQ = √((4-8)^2 + (8-3)^2) = √((-4)^2 + (5)^2) = √(16+25) = √41

Once we have the lengths of the sides of the triangle, we can use the Heron's formula to find its area:

s = (OP + OQ + PQ)/2

Area = √(s(s-OP)(s-OQ)(s-PQ))

s = (√26 + √17 + √41)/2 = (√44)/2 = 4√11

Area = √(4√11(4√11-√26)(4√11-√17)(4√11-√41))

Area = √(4√11 * √(44-26) * √(44-17) * √(44-41))

Area = √(4√11 * √18 * √27 * √3)

Area = √(4√11 * 3√2 * 3√3 * √3)

Area = 4*11 = 44 square units

Hence, the area of triangle OPQ is 44 square units.

To learn more about Area of triangle, Visit

https://brainly.com/question/17335144

#SPJ1

The value on simplifying the fraction expression 5/6 - 7/12 is obtained as 1/4.

What is a fraction?

In mathematics, a fraction is represented by a number that identifies a portion of a whole. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object.

The fraction expression is given as 5/6 - 7/12.

5/6 - 7/12

First take the LCM of the denominator -

LCM = 12

Now, multiply 2 by 5 in first fraction numerator, as 6 multiplied by 2 is 12 (LCM) -

10/12 - 7/12

Now, use the arithmetic operation of subtraction -

(10 - 7)/12

3/12

Divide numerator and denominator by 3 -

1/4

Therefore, the final value as a fraction is obtained as 1/4.

To learn more about fraction from the given link

https://brainly.com/question/28699958

#SPJ1

The additive inverse of a complex number is the opposite of the complex number. The complex conjugate of a complex number is which is the real part plus the opposite of the imaginary part of the complex number.

The additive inverse of a number is its opposite number. If a number is added to its additive inverse, the sum of both numbers becomes zero.

When the sum of two real numbers is zero, then each real number is said to be the additive inverse of the other. So, we have R + (-R) = 0, where R is a real number.

A complex conjugate of a complex number is another complex number whose real part is the same as the original complex number and the magnitude of the imaginary part is the same with the opposite sign.

To know more about the difference between additive inverse and complex conjugate:

https://brainly.com/question/20013194

#SPJ4

The length of the yard as calculated from the given data is found out to be as 5 yards long.

let the length of the yard be , 27 - 9x

and the width of the yard is x.

Given , the are of the yard = 360.

Therefore, we can say that

=>x(27 - 9x) = 360

=>27x - 9x² = 360

=> 3x - x²  = 40

=> x²  - 3x + 40 = 0

=>x²  + 5x - 8x + 40 = 0

=> x ( x - 5) -8 ( x - 5 )

Therefore, the value of x will be 5 or 8.

On putting these values in the equation we get that , the length being 5 is the correct answer.

T learn more about length

brainly.com/question/29248993

#SPJ4

The solution to the system of equation 4y + x = 15 and x = 8y + 3 is (11, 1)

An equation shows the relationship between numbers and variables in an expression.

The standard form of a linear equation is:

Ax + By = C

Where A, B and C are constants

Given that:

4y + x = 15

multiply by 2:

8y + 2x = 30    (1)

Also:

x = 8y + 3

8y - x = -3     (2)

Subtract equation 2 from 1 to solve using elimination method:

3x = 33

x = 11

put x = 11 in equation 2:

8y - 11 = -3

y = 1

The solution is (11, 1)

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

The steps to convert the graph a quadratic equation in factored form is explained below.

Factored form in math is defined as the process of expressing a given number or algebraic expression as the product of its factors is called factoring.

Here we need to explain the process of graph a quadratic equation in factored form.

There are three ways are defined to convert them.

The very first way to When every term of the equation has GCD ≠ 0 then it can be factored by taking out GCD as a common factor.

the next way is to use the Identity that is a² - b² = (a + b) (a - b)

The last way is to use the Identity (x + a)(x + b)

To know more about equation here.

https://brainly.com/question/10413253

#SPJ4

The algebraic expression to represent how much time he has left to drive as function is given as f(g) = g - 21.

Given is that Greg will travel on his trip across the country to attend his cousin's wedding. The first day he travels 8 hours. The second day he travels 9 hours. The third day he had mechanical problems and only drove 4 hours.

We can write an algebraic expression to represent how much time he has left to drive as function f(g). We can write -

f(g) = g - (8 + 9 + 4)

f(g) = g - 21

Therefore, the algebraic expression to represent how much time he has left to drive as function is given as f(g) = g - 21.

To solve more questions on expressions, visit the link below -

brainly.com/question/1041084

#SPJ1

The introduction of harmful chemicals into the air is known as air pollution.

The chief causes of man-made air pollution include vehicle emissions, fuel oils and natural gas used to heat houses, byproducts of manufacturing and electricity generation, notably coal-fueled power plants, and odors from chemical manufacture.Industrial emissions, automobile emissions, and any other place where fossil fuels are burnt are all sources of atmospheric pollution, or air pollution. Another major contaminant that can cause ozone depletion is methane, which is released by landfills and cattle.

Air pollution can have long-term harmful consequences, such as acid rain, which pollutes the Earth’s bodies of water and ruins infrastructure.

To learn more about Air pollution to refer:

https://brainly.com/question/21683809

#SPJ1

If the factor distributes 5% of its profits as dividends among its 500 shareholders with an equal number of shares, the dividend per shareholder is Rs. 1,200.

Dividends refer to the profits declared for sharing among partners or more specifically among shareholders.

Dividends are a means for repaying shareholders for their shareholding interest in the company.

Companies declare dividends when sufficient profits are generated.

The profit per month = Rs 1,000,000

The total profit for the year = Rs 12,000,000 (Rs. 1,000,000 x 12)

Dividends payout = 5%

Dividends declared = Rs. 600,000 (Rs. 12,000,000 x 5%)

The number of shareholders with equal shares = 500

Dividends per shareholder = Rs. 1,200 (Rs. 600,000/500)

Thus, the dividends per shareholder is the quotient of the total dividends and the number of shareholders.

Learn more about dividends for shareholders at https://brainly.com/question/3161471

#SPJ1

The length of each leg, just divide the hypotenuse, 12 , by the square root of 2. Then to remove the radical from the denominator, multiply both numerator and denominator by square root of 2.

Find the length of each leg?

To learn more about length refers to:

https://brainly.com/question/16651806

#SPJ1

The answer is: Yes, Yes, Yes, No.

The expression -8 + 5 shows the sum of two integers. This expression has a value of -3. Because -3 is also an integer, the set of integers appears to be closed under addition.

The expression 9 − (-11) shows the difference between two integers. This expression has a value of 20. Because 20 is also an integer, the set of integers appears to be closed under subtraction.

The expression 3 · (-4) shows the product of two integers. This expression has a value of -12. Because -12 is an integer, the set of integers appears to be closed under multiplication.

The expression, -1 ÷ 6, shows the quotient of two integers. This expression has a value of -1/6, Because -1/6 is not an integer, the set of integers is not closed under division.

To know more about Athematic Oprations:

https://brainly.com/question/16738751

#SPJ4

The rule of the functions for the ordered pairs will be f(x) = (2/3)².

An ordered pair is made up of the ordinate and the abscissa of the x coordinate, with two values written in parentheses in a specific order. In order to understand a point visually, it can be helpful to locate it on the Cartesian plane. An ordered pair's numerical values may be fractions or integers.

Given that the ordered pairs are (1,2/3), (2,4/9),(3,8/27),(4,16/81) (5,32/243).

x          y

1        2/3        = (2/3)^1

2        4/9        = (2/3)^2

3        8/27      = (2/3)^3

4        16/81    = (2/3)^4

5        32/243  = (2/3)^5

Function rule is f(x) = (2/3)²

To know more about ordered pairs follow

https://brainly.com/question/11139505

#SPJ1

The solution for the system of equations is x = -6 and y = 8.

When an algebraic equation is graphed, it always results in a straight line since each term in a linear equation has an exponent of 1. For this reason, it is referred to as a "linear equation."

There are both one-variable and two-variable linear equations.

Given the equations,

-2x + 5y = 52

x + 4y = 26

solving by elimination method,

multiply by 2 in equation x + 4y = 26

= 2x + 8y = 52

now add both equations,

-2x + 5y + 2x + 8y = 52 + 52

13y = 104

y = 104/13

y = 8

substitute the value of y in equation x + 4y = 26

x + 4(8) = 26

x = 26 - 32

x = -6

Hence the solution of an equation is at x = -6 and y = 8.

Learn more about linear equations;

https://brainly.com/question/29739212

#SPJ1

Three cards are randomly selected from a standard deck of 52 cards. The probability that each card is a king (k) if the sampling is done without replacement is  1/5525

Probability measures the likelihood of the occurrence of an event. The probability is defined as:

p(A) = n(A) / n(S)

Where:

n(A) = number of possible ways an event A can happens

n(S) = number of possible outcomes.

In a standard deck, there are 4 kings. Hence,

1st draw, the probability it is a king = 4/52

Suppose, that the first card is a king, then the remaining kings are 3 and the remaining cards are 51.

Hence, at 2nd draw, the probability it is a king = 3/51.

Similarly, at 3rd draw, the probability it is a king = 2/50

The probability that each card is a king:

P (3 kings) = 4/52 x 3/51 x 2/50

                  = 24/13260

                  = 1/5525

Learn more about probability here:

https://brainly.com/question/251701

#SPJ4

Answer: Probability that she attended class regularly given that she receives A grade is 0.9286.

Step-by-step explanation: i looked it up man ‍♀️

The total of all the angles created on a transverse that are inside either of the two parallel lines is always 180 degrees.

Lines that are parallel to one another on a plane do not intersect or meet at any point. They are always equidistant from one another and parallel. Non-intersecting lines are parallel lines. Parallel lines can also be said to meet at infinity.

When a transversal intersects two parallel lines, the angles that are created inside are equal to the alternate pairings of that transversal. Alternate interior angles are what they are termed.

When a transversal intersects two parallel lines, co-interior angles result between the lines. On the same side of the transversal, the two angles always sum to 180 degrees.

To learn more about parallel lines link is here

brainly.com/question/16701300

#SPJ4

It is been proved that c(a+b) = ab.

Prove:-

c(a+b) = ab.

it is given that ∠ ABD = ∠ XYD = ∠ CDB = 90°

So, Lines AB, XY, and CD are parallel to Each other.

→ AB || XY || CD

Now In ΔABD, we have,

→ AB || XY

So,

→ DY/BD = c/a

→ DY = (c/a)*BD ----------------------- Equation (1)

In Δ BDC we have

→ CD || XY

So,

→ BY/BD = c/b

→ BY = (c/b)*BD ----------------------- Equation (2)

______________________

Adding Equation(1) and Equation(2) now, we get

→ DY + BY = (c/a)*BD + (c/b)*BD

taking (c * BD) common From LHS, we get,

→ BD = c * BD(1/a + 1/b)

BD will be canceled from both sides,

→ 1/c = 1/a + 1/b

→ 1/c = (a+b)/ab

→ c(a+b) = ab

Know more about Angles:

https://brainly.com/question/18922904

#SPJ4

The Question is incomplete although I've found a similar question of it.

: Picture attached:

The function that could be used to define and continue this function is f(n) = 1.25n -3

An arithmetic sequence is sequence of integers with its adjacent terms differing with one common difference.

Thus, the nth term of arithmetic sequence is given by:

Tₙ  = a + (n-1)d         (for all positive integer values of n)

where a is the first term, n is the number of term and d is common difference

d is the constant difference between each subsequent terms. That is:

d = -0.5 - (-1.75) = 1.25

Tₙ  = -1.75 + (n - 1)1.25

Tₙ  = -1.75 + 1.25n - 1.25

Tₙ  = 1.25n - 3

If we take Tₙ = f(n) , then the function that gives the nth term is:

is f(n) = 1.25n + 3

Learn more about arithmetic sequence on:

brainly.com/question/3702506

#SPJ1

For f(-7), it's 20. For determining x, it's 8.

For f(-7), plug-in -7 to x, and you get -3(-7), which is 21, and minus 1 is 20.

For determining x, plug in 8, you get -3(8), which is -24, minus 1 is -25.

Answer:

2790 ft²

Step-by-step explanation:

Area of rectangle with length L and width W:

area = LW

area = 45 ft × 62 ft

area = 2790 ft²

Answer:

4x²+4x+3

Step-by-step explanation:

g(f(x))= (2x+1)²+2

= 4x²+4x+1+2

=4x²+4x+3

Answer:12

Step-by-step explanation:

Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.

12

The polynomial 2x³ + x² -3x +14 must be added to (x³ + 3x -8) to obtain (3x³ + x² +6).

Quadratics are polynomial equations of the second degree, which means that they contain at least one squared term. Quadratic equations are another name for it. The general form of the quadratic equation is:  ax² + bx + c = 0,

where x is an unknown variable and a, b, c are numerical coefficients.

The polynomial equation whose highest degree is two is called a quadratic equation or sometimes just quadratics.

Let a polynomial P must be added.

Therefore, according to the question,

P+ (x³ + 3x -8) = (3x³ + x² +6)

=> P= (3x³ + x² +6) - (x³ + 3x -8)

=> P= (3-1)x³ + x² -3x +(6-(-8) )

=> P= 2x³ + x² -3x +14

Thus, the polynomial 2x³ + x² -3x +14 must be added to (x³ + 3x -8) to obtain (3x³ + x² +6).

To know more about quadratic equations visit: brainly.com/question/30098550

#SPJ4