How is the total price including sales tax calculated? a. (purchase price) times (percent sales tax); then added to original amount c. (purchase price) times (percent sales tax); then divided by the original amount b. (purchase price) times (percent sales tax); then subtracted from original amount d. (purchase price) times (percent sales tax); then multiplied by the original amount

Answer:

[tex](r \;\circ\;q)(4) = \boxed{5}\\\\(q \;\circ\;r)(4) = \boxed{13}\\[/tex]

Step-by-step explanation:

We have the following functions

[tex]q(x) = x^2+4\\\\and\\\\r(x) = \sqrt{x+5}\\\\[/tex]

1. To find
[tex](r \;\circ \;q)(4) = r(\;q(4)\;)[/tex]

First find
[tex]q(4) = 4^2 + 4 = 16 + 4 = 20[/tex]

Substitute this value for x in r(x)

[tex]r(20) = \sqrt{20 + 5} = \sqrt{25} = 5[/tex]

So
[tex]\bold{(r \;\circ \;q)(4) = 5}[/tex]

2. To find
[tex](q \;\circ\;r)(4) = q(\;r(4)\;)[/tex]

First find
[tex]r(4) = \sqrt{4 + 5} = \sqrt{9} = 3\\\\[/tex]

Substitute this value for x in q(x)

[tex]q(3) = 3^2 + 4 = 9 + 4 = 13\\\\\bold{(q \;\circ\;r)(4) = 13}[/tex]

The compositions of functions are:

Here we have the two functions:

q(x) = x² + 4

r(x)=  √(x + 5)

We want to find the two compositions:

(r o q)(4) = r(q(4))

First let's find:

q(4) = 4² + 4 = 16 + 4 = 20

Then:

r(q(4)) = r(20) =  √(20 + 5) = 5

And the other composition is:

(q o r)(4) = q(r(4))

First, r(4) = √(4 + 5) = 3

Then:

q(r(4)) = q(3) = 3² + 4 = 9 + 4 = 13

Learn more about compositions at:

https://brainly.com/question/10687170

#SPJ1

Since the sum of a triangle's internal angles is always 180 degrees, x has a value of 40 degrees.

The polygonal shape of a triangle has three edges and three angles. It is one of the most fundamental and significant geometric shapes and is utilised in a wide range of mathematical, scientific, and engineering fields. The edges and angles of a triangle can be used to classify it in various ways. Triangles can be categorised in one way by their sides: Three equal sides make up an equilateral triangle. Two of the edges of an isosceles triangle are equal. Three of the edges of a scalene triangle are unequal.

given

The property of angles in a triangle, which says that the sum of a triangle's interior angles is always 180 degrees, can be used to determine the value of x in the given figure.

Triangle ABC consists of:

∠A + ∠B + ∠C = 180

Since we know that A = 50 degrees and B = 90 degrees, we can use these numbers as a substitute:

50 + 90 + ∠C = 180

When we simplify the solution, we obtain:

140 + ∠C = 180

140 from both sides is subtracted, giving us:

∠C = 40

Since the sum of a triangle's internal angles is always 180 degrees, x has a value of 40 degrees.

To know more about triangle visit:

https://brainly.com/question/2773823

#SPJ1

Answer:

you go queen

Step-by-step explanation:

yas

The yield to maturity (YTM) of the bonds is 10.77%.

To calculate the yield to maturity (YTM), we need to use the following formula:

YTM = [(Annual Interest Payment + (Par Value - Market Price) / Years to Maturity) / (Par Value + Market Price) / 2] x 100%

Where:

Annual Interest Payment = Coupon rate x Par value

Par value = RM1,000

Market Price = RM980

Years to Maturity = 3

Coupon rate = 10%

First, let's calculate the annual interest payment:

Annual Interest Payment = Coupon rate x Par value = 10% x RM1,000 = RM100

Next, we can substitute the given values in the formula:

YTM = [(100 + (1,000 - 980) / 3) / (1,000 + 980) / 2] x 100%

YTM = 10.77%

Therefore, the yield to maturity (YTM) of the bonds is 10.77%.

Learn more about yield to maturity (YTM) on:

https://brainly.com/question/457082

#SPJ1

In response to the aforementioned query, we may say that The future interest value of the loan, or the total amount due after three months, is $8140.

By dividing the principal by the interest rate, the passage of time, and other factors, simple interest is determined. Simple return equals principle plus interest plus hours is the formula used in marketing. The easiest way to compute interest is by using this method. The most typical method for calculating interest is as a portion of the principle amount. For example, if he borrows $100 from a buddy and agrees to pay back the loan at 5% interest, he will only pay his share of the 100% interest. $100 (0.05) = $5. When you borrow money, you must pay interest, and you must charge interest when you lend it. Typically, interest is determined as an annual percentage of the loan total. The loan's interest is the name given to this percentage.

The following formula can be used to determine a loan's future value A:

[tex]A = P + Prt[/tex]

When P is the principal borrowed, r denotes the interest rate in decimal form, and t denotes the length of time in years.

P equals $8,000, r equals 0.07 (because the interest rate is specified as 7%), and t equals 3/12 to 0.25 years in this example (since the time period is given in months and we need to convert it to years).

With these values entered into the formula, we obtain:

[tex]A = $8000 + $80000.070.25\\A = $8000 + $140 \sA = $8140[/tex]

The future value of the loan, or the total amount due after three months, is $8140.

To know more about interest visit:

https://brainly.com/question/28792777

#SPJ1

Using the concept of rotational symmetry, the angle of rotation about the center that results in an image that matches the original figure is; Option A:  90

Rotational symmetry is defined as a process that requires the rotation of a given object about a reference point to produce its image which has the same characteristics. This tells us that its dimensions, measure of internal angles and size do not change except its orientation. The orientation depicts the way in which the object is positioned.

here, we have,

The sum of an angle formed at a point is 360 degrees.

Thus turning a given object about a point implies its rotation with respect to a measured  angle.

Thus in the diagram given in the question, the pattern shown divides the angle at the centered point into four equal parts.

Thus;

Angle of rotation = 360/4 = 90 degrees

Read more about rotational symmetry at; brainly.com/question/29977243

#SPJ1

Therefore , the solution of the given problem of  expressions comes out to be option C. 69x is the right response.

Calculations like multiplying, dividing, joining, and presently removing are required. If they were put together, it would say: An equation, some statistics, and a mathematical formula A statement of truth is composed of values, components, and mathematical processes like additions, subtractions, errors, subdivisions, and arithmetic formulas. Words and phrases can be evaluated and analysed.

Here,

The formula 21x + 19(2x) + 2(5x) can be made simpler as follows:

=> 21x + 38x + 10x = 69x

Maliq's total scores can therefore be written as 69x.

To determine which decision is equivalent to 69x, we can also look through the answer options.

A.

=> (21+19)2x + 10x = 40(2x) + 10x = 80x + 10x = 90x,

which is not equivalent to 69x..

B. 42x and 69x are not equal.

C. 69x is the same as 69x.

D. The sum of

=> (21+19+2)(x+2x+5x) = 42(8x) = 336x does not equal 69x.

Therefore, C. 69x is the right response.

To know more about expressions visit :-

brainly.com/question/14083225

#SPJ1

Answer:

Step-by-step explanation:

To solve this problem, we need to standardize the values using z-scores and then find the area under the standard normal distribution curve between those z-scores.

First, we need to find the z-scores for the values 3.2 and 6.2 using the formula:

z = (x - μ) / σ

where x is the value, μ is the mean, and σ is the standard deviation.

For x = 3.2:

z = (3.2 - 5.2) / 1 = -2

For x = 6.2:

z = (6.2 - 5.2) / 1 = 1

Next, we use a standard normal distribution table or calculator to find the area under the curve between these two z-scores. The area represents the probability of a randomly chosen Fluorescent lighbulb lifetime being between 3.2 and 6.2.

Using a standard normal distribution table, we can find that the area between z = -2 and z = 1 is approximately 0.8186.

Therefore, the probability that a randomly chosen Fluorescent lighbulb lifetime will be between 3.2 and 6.2 is approximately 0.8186 or 81.86%.

The sum of the first 30 consecutive whole numbers is 465.

What are consecutive numbers?

Consecutive numbers are numbers that follow each other in order without interruption, with a difference of 1 between each two adjacent numbers. For example, 3, 4, 5, 6, and 7 are consecutive numbers.

The formula n x (n+1)/2 is used to find the sum of the first n consecutive whole numbers because it provides a quick and efficient way to calculate the sum without having to add all the numbers individually.

To understand why the formula works, consider the sum of the first n numbers: 1 + 2 + 3 + ... + (n-1) + n. We can rewrite this sum in reverse order, starting with n and working down to 1: n + (n-1) + (n-2) + ... + 2 + 1.

If we add these two expressions together, we get:

(1 + n) + (2 + n-1) + (3 + n-2) + ... + (n-1 + 2) + (n + 1)

Notice that each pair of terms in parentheses adds up to n+1. There are n/2 pairs of terms, so the sum of the first n numbers is:

n/2 x (n+1)

Simplifying this expression gives the formula:

n x (n+1)/2

So to find the sum of the first 30 consecutive whole numbers, we can substitute n=30 into the formula:

30 x (30+1)/2 = 15 x 31 = 465

Therefore, the sum of the first 30 consecutive whole numbers is 465.

To learn more about Consecutive numbers from given link.

https://brainly.com/question/29775116

#SPJ1

274 students had not signed up for any of the three courses.

A counting method called the inclusion-exclusion principle is used to determine how many items there are in the union of two or more sets. The basic concept is to start by counting the components in each set, but we then need to adjust for any items that are in multiple sets. The number of elements in the intersection of any two sets must be subtracted in order to make this repair, and the items in the intersection of any three sets must be added back in. When it comes to combinatorics and probability theory counting difficulties, the inclusion-exclusion principle is a helpful tool.

The total number of students signed up for the course is:

73 + 54 + 34 = 161

This includes multiple courses together. To get the accurate number we subtract the number of students that signed up for 2 courses.

(17 + 9 + 9) + 4 = -22 + 4 = -18

The negative count means we have overcounted, so we need to subtract this number from the total number of surveyed students:

292 - 18 = 274

Hence, 274 students had not signed up for any of the three courses.

Learn more about probability here:

https://brainly.com/question/14210034

#SPJ1

The amount of water left in the cubical tank would be; 3040000 mm³

A cube is a three-dimensional representation of a square. it has 6 faces 2 on the bottom and top, 4 on the sides faces.

We know that Volume of a cube = a³ ; a = size of edge

Volume of cubical tank = 12³

= 1728 cm³

Now, Half filled cube = 1728 / 2

= 864 cm³

Volume is f rectangular tank :

V = length x width x height

V = 10 * 8 * 7 = 560 cm³

Volume of water left in cubical tank will be;

(864 - 560) = 304cm³

1cm³ = 1000mm³

Therefore,

304cm³ = 304 x 1000 = 3040000mm³

Learn more about cubes;

https://brainly.com/question/22940499

#SPJ9

The cost price of an item is the sum paid to acquire it or the cost at which it was produced. The cost price is denoted by the letter C.P. 

we made money when we sold a product we used the formula are :

we lose money while selling a product. we used formula are :

The profit (gain) percentage and selling price are :

The loss percentage and SP are :

Given:-

[tex] \: [/tex]

[tex] \: [/tex]

Solution:-

now , put the given values of x = -2 nd y = 5 in equation :

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

━━━━━━━━━━━━━━━━━━━━━━━━━━━

hope it helps! :)

Answer:-45

Step-by-step explanation:

first plug in the x and the y values

4(-2)(5)-(-2+7)

The start using pemdas to simplify

*or bodmas depends on what you learned

Then you should arrive to this

4(-2)(5)+ -(5)

-8(5)+ -5

-40-5= -45

Hope that helps

The scale factor between the original and resulting points is equal to 4 / 3.

In this problem we find a representation of a quadrilateral and its image depicted in Cartesian plane. According to the statement, the coordinates of the original and resulting points are, respectively:

B(x, y) = (- 3, 6), B'(x, y) = (- 4, 8)

Then, the scale factor can be found by means of the following formula:

B'(x, y) = k · B(x, y)

(- 4, 8) = (- 3 · k, 6 · k)

k = 4 / 3

To learn more on dilations: https://brainly.com/question/13176891

#SPJ1

The required correct match for the given problem has been shown below.

A number system is described as a process of composing to designate digits. It is the mathematical inscription for describing the numbers of a given set by using numbers or other symbols in a uniform method. It delivers a special presentation of every digit and describes the arithmetic structure.

Here,
3 2/7 = 23/7 = 3.2                      between 3 and 4
-3 7/8 = -31/8 = -3.875               between -3 and -4

-3/8 = -0.375                             between 0 and -1
-0.9                                          between 0 and -1
1/7                                             between 0 and 1.

Learn more about the number system here:

https://brainly.com/question/22046046

#SPJ1

We can say that approximately 4.29 inches of rain fell in 15 minutes.

We can apply a proportion to determine the amount of rain that fell in 15 minutes.

We can calculate the proportion because we know that 12 inches of rain fell in 42 minutes:

x inches in 15 minutes equals 12 inches in 42 minutes.

where x is how much rain fell in 15 minutes.

We can cross-multiply and simplify to find x's value:

42 minutes equals 12 inches times 15 minutes (x inches)

180 = 42x

x = 180 / 42

x = 4.2857...

We may estimate that 4.29 inches of rain, rounded to the nearest hundredth, fell in 15 minutes.

To know more similar question visit:

https://brainly.com/question/3614551

#SPJ1

The answer in a fraction or whole number. is P(odd) = 1/3.

Fractions represent the parts of a whole or collection of objects. A fraction has two parts. The number on the top of the line is called the numerator. It tells how many equal parts of the whole or collection are taken.  

The number below the line is called the denominator.  It shows the total number of equal parts the whole is divided into or the total number of the same objects in a collection

According to the fundamental principle of fractions, a fraction retains its value whenever its numerator or denominator were multiplied by a single non-zero number. It can be used to multiply or divide two fractions.

Only 3 is odd among the integers 2, 3, and 4. As a result, there is a 1/3 chance of selecting an odd number (1 out of 3).

P(odd) is equal to 1/3 as a result.

To know more about Fraction visit:

brainly.com/question/17205173

#SPJ1

Answer:

To find the area of the shaded segment of the circle, we need to first find the area of the sector formed by the 60 degrees angle, and then subtract the area of the triangle formed by the radii and the chord.

The formula for the area of a sector of a circle is:

A_sector = (θ/360) x πr^2

where θ is the central angle in degrees, and r is the radius.

Substituting the given values, we get:

A_sector = (60/360) x π x 18^2

A_sector = 113.04 cm^2

Next, we need to find the area of the triangle formed by the radii and the chord. To do this, we need to first find the length of the chord using the formula:

c = 2r sin(θ/2)

where θ is the central angle in radians.

Converting the given 60 degrees angle to radians, we get:

θ = 60 x (π/180) = π/3 radians

Substituting the values, we get:

c = 2 x 18 x sin(π/6)

c = 18√3 cm

Now, we can find the area of the triangle using the formula:

A_triangle = (1/2) x base x height

where the base is the chord length c, and the height is half the length of the chord, which is:

h = r - r cos(θ/2)

Substituting the values, we get:

h = 18 - 18 cos(π/6)

h = 18 - 9√3 cm

Therefore, the area of the triangle is:

A_triangle = (1/2) x 18√3 x (18 - 9√3)

A_triangle = 243 cm^2

Finally, the area of the shaded segment is the difference between the area of the sector and the area of the triangle:

A_shaded = A_sector - A_triangle

A_shaded = 113.04 - 243

A_shaded = -129.96

However, the result is negative because the triangle is larger than the sector in this case. Therefore, there is no shaded area in this situation.

Step-by-step explanation:

The Simple Interest is $112.5

What is Simple Interest?

Simple Interest is is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.

In simple interest, the principal amount is always the same, unlike compound interest where we add the interest of previous years principal to calculate the interest of the next year.

Simple Interest = P * R * T/100

Where P = Principal = $2500

Rate = 1.5%

Time = 3 years

Simple Interest = 2500 * 1.5 * 3/100

Simple Interest = 11250/100

Simple Interest = $112.5

Read more about Simple Interest

https://brainly.com/question/30810708

#SPJ1

When Five dozen eggs cost R60 [r/dozen], the value of R is 3600.

The term "dozen" or "dz" refers to a group of twelve.

Because there are roughly 12 lunar cycles (or months) in each solar cycle (or year), the number 12 may be one of the earliest primitive integer groupings. Twelve is useful because it has the most divisors among numbers up to its double, a characteristic that is only true of the numbers 1, 2, 6, 12, 60, 360, and 2520.

The duodecimal system, also known as the dozenal, was developed in Mesopotamia and uses the number twelve as its base (see also sexagesimal). By counting each finger bone with one's thumb, one can quickly count in base-12 on their hands.

Given 5 dozen of egg costs = R/60

That is

5 × 12 = R/60

60 = R/60

R = 60 × 60

R = 3600

Thus, When Five dozen eggs cost R60 [r/dozen], the value of R is 3600.

Learn more about dozen

https://brainly.com/question/22813421

#SPJ1

Complete question:

Five dozen eggs cost R60 [R/dozen]. Find the value of R.

Answer:57

Step-by-step explanation:

Given, P(X=15) and using the probability mass function we get

(27C15)(0.546)¹⁵(1-0.546)²⁷⁻¹⁵=0.1523

What is Probability?

Probability is simply how likely something is to happen. The occurrence of an event will be in the range of 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

What is the Probability mass function?

The probability distribution of a discrete random variable, or probability mass function, gives the potential values and the corresponding probabilities. 

According to the problem,

Let X be the random variable of interest, on this case we know that:

 X∼Binom (n=27,p=0.546)

The probability mass function for the Binomial distribution is given as:

                              P(X)=(nCx) (pˣ) (1-p)ⁿ⁻ˣ,

                              here,

                                      (nCx) =  n !/(n-x)!( x)!

For finding Probability and by using the mass function :

P(X=15) = (27C15)(0.546)¹⁵(1-0.546)²⁷⁻¹⁵ = 0.1523

The value of p will be 0.546

To know more about binomial distribution visit:

https://brainly.com/question/16759552

#SPJ1

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$900\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.10\\ t=years\dotfill &1 \end{cases} \\\\\\ A = 900[1+(0.10)(1)] \implies A = 990[/tex]

Answer:

The answer you're looking for is 40%

Step-by-step explanation:

If you divide 12(numerator) by 30(denominator), you get 0.4.
After that, if you want to convert the decimal to a percent you always have to multiply by 100.

[tex]\frac{12}{30} =0.4=0.4 x 100=40%[/tex]

I hope this was helpful!

Answer:

6.25 seconds

Step-by-step explanation:

Using the the equation

h = 100t − 16t^2

The ball hits the ground, when h = 0, solving below equation:

100t − 16t^2 = 0

4t(25 - 4t) = 0

t = 0 seconds, this is the starting point when ball was hit

25 - 4t = 0 ⇒ 4t = 25 ⇒ t= 25/4 = 6.25 seconds later the ball hits the ground

The value of x in the chord is 2.8 units

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

The circle and the chords

Represent the radius of the circle with r

Next, we calculate the radius using each chord using the Pythagoras theorem

Using the above as a guide, we have the following:

r² = x² + (38/2)²

r² = 12² + (30/2)²

By substitution, we have

x² + (38/2)² = 12² + (30/2)²

So, we have

x² = -(38/2)² + 12² + (30/2)²

Evaluate

x² = 8

Take the square root of both sides

x = 2.8

Hence, the value of x is 2.8 units

Read more about chords at

brainly.com/question/13950364

#SPJ1

Answer:

Approximately 13%

Step-by-step explanation:

Troy meant to make 15, but only made 13, meaning that he was off by 2. To find the percent error here, we will divide how off Troy was by the amount Troy meant to make:

2/15=0.133333333, or approximately 13% (multiply the decimal by 100 to find the percent, then round to the nearest integer.)

1) The amount is 307 g

2) The rate of change is 0.088

3) The time taken  is 8 days

Exponential decay is a mathematical process in which the value of a quantity decreases over time or space at a rate proportional to its current value.

We know that the exponential decay can be given by;

N =No[tex]e^-0.088t[/tex]

After 3 days;

N =400[tex]e^-0.088(3)[/tex]

N = 307 g

The rate of change after 3 days;

307 = 400[tex]e^-3r[/tex]

307/400 = [tex]e^-3r[/tex]

0.7675 =[tex]e^-3r[/tex]

-3r = ln(0.7675)

r = ln(0.7675)/-3

r = 0.088

1/2(400) = 400[tex]e^-0.088t[/tex]

200/400 = [tex]e^-0.088t[/tex]

1/2 =[tex]e^-0.088t[/tex]

t = ln0.5/-0.088

t = 8 days

Learn more about exponential function:https://brainly.com/question/14355665

#SPJ1

Answer:

Where is the picture???

Step-by-step explanation:

The Area would be 4ft because 2x2=4 its basic multiplication,

And I don't really understand why you also put 6ft but if you're saying 2ft x 6ft then that would be 12ft.

Hope that helps <3