Charlotte works in a department store selling clothing. She makes a guaranteed salary of $500 per week, but is paid a commission on top of her base salary equal to 30% of her total sales for the week. How much would Charlotte make in a week in which she made $1575 in sales? How much would Charlotte make in a week if she made
x
x dollars in sales?

The limit does exist for lim x→49 (x^2 - 7x - 49) and it approaches value of 2009.

The limit can be found using algebraic manipulation. First we will try plug in the value and see if we can determine the limit. We have:

lim x→49 (x^2 - 7x - 49) = 49^2 - 7×49 - 49 = 2009

So limit exist at x^2 - 7x - 49 and it can be found out by simple substitution.

So, as x approaches 49, the expression x^2 - 7x - 49 approaches 2009.

Therefore, lim x→49 x^2 - 7x - 49 = 343.

To know more on limit

https://brainly.com/question/12207539

#SPJ4

Answer:the answer of this slope is  7 an 24

Step-by-step explanation:

The complete table is shown below.

The equation is: y= 53.x + 250.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

Mai must spend $250 on wire and $5.30 per bracelet for beads.

a) 5.3 x 20 + 250 = 356 dollar

5.3 x 40 + 250 = 462 dollar

5.3 x 60 + 250 = 568 dollar

so, the complete table is

 Number of bracelets      cost in dollar

                 20                          356

                 40                          462

                 60                          568

b) let the number of bracelets be x and the cost is y dollar

so, the equation is

y= 53.x + 250

Learn more about Equation here:

https://brainly.com/question/29657992

#SPJ1

Answer:

The expression is:

4K

But as an equation, it would be:

T = 4K

Step-by-step explanation:

K = Kelli's age

T = Trey's age

Trey is 4 times older than Kelli

T = (4)(K)

Step-by-step explanation:

The slope of a line can be calculated as the difference of the y-coordinates divided by the difference of the x-coordinates of two points on that line. In this case, we have two points: (10,23) and (20,36).

So, the slope of the line would be:

(36 - 23) / (20 - 10) = 13 / 10 = 1.3.

Therefore, the slope of the line that has the coordinates of (10,23) and (20,36) is 1.3

Answer:

matt needs to use more than 2% mixture for his aquarium

Step-by-step explanation:

The kind of data we have is Categorical data. Data that can be broken down into groups or categories is known as categorical data.

There are three categories in this case: eggs, cereal, and no breakfast These groups include the 10 students who ate cereal, 5 students who ate eggs, and 3 students who did not eat breakfast at all.

A categorical variable is a variable in statistics that can have one of a limited, typically fixed number of possible values and assign each observational unit to a specific group or nominal category based on some qualitative property.

Learn more about Categorical data:

https://brainly.com/question/3882981

#SPJ4

The equation in standard form of the line that passes through the point (6, 1) and is parallel to the line represented by 8x + 3y= 15 is equal to y = -8x + 43.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

From the information provided above, we have the following slope and data points on the line:

In Geometry, two (2) lines are parallel under the following conditions:

m₁ = m₂ ⇒ -8 = -8

At data point (6, 1), a linear equation of this line can be calculated in point-slope form as follows:

y - 1 = -8(x - 6)

y - 1 = -8x + 42

y = -8x + 42 + 1

y = -8x + 43

Read more on slope here: brainly.com/question/3493733

#SPJ1

The answer is B. Both Charlie and Annabeth will have travelled for the same amount of time.

They will have travelled the same amount of time. This is because the time spent traveling is determined by the total distance travelled, not the direction of travel. In this case, the distance between New York and the travellers' current location is decreasing at first and then increasing, suggesting that they have reached their destination and are now returning. Since the total distance travelled is the same regardless of the direction, the time spent traveling will also be the same for both travellers. Therefore, both Charlie and Annabeth will have travelled for the same amount of time.

Learn about time here:

https://brainly.com/question/26941752

#SPJ4

Answer:The number of dollar bills, d, is the independent variable.

The quarters, q, is the dependent variable.

Step-by-step explanation:

The number of dollar bills, d, is the independent variable.

The quarters, q, is the dependent variable.

Answer:

Step-by-step explanation:

dependent then independent because i passes the lesson.

Answer: 0.56

Step-by-step explanation: convert from fraction to decimal

The probability of exactly 2 couples dancing together is 100/45 = 20/9.

To find the probability of the total number of ways to form pairs of 5 couples is C(10, 2) = 45, because there are 10 people and we need to choose 2 at a time.

The number of ways to form exactly 2 couples dancing together is C(5, 2) * C(5, 2) = 10 * 10 = 100. This is because we first choose 2 couples out of the 5 couples and then pair the males and females within each chosen couple.

So the probability of exactly 2 couples dancing together is 100/45 = 20/9.

To learn more about the probability, visit:

brainly.com/question/30034780

#SPJ4

The probability of exactly 2 couples dancing together is 100/45 = 20/9.

To find the probability of the total number of ways to form pairs of 5 couples is C(10, 2) = 45, because there are 10 people and we need to choose 2 at a time.

The number of ways to form exactly 2 couples dancing together is C(5, 2) * C(5, 2) = 10 * 10 = 100. This is because we first choose 2 couples out of the 5 couples and then pair the males and females within each chosen couple.

So the probability of exactly 2 couples dancing together is 100/45 = 20/9.

To learn more about Probability

brainly.com/question/30034780

#SPJ4

The probability that their meeting will be held at the station would be = 1/4

Probability is defined as the representation of an expression which shows the possible outcome of an event.

The random time for the arrival of both friends at the station = ,7:20 - 7:00

= 20 minutes.

The extra minutes used to wait for each other which is outside the random time needed to arrive at the station = 5 min.

Therefore the probability for both of them meeting at the station = 5/20 = 1/4.

Learn more about probability here:

https://brainly.com/question/24756209

#SPJ1

Answer:

The total number of markers along the 5-mile walkway is 6.

This includes markers at each mile (5 markers) and one marker at the east end of the walkway.

The simplifies expression is -5x/6 - 8

The expression "quantity negative two thirds times x minus 6 end quantity minus quantity negative 14 plus one sixth times x end quantity" represents:

-(2/3)x - 6 - ( -14 + (1/6)x)

The process of simplifying an expression involves reducing the expression to its simplest form, making it easier to understand and manipulate. To simplify an expression, we combine like terms by adding or subtracting the coefficients.

We need to simplify this expression into its simplest form.

Thus,

-(2/3)x - 6 - ( -14 + (1/6)x) equals,

= -2x/3 - 6 +14 - x/6

= -(4+1)x/6 - 8

= -5x/6 - 8

Read more about Simplification:

https://brainly.com/question/18077352

#SPJ4

The antiderivative of f(x) = tan(eˣ + π/2) on 0≤x≤ln(π/2) is:

⇒  ln |sec([tex]e^{\pi /2}[/tex])| / [tex]e^{\pi /2}[/tex]

Now, For the antiderivative of f(x) = tan(eˣ + π/2) on the interval 0≤x≤ln(π/2), we need to integrate the given function.

Now, using the substitution u = eˣ + π/2.

Then, we have:

du/dx = eˣ

dx = du / eˣ

Using this substitution, we can rewrite the original function as:

f(x) = tan(eˣ + π/2) dx = tan(u) du / eˣ

Now let's integrate this function:

∫tan(u) du / eˣ = - ln |cosec(u)| / eˣ + C

Substituting back u = eˣ+π/2:

ln |cosec(eˣ + π/2)| / eˣ + C

= - ln |cosec(eˣ + π/2)| / eˣ + C

Now we need to evaluate this expression at the limits of integration x = 0 and x = ln(π/2):

F(ln(π/2)) - F(0)

= - ln |cosec([tex]e^{\pi /2 } + \frac{\pi }{2}[/tex])| / [tex]e^{\pi /2}[/tex] + C - (- ln |cos(0)| / [tex]e^{\pi /2}[/tex] + C)

= - ln |sec([tex]e^{\pi /2}[/tex])| / [tex]e^{\pi /2}[/tex] + ln |cos(0)| / [tex]e^{\pi /2}[/tex]

= - ln |sec([tex]e^{\pi /2}[/tex])| / [tex]e^{\pi /2}[/tex] + ln(1) / [tex]e^{\pi /2}[/tex]

=  ln |sec([tex]e^{\pi /2}[/tex])| / [tex]e^{\pi /2}[/tex]

So, the antiderivative of f(x) = tan(eˣ + π/2) on 0≤x≤ln(π/2) is:

⇒  ln |sec([tex]e^{\pi /2}[/tex])| / [tex]e^{\pi /2}[/tex]

Learn more about the function visit:

https://brainly.com/question/11624077

#SPJ12

The total number of twenty questions prepared by Josh can be find by using the expression k = 20 * P(getting a question right) / (1 + 20 * 0.08 / 0.92), where, k = total question prepared by Josh

Let's call the number of questions Josh was prepared for as "k".

The probability of Josh getting a question right given that he knew the answer is 0.92,

So the probability of him getting a question right by guessing is

1 - 0.92 = 0.08.

The overall probability of Josh getting a question right is the sum of the probability of him getting it right given that he was prepared and the probability of him getting it right by guessing:

P(getting a question right) = P(getting a question right | prepared) * P(prepared) + P(getting a question right | guessed) * P(guessed)

Since each question is either prepared or guessed, the sum of P(prepared) and P(guessed) is 1:

P(getting a question right) = 0.92 * P(prepared) + 0.08 * (1 - P(prepared))

Simplifying the expression:

P(getting a question right) = 0.92 * P(prepared) + 0.08

Since the overall probability of Josh getting a question right is the same for every question,

it must be the same for all twenty questions:

So, we can write it as:

0.92 * P(prepared) + 0.08

= 0.92 * k/20 + 0.08 * (20-k)/20

Dividing both sides by 0.92:

P(prepared) = k/20 = (0.92 * k + 0.08 * 20 - 0.08) / 0.92

Isolating k:

k = 20 * P(prepared) / (1 + 20 * 0.08 / 0.92)

Plugging in the overall probability of Josh getting a question right, we have:

k = 20 * P(getting a question right) / (1 + 20 * 0.08 / 0.92)

For more questions on conditional probability

https://brainly.com/question/28339868

#SPJ4

The maturity date of the loan is July 31st.

To find the maturity date, you first need to find the number of days between May 11th and the maturity date. The loan was taken out for 82 days, so you add 82 days to May 11th to find the maturity date.

For example, if May 11th is day 1, then day 82 would be July 31st. Therefore, the maturity date of the loan is July 31st.

To learn more about interest, visit:

https://brainly.com/question/29480777#

#SPJ11

The average of the 3-day simple moving averages for these five days to the nearest $0.01 is $105.99, $107.19 and $110.40.

What is a Simple Moving Average?

By dividing the number of periods inside the range by the average of the range of prices, simple moving averages are used.

We are given closing prices of a stock over a 5-day period.

So, 3-day simple moving averages are

For Monday - $104.67

For Tuesday - $103.95

For Wednesday - ($104.67 + $103.95 + $109.35)/3 = $105.99

For Thursday - ($103.95 + $109.35 +$108.27)/3 = $107.19

For Friday - ($113.58 + $109.35 +$108.27)/3 = $110.4

Hence, the average of the 3-day simple moving averages for these five days to the nearest $0.01 is $105.99, $107.19 and $110.40.

Learn more about Simple Moving Average from the given link

https://brainly.com/question/15213589

#SPJ1

Let P be the principal Vanilla Ice borrowed. The interest charge is calculated as P * 10.3% * 240/365.

So, 330 = P * 10.3% * 240/365

Solving for P, we get:

P = 330 / (10.3% * 240/365) = $3,116.71

Therefore, Vanilla Ice borrowed a principal of $3,116.71.

Simple Interest (SI) is calculated based on the principal amount only, and the interest rate stays constant throughout the tenure. The formula for Simple Interest is:

SI = P * R * T

Where:

P = Principal amount

R = Interest rate

T = Time (in years)

Compound Interest (CI) is calculated based on the principal amount and the interest earned on it in previous periods. The interest earned in each period is added to the principal, and the new amount becomes the principal for the next period. This leads to an exponential growth of the invested amount. The formula for Compound Interest is:

CI = P * (1 + R/n)^(nt)

Where:

P = Principal amount

R = Interest rate

n = Number of compounding periods per year

t = Time (in years)

In summary, the main difference between simple and compound interest is that simple interest is calculated only on the principal amount, whereas compound interest is calculated on the principal amount and the accumulated interest.

To know more about Interest formula:
https://brainly.com/question/25793394
https://brainly.com/question/2277782

Answer: The numeric coefficient is 3.

Step-by-step explanation:

(f ◦ g)(x) = -2x^2 + 11.

What is Composition of two functions ?

The new function obtained by performing f first and then g is the combination of two functions g and f.

The composition of two functions f and g, denoted by (f ◦ g)(x), is defined as the function that maps x to f(g(x)).

Given the functions f(x) = 2x + 3 and g(x) = -x^2 + 5, the composition of these two functions is:

(f ◦ g)(x) = f(g(x)) = f(-x^2 + 5) = 2(-x^2 + 5) + 3 = -2x^2 + 11

So, (f ◦ g)(x) = -2x^2 + 11.

To know more about Composition functions visit,

https://brainly.com/question/28138588

#SPJ4

For the given function; Domain: -4 ≤ x ≤ 4, Range: 0 ≤ y ≤ 3, Relative max: x = 0, y=3, and Relative min: x = -2, y=0 and x = 2, y =0.

The range of values that we are permitted to enter into our function is known as the domain of a function.

The x values for a function like f make up this set (x).

A function's range is the collection of values it can take as input. The values in this set

Hence, once we input an x value, the function returns. The y values are those.

The domain of the function is the input values, that is the x-coordinates thus,

Domain: -4 ≤ x ≤ 4

Range of the function is the output values, that is the y-coordinate thus,

Range: 0 ≤ y ≤ 3

Relative max is a point where the function changes from increasing to decreasing thus,

Relative max: x = 0, y=3

Relative min is a point where the function changes from decreasing to increasing, thus,

Relative min: x = -2, y=0 and x = 2, y =0

Hence, the Domain: -4 ≤ x ≤ 4, Range: 0 ≤ y ≤ 3, Relative max: x = 0, y=3, and Relative min: x = -2, y=0 and x = 2, y =0.

Learn more about domain here:

https://brainly.com/question/29143732

#SPJ1

The inequality is equivalent to the given inequality? -4(x+7)< 3(x-2) is x>-22/7

Inequality is a mathematical statement which shsow that two quantities are not the same or that they are not equal.

The given inequality is -4(x+7) < 3(x-2)

Opening the brackets to have

-4x-28<3x-6

Collecting like terms to have

-4x-3x<-6+28

This shows that -7x<22

Making x the subject of the relation we have

x>-22/7

The inequality that satisfies the given inequality is x>-22/7

Learn more about inequality on https://brainly.com/question/30231190

#SPJ1

Triangle ABC is similar to triangle DEF because their corresponding angles, ∠A and ∠D, and ∠B and ∠E, are equal.

The AAA similarity is a theorem of a triangle which means "angle-angle-angle", that is, two triangles are similar to each other if they both have three corresponding angles that are congruent to each other.

The line BC divides the line AD and AE, we can state that the two triangles are similar by the Angle-Angle-Angle (AAA) Similarity Theorem.

The AAA Similarity Theorem states that if the three angles of one triangle are equal to the three angles of another triangle, then the two triangles are similar.

Here is an example similarity statement based on the Angle-Angle-Angle (AAA) Similarity Theorem: "Triangle ABC is similar to triangle DEF because they both have equal corresponding angles, ∠A and ∠D, ∠B and ∠E, and ∠C and ∠F, and because the line BC divides the line AD and AE."

Hence, Triangle ABC is similar to triangle DEF because their corresponding angles, ∠A and ∠D, and ∠B and ∠E, are equal.

To learn more about the similarity of triangles visit,

https://brainly.com/question/21874653

#SPJ1

Multiply the mass in kilogrammes by 2.2046226218 to convert 50 kg to pounds.

To learn more about Kilogram refer to:

https://brainly.com/question/20550400

#SPJ4

Answer:

q is independent var, r is dependent

Step-by-step explanation: