a varies inverselv as b^3. If a =
3/2 when b = 2, find a
when b is 3

Answer:

The commission rate is of 12%.

Step-by-step explanation:

Commission rate:

The commission rate is given by the commission value multiplied by 100% and divided by the value of merchandise sold.

In this question:

$252 in commission for selling $2100 in merchandise. So

252*100%/2100 = 12%

The commission rate is of 12%.

Answer:

13 is a prime number, not divisible by any number greater than 1 or less than 13. So the prime factorisation of 78 is: 78 = 2 ⋅ 3 ⋅ 13 This can also be represented by a factor tree:

Step-by-step explanation:

Answer:

78 = 2 ⋅ 3 ⋅ 13

Step-by-step explanation:

78  ends with an even digit, so is divisible by  2 and we find:  78 = 2 ⋅ 39

39  ends with an odd digit, so is not divisible by  2 .

The digits of  39  add up to a multiple of  3 , namely  3 + 9 = 12 . So we can tell that  39  is divisible by  3 : 39 = 3 ⋅ 13

13  is a prime number, not divisible by any number greater than  1  or less than  13 .

So the prime factorization of  

78  is:

78= 2 ⋅ 3 ⋅ 13

The last row of the table will show the total interest paid, which is approximately $243.11.

The correct option is C.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

To calculate the total interest paid,

we need to first find out how many months it will take to pay off the entire balance.

We can use the following formula to calculate the number of months:

N = -log(1-(r×b/p))/log(1+r)

where N is the number of months, r is the monthly interest rate (which is the annual percentage rate divided by 12), b is the balance, and p is the payment.

In this case,

r = 0.1799/12 = 0.01499 (monthly interest rate), b = $1,800, and p = $125.

Plugging these values into the formula, we get:

N = -log(1-(0.01499 × 1800/125))/log(1+0.01499) ≈ 16.24

So it will take about 16.24 months to pay off the entire balance.

Using a spreadsheet, we can create a table with the following columns:

Month: 1 to 16

Balance: starting with $1,800 and decreasing by $125 each month

Interest: calculated as the monthly interest rate times the balance

Payment: $125

Total Interest: calculated as the sum of the interest for all previous months

The last row of the table will show the total interest paid, which is approximately $243.11.

Therefore, the value is (C) $243.11.

To learn more about the percentage;

https://brainly.com/question/24159063

#SPJ1

Answer: Option C is correct $243.11

Step-by-step explanation: I got it right On the test!!!

The graph of the system of the inequalities is attached.

To graph the inequalities y < -x - 4 and y ≥ (3/5)x + 4, we can start by graphing the corresponding equations and then shade the appropriate regions based on the inequality signs.

Let's begin with the equation y = -x - 4:

Choose a range of x-values to plot.

For simplicity, let's use x-values from -10 to 10.

Substitute different x-values into the equation to find corresponding y-values.

For example:

When x = -10, y = -(-10) - 4 = 10 - 4 = 6.

When x = 0, y = -(0) - 4 = -4.

When x = 10, y = -(10) - 4 = -10 - 4 = -14.

Plot these points on the coordinate plane and draw a straight line passing through them.

This line represents the equation y = -x - 4.

Next, let's graph the equation y = (3/5)x + 4:

Again, choose a range of x-values to plot. Let's use the same range of -10 to 10.

Substitute different x-values into the equation to find corresponding y-values. For example:

When x = -10, y = (3/5)(-10) + 4 = -6 + 4 = -2.

When x = 0, y = (3/5)(0) + 4 = 0 + 4 = 4.

When x = 10, y = (3/5)(10) + 4 = 6 + 4 = 10.

Plot these points on the coordinate plane and draw a straight line passing through them.

This line represents the equation y = (3/5)x + 4.

Now, let's shade the regions based on the inequalities:

For y < -x - 4, we need to shade the region below the line y = -x - 4.

For y ≥ (3/5)x + 4, we need to shade the region above or on the line y = (3/5)x + 4.

Hence, the region where the shaded regions overlap represents the solution to both inequalities.

Learn more about system of inequalities click;

https://brainly.com/question/29785389

#SPJ1

Answer: the first option is correct

Y+ 11> -9 this answer is most likely right.

Step-by-step explanation: -25 + 11 = 14 so that makes it bigger that -9 and that it has -25 in the solution set. Let me know if this is for Edmonton.

Answer:

It was D

Step-by-step explanation:

The volume contained in a cup of oil is a fraction of the volume

contained in a pint of oil.

Correct response:

The measure of the volume of oil the car holds = Pints of oil

The measurement the man has for use = Cups of oil

Required:

The number of cups equal to three pints.

Solution;

1 pint of oil = 2 cups of oil

Therefore;

3 pints of oil = 3 × 2 cups of oil = 6 cups of oil

Learn more about units conversion here:

https://brainly.com/question/4845674

Answer:

See below

Step-by-step explanation:

x = part 1

3x = part 2

x + 3x  = part 3       summed, they equal 1000

x    +     3x      +   x + 3x = 1000

8x = 1000

x = 125       3x = 385      third part = 500

Example: (2x - 4) x=7 so (2x (x=7) - 4) =18

Answer:

the answer 24 squared

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Add 11 on both sides, therefore getting x is less than or equal to 11.  Now find the graph that fits the description - therefore D.  

Answer:

y = 3/2x + 7

Step-by-step explanation:

The slops is rise over run, so in this case the slope is 3/2 because it goes up 3 units while going 2 units to the right.

The points (0,7) is on the y axis. This means that 7 is the y intercept

With this information, we can follow the format of the slope intercept equation: y = mx + b

m stands for the slope and b stands for the y intercept. Plugging the information in, our equation is:

y = 3/2x + 7

The least common multiple of 3z² - 75 and z + 5 is 3z² - 45.

The least common multiple of 3z² - 75 and z + 5, we first need to factor each polynomial:

3z² - 75 = 3(z² - 25)

= 3(z - 5)(z + 5)

z + 5 = 1(z + 5)

Next, we identify the common factors between the two polynomials and take the highest power of each:

3(z - 5)(z + 5) has factors of 3, (z - 5), and (z + 5)

1(z + 5) has factors of 1 and (z + 5)

The least common multiple of these two polynomials is the product of the highest powers of each factor.

The least common multiple is:

LCM = 3(z - 5)(z + 5)

= 3z² - 45

We must first factor each polynomial to get the least common multiple of 3z²  - 75 and z + 5.

Z + 5 = 1(z + 5)

= 3z²  - 75

= 3(z² - 25)

= 3(z - 5)(z + 5)

The greatest power of each polynomial is then selected after determining the elements that the two polynomials have in common:

3(z - 5) Factors of (z + 5) include 3, (z - 5), and (z + 5).

The components of 1(z + 5) are 1 and (z + 5).

The sum of the greatest powers of each factor produces the least frequent multiple of these two polynomials.

This is the least frequent multiple:

LCM is equal to 3(z - 5)(z + 5) = 3z² - 45.

For similar questions on least common multiple

https://brainly.com/question/10749076

#SPJ11

Answer:

A) \(\frac{7}{tan55^\circ}\)

Step-by-step explanation:

\(tan\theta=\frac{opposite}{adjacent}\\ \\tan55^\circ=\frac{7}{BC}\\ \\BC*tan55^\circ=7\\\\BC=\frac{7}{tan55^\circ}\)

Answer:

Factors of 20 and 10: P ∪ Q

Factors of 20 but not 10: U ∩ (P ∪ Q)c

Neither factors of 20 or 10: (P ∪ Q)c

Opportunity cost when 3 military outfits are produced is 30

Opportunity cost when 4 military outfits are produced is - 35.

Opportunity cost when 5 military outfits are produced  is -50.

As military outfit increases, opportunity cost declines.

Opportunity cost of the next best option forgone when one alternative is chosen over other alternatives

Opportunity cost = change in the total pounds of butter produced /  change in total outfit produced

Opportunity cost when 3 military outfits are produced = (85 - 115) / (3 - 2) = 30

Opportunity cost when 4 military outfits are produced = (50 - 85) / (4 - 3) = - 35

Opportunity cost when 5 military outfits are produced = (0 - 50) / (5 - 4) = -50

To learn more about opportunity cost, please check: https://brainly.com/question/26315727

The calculated bill for a person who uses 600kWh in a month is $80

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

b(x) = 0.10x, x ≤ 200

b(x) = 0.15(x - 200) + 20, x > 200

For a person that uses 600kWh per month, we make use of the function

b(x) = 0.15(x - 200) + 20

This is because it is valid for x > 200

Substitute the known values in the above equation, so, we have the following representation

b(600) = 0.15(600 - 200) + 20

Evaluate

b(600) = 80

Hence, the bill for a person who uses 600kWh in a month is $80

Read more about piecewise function at

brainly.com/question/27262465

#SPJ1

Answer:

(3, 6)

Step-by-step explanation:

The vertex form of a quadratic is y = a(x-h)^2 + k

where (h, k) is the point of the vertex. So the answer is (3,6)

The sixth term of the geometric sequence is 2048.

The given geometric sequence is 2, 8, 32, 128. We can observe that each term is obtained by multiplying the previous term by 4. Therefore, the common ratio (r) of the sequence is 4.

The formula for the nth term (an) of a geometric sequence is given by:

an = a1 * r^(n-1)

where a1 is the first term and r is the common ratio.

For this sequence, a1 = 2 and r = 4. Plugging in these values into the formula, we get:

an = 2 * 4^(n-1)

To find a6, we substitute n = 6 into the formula:

a6 = 2 * 4^(6-1)

  = 2 * 4^5

  = 2 * 1024

  = 2048

For more such questions on geometric,click on

https://brainly.com/question/19241268

#SPJ8

The Probable question may be:
Write an equation for the nth term of the geometric sequence 2, 8, 32, 128,

Then find a6. Round to the nearest tenth if necessary.

a = 5×4 X

a1 = n-1 X

Answer:

17.8

Step-by-step explanation:

You have to add 9.2 and 63 and the subtract from 90. Hope this helped! <3

Answer:

0.024 represents the amount of snow that is added to the lawn every minute.

Step-by-step explanation:

Emily observed the amount of snow on her lawn during a blizzard. So, 0.024 in the equation shows the rate at which snow is coming with the number of minutes passing.

Equations are mathematical expressions that have two algebras on either side of an equal (=) sign. The expressions on the left and right are shown to be equal to one another, demonstrating this relationship. L.H.S. = R.H.S. (left-hand side = right side) is a fundamental simple equation.

For an unknown quantity represented by an unknown variable, equations are then solved to determine its value. It is clear that a statement is not even an equation if there is no "equal to" sign in it.

As per the given equation in the question,

S is the snow in inches.

x shows the time in minutes and,

0.024 is the rate along with the time at which the snow is accumulating in the lawn and 7 in the equation is the constant value.

To know more about an equation:

https://brainly.com/question/14686792

#SPJ2

Most people on this website are living in the UK, Australia, America, or Canada. There might be a language setting, but I am not sure.

Answer:

Step-by-step explanation:

a) If a driver uses a full tank of gas every day, the fraction of a tank he will use in 3 days is 3/1, or 3/1 of a tank.

b) If a driver uses a full tank of gas every day, the fraction of a tank he will use in 1 week is 7/1, or 7/1 of a tank.

It's worth noting that tanks of gas come in different sizes, so the amount of gas consumed in a day, week, or any other period of time will depend on the size of the tank, and the consumption of the car, so this answer is based on the assumption that a full tank is used every day.

\(20^{\tfrac 52}\\\\=(20^5)^{\tfrac 12}\\\\=\left(20^4 \cdot 20 \right)^{\tfrac 12}\\\\=20^{\tfrac 42} \cdot 20^{\tfrac 12}\\\\=20^2 \sqrt{20}\\\\=400\sqrt{4 \times 5}\\\\=400 \times 2\sqrt 5\\\\=800\sqrt 5\)

Answer:

\(800\sqrt{5}\)

Step-by-step explanation:

Given: \(\large (20)^\text{$ \dfrac{5}{2} $}\)

Properties of Exponents:

Rational Exponent Property: \(\large x^\text{$ \dfrac{m}{n} $} = \large \text{$ \sqrt[n]{x^m} $}\)

Product of Powers Property:

1. Convert into a radical:

\(\sqrt[2]{20^5} \implies \sqrt{20^5}\)

2. Simplify the expression:

\(\sqrt{20^2\times20^2\times20^1}\\\\\implies \sqrt{20^4\times20}\\\\\implies 20^2\sqrt{20}\\\\\implies 20^2\sqrt{4\times5}\\\\\implies 20^2\times2\sqrt{5}\)

3. Evaluate the power:

\(20\times20\times2\sqrt{5}\\\\\implies 400\times2\sqrt{5}\)

4. Multiply:

\((400\times2)\sqrt{5}\\\\\implies800\sqrt{5}\)

A formula without free variables is a formula that does not contain any variables that are not quantified.

Sentences are commonly referred to as formulas devoid of any unrestricted variables. These statements hold a truth value independent of the variable values, hence the reason.

Open formulas are frequently referred to as formulas with free variables. These are not actually declarations; instead, they are arrangements that can transform into declarations by allotting definite values to the independent variables.

Formulas without free variables are often easier to work with than formulas with free variables.

Find out more on formula variables at https://brainly.com/question/30700385

#SPJ1

Answer:

3n+4

Step-by-step explanation:

four more than three times a number.

3n + 4

We provide recruitment solutions for your Future Talent and Volume Hiring needs. Platform. Services.

Define Decimal place?

To learn more about decimal place refers to:

https://brainly.com/question/29423712

#SPJ1

Answer:

first off theres two ways of doing it the equation is more fun though

14.5 = x + 4.5

14.5 = x(5) -4.5

-4.5

10 = 5x

divide by 5

you get

2x or $2

other way was to just -4.5 and divide by 5 but thats no fun