A salesperson is paid a weekly salary of $800, plus a commission of 4% of all their sales for the
week.
Express their weekly income in terms of the weekly sales revenue. Make sure to define your variables in terms of what the letters mean relative to the context of the problem. Note that
variable meanings are not numbers.

The annual rate of decline is 5.3%.

What is exponential ?

Exponential refers to a mathematical function where the variable is in the exponent. Exponential functions have the general form:

\(f(x) = a^{x}\)

here "a" is a constant called the base, and "x" is the variable. When the base "a" is a positive number greater than 1, the function grows exponentially as "x" increases. When the base "a" is a number between 0 and 1, the function decays exponentially as "x" increases.

We can start by using the formula for exponential decay:

\(N(t) = N0 * (1 - r)^{t}\)

where N(t) is the population after t years, N0 is the initial population, r is the annual rate of decay (as a decimal), and t is the time in years.

We are given that the initial population is 670, so N0 = 670. After 4 years, the population has reduced to 557, so N(4) = 557. We can plug these values into the formula and solve for r:

\(557 = 670 * (1 - r)^{4}\)

\((557/670)^{1/4} = 1 - r\)

\(0.947 = 1 - r\)

\(r = 0.053\)

So the annual rate of decline is 5.3%.

To learn more about exponential visit the link:

https://brainly.com/question/11975096

#SPJ1

The height of the cylinder is the sum of the diameters of the spherical balls, which is 7cm+7cm+7cm=21cm.

The radius of the cylinder is half of the diameter of the spherical balls which is 3.5cm.

The volume of cylinder is given by the formula:

The volume of sphere is given by the formula:

There are three(3) spherical balls in the cylinder, thus, the volume of the 3 spherical balls will be:

Hence, the volume of the space inside the cylinder, not filled by the balls is:

An eating disorder characterized by bingeing and purging is called bulimia nervosa.

The minimum amount of body fat needed for good health is variable and can depend on factors such as age, gender, and individual circumstances. However, essential body fat is typically estimated to be around 3-5% for men and 8-12% for women.

The term used to describe a person who is very overfat is obese. Obesity refers to having excessive body fat, which can have negative effects on health.

People with anorexia nervosa, an eating disorder characterized by restrictive eating and an intense fear of gaining weight, often see themselves as too fat even when they are extremely thin. This distorted body image is a characteristic feature of anorexia nervosa.

A technique for assessing body fat levels that involves being weighed under water is called hydrostatic weighing or underwater weighing. It is considered one of the more accurate methods for determining body composition.

To know more about bulimia nervosa., refer here:

https://brainly.com/question/32013975#

#SPJ11

A second linearly independent solution of y₂ is \(-\frac{1}{6x^3}\)

The general Equation is y" + P(x)y' + q(x)y = 0 ...............(i)

where P(x), Q(x) are continues in the internal I ≤ R.

If y₁(x) is a solution of equation 1 in I then y₁(x) ≠ 0.

Then y₂(x) = y₁(x)\(\int{\frac{e^{-\intP(x)dx}}{(y_{1}x)^2}}dx\) is another solution.

The differential equation is x²y" + xy' – 9y = 0 where x > 0.

As y₁(x) = x³ is one solution of differential equation.

Divide throughout by (x²) to given differential equation.

1/x² (x²y" + xy' – 9y = 0)

y" + (y'/x) – (9/x²)y = 0 ................(ii)

By comparing equation (i) & (ii) we get:

p(x)=1/x , q(x)= –are continuous for x>0

So, another solution,

y₂(x) = y₁(x)\(\int{\frac{e^{-\intP(x)dx}}{(y_{1}x)^2}}dx\)

Now putting the values of P(x) And Q(x)

y₂(x) = \(x^3\int\limits {\frac{e^{\int(1/x)dx} }{(x^3)^2}} \, dx\)

y₂(x) = \(x^3\int\limits {\frac{\frac{1}{x} }{x^6} }} \, dx\)

y₂(x) = \(x^3\int\limits {\frac{1}{x^7} }} \, dx\)

y₂(x) = \(x^3\int\limits {x^-7} } \, dx\)

y₂(x) = \(x^3\left[\frac{x^{-7+1}}{-7+1}\right]\)

y₂(x) = \(-\frac{1}{6}(x^3\times x^{-6})\)

y₂(x) = \(-\frac{1}{6x^3}\)

So, the answer of this question is \(-\frac{1}{6x^3}\).

To learn more about Differential equation link is here:

brainly.com/question/14620493

#SPJ4

The vertex of the Quadratic function with a y-intercept of (5, 0) and an x-intercept of (0, 80) is located at the point (0, 0).

The vertex of a quadratic function given the y-intercept and x-intercept, we need to determine the axis of symmetry, which is the line that passes through the vertex. The x-coordinate of the vertex will be the midpoint between the x-intercepts, while the y-coordinate will be the same as the y-intercept.

Given that the y-intercept is (5, 0) and the x-intercept is (0, 80), we can determine the x-coordinate of the vertex by finding the midpoint of the x-intercepts. The x-coordinate of the midpoint is simply the average of the x-values:

x-coordinate of vertex = (0 + 0) / 2 = 0 / 2 = 0

Since the y-coordinate of the vertex is the same as the y-intercept, the vertex will have the coordinates (0, 0).

Therefore, the vertex of the quadratic function is (0, 0).

In conclusion, the vertex of the quadratic function with a y-intercept of (5, 0) and an x-intercept of (0, 80) is located at the point (0, 0).

To know more about Quadratic function.

https://brainly.com/question/25841119

#SPJ8

Answer:

A

Step-by-step explanation:

bcz 7 times 7 times 7  3 times

Answer:

A)

Step-by-step explanation:

The expression would be 7x7x7 because exponents work that way in steps of using multiplication. It an expression used to say "3 times more" that the real amount. 7³ = to the the expression of 7x 7 x 7.

Note:

Hope this helps!

-kiniwih426

Answer:

white sold = 16

yellow sold = 12

Step-by-step explanation:

w = # of white sold

y = # of yellow sold

w + y = 28   solve this for w

w = 28 - y

9.95w + 13.5y = 321.20     substitute w = 28-y into this expression and solve for y

9.95(28-y) + 13.5y = 321.20

278.60 - 9.95y + 13.50y = 321.20

278.60 + 3.55y = 321.20

3.55y = 321.20 - 278.60 = 42.60

y = 42.60/3.55 = 12   substitute this into w = 28 - y and solve for w

w = 28 - 12 = 16

Yes, you can solve for the y-intercept using the slope, one ordered pair, and the slope-intercept equation.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Here Rin says that you can solve for the y-intercept using the slope, one ordered pair, and the slope-intercept equation.

The statement is right because for the calculation of the y-intercept we need one point to pass through the line and the slope of the line.

To know more about an equation of the line follow

https://brainly.com/question/18831322

#SPJ1

To break even, 29 units must always be sold. The cost will be $850 per unit, or $24,650.

For the given question-

Total cost c: c = 850x + 250000

Total revenue R: R = 9502x

The point during which costs equal revenues is known as the break-even point.

850x + 250000 = 9502x

9502x - 850x = 250000

8652x = 250000

x = 28.29

x = 29

Thus, to break even, 29 units must always be sold. The cost will be $850 per unit, or $24,650.

To know more about the break even point, here

https://brainly.com/question/15281855

#SPJ4

Answer:

36 red, 22 blue

37 red, 21 blue

38 red, 20 blue

39 red, 19 blue

40 red, 18 blue

Step-by-step explanation:

Total number of pens: 58

More red pens than blue pens.

At least 36 red pens.

No more than 40 red pens.

Possible number of pens:

36 red, 22 blue

37 red, 21 blue

38 red, 20 blue

39 red, 19 blue

40 red, 18 blue

Therefore the probability that  she buys at least one of the previous items is 0.1333

The area of mathematics known as probability deals with numerical descriptions of the likelihood that an event will occur or that a statement is true .A number between 0 and 1 is the likelihood of an event, where, broadly speaking, 0 signifies the event's impossibility and 1 denotes its certainty.

Given:

event A: she buys  red dress.

event B: she buys a blue dress.

event C: she buys a necklace.

the probability she will buy a red dress is 0.2,

the probability she will buy a blue dress is 0.4

there is 10% chance  she will buy a necklace =0.10

The probability she wants to buy at most one dress,

P(A or B or C) =0.2 +0.4 +0.1 -(0.08 -0.04 -0.02 +0.08)

P(A or B or C) =0.568

the probability she buys at least one of the previous items is

\(\frac{P(A or B or C)}{P(AorB andC)}\) = \(\frac{0.2 * 0.1 * 0.4}{(0.2 * 0.1)+(0.1 *0.4)}\)

 \(\frac{P(A or B or C)}{P(AorB andC)}\)= 2/15 =0.133

Therefore the probability that  she buys at least one of the previous items is 0.1333

To know more about probability , visit

https://brainly.com/question/11234923

#SPJ4

Answer:

y+2=1/2(x+3)

Why?

Point slope form is written as (y-y1) = m(x-x1) with y1 being the value of y at a certain point, x1 being the value of x at a certain point, and m being slope. y1 and x1 are given to us by the point (-3, -2) letting us know that y1=-2 and x1=-3. The only thing left to find is slope. Parallel lines have the same slope. If the line we are trying to find is parallel to the one given in the question, we just need to find the slope of the equation given. That equation is given in slope-intercept form which is y = mx + b. m is still slope so we can see that the slope is 1/2. Now we can plug m, x1 and y1 into the point slope form equation to get y + 2 = 1/2(x + 3)

Answer:

x=2 or x=−6

Step-by-step explanation:

The hypothesis of continental drift was initially not accepted by many scientists due to the lack of a comprehensive mechanism, conflicting with established beliefs, and limited supporting evidence.

During the early stages of the continental drift theory, scientists struggled to find a satisfactory mechanism that could explain how continents could move across the Earth's surface.

The concept seemed implausible without a clear understanding of the driving forces behind such movement. Without a solid mechanism, many scientists were hesitant to accept the hypothesis.

Additionally, the theory of continental drift contradicted the prevailing scientific belief of a fixed and unchanging Earth.

The concept challenged the long-held notion of a static planet and required a paradigm shift in scientific thinking, which met with resistance from some scientists who were reluctant to abandon established ideas.

Furthermore, the available evidence supporting continental drift was limited and fragmented.

While Alfred Wegener presented compelling evidence such as the fit of coastlines, fossil distributions, and geological similarities, skeptics argued that these observations could be explained by alternative mechanisms or coincidences rather than actual continental movement.

Over time, advancements in plate tectonics, geophysical studies, and technological innovations provided more substantial evidence and a better understanding of Earth's dynamics, leading to widespread acceptance of the theory.

The accumulation of data and the development of a comprehensive mechanism helped address the initial concerns and skepticism surrounding the hypothesis of continental drift.

Learn more about hypothesis of continental drift

brainly.com/question/769922

#SPJ11

Answer:

If s = 1 over 3 unit and A = 18s² what is the value of A, in square units? ____ square unit(s).Step-by-step explanation:

The solution to the given system of differential equations is x(t) = e^(t^2/2) * (8 - t^2/2) + e^(t^2/2) and y(t) = 8 * e^t. The initial conditions are x(0) = 9 and y(0) = 8.

To solve the system of differential equations x' = y - x*t and y' = y with initial conditions x(0) = 9 and y(0) = 8, we can use the method of integrating factors.

First, let's solve the second equation y' = y, which has the general solution y = C*e^t, where C is a constant determined by the initial condition y(0) = 8. Plugging in this value, we get C = 8.

Now, we can use this solution for y to find an integrating factor for the first equation x' = y - x*t. Multiplying both sides by e^(-t^2/2), we get

e^(-t^2/2)*x' - e^(-t^2/2)tx = e^(-t^2/2)*y - e^(-t^2/2)ty

The left-hand side can be simplified using the product rule

(d/dt)[e^(-t^2/2)*x] = e^(-t^2/2)*x' - e^(-t^2/2)tx

So, we can rewrite the equation as

(d/dt)[e^(-t^2/2)*x] = e^(-t^2/2)*y - e^(-t^2/2)ty

Integrating both sides with respect to t, we get

e^(-t^2/2)*x = ∫[e^(-t^2/2)*y - e^(-t^2/2)ty] dt + C

Using the solution for y we found earlier, we can simplify the integral

e^(-t^2/2)*x = e^t * (8 - t^2/2) + C

Now, we can use the initial condition x(0) = 9 to find C

e^0 * 9 = e^0 * (8 - 0/2) + C

C = 9 - 8 = 1

Therefore, the solution to the system of differential equations x' = y - x*t and y' = y with initial conditions x(0) = 9 and y(0) = 8 is:

x = e^(t^2/2) * (8 - t^2/2) + e^(t^2/2)

y = 8 * e^t

To know more about differential equation:

https://brainly.com/question/2273154

#SPJ4

At t = 1 second, the particle's position is -2 meters, its velocity is 24π - 6 m/s, and its acceleration is -12 m/s².

To find the particle's position, velocity, and acceleration at the time t = 1, we'll need to calculate the corresponding values using the given formula. Let's go through each of them:

a) To find the particle's position, we substitute t = 1 into the given formula:

x(t) = 4sin(6πt) - 2t³

x(1) = 4sin(6π(1)) - 2(1)³

     = 4sin(6π) - 2

     = 4sin(6π) - 2

     = 4(0) - 2

     = -2

Therefore, at t = 1 second, the particle's position is -2 meters.

b) To find the particle's velocity, we need to differentiate the position function with respect to time (t):

v(t) = dx(t)/dt

Using the given formula, we have:

x(t) = 4sin(6πt) - 2t³

Taking the derivative:

v(t) = d/dt [4sin(6πt) - 2t³]

     = 4(6πcos(6πt)) - 6t²

Now, substitute t = 1 into the velocity function:

v(1) = 4(6πcos(6π(1))) - 6(1)²

     = 4(6πcos(6π)) - 6

     = 4(6π(1)) - 6

     = 24π - 6

Therefore, at t = 1 second, the particle's velocity is 24π - 6 m/s.

c) To find the particle's acceleration, we need to differentiate the velocity function with respect to time (t):

a(t) = dv(t)/dt

Using the velocity function derived earlier:

v(t) = 4(6πcos(6πt)) - 6t²

Taking the derivative:

a(t) = d/dt [4(6πcos(6πt)) - 6t²]

     = -24π²sin(6πt) - 12t

Now, substitute t = 1 into the acceleration function:

a(1) = -24π²sin(6π(1)) - 12(1)

     = -24π²sin(6π) - 12

     = -24π²(0) - 12

     = -12

Therefore, at t = 1 second, the particle's acceleration is -12 m/s².

Learn more about derivative here: https://brainly.com/question/29144258

#SPJ11

The number of children in the town with population 1,98,568 is 1,17,578.

It is given in the question that the total population of the town is 1,98,568 and the number of men are 45,312 and  the number of women are 35,678.

We know that,

Total population of the town = Total number of men the town + Total number of women in the town + total number of children in the town

Hence,

1,98,568 = 45,312 + 35,678 +  total number of children in the town

1,98,568 = 80,990 +  total number of children in the town

Total number of children in the town = 1,98,568 - 80,990

Total number of children in the town = 1,17,578

To learn more about children, here:-

https://brainly.com/question/4260407

#SPJ4

42 red blood cells are needed to make a line 1 inch long

The diameter of a red blood cell is 6 x \(10^{-6}\) m,

so we need to determine how many cells can fit in a

line 1 inch long (2.54 x\(10^{-5}\) m).

Dividing the length by the diameter gives the number of cells:

2.54 x \(10^{-5}\) m / 6 x \(10^{-6}\) m = 42.33.

So, approximately 42 red blood cells are needed to make a line 1 inch long.

This highlights the small size of red blood cells and the remarkable ability of the human body to produce and maintain billions of these cells for proper blood circulation and oxygen delivery.

Red blood cells, also known as erythrocytes, are one of the main types of blood cells. They are biconcave discs with a diameter of about 7.5 micrometers, and their primary function is to transport oxygen from the lungs to the tissues and carbon dioxide from the tissues to the lungs.

To know more on red blood cells follow this link

https://brainly.com/question/17890844#

#SPJ11

Answer:

24

Step-by-step explanation:

144/12 = 12

Then 12 times 2 = 24

Hope this helps!

Answer:

24

Step-by-step explanation:

144/12=12

12*2=24

Answer:

18

Step-by-step exp18lanation:

1) Simplify 2 - 4 to -2.

3 - 5 × -2 ÷ 2 × 3

2) Simplify 5 × -2 to -10.

3 - (-10 ÷ 2 × 3)

3) Simplify -10 ÷ 2 to -5.

3 - (-5 × 3)

4) Simplify -5 × 3 to -15.

3 - (-15)

5) Remove parentheses.

3 =+15

6) Simplify.

18

Answer:

24

simple explanation:

{3+[-5(2-4)÷2}×3

{3+[-5(-2)÷2}×3

{3+[-10]÷2)×3

3+5×3

8×3

=24

The size of each house of the Texas legislature is as follows:

There are 150 members in the House and 31 members in the Senate.

The Texas legislature consists of two houses: the House of Representatives and the Senate. The size of each house is determined by the number of members serving in it.

In the given choices:

Option 1: There are 181 members in the House and 30 members in the Senate. This option does not match the commonly known structure of the Texas legislature.

Option 2: There are 150 members in the House and 31 members in the Senate. This option matches the commonly known structure of the Texas legislature.

Option 3: There are 150 members in both the House and the Senate. This option implies that both houses have the same number of members, which is not the case in the Texas legislature.

Option 4: There are 150 members in the Senate and 31 members in the House. This option contradicts the typical arrangement of the Texas legislature.

The size of each house of the Texas legislature is as follows:

There are 150 members in the House and 31 members in the Senate.

To know more about Senate, visit

https://brainly.com/question/22932886

#SPJ11

Answer:

1³ = 1

2³ = 8

3³ = 27

4³ = 64

5³ = 125

6³ = 216

Step-by-step explanation:

Answer:

The cube of first six natural numbers are

1, 8, 27, 65, 125, 216

Step-by-step explanation:

Natural Numbers are known as 1, 2, 3, 4, ..., ∞

Now,

For Cube of first six natural numbers

1³ = 1

2³ = 8

3³ = 27

4³ = 64

5³ = 125

6³ = 216

Thus, The cube of first six natural numbers are

1, 8, 27, 65, 125, 216

-TheUnknownScientist

The unit of measurement used to describe how far a set of values are from the mean is the standard deviation. Therefore, the correct answer is (b) standard deviation.

The variance is another measure of spread, but it is not in the form of the original units of measurement. The median is a measure of central tendency and not a measure of spread. The mode is the most frequently occurring value in a set and is also not a measure of spread.
The unit of measurement used to describe how far a set of values are from the mean is the Standard Deviation (b). It is calculated by taking the square root of the variance and provides a measure of the average distance between each value in the set and the mean. The Median (c), on the other hand, is the middle value in a set when the values are arranged in numerical order.

Learn more about Standard Deviation:

brainly.com/question/23907081

#SPJ11

Answer:

g=dx

Or, if you'r wanting the solved equation..

12 = 0.5 x 24

Step-by-step explanation:

If she has 12 gallons in her tank and you look at what it's asking us to do, "..number of gallons of gas, g" pairs up with the 12 gallons while the 0.5 gallons used per day pairs with "...the number of days, d, she has driven to school."

Hope this helped!

Answer:

Step 1: Locate and underline the whole numbers place (2) then look at the digit to the right (6):

2.6

Step 2: In this case, the digit to the right (6) is 5 or above. So, we add 1 to the whole numbers place (2). The digit(s) after the (2) are replaced by zeros (or dropped). Thus, we get 3 as the answer.

In short: 2.6 rounded to the nearest whole number is 3.

In order from top to bottom, your answer should be:

A

C

B

The leading coefficient of a polynomial is the coefficient of the term with the highest degree. It can tell us a lot about the graph of the polynomial, it can mainly tell us whether the graph is in a downward direction or upward direction.

If the leading coefficient is positive, then the graph will start at the origin and will extend upwards, with the degree of the polynomial determining how steep the graph is. If the leading coefficient is negative, then the graph will start at the origin and extend downwards.

If the leading coefficient is 0, then the graph will be a horizontal line. The leading coefficient can also tell us about the end behavior of the graph. If the degree of the polynomial is even, then the end behavior will be a horizontal line. If the degree of the polynomial is odd, then the end behavior will be a vertical line. Knowing the leading coefficient of a polynomial gives us a basic idea of what the graph of the polynomial will look like.

Learn more about leading coefficient:

https://brainly.com/question/24881460

#SPJ4

Answer:

903

Step-by-step explanation:

Answer:

129 x 6=774

774+1=775

Step-by-step explanation:

Hope this helps