The Pool Fun Company has learned​ that, by pricing a newly released Fun Noodle at $ 3 comma sales will reach 7000 Fun Noodles per day during the summer. Raising the price to $ 4 will cause the sales to fall to 5000 Fun Noodles per day. a.  Assume that the relationship between sales​ price, x, and number of Fun Noodles​ sold, ​ y, is linear. Write an equation in​ slope-intercept form describing this relationship. Use ordered pairs of the form​ (sales price, number​ sold).

The question involves hypothesis testing for proportions. The p-value is calculated using the normal distribution for proportions. In this case, the p-value is found to be 0.0417.

The question involves hypothesis testing for proportions. The null and alternative hypotheses need to be defined for the study.

The p-value is calculated using the normal distribution for proportions.

In this case, the p-value is found to be 0.0417. We can conclude that there is sufficient evidence to reject the null hypothesis and conclude that there is a difference between the proportions of households in the two communities.

Answer:

17

Step-by-step explanation:

There are 5 different triangles formed by drawing all of the diagonals from a vertex of a hexagon.

To find the number of triangles formed by drawing all of the diagonals from a vertex of a hexagon, we need to determine the number of different combinations of vertices that can form triangles.

For a hexagon, there are 4 vertices that can be chosen as one of the vertices of the triangle. The other 2 vertices can be chosen from the remaining 5 vertices. The order in which the vertices are chosen doesn't matter, so we need to divide by 2 to avoid overcounting.

Using the combination formula, we get:

C(5, 2) / 2 = 10 / 2 = 5

Therefore, there are 5 different triangles formed by drawing all of the diagonals from a vertex of a hexagon.

Annual income of Mason is 70,000 dollars.

He saves 7% of his annual earnings into a saving account.

So, his savings would be 7% of 70,000 = 0.07 x 70,000 = 4,900 dollars.

The saving account gives an interest rate of 3% per annum.

So the interest accrued on 4900 dollars over the year would be 3% of 4,900 = 0.03 x 4,900 = 147 dollars.  

Total amount in the saving account would be sum of principal amount and interest accrued.

Total balance = principal amount + interest accrued.

Total balance = 4900 + 147 = 5,047 dollars.

Hence, option C is correct i.e. 5,047 dollars.

The solution to the system of equations is:

x = 0

y = 6

To solve the system of equations:

-6y + 11x = -36

-4y + 7x = -24

You can use the method of substitution or elimination. I'll use the elimination method here.

First, multiply the second equation by 3 to make the coefficients of y in both equations equal:

-6y + 11x = -36

-12y + 21x = -72

Now, you can subtract the first equation from the second equation to eliminate x:

(-12y + 21x) - (-6y + 11x) = (-72) - (-36)

Simplify:

-12y + 21x + 6y - 11x = -72 + 36

Combine like terms:

-6y + 10x = -36

Now, divide both sides by 2 to simplify:

(-6y + 10x) / 2 = (-36) / 2

-3y + 5x = -18

Now you have a simplified system of equations:

-6y + 11x = -36

-3y + 5x = -18

You can solve this system using either the substitution or elimination method. Let's use the elimination method again. Multiply the second equation by 2 to make the coefficients of x equal:

-6y + 11x = -36

-6y + 10x = -36

Now, subtract the first equation from the second equation:

(-6y + 10x) - (-6y + 11x) = (-36) - (-36)

Simplify:

-6y + 10x + 6y - 11x = -36 + 36

Combine like terms:

-1x = 0

Now, solve for x:

x = 0

Now that you know the value of x, you can substitute it into one of the original equations to find the value of y. Let's use the first equation:

-6y + 11x = -36

-6y + 11(0) = -36

Simplify:

-6y = -36

Now, solve for y:

y = (-36) / (-6)

y = 6

for such more question on system of equations

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To create 9 gallons of a 30% alcohol solution, mix 6 gallons of the 20% alcohol solution with 3 gallons of the 50% alcohol solution by setting up and solving a system of equations based on volumes and concentrations.

To find out how many gallons of 20% alcohol solution and 50% alcohol solution must be mixed to get 9 gallons of a 30% alcohol solution, we can set up a system of equations based on the volumes and concentrations of the solutions. Let's let x represent the volume of the 20% solution and y represent the volume of the 50% solution.

Since the total volume of the mixture should be 9 gallons, we have our first equation:

Next, we consider the concentration of alcohol in the final mixture. The amount of pure alcohol from the 20% solution is 0.20x gallons, and from the 50% solution, it is 0.50y gallons. The final mixture has a concentration of 30%, so the total amount of alcohol in the 9 gallons mixture is 0.30 * 9 gallons. This gives us our second equation:

Now we have a system of two equations with two variables that can be solved using methods such as substitution or elimination. After solving, we find that x = 6 gallons and y = 3 gallons. Therefore, to obtain 9 gallons of a 30% alcohol solution, you'd need to mix 6 gallons of the 20% alcohol solution with 3 gallons of the 50% alcohol solution.

The landscaper will need to add more herbicide after approximately 14 weeks, as the level of herbicide will then have degraded from 200 gallons to below the threshold of 50 gallons due to a weekly degradation rate of 10%.

The landscaper pours 200 gallons of herbicide into a pond, and this herbicide degrades at a rate of 10% each week. To find out in how many weeks the herbicide level will drop below 50 gallons, a simple mathematical model that describes exponential decay can be used.

To calculate this, we can use the formula [tex]A = P(1 - r)^n[/tex], where A is the amount of herbicide after n weeks, P is the initial amount of herbicide, and r is the percentage rate of degradation per week.

Starting with 200 gallons and wanting to find when it falls below 50 gallons, we set up the equation 50 = 200(1 - 0.10)^n. Simplifying this yields 50 = 200(0.9)^n. Dividing both sides by 200 gives us 0.25 = (0.9)^n.

To solve for n, we can take the logarithm of both sides. Using the natural logarithm, we get ln(0.25) = n ln(0.9). Then, divide by ln(0.9) to isolate n, giving us n = ln(0.25) / ln(0.9), approximately 13.51.

Since we cannot have a fraction of a week, we round up to the next whole week, thus the landscaper will need to add more herbicide after 14 weeks.

files are attached below

Answer:

The graph as shown below.

Step-by-step explanation:

Given : The function [tex]f(x)=\frac{1}{x-3}-2[/tex]

We have to plot the graph for the given function   [tex]f(x)=\frac{1}{x-3}-2[/tex]  

Consider the given function [tex]f(x)=\frac{1}{x-3}-2[/tex]

Domain of function [tex]f(x)=\frac{1}{x-3}-2[/tex]

DOMAIN is set of input values for which the function is real and has defined values.        

So, The given function is undefined at x = 3

So, Domain is [tex]x<3\quad \mathrm{or}\quad \:x>3[/tex]

RANGE is the set of values of dependent variable  for which the function is defined.

Inverse of given function is  [tex]y=\frac{3x+7}{x+2}[/tex]

Now, domain of inverse function is [tex]f\left(x\right)<-2\quad \mathrm{or}\quad \:f\left(x\right)>-2[/tex]

Now, x intercept and y- intercepts

x intercept where y = 0 and y- intercept where x= 0

Let f(x) = y

Then [tex]y=\frac{1}{x-3}-2[/tex]

Put x = 0

thus y- intercept is [tex]\left(0,\:-\frac{7}{3}\right)[/tex]

Now put y = 0

Then  x- intercept is [tex]\left(\frac{7}{2},\:0\right)[/tex]

Now, Calculate the vertical and horizontal asymptotes,

Vertical asymptotes,

Go over every undefined point and check if at least one of the following statements is satisfied.

[tex]\lim _{x\to a^-}f\left(x\right)=\pm \infty[/tex]

[tex]\lim _{x\to a^+}f\left(x\right)=\pm \infty[/tex]

Thus, The vertical asymptotes is x = 3

And For horizontal asymptotes,

[tex]\mathrm{Check\:if\:at\:}x\to \pm \infty \mathrm{\:the\:function\:}y=\frac{1}{x-3}-2\mathrm{\:behaves\:as\:a\:line,\:}y=mx+b[/tex]

We have y = -2 as horizontal asymptotes.

Plot we get the graph as shown below.

Since there are 200 units and variable costs are $500, we do a simple division, like this:

500/200 = 2.5.

So the answer is: 2.5

Hope this helped! c:

Answer:0.2

Step-by-step explanation: