You are looking to build a storage area in your back yard. This storage area is to be built out of a special type of storage wall and roof material. Luckily, you have access to as much roof material as you need. Unfortunately, you only have 26.7 meters of storage wall length. The storage wall height cannot be modified and you have to use all of your wall material.
You are interested in maximizing your storage space in square meters of floor space and your storage area must be rectangular
What is your maximization equation and what is your constraint? Write them in terms of x and y where x and y are your wall lengths.
Maximize z = _____
Subject to the constraint:
26.7 ______
Now solve your constraint for y:
y= ___________
Plug your y constraint into your maximization function so that it is purely in terms of x. Maximize z= _______
Using this new maximization function, what is the maximum area (in square meters) that your shed can be? Round to three decimal places.
Maximum storage area (in square meters) = _____

\(~~~~~~ \stackrel{\textit{\LARGE Quarterly}}{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$7000\\ r=rate\to 9\%\to \frac{9}{100}\dotfill &0.09\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &12 \end{cases}\)

\(A = 7000\left(1+\frac{0.09}{4}\right)^{4\cdot 12} \implies A=7000(1.0225)^{48}\implies \boxed{A \approx 20367.48} \\\\[-0.35em] ~\dotfill\)

\(~~~~~~ \stackrel{\textit{\LARGE Annually}}{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$7000\\ r=rate\to 9\%\to \frac{9}{100}\dotfill &0.09\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &12 \end{cases}\)

\(A = 7000\left(1+\frac{0.09}{1}\right)^{1\cdot 12}\implies A=7000(1.09)^{12} \implies \boxed{A \approx 19688.65} \\\\[-0.35em] ~\dotfill\\\\ 20367.48~~ - ~~19688.65 ~~ \approx ~~ \text{\LARGE 678.83}\)

After 20 years, the value of the fox population will be 640.

The population of the fox after 20 years is calculated as follows;

The given function is;

y = 40 x 4ˣ

Where;

how many 10 years period make up 20 years?

x = 2

The value of the fox population is calculated as follows

y = 40 x 4²

y = 40 x 16

y = 640

Learn more about population growth here: https://brainly.com/question/25630111

#SPJ1

Answer:

Use desmos in the future to figure this out

Step-by-step explanation:

Desmos is a miracle for graphing assignments.

Also, (2, 7)

Just substitute every one of them in!

3*-5+4*1 is not bigger than 20

0^-5+-3*4 is not bigger than 20

3*-4+4*-2 is not bigger than 20

3*2+4*7=34 is bigger than 20

Therefore choosing answer D!

The phrase "twelve less than the product of three and a number" can be translated into an algebraic expression 3x - 12. We can use this expression to find the value of the expression for a given value of x or to write and solve an equation involving this expression.

The phrase "twelve less than the product of three and a number" can be translated into an algebraic expression. To do this, we need to assign a variable to the unknown number and then use multiplication and subtraction to represent the given information.

Let x be the unknown number. The product of three and x is 3x. Twelve less than 3x is 3x - 12. Therefore, the algebraic expression for "twelve less than the product of three and a number" is 3x - 12. This expression represents a value that is 12 less than three times the number x.

For instance, if we know that a number is 7, we can use this expression to find the value of "twelve less than the product of three and 7."3x - 12 = 3(7) - 12= 21 - 12= 9Therefore, the value of "twelve less than the product of three and 7" is 9. We can also use this expression to write an equation and solve for x. For example, if we know that the value of "twelve less than the product of three and a number" is 33, we can write an equation:3x - 12 = 33Then, we can solve for x:3x = 33 + 123x = 45x = 15. Therefore, the unknown number is 15.

To summarize, the phrase "twelve less than the product of three and a number" can be translated into an algebraic expression 3x - 12. We can use this expression to find the value of the expression for a given value of x or to write and solve an equation involving this expression.

Learn more about product from the given link

https://brainly.com/question/20451763

#SPJ11

Paper Company will make the following entry:

Debit: Notes Receivable - Dame Company $4,700

Credit: Accounts Receivable $4,700

What is an entry?

An "entry" in accounting refers to the recording of a financial transaction or event in the company's books or accounting system. It is the process of documenting the impact of a transaction on the financial statements.

1. Debit: Notes Receivable - Dame Company ($4,700) - This account represents the amount owed to Paper Company by Dame Company and is classified as a noncurrent asset since it will be settled in more than one year.

2. Credit: Accounts Receivable ($4,700) - This account represents the open accounts receivable from Dame Company, which is now being settled through the promissory note.

By making this entry, Paper Company acknowledges the receipt of the promissory note and removes the outstanding accounts receivable from their books, replacing it with a notes receivable asset.

learn more about debit here:

https://brainly.com/question/3069919

#SPJ4

74.5kg

Step-by-step explanation:

(140kg ÷ 2 = 70kg) 70kg - 4.5kg = 65.5 (65.5 is raima's weight) 70kg +4.5kg = 74.5kg (74.5kg is sia's weight)

Answer:

Wheres the question?

Step-by-step explanation:

In this scenario, we are given the following information: sample size (n) is 49, sample mean (P) is 50, sample standard deviation (s) is 7, null hypothesis (H₀) states that the population mean (μ) is greater than or equal to 52, and the alternative hypothesis (Hₐ) states that the population mean is less than 52.

The test statistic for this situation is the t-statistic, which measures the difference between the sample mean and the hypothesized population mean, taking into account the sample size and the sample standard deviation. It is used to assess the evidence against the null hypothesis. In this case, since the alternative hypothesis states that the population mean is less than 52, we have a left-tailed test. To calculate the t-statistic, we use the formula:

t = (P - μ) / (s / √n)

Plugging in the given values:

t = (50 - 52) / (7 / √49) = -2 / (7 / 7) = -2

Therefore, the test statistic for the provided information is -2. This value represents the standardized difference between the sample mean and the hypothesized population mean, accounting for the sample size and standard deviation. It indicates that the sample mean is 2 standard deviations below the hypothesized population mean of 52.

Learn more about null hypothesis here: brainly.com/question/30821298

#SPJ11

To find a value of c such that P(z ≥ c) = 0.55, we need to use a standard normal distribution table or calculator.From the standard normal distribution table, we find that the z-score corresponding to a right-tailed area of 0.55 is approximately 0.126.

Therefore, we have:

P(z ≥ c) = 0.55

P(z ≤ c) = 1 - P(z ≥ c) = 1 - 0.55 = 0.45

Using the standard normal distribution table, we find that the z-score corresponding to a left-tailed area of 0.45 is approximately -0.126.

So, c = -0.126.

Therefore, the value of c that satisfies P(z ≥ c) = 0.55 is approximately -0.126.

To learn more about distribution : brainly.com/question/29664127

#SPJ11

Answer:

9 is answer . . . . . . . ........

The numerical values of the circumference and area are equal.

Answer:

To simplify it a

Step-by-step explanation:

To estimate the number of new users that would be added during time period 7, we can use the Bass diffusion model, which is commonly used to model the adoption of new products or technologies.

The Bass diffusion model is given by the formula:

\(\[N(t) = \frac{{p \cdot q}}{{q + (p/q) \cdot e^{-((p+q) \cdot t)}}}\]\)

where:

- N(t) represents the cumulative number of adopters at time \(t\).

- p is the innovation parameter, representing the coefficient of innovation.

- q is the imitation parameter, representing the coefficient of imitation.

- e is the base of the natural logarithm.

Given a population size of 67 million, an innovation parameter of 0.005, and an imitation parameter of 0.84 for Color TV, we can substitute these values into the Bass diffusion model and calculate the number of new users added during time period 7.

\(\[N(7) - N(6) = \frac{{p \cdot q}}{{q + (p/q) \cdot e^{-((p+q) \cdot 7)}}} - \frac{{p \cdot q}}{{q + (p/q) \cdot e^{-((p+q) \cdot 6)}}}\]\)

Substituting the given values into the equation:

\(\[N(7) - N(6) = \frac{{0.005 \cdot 0.84}}{{0.84 + (0.005/0.84) \cdot e^{-((0.005+0.84) \cdot 7)}}} - \frac{{0.005 \cdot 0.84}}{{0.84 + (0.005/0.84) \cdot e^{-((0.005+0.84) \cdot 6)}}}\]\)

Evaluating the expression will give us the estimated number of new users added during time period 7.

In LaTeX, the solution can be represented as:

\(\[N(7) - N(6) = \frac{{0.005 \cdot 0.84}}{{0.84 + (0.005/0.84) \cdot e^{-((0.005+0.84) \cdot 7)}}} - \frac{{0.005 \cdot 0.84}}{{0.84 + (0.005/0.84) \cdot e^{-((0.005+0.84) \cdot 6)}}}\]\)

After evaluating this expression, you will obtain the estimated number of new users added during time period 7.

To know more about LaTex visit-

brainly.com/question/18882901

#SPJ11

The variable which the scientist willfully modifies is referred to as the independent variable. Every variable observed throughout the experiment seems to be the dependent variable.

A symbol (often a letter) used in mathematics to represent an unknowable quantitative score in such an equation or algebraic statement. A variable can be defined as a quantity that is changeable and not fixed.

Examples of variables include age, gender, company revenue and costs, the country of birth, expenditures, class grades, eye color, and vehicle kind. Because the amount may differ between data units within a population and may change over time, it is referred to as a variable.

To know more about variable visit:

https://brainly.com/question/29896953

#SPJ4

The two equivalent expressions are the second one and the last:

(56x + 24)/8 and 3 + 7x

We want to find an equivalent expression to 56x + 24 divided by 8, so we want to simplify the expression:

(56x + 24)/8   (that is the second expression)

We can distribute that division so we get:

(56x + 24)/8 = (56x)/8 + 24/8

Now we can simplify these two quotients so we get:

(56x)/8 + 24/8 = 7x + 3  (that is the last expression).

Then the two equivalent expressions are:

(56x + 24)/8 and 3 + 7x

Learn moer about equivalent expressions at:

https://brainly.com/question/2972832

#SPJ1

The weight of food packed in certain containers is a random variable with a mean of 16 0z. and a standard deviation of 0.6 oz. If 36 packages are randomly selected, the probability that the mean will be greater than 16.2 oz is 2.28%.

Given that the weight of food packed in containers is a random variable with a mean (µ) of 16 oz. and a standard deviation (σ) of 0.6 oz, we want to find the probability that the mean weight of a sample of 36 packages (n) will be greater than 16.2 oz.
Step 1: Calculate the standard error (SE) of the sample mean.
SE = σ / √n = 0.6 / √36 = 0.6 / 6 = 0.1
Step 2: Calculate the z-score for 16.2 oz.
z = (sample mean - population mean) / SE = (16.2 - 16) / 0.1 = 2
Step 3: Find the probability that the mean weight will be greater than 16.2 oz.
To find the probability for a z-score of 2, we can look it up in a standard normal (z) table or use a calculator that provides the area to the left of the z-score.
Using the table or calculator, we find the area to the left of the z-score 2 is approximately 0.9772. Since we are looking for the probability of the mean weight being greater than 16.2 oz, we want the area to the right of the z-score. To find this, subtract the area to the left from 1:
1 - 0.9772 = 0.0228
So, the probability that the mean weight of the 36 packages will be greater than 16.2 oz is approximately 0.0228 or 2.28%.

To learn more about probability, refer to:-

https://brainly.com/question/30034780

#SPJ11

Answer:

8.89 feet

Step-by-step explanation:

\(\sqrt{79}\) = 8.888, rounded to nearest hundredth would be 8.89

Answer:

$400

Step-by-step explanation:

We will make this question into a function by setting 'p' as the initial price before sale and converting the percent to a decimal (60*0.01).

Because the final price was calculated by multiplying the initial price by 60%, we can represent that with the function:

0.6p=240

All we need to do now is isolate p by dividing out 0.6.

p=400

Giving us an answer of $400 (that's an expensive jacket )

It is requred to test the exactness of the given ODE and then find its general solution. Then, if the given ODE is not exact, an integrating factor must be used to make it exact.

This given ODE is:(2xy - 2y²e^(3x))dx + (x² - 2ye^(2x))dy = 0.To verify the exactness of the given ODE, we determine whether or not ∂Q/∂x = ∂P/∂y, where P and Q are the coefficients of dx and dy respectively, as follows: P = 2xy - 2y²e^(3x) and Q = x² - 2ye^(2x).Then, we have ∂P/∂y = 2x - 4ye^(3x) and ∂Q/∂x = 2x - 4ye^(2x).Thus, since ∂Q/∂x = ∂P/∂y, the given ODE is exact.To solve the given ODE, we have to find a function F(x,y) that satisfies the equation Mdx + Ndy = 0, where M and N are the coefficients of dx and dy respectively. This is accomplished by integrating both P and Q with respect to their respective variables. We have:∫Pdx = ∫(2xy - 2y²e^(3x))dx = x²y - y²e^(3x) + g(y), where g(y) is a function of y. We differentiate both sides of this equation with respect to y, set it equal to Q, and then solve for g(y). We have:(d/dy)(x²y - y²e^(3x) + g(y)) = x² - 2ye^(2x)Thus, g'(y) = 0 and g(y) = C, where C is a constant.Substituting the value of g(y) in the equation above, we get:x²y - y²e^(3x) + C = 0, as the general solution.The given ODE is exact, so we can solve it by finding a function that satisfies the equation Mdx + Ndy = 0. After integrating both P and Q with respect to their respective variables, we find that the general solution of the given ODE is x²y - y²e^(3x) + C = 0.

To know more about integrating factor visit:

brainly.com/question/32554742

#SPJ11

There are four 1/4’s per hour

Multiply the miles by 4:

15 3/4 x 4 = 63 miles per hour

Answer:

(-4,-5)

Step-by-step explanation:

(x-coordinate, y-coordinate)

-4 is C's x-coord and -5 is C's y-coordinate

Answer:

thx

Step-by-step explanation:

Answer:

n-13

Step-by-step explanation:

im not up for this bc didn't sleep a lot hope i did ok

In programming, a loop is a control structure that allows us to execute a block of code repeatedly. A for loop is a type of loop that is commonly used when we need to repeat a set of instructions for a specific number of times.

In this case, we want to print the integers 0 through 39, each value on a separate line.

Here's an example of a for loop in Python that accomplishes this:

for i in range(40):

   print(i)

In this loop, the variable `i` takes on the values 0 through 39, one at a time, on each iteration of the loop. The range(40) function generates a sequence of integers from 0 to 39, which is used to control the loop.

The print() function outputs the value of `i` to the console on each iteration, followed by a newline character which creates a new line for each value.

To break this down further, the 'for' keyword initiates the loop and the `in` keyword specifies the range of values for the loop. The `range()` function generates a sequence of integers starting at 0 and ending at 39.

The `print()` function outputs each value to the console followed by a newline character which creates a new line for each value. This loop will execute a total of 40 times, printing each value on a separate line.

In summary, the for loop is a powerful and flexible tool in programming that allows us to automate repetitive tasks. In this example, we used a for loop to print the integers 0 through 39, each on a separate line, in a concise and efficient manner.

To know more about loop refer here:

https://brainly.com/question/14390367?#

SPJ11

Answer:

√27

Step-by-step explanation:

3 × √3

The square of 3 is 9.

√9 × √3

√(9 × 3)

Multiply.

√27

3√3 as a whole radical is √27.

Answer:

x = 7
y = -7

Step-by-step explanation:

Answer: 5280 miles

Step-by-step explanation:

Answer:

\(f(x)=x^3-9x^2+8x+60\)

Step-by-step explanation:

The zeros of a function are the x-values when f(x) = 0.

Factor Theorem

If f(x) is a polynomial, and f(a) = 0, then (x – a) is a factor of f(x).

If the zeros of the polynomial are -2, 5 and 6 then (x + 2), (x - 5) and (x - 6) are factors of the polynomial.

Therefore, the polynomial in factored form is:

\(f(x)=a(x+2)(x-5)(x-6)\)

where a is the leading coefficient.

Given a = 1:

\(f(x)=(x+2)(x-5)(x-6)\)

Expand the parentheses to express the polynomial in standard form:

\(f(x)=(x+2)(x-5)(x-6)\)

\(f(x)=(x^2-3x-10)(x-6)\)

\(f(x)=x^3-6x^2-3x^2+18x-10x+60\)

\(f(x)=x^3-9x^2+8x+60\)

Answer:

Step-by-step explanation:

A teacher buys a yogurt cup for $2.00 and a textbook for $13.00 for each student in their classroom. The teacher spends a total of $405.00 for all of the yogurt cups and textbooks. How many students are in the teacher's class?

expenditure for each student 2 + 13 = 15.

We divide the total expenditure by the number of students

405: 15 = 27 $ (your answer)

Answer:

27

Step-by-step explanation:

The diameter, in inches, of a circle with a circumference of 84.78 inches is equal to 27 inches.

In order to calculate the diameter of any circle, you should use the formula for the circumference of a circle. Mathematically, the circumference of a circle can be calculated by using this mathematical expression:

C = πD

Where:

By making diameter (D) the subject of formula, we have the following:

D = C/π

Note: The value of pie (π) is equal to 3.14.

Substituting the given parameters into the formula, we have the following;

Diameter (D) = 84.78/3.14

Diameter (D) = 27 inches.

Read more on a circle here: brainly.com/question/6615211

#SPJ1

Answer:

Step-by-step explanation:

strategy:  Find the area of the entire dartboard, then subtracted the inner circle from that whole.    we will have the entire outer circle,  so divide that by 2 for half of it.   Next divide the inner circle by 4 . Then add that to the outer circle answer from above.

whole circle = \(\pi\)*\(20^{2}\) = 1257.142857 \(cm^{2}\)

inner circle = \(\pi\)*\(10^{2}\) = 314.2857143 \(cm^{2}\)

1257.142857 - 314.2857143 = 942.8571427 outer circle

942.8571427 / 2 = 471.4285 ( half of the outer circle)

now find quarter of the inner circle

314.2857143 / 4 = 78.57142855

add the two parts together

78.57142855 + 471.4285  = 549.9999

The shaded regions = 550 \(cm^{2}\)

The 2021st term of the sequence is (- n - 2017).

Given,

A sequence is constructed by listing all the possible numbers that contain no digit greater than 3 in ascending order.

We need to find out what is the 2021st term of this sequence.

An arithmetic sequence is a sequence where the difference between the consecutive terms is the same.

Example: 2, 4, 6, 8, 10

4 - 2 = 2

6 - 4 = 2

8 - 6 = 2

The nth term of an arithmetic sequence is given by:

= a + ( n - 1 ) d

Where a = the first term

d = common difference

Let the sequence that contains no digit less than 3 in ascending order be:

3 - n, 3 - (n + 1), 3 - (n+2), 3 - (n+3), 3 - (n+4),......

Where n = any real number from 1.

We see that the common difference is -1.

3 - (n+1) - (3 - n)

= 3 - n - 1 - 3 + n

= -1

3 - (n+2) - [3-(n+1)]

= 3 - n - 2 - 3 + n + 1

= -1

Find the 2021st term.

We have,

a = 3 - n

d = -1

n = 2021

= a + ( n - 1 ) d

= (3 - n) + ( 2021 - 1 ) (-1)

= 3 - n - 2020

= - n - 2017

Thus the 2021st term of the sequence is - n - 2017.

Learn more about arithmetic sequence here:

https://brainly.com/question/10396151

#SPJ4