9. At a scouts' camp. there is sufficient food to last 72 scouts for 6 days. If 18 scouts do not turn up for the camp, how much longer can the food last for the other scouts?​

(a) The break-even points are approximately 1,581 and 2,809 units produced.

(b)  The maximum revenue is approximately $2,088,931.47.

(c) P(x) = -5/9x² + 919x - 49,400

(d) The price that will maximize the profit is approximately $1,829.17 per unit.

An algebraic expression is when we use numbers and words in solving a particular mathematical question.

(a) To find the break-even points, we need to find the values of x at which the total revenue equals the total cost. The total revenue is the product of the selling price and the number of units sold, while the total cost is the sum of the fixed cost and the variable cost per unit multiplied by the number of units sold. Thus, we have:

Total revenue = Selling price × Number of units sold = (2148 - 5/9x)x

Total cost = Fixed cost + Variable cost per unit × Number of units sold = 49,400 + (49x/9 + 222)x

Setting the total revenue equal to the total cost, we get:

2148x - 5/9x² = 49,400 + (49x/9 + 222)x

Multiplying both sides by 9, we get:

19332x - 5x² = 445,110

Simplifying, we get:

5x²- 19332x + 445,110 = 0

Using the quadratic formula, we get:

x = (19332 ± sqrt(19332² - 4(5)(445,110))) / (2(5))

x ≈ 2808.6 or x ≈ 1581.4

Hence, the break-even points are approximately 1,581 and 2,809 units produced.

(b) The revenue function is given by:

R(x) = (2148 - 5/9x)x

To find the maximum revenue, we can take the derivative of the revenue function with respect to x, set it equal to zero, and solve for x:

R'(x) = 2148 - 10/9x = 0

x = 19332/10 ≈ 1933.2

Substituting this value of x into the revenue function, we get:

R(1933.2) ≈ $2,088,931.47

Hence, the maximum revenue is approximately $2,088,931.47.

(c) The profit function P(x) is given by:

P(x) = R(x) - C(x) = (2148 - 5/9x)x - (49,400 + (49x/9 + 222)x)

Simplifying, we get:

P(x) = -5/9x² + 919x - 49,400

(d) To find the maximum profit, we can take the derivative of the profit function with respect to x, set it equal to zero, and solve for x:

P'(x) = -10/9x + 919 = 0

x = 8265

Substituting this value of x into the profit function, we get:

P(8265) ≈ $1,077,927.78

Therefore, the maximum profit is approximately $1,077,927.78.

To find the price that will maximize the profit, we need to substitute the value of x into the selling price function:

Selling price = 2148 - 5/9x = 2148 - 5/9(8265) ≈ $1,829.17

Hence, the price that will maximize the profit is approximately $1,829.17 per unit.

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Answer:

19107

Step-by-step explanation:

First, we need to find the common difference (d), which we can find by subtracting two consecutive terms.  Thus, we can do d = 1 - (-3) = 4.

Now, we need to know how many terms are in the arithmetic series.  We can find the number using nth term formula, which is

[tex]a_{n}=a_{1}+(n-1)*d[/tex], where a1 is the first term, n is the term position (e.g., 1st, 2nd).

Although we don't know the term position of 389, we can still plug it into the formula and solving for n will reveal it's term number and the total number of sums in the sequence:

[tex]389=-3+(n-1)*4\\392=(n-1)*4\\392=4n-4\\396=4n\\99=n[/tex]

Now, we can find the sum using the sum formula, which is

[tex]S_{n}=n/2*(a_{1}+a_{n})[/tex]

Sn can become S99 since there are 99 terms and we can let an = a99, which we know is 389.

Now, we must solve for S99:

[tex]S_{99}=\frac{99}{2}*(-3+389)\\ S_{99}=\frac{99}{2}*(386)\\ S_{99}=19107[/tex]

The value of ∠ GPY, given the angle measures on the figure, can be found to be 118 °

The angles ∠ GPY and ∠ KPR are congruent, which means that they are the same.

The angle ∠ GPY can therefore be found by equating both angles to themselves:

8 p + 94 = 5 p + 103

Collect like terms ;

8 p - 5 p = 103 - 94

3 p = 9

p = 9 / 3

p = 3

The value of ∠ GPY is therefore :

= 5 ( 3 ) + 103

= 15 + 103

= 118 °

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The solution is, the capacity of the largest container that can fill the tanks an exact number of times is, 44 litres.

In mathematics, the greatest common divisor of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For two integers x, y, the greatest common divisor of x and y is denoted {\displaystyle \gcd}.

here, we have,

We subtract the remainders from the amounts.

447 - 7 = 440

577 - 5 = 572

669 - 9 = 660

Now we need the GCF of 440, 572, 660

440 = 2³ × 5 × 11

572 = 2² × 11 × 13

660 = 2² × 3 × 5 × 11

GCF = 2² × 11 = 44

The greatest common factor is 44.

Answer: 44

Check:

447/44 = 10 reminder 7

577/44 = 13 remainder 5

669/44 = 15 remainder 9

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Answer:

55 cards

Step-by-step explanation:

Answer:

-3, 1

Step-by-step explanation:

these are points where the curve cuts the x-axis

at this point the value of y=0

The slope-intercept form of the equation of the line through (5, 0) and perpendicular to y = -5/3x is y = 3/5x - 3.

What is the slope-intercept form of a linear equation, and how can we determine the equation of a line perpendicular to another line?

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. This form is useful for graphing lines and solving problems involving linear relationships.

To determine the equation of a line perpendicular to another line, we use the fact that the slopes of perpendicular lines are negative reciprocals of each other. In other words, if the slope of one line is m, then the slope of a line perpendicular to it is -1/m.

Calculate the slope-intercept form:

We are given that the line we are looking for passes through the point (5, 0) and is perpendicular to the line y = -5/3x. To find the equation of the line, we need to determine its slope and y-intercept.

The slope of the given line is -5/3, so the slope of the line perpendicular to it is:

-1/(-5/3) = 3/5

Therefore, the slope of the line we are looking for is 3/5.

Next, we can use the point-slope form of the equation of a line to find the equation of the line:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is a point on the line. We can substitute m = 3/5 and (x1, y1) = (5, 0) to get:

y - 0 = 3/5(x - 5)

Simplifying this equation, we get:

y = 3/5x - 3

which is the slope-intercept form of the equation of the line we were looking for.

Therefore, the slope-intercept form of the equation of the line through (5, 0) and perpendicular to y = -5/3x is y = 3/5x - 3.

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1. The decrease in the balance would be $11.25 2. The interest on the average daily balance would be $28.77. 3. The total interest paid would be $214,960. 4. The payment would be $1,978.

Interest refers to the amount of money that is charged or earned for the use of borrowed money. It is a fee paid by a borrower to a lender for the use of funds, or a payment received by a depositor from a bank for the use of their money.

Interest rates are typically expressed as a percentage of the principal amount and can be fixed or variable, depending on the terms of the loan or investment. The interest rate charged on a loan is determined by a number of factors, including the creditworthiness of the borrower, the length of the loan, and prevailing market conditions.

1. The decrease in the balance would be $11.25.

Calculation:

Minimum payment = 2.5% of $450 = $11.25

New balance after paying the minimum = $450 - $11.25 = $438.75

The decrease in the balance would be $450 - $438.75 = $11.25.

2. The interest on the average daily balance would be $28.77.

Calculation:

The balance for the first 14 days of the month = $2000

The balance for the last 16 days of the month = $1400

Average daily balance = (14 * 2000 + 16 * 1400) / 30 = $1666.67

Interest for the month = 0.23 / 12 * $1666.67 = $28.77

3. The total interest paid would be $214,960.

Calculation:

No. of payments = 30 * 12 = 360

Total amount paid = $876 * 360 = $315,360

Total interest paid = $315,360 - $125,000 = $190,360

4. The payment would be $1,978.

Calculation:

Monthly interest rate = 7.3% / 12 = 0.6083%

Number of payments = 30 * 12 = 360

Payment = $275,000 * 0.006083 / (1 - (1 + 0.006083)^-360) = $1,977.54 (rounded to nearest dollar: $1,978)

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Answer: less then

Step-by-step explanation: Less than means subtraction, whereas more than means addition. · Saying twice a number means that you are multiplying that number by 2.

The Length of wooden strip based on the information is 106 cm.

The perimeter of a shape is simply the total length of the boundary that the shape has. It should be noted that in this case, it's gotten by adding all the length that the shape has.

Length of wooden strip = Perimeter of a rectangular table.

= 2(Length+Breadth)

= 2(32+21)

= 2(53)

= 106 cm

Length of wooden strip is 106 cm.

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What is the length of the wooden strip required to frame a photograph of length and breadth 32 cm and 21 cm respectively?

Answer:

A. the graph of the function does not form a straight line.

Step-by-step explanation:

The calories burned per hour is 30 calories per hour

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

Calories at 7 = 25 calories

Calories at 9 = 85 calories

Using the above as a guide, we have the following:

Rate = Difference in calories/Difference in time

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

Rate = (85 - 25)/(9 - 7)

Evaluate

Rate = 30

Hence, the rate is 30 calories per hour

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Barbara's weekly average for the four-week period is 65 minutes.

What is the average?

The average, also known as the arithmetic mean, is a measure of central tendency that represents the typical value of a set of numbers. It is calculated by adding up all the numbers in the set and then dividing the sum by the total number of numbers.

To find Barbara's weekly average for the four-week period, we need to add up her weekly totals and divide the sum by 4 (since there are four weeks in the period):

Average = (48 + 115 + 62 + 35) / 4

= 260 / 4

= 65

Therefore, Barbara's weekly average for the four-week period is 65 minutes.

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Therefore , the solution of the given problem of unitary method comes out to be amount billed to the client.

To finish the job using the unitary technique, the equation from this nano section should be multiplied by two. In essence, when a wanted object is present, both the characterised by either a group and the pigment sections are omitted from the unit method. A variable fee of Inr ($1.01), for instance, would be paid for 40 pens. It's conceivable that one nation will have complete control over the strategy used to achieve this. Almost all living things have a unique trait.

Here,

$3,300 is debited from Accounts Payable - Client's Name.

Credit: $3,300 in revenue

This shows the revenue earned by the law company for the job done and records the increase in accounts receivable for the amount billed to the client.

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Step-by-step explanation:

To write the expression (-4-7i)+(-1-4i) in a+bi form, we need to simplify the expression by adding the real parts and the imaginary parts separately.

(-4-7i)+(-1-4i) = -4 - 1 - 7i - 4i = -5 - 11i

Therefore, (-4-7i)+(-1-4i) can be written in a+bi form as -5 - 11i.

Answer:

a= -24

b= 23

Step-by-step explanation:

(-4-7i)(-1-4i)

4+16i+7i-28

-24i+23i

Answer:

Step-by-step explanation:

The diameter of the circle is twice the length of the radius, so we can write:

2r = d

where r is the radius and d is the diameter.

Substituting the given diameter of 11 4/5 ft, we get:

2r = 11 4/5 ft

To find the length of the radius, we can divide both sides by 2:

r = (11 4/5) / 2

r = 5 9/10 ft

We also know that the length of the radius is z + 3.6, so we can set up the equation:

z + 3.6 = 5 9/10

Subtracting 3.6 from both sides, we get:

z = 5 9/10 - 3.6

z = 2 3/10

Therefore, the value of z is 2 3/10 or 2.3 as a decimal.

Answer: The correct answer is 2.3

Step-by-step explanation: Answer confirmed correct on test so no worries

Answer:

The length of the garden would be 480 ft and the width would be 320 ft.

Step-by-step explanation:

The longest pipe can fit in the prism is 11.7 ft, so, 12 ft long pipe does not fit.

The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.

From the given figure,

By considering base of the prism, we get

c²=6²+6²

c²=72

c=6√2 ft

Now, d²=c²+8²

d²=72+64

d²=136

d=√136

d= 11.7 ft

Hence, the longest pipe can fit in the prism is 11.7 ft, so, 12 ft long pipe does not fit.

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Answer:

9,646

Step-by-step explanation:

1378 acorns x 7 years = 9,646 acorns

The total cost of the tablet is $684.48

The first step is to write out the parameters given in the question

The cost of the tablet computer is $713

The tablet computer is on sale at 11%

Next is to multiply the total cost by the sales percent

11/100 × 713

= 0.11 × 713

= 78.43

= 713 - 78.43

= 634.57

The local sales tax rate is 7%

= 7/100 × 713

= 0.07 × 713

= 49.91

The total cost can be calculated as follows

= 49.91 + 634.57

= 684.48

Hence the total cost of the tablet is $684.48

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The function y=3x+12 in factored form is (3x+12) and the zero of the function is -4.

A linear function is a polynomial of degree 1, or a mathematical expression that describes a relation between two variables. It is often written in the form y = mx + b, where m is the slope, x is the independent variable, and b is the y-intercept.

The factored form of a linear equation is the same as the standard form of the equation, with the exception that the coefficients of the variables are each expressed as a product of their prime factors. In the case of y=3x+12, the factored form is (3x+12). The zero of the function (also known as the root of the equation) is the value of the variable that will result in a value of 0 for the equation. To find the zero of the function, we need to set the equation equal to 0 and solve for the value of x. When we set y=0, we get 3x+12=0, which can be solved to get x=-4. Therefore, the zero of the function is -4.

The function y=3x+12 in factored form is (3x+12) and the zero of the function is -4.

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Answer:

y=x+5 x=3

Plug 3 into x

y=3+5

5+3=8

Step-by-step explanation:

The probability that fewer than 3 of the selected consumers believe that cash will be obsolete in the next 20 years IS 0.528.

The binomial probability formula is used to calculate the probability of getting exactly k successes in n independent trials, where each trial has only two possible outcomes (success or failure) and the probability of success is denoted as p. The formula is:

Here we have  

39.6​% of consumers believe that cash will be obsolete in the next 20 years.

Let p be the probability that a consumer believes that cash will be obsolete

=> p = 39.6% or 0.396.

Then, the probability that a consumer does not believe that cash will be obsolete is q = 1 - p = 0.604.  

We need to find the probability that less than 3 of the selected consumers believe that cash will be obsolete.

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

Using the binomial probability formula, we have:

[tex]P(X = k) = C(n,k) \times p^k\times q^{(n-k)[/tex]

=> P(X = 0) = C(6, 0) × (0.396)⁰ × (0.604)⁶ = 0.048

=> P(X = 1) = C(6, 1) × (0.396)¹ × (0.604)⁵ = 0.18

=> P(X = 1) = C(6, 2) × (0.396)² × (0.604)⁴ = 0.3

P(X < 3) = 0.048 + 0.18 + 0.3 = 0.528        

Therefore,

The probability that fewer than 3 of the selected consumers believe that cash will be obsolete in the next 20 years IS 0.528.

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The probability that Oliver will receive no emails in between 9.00am and 11.30am is 2.599%.

Poisson Distribution is defined as a discrete distribution which measures the likelihood of happening an event in a certain period of time.

The formula for Poisson distribution is,

P(x) = (e^(-λ) λˣ) / x!

Given that,

Average rate of arrival of emails in an hour = 1.46 per hour

Between 9.00 am and 11.30 am, there are 2.5 hours.

Average rate of arrival of emails in 2.5 hours = 2.5 × 1.46

                                                                           = 3.65

So, λ = 3.65

x = 0  (since no emails.)

P(0) = (e^(-3.65) (3.65)⁰) / 0!

      = e^(-3.65)

      = 0.02599

      = 2.599%

Hence the probability is 2.599%.

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The area of the shaded region in factored form is 9x^2(9 - 4π)

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

Square length = 9x

Radius of circle = 6x

The area of the square is given by (side length)^2.

Since the square has 9x as a side length, its area is:

Area 1 = (9x)^2 = 81x^2

For the circle, we have

Area 2 = π(6x)^2

Area 2 = 36πx^2

The area of the shaded region is the area of the original square minus the area of the circle, which is:

Shaded = 81x^2 - 36πx^2

Factorize

Shaded = 9x^2(9 - 4π)

Hence, the area is 9x^2(9 - 4π)

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The domain and range for the mapping diagram are given as follows:

The diagram represents a function, as each value of the input is mapped to a single value of the output.

The concepts for the domain and the range of the diagram are defined as follows:

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Answer:

-1/3x + 62/3

Step-by-step explanation:

Interchange the variables:  y = -3x + 62

Swap the sides:  -3y + 62

Move constant:  -3y + 62 = x

Divide and simplify:  -3y = x - 62

Answer: -1/3x + 62/3

Please help me with my answer.  I'm stuck and really need help on it.

Answer:

-3 = slope, 62 = y intercept

Step-by-step explanation:

The equation rewritten as a function of x is

[tex]y \ln \left(-2 x+x^2+2 y \right)=\ln (x)[/tex]

Generally, In the field of mathematics, an assignment of one element from set Y to each and every element in set X is the definition of a function. This particular set, X, is referred to as the function's domain, and this particular set, Y, is referred to as the function's codomain.

Historically, functions have been seen as an idealization of the way in which one variable relies on another variable. Wikipedia

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As a result, y = -x + 1/2 is the equatiοn οf the tangent line tο the curve x² + y² = (2x² + 2y² - x)² at the pοsitiοn (0,1/2).

An equatiοn in mathematics is a claim that twο mathematical expressiοns are equivalent. An equatiοn has an equal sign, typically has οne οr mοre factοrs, and can be sοlved fοr by applying algebraic οr numerical techniques. Equatiοns are used tο represent real-wοrld phenοmena, resοlve issues, and make predictiοns in many branches οf mathematics, science, and engineering.

given:

We must first use implicit differentiatiοn tο determine the derivative οf the curve in οrder tο determine the equatiοn οf the tangent line tο the curve at the pοsitiοn (0,1/2).

By taking the derivative οf the equatiοn's twο sides with regard tο x, we arrive at:

dy/dx = 2x + 2y

(2x² + 2y²- x) * (4x - 1) (4x - 1)

When we sοlve fοr dy/dx and simplify this equatiοn, we get:

[(1 - 4x)(2x + 2y)] Equals dy/dx / [4(2x² + 2y² - x) - 2y(1 - 4x)]

The slοpe οf the tangent line at the pοint (0,1/2) can nοw be calculated by plugging in the numbers x = 0 and y = 1/2:

dy/dx = [(1 - 4(0))

(2(0) + 2(1/2))] / [4(2(0)² + 2(1/2)² - 0) - 2(1/2)(1 - 4(0))] = -1

Therefοre, the tangent line's slοpe at the pοsitiοn (0,1/2) is negative οne. We can use the pοint-slοpe fοrm οf a line tο determine the equatiοn οf the tangent line:

where (x1,y1) is the tangency pοint and m is the inclinatiοn οf the tangent line. When we enter the numbers we have, we οbtain:

y - 1/2 = -1(x - 0) (x - 0)

When we simplify this sοlutiοn, we οbtain:

y = -x + 1/2

As a result, y = -x + 1/2 is the equatiοn οf the tangent line tο the curve x² + y2 = (2x² + 2y² - x)² at the pοsitiοn (0,1/2).

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Jack has enough rope for both projects.

Multiplication is a type of mathematical operation. The repetition of the same expression types is another aspect of the practice.

For instance, the expression 2 x 3 indicates that 3 has been multiplied by two.

Given:

Jack has 7 yards of rope.

He wants to cut it into pieces of different sizes.

Jack needs 84 inches of rope to tie some packages and 4 feet of rope for another project.

First, we need to convert all the measurements to the same units.

Let's convert yards to inches and feet to inches:

7 yards = 21 feet = 252 inches

4 feet = 48 inches

Now, let's add up the lengths of rope that Jack needs:

84 inches + 48 inches = 132 inches

So Jack needs a total of 132 inches of rope.

Since 132 inches is less than the total length of rope that Jack has (252 inches).

Therefore, he does have enough rope for both projects.

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