Mrs. Sanders has three grandchildren, who call her regularly. One calls her every three days, one calls her every four days, and one calls her every five days. All three called her on December 31, 2016. On how many days during the next year did she not receive a phone call from any of her grandchildren

Answers

Answer 1

By probability, she will not receive a phone call from any of her grandchildren after 146 days

How does probability affect our lives?

In those circumstances, probability helps in assessing the likelihood of an event. Probability plays a significant role in daily life. political strategy analysis, blood type determination, sports and gaming strategies, insurance buying or selling, online shopping, and online gaming.

There is a [tex]\frac{2}{3}[/tex] chance that the first child won't call, a [tex]\frac{3}{4}[/tex] chance that the second child won't call, and a [tex]\frac{4}{5}[/tex] chance that the third child won't call on any given day. There is a [tex]\frac{2}{3} *\frac{3}{4} * \frac{4}{5} = \frac{2}{5}[/tex] chance that no child calls her on a randomly selected day.

When we consider a sample of 360 days, in particular, this "unrigorous" reasoning becomes rigorous due to linearity of expectation; over the first 360 days, 360 * 2/5 = 144 days will pass without a phone call. Now, we just check the remaining days. On days $361 and $362, no one calls her. On days 363 and 364, she receives calls from children every three and four days, respectively. On day 365, she receives calls every five days. Therefore, to get our answer of 146, we two more days in  144.

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Related Questions

Question 1(Multiple Choice Worth 4 points) (02.05 LC) A surgeon performed two types of surgeries to treat large kidney stones and small kidney stones. Treatment A on large stones was successful 73% of the time, but on small stones it was successful 93% of the time. Treatment B was successful on large stones 69% of the time, but on small stones it was successful 87% of the time. The overall report stated treatment B was more successful. What may make this claim possible? Sampling error Cause-and-effect relationship Convenience error Confounding Simpson's Paradox

Answers

The correct option is Simpson's Paradox because the concept of the other options don't depict the paradox displayed in the question.

Simpson's paradox

it is simply a phenomenon in probability and statistics, whereby a trend appears in several different groups of data but will disappear or reverse when these groups are combined.

This result is often encountered in many areas of statistics and is very problematic especially when frequency data is given causal interpretations. The paradox can be resolved when causal relations are appropriately addressed in the statistical modeling.

It concluded that treatment B was more successful than treatment A without considering the conditions under which both treatments were carried out neither did it consider the severity of cases of patients involved in the treatment.

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a line is parallel to the y=x-8 and intersects the point (4,-9). What is the equation of this parallel line? Start by entering this into point-slope form

Answers

Answer:

sry i dont no

Jane had 27 stickers two weeks ago. Then she bought stickers every day for two weeks. She bought 3 stickers two weeks ago, and on each day after that, Jane bought two more stickers than she had bought on the previous day. How many stickers does Jane have now

Answers

Answer:

Jane has 251

Step-by-step explanation:

Stickers Initially = 27 Jane bought stickers on 1st day = 3 Remaining days = 13 Each next day she bought 2 more stickers than the previous day, so: Stickers bought in the last 2 weeks (14 days) = n+(n+2)+(n+2+2)+(n+2+2+2)+.............+(n+2(13))here n =3 So:Stickers bought in the last 2 weeks (14 days) = 3+5+7+9+11+13+15+17+19+21+23+25+27+29Stickers bought in the last 2 weeks (14 days) = 224 At Present Jane has Total Stickers = Stickers Initially+ Stickers bought in the last 2 weeks (14 days)At Present Jane has Total Stickers = 27+224

hellppppp gangyy nnn

Answers

The correct answer is option c as DE/AE=BC/AC

What is the slope of the line?

In Mathematics, a slope of a line is the change in y coordinate with respect to the change in x coordinate. The net change in y-coordinate is represented by Δy and the net change in x-coordinate is represented by Δx. Where “m” is the slope of a line. So, tan θ to be the slope of a line.

Given here ΔADE ≈ΔABC and thus  DE/AE=BC/AC

but tanθ = DE/AE=BC/AC where tan θ is the slope of the line thus both the lines have identical slopes.

Hence, The correct answer is option c)  ΔADE ≈ΔABC thus DE/AE=BC/AC Therefore the slope of AD is the same as the slope of AB

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determine whether each table represents a linear or non-linear function explain

Answers

Each of the tables is classified as linear or non-linear on the image presented at the end of the answer.

How to classify the functions as linear or non-linear?

A function is classified as linear or non-linear depending on the rate of change of the function.

If the rate of change of the function is constant, that is, when x changes by one amount, y always changes by the same amount, then the function is classified as linear.

Conversely, if the rate of change of the function is different for different intervals, then the function is classified as non-linear.

For example, the top-left function is non linear, as when x changes by one from x = 1 to x = 2, y changes by 3, from y = 1 to y = 4, while when x changes by one from x = 2 to x = 3, y changes by 5.

The bottom-right function is linear, as for each increase of x by 5, the value of y decays by 4.

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How do you make an XY graph in Excel?

Answers

Select the data for which you want to create a chart slope . Click INSERT > Recommended Charts. On the Recommended Charts tab, scroll through the list of charts that Excel recommends for your data

When you find the chart you like, click it > OK.

The formula for a horizontal line at y=4 is as follows: There is no slope. 4.0 is the y-intercept.

What are the Slope and intercepts ?

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

The slope expresses how quickly the dependent variable changes when the independent variable changes. The Greek capital letter D or D is frequently used by mathematicians and economics to represent change. Slope contrasts the change in the vertical axis, y, with the change in the horizontal axis, x.

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need to find domain
O 2. 20 18 16 14 12 10 8 6 4 2 2 4 6 8 10 12 14 16 18 20 3. -5-4 D:​

Answers

The collection of values that can be plugged into a function's domain are called its parameters.

How do you find domain?

A specific area of thinking, action, or interest is referred to as a domain, particularly one over which someone has authority. [formal]...the great artists who experimented with several mediums. Alternative words: region, globe, field, department [informal] More Domain synonyms.

The domain is used to facilitate user navigation and increase accessibility. Slugs are links that consist of the domain plus the text "/text."

Let y = f(x) be a function where x and y are the independent and dependent variables. The chosen x-value is said to fall within the domain of f if a function f offers a means of effectively producing a single value y while using a value for x to that end.

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A cone whose apex lies along its center axis and whose axis is perpendicular to its base is called a __________ cone.

Answers

A right cone is a cone whose apex is located along its center axis and whose axis is perpendicular to its base.

What is meant by right cone?When the line connecting the vertex to the circular base's midpoint forms the cone's axis, the cone is said to be right circular. In other words, the apex of the cone and the centre point of the circular base meet and form a right angle. Having a circular base and an apex or vertex, a cone is a three-dimensional solid. The cone whose axis line is parallel to the base is referred to as the right circular cone. In mathematics, a cone is a recognizable three-dimensional geometric shape having a smooth and curving surface pointing upward. The word "cone" comes from the Greek word "konos," which denotes a peak or a wedge.

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Today in class, we did calculations with decimals. Reflect on how you made these calculations:

How did we compute products of dollar amounts that were not whole numbers?

For example, how would you compute the product of 3 student tickets at $4. 25 per ticket?

Use this example to explain your strategy.

Answers

As per the decimal number system, the cost of 25 tickets is $32.5

The term decimal in math is defined as the numbers, which consist of two parts namely, a whole number part and a fractional part separated by a decimal point.

Here we have given that the product of 3 student tickets at $4.

Here we have know that the ticket cost for 3 students is $4.

Then the cost of one person is calculated by dividing the cost by the number of students then we get,

=> 4/3

=> 1.3

So, if the cost for one person or ticket is $1.3 then the cost of 25 tickets is calculated as,

=> 25 x 1.3

=> 32.5

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Find the equation of the line passing through the given point and parallel to the given line.​

Answers

Answer:

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

Step-by-step explanation:

[tex]x+2y=5 \\ \\ 2y=-x+5 \\ \\ y=-\frac{1}{2}x+\frac{5}{2}[/tex]

The slope of the given line is [tex]-\frac{1}{2}[/tex].

This means the slope of any line parallel to the given line is also [tex]-\frac{1}{2}[/tex].

Using point-slope form, the equation is [tex]y-2=-\frac{1}{2}(x-3)[/tex].

Find the 35th term for the sequence: 12, 9.5, 7, 4.5...

Answers

Answer:

-73

Step-by-step explanation:

So to begin you must find where you start on a graph. To do this you can go backwards from your first number and in this situation it would be 14.5 because the slope is -2.5x. I will use y as the answer.

y=-2.5x+14.5

From here you plug in how many terms are neeeded for the correct answer. In this situation there is 35 terms needed.

y=-2.5(35)+14.5

Solve this equation to get your answer.

y=-73

Answer:

The 35th term is - 73.

----------------------------

Given sequence:

12, 9.5, 7, 4.5...

This is an AP with the common difference of:

d = 4.5 - 7 = 7 - 9.5 = 9.5 - 12 = - 2.5

The first term is a = 12.

Use the nth term equation to find the 35th term:

aₙ = a + (n - 1)da₃₅ = 12 + (35 - 1)(- 2.5) = 12 - 34*2.5 = 12 - 85 = - 73

How do you identify an exponential graph?

Answers

Exponential graph is identified by its curve.

An exponential graph is a graph that shows a rapid increase or decrease of a value over time, where the rate of change is proportional to the current value. It is usually represented by a curve that bends upward or downward.

The key characteristic of an exponential graph is that the Y-axis is on a logarithmic scale, and the curve of the graph is a steep curve going either up or down. The equation of an exponential graph is usually of the form y = ab^x, where a is the initial value, b is the growth or decay factor, and x is the independent variable.

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ACTIVITY 6: Modeling Real Life

A company is loading recliners and sofas onto a trailer that has a volume of about 3800 cubic feet. Each recliner takes up about 40 cubic feet and each sofa takes up about 80 cubic feet. The company wants the shipment to have at least 30 recliners and more than 25 sofas. Write and graph a system that represents the situation. Give one example of the numbers of recliners and sofas the company can have in the shipment.

Answers

The equation is 80x + 1200 = 3800. And the numbers of at least 30 recliners and 32 sofas the company can have in the shipment.

What is linear equation?

Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.

Given:

A company is loading recliners and sofas onto a trailer that has a volume of about, 3800 cubic feet.

Each recliner takes up about 40 cubic feet and each sofa takes up about 80 cubic feet.

The company wants the shipment to have at least 30 recliners and more than 25 sofas.

The equation that represents the situation is,

80x + 40y = 3800,

where x is the volume of a sofa and y is the volume of a recliner.

If y = 30 then,

80x + 1200 = 3800

80x = 2600

x = 2600/80

x = 32.5

x ≈ 32

Therefore, 30 recliners and 32 sofas.

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Quadrilateral FGHI is similar to quadrilateral JKLM. Find the measure of side JK. Figures are not drawn to scale.

Answers

The measure of side KL in the given quadrilateral is 31.88 units.

What is a Quadrilateral?

A quadrilateral is a four-sided polygon with four edges and four corners that is used in geometry.

The Latin words Quadri, a variation of four, and latus, meaning "side," are the source of the name.

A two-dimensional shape with four sides, four vertices, and four angles is referred to as a quadrilateral.

Convex and concave are the two main forms.

Convex quadrilaterals can also be divided into a number of subgroups, including trapezoids, parallelograms, rectangles, rhombus, and squares.

So, according to the given figure of FGHI and JKLM:

FG/JK = GH/KL = HI/LM = FI/JM

GH/KL = HI/LM

7/KL = 9/41

KL = 7*41/9 = 31.888

Therefore, the measure of side KL in the given quadrilateral is 31.88 units.

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Correct question with a diagram:

Quadrilateral FGHI is similar to quadrilateral JKLM. Find the measure of side KL. Round your answer to the nearest tenth.

Brigid has a 25-foot ladder she will use to paint the side of her house. What angle does the ladder need to make with house so she can reach 18 feet up the side of her house

Answers

The ladder needs to make an angle of approximately 54.7 degrees with the house in order for Brigid to reach 18 feet up the side of the house.

To determine the angle the ladder needs to make with the house, we can use the tangent function.

First, we'll need to determine the opposite side (the height that the ladder needs to reach) and the adjacent side (the distance from the base of the ladder to the house) of the triangle formed by the ladder and the house.

Opposite side = 18 feet

Adjacent side = 25 feet

We can then use the tangent function to find the angle:

tan(angle) = opposite / adjacent

Solving for the angle, we get:

angle = arctan(18/25) = approximately 54.7 degrees

Therefore, the ladder needs to make an angle of approximately 54.7 degrees with the house in order for Brigid to reach 18 feet up the side of the house.

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Pat is making rectangular placemats each with area 1200cm2 she wants to braid trim around the edges how much trim does pat need for the placemat

Answers

Pat needs 16[tex]\sqrt{1200}[/tex]cm of trim for each placemat to braid trim around the edges.

To find out how much trim Pat needs for each placemat, we need to first find the perimeter of the rectangle.

The area of the rectangle is given as 1200 [tex]cm^2[/tex].

The perimeter of the rectangle is the sum of all four sides of the rectangle. If the length and breadth of the rectangle are L and B respectively, then the perimeter P can be calculated using the formula:

P = 2(L+B)

Now, let's find the length and breadth of the rectangle using the area formula,

Area = LB = 1200 [tex]cm^2[/tex]

so LB = 1200 [tex]cm^2[/tex]

Now we can substitute the value of L and B in the perimeter formula

P = 2(L+B) = 2(sqrt(1200)+sqrt(1200))

As the area of the rectangle is given as 1200[tex]cm^2[/tex] , the length and breadth can be calculated as [tex]\sqrt{1200}[/tex]cm.

So the perimeter of the rectangle is

P = 2*([tex]\sqrt{1200}[/tex] + [tex]\sqrt{1200}[/tex])

  = 2*2[tex]\sqrt{1200}[/tex]

  = 4[tex]\sqrt{1200}[/tex]cm

To find the total length of trim Pat needs for the placemat, we need to multiply the perimeter by the number of edges that need a trim. Since the edges are around the rectangular placemat, so it will be 4 edges.

So, the total length of trim Pat needs for the placemat is

P4 = 4[tex]\sqrt{1200}[/tex]*4 = 16[tex]\sqrt{1200}[/tex]cm

So Pat needs 16[tex]\sqrt{1200}[/tex]cm of trim for each placemat.

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How many real solutions of 2x 3y 5 are possible?

Answers

The equation 2x + 3y = 5 has one real solution.

To find it, you can solve the equation for one of the variables (either x or y) and then substitute the result into the equation to find the other variable.

For example, you can solve for y to get y = (5 - 2x)/3, and then substitute this into the equation to get 2x + 3((5 - 2x)/3) = 5, which you can then solve for x. Doing this will give you x = 5/4, which means that the solution is (5/4, 5/3).

Linear equations are equations that involve two variables and can be expressed in the form ax + by = c, where a and b are constants and x and y are the variables. These equations have one real solution, which can be found by solving for one of the variables and then substituting the result into the equation to find the other variable. Once both variables are known, the solution to the equation is the point (x,y) that satisfies both equations.

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Given this unit circle, what is
the value of x?
(x,-√2)
X =
(1,0)
[?]
Enter

Answers

Answer:

x = - √2/2

Step-by-step explanation:

We know that x = rcosθ and y = rsinθ. The unit circle always have radius of 1 unit. Therefore, r = 1 as defined. Hence:

x = cosθ, y = sinθ

x = cosθ, θ = arcsin(y)

x = cos{arcsin(-√2/2)}

Find the measurement or θ that makes sinθ = -√2/2 and that is π + π/4 = 5π/4.

x = cos(5π/4)

And cos(5π/4) = - √2/2 as well. Hence, x = - √2/2.

Tues
1.There were 32 brown ducklings at a pond. Twice as
many white ducklings arrived., 1/2 of the brown ducklings
flew away. How many ducklings are there now, at the
pond?

Answers

Answer:

80 ducks (16+64)

Step-by-step explanation:

So if there were 32 brown ducks in the pond at first, then twice the amount of brown ducks (32).

32x2=64 white ducks

So now their are 64 white ducks at the pond. We still have to add how many brown ducks their were so…

64+32=96 ducks in total

But then as the white ducks came in half of the brown ducks flew away.

32/2=16 brown ducks left in the pond.

Lastly add the remaining brown ducks with the white ducks and that is you answer!
16+64=80 total amount of ducks

Final Answer:

80 ducks

I hope this helps! I am sorry if I got it wrong!

PLEASE HELP I AM DESPERATE!
Question is in the picture please help!!!

Answers

Answer:

  (a)  (5, 9)

Step-by-step explanation:

You want the solution to the system ...

x = 5y = 2x -1

Solution

The value of x is already given, so no work is required to find that.

The value of y is found by using that value of x in the equation for y:

  y = 2x -1

  y = 2·5 -1 = 10 -1 = 9

The solution is (x, y) = (5, 9).

What is the measure or a

Answers

The measures of the angles of the parallelogram are

The measure of ∠A = 72°

The measure of ∠B = 108°

What is a Parallelogram?

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure

The four types are parallelograms, squares, rectangles, and rhombuses

Properties of Parallelogram

Opposite sides are parallel

Opposite sides are congruent

Opposite angles are congruent

Same-Side interior angles (consecutive angles) are supplementary

Each diagonal of a parallelogram separates it into two congruent triangles

The diagonals of a parallelogram bisect each other

Given data ,

Let the parallelogram be represented as ABCD

Now , the measure of ∠A = ( 5y - 3 )°

The measure of ∠C = ( 3y + 27 )°

For a parallelogram , opposite angles are congruent

So , measure of ∠A = measure of ∠C

Substituting the values in the equation , we get

( 5y - 3 )° =  ( 3y + 27 )°

On simplifying the equation , we get

( 5y - 3 ) =  ( 3y + 27 )

Subtracting 3y on both sides of the equation , we get

2y - 3 = 27

Adding 3 on both sides of the equation , we get

2y = 30

Divide by 2 on both sides of the equation , we get

y = 15

So , the measure of ∠A = ( 5y - 3 )°

The measure of ∠A = ( 5 ( 15 ) - 3 ) )°

The measure of ∠A = ( 75 - 3 )°

The measure of ∠A = 72°

Now , for a parallelogram , same-side interior angles (consecutive angles) are supplementary

So , the measure of ∠A + the measure of ∠B = 180°

Substituting the values in the equation , we get

72° + the measure of ∠B = 180°

Subtracting 72° on both sides of the equation , we get

The measure of ∠B = 108°

Hence , the measures of angles of the parallelogram are 72° and 108° respectively

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What is the correct equation for a slope of 2 and a y-intercept of -7

Answers

Answer:

y=2x-7

Step-by-step explanation:

y=mx+b  ==> m is the slope and b is the y-intercept

y=(2)x + (-7)  ==> plugin 2 for m=slope and -7 for b = y-intercept

y=2x-7 ==> simplify

Jack spends a total of $16.50 on one bag of popcorn and three drinks.
Jill spends a total of $29.75 for two bags of popcorn and five drinks.
Write a system of equations. Determine and state the price of a bag of popcorn and the price of a drink, to the nearest cent.

Answers

Answer:

Sure! Here's a system of equations we can set up to represent this situation:

Let x be the price of a bag of popcorn and y be the price of a drink.

Then we can set up the following system of equations:

x + 3y = 16.50 (equation for Jack's purchases)

2x + 5y = 29.75 (equation for Jill's purchases)

To solve this system of equations, we can use the substitution method.

First, we can solve for x in equation 1:

x = 16.50 - 3y

Then, we can substitute this expression for x into equation 2:

2(16.50 - 3y) + 5y = 29.75

Simplifying this equation, we get:

33 - 6y + 5y = 29.75

Combining like terms, we get:

33 - y = 29.75

Subtracting 29.75 from both sides, we get:

33 - 29.75 - y = -y

Simplifying, we get:

3.25 - y = 0

Subtracting 3.25 from both sides, we get:

-y = -3.25

Dividing both sides by -1, we get:

y = 3.25

So, the price of a drink is $3.25.

Now we can substitute this value for y back into equation 1 to solve for x:

x + 3(3.25) = 16.50

Simplifying, we get:

x + 9.75 = 16.50

Subtracting 9.75 from both sides, we get:

x = 6.75

So, the price of a bag of popcorn is $6.75.

To the nearest cent, the price of a bag of popcorn is $6.75 and the price of a drink is $3.25.

Step-by-step explanation:

in atwo digits Number The sum of the digits is 13 twice the term digits excceds
the units digits by one find the number

Answers

The two-digit number is 34.

What are integers?

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. The boldface Z is a common way to represent the set of integers in mathematical terms.

What are whole numbers?

If p and q are integers and q is not equal to 0, then the number is in the form of p/q and is said to be rational. Among the rational number examples are 1/3, 2/4, 1/5, 9/3, and so on.

The given information can be translated into the following equation:

(10x + y) + (2x - y - 1) = 13

Where x is the tens digit and y is the units digit.

Solving for x and y, we get:

x = 3 and y = 4

So the number is 34.

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Could you help me solve this

Answers

Answer: The middle number is 15

Step-by-step explanation:

45/3= 15 so the three numbers will be around there.

14+15+16= 45

A 20% acid solution is mixed with a 70% acid solution to get 50 liters of a 40% solution.


How much of the 70% solution is used?
A)30 liters
B)20 liters
C)25 liters

Answers

x = liters of solution at 20%

y = liters of solution at 70%

[tex]\begin{array}{lcccl} &\stackrel{liters}{quantity}&\stackrel{\textit{\% of liters that is}}{\textit{acid only}}&\stackrel{\textit{liters of}}{\textit{acid only}}\\ \cline{2-4}&\\ \textit{Sol'n at 20\%}&x&0.2&0.2x\\ \textit{Sol'n at 70\%}&y&0.7&0.7y\\ \cline{2-4}&\\ mixture&50&0.4&20 \end{array}~\hfill \begin{cases} x + y = 50\\\\ 0.2x+0.7y=20 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{using the 1st equation}}{x+y=50\implies x=50-y}\hspace{5em}\stackrel{\textit{substituting on the 2nd equation}}{0.2(50-y) + 0.7y=20} \\\\\\ 10-0.2y+0.7y=20\implies -0.2y+0.7y=10\implies 0.5y=10 \\\\\\ y=\cfrac{10}{0.5}\implies \boxed{y=20}[/tex]

The width of a rectangle is represented by 5k4h 6r; the length of the rectangle is represented by 7k4h 6r. Which of the following expressions represents the perimeter of the rectangle

Answers

5k4h 6r + 7k4h 6r + 5k4h 6r + 7k4h 6r = The perimeter of the rectangle is 24k8h 24r.

1. 5k4h 6r + 7k4h 6r = 12k8h 12r

2. 12k8h 12r + 5k4h 6r = 17k12h 18r

3. 17k12h 18r + 7k4h 6r = 24k8h 24r.

Therefore, the perimeter of the rectangle is 24k8h 24r.

The width of a rectangle is represented by 5k4h 6r, and the length of the rectangle is represented by 7k4h 6r. To find the perimeter of the rectangle, we need to add the width and length of the rectangle together. This can be done by adding 5k4h 6r and 7k4h 6r. The answer to this addition is 12k8h 12r. We then need to add the width and length of the rectangle together again. To do this, we add 12k8h 12r and 5k4h 6r. The answer to this addition is 17k12h 18r. Finally, we need to add the width and length of the rectangle together again. This is done by adding 17k12h 18r and 7k4h 6r. The answer to this addition is 24k8h 24r. Therefore, the perimeter of the rectangle is 24k8h 24r.

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consider the line -7x-2y=6
find the equation of the line that is parallel to this line and passes through the point (-2,-6)
find the equation of the line that is perpendicular to this line and passes through the point (-2.-6)

Answers

The equations are;

a) y = -7/2x - 13

b) -2/7x - 46/7

What is the equation of the line?

We know that the equation of the line that we have here can be written in the general form as the equation that is given as; y = mx + c

We have that

m = slope of the line

c = intercept of the line

As such, we have;

-7x-2y=6 or y = 6 + 7x/-2

or

y = -3 - 7x/2

For the parallel line m = - 7/2

y - (-6) = -7/2(x - (-2))

y + 6 = -7/2x - 7

y = -7/2x - 13

For the perpendicular line m = - 2/7

y - (-6) = -2/7(x - (-2))

y + 6 = -2/7x - 4/7

y = -2/7x - 46/7

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A box with an open top is to be constructed from a square piece of cardboard, 3 ft wide, by cutting out a square from each of the four corners and bending up the sides. Find the largest volume that such a box can have. Let x denote the length of the side of the square being cut out. Let y denote the length of the base.
a) Write an expression for the volume V in terms of both x and y.
b) Use the given information to write an equation that relates the variables.
c) Use part (b) to write the volume as a function of only x.
d) Finish solving the problem by finding the largest volume that such a box can have.

Answers

The required maximum volume of the box is 2ft³.

What is volume?

Volume is a measurement of how much space an object takes up.

We can calculate the amount of something needed to fill it, like water for a bottle, tank, or aquarium.

Amount of space that stuff takes up - that's what we mean when we talk about volume.

Stuff is anything that has mass and takes up room.

When scientists are measuring volume, they usually use cubic meters.

So, calculate as:

V=x·y²

2x+y=3

y=3-2x

V = x·(3-2x)² = x·(9-12x+4x²) = 9x - 12x²+4x

V ` = 9-24x+12x² = 3(4x²-8x+3) = 3(4x²-6x-2x+3)

= 3[2x(2x-3)-(2x-3)] = 3(2x-3)(2x-1)

When the most amount is present: V ` = 0

Then,

2x-3 = 0  

2x = 3              

x = 1.5 (That's wrong, 'cause y = 0.)

or: 2x-1 = 0

2x = 1

x = 0.5,  y = 3 - 2 · 0.5 = 3 - 1 = 2

V max = 0.5 · 2² = 0.5 · 4 = 2 ft³

Therefore, the required maximum volume of the box is 2ft³.

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Part A) based on your answer to answer to part a, are there any values that can be eliminated from the solution set

Answers

The values that can be eliminated from the solution set of the inequality are given as follows:

Values of x ≤ 0.

How to calculate the perimeter of a rectangle?

The perimeter of a rectangle of length l and height h is given by the formula presented as follows:

P = 2(l + h).

The dimensions for this problem are given as follows:

Length l = x + 4.Height h = x.

The perimeter must be less than 120, hence the inequality is given as follows:

2(x + 4 + x) < 120

4x + 8 < 120

4x < 112

x < 28.

However, a side length must assume positive values, meaning that values of x ≤ 0, that is, zero and negative values, are eliminated from the solution.

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