If 2/5 cup of coconut shavings covers 1/4 of a cake, then how much coconut shavings are needed for one cake? A. 3/5 cup B. 5/8 cup C. 1 3/5 cup D. 10 cups

The enclosed region has an area of zero.

Here, we have,

To find the area of the enclosed region between the two parabolas, we need to calculate the definite integral of the difference of the two functions over the interval where they intersect.

The two parabolas are given by:

y=6x²

y=x² + 9

To find the intersection points, we set the two equations equal to each other:

6x² =x² + 9

Now, let's solve for

6x² =x² + 9

=> 6x² - x² = 9

=> 5x² = 9

=> x² = 9/5

=> x = ±√9/5

Since we are looking for the area between the two curves, we only need to consider the positive x value:

x = √9/5

=> x = 3/√5

Now, the definite integral to find the area between the curves is given by:

[tex]A = \int\limits^b_a {(y_2 - y_1)} \, dx[/tex]

where [tex]y_2[/tex] and [tex]y_1[/tex] are the equations of the two curves, and a and b are the x-coordinates of the intersection points.

In this case,

[tex]y_2 = x^2+9 \\ y_1 = 6x^2[/tex]

So, the area A is:

A = [tex]\int\limits^\frac{3}{\sqrt{5} } _0 {(9-5x^2)} \, dx[/tex]

Now, integrate with respect to x:

[tex]A = [9x - \frac{5x^3}{3} ]^{\frac{3}{\sqrt{5} }}_0[/tex]

solving we get,

A = 0

The enclosed region has an area of zero.

This result may seem counterintuitive, but it means that the two parabolas intersect at a point and do not enclose any finite area between them.

Instead, they share a single point in the coordinate plane.

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The area of the fenced field, enclosed by the parabolas y=6x² and y=x²+9, can be found by integrating the difference of the two functions from their points of intersection, which are x=-3 and x=3.

The subject of this question is Mathematics, more specifically it's an application of calculus. To find the area enclosed by two curves, we need to integrate the difference of the two functions from where they intersect. In this case, the two parabolas y=6x² and y=x²+9. To find the points of intersection X₁ and X₂, we make the two equations equal and solve for x, which gives us x= -3 and x=3.

Then we take the integral of (6x² - (x² + 9)) from -3 to 3. The result of this integral will give us the area between these two parabolas, which represents the area of the fenced field.

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The amount of time spent reading email to the amount of time spent watching television is 1/12

Step-by-step explanation:

Given

Time to read email = 15 minutes

Time on television =  3 hours = 3*60 minutes = 180 minutes

Ration is the fraction between two things. In this case, the ration is from the amount of time spent reading email to the amount of time spent watching television

So,

Required ratio will be: 15/180

Simplifying => 1/12

So,

The amount of time spent reading email to the amount of time spent watching television is 1/12

Keywords: Ratio, fractions

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Answer:

sin2θ = -24/25

cos2θ = 7/25

tan2θ =  -24/7

Step-by-step explanation:

sinθ = 3/5

θ is in Quadrant II. So 2θ is in Quadrant III or IV. So sin2θ is negative. Nothing can be said about cos and tan yet.

sin135 = 0.707 > 3/5.

So θ > 135.

2θ lies in Quadrant IV. So cos2θ is positive and tan2θ is negative.

cosθ = √(1 - sin²θ)

        = -4/5

sin2θ = 2sinθcosθ = 2x(3/5)x(-4/5) = -24/25

cos2θ = 1 - 2sin²θ = 1 - 2x(3/5)² = 7/25

tan2θ = sin2θ/cos2θ = -24/7

Answer:  The correct option is

(A)  If F and G differ by a constant, then f = g.

Step-by-step explanation:  According to the given condition, we have

[tex]F'(x)=f(x)~~~\textup{and}~~~G'(x)=g(x).[/tex]

We are to select the correct statement.

Let F(x) = p(x)  and  G(x) = p(x) + c, c - constant.

Then, we get

[tex]F'(x)=p'(x)~~~\textup{and}~~~G'(x)=p'(x).[/tex]

Therefore,

[tex]F'(x)=G'(x)\\\\\Rightarrow f(x)=g(x)\\\\\Rightarrow f=g.[/tex]

Thus, if F and G differ by a constant, then f = g.

Option (A) is CORRECT.

Answer:I think this is the nswer

Step-by-step explanation:

C. Your carpet is ruined because your roommate negligently left her wet boots, umbrella, and raincoat

sitting in a pile on the rug all afternoon

The statement of rain-related losses that WOULD be covered under this renters insurance policy is when your mattress is ruined because part of the apartment's roof blew off during a major rainstorm, creating a stream of water landing directly on your bed.

Basically, the renter's insurance is similar to the homeowner's insurance, but it is for people who rent or lease properties, such as houses and apartments. A renter's insurance refers to an insurance policy that can cover theft, water backup damage, certain natural disasters, bodily injuries and more in a rented property.

If we rent an apartment, home or even a dorm, the renter's insurance are more recommended for protecting your space and belongings in the event of a covered accident. Therefore, the Option B is correct.

Missing options "a. Your laptop is ruined because you left your window open during a moderate rain shower b. Your mattress is ruined because part of the apartment's roof blew off during a major rainstorm, creating a stream of water landing directly on your bed C. Your carpet is ruined because your roommate negligently left her wet boots, umbrella, and raincoat sitting in a pile on the rug all afternoon D. You lose a day's wages because a horrible rainstorm makes it impossible to get to your job"

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Answer

On the upper edge of a glass cylindrical glass there is a drop of honey. At the diametrically opposite point, a fly has stopped, as shown in the figure. If the fly advances (without flying) over the upper edge of the glass to the drop of honey, say how far it would have to travel. Consider that the diameter of the vessel is 10 cm.

Step-by-step explanation:

To make a mixture of 50 pounds of chocolates with a price of $4.54 per pound, the grocer needs to use 12.5 pounds of milk chocolate, 12.5 pounds of dark chocolate, and 12.5 pounds of dark chocolate with almonds.

Let's assume the grocer uses:

Given that the mixture needs to contain as many pounds of dark chocolate with almonds as milk chocolate and dark chocolate combined, we have the equation:

y = x + y

The total cost of the mixture is:

2.50x + 4.30y + 5.50y = 4.54 * 50

Simplifying the equation and solving the system of equations, we can find the values of x and y:

x = 12.5 pounds, y = 12.5 pounds

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Using the system of equations method, we use the given conditions to form three equations. By solving these equations, we can determine the quantities of each type of chocolate the grocer needs to use in their mixture.

Identifying this problem as a system of equations problem, we can use three unknowns: M for milk chocolate, D for dark chocolate, and A for dark chocolate with almonds.

Given that he wants to make a 50-pound mixture, the first equation can be represented as M + D + A = 50.

The second equation is derived from the condition that the mixture should contain as many pounds of dark chocolate with almonds as milk chocolate and dark chocolate combined, which gives us: A = M + D.

The third equation is obtained by acknowledging that a weighted average of the mixture's component prices matches the price per pound of the mixture. That equation is 2.5M + 4.3D + 5.5A = 4.54*50.

Finally, by solving this system of equations, we can determine the quantities of each type of chocolate required.

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Answer:

0.8802

Step-by-step explanation:

given that the Police estimate that 84​% of drivers wear their seatbelts.

when they stop 140 cars, no of trials = no of cars checked = 140

Each car is independent of the other

Hence X no of cars with drivers wearing seat belts is binomial with p = 0.85

Required probability =

the probability they find at least 27 drivers not wearing their​ seatbelts

Since normal approximation is required we can approximate to

X is Normal with mean = np = [tex]140(0.84)\\=117.6[/tex]

std dev = [tex]\sqrt{npq} =4.338[/tex]

Required probability =atelast 27 drivers not wearing their​ seatbelts

= P(X>(140-27))

= P(X>113)

[tex]=P(X>112.5)\\=1- 0.1198\\=0.8802[/tex]

Answer:

Answer is a continuous random variable x the height of the function named the probability density function f(x)

Step-by-step explanation:

A continuous random variable takes infinite number of possible values.

example include  height , weight amount of sugar in an orange time required to run a mile.

Continues random variable named probability function f(x).

The height of a function at a certain value of x in the case of a continuous random variable represents the probability density at that point, not the actual probability. The area under the curve of the function between two points gives the actual probability that x falls between those points. The total probability (the total area under the curve) is always 1.

For a continuous random variable x, the height of the function at a certain value of x is named the probability density function f(x) which describes the probabilities for continuous random variables. The value does not represent a direct probability but the density of probability around that point, and the area under the curve between two given points gives the probability that x would fall between those points. This is represented by the notation P(c < x < d), where c and d are the boundaries of the interval.

It is essential to note that for any specific value of a continuous random variable, the probability is always 0, represented as P( x = c )= 0, which means the height of the function at a particular x does not represent the exact probability at that point but just the density.

The total probability of a continuous random function is always 1, thus, the total area under the probability density function curve equals one. And the value of the function at any given point can be less or greater than 1 given the function's shape and range.

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Answer:

How many seconds did it take the paper airplane to reach the ground?

40 Seconds.

Step-by-step explanation:

When the paper airplane touches the ground is equivalent to having a height equal to zero (y=0). So replacing in the equation:

[tex]y= -1.5x+60\\0= -1.5x+60\\1.5x=60\\x=\frac{60}{1.5} \\x=40[/tex]

The function y= -1.5x+60 describes the downward trajectory of a paper airplane. The '-1.5' represents the falling speed per second, and '+60' represents the initial height. To find the paper airplane's height at any time, substitute the time into the equation.

The question deals with the concept of linear equations and gravity, a physics concept represented in mathematical terms. The function y= -1.5x+60 describes the trajectory of a paper airplane thrown from a building. This function means that the height y of the airplane above the ground, after x seconds, decreases by 1.5m each second, starting from an initial height of 60m.

The coefficient -1.5 represents the speed of the plane, which is downwards due to negative sign. After each second, the paper airplane will be 1.5 m lower than it was the previous second. The '+60' means the paper airplane was initially 60m off the ground.

To use this function for any given time (x), simply substitute the time into the equation. For example, for 5 seconds (x=5), the height y would be -1.5*5+60 = -7.5 + 60 = 52.5m

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Answer:

6 cups

Step-by-step explanation:

[tex](18 \times \frac{2}{3} ) \div 2 = [/tex]

[tex]12 \div 2 = [/tex]

[tex]6[/tex]

Answer:

a) ZY = 27

b) WY = √2×27 = 38.18

c) RX = √2×27 ÷ 2 = 19.09

d) m∠ WRZ = 90°

e) m∠ XYZ = 90°

f) m∠ ZWY = 45°

Step-by-step explanation:

Properties of a Square:

We have [] WXYZ is a SQUARE with side = WZ = 27

Therefore By Applying the above Properties we will get the required Answers.

a) ZY = 27                       .........{ From 1 above properties}

b) WY = √2×27 = 38.18    .......{ From 5 above properties}

c) RX = √2×27 ÷ 2 = 19.09  ...{ From 3 above properties}

d) m∠ WRZ = 90°          ...........{ From 3 above properties}

e) m∠ XYZ = 90°             .........{ From 2 above properties}

f) m∠ ZWY = 45°            .........{ From 4 above properties}

The answer is mean.

Mean is the most commonly used measure of central tendency. It represents the average of the given collection of data. Median: Given that the data collection is arranged in ascending or descending order, the following method is applied:

• If number of values or observations in the given data is odd, then the median is given by [(n+1)/2]th observation.

• If in the given data set, the number of values or observations is even, then the median is given by the average of (n/2)th and  [(n/2) +1]th observation.

Given here: Shop A Shop B

                      55         36

                      52         40

                      50         34

                      47         39

                      51         44

                      48        41

                      53        40

                      53       38

Total =           409      312

Since the data is not skewed mean will provide more accurate data then median.

Therefore the respective means are Shop A =51.125 Shop B=39

Hence, The answer is mean.

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Answer:

the answer is d.

Step-by-step explanation:

Monthly checking account statements include:

- A period

- A beginning balance and an ending balance

- A detailed list of debits and credits during the period

so it is d since it is all three.

Answer:

  1770

Step-by-step explanation:

No calculator is needed.

When you fill in the numbers, you get ...

  1 = (x/1770)^(-0.8)

The only way the value will be 1 is if the fraction is 1:

  x/1770 = 1

The only way the fraction will be 1 is x = 1770.

1770 mg Zn ions per liter will be lethal in 1 minute.

_____

Check

You know the answer will be slightly more than 1743 from your answer to the second part of the first question.

Answer: A sixty day supply of cat food for her two cats will cost her $125

Step-by-step explanation:

Carol has two cats Rover and Bobo.

Let x = the quantity of a can of fast food.

Rover eats three fourths of a can of cat food each day. This means that Rover eats 3x/4 each day. Bobo eats a half of a can of cat food each day. This means that bobo eats x/2 each day.

Cat food costs five dollars for three cans. This means that 3x = 5

Total number of cans consumed by both dogs in a day is 3x/4 + x/2 =5x/4

That means the cost per day would be

(5x/4 × 5)/3x = 25x/4 ×1/3x

= 25/12

It costs her $25/12 per day

To determine the cost for 60 days, we would multiply the cost per day by 60. It becomes

25/12 × 60 = $125

Answer: the bus traveled 144 miles at a speed of 60 miles per hour and 144 miles at a speed of 40 miles per hour

Step-by-step explanation:

The bus traveled at an average rate of 60 miles per hour and then reduced its average rate to 40 miles per hour for the rest of the trip.

Let x miles = distance travelled at 60 miles per hour.

Let y miles = distance travelled at 40 miles per hour.

Total distance travelled = 288 miles.

Therefore,

x + y = 288 - - - - - - - 1

Total time spent in travelling 288 miles = 6 hours

Speed = distance /time

Time = distance / speed

Time spent when travelling x miles at a speed of 60 miles per hour = x/60

Time spent when travelling y miles at a speed of 40 miles per hour = y/40

Since total time is 6 hours, this means that

x/60 + y/40 = 6

(2x + 3y)/120 = 6

2x + 3y = 6 × 120 = 720 - - - - - - - 2

Substituting x = 288-y from equation 1 into equation 2, it becomes

2(288-y) + 3y= 720

576 - 2y + 3y = 720

- 2y + 3y = 720 - 576

y = 144 miles

x = 288 - y = 288-144

x = 144 miles

Answer:

Step-by-step explanation:

Given that in a rural area, only about 30% of the wells that are drilled find adequate water at a depth of 100 feet or less.

The sample size n = 80

no of wells less than 100 feet deep=27

Sample proportion = [tex]\frac{27}{80} =0.3375[/tex]

a) Create hypotheses as

[tex]H_0: p = 0.30\\H_a: p >0.30\\[/tex]

(Right tailed test)

p difference [tex]= 0.3375-0.30 = 0.0375[/tex]

Std error of p = [tex]\sqrt{\frac{0.3(0.7)}{80} } =0.0512[/tex]

b) Assumptions: Each trial is independent and np and nq >5

c) Z test can be used.

Z= p diff/std error = [tex]\frac{0.0375}{0.0512} =0.73[/tex]

p value = 0.233

d) p value is the probability for which null hypothesis is false.

e) Conclusion: Since p >0.05 we accept null hypothesis

there is no statistical evidence which support the claim that more than 30% are drilled.

that's cool I saw what you did your a nice friend lol

Answer:

dam it

Step-by-step eddqowd23r43tttt5xplanation:

Answer:

A=(-1,3)

B=(5,3)

C=(5,-5)

Step-by-step explanation:

Answer:

The answer to your question is (2, -1)

Step-by-step explanation:

1.- Find half points

AB

Between A and B there are 6 units, then the half point is three units from point A to the right

                                (2, 3)

BC

Between B and C there are 8 units, then the half point is four units below the point B.

                               (5, -1)

AC

Xm = -1 + 5 / 2 = 4 / 2 = 2

Ym = 3 - 5 / 2 = - 2 / 2 = - 1

                               (2, -1)

2.- Find the equations of the mediatrices

AB

          x = 2                     because the line must be perpendicuar to AB

BC

          y = - 1                    because the line must be perpendicular to BC

AC

          slope        m =[tex]\frac{-5 - 3}{5 + 1}[/tex]

                           m = [tex]\frac{-8}{6}[/tex]

                           m = [tex]\frac{-4}{3}[/tex]

mediatrix AC

                           y + 1 = -4/3 (x -2)

                          3y + 3 = -4x + 8

                           4x + 3y = 8 - 3

                           4x + 3y = 5

3.- Find the circumcenter

When x = 2

                         4(2) + 3y = 5

                           8 + 3y =5

                                 3y = 5 - 8

                                 3y = -3

                                   y = -3/3

                                   y = -1

When y = -1

                        4x + 3(-1) = 5

                        4x - 3 = 5

                        4x = 5 + 3

                        4x = 8

                        x = 8/4

                       x = 2

Circumcenter    (2, -1)

Answer:

b

Step-by-step explanation:

Answer:straight angle

Step-by-step explanationbecause it’s straight

Answer:

[tex]\overline {JL} \cong \overline{MO}[/tex] is the only correct statement.

Step-by-step explanation:

When the two triangles are congruent then their Vertices are correspondence to each other. the correspondence of vertices are as

For, Δ JKL ≅ Δ MNO

J ↔ M

K ↔ N

L ↔ O

The true statement with respect to the correspondence are as

For, Δ JKL ≅ Δ MNO

∠JKL ≅ ∠MNO

∠JLK ≅ ∠MON

∠KJL ≅ ∠NMO

[tex]\overline {JL} \cong \overline{MO}[/tex]

[tex]\overline {KL} \cong \overline{NO}[/tex]

[tex]\overline {JK} \cong \overline{MN}[/tex]        

These all are corresponding parts of congruent triangles (c.p.c.t).

Answer:

f(t) = 250[tex]e^{-0.007752t}[/tex]

Step-by-step explanation:

Let f(t) = [tex]\alpha[/tex][tex]e^{\beta t }[/tex]

where f is the amount of radioactive substance in grams

and t is the time in minutes

initially (at t=0), f = 250 grams

⇒f(0) = 250 grams

⇒[tex]\alpha[/tex][tex]e^{0\beta}[/tex] = 250

⇒[tex]\alpha[/tex][tex]e^{0}[/tex] = 250

⇒[tex]\alpha[/tex] = 250 grams {∵[tex]e^{0} = 1[/tex]}

⇒f(t) = 250[tex]e^{\beta t }[/tex]

At t = 250 minutes, f = 36 grams

⇒f(250) = 36 grams

⇒250[tex]e^{250\beta}[/tex] = 36

⇒[tex]e^{250\beta}[/tex] = [tex]\frac{36}{250}[/tex] = 0.144

⇒250[tex]\beta[/tex] = ㏑ 0.144 = -1.938

⇒[tex]\beta[/tex] = -[tex]\frac{1.938}{250}[/tex] = -0.007752 [tex]min^{-1}[/tex]

∴f(t) = 250[tex]e^{-0.007752t}[/tex]

Answer:

Step-by-step explanation:

The increase in the number of books sold each year follows an arithmetic progression, hence it is linear.

The formula for the nth term of an arithmetic progression is expressed as

Tn = a + (n - 1)d

Where

Tn is the nth term of the arithmetic sequence

a is the first term of the arithmetic sequence

n is the number of terms in the arithmetic sequence.

d is the common difference between consecutive terms in the arithmetic sequence.

From the information given,

a = 500 (number of books in the first year.

T5 = 1000 (the number of books at 2014 is)

n = 5 (number of terms from 2010 to 2014). Therefore

T5 = 1000 = 500 + (5 -1)d

1000 = 500 + 4d

4d = 500

d = 500/4 =125

The linear function that represents the number of yearbooks sold per year will be

T(n) = 500 + 125(n - 1)

The correct linear function that represents the number of yearbooks sold per year is [tex]\( f(t) = 100t + 500 \)[/tex], where [tex]\( t \)[/tex] is the number of years since 2010.

To determine the linear function, we need to find the slope (rate of change) and the y-intercept (initial value) of the function.

 Given that in 2010, 500 yearbooks were sold, we can denote this point as (0, 500) since 0 years have passed since 2010. This gives us the y-intercept of the function.

 Next, we look at the year 2014, where 1000 yearbooks were sold. This is 4 years after 2010, so we can denote this point as (4, 1000).

 The slope of the line (m) is calculated by the change in the number of yearbooks sold divided by the change in time (years). So, we have:

[tex]\[ m = \frac{1000 - 500}{4 - 0} = \frac{500}{4} = 125 \][/tex]

 This means that the number of yearbooks sold increases by 125 each year.

 Now, we can write the linear function using the slope-intercept form [tex]\( f(t) = mt + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.

 Substituting the values we have:

[tex]\[ f(t) = 125t + 500 \][/tex]

However, to make the function more general and to avoid dealing with fractions, we can express the slope as a multiple of 100. Since 125 is the same as [tex]\( \frac{5}{4} \times 100 \)[/tex], we can rewrite the function as:

[tex]\[ f(t) = \frac{5}{4} \times 100t + 500 \][/tex]

 Simplifying this, we get:

[tex]\[ f(t) = 100t + 500 \][/tex]

 This function represents the number of yearbooks sold each year, where [tex]\( t \)[/tex] is the number of years since 2010. For example, in 2011 (t=1), the function would predict [tex]\( f(1) = 100(1) + 500 = 600 \)[/tex] yearbooks sold.

Is this a question or a statement?

Answer:

The dimensions of the poster of the smallest area would be 24×36 cm.

Step-by-step explanation:

Let x and y be the width and height respectively of the printed area, which has fixed area.

If the area of the printed material on the poster is fixed at 384 square centimeters.

i.e. [tex]xy=384\ cm^2[/tex]

[tex]\Rightarrow y=\frac{384}{x}[/tex]

The top and bottom margins of a poster are 6 cm each is y+1.

The total width of the poster including 4 cm at sides is x+8.

The area of the total poster is [tex]A=(x+8)(y+12)[/tex]

Substitute the value of y,

[tex]A=(x+8)(\frac{384}{x}+12)[/tex]

[tex]A=384+12x+\frac{3072}{x}+96[/tex]

[tex]A=12x+\frac{3072}{x}+480[/tex]

Derivate w.r.t x,

[tex]A'=12-\frac{3072}{x^2}[/tex]

Put A'=0,

[tex]12-\frac{3072}{x^2}=0[/tex]

[tex]\frac{3072}{x^2}=12[/tex]

[tex]x^2=\frac{3072}{12}[/tex]

[tex]x^2=256[/tex]

[tex]x=16[/tex]

Derivate again w.r.t x,

[tex]A''=\frac{2(3072)}{x^3}[/tex] is positive for x>0,

A is concave up and x=16 is a minimum.

The corresponding y value is

[tex]y=\frac{384}{16}[/tex]

[tex]y=24[/tex]

The total poster width is x+8=16+8=24 cm

The total poster height is y+12=24+12=36 cm

Therefore, the dimensions of the poster of the smallest area would be 24×36 cm.

To find the dimensions of the poster with the smallest area, subtract the margin widths from the total dimensions. Set up and solve an equation to find the dimensions. The smallest area occurs when the expression 2x + 3y - 72 is minimized.

To find the dimensions of the poster with the smallest area, we need to subtract the margin widths from the total dimensions. The top and bottom margins are 6 cm each, and the side margins are 4 cm each. Let the length of the printed material be x and the width be y. Then, the length of the poster is x + 2(6) = x + 12, and the width of the poster is y + 2(4) = y + 8. We know that the area of the printed material is fixed at 384 square centimeters, so we have the equation (x + 12)(y + 8) = 384. We can solve this equation to find the dimensions of the poster.

Expanding the equation, we get xy + 8x + 12y + 96 = 384. Rearranging the terms and isolating xy, we have xy = 384 - 8x - 12y - 96. Rearranging the terms again, we get xy = -8x - 12y + 288. Factoring out a -4, we have xy = -4(2x + 3y - 72). Now, we want to minimize the area of the poster, which means we want to minimize the value of xy. So, we need to minimize the expression 2x + 3y - 72 to find the minimum dimensions of the poster.

There are various methods to minimize this expression, such as using calculus or graphing techniques. Using calculus, we can take the partial derivatives of the expression with respect to x and y, set them equal to 0, and solve for x and y. However, since this is a high school level question, we can use a simpler method by observing that the expression 2x + 3y - 72 represents a straight line. The minimum value of this expression occurs at the point where the line intersects the x and y axes. So, to find the minimum dimensions of the poster, we can set 2x + 3y - 72 = 0 and solve for x and y. Solving this equation, we get x = 36 and y = 16. Therefore, the dimensions of the poster with the smallest area are 36 cm by 16 cm.

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Answer:3 significant figures

Step-by-step explanation:got it right!!

Answer:

Since we FAIL to reject the null hypothesis, then if we construct an interval of 95% of confidence, the 0 should be included, because on the test hypothesis we conclude that there would be no significant difference between the means of the two groups analyzed, and the results obtained on the hypothesis test needs to be consistent with the confidence interval.

Step-by-step explanation:

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".  

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".

[tex]\bar x_{meat}=111.7[/tex] represent the sample mean of calories for the meat hot dogs

[tex]\bar x_{beef}=135.4[/tex] represent the sample mean of calories for the beef hot dogs

The system of hypothesis on this case would be:

Null hypothesis: [tex]\mu_{meat}-\mu_{beef}=0[/tex]

Alternative hypothesis: [tex]\mu_{meat}-\mu_{beef}\neq 0[/tex]

On this case we have the p value obtained, after calculate the statistic and we got that [tex]p_v =0.124[/tex] if we select a 5% significance level [tex]\alpha=0.05[/tex] we see that [tex]p_v >\alpha[/tex] and on this case we can FAIL to rejec the null hypothesis, so there is not a significant difference between the mean of the two tpes of hot dogs analyzed at 5% of significance.

And since we FAIL to reject the null hypothesis, then if we construct an interval of 95% of confidence, the 0 should be included, because on the test hypothesis we conclude that there would be no significant difference between the means of the two groups analyzed, and the results obtained on the hypothesis test needs to be consistent with the confidence interval.

A 95% confidence interval for μMeat - μBeef including 0 indicates no significant difference in calorie content between meat and beef hot dogs.

A 95% confidence interval for μMeat - μBeef that includes 0 suggests that there is no significant difference in the mean calorie content between meat and beef hot dogs. In this case, the difference in mean calorie content between the two types of hot dogs is not statistically significant, as the null hypothesis is not rejected. The P-value of 0.124 suggests that there is a 12.4% chance of observing a difference in mean calorie content as extreme as the one observed if the null hypothesis were true. Therefore, we cannot conclude that there is a significant difference in the mean calorie content between meat and beef hot dogs.

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Answer:

412 ft³

Step-by-step explanation:

Diameter = 5 ft

Radius = D/2 = 5/2 = 2.5 ft

Volume of a Cylinder = 2πr²*h

Plug in values

2(3.14)(2.5)^2*21 = 412.33 ft^3

Volume of the pipe is 412 cubic feet rounded to nearest whole number.

The volume of the cylindrical construction pipe is 330 cubic feet.

To find the volume of a cylindrical construction pipe, we can use the formula:

Volume = π * [tex](radius)^2[/tex] * height

Given that the diameter is 5 ft, the radius of the pipe is half of the diameter, which is 2.5 ft.

The height of the pipe is given as 21 ft.

Plugging these values into the volume formula:

Volume = 3.14 *[tex](2.5)^2[/tex] * 21 = 330 ft³

Therefore, the volume of the cylindrical construction pipe is 330 cubic feet.

Learn more about Volume of a cylinder here:

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Answer:

Option d is right

Step-by-step explanation:

Given that a  local news agency conducted a survey about unemployment by randomly dialing phone numbers until they had gathered responses from 1000 adults in their state. In the survey, 19% of those who responded said they were not currently employed. In reality, only 6% of the adults in the state were not currently employed at the time of the survey.

The reason more approporiate woul dbe

(d) The difference is due to nonresponse bias. Adults who are employed are less likely to be available for the sample than adults who are unemployed.

would be the correct option.

Adults who are employed will lie is absurd may be reverse true.  Since survey done for adults, eligible teenagers also included.  Voluntary response is also wrong as given 1000 persons selected.

The difference in percentages is due to sampling variability. Random sampling may not perfectly represent the population, resulting in differences in the percentages.

The difference in percentages is best explained by (a) sampling variability. When conducting a survey, it is expected that there will be some variability between the sample results and the true population values. Even with random sampling, there is a chance that the sample may not perfectly represent the entire population. In this case, the survey respondents may not be an accurate reflection of the overall population, resulting in a difference in the percentages.

For example, if the survey happened to include a higher proportion of unemployed individuals in the sample, the percentage of unemployed respondents would be higher than the true population percentage.

Sampling variability is common in statistics and can be mitigated by increasing the sample size to reduce the margin of error.

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