On the square baseball diamond shown below, the distance from first base to second base is 90 feet. How far does the catcher have to throw the ball from home plate to reach second base? Round your answer to the nearest 10th. Show your work

The critical values for a Chi-square distribution with 80% confidence level and sample size of 15 (thus 14 degrees of freedom) are: χ2L = 18.475 and χ2R = 8.897.

The question is asking for the critical values for a Chi-square distribution which can be found using Chi-square tables usually found in statistics textbooks or online. The critical values refer to the boundary values for the acceptance region of a hypothesis test.

When trying to find the critical values for an 80% confidence level with 14 degrees of freedom (since degrees of freedom = n - 1 for sample, thus 15 - 1 = 14), you need the 90th percentile for the χ2L and the 10th percentile for the χ2R (since α = 20%, then α/2 = 10%).

Using a Chi-square table for these percentiles, we get:

χ2L = 18.475

χ2R = 8.897

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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}

Answer:

ΔNAS≅ΔSEN by SSA axiom of congruency.

Step-by-step explanation:

Consider ΔNAS and ΔSEN,

NS=SN(Common ie . Both are the same side)

SA=NE( Given in the question that SA≅ NE)

∠SNA=∠NSE( Due to corresponding angle property where SE ║ NA)

Therefore, ΔNAS ≅ΔSEN by SSA axiom of congruency.

∴ NA≅SA by congruent parts of congruent Δ. Hence, proved.

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:

50

Step-by-step explanation:

There are 434 different ways to distribute 15 identical stuffed animals among six children so that each child receives at least one but no more than three stuffed animals.

1. Define the generating function for distributing stuffed animals to each child as:

 [tex]\[ (x + x^2 + x^3)^6 \][/tex]

  This represents the options for each child receiving 1, 2, or 3 stuffed animals, and there are 6 children.

2. Expand the generating function using the binomial theorem:

  [tex]\[ (x + x^2 + x^3)^6 = \binom{6}{0}x^0 + \binom{6}{1}x^1 + \binom{6}{2}x^2 + \binom{6}{3}x^3 + \binom{6}{4}x^4 + \binom{6}{5}x^5 + \binom{6}{6}x^6 \][/tex]

  Simplify to:

  [tex]\[ 1 + 6x + 21x^2 + 56x^3 + 126x^4 + 252x^5 + 462x^6 \][/tex]

3. The coefficient of [tex]\( x^{15} \)[/tex] in the expansion represents the number of ways to distribute 15 stuffed animals among six children.

4. Identify the terms that contribute to [tex]\( x^{15} \)[/tex]:

  [tex]\[ 56x^3 + 126x^4 + 252x^5 \][/tex]

5. Add the coefficients:

  56 + 126 + 252 = 434

Therefore, there are 434 different ways to distribute 15 identical stuffed animals among six children so that each child receives at least one but no more than three stuffed animals.

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.

Is this a question or a statement?

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

Answer:

dam it

Step-by-step eddqowd23r43tttt5xplanation:

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.

The solution of p is given by the equation p = 2

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

17 - 2p = 2p + 5 + 2p   be equation (1)

Adding 2p on both sides , we get

2p + 2p + 2p + 5 = 17

On simplifying , we get

6p + 5 = 17

Subtracting 5 on both sides , we get

6p = 17 - 5

6p = 12

Divide by 6 on both sides , we get

p = 12 / 6

p = 2

Therefore , the value of p is 2

Hence , the solution is p = 2

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Answer:

b

Step-by-step explanation:

Answer:straight angle

Step-by-step explanationbecause it’s straight

Answer:

x+2

Step-by-step explanation:

A factor of a polynomial can be thought of as the value of x at which the polynomial is equal to zero.

So, you can use the values in the options given and put them in the polynomial from the question.

for example: try, part a) x-1, here x=1 since the factor is x-1=0

put this value in the polynomial to see if it results to zero.

[tex](1)^3 + 3(1)^2 - 2(1) - 8\\ -6[/tex]

so this isn't the answer.

now try, part d) x + 2, here, x = -2

[tex](-2)^3 + 3(-2)^2 - 2(-2) - 8\\ 0[/tex]

you'll see this is the factor!

Answer:

  d.  x+2

Step-by-step explanation:

The question is essentially asking which of -2, -1, 1, 2 is a zero of the polynomial. All of them are plausible, because all are factors of -8, the constant term.

So, we don't have much choice but to try them. That means we evaluate the function to see if any of these values of x make it be zero.

±1:

The value 1 is easy to substitute for x, as it makes all of the x-terms equal to their coefficient. Essentially, you add all of the coefficients. Doing that gives ...

  1 +3 -2 -8 = -6

Similarly, the value -1 is easy to substitute for x, as it makes all odd-degree terms equal to the opposite of their coefficient. Here, ...

  f(-1) = -1 +3 -(-2) -8 = -4

Neither one of these values (-1, +1) is a zero of the polynomial, so choices A and B are eliminated.

__

(x-2):

To see if this is a factor, we need to see if x=2 is a zero. Evaluation of a polynomial is sometimes easier when it is written in Horner form:

  ((x +3)x -2)x -8

Substituting x=2, we get ...

  ((2 +3)2 -2)2 -8 = (8)2 -8 = 8 . . . not zero

This tells us there is a zero between x=1 and x=2, but that is not what the question is asking.

__

(x+2):

We can similarly evaluate the function for x=-2 to see if (x+2) is a factor.

  ((-2 +3)(-2) -2)(-2) -8 = (-4)(-2) -8 = 0

Since x=-2 makes the function zero, and it makes the factor (x+2) equal to zero, (x+2) is a factor of the polynomial.

So, the factor (x+2) is a factor of the given polynomial.

_____

I find that a graphing calculator answers questions like this quickly and easily. If you're allowed one, it is a handy tool.

Answer:

Glen uses 15.65 inches fabrics for headbands and 9.68 inches for each player

Explanation:

Given the fabric used are:

For headbands, 641.65 inches for 41 people (39 players and 2 coach)

Therefore, applying the concept of unitary method  

41 people = 641.65 inches

1 person = [tex]\frac{641.65}{41} inches[/tex]= 15.65 inches

For wristbands, 377.52 inches for 39 players

39 players = 377.52 inches

1 player = [tex]\frac{377.52}{39} inches[/tex] = 9.68 inches

Therefore, Glen uses 15.65 inches fabrics for headbands and 9.68 inches for each player

The complete question is written below:

While on vacation, Enzo sleeps 115% as long as he does while school is in session. He sleeps an average of s hours per day while he is on vacation. Which of the following expressions could represent how many hours per day Enzo sleeps on average while school is in session?

A.1.15s

B.s/1.15

C.100/115s

D.17/20s

E.(1.15-0.15)s

Answer:

B. [tex]\dfrac{s}{1.15}[/tex]

Step-by-step explanation:

Let the hours per day slept while school is in session be [tex]x[/tex].

Given:

Hours slept per day on vacation = [tex]s[/tex]

Enzo sleeps 115% as long in vacation as he does in school. Therefore, as per question,

[tex]s=115\%\ of\ x\\\\s=\frac{115}{100}x\\\\s=1.15x\\\\x=\dfrac{s}{1.15}[/tex]

Hence, the number of hours Enzo sleeps while school is in session is given as:

[tex]x=\dfrac{s}{1.15}[/tex]

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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Answer:3 significant figures

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

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:

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.

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:

  50 cm²

Step-by-step explanation:

The area of a trapezoid can be figured from the formula

  A = (1/2)(b1 +b2)h

Filling in the given numbers and doing the arithmetic, we get ...

  A = (1/2)(10.2 +9.8)(5) = 50 . . . . square centimeters

The area is 50 cm².

Answer: Charlie have to drive at a speed of 80miles per hour in order to reach there on time.

Step-by-step explanation:

At 4pm Charlie realizes he has half an hour to get to his grandmothers house for diner. Knowing that the time he has left is 30 minutes and the distance to his grandmother's place is 40 miles, the only thing that he can control is his speed

Speed = distance travelled / time taken

40/0.5 = 80 miles per hour

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.

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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

The school uses 23,070 pieces of paper in all.

Here's an explanation:

It is already given that the school uses 13,270 pieces of white paper. Then it says that there are 7,570 fewer pieces of blue paper than white paper. So if you subtract 7,570 from 13,270, you get that the school used 5700 pieces of blue paper. Then it says that there are 1,600 fewer pieces of yellow paper than blue paper. So when you subtract 1,600 from 5,700, you get that the school used 4,100 pieces of yellow paper. So if you do 13,270+5,700+4,100, you get that the school used 23,070 pieces of paper in total.

The school uses a total of 23,070 pieces of paper, which is calculated by adding 13,270 pieces of white paper, 5,700 pieces of blue paper, and 4,100 pieces of yellow paper.

The school used 13,270 pieces of white paper. It is stated that they use 7,570 fewer pieces of blue paper than white paper, which means they used 13,270 - 7,570 = 5,700 pieces of blue paper. For yellow paper, they use 1,600 fewer pieces than blue paper, which means they use 5,700 - 1,600 = 4,100 pieces of yellow paper. To get the total number of pieces of paper the school used, you would add all these together: 13,270 white paper pieces + 5,700 blue paper pieces + 4,100 yellow paper pieces = 23,070 pieces of paper in total.

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Answer:

  12

Step-by-step explanation:

The degree of the polynomial is 12, so the theorem tells you it has 12 zeros.

Answer:

[tex]\displaystyle 12[/tex]

Step-by-step explanation:

You base this off of the Leading Coefficient's degree.

I am joyous to assist you anytime.

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:

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:

Step-by-step explanation:

The estimated cost is ...

  $14000 +12600 +6200 = $32800

The actual cost is ...

  $13860 +12420 +6500 = $32780

The variance is the difference between actual cost and predicted cost:

  $32,780 - 32800 = -$20.

It is favorable when actual costs are lower than predicted.

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:

Estimated 5 hours

Step-by-step explanation:

780 miles = 12 hours

1 mile = 0.0154hr (3s.f)

325 miles = 0.0154 × 325

= 5.01hr