A field bordering a straight stream is to be enclosed. The side bordering the stream is not to be fenced. If 1000 yards of fencing material is to be used, what are the dimensions of the largest rectangular field that can be fenced? What is the maximum area?

Answers

Answer 1

Answer:

x  =  500 yd

y  =  250 yd

A(max) = 125000 yd²

Step-by-step explanation:

Let´s call x the side parallel to the stream ( only one side to be fenced )

y the other side of the rectangular area

Then the perimeter of the  rectangle  is  p  =  2*x  + 2* y  ( but only 1 x will be fenced)

p  =  x  +  2*y

1000  =  x   +  2 * y         ⇒    y  =  (1000 - x )/ 2

And   A(r)  =  x * y

Are as fuction of x

A(x)  =  x  *  (  1000  -  x ) / 2

A(x)  =   1000*x / 2 -  x² / 2

A´(x)  =  500  -  2*x/2

A´(x)  =  0              500   -  x   =  0

x  =  500 yd

To find out if this value will bring function A to a maximum value we get the second derivative

C´´(x)  =  -1         C´´(x) < 0  then efectevly we got a maximum at  x  = 500

The side  y  = ( 1000  -  x ) / 2

y  =  500/ 2

y  =  250 yd

A(max)  =  250 * 500

A(max) = 125000 yd²


Related Questions

which of the following graphs dont belong and why?​

which of the following graphs dont belong and why?

Answers

Answer:

Upper Right

Step-by-step explanation:

All of them have different dips, therefore the one facing in a different direction must be the odd one out.

Answer:

top right graph

Step-by-step explanation:

3 of the 4 graphs start at negative infinity for negative x, and approach infinity as x approaches infinity.

The top right graph starts at infinity for negative x and approaches negative infinity as x approaches infinity.

Answer: top right graph

Find the area also if you can do a step by step explanation thanks

Find the area also if you can do a step by step explanation thanks

Answers

Answer:

Rhombus=60 squared

Step-by-step explanation:

There are two areas right there.

First multiply the 6 and the 5.

6(5)=30 in squared

10(6) for the Rhombus

=60

You only need the area for the Rhombus because that is the entire area, the triangle is just taking up space inside the shape.

f scores are normally distributed with a mean of 35 and a standard deviation of 10, what percent of the scores is: (a) greater than 34?

Answers

The percentage of scores greater than 34 is 0.5398 or 53.98%.

Given that the mean of scores (μ) = 35 and the standard deviation (σ) = 10. We need to find the percentage of scores greater than 34. Since the scores are normally distributed, we can standardize the variable by using the z-score formula.

z = (x - μ) / σ

Here, x = 34, μ = 35 and σ = 10z = (34 - 35) / 10z = -0.1

We need to find the area to the right of the z-score line on the standard normal distribution table. The standard normal distribution table provides the probabilities corresponding to the z-scores, i.e. the area under the curve to the right or left of the z-score line on the distribution table. The area to the right of the z-score line represents the percentage of scores that are greater than the given value. Using the standard normal distribution table, the area to the right of the z-score line -0.1 is 0.5398.

The percentage of scores greater than 34 is 0.5398 or 53.98%.

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How long would it take R20000 invested today at a simple interest rate of 9% p.a. to reach an investment goal of R30000.
A Approximately 5.6 years
B Approximately 6.1 years
C Approximately 4.7 years
D Approximately 5.1 years

Answers

\(~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 30000\\ P=\textit{original amount deposited}\dotfill & \$20000\\ r=rate\to 9\%\to \frac{9}{100}\dotfill &0.09\\ t=years \end{cases} \\\\\\ 30000 = 20000[1+(0.09)(t)] \implies \cfrac{30000}{20000}=1+0.09t\implies \cfrac{3}{2}=1+0.09t \\\\\\ \cfrac{3}{2}-1=0.09t\implies \cfrac{1}{2}=0.09t\implies \cfrac{1}{2(0.09)}=t\implies 5.6\approx t\)

Does the equation 7/8 = 8.75/3.75 represent a proportional relationship? Why or why not? CHECK PICTURE

Does the equation 7/8 = 8.75/3.75 represent a proportional relationship? Why or why not? CHECK PICTURE

Answers

Answer:

It's the forth one

Step-by-step explanation:

Yes it is proportional because 7/3 = 8.75/3.75

How do you tell if an equation is a proportional relationship?

To know if a relationship is proportional, you should look at the ratios between the two variables. If the ratio is always the same, the relationship is proportional. If the ratio changes, the relationship is not proportional.

every hour a clock chimes as many times as the hour. how many times does it chime from 1 a.m. through midnight (including midnight)?

Answers

The total number of chimes made by the clock from 1 a.m. to midnight (including midnight) is 156 chimes.

Starting from 1 a.m. and ending at midnight (12 a.m.), we need to calculate the total number of chimes made by the clock.

We can break down the calculation into the following:

From 1 a.m. to 12 p.m. (noon):

The clock chimes once at 1 a.m., twice at 2 a.m., three times at 3 a.m., and so on until it chimes twelve times at 12 p.m. So, the total number of chimes in this period is:

1 + 2 + 3 + ... + 12 = 78

From 1 p.m. to 12 a.m. (midnight):

The clock chimes once at 1 p.m., twice at 2 p.m., three times at 3 p.m., and so on until it chimes twelve times at 12 a.m. (midnight). So, the total number of chimes in this period is:

1 + 2 + 3 + ... + 12 = 78

Therefore, the total number of chimes made by the clock from 1 a.m. to midnight (including midnight) is:

78 + 78 = 156 chimes.

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From 1 a.m. through midnight (including midnight), the clock will chime 156 times. This is because it will chime once at 1 a.m., twice at 2 a.m., three times at 3 a.m., and so on, until it chimes 12 times at noon. Then it will start over and chime once at 1 p.m., twice at 2 p.m., and so on, until it chimes 12 times at midnight. So, the total number of chimes will be 1 + 2 + 3 + ... + 11 + 12 + 1 + 2 + 3 + ... + 11 + 12 = 156.


1. From 1 a.m. to 11 a.m., the clock chimes 1 to 11 times respectively.
2. At 12 p.m. (noon), the clock chimes 12 times.
3. From 1 p.m. to 11 p.m., the clock chimes 1 to 11 times respectively (since it repeats the cycle).
4. At 12 a.m. (midnight), the clock chimes 12 times.

Now, let's add up the chimes for each hour:

1+2+3+4+5+6+7+8+9+10+11 (for the hours 1 a.m. to 11 a.m.) = 66 chimes
12 (for 12 p.m.) = 12 chimes
1+2+3+4+5+6+7+8+9+10+11 (for the hours 1 p.m. to 11 p.m.) = 66 chimes
12 (for 12 a.m.) = 12 chimes

Total chimes = 66 + 12 + 66 + 12 = 156 chimes

So, the clock chimes 156 times from 1 a.m. through midnight (including midnight).

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What i the meaure in radian for the central angle of a circle whoe radiu i 9 cm and intercepted arc length i 7. 2 cm?

Enter your anwer a a decimal in the box. Radian

Answers

The central angle (in radians ) is 0.8 radians.
What is a cricle ?

A circle is a basic 2D shape measured by its radius. A circle divides the plane into two areas: interior and exterior. Similar to line type. Imagine a line segment bending until the ends connect. Arrange the loops so that they form a perfect circle.

we know that,

arc length = radius *  central angle (in radians)

and central angle (in radians) = arc length / radius

by substituting the given values

arc length = 7.2

radius=9

we get,

central angle (in radians) = 7.2 / 9

=0.8 radians

Hence , the central angle = 0.8 radians

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Angela shared a cab with her friends. When they arrived at their destination, they evenly divided the $63fare among the x of them. Angela also paid a $8tip. How much did Angela pay in total? Write your answer as an expression

Answers

1.if tip included in fare, total amount paid by Angela =(55$/x) +8$

if tip is not included in fare than total amount paid by angela = (63$/x)+8$

Explanation :-

According to qus

Total friends included Angela = x

Total fare paid by them =63$

If tip included in total fare, than total fare without tip=63-8

= 55$

Sothat,

amont paid by individual =total fare /total friends. 55$/x

If tip not include in total fare than total amount paid by individual =63$/x

Cookies cost $3.50 per package. How many packages of cookies can Gail buy if she has \$42 .00? Write an equation and solve.

Answers

Answer:

Solve: 12 packagesEquation: n = $42.00¢

Step-by-step explanation:

Given

1 package = $3.50¢

∴, ? package = 42.00¢

Equation

Identify the variable. Let n be the variables, then, the equation is: n=$42.00¢

Solve

Since 1 is 3.50

To find 42.00

Divide 42.00 by 3.50

42.00 ÷ 3.50 = 12

Therefore, Gail can buy 12 packages with $42.00¢

1. Dilate A using
Pas the center
of dilation and a
scale factor of 3.
Label the new
point P.
B.
Pear Deck Interactive Side
Do not remove the
Students, draw anywhere on this slide!

1. Dilate A usingPas the centerof dilation and ascale factor of 3.Label the newpoint P.B.Pear Deck Interactive

Answers

Pas the center , pear deck interactive side

Number 8 iready mathbook 8th grade. Graph the equation y = 20x + 500

Answers

A graph of the linear equation y = 20x + 500 in slope-intercept form is shown in the image attached below.

What is a graph?

In Mathematics, a graph can be defined as a type of chart that is typically used for the graphical representation of data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis respectively.

Next, we would use an online graphing calculator to plot the given function as shown in the graph attached below.

In conclusion, the slope of this linear equation is equal to 20 and it does not represent a proportional relationship.

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Number 8 iready mathbook 8th grade. Graph the equation y = 20x + 500

when estimating a population​ mean, are you more likely to be correct when you use a point estimate or an interval​ estimate? explain your reasoning.

Answers

In estimating a population mean, an interval estimate is more likely to be correct than a point estimate. An interval estimate provides a range of values within which the true population mean is likely to fall, while a point estimate provides only a single value.

When estimating a population mean, using an interval estimate is more likely to be correct because it accounts for the uncertainty associated with the estimate. A point estimate, on the other hand, provides a single value that is assumed to represent the true population mean. However, due to sampling variability and potential errors in measurement, a point estimate is prone to error and may not accurately reflect the true population mean.

By using an interval estimate, which includes a range of values, we have a measure of uncertainty. The range is typically constructed based on a certain level of confidence, such as a 95% confidence interval. This means that if we were to repeat the sampling and estimation process many times, the true population mean would be expected to fall within the estimated interval in 95% of those repetitions.

The interval estimate takes into account the variability in the data and provides a more realistic representation of the true population mean. It provides a margin of error and acknowledges that the point estimate is just one possible value among many that could have been obtained through sampling.

Therefore, when estimating a population mean, an interval estimate is preferred because it not only provides a point estimate but also quantifies the uncertainty associated with that estimate, leading to a higher likelihood of being correct.

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Solve the following exponential equation by expressing each side as a power of the same base and then equating exponents. 53−x=251​ The solution set is White an equation for line L in point-slope form and slope-intercept form. Lis perpendicular lo y=4x. White an equation for line t in point-slope farm. y=−41​x+c (Sumplyy your onswer. Use integors or tractons for arty rumbers in the equation) Wile an equation for ine L in slopesindoreept form y−y1​=−41​(x−x1​) (5mplfy vour answer. Use integprs or fractions for any nurbers ti the equation)

Answers

The equation for line L in slope-intercept form is y = -1/4x + x₁/4 + y₁

The exponential equation is 53−x=251. Therefore, we need to express each side as a power of the same base and then equate exponents. Let's express both sides with the same base 5. We know that 251 is the same as 5². Thus, the equation can be rewritten as:

53−x=251=5².

We need to express 53−x as a power of 5. To do that, we can write it as:

53−x = 5³/x.

Now, we can substitute this expression into our equation to get:

5³/x=5²

Let's multiply both sides of the equation by x to eliminate the fraction:

5³=5²x.

Divide both sides by 5² to get:x = 5. We can check our solution by plugging it back into the original equation:

53−5=25, which is true.

Thus, the solution set is {5}.The equation for line L in the point-slope form: We know that L is perpendicular to y=4x. Thus, the slope of L is -1/4. We also know that L passes through a point (x₁, y₁). Let's write the point-slope form of the equation:

y - y₁ = -1/4(x - x₁).

The equation for line L in slope-intercept form: Let's solve this equation for y to get it in slope-intercept form:

y - y₁ = -1/4(x - x₁).

Multiply both sides by 4 to eliminate the fraction:

4y - 4y₁ = -x + x₁.

Simplify by moving -x + x₁ to the right side:

4y = x₁ - x + 4y₁.

Add x to both sides:

4y + x = x₁ + 4y₁

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What is the edge length of
a cube of 1/8 m^3

Answers

Step-by-step explanation:

The volume of a cube is the edge³, so to find the edge, you need to calculate the cubic root of it:

\( \sqrt[3]{ \frac{1}{8} } = \frac{1}{2 } \)

sophia got 8 presents for her birthday . There were 3 shirts in each present. she wants to organize her new shirts and will put 4 shirts in each of her drawers. How many drawers of 4 shirts will she fill ?

Answers

Answer:

6 drawers

Step-by-step explanation:

Total no. of shirts = 8×3

= 24

No. of drawers of shirts filled

= 24÷4

=6

answer- 6

8 x 3 = 24 shirts
24 divided by 4 = 6

a train is moving at a speed of 65 mph. the ticket collector is walking 2 mph toward the front of the train. how fast, in mph is the ticket collector moving from the point of view of a person on the train?

Answers

The relative velocity between the ticket collector moving from the point of view of a person on the train is 63mph

Since a train is moving at a speed of 65 mph

Also,the ticket collector is walking 2 mph toward the front of the train

So, the relative velocity for the ticket collector moving from the point of view of a person on the train = velocity of train - velocity of ticket collector

So, V = u - v

V = + 65mph - (+ 2 mph)

V = 63mph

So, the relative velocitybetween the ticket collector moving from the point of view of a person on the train is 63mph

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This graph shows the amount of rain that falls in a given amount of time.

What is the slope of the line and what does it mean in this situation?

Select from the drop-down menus to correctly complete each statement.

The slope of the line is
Choose...
.

This means that
Choose...
mm of rain falls every
Choose...
.

This graph shows the amount of rain that falls in a given amount of time.What is the slope of the line

Answers

The slope of the line is

3

This means that

6mm

of rain falls every

1hr

Write the multiplication expression for each model then solve

Write the multiplication expression for each model then solve

Answers

Answer:

2/3 * 3 = 2

Step-by-step explanation:

We see that one model has 3 parts and 2 of the 3 parts are shaded.  Thus, the fraction for one of the models by itself is 2/3, where 2 is the part shaded, and 3 is the whole (shaded parts + non-shaded parts).  

Since we have three models with the same form and the same part shaded, we can simply multiply 2/3 by 3, which is our multiplication expression and solve:

2/3 * 3 = 6/3 = 2

Please help!! I'm so bad at math!
find the product of (5x-7)(2x+4)

Answers

Answer:

10x²+6x-28

I think that's right, sorry if not.

Answer:

Its 10x^2+6x+28

Step-by-step explanation:

You can see the picture for further explanation .

Please help!! I'm so bad at math!find the product of (5x-7)(2x+4)

Find an equation of the ellipse. find its foci. smaller x-value (x, y) = larger x-value (x, y) =

Answers

An equation of this ellipse is equal to x²/16 + y²/25 = 1.The foci of this ellipse are equal to (0, 3) and (0, -3).

How to determine the equation of an ellipse?

Mathematically, the standard form of the equation of this ellipse is given by:

\(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\)

This ultimately implies that, the major axis of this ellipse is the x-axis. By critically observing the graph (see attachment), we can logically deduce the following values:

a = 4b = 5

Substituting the parameters into the standard equation of an ellipse, we have;

x²/4² + y²/5² = 1

x²/16 + y²/25 = 1

For the eccentricity, we have:

e² = 1 - a²/b²

e² = 1 - 4²/5²

e² = 1 - 16/25

e² = 9/25

e = √(9/25)

e = 3/5.

Therefore, the foci with smaller y-value is given by:

Foci = (0, be)

Foci = 0, 5 × 3/5)

Foci = (0, 3).

With larger y-value:

Foci = (0, -be)

Foci = 0, -5 × 3/5)

Foci = (0, -3).

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Find an equation of the ellipse. find its foci. smaller x-value (x, y) = larger x-value (x, y) =

To start, which measurement does Tommy need to
know about the soup cans?
O weight
O circumference
O volume
O surface area

Answer FAST

Answers

Answer:

C. volume

Step-by-step explanation:

when youre starting your measurements you want to start the volume first.

Answer:

C

Step-by-step explanation:

got it right

The directors of the Ashborne Community Center are raising money for a new outreach
program. To meet their goal of $2,400, they are selling tickets to an event hosted by a local
celebrity. They know from previous fundraisers that the expression -4p +220 can be used to
estimate the number of tickets they will sell based on the price per ticket, p.
What two ticket prices will make the community center exactly $2,400 in revenue?

Answers

Answer:

15 or 40

Step-by-step explanation:

Melissa walks 3 miles to the house of a friend and returns home on a bike. She averages 4 miles per hour faster when cycling than when walking, and the total time for both trips is two hours. Find her walking speed (HINT: Write an expression that represents the time it takes for Melissa to walk to her friends house, and then write an expression for the time it takes to cycle back. The sum of these expressions is equal to the total time of the trip.)

Answers

Answer:

walking speed is 2 m/s

Step-by-step explanation:

given data

distance between Melissa and friend = 3 mile

total time of the trip = 2 hour

solution

we consider here

walking speed = s₁

bike speed = s₂  

so s₂ = s₁ + 4    .................1

and

time is express as

time = distance ÷ speed      .................2

so time for Melissa to friend reach = 3 ÷ s₁    

and time for return from her friend =  3 ÷ s₂  

so put this value in equation 2 we get

time = 3 ÷ s₁  + 3 ÷ s₂  

2 = \(\frac{3}{s_1} + \frac{3}{s_1 + 4}\)    

solve it and we will get

s₁² + s₁ - 6 = 0

s₁ = 2 m/s

so walking speed is 2 m/s

Suppose you want to figure out how likely it would be to spin red and flip tails. We call red and tails the event.

Suppose you want to figure out how likely it would be to spin red and flip tails. We call red and tails

Answers

Answer with Explanation: We need to find the probability of obtaining the red and tails when the two are flipped at the same time:

\(\begin{gathered} P\left(R\right)=\frac{1}{2} \\ P\left(T\right)=\frac{1}{2} \end{gathered}\)

The probability of the red and tails or P(Red and Tails) is as follows:

\(\begin{gathered} P\left(R\text{ and }T\right?=P\left(R\right)\times P\left(T\right) \\ \therefore\rightarrow \\ P\left(R\text{ and }T\right?=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4} \\ P\left(R\text{ and }T\right?=\frac{1}{4} \end{gathered}\)

Conclusion: Therefore the probability is (1/4) or 25%.

U7L2 Cool Down
The measure of the arc from B to A not passing through C is 26 degrees.

1. What is the measure of angle BOA ?
2. What is the measure of angle BDA?
3. What is the measure of angle BCA ?
degrees
degrees
degrees

Answers

Using the inscribed angle theorems, the measure of the indicated angles are:

1. m∠BOA = 26°

2. m∠BDA = 13°

3. m∠BCA = 13°

What is the Inscribed Angle Theorems?

Based on the inscribed angle theorem, the following relationships are established:

Inscribed angle = 2(measure of intersected arc)Central angle = measure of intersected arc

Given:

Intercepted arc BA = 26°

1. ∠BOA is central angle

Thus:

m∠BOA = 26° (inscribed angle theorems)

2. ∠BDA is inscribed angle.

m∠BDA = 1/2(30) = 13° (inscribed angle theorems)

3. m∠BCA = m∠BDA = 13° (inscribed angle theorems)

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helppppppppppp plssssssssssssssssssssssssssss

helppppppppppp plssssssssssssssssssssssssssss

Answers

Answer:

answer is 5

Step-by-step explanation:

The answer is 5 hope this helps!

PLS HELPP!!!! *PICTURE BELOWW‼️‼️)

Two friends went shopping for t-shirts and baseball caps. Each t-shirt costs the same amount, and each
baseball cap costs the same amount.
● The first friend paid $82.22 for 5 t-shirts and 3 baseball caps.
. The second friend paid $51.73 for 3 t-shirts and 2 baseball caps.
What was the cost in dollars of each baseball cap?
O $12.67
O $9.25
O $11.99
O$10.28

PLS HELPP!!!! *PICTURE BELOWW)Two friends went shopping for t-shirts and baseball caps. Each t-shirt

Answers

The cost of each baseball in dollars is $11.99.

What is an equation?

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 9 is an equation.

We have,

Cost of one t-shirt = x

Cost of one baseball cap = y

We can make two equations.

5x + 3y = 82.22 ____(1)

3x + 2y = 51.73 _____(2)

Solving by elimination method.

Multiply 2 on (1)

Multiply 3 on (2)

  10x + 6y = 164.44

  9x + 6y = 155.19

 (-)    (-)      (-)

          x = 9.25

Now,

x = 9.25 in (1) we get,

5x + 3y = 82.22

5 x 9.25 + 3y = 82.22

46.25 + 3y = 82.22

3y = 82.22 - 46.25

3y = 35.97

y = $11.99

Thus,

The cost of one baseball cup is $11.99.

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Stacy baked 6 chocolate chip cookies. Each cookie had 2.3 grams of chocolate chips. If each large square equals one whole, which model represents the total number of chocolate chips Stacy used?

Answers

The shaded squares within each large square represent the 2.3 grams of chocolate chips in each cookie.

To represent the total number of chocolate chips Stacy used, we can use a visual model. Since each cookie had 2.3 grams of chocolate chips, we can represent each gram with a small square and each whole cookie with a large square.

Therefore, the model that represents the total number of chocolate chips Stacy used would be 6 large squares, with each large square divided into 10 equal smaller squares, and 2.3 of these smaller squares shaded in to represent the 2.3 grams of chocolate chips in each cookie.

Visually, the model would look like this:

 |   |   |   |   |   |   |

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

       |   |   |   |   |   |   |   |

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

       |   |   |   |   |   |   |   |

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

       |   |   |   |   |   |   |   |

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

       |   |   |   |   |   |   |   |

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

       |   |   |   |   |   |   |   |

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

         1   2   3   4   5   6   7

Each large square represents one cookie, and each small square within the large square represents 0.1 grams of chocolate chips. The shaded squares within each large square represent the 2.3 grams of chocolate chips in each cookie.

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if AB = 3 centimeters and AC = 2 centimeters, what is the largest possible perimeter, in centimeters, of isosceles triangle ABC?

Answers

Answer:

8

Step-by-step explanation:

AB is 3 cm and AC is 2 cm, and since triangle ABC is an isosceles triangle, BC can either be 3 cm or 2 cm. We want the longest perimeter possible, so make BC 3 cm, and add the side lengths to find the perimeter.

P = 3 + 3 + 2 = 8.

The calculation answer obtained from multiplying the measurements 64.49 and 6.57 is 423.70. Given the operational rules governing significant figures, this answer

Answers

The answer obtained from multiplying the measurements 64.49 and 6.57 is 423.70.

 

 

According to the rules governing significant figures, the result of a multiplication or division should have the same number of significant figures as the measurement with the fewest significant figures.

In this case, both measurements, 64.49 and 6.57, have four significant figures each. When multiplied together, the result is 423.6993. However, since the measurement 6.57 has the fewest significant figures, the final answer should be rounded to match that.

Therefore, the answer is rounded to three decimal places, resulting in 423.700. The zero at the end is included to indicate that the measurement is known to that level of precision.

Hence, considering the rules of significant figures, the answer obtained from multiplying the measurements 64.49 and 6.57 is 423.700.

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