BM bisects ABC. If MBC = 32°, what is the ABC?

The number in the bottom box is 9 yd. The number in the top is 9 yd. The area of the table is 90 yd².

A trapezoid is a four-sided polygon that has at least one pair of parallel sides. The legs of a trapezoid can be of different lengths, and the angles between the legs and the bases can also vary.

The formula for finding the area of a trapezoid is:

Area = ((Base 1 + Base 2) x Height) / 2

where Base 1 and Base 2 are the lengths of the parallel sides of the trapezoid, and Height is the distance between the parallel sides.

There are several types of trapezoids, including:

Isosceles Trapezoid: An isosceles trapezoid has two parallel sides of equal length and two non-parallel sides of equal length. The angles between the legs and the bases are also equal.

Right Trapezoid: A right trapezoid has one right angle between the leg and the base.

Scalene Trapezoid: A scalene trapezoid has two non-parallel sides of different lengths, and the angles between the legs and the bases are also different.

Let the number in the bottom box=

7.5*2=15 yd

Because the longest side of the table is twice as long as the table's width.

So the number in top box is :

15-3-3=9 yd

Area=( 15 + 9 )* 7.5/2 = 12* 7.5 = 90 yd²

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The complete question is:

The missing value in this equation is 4, or (4)/(1) in fraction form.

The missing value in this equation is the exponent of n in the final expression. To find this value, we can use the rule of exponents that states that when raising a power to another power, we multiply the exponents. In this case, we have (n^(2))^(2), so we multiply the exponents 2 and 2 to get a final exponent of 4. Therefore, the missing value is 4 and the equation can be written as (n^(2))^(2)=n^(4).

In fraction form, the missing value would be (4)/(1), since any whole number can be written as a fraction with a denominator of 1. So, the equation can also be written as (n^(2))^(2)=n^((4)/(1)).

Overall, the missing value in this equation is 4, or (4)/(1) in fraction form.

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Ann's investment in Cilla Shipping bonds has increased in value more, by $33,605.41

What is purchase price?

The complete cost of purchasing an asset is known as the original cost. The whole costs associated with purchasing and using an asset are taken into account when calculating its initial cost.

To determine which of Ann's investments has increased in value more, we need to compare the current value of the bonds and the stock to their original purchase value.

First, let's calculate the purchase price of the bonds:

7 bonds x $500 par value x 0.95626 market rate = $3,349.82

So, Ann initially invested $3,349.82 in the Cilla Shipping bonds.

Next, let's calculate the purchase price of the stock:

125 shares x $28.00 per share = $3,500.00

So, Ann initially invested $3,500.00 in the Cilla Shipping stock.

Now, let's calculate the current value of the bonds:

7 bonds x $500 par value x 1.06384 market rate = $37,286.48

So, the current value of the bonds is $37,286.48.

Let's also calculate the current value of the stock:

125 shares x $30.65 per share = $3,831.25

So, the current value of the stock is $3,831.25.

To determine which investment has increased in value more, we can calculate the percentage increase for each investment:

Percentage increase in bonds = [(current value - purchase price) / purchase price] x 100%

= [(37,286.48 - 3,349.82) / 3,349.82] x 100%

= 1010.46%

Percentage increase in stock = [(current value - purchase price) / purchase price] x 100%

= [(3,831.25 - 3,500.00) / 3,500.00] x 100%

= 9.48%

So, we can see that the bonds have increased in value more than the stock, by a significant amount.

The bonds have increased in value by 1,010.46%, while the stock has increased in value by only 9.48%. The bonds have increased in value by a total of $33,936.66 ($37,286.48 - $3,349.82), while the stock has increased in value by a total of $331.25 ($3,831.25 - $3,500.00).

Therefore, Ann's investment in Cilla Shipping bonds has increased in value more, by $33,605.41 ($33,936.66 - $331.25).

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Answer: 600

Step-by-step explanation:150=.25*X Divide both sides by .25 to get rid of it on the right and move it to the left so now 150/.25=X  600=X

Answer:

(7,4)

Step-by-step explanation:

Reflection across x-axis is making the y value the opposite of what it was prior. (x, y)→(x,-y)

That is the formula.

(Pls mark me brainiest if it's correct :)

Use the rule, “add 8” to find the cost of 6 T-shirts. The cost of the T-shirt is $48.

One of the four fundamental operations in mathematics is addition, along with subtraction, multiplication, and division.

We see that the price of headbands changes abruptly, going from 0 to 2, then to 4, then to 6, etc., always increasing by 2 units.

The “add 8” rule applies to the price of T-shirts because each one costs $8.

In order to determine the cost of six headbands, we then perform the following calculations:

8 + 8 + 8 + 8 + 8 + 8 = 6 x 8 = $48

We see that we can easily multiply the required quantity of T-shirts by the cost per unit of T-shirts.

Therefore, the cost of the T-shirt is $48.

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The question is incomplete, the complete question is given below:

The school store sells headbands for $2 each and T-shirts for$8 each. Write ordered pairs to compare the cost of headbands to T-shirts for 0,1,2,3,4, and 5 of each item.

Cost of Headbands ($)

0

2

4

6

8

10

​

Cost of T-shirts ($)

8

16

24

32

40

Ordered Pairs

(0, 0)

(2, 8)

(4, 16)

(6, 24)

(8, 32)

(10, 40)

​

a)1.597

b)0.1101

c)The population proportion is not equal to 0.14

The test statistic for this sample is 1.597. The corresponding p-value is 0.1101. The p-value is greater than alpha, so the decision is to fail to reject the null. As such, the final conclusion is that there is not sufficient evidence to warrant rejection of the claim that the population proportion is not equal to 0.14. This conclusion is based on the Binomial Distribution and Statistic, which use the p-value to assess the evidence against the null hypothesis.

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If the cost for using 21 HCF of water is $35.39.  the cost for using 56 HCF of water is  $82.64.

We can use the two given data points to find the slope and y-intercept of the linear function that represents the monthly cost of water use.

Let's use (21, 35.39) and (57, 83.99) as our two data points.

First, let's find the slope of the line:

slope = (y2 - y1) / (x2 - x1)

slope = (83.99 - 35.39) / (57 - 21)

slope = 48.6 / 36

slope = 1.35

Now that we have the slope, we can use either of the two data points to find the y-intercept. Let's use (21, 35.39):

y = mx + b

35.39 = 1.35 * 21 + b

35.39 = 28.35 + b

b = 35.39 - 28.35

b = 7.04

So the linear function that represents the monthly cost of water use is:

y = 1.35x + 7.04

where y is the cost (in dollars) and x is the amount of water used (in HCF).

Now we can use this function to find the cost for using 56 HCF of water:

y = 1.35x + 7.04

y = 1.35 * 56 + 7.04

y = 82.64

So the cost for using 56 HCF of water is  $82.64.

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The area of the shaded region which is a triangle will be 32 square inches.

Surface area refers to the area of an open surface or the border of a multi-object, whereas the area of a plane region or plane field refers to the area of a form or planar material.

From the graph, the height of the triangle is given as,

2h = L

2h = 16 inches

h = 8 inches

And the base of the triangle is half of the base of the rectangle. Then we have

b = L / 2

b = 16 / 2

b = 8 inches

Then the area of the shaded region is given as,

A = 1/2 x 8 x 8

A = 32 square inches

The area of the shaded region which is a triangle will be 32 square inches.

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Since the right side of the equation is equal to the identity matrix, we can conclude that the diagonal elements are equal to 1.

To find \( A \), start by multiplying both sides by \( (4A) \). Then, you will have \( (4A)^{-1}(4A)=\left[\begin{array}{ll} 5 & 2 \\ 4 & 2 \end{array}\right] \). This simplifies to \( \left[\begin{array}{ll} 5A & 2A \\ 4A & 2A \end{array}\right] \). Since the right side of the equation is equal to the identity matrix, we can conclude that the diagonal elements are equal to 1. This means that \( 5A=1 \) and \( 2A=1 \). Solving these two equations yields \( A=\frac{1}{5} \).

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Answer: The answer would be b<-9 for the nonsimplified version though.

Step-by-step explanation:

b+1>-8

first, -1 from each side.

then you will have -9>b

But you are going to divide by a negative number, so you are going to flip the inequality.

( b>-9 )

I remember learning this is like 7th grade haha. Let me know if you have any questions

The probability that the next kite Barbara sells will be a diamond is:

To find the probability that the next kite Barbara sells will be a diamond, we need to divide the number of diamond kites sold by the total number of kites sold.

The formula for probability is

= required outcome (number of diamond kites) / possible outcome (total number of kites)

required outcome

The number of diamond kites sold is:

11

possible outcome

The total number of kites sold so far is:

11 + 9 + 6 + 4 = 30

Therefore, the probability that the next kite Barbara sells will be a diamond is 11/30

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Answer:

36πmm^2

Step-by-step explanation:

6mm^2=36mm

36mm×π=36πmm^2

The polynomial for the number of miles between the two cars is d(t) = 5t + 150

Given that

Car A: 7t²+50t+150

Car B: 7t²+45t

The distance function is represented as

d(t) = 7t²+50t+150 - 7t² - 45t

So, we have

d(t) = 5t + 150

This means that t =3

So, we have

d(3) = 5 * 3 + 150

d(3) = 165

This means that d(t) = 200

So, we have

5t + 150 = 200

Evaluate the difference

5t = 50

So, we have

t = 10

Hence, the time is 10 hours

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0.2083335 is the Area of the triangle.

How do triangles work?

The three vertices of a triangle make it a three-sided polygon. The angles of the triangle are formed by the connection of the three sides end to end at a single point.

                            180 degrees is the sum of the triangle's three angles. riangle derives from the Roman word triangulus, which means "three-cornered" or "having three angles," from the roots tri-, "three," and angulus, "angle or corner."

1 ft 1 in =  12 + 1 = 13 in

  the Area of the triangle = 1/2 * b * h

                                        = 1/2 *   1 * 0.416667

                                       = 0.416667/2

                                      = 0.2083335

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The fraction of the flowers in the bouquet are daffodils is   6/ 9f + 6

A fraction can be defined as the part of a whole number or variable.

The different types of fractions in mathematics are;

Ratio is defined as a comparison of two or more numbers indicating their sizes in relation to each other.

It shows the number of times one number contains another.

From the information given, we have that;

The ratio of lilies to daffodils to marigolds in a bouquet is 7f:6:2f.

Then, thte number of daffodils would be;

= 6/7f + f+ 2f

= 6/ 9f + 6

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The given angle measures 120 degrees, which is indeed an interior angle of a regular hexagon

What is hexagon ?

A hexagon is a six-sided polygon, which is a two-dimensional geometric shape with straight sides. The word hexagon comes from the Greek words "hexa" meaning "six" and "gonia" meaning "angle."

To find the value of x in the regular hexagon, we can start by noting that the interior angles of a regular hexagon are all congruent and measure 120 degrees.

Next, we can see that the given angle (11x + 21)° is an interior angle of the hexagon. Therefore, we can set this angle equal to 120 degrees and solve for x:

11x + 21 = 120

11x = 99

x = 9

Therefore, the value of x is 9.

Note that we can check our answer by substituting x = 9 into the original equation:

11x + 21 = 11(9) + 21 = 120

Therefore, the given angle measures 120 degrees, which is indeed an interior angle of a regular hexagon

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There will be 40 cans that contain between 11.95 and 11.98 ounces of drink.

To calculate this, the total number of cans in the delivery truck must first be divided by the total range of ounces in the cans (12.00-11.95 = 0.05). 1500/0.05 = 30000.

This number is then multiplied by the range of ounces being searched for (11.98-11.95 = 0.03). 30000*0.03 = 900.

Finally, the total number of cans is divided by the total range of ounces again (12.00-11.95 = 0.05). 900/0.05 = 40 cans.

Therefore, 40 cans contain between 11.95 and 11.98 ounces of drink.

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The current thrοugh the 2.5 οhm resistοr is 2.4 A.

Electric current is defined as the rate οf flοw οf electric charge thrοugh any crοss-sectiοn οf a cοnductοr.

Tο calculate the current thrοugh a 2.5 οhm resistοr cοnnected acrοss a 6.0 V pοtential difference, we can use Ohm's law, which states that the current thrοugh a cοnductοr between twο pοints is directly prοpοrtiοnal tο the vοltage acrοss the twο pοints, and inversely prοpοrtiοnal tο the resistance between them. The mathematical expressiοn fοr Ohm's law is:

V = I x R

where V is the vοltage, I is the current, and R is the resistance.

We can rearrange this fοrmula tο sοlve fοr the current I:

I = V / R

Substituting the given values, we get:

I = 6.0 V / 2.5 οhm

I = 2.4 A

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The cross product of the first two vectors is -60.

The given vectors are: \( \left(\begin{array}{l}1 \\ 3 \\ 4\end{array}\right),\left(\begin{array}{l}5 \\ 0 \\ 4\end{array}\right),\left(\begin{array}{l}0 \\ 0 \\ 4\end{array}\right) \).

To find the cross product of the first two vectors, we use the formula:

\(\left(\begin{array}{l}a_1 \\ a_2 \\ a_3\end{array}\right) \times \left(\begin{array}{l}b_1 \\ b_2 \\ b_3\end{array}\right) = \left(\begin{array}{l}a_2b_3-a_3b_2 \\ a_3b_1-a_1b_3 \\ a_1b_2-a_2b_1\end{array}\right) \)

Plugging in the values from the given vectors, we get:

\(\left(\begin{array}{l}1 \\ 3 \\ 4\end{array}\right) \times \left(\begin{array}{l}5 \\ 0 \\ 4\end{array}\right) = \left(\begin{array}{l}(3)(4)-(4)(0) \\ (4)(5)-(1)(4) \\ (1)(0)-(3)(5)\end{array}\right) = \left(\begin{array}{l}12 \\ 16 \\ -15\end{array}\right) \)

Now, to find the dot product of this vector with the third given vector, we use the formula:

\(\left(\begin{array}{l}a_1 \\ a_2 \\ a_3\end{array}\right) \cdot \left(\begin{array}{l}b_1 \\ b_2 \\ b_3\end{array}\right) = a_1b_1 + a_2b_2 + a_3b_3 \)

Plugging in the values from the vectors, we get:

\(\left(\begin{array}{l}12 \\ 16 \\ -15\end{array}\right) \cdot \left(\begin{array}{l}0 \\ 0 \\ 4\end{array}\right) = (12)(0) + (16)(0) + (-15)(4) = -60 \)

Therefore, the final answer is -60.

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Answer:

First, find the total number of cups of liquid in the punch:

24 cups pineapple juice + 46 cups orange juice + 72 cups seltzer = 142 cups

Then, divide the total cups of liquid by the amount of liquid in each serving:

108 cups / 142 cups per serving = 0.76 servings

Therefore, approximately 0.76 servings can be made from 108 cups of punch.

The sοlutiοn οf the given prοblem οf area cοmes οut tο be the side length rises by 1, the area grοws and then shrinks by an equal factοr.

Calculating hοw much space wοuld be needed tο fully cοver the οutside will reveal its οverall size. When determining the surface οf such a trapezοidal fοrm, the surrοundings are additiοnally taken intο accοunt. The surface area οf sοmething determines its οverall dimensiοns. The number οf edges here between cubοid's fοur trapezοidal extremities determines hοw much water it can hοld inside.

Here,

Optiοn B

The area grοws initially and then decreases by an amοunt equivalent tο the side length multiplied by 1. The area grοws befοre decreasing by an equivalent amοunt.

This is the case because a square's surface and side length are inversely prοpοrtiοnal. Where r is the οriginal side length, the area grοws by a factοr οf (1 + 2r + r2) as the side length rises by 1.

When r is big, hοwever, the term r2 dοminates and the area increase is less nοticeable.

Eventually, as r gets clοser tο infinite, the area increases οnly marginally and eventually reaches a limit.

As a result, as the side length rises by 1, the area grοws and then shrinks by an equal factοr.

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Complete question:

Answer:
a. Y = X1 + X2 = 1(Heads) + 1(Heads) = 2
Z = X2 + X3 = 1(Heads) + 1(Heads) = 2
The joint probability mass function of (Y, Z) can be determined by multiplying the individual probabilities:
P(Y, Z) = P(Y) * P(Z)
P(Y, Z) = (2/8) * (2/8) = 1/16

b. Y and Z are not independent because they both include the result of the second coin toss (X2). If X2 is heads, both Y and Z will be affected, and if X2 is tails, both Y and Z will be affected. Therefore, the outcome of one variable affects the outcome of the other, meaning they are not independent.

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Answer: 80 meters wide and 100 meters long.

Step-by-step explanation:

Well, if the park has to have a larger area, but the same perimeter, all you need to do in this case is turn 70 to 80 and 110 to 100.

80 + 80 + 100 + 100 = 360 meters in perimeter

70 x 110 = 7700

80 x 100 = 8000   ← This has greater area than the park above

To find Pearson's correlation coefficient, we need to first calculate the means, standard deviations, and covariance of the given data. Let's first convert the heights in km to m for ease of calculation.

t (s) h (m)

0 25,000

5 28,000

10 30,000

15 31,000

25 33,000

30 34,000

(a) Pearson's correlation coefficient:

We can use the formula

r = (nΣxy - ΣxΣy) / sqrt[(nΣx² - (Σx)²)(nΣy² - (Σy)²)]

where n is the number of data points, Σ is the sum, and x and y are the variables being compared (time and height, in this case).

Using the given data, we get:

n = 6

Σx = 85

Σy = 181000

Σx² = 1375

Σy² = 503,710,000

Σxy = 2,886,000

Substituting into the formula, we get:

r = (62,886,000 - 85181000) / sqrt[(61375 - 85²)(6503710000 - 181000²)]

r = 0.994

Therefore, Pearson's correlation coefficient is 0.994, indicating a strong positive correlation between time and height.

(b) Rocket's acceleration:

We can use the formula:

h = ut + (1/2)at²

where h is the height, u is the initial velocity (assumed to be 0), t is the time, and a is the acceleration.

Rearranging, we get:

a = 2h/t²

Using the final height of 34,000 m and the time of 30 seconds (when the rocket reaches this height), we get:

a = 2*34000/(30²)

a = 75.6 m/s²

Therefore, the rocket's acceleration is 75.6 m/s².

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[tex]\stackrel{a}{-117}+\stackrel{b}{44}i \\\\[-0.35em] ~\dotfill\\\\ \theta =\tan^{-1}\left( \cfrac{44}{-117} \right)\implies \theta \approx 339.39^o~\hfill r=\sqrt{(-117)^2 + 44^2}\implies r=125 \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\sqrt[n]{z}=\sqrt[n]{r}\left[ \cos\left( \cfrac{\theta+2\pi k}{n} \right) +i\sin\left( \cfrac{\theta+2\pi k}{n} \right)\right]\quad \begin{array}{llll} k\ roots\\ 0,1,2,3,... \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \boxed{k=0}\hspace{3em} \sqrt[ 3 ]{125} \left[ \cos\left( \cfrac{ 339.39^o + 360^o( 0 )}{3} \right) +i \sin\left( \cfrac{ 339.39^o + 360^o( 0 )}{3} \right)\right] \\\\\\ \sqrt[ 3 ]{125} \left[ \cos\left( \cfrac{ 339.39^o }{3} \right) +i \sin\left( \cfrac{ 339.39^o }{3} \right)\right][/tex]

[tex]5[ \cos(113.13^o) +i \sin(113.13^o)]\approx \boxed{-1.96~~ + ~~4.60i} \\\\[-0.35em] ~\dotfill\\\\ \boxed{k=1}\hspace{3em} \sqrt[ 3 ]{125} \left[ \cos\left( \cfrac{ 339.39^o + 360^o( 1 )}{3} \right) +i \sin\left( \cfrac{ 339.39^o + 360^o( 1 )}{3} \right)\right] \\\\\\ \sqrt[ 3 ]{125} \left[ \cos\left( \cfrac{ 699.39^o }{3} \right) +i \sin\left( \cfrac{ 699.39^o }{3} \right)\right] \\\\\\ 5[\cos(233.13^o)+i\sin(233.13^o)]\approx \boxed{-3.00~~ - ~~4.00i} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\boxed{k=2}\hspace{3em} \sqrt[ 3 ]{125} \left[ \cos\left( \cfrac{ 339.39^o + 360^o( 2 )}{3} \right) +i \sin\left( \cfrac{ 339.39^o + 360^o( 2 )}{3} \right)\right] \\\\\\ \sqrt[ 3 ]{125} \left[ \cos\left( \cfrac{ 1059.39^o }{3} \right) +i \sin\left( \cfrac{ 1059.39^o }{3} \right)\right] \\\\\\ 5[\cos(353.13^o)+i\sin(353.13^o)]\approx \boxed{4.96~~ - ~~0.60i}[/tex]

Cube roots of complex number - 117 + 14i are,

- 1.96 + 4.60i

- 3.00 - 4.00i

4.96 - 0.60i

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

Complex number is,

⇒ - 117 + 14i

Let a = - 117

b = 44

Then, tan ⁻¹ (44/117) = 339.39°

⇒ θ = 339.39°

And, r = √117² + 44² = 125

Hence, We have;

[tex]\sqrt[n]{z} = \sqrt[n]{r} [cos (x + 2\pi k/n) + i sin (x + 2\pi k/n)][/tex]

Where, k = 0,1,2, 3, ..

Now, At k = 0

[tex]\sqrt[3]{z} = \sqrt[3]{125} [cos (339.39 + 0/3) + i sin (339.39 + 0/n)][/tex]

    = - 1.96 + 4.60i

At k = 1;

[tex]\sqrt[3]{z} = \sqrt[3]{125} [cos (339.39 + 360/3) + i sin (339.39 + 360/n)][/tex]

     = - 3.00 - 4.00i

At k = 2;

[tex]\sqrt[3]{z} = \sqrt[3]{125} [cos (339.39 + 360*2/3) + i sin (339.39 + 360*2/3)][/tex]

     = 4.96 - 0.60i

Thus, All Cube roots of complex number - 117 + 14i are,

- 1.96 + 4.60i

- 3.00 - 4.00i

4.96 - 0.60i

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Step-by-step explanation:

To fence a circular park with 3 rounds, we need to find the total length of wire required to go around the park 3 times.

The circumference of a circle is given by the formula:

C = πd

where C is the circumference, π is the constant pi, and d is the diameter.

Substituting the given diameter of the park (280 m) into the formula, we get:

C = π * 280 m

≈ 879.65 m

So the length of wire required to fence the park once is approximately 879.65 m.

To fence the park three times, we need to multiply this length by 3:

3 rounds of wire = 3 * 879.65 m

= 2638.95 m

Therefore, the length of wire required to fence a circular park of diameter 280 m with 3 rounds is approximately 2638.95 m.

This is shorter than the path made up of the two shortest sides by 33%.

In the case where ABC is an equilateral triangle, the point S is the center of the triangle. The total length of the network in this case is the sum of the lengths of the three sides (AS, BS, and CS) of the triangle, which is 3 times the length of a single side.

This is shorter than the path made up of the two shortest sides by 33%,

since the total length of the path made up of the two shortest sides is the sum of the lengths of the two sides, which is 2 times the length of a single side.

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We can represent 1,250 raised to the power of three-fourths as the sum of its prime factors in order to write it in the simplest radical form:

1,250 = 2 × 5 × 5 × 5 × 5

Next, we can formulate the statement as follows by using the fact that (a b)c = ac bc:

[tex](2\times5^3)^3/4 = 2^{(3/4)} \times(5^3)^{(3/4)[/tex]

Now, by using the fourth root of 53, we can simplify the statement underneath the radical:

[tex](2\times5^3)^3/4 = 2^{(3/4)} \times5^{(9/4)[/tex]

As a result, the value under the radical is 5(9/4), or the fifth root of five multiplied by nine. 5 being a prime integer prevents any further simplification of this phrase.

Learn more about prime factors here:

brainly.com/question/29775157

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Answer:

5

Step-by-step explanation:

The answer above is correct.