Classify the numbers as prime or composite

Answer:

(A) 72

Step-by-step explanation:

Find the middle(or middle two) values:

67 67 68 71 72 72 72 72 73 76

1   2   3   4   5   6   7   8   9   10

                    ^    ^

Now find the mean of the two middle values: (72+72)/2 = 72.

Therefore, the median value is 72 or (A).

Final answer:

The median score of the top ten finishers in the golf tournament is 72.

Explanation:

To find the medianscore, we need to arrange the scores in ascending order. The scores are: 67, 67, 68, 71, 72, 72, 72, 72, 73, 76. The middle score is the median. Since there are 10 scores, the middle score is the 5th score in the ordered list, which is 72. Therefore, the median score is 72.

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The constant of proportionality is k = 490 and the equation is y = 490x where x is the number of hours and y is the total number of miles

The time required is 12 hours

What is Proportion?

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

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

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the distance of the aircraft be = x

Let the total time taken by the aircraft be = y

Let the constant of proportionality be k

when x = 1 ,

y = 490

So , the equation will be y = kx

Substituting the values in the equation , we get

y = 490x

when x = 2

y = 490 ( 2 )

y = 980

Now , the time taken by aircraft to travel 5,880 miles is

Substitute the value of y as 5880 in the equation , we get

5880 = 490x

Divide by 490 on both sides of the equation , we get

x = 5880 / 490

x = 12

Therefore , the time taken is 12 hours

Hence , the constant of proportionality is 490

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Answer:

The constant of proportionality is 490

The jet will take 12 hours to travel 5,880 miles

Step-by-step explanation: The miles multiply by 490 each time.

490 x 12 is 5,880

Answer:

(x^2+8) ( y+4)

Step-by-step explanation:

x^2y + 8y+ 4x^2 +32

Splitting into two groups

x^2y + 8y+      4x^2 +32

Factor y out of the first group  and 4 out of the second group

y( x^2+8)    + 4(x^2+8)

Factor out (x^2+8)

(x^2+8) ( y+4)

Answer:

(x^2+4)(y+3)

Step-by-step explanation:

x^2y+4y+3x^2+12

factor by grouping

=x^2y+4y + 3x^2+12

left. right

take common in left y and in right 3

=y(x^2+4) + 3(x^2+4)

now common term is (x^2+4)

=(x^2+4) (y+3) answer

The magnitude of the resultant force is 2930 pounds.

What is the resultant force?

The resultant force is the single force that has the same effect as two or more forces acting together. Two forces that act in the same direction produce a resultant force that is larger than either individual force.

If one bulldozer exerts force in west direction of magnitude 1250 pounds and the other exerts a force in north direction of magnitude 2650 pounds .

let F=  1250 pounds  and F= 2650 pounds

Using magnitude,

|F|=√F²+  F²

|F|= √1250²+2650²

   = √1562500+7022500

  =√2*2*5*5*5*5*5*5*5*5+2*2*5*5*5*5*53*53

=√2*2*5*5*5*5(5*5*5*5+53*53)

=50√3434

= 2930.017 pounds.

Hence, the magnitude of the resultant force is approximately equal to 2930 pounds.

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