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5 days ago

5

The final score of a figure skating competition is determined by finding the average of six judges' scores. Write a formula for

the average A
of six scores x1, x2, x3, x4, x5, and x6. Then solve the formula for x4, the fourth judge's score.
A=

x4=

The table shows the scores given to a figure skater by the judges. The skater receives a final score of 5.7. Find the score given by the fourth judge.

Judge 1 2 3 4 5 6
Score 5.6 5.8 5.6 x4 5.9 5.4

2 answers:

PIT_PIT [3.9K]5 days ago

3 0

Answer:

a) $\text{Average of Scores} = \frac{\text{Sum of all scores}}{\text{Total Number of scores}}\\\\ = \frac{x_1+x_2+ x_3+ x_4+ x_5+ x_6}{6}$

$x_4 = 6A - (x_1+x_2+x_3+x_5,+x_6)$

b) $x_4 = 5.9$

Detailed explanation:

a) The judges provided a total of six scores: $x_1, x_2, x_3, x_4, x_5, x_6$

We need to calculate the average of these scores:

$\text{\bold{Average of Scores}} = \frac{\text{Sum of all scores}}{\text{Total Number of scores}}\\\\ = \frac{x_1+x_2+ x_3+ x_4+ x_5+ x_6}{6}$

To determine the fourth judge's score, we can rearrange the formula to yield $x_4$

$x_4 = 6A - (x_1+x_2+x_3+x_5,+x_6)$

b) The computed average score = 5.7

Judge: 1 2 3 4 5 6

Score: 5.6 5.8 5.6 x 5.9 5.4

Substituting the values into the equation provides us with:

$x = 6(5.7) - (5.6+5.8+5.6+5.9+5.4)$

x = 5.9

This indicates the score recorded by the fourth judge is 5.9

$x_4 = 5.9$

AnnZ [3.9K]5 days ago

3 0

The average A is calculated by adding the scores given by each judge and dividing by the total number of judges.

Hence $A =\frac{x1 + x2 + x3 + x4 + x5 + x6}{6}$

To determine the score given by judge 4, we need the final average score (A) and the scores from the other five judges.

The overall score A comes to 5.7

The scores from judges 1, 2, 3, 5, and 6 are 5.6, 5.8, 5.6, 5.9, and 5.4 respectively.

With this information, we can compute x4:

$x4=6A-x1-x2-x3-x5-x6$

$x4=6*5.7 -5.6-5.8-5.6-5.9-5.4$

$x4=5.9$

Thus, the fourth judge's score was $x4=5.9$

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AnnZ [3900]

The tension does not approach infinity.
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For m₁: m₁*g - T = m₁*a

For m₂: T - m₂*g = m₂*a

Assuming a massless cord and pulley without friction, the accelerations are the same.

From the second equation: a = (T - m₂*g) / m₂

Substitute into the first:
m₁*g - T = m₁ * [(T - m₂*g) / m₂]
Rearranging:
m₁*g - T = (m₁*T)/m₂ - m₁*g
2*m₁*g = T * (1 + m₁/m₂)
2*m₁*m₂*g = T * (m₂ + m₁)
T = (2*m₁*m₂*g) / (m₂ + m₁)
Taking the limit as m₁ approaches infinity:
T = 2*m₂*g

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5 0

14 days ago

If the volume of a cube is increased by a factor of 10, by what factor does the surface area per unit volume change

tester [3938]

Answer:

(1/10)∛100 ≈ 0.4642

Step-by-step explanation:

For a cubic shape with volume V, the edge length is defined as...

s = ∛V

and the surface area is given by...

A = 6s² = 6V^(2/3)

The area-to-volume ratio is therefore...

r1 = A/V = 6V^(2/3)/V = 6V^(-1/3)

When the volume V is increased by a factor of 10, the new area-to-volume ratio becomes...

r2 = 6(10V)^(-1/3)

Consequently, the change factor for the ratio is...

r2/r1 = (6(10V)^(-1/3))/(6V^(-1/3)) = 10^(-1/3) = (1/10)∛100

The change in surface area per unit volume results in a factor of (∛100)/10.

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Example

For a cube with side length 2, the corresponding volume equals 2³ = 8, with a surface area of 6·2² = 24. The resulting area-to-volume ratio is 24/8 = 3.

<pif we="" multiply="" the="" edge="" length="" by="" new="" volume="" equals="" and="" surface="" area="" equates="" to="" so="" area-to-volume="" ratio="" becomes...="">

The area-to-volume ratio changed by a factor of (0.3∛100)/3 = (∛100)/10, as previously noted.

</pif>

8 0

10 hours ago

A factory received a shipment of 38 sprockets, and the vendor who sold the items knows there are 5 sprockets in the shipment tha

tester [3938]

Answer:

a) 0.00019923%

b) 47.28%

Step-by-step explanation:

a) To determine the likelihood that all sockets in the sample are defective, we can use the following approach:

The first socket is among a group that has 5 defective out of 38, leading to a probability of 5/38.

The second socket is then taken from a group of 4 defective out of 37, following the selection of the first defective socket, resulting in a probability of 4/37.

Extending this logic, the chance of having all 5 defective sockets is computed as: (5/38)*(4/37)*(3/36)*(2/35)*(1/34) = 0.0000019923 = 0.00019923%.

b) Using similar reasoning as in part a, the first socket has a probability of 33/38 of not being defective as it's chosen from a set where 33 sockets are functionally sound. The next socket has a proportion of 32/37, and this continues onward.

The overall probability calculates to (33/38)*(32/37)*(31/36)*(30/35)*(29/34) = 0.4728 = 47.28%.

5 0

7 days ago

What is 3.242424 as a mixed number

Zina [3917]

Response:

Detailed explanation:

The final result is 3 /8/33.

step by step breakdown

Initially, we write:

x

=

3

.

¯¯¯¯

24

After that, we will multiply each side by

100

leading to:

100

x

=

324

.

¯¯¯¯

24

Subsequently, we will subtract the first equation from the second equation:

100

x

−

x

=

324

.

¯¯¯¯

24

−

3

.

¯¯¯¯

24

We can then solve for

x

in the following manner:

100

x

−

1

x

=

(

324

+

0

.

¯¯¯¯

24

)

−

(

3

+

0

.

¯¯¯¯

24

)

(

100

−

1

)

x

=

324

+

0

.

¯¯¯¯

24

−

3

−

0

.

¯¯¯¯

24

99

x

=

(

324

−

3

)

+

(

0

.

¯¯¯¯

24

−

0

.

¯¯¯¯

24

)

99

x

=

321

+

0

99

x

=

321

99

x

99

=

321

99

99

x

99

=

3

×

107

3

×

33

x

=

3

×

107

3

×

33

x

=

107

33

Next, we convert this improper fraction to a mixed numeral:

x

=

107

33

=

99

+

8

33

=

99

33

+

8

33

=

3

+

8

33

=

3

8

33

3

.

¯¯¯¯

=

3

8

33

6 0

10 hours ago

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For each store what is the ratio of the number of cans to the price? Super saver 12 pack 4 for $10, shop smart 24 pack 2 for $9,

tester [3938]

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4 0

7 days ago