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3 years ago

Lawrence High prevailed in Saturday's track

Mathematics

1 answer:

Serggg [28]3 years ago

4 0

Answer:

The answer is below

Step-by-step explanation:

Let x represent a first place finish, y represent a second place finish and z represent a third place finish.

Since there is a total of 20 individual events, hence:

x + y + z = 20 (1)

A first place finish is 5 point, a second place finish is 3 point and third place finish is 1 point. Therefore:

5x + 3y + z = 68 (2)

The second place finishers is as much as first and third-place finishers combined. Hence:

y = x + z (3)

Solving equation 1, 2 and 3 simultaneously gives:

x = 7, y = 10 and z = 3

This means the number of first place finishes was 7, second place finishes was 10 and third place finishes was 3

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There are 8 blue marbles and 7 red marbles in a bag. Julie pulls two marbles at random from the bag first. What is the probabili

konstantin123 [22]

Answer:

either a ratio 8;7. or a percentage of 53% for picking the blue marble first i think and a 50/50 chance if you keep that blue marble out.

Step-by-step explanation:

4 0

3 years ago

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John and Nathan share a reward of $140 in a ratio of 2:5. What fraction of total

nydimaria [60]

Answer:

2/7

Step-by-step explanation

2+5 = 7

Fraction that goes to John = 2/7 of $140

Fraction that goes to Nathan = 5/7 of $140

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4 years ago

Please help with math problem

e-lub [12.9K]

Answer:

$a_0 = -8$

$a_1=-6$

$x^2 +y^2 -8x - 6y = 0$

Step-by-step explanation:

The equation of the circle has the following form

$x^2 + y^2 + a_0x + a_1y=0$

The equation of the circle has the following form

We know that the circle goes through the following points

(1, 7)

(8, 6)

(7, -1).

Then we substitute the values of x and y in the equation

$(1)^2 + (7)^2 + a_0(1) + a_1(7)=0$

$1 + 49 + a_0 + 7a_1=0$

$a_0 + 7a_1=-50$ (1)

$(8)^2 + (6)^2 + a_0(8) + a_1(6)=0$

$64 + 36 + 8a_0 + 6a_1=0$

$8a_0 + 6a_1= -100$ (2)

With these equations is enough to solve the system

$a_0 + 7a_1=-50$ (1)

$8a_0 + 6a_1= -100$ (2)

Multiply the equation (1) by -8 and add it to the equation (2)

$-8a_0 - 56a_1=400$ (1)

$8a_0 + 6a_1= -100$ (2)

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

$-50a_1 = 300\\\\a_1 = -6$

Then

$a_0 + 7(-6) = -50\\\\a_0 = -50+42\\\\a_0=-8$

Finally the equation is:

$x^2 +y^2 -8x - 6y = 0$

7 0

3 years ago

Look at this triangle work out length BC

Andreas93 [3]

Answer:

The length of BC is √105 cm or 10.2 cm.

Step-by-step explanation:

You have to apply Pythagoras Theorem, c² = a² + b² where c represents hypotenuse, a and b are the sides :

${c}^{2} = { a}^{2} + {b}^{2}$

$let \:a =BC \:, \: b = 8 \: , \: c = 13$

${13}^{2} = {BC}^{2} + {8}^{2}$

$169 = {BC}^{2} + 64$

${BC}^{2} = 169 - 64$

${BC}^{2} = 105$

$BC = \sqrt{105}$

$BC = 10.2 \: cm \: (3s.f)$

7 0

3 years ago

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Find the future value of an annuity due of $7,000 paid at the beginning of each 6-month period for 8 years if the interest rate

Oliga [24]

Answer: Im not sure but i think its 120,960

Step-by-step explanation: i know that there is 2 of the 6-month periods in a year and multiplied that by 8 and got 16. Then i did 7000x.08=560 and then i added that to 7000 and got 7560. FInally i multiplied that by 16 and got 120,960.

4 0

3 years ago