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2 years ago

At a competition with 5 runners

Mathematics

2 answers:

kenny6666 [7]2 years ago

7 0

Answer:

Permutation; number of ways = 60

Step-by-step explanation:

ankoles [38]2 years ago

5 0

Answer:

B: Permutation; Number of ways = 60

Step-by-step explanation:

First we have to decide if this is a problem of permutation or combination. The rule is:

If the order matters, permutations will be used
If order does not matter, combinations will be used

In this problem, they order of awarding the medals matters, so this is a permutation problem.

We have to award 3 medals among 5 runners. So this can be done in 5P3 ways:

$nPr=\frac{n!}{(n-r)!}\\ \\ so\\ \\ 5P3=\frac{5!}{(5-3)!}=60$

Therefore, there are 60 ways to award the medal. Therefore, the correct answer is B.

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What is the equation of the line that is perpendicular to y=2/3x-5 and passes through (6,-1)?

riadik2000 [5.3K]

Answer: 2y + 3x - 16 = 0

Step-by-step explanation:

Equation of the line is y = 2x/3 - 5

From the equation , the slope m₁ = 2/3. therefore recall, from condition for perpendicularity, m₁m₂ = -1

The product of their gradient must be (-1).

Now since m₁ = 2/3 and m₁m₂ =-1

2m₂/3 = -1

Therefore , m₂ = -3/2.

Since the equation passes through the coordinate of (6,-1)

we now substitute for x and y in the equation of a line to get the y intercept (c)

y = mx + c

-1 = -3x/2 +c

-1 = -3/2 x 6 + c

-1 = -9 + c

-1 + 9 = c

Therefore c = 8

Now to get the equation of line that is perpendicular to y = 2x/3 - 5

y = -3x/2 + 8

making it a linear equation,

2y = -3x + 16

2y +3x - 16 = 0

6 0

3 years ago

Use the compound interest formulas A = P 1 + r n nt and A = Pe rt to solve. 2) Suppose that you have $8000 to invest. Which inve

Gnoma [55]

Answer: A

Compound interest simply defined as the interest added at regular interval. Compound interested can be calculated using

Compound interest = P (1+) ^nt and Pe ^rt

P = Initial balance

r = Annual interest rate

n = Number of times the interest is compounded per year

t =Number of year money is invested

Using

Compound interest = P (1+ ) ^nt

Continuous

P= $ 8000

t = 6

r = 6.25%

= 0.0625

n = 1

Compound interest = 8000 (1+) ^1×6

= 8000 (1 + 0.0625) ^6

= 8000 (1.0625) ^ 6

= 8000× 1.4387

= $11,509.6

Semi- annually

P= $ 8000

t = 6

r = 6.3%

= 0.063

n = 2

Compound interest = 8000 (1+) ^2×6

= 8000 (1 + 0.063) ^12

= 8000 (1.063) ^12

= 8000× 1.4509

= $11,607.0

Investing $ 8000 semi-annually at 6.3% for 6 years yields greater return

Therefore the answer is (A)

3 0

2 years ago

Divide. −2 4/7 Enter your answer as a mixed number, in simplified form, in the box.

Katarina [22]

Answer:
-3 $\frac{3}{7}$

Explanation:
$\frac{-24}{7}$ = -3 $\frac{3}{7}$
So first make the improper fraction into a mixed number by taking out all the whole numbers from the numerator (3) and making sure the proper sign is in front of the answer (- 3) your remainder is the original numerator minus the product of the answer times the denominator: 24 - (3 • 7) = 24 - 21 = 3. Rewrite the mixed number.

3 0

2 years ago

Ian purchased cans of soda for a party he was having. For every 12 cans of soda she paied $4.98. What is the cost per can of sod

adelina 88 [10]

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2 years ago

How do you do 3(4y-7)=15y+6

cestrela7 [59]

Answer:

y = 27/7

Step-by-step explanation:

Perform the indicated multiplication:

3(4y-7)=15y+6 becomes:

12y - 21 = 5y + 6

Combining like terms, we get:

7y = 27, so that y = 27/7

7 0

3 years ago