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3 years ago

Last year the local dance club had 64 members. this year it has 73 members. Calculate the percentage increase in the membership.

Mathematics

1 answer:

lozanna [386]3 years ago

6 0

Answer:

14.06%

Step-by-step explanation:

To find the percent increase, find the difference between the original and new amounts, divide it by the original amount, then multiply by 100:

73 - 64 = 9, so the difference is 9.

Divide this by the original and multiply by 100:

(9 / 64) x 100

= 14.06

So, the percent increase in the membership is 14.06%

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2 years ago

Find the number of terms, n, in the arithmetic series whose first term is 13, the common difference is 7, and the sum is 2613.

siniylev [52]

Answer:

Step-by-step explanation:

Recall that the sum of an arithmetic series is given by:

$\displaystyle S = \frac{n}{2}\left(a + x_n\right)$

Where n is the number of terms, a is the first term, and x_n is the last term.

We know that the initial term a is 13, the common difference is 7, and the total sum is 2613. Since we want to find the number of terms, we want to find n.

First, find the last term. Recall that the direct formula for an arithmetic sequence is given by:

$x_n=a+d(n-1)$

Since the initial term is 13 and the common difference is 7:

$x_n=13+7(n-1)$

Substitute:

$\displaystyle S = \frac{n}{2}\left(a + (13+7(n-1)\right)$

We are given that the initial term is 13 and the sum is 2613. Substitute:

$\displaystyle (2613)=\frac{n}{2}((13)+(13+7(n-1)))$

Solve for n. Multiply both sides by two and combine like terms:

$5226 = n(26+7(n-1))$

Distribute:

$5226 = n (26+7n-7)$

Simplify:

$5226 = 7n^2+19n$

Isolate the equation:

$7n^2+19n-5226=0$

We can use the quadratic formula:

$\displaystyle x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}$

In this case, a = 7, b = 19, and c = -5226. Substitute:

$\displaystyle x =\frac{-(19)\pm\sqrt{(19)^2-4(7)(-5226)}}{2(7)}$

Evaluate:

$\displaystyle x = \frac{-19\pm\sqrt{146689}}{14} = \frac{-19\pm 383}{14}$

Evaluate for each case:

$\displaystyle x _ 1 = \frac{-19+383}{14} = 26\text{ or } x _ 2 = \frac{-19-383}{14}=-\frac{201}{7}$

We can ignore the second solution since it is negative and non-natural.

Therefore, there are 26 terms in the arithmetic series.

Our answer is A.

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2 years ago

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mars1129 [50]

B is the answer to this question

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3 years ago

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makkiz [27]

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3 years ago

Mrs. Konings likes to eat Nerds (the candy, not her people). There are 1,000 Nerds in the box. The amount of Nerds left in the b

Sveta_85 [38]

Answer:

$y-\frac{1}{3}+y=1000$

x=499.83

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Step-by-step explanation:

We can solve this problem with a system of equations:

The total quantity of Nerds in the box:

$x+y=1000$ (1)

The amount of Nerds left in the box: $y$

The number of portions Mrs. Konings has taken: $x$

The amount of Nerds left in the box decreases by a third each time she dumps out a portion:

$x=y-\frac{1}{3}$ (2)

Substituting (2) in (1):

$y-\frac{1}{3}+y=1000$ (3) This is the equation

Let's find $y$ :

$y=\frac{3001}{6}=500.16$ (4)

Now let's find $x$ by substituting (4) in (2):

$x=500.16-\frac{1}{3}=499.83$ (5)

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3 years ago

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