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3 years ago

A basketball player made 75% of her free throws in 10 games. She had 36 free throw tries. How many did she make?

1 answer:

5 0

If she had 36 free throw tries and made 75% of them, you would multiply 36 by 0.75. Percentages are really just parts out of 100, so 75 in decimal form would be 0.75 (out of 1.0).

36 x 0.75 = 27 ( the same as 3/4 of 36 )

So, the basketball player made 27 free throws.

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Find the 13th term of the arithmetic sequence -3x – 1,42 + 4,112 + 9, ...

Strike441 [17]

Answer:

The 13th term is 81x + 59.

Step-by-step explanation:

We are given the arithmetic sequence:

$\displaystle -3x -1, \, 4x +4, \, 11x + 9 \dots$

And we want to find the 13th term.

Recall that for an arithmetic sequence, each subsequent term only differ by a common difference d. In other words:

$\displaystyle \underbrace{-3x - 1}_{x_1} + d = \underbrace{4x + 4} _ {x_2}$

Find the common difference by subtracting the first term from the second:

$d = (4x+4) - (-3x - 1)$

Distribute:

$d = (4x + 4) + (3x + 1)$

Combine like terms. Hence:

$d = 7x + 5$

The common difference is (7x + 5).

To find the 13th term, we can write a direct formula. The direct formula for an arithmetic sequence has the form:

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

Where a is the initial term and d is the common difference.

The initial term is (-3x - 1) and the common difference is (7x + 5). Hence:

$\displaystyle x_n = (-3x - 1) + (7x+5)(n-1)$

To find the 13th term, let n = 13. Hence:

$\displaystyle x_{13} = (-3x - 1) + (7x + 5)((13)-1)$

Simplify:

$\displaystyle \begin{aligned}x_{13} &= (-3x-1) + (7x+5)(12) \\ &= (-3x - 1) +(84x + 60) \\ &= 81x + 59 \end{aligned}$

The 13th term is 81x + 59.

3 0

3 years ago

Anybody body willing to help i have to do 1-3 and 14-17 for all of my hw

Ymorist [56]

I will help, what is your book called?

6 0

3 years ago

A cylindrical can has a volume of 2in^(3). Express the surface area of the can as a function of its radius,r.

noname [10]

$V=2 \text{ in}^3\\
A=2\pi r (r+h)\\
h=?\\\\
V=\pi r^2h=2\\
\pi r^2h=2\\
h=\dfrac{2}{\pi r^2}\\
A=2\pi r\left(r+\dfrac{2}{\pi r^2}\right)\\
\boxed{A=2\pi r^2+\dfrac{4}{r}}
 
$

7 0

3 years ago

Which of the following is a rational number? 8 15 44 45 π

sveta [45]

All of them are, except ' π ' (pi) ... which gives you an idea of why
that one is usually written as a symbol and not as digits.

Here's a useful factoid regarding the other numbers on the list:
-- ANY number that you can write down on paper, completely,
using digits, is a rational number.

4 0

3 years ago

Read 2 more answers

A sign in a bakery gives these options: • 12 cupcakes for $29 • 24 cupcakes for $56 • 50 cupcakes for $129 Find each unit price

crimeas [40]

Answer:

a) $2.44 per cupcake

b) $2.33 per cupcake

c) $2.58 per cupcake

Step-by-step explanation:

We are given the following in the question:

We have to calculate the unit price of the cupcakes.