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2 years ago

A ballroom has a square dance floor. The area of the floor is 400 square feet.

Mathematics

1 answer:

Ilya [14]2 years ago

6 0

It is given in the qustion that

A ballroom has a square dance floor. The area of the floor is 400 square feet.

And the formula of area of square is side square.

So we will get

$400 = side^2$

Taking square root on both sides,

$side = 20$

And on increasing the side length by one foot , we will get side length of 21 feet .

And it is not a perfect square .

And the area is

$Area= 21^2 = 441 ft^2$

And 441 is a perfect square and a rational number .

Therefore true statements are A and E .

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The sum of an infinite geometric sequence is seven times the value of its first term.

Radda [10]

Answer:

a). r = $\frac{6}{7}$

b). At least 5 terms should be added.

Step-by-step explanation:

Formula representing sum of infinite geometric sequence is,

$S_{\inf}=\frac{a}{1-r}$

Where a = first term of the sequence

r = common ratio

a). If the sum is seven times the value of its first term.

$7a=\frac{a}{1-r}$

$7=\frac{1}{1-r}$

7(1 - r) = 1

7 - 7r = 1

7r = 7 - 1

7r = 6

r = $\frac{6}{7}$

b). Since sum of n terms of the geometric sequence is given by,

$S_{n}=\frac{a(1-r^{n})}{1-r}$

If the sum of n terms of this sequence is more than half the value of the infinite sum.

$\frac{a[1-(\frac{6}{7})^{n}]}{1-\frac{6}{7}}$ > $\frac{7a}{2}$

$\frac{1-(\frac{6}{7})^{n}}{1-\frac{6}{7}}> \frac{7}{2}$

$\frac{1-(\frac{6}{7})^{n}}{\frac{1}{7}}> \frac{7}{2}$

$1-(\frac{6}{7})^{n}> \frac{7}{2}\times \frac{1}{7}$

$1-(\frac{6}{7})^{n}> \frac{1}{2}$

$-(\frac{6}{7})^{n}> -\frac{1}{2}$

$(\frac{6}{7})^{n}< \frac{1}{2}$

$(0.85714)^{n}< (0.5)$

n[log(0.85714)] < log(0.5)

-n(0.06695) < -0.30102

n > $\frac{0.30102}{0.06695}$

n > 4.496

n > 4.5

Therefore, at least 5 terms of the sequence should be added.

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2 years ago

Let the function f(x) have the form f(x) = Acos(x-C). To produce a graph that

Gala2k [10]

Answer:

A has to be 2

Step-by-step explanation:

In the expression $f(x)=A*cos(x-C)$ , the multiplicative factor A represents what is called the "amplitude of the wave-shaped function that you obtain as the graph. Such amplitude is understood as half of the crest-to-through distance of the wavy curve.

From the drawing, the crest is at y=2 and the through at y=-2 (a distance of 4 units) therefore the value of A should be half of that distance: 4/2 = 2

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2 years ago

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SPORTS A coach uses a metric to determine the athletes that make the Varsity, Junior Varsity A, and Junior Varsity B teams. The

Harman [31]

Answer:

there is no picture. :)

Step-by-step explanation:

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1 year ago

The City Library ordered a new computer system costing $158,000; it will be delivered in 6 months. The full amount will be due 3

Nana76 [90]

Answer:

$151,257.12

Step-by-step explanation:

7.5% is the annual interest rate, the monthly interest rate is:

$r= \frac{0.075}{12} =0.00625$

The amount (P) that must be deposited into an account at a rate 0.625% per month for 7 months in order to obtain $158,000 is given by:

$158,000 = P*(1+0.00625)^7\\P=\$151,257.12$

$151,257.12 must be deposited into the account today.

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2 years ago

Harper has $15.00 to spend at her grocery store. She is going to buy bags of fruit that cost $4.75 each and one box of crackers

Andrej [43]

First write the inequality: 15 $\leq$ 4.75x +3.50

Then to solve, first subtract 3.50 from both sides to get:

11.50 $\leq$ 4.75x

Then divide by 4.75 to get 2.42, and since you can't buy .42 of a bag of fruit, you round down. So your final answer would be 2 bags of fruit.

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2 years ago

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