MATHEMATICS HIGH SCHOOL

In yesterday's basketball game, Raul made 77.7% of his shots.What fraction of his shots did he make?
1. How would you write 77.7% as a decimal? Set that decimal equal
to x. What digit or digits repeat?
2. Multiply each side of the equation by a power of 10 to get the
repeating digit(s) to the left of the decimal point. Since you only
need to move one place, multiply each side by 10.
3. Subtract the equation in Exercise 1 from the equation in Exercise 2.
Then simplify.
4. Divide each side of the equation by 9 to solve for x. What fraction is
equal to x? Show your work.
5. What fraction of Raul's shots did he make?
On the Back!
6. This season, Jenny's lacrosse team had a winning percentage of
0.83. What fraction of their games did Jenny's team win?

Answers

Answer 1

Answer:

Answer:

FEEL FREE TO CORRECT ME IF I'M WRONG! (in the comments)

1. 0.777, the thousandths place value repeats

2. 7.77

3. x = 0.60 (0.0603729)

6. 83%

-did my best-

Step-by-step explanation:

Answer 2

Answer:

Final answer:

Raul made 7/9 of his shots in yesterday's basketball game and Jenny's lacrosse team won 83/100 of their games this season.

Explanation:

To answer the question about what fraction of shots Raul made, we need to convert the percentage into a decimal and then a fraction. To first convert 77.7% into a decimal, we move the decimal point two places to the left, getting 0.777.

Now, to put this into fraction form, knowing that the decimal 0.777 is repeating, we let x = 0.777. Multiply each side by 10 to get 10x = 7.777. Subtracting the first equation from this gives us 9x = 7, hence x = 7/9. So, the fraction of shots Raul made is 7/9.

For Jenny's lacrosse team, the winning percentage is 0.83. It’s a non-repeating decimal so it's straightforward to convert this into a fraction. To convert the decimal to a fraction, we consider the numbers after the decimal point. Since there are two digits (.83), we write it as 83/100. But, it can be simplified by dividing both the numerator and the denominator by their greatest common factor (GCF), which is 1 in this case. So, the fraction of games Jenny's team won is 83/100.

Learn more about Converting percentages to fractions:

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Convert 6.42 kilograms to grams. 0.00642 g 64.2 g 642 g 6,420 g

Use the number line below, where RS = 5y + 2, ST = 3y + 6, and RT = 48

Answers

RS+ST= RT

(7Y+3)+(2Y+9)= 14Y-8

9Y+12=14Y-8

5Y=20

Y=4

Laurie is trying to stay within 10 feet of her current diving depth of –30 feet (with regard to sea level) so that the light is still good but she can be close to the sea life during her scuba dive. Which two equations can be used to find the minimum and maximum depths Laurie wants to stay between?A. x + 30 = 10 and x + 30 = –10
B. x – 30 = 10 and x – 30 = –10
C. x + 10 = 30 and x + 10 = –30
D. x – 10 = 30 and x – 10 = –30

Answers

ANSWER
A. x + 30 = 10 and x + 30 = –10

EXPLANATION
If x represents the depth of Laurie at a given moment, then the distance between his current depth and -30 feet is given by

| x - (-30) |

which can be simplifed into

| x + 30 |

We use absolute value because distance cannot be negative.

Laurie must stay within 10 feet. Therefore, the distance x is from -30 feet has to be equal to 10 to find the maximum and minimum depths that Laurie can stay between:

| x + 30 | = 10

When we solve this absolute value equation, we work with two cases.

Case 1: When x + 30 is positive, then |x+30| = x+30 (no change) and we have the equation
x + 30 = 10

Case 2: When x + 30 is negative, then |x+30| = -(x+30) so as to force the distance into a positive number. Then this gives us the equation
-(x+30) = 10
which we can multiply both sides by -1 to get
x + 30 = -10

How do you factor 64-x^2 completely?

Answers

$64-x^2$

$This \ fits \ the \ form \ a^2-b^2$

$Rewrite \ it \ where \ a=8 \ and \ b=x$

$Use \ Difference \ of \ Squares$ $a^2-b^2=(a+b)(a-b)$

$(8+x)(8-x)$

A plumber needs to drill a hole that is just slightly larger than 3/16 of an inch in diameter. Which measurement is the smallest but still larger than 3/16?5/16 inch. 13/64 inch. 9/32 inch.

Answers

All we need to do is to find a common denominator for each of the fractions. It's quite easy in this case because each denominator is an iteration of 16, so so LCD is 64:

5/16 = 20/64
13/64 stays the same
9/32 = 18/64
And the hole's size: 3/16 = 12/64

12/64 < 13/64 < 18/64 < 20/64

So the smallest measurment but still larger than 3/16 (12/64) is 13/64 inch.

What is the measure of an interior angle of a regular pentagon? 72° 540° 108° 180°?

Answers

The answer is most likey 108. A pentagon has a sum of 540, and 540 divided by 5 is 108.

The sum of pentagon angles is 540

So you can exclude 540 as an answer

180 is a straight line in a pentagon there is no straight line angle so exclude that
72 and 108 both feasible id say

Suppose theta is in the interval (90, 180). Choose whether the sign of tan(theta/2) is positive or negative.

Answers

$90^\circ<\theta<180^\circ\implies45^\circ<\frac\theta2<90^\circ$

$\tan\theta>0$ for $\theta$ in this interval.

Final answer:

When theta is in the interval (90, 180), the sign of tan(theta/2) is negative.

Explanation:

When theta is in the interval (90, 180), the sign of tan(theta/2) is negative.

To understand why, we can use the half-angle identity for tangent:

tan(theta/2) = (-1 - cos(theta))/(sin(theta))
Since theta is in the second quadrant (90 < theta < 180), both sine and cosine are positive.
The numerator (-1 - cos(theta)) is negative, while the denominator (sin(theta)) is positive.
Therefore, the overall expression tan(theta/2) is negative.

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