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Alecsey [184]
3 years ago
13

A group of students calculated their average score at a spelling bee. They realized that if one of them scored 9 more points, th

eir average score would be 81 points. If one of them scored 3 points less, their average score would be 78 points. How many students were in the group?
Mathematics
1 answer:
alukav5142 [94]3 years ago
8 0

Answer: There are 4 students in the group.

Step-by-step explanation:

Let the number of students in the group be n

If one of them scored 9 more points , their average score would be 81 points.

So, our equation (1) will be

\frac{\sum x+9}{n}=81\\\\\sum x+9=81n

Similarly,

If one of them scored 3 points less, their average score would be 78 points.

So, our equation (2) will be

\frac{\sum x-3}{n}=78\\\\\sum x-3=78n

So, from equation (1) and (2) we get:

81n-9=\sum x=78n+3\\\\81n-9=78n+3\\\\81n-78n=3+9\\\\3n=12\\\\n=\frac{12}{3}\\\\n=4

Hence, there are 4 students in the group.

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John made a triangle with all three sides the same length, 1 \frac{2}{3} ft. What is the perimeter of the triangle?
UNO [17]

Answer:

5 ft

Step-by-step explanation:

If all sides are of the same length, we can multiply the value of one side by 3, because a triangle has three sides (and the perimeter is all sides added together), to find the perimeter.

1\frac{2}{3} × 3

1\frac{2}{3} can be rewritten as \frac{5}{3}, so:

\frac{5}{3} × \frac{3}{1}

= \frac{15}{3}

The numerator & denominator share a common factor of 3, so:

5 ft is the final answer/perimeter.

hope this helps!

7 0
2 years ago
(-3 * 10 to the power of 4) * (2 * 10 to the power of -3)
gayaneshka [121]
-3*10= -30 to the 4th power is 810,000
10 to the -3 power is -1000 * 2 is -2000

810,000 * -2000 = -1,620,000,000
8 0
4 years ago
What is the value of x in the diagram below?
VARVARA [1.3K]

Answer:

<h2>7.2</h2>

option B is the right option.

Step-by-step explanation:

<h3>Using leg rule</h3>

\frac{bc}{ab}  =  \frac{ab}{bd}

Plug the values:

\frac{20}{12}  =  \frac{12}{x}

Apply cross product property

20 \times x = 12 \times 12

Calculate the product

20x = 144

divide both sides of the equation by 20

\frac{20x}{20}  =  \frac{144}{20}

Calculate:

x = 7.2

hope this helps..

Good luck...

4 0
3 years ago
Read 2 more answers
a line passes through the point (4 –6) and has a slope of -<img src="https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B4%7D" id="TexFormu
yulyashka [42]

Answer:

y = \frac{5}{4}x - 1

Step-by-step explanation:

A line that passes through the point (4,-6) has a slope of 5/-4. Which of the following gives the equation of the line?

With the slope of 5/-4, and the ordered pair (4,-6) :  

let m = 5/-4 (slope),  

x1 = 4

y1 = -6

We can use those given values into the point-slope formula:

y - y1 = m(x - x1)

Plugging in those values will give you the answer:  

y - (-6) = \frac{5}{-4} (x - 4)

Distribute \frac{5}{-4}  into the terms inside the parenthesis:

y + 6 = \frac{ 5}{-4}x  + 5  

  Subtract 6 from both sides to isolate y:

y + 6 - 6 = -\frac{ 5}{4}x +5 - 6

The equation of the line in slope-intercept form is:

y = -\frac{ 5}{4}x - 1  

6 0
3 years ago
(16 \8) + (24 \ 6)<br> 2<br> DONE
Marina86 [1]

Answer:

6

Step-by-step explanation:

Remember the Order of Operations:

Parentheses

Exponents

Multiplication/Division (whichever comes first)

Addition/Subtraction (whichever comes first)

In this case, we start by simplifying what is in the parentheses:

(16÷8)+(24÷6)

2+4

6

3 0
3 years ago
Read 2 more answers
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