MATHEMATICS HIGH SCHOOL

six girls and four boys have entered the science fair. first, second, and third place awards are to be given out. what is the probability that exactly one girl and two boys will recite awards? express your answer as a percent

Answers

Answer 1
Answer:

The probability  that exactly one girl and two boys will recite awards is 10%.

Probability

Given:

6 girls +4 boys

Hence:

Probability of a girl  getting the first place =6/10

Probability of a boy  getting the second place=4/9

Probability of a boy  getting the third place=3/8

Total probability:

Total probability=6/10×4/9×3/8

Total probability=0.1×100

Total probability=10%

Therefore the probability  that exactly one girl and two boys will recite awards is 10%.

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Answer 2
Answer:

Answer:

10%

Step-by-step explanation:

was right on edge

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Round the fraction to the nearest whole number. 5 2/7
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A right rectangular prism has base dimensions of 3 inches by 12 inches. An oblique rectangular prism has base dimensions of 4 inches by 9 inches.If the prisms are the same height, how do their volumes compare?The volumes are equal, because the bases are congruent.The volumes are equal, because the heights are equal and the horizontal cross-sectional areas at every level are also equal.The volumes are not equal, because their horizontal cross-sectional areas are not the same at every level.

What is the least positive integer with a square root greater than 4?

Answers

The least positive integer will be 17.

Explanation

Lets assume, the integer is x

As the square root of this integer needs to greater than 4, that means....

√(x) >4\n \n x>4^2\n \n x>16

Thus, the integer should be greater than 16

So, the least positive integer with a square root greater than 4 will be 17.

In a right triangle, the length of one leg is 6 units. The length of the other leg is 8 units. What is the length of the hypotenuse (hint: use Pythagorean Theorem)?

Answers

The length of the hypotenuse of given right triangle is 9.2 units.

Given that, in a right triangle, the length of one leg is 6 units. The length of the other leg is 8 units.

What is the Pythagoras theorem?

The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angledtriangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.

Let the length of the hypotenuse be x.

Now, using Pythagoras theorem, we get

x²=6²+7²

⇒x²=36+49

⇒x²=85

⇒x=√85

⇒x=9.2 units

Therefore, the length of the hypotenuse of given right triangle is 9.2 units.

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hypotenuse = √(6^2+8^2)= √(36+64)= √(100)=10 \ units

Simplify the expression below as much as possible.(7-6i) + (-1 + 4i) -(4-7i)
A. 10 + 5i
B. 2 - 9i
C. 10-9i
D. 2 +5i

Answers

The answer is D hope this helped
B. 2-9i. Is the correct answer

4a+b-3=2b
is this a linear equation?

Answers

4a+b-3=2b\n\n4a-3=2b-b\n\nb=4a-3\n\nthis\ is\ a\ linear\ eqation

According to the Rational Root Theorem, the following are potential fox) 2x2 +2x 24.roots of -4, -3, 2, 3, 4Which are actual roots of f(x)?O 4 and 34, 2, and 3O 3 and 43, 2, and 4

Answers

Correct Answer:First Option

Explanation:

There are two ways to find the actual roots:

a) Either solve the given quadratic equation to find the actual roots

b) Or substitute the value of Possible Rational Roots one by one to find out which satisfies the given equation.

Method a is more convenient and less time consuming, so I'll be solving the given equation by factorization to find its actual roots. To find the actual roots set the given equation equal to zero and solve for x as given below:

2x^(2) +2x-24=0\n \n 2(x^(2) +x-12)=0\n \n x^(2) +x-12=0\n \n x^(2) +4x-3x-12=0\n \n x(x+4)-3(x+4)=0\n \n (x-3)(x+4)=0\n \n x-3=0, x=3\n \n or\n\nx+4=0, x=-4

This means the actual roots of the given equation are 3 and -4. So first option gives the correct answer.
The correct answer for the question that is being presented above is this one: "-4 and 3." According to the Rational Root Theorem, the following are potential f(x) 2x2 +2x 24. The actual roots of the quadratic equation based on the Rational Root Theorem are -4 and 3.

Jeff's club had $370 to divide equally among 2 people. About how much did each person receive? First, round the amount to the nearest hundred dollars. Each person received approximately $______.

Answers

Answer:

$185.

Step-by-step explanation:

To find out how much each person received, we can divide the total amount of money, which is $370, by the number of people, which is 2.

370 ÷ 2 = 185

Therefore, each person received approximately $185.
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