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patriot [66]
3 years ago
15

Please help....There are 42 boys and girls participating in an essay-writing competition. Of the competitors, 21 are in seventh

grade, 14 are in eighth grade, and 7 are in ninth grade. What is the probability of an eighth grader winning the competition? Which simulation(s) can be used to represent this situation?
1.The probability is 1/3 . Simulate this situation by rolling a 6-sided die, with odd numbers representing seventh graders and even numbers representing eighth graders.
2. The probability is 1/6 . Simulate this situation by picking a card from a deck of cards, with hearts representing seventh graders, diamonds representing eighth graders, and spades representing ninth graders.
3. The probability is 1/3 . Simulate this situation by spinning a spinner with six equal sections, with one section representing ninth graders, two sections representing eighth graders, and three sections representing seventh graders.
4. The probability is 1/6. Simulate this situation by using a number generator with numbers from 1 to 6, with 1 through 3 representing seventh graders, 4 and 5 representing eighth graders, and 6 representing ninth graders.
Mathematics
2 answers:
almond37 [142]3 years ago
7 0
The probability of an 8th grader winning is : 14/42 which reduces to 1/3

the simulation would be : # 3 <====

because u will have 6 equal sections on ur spinner...with each section representing 7 people
one section representing 9th graders...so their is 7 of them
2 sections representing 8th graders....so their is 7 * 2 = 14 of them
and 3 sections representing 7th graders....7 * 3 = 21 of them

a_sh-v [17]3 years ago
5 0

Answer:

The answer is C.

Step-by-step explanation:

Have a nice day ( : <3

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∠ACD= ∠BAC ( reason: CPCTC)

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3 years ago
What does 8 3/4 equal to as a improper fraction
Paul [167]

Answer:

35/4

Step-by-step explanation:

6 0
2 years ago
1)-5.5 - 11.2 =<br> on<br> a.) 5.7<br> b.)-5.7<br> c.) 16.7<br> d.) -16.7
Bingel [31]

Answer:

C

Step-by-step explanation:

-5.5-11.2

change the subtraction to addition

5.5+11.2= 16.7

6 0
3 years ago
Read 2 more answers
Solve the equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are locat
eimsori [14]

Answer:

There are NO real roots for this equation. The only roots have imaginary parts and therefore cannot be represented on the real x-axis.

Step-by-step explanation:

We notice that the expression on the left of the equation is a quadratic with leading term 2x^2, which means that its graph is that of a parabola with branches going up.

Therefore, there can be three different situations:

1) if its vertex is ON the x axis, there would be one unique real solution (root) to the equation.

2) if its vertex is below the x-axis, the parabola's branches are forced to cross it at two locations, giving then two real solutions (roots) to the equation.

3) if its vertex is above the x-axis, it will have NO real solutions (roots) but only non-real ones.

So we proceed to examine the vertex's location, which is also a great way to decide on which set of points to use in order to plot its graph efficiently.

We recall that the x-position of the vertex for a quadratic function of the form  f(x)=ax^2+bx+c is given by the expression:

x_v=\frac{-b}{2a}

Since in our case a=2 and b=-3, we get that the x-position of the vertex is:

x_v=\frac{-b}{2a}\\x_v=\frac{-(-3)}{2(2)}\\x_v=\frac{3}{4}

Now we can find the y-value of the vertex by evaluating this quadratic expression for x = 3/4:

y_v=f(\frac{3}{4})=2( \frac{3}{4})^2-3(\frac{3}{4})+4\\f(\frac{3}{4})=2( \frac{9}{16})-\frac{9}{4}+4\\f(\frac{3}{4})=\frac{9}{8}-\frac{9}{4}+4\\f(\frac{3}{4})=\frac{9}{8}-\frac{18}{8}+\frac{32}{8}\\f(\frac{3}{4})=\frac{23}{8}

This is a positive value for y, therefore we are in the situation where there is NO x-axis crossing of the parabola's graph, and therefore no real roots.

We can though estimate a few more points of the parabola's graph in order to complete the graph as requested in the problem. For such we select a couple of x-values to the right of the vertex, and a couple to the right so we can draw the branches. For example: x = 1, and x = 2 to the right; and x = 0 and x = -1 to the left of the vertex:

f(-1) = 2(-1)^2-3(-1)+4= 2+3+4=9\\f(0)=2(0)^2-3(0)+4=0+0+4=4\\f(1)=2(1)^2-3(-1)+4=2-3+4=3\\f(2)=2(2)^2-3(2)+4=8-6+4=6

See the graph produced in the attached image.

4 0
3 years ago
Use one method to find the LCM of the first set of numbers below. Use the other method to find the LCM of the second set. Show W
Nat2105 [25]

Answer:

The least common multiple (LCM) of two or more non-zero whole numbers is the smallest whole number that is divisible by each of those numbers. In other words, the LCM is the smallest number that all of the numbers divide into evenly.

Step-by-step explanation:

The LCM of 13 AND 17 is 221

The LCM of 40 AND 60 is 120

lcm (40; 60) = 120 = 23 × 3 × 5

4 0
3 years ago
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