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3 years ago

13

There are 42 boys and girls participating in an essay-writing competition. Of the competitors, 21 are in seventh grade, 14 are i

n 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?

2 answers:

Aleks [24]3 years ago

7 0

Answer: Our required probability is 0.34.

Step-by-step explanation:

Since we have given that

Number of seventh grade student s= 21

Number of eight grade students = 14

Number of ninth grade students = 7

Total number of boys and girls = 42

Probability of an eigthth grader winning the competition would be

$\dfrac{14}{42}\\\\=\dfra{1}{3}\\\\=0.3333333..................\\\\\approx 0.34$

Hence, our required probability is 0.34.

Masja [62]3 years ago

6 0

P(8th grader winning) = 14/42...reduces to 1/3

simulate this by using a number generator with numbers 1 - 6.....with 1 - 3 representing 7th graders, 4 and 5 representing 8th graders, and 6 representing 9th graders

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Good Treads and Speed Tracks manufacture tires. Good Treads claims that their tires last longer than Speed Tracks tires. A car c

Crazy boy [7]

The answer is B... good treads claim is false therefore it can be concluded that speed tracks tires last longer than good treads tires

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3 years ago

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The cost to manufacture t shirts can be represented by the function c(x)=10.5x complete the following statement about the functi

Advocard [28]

For this case we have:

Cost of manufactures of T-shirts $C(x)=10.5x$

where x represents the number of T-shirts

Part A:

Substituting $x = 8$ in the total cost equation you have to:

$C (8) = (10.5) (8)\\\\C (8) = 84\\$

Thus, the cost of 8 shirts will be $C (8) = 84\\$

Part B:

If $x = 12$ then

$C (12) = (10.5) (12)\\\\C (12) = 126\\$

Thus, the cost of 12 shirts will be $C (12) = 126\\$

Answer:

$C (8) = 84\\\\C (12) = 126\\\\$

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3 years ago

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PLease evaluate this math problem for me!!

umka2103 [35]

8(1/4)

=(8/1)

=(8)(1)/(1)(4)

=8/4

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3 years ago

Dmitry [639]

Answer:

$8,000

Step-by-step explanation:

Let the store earned $x in December.

Therefore,

Money spent to buy new inventory $=\frac{1}{4} x$

Remaining money $= x - \frac{1}{4} x =\frac{3}{4} x$

Money used to pay bills $=\frac{1}{2} \times \frac{3}{4} x=\frac{3}{8} x$

Money still left over = $3,000

Total money earned in December $= \frac{1}{4} x+ \frac{3}{8} x+3,000$

$\therefore x= \frac{1}{4} x+ \frac{3}{8} x+3,000$

$\therefore x= \frac{2}{8} x+ \frac{3}{8} x+3,000$

$\therefore x= \frac{5}{8} x+ 3,000$

$\therefore x- \frac{5}{8} x=3,000$

$\therefore \frac{8x-5x}{8} =3,000$

$\therefore \frac{3x}{8} =3,000$

$\therefore x =3,000\times \frac {8}{3}$

$\therefore x =1,000\times 8$

$\therefore x =\$8,000$

Thus, total money earned in December is $8,000.

3 0

2 years ago

What is the value of x?

Nikolay [14]

Answer: 7 centimeters

Explanation:

Let triangle ABC and triangle CDE form a bow tie such that
- triangle ABC is smaller than triangle CDE
- Segment AC and segment CD are the north sides
- Segment BC and segment CE are the bottom sides
- AC = 6, CD = 42, CE = 36, BC = x

Since angle ACB and angle ECD are formed by intersecting segment AE and segment BD at point C, they are vertical angles. (See the attached picture) So, angle ACB and angle ECD are congruent.

Moreover when we form our bowtie, point A is in the north side and point E is in the bottom sides and this implies that angle BAC and angle CED are alternate interior angles as shown in the attached figure.

Since it is given in the problem that alternating interior angle are congruent, angle BAC and angle CED are congruent.

Now, we have the following pairs of angles in triangle ABC and triangle CDE that are congruent:

- angle BAC and angle CED
- angle ACB and angle ECD

By AA Similarity theorem, when we have two pairs of congruent angles for two triangles, then the two triangles are similar. So, triangle ABC and triangle CDE are similar.

In similar triangles, the sides that are opposite to the congruent angles are proportional to each other. So,

$\frac{BC}{CD} = \frac{AC}{CE} 


$ (1)

Since $AC = 6, CD = 42, CE = 36, BC = x$ , we can substitute these values to equation (1). So, equation (1) becomes

$\frac{x}{42} = \frac{6}{36}$
$\frac{x}{42} = \frac{1}{6}$ (2)

SInce we are solving for x, we can multiply both sides of equation (2) by the denominator at the left side which is 42 so that

x = 42(1/6)
x = 7 centimeters

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2 years ago