MATHEMATICS COLLEGE

There are 80 participants in a competition. The average score of each participant is 58.5. The average score of the male participants is 64 and the average score of the female participants is 56. How many male participants are there in the competition?

Answers

Answer 1

Answer:

Answer:

Step-by-step explanation:

Given

Total number of participants= 80
Male = x
Female = 80 - x
Average = 58.5
Average for male = 64
Average for female = 56

Equation to reflect the sum:

64x + 56(80 - x) = 80*58.5
64x - 56x = 80*(68.5 - 56)
8x = 80*2.5
x = 25

The answer is 25 male participants

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Given f '(x) = (2 - x)(6 - x), determine the intervals on which f(x) is increasing or decreasing. (2 points)Decreasing (-∞, 2); increasing on (6, ∞)
Decreasing (2, 6); increasing on (-∞, 2) U (6, ∞)
Decreasing (-∞, 2) U (6, ∞); increasing on (2, 6)
Increasing (-∞, -2) U (-6, ∞); increasing on (-2, -6)

Answers

Answer:

Decreasing (2, 6); increasing on (-∞, 2) U (6, ∞)

Step-by-step explanation:

To determine where $f(x)$ is increasing or decreasing, we set $f'(x)=0$ and check for the intervals.

We see that $f'(x)=0$ when either $x=2$ or $x=6$ . Therefore, we'll need to check the intervals $(-\infty,2)$ , $(2,6)$ , and $(6,\infty)$

For the interval $(\infty,2)$ , we can pick $x=0$ . This means that $f'(0)=(2-0)(6-0)=(2)(6)=12>0$ , showing that $f(x)$ increases on the interval $(-\infty,2)$

For the interval $(2,6)$ , we can pick $x=4$ . This means that $f'(4)=(2-4)(6-4)=(-2)(2)=-4<0$ , showing that $f(x)$ decreases on the interval $(2,6)$

For the interval $(6,\infty)$ , we can pick $x=7$ . This means that $f'(7)=(2-7)(6-7)=(-5)(-1)=5>0$ , showing that $f(x)$ increases on the interval $(6,\infty)$

Therefore, $f(x)$ is increasing on $(-\infty,2)\cup(6,\infty)$ and is decreasing on $(2,6)$ .

-2 1/2 x (-1 2/3) what is the answer for this question

Answers

Answer: 4 1/6

Step-by-step explanation:

Let X∼ Exponential (λ )and let t be a constant with 0 0 be any value.

Answers

Answer:

Hello! Hope you are having a good day. Your answer is F. I just did this. Good luck!

Step-by-step explanation:

A particular concentration of a chemical found in polluted water has been found to be lethal to 40% of the crayfish that are exposed to the concentration for 24 hours. 22 crayfish are placed in a tank containing this concentration of chemical in the water. (a) What is the probability that 13 or 17 survive?
(b) What is the probability that at least 17 survive?
(c) What is the probability that at most 16 survive?
(d) What number of crayfish are expected to survive?
(e) What is the variance in the number of crayfish that are expected to survive? No actual crayfish were harmed in the making of this question.

Answers

Answer:

a) $P(X=13)=(24C13)(0.4)^(13) (1-0.4)^(24-13)=0.0608$

$P(X=17)=(24C17)(0.4)^(17) (1-0.4)^(24-17)=0.0017$

$P(X=13 U X=17) = 0.0608+0.0017=0.0624$

b) $P(X \geq 17)=0.000427$

c) $P(X \geq 16)= 1-0.000427=0.9996$

d) $E(X)= np = 22*0.4=8.8$

e) $Var(X) = np(1-p)= 22*0.4*(1-0,4)=5.28$

Step-by-step explanation:

1) Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

2) Solution to the problem

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=24, p=0.4)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^(n-x)$

Where (nCx) means combinatory and it's given by this formula:

$nCx=(n!)/((n-x)! x!)$

3) Part a

$P(X=13)=(22C13)(0.4)^(13) (1-0.4)^(22-13)=0.0336$

$P(X=17)=(22C17)(0.4)^(17) (1-0.4)^(22-17)=0.00035$

$P(X=13 U X=17) = 0.0336+0.00035=0.0340$

4) Part b

$P(X \geq 17)=P(X=17)+P(X=18)+P(X=19)+P(X=20)+P(X=21)+P(X=22)$

$P(X=17)=(22C17)(0.4)^(17) (1-0.4)^(22-17)=0.00035$

$P(X=18)=(22C18)(0.4)^(18) (1-0.4)^(22-18)=0.0000651$

$P(X=19)=(22C19)(0.4)^(19) (1-0.4)^(22-19)=0.00000914$

$P(X=20)=(22C20)(0.4)^(20) (1-0.4)^(22-20)=0.000000914$

$P(X=21)=(22C21)(0.4)^(21) (1-0.4)^(22-21)=5.81x10^(-8)$

$P(X=22)=(22C22)(0.4)^(22) (1-0.4)^(22-22)=1.76x10^(-9)$

$P(X \geq 17)=0.000427$

5) Part c

$P(X \leq 16)=1-P(X>16)=1-P(X\geq 17) = 1-[P(X=17)+P(X=18)+P(X=19)+P(X=20)+P(X=21)+P(X=22)]$

$P(X \geq 16)= 1-0.000427=0.9996$

6) Part d

The expected value is:

$E(X)= np = 22*0.4=8.8$

7) Part e

The variance is given by:

$Var(X) = np(1-p)= 22*0.4*(1-0,4)=5.28$

20 POINTS! You are planning to use a ceramic tile design in your new bathroom. The tiles are equilateral triangles. You decide to arrange the tiles in a hexagonal shape as shown. If the side of each tile measures 9 centimeters, what will be the exact area of each hexagonal shape?

Answers

Answer:

210.33 cm^2

Step-by-step explanation:

We know that 6 equilateral triangles makes one hexagon.

Also, an equilateral triangle has all its sides equal.

If the tile of each side of the triangular tile measure 9 cm, then the height of the triangular tiles can be gotten using Pythagoras's Theorem.

The triangle formed by each tile can be split along its height, into two right angle triangles with base (adjacent) 4.5 cm and slant side (hypotenuse) of 9 cm. The height (opposite) is calculated as,

From Pythagoras's theorem,

$hyp^(2) = adj^(2) + opp^(2)$