A student-faculty government committee of 4 people is to be formed from 20 student
volunteers and 5 faculty volunteers.
a. If one person from the group of volunteers is chosen at random to draw the names
out of a hat, what is the probability that the person drawing the names is a student?
b. How many ways can the committee of four be formed if there are no restrictions on
composition.
C. How many ways can two of the students be chosen?
d. How many ways can 2 faculty be chosen?
e. What is the probability that the random selection of the four-person committee will
result in two students and two faculty?

Answer:

Step-by-step explanation:

Answer:9

Step-by-step explanation: 18/6=3 so 27/3 should equal the answer. If u know ur multiplication, the answer would be 9

Answer: 75%

Step-by-step explanation:

186.75/249 =.75

.75x100

75%

Answer:

Step-by-step explanation:

The distance between trains increases by 65+85 = 150 mph.

450 miles × (1 hour)/(150 miles) = 3 hours

Answer:

the x-intercepts are at

x = -3

x = 0

x = 1

Step-by-step explanation:

ask the points, where the functional value is 0.

2x³ + 4x² - 6x = 0

we see that every term contains an expression of x. so, we can simplify this

x × (2x² + 4x - 6) = 0

so, one solution is plainly visible : x=0

for the other solutions we need to solve the square equation

2x² + 4x - 6 = 0

or even simpler

x² + 2x - 3 = 0

the solution of a square equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a=1

b=2

c=-3

x = (-2 ± sqrt(2² - 4×1×-3))/(2×1) = (-2 ± sqrt(4 + 12))/2 =

= (-2 ± sqrt(16))/2 = (-2 ± 4)/2 = -1 ± 2

x1 = -1 + 2 = 1

x2 = -1 - 2 = -3

Evaluating the limand directly at x = 0 yields the indeterminate form 0/0. If L'Hopital's rule is known to you, you can compute the limit by applying it twice:

[tex]\displaystyle\lim_{x\to0}\frac{x\left(e^{3x}-1\right)}{2-2\cos(x)} = \lim_{x\to0}\frac{3xe^{3x}+e^{3x}-1}{2\sin(x)} \\\\\\ = \lim_{x\to0}\frac{9xe^{3x}+6e^{3x}}{2\cos(x)} = \frac62=\boxed{3}[/tex]

Answer:

1/2 or 50-50

Step-by-step explanation:

1/4 +1/4 = 1/2 or 50-50

Answer:

15x - 12

Step-by-step explanation:

3(5x-4)

We can find an equivalent expression by distributing the 3 to what's inside of the parenthesis (5x and -4)

3(5x-4)

* Distribute *

3 * 5x = 15x

3 * -4 = -12

An equivalent expression would be 15x -12

Answer:

- 3.027

Step-by-step explanation:

First price = 10000 ; second price = 700

Number of tickets sold = 11000

Ticket cost = $4

Probability that a ticket wins grand price = 1 / 11000

Probability that a ticket wins second price = 1 / 11000

X ____ 10000 _____ 700

P(x) ___ 1 / 11000 ___ 1/11000

Expected winning for a ticket buyer :

E(X) = Σx*p(x)

E(X) = (1/11000 * 10000) + (1/11000 * 700) - ticket cost

E(X) = 0.9090909 + 0.0636363 - 4

E(X) = - 3.0272728

E(X) = - 3.027

Answer:

5.6

Step-by-step explanation:

( 9 + 6 + 3 + 9 + 7 + 2 + 1 + 5 + 6 + 8 ) / 10

= 56 / 10

= 5.6

Answer:

-2 is the answer.

Step-by-step explanation:

#CarryOnLearning

Answer:

24

Step-by-step explanation:

To find the range, you must subtract the lowest value from the highest value in the data set. If you organize the set from least to greatest, 72 is the lowest, and 96 is the highest.

So, 96 - 72 = 24, which is the range.

The x-intercepts are the points on the plot of a function f(x) where the graph crosses the x-axis. In other words, they're the values of x that make f(x) = 0.

In this case, the x-intercepts are the two roots of the parabola,

(x - 4) (x - 5) = 0 … … … (this is what the hint is referring to)

==>   x - 4 = 0   or   x - 5 = 0

==>   x = 4   or   x = 5

The intercepts themselves are points (x, f(x)), so you can report them as (4, 0) and (5, 0).

Answer:

huh ano yan huhu paki ayos ng sagot

Step-by-step explanation:

hahahhaa

Answer:

B

Step-by-step explanation:

Divide both sides by 3

Take square root of both sides.

Add 9 to both sides.

Answer:

Train A speed = x + 20

Train B = x

We know the 46 minutes is 23/30 of an hour.

Use D = rt

Take it from it, hope its helped, have a great day!

Answer:

[tex]8^{3(n-1)+1}[/tex]

Step-by-step explanation:

Answer:

Solution given:

f(x)=x²

g(x)=x+5

h(x)=4x-6

now

23:

(fog)(x)=f(g(x))=f(x+5)=(x+5)²=x²+10x+25

24:

(gof)(x)=g(f(x))=g(x²)=x²+5

25:

(foh)(x)=f(h(x))=f(4x-6)=(4x-6)²=16x²-48x+36

26:

(hof)(x)=h(f(x))=h(x²)=4x²-6

27;

(goh)(x)=g(h(x))=g(4x-6)=4x-6+5=4x-1

28:

(hog)(x)=h(g(x))=h(x+5)=4(x+5)-6=4x+20-6=4x-14

Answer:

the answer is 4x - 4

Step-by-step explanation:

Answer:

B is the answer

the graph is shifted up +3

the graph is curving upward, so the power has to be positive

Answer:

See attachment for graph

The height of the arch is: 120 m

The width to the nearest meter, at the base of the arch is 22 m

Step-by-step explanation:

Given

[tex]h = -0.06d^2 + 120[/tex]

Solving (a): The graph

See attachment for graph

Variable h is plotted on the vertical axis while variable d is plotted on the horizontal axis.

Solving (b): The height

The curve of [tex]h = -0.06d^2 + 120[/tex] opens downward. So, the maximum point on the vertical axis represents the height of the arch,

Hence:

[tex]height = 120[/tex]

Solving (c): The width

The curve touches the horizontal axis at two different points.

[tex]x_1 = -11[/tex]

[tex]x_2 = 11[/tex]

The absolute difference of both points represents the width.

So:

[tex]Width = |x_2 - x_1|[/tex]

[tex]Width = |11 - -11|[/tex]

[tex]Width = |11 +11|[/tex]

[tex]Width = |22|[/tex]

Hence:

[tex]Width = 22[/tex]

Answer:

[tex]E(x) = 1.5\\[/tex]

Step-by-step explanation:

Given

[tex]n = 9[/tex] -- number of rolls

Required

The mean of 2's

The distribution follows binomial distribution where:

[tex]X \to Binomial(n,p)[/tex]

In this case:

[tex]p= \frac{1}{6}[/tex] ---- the theoretical probability of rolling 2

So, the mean of 2's is calculated using:

[tex]E(x) = np[/tex]

[tex]E(x) = 9 * \frac{1}{6}[/tex]

[tex]E(x) = \frac{9}{6}[/tex]

Simplify

[tex]E(x) = \frac{3}{2}[/tex] or

[tex]E(x) = 1.5\\[/tex]

Answer:

c is answer

Step-by-step explanation:

yes

Answer:

C

Step-by-step explanation:

took test

Given:

After deduction of 4 paisa in a Rupee a sum of Rs 720 is left.

To find:

The original amount.

Solution:

We know that,

1 Rs. = 100 paisa

After deduction of 4 paisa in a Rupee, we get

[tex]100-4=96[/tex]

It means Rs. 720 is the 96% of the original amount.

Let x be the original amount.

[tex]720=\dfrac{96}{100}x[/tex]

[tex]72000=96x[/tex]

[tex]\dfrac{72000}{96}=x[/tex]

[tex]750=x[/tex]

Therefore, the original amount is Rs. 750.

Answer:

Bunny Hill Ski Resort:

y = 10x + 35

Diamond Ski Resort:

y = 5x + 40

Point where the cost is the same:

(1, 45)

Step-by-step explanation:

The question tells us that:

$35 and $40 are initial fees

$10 and $5 are hourly fees

This means that x and y will equal:

x = number of hours

y = total cost of ski rental after a number of hours

So we can form these 2 equations:

y = 10x + 35

y = 5x + 40

Now we are going to use System of Equations to find what point the cost of both ski slopes is the same.

Because they both equal y, we can set the equations equal to each other:

10x + 35 = 5x + 40

And we use basic algebra to solve for x:

10x + 35 = 5x + 40

(subtract 5x from both sides)

5x + 35 = 40

(subtract 35 from both sides)

5x = 5

(divide both sides by 5)

x = 1

Remember, x equals the number of hours.

That means when your rent out the skis for 1 hour, you will get the same price of $45 (you find the price by plugging in 1 into both of the equations)

Hope it helps (●'◡'●)

Answer:

X o punto Y O punto z

Step-by-step explanation:

Answer:

The answer is "1035.76 miles"

Explanation:

The aircraft flies at 120 mph for 1.5 hours at a [tex]10^{\circ}[/tex] bearing, then flies at the very same speed at [tex]100^{\circ}[/tex] bearings for 8.5 hours.

However an angle of [tex]100-10 = 90^{\circ}[/tex] between displacements

First shifts[tex]= 1.5 \times 120 = 180\ miles.[/tex]

Second shift [tex]= 8.5\times 120 = 1020\ miles.[/tex]

These two shifts are at [tex]90^{\circ}[/tex] and therefore the final shift is:

[tex]\to \sqrt{180^2+1020^2}=1035.76 \ miles[/tex]

Answer:

a) The probability that with heavy use, the battery life exceeds 11 hours is 0.4602.

b) Using the standard normal table, After 6.8 hours should you plan to recharge your phone.

Step-by-step explanation:

a) The probability that with heavy use, the battery life exceeds 11 hours:-

P(x > 11) = 1 - p( x< 11)  

[tex]=1- p P[(x - \mu) / \sigma < (11 - 10.75) / 2.4]\\\\=1- P(z < 0.10)[/tex]  

Using z table distribution,    

= 1 - 0.5398  

= 0.4602  

b) Using the standard normal table,  

[tex]P(Z < z) = 5%\\\\\\\\= P(Z < -1.645 ) = 0.05 \\z = -1.645[/tex]

Using the z-score formula,  

[tex]x = z \times \sigma + \mu\\x = -1.645 * 2.4 + 10.75\\x = 6.8 hours.[/tex]

Answer:

Step-by-step explanation:

9514 1404 393

Answer:

  (c)  5x and 3x, and 4 and 1

Step-by-step explanation:

Like terms have the same variable(s) to the same power(s).

The terms of this expression are ...

The like terms are {5x, -3x}, which have the x-variable to the first power, and {4, -1}, which have no variable.