A professor divided the students in her business class into three groups: those who have never taken a statistics class, those who have taken only one semester of a statistics class, and those who have taken two or more semesters of statistics. The professor randomly assigns students to groups of three to work on a project for the course. 65% of the students have never taken a statistics class, 15% have taken only one semester of a statistics class, and the rest have taken two or more semesters of statistics. Round your answers to three decimal places.
a. What is the probability that the first groupmate you meet has studied at least two semesters of statistics?
b. What is the probability that the first groupmate you meet has studied some statistics?
c. What is the probability that neither of your two groupmates has studied any statistics?
d. What is the probability that your two groupmates have studied at least one semester of statistics?
e. What is the probability that at least one of your two groupmates has studied more than one semester of statistics?

Answer:

Approximately [tex]30\; \rm N[/tex] toward the center of the object.

Step-by-step explanation:

Look up the gravitational constant and the mass of the earth:

[tex]\begin{aligned}G &\approx 6.67 \times 10^{-11}\; \rm m^{3} \cdot kg^{-1} \cdot s^{-2} \\ &= 6.67 \times 10^{-11} \; \rm N \cdot m^{2} \cdot kg^{-2}\end{aligned}[/tex].

[tex]M \approx 5.97 \times 10^{24}\; \rm kg[/tex].

Convert the unit of distance to standard units:

[tex]\begin{aligned}r &= 25600\; \rm km \\ &= (25600 \times 10^{3})\; \rm m \\ &= 2.56 \times 10^{7}\; \rm m\end{aligned}[/tex].

Consider two spherical objects with mass [tex]m_{1}[/tex] and [tex]m_{2}[/tex]. Let [tex]r[/tex] denote the distance between the centers of the two objects. By Newton's Law of Universal Gravitation, the size of the gravitational force between these two objects would be:

[tex]\begin{aligned}F &= \frac{G \cdot m_{1} \cdot m_{2}}{r^{2}}\end{aligned}[/tex].

Thus, the size of the gravitational force between this object and the earth would be:

[tex]\begin{aligned}F &= \frac{G \cdot m \cdot M}{r^{2}} \\ &\approx \frac{1}{2.56\times 10^{7}\; \rm m} \\ &\quad \times 6.67 \times 10^{-11}\; \rm N \cdot m^{2}\cdot kg^{-2} \\ &\quad \times 50\; \rm kg \times 5.97 \times 10^{24}\; \rm kg \\ &\approx 30\; \rm N\end{aligned}[/tex].

Since gravitational force is attractive, the [tex]50\; \rm kg[/tex] object in this question would attract the earth through the gravitational force. Thus, this force would point towards the center of this [tex]50\; \rm kg\![/tex] object.

Answer:

b

Step-by-step explanation:

The answer could be 2 i don’t know really

Answer:

x = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

The opposite sides of a rectangle are congruent , then

10x - 1 = 4x + 2 ( subtract 4x from both sides )

6x - 1 = 2 ( add 1 to both sides )

6x = 3 ( divide both sides by 6 )

x = [tex]\frac{3}{6}[/tex] = [tex]\frac{1}{2}[/tex] ( = 0.5 )

Answer:

Part A: 6250

Part B: No

Step-by-step explanation:

Part B: When Time is  2 Hours, the cost is $30.

            30x3=90 < 100

         So the unlimited weekly pass is not cheaper

                  (Find the value of y by given x)

Answer:

[tex]\frac{4\pi (3)^{3} }{3}[/tex]

Step-by-step explanation:

Because radio=6/2=3 cm (half of diameter)

I hope this help you

Answer:

9 i think

Step-by-step explanation:

Answer:

= 3

Step-by-step explanation:

Answer:

the length of missing side is √115(ie.10.723)

Answer:

3 hours and 45 minutes i hope i helped you :)))

Step-by-step explanation:

Answer: y=140!!!

:)

Hope you have a good one <3

Answer:

A 4

Step-by-step explanation:

-1/-4 = 4

It's very difficult to understand the chart.Can you please take a screenshot of the chart?

Answer: The equation would be L = 85H + 60

Step-by-step explanation:

Answer:

1. 6+x, 2. 8 + 7x^2 - 2x + 5x^3, 3. 16x^3+11x^2-17x-12, 4. (x-2)(x+9), 5. 2x+3)(2x-3), 6. 2x(x+2)(x+5)

Step-by-step explanation:

Number 1

1. 2-3x+5+7+4x-8

2. 7-3x+7+4x-8

3. 14-3x+4x-8

4. 14+x-8

5. 6+x

Number 2

1. 8+3x^2+x -5x^3+4x^2-3x

2. 8+7x^2+x+5x^3-3x

3. 8+7x^2-2x+5x^3

Number 3

1.(simplify) 10x^3 + 5x^2 - 20x + 6x^2 + 3x - 12

2. 16x^3+5^2-20x+6^2+3x-12

3. 16x^3+11x^2-20x+3x-12

4. 16x^3+11x^2-17x-12

Number 4

(x-2)(x+9)

Number 5

(2x+3)(2x-3)

Number 6

2x(x^2+7x+10) or 2x(x+2)(x+5)

Answer:

No, The domains of a same number are said twice.

Step-by-step explanation:

If it is the range (y) it doesn't matter twice or not.

Answer:

The given relation is not a function.

Step-by-step explanation:

Given the relation: {(3,2) (8,16) (13,8) (14,14) (20,5) (24,8) (27,2) (31,6) (31,3)}

A relation is any set of ordered pairs, which can be thought of as (input, output).

A function is a relation in which no two ordered pairs have the same first component (x-values or input) and different second components (y-values or output).

Another way to find out whether a relation or a set of given points represent a function through the Vertical Line Test.  If a vertical line intersects the graph in all places at exactly one point, then the relation is a function.

To use the vertical-line test, imagine dragging a ruler held vertically across the  graph from left to right. If the graph is that of a function, the edge of the ruler would hit the graph only once for every x -value. If you do this for the given set of points, every vertical line intersects the graph in at most one point, except for the x-value = 31, where the vertical line contains two points (in red dots) in it:  (31,6) and (31,3).  The given graph fails the Vertical Line Test, which means that it is not a function.

Attached is a screenshot of the graph where I performed the Vertical Line Test.  

Please mark my answers as the Brainliest if you find my explanation helpful :)

Answer:

[tex] - 7 + 3x - 2(3x + 4) = 5(2x - 3) + 4(3x - 1) - 4 \\ - 7 + 3x - 6x - 8 = 10x - 15 + 12x - 4 - 4 \\ - 3x - 15 = 22x - 15 - 8 \\ 25x = 8 \\ x = \frac{8}{25} [/tex]

Answer:

B

Step-by-step explanation:

With answer B, x is marked 4 on the x-axis and because there was no given y-intercept, the line must be vertical.

Answer:

see below

Step-by-step explanation:

2/5 + 1/3 + x = 1

Get a common denominator of 15

2/5 * 3/3 + 1/3 *5/5 +x = 1

6/15 + 5/15 +x = 1

11/15 + x = 1

Subtract 11/15 from each side

11/15 +x-11/15 =15/15-11/15

x = 4/15

Answer: £784.08

Step-by-step explanation:

First find 1% of 800, which is 800/100=£8

800-8= £792 after 1 year

find 1% of 792, which is 792/100=£7.92

792-7.92= £784.08

Answer:

8

Step-by-step explanation:

If you're evaluating, then substitute x=2 into the equation.

That gets you 3(2)^2-4

Then do 2^2 and multiply by 3, that should get you 12

After that, subtract 4 from 12, which gets you 8

Answer:

35/18

Step-by-step explanation:

Answer:

D. 16

Step-by-step explanation:

1. Because these are vertical angles (opposite pair of angles that are formed by intersecting lines), these are congruent. That means (8x-8) = (7x+8).

2. (Solving)

Step 1: Subtract 7x from both sides.

Step 2: Add 8 to both sides.

Step 3: Check if solution is correct.

Therefore, the answer is D. 16.

Answer:

9 dollars per pound of salmon

Answer:

I think C has the best buy

Answer:

not a real number

Step-by-step explanation:

any negative number under a square root sign, except for 0, isn't real

On evaluating the given roots,

(a) [tex]$-(\sqrt[3]{8}) = -2$[/tex]

(b) [tex]$\sqrt[4]{-81}$[/tex] is not a real number

(a) [tex]$-(\sqrt[3]{8})$[/tex]:

The cube root of 8 is the number that, when raised to the power of 3, equals 8. In this case, the cube root of 8 is 2, because [tex]2^3 = 8[/tex].

Since we have a negative sign in front of the cube root, the result will be the negative value of the cube root of 8.

Therefore, [tex]$-(\sqrt[3]{8}) = -2$[/tex].

(b) [tex]$\sqrt[4]{-81}$[/tex]:

The fourth root of a number is the number that, when raised to the power of 4, equals the given number.

In this case, we are looking for the fourth root of -81.

However, the fourth root of a negative number is not a real number. This is because raising a positive number to an even power (in this case, 4) will always result in a positive value, and there is no real number that, when raised to the power of 4, gives a negative result.

Therefore, the fourth root of -81 is not a real number.

To know more about roots, refer here:

https://brainly.com/question/12105008

#SPJ2

Answer:

She makes 30 portions.

Step-by-step explanation:

To find, you would multiply the amount of tuna you need by the number of onions nicole used.

6/5x2 = 12/5

12/5 ÷ 2/5 = 6

6x5 = 30

She makes 30 portions.

Answer:

1

Step-by-step explanation:

that's the lowest number