Let the sample space be S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10). Suppose the outcomes are equally likely. Compute the probability of the event E = {1,4,7,9).

P(E)= ____?

(Type an integer or a decimal. Do not round.)

Answer:

Tres respuestas posibles son:

2 y 3x^2 + x

2x y 3x + 2

x y 6x + 2

y hay muchas mas.

Step-by-step explanation:

Hay muchas respuestas posibles.

6x^2 + 2x = 2(3x^2 + x) = 2x(3x + 2) = x(6x + 2)

Answer:

x = 1, y = -15

Step-by-step explanation:

7x + y = -8 ⇒ y = -7x-8

2x + 5y = -7

substitute -7x-8 for y:

2x + 5(-7x-8) = -7

2x - 35x - 40 = -7

-33x - 40  = -7

-33x = -33

x = 1

y = -7x-8 = -15

Answer:

a volleyball is $16.5

Step-by-step explanation:

6b+2v= 114

v=b-3

6b+2(b-3)= 114

6b + 2b - 6

8b - 6 = 114

8b = 108

b= 13.5

substitute b in

6(13.5) + 2v = 114

81 + 2v = 114

2v = 33

v= 16.5

Answer: x=1/3

Step-by-step explanation:

Step 1: Simplify both sides of the inequality.

3x−1<0

Step 2: Add 1 to both sides.

3x−1+1<0+1

3x<1

Step 3: Divide both sides by 3.

3x/3 <1/3

x/1/3

Answer:

Step-by-step explanation:

First find out what an 11% return on $30,000 is.

= 11% * 30,000

= $3,300

Use simultaneous equations.

Assume the amount to be invested in to make a 7% interest is x and the amount for a 13% interest is y.

0.07x + 0.13y = 3,300

x + y = 30,000

y = 30,000 - x

0.07x + 0.13 (30,000 - x) = 3,300

0.07x + 3,900 - 0.13x = 3,300

0.07x - 0.13x = 3,300 - 3,900

-0.06x = -600

x = -600 / -0.06

x = $10,000

y = 30,000 - x

= 30,000 - 10,000

y = $20,000

It's True True True True True True True

Answer:

20 boys in the class

Step-by-step explanation:

40% of 50 is 20

Answer:

a) 0.4545 = 45.45% probability that a random committee is made up of 2 women and 1 man.

b) 0.1515 = 15.15% probability that the Chairperson and Vice Chairperson are both women and the Treasurer is a man

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

If the order of the people chosen is important, we use the permutations formula. If the order is not important, we use the combinations formula.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

(a) What is the probability that a random committee is made up of 2 women and 1 man?

Order is not important, so we use the combinations formula.

Desired outcomes:

2 women from a set of 6, and a men from a set of 5. So

[tex]D = C_{6,2}*C_{5,1} = \frac{6!}{2!4!}*\frac{5!}{1!4!} = 15*5 = 75[/tex]

Total outcomes:

3 people from a set of 6 + 5 = 11. So

[tex]T = C_{11,3} = \frac{11!}{3!8!} = 165[/tex]

Probability:

[tex]p = \frac{D}{T} = \frac{75}{165} = 0.4545[/tex]

0.4545 = 45.45% probability that a random committee is made up of 2 women and 1 man.

(b) Suppose now that the committee consists of different positions: Chairperson, Vice-Chairperson, and Treasurer. What is the probability that the Chairperson and Vice Chairperson are both women and the Treasurer is a man?

Now, the order is important, which means that we use the permutations formula.

Desired outcomes:

2 women from a set of 6, and a men from a set of 5. So

[tex]D = P_{6,2}*P_{5,1} = \frac{6!}{4!}*\frac{5!}{4!} = 30*5 = 150[/tex]

Total outcomes:

3 people from a set of 11. So

[tex]T = P_{11,3} = \frac{11!}{8!} = 990[/tex]

Probability:

[tex]p = \frac{D}{T} = \frac{150}{990} = 0.1515[/tex]

0.1515 = 15.15% probability that the Chairperson and Vice Chairperson are both women and the Treasurer is a man

Answer:

A

Step-by-step explanation:

there is no intersection which means no solution...i dont knwo how to explain sorry

Answer:

x = 5

Step-by-step explanation:

3x – 4y = 31

y = -2x + 6

Plug in Y

3x – 4(-2x + 6) = 31

Distribute

3x +8x-24= 31

Add like terms

11x - 24 = 31

Add 24 on both sides

11x = 55

Divide both sides by 11

x = 5

Answer:186.66is answer

p=14000

r=8%

time=60days=2month/12=1/6year

Step-by-step explanation:

simple interest=ptr/100=14000×8×1/600=186.666

Answer:

mineeeeeeeeeeee

Step-by-step explanation:

Answer:

40_ page 302

Step-by-step explanation:

mathematics teacher and she said that to me and happy holidays so we can get the text on

Answer:

im sry

Step-by-step explanation:

Answer: 3 1/30

Step-by-step explanation:

Hi, IReady sucks. So I am gonna help you. I got 3 1/30 when you add them together. I would also recommend using a Fraction Calculator online. ;) it helps a lot!

Answer:

4 hours

Step-by-step explanation:

Answer:

n=10

Step-by-step explanation:

For a regular polygon with n sides, each interior angle, x, is given by

[tex]x=180\frac{n-2}{n}[/tex]

This can be solved for n

[tex]n=\frac{360}{180-x}[/tex]

For the pentagons

x(5)=180(3/5)=108 degrees.

The angles around P sum to 360, so

2(x(5))+x(A)=360

x(A)=360-2(108)=144.

Substitue in the equation for n.

n=360/(180-144)=10

The number of sides in this polygon is 10.

For any polygon, the sum of interior angles is given as,

[tex]\bold{Sum\ of\ interior\ angles= {(n-2)}\times {180^o}}[/tex]

where,

n = number of sides,

We know that for a pentagon, the number of sides is 5.

thus, substituting the values in the sum of interior angle formula we get,

[tex]{Sum\ of\ interior\ angles= {(n-2)}\times {180^o}}[/tex]

[tex]{Sum\ of\ interior\ angles= {5-2}\times{180^o}}\\= 3 \times {180^o} = 540^o[/tex]

therfore, each angle in a regular pentagon,

[tex]\dfrac{Sum\ of\ interior\ angles}{Number\ of\ Sides} = \dfrac{540^o}{5} = 108^o[/tex],

Let's assume that polygon A is having x number of sides.

At point P, the sum of the angles must be 360°.

The sum of the angles at point P

          = interior angle of the first pentagon

          + interior angle of the second pentagon

          + interior angle of the polygon A with x sides

Substituting the values,

360° = 108° + 108° + z

z = 360° - 108° - 108°

z = 144°

Thus, the interior angle of the x sided polygon is z = 144°.

For a regular polygon, all the interior angles are equal,

so, for a polygon with sides x.

the sum of interior angle = measure of interior angle x Number of sides

                                         = [tex]144^o \times x[/tex]

Also, we know

[tex]{Sum\ of\ interior\ angles= {(n-2)}\times {180^o}}[/tex]

Substituting, the values for an x number of side  polygon,

[tex]{Sum\ of\ interior\ angles= {(n-2)}\times {180^o}}\\{144^o \times x = {(x-2)}\times {180^o}}\\144x = 180x - 360\\360 = 180x- 144x\\x = \dfrac{360}{36}\\x = 10[/tex]

Hence, the number of sides in this polygon is 10.

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Answer:

b

Step-by-step explanation:

beacause 2x+60 thats the answer

Answer:

179

Step-by-step explanation:

(x+35)^0=1

supplement=

180-1

179

Answer:

Step-by-step explanation:

The missing equation is:

[tex]S = \int ^b_a 2 \pi f(y) \sqrt{1 + f' (y)^2 } \ dy[/tex]

Suppose f = nonnegative function whose first derivative is within (a,b) and it is continuous, Then the area of the surface generated is revolved about the x-axis:

The area of the surface revolution is:

[tex]S = \int ^b_a 2 \pi f(x) \sqrt{1 + f' (x)^2 } \ dx[/tex]

So; if  [tex]x = g(y)[/tex] for [tex]y \ \varepsilon \ [c,d][/tex]

Then; substituting a with c and b with d; f(x) also with g(y) and dx with dy;

Then;

[tex]S = \int ^d_c 2 \pi g(y) \sqrt{1 + g' (y)^2 } \ dy[/tex]

SInce;

[tex]g(y) \ne f(y)[/tex]; Then the statement is false.

Provided that the semicircle [tex]y = \sqrt{1-x^2}[/tex] isn't on [tex][-1,1][/tex] interval.

Then, the solid generated by the revolution about the x-axis is a sphere.

However, the surface is well defined and the statement is false.

Answer:

He spent 60% on fruit

Step-by-step explanation:

Answer:

Step-by-step explanation:

65-39=26

26/100=0.26

Answer:

A. c = 60 / p

Step-by-step explanation:

If p=2, the equation would read... c = 60 / 2, which mean c = 30. If c = 12, the equation would read... 12 = 60 / p, and p = 5, and so on, 20 = 60 / 3, and 15 = 60 / 4.

Answer:

Step-by-step explanation:

Slope-intercept form:

Take two points from the graph:

Find the slope:

The y-intercept is b = 5

The line is:

Answer:

[tex]T > 45[/tex]

Step-by-step explanation:

Given

[tex]\frac{T}{3} > 15[/tex]

Required

Graph the solution

[tex]\frac{T}{3} > 15[/tex]

Multiply both sides by 3

[tex]3 * \frac{T}{3} > 15*3[/tex]

[tex]T > 15*3[/tex]

[tex]T > 45[/tex]

See attachment for graph (Assume T is on the x-axis)

Answer:

x=0.3

Step-by-step explanation:

6x+3+4x=1/2(9+10x)

10x+3=4.5+5x

5x=1.5

x=0.3

Answer:

x=0.3

Step-by-step explanation:

6x+3+4x=1/2(9+10x)

10x+3=4.5+5x

subtract 5x and 3 from both sides

5x=1.5

x=0.3

Answer: =−3x^3−9x^2+3

Step-by-step explanation:

Distribute the Negative Sign:

=5x^3−7x^2+3x−4+−1(8x^3+2x^2+3x−7)

=5x^3+−7x^2+3x+−4+−1(8x^3)+−1(2x^2)+−1(3x)+(−1)(−7)

=5x^3+−7x^2+3x+−4+−8x^3+−2x^2+−3x+7

Combine Like Terms:

=5x^3+−7x^2+3x+−4+−8x^3+−2x^2+−3x+7

=(5x^3+−8x^3)+(−7x^2+−2x^2)+(3x+−3x)+(−4+7)

=−3x^3+−9x^2+3

Answer:

91 km per hour

Step-by-step explanation:

45 miles per hour is the same as 72 kilometers per hour (metric), so pick any value greater than 72 km per hour.