A poll is given, showing 30% are in favor of a new building project.

If 5 people are chosen at random, what is the probability that exactly 4 of them favor the new building project?

Answer:

Approximately [tex]35.2[/tex] points.

Step-by-step explanation:

Let random variables [tex]X_{1},\, \dots,\, X_{30}[/tex] denote the score of those [tex]30[/tex] test-takers. These random variables are independently and identically distributed. In other words, the scores follow the same distribution and are independent from one other.

While the exact distribution of each score is unknown, the mean and variance of this distribution are given: [tex]\mu = 1083[/tex] and [tex]\sigma = 193[/tex].

By the Central Limit Theorem, the mean (average) [tex]\overline{X}_{n}[/tex] of a sufficiently large number of such observations would follow a normal distribution. The mean of that distribution would be [tex]\mu[/tex] (same as the mean of the observations) while the variance [tex]{\rm Var}(\overline{X}_{n})[/tex] would be [tex](\sigma^{2} / n)[/tex].

Take the square root of variance to find the value of the corresponding standard deviation:

[tex]\begin{aligned}& \sqrt{{\rm Var}(\overline{X}_{n})} \\ =\; & \sqrt{\frac{\sigma^{2}}{n}} \\ =\; & \sqrt{\frac{193^{2}}{30}}\\ \approx\; & 35.2\end{aligned}[/tex].

Answer:

X = ( 40/11 )

Y = ( -58/11 )

Step-by-step explanation:

6x + 3y = 6

7x + 9y = -22

-------------------------

-3(6x + 3y = 6)

= -18x - 9y = -18

-------------------------

-18x - 9y = -18

7x + 9y = -22

-11x = -40

÷-11   ÷-11

x = ( 40/11 )

------------------------

6( 40/11 ) + 3y = 6

( 240/11 ) + 3y = 6

-( 240/11 )      -( 240/11 )

3y = ( -174/11 )

÷3          ÷3

y =  ( -58/11 )

---------------------------

I hope this helps!

Answer:

[tex]x=\frac{40}{11}[/tex]
[tex]y=-\frac{58}{11}[/tex]

Step-by-step explanation:          [tex]\left \{ {{6x+3y=6} \atop {7x+9y=-22}} \right.[/tex]

Multiply both sides of the equation by a coefficient

[tex]\left \{ {{3\left(6x+3y\right)=6\times3} \atop {7x+9y=-22}} \right.[/tex]

Apply the Distributive Property
[tex]\left \{ {{18x+9y=6\times3} \atop {7x+9y=-22}} \right.[/tex]

Calculate the product or quotient

[tex]\left \{ {{18x+9y=18} \atop {7x+9y=-22}} \right.[/tex]

Subtract the two equations
[tex]18x+9y-(7x+9y)=18-(-22)[/tex]

Remove parentheses
[tex]18x+9y-7x-9y=18+22[/tex]

Cancel one variable
[tex]18x-7x=18+22[/tex]

Combine like terms
[tex]11x=18+22[/tex]

Calculate the sum or difference
[tex]11x=40[/tex]

Divide both sides of the equation by the coefficient of variable
[tex]x=\frac{40}{11}[/tex]

Substitute into one of the equations
[tex]7\times\frac{40}{11}+9y=-22[/tex]

Write as a single fraction
[tex]\frac{7\times40}{11}+9y=-22[/tex]

Calculate the product or quotient
[tex]\frac{280}{11}+9y=-22[/tex]

Multiply both sides of the equation by the common denominator
[tex]\frac{280\times11}{11}+9y\times11=-22\times11[/tex]

Reduce the fractions
[tex]280+9y\times11=-22\times11[/tex]

Multiply the monomials
[tex]280+99y=-22\times11[/tex]

Calculate the product or quotient
[tex]280+99y=-242[/tex]

Rearrange variables to the left side of the equation
[tex]99y=-242-280[/tex]

Calculate the sum or difference
[tex]99y=-522[/tex]

Divide both sides of the equation by the coefficient of variable
[tex]y=-\frac{522}{99}[/tex]

Cross out the common factor
[tex]y=-\frac{58}{11}[/tex]

The solution of the system is
[tex]\left \{ {{x=\frac{40}{11}} \atop {y=-\frac{58}{11}}} \right.[/tex]

I hope this helps you

:)

Answer:

You are so dum i can answer it in less than 5 seconds.

Step-by-step explanation:

Answer:

Step-by-step explanation:

P(E') = 1 - P(E)

       [tex]= 1-\dfrac{5}{13}\\\\\\=\dfrac{13}{13}-\dfrac{5}{13}\\\\\\=\dfrac{8}{15}[/tex]

P(E') -> complement of the event.

Answer :

⠀

Explanation :

[tex]\longrightarrow \sf \qquad {x}^{2} + 10x - 39 = 0[/tex]

⠀

We have to find the two numbers a and b such that,

[tex]\longrightarrow \sf \qquad a + b = 10[/tex]

[tex]\longrightarrow \sf \qquad a b = 39[/tex]

⠀

Obviously, the two numbers are 3 and 13.

[tex]\longrightarrow \sf \qquad {x}^{2} - 3x + 13x - 39 = 0[/tex]

[tex]\longrightarrow \sf \qquad {x}(x - 3)+ 13(x - 3) = 0[/tex]

[tex]\longrightarrow \sf \qquad ({x}+ 13)(x - 3) = 0[/tex]

⠀

Whether, the value of x :

[tex]\longrightarrow \sf \qquad {x}+ 13 = 0[/tex]

[tex]\longrightarrow \pmb{\bf \qquad {x} = - 13}[/tex]

⠀

Whether, the value of x :

[tex]\longrightarrow \sf \qquad {x} - 3 = 0[/tex]

[tex]{\longrightarrow { \pmb{\bf \qquad {x} = 3}}}[/tex]

⠀

We are given with the equation x² + 10x - 39 = 0 and need to find x, so let's start ;

[tex]{:\implies \quad \sf x^{2}+10x-39=0}[/tex]

By using splitting the middle term method, Rewrite as ;

[tex]{:\implies \quad \sf x^{2}+13x-3x-39=0}[/tex]

[tex]{:\implies \quad \sf x(x+13)-3(x+13)=0}[/tex]

[tex]{:\implies \quad \sf (x+13)(x-3)=0}[/tex]

So, here either (x + 13) = 0 or (x - 3) = 0, when you equate both of them with 0, you will get x = -13 and x = 3

Hence, The required answer is -13 and 3

Answer:

No

Step-by-step explanation:

Knowing that 1.5 can also be written as 1.500

Thus, 0.968 < 1.500

Also can say 0.968 is less than 1.500

[RevyBreeze]

Answer:

Not worth 40 points. Poster is a liar.

R=15 --> 30/2 , H=320

Anyways, because you lied, I won't show my work.

Volume= 72,000pi or 226194.6711

Answer:

  150 in³

Step-by-step explanation:

We want to find half the volume of a rectangular pyramid. The volume of the whole pyramid is given by the formula ...

  V = 1//3LWH

  V = 1/3(5 in)(15 in)(12 in) = 300 in³

Then the volume of the half that is not filled with marbles is ...

  1/2V = 1/2(300 in³) = 150 in³

150 cubic inches of marbles are needed to finish filling the container.

Answer:

24

Step-by-step explanation:

LCM of 4, 6, and 8 by Prime Factorization

LCM of 4, 6, and 8 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 23 × 31 = 24. Hence, the LCM of 4, 6, and 8 by prime factorization is 24.

Answer:

4 and 5/12

Step-by-step explanation:

Find them as an improper fraction then find the LCD and add

Answer:

3.63333 is the answer in Desamole form

Answer:

Give me the diagram so i can answer the question please

Answer:

those weights sure are mean

Step-by-step explanation:

they say their mean so their mean

Probability of getting the keychain = 1/2

Probability of getting red hat = 1/3

Probability of getting black sweatshirt = 1/2

Probability of all 3 = 1/2 x 1/3 x 1/2 = 1/12

Answer: A. 1/12

Answer: a

Step-by-step explanation: i did it

Answer:

7.5 miles per hour

Step-by-step explanation:

7.5 = 1 mile + 7.5= 1 mile =15= 2 miles

Answer:

FOUR HUNDRED FORTY-FOUR THOUSAND FOUR HUNDRED FOUR

Step-by-step explanation:

Answer:

The correct word form is:

Four hundred and forty-four my four hundred and four

---

Thank you so much for participate in the community of Brainly.com

I hope help you :)

Kind regards, Antonio.

Answer:

85%

Step-by-step explanation:

Johny answered [tex]\frac{17}{20}[/tex] questions correctly. To change this into percent, just multiply both the numerator and denominator by the number that makes the denominator equal 100. In this case, 5 would make 20 equal 100, so we multiply both the top and bottom by 5.

[tex]\frac{17}{20} *\frac{5}{5}=\frac{85}{100}[/tex]

Your numerator will be your percentage if the denominator is 100.

Answer:

11,200

Step-by-step explanation:

You can look up "Meters to Centimeters" and that should help you in the future

Answer:

11,200

Step-by-step explanation:

Answer:

C .6 inches

Step-by-step explanation:

I'm not sure of my answer

Answer:

D

Step-by-step explanation:

First, if you asked to divide a fraction then the fraction on the right will be inversed

[tex] - 3 \div ( - \frac{2}{5} ) = - 3 \times - \frac{5}{2} [/tex]

then from here, you multiply the fraction

[tex] = \frac{15}{2} [/tex]

or

[tex]7 \frac{1}{2} [/tex]

pls give brainliest

[tex] \rightarrow4 \times \frac{3}{5} = 12 \times \frac{1}{5} \\ [/tex]

[tex] \rightarrow \frac{12}{5} = \frac{12}{5} \\ [/tex]

[tex] \rightarrow \: lhs \: = \: rhs[/tex]

Hence , 4 x 3/5 =12 ×1/5

Let's see

We know

So

Hence verified

Answer:

See below.

Step-by-step explanation:

You have to find the unit price.

1750/7=250

Now, multiply the unit price by the desired amount.

250*12=3000

So, 12 calculators will cost 3,000.

-hope it helps

Answer:

C

Step-by-step explanation:

This is because C is the only answer that equals 2 2/3

Option C (2 2/3 = 1 + 1 +1/3 + 1/3) is the correct equation.

A) 2 + 2 + 3 = 7

B) 1 + 1 + 2 + 3 = 7

C) 1 + 1 + 1/3 + 1/3 = 2 2/3

D) 1 + 1 + 1/3 = 2 1/3

I attached a picture to make it simpler!

—————

Please remember to revise this and make it in your own words if you want! I hope this helps you. -Doodle

—————

Answer:

The third option

Step-by-step explanation:

I did the math x less than or equal to 0.5

Answer:

A) Carla: y = 1.5x + 30   <-- y is the total money, and x is the number of weeks

Darla: y = 3x   <-- y is the total money, and x is the number of weeks

B) No, they start with a different amount of money and also save different amounts each week. They will not always have the same amount of money.

C) See attachment

Step-by-step explanation:

We'll start with Carla.

Carla saves $1.5 every week. That means that if we multiply the number of weeks she has saved by 1.5 we'll get the amount of money she has. However, she starts at 30 so we have to add 30 to that at the beginning. So, Carla's equation is y = 1.5x + 30. y is the total money, and x is the number of weeks

Darla saves $3 every week. That means that if we multiply the number of weeks she has saved by 3 we'll get the amount of money she has. Unlike Carla, Darla starts at $0, so there is no need to add anything. So, Darla's equation is y = 3x. y is the total money, and x is the number of weeks

Since Carla and Darla start with a different amount of money and save different amounts each week, they won't always have the same amount of money. However, they will cross at some point. You can actually see this in the graph. Carla, there is red, and Darla is blue.

Now let's graph the 2 equations. First, we'll do Carla. her equation is y = 1.5x + 30. Since it is in the slope-intercept form we can just use y = mx + b to tell how we're going to graph this. In this formula, m is the slope, and b is the y-intercept. As you can see when you look back at Carla's equation, m is 1.5 and b is 30. First, we'll take the y-intercept, b, which is 30 as we just figured out, and plot it on the graph. All you have to do here is count 30 units up the y-axis (the one going up and down) and put a point there. Now we take the slope (1.5) and we start putting in points that the line will go through. 1.5 in fraction form is 3/2 meaning (starting from that point we marked earlier) we will go 3 units up, and 2 units to the right and put another point there. You can now take a ruler, line up the 2 points you marked and draw a big line through them that keeps going on forever on both sides (just put an arrow at both ends to mark that).

Now we'll do the same with Darla's equation. Her's is y = 3x. When we compare this with or slope-intercept formula, y = mx + b, we'll notice there is no b. That means it is 0 and that the y-intercept is also 0. So go ahead and mark a point in the middle of the graph where the 2 big lines cross. 3 in fraction form is just 3/1 meaning that we'll go 3 up and 1 to right (from the point you just marked) and put another point there. Now draw another big line through both of those points (WITH A RULER) and mark the ends with arrows.

Answer:

9 square units

Step-by-step explanation:

Create a rectangle around the polygon of the dimensions:

4 spaces wide, 4 spaces tall

The area of the rectangle is 4 * 4 = 16.

Subtract the non shaded triangles which aren't taken up by the polygon:

There are two 1 by 3 triangles, one 2 by 1 triangle, and one 2 by 3 triangle.

The total sum of these areas is:

2 * [(1 * 3) / 2] + [(2 * 1) / 2] + [(2 * 3) / 2]

= 3 + 1 + 3

= 7

So, the area of the polygon is 16 - 7 = 9 square units.

Answer:

9 sq units

Step-by-step explanation:

entered it in rsm its correct

Answer:

Bobby has 45 beads

Step-by-step explanation:

Let x be the number of beads Bobby has.

Then, (x + 30) is the number of beads Alvin has.

Then, 3 (x + 30) is the number of beads Cathy has.

3 (x + 30) + (x + 30) + x = 345

3x + 90 + x + 30 + x = 345

5x + 120 = 345

5x = 225

x = 45

Therefore, Bobby has 45 beads.