At a party there are 30 students over age 21 and 20 students under age 21. You choose at random 3 of those over 21 and separately choose at random 2 of those under 21 to interview about attitudes toward alcohol. You have given every student at the party the same chance to be interviewed: what is that chance

Answer: [tex]0.416655[/tex]

Step-by-step explanation:

If random variable X has the binomial distribution B(n, p), then

[tex]P(X=x)=\ ^nC_xp^x(1-p)^{n-x}[/tex]

, where  n= Total number of trials, x = number of successes , p= probability of success in each trial.

Given: The random variable R has the binomial distribution B (12,0.35).

n= 12, = 0.35

[tex]P(R>4)=1-P(R\leq4)\\\\=1-[P(R=0)+P(R=1)+P(R=3)+P(R=4)]\\\\\\=1-[^{12}C_0(0.35)^{0}(1-0.35)^{12}+^{12}C_1(0.35)^{1}(1-0.35)^{11}+^{12}C_2(0.35)^{2}(1-0.35)^{10}+^{12}C_3(0.35)^{3}(1-0.35)^{9}+^{12}C_4(0.35)^{4}(1-0.35)^{8}]\\\\= 1-[(1)(0.65)^{12}+(12)(0.35)(0.65)^{11}+\dfrac{12!}{2!10!}(0.35)^2(0.65)^{10}+\dfrac{12!}{9!3!}(0.35)^3(0.65)^{9}+\dfrac{12!}{8!4!}(0.35)^4(0.65)^{8}]\\\\=1-0.583345\\\\\approx0.416655[/tex]

Hence, P(R>4)=0.416655

Answer:

[tex]c = 2[/tex]

Step-by-step explanation:

In order to find the answer to this question you must add 7 on both sides.

[tex]c-7=-9[/tex]

[tex]+ 7 + 7[/tex]

[tex]-9 + 7 = -2[/tex]

[tex]c = -2[/tex]

Hope this helps.

Answer:

x=2y

Step-by-step explanation:

Answer:

8 hours

Step-by-step explanation:

it can't be 36 as the answer, and the next multiple before 36 is 32. And if you do 32 divided by 4 then you get 8. The answer is 8 hours.

Answer:

x = -1

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

_+(-4) = -1

_-4 = -1

_ = 3

Answer:

24,823

Step-by-step explanation:

Since we know the answer and the what we're subtracting from we can make an equation like this 65,823 - b = 41,000. Now you solve it by subtracting 65,823 - 41,000 = b. 24,823 = b because if we were to add the smaller numbers like this: 41,000 + 24,823 we would get 65,823 making our answer correct.

Answer:

The answer is B

Step-by-step explanation

As it shows in the table each week the amount adds to 75$. in the table it only shows 4 weeks amount. and the question asks you whats the amount going to be in the 7th week . the amount will be 825.

9514 1404 393

Answer:

  second step is wrong; x = 5

Step-by-step explanation:

The correct solution is ...

  3(x -3) +9 = 15

  3x -9 +9 = 15 . . . . . . . not 3x -3

  3x = 15

  x = 5

_____

Jeremy did what a lot of students do -- failed to apply the outside factor to all of the terms in parentheses.

Answer:

13 = x      15 - x = 2

Step-by-step explanation:

15-x=2

15-13=2

Using the law of sines, equation A). [tex]\frac{sin(51)}{2.6} = \frac{sin(76)}{z}[/tex] is correct and can be used to solve for the value of z.

The law of sine or the sine law states that the ratio of the side length of a triangle to the sine of the opposite angle, which is the same for all three sides. It is also known as the sine rule.

[tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}[/tex]

Similarly, In triangle XYZ,

[tex]\frac{sin(51)}{2.6} = \frac{sin(76)}{z}=\frac{sin(53)}{x}[/tex]

Learn more about law of sines here

https://brainly.com/question/17289163

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Answer:

[tex]P(x = 1) = 0.10[/tex]

Step-by-step explanation:

Given

[tex]\begin{array}{ccccc}x & {1} & {2} & {3} & {4} \ \\ P(x) & {0.10} & {0.30} & {0.40} & {0.20} \ \ \end{array}[/tex]

Required

Determine the probability of selling exactly 1 batch

This probability is represented with [tex]P(x = 1)[/tex]

From the table:

When x = 1; P(x) = 0.10

Hence:

[tex]P(x = 1) = 0.10[/tex]

In other words, the probability of selling exactly 1 is 0.10

Answer:

384 cm^3

Step-by-step explanation:

(16 times 4) times 6 = 384   :D

Answer:

2.53%

Step-by-step explanation:

all you have to do is 1 / 39.51 = about 0.0253 = 2.53%

Answer: -25•2^n-1 is the awnser

The explicit formula of the geometric sequence is -25 × 2ⁿ⁻¹.

Let's find the explicit formula for the geometric sequence as follows:

-25, -50, -100,- 200, ...

Using the geometric sequence formula,

nth term = arⁿ⁻¹

where

Therefore,

a = -25

r = -50 / -25 = 2

Hence,

nth term = -25 × 2ⁿ⁻¹

learn more on geometric sequence here: https://brainly.com/question/27197371

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Answer:0

Step-by-step explanation:

Annually compounded interest: 4,031.75

Simple interest: 3,900.00

Answer:

42/55

Step-by-step explanation:

6/5 times 7/11 = 42/55

Answer:

-2

Step-by-step explanation:

2-4=-2

Answer:

Step-by-step explanation:

There are 12 months in one year, so there would be 12*y in y years.

Answer:

there 12 months in one 1 year

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Answer:

First the line is positive so you can eliminate all negative choices for slope

Now start from a random point that lands on the graph

Now it can’t be 1 becuase it has am extra box but that line isn’t on a point

Now 1/2 it can’t be becuase if you rise 1 and go right 2 it’ll not land ona. Point

But for 2, you rise up 2 and right 1 and you land on a point on the graph so the final answer is 2

9514 1404 393

Answer:

  a) f(-2.5) = 62.6875; f(-1.5) = -13.0625; (-2.5, -1.5) contains a real root

  b) there are 1 each of positive and negative real roots; 2 complex roots

  c) -2 and 1/3 are the rational real roots

  d) x ∈ {-2, 1/3, -1/3 +i(√2)/3, -1/3 -i(√2)/3}

Step-by-step explanation:

a) f(-2.5) = 62.6875; f(-1.5) = -13.0625. The function changes sign between -1.5 and -2.5, so there is a real root in that interval.

__

b) The given coefficients have one sign change, so there is one positive real root. Changing the signs of odd-degree terms makes the signs + - + - -, so there are three sign changes. There are 1 or 3 negative real roots, and possibly 2 complex roots. The constant term is non-zero, so zero is not a root. Here's your table:

  positive real roots: 1

  negative real roots: 1 or 3

  complex roots: 2 or 0

  zero roots: none

The graph is attached. It shows 2 real roots, one positive and one negative, so there are 2 complex roots. (There are 4 roots in total, so if only 2 are real, the other 2 are complex.)

__

c) Possible rational roots are of the form ...

  ±{1, 2}/{1, 3, 9}

Listed, they are ...

  ±{1/9, 2/9, 1/3, 2/3, 1, 2}

The actual real roots are -2 and 1/3.

__

d) The graph shows the real roots to be -2 and 1/3. The original leading coefficient of 3 is the product of the leading coefficients of the factors. Writing the factor (x -1/3) as (3x -1) lets us reduce the leading coefficient of the quadratic term from 9 to 3. The result of dividing factors (x+2) and (3x-1) from the original function is shown in the attachment. It is a parabola with vertex (-1/3, 2/3), so the factorization is ...

  f(x) = (x +2)(3x -1)(3(x +1/3)² +2/3)

The roots of the quadratic term are ...

  3(x +1/3)² = -2/3

  x +1/3 = ±√(-2/9)

  x = (-1 ±i√2)/3

So, the entire list of roots is ...

  x ∈ {-2, 1/3, -1/3 +i(√2)/3, -1/3 -i(√2)/3}

_____

Additional comment

The roots of a quadratic are easily found by knowing its leading coefficient and its vertex. If factoring known real roots from a higher-degree polynomial results in a quadratic, then the remaining complex roots are easily found. A graphing calculator is a wonderful tool for this process.

Answer:

The cost of 80 oranges =  480 nairas

Step-by-step explanation:

Given

The cost of 5 oranges = 30 naira

Determine

The cost of 80 oranges

Given that the cost of 5 oranges = 30 naira

so,

Unit rate = 30 nairas / 5 oranges

               = 6 nairas per orange

∴ The cost of 1 orange = 6 nairas

As the cost of 1 orange = 6 nairas

Thus,

The cost of 80 oranges = 6 × 80 = 480 nairas

Hence,

The cost of 80 oranges =  480 nairas

Answer:

it is %224 profit on the skates

Step-by-step explanation:

Answer:

y = 60°

x = 12

Step-by-step explanation:

opposite angles of a parallelogram are equal

opposite sides of a parallelogram are equal

Step-by-step explanation:

the answer of this question is 5.39

Answer:

Variability

Step-by-step explanation:

Variability in simple terms may be described as differences in measurement or reading of a certain construct or phenomenon. Variability measures include range, standard deviation or variance. In most cases, variation or degree of Variability is measured about a central value called the mean. This is because same measurement about a certain phenomenon or study would usually not yield the same result value. Hence, the mean is used to record the average of these measurement and the differences in each measurement from the mean is also recorded, this is called the standard deviation which is a Variability measure.

Thus VARIABILITY means successive observation of a phenomenon do not yield exactly the same result.