what is the value of a, if 5a-b-c=36 and b=c=1/2a

Answer:

a) The probability that at least 2 of them started smoking before 21 years of age is 0.1875 = 18.75%.

b) The probability that at most 4 of them started smoking before 21 years of age is 0.96875 = 96.875%.

c) The probability that exactly 3 of them started smoking before 21 years of age is 0.3125 = 31.25%.

Step-by-step explanation:

For each smoker, there are only two possible outcomes. Either they started smoking before 21 years old, or they did not. Smokers are independent, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [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]

And p is the probability of X happening.

50% of adult smokers started smoking before 21 years old.

This means that [tex]p = 0.5[/tex]

5 smokers 21 years old or older are randomly selected, and the number of smokers who started smoking before 21 is recorded.

This means that [tex]n = 5[/tex].

a) The probability that at least 2 of them started smoking before 21 years of age is

This is:

[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]

In which

[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{5,0}.(0.5)^{0}.(0.5)^{5} = 0.03125[/tex]

[tex]P(X = 1) = C_{5,1}.(0.5)^{1}.(0.5)^{4} = 0.15625[/tex]

[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.03125 + 0.15625 = 0.1875[/tex]

The probability that at least 2 of them started smoking before 21 years of age is 0.1875 = 18.75%.

b) The probability that at most 4 of them started smoking before 21 years of age is

This is:

[tex]P(X \leq 4) = 1 - P(X = 5)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 5) = C_{5,5}.(0.5)^{5}.(0.5)^{0} = 0.03125[/tex]

[tex]P(X \leq 4) = 1 - P(X = 5) = 1 - 0.03125 = 0.96875[/tex]

The probability that at most 4 of them started smoking before 21 years of age is 0.96875 = 96.875%.

c) The probability that exactly 3 of them started smoking before 21 years of age is

This is P(X = 3). So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 3) = C_{5,3}.(0.5)^{3}.(0.5)^{2} = 0.3125[/tex]

The probability that exactly 3 of them started smoking before 21 years of age is 0.3125 = 31.25%.

Answer:

- Top Hat

- 14

- 37

Step-by-step explanation:

Answer:

12inches

Step-by-step explanation:

Answer:

    36.07

Step-by-step explanation:

    Method 1:

         [tex]A_1 = b * h = 3.1 * 3.4 = 10.54[/tex]

         [tex]A_2 = b * h = 3.8 * 3.7 = 14.06[/tex]

         [tex]A_3 = b * h = 3.1 * 3.7 = 11.47[/tex]

         [tex]A = A_1 + A_2 + A_3 = 10.54 + 14.06 + 11.47 = 36.07[/tex]

    Method 2:

         [tex]A_1 = b * h = (3.1 + 3.8)(3.4 + 3.7) = 6.9 * 7.1 = 48.99[/tex]

         [tex]A_2 = b * h = 3.4 * 3.8 = 12.92[/tex]

         [tex]A = A_1 - A_2 = 48.99 - 12.92 = 36.07[/tex]

Both solutions point to the same answer, so we can confirm it's correct

====================================================

Explanation

Consider three scenarios:

These scenarios cover all the possible cases of what x could be. It's either the min, the max, or somewhere in between the min and max.

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

We'll start with scenario A.

If x is the min, then that must mean 39 is the max as it's the largest of the set {18, 36, 16, 39, 27, 8, 34}

The range is 56, so,

range = max - min

56 = 39 - x

56+x= 39

x = 39-56

x = -17  which is one possible answer

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

If instead we go with scenario B, then x is the max and 8 is the min

range = max - min

56 = x - 8

56+8 = x

64 = x

x = 64 is the other possible answer

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

Lastly, let's consider scenario C. If x is not the min or the max, then it's somewhere between the min 8 and max 39. in short, 8 < x < 39.

Note that range = max - min = 39-8 = 31 which is not the range of 56 that we want. So there's no way scenario C can be possible here.

Answer:

-$7

Step-by-step explanation:

20 - 15 = 5

5 + 5 = 10

10 - 10 = 0

0 - 7 = -7

9514 1404 393

Answer:

  1/12 box

Step-by-step explanation:

Each brother gets 1/4 of the remaining 1/3 box, so ...

  (1/4)(1/3 box) = 1/(4·3) box = 1/12 box

Each brother gets 1/12 of the original box.

Answer:

1/12

Step-by-step explanation:

3/36=1/12

Answer:

B would be 72 using a^2+b^2=c^2

Step-by-step explanation:

30^2 + x =78^2

in other words

900 + x =6084

6084-900= 5184

The square root of 5184 is 72

Answer:

Step-by-step explanation:Herely/3fcEdSx's li[tex]^{}[/tex]nk to the answer:

bit.[tex]^{}[/tex]

The radius divides the diameter into 2, and the radius of the circle is 16 units

The radius of the circle and the tangent line meet at a right angle.

This means that:

CE² = r² + DE² ------ Pythagoras theorem

So, we have:

34² = r² + 30²

Evaluate the squares

1156 = r² + 900

Rewrite as:

r² = 1156 - 900

Evaluate

r² = 256

Take the square root of both sides

r = 16

Hence, the radius of the circle is 16 units

Read more about radius at:

https://brainly.com/question/9554871

#SPJ2

Step-by-step explanation:

If it's a straight line the use formula

[tex]y = mx + c[/tex]

m= gradient of line

c = y-intercept

we know that y-intercept is 4 so coordinate is

(0,4)

Equation also passes (2,10)

Use both coordinate to find gradient

m= vertical distance / horizontal distance

= (10-4) / (2-0)

= 3

y = 3x + 4

Answer:0.75

Step-by-step explanation:

trust me

Answer:

20

Step-by-step explanation:

25*4/5=5*4=20

Answer:

20

Step-by-step explanation:

25 x 4/5=100/5=20

Answer:

1.875

Step-by-step explanation:

The rate of change is the derivative of the function.

[tex]f(x) = \frac{10}{x-4}\\\\f'(x)=10\times \frac {d}{dx}\frac{1}{x-4}\\\\f'(x)=\frac{-10}{(x-4)^{2}}\\\\f'(2) = \frac{-10}{(2-4)^{2}} =-2.5\\\\f'(8)= \frac{-10}{(8-4)^{2}} =-0.625\\[/tex]

So, the rate of change is

f'(8) -  f'(2) = - 0.625 + 2.5 = 1.875

Answer:

Number of shopper buy from sale [3,000shopper] = 600 (Approx.)

Step-by-step explanation:

Given:

Number of shopper in mall = 60

Number of shopper buy from sale = 12

Find:

Number of shopper buy from sale if total number number of shopper are 3,000

Computation:

Number of shopper buy from sale [3,000shopper] = 3000[Number of shopper buy from sale/Number of shopper in mall]

Number of shopper buy from sale [3,000shopper] = 3000[12 / 60]

Number of shopper buy from sale [3,000shopper] = 3000[1/5]

Number of shopper buy from sale [3,000shopper] = 600 (Approx.)

Answer:

Step-by-step explanation:

yes,      (given number) / 5

Answer:

Alternate interior angles.

Step-by-step explanation:

Answer:

[tex]d = 0.112* 10^3[/tex]

Step-by-step explanation:

Given

[tex]h = 8.4 * 10^3[/tex]

[tex]d = \sqrt{\frac{3h}{2}}[/tex]

Required

Find d

We have:

[tex]d = \sqrt{\frac{3h}{2}}[/tex]

Substitute: [tex]h = 8.4 * 10^3[/tex]

[tex]d = \sqrt{\frac{3*8.4 * 10^3}{2}}[/tex]

[tex]d = \sqrt{\frac{25.2 * 10^3}{2}}[/tex]

[tex]d = \sqrt{12.6 * 10^3}[/tex]

Express as:

[tex]d = \sqrt{1.26 *10* 10^3}[/tex]

[tex]d = \sqrt{1.26 *10^4}[/tex]

Split

[tex]d = \sqrt{1.26} *\sqrt{10^4}[/tex]

[tex]d = 1.122* 10^2[/tex]

To write in form of: [tex]a * 10^b[/tex]

The value of a must be: [tex]0 \le a \le 1[/tex]

So, we have:

[tex]d = 0.1122* 10 * 10^2[/tex]

[tex]d = 0.1122* 10^3[/tex]

Approximate

[tex]d = 0.112* 10^3[/tex]

Answer: The test statistic for this hypothesis test =1.597

Step-by-step explanation:

When population standard deviation is unknown, we use t-test statistic:

[tex]t=\dfrac{\overline{x}-\mu}{\dfrac{s}{\sqrt{n}}}[/tex]

[tex]\overline{x}[/tex] = sample mean, [tex]\mu[/tex] = population mean , s= sample standard deviation, n = sample size.

As per given,

[tex]t=\dfrac{10.7-10}{\dfrac{3.1}{\sqrt{50}}}\\\\=1.59669273171\approx1.597[/tex]

Hence, the test statistic for this hypothesis test =1.597

Answer:

7:55 PM

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

5[tex]ft^2[/tex] is the area of the original piece of fabric.

Step-by-step explanation:

0.625 x 8 = 5

=================================================

Explanation:

There are B = 3+5+4 = 12 marbles total, of which A = 12-5 = 7 are not black. Or you could note that we have A = 3 red + 4 white = 7 marbles that are not black.

The probability of selecting a non-black marble is A/B = 7/12

7/12 = 0.5833 = 58.33% approximately

Answer: 2/5

Step-by-step explanation:

Answer: 6/15

1. Drawing a red marble from a bag that contains 3 red marbles and 5 purple marbles. ... 4. A bag contains 6 red chips, 9 white chips, and 5 blue chips. A chip is selected and then replaced. ... from the box without replacement of the first draw. ... d. green first, purple second. E. -DO. 6. Find the probability of each event for more than one

Answer:

Step-by-step explanation:

x − 5 = 0   ⇒   x1 = 5

3x + 1 = 0   ⇒   x2 = −1

3

≈ −0.333333

Factorization:

(x − 5)(3x + 1) = 0

Standard form:

3x2 − 14x − 5 = 0

Extrema:

Min = (2.333333, −21.333333)

Answer:

( 3 x + 1 )  ( x − 5 )

Volume of the new similar cylinder is equals to 340,426.24 in.³.

" Volume is defined as the total space occupied by any three dimensional objects enclosed in it."

Formula used

Volume of the cylinder = πr²h

r = radius of the cylinder

h = height of the cylinder

value of π = 3.14

According to the question,

radius of the cylinder = 11 in.

height of the cylinder = 14 in.

Dimensions of new cylinder are quadrupled means 4times.

New radius = 44 in.

New height = 56 in.

Substitute the value in the formula we get,

Volume of the new cylinder = (3.14) ×(44)² × (56)

                                      = 340,426.24 in.³

Hence, volume of the new similar cylinder is equals to 340,426.24 in.³.

Learn more about volume here

https://brainly.com/question/1578538

#SPJ2

Answer:

H1 : μ < 1225

Step-by-step explanation:

The alternative hypothesis in carrying out a statistical test could be explained as a notion which aims to displace or rival an initial position, the null hypothesis.

When declaring an hypothesis, the statement compares the initial or population mean in the hypothesis statement and not the result or outcome of the sample statistic.

In the scenario above :

The null is of the notion that :

H0 : μ = 1225 ;

Hence, the stance of the alternative which is that the mean is lower or less will be written as :

H1 : μ < 1225

The hypothesis test is carried out by the students where the alternate hypothesis is [tex]\rm H_1 : \mu < 1225[/tex] and this can be determined by using the given data.

Given :

Given that the office of the Registrar estimates that on average it costs students $1,225 per month to live off-campus that means the mean is 1225.

The hypothesis test is carried out by the students where the null hypothesis and alternate hypothesis is given by:

Null hypothesis is given by --   [tex]\rm H_0 : \mu = 1225[/tex]

Alternate Hypothesis is given by --   [tex]\rm H_1 : \mu < 1225[/tex]

The hypothesis test is carried out by the students where the alternate hypothesis is [tex]\rm H_1 : \mu < 1225[/tex].

For more information, refer to the link given below:

https://brainly.com/question/23017717

Answer:

Solution given:

perpendicular [P]=15m

base[B]=8m

hypotenuse [H]=17m

rate :4 plants per square metre

no of plants=?

we have

Area of triangular garden: ½(P*B)=½(15*8)=60m²

Now

Total no of plants =rate ×Area =4×60=240

Michael needs 240 plants in the garden

Answer:

no

Step-by-step explanation: