6a + 2b = 30
6a + 9b = 51
What are a and b

Answer:

a) 0.7847 = 78.47% probability that no samples are mutated.

b) 0.9769 = 97.69% probability that at most one sample is mutated.

c) 0% probability that more than half the samples are mutated.

Step-by-step explanation:

For each sample, there are only two possible outcomes. Either they are mutated, or they are not. The probability of a sample being mutated is independent of any other sample, 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.

2% of cases.

This means that [tex]p = 0.02[/tex]

12 samples are studied

This means that [tex]n = 12[/tex].

(a) No samples are mutated.

This is [tex]P(X = 0)[/tex]. So

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

[tex]P(X = 0) = C_{12,0}.(0.02)^{0}.(0.98)^{12} = 0.7847[/tex]

0.7847 = 78.47% probability that no samples are mutated.

(b) At most one sample is mutated.

This is:

[tex]P(X \geq 1) = P(X = 0) + P(X = 1)[/tex]

Then

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

[tex]P(X = 0) = C_{12,0}.(0.02)^{0}.(0.98)^{12} = 0.7847[/tex]

[tex]P(X = 1) = C_{12,1}.(0.02)^{1}.(0.98)^{11} = 0.1922[/tex]

[tex]P(X \geq 1) = P(X = 0) + P(X = 1) = 0.7847 + 0.1922 = 0.9769[/tex]

0.9769 = 97.69% probability that at most one sample is mutated.

(c) More than half the samples are mutated.

This is:

[tex]P(X > 6) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12)[/tex]

So

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

[tex]P(X = 0) = C_{12,7}.(0.02)^{7}.(0.98)^{5} \approx 0[/tex]

So the others(greater than 7) wil be 0 too

0% probability that more than half the samples are mutated.

Answer:

x=3

Step-by-step explanation:

Answer:

SSS (side, side, side)

hope it helps:))!!!

Answer:

Following are the responses to the given question:

Step-by-step explanation:

Mean Absolute Deviation MAD

[tex]MAD = \sum_{i=1}^{n} \frac{\left | actual_{i}-forecast_{i} \right |}{n}[/tex]

Mean squared error  

[tex]MSE=\Sigma^{n}_{i=1} \frac{(Actual_i - Forecast_i)^2}{(n - 1)}[/tex]

linear trend equation is [tex]Ft = 124 + 2t[/tex]

[tex]MAD = \frac{23}{10} = 2.3\\\\MSE = \frac{91}{9}= 10.11\\\\[/tex]

Naive method

[tex]MAD = \frac{36}{9} = 4\\\\MSE = \frac{202}{8}=25.25\\\\MAD (Naive) = 4\\\\MAD (Linear) =2.3\\\\MSE (Naive)=25.25\\\\MSE (Linear)=10.11\\\\[/tex]

Please find the attached file.

Answer:

x = -1

Step-by-step explanation:

Add two on both sides. This makes the equation 7x + 6 = x. Now subtract 7x on both sides. This equals 6 = -6x. Divide by -1 on both sides. x = -1.

Answer:

132.

Step-by-step explanation:

That would be the number of permutations of 2 from 12.

12P2 = 12! / (12-2)!

= 132.

Answer:

f(g(x)) = 15x + 2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Distributive Property

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

f(x) = 5x + 7

g(x) = 3x - 1

Step 2: Find

Answer:

Step-by-step explanation:

n + d = 12

0.05n + 0.1d = 1    ║ × ( - 10 )

n + d = 12 ..... (1)

- 0.5n - d = - 10 ..... (2)

(1) + (2)

0.5n = 2 ⇒ n = 4

d = 12 - 4 = 8

There are 4 nickels and 8 dimes in the pocket.

Answer:

161 speed of plain in still air

Mark in brainlist

9514 1404 393

Answer:

  (x^(1/2))(x^(1/2)) = x^(1/2 +1/2) = x^1 = x

Step-by-step explanation:

The rule of exponents is ...

  (x^a)(x^b) = x^(a+b)

From which ...

  (x^a)(x^a) = x^(a+a) = x^(2a)

So, if we want two identical factors that have a product of x = x^1, then the exponents of those factors will be such that ...

  x^(2a) = x^1

  2a = 1

  a = 1/2

The square root is defined as one of two identical factors that have a product equal to the specified value. That is ...

  (√x)(√x) = x

Above, we have shown that ...

  (x^(1/2))(x^(1/2)) = x

so, we can conclude ...

  √x = x^(1/2)

_____

Additional comment

In like fashion, we can show that the n-th root of a number is the same as that number to the 1/n power. It's really a matter of definition. Since the square of x^(1/2) is x, we call x^(1/2) the square root. It is used commonly enough that it has its own symbol: √x.

Answer:

Squaring and square root are inverses, so one should "undo" the other. That is, squaring the square root of a number results in the number. Using the power of a power rule, you multiply the exponents. Since a number to the first power is itself, the product of the exponents must equal 1. This means that the power of the square root must be the reciprocal of 2, or one half.

Step-by-step explanation:

Answer:11 degrees at sunrisde the temp was -1 degree

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given that the adult dosage = 15 mg/day.

1. The pediatric dosage for a child weighing 52 pounds can be determined by;

Pediatric Dosage = (Child weight divided by 150 lbs.) x Adult Dose

                             = [tex]\frac{52}{150}[/tex] x 15 mg/day

                             = 5.2 mg/day

The pediatric dosage of the medication for a child weighing 52 pounds is 5.2 mg per day.

2. The medication can be consume by either an adult or a  pediatric at a measured quantity. If an adult takes 15 mg of the medication per day, then any child whose weight is 52 pounds can take a maximum quantity of 5.2 mg of the medication per day. This implies that a child of the measured weight should not take more than 5.2 mg of the medication per day, and probably not at once.

The dosage of the medication for a pediatric can be determined by;

Pediatric Dosage = (Child weight divided by 150 lbs.) x Adult Dose

That is, once the weight of a child is determined, the dosage can be calculated.

Answer:

20

Step-by-step explanation:

your mom

Answer:

I believe that It would be b

Answer:

true.

hope it helps..

Answer:

Yes, the result does not have statistical significance

Yes, the result has practical significance

Step-by-step explanation:

An experiment or claim may be said to be statistically significant if it's occurence is likely not due to chance for a certain level of stated significance. From the scenario described, it is stated that if vegetarian diet has no effect on blood, then the result obtained wipukd likely occur in less Than 1 of 100 ; this is < 0.01. This means that the effect of vegetarian diet on blood could not have occurred by chance. Hence, result is statistically significant.

The result does have practical significance too, since there is a distinctive difference in blood pressure of non - vegetarians(138mmHg) and Vegetarians (124mmHg).

-4x²+16x-16=0

X=2

The choose (2,0)

Answer:

Mean = 21.413

Median = 16.5

Standard deviation = 19.182

0.768

Step-by-step explanation:

Given the data :

Ordered data, X : 4.3 6.1 7.4 10.7 13.1 13.6 14.7 16.5 17.1 17.4 18.7 22.3 36.7 43.2 79.4

The sample size, n = 15

The mean, m= ΣX / n = 321.2 / 15 = 21.413

The median, Md:

1/2(n + 1)th term

1/2 (15 +1) th term

1/2(16) = 8th term

Median = $16.5

The standard deviation, s = √[Σ(x - m)²/ n]

The standard deviation obtained using a calculator is ; 19.182

Coefficient of skewness : = 3(m - Md) / s

= 3(21.413 - 16.5) / 19.182

= 14.739 / 19.182

= 0.768

Step-by-step explanation:

everything can be found in the picture

Answer:

11, 12, 13, 21, 22 and 23

Step-by-step explanation:

Given

[tex]Procedures = 2[/tex]

[tex]1 \to[/tex] Step 1

[tex]2 \to[/tex] Step 2

[tex]3 \to[/tex] Step 3

Required

List all possible experimental outcomes

From the question, we understand that:

[tex]Procedure\ 1 = 3\ steps[/tex]

[tex]Procedure\ 2 = 2\ steps[/tex]

So, the total possible steps (n) are:

[tex]n=Procedure\ 1 * Procedure\ 2[/tex]

[tex]n = 3 * 2[/tex]

[tex]n = 6\ steps[/tex]

Such that the 2nd steps cannot take the value of 3.

So, the outcomes are: 11, 12, 13, 21, 22 and 23

Answer:

Thus, The steps applied to ABCD to obtain A'B'C'D' is shifted x coordinate 2 units to right and y coordinate 3 units down

Answer:

Population = All Sandhill cranes bred and hatched in Alaska that migrate south

Sample = The 50 crane samples which are tagged yearly.

Step-by-step explanation:

The population refers to all members or subjects which belongs to a defined study. Each and every subject which meets the requirement of a study makes up the population.

The sample however, is a subset of the population, the sample is a smaller group of subject which is selected from the population randomly to for a representative sample of the population. Here, it is the 50 sampled sandhill cranes bed per year.

Answer:

These are the answers

Step-by-step explanation:

Answer:

Step-by-step explanation:

mean = sum of data / no of data

=3 + 5 + 2 + 10 + 6 + 3 + 7 + 3/8

=36/8

4.5

to calculate the given data must be arranged in ascending to descending order . So , the data are

2 , 3 , 3 , 3 , 5 , 6 , 7 , 10

Median = N + 1/2    (N means no of data)

=8 + 1/2

=9/2

=4.5

=(4 + 5) th term / 2

=3 + 5/2

=8/2

=4

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Answer:

  (64x^28)/(5y^22)

Step-by-step explanation:

The applicable rules of exponents are ...

  (a^b)^c = a^(bc)

  (a^b)(a^c) = a^(b+c)

  (a^b)/(a^c) = a^(b-c)

__

First, eliminate the outside exponent on the left factor. Then use the above rules to combine factors with the same base.

  [tex]\displaystyle\left(\frac{4x^4}{5y^6}\right)^5\cdot\left(\frac{5^4y^8}{4^2x^{-8}}\right)=\frac{(4^5x^{20})(5^4y^8)}{(5^5y^{30})(4^2x^{-8})}=4^{5-2}5^{4-5}x^{20-(-8)}y^{8-30}\\\\=4^35^{-1}x^{28}y^{-22}=\boxed{\frac{64x^{28}}{5y^{22}}}[/tex]

Answer:

3a - b = 1

Step-by-step explanation:

a = (2-3)

b = (1-5)

Substitute the values of a and b to the 3a-b.

3(2-3) - (1-5)

6-9 - (-4)

6 - 9 + 4

-3 + 4

= 1

Therefore, 1 is the answer.

Step-by-step explanation:

Solution :

Given,

a= (2 - 3)

b= (1 - 5)

Now,

3a-b

= 3(2 - 3) -(1 - 5)

= 3×(-1) - (-4)

= -3+4

= 1

.

. .The value of 3a-b is 1