Rectangle ABCD translates 4 units down and 2 units to the right to form rectangle A'B'C'D'. The vertices of rectangle ABCD are labeled in alphabetical order going clockwise around the figure. If AB = 3 units and AD = 5 units, what is the length of B'C'?

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:

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:

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:

c. The data are continuous because the data can take on any value in an interval.

Step-by-step explanation:

Discrete data are those which can take up only specific values. Discrete data values may include the number of children in a particular school, the number of visitors received per day. All this values are specific and cannot just take up any number one f values within an interval. Continous data on the other hand can take up any number of data values between an interval. Continous data types are usually height temperature, length(distance data). There can be infinite number of possible data within interval values.

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:

* Giống nhau: đều là biểu hiện bằng tiền về lao động sống và lao động hóa trong quá trình sản xuất

* Khác nhau:

+ Về thời gian: chi phí sản xuất gắn liền với từng thời kỳ, còn giá thành sản phẩm gắn với thời hạn hoàn thành sản phẩm. ...

+ Có những chi phí được tính vào giá thành nhưng không được tính vào chi phí kỳ này.

+ Mối quan hệ chi phí và tính giá thành sản phẩm: Chi phí là cơ sở để tính giá thành, giá thành là thước đo chi phí sản xuất mà doanh nghiệp bỏ ra để có được khối lượng hoàn thành.

+ Có nhiều chi phí phát sinh trong kỳ nhưng chưa có sản phẩm hoàn thành do đó chưa có giá thành.

Step-by-step explanation:

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:

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

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

Step-by-step explanation:

Answer:

x=3

Step-by-step explanation:

Answer:

I believe that It would be b

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

Answer:

1. 8

2 . 11

[tex]3 . \sqrt{128} \ or \ 8 \sqrt2[/tex]

Step-by-step explanation:

[tex]Distance = \sqrt{(x_2 -x_1)^2 + (y_2 - y_1)^2 }[/tex]

1 . ( 5 , - 2 ) and ( 5 , 6 )

  [tex]Distance = \sqrt{(5 -5)^2 + ( 6-(-2))^2} = \sqrt{ 0 + 8^2 } = \sqrt{64} = 8[/tex]

2 . ( 8 , 6 ) and ( - 3 , 6 )

  [tex]Distance = \sqrt{( -3 -8)^2 + ( 6 - 6)^2 } = \sqrt{ (-11)^2 + 0 } = \sqrt { 121 } = 11[/tex]

3. ( 5 , - 2 ) and ( -3 , 6 )

  [tex]Distance = \sqrt{(-3 - 5)^2 + ( 6 --2)^2} = \sqrt{(-8)^2 + ( 8)^2} = \sqrt{ 64 + 64 } = \sqrt{128}[/tex]

          [tex][ \ \sqrt{128} = \sqrt{ 2 \times 64} = \sqrt{ 2 \times 8^2 } = 8 \sqrt{2} \ ][/tex]

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.

Step-by-step explanation:

7x-21 = 5x +15

7x-5x = 15 + 21

2x = 36

x = 36/2

x = 18

Answer:

x=18

Step-by-step explanation:

Distribute 7 through the parentheses

7x-21=5(x+3)

Move the variable to the left -hand side and change its sign

7x-21-5x=15

Collect like terms

2x=15+21

divide both sides of the equation by 2

x=18

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:

132.

Step-by-step explanation:

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

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

= 132.

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.

-4x²+16x-16=0

X=2

The choose (2,0)

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:

9514 1404 393

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:

I thikn the answer is B

Step-by-step explanation:

For a geometric series to diverge the absolute value of the common ratio has to be 1 or greater

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).

Answer:

Step-by-step explanation:

sine 30° = opposite / hypotenuse = 4/8 = 1/2

cosine 30° = adjacent / hypotenuse = 4sqrt(3) / 8 = sqrt(3) / 2

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.