Subtract the complex numbers.

(5 + 4i) - (7 + 8i)

Answer:

72%

Step-by-step explanation:

Answer:

[tex]\mathbf{ \sqrt{\dfrac{15.7}{4} + \dfrac{10.6}{3}} }[/tex]

Step-by-step explanation:

Given that:

[tex]\overline x_1 =[/tex] the average diameter of 4 randomly select sequoia trunk from giant trees

[tex]\overline{x_2}[/tex] = the average diameter of 3 randomly selected trunk in California trees.

Thus;

sample size [tex]\mathbf{n_1 = 4 \ \ \& \ \ n_2 = 3}[/tex]

Variance:

[tex]\mathbf{\sigma_1^2 = 15.7 }[/tex]

[tex]\mathbf{\sigma_2^2 = 10.6 }[/tex]

Recall that:

[tex]\mathbf {( \overline x_1 - \overline x_2) \sim Normal \Big ( \mu_1 -\mu_2 \ , \ \dfrac{\sigma_1^2}{n_1} + \dfrac{\sigma_12^2}{n_2} \Big )}[/tex]

[tex]\mathbf{Mean ( \overline x_1 - \overline x_2) = \mu_1 - \mu_2}[/tex]

Therefore:

The standard deviation [tex]\mathbf{ \overline x_1 - \overline x_2 = \sqrt{\dfrac{\sigma_1^2}{n_1} + \dfrac{\sigma_2^2}{n_2} } }[/tex]

[tex]\mathbf{ \overline x_1 - \overline x_2 = \sqrt{\dfrac{15.7}{4} + \dfrac{10.6}{3}} }[/tex]

The standard deviation of the sampling distribution of the difference in the sample means is 9.95

The given parameters are:

For a normal distribution we have:

[tex]\bar x_1 - \bar x_2 = \sqrt{\frac{\sigma_1^2}{n_1} +\frac{\sigma_2^2}{n_2}}[/tex]

So, the equation becomes

[tex]\bar x_1 - \bar x_2 = \sqrt{\frac{15.7^2}{4} +\frac{10.6^2}{3}}[/tex]

Evaluate the exponents

[tex]\bar x_1 - \bar x_2 = \sqrt{\frac{246.49}{4} +\frac{112.36}{3}}[/tex]

[tex]\bar x_1 - \bar x_2 = \sqrt{61.62+37.45}[/tex]

Evaluate the sums

[tex]\bar x_1 - \bar x_2 = \sqrt{99.07}[/tex]

Evaluate the square roots

[tex]\bar x_1 - \bar x_2 = 9.95[/tex]

Hence, the standard deviation of the sampling distribution of the difference in the sample means is 9.95

Read more about sampling distribution at:

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Answer:

PV= $72,866.33

Step-by-step explanation:

Giving the following information:

Interest rate= 6% compounded semiannually

Number of periods= 26*2= 52 semesters

Future value= 338,893

To calculate the initial investment (PV), we need to use the following formula:

PV= FV/(1+i)^n

i= 0.06/2= 0.03

PV= 338,893 / (1.03^52)

PV= $72,866.33

Answer:

The correct answer is $72,866.33

Answer:

Yes. Felix is correct.

Step-by-step explanation:

Find out how much ml does a can of lemonade have, I would assume its 330ml since I searched up the ml of a lemonade can.

Find out how much cans of lemonade there are in 2 packs of 8.

2 packs = 8 x 2 = 16 cans of lemonade

Now find out how much ml 16 lemonade cans equal to.

1 can of lemonade = 330ml

16 cans of lemonade = 330 x 16 = 5280ml

Now let's find 5 bottles of 1 litre.

1 litre x 5 = 5 litres.

5280 = 5 litres and 280ml

So Felix is correct about 2 packs of 8 cans is more than 5 bottles of 1 litre.

Answer:

0.45 and 0.5

Step-by-step explanation:

plato/edmentum

The 90% confidence interval for the true proportion of club members who use compost is given as (0.4, 0.507)

This refers to the probability of a parameter falling across a set of values around the mean.

To find the 90% confidence interval,

Probability=  45%= 0.45

Level of significance= 90%

1-0.90

= 0.10

[tex]z\alpha /2 = z(0.1/2) = 0.05[/tex]

The value of 0.05

P0.05= 1.645

P ± 1.645 x [tex]\sqrt{P0-p/n}[/tex]

0.45 ± 1.645 * [tex]\sqrt{0.48 (1-0.45)/200}[/tex]

0.45 ± 1.645 * 0.035178

0.45 ± 0.0578

0.45 - 0.0578, 0.45 + 0.0578

(0.4, 0.507)

Read more about confidence intervals here:

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Answer: 234 in^3

Step-by-step explanation:

The area of a parallelogram is simply length * height.

Answer:

$65.60

Step-by-step explanation:

4×16.40 = 4×(16+0.40) = (4×16) + (4×0.40) = 64 + 1.60 = 65.60

9514 1404 393

Answer:

  7

Step-by-step explanation:

The total length of ribbon is ...

  (10)(2.1 ft) = 21 ft

There are 3 feet in a yard, so the number of yards is ...

  (21 ft)×(1 yd)/(3 ft) = 7 yd

Answer:

La ética es una rama de la filosofía que se ocupa de la reflexión crítica sobre las acciones de los hombres. En un sentido general, la ética busca establecer los criterios para juzgar si una acción puede calificarse de correcta o incorrecta, y para evaluar los motivos y consecuencias de dicha acción. Las cuestiones éticas también juegan un papel importante en la política, los negocios y la medicina, y en campos de la ciencia y el estudio como la historia, la biología y la sociología, la ética de la profesión es ocasionalmente un tema de discusión.

Así, la ética implica una evaluación de las acciones de las personas, calificándolas como correctas o incorrectas a los ojos de la sociedad. De esta manera, influye en la forma en que las personas realizan o dejan de realizar una determinada acción, ya que estas consideran sus consecuencias positivas o negativas al momento de realizarla.  

Answer:

A

Step-by-step explanation:

I think letter C the die is consisting of 6 number 1,2,3,4,5,6 and the coin H,T. The probability of tossing a coin are only two while rolling a die has six probability that it will land either three or fou.r

Answer:

Cystic fibrosis probability is remote in current case.

Step-by-step explanation:

Cystic fibrosis is the disease in which patient suffers lung and intestine clog due to mucus. There is chance of cystic fibrosis in children when one of parent has history of such a disease. If one parent has defective genes and other parent has healthy genes then there is very remote chances of this disease in child.

This question is incomplete, the complete question is;

Nine pieces of 8-in. × 12-in. duct that is 2[tex]\frac{2}{3}[/tex] ft in length is needed for a building. What is the total length (in ft) needed?

Answer:

the total length needed is 24 ft

Step-by-step explanation:  

Given the data in the question;

the length of one piece of 8-in. × 12-in. duct is 2[tex]\frac{2}{3}[/tex] ft

Now to find the total length for nine pieces of the duct;

we simple multiply 2[tex]\frac{2}{3}[/tex] ft  by nine

so

Total length = 9 × 2[tex]\frac{2}{3}[/tex]  

we convert the mixed fraction to improper fraction

2[tex]\frac{2}{3}[/tex]  = 8/3

so

Total length = 9 × (8/3) ft

Total length = 24 ft

Therefore, the total length needed is 24 ft

Step-by-step explanation:

3rd one is the answer

-2x+1

Answer:

f(x) = 2x + 1

Step-by-step explanation:

You can plug in the value to each one and see if the function is true. The only one in which the function is true is f(x) = 2x + 1, so the answer is 2x + 1.

Answer:

5:6

Step-by-step explanation:

since you are dividing it by 4

Answer:

105

Step-by-step explanation:

0.2(x)=21

x=21/0.2

x=105

Answer:

12.

Step-by-step explanation:

This is how to round 12.36 to the nearest whole number. In other words, this is how to round 12.36 to the nearest integer.

12.36 has two parts. The integer part to the left of the decimal point and the fractional part to the right of the decimal point:

Integer Part: 12

Fractional Part: 36

Our goal is to round it so we only have an integer part using the following rules:

If the first digit in the fractional part of 12.36 is less than 5 then we simply remove the fractional part to get the answer.

If the first digit in the fractional part of 12.36 is 5 or above, then we add 1 to the integer part and remove the fractional part to get the answer.

The first digit in the fractional part is 3 and 3 is less than 5. Therefore, we simply remove the fractional part to get 12.36 rounded to the nearest whole number as:

12

Answer:

From what I know the answer is no

Step-by-step explanation:

A quadrilateral  is a shape with four equal sides, the sides on a trapezoid are not equal therefore, its not a  quadrilateral .

Answer:

True

Step-by-step explanation:

     A quadrilateral is any shape with four sides. A trapezoid does have four sides, and therefore is a quadrilateral. The difference between a trapezoid and a "regular quadrilateral" is a trapezoid only has one pair of parallel sides, why a quadrilateral like a square or rectangle has two pairs.

Have a nice day! - I know that this is late, but this problem popped up on my dashboard and I thought I would answer :)

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Answer:

bruno

Step-by-step explanation:

1+2+1+2+1+2+5+1+6+5+1+6+5+1+6=45

Answer:

36

Step-by-step explanation:

18 × 2 = 36

Because 1/2 is half of 1 kg so multiply by 2 it makes 1 kg

Answer:105

explanation: -45

+150

_ ___

105

Answer:

$33.01

Step-by-step explanation:

Answer:

33.01

Step-by-step explanation:

Answer:

42

Step-by-step explanation:

Answer:

3/4

Step-by-step explanation:

3 divided by 4

Answer:

5

Step-by-step explanation:

Answer:

$1,420.11

Step-by-step explanation:

I just took the test and got it right

Cassidy's approximate monthly payment is $1420.11 if Cassidy is planning to obtain a loan from her bank for $210,000 for a new home option (D) is correct.

It is defined as the systematic way of representing of loan payments according to the time in which the principal amount and interest are mentioned in a list manner

It is given that:

Cassidy is planning to obtain a loan from her bank for $210,000 for a new home.

A fixed annual interest rate of 2.7% compounded monthly for 15 years.

The formula is:

[tex]P=\rm \dfrac{Fp(i)}{1-(1+i)^{-1}}[/tex]

Plug all the values in the above formula:

[tex]P=\rm \dfrac{210000(2.7\%/12)}{1-(1+(2.7\%/12))^{-15\times12}}[/tex]

After calculating:

P = $1420.11

Thus, Cassidy's approximate monthly payment is $1420.11 if Cassidy is planning to obtain a loan from her bank for $210,000 for a new home.

Learn more about the amortization schedule here:

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Answer:

A) 0.8131 ≈ 0.81

B) 0.6322 ≈ 0.63

C)  0.7639 ≈ 0.77

Step-by-step explanation:

A)

Total number of  units

= 55 + 32 + 17 + 3

 = 107

hence the probability that the failure involves a gas leak

= ( 55 + 32 ) / 107

= 0.8131

B) probability that there is evidence of electrical failure given tat there is a gas leak

P ( A / B ) = [tex]\frac{P(A n B)}{P(B)}[/tex]

P( A∩B ) = 55/107 = 0.5140

P ( B ) = ( 55 + 32 ) / 107 = 0.8131

hence P ( A / B ) = 0.5140 / 0.8131 = 0.6322

A = failure due to electrical

B = failure due to gas leak

C)  Probability of a gas leak given that there is evidence of electrical failure

P ( B / A ) =  [tex]\frac{P(BnA)}{P(A)}[/tex]

P ( B ∩ A ) = 0.5140

P( A ) = ( 55 + 17 ) / 107  = 0.6729

hence P ( B / A ) = 0.5140 / 0.6729 = 0.7639

Answer: 1720

Step-by-step explanation: