Solve each equation for the specified variable

Answer:

18c^3d^9

Step-by-step explanation:

2c^3 d^2 * 9d^7

We know that  we add the exponents when the base is the same

2*9  c^3 d^(2+7)

18c^3d^9

Here are the complex numbers with their simplified differences

(7 -3i) - (6 - 4i) = 1 + i

(4 + 3i) - (6 +2i) = -2 - i

(4 + 5i) - (3 - 4i) = 1 + 9i

(5 + 4i) - (9 + i) = -4 + 3i

A complex number is when a real number and an imaginary number are added together

Complex numbers are usually in the form : a + bi

where a and b are real numbers and i is an imaginary number

An example of a complex number:

in this complex number : (7 -3i)

7 and 3 are real numbers while i is the imaginary number

How to simplify complex numbers

In order to simplify these set of complex numbers, remember that when there is a bracket in mathematics it signifies multiplication.

Here are the set of rules that guide multiplication :

1. When a negative value is multiplied by a positive value, the value becomes a negative value

For example, -1 x 1 = -1

2. When a positive value is multiplied by a positive value, the value remains a positive value

For example, 1 x 1 = 1

3. When a negative value is multiplied by a negative value, the value becomes a negative value

For example,-1 x -1 = 1

Solution to the questions:

Using the above information, the complex numbers can now be simplified

1. (7 -3i) - (6 - 4i)

this above equation becomes :

7 - 3i - 6 + 4i

add like terms together

7 - 6 - 3i + 4i  = 1 + i

2. (4 + 3i) - (6 +2i)

this above equation becomes :

4 + 3i - 6 - 2i

add like terms together

4 - 6 +3i - 2i = -2 - i

3. (4 + 5i) - (3 - 4i)

this above equation becomes :

4 + 5i - 3 + 4i

add like terms together

4 - 3 + 5i + 4i  = 1 + 9i

4. (5 + 4i) - (9 + i)

this above equation becomes :

5 + 4i -9 -i

add like terms together

5 -9 + 4i - i  = -4 + 3i

In order to solve for complex numbers remember that a bracket in mathematics means that a multiplication operation should be carried out. Also, pay cognisance to the rules guiding the multiplication of negative and positive numbers

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Answer: Choice A) M = 0.25n + 100

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

Explanation:

For now, I'll treat n as x, and M as y.

In other words,

Let's select two points from this graph. I'll pick (200,150) and (400,200)

The slope of the line through those points is

m = (y2-y1)/(x2-x1)

m = (200-150)/(400-200)

m = 50/200

m = 0.25

Now we'll use the point (x,y) = (200,150) along with that slope value to find the y intercept b

y = mx+b

150 = 0.25*200+b

150 = 50+b

150-50 = b

100 = b

b = 100

You could also use (x,y) = (400,200) and you should get the same b value.

In fact, any other point from this graph works as well.

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

Since m = 0.25 and b = 100, we go from y = mx+b to y = 0.25x+100

This then translates over to M = 0.25n + 100 which is choice A

To help verify this, let's say we plugged in n = 100

M = 0.25*n + 100

M = 0.25*100 + 100

M = 25 + 100

M = 125

Which is confirmed by what the graph shows. I'll let you check the other points as well.

100 = 10², so the sum you're considering is the sum of squared integers starting with 10.

[tex]\displaystyle 100+121+144+168+\cdots+n^2+\cdots = \boxed{\sum_{k=10}^\infty k^2}[/tex]

The [tex]\pm[/tex] symbol means "plus minus".

Writing [tex]1.5 \pm 0.85[/tex] is the same as saying [tex]1.5 + 0.85\ \text{ or } \ 1.5 - 0.85[/tex]

The lower bound, or left endpoint, is 1.5 - 0.85 = 0.65

The upper bound, or right endpoint, is 1.5 + 0.85 = 2.35

Based on what you have, it looks like you probably followed those steps. However, you have the items in the wrong order. You should have 0.65 listed first and 2.35 listed last. Also, you need to have "or equal to" as part of the inequality sign.

So you should have [tex]0.65 \le x \le 2.35[/tex]

As for your graph, you have the endpoints in the wrong spot.

The left endpoint should be between the 0.6 and 0.7 to indicate 0.65

The right endpoint should be between 2.3 and 2.4 to indicate 2.35

See the diagram below.

Answer:

a) 0.55 = 55% probability that the person is traveling on business

b) 0.14 = 14% probability that the person is traveling for business on a privately owned plane.

c) 0.2545 = 25.45% probability that the person arrived on a privately owned plane, given that the person is traveling for business reasons.

d) 0.2 = 20% probability that the person is traveling on business, given that the person is flying on a commercially owned plane.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

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

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

Question a:

50% of 60%(major airlines)

70% of 20%(privately owned airplanes)

80% of 100 - (60+20) = 20%(comercially owned airplanes). So

[tex]p = 0.5*0.5 + 0.7*0.2 + 0.8*0.2 = 0.55[/tex]

0.55 = 55% probability that the person is traveling on business.

Question b:

70% of 20%, so:

[tex]p = 0.7*0.2 = 0.14[/tex]

0.14 = 14% probability that the person is traveling for business on a privately owned plane.

Question c:

Event A: Traveling for business reasons.

Event B: Privately owned plane.

0.55 = 55% probability that the person is traveling on business.

This means that [tex]P(A) = 0.55[/tex]

0.14 = 14% probability that the person is traveling for business on a privately owned plane.

This means that [tex]P(A \cap B) = 0.14[/tex]

Desired probability:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.14}{0.55} = 0.2545[/tex]

0.2545 = 25.45% probability that the person arrived on a privately owned plane, given that the person is traveling for business reasons.

Question d:

Event A: Commercially owned plane.

Event B: Business

80% of those arriving on other commercially owned planes are traveling for business reasons.

This means that:

[tex]P(B|A) = 0.2[/tex]

0.2 = 20% probability that the person is traveling on business, given that the person is flying on a commercially owned plane.

Answer:

Option B, 15.6

Step-by-step explanation:

Using the Pythagoras theorem,

√(11²+11²)

= √(121+121)

= √(2×121)

= √121×√2

= 11√2

= 15.6

Answered by GAUTHMATH

Option B - 15.6 is Correct.

We have a figure in which a right angled triangle is shown with it base (b) = 11 and perpendicular(p) = 11.

We have to find the value of c or hypotenuse (h).

According to the Pythagoras theorem : for a right angled triangle -

[tex](h)^{2} = (b)^{2} +(p)^{2}[/tex]

According to the question -

[tex]b =11\\p =11\\h=c[/tex]

Substituting the values, we get -

[tex]c^{2} = (11)^{2} + (11)^{2} \\c^{2} = 121 + 121\\c^{2} =242\\c=15.55[/tex]

Rounding to nearest 10, we get -

c = 15.6

Hence , Option B is correct.

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Answer:

(42% ; 48%)

We are 99% confident that the percentage of all adults in the country who favor a plan to break up the megabanks is between 42% and 48%

Step-by-step explanation:

The confidence interval is used to estimate the range of values for which the population value may lie at a certain level of confidence.

Given that :

Phat = 45%

Margin of error = ±3%

The confidence interval is defined as :

C. I = Phat ± margin of error

C. I = 45% ± 3%

Lower boundary :

45% - 3% = 42%

Upper boundary :

45% + 3% = 48%

C.I = (42% ; 48%)

We are 99% confident that the percentage of all adults in the country who favor a plan to break up the megabanks is between 42% and 48%

Let the number be x

ATQ

[tex]\\ \sf\twoheadrightarrow 6x-18=96[/tex]

[tex]\\ \sf\twoheadrightarrow 6x=96+18[/tex]

[tex]\\ \sf\twoheadrightarrow 6x=112[/tex]

[tex]\\ \sf\twoheadrightarrow x=\dfrac{112}{6}[/tex]

[tex]\\ \sf\twoheadrightarrow x=7[/tex]

Answer:

can you say again please

Answer:

arcsin0.616

Step-by-step explanation:

arcsino.616

9514 1404 393

Answer:

  dy/dx = 2x +1

Step-by-step explanation:

The power rule can be used.

  d/dx(x^n) = n·x^(n-1)

Then the derivative of x² is 2x¹ = 2x, and the derivative of x = 1x⁰ = 1.

The derivative of the function is ...

  dy/dx = 2x +1

Answer:

A. Increase the level of confidence

Step-by-step explanation:

The margin of error is given by:

The margin of error is:

[tex]M = \frac{Ts}{\sqrt{n}}[/tex]

In which T is related to the level of confidence(the higher the level of confidence, the higher T is), s is the standard deviation of the sample and n is the size of the sample.

Increase the width:

That is, increasing the margin of error, as the width is twice the margin of error, the possible options are:

Increase T -> increase confidence level.

Increase s -> Increase the standard deviation of the sample.

Decrease n -> Decrease the sample size.

Thus, the correct answer is given by option A.

9514 1404 393

Answer:

  C

Step-by-step explanation:

The graph shows two vertical asymptotes, so the relevant function will be zero in the denominator for two different x-values. The only possibility is ...

  [tex]F(x)=\dfrac{1}{(x-1)(x+1)}[/tex]

Answer

33 percent

Step-by-step explanation:

Answer:

33 squares are shaded 23%

Step-by-step explanation:

I hope this answer works out for you if it doesn't I'm really sorry have a great day

Answer:

Rational number

Step-by-step explanation:

Given

[tex]5\frac{3}{8}[/tex]

Required

The subset it belongs to

Express as improper fraction

[tex]5\frac{3}{8} = \frac{43}{8}[/tex]

The above number is rational because it is represented by the division of 2 integers, i.e. 43 and 8 are integers

Express as decimals

[tex]5\frac{3}{8} = 5.375[/tex]

The above number cannot be classified as integers or whole because it has decimal parts

Answer:

(-16, 17)

Step-by-step explanation:

The range of the function will be (-16, 17)

The range of function f(x) = 3x + 2 overthe interval -6 < x < 5 is (-13,14)

The difference between the highest and lowest values.

The given function is  f(x) = 3x + 2

f(x) equal tp three times of x plus two.

The given interval is minus six less than x less than five.

-6 < x < 5

Which means the x values are -5, -4, -3, -2, -1, 0, 1, 2,3,4

Plus in the function

f(-5)=-15+2=-13

f(-4)=-10

f(-3)=-9+2=-7

f(-2)=-6+2=-4

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

f(0)=0+2=2

f(1)=3+2=5

f(2)=6+2=8

f(3)=9+2=11

f(4)=12+2=14

Hence the range of function f(x) = 3x + 2 overthe interval -6 < x < 5 is (-13,14)

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Answer:

5 cups

Step-by-step explanation:

sammy + 4 friends = 5 people

21/5 = 4.2

we rounded it off to 5 cups.

Answer:

( 0.742, 0.849 )

Step-by-step explanation:

sample size = 220

number of voters with positive response ( i.e. number of voters who believe the government is doing right )  = 175

Calculate the 95% confidence interval

P = 175 / 220 = 0.796

the 95% confidence interval = ( 0.796 ± 0.054 )

attached below is the detailed solution

Let x and y be the required amounts of the 35% and 60% acid solutions, respectively.

x liters of 35% acid solution contains 0.35x L of acid.

y liters of 80% acid solution contains 0.80y L of acid.

Together, a combined (x + y) L of mixed solutions contains (0.35x + 0.80y) L of acid.

You want to end up with 60 L of 65% acid solution, which means

x + y = 60

0.35x + 0.80y = 0.65 × 60 = 39

Solve for x and y :

y = 60 - x

0.35x + 0.80 (60 - x) = 39

0.35x + 48 - 0.80x = 39

0.45x = 9

x = 20

y = 40

Answer:

The only limitation is x≠0

The interval notation is (-∞,0)∪(0,∞)

Step-by-step explanation:

Set up the expression.

[tex](x+7)*(\frac{1}{x}-13)[/tex]

Multiply using FOIL.

[tex](x*\frac{1}{x})+(x*-13)+(7*\frac{1}{x})+(7*-13)[/tex]

[tex]1-13x+\frac{7}{x}-91[/tex]

[tex]-13x+\frac{7}{x}-91[/tex]

Find the Domain.

The only limitation is x≠0

The interval notation is (-∞,0)∪(0,∞)

Answer:

It will be 31.4 cm rounded off for circumference

It will be 78.53 cm2 rounded off for area

Step-by-step explanation:

Diameter = 10 cm

Radius = 10/2 cm = 5 cm

Circumference = 2×pi×radius

= 2pi×5

= 31.4 cm

Area = pi × r square

= 25 pi

= 78.53cm2

Answer:

-0.56

Step-by-step explanation:

Answer:

"She's really angry; she ordered the product last Wednesday, Don in customer  service said it would arrive a week later. It was a dollhouse for her niece, Can you take it from here?" is the best option

Step-by-step explanation:

Answer:

a. The average daily amount of time an adult spends on the internet is different than 4.5 hours.

Step-by-step explanation:

An internet provider states that, on average, the daily amount of time an adult spends on the internet is 4.5 hours.

At the null hypothesis, it is claimed that the mean is of 4.5 hours, that is:

[tex]H_0: \mu = 4.5[/tex]

A sociologist studying the behaviors of internet consumers believes the average daily amount an adult spends on the internet is different than the amount stated by the internet provider.

At the alternative hypothesis, the sociologist claim, is that the mean is different of 4.5, that is:

[tex]H_1: \mu \neq 4.5[/tex]

Thus, the correct answer is given by option a.

The partial fraction expansion takes the form

-6x/((x + 2) (x + 8)) = a/(x + 2) + b/(x + 8)

Both factors in the denominator are linear, so the numerators in the corresponding partial fractions have degree 1 - 1 = 0 and are thus constants.

Combine the fractions on the right side into one with a common denominator, then set the numerators on both sides of the equation equal to each other:

-6x = a (x + 8) + b (x + 2)

Expand the right side and collect terms by powers of x :

-6x = (a + b) x + (8a + 2b)

It follows that

a + b = -6   and   8a + 2b = 0

==>   a = -2   and   b = 8

So we end up with

-6x/((x + 2) (x + 8)) = -2/(x + 2) + 8/(x + 8)

9514 1404 393

Answer:

Step-by-step explanation:

1a. Vertical angles share a vertex and are composed of opposite rays. Here, angles 2 and 4 are vertical angles.

1b. Consecutively numbered angles are adjacent, as are angles 1 and 5. The pairs of interest can be chosen from ...

  1&2, 2&3, 3&4, 4&5, 5&1

__

2. Angles 1 and 3 have the same measure, because they are vertical angles. Then we have ...

  78° = (5x -2)°

  80 = 5x . . . . . . . divide by °, add 2

  16 = x . . . . . . . divide by 5

Answer:

12.04

Step-by-step explanation:

Find the number in the hundredth place  4  and look one place to the right for the rounding digit  1 . Round up if this number is greater than or equal to  5  and round down if it is less than  5 .