What's (6+5i)(6-5i) using the foil method

To accumulate $400,000 for retirement in 35 years with a 6% interest rate, you would need to save approximately $2,090.77 per year.

We can use the formula for calculating the future value of an ordinary annuity.

The formula for the future value of an ordinary annuity is:

FV = P * ((1 + r)^n - 1) / r

In this scenario:

FV = $400,000

r = 6% = 0.06

n = 35 years

Let's substitute the values into the formula and solve for P:

\($400,000 = P * ((1 + 0.06)^35 - 1) / 0.06\)

Solving for the annual payment (P) required:

\(P = ($400,000 * 0.06) / ((1 + 0.06)^{35} - 1)\)

Using a calculator, we can evaluate this expression:

P ≈ $2,090.77

Therefore, to accumulate $400,000 for retirement in 35 years with a 6% interest rate, you would need to save approximately $2,090.77 per year.

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Hence, there is a 0.68 percent probability that the fifth driver will be the one that police officer summons over while wearing a safety belt.

The word "probability" derives from the Latin word "propitiate," which means "credibility, probability," from the noun probabilism in the 14th century (see probable). The phrase was first used in a mathematical meaning in 1718.

Part A:

The likelihood that precisely 3 drivers are buckled up can be determined using the binomial probability formula:

P(X = 3) = (5 choose 3) × (0.68)³ × (0.32)²

Where (5 choose 3) = 10 is the number of ways to choose 3 drivers out of 5.

P(X = 3) = 10 × 0.68³ × 0.32²

P(X = 3) = 0.267

Consequently, there is a 0.267 percent chance that all 3 drivers are buckled up.

Part B:

The fifth driver will be pulled by by the police officer since 4 other drivers have already been stopped. We are looking for the likelihood that the motorist is wearing a safety belt.

Since 68% of drivers are safety belt wearers, there is a 0.68 percent chance that the following motorist will be as well.

Thus, there is a 0.68 percent chance that the next vehicle the police officer pulls over is driven by a person wearing a safety belt.

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The equations that has the same value as x in 2/3(6x+12)=-24 are 4x+8 = -24 and 4x = -32 , option(a) and (e) are correct .

In the question ,

the equation 2/3(6x+12)=-24 is given

on solving for x ,we get

4x+8 = -24

4x = -24-8

4x = -32

x = -8 .

Solving option(a)

4x+8 = -24

4x = -24-8

4x = -32

x = -8

Solving for option(b)

9x+18 = -24

9x = -24-18

9x = -42

x = -42/9

solving for option(c)

4x = -16

x = -4

solving for option(d)

(18x+36)/2 = -24

18x + 36 = -48

18x = -48-36

18x = -84

x = -84/18

solving for option(e)

4x = -32

x = -32/4

x = -8

we can see that only option (a) and option(e) , given the value of x as -8 .

Therefore , the equations that has the same value as x in 2/3(6x+12)=-24 are 4x+8 = -24 and 4x = -32 , option(a) and (e) are correct .

The given question is incomplete , the complete question is

Which equation has the same value as X 2/3(6x+12)=-24 ?

Select two options

(a) 4x+8 = -24

(b) 9x+18 = -24

(c) 4x = -16

(d) (18x+36)/2 = -24

(e) 4x = -32

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TJohn's age is approximately 23.33 years, and Sharon's age is approximately 93.33 years.

And the correct graph is D.

To represent the given problem as a system of equations, we can use the following information:

John is 70 years younger than Sharon: j = s - 70

Sharon is 4 times as old as John: s = 4j

Let's plot the graph for this system of equations:

First, let's solve equation (2) for s:

s = 4j

Now substitute this value of s in equation (1):

j = s - 70

j = 4j - 70

3j = 70

j = 70/3

Substitute the value of j back into equation (2) to find s:

s = 4j

s = 4(70/3)

s = 280/3

The solution to the system of equations is j = 70/3 and s = 280/3

In the graph d, the solution to the system of equations is represented by the point (70/3, 280/3), which is approximately (23.33, 93.33) on the graph.

Therefore, John's age is approximately 23.33 years, and Sharon's age is approximately 93.33 years.

And the correct graph is D.

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The grams of cocoa does it contains is 36.57 grams

From the question, we have the following parameters that can be used in our computation:

Weight of the chocolate bar = 69

Proportion = 53%

This implies that

Grams of cocoa = weight of the chocolate bar * Proportion

Substitute the known values in the above equation, so, we have the following representation

Grams of cocoa = 53% * 69

Evaluate the products

Grams of cocoa = 36.57

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Answer:

i measures of the third angle is 18degrees

The coordinates of the y-intercept are (0, 3.5) and the coordinates of the x-intercepts are (-17.5, 0). Using these coordinates, the graph of the equation is shown below.

From the question, we are to graph the given linear equation.

To graph the equation,

We will determine the coordinates of the x-intercepts and y-intercepts.

When x = 0

y = 1/5x + 3.5

y = 1/5(0) + 3.5

y = 3.5

(0, 3.5)

When y = 0

y = 1/5x + 3.5

0 = 1/5x + 3.5

Multiply through by 5

0 = x + 17.5

x = -17.5

(-17.5, 0)

Using the coordinates of the x-axis and y-axis, the graph of the equation is shown below.

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Answer: There are no solutions.

Step-by-step explanation:

1/4(8x - 4) = 2x + 1

2x - 1 = 2x + 1

-1 = 1

Answer:

(1,-3) and (-1,-3)

Step-by-step explanation:

Since both y-values are less than 0, they will be lower than the x-axis. This works for all points.

Answer:

(1,-8)

Step-by-step explanation:

(-2,3) T<-4,-7> = (-6.-4)

(5,-1) T<-4,-7> = (1,-8)

The present value of the security that pays an annual dividend of $190 is $4750.

An annuity is when a series of payment is made over a period of time. An annuity can be for a specified period of time or forever.

Present value is the sum of discounted cash flows. In order to determine the present value of the annual dividend, divide the annual dividend by the security's annual return.

Present value = annual dividend / security's annual return

$190 / 0.04 = $4,750

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Answer:

Step-by-step explanation:

2y-17 and 40 are vertical angles so they are congruent:

2y-17=40 and

2y=57 so

y=28.5

2y-17 + 70 + 4x = 180 and we already know y is 28.5, so:

2(28.5)-17 + 70 + 4x = 180 and

57-17+70+4x=180 and

110+4x=180 and

4x=70 so

x=17.5

Answer:

he spent 2hours 50minutes snowboarding

the time he spent skiing and snowboarding minus the time he skied

5hours minus 2hours 10minutes

Answer:

Calculated value Z = 2.1097 > 1.96 at 0.05 level of significance

There is a difference between the means

Step-by-step explanation:

Step(i):-

Given that mean of the Population = 5.9pounds/square inch

Given mean of the sample = 6.0pounds/square inch

Given that variance of the Population = 0.36

The standard deviation of the Population = √0.36 =0.6

critical value (Z₀.₀₅)= 1.96

Step(ii):-

Null Hypothesis:H₀: x⁻ = μ

Alternative Hypothesis:H₁:  x⁻ ≠ μ

Test statistic

              \(Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }\)

               \(Z = \frac{6.0-5.9 }{\frac{0.6}{\sqrt{160} } }\)

              Z  =  2.1097

Final answer:-

Calculated value Z = 2.1097 > 1.96 at 0.05 level of significance

The null hypothesis is rejected

There is a difference between the means

18-3n

1) Let's apply the Distributive Property, a.k.a FOIL for this:

We always multiply the exterior factor by each number/variable and then we subtract.

2)Hence, the answer is 18-3n

Answer:

$0.40

I had the same question and it was $0.40

Answer:

$0.55

Got it on the test, hope this helps :)

Answer: = ( $52,474.75 , $69,225.25)

Therefore at 90% confidence interval = ( $52,474.75 , $69,225.25)

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean x = $60,850

Standard deviation r = $16,100.22

Number of samples n = 10

Confidence interval = 90%

z(at 90% confidence) = 1.645

Substituting the values we have;

60,850+/-1.645(16,100.22/√10)

60,850+/-1.645(5091.336602979)

60,850+/-8375.248711901

$60,850+/-8375.248711901+/- $8375.25

= ( $52474.75 , $69225.25)

Therefore at 90% confidence interval = ( $52474.75 , $69225.25)

Rate of change

Exponential functions increase faster than linear functions because the variable is at the exponent.

We have two exponential functions and two linear functions.

The exponential functions are

And

We can compare which of the exponential function grow faster by substituting x for two values.

Select x=1 and x=2

The first equation for both values is:

Now for the second function:

Therefore, the function that increases the fastest is

you cannot see the messages?

no problem, let's talk from here

did you follow the above explanation?

ok now we only have to compare both exponential functions

The answer is complete

Hope I could help you

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Answer:

\(21.7 x 10^5\)

Step-by-step explanation:

(6.2 x 10²) x (3.5 x 10³)

First, multiply the coefficients: 6.2 x 3.5 = 21.7.

Then, add the exponents: 10² x 10³ = 10^(2+3) = 10^5.

Therefore, the result is 21.7 x 10^5.

Answer:

3286000

Step-by-step explanation:

The exact solutions of the qudratic equation 3x^2 - 6x + 2 = 0 are:

a. negative 1 plus or minus the square root of 3 divided by

3 (x = (-1 ± √3) / 3) .So, option a is the correct answer.

To find the solutions of the quadratic equation 3x^2 - 6x + 2 = 0, we can use the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the solutions are given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 3, b = -6, and c = 2. Substituting these values into the formula, we have:

x = (-(-6) ± √((-6)^2 - 4(3)(2))) / (2(3))

x = (6 ± √(36 - 24)) / 6

x = (6 ± √12) / 6

x = (6 ± 2√3) / 6

x = (3 ± √3) / 3

Therefore, the exact solutions of the equation 3x^2 - 6x + 2 = 0 are:

a. negative 1 plus or minus the square root of 3 divided by 3 (x = (-1 ± √3) / 3)

So, option a is the correct answer.

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The equation of the line having slope 0 and passing through (-3,-2) is f(x) = -2.

Any horizontal line has the same y-value for every point on the line. We are given that the line passes through the point (-3,-2). This means that f(-3) = -2, since the y-value of the point (-3,-2) corresponds to the value of the function at x = -3.

This is because no matter what x-value we plug into the function, the output (y-value) will always be -2. Therefore, the equation of the line in function notation is f(x) = -2.

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None of the ordered pairs (1, 0), (-1, 1), (2, 2), and (0, 3) make both inequalities true.

To determine which ordered pair makes both inequalities true, we can substitute the given values into the inequalities and check for validity:

1. (1, 0):

  For y > -3x + 3: 0 > -3(1) + 3 -> 0 > 0, which is not true.

  For y < 2x - 2: 0 < 2(1) - 2 -> 0 < 0, which is not true.

  Therefore, (1, 0) does not satisfy both inequalities.

2. (-1, 1):

  For y > -3x + 3: 1 > -3(-1) + 3 -> 1 > 6, which is not true.

  For y < 2x - 2: 1 < 2(-1) - 2 -> 1 < -4, which is not true.

  Therefore, (-1, 1) does not satisfy both inequalities.

3. (2, 2):

  For y > -3x + 3: 2 > -3(2) + 3 -> 2 > -3, which is true.

  For y < 2x - 2: 2 < 2(2) - 2 -> 2 < 2, which is not true.

  Therefore, (2, 2) does not satisfy both inequalities.

4. (0, 3):

  For y > -3x + 3: 3 > -3(0) + 3 -> 3 > 3, which is not true.

  For y < 2x - 2: 3 < 2(0) - 2 -> 3 < -2, which is not true.

  Therefore, (0, 3) does not satisfy both inequalities.

None of the given ordered pairs satisfy both inequalities simultaneously.

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Answer:

0

Step-by-step explanation:

sin²θ + cos²θ = 1

secθcosθ = (1/cosθ)cosθ = 1

1 - 1 = 0

Answer:

Step-by-step explanation:

[x² + 2( \(\frac{7}{2}\) ) x + ( \(\frac{7}{2}\) )²] - ( \(\frac{7}{2}\) )² + 36 =

( x + 3.5)² + 23.75

or

( x + \(\frac{7}{2}\) )² + \(\frac{95}{4}\)

The table can be summarized as follows:

|          | Has a dog | Does not have a dog |

|----------|-----------|---------------------|

| Has a cat     | 2         | 3                   |

| Does not have a cat | 12        | 10                  |

To find the probability that a student chosen randomly from the class has a cat, we need to find the total number of students who have a cat (regardless of whether or not they have a dog), and divide it by the total number of students in the class.

The number of students who have a cat is 2 (those who have a dog and a cat) + 3 (those who have a cat but do not have a dog) = 5.

The total number of students in the class is the sum of all four categories: 2 (has a cat and a dog) + 3 (has a cat, does not have a dog) + 12 (does not have a cat, has a dog) + 10 (does not have a cat, does not have a dog) = 27.

So, the probability that a student chosen randomly from the class has a cat is 5/27.

Answer:

Grams

Step-by-step explanation:

Pencils are pretty light, so they should be measured in grams.

Answer:

grams :)

Step-by-step explanation:

I looked it up

Answer:

The maximum distance between supports for the beam to support a weight of 1600 lb is also 4.5 feet.

Step-by-step explanation:

We are given that weight P is inversely proportional to the distance D between the supports of the beam, and for this certain type of wooden beam, we have:

P = 7200/D

To find the distance between supports needed to carry 1600 lb, we can substitute P = 1600 in the above equation and solve for D:

1600 = 7200/D

D = 7200/1600

D = 4.5 feet

So the distance between supports needed to carry 1600 lb is 4.5 feet.

To find the maximum distance between supports for the beam to support a weight of 1600 lb, we can use the same equation and solve for P = 1600:

1600 = 7200/D

D = 7200/1600

D = 4.5 feet

Therefore, the maximum distance between supports for the beam to support a weight of 1600 lb is also 4.5 feet.

The original value for the first angle so that the angle measures form a triangle is 39.5°

For any triangle to be formed, its three interior angles must sum up to 180°. Thus the sum of the interior angles of a triangle is 180°

Considering, the angles: 115.1°, 47.5° and 93°, their sum which is 255.6° is not equal to 180° so they cannot form a triangle.

but a new value represented by x for the first angle 115.1° can be derived as follows;

x + 47.5° + 93° = 180°

x + 140.5 = 180° {subtract 140.5° from both sides}

x = 180° - 140.5°

x = 39.5°

Therefore, the new value for the first angle 115.1° that will make the angle measures form a triangle is 39.5°

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the awnser is -12,x-1{+8}