now examine |a + bi| and complete the definition below. the absolute value of any complex number a + bi is the from (a, b) to (0, 0) in the complex pl

Answer:

16 years

Step-by-step explanation:

We can use the formula for compound interest to solve this problem:

A = P(1 + r/n)^(nt)

where A is the final amount, P is the principal (initial amount), r is the annual interest rate (as a decimal), n is the number of times per year the interest is compounded, and t is the number of years.

In this case, P = $5000, r = 0.05 (since the annual interest rate is 5%), n = 12 (since the interest is compounded monthly), and we need to solve for t when A = $6,568.52.

Plugging in the values, we get:

$6,568.52 = $5000(1 + 0.05/12)^(12t)

Dividing both sides by $5000 and taking the natural logarithm of both sides, we get:

ln(1.313704) = ln(1 + 0.05/12)^(12t)

Using the logarithmic identity ln(a^b) = b ln(a), we can simplify the right side:

ln(1.313704) = 12t ln(1 + 0.05/12)

Dividing both sides by 12 ln(1 + 0.05/12), we get:

t = ln(1.313704) / (12 ln(1 + 0.05/12)) = 16.0

Therefore, it will take Mr. Sanchez 16 years to have $6,568.52 in the college fund, if he does not make any deposits or withdrawals. The answer is 16 years.

The square root of 169 is indeed 13.When simplifying the square root of a perfect square (a number that has an exact integer square root), we find the square root by identifying the largest perfect square factor of the given number. In this case, 169 is a perfect square because it can be expressed as 13^2.

To simplify the expression √169, we need to find the square root of 169. The square root of a number is a value that, when multiplied by itself, equals the original number.

In this case, we can calculate the square root of 169 as follows:

√169 = 13

So, the simplified form of the expression √169 is 13.

To verify this result, we can square 13 to check if it equals 169:

13^2 = 169

Therefore, the square root of 169 is indeed 13.

In general, when simplifying the square root of a perfect square (a number that has an exact integer square root), we find the square root by identifying the largest perfect square factor of the given number. In this case, 169 is a perfect square because it can be expressed as 13^2.

Taking the square root of a perfect square yields the positive and negative square roots of that number. However, when referring to the principal square root (which is typically denoted by the radical symbol), we consider only the positive square root.Hence, the simplified form of √169 is 13.

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Answer:

24 and 25

Step-by-step explanation:

I hope this helps!

Answer:

81/6250

Step-by-step explanation:

To compute the volume of the solid generated by revolving the region bounded by the curves y = 2x and y = x^2 about each coordinate axis, we'll use the shell method and the washer method separately.

a. Shell Method:

When using the shell method, we integrate along the axis of revolution (in this case, the y-axis). The volume of each shell is given by 2πrh, where r is the radius of the shell and h is its height. In this case, the radius is x, and the height is the difference between the curves y = 2x and y = x^2.

To find the volume of the solid generated by revolving the region about the y-axis, we need to determine the limits of integration. The region is bounded by y = 2x and y = x^2. By equating these two equations, we find the points of intersection:

2x = x^2

x^2 - 2x = 0

x(x - 2) = 0

This equation yields two solutions: x = 0 and x = 2. These will be the limits of integration.

The volume (V) can be calculated as follows:

V = ∫[a,b] 2πx (2x - x^2) dx

  = 2π ∫[0,2] (2x^2 - x^3) dx

  = 2π [2/3 x^3 - 1/4 x^4] |[0,2]

  = 2π [(2/3 * 2^3 - 1/4 * 2^4) - (2/3 * 0^3 - 1/4 * 0^4)]

  = 2π [(16/3 - 16/4)]

  = 2π [16/12]

  = 8π/3

Therefore, the volume of the solid generated by revolving the region about the y-axis using the shell method is 8π/3.

b. Washer Method:

When using the washer method, we integrate along the axis perpendicular to the axis of revolution (in this case, the x-axis). The volume of each washer is given by π(R^2 - r^2)h, where R is the outer radius, r is the inner radius, and h is the height of the washer. In this case, the outer radius R is 2x, the inner radius r is x^2, and the height h is dx.

To find the volume of the solid generated by revolving the region about the x-axis, we need to determine the limits of integration. The region is bounded by y = 2x and y = x^2. By equating these two equations, we find the points of intersection:

2x = x^2

x^2 - 2x = 0

x(x - 2) = 0

This equation yields two solutions: x = 0 and x = 2. These will be the limits of integration.

The volume (V) can be calculated as follows:

V = ∫[a,b] π((2x)^2 - (x^2)^2) dx

  = π ∫[0,2] (4x^2 - x^4) dx

  = π [4/3 x^3 - 1/5 x^5] |[0,2]

  = π [(4/3 * 2^3 - 1/5 * 2^5) - (4/3 * 0^3 - 1/5 * 0^5)]

  = π [(

32/3 - 64/5)]

  = π [(160/15 - 96/15)]

  = π [64/15]

Therefore, the volume of the solid generated by revolving the region about the x-axis using the washer method is 64π/15.

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h(x) = -7/6x - 25/6.

Given h(-1)=-2 and h(-7)=-9

For linear function h(x), we can use slope-intercept form which is y = mx + b, where m is the slope and b is the y-intercept.

To find m, we can use the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

h(-1) = -2 is a point on the line, so we can write it as (-1, -2).

h(-7) = -9 is another point on the line, so we can write it as (-7, -9).

Now we can find m using these points: m = (-9 - (-2)) / (-7 - (-1)) = (-9 + 2) / (-7 + 1) = -7/6

Now we can find b using one of the points and m. Let's use (-1, -2):

y = mx + b-2 = (-7/6)(-1) + b-2 = 7/6 + b

b = -25/6

Therefore, the linear function h(x) is:h(x) = -7/6x - 25/6

We can check our answer by plugging in the two given points:

h(-1) = (-7/6)(-1) - 25/6 = -2h(-7) = (-7/6)(-7) - 25/6 = -9

The answer is h(x) = -7/6x - 25/6.

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The given values are 2,6,5,3,0,3,4,3,2,4,5,2,4

There are the following values as shown in the given data.

To find the mode first we have to assign each value that how many times it appears.

1. 2-3 the number 2 appears only Three times.

2. 6-1 the number 6 appears one time.

3. 5-2 the number 5 appears only two times.

4. 3-3 the number 3 appears only three times.

5. 0-1 the number 1 appears only one time.

6. 4-3 the number 4 appears only Three times.

So, the mode of the given data is 4,3,2 as it appears the most number of times.

If a given set of values with two modes is bimodal, a given set of numbers with three modes is trimodal, and any set of numbers with more than one mode is multimodal.

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The estimate of the population proportion of defectives is 0.05.

Given that,

There are 10 different samples of 50 observations, that is, total of 500 observations.

To find : The estimate of the population proportion of defectives

And total number of defectives from 500 observations is (5+1+1+2+3+3+1+4+2+3) = 25

Thus, the point estimate for the population proportion defectives will be,

=25/500=0.05

or just obtain the individual proportion of each sample and then take their average to obtain the same result.

Thus, the point estimate for the population proportion defectives will be 0.05

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Answer:

There are 3 terms

Step-by-step explanation:

Answer:

Purchase rate of the house is $480000.

Step-by-step explanation:

Let the purchase rate of the house = $p

Current value of the house = $648000

If the current rate of the house has increased by 35% of the purchase rate,

Current rate = Purchase rate +  35% of the purchase rate

648000 = p + (35% of p)

648000 = p + \(p\times \frac{35}{100}\)

648000 = p + 0.35p

648000 = (1.35)p

p = \(\frac{648000}{1.35}\)

p = $480000

Therefore, purchase rate of the house is $480000.

(a) The test statistic is calculated as follows -1.83

b. The P-value is approximately 0.067.

C. There is not sufficient evidence to determine whether the antidepressant drug had an effect on changing smoking habits after one year. The correct option is A.

(a) The test statistic is calculated as follows:

z = (pdrug - pplacebo) / √(p(1-p) * (1/ndrug + 1/nplacebo))

Plugging in the values from the question, we get:

z = (55/223 - 213/677) / √0.5 * (1-0.5) * (1/223 + 1/677))

z = -1.83

(b) The P-value is the probability of obtaining a test statistic at least as extreme as the one observed, assuming that the null hypothesis is true. The P-value can be calculated using a statistical calculator or software program. In this case, the P-value is approximately 0.067.

(c) Since the P-value is greater than the significance level of 0.03, we cannot reject the null hypothesis. Therefore, there is not sufficient evidence to determine whether the antidepressant drug had an effect on changing smoking habits after one year.

The final conclusion is therefore:A. There is not sufficient evidence to determine whether the antidepressant drug had an effect on changing smoking habits after one year.

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To calculate the cost of holding stock for a year, we need to determine the carrying cost per unit and multiply it by the number of units being held in stock.

First, let's calculate the economic order quantity (EOQ) for the computing systems:

EOQ = sqrt((2DS)/H)

where

D = annual demand = 25 systems

S = setup cost per order = $6,000

H = holding cost per unit per year = ?

Assuming a holding cost of 20% of the unit cost, we have:

H = 20% of unit cost = 0.20*$6,000/46 = $24.78 per unit per year

So, the EOQ is:

EOQ = sqrt((225$6,000)/$24.78) = 46.17 (rounded to 46)

Since the EOQ is 46 systems, we need to order 46 systems at a time to minimize our total inventory costs.

The cost of holding stock for a year is then:

Cost of holding stock = number of units held in stock * holding cost per unit per year

= 46 * $24.78

= $1,139.88

Therefore, it will cost your company $1,139.88 to hold 46 computing systems in stock for a year.

The sum is 3/4 in simplest form.

This is an infinite geometric series with the first term of 1/1.3 and a common ratio of -2.2/3.

The sum of an infinite geometric series can be discovered utilising the formula:

S = a / (1 - r)

Where a is first term, and r is common ratio.

Plugging in the values, we have:

S = 1/1.3 / (1 - (-2.2/3)) = 1/1.3 / (1 + 2.2/3) = 1/1.3 / (5.2/3) = 3 / (5.2 * 1.3) = 3 / (6.76) = 3 / (4 * 1.69) = 3 / 6.76 = 3 * 1.69 / 6.76 = 3/4.

So the sum is 3/4 in simplest form.

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--The given question is incomplete; the complete question is

"Find the sum of 1/1.3 + 1/3.5 + 1/5.7 +...... express your answer as a fraction in simplest form."--

The minimum sterilization time required to achieve a 99.9% confidence level in successfully sterilizing 50 L of medium containing 10^6 contaminating organisms is approximately 1.95 minutes.

To calculate the minimum sterilization time required to yield 99.9% confidence of successfully sterilizing 50 L of medium containing 10^6 contaminating organisms, we need to use the concept of decimal reduction time (D-value) and the number of organisms.

The D-value represents the time required to reduce the population of microorganisms by one log or 90%. In this case, the given D-value is 0.65 minutes.

To achieve a 99.9% confidence level, we need to reduce the population of microorganisms by three logs or 99.9%, which corresponds to a 10^-3 reduction.

To calculate the minimum sterilization time, we can use the following formula:

Minimum Sterilization Time = D-value × log10(N0/Nf)

Where:

D-value is the decimal reduction time (0.65 minutes).

N0 is the initial number of organisms (10^6).

Nf is the final number of organisms (10^6 × 10^-3).

Let's calculate it step by step:

Nf = N0 × 10^-3

= 10^6 × 10^-3

= 10^3

Minimum Sterilization Time = D-value × log10(N0/Nf)

= 0.65 minutes × log10(10^6/10^3)

= 0.65 minutes × log10(10^3)

= 0.65 minutes × 3

= 1.95 minutes

Therefore, the minimum sterilization time required to yield 99.9% confidence of successfully sterilizing 50 L of medium containing 10^6 contaminating organisms using this procedure is approximately 1.95 minutes

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Answer:

Yes

Step-by-step explanation:

Answer:

\({\underline{\textsf{\textbf{True }}}}\)

Your answer is 25% loss

Step-by-step explanation:

Proof :

Given that,

A cycle was bought for ₹1,600

And it's S. P. (selling price) is ₹1,200

As the C. P. (cost price) is more than the S. P.

Therefore,

➡ Loss = C. P. - S. P.

➡ Loss = 1,600 - 1,200

➡ Loss = ₹400

And also,

➡ Loss% = loss*100/C. P.

➡ Loss% = 400*100/1,600

➡ Loss% = 25%

Hence proved :)

Answer:

It is d. 3/2

Step-by-step explanation:

slope formula is rise over run or x2-x1/y2-y1. So it would be 6-0/4-0. That equals 6/4. You just need to simplify that by dividing both 6 and 4 by 2 and you get 3/2.

Answer:

Zelie should have divided both numbers by 14

Step-by-step explanation:

Given

\(Actual = 28\)

\(Measured = 14\)

Required

Spot and correct Zelie's mistake

\(Zelie = \frac{28 - 7}{14 - 7} = \frac{21}{7}\)

Scale is calculated as:

\(Actual = Measured * Scale\)

\(28 = 14 * Scale\)

Divide 28 and 14 by 14

\(28/14 = 14/14 * Scale\)

\(2 = 1 * Scale\)

\(2 =Scale\)

\(Scale = 2\)

Notice at this point:

\(28/14 = 14/14 * Scale\)

Both sides were divided by 14.

Hence, option A answers the question.

Answer:

A. Zelie should have divided both numbers by 14.

Explanation:

I took the quiz and got it right.

Hope this Helps!

John's savings amount as a function of time is S(t) = $24,000 / 25. Initially, he needs to save $24,000 for a new car. After the first month, he has saved $1,000. The savings amount is directly proportional to the time elapsed. The constant of proportionality is 1/24. Thus, John's savings amount can be determined based on the remaining amount he needs to save.

John's savings amount can be represented as a function of time and is proportional to the amount he still needs to save. Let's denote the amount John needs to save as N(t) at time t, and his savings amount as S(t) at time t. Initially, John needs to save $24,000, so we have N(0) = $24,000.

We know that John has saved $1,000 after the first month, which means S(1) = $1,000. Since his savings amount is proportional to the amount he still needs to save, we can write the proportionality as:

S(t) = k * N(t)

where k is a constant of proportionality.

We need to find the value of k to determine John's savings amount at any given time.

Using the initial values, we can substitute t = 0 and t = 1 into the equation above:

S(0) = k * N(0)  =>  $1,000 = k * $24,000  =>  k = 1/24

Now we have the value of k, and we can write John's savings amount as a function of time:

S(t) = (1/24) * N(t)

Since John's savings amount is proportional to the amount he still needs to save, we can express the amount he still needs to save at time t as:

N(t) = $24,000 - S(t)

Substituting the expression for N(t) into the equation for S(t), we get:

S(t) = (1/24) * ($24,000 - S(t))

Simplifying the equation, we have:

24S(t) = $24,000 - S(t)

25S(t) = $24,000

S(t) = $24,000 / 25

Therefore, John's savings amount at any given time t is S(t) = $24,000 / 25.

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Answer:

Step-by-step explanation:

You want values of ∆y and dy for y = x² -6x and x = 5, ∆x = dx = 0.5.

The value of dy is found by differentiating the function.

  y = x² -6x

  dy = (2x -6)dx

For x=5, dx=0.5, this is ...

  dy = (2·5 -6)(0.5) = (4)(0.5)

  dy = 2

The value of ∆y is the function difference ...

  ∆y = f(x +∆x) -f(x) . . . . . . . where y = f(x) = x² -6x

  ∆y = (5.5² -6(5.5)) -(5² -6·5)

  ∆y = (30.25 -33) -(25 -30) = -2.75 +5

  ∆y = 2.25

__

Additional comment

On the attached graph, ∆y is the difference between function values:

  ∆y = -2.75 -(-5) = 2.25

and dy is the difference between the linearized function value and the function value:

  dy = -3 -(-5) = 2.00

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Answer:

no they do not :) :) :)

Answer:

-4,-2,1

Step-by-step explanation:

It crosses the x-axis at -4,-2 and 1

The distance from Marcel and Katya is 34 metres

From the given diagram, we have the following

Acute angle given = 42 degrees

According to SOH CAH TOA identity

sin theta = opp/hyp

sin 42 = x/50

x = 50sin42

x = 50(0.6691)

x = 33.46

Hene the distance from Marcel and Katya is 34 metres

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Time-series plots are used for several reasons:

B. Time-series plots are used to identify any outliers in the data.

C. Time-series plots are used to identify trends in the data over time.

D. Time-series plots are used to present the relative frequency of the data in each interval or category.

First, we need to know that quantitative variable is required when drawing a time-series plot.

We need to also know that data points are graphically represented as time-series plots, with the variable of interest drawn on the y-axis and time commonly depicted on the x-axis. They demonstrate the variable's evolution over time.

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The total area of the ribbon is equals to 46 sq. inches with a 4 square inches of school logo in between.

The four-sided polygonal shape known as a quadrilateral has four edges and four corners. The Latin words quadri, a variation of four, and latus, meaning "side," were used to create the term.

In American and Canadian English, a quadrilateral having at least one set of parallel sides is referred to as a trapezoid. It is referred to as a trapezium in British and other varieties of English. In Euclidean geometry, a trapezoid is a convex quadrilateral by definition. The bases of the trapezoid are the parallel sides.

The total area of the ribbon = area of the top square + area of the bottom trapizium

Area of the square = 4*4 = 16 sq. inches

Area of the trapizium = (1/2)*(sum of parallel sides)*height = (1/2)*(4+8)*5 = 30 sq. inches.

The total area of the ribbon is equal to 30 + 16 = 46 sq. inches with a 4 square inches of school logo in between.

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Answer:

a=18

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

Step 1: Write out your equation

3a=a+36

Step 2: Subtract a on both sides

2a=36

Step 3: Divide by 2 on both sides

a=18

Hope I helped