In which quadrant is the number 6 – 8i located on the complex plane?

Answer:

8

Step-by-step explanation:

1/2(12)=6

Answer:

8

Step-by-step explanation:

1/2(8+4)=6

The system of equations that satisfies the solution (3, -4) is:

4x + 1y = 8

2x - 3y = -17

To create a system of equations where the solution is (3, -4), we can assign arbitrary values to the coefficients of the equations. Let's use the following values:

Equation 1: 4x + 1y = 8

Equation 2: 2x - 3y = -17

By plugging in the values (3, -4) into these equations, we can find the missing coefficients:

Equation 1: 4(3) + 1(-4) = 12 - 4 = 8

Equation 2: 2(3) - 3(-4) = 6 + 12 = 18 - 17 = -17

Therefore, the system of equations that satisfies the solution (3, -4) is:

4x + 1y = 8

2x - 3y = -17

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Answer:

81

Step-by-step explanation:

Area is multiplying all side

9 x 9 = 81

The virtual condition for the .376² MMC pin with a perpendicularity tolerance of .008² diameter at MMC is approximately .001131.

To determine the virtual condition for a .376² MMC (Maximum Material Condition) pin with a perpendicularity tolerance of .008² diameter at MMC, we need to calculate the tolerance zone.

The perpendicularity tolerance specifies the allowable deviation of the pin from a perfect perpendicular orientation. The tolerance zone is defined as a cylindrical volume around the pin, with a diameter equal to the perpendicularity tolerance.

In this case, the perpendicularity tolerance is given as .008² diameter at MMC. Since the diameter at MMC is .376², we can calculate the tolerance zone as follows:

Tolerance zone = .008² * .376²

Simplifying the calculation:

Tolerance zone = .008 * (.376 * .376)

Tolerance zone = .008 * .141376

Tolerance zone = .001131

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Step-by-step explanation:

y+7=6(x-4)

y+7=6x-24

y=6x-31

Answer: y + 7 = 6(x - 4)

Step-by-step explanation:

      The point-slope formula is y - \(y_1\) = m(x - \(x_1\)) where m is the slope and ( \(x_1\), \(y_1\)) is a point on the graph.

      Using the formula, we will plug in our known values to write our equation.

y - \(y_1\) = m(x - \(x_1\))

y - (-7) = (6)(x - (4))

y + 7 = 6(x - 4)

The sum of the NPV and false omission rate for any test will always be 100%.

The NPV (Negative Predictive Value) is the proportion of people who test negative for a condition and actually do not have it, while the false omission rate is the proportion of people who have the condition but test negative for it.

When we add together the NPV and the false omission rate for any test, we are essentially considering all the cases where the test result is negative.

The NPV represents the proportion of people who truly do not have the condition and test negative for it, while the false omission rate represents the proportion of people who actually have the condition but test negative for it.

Together, these two values cover all possible cases where the test result is negative, which means that they represent the entirety of the negative results for the test.

Since the sum of all probabilities for an event must always equal 100%, the sum of the NPV and false omission rate must also equal 100%.

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Answer: Tonya's house is 2.37 miles farther from the school than Jamal's house.

Step-by-step explanation: To solve this problem using a quick picture, we can draw a line segment to represent the distance from the school to Tonya's house, and another line segment to represent the distance from the school to Jamal's house. We can then use a ruler to measure the length of each line segment and subtract the length of the line segment representing the distance to Jamal's house from the length of the line segment representing the distance to Tonya's house.

For example, if we draw a line segment that is 3.64 inches long to represent the distance from the school to Tonya's house and a line segment that is 1.27 inches long to represent the distance from the school to Jamal's house, then we can use a ruler to measure the lengths of the line segments and find that the line segment representing the distance to Tonya's house is 3.64 - 1.27 = 2.37 inches longer than the line segment representing the distance to Jamal's house. This means that Tonya's house is 2.37 miles farther from the school than Jamal's house.

Step-by-step explanation:

Since there are in arithmetic progression, 2(2x + 9) = (3x + k) + (x + 13).

=> 4x + 18 = 4x + 13 + k

Hence k = 5.

Step-by-step explanation:

i guss first

(4/5)^6

4^6/5^6 (because it is equal power of 4and5)

4095/15625

0.27208

The main difference in calculations for the independent samples t-test when the variances are equal and the variances are unequal is the method used to calculate the pooled variance, the t-value, and the degrees of freedom.

1. When variances are equal (also called pooled variance):
- Calculate the pooled variance using the formula:

\(Sp^2 = [(n1-1) × s1^2 + (n2-1) × s2^2] / (n1 + n2 - 2)\)
- Calculate the t-value using the formula:

\(t = (M1 - M2) / sqrt(Sp^2 × (1/n1 + 1/n2))\)
- Determine the degrees of freedom using the formula:

df = n1 + n2 - 2
2. When variances are unequal (also called Welch's t-test):
- Calculate the t-value using the formula:

\(t = (M1 - M2) / sqrt((s1^2 / n1) + (s2^2 / n2))\)
- Determine the degrees of freedom using the formula:

\(df = [(s1^2 / n1 + s2^2 / n2)^2] / [(s1^2 / n1)^2 / (n1 - 1) + (s2^2 / n2)^2 / (n2 - 1)]\)
In summary, the main difference in calculations for the independent samples t-test when the variances are equal and the variances are unequal is the method used to calculate the pooled variance, the t-value, and the degrees of freedom.

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Answer:

\(Gallons = 2.305\)

Step-by-step explanation:

Given

Rate = 130.16 miles for 5 gallons

Required

Number of gallons used for a journey of 60 miles

The rate in miles per gallon is calculated as:

\(Rate = \frac{Distance}{Gallons}\)

When distance = 130.16 and gallons = 5, we have:

\(Rate = \frac{130.16}{5}\)

\(Rate = 26.032\)

When distance = 60 miles.

Substitute 60 for distance and 26.032 for rate in \(Rate = \frac{Distance}{Gallons}\)

\(26.032 = \frac{60}{Gallons}\)

Cross Multiply

\(Gallons * 26.032 = 60\)

\(Gallons = \frac{60}{26.032}\)

\(Gallons = 2.305\) --- approximated

x - 12 = 18 is the the equation that represents ."Twelve less than a number, ×, is 18."

given the number is x

the equation of the given statement

x - 12 = 18

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The probability that a randomly selected proofreader's age will be between 35.5 and 37 years is approximately 0.1512, or 15.12%.

To find the probability that a randomly selected proofreader's age is between 35.5 and 37 years, we can use the standard normal distribution and convert the ages to z-scores.

First, let's calculate the z-score for the lower age limit of 35.5 years:

z1 = (35.5 - 36) / 3.7

z1 ≈ -0.1351

Next, let's calculate the z-score for the upper age limit of 37 years:

z2 = (37 - 36) / 3.7

z2 ≈ 0.2703

Using the z-table or a calculator, we can find the area under the standard normal curve between these two z-scores:

P(35.5 ≤ X ≤ 37) = P(-0.1351 ≤ Z ≤ 0.2703)

Looking up the z-scores in the standard normal distribution table, we find the corresponding probabilities:

P(-0.1351 ≤ Z ≤ 0.2703) ≈ 0.5557 - 0.4045

P(-0.1351 ≤ Z ≤ 0.2703) ≈ 0.1512

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The expression that shows John's score will be 2x + 9.

It is vital to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information.

In this case, it is vital to note that they have at least two terms which have to be related by through an operator.

In this case, Mai has a score of x while John has 9 more than twice mai's score.

The expression for this relationship will be:

= (2 × x) + 9

= 2x + 9

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Complete question

Mai has a score of x. John has 9 more than twice mai's score. Illustrate the expression for Johnsc score.

a) To compute R, we use the given values: μ = 1.1, v2f = 23.62 ± 0.98 m/s, and v1i = 30.57 ± 0.76 m/s. Plugging these values into the equation R = μv1^2/v2^2, we get:

R = (1.1 * 30.57^2) / (23.62^2)

≈ 1.1 * 936.4049 / 557.3444

≈ 1029.0454 / 557.3444

≈ 1.8479

b) To compute δR, we need to consider the uncertainties in the given values. Using error propagation, we can calculate δR:

δR = |R| * √((2 * δμ / μ)^2 + (2 * δv1i / v1i)^2 + (2 * δv2f / v2f)^2)

Substituting the given uncertainties, we have:

δR = 1.8479 * √((2 * 0 / 1.1)^2 + (2 * 0.76 / 30.57)^2 + (2 * 0.98 / 23.62)^2)

= 1.8479 * √(0 + 0.0384 + 0.0837)

≈ 1.8479 * √0.1221

≈ 1.8479 * 0.3496

≈ 0.6461

c) Therefore, the result, R ± δR, is approximately 1.8479 ± 0.6461. Since we have two significant figures in the uncertainty (0.6461), we should round the result to two significant figures as well. Thus, the final result is R = 1.8 ± 0.6. The unit of R will depend on the units of the given velocities (m/s in this case).

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The area of the irregular shape is 84 ft square.

The diagram is a trapezium. A trapezium is a quadrilateral. Therefore, the area of the trapezium can be found as follows:

area of the trapezium = 1 / 2 (a + b)h

where

Therefore,

a = 10 ft

b = 18 ft

c = 6 ft

area of the trapezium = 1 / 2 (10 + 18)6

area of the trapezium = 1 / 2 (28)6

area of the trapezium = 168 / 2

area of the trapezium = 84 ft²

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Risk probability is the level of probability that an investment will not produce the expected gain.

Risk probability refers to the likelihood that an investment will not generate the expected returns. It is an important concept in investment analysis and decision-making.  When making investment decisions, it is crucial to assess the potential risks involved. Risk probability helps us evaluate the likelihood of an investment not meeting our expectations. It provides an estimate of the chances of experiencing a loss or not achieving the desired level of gain.

For example, let's say you are considering investing in stocks. Before making a decision, you would analyze various factors such as market trends, company performance, and economic indicators. By assessing the risk probability, you can determine the likelihood of the investment not producing the expected returns. Also understanding the risk probability, investors can better manage their investment portfolios and make more informed decisions.

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Raw data can be calculated by using mathematical operations such as addition, subtraction, multiplication, and division.

This can be done manually or by using a calculator or a computer program .Additionally, statistical methods such as mean, median, mode, and standard deviation can be used to calculate raw data.Raw data can also be manipulated in various ways. For example, data can be sorted, filtered, and organized into categories or hierarchies. Data can also be visualized in graphs, charts, and diagrams to make patterns and trends easier to identify. Statistical methods such as correlation and regression can also be used to analyze and interpret raw data. Additionally, data can be combined with other data sets to create new insights and relationships. Finally, machine learning and predictive analytics can be used to make predictions about future outcomes based on existing data.

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Answer:

Outlier, clusters, and gap in your value.

Step-by-step explanation:

An OUTLIER is a data point that falls away from the rest of the points in a scatter plot. It doesn't seem to fit with the rest of the points. DATA CLUSTERS are groups of points that are all graphed close together. A GAP IN VALUE occurs when there are points clustered at two different spots on a scatter plot.

Answer: The final price is less than the original

Step-by-step explanation:

    Let us break this down a bit.

The original price is $500

-> At the beginning, the price was marked up by 20%

-> At the end, the price at the beginning of the season is marked down by 20%

    We are solving for: "How does the final price compare with the original price of $500​"

        First, we will find the price at the beginning.

-> Please note a percent divided by 100 becomes a decimal

20% / 100 = 0.2

$500 * 0.2 = $100

$500 + $100 = $600

     Now, we will find the price at the end.

$600 * 0.2 = $120

$600 - $120 = $480

     The final price is less than the original price of $500.

Answer:

Step-by-step explanation:

price marked up by 20%= 500+ \(\frac{20}{100}\)×500

                                        =$600

price marked down by 20%= 600- \(\frac{20}{100}\)×600

                                             =$480

the final price is less than the original price

Let:

The slope m is given by:

So, we can conclude the slope of the line from point B to point A is -1/4

Answer:

- 21

Step-by-step explanation:

The minimum value occurs at the vertex of the function

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

To obtain this form use the method of completing the square

Given

f(x) = x² - 6x - 12

add/ subtract ( half the coefficient of the x- term)² to x² - 6x

f(x) = x² + 2(- 3)x + 9 - 9 - 12

     = (x - 3)² - 21

with vertex = (3, - 21 )

The minimum is the value of k, that is minimum value = - 21

Hey there! I'm happy to help!

The domain is any possible number you can input into the function to get a real output. The domain of h just means the domain of this entire function, which is called h.

Let's look at the answer options.

OPTION A

All real values of x such that x≠0.

The only way to make it so that we do not have a real output is if we get a negative square root. You cannot multiply any number by itself to get a negative number unless you use imaginary numbers, but using imaginary numbers makes our output not real.

Anyways, plugging in 0 would give us √-10, which is not a real number. That part is correct, but this option says ALL REAL NUMBERS except for 0. The problem is is that we can take any number less than ten and plug it in and we would get a negative square root, a fake number. So, this option is incorrect.

OPTION B

All real values of x such that x≥10.

Let's say we use 10 for our x and plug it in. This gives us √0, which is 0, a real output. Anything bigger than this 10 will give us a real output as well, so this option is correct.

We don't even need to check the other options because we have already found the correct answer. C,D, and E are all incorrect though because they include values less ten, which would give us a negative square root, a fake number.

I hope that this helps! Have a wonderful day!

You must leave the money in the account for(Time) 20 years to earn $ 900 in Simple interest.

To calculate the simple interest use formula :-

I = (P×R×T)/100 , I is the Simple Interest ,where P is the principal amount, R is the rate of interest and T is time (in years).

Given : P= $1500   ; R = 3%= 3/100    and  I =$900

To find : Time

From the above formula , we have

900 =  (1500 ×3×T)/100

900 = 1500 × 0.03T

T = 900/(1500×0.03) = 20

T= 20 years

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It takes Lena to compress the accordion completely and then stretch it back out to a length of 50cm.

It takes Lena 4.1 seconds to compress the accordion completely and then stretch it back out to a length  of 50cm.

I am assuming the function without a T: \(A(t) = 25_{cos}(t)+65\)

The function is graphed in the figure attached, and the blue line is \(y = 50cm\).

From the graph we see that the accordion is completely stretched  (has minimum length) at \(t = \pi\) seconds, and stretches back  to 50cm at \(t = 4.069s\); therefore, it takes Lena 4.069 seconds to stretch the accordion back again, which to the nearest tenth of a second is  4.1s.

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Answer: 1.3s

Step-by-step explanation:

If you're solving for  \(A(t)=25cos( \pi t)+65\\\)

Answer:

z= 23°

y= 120°

Step-by-step explanation:

For z, the measures of the angles are alternate interior angles, they equal each other. So, the equation would be:

66= 3z-3

Step 1- Add 3 to both sides.

66= 3z-3

+3       +3

69= 3z

Step 2- Divide both sides by 3.

69= 3z

3     3

z= 23°

For y, the measures of 66 and y are alternate exterior angles, they sum up to 180 degrees. So, the equation would be:

180= 60+y

Step 1- Subtract 60 to both sides.

180= 60+y

-60   -60

y= 120°

Hope this helps!

We will solve as follows:

a. We will find the measure of the angle using the following expression:

Here a, b & c are the sides delimited by the triangle formed inside the circle and the points given and C is the angle between them. Now, we solve for C, then replace and solve[This can be seen in the following graph]:

Now, we determine the values of a. b and c using the points given and the vertex:

Now, we replace the values on the formula and solve for C:

And that in radians is:

So, the angle is approximately 1.89 radians.

b.

We will find the distance he traveled along the arc as follows:

Here s is the arc length, theta the angle and r the radius, now we replace:

So, he traveled approximately 39.69 feet.

The Area of Trapezium is 50, 267 mm².

We have,

base 1 = 224 mm

base 2 = 77 mm

Height = 334 mm

Now, Area of Trapezium

= 1/2 (Sum of parallel side) x height

= 1/2 (224 + 77) x 334

= 1/2 x 301 x 334

= 50, 267 mm²

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