Simplify. (Use the form a + bi.)
3 − 6i
−7i

Answer:

25.6 km/h

Step-by-step explanation:

Omani:

First, 1.5 hours = 1 hour and 30 minutes

and 66 miles = 105.6 km (66 x 1.6 = 105.6)

105.6 / 1.5 = 70.4 km/h

Omani's speed is 70.4 km/h

Adedi:

1 hour and 15 minutes is 1.25 hours

she drives 56 km in 1.25 hours

So 56 / 1.25 = 44.8 km/h

Adedi's speed is 44.8 km/h

Difference:

70.4 - 44.8 = 25.6 km/h

Omani is faster than Adedi with 25.6 km/h

Below are some authorial techniques that can be used to create mystery, tension, or surprise in literature.

Order of events: The order in which events are presented can create a sense of mystery or suspense.

Pacing: The pace of a story can also be used to create suspense. A slow-paced story can build tension by allowing the reader to dwell on the details of a situation, while a fast-paced story can create excitement and surprise by keeping the reader guessing what will happen next.

Structure: The structure of a story can also be used to create mystery, tension, or surprise. For example, a story that is told in flashback can create a sense of mystery by revealing information about the past that is relevant to the present.

Time manipulation: The manipulation of time can also be used to create suspense.

Language: The language that an author uses can also be used to create mystery, tension, or surprise. For example, an author might use vague or ambiguous language to create a sense of mystery, or use strong language to create a sense of tension or surprise.

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Answer:

it would be positive

Step-by-step explanation:

Answer:

Step-by-step explanation:

A positive plus a negative equals a negative:

4 + (-3) = 1

A positive plus a positive equals a positive:

4 + 4 = 8

A negative plus a negative equals a negative:

(-2 )+ (-2) = -4

If two number have the same absolute value, they will equal zero:

-3 + 3 = 0

- 2 + 2 = 0

The recursive formula for the nth term of the sequence is \(a_n=\frac{1}{4}a_{n-1}\)

The sequence is

80, 20, 5...

The first term = 80

The second term = 20

Consider the nth term as \(a_n\)

The common ratio = The second term / The first term

Substitute the values in the equation

The common ratio = 20/80

Divide both numerator and denominator of the term by 20

= 1/4

Therefore the nth term will be the 1/4 of the previous term. If the nth  term of the sequence is  \(a_n\) and previous term (n-1) term is \(a_{n-1}\)

Then the nth term of the sequence

\(a_n=\frac{1}{4}a_{n-1}\)

Hence, the recursive formula for the nth term of the sequence is \(a_n=\frac{1}{4}a_{n-1}\)

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Answer:

9.43ft

Step-by-step explanation:

Given

\(d = 3ft\)

Required

Determine the perimeter

To do this, we simply calculate the circumference;

This gives:

\(C = \pi d\)

\(C = \frac{22}{7} *3\)

\(C = \frac{66}{7}\)

\(C = 9.43ft\)

6x + 9

I hope this helps!

Answer:

= 6x +9

Step-by-step explanation:

1. you need to multiply -3 by x² + 2x - 3

so you got -3x² -6x + 9

2. Then, you need to multiply 3 by (x²+4x)

= 3x² + 12x

3. -3x² - 6x + 9 + 3x² + 12x

4. then you need to solve with the same

= - 3x² + 3x²

= 0

= - 6x + 12x

= 6x

5. lastly you will got the answer.

# = 6x +9

There are four degrees of freedom for the chi-square goodness-of-fit test in this study. So, correct option is B.

For a chi-square goodness-of-fit test in the context of testing the fairness of a spinner with five sections, the number of degrees of freedom can be determined by subtracting 1 from the number of categories being tested.

In this case, since the spinner has five sections, there are five categories. Therefore, the degrees of freedom for the chi-square goodness-of-fit test would be:

Degrees of freedom = Number of categories - 1

= 5 - 1

= 4

Degrees of freedom represent the number of values in the final calculation of the chi-square test statistic that are free to vary. It determines the critical values and the distribution of the test statistic.

In the case of the chi-square goodness-of-fit test, the test compares the observed frequencies in each category with the expected frequencies under the assumption of fairness. By comparing these frequencies, the test determines if there is a significant deviation from the expected distribution, indicating unfairness in the spinner.

So, correct option is B.

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Answer:

The store sells 12 bottles of purple paint

Step-by-step explanation:

Answer:

i don't know sorry

Step-by-step explanation:

Answer:

Step-by-step explanation:

1) The first option comprises of seven like terms and one 6, which would result in 7z + 6.

2) The second option is blank.

3) The third option comprises of two numbers with like terms that actually do add up to 6z.

4) The fourth option is z multiplied by itself 6 times, which is z to the power of 6 or z⁶.

5) The fifth option is z divided by 1/6, which is \(\frac{z}{6}\).

I hope this helps! Have a blessed day!

The cost per second to power such a circuit during the peak usage period is approximately \(2.376 x 10^-6\)$/s. The cost per second to power the circuit during the peak usage period can be calculated using the following steps:

Calculate the power consumption of the device-The power consumption of the device can be calculated using the formula: Power = Voltage x Current. P = V x I, Substituting the given values:

P = 110V x 0.12A

= 13.2 W

Calculate the cost per second-The cost per second can be calculated using the formula:

Cost per second = Power x Cost per Joule

C = P x CC

= 13.2 W x 1.8 x \(10^-7\) $/J

≈ 2.376 x 10^-6 $/s

Therefore, the cost per second to power such a circuit during the peak usage period is approximately 2.376 x\(10^-6\) $/s.

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The vertex form of the quadratic equation, for the vertex points at which the parabola crosses its symmetry, is,

\(\rm f(x)=8[(x+\dfrac{1}{4})^2]-\dfrac{1}{2}\)

Vertex form of the parabola is the equation form of the quadratic equation which is used to find the coordinate of vertex points at which the parabola crosses its symmetry.

The standard equation of the vertex form of the parabola is given as,

\(\rm y=a(x-h)^2+k\)

Here, (h, k) is the vertex point.

The given quadratic equation in the problem is,

\(\rm f(x)=8x^2+4x\)

To isolate the term, take out the common number 8 from the equation,

\(\rm f(x)=8(x^2+0.5x)\)

Add and subtract 0.5/2 in the equation as;

\(\rm f(x)=8(x^2+0.5x+\dfrac{0.5}{2}-\dfrac{0.5}{2})\\\\f(x)=8(x^2+0.5x+\dfrac{1}{16}-\dfrac{1}{16})\\\\f(x)=8((x^+0.5x)^2-\dfrac{1}{16})\\\\f(x)=8[(x+\dfrac{1}{4})^2]-\dfrac{1}{2}\)

The above equation is the vertex form of the given quadratic equation. Thus, option A is the correct option.

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The missing angles and side of the triangle are;

m∠FXD = 44°

EG = 14

m∠FZG = 32°

We are told that the angle bisectors of ΔXYZ are XG, YG and ZG

The parameters are;

∠DYE = 94°

∠FXG = 22°

Thus;

m∠FXD = 2* 22°

m∠FXD = 44°

The sum of angles in a triangle is 180 degrees. Thus;

m∠FZE + 94 + 22 = 180

m∠FZE = 180 - (94 + 22)

m∠FZE = 64°

Thus;

m∠FZG = 64°/2

m∠FZG = 32°

The incenter of a triangle lies at equal distances from the three line segments forming the sides of the triangle, and also from the three lines containing those segments. Thus;

DG = EG = FG = 14

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Answer:

4 = 68

5 = 112

7 = 112

Step-by-step explanation:

Hope it helps

I hope it's helpful .....

The first matrix given cannot be diagonalized because it does not have a complete set of linearly independent eigenvectors.

To diagonalize a matrix, we need to find a matrix P such that P^(-1)AP = D, where A is the given matrix and D is a diagonal matrix. In the first matrix provided, the real eigenvalues are given as 0, -3, and 6. To diagonalize the matrix, we need to find linearly independent eigenvectors corresponding to these eigenvalues. However, it is stated that the matrix has only one eigenvector associated with the eigenvalue 6. Since we don't have a complete set of linearly independent eigenvectors, we cannot diagonalize the matrix. Therefore, option C, "The matrix cannot be diagonalized," is the correct choice.

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Answer:

The area is 56.25 \(mm^{2}\)

Step-by-step explanation:

Hope this helps!! Please mark brainliest.

Answer:

106°

Step-by-step explanation:

hence it is a iso circle, the < J and < L to be equal one to another.

so 10x - 13 = 3x +22

7x = 45

x = 35/7

x = 5

so the inner < sum is equal to 180.

so 10x - 13° + 3x + 22° + < K = 180°

10 (5)° - 13° + 3(5)° + 22° + <K = 180°

50° -13° +15° +22° +<K = 180°

<K = 180° - 74°

<K = 106°

Answer:

The correct option is;

C. $0.19 per KWH

Step-by-step explanation:

The given data are;

KWH   \({}\)               Billing

578   \({}\)                 $109.82

1,033   \({}\)               $196.27

1,475   \({}\)               $280.25

1,754   \({}\)               $333.26

Therefore, we have the rate of change, m, given as follows;

m =(Change in the amount paid)/(Change in the electric usage in the same period)

For the first and second month, the rate of change is therefore;

m = ($196.27 - $109.82)/(1,033 - 578) = $0.19 per kWH

Between the first and third month, the rate of change is given as follows;

m = ($280.25 - $109.82)/(1,475 - 578) = $0.19 per kWH

Between the first and fourth month, the rate of change is given as follows;

m = ($333.26 - $109.82)/(1,754 - 578) = $0.19 per kWH

Therefore;

The rate of change is constant and is $0.19 per kWH

Answer:

1. 200

2. 78

3. 50%

4. 20%

5. 14.52

6. 72

7. 30

8. 27

9. 50%

10. 20%

I hope this helps:D

The time zone at the prime meridian is called Greenwich Mean Time (GMT), serving as the global reference point for our time system. GMT is based on the 0 degree longitude measurement at the Royal Observatory in Greenwich, London.

Greenwich Mean Time (GMT) is the time at the prime meridian, which is located at 0 degrees longitude. It serves as the global reference point for our time system. GMT is based on the concept of using the prime meridian as a standard reference for timekeeping worldwide.

The establishment of GMT can be attributed to the Royal Observatory in Greenwich, London, where the prime meridian is defined. The observatory's location was selected as the reference point in 1884 during the International Meridian Conference. This decision aimed to provide a universal standard for time measurement and facilitate global coordination.

GMT is often used as the basis for determining time zones around the world. Time zones are typically measured in relation to GMT, with some regions ahead or behind by a certain number of hours. For example, time zones ahead of GMT are designated as GMT+1, GMT+2, and so on, while those behind are labeled as GMT-1, GMT-2, and so forth.

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Answer:

The helicopter must cover a straight line distance of approximately 61.270 miles from the hospital to the wreck site.

Step-by-step explanation:

Let suppose that Air Care helicopter travels in straight line from the hospital to the wreck site, we can determine that distance (\(d\)), measured in miles, by using the following Pythagorean identity from Analytical Geometry:

\(d = \sqrt{(x_{W}-x_{H})^{2}+(y_{W}-y_{H})^{2}}\)

Where:

\(x_{W}\), \(y_{W}\) - Location of the wreck site, measured in miles.

\(x_{H}\), \(y_{H}\) - Location of the hospital, measured in miles.

If the location of the wreck site and the hospital are \((13, -14)\) and \((-42, 7)\), respectively. The distance that helicopter must cover is:

\(d = \sqrt{[13-(-42)]^{2}+[(-14)-13]^{2}}\)

\(d \approx 61.270\,mi\)

The helicopter must cover a straight line distance of approximately 61.270 miles from the hospital to the wreck site.

Answer:

Step-by-step explanation:

since the bucket of water is 10 inch and the fish tank is 30 then

A mathematical puzzle, where the rational numbers are used is attached with the answer.

A puzzle is a game, problem, or toy that tests a person's ingenuity or knowledge.

In a puzzle, the solver is expected to put pieces together in a logical way, in order to arrive at the correct or fun solution of the puzzle.

Given is to investigate a mathematical puzzle where rational numbers are used.

Refer to the image attached. It shows a mathematical puzzle attached where the rational numbers are used.

Therefore, a mathematical puzzle, where the rational numbers are used is attached with the answer.

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{Question in english -

Investigate a mathematical puzzle where rational numbers are used.}

The researcher should analyze the data obtained from 933 people who were asked about their favorite type of TV program, with the condition that they could only choose one answer. The appropriate statistical test to analyze these data is c. Chi-square test.

The Chi-square test is used for analyzing categorical data, which is the case in this scenario where individuals have to choose among news, documentary, soap, or sports. The test will help the researcher determine if there is a significant difference in preferences for TV program types among the respondents.

The specific techniques and statistical tests used may vary depending on the goals of the research and the nature of the data.

Therefore option c is correct.

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ANSWER:

STEP-BY-STEP EXPLANATION:

In this case, we can make a proportion, since we know the time when there are 5 people, we need to know the time when there are two people

solving for x:

Answer:

3

Step-by-step explanation:

We do do -3 on both sides and get 7b = 21. Then we multiply by the reciprocal (divide) (7b * 1/7 = 21 * 1/7) . We get b = 21/7 cause the 7's cancel out. b = 3 cause 21/7 = 3

Answer:

Yes

Step-by-step explanation:

Points D and E are on plane F.

Answer:

d

Step-by-step explanation:

up 2 right 1

Answer:

y=1/2x

Step-by-step explanation:

Infinite series, the total of an infinite number of numbers connected in a specific method and listed in a specific order.

We get,

a)  \($\sum_{n=0}^{\infty}$\)

Infinity

b)  \($\sum_{n=1}^{\infty}\left(\frac{4}{2^n}\right)$\)

\(\sum_{n=1}^{\infty} \frac{4}{2^n}\)

\(& =4 \cdot \sum_{n=1}^{\infty} \frac{1}{2^n} \\\)

\(& \sum_{n=k}^{\infty}\left(a_n\right)=\sum_{n=0}^{\infty}\left(a_n\right)-a_0-a_1- \\\)

\(& =4\left(\sum_{n=0}^{\infty} \frac{1}{2^n}-\frac{1}{2^0}\right)\)

\(& \sum_{n=0}^{\infty} \frac{1}{2^n}=2 \\\)

\(& =4\left(2-\frac{1}{2^0}\right)\)

Then we get,

=4

c) \($\sum_{n=1}^{\infty}\left(\frac{7}{10^n}\right)$\)

\($\sum_{n=1}^{\infty} \frac{7}{10^n}\)

\(& =7 \cdot \sum_{n=1}^{\infty} \frac{1}{10^n} \\\)

\(& \sum_{n=k}^{\infty}\left(a_n\right)=\sum_{n=0}^{\infty}\left(a_n\right)-a_0-a_1- \\\)

\(& =7\left(\sum_{n=0}^{\infty} \frac{1}{10^n}-\frac{1}{10^0}\right)\)

\(& \sum_{n=0}^{\infty} \frac{1}{10^n}=\frac{10}{9} \\\)

\(& =7\left(\frac{10}{9}-\frac{1}{10^0}\right)\)

Simplify

\($7\left(\frac{10}{9}-\frac{1}{10^0}\right): \quad \frac{7}{9}$\)

= 7/9

Therefore,

a) infinity, b) =4, and c) = 7/9

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Let X be the number of customers who will order the chicken entree in the next 10 customers. Suppose a restaurant has 4 possible entrées, chicken, beef, pork, and tofu, and the manager believes that each customer will independently order any one of them with probabilities 0.3, 0.4, 0.2, and 0.1, respectively.

The probability that a customer will order the chicken entree is 0.3. The probability that a customer will not order the chicken entree is 0.7. Since each customer's order is independent, X follows a binomial distribution with parameters n = 10 and p = 0.3. Thus,X ~ B(10, 0.3).a) Distribution:

The probability distribution of X is given by:

P(X = 0) = (0.7)^10

= 0.0282P(X = 1)

= 10C1 (0.3) (0.7)^9

= 0.1211P(X = 2)

= 10C2 (0.3)^2 (0.7)^8

= 0.2335P(X = 3)

= 10C3 (0.3)^3 (0.7)^7

= 0.2668P(X = 4)

= 10C4 (0.3)^4 (0.7)^6

= 0.2001P(X = 5)

= 10C5 (0.3)^5 (0.7)^5

= 0.1029P(X = 6)

= 10C6 (0.3)^6 (0.7)^4

= 0.0367P(X = 7)

= 10C7 (0.3)^7 (0.7)^3

= 0.0090P(X = 8)

= 10C8 (0.3)^8 (0.7)^2

= 0.0015P(X = 9)

= 10C9 (0.3)^9 (0.7)^1

= 0.0002P(X = 10)

= (0.3)^10

= 0.0000

The mass function of X is given by:

f(x) = P(X = x)

where x = 0, 1, 2, ..., 10.b)

Expected Value:μ = E(X) = np = 10 x 0.3 = 3

Variance:V(X) = npq = 10 x 0.3 x 0.7 = 2.1

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The difference of the maximum and minimum values is divided by the number of bins.

1. Identify the maximum and minimum values of the quantitative data

2. Subtract the minimum value from the maximum value to get the difference

3. Divide the difference by the number of bins to get the approximate width of each bin

The width of the bins in a frequency distribution of quantitative data can be estimated by dividing the difference between the maximum and minimum values of the data by the desired number of bins. This will provide an approximate size for each bin, which can then be used to construct the frequency distribution.

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