what is the sum of 3 - 2i and -5 + 6i?

The surface area of a sphere with a radius of 10 feet is approximately 1,256 ft².

The surface area of a sphere refers to the total area that covers the surface of the sphere. It is the sum of all the areas of the small flat faces that make up the sphere.

To find the surface area of a sphere with a radius of 10 feet, we need to use the formula:

Surface Area = 4πr²

Where r is the radius of the sphere.

Plugging in the value of r=10 into the formula, we get:

Surface Area = 4π(10) = 400π

Since π is an irrational number, we cannot calculate its exact value. However, we can approximate it to 3.14. Therefore,

=> Surface Area = 400 * 3.14 = 1256

Rounding to the nearest whole number, we get the surface area of the sphere with a radius of 10 feet as 1,256 ft², which is option (a).

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Step-by-step explanation:

(3-2)^2+y^2=4

(9-4)+y^2=2^2

the power of y and 2 should be cut now

5+y=2

5-2=y

3=y

y=3

:. the area of enclosed by a circle is 3 cm

The system of linear equations using matrix inversion can be represented as the equations in matrix form as AX = B, where A is the coefficient matrix, X is the variable matrix, and B is the constant matrix.

(a)
The coefficient matrix A is:
| -1 -4 2 |
| 1 2 -1 |
| 1 1 -1 |

The variable matrix X is:
| x |
| y |
| z |

The constant matrix B is:
| 6 |
| 1 |
| 6 |

To solve for X, we can use the formula X = A^(-1) * B, where A^(-1) is the inverse of A.

First, we need to find the inverse of A. Inverse of A, denoted as A^(-1), is found by using matrix inversion.

Next, we calculate the product of A^(-1) and B to find X.

(b)
The coefficient matrix A is:
| -1 -4 2 |
| 1 2 -1 |
| 1 1 -1 |

The variable matrix X is:
| x |
| y |
| z |

The constant matrix B is:
| -8 |
| 7 |
| 2 |

We can follow the same steps as in part (a) to find X.

(c)
The coefficient matrix A is:
| -1 -4 2 |
| 1 2 -1 |
| 1 1 -1 |

The variable matrix X is:
| x |
| y |
| z |

The constant matrix B is:
| 0 |
| 0 |
| 0 |

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The confidence interval size shrank from 0.99 to 0.90, is the right answer. Confidence interval: 0.88

A confidence interval in frequentist statistics is a range of estimates for an unknown parameter. A confidence interval is calculated at a specified degree of confidence; the most popular level is 95%, but other levels, such as 90% or 99%, are occasionally used.

Therefore, the correct choice is option B which states that From 0.99 to 0.90 the confidence interval size became smaller

In statistics, confidence is another word for probability. If you create a confidence interval, for instance, with a 95% level of confidence, you can be sure that 95 out of 100 times, the estimate will fall between the upper and lower values indicated by the confidence interval.

It can be calculated as:

df=n-1=19

t critical value 0.12 (two tail) = 1.62797

M = 51.5

sM = √(6.842 / 20) = 1.53

μ = M ± Z (sM)

μ = 51.5 ± 1.62797 * 1.53

μ = 51.5 ± 2.49

Therefore, CI { 49.01 and 53.99 }

Therefore, the confidence interval size shrank from 0.99 to 0.90, is the right answer. Confidence interval: 0.88

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Answer:

Highest: 1277 meters. Closer to sea level: -969 meters

The Values of (a+b)ab are undefined.

Given that, a = 3an and db = -2We need to find the values of (a+b)

Now, we have a = 3an... equation (1)Also, we have db = -2... equation (2)From equation (1), we get: n = 1/3... equation (3)Putting equation (3) in equation (1), we get: a = a/3a = 3... equation (4)Now, putting equation (4) in equation (1), we get: a = 3an... 3 = 3(1/3)n = 1

From equation (2), we have: db = -2=> d = -2/b... equation (5)Multiplying equation (1) and equation (2), we get: a*db = 3an * -2=> ab = -6n... equation (6)Putting values of n and a in equation (6), we get: ab = -6*1=> ab = -6... equation (7)Now, we need to find the value of (a+b).For this, we add equations (1) and (5),

we get a + d = 3an - 2/b=> a + (-2/b) = 3a(1) - 2/b=> a - 3a + 2/b = -2/b=> -2a + 2/b = -2/b=> -2a = 0=> a = 0From equation (1), we have a = 3an=> 0 = 3(1/3)n=> n = 0

Therefore, from equation (5), we have:d = -2/b=> 0 = -2/b=> b = ∞Now, we know that (a+b)ab = (0+∞)(0*∞) = undefined

Therefore, the values of (a+b)ab are undefined.

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The sampling soldiers until her margin of error for a 82% confidence interval is less than 0.004, soldiers should Haley sample is 12,724 soldiers.

The degree of inaccuracy in survey findings from random sampling is known as the margin of error in statistics. A wider margin of error in statistics denotes a reduced chance of relying on a survey's or poll's findings, meaning that there will be less trust in the results' ability to accurately reflect a community. It is a very important tool for market research since it shows the degree of assurance that should be placed in survey data by the researchers.

A confidence interval is a measure of how unpredictable a given statistic is. It is typically used in conjunction with the margin of error to indicate how confidently a statistician feels that the findings of an online survey or online poll are worthy of being considered representative of the total population.

In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi (1-\pi)}{n} }\)

In which, z is the z-score that has a p-value of 1+∝/2.

The margin of error is of:

\(M=z\sqrt{\frac{\pi (1-\pi)}{n} }\)

Estimate of the proportion of 64%, hence π = 0.64.

94% confidence level

So , ∝ = 0.94 z is the value of Z that has a p-value of , so z = 1.88

Margin of error of less than 0.008 is wanted, hence, we have to find n when M = 0.008.

\(M=z\sqrt{\frac{\pi (1-\pi)}{n} }\\0.008 =1.88\sqrt{\frac{0.64(0.36)}{n} } \\0.008\sqrt{n} = 1.88\sqrt{0.64(0.36)} \\n = 12723.84\\\)

Therefore, Haley should sample 12,724 soldiers.

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Answer:

8 hours

Step-by-step explanation:

The scenario that is being described can be fully made into an equation using three variables. These would be w for the number of weeks, b for the number of hours she babysat that week, and x for the total amount of hours worked. Like so...

5w + t = x

Since we are told that we need to find the total hours worked for a single week (w = 1) and that Erica babysat for 8 hours that week (b = 8), then we only need to solve for the total amount of hours worked (x)

5(1) + 8 = x

5+8 = x

13 = x

Erica worked a total of 8 hours.

The sine of the angle theta is given by the ratio of the opposite leg to the hypotenuse side of the right triangle formed by the terminal segment.

Reasons:

The given parameters are;

The sine value of the given angle = One-half

Required: To select the true statement of the location of the terminal side.

Solution:

Given that sin(θ) = 0.5, we have;

The sine of an angle is positive in Quadrant I and Quadrant II

The reference angle, is the angle formed between the angle's terminal side and x-axis

By trigonometric ratios, considering the reference angle, we have;

θ = arcsin(0.5) = 30°

Therefore;

The option that gives the true location of the terminal side of an angle, that have a sine value of One-half is; Theta has a reference angle of 30° and is in Quadrant I or II.

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Answer:

a

Step-by-step explanation:

edge

Maya drove on the mountains for her trip. Due to traffic, her average rate of miles per hour was faster at the time of coming back to her home than going on her trip. Thus, The distance between where she lives and the mountains is

288 miles .

Let's consider that Maya live x miles from the mountains.

Let her rate to mountains be y miles/h.

we have given that

Driveing time taken by Maya going from home to trip location= 9 hours due to traffic

total return time taken by her = 4 hours

average rate = 40 miles/hour

Using rate formula,

Rate = distance/time

=> distance (d) = rate (r) × time (t)

so, x/y = 9

=> x=9y --(1)

Return trip 4 hours then rate = y+40

=> x/(y+40) =4 --(2)

using Substitution method, x= 3 substitute in (2)

=> 9y/(y+40)=4

=> 9y=4y+160

=> 9y-4y=160

=> 5y=160

=> y= 160/5

=> y=32

Now, x=9y

x=9×32= 288 miles

Hence, distance to the mountain is 288 miles.

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Complete question:

Maria drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 9 hours. When Maria drove home, there was no traffic and the trip only took 4 hours. If her average rate was 40 miles per hour faster on the trip home, how far away does Maria live from the mountains?

Do not do any rounding.

Answer:

I think that the answer is c

Step-by-step explanation:

Answer:

there is no table so we are therefore unable to answer this question

Step-by-step explanation:

sorry

Answer:

answer is 21= 5x- y

Step-by-step explanation:

y+6=5(x-3)

y+6=5x-15

y = 5x-15-6

y = 5x-21

rearrange this equation as formAx+By=C

5X - y = 21

Answer:

Yes(-1,-1)

Yes (0,-40)

No - (1,1600)

Step-by-step explanation:

Answer:

x = -2

Step-by-step explanation:

3/2 (x-5) - 3/2 = 9x/2

3x/2 - 15/2 - 3/2 = 9x/2 ... alldenominator

are 2 so we can multiply all term by 2

2(3x/2 - 15/2 - 3/2 = 9x/2)

3x - 15 - 3 = 9x ... simplify it

3x - 12 = 9x

-12 = 9x - 3x ... take 3x to the left

-12 = 6x ... simplify

6x/6 = -12/6 ... dividing both side by 6

x = -2 ... simplify and solve x

Answer:

-11

Step-by-step explanation:

-20-(-9)= -11

Answer:

a.

\(f(t) = 21000( {.918}^{t} )\)

b.

\(f(4) = 21000( {.918}^{4}) = 14913.86\)

The value of x is 7/3, which can be rounded to two decimal places as approximately 2.33.

To solve the equation 2x + 8 + 4x = 22, we need to combine like terms and isolate the variable x.

Combining like terms, we have:

6x + 8 = 22

Next, we want to isolate the term with x by subtracting 8 from both sides of the equation:

6x + 8 - 8 = 22 - 8

6x = 14

To solve for x, we divide both sides of the equation by 6:

(6x) / 6 = 14 / 6

x = 14/6

Simplifying the fraction 14/6, we get:

x = 7/3

Therefore, the value of x is 7/3, which can be rounded to two decimal places as approximately 2.33.

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The test variable in part 1 of the investigation is the type of fertilizer used, while the responding variable is the growth rate of the plants.

In part 1 of the investigation, the experiment aims to study the effect of different fertilizers on plant growth. The test variable, or the independent variable, is the type of fertilizer being used. The researcher would manipulate this variable by selecting and applying different types of fertilizers to the plants. The responding variable, or the dependent variable, is the growth rate of the plants.

This variable is expected to change in response to the manipulation of the test variable. The researcher would measure and observe the growth rate of the plants in order to determine the impact of the different fertilizers on their development.

By identifying and controlling the test and responding variables, the experiment allows for a systematic analysis of the relationship between the fertilizer type and plant growth, providing valuable insights for agricultural practices or gardening.

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Given:

Slope of a straight line is \(\sqrt{3}\).

The line passing through the point (-1,5).

To find:

The equation of the straight line.

Solution:

The point slope form of a line is:

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

Where, m is the slope and \((x_1,y_1)\) is the point.

The line passing through the point (-1,5) with slope \(\sqrt{3}\). So, the equation of the line is:

\(y-5=\sqrt{3}(x-(-1))\)

\(y-5=\sqrt{3}(x+1)\)

\(y=\sqrt{3}x+\sqrt{3}+5\)

Therefore, the equation of the straight line is \(y=\sqrt{3}x+\sqrt{3}+5\).

Answer:

If c=2 than x=5 because 2x5=10 and 10-7=3 and 3x3=9

Step-by-step explanation:

Answer:

A. 150

Step-by-step explanation:

Calculate the probability of landing on an odd number: 1/2.

Multiply the probability by the number of trials: (1/2) * 300.

Simplify the expression: 150.

Therefore, a reasonable prediction is that the event of landing on an odd number will occur 150 times out of the 300 rolls of the fair 6-sided die.

Answer: Option B

Step-by-step explanation:

Answer:

£3.9

Step-by-step explanation:

Philip went to the shop with £9.60

spent £5.70

Money left = £9.60 -£ 5.70

                  =£3.9

Hence,

He came home with £3.9

The probability that a card is a spade or a king, given that it is black is 3/26 or 0.1154 or 11.54%

In a standard deck of cards, we have the following readings

Black cards = 26

Black spade or king = 3

So, we have the probability formula to be

Probability = Black spade or king/Black cards

This gives

Probability = 3/26

Evaluate

Probability = 0.1154

Express as percentage

Probability = 11.54%

Hence, the probability that a card is a spade or a king, given that it is black is 3/26

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Answer:

ther is no dot plot

Step-by-step explanation:

The last term is 300

The sum of all the terms is 15150.0

The average of all the terms is 151.5

Here is an example solution in Python that follows the given pseudocode:

# Prompt for and read the first term

first_term = int(input("Enter first term: "))

# Prompt for and read the common difference

common_difference = int(input("Enter common difference: "))

# Prompt for and read the number of terms

number_of_terms = int(input("Enter number of terms: "))

# Calculate the last term

last_term = first_term + (number_of_terms - 1) * common_difference

# Calculate the sum of all the terms

sum_of_terms = number_of_terms * (first_term + last_term) / 2

# Calculate the average of all the terms

average_of_terms = sum_of_terms / number_of_terms

# Display the results

print("The last term is", last_term)

print("The sum of all the terms is", sum_of_terms)

print("The average of all the terms is", average_of_terms)

If you run this code and enter the values from the sample run (first term: 3, common difference: 3, number of terms: 100), it will produce the following output:

The last term is 300

The sum of all the terms is 15150.0

The average of all the terms is 151.5

The program prompts the user for the first term, common difference, and number of terms. Then it calculates the last term using the given formula. Next, it calculates the sum of all the terms and the average of all the terms using the provided formulas. Finally, it displays the calculated results.

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Answer:

Area of gray region = \(8x^2+8x-7\)

Step-by-step explanation:

The area covered by the furniture can be subtracted from the total area of the room to calculate the area of the gray region.

Total area of the room: \(13x^2+7x-2\)

Area taken up by furniture: \(5x^2-x+5\)

Area of gray region = total area of the room - area taken up by furniture

Area of gray region = \(13x^2+7x-2-(5x^2-x+5)\)

Remember to distribute the negative sign:

Area of gray region = \(13x^2+7x-2-5x^2+x-5\)

Combine like terms:

Area of gray region = \(8x^2+8x-7\)

Answer:

8x^2+6x+3

Step-by-step explanation:

 13x^2+7x-2

-  5x^2-   x+3

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

8x^2=6x=3

Answer:

Summary:

Step-by-step explanation:

We know that the diagonals of a parallelogram bisect each other.

As

The parallelogram PQRS is given, so

RT = TP

Given

plug in RT = x and TP = 5x-28 in the equation RT = TP

RT = TP

x = 5x-28

switch the sides

5x-28 = x

adding 28 in both sides

5x-28+28 = x+28

simplify

5x = x+28

subtract x from both sides

5x-x = x+28-x

4x = 28

divide boh sides by 4

4x ÷ 4 = 28  ÷ 4

simplify

x = 7

Therefore, we conclude that the value of x is: x = 7

Similarly,  

QT = TS

Given

plug in QT = 5y and TS = 2y+12 in the equation QT = TS

QT = TS  

5y = 2y+12

subtract 2y from both sides

5y - 2y = 2y+12-2y

simplify

3y = 12

divide both sides by 3

3y ÷ 3 = 12 ÷ 3

simplify

y = 4

Therefore, we conclude that the value of y is: y = 7

Summary: