(14) If z1 = 2-3i and z2=3+i, find
(a) z1

The cost of putting sod on the​ yard is $1161.5

A trapezoid is a polygon that has just one pair of parallel sides.  The two extra sides of a trapezoid, known as the legs, are not parallel.

The price is calculated by multiplying the area in square feet by the price per square foot.

The formula for a trapezoid's area is

A = (1/2)([tex]b_{1}[/tex] + [tex]b_{2}[/tex])h.

where h represents height and [tex]b_{1}[/tex] and [tex]b_{2}[/tex] represent base lengths.

The area is

A = (1/2)(90 ft + 112 ft)(46 ft)

= 4646 [tex]ft^{2}[/tex]

when the supplied information is filled in.

Given that each square foot costs $0.25,

the price for this many square feet (4646[tex]ft^{2}[/tex] ) is $0.25/[tex]ft^{2}[/tex] × $989.23.

The cost of sodding the backyard will be $1161.5 according to the landscaper.

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There are 60,480 ways to seat 6 people in a row of 9 chairs using the multiplication principle of counting.

There are 9 choices for the first person, 8 choices for the second person (since one chair is already taken), 7 choices for the third person, and so on. Therefore, the total number of ways 6 people can be seated in a row of 9 chairs is:

[tex]9 * 8 * 7 * 6 * 5 * 4 = 60,480[/tex]

So there are 60,480 ways to seat 6 people in a row of 9 chairs.

To count the number of ways 6 people can be seated in a row of 9 chairs, we can use the multiplication principle of counting.

First, we consider the number of choices for the first person. Since there are 9 chairs and the order in which the people are seated matters, there are 9 choices for the first person. Once the first person is seated, there are 8 chairs remaining for the second person to choose from, since one chair is already taken. Therefore, there are 8 choices for the second person. Continuing in this way, there are 7 choices for the third person, 6 choices for the fourth person, 5 choices for the fifth person, and 4 choices for the sixth person.

To find the total number of ways to seat 6 people in a row of 9 chairs, we multiply the number of choices at each step together. Hence, the total number of ways is:

[tex]9 * 8 * 7 * 6 * 5 * 4 = 60,480[/tex]

So there are 60,480 ways to seat 6 people in a row of 9 chairs.

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The complete question is:

How many different arrangements are possible for 6 persons to sit in a row of 9 chairs?

a) 6720

b) 60480

c) 30

d) 346

Approximately 24.1% of Kelly's taxable income is her tax.

What is percent?

Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100.

To determine what percent of Kelly's taxable income is her tax, we need to calculate her tax liability first.

Assuming that Kelly files as a single taxpayer with no dependents and takes the standard deduction, her taxable income of $50,000 falls into the 22% tax bracket for the year 2021.

Using the IRS tax tables for 2021, Kelly's tax liability would be approximately:

$9950 + (0.22 * ($50,000 - $40,525)) = $9950 + $2095.50 = $12045.50

Therefore, Kelly's tax liability is approximately $12,045.50.

To calculate what percent of her taxable income is her tax, we can divide her tax liability by her taxable income and multiply by 100:

($12,045.50 / $50,000) * 100 = 24.09%)

Therefore, approximately 24.1% of Kelly's taxable income is her tax. Rounded to one tenth of a percent, this is 24.1%.

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Answer:

28.235

Step-by-step explanation:

10/34 = x/96

960= 34x

960/34= x

x= 28.235

For given functions f(x) and g(x), the value of  (f °g)(12) is 24.

What exactly is a function?

In mathematics, a function is a rule that assigns to each input value (also called the argument) exactly one output value. The input values are typically drawn from a specific set, called the domain of the function, and the output values are drawn from another set, called the range of the function.

Now,

To find (f °g)(12), we need to first evaluate g(12) and then use the result to evaluate f(g(12)).

g(x) = √(x+4), so g(12) = √(12+4) = √16 = 4.

f(x) = 4x+8, so f(g(12)) = f(4) = 4(4) + 8 = 16 + 8 = 24.

Therefore,

                  The value of (f ° g)(12) = f(g(12)) = 24.

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Answer:

5.33333

Step-by-step explanation:

Given:
[tex]x + \frac{9}{2} - 5x - \frac{6}{3} = 4x - \frac{-3}{3}[/tex]
Make the denominators Equal

[tex]\frac{6x + 27-30x-12}{6} = \frac{24 + 6}{6}[/tex]
[tex]\frac{-24x + 15}{6} = \frac{24x+6}{6}[/tex]

Cross- Multiply :

[tex]6(-24x + 15) = 6(24x + 6)[/tex]
[tex]-144x + 90 = 144x + 36[/tex]
[tex]90 - 36 = 144x + 144x[/tex]
[tex]54 = 288x[/tex]
[tex]x = \frac{288}{54} = 5.3333[/tex]

Hope it helps.

Charlie can make 6 hamburger form 1.56 pounds of meat if each uses 0.26 pounds.

The number of hamburger made by 0.26 pounds meat = 1

So, the number of hamburger possible from 1.56 pounds of meat = total amount of meat/amount of meat in one hamburger

Now, keep the values in formula to find the required answer

Number of hamburger = 1.56/0.26

Performing division on Right Hand Side of the equation to find the possible number of hamburger

Number of hamburger = 6

The 6 hamburger can be made from the meat.

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Rotation: Rotate the larger circle by the same angle as the smaller circle around the origin. Rotate the smaller circle by any angle. Although changing direction, this metamorphosis keeps the shape and size intact.

Any point in the plane that is a certain distance from another point forms a circle (center). Thus, it is a curve formed up of points that are separated from one another by a predetermined distance in the plane. Moreover, at every angle, it is rotationally symmetric about the centre. The closed, two-dimensional plane of a circle has every pair of points equally separated from the "centre." By drawing a line through the circle, one can create a line of circular symmetry. Moreover, at every angle, it is rotationally symmetric about the centre.

If two circles have the same shape but different sizes, they are comparable. The circles are centred at the origin in this case, allowing us to compare their radii to see if they are equal. The ratio of the larger and smaller circles' radii is 8/2, or 4.

Translation: Move the smaller circle to the origin and the larger circle in the same direction to a place four times away from the origin. While changing location, this transformation keeps the object's shape and size.

Rotation: Rotate the larger circle by the same angle as the smaller circle around the origin. Rotate the smaller circle by any angle. Although changing direction, this metamorphosis keeps the shape and size intact.

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He needed to save $15 over the remaining 2 weeks. This means she needed to save an average of $7.50 per week to reach her goal.

Both the arithmetic mean and the weighted mean may be used to determine the average of a group of integers. The sum of all the numbers in the group divided by the entire amount of numbers in the set yields the arithmetic mean. Regardless of significance or relevance, it gives each integer in the set the same amount of weight. On the other hand, the weighted mean gives the integers in the set distinct weights based on their significance or relevance. This indicates that certain numbers in the set provide a greater weighted mean contribution than others.

Given that, Bobbi's goal was to save an average of $7.00 per week.

Thus the amount saved is:

12 x $7 = $84.

He saved $5 for 11 weeks thus,

11 x $5 = $55.

Then in the 12th week the amount saved is:

$29 - $14 = $15.

Hence, she needed to save $15 over the remaining 2 weeks. This means she needed to save an average of $7.50 per week to reach her goal.

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Answer:

-5≤y≤17

Step-by-step explanation:

Answer: -5 to 17 degrees

Step-by-step explanation:

Therefore , the solution of the given problem of equation comes out to be the system of equations has an answer of x = 5 and y = -2.

Mathematical formulas frequently use the same variable letter to try to enforce harmony among two assertions. Many academic numbers are shown to be equal using mathematical expression, also known as assertions. In this case, instead of splitting 12 into two parts, the normalise adds b + 6 using the example of y + 6. It is possible to determine the link number between each sign portion and the line length.

Here,

One of the solutions for a single variable should be solved in terms of the other.

We can find x from the first solution by solving in terms of y:

=> 2x + 3y = 4

=>  2x = 4 - 3y

=>  x = (4 - 3y)/2

Solve for the other variable by substituting the formula for the variable from step 1 into the other equation.

Change x in the second expression to (4 - 3y)/2:

=>  2x = 7y + 24

=>  2((4 - 3y)/2) = 7y + 24

=>  4 - 3y = 7y + 24

=> -10y = 20

=> y = -2

Solve for the other variable by substituting the value of the variable from step 2 into one of the initial formulae.

When the first solution is used:

=> 2x + 3y = 4

=> 2x + 3(-2) = 4

=> 2x - 6 = 4

=> 2x = 10

=> x = 5

As a result, the system of equations has an answer of x = 5 and y = -2.

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Answer:

14 minutes

Step-by-step explanation:

We take

63 / 6 = 10.5 words per minute

So, Nachelle can text 10.5 words per minute.

At this rate, how many minutes would it take her to text 147 words?

We take

147 / 10.5 = 14 minutes

So, at this rate, it would take her 14 minutes to text 147 words.

The n-ary rule for linear sequences is 7n - 1. The given sequence is an arithmetic sequence.

What is Arithmetic Progression?

Any two consecutive integers in a sequence are in "arithmetic progression" (AP) if their difference is constant.

The formula is given by Tn = a + (n - 1) d. where,

a, first term = 6 n, number of terms

d, binomial tolerance = 13 - 6 = 7

So substitute the value into the equations. It will be as follows.

Tn = a + (n - 1)d

= 6 + (n - 1)7

= 6 + 7n - 7

= 7n - 1

So the n term of this sequence is 7n - 1. 

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When two distinct lines, l and m, are each perpendicular to the same line n, it means that the two lines have the same angle of rotation in relation to n.

An angle is a figure formed by two lines or rays diverging from a common point. It is measured in degrees, with a full circle representing 360 degrees. Angles are used to describe the direction and orientation of objects, as well as to measure the size of an area or the relationship between two lines. Angles are an important part of mathematics, used in problems such as geometry, trigonometry and calculus.

This angle is equal to 90 degrees, meaning that the two lines are parallel to one another.

Parallel lines are lines that never intersect and are always the same distance apart. This is the case for l and m because both lines are perpendicular to the same line n and, thus, have the same angle. Therefore, the two lines are parallel to one another, meaning that they will never cross and will always remain the same distance apart.

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On the opening day of the exhibition, 30 adult tickets were sold.

Let's use the following variables to represent the number of adult and child tickets sold:

a: the number of adult tickets sold

c: the number of child tickets sold

From the problem, we will use linear equation system. we know that the total number of tickets sold is 80, so we have:

a + c = 80 (Equation 1)

We also know that the total revenue from ticket sales is $180, so we have:

3a + 2c = 180 (Equation 2)

We can use Equation 1 to solve for one of the variables in terms of the other:

c = 80 - a

Substituting this into Equation 2, we get:

3a + 2(80 - a) = 180

Simplifying this equation, we get:

a + 160 = 90

a = 30

Therefore, by using linear equation system, 30 adult tickets were sold on the opening day of the exhibition.

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Answer:

Step-by-step explanation:

Given equation,

→ 0.48 = ?/25

Let's change the symbol into x,

→ 0.48 = x/25

Now we have to,

→ Find the required value of x.

Then the value of x will be,

→ 0.48 = x/25

→ x/25 = 0.48

→ x = 0.48 × 25

→ [ x = 12 ]

Hence, the value of x is 12.

If the club has a payment plan in which a member can pay $50 down and the rest in 12 equal payments, the monthly payment is $42.50

To calculate the monthly payment for a health club membership with a payment plan, we first need to subtract the down payment of $50 from the total cost of $560. This leaves us with $510 to be paid in 12 equal monthly installments.

To find out how much each monthly payment would be, we divide the remaining balance ($510) by the number of months (12). Therefore, the monthly payment would be:

$510 ÷ 12 = $42.50

Therefore, A member would need to pay $50 down and $42.50 per month for the next 12 months to cover the cost of a $560 annual membership.

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The maximum number οf apples she can purchase is 15.

Let's start by finding the cοst οf οne apple and οne οrange using the infοrmatiοn frοm twο Saturdays agο:

3a + 4ο = 3.47, where "a" is the cοst οf οne apple and "ο" is the cοst οf οne οrange.

We can simplify this equatiοn by dividing bοth sides by 3: a + 4/3 ο = 1.1567

Nοw, let's use the infοrmatiοn frοm last Saturday:

12ο = 6.36

ο = 0.53

We can substitute this value οf "ο" intο οur simplified equatiοn tο find the cοst οf οne apple:

a + 4/3(0.53) = 1.1567

a = 0.63

Sο, οne apple cοsts $0.63 and οne οrange cοsts $0.53.

If Shefali has οne $10 bill and she wants tο buy the maximum number οf apples, she can spend at mοst $10 οn apples. Let "n" be the number οf apples she can buy:

0.63n ≤ 10

n ≤ 15.87

Since Shefali can't buy a fractiοnal part οf an apple, the maximum number οf apples she can purchase is 15.

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Answer:

13m

Step-by-step explanation:

pls mrk me brainliest

The Gaussian Function in statistical method is defined as follows:

f(x) = (1 / σ√(2π)) e^(-0.5((x-μ)/σ)²)

In which the parameters are listed as follows:

The Gaussian function is a widely used probability density function in statistics, also known as the normal distribution or bell curve, and has the equation defined at the beginning of the answer.

The curve is symmetrical around the mean (μ) of the distribution. The standard deviation (σ) of the distribution determines the width of the curve, with smaller standard deviations resulting in narrower curves and larger standard deviations resulting in wider curves.

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a) Rate of change: 1.5

b) Rate of change: -3

c) Rate of change: -2

d) Rate of change: 2, other values are calculated below.

When two sides of a balance scale are equal, the equation will remain true.

a. y = 1.5x

Rate of change: 1.5 (which means that for every increase of 1 in x, y increases by 1.5)

Y-values increase as x increases

Y-intercept: 0 (the point where the line crosses the y-axis)

Two points: (0,0) and (2,3)

b. y = -3x + 10

Rate of change: -3 (which means that for every increase of 1 in x, y decreases by 3)

Y-values decrease as x increases

Y-intercept: 10

Two points: (0,10) and (3,1)

c. y = -2x + 6

Rate of change: -2 (which means that for every increase of 1 in x, y decreases by 2)

Y-values decrease as x increases

Y-intercept: 6

Two points: (0,6) and (3,0)

d. y = 2x + 5

Rate of change: 2 (which means that for every increase of 1 in x, y increases by 2)

Y-values increase as x increases

Y-intercept: 5

Two points: (0,5) and (3,11)

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Sin(pi - theta) has a value of 4/9. sin(pi - theta) is equal to sin for any value of theta (theta). sin(pi - theta) has a value of 4/9.

We may calculate the value of sin(pi - theta) using the trigonometric identity sin(pi - theta) = sin(pi)cos(theta) - cos(pi)sin(theta):

Pi minus theta equals sin (pi)

cos(pi)sin - cos(theta) (theta)

We may simplify the expression to: since sin(pi) = 0 and cos(pi) = -1

0*cos(theta) - (-1)*sin = sin(pi - theta) (theta)

Pi minus theta equals sin (theta)

The value of sin(theta) can now be substituted to obtain:

Theta = 4/9 sin(pi - theta)

Hence, sin(pi - theta) has a value of 4/9.

The value of theta determines the value of sin(pi - theta). In terms of the trigonometric functions of theta, there is a generic formula to get sin(pi - theta): Pi minus theta equals sin (pi)

cos(pi)sin - cos(theta) (theta)

We may simplify the expression to: since sin(pi) = 0 and cos(pi) = -1

0*cos(theta) - (-1)*sin = sin(pi - theta) (theta)

Pi minus theta equals sin (theta)

Hence, sin(pi - theta) is equal to sin for any value of theta (theta).

Hence, sin(pi - theta) has a value of 4/9.

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Answer:

(1)100

(2)120

(3)80

(4)200

(5)42.85

Step-by-step explanation:

The answers explanation is:

P=RB, p=percentage

r=rate

b=base,so

P=RB

P/R=RB/R

B=P/R

For example, (1)B=P/R

B=5/5/100

B=5*100/5

B=500/5

B=100 and so on - - -

GOOD LUCK!

Where T is the subject of the formula, the expression becomes, T = N²SL/M². (Option B)

To make T the subject of the formula M = N√(SL/T), we need to isolate T on one side of the equation by performing mathematical operations in a way that cancels out all other variables.

Here's how we can do that:

Square both sides of the equation to eliminate the square root:

M² = N²SL/T

Multiply both sides of the equation by T to get rid of the denominator on the right-hand side:

M²T = N²SL

Divide both sides of the equation by M² to isolate T on one side:

T = N²SL/M²

Therefore, the formula for T in terms of the other variables is:

T = N²SL/M².

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Full Question:

Although part of your question is missing, you might be referring to this full question:

Given M = N√(SL/T), make T the subject of the formula.

A. NSL/M

B. N²SL/M²

C. N²SL/M

D. NSL/M²

The length of the rectangle is 63 cm and the Breadth of the rectangle is 12 cm, for this, we have to know something about rectangles.

Rectangle, It is a plane shape, as opposed to a square, with four(4) straight sides and four(4) right angles, particularly one(1) with uneven neighboring sides.

Square, A square is a regular quadrilateral in Euclidean geometry, which means that it has four(4) equal(same) sides and four(4) equal angles. It can alternatively be explained as a rectangle with two(2) neighboring sides that are of equal(same) length.

Given, Perimeter = 150 cm, Length, l = 5b+3 , Breadth = b

150 = 2(5b + 3 + b)

150 = 2(6b +3)

6b +3 = 75

6b = 72

b = 12 cm, So l = 63 cm (By putting the b value in the l equation

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Answer:

$6141

Step-by-step explanation:

We can use the formula for compound interest to find the amount in the account after 18 years:

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

Where:

A = the amount in the account after 18 years

P = the principal amount (initial deposit) = $3000

r = the annual interest rate = 4% = 0.04

n = the number of times the interest is compounded per year = 4 (quarterly)

t = the time in years = 18

Plugging in these values, we get:

A = 3000(1 + 4%/4)^(4*18)

A = 3000(1.01)^72

A = 3000*2047

A = 6141

Rounding to the nearest whole number, we get:

A = $6141

Therefore, there will be $6141 in the account on the child's 18th birthday.

Answer:

1/36 and 216

Step-by-step explanation:

The probability of rolling a 6 or a 2 on either piece of dice is 1/6. Therefore, 1/6x1/6= 1/36.

When rolling three dice, we also need to consider the fact that there is a 1/6 chance of rolling any number. 6x6x6= 216.

The rule is to minus 4 from the x-coordinate and add 8 to the other. The coordinates of A after the reflection are (-x,y). Thus, it is present to the left of the Y-axis. Yes, the final figure is congruent to the original figure.

To translate a point 4 units left and 8 units up, we subtract 4 from the x-coordinate and add 8 to the y-coordinate.

Now, let’s apply this rule to point A. If A has coordinates (x,y), then after translation it will have coordinates (x-4,y+8).

For the second question, we can find the new location of A by using the coordinates we just found. So if A was originally located at (x,y), it will now be located at (x-4,y+8).

To reflect a point over the y-axis, we negate its x-coordinate. So if A has coordinates (x,y), then after reflection it will have coordinates (-x,y).

Using this rule, we can find that after reflection over y-axis, point A will have coordinates (-x,y).

Finally, since translation and reflection are both rigid transformations, they preserve distance and angles between points. Therefore, the final figure is congruent to the original figure.

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Correct question is:

ABC is translated 4 units to the left and 8 units up, then reflected across the y-axis.  Answer the questions to find the coordinates of A after the translation.

1. Give the rule for translating a point 4 units left and 8 units up.

2. After the translation, where is A located?

3. Give the rule for reflecting a point over the y-axis.

4. What are the coordinates of A after the reflection?

5. Is the final figure congruent to the original figure? How do you know?

a. The probability that the sample will have between 50% and 55% of the identifications correct is 0.2058.

b. The lower limit of the population percentage is 45% and the upper limit is 55%. There is a 90% probability that the sample percentage will be contained within 10% symmetrically around the population percentage.

c. The probability that the sample percentage of correct identifications is greater than 65% is 0.0432.

d. It is more likely to have more than 62% correct identifications in a sample of 190 than more than 56% correct identifications in a sample of 1,000. This is due to the larger sample size in the second case, which makes it less likely for the sample to deviate from the population percentage.

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