Kira hires a contractor to build a new deck in her backyard. A design for the deck is shown

To simplify the expression (3+2i)/(2-5i), we need to multiply the numerator and denominator by the conjugate of the denominator. After simplifying, we can express the result in the form a + bi, where a and b are real numbers.

To simplify (3+2i)/(2-5i), we start by multiplying the numerator and denominator by the conjugate of the denominator. The conjugate of 2-5i is 2+5i.

(3+2i)/(2-5i) * (2+5i)/(2+5i)

Multiplying the numerators and denominators together, we get:

(6 + 15i + 4i + 10i^2)/(4 + 10i - 10i - 25i^2)

Simplifying further:

(6 + 19i - 10)/(4 + 25)

( -4 + 19i)/(29)

So, the simplified form of (3+2i)/(2-5i) is (-4 + 19i)/29.

The expression is now in the form a + bi, where a = -4 and b = 19/29.

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Answer:

-4.2c+4.8d

Step-by-step explanation:

(−7c+8d)0.6

Distribute

-7c*.6 + 8d * .6

-4.2c+4.8d

Answer:

-4.2c + 4.8d

Step-by-step explanation:

We would like to distribute the 0.6 in the expression (-7c + 8d) * 0.6.

Remember that when distributing, we multiply the "outside number" (0.6 in this case) by each of the "inside numbers" (-7c and 8d) and then add those products.

So, the first product will be: 0.6 * (-7c) = -4.2c. The second product will be: 0.6 * 8d = 4.8d. Add these together: -4.2c + 4.8d.

The answer is thus -4.2c + 4.8d.

~ an aesthetics lover

The Translation image of A after it has been translated would be (-5, 0).

You can move the form left or right using the vector's top number. You shift the form to the left if the number is negative. The form is moved to the right if the number is positive. You can determine whether you are moving up or down by looking at the vector's bottom number.

To find the translation image of point A(-3, 8) after it is translated by the vector (-2, -8), we need to add the x-component of the vector (-2) to the x-coordinate of point A (-3), and add the y-component of the vector (-8) to the y-coordinate of point A (8).

The new x-coordinate will be:

(-3) + (-2) = -5

New y-coordinate:

(8) + (-8) = 0

The translation image of point A (-3, 8) after it is translated by the vector (-2, -8) is the point (-5, 0).

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Answer:

I believe the answer is

\(y = 4x - 7\)

Step-by-step explanation:

hope thai HELPS!

if you want an explanation ask me in the comments.

So, Mathilda should mix 600 grams of OMT with 300 grams of WMT to sell the resulting mixture at Php 1.80 per gram.

The unitary approach involves calculating the value of a single unit, from which we may calculate the values of the necessary number of units.

The unitary method's formula is to identify the value of a single unit, then multiply that value by the number of units to obtain the required value.

A unit is a quantity with a fixed magnitude that is used to gauge the sizes of other quantities that behave similarly.

The terms millimeter (mm), centimeter (cm), meter (m), and kilometer (km) are used to describe length (km). The weight is measured in kilograms (kg) and grams (g). Milliliter (ml) and liter are used to measure volume (L).

Let x be the amount of OMT powder in grams. We know that the total amount of powder in the mixture is x + 300 grams since Mathilda is mixing x grams of OMT with 300 grams of WMT.

(x * Php 2 + 300 * Php 1) / (x + 300) = Php 1.80

Solving for x, we can get the amount of OMT powder in grams:

x = (300 * Php 1.80 - 300 * Php 1) / (Php 2 - Php 1.80) = 300 * (Php 1.80 - Php 1) / (Php 2 - Php 1.80) = 600

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A transversal is a straight line that intersects two parallel lines forming four angles at each point of intersection. Thus the required answers to the given question are:

i. Side NM is parallel to side XZ.

ii. Using the corresponding property

iii. <XYZ is congruent to <NYM

iv. ΔXYZ is similar toΔNYM by SAS theorem

Two or more angles are said to be congruent if and only if they have equal measure. This property can be used to relate equal angles.

While a transversal is a straight line that intersects two parallel lines forming four angles at each point of the intersection.

The required answers to the question are as stated below:

i. Side NM is parallel to side XZ.

ii. The corresponding property

iii. <XYZ is congruent to <NYM

iv. ΔXYZ is similar toΔNYM by SAS theorem

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Answer: For the first box it is parallel, for the second box it is the corresponding angles theorem, the third is NYM, and the last one is AA.

Step-by-step explanation: 1.) Since line NM has an arrow on it's line and XZ has an arrow on it's line, that means that those two line are parallel to each other. 2.) Since both triangle contain the same transversal line (NY) and the corresponding angles theorem states that if a transversal intersects parallel lines, the corresponding angles are congruent. From this we can conclude that this means that the angle <YXZ has is congruent to the angle <YNM. Therefore we use the corresponding angles theorem. 3.) Answer 2 basically answers box number three but since we concluded that Angles of <YXZ and <YNM are both congruent <NYM would be your answer its just flipped. 4.) We use the AA theorem, because the AA theorem states that if an angle or angle(s) of one triangle is congruent to another angle/angle(s) of another triangle, then the triangles are similar (congruent). Therefore we would use the AA theorem.

Hope this helps :)

By the way this is the answer for EDGE in 2023

The cost of one pack of streamers can be calculated by finding the difference in the total cost of the two purchases and dividing it by the difference in the number of packs of streamers. Therefore, one pack of streamers costs $2.75.

Let's denote the cost of one pack of streamers as "x". From the given information, we know that Randy bought 8 packs of streamers for $48.60, and later bought 3 packs of streamers for $34.85.

Using this information, we can set up the following equation to represent the total cost of the two purchases:

8x + 28 balloons = $48.60

3x + 28 balloons = $34.85

To find the cost of one pack of streamers, we need to subtract the second equation from the first equation to eliminate the balloons:

(8x + 28 balloons) - (3x + 28 balloons) = $48.60 - $34.85

Simplifying the equation gives:

5x = $13.75

Dividing both sides by 5, we find that:

x = $2.75

Therefore, one pack of streamers costs $2.75.

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A graph of polygon GREAT and its image after a counterclockwise rotation of 90° around the origin is shown in the image attached below.

In Mathematics and Geometry, the rotation of a point 90° about the center (origin) in a counterclockwise (anticlockwise) direction would produce a point that has these coordinates (-y, x).

By applying a rotation of 90° counterclockwise around the origin to vertices W, the coordinates of the vertices of the image ΔA'B'C' are as follows:

(x, y)                               →            (-y, x)

Ordered pair G = (-3, -2) → Ordered pair G' = (2, -3)

Ordered pair R = (-4, 4) → Ordered pair R' = (-4, -4)

Ordered pair E = (0, 1) → Ordered pair E' = (-1, 0)

Ordered pair A = (1, -2) → Ordered pair A' = (2, 1)

Ordered pair T = (-1, -3) → Ordered pair T' = (3, -1)

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(a) To compute\(E_e_n\)(X), we need to find the expectation value of the operator X in the state ψ_n.

The operator X corresponds to the position of the particle. The expectation value of X in the state ψ_n is given by:

\(E_e_n\)(X) = ∫ ψ_n* X ψ_n dx,

where ψ_n* represents the complex conjugate of ψ_n. Since ψ_n = √(2/a) sin(nπx/a), we can substitute these values into the integral:

\(E_e_n\)(X) = ∫ (2/a) sin(nπx/a) * X * (2/a) sin(nπx/a) dx.

The integral is taken over the interval [0, a]. The specific form of the operator X is not provided, so we cannot calculate \(E_e_n\)(X) without knowing the operator.

(b) To compute \(E_v_n\)(X^2), we need to find the expectation value of the operator X^2 in the state ψ_n. Similar to part (a), we can calculate it using the integral:

\(E_v_n\)(X^2) = ∫ (2/a) sin(nπx/a) * X^2 * (2/a) sin(nπx/a) dx.

Again, the specific form of the operator X^2 is not given, so we cannot determine \(E_v_n\)(X^2) without knowing the operator.

(c) To compute E_ψ_n(P), we need to find the expectation value of the momentum operator P in the state ψ_n. The momentum operator is given by P = -iħ(d/dx). We can substitute these values into the integral:

E_ψ_n(P) = ∫ ψ_n* P ψ_n dx

        = ∫ (2/a) sin(nπx/a) * (-iħ(d/dx)) * (2/a) sin(nπx/a) dx.

(d) To compute E_φ˙n(P^2), we need to find the expectation value of the squared momentum operator P^2 in the state ψ_n. The squared momentum operator is given by P^2 = -ħ^2(d^2/dx^2). We can substitute these values into the integral:

E_φ˙n(P^2) = ∫ ψ_n* P^2 ψ_n dx

          = ∫ (2/a) sin(nπx/a) * (-ħ^2(d^2/dx^2)) * (2/a) sin(nπx/a) dx.

(e) The uncertainty relation in quantum mechanics is given by the Heisenberg uncertainty principle:

ΔX ΔP ≥ ħ/2,

where ΔX represents the uncertainty in the position measurement and ΔP represents the uncertainty in the momentum measurement. To determine the state ψ_n for which the uncertainty is a minimum, we need to find the values of ΔX and ΔP and apply the uncertainty relation. However, the formulas for ΔX and ΔP are not provided, so we cannot determine the state ψ_n for which the uncertainty is a minimum without further information.

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Answer:

   So where's the line?

Let's start by setting up some equations to represent the information given in the problem.

Let's assume that Mitchell read x sports books last year. According to the problem, he read 5 mysteries for every 2 sports books, so he must have read (5/2)x mysteries.

We also know that he read 12 more mysteries than sports books, so:

(5/2)x - x = 12

Simplifying this equation, we get:

(3/2)x = 12

Multiplying both sides by 2/3, we get:

x = 8

So Mitchell read 8 sports books last year. To find out how many mysteries he read, we can use the equation we derived earlier:

(5/2)x = (5/2)(8) = 20

Therefore, Mitchell read 20 mysteries last year.

Comparing the means of the two samples, we find that the difference between the means is significant. Therefore, we can reject the claim and conclude that male and female high school students have different exam scores.

To perform the two-sample t-test, we first calculate the standard error of the difference between the means using the formula:

SE = sqrt((s1^2 / n1) + (s2^2 / n2))

Where s1 and s2 are the population standard deviations of the male and female students respectively, and n1 and n2 are the sample sizes. Plugging in the values, we have:

SE = sqrt((47^2 / 49) + (4.3^2 / 53))

Next, we calculate the t-statistic using the formula:

t = (x1 - x2) / SE

Where x1 and x2 are the sample means. Plugging in the values, we have:

t = (239 - 21.1) / SE

We can then compare the t-value to the critical t-value at α = 0.01 with degrees of freedom equal to the sum of the sample sizes minus 2. If the t-value exceeds the critical t-value, we reject the null hypothesis.

In this case, the t-value is calculated and compared to the critical t-value using the provided standard normal distribution table. Since the t-value exceeds the critical t-value, we can reject the claim that male and female high school students have equal exam scores.

Therefore, the correct answer is:

B. Male and female high school students have different exam scores.

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The correct answer is option c) infinitely many solutions..

To solve the system of equations using the substitution method, we'll substitute the value of y from the second equation into the first equation and solve for x.

Given:

-6x + 2y = 8 ---(1)

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

Substitute equation (2) into equation (1):

-6x + 2(3x + 4) = 8

Simplify:

-6x + 6x + 8 = 8

8 = 8

We obtained a true statement (8 = 8), which means the two equations are equivalent. This solution shows that the system has infinitely many solutions.

Therefore, the correct answer is option c) infinitely many solutions..

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The probability of getting one defective component per customer is very low, less than 1/14,254. The probability of getting five defective components to a single customer is also low, 1/14,254. And the probability of getting two defective components to two different customers and the rest of the customers getting none is 10/14,254.

(a) The probability that each customer will receive one defective component is the probability that the five defective components will be drawn in a specific order, divided by the total number of ways the 50 components can be drawn. There are 5049484746 ways that the 50 components can be drawn, and 5! (5 factorial) ways that the defective components can be drawn in a specific order. So the probability is (5!)/(5049484746) = 1/14,254.

(b) The probability that one customer will have drawn five defective components is the probability that all five defective components will be drawn in a row, divided by the total number of ways the 50 components can be drawn. There are 5049484746 ways that the 50 components can be drawn, and 5! (5 factorial) ways that the defective components can be drawn in a row. So the probability is (1!)/(5049484746) = 1/14,254,

(c) The probability that two customers will receive two defective components each, two none, and the other one, is the probability that the five defective components will be drawn in a specific order and then divided among the five customers in a specific way, divided by the total number of ways the 50 components can be drawn. The number of ways to divide the defective components among the customers is 5!/(2!2!1!) = 10. There are 5049484746 ways that the 50 components can be drawn, and 5! (5 factorial) ways that the defective components can be drawn in a specific order, so the probability is (105!)/(50494847*46) = 10/14,254.

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Range: All real numbers greater than or equal to 3. The Option C.

To find the range of the function, we need to determine the set of all possible y-values that the function takes.

Since the line crosses the y-axis at (0, 2), we know that the function's range includes the value 2. Also, since the line turns at (-1, 3), the function takes values greater than or equal to 3.

Therefore, the range of the function is all real numbers greater than or equal to 3.

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Imani uses less flour in her cookies than Vic because vic uses 25 / 17 g of flour while Imani uses 25 / 21 g of flour.

How much "stuff" is contained in a specific quantity of space is determined by its density. For instance, a block of the harder, lighter element gold (Au) will be denser than a block of the heavier element lead (Pb) (Au). Styrofoam blocks are less dense than bricks. Mass per unit volume serves as its definition.

A substance's density is a measurement of how heavy it is in relation to its size. When placed in water, an object will float if its density is lower than that of the water, whereas it will sink if its density is higher.

if we see Vic's recipe:

170 g of butter = 250 g of flour

1 g of butter = 250 ÷ 170

= 25 / 17 g of flour

and Imani's recipe:

630 g of butter = 750 g of flour

1 g of butter = 750 ÷ 630 = 25 / 21 g of flour

Compare:

25 / 21 < 25 / 17

so Imani uses less flour in her cookies than Vic

moreover imani's cookies are more dense.

Therefore, we get that Vic uses more flour than imani.

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Answer:

Write the dividend under the bar and the divisor to the left. Each is written in descending order of powers of

x

. If any power of

x

is missing, then include it with a

0

coefficient. For example, if you were dividing by

x

2

−

1

, then you would express the divisor as

x

2

+

0

x

−

1

.

Choose the first term of the quotient to cause leading terms to match. In our example, we choose

x

2

, since

(

x

−

1

)

⋅

x

2

=

x

3

−

x

2

matches the leading

x

3

term of the dividend.

Write the product of this term and the divisor below the dividend and subtract to give a remainder (

2

x

2

).

Bring down the next term (

−

x

) from the divisor alongside it.

Choose the next term (

2

x

) of the quotient to match the leading term of this remainder, etc.

Stop when there is nothing more to bring down from the dividend and the running remainder has lower degree than the divisor.

In our example, the division is exact. We are left with no remainder.

Step-by-step explanation:

i did the test

Answer:

45

Step-by-step explanation:

Answer:

45

Step-by-step explanation

Juan has just completed a 15 kilometer race in 20 minutes.  What was his average speed in kilometers per hour?

Solution

First, 15 kilometers is a distance, so

       d  =  15

Next, we are given 20 minutes and we are asked to present the speed in kilometers per hour rather than kilometers per minute.  We need to convert 20 minutes to hours.  Since there are 60 minutes per hour, we divide by 60 to find out how many hours it took

t  =  20 minutes / 60 minutes per hour =  1/3 hours

Now we can use the d=rt equation:

15  =  (r)(1/3)

If we multiply both sides

(3)(5)  =  (r)(1/3)(3)  or  r  =  45

Juan's average speed was 45 kilometers per hour.

(-8x-104=6x-14) is equivalent to the given equation (-8(x+13)=2(x-7)+4x).Option C is correct.

A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.

Given equation;

⇒-8(x+13)=2(x-7)+4x

⇒-8x-13×8 = 2x-2×7+4x

⇒-8x-104=2x-14+4x

⇒-8x-104=6x-14

(-8x-104=6x-14) is equivalent to the given equation (-8(x+13)=2(x-7)+4x).

Hence, option C is correct.

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The 95% prediction interval for 2015's return is approximately 6.13% to 20.61%.

To calculate the 95% prediction interval for 2015's return based on the average return and standard deviation of the S&P 500 from 2010 to 2014, we'll use the normal distribution and assume that returns follow a normal distribution.

Given information:

Average return (μ) = 13.37%

Standard deviation (σ) = 7.13%

Sample size (n) = 5 years (2010 to 2014)

To calculate the prediction interval, we need to consider the sampling distribution of the mean. The formula for the prediction interval is:

Prediction Interval = x ± Z * (σ / √n)

Where:

x is the sample mean (average return)

Z is the z-score corresponding to the desired confidence level (95% confidence level corresponds to a z-score of approximately 1.96)

σ is the standard deviation

n is the sample size

Let's calculate the prediction interval for 2015's return:

Prediction Interval = 13.37% ± 1.96 * (7.13% / √5)

Calculating the standard error (σ / √n):

Standard Error = 7.13% / √5

Substituting the values:

Prediction Interval = 13.37% ± 1.96 * (7.13% / √5)

Calculating the values:

Standard Error = 7.13% / √5 ≈ 3.19%

Prediction Interval = 13.37% ± 1.96 * 3.19%

Calculating the lower and upper bounds of the prediction interval:

Lower bound = 13.37% - (1.96 * 3.19%)

Upper bound = 13.37% + (1.96 * 3.19%)

Lower bound ≈ 6.13%

Upper bound ≈ 20.61%

Therefore, the 95% prediction interval for 2015's return is approximately 6.13% to 20.61%.

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The time Jodie have left to match the record of Mandy is 15.11 seconds

Jodie:

= 40.25 seconds

Time spent on the rope = 12.84 seconds

Total time spent = 40.25 seconds + 12.84 seconds

= 53.09 seconds

Total time she have left to match the record = Mandy's obstacle course - Total time spent

= 68.2 seconds - 53.09 seconds

= 15.11 seconds

Therefore, the time Jodie have left to match the record of Mandy is 15.11 seconds

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Answer:

The answer is 24/7

Answer:

3.428

Step-by-step explanation:

A number minus 8 is the same as a number divided by 2.

We have to find that number\(.\)

Let the number be x.

From the given question,

1. Number minus 8

2. Number divided by 2

ATQ : (I) = (II)

⭆ x - 8 = x/2

⭆ 2(x -8) = x

⭆ 2x - 16 = x

⭆ 2x - x = 16

⭆ x = 16

The sum of the angle measures of the polygon is 540°, the value of x is 5.

The sum of the angle measures of the polygon is 540°.

We know that the sum of the interior angles of a polygon of n sides = (n – 2) × 180°. = 3× 180°= 540°

If a polygon has x sides, then the sum of its angle measures can be found using the formula:

Therefore, for a polygon with x sides, the equation becomes:

⇒(x-2) * 180° = 540°

Solving for x, we get:

⇒x = (540° + 360°) / 180° + 2

⇒x = 3 + 2

⇒x = 5

So, the polygon has 5 sides.

Therefore, the value of  x is 5.

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The total number of ways to line up the 11 people such that the bride is next to the maid of honor and the groom is next to the best man is:

9! * 2! * 2! = 40,320.

If we consider the bride and the maid of honor as a single entity, there would be 10 entities in total to be arranged in a row.

Similarly, if we consider the groom and the best man as a single entity, there would be 10 entities in total to be arranged in a row.

Now, we need to consider that the bride and the maid of honor are together, and the groom and the best man are together.

This means that we have two entities (bride and maid of honor, groom and best man) that must be kept together in the arrangement.

We can treat these two entities as single units, which gives us a total of 9 units to arrange.

We can arrange these units in 9! ways.

However, within each of the two units, the bride and the maid of honor can be arranged in 2! ways, and the groom and the best man can be arranged in 2! ways.

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Answer:

[In Picture]

Step-by-step explanation:

There are no given options.

However, I am able to recreate the best answer for the question given.

There would be arrow going to the left from -3. The arrow will include all numbers less than -3.

Since there is a less than sign, the circle at the beginning of the arrow is open.

Choose the option that closely matches the line shown.

The number line is the representation of numbers in real order.

The difference between the consecutive numbers in a number line is always positive.

The number line of n < - 3 is n less than -3.

The graph of the number line is given below.

It is the representation of numbers in real order.

The difference between the consecutive numbers in a number line is always positive.

We have,

n < - 3

This is read as,

n is less than -3.

The graph of the number line is given below.

Thus,

The number line of n < - 3 is n less than -3.

The graph of the number line is given below.

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Answer:

2.05m

Step-by-step explanation:

Answer:

63 square units

Step-by-step explanation:

Area of the rhombus = Base × Height

Given

Base = x = 9unit

Height = h = 7units

Substitute into the formula

Area of the rhombus = 9×7

Area = 63units²

Hence the required area of the rhombus is 63 square units