5. Given Z₁ = 6(cos 26° + i sin 26°) and z₂ = 3 (cos 12° + i sin 12°), find each of the following. Leave your answers in polar form. a) Z₁ Z₂ Z1 b) 21 22

Answer:

3

Step-by-step explanation:

To find the answer, heres what you need to do.

Basically, you divide each number on the right by the number on the left.

15/5= 3

24/8=3

36/12=3

72/24=3

Since all of the answers are 3, your answer is 3

Answer:

3

Step-by-step explanation:

Slope Formula:

y2 - y1/x2 - x1

Let's use (5, 15) and (8,24)

(x1, y1) = (5, 15)

(y1, y2) = (8, 24)

Substitute:

y2 - y1/x2 - x1

24 - 15/8 - 5

Solve:

24 - 15/8 - 5

9/3

= 3

Therefore the slope, or constant rate is 3.

Tip: look at the relationship between Cost and Time.

15/5 = 3

24/8 = 3

36/12 = 3

72/24 = 3

Dividing is a simple way to find the slope!

Answer:

{(0, -4), (1, -2), (2, 0), (3, 2), (4, 4)}

Input values (x) = {0, 1, 2, 3, 4}

Output values (y) = {-4, -2, 0, 2, 4}

Step-by-step explanation:

Given the linear equation, y = 2x - 4, you could practically choose any input value (for x), to have an output value (for y).

If x = 0:

y = 2(0) - 4

y = 0 - 4

y = -4

First ordered pair: y-intercept =  (0, -4)

If x = 1:

y = 2(1) - 4

y= 2 - 4

y = -2

Second ordered pair: (1, -2).

If x = 2:

y = 2(2) - 4

y= 4 - 4

y = 0

Third ordered pair: x-intercept =  (2, 0).

If x = 3:

y = 2(3) - 4

y = 6 - 4

y = 2

Fourth ordered pair: (3, 2).

If x = 4:

y = 2(4) - 4

y = 8 - 4

y = 4

Fifth ordered pair: (4, 4).

Your input values (x) = {0, 1, 2, 3, 4}

Your output values (y) = {-4, -2, 0, 2, 4}

B. 4y - 2

Hope this helps! :)

Answer:

B. 4y - 2

Step-by-step explanation:

2( y + 1 ) + 2( y - 2 )

= 2y + 2 + 2y - 4

= 2y + 2y + 2 - 4

= 4y - 2

= 4y - 2

Answer:

42'

Step-by-step explanation:

 First you draw a box with the dimensions given and then draw the walkway around it. You then as 5 feet to both the 5 and 6 because you are adding 2.5 feet on the left and right side on both sides of your garden. This then leaves you with the dimensions of 10 by 11. Two sides equal 11 and two equal 10. You then find the perimeter. 10+10+11+11 = 42.                

Answer: 32 feet

Step-by-step explanation:

Perimeter of a rectangle = 2 (l + b)

= 2 (7.5 + 8.5)

32 feet

Answer:12

Step-by-step explanation:

Based on the calculations, the number of degrees that the auto-aim feature would adjust the shot is 12°.

Based on the triangle attached in the image above, we can deduce the following parameters:

Side AT = 15 m.

Side CA = 50 m.

Side CT = 60 m.

In this scenario, we would apply the cosine trigonometry function by using this mathematical expression:

AT² = CA² + CT² - 2(CA)(CT)COSθ

15² = 50² + 60² - 2(50)(60)COSθ

225 = 2500 + 3600 - 6000COSθ

6000COSθ = 6100 - 225

6000COSθ = 5875

θ = COS⁻¹(5875/6000)

θ = COS⁻¹0.9792

θ = 11.72 ≈ 12°

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x=-2/3

Step-by-step explanation:

6(x+4)=20

x+4=20/6( aka 10/3)

x=10/3-4=-2/3

The dimensions of the box are approximately: side length = 9.36 inches, and height = 14.62 inches.

Let's denote the side length of the square base as s, and the height of the box as h.

We are given the volume of the box as 150 cubic inches, so we can write the equation:

Volume = s^2 * h = 150.

The surface area of the box is given as 145 square inches, which consists of the base area (s^2) and four equal side areas (4s * h):

Surface Area = s^2 + 4s * h = 145.

We also know that the height of the box must be larger than 8 inches, so we have the condition:

h > 8.

Now, let's solve these equations simultaneously. We can rearrange the second equation to express h in terms of s:

h = (145 - s^2) / (4s).

Substituting this expression for h into the volume equation, we have:

s^2 * [(145 - s^2) / (4s)] = 150.

Simplifying this equation, we get:

s^3 - 600s + 580 = 0.

This is a cubic equation, and solving it can be quite complex. We can use numerical methods or calculators to approximate the solution. After solving, we find that the side length of the square base is approximately 9.36 inches and the height of the box is approximately 14.62 inches.

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

Work Shown:

4x^2 - y^2

(2x)^2 - (y)^2

(2x-y)(2x+y)

When going from the second step to the third step, I used the difference of squares rule. That rule is a^2-b^2 = (a-b)(a+b). In this case, a = 2x and b = y.

Side note: (2x-y)(2x+y) is the same as (2x+y)(2x-y). We can multiply in any order.

The formula for the area of a regular pentagon is:

A = (1/2)Pa

where A is the area of the pentagon, P is the perimeter of the pentagon, and a is the apothem (the distance from the center of the pentagon to the midpoint of a side).

If the apothem of the pentagon is 3√2, then we need to know the perimeter of the pentagon in order to calculate its area.

Unfortunately, the apothem alone is not enough information to determine the perimeter of a pentagon. However, if we assume that the pentagon is regular, then we know that all of its sides and angles are equal, and we can use the following formula to find its perimeter:

P = 5s

where P is the perimeter and s is the length of a side.

To find the length of a side, we can use the fact that the apothem is perpendicular to a side and bisects it. This means that the triangle formed by the apothem, half a side, and the center of the pentagon is a right triangle. The hypotenuse of this triangle is the length of a side, and the legs are half a side and the apothem:

s/2 = 3√2

s = 6√2

Now we can use the equation for the perimeter of a pentagon:

P = 5s = 5(6√2) = 30√2

Finally, we can use the formula for the area of a regular pentagon:

A = (1/2)Pa = (1/2)(30√2)(3√2) = 45

Therefore, the area of the pentagon is 45 square units, assuming that it is a regular pentagon with an apothem of 3√2.

Answer: A: x=4

Step-by-step explanation:

5(4)-5=15

20-5=15

15=15

Answer:

N+1

Step-by-step explanation:

It begins with = 2

then n+1=3

then n+2=4 and so on it is n+1

Therefore, there are 216 different choices of combination in total.

To determine the total number of choices, you need to multiply the number of options for each category together. In this case, you have 6 choices for waist sizes, 6 choices for lengths, and 6 choices for colors.

The total number of choices can be calculated as follows:

Total choices = Number of waist sizes × Number of lengths × Number of colors

= 6 × 6 × 6

= 216

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Answer:

∠A≅∠Y          AB≅YZ

∠B≅∠Z          AC≅YX

∠C≅∠X          BC≅ZX

ΔABC≅ΔYZX

Step-by-step explanation:

congruent is identical in form so if the angle has one dash than look for the identical version on the other triangle

a) Here is the chart showing the number of bacteria after 0 to 4 hours:

| Time (hours) | Number of bacteria |

|--------------|--------------------|

| 0 | 50 |

| 1 | 150 |

| 2 | 450 |

| 3 | 1,350 |

| 4 | 4,050 |

b) To write an expression that models the number of bacteria after a number of hours, n, we can use the formula:

In this case, the initial number of bacteria is 50, and the growth factor is 3 (since the number of bacteria triples every hour). Therefore, the expression that models the number of bacteria after n hours is:

c) To determine the number of bacteria that are present after 12 hours using the expression we derived in part b), we can substitute n = 12 into the expression:

= 26572050

The equivalent expression for the new price of the item is 0.57b. With b be the original price of the item.

The original price of the item is represented by "b". Paul received a coupon for "43 percent" off one item at a clothing store. This means that the new price of the item will be the "original price" minus the discount. The discount is calculated by multiplying the original price by the percentage discount.
So, the discount is:
43 percent of b = 0.43 * b

The new price of the item is the original price minus the discount:
b - 0.43 * b = b - 0.43b

This expression can be simplified by combining the like terms. The like terms in this expression are b and -0.43b.
To combine like terms, we add the coefficients of the like terms:
1b + (-0.43)b = 0.57b

So, the equivalent expression for the new price of the item is:
0.57b

This means that the new price of the item is 57% of the original price. Therefore, the equivalent expression for the new price of the item is 0.57b.

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Given:

Quadrilateral WXYZ has 4 vertices:

W(1, 1), X(1,4), Y(2,3), and Z(2,2).

There are two transformations:

Translation: (x,y) = (x-2, y-1)

Dilation: (x,y) = (3x,3y)

To find:

We need to identify the coordinates after the transformation:

Step-by-step solution:

1) After the first transformation:

(x,y) = (x-2, y-1)

W(1, 1) = (-1, 0)

X(1,4) = (-1, 3)

Y(2,3) = (0, 2)

Z(2,2) = (0, 1)

2) After the Second transformation:

(x,y) = (3x,3y)

W(1, 1) = (3, 3)

X(1,4) = (3, 12)

Y(2,3) = (6, 9)

Z(2,2) = (6, 6)

Here we have finally classified all the different points into different categories.

I think that the answer would be 14

Answer:

(18-4+5)+(2/7 j-6/7 j)=

19 +(-4/7 j)=

The test to use when there's an independent group design and ordinal data is the Kruskal Wallis test

Given: Independent group and ordinal data. To find which test to use.

What's the Kruskal Wallis test?

The Kruskal Wallis test is used when you have one independent variable with two or further situations and an ordinal dependent variable. In other words, it's thenon-parametric interpretation of ANOVA and a generalized form of the Mann- Whitney test system since it permits two or further groups.

The Kruskal Wallis test is used when you have one independent variable with two or further situations and an ordinal dependent variable. In other words, it's thenon-parametric interpretation of ANOVA and a generalized form of the Mann- Whitney test system since it permits two or further groups.

The null thesis for the Kruskal- Wallis test simply states that there are no methodical or harmonious differences among the treatments being compared.

How to calculate the Kruskal Wallis test?

The computation of the Kruskal- Wallis statistic requires

Hence as is mentioned for an independent group design and ordinal data so we use the Kruskal Wallis test.

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We can use the Kruskal Wallis test when we have an independent group design and ordinal data.

We are given an independent group design and ordinate data.

We need to tell which test to use on them.

The Kruskal Wallis test is used when you have one independent variable with two or more situations and one ordinal dependent variable. In other words, it is an interpretation of ANOVA table and a generalized form of the Mann- Whitney test system.

The null hypothesis for the Kruskal- Wallis test tells us that:

There are no methodical or harmonious differences among the treatments being compared.

Therefore, we can use the Kruskal Wallis test when we have an independent group design and ordinal data.

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(A) A normal distribution centered at 1/3 with a standard deviation of about 0.0351.

Normal Distribution:

The normal distribution, also known as the Gaussian distribution, is a probability distribution symmetrical about the mean, indicating that data near the mean occurs more frequently than data far from the mean. The normal distribution model is important in statistics and is the key to the central limit theorem (CLT). The theory states that means computed from independent, identically distributed random variables have an approximately normal distribution, regardless of the type of distribution from which the variable is sampled (provided it has finite variance). Mean (average value), median (center), and mode (most frequent observation) are all equal. Moreover, these values ​​all represent the peak or highest point of the distribution.

Standard Deviation:

The standard deviation (or σ) is a measure of the distribution of data from the mean. A low standard deviation means the data is clustered around the mean, and a high standard deviation means the data is more scattered. A standard deviation close to zero indicates that the data points are close to the mean, while a high or low standard deviation indicates that the data points are above or below the mean, respectively.  The top curve is more spread out and therefore has a higher standard deviation, while the bottom curve is more concentrated around the mean and therefore has a lower standard deviation.

Complete Question:

A successful waffle-man has recently developed a new recipe for waffles. To test the popularity of this new waffle compared to two other tried-and-true types of waffles, our friend the waffle-man randomly selected 180 lucky customers to vote on which of the three waffle types they liked best. Exactly 35% of these customers (or 63 in total) voted in favor of the new waffle. If all waffles were equally tasty, then the waffle-man knows to expect that each waffle would receive around 1/3 of the votes (so around 60 votes per waffle).

Are 63 votes for the new waffle enough to conclude that significantly more customers like it compared to the others? Luckily, our friend the waffle-man triple-majored in waffles, statistics, and clinical neurophysiology and knows how to objectively answer this question. He conducts a hypothesis test for proportions,

H0:p=1/3 H0:p=1/3, Ha :p>1/3 Ha: p>1/3

with a sample proportion of 63/180.

In carrying out this test, what null distribution for p^p^ should he use? In other words, what is the distribution of the sample statistic assuming the null hypothesis is true? (Be sure to use at least four decimal places in your calculations.)

Select one:

a)A normal distribution centered at 1/3 with a standard deviation of about 0.0351

b)A normal distribution centered at 1/3 with standard deviation of about 0.0356

c)A normal distribution centered at 0.35 with standard deviation of about 0.0356.

d)A normal distribution centered at 0.35 with standard deviation of about 0.0351.

e)We cannot use a null distribution in this problem because the population is not normally distributed.

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The probability that at least 68 will shoplift again during the next five-year period is 0.0082

We are given that the probability of a convicted shoplifter repeating the crime within 5 years is 0.30.Using the formula of mean and variance of binomial distribution;Mean, μ = np = 200 x 0.30 = 60Var (Binomial) = npq = 200 x 0.30 x 0.70 = 42

Using the normal approximation to the binomial, we can calculate the probability as:P(X ≥ 68)

We can write this as:P(X > 67.5) = P(Z > (67.5-60)/6.4807) = P(Z > 1.1582) Where Z is the standard normal random variable.To calculate this, we need to refer to the standard normal distribution table of values, which gives:P(Z > 1.16) = 0.1230

Therefore,P(X > 67.5) = 0.1230

Hence, the probability that at least 68 will shoplift again during the next five-year period is 0.0082

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Answer:

The 1 liter bottle is better value

Step-by-step explanation:

Cost of 750 ml = £1.90

Cost of 1 liter = £2.50

1000 ml = 1 liter

Cost per 250 ml

750 ml / 3 = £1.90 / 3

250 ml = £0.6333333333333

Approximately,

£ 0.633

Cost per 250 ml

1 liter / 4 = £2.50 / 4

250 ml = £0.625

The 750 ml bottle is not a better value

The 1 liter bottle is better value

The partial derivative diffusivity equation for spherical flow is ∂²p/∂r² + (1/r) ∂p/∂r = ϕμC/k ∂p/∂t, and for hemispherical flow, it is the same equation.

1. The partial derivative diffusivity equation for spherical flow is derived from the spherical coordinate system and applies to radial flow in a spherical geometry. It can be expressed as ∂²p/∂r² + (1/r) ∂p/∂r = ϕμC/k ∂p/∂t.

2. The partial derivative diffusivity equation for hemispherical flow is derived from the hemispherical coordinate system and applies to radial flow in a hemispherical geometry. It can be expressed as ∂²p/∂r² + (1/r) ∂p/∂r = ϕμC/k ∂p/∂t.

1. For the derivation of the partial derivative diffusivity equation for spherical flow, we consider a spherical coordinate system with the radial direction (r), the azimuthal angle (θ), and the polar angle (φ). By assuming steady-state flow and neglecting the other coordinate directions, we focus on radial flow. Applying the Laplace operator (∇²) in spherical coordinates, we obtain ∇²p = (1/r²) (∂/∂r) (r² ∂p/∂r). Simplifying this expression, we arrive at ∂²p/∂r² + (1/r) ∂p/∂r.

2. Similarly, for the derivation of the partial derivative diffusivity equation for hemispherical flow, we consider a hemispherical coordinate system with the radial direction (r), the azimuthal angle (θ), and the elevation angle (ε). Again, assuming steady-state flow and neglecting the other coordinate directions, we focus on radial flow. Applying the Laplace operator (∇²) in hemispherical coordinates, we obtain ∇²p = (1/r²) (∂/∂r) (r² ∂p/∂r). Simplifying this expression, we arrive at ∂²p/∂r² + (1/r) ∂p/∂r.

In both cases, the term ϕμC/k ∂p/∂t represents the source or sink term, where ϕ is the porosity, μ is the fluid viscosity, C is the compressibility, k is the permeability, and ∂p/∂t is the change in pressure over time.

These equations are commonly used in fluid mechanics and petroleum engineering to describe radial flow behavior in spherical and hemispherical geometries, respectively.

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Answer: A

Step-by-step explanation: I would say A because the angle is greater than 90 degrees

Answer:

We have supplementary angles.

76 + 3x + 2 = 180

3x + 78 = 180

3x = 102

x = 34

Answer:

6 weeks

Step-by-step explanation:

end goal = $76

how much he has in the bank = $30

how much he earnes per week = $8

first, subtract 30 from 78 to figure out how much he has left to ear:

$78 - $30 = $48

then take the difference and divide it by 8 since he earned $8 per week:

48 ÷ 8 = 6

It will take him 6 remaining weeks to complete his end goal.

Answer:

Line d : y = -3x - 3

Line e : y = -3x - 2

Line f  : y= -3x + 2

Step-by-step explanation:

Given that,

The slope of each line is -3.

Now,

We know that,

Equation of line is represented by y = mx + c

where m is the slope and c is the y-intercept.

Now,

Given that,

Line d goes through (0, - 3) and (- 1, 0).

So,

y-intercept of Line d is -3

∴ we get

Equation of Line d is : y = -3x -3

Now,

Given that,

Line e goes through (-1, 2) and (0, -2).

So,

y-intercept of Line e is -2

∴ we get

Equation of Line e is : y = -3x - 2

Now,

Given that,

Line f goes through (0, 2) and (1, -1).

So,

y-intercept of Line e is 2

∴ we get

Equation of Line f is : y = -3x + 2

Answer:

The person above me is correct except for the fact that line e is wrong because I put it and is wrong

The selling price of the game is (d) $111.80

The given parameters are:

Discount = 30%

Selling price = $86.00

Since the item is sold less, then the original price would be more.

So, we have:

Price = Selling price * (1 + Discount)

This gives

Price = $86.00 * (1 + 30%)

Evaluate

Price = $111.80

Hence, the selling price is (d) $111.80

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Answer:

Thanks for free points have a nice day :)

Answer:

The answer is 59 ½

Step-by-step explanation:

4×4×4-2×1 ½×1 ½

= 64 - 2× 3/2 × 3/2

= 64 - 9/2

= 128/2 - 9/2

= 119/2

= 59 ½ in3

Hope this helped :)

Answer:

area of a triangle

1/2 base ×height

1/2×15×8.5

=63.75cm ^2

Answer:

63.75cm^2 / square centimeters

Step-by-step explanation:

The area of a triangle is calculated by multiplying 1/2 times the base, times the height.

A = (1/2)(base)(height)

A = (0.5)(15)(8.5)

A =63.75