11) Find the quotient of 30(cos(-70°) + i sin(-70°)) and 6(cos 20° + i sin 20°). Write the result in rectangular form.

Answer:

The answer is

Step-by-step explanation:

\( - 12( \frac{5}{6} x - 5) + 2x\)

Using FOIL multiply the terms in the bracket

That's

\( - 12( \frac{5}{6} x) + 12(5) + 2x \\ \rarr \: \: - 10x + 60 + 2x\)

Group like terms

That's

\(60 + 2x - 10x\)

We have the final answer as

Hope this helps you

The second lawn that Makayla mows has a length of 70 feet.

If the first lawn Makayla mows is 10 feet long and 7 feet wide, use the formula for the area of rectangle to know the area of the first lawn.

A = l x w

Area of first lawn = 10 feet x 7 feet

Area of first lawn = 70 ft^2

If the area of the second lawn is 7 times as big as the first, then the area of the second lawn is:

Area of second lawn = 7 x Area of first lawn

Area of second lawn = 7 x 70 ft^2

Area of second lawn = 490 ft^2

If the second lawn has the same width as the first, which is 7 feet, using the formula for the area of a rectangle, solve for the length of the second lawn.

A = l x w

Area of second lawn = l x w

490 ft^2 = l x (7 feet)

l = 70 feet

Learn more about area of rectangle here: https://brainly.com/question/25292087

#SPJ4

Answer:

To determine which equation the graph of the system of equations solves, we need to solve the system of equations and see which equation represents the graph at the point of intersection.

The system of equations can be written as:

-1/2x + 3 = 3x - 4

-1/2x - 3 = -3x + 4

We can simplify the first equation by adding 1/2x and 4 to both sides:

3.5x = 7

x = 2

Substituting x = 2 into the second equation:

-1/2(2) - 3 = -3(2) + 4

-1 - 3 = -6 + 4

-4 = -2

Since -4 does not equal -2, we know that there is no solution to this system of equations. Therefore, the graph of the system of equations does not solve any of the given equations.

Explanation:

This is because

The dimensions of building lot are 396 feet width and 1980 feet length.

Let the width of building lot be x. So, the length of the same building lot will be 5x. According to the formula, the area will be length × width.

18 acre = x×5x

Keep the value of acre in the above mentioned relation

18 × 43,560 = 5x²

Performing multiplication on Left Hand Side of the equation

784,080 = 5x²

Performing division by 5

x² = 156,816

Now taking square root to find the value of x

x = ✓156,816

x = 396 ft

Thus, the width of building lot is 396 feet

The length of building lot = 5×396

Performing multiplication

The length of building lot = 1980 feet

Therefore, the length and width of building lot is 1980 feet and 396 feet respectively.

Learn more about area -

https://brainly.com/question/25292087

#SPJ1

The equations test observation (4, 4) belongs to class 1.

To assign a class to the test observation (4, 4),  to evaluate the equations of the support vector classifiers (SVCs) and determine which one(s) the observation satisfies.

Let's go through each SVC and check if the observation lies on the positive side or the negative side of the decision boundary.

SVC for class 1(+) vs 2(-): 2x + 3y = 0

Substituting the values of x = 4 and y = 4

2(4) + 3(4) = 8 + 12 = 20

Since 20 is positive, the test observation (4, 4) lies on the positive side of this decision boundary.

SVC for class 1(+) vs 3(-): 3x + 2y = 0

Substituting the values of x = 4 and y = 4

3(4) + 2(4) = 12 + 8 = 20

Again, 20 is positive, so the test observation (4, 4) also lies on the positive side of this decision boundary.

SVC for class 2(+) vs 3(-): x + y = 0

Substituting the values of x = 4 and y = 4

4 + 4 = 8

Since 8 is positive, the test observation (4, 4) lies on the positive side of this decision boundary as well.

Based on these results, the test observation (4, 4) satisfies all three decision boundaries and lies on the positive side of each. Therefore,  assign it to class 1, which is the common positive class across all three classifiers.

To know more about equations here

https://brainly.com/question/29538993

#SPJ4

The total cost paid by Alexander is 1080 dollars.

Alexander had a total of 216 potatoes in 6 shipments. Let's assume x represents the cost of each potato in the first three shipments, and y represents the cost of each potato in the next three shipments.

Since one shipment cost him 3 dollars per potato, the total cost of the first three shipments would be 216 * x. Similarly, the total cost of the next three shipments would be 216 * y.

We are given that the total cost for the first three shipments is 5 dollars per potato, so we can write the equation:

216 * x = 3 * 216.

Simplifying the equation, we have: 216x = 648.

Solving for x, we find that x = 3.

We are also given that the last two shipments were free, so the total cost for the last two shipments is 0.

To find the total cost paid by Alexander, we need to add the cost of the first three shipments (216 * 3) and the cost of the next three shipments (216 * y), which equals 648 + 0 + 216 * y.

Since the total cost is 5 dollars per potato, we can write the equation: 648 + 0 + 216 * y = 5 * 216.

Simplifying the equation, we have: 648 + 216y = 1080.

Solving for y, we find that y = 2.

Therefore, the total cost paid by Alexander is 648 + 0 + 216 * 2, which equals 1080.

The total cost paid by Alexander is 1080 dollars.

learn more about total cost here:

https://brainly.com/question/16526817

#SPJ11

Answer:

B. 7/20

Step-by-step explanation:

P(A | B) = P(A∩B) / P(B) is the formula for conditional probability

             = (7/40) / (1/2)

Copy dot flip

              = 7/40 * 2/1

              =7/20

The length of side XZ is 5 units and side YZ is 6 units.

A triangle is a three-sided polygon, which has three vertices. The angles of the triangle are formed by connecting the three sides end to end at a point. The total of the three angles of the triangle is equal to 180 degrees. To study about and build the world's seven sorts of triangles: equilateral, right isosceles, obtuse isosceles, acute isosceles, right scalene, obtuse scalene, and acute scalene. The hypotenuse is the longest side of a right triangle, a "opposite" side is the one across from a given angle, and a "adjacent" side is the one close to a given angle.

Here,

XZ=3-(-2)

XZ=5 units

YZ=4-(-2)

YZ=6 units

Side XZ is 5 units long and Side YZ is 6 units long.

To know more about triangle,

https://brainly.com/question/28600396

#SPJ1

Answer:

B

Step-by-step explanation:

I would say B because they're only 2 options head and tails.

✩brainliest appreciated ✩

The main function is given by:

f (x) = sine (x)

We then have the following transformations:

Reflections:

Reflection or turning is the mirror image of a figure. It can also be said that it is the turning of points and graphs around the axes.

To graph y = -f (x), reflect the graph of y = f (x) on the x-axis. (Vertical reflection)

f (x) = - sine (x)

Expansions and vertical compressions:

To graph y = a*f (x)

If a> 1, the graph of y = f (x) is expanded vertically by a factor a.

f (x) = - 2 * sine (x)

Vertical translations

Suppose that k> 0

To graph y = f (x) + k, move the graph of k units up.

f (x) = - 2 * sine (x) + 3

Answer:

C. reflection across the x-axis, vertical stretching by a factor of 2, vertical translation 3 units up

The set of transformations which is needed to graph f(x) = –2sin(x) + 3 is reflection across the x-axis, vertical stretching by a factor of 2, vertical translation 3 units up, the correct option is C.

A rigid transformation (also called an isometry) is a transformation of the plane that preserves length. In a rigid transformation the pre-image and image are congruent (have the same shape and sizes).

We are given that;

The function= f(x) = –2sin(x) + 3

Now,

To graph f(x) = –2sin(x) + 3 from the parent sine function y = sin(x), we need to apply the following transformations:

A reflection across the x-axis, because of the negative sign in front of the 2.

A vertical stretching by a factor of 2, because of the absolute value of the coefficient of sin(x), which is 2.

A vertical translation 3 units up, because of the constant term 3.

Therefore, by transformations answer will be Reflection across the x-axis, vertical stretching by a factor of 2, vertical translation 3 units up.

Learn more about rigid transformations;

https://brainly.com/question/7070983

#SPJ5

Aya can make 14 mats of 1 foot long.

Division is one of the fundamental arithmetic operation, which is performed to get equal parts of any number given, or finding how many equal parts can be made. It is represented by the symbol "÷" or sometimes "/"

Given that, Aya has 14\(\frac{2}{5}\) feet of chain. She wants to make pieces foot long mat.

Let can make x mats out of the given chain, since each mat is 1 foot long, so,

1×x =  14\(\frac{2}{5}\)

x = 72/5

x = 14.4

x ≈ 14

Hence, She can make 14 mats out of the given chain.

For more references on division, click;

https://brainly.com/question/21416852

#SPJ1

A dot density map uses dots to show the number of people living in a certain area.

A dot density map is a cartographic technique used to represent the number of people living in a specific area. It employs dots to visually depict the population distribution across a region.

The density of dots in a given area corresponds to a higher concentration of people residing there.

This method allows for a quick and intuitive understanding of population patterns and can be used to analyze population distribution, identify densely populated areas, or compare population densities between different regions.

It is important to note that dot density maps specifically focus on representing population and do not convey information regarding the ratio of land to water, types of resources, or climate in an area.

for such more question on density map

https://brainly.com/question/1354972

#SPJ8

Answer:

Step-by-step explanation:

it is infinite having only one line

The given expression is 4(8x + 5). This is a product of a coefficient and a binomial expression. In mathematics, a binomial is a polynomial with two terms.

They are represented as ax + b or a + bx or (a + b) etc. Given expression is 4(8x + 5). We can simplify this by applying the distributive property. It is given as follows; The distributive property of multiplication states that a(b + c) = ab + ac To simplify the given expression, we need to multiply the coefficient 4 with each term in the parentheses.

It can be done as follows; 4(8x + 5) = 4*8x + 4*5 We multiply 4 with 8x and 4 with 5 to obtain; 32x + 20 This is the main answer. Therefore, the simplified form of 4(8x + 5) is 32x + 20. To simplify the given expression 4(8x + 5), we can use the distributive property. According to this property, the product of a number with the sum of two or more terms is equal to the sum of the products of that number with each term of the sum. In other words, a(b + c + …) = ab + ac + … In the given expression, 4 is multiplied with the binomial (8x + 5). Hence,

4(8x + 5) = 4*8x + 4*5

= 32x + 20

Hence, the simplified form of 4(8x + 5) is 32x + 20.

To know more about expression visit:

https://brainly.com/question/28170201

#SPJ11

Answer:

I think 15 I am sure

Step-by-step explanation:

The number of insects consumed by pitcher plants is essential for their survival and growth, and it is fascinating to observe this unique aspect of their carnivorous nature.

Pitcher plants are carnivorous plants that trap and digest insects to obtain nutrients. The exact number of insects consumed by pitcher plants in a month can vary depending on factors such as the species of pitcher plant, its size, and the local environment. However, studies have estimated that a single pitcher plant can consume anywhere from a few dozen to hundreds of insects per month.

The mechanism of the pitcher plant is quite interesting. Insects are lured into the plant by its color and sweet-smelling nectar. Once inside, the insect becomes trapped and is unable to escape due to the slippery inner walls of the pitcher. The plant then secretes digestive enzymes that break down the insect's tissues, allowing the plant to absorb the nutrients.

Interestingly, not all insects are consumed by pitcher plants. They tend to prefer smaller insects such as ants and flies, but larger insects such as bees and wasps may occasionally become trapped as well.

To learn more about : pitcher

https://brainly.com/question/29659060

#SPJ11

The area of the barn quilt is 3 sq.ft.

The amount of sugar needed to make 1/2 of a batch of cookies is 1/5 of a cup.

Number of boys are practicing hitting the ball = 4

Number of bags of lemons used by Rachel on Tuesday = 1\(\frac{3}{4}\)

1. A painted barn blanket needed to be 1 1/3 feet by 2 1/4 feet in size.

Area of the barn quilt = 1 1/3*2 1/4

                                  = 4/3*9/4

                                  = 3 sq. ft.

2. The recipe for Mrs. Smith's oatmeal cookies asks for 2/5 cups of sugar.

Sugar needed for making 1/2 of a batch of cookies = 1/2*2/5

                                                                                 = 1/5 of a cup

3. Six boys are practicing baseball throwing, catching, and hitting in the park. Two thirds of those six youngsters are practicing hitting.

Number of boys practicing hitting the ball = 6*2/3 = 4

4. At the park's lemonade kiosk, Rachel works. She used 1 and 2/5 bags of lemons on Monday. She used 1 and 1/4 times as many lemons on Tuesday as she did on Monday.

Number of bags of lemon used on Tuesday = 7/5*5/4

                                                                     = 7/4

                                                                     = 1 and 3/4 bags

Learn more about area here:

https://brainly.com/question/25292087

#SPJ1

Answer:

a

Step-by-step explanation:

Answer:

A.   L = 240 m

Step-by-step explanation:

use similar triangle

L / 60 = 80 / 20

L = (80 * 60) / 20

L = 240 m

The approximate percentage of lightbulb replacement requests numbering between 35 and 62 would be approximately the same as the percentage within one standard deviation of the mean, which is 68%.

Here, we have,

To determine the approximate percentage of lightbulb replacement requests numbering between 35 and 62, we can utilize the 68-95-99.7 rule, also known as the empirical rule or the three-sigma rule.

According to this rule:

Approximately 68% of the data falls within one standard deviation of the mean.

Approximately 95% of the data falls within two standard deviations of the mean.

Approximately 99.7% of the data falls within three standard deviations of the mean.

Given that,

the mean is 62 and the standard deviation is 9, we can calculate the range within one standard deviation of the mean:

Lower Limit = Mean - Standard Deviation = 62 - 9 = 53

Upper Limit = Mean + Standard Deviation = 62 + 9 = 71

The range within one standard deviation of the mean is from 53 to 71.

Since 35 falls below the lower limit of one standard deviation, we can assume it lies beyond the range of interest in this case.

Therefore, the approximate percentage of lightbulb replacement requests numbering between 35 and 62 would be approximately the same as the percentage within one standard deviation of the mean, which is 68%.

Hence, the approximate percentage is 68.

Learn more about standard deviation here:

brainly.com/question/23907081

#SPJ4

Answer:

answer is 1.1

Step-by-step explanation:

that you can divide and see the answer

The explicit formula for f^-1 is (x-3)^(1/4) and this is obtained by switching the roles of x and y and solving for y in terms of x.

To find the inverse function of f(x)=x^4+3, we need to switch the roles of x and y, and solve for y.
Let y = x^4+3
Subtract 3 from both sides to get:
y - 3 = x^4
Take the fourth root of both sides to isolate x:
(x^4)^(1/4) = (y-3)^(1/4)
Simplify:
x = (y-3)^(1/4)
So the inverse function of f(x) is:
f^-1 (x) = (x-3)^(1/4)
This is the explicit formula for the inverse function of f(x).
To know more about explicit formula visit:

https://brainly.com/question/18069156

#SPJ11

To find the Taylor expansion of f(x) = 2tan(x) around a = 7π/4, we need to compute the derivatives of f(x) at the given point. The general formula for the nth derivative of tan(x) is:

f^(n)(x) = 2n! sec^2(x) tn-1(x)

Let's compute the derivatives and evaluate them at x = 7π/4:

f(x) = 2tan(x)

f'(x) = 2sec^2(x)

f''(x) = 4sec^2(x)tan(x)

f'''(x) = 8sec^4(x) + 8sec^2(x)tan^2(x)

Now, let's evaluate these derivatives at x = 7π/4:

f(7π/4) = 2tan(7π/4) = 2(-1) = -2

f'(7π/4) = 2sec^2(7π/4) = 2(1) = 2

f''(7π/4) = 4sec^2(7π/4)tan(7π/4) = 4(1)(-1) = -4

f'''(7π/4) = 8sec^4(7π/4) + 8sec^2(7π/4) tan^2(7π/4) = 8(1) + 8(1)(-1) = 0

Now we can write the Taylor expansion for f(x) around x = 7π/4:

f(x) ≈ f(7π/4) + f'(7π/4)(x - 7π/4) + (1/2)f''(7π/4)(x - 7π/4)^2 + (1/6)f'''(7π/4)(x - 7π/4)^3

Substituting the values we computed earlier, we get f(x) ≈ -2 + 2(x - 7π/4) - 2(x - 7π/4)^2

Therefore, the first three nonzero terms of the Taylor expansion for f(x) = 2tan(x) around a = 7π/4 are -2 + 2(x - 7π/4) - 2(x - 7π/4)^2.

To know more about Taylor expansion visit:

https://brainly.com/question/31953134

#SPJ11

Using sampling concepts, it is found that the population and the sample are given by:

Population: all the chicken meat; Sample: three random places in the chicken.

It is a common statistics practice, when we want to study something from a population, we find a sample of this population, which is a group containing elements of a population.

In this problem, a group of 3 chicken meat is taken from all the chicken meat, which is the population, hence the correct option is given by:

Population: all the chicken meat; Sample: three random places in the chicken.

More can be learned about sampling concepts at https://brainly.com/question/25122507

#SPJ1

C. The probability of the type I error best defines the notion of the significance position of a thesis test.

The significance position, denoted by alpha( α), is the probability of rejecting the null thesis(H_o) when it's actually true. This is also known as a type I error, which occurs when we inaptly reject a true null thesis.

Option a isn't correct because the probability of rejecting H_o, whether it's true or not, isn't fixed and depends on the sample and the chosen significance position.

Option b isn't correct because it describes the p- value, which is a affiliated conception but not the significance position. The p- value is the probability of observing a sample statistic as extreme or more extreme than the one actually attained, assuming the null thesis is true.

Option d is also not correct because it describes the probability of a type II error, which occurs when we fail to reject a false null thesis. The probability of a type II error is denoted by beta( β) and is told by factors similar as sample size and effect size.

Learn more about hypothesis test:-

https://brainly.com/question/4232174

#SPJ4

The expression 2^7 times 19 can be simplified by first evaluating the exponential term, 2^7, which is equal to 128. Therefore:2^7 times 19 = 128 * 19We can then evaluate the product of 128 and 19 using multiplication. When we do that, we get:2^7 times 19 = 2432Therefore, the choice that is equivalent to the expression 2^7 times 19 is 2432

Answer: x = 6.56

Step-by-step explanation: -0.4x - 0.5 + x = 3.63

-0.4x^2 - 0.5 = 3.63

-0.4x^2 = 4.13

0.63x = 4.13

x = 6.56