Write the trigonometric form of the complex number. (Let 0 ≤ < 2.)1 − √3iradical 3i

Answer:

= 1.21577e19

Step-by-step explanation:

I used a calculator that should tell you. :))

(a) The probability that all 4 missiles will fire is 0.2098 and (b) The probability that at most 2 will not fire is 0.0099.

Here we need to use the concept of combinations to get our required answer.

Here we have been given that 4 out of 14 missiles are defective.

Hence 10 missiles are working.

A sample of 4 missiles was chosen

Hence the simple can be chosen in ¹⁴C₄ ways

a)

The probability that all 4 missiles will fire is

¹⁰C₄/¹⁴C₄

= 0.2098

b)

The probability that at most 2 will not fire is

1 - the probability of including all three defective missiles

= 10³C₃/¹⁴C₄

= 0.0099

To learn more about Probability visit

https://brainly.com/question/30034780

#SPJ4

(a) Probability all 4 fire: 0.3297. (b) Probability at most 2 not fire: 0.9591.

(a) To track down the chance that all of the 4 rockets will fire, we actually need to do not forget the quantity of methods we can select 4 operating rockets out of the eleven that are not unsuitable, isolated by the all out range of approaches we will select four rockets out of the whole component.

The amount of ways of selecting four operating rockets out of the eleven that aren't improper is given by way of the combination recipe:

C(eleven,four) = 330

The absolute quantity of methods of selecting four rockets out of the entire part is given via:

C(14,4) = 1001

Subsequently, the chance that each one of the four rockets will hearth is:

P(all four hearth) = C(11,four)/C(14,4) = 330/1001 ≈ zero.3297

(adjusted to 4 decimal spots)

(b) To find the likelihood that at most 2 rockets might not fire, we need to remember every one of the potential conditions in which 0, 1, or 2 poor rockets are selected, and afterward song down the likelihood of every case and upload them up.

Case 1: No defective rockets are selected

The amount of ways of selecting four working rockets out of the eleven that are not faulty is given through the mixture recipe:

C(11,four) = 330

Subsequently, the chance of choosing no defective rockets is:

P(0 inadequate) = C(eleven,4)/C(14,four) ≈ 0.3297

Case 2: One defective rocket is chosen

The quantity of ways of selecting three operating rockets out of the eleven that are not poor is given with the aid of the combo equation:

C(eleven,three) = 165

The amount of ways of selecting 1 damaged rocket out of the three that are available is given through the mix equation:

C(three,1) = 3

Subsequently, the all out number of approaches of selecting 1 insufficient and three running rockets is:

C(eleven,three) × C(3,1) = 495

Thusly, the probability of choosing one deficient rocket and three running rockets is:

P(1 deficient) = C(eleven,three) × C(three,1)/C(14,4) ≈ 0.4655

Case three: Two poor rockets are selected

The amount of approaches of choosing 2 poor rockets out of the three which might be handy is given through the combination recipe:

C(3,2) = 3

The amount of ways of choosing 2 running rockets out of the 11 that aren't faulty is given via the mix recipe:

C(11,2) = 55

In this way, the all out number of methods of selecting 2 broken rockets and 2 working rockets is:

C(3,2) × C(eleven,2) = one hundred sixty five

Subsequently, the chance of choosing two incorrect rockets and two operating rockets is:

P(2 insufficient) = C(3,2) × C(11,2)/C(14,four) ≈ 0.1638

Subsequently, the likelihood that at maximum 2 rockets might not fireplace is:

P(at maximum 2 don't fire) = P(zero imperfect) + P(1 blemished) + P(2 deficient) ≈ 0.9591

(adjusted to 4 decimal spots).

To learn more about probability, refer:

https://brainly.com/question/1581511

#SPJ4

Answer:

A ^ ( m+n)

Step-by-step explanation:

When we are multiplying terms with exponents and the bases are the same, we can add the exponents

A^m * A^n =

A ^ ( m+n)

Answer:

m and n

Step-by-step explanation:

Exponents are the raised numbers or letters.

So it is m and n

The intersection and the union of the intervals (-7, 0) and (-3, 5) are (-3,0) and (-7,5) respectively

Given,

The intervals = (-7,0) and (-3,5)

Draw the intersection and union of the intervals in the number line

The intersection is an interval that lies within the both intervals (-7,0) and (-3,5)

Intersection of the intervals (-7,0) and (-3,5)  = (-3,0)

The union is the set that consist of all the elements in the first interval and all the elements in the second interval

Union of the intervals (-7,0) and (-3,5) = (-7,5)

Hence, The intersection and the union of the intervals (-7, 0) and (-3, 5) are (-3,0) and (-7,5) respectively

Learn more about number line here

brainly.com/question/13206357

#SPJ1

The solution to this question is as the function could be horizontally translated to the left as follows: Therefore,g(x) = 3x +6

The term "function" refers to the relationship between a collection of inputs and outputs with one each. Simply described, a function is an association of inputs where each input is coupled with exactly one output. Every function has an associated domain, codomain, or range. The most common way to represent a function is as f(x), where x represents the input..

Here,

f(x)=3x+4

As we have to find g(x) a horizontal translation 2 units to the left.

Therefore

g(x)=f(x)+2

g(x)=(3x+2)+4

g(x)=3x+6

Therefore ,solution is g(x) = 3x +6

To know more about function ,visit

https://brainly.com/question/23712366

#SPJ4

Answer:

94/45

Step-by-step explanation:

Answer:

23

Step-by-step explanation:

The amount of children's tickets is x, while the amount of adults' tickets is 2x

5.1*x- the amount of money from children

9.6*2x= 19.2x- the amount of money from adults

5.1x+19.2x= 558.9

x=23 - child tickets

Therefore, the area between the large loop and the small loop of the curve r = 2 + 4cos(3θ) is 70π/3.

To find the area between the large loop and the small loop of the curve, we need to find the points of intersection of the curve with itself.

Setting the equation of the curve equal to itself, we have:

2 + 4cos(3θ) = 2 + 4cos(3(θ + π))

Simplifying and solving for θ, we get:

cos(3θ) = -cos(3θ + 3π)

cos(3θ) + cos(3θ + 3π) = 0

Using the sum to product formula, we get:

2cos(3θ + 3π/2)cos(3π/2) = 0

cos(3θ + 3π/2) = 0

3θ + 3π/2 = π/2, 3π/2, 5π/2, 7π/2, ...

Solving for θ, we get:

θ = -π/6, -π/18, π/6, π/2, 5π/6, 7π/6, 3π/2, 11π/6

We can see that there are two small loops between θ = -π/6 and π/6, and two large loops between θ = π/6 and π/2, and between θ = 5π/6 and 7π/6.

To find the area between the large loop and the small loop, we need to integrate the area between the curve and the x-axis from θ = -π/6 to π/6, and subtract the area between the curve and the x-axis from θ = π/6 to π/2, and from θ = 5π/6 to 7π/6.

Using the formula for the area enclosed by a polar curve, we have:

A = 1/2 ∫[a,b] (r(θ))^2 dθ

where a and b are the angles of intersection.

For the small loops, we have:

A1 = 1/2 ∫[-π/6,π/6] (2 + 4cos(3θ))^2 dθ

Using trigonometric identities, we can simplify this to:

A1 = 1/2 ∫[-π/6,π/6] 20 + 16cos(6θ) + 8cos(3θ) dθ

Evaluating the integral, we get:

A1 = 10π/3

For the large loops, we have:

A2 = 1/2 (∫[π/6,π/2] (2 + 4cos(3θ))^2 dθ + ∫[5π/6,7π/6] (2 + 4cos(3θ))^2 dθ)

Using the same trigonometric identities, we can simplify this to:

A2 = 1/2 (∫[π/6,π/2] 20 + 16cos(6θ) + 8cos(3θ) dθ + ∫[5π/6,7π/6] 20 + 16cos(6θ) + 8cos(3θ) dθ)

Evaluating the integrals, we get:

A2 = 80π/3

Therefore, the area between the large loop and the small loop of the curve r = 2 + 4cos(3θ) is:

A = A2 - A1 = (80π/3) - (10π/3) = 70π/3

To know more about area,

https://brainly.com/question/31479047

#SPJ11

Answer:

(a + 8)(a - 5)

Step-by-step explanation:

a² + 3a - 40 =

= (a      )(        )

Find two numbers that multiply to -40 and add to 3.

They are 8 and -5.

= (a + 8)(a - 5)

solution :

a²+3a-40

find the roots (2 numbers in which you can add and multiply to give 3a and 40)

(a-5) (a+8)

substitute the roots with 3a and multiply 40 by a²

a²-5a+8a-40a²

a(a-5) +8(a-40a²)

(a-5) (a+8)

The grumbling sensation in Zoe's stomach triggers a series of neural, hormonal, and cognitive processes that lead to her awareness of hunger and subsequent behavioral response to satisfy her body's need for food.

After feeling a grumbling in her stomach, Zoe realizes she is hungry.

Zoe is going through a physiological process known as hunger, which involves several steps:

Stimulus:

The grumbling sensation in Zoe's stomach acts as a stimulus, indicating a need for nourishment.

Neural Signaling:

The sensation of hunger triggers nerve signals from the stomach and intestines to the brain, specifically the hypothalamus, which plays a vital role in regulating appetite.

Hypothalamic Response:

The hypothalamus receives the signals and initiates various physiological and behavioral responses to address the hunger.

It releases neuropeptides and hormones such as ghrelin, which stimulate the appetite and signal the body to seek food.

Cognitive Awareness:

As a result of the neural signaling and hypothalamic response, Zoe becomes cognitively aware of her hunger.

She recognizes the sensations and interprets them as a need for food.

Behavioral Response:

Zoe's realization of hunger prompts her to seek food and engage in behaviors aimed at obtaining nourishment, such as planning a meal, preparing food, or seeking a restaurant or grocery store.

In summary, the grumbling sensation in Zoe's stomach triggers a series of neural, hormonal, and cognitive processes that lead to her awareness of hunger and subsequent behavioral response to satisfy her body's need for food.

Learn more about physiological process from this link:

https://brainly.com/question/31437946

#SPJ11

Using the Integral Test, the correct choice is B. Since the integral ∫(k+7)dx diverges, the series also diverges.

We are supposed to use Integral Test to determine the convergence or divergence of the series, ∑(k+7)dx.

We can use the Integral Test to test for the convergence of series if the function in the series is continuous, positive, and decreasing for all x greater than or equal to some value N.

The Integral Test states that a series converges if and only if the integral of the series term is convergent, i.e. if the integral of u(x)dx is convergent. Also, if the integral of u(x)dx diverges, the series is divergent.

So we need to check whether the function in the given series is continuous, positive, and decreasing for all x greater than or equal to some value N.

If we integrate the series, ∑(k+7)dx, we get:∫(k+7)dx= ∫k

dx + ∫7dx= (k²/2) + 7x+ C

where C is the constant of integration.

Since the value of C is not given, we cannot say anything about the exact value of the integral.

However, the value of the constant of integration does not matter in this case as we only need to determine whether the integral converges or diverges.

Therefore, we can use the Integral Test to determine the convergence or divergence of the series.

Using the Integral Test, the correct choice is B.

Since the integral ∫(k+7)dx diverges, the series also diverges.

Know more about Integral Test here:

https://brainly.com/question/31381575

#SPJ11

Rounded to the nearest whole number, the area of the shaded face of the cylinder is approximately 381 mm^2.

To determine the area of the shaded face of the cylinder, we need more information about the shape and position of the shaded region. Without a specific description or visual representation of the shaded face, it is not possible to accurately calculate its area.

However, if we assume that the shaded face represents the circular base of the cylinder, we can calculate its area. The area of a circle is given by the formula:

A = πr^2,

where A represents the area and r represents the radius of the circle.

Given that the diameter of the circle is 22 mm, we can calculate the radius by dividing the diameter by 2:

r = 22 mm / 2 = 11 mm.

Now we can calculate the area of the shaded face:

A = π(11 mm)^2

≈ 121π mm^2.

To provide the answer to the nearest whole number, we can approximate the value of π as 3.14:

A ≈ 121 × 3.14 mm^2

≈ 380.94 mm^2.

Rounded to the nearest whole number, the area of the shaded face of the cylinder is approximately 381 mm^2.

for such more question on area

https://brainly.com/question/15822332

#SPJ8

Answer:

the numerator is: 22

the denominator is : 30

___________________

the simplified numerator is: 11

the simplified denominator is: 15

Step-by-step explanation:

Answer: 22/30 reduced is 11/15

Step-by-step explanation: Half 22/30 to get 11/15, (so 22/2=11 and 30/2=15) Your numerator would be 11, and your denominator is 15.

Hope this helps!

Step-by-step explanation:

How to Calculate the Semi Interquartile Range / Quartile Deviation. As the SIR is half of the Interquartile Range, all you need to do is find the IQR and then divide your answer by 2. Note: You might see the formula QD = 1/2(Q3 – Q1). Algebraically they are the same.

Answer:

$10

Step-by-step explanation:

This question has missing details.

The given parameters from the complete question is:

\(Slushy\ Cup = \$5\)

\(Refill = \$1\)

Required

Total amount for 1 cup and 5 refills

Let

\(x \to\) Slushy Cup

\(y \to\) Refill

So, the expression for the total amount is:

\(Total = 5x + y\)

\(x =1\) -- 1 cup

\(y = 5\) -- 5 refills

So, the total is:

\(Total = 5 * 1 + 5\)

\(Total = 5 + 5\)

\(Total = 10\)

The given statement is False, because the description only applies to one solution. The solution set contains all conceivable solutions.

A linear number pattern is a succession of numbers with the same difference between each term. As an example, consider the numbers 1, 3, 5, 7, 9,... Every phrase differs by a factor of two. These are also known as linear numbers. Another example would be 7, 17, 27, 37,...

A formula can be found for linear sequences, that is, sequences in which the difference between succeeding terms is always the same. would have resulted in the formula un = 3n + 35. produces the formula un = 3n - 10, where c is either positive or negative.

To obtain the remaining phrases, you simply keep using the addition of 1 method.

Here are a few further illustrations of linear number patterns:

Beginning with three points and a two-point difference:

3, 5, 7, 9, … Starting with five and a three-point difference:

5, 8, 11, 14, …

To learn more about linear number pattern visit:

https://brainly.com/question/24505121

#SPJ4

Answer:

x = 19√3

y = 38

Step-by-step explanation:

x/19 = cot 30° = √3

x = 19√3

sin 30° = 19/y

1/2 = 19/y

y = 38

The disparities between the actual and anticipated values in a regression model were referred to as residuals in the context Tufte provided.

American statistician Edward Rolf Tufte is a retired professor of political science, statistics, and computer science at Yale University.

Tufte talked about the idea of residuals. The discrepancies between the actual value and the projected value are known as residuals in statistics. Depending on whether the observed value is higher or lower than the projected value, they might be either positive or negative.

A model's residuals offer a gauge of how well it matches the data. According to him, residual plots are a great tool for seeing issues with the model fit and spotting outliers that might be skewing the results.

In contrast to relying exclusively on statistical tests, Tufte emphasised the significance of visually evaluating residuals since graphs can highlight patterns and correlations that may be missed in the numbers.

Overall, residuals are a key idea in statistics since they may be used to evaluate a model's reliability and point out its flaws.

Learn more about residuals from the given link :

https://brainly.com/question/1447173

#SPJ11

Answer:

8x4

Step-by-step explanation:

i got you

big brain

Answer:

8x(8)

Step-by-step explanation:

Answer:

the answer would be 160H

The cost of a job that lasts 1.5 hours is  $ 192.5

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

The charge of each job by the plumbing company = $ 95

The charge on each hour for each job = $ 65

The equation for the cost of a job is = 65h + 95

where h is the number of hours for the job

Now , to calculate the cost of job that lasts 1.5 hours ,

substitute the value of h as 1.5

And , the equation becomes

= 65h + 95

= 65 ( 1.5 ) + 95

= 97.5 + 95

= $ 192.5

Hence , the cost of a job that lasts 1.5 hours is  $ 192.5

To learn more about equations click :

https://brainly.com/question/10413253

#SPJ3

Answer:

5(x - 5)(x + 2)

Step-by-step explanation:

5x² - 15x - 50

5(x² - 3x - 10)

5(x - 5)(x + 2)

(i) True.

(ii) False.

The first statement is true.

It is a well-known fact that for any random variable X, the covariance of X with itself is equal to the variance of X. This can be easily shown by applying the definition of covariance and variance and using the fact that the correlation between X and X is always 1.

The second statement is false. The mean of an exponential random variable is equal to 1/λ, where λ is the rate parameter. On the other hand, the standard deviation of an exponential random variable is equal to 1/λ as well. These two values are not equal, unless λ=1. Therefore, the statement is false.

In summary, the first statement is true, while the second statement is false. The covariance of a random variable with itself is equal to its variance, but the mean and standard deviation of an exponential random variable are not equal unless λ=1.

To learn more about standard deviations click brainly.com/question/14747159

#SPJ11

Answer:

Step-by-step explanation:

Exact Form:

1/2

Decimal Form:

-0.5

Answer:

- 2

Step-by-step explanation:

using the rule of logarithms

\(log_{b}\) x = n ⇒ x = \(b^{n}\)

given

\(log_{\frac{1}{7} }\) 49 = n , then

49 = \((\frac{1}{7}) ^{n}\)

49 = \((7^-1)^{n}\) , that is

7² = \(7^{-n}\)

since bases on both sides are equal then equate exponents

- n = 2 ( multiply both sides by - 1 )

n = - 2

To compute the chi-square (χ2) statistic for a contingency table, the entries in the table should be non-negative whole numbers and should represent counts or frequencies.

The entries should indicate the number of observations falling into each category or combination of categories. It is important to note that the χ2 test is a statistical test used to analyze the association between categorical variables, and it requires the data to be in the form of a contingency table with appropriate counts or frequencies.

The χ2 test is commonly used to examine the relationship between two categorical variables. The contingency table is a table that summarizes the observed frequencies or counts for each combination of categories of the variables. The entries in the contingency table should fulfill certain requirements to ensure the validity of the χ2 test. Firstly, the entries in the table should be non-negative whole numbers, as they represent counts or frequencies of occurrences. Negative values or non-integer values are not meaningful in this context.

Secondly, the entries should reflect the number of observations falling into each category or combination of categories. Each cell in the table represents the count or frequency of observations falling into a specific combination of categories. By ensuring that the entries in the contingency table satisfy these criteria, we can accurately compute the χ2 statistic and perform the appropriate statistical analysis to assess the association between categorical variables.

Learn more about chi-square here: brainly.com/question/32379532

#SPJ11

Answer: C, 224 inches squared

Step-by-step explanation:

When formed into a solid, the triangles are folded upwards to make a pyramid. You can find the surface area by finding the areas of the individual shapes.

There are four triangles with a height of 10 inches and a base of 8 inches.

There is one square with a side length of 8 inches.

Triangle area formula : A = (b * h) / 2

Square area formula: A = s^2

(10 * 8) / 2 = 40

8 ^ 2 = 64

There are four triangles with area of 40 and one square with area of 64.

40 + 40 + 40 + 40 + 64 = 224 inches squared. The correct answer choice is C.

The surface area of the pyramid is 224 in².

The surface area of a solid object is a measure of the total area that the surface of the object occupies.

Given net will form a square pyramid, so we will find the surface area of the square pyramid.

Therefore,

The area of the pyramid = side² + 2 × side × height

= 8² + 2 × 8 × 10

= 64 + 160

= 224

Hence the surface area of the pyramid is 224 in².

Learn more about surface area click;

https://brainly.com/question/29298005

#SPJ3

Answer:

D. 2 7/12

Step-by-step explanation:

8 1/4 - 5 2/3

Turn to improper fractions.

33/4 - 17/3

Make the denominators equal.

99/12 - 68/12

Subtract the fractions since denominators are equal.

31/12

= 2 7/12

Answer:

\( 2 \frac{7}{12} \)

Answer D is correct.

Step-by-step explanation:

\(8 \frac{1}{4} - 5 \frac{2}{3} \\ \frac{33}{4} - \frac{17}{3} \\ \frac{99 - 68}{12} \\ \frac{31}{12} = 2 \frac{7}{12} \)

Answer:

RR' || SS'

Step-by-step explanation:

because if you look at the image you see that RR' is parallel to SS'

Answer:

\((a)\ y = 2x +8\)

\((b)\ y = 0\)

\((c)\ y = -5\)

Step-by-step explanation:

Given

\(y = x^2\)

First, graph \(y = x^2\) (See attachment)

We are not limited to any particular linear equation; as long as we meet the required condition

Solving (a): Equation of a line that intersects \(y = x^2\) at two points

Select any two points on opposite sides of the curve

The selected points are:

\((x_1,y_1) = (-2,4)\)

\((x_2,y_2) = (4,16)\)

Calculate slope (m)

\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

\(m = \frac{16 - 4}{4 - -2}\)

\(m = \frac{12}{6}\)

\(m = 2\)

The equation is then calculated using:

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

This gives:

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

\(y = 2(x +2) + 4\)

Open bracket

\(y = 2x +4 + 4\)

\(y = 2x +8\)

Solving (b): Equation of a line that intersects \(y = x^2\) at one point

A good illustration of this is x-axis

Because it intersects with the line at just one point, which is origin (0,0).

The equation of line at this point is:

\(y = 0\)

Solving (c): Equation of a line that does not intersect \(y = x^2\)

Here, we make use of any horizontal line below the x-axis

Select any two horizontal points below the x-axis

\((x_1,y_1) = (-5,-5)\)

\((x_2,y_2) = (5,-5)\)

Calculate slope

\(m = \frac{-5--5}{5--5}\)

\(m = \frac{0}{10}\)

\(m = 0\)

The equation is then calculated using:

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

\(y = 0(x - -5) + (-5)\)

\(y = 0-5\)

\(y = -5\)

The given expression is 9x^4 - 13x^2 + 4. To find the sum of the factors, we need to factorize the expression and add up the individual factors.

The factored form of the expression is (3x - 2)(3x + 2)(x - 1)(x + 1). Therefore, the sum of the factors is 3x - 2 + 3x + 2 + x - 1 + x + 1, which simplifies to 8x.

To find the factors of the expression 9x^4 - 13x^2 + 4, we can rewrite it as (3x^2)^2 - 2(3x^2)(2) + (2)^2 - (x)^2 + (1)^2. This can be further simplified as (3x^2 - 2)^2 - (x - 1)^2. Now we have a difference of squares. Using the identity a^2 - b^2 = (a + b)(a - b), we can factorize the expression as (3x^2 - 2 - x + 1)(3x^2 - 2 + x - 1). Simplifying this, we get (3x - 2)(3x + 2)(x - 1)(x + 1).

To find the sum of the factors, we add up the individual factors: (3x - 2) + (3x + 2) + (x - 1) + (x + 1). Simplifying this, we get 8x. Therefore, the sum of the factors of 9x^4 - 13x^2 + 4 is 8x.

To learn more about factors click here:

brainly.com/question/31931315

#SPJ11