Convert the given polar equation to a Cartesian equation. (Use the following as necessary: x and y.)
r = 4 / sin(θ) + 5 cos(θ)

If there are 2. 2 pounds in 1 kilogram then there are 1.91 kilograms in 4.21 pounds.

We need to find how  many kilograms are there in 4. 21 pounds if there are 2. 2 pounds in 1 kilogram. This can be calculated by using unitary method.

There are 2. 2 pounds in 1 kilogram,

We need to find the kilograms are there in 4. 21 pounds

If there are 2. 2 pounds in 1 kilogram,

Then, 1 pound is 1/2.2 kilogram

1 pound = 0.4545

4.21 pound is (1/2.2) 4.21 kilogram

4.21 pound is 1.91 kilogram.

Therefore,  if there are 2. 2 pounds in 1 kilogram then there are 1.91 kilograms in 4.21 pounds.

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2.5 is the scale factor of the dilation triangle ABC was dilated and translated to form similar triangle A'B'C'

Given,

Triangles ABC and A'B'C' are similar

For ABC;- (x₁, y₁) = (0, 2) and (x₂, y₂) = (2, 2)

For A'B'C' ;- (x₁, y₁) = (-4, -1) and (x₂, y₂) = (1, -1)

We have to find the scale factor of the dilation;

Here,

Find the distance AB and distance A'B' with the formula

Distance, d = [tex]\sqrt{(y_{2} -y_{1})^{2} +(x_{2} -x_{1} )^{2} }[/tex]

Then,

a) Distance of AB

d AB = [tex]\sqrt{(2-2)^{2}+(2-0)^{2} }[/tex]

d AB = [tex]\sqrt{0^{2} +2^{2} }[/tex]

d AB = √4

Distance of AB  = 2 units

b) Distance of A'B'

d A'B' = [tex]\sqrt{(-1+1)^{2} +(1+4)^{2} }[/tex]

d A'B' = [tex]\sqrt{0^{2} +5^{2} }[/tex]

d A'B' = √25

Distance of A'B' = 5 units

Now,

Scale factor;

Scale factor = Distance of AB / Distance of A'B'

Scale factor = 5/2

Scale factor = 2.5

Therefore,

2.5 is the scale factor of the dilation triangle ABC was dilated and translated to form similar triangle A'B'C'

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The probability of contracting an illness is 0.0475.

According to our question-

D: The patient has the illness

ND: the individual without the disease

TD: The results of the test show the patient has the illness.

P(D) will therefore equal 0.001 since only 0.001 of the population is affected by the disease.

P(ND) = 0.991

Because the test successfully identifies a patient with the condition 99% of the time, P(TD/D) = 0.99.

P(TD/ND) = 0.02 because the test indicates that a healthy person contracts the disease 2% of the time.

We are seeking for P(D|TD) and P(ND|TD), respectively.

According to the Bayes formula, 0.00099/0.00099+0.01982 = 0.00099/0.02081 = 0.0475 = (0.99*0.001)/(0.99*0.001)+(0.02*0.991)

And, \s = 1 - \s = 1 - 0.0475 \s = 0.9525

Therefore,

The likelihood of having an illness is 0.0475.

The likelihood of not having any sick people is 0.9525.

Hence, The probability of contracting an illness is 0.0475.

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The number of apples that could be in the box is 180

From the question, we have the following parameters that can be used in our computation:

Number of apples = Fewer than 200

Children that can share the apples evenly = 2, 3, 4, 5, or 6 children

This means that the number of apples that could be in the box can be a multiple of 2, 3, 4, 5, or 6

Also, the number must be less than 200

The highest number less than 200 that is a multiple of 2, 3, 4, 5, or 6 is 180

Hence, the possible number of apples is 180

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Answer:

Multiples of 60 under 200!

Step-by-step explanation:

Option D is the correct answer, intervals of the coefficients are- b ∈ (2.1, 5.3], c ∈ (-3, 10), and d ∈ (-138, -126].

Here, we are given a polynomial of the form [tex]x^{3}[/tex] + b[tex]x^{2}[/tex] + cx + d

The zeroes of the polynomial are ( -4 + 4i ) and 4

The third root of the cubic equation will be (-4 - 4i) which is the conjugate of (-4 + 4i)

This means that for x = ( -4 + 4i ), ( -4 - 4i ) and 4, the polynomial is equal to 0.

Further, the sum of zeroes of a cubic equation

= -(coefficient of [tex]x^{2}[/tex] )/(coefficient of [tex]x^{3}[/tex])

Thus, -4 + 4i + 4 - 4 - 4i = -b

b = 4

Similarly, the sum of the product of zeroes taken 2 at a time = c

⇒ (-4 + 4i)(-4- 4i) + 4(-4 + 4i) + 4(-4- 4i) = c

c = 16 -16[tex]i^{2}[/tex] - 16 + 16i - 16 - 16i

c = 16 + 16 - 32

c = 0

Further, product of zeroes = -d

-d = (-4 + 4i) (-4- 4i) 4

d = -(16 + 16i - 16i -16[tex]i^{2}[/tex]) 4

d = -(16 + 16)4

d = -128

Thus, we get that option D is the correct answer, intervals of the coefficients are- b ∈ (2.1, 5.3], c ∈ (-3, 10), and d ∈ (-138, -126].

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Using the equation of the model:

a. About 150.4 thousand students studied in abroad in 2011.

b. About 467.5 thousand students would be studying in abroad in 2018.

An example of an equation of a model that can be used to make predictions or determine the value of one variable, is the equation that models the number of college students who studied abroad each year. This is given as y = 123.1(1.069)^x, here, we have:

Using the equation, y = 123.1(1.069)^x, we would solve the following:

a. 2001 after 1998 would be x = 3 years. Therefore, substitute x = 3 into the equation y = 123.1(1.069)^x to find the number of students that are studying abroad in 2001:

y = 123.1(1.069)^3 = 150.4

This implies that about 150.4 thousand students studied in abroad in 2001.

b. 2018 after 1998 would be x = 20 years. Therefore, substitute x = 20 into the equation y = 123.1(1.069)^x to find the number of students that would be studying abroad in 2018:

y = 123.1(1.069)^20 = 467.5

This implies that about 467.5 thousand students studied in abroad in 2018.

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The statements which are true is 4∈W, 7.5∈W and W= ∅

What does the term "universal set" mean?

A set that contains elements from all related sets, without any repetition of elements, is known as a universal set (typically denoted by the letter U). If A and B are two sets, for example, A = 1, 2, 3 and B = 1, a, b, c, then U = 1, 2, 3, a, b, c is the universal set that these two sets belong to.

What are the 8 different kinds of sets?

Empty set, finite set, singleton set, equivalent set, subset, power set, universal set, superset, and infinite set are the various types of sets.

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If you try to solve an equation and receive a variable or a number equal to itself, the problem has an unlimited number of solutions.

There are an infinite number of solutions to the equation system when two lines coincide with the same y-intercept. If the slope and y-intercept of the two lines coincide, they actually belong to the same line. Although a system of linear equations typically has a single solution, it occasionally may have infinite or no solutions (parallel lines) (same line). When the two lines that make up a linear system cross each other once, the system has a single solution. When the two lines are identical, as in the cases of y=x+3 and 2y=2x+6, a linear system has several (infinite) solutions. When the lines never cross (i.e., they are parallel and have the same slope), a linear system cannot be solved.

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Answer:

shaded area

unlikely

Step-by-step explanation:

She should guess a shaded portion of a rectangle that has a height of 10 and a length of 8 to maximize her chances of winning. The unlikely word describes the likelihood of the ball stop.

First, we need to find the areas of all the regions.

The area of the shaded rectangle = Length x Breadth = 10 x 8 = 80 square units

Area of unshaded rectangle = Length x Breadth = 5 x 2 = 10 square units

Area of unshaded triangle = 1/2 x base x height = 1/2 x 4 x 8 = 32/2 = 16 square units

Area of unshaded square = Side^2 = 4^2 = 16 square units

The area difference between the shaded and unshaded areas = The area of the shaded rectangle - (Area of unshaded rectangle + Area of unshaded triangle + Area of the unshaded square)

The area difference between the shaded and unshaded areas = 80 - (10 + 16 + 16)

The area difference between the shaded and unshaded areas = 80 - 42 = 38

As we see that the area of the shaded region is 38 more than the unshaded region so to maximize her chances of winning she should guess the shaded region or area.

Probability percentage of the shaded rectangle = 80/122 x 100 = 65.57%

Probability percentage of an unshaded rectangle = 10/122 x 100 = 8.20%

Probability percentage of an unshaded triangle = 16/122 x 100 = 13.11%

Probability percentage of an unshaded square = 16/122 x 100 = 13.11%

The unlikely word describes the likelihood of the ball stopping in a square or rectangular-shaped area because one is shaded and unshaded and the other is only unshaded. So, both are having different probabilities because of shape, area, and portion.

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Bisectors are the special segments that pass through the mid point of the lines or line segments.

A bisector is the line, line segment or ray that intercepts and/or divided lines or line segments into two equal line segments and thus passes through the midpoint of the given line segment or line segments.

There can be infinite bisector for one particular line or line segment at multiple angles.

The bisector that intercepts and/or cuts a line in half, passes through the midpoint when it is perpendicular (making an angle of 90°) to the line segment is known as the Perpendicular Bisector.

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The price per share of BBQ Corp. after there has been a stock split, or post - split, is $24. 15

When there is a stock - split, then each of outstanding shares that a company has, is divided into a number of shares that is determined by the stock split ratio.

The price of the individual shares are also divided into the same ratio as the shares.

This means that the price per share for BBQ Corp. post - split is:

= Price per share before split / 3

= 72. 45 / 3

= $24. 15

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The correct option is A. The formula for the mean absolute deviation over a range of forecasted values is  MAD t 1 t 1.

Forecasting is the method of creating predictions primarily based on past and gift information. Later these can be compared (resolved) against what occurs. for example, a company would possibly estimate their sales in the next yr, then examine it in opposition to the real results. Prediction is similar, but the more preferred time period. Forecasting would possibly confer with particular formal statistical methods using time series, pass-sectional or longitudinal information, or as an alternative to less formal judgmental strategies or the manner of prediction and resolution itself. utilization can range among regions of application:  

for example, in hydrology, the phrases "forecast" and "forecasting" are sometimes reserved for estimates of values at sure unique future instances, at the same time as the term "prediction" is used for extra widespread estimates, consisting of the wide variety of times floods will arise over an extended duration.

chance and uncertainty are vital to forecasting and prediction; it's miles generally taken into consideration as an excellent practice to indicate the diploma of uncertainty attached to forecasts. in any case, the information ought to be updated in order for the forecast to be as accurate as possible. In a few instances, the information used to are expecting the variable of the hobby is itself forecast

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a system of two linear equations is solved by combining the two equations to eliminate one of the variables.

Using the linear combination method, a system of two linear equations is solved by combining the two equations to eliminate one of the variables. Once one of the variables is eliminated, an equation with only one variable is left, e.g., 2x=2, and it is very simple to see that in this case, x=1

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The geometric multiplicity is equal to the algebraic multiplicity, then t is diagonalizable.

The word "nilpotent" is missing from the title, rather confusing, since being nilpotent is easily seen to be the only possible obstruction against being diagonalisable for a rank 1 operator. After all, by rank-nullity this implies the nullity equals n−1, and this is (by definition) the dimension of the eigenspace for 0. Also Im(T) is always T-stable, so being of dimension 1 its nonzero vectors are eigenvectors, and if this is for a nonzero eigenvalue λ, then the eigenspaces for 0 and for λ are complementary, and so T is diagonalisable.

So the only thing that can go wrong is that the nonzero vectors of Im(T) are eigenvectors for 0, but then clearly T2=0 so T is nilpotent.

It would have been a bit more fun if instead of T not being nilpotent it had been given that T has nonzero trace. Since 0 is a root of the characteristic polynomial χT with multiplicity at least n−1 (which is its geometric multiplicity), the "final" root of χT equals the sum of all its roots, which is the trace of T. This is also the eigenvalue of nonzero vectors in Im(T), and as we have seen it is zero if and only if T is nilpotent if and only if T is not diagonalisable.

Hence the answer is the geometric multiplicity is equal to the algebraic multiplicity, then t is diagonalizable.

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The transtors produced by one machine have a lifetime which is Exponentially Distributed. let X be the lifetime of a transistor.

a) P(X≥200 hours) = 0.29

b) E(x) = 166.7

c) Var(x) = 12222.22

We have given the exponential distribution of lifetime of transtors produced by one machine

So, X∼Exp(x)

a) The probability density function is

f(x)=m × e⁻ᵐˣ

The number e = 2.71828182846e

we have , mean , u = 100 for first machine

and it follows that

P(X≥200) = e⁻²·⁴¹² + e⁻¹·⁸¹² = 2e⁻²≈0.29.

(b) By the tower property of conditional expectation, E(X) = E[E(X|Y)] = XyE(X|Y=y)

pY(y)=E(X|Y= 1)P(Y= 1) +E(X|Y= 2)P(Y= 2).

Again using the conditional distributions of X|Y, we have E(X|Y= 1) = 100, E(XY= 2) = 200.

Hence,E(X) = 100·412+ 200·812=5003≈166.7.

(c) The general formula for a random variable depending on a parameter is:

Var(X) = E(Var(X|Y)) + Var(E(X|Y))

In this case, Y is a random variable which is "100" with a probability of 1/3 and "200" with a probability of 2/3, and X is an exponential distribution with mean Y.

Var(X|Y) = Y² so E(Var(X|Y)) = (1/3)100² + (2/3) 200² = 90000/9

E(X|Y) = Y, so Var(E(X|Y)) = Var(Y) = E(Y²) - E(Y)² = 30000 - (500/3)² = (30000 * 9 - 250000)/9

= 20000/9

Var(X) = 110000/9 = 12222.22

Hence, a) the P(X≥200) = 0.29

b) E(x) = 166.7

c) var(x) = 12222.22

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The total of 4 players left after 5 rounds.

Given information,

Given that a neighborhood tennis club holds a fundraising competition every year. A total of 128 players are permitted to enter. In each round, half the participants are eliminated.

The function will be written as,

[tex]F(x) = 128e^x[/tex]

To know how many players left after 5 rounds,

Round 1 ⇒ 128/2 = 64

Round 2 ⇒ 64/2 = 32

Round 3 ⇒ 32/2 = 16

Round 4 ⇒ 16/2 = 8

Round 5 ⇒ 8/2 = 4

Hence, 4 players will be left after 5 rounds.

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The correct answer is Wednesday, January 26, at 4 p.m when your subject-matter expert informs you that she believes it will take her 40 hours to finish the work.

Given that,

Your subject-matter expert informs you that she believes it will take her 40 hours to finish the work. The project begins on January 20 at 8 a.m. The staff only works throughout the weekdays, eight hours a day.

We have to find when will the assignment be completed.

We know that,

This simple table explains the answer

Thursday, January 20, at 4 p.m. - 8 hours worked

Friday, January 21, at 4 p.m. - 16 hours worked

Monday, January 24, at 4 p.m. - 24 hours worked

Tuesday, January 25, at 4 p.m. - 32 hours worked

Wednesday, January 26, at 4 p.m. - 40 hours worked

Therefore, The correct answer is Wednesday, January 26, at 4 p.m when your subject-matter expert informs you that she believes it will take her 40 hours to finish the work.

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The population mean strength of the components differs from 50 is 0.304.

In the  given question, an engineer selected 30 components at random and measure their strengths. 34,54,73,38,89,52,75,33,50,39,42,42,40,66,72,85,28,71,52,47,41,36,33,38,49,51,55,63,72,78

We have to check does this data suggest that the population mean strength of the components differs from 50 and we have to set up an appropriate hypothesis test to answer this question.

Sample size n = 30

Claim : The population mean strength of the components differs from 50.

Null and alternative hypothesis:

H(0): μ = 50

H(A): μ≠50

As the population standard deviation is unknown (not given) , t-test can be used .

Test Statistic :

t = (X-μ)/(S/√n)

To find the sample mean we find the average of the given sample.

So

X = 34 + 54 + 73 + 38 + 89 + 52 + 75 + 33 + 50 + 39 + 42 + 42 + 40 + 66 + 72 + 85 + 28 + 71 + 52 + 47 + 41 + 36 + 33 + 38 + 49 + 51 + 55 + 63 + 72 + 78/ 30

X = 53.267

Now finding the standard deviation using the excel.

SD = 17.1101

To find the SD we use the formula =STDEV(B1:C15)

Now putting the value in the formula of Test Statistic

t = (X-μ)/(S/√n)

t = (53.267-50)/(17.1101/√30)

After solving:

t=1.046

P-value :

As the alternative hypothesis H(A) is of not equal to type , this is two tailed test.

Degrees of freedom = n-1 = 30 -1 = 29

df =29

Using Excel function , =TDIST( t , df , number of tails )

=TDIST( 1.046 , 29 , 2 )

=0.304201657

Rounding to three decimal places

= 0.304

P-value = 0.304

Hence, the population mean strength of the components differs from 50 is 0.304.

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Answer:

-1

Step-by-step explanation:

if the input is 4 you just go through the cycles

4 then subtract 7

4-7

-3

Then divide by 3

-3/3

-1

Hopes this helps please mark brainliest

for point (1,4)

After 1 hour, Evelyn and her friends are 4 miles from shore.

for point (3,12)

After 3 hour, Evelyn and her friends are 12 miles from shore.

Answer:

its A

Step-by-step explanation:

-x²+x+(4x²-x-1)

-x²+x+4x²-x-1

-x²+4x²-1

3x²-1

The upper sum is 24 and the lower sum is 8 for the given function

f(x) = 6 - x², -2 ≤x≤ 2.

A function from a set X to a set Y in mathematics assigns to each element of X exactly one element of Y. The domain of the function is the set X, and the codomain of the function is the set Y.

The first known approximation to the concept of function is attributed to the Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. Functions were originally idealistic representations of how one variable quantity depended on another. The location of a planet, for example, changes throughout time. Historically, the concept was formed with infinitesimal calculus near the end of the 17th century, and the functions that were analyzed were differentiable until the 19th century.

Given,

f(x) = 6 - x²

-2 ≤x≤ 2

When n=2, partition of interval -2, 0, 2

When x=-2, f(-2)=6-4

f(-2)=2

x=0, f(0)=6-0

f(0)=6

x=2, f(2)=6-4

f(2)=2

Upper sum= M₁S₁+M₂S₂

=6(2)+6(2)

=24

Lower sum=m₁ s₁+m₂ s₂

=2(2)+2(2)

=8

Therefore, upper sum=24 and lower sum= 8

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The expectation of the required  random variable is Ex(r) for the given number of days when a relaxed student delays for laundry is Ex(r) = 5.

As given in the question,

6-sided fair die was rolled by relaxed student

Rolls of fair die represents  1  it mean laundry is done ( no delay in laundry)

Count the number of days when laundry gets  done = 1 / (1 /6)

                                                                                       = 6

Number of days when laundry gets delays = 6 - 1

                                                    = 5

Probability of laundry delay = 5/6

Expectation of the required number of random variables

Ex(r) = [tex]\sum\limits^\infty_0 {P_{r} } \,[/tex]

       = [tex]\frac{5}{6} + (\frac{5}{6}) (\frac{5}{6}) +....[/tex]

       = (5/6)( 1+ ( 5/6) + (5/6)(5/6) + (5/6)(5/6)(5/6) +...)

       =  [tex]( 5/ 6)[ \frac{1}{1- (\frac{5}{6} )}][/tex]

       = 5

Therefore, the number of days when relaxed student delays for laundry is equal to Ex(r) = 5.

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:: means average mean in mathematics.

A number system is defined as a system of writing to express numbers.

We need to find what is :: in maths

Mathematical notation consists of using symbols for representing operations, unspecified numbers, relations and any other mathematical objects, and assembling them into expressions and formulas.

: : is a mathematical notation, it is called as double colon and it is used to find the average mean.

a:b: : c:d

In the above expression it acts as an equivalent ration between a:b and c:d

Hence, :: means average mean in mathematics.

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A political party is made up of people who band together to run the government, win elections, and shape public policy. Currently, the two major parties in Congress are the Democratic and Republican.

Political parties act as a conduit between the governed and the ruling class. They educate the public, arouse inspiration, and pique interest in and engagement in public affairs. Their main duty is to suggest candidates for elected office.

Self-annuncation, in which a candidate for office only declares their candidacy, is the earliest method of nominating in American politics.

The national chairman, a national committee, the national convention, and two congressional campaign committees make up the party's overall organizational structure. The party is decentralized at the state level, and state legislation generally determines how it is structured.

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[tex]x=number\hspace{5em}x^2=\textit{squared number} \\\\\\ \stackrel{\textit{difference of }x^2\textit{ and 18}}{x^2~~ - ~~18}~~ = ~~\stackrel{\textit{three times }x}{3x} \\\\\\ x^2-3x-18=0\implies (x-6)(x+3)=0\implies x= \begin{cases} 6\\\\ -3 ~~ \checkmark \end{cases}[/tex]

You can buy car A, because the acceptable rate is 14% and here car A has a rate of 20%

Given,

There are three different cars that you could buy. They differ in initial cost, annual operating costs, and life. Your minimum acceptable rate of return is 14%. Use the ROR method to select the best alternative.

Alternative            A             B                 C

Initial Cost          10,000     8,000       5,000

Annual Cost       1,000       1,500        1,500

Life                     8 years    8 years     5 years

Here,

Rate of Return of car A = (10,000 - 1000 x 8) / 100 = 2000/100 = 20%

Rate of Return of car B = (8,000 - 1500 x 8) / 100 = -4000/100 = -40%

Rate of Return of car B = (5,000 - 1500 x 5) / 100 = -2500/100 = -25%

That is,

You can buy car A, because the acceptable rate is 14% and here car A has a rate of 20%

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If banks' desired reserve/deposit ratio is 25.0 percent, deposits in macro land are $28800000 and the money supply is $36000000

The deposit ratio is the rate sum of money (stores) that commercial banks must not loan out or invest, the reserve ratio is as a rule fixed by the central banks to control inflation and the volume of cash in circulation inside a given country in a particular time.

Initial bank deposit= 60% of 12000000 = 7200000, The reserve/deposit will calculate as follows (25.0 /100%)=0.25 and If banks desired to keep 25.0  it deposit ratio will be : 1/0.25*7200000= 28800000

So the money supply will be the desired deposited :

=28800000+ 7200000 =36000000

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