eliminate the parameter in the equations x=5cos(t) -7 and y=5sin(t)+9. how can the rectangular equation be described?
circle
ellipse
parabola
hyperbola

27a³ + 189a²b + 441ab² + 343b³ = (3a + 7b)³

27a³ + 189a²b + 441ab² + 343b³

Therefore,

27a³  = (3a)³

189a²b  = 3(3a)²(7b)

441ab² = 3(3a)(7b)²

343b³ = (7b)³

(3a)³ + (7b)³ + 3(3a)²(7b) + 3(3a)(7b)²

a³ + b³ + 3a²b + 3ab²  = (a + b)³

Therefore,

27a³ + 189a²b + 441ab² + 343b³ = (3a + 7b)³

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a) The length of p is 21.4 cm

b) The measure of angle P is 45.6°

From the question, we are to determine the length of p

From the Pythagorean theorem, we can write that

30² = 21² + p²

p² = 30² - 21²

p² = 900 - 441

p² = 459

p = √459

p = 21.4 cm

∴ The length of p is 21.4 cm

b)

Measure of angle P

Using SOH CAH TOA

[tex]cos P= \frac{21}{30}[/tex]

cos P = 0.7

P = cos⁻¹(0.7)

P = 45.6°

Hence, the measure of angle P is 45.6°

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The number of robots have have for a city of 75 square miles would be 10 robots.

The first step is to determine how many robots are needed for 1 square mile: 4/30.

The second step is to multiply this fraction by 75

4/30 x 75 = 10 robots

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Answer: B

Step-by-step explanation:

When you evaluate f(-1)=2x^4+x^2-5 we will get -2 in basic notation (-1,-2). We need to find the root of the function to find the other roots or factors, where y=0.

Answer:

Step-by-step explanation:

this is independent  

20/50= 2/5= 40% of getting pink, probability of getting 2= 20%

13/50=0.26= 26% of getting blue, probability of getting 2= 13%

17/50=0.34=34% of getting purple, probability of getting 2 = 17%

70%

Answer:

1st quartile is 136

The second quartile is also the median 142

The third quartile is 162

The interquartile range is the difference between the 3rd and first quartile or 26

Step-by-step explanation:

Answer:

the value of the variable x is 16

Step-by-step explanation:

[tex]given \: expression \\ \frac{5}{8}x = \frac{1}{2} x + 2 \\ substract \: \frac{1}{2} x from \: both \: sides \\ \frac{5}{8}x - \frac{1}{2} x = \frac{1}{2} x - \frac{1}{2} x + 2 - \frac{1}{2} x \\ factor \: out \: common \: x \\ x( \frac{5}{8} - \frac{1}{2} ) = \frac{1}{8} \\ simplify \\ \frac{1}{2} x + 2 - \frac{1}{2} x \: \frac{1}{2} x - \frac{1}{2} x = 0 = 2 \\ \frac{1}{8} x = 2 \\ multiply \: both \: sides \: by \: 8 \\ 8. \frac{1}{8} x = 2.8 \\ simplify \\ x = 16.[/tex]

The value of c is 5 when we simplify the  logarithmic equation              log(-c) + log8= log (7c-75). This can be obtained using the properties of the logarithm.

Given that,

log(-c) + log8 = log (7c-75)

log (-8c) = log (7c-75)  (∵ log a + log b = log ab)

- 8c = 7c - 75              

(8+7)c = 75

15c = 75

⇒ c = 5

Hence the value of c is 5 when we simplify the  logarithmic equation              log(-c) + log8= log (7c-75).

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Answer:

(a) C=88pi

    A=1936pi

(b) Area

(c) Circumference

Step-by-step explanation:

Circumference formula = 2r(pi)

Area formula = pi(r^2)

Circumference = 2(44)(pi) = 88pi

Area = pi(44^2) = 1936pi

When something is paved it is the whole area not just the border so AREA

The chain will surround the place not fill it up so CIRCUMFERENCE

The amount of medicine infused in 8 hours is 1000ml.

According to the statement

we have given that the medicine normal saline (ns) iv to infuse at 125 ml/hr.

and we have to find the total amount of medicine infuse in the 8 hours in the whole number value.

So,

An infusion is the creation of a new substance by steeping another substance in a liquid, usually water

we have given a rate of infusion of medicine per hour which is 125 ml/hr.

And

Amount of medicine infuse in 1 hour is 125 ml

And the Amount of medicine infuse in 8 hours = 125*8

Amount of medicine infuse in 8 hours = 1000 ml.

So, The amount of medicine infused in 8 hours is 1000ml.

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The value of λ in the vector is 0.2

Vectors are the opposite of scalar quantities and they are quantities that have directions and magnitude

The vector a is given as:

a = (−6, 8)

The magnitude of vector a is calculated using

|a| = √(x^2 + y^2)

So, the equation becomes

|a| = √((-6)^2 + 8^2)

Evaluate the exponent

|a| = √(36 + 64)

Evaluate the sum

|a| = √100

Take the square root of both sides

|a| = 10

Given that

λa = 5

This means that

λ * 10 = 5

Divide both sides by 10

λ = 0.2

Hence, the value of λ is 0.2

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Answer:

12ft

Step-by-step explanation:

It takes 10 minutes for each plant and she spent 1 hour in total or 60 minutes: 60/10 = 6 plants

If each of the plants is 2 feet apart and there are 6 plants: 2ft*6 = 12ft

1/3 portion of the mixture, costing $\$6$ contains chocolate.

Assume that, in a mixture:

chocolate = x pound

nuts = y pound

mixture= x+y

The desired value is found by dividing the weight of the chocolate by the overall weight, or x/(x+y).

From the given data,

cost of x pound chocolate at $\$10$per pound = 10x

cost of y pound nuts at $\$4$ per pound = 4y

cost of x+y pound mixture at $\$6$ = 6(x+y)

As per condition,

⇒10x + 4y = 6(x+y)

⇒10x + 4y = 6x+ 6y

⇒4x = 2y

⇒y = 2x

The fraction of the chocolate in the mixture is

[tex]x/(x+y)[/tex] = [tex]x/(x+2x)[/tex] = [tex]x/3x[/tex] = 1/3

Therefore, chocolate makes  1/3 of the mixture's weight.

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Answer:

1/3

Step-by-step explanation:

The value of the fund in 18 years as required by the task is; $1553.5.

Since, the interest rate is compounded annually as described, the value of the fund in 18 years can be calculated by means of the compound interest formula as;

Value = 500(1.065)^18.

Hence, we have; Value = $1553.5.

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The  total cost of using both appliances for 6 days is about 3000-4000 watt.

According to the statement

Brianne uses her computer for 3 hours

Brianne uses hair dryer for 10 minutes

Now we use the formula

C = wtc/1000

substitute the values in it

then

C = 600*6/1000

C = 3.6

and same for hair dryer

So, The  total cost of using both appliances for 6 days is about 3000-4000 watt.

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The sample is the randomly selected customers.

Sampling:  

Suppose I want to estimate the proportion of New York state residents who are Buffalo Bills fans. So i ask, lets say, 1000 randomly selected New York state residents whether they are Buffalo Bills fans, and expand this to the entire population of New York State residents.

Sampling is a process used in statistical analysis in which a predetermined number of observations are taken from a larger population. The methodology used to sample from a larger population depends on the type of analysis being performed, but it may include simple random sampling or systematic sampling.

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Company's average operating assets for last year is $193000, company's margin is 15%, return on investment is 42%, company's residual income for last year is $521000.

Given the balance sheet and income statement of Joel de Paris and we have to calculate company's average operating assets for last year, company's margin,return on investment and company's residual income for last year.

1) Company's average operating assets=

(beginning operating assets+closing operating assets)/2

={(2562000-349000-253000)+(2634000-434000-25000)}/2

=(1910000+1950000)/2

=3860000/2

=$1930000

2)Company's margin= net operating income/ sales

=810000/540400

=15%

3)Turnover=sales/average inventory

=540400/1930000*100

=27.9%

=28%

4) Return on investment=margin* turnover

=15% of 28%

=42%.

Hence company's average operating assets for last year is $193000, company's margin is 15%, return on investment is 42%, company's residual income for last year is $521000.

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The question is incomplete and the information of question is in figure.

The ratio of lunch interval to the total times of class periods is 1:10

Given that timing of school opens is 10am , the timing of school closes is 3:30pm and the lunch interval is 30 minutes

We need to find the ratio of lunch interval to the total times of class periods.

Now,

Timing of a school(10.a.mto3.30p.m)=5hours30minutes

Timing for lunch interval=30minutes

Total time of the class periods=5hours30minutes−30minutes

=5hours

=60×5=300 minutes.

Ratio of lunch interval to total time of the class period=30minutes:300 minutes=1:10

Hence the ratio of lunch interval to the total times of class periods is 1:10

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The change in the scale factor from the old scale to the new scale is 3.

A scale drawing is a reduced form in terms of dimensions of an original image / building / object. The scale drawing is usually reduced at a constant dimension.

The change in the scale factor = larger scale / smaller scale

3.3 / 1.1 = 3

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Answer:

$1,194

Step-by-step explanation:

The area of the parking lot is 253.5(176.5) which equals 44,472.75. You then divide 44,472.75 by 4000 to see how many gallons you need to cover the parking lot. The answer to that was about 11.2 and since you can only purchase full drums you have to round it up to 12 to have enough. Finally, you multiply 12 by 99.50 and get your answer.

Answer:

Option (3)

Step-by-step explanation:

Since the base of the exponential is less than 1, the function is decreasing for all x.

See below for the table of -csc theta

The function is given as:

-csc theta

Rewrite properly as:

[tex]-\csc(\theta)[/tex]

This is calculated as:

[tex]-\csc(\theta) = -\frac{1}{\sin(\theta)}[/tex]

Set [tex]\theta[/tex] to 0, 30, 45, 60 and 90

[tex]-\csc(0) = unde fined[/tex]

[tex]-\csc(30) = -2[/tex]

[tex]-\csc(45) = -\sqrt 2[/tex]

[tex]-\csc(60) = -\frac{2\sqrt 3}{3}[/tex]

[tex]-\csc(90) = -1[/tex]

So, the table of -csc theta is

Angle      -csc theta

0              undefined

30            -2

45            -√2

60             -2/3 √3

90             -1

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30 pounds of coffee A and 60 pounds of coffee B used.

According to statement

Type A coffee costs Charmaine $4.25 per pound

Type B coffee costs $5.40 per pound.

Total cost of month on coffee is $451.50

AND

B=2A -(1)

Let's form the equation

4.25A + 5.40B = 451.50

Put equation 1 in it then

4.25A + 5.40*2A = 451.50

15.05A = 451.50

A = 30 pounds then

B = 60 pounds.

So, 30 pounds of coffee A and 60 pounds of coffee B used.

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In a proportionate stratified sample of 120, there are 72 Whites, 24 Latinos, 18 Blacks and 6  others.

Proportionate Stratified Sample

A proportionate stratified sample is one in which the size of the strata in the sample is proportional to the size of the strata in the population; in other words, the chance of selecting a unit from a stratum depends on the relative size of that stratum in the population.

Calculating the Proportionate Stratified Sample

The given percentage of -

Whites = 60%

Latinos = 20%

Blacks = 5%

Strength of the sample = 120

⇒ Number of Whites = 60% of 120

= 0.6 × 120

=72

Number of Latinos = 20% of 120

= 0.2 × 120

=24

Proportionate Stratified Sample of Blacks and Others

Count of Blacks = 15 % of 120

= 0.15 × 120

= 18

Count of others = 5% of 120

= 0.05 × 120

6

Thus, in a Proportionate Stratified Sample of 120, 72 are Whites, 24 are Latinos, 18 are Blacks, and 6 are others.

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The dimensions of the rectangle are: length= 18 in and width =1 in.

There are different types of quadrilaterals, for example, square, rectangle, rhombus, trapezoid, and parallelogram.  Each type is defined accordingly to its length of sides and angles. For example, in a rectangle,  the opposite sides are equal and parallel and their interior angles are equal to 90°.

The area of a rectangle can be found for the formula : l*w, where b = length and w =width. The question gives that the area is 18 in².

For this question, the length exceeds its width by 17 inches - l=w+17. Thus,  from the value of area given, you can find the values of the length and width of the rectangle.

A=l*w

18=(w+17)*w

18=w²+17w

w²+17w-18=0

Next step will be solve the previous equation ( W²+17W-18=0)

[tex]w_{1,\:2}=\frac{-17\pm \sqrt{17^2-4\cdot \:1\cdot \left(-18\right)}}{2\cdot \:1}\\ \\ w_{1,\:2}=\frac{-17\pm \:19}{2\cdot \:1}[/tex]

Therefore,

[tex]w_1=\frac{-17+19}{2\cdot \:1}=1\\ \\ \\ w_2=\frac{-17-19}{2\cdot \:1}=-18[/tex]

For dimensions, only positive numbers must be used. Then, the width is equal to 1 inch.

As, the area (l*w) is 18 in², you have.

18=l*w

18=l*1

l=18 in

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Answer:

Step-by-step explanation:

1a+1b(a+b-c)+1b+1c(b=c-a)+ 1a+1c(c+a-b)

1a+1b-c+1b +1c-a+1a+1c-b

1a+2b-c+a+1c-b

2a+1b+c this is the answer I think lol

Using the normal distribution, there is a 0.2148 = 21.48% probability that the sum of the 40 values is less than 7,100.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

For this problem, these parameters are given as follows:

[tex]\mu = 180, \sigma = 20, n = 40, s = \frac{20}{\sqrt{40}} = 3.1623[/tex]

A sum of 7100 is equivalent to a sample mean of 7100/40 = 177.5, which means that the probability is the p-value of Z when X = 177.5, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{177.5 - 180}{3.1623}[/tex]

Z = -0.79

Z = -0.79 has a p-value of 0.2148.

There is a 0.2148 = 21.48% probability that the sum of the 40 values is less than 7,100.

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The Width of plot B is 183 ft.

According to the statement

we have given that the Plot A has a square footage of 46,060, and Plot B has a square footage of 43,005. The common boundary they share is 235 feet long.

And we have to find the width of the Plot B

We know that

Area of plot A = 46,060 square footage.

Area of plot B = 43005 square footage.

Common area share by both Plot = 235 feet long.

So, Now

The width of Plot B = Area of plot B / Common area

Substitute the values in it then

width of Plot B = Area of plot B / Common area

width of Plot B = 43005 / 235

width of Plot B = 183 feet.

So, The Width of plot B is 183 ft.

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Answer:

since those 2 lines are parrelel that means the angles are the same so

8x+6=4x+38

minus 6

8x=4x+32

minus 4x

4x=32

divide by 4

x=8

Hope This Helps!!!

The value of the x is 11 and the measure of the angle B is 82 degrees.

It is defined as the angles when two lines intersect each other and at the intersecting point, some pair of angles are formed which we call vertically opposite angles, as the name describes that they have vertically opposite angles.

We have:

The angle measurements in the diagram are represented by the following expressions:

Angle A = 8x - 6

Angle B = 4x + 38

By using the vertically opposite angle property in angle B

As we know the alternate exterior angle are equal

8x - 6 = 4x + 38

4x = 44

x =11

Measure of angle B = 4(11) + 38 = 82 degrees

Thus, the value of the x is 11 and the measure of the angle B is 82 degrees.

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