Find the perimeter and area of the figure.

The polar coordinates of (1, -9) are (9.06, -1.47 radians).

To convert from rectangular coordinates to polar coordinates, we can use the following formulas:

r = √(x² + y²)

θ = tan⁻¹(y/x)

where r is the distance from the origin to the point, and θ is the angle between the positive x-axis and the line connecting the origin to the point.

In this case, x = 1 and y = -9. Plugging these values into the formulas, we get:

r = √(1² + (-9)²) = √82 ≈ 9.06

θ = tan⁻¹((-9)/1) ≈ -1.47 radians

Therefore, the polar coordinates of (1, -9) are (9.06, -1.47 radians). The distance from the origin to the point is approximately 9.06 units, and the angle between the positive x-axis and the line connecting the origin to the point is approximately -1.47 radians (or approximately -84.26 degrees).

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Answer:

C

Step-by-step explanation:

x + 9 = 4(x-1)²

x + 9 = 4(x² - 2x + 1)                  Multiply (x - 1) times (x - 1)

x + 9 = 4x² - 8x + 4                  

4x² - 9x - 5 = 0                          Subtract x + 9 from both sides

The probability of 3 or more deaf people in a sample of 100 is given as follows:

0.3633 = 36.33%.

The mass probability formula, giving the probability of x successes, is of:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are given by:

The values of the parameters for this problem are given as follows:

p = 0.02, n = 100.

The probability of 3 or more deaf people are given as follows:

P(X >= 3) = 1 - P(X < 3).

In which:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2).

Hence:

Thus:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

P(X < 3) = 0.1326 + 0.2707 + 0.2334

P(X < 3) = 0.6367.

P(X >= 3) = 1 - P(X < 3).

P(X >= 3) = 1 - 0.6367.

P(X >= 3) = 0.3633.

We suppose that 2% of the population is deaf, and want to find the probability of 3 or more deaf people in a sample of 100.

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Answer:

Step-by-step explanation:

3x  +  5  +  x  -  25  =  180

4x  -  20  =  180

4x  =  200

x  =  50

Answer:

+4

Step-by-step explanation:

F(x,y)   = 3x+y      and y <= -2x+ 4     sub in for 'y'

          = 3x  + (-2x+4)

          = x + 4

If you look at the graph for   y <= - 2x+4   ( see below)

    you will see that the domain (x values ) can only go from 0 to 4 and the max value is +4     ( rememeber too that y is restricted to >= 0  as is x )

Answer:

The slope is 4 and the y-intercept is (0,-2)

Amy’s monthly budget for textbooks equals $900.00

Amy's monthly budget for rent, utilities and food equals $12,798.

Her monthly budget for a personal & miscellaneous cost equals  $2,259.

Her total monthly budget equals $15,957.

A budget is refers to an estimation of the revenue and expenses over a specified future period of time and is usually compiled and re-evaluated on a periodic basis.

Budget for textbooks:

= $900.00

Budget for rent, utilities and food:

= $12,798.

Budget for personal and miscellaneous cost:

= $2,259.

Total monthly budget:

= $900 + $12,798 + $2,259

= $15,957

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Answer:

My answer would be; the performer displays rapid initial improvement followed by a decline in the rate of improvement.

Step-by-step explanation:

Usually a learning curve means that struggles are occurring after time of understanding and if we were creating a linear graph of this learning curve, it would be decreasing.

Autumn's bank registry will be :

Transaction Amount Balance

Paycheck $1275.00 $1275.00

Rent $400.00 $875.00

Utilities $75.00 $800.00

Cell Phone $80.00 $720.00

Subway Pass $120.00 $600.00

Groceries $200.00 $400.00

Work Clothes $100.00 $300.00

Entertainment $100.00 $200.00

Savings $200.00 $0.00

As you can see, Autumn has $0.00 left over at the end of the month. This means that she is spending more money than she is earning. In order to create a budget that works for her, Autumn will need to find ways to cut back on her expenses. Some possible areas where she could cut back include:

Autumn could look for a cheaper apartment or move in with more roommates. Autumn could turn off lights and appliances when she's not using them and seal up any cracks or holes in her apartment to keep the heat in during the winter and the cool air in during the summer.

By cutting back on her expenses, Autumn can create a budget that works for her and save money for the future.

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Notice that for this question, they are providing you with:

1) The slope of the line (4)

2) a point on the plane through which the line goes (6, -2)

So you can directly use for this the "point-slope" form of a line which is as follows:

This includes m as the slope, and the pair (x0, y0) as the pair representing the point the line goes through.

So, let's use the info they gave you to complete this:

which we can work out a little more:

And even a little more to finish the equation of the line in its standard slope-intercept form:

So the equation of the line is:

Answer:

Answer is c, 67.

Step-by-step explanation:

So angle L and K are going to be the same, and so its going to be:

46+2n=180, since 180* inside a triangle and n= both L and K.

180-46=134

134/2=67

Both K and L will be 67.

Answer is c, 67.

To check, 46+67+67=180

The measure of angle JLK is 67 degree.

A triangle is a polygon that has three sides and three vertices. It is one of the basic figures in geometry.

The angle L and K are going to be the same;

46+2n=180,

Since 180 inside a triangle and n= both L and K.

180-46=134

134/2=67

Both K and L will be 67.

The answer is c, 67.

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Answer:

the missing number is 47............

Answer:

47

Step-by-step explanation:

46+10=56. That means that ?+9 needs to equal 56.

56-9=47 which is the missing number.

Answer:

The sum will be close to 1/4

Step-by-step explanation:

1/8+1/6 is 7/24, and 1/4th of that is 6/24, so it is very close.

Answer: The sum will be close to 1/4

Step-by-step explanation:

You can start by making the fractions have the same denominator, (8*6) which gets you 48

You then want to use the butterfly method, so 1/8 becomes 6/48 and 1/6 becomes 8/48. You then add these up to 14/48.

12/48 is 1/4, and 14/48 is close to 12/48, thus making the answer the first option.

Answer:

The expression that can be used it -12.6+-8.7=-21.3

Step-by-step explanation:

Make sure you look at what I put because it is negative 12.6 AND negative 8.7 which is why there is an addition mark in between them both

Answer:

B: –12.6 – 8.7

The equation of logarithm are solved and

a) A = 2 + 3 log x + 4 log b

b) B = ( 36 + x + y ) ( log 6 )

c) C = ( 1/2 )x log 5

d) D = ln ( x⁴ / y² )

Given data ,

Let the logarithmic equation be represented as A

Now , the value of A is

a)

A = 2 log 10 + 3 log x + 4 log b

The base of the logarithm is 10 , so

A = 2 + 3 log x + 4 log b

b)

B = log 6³⁶ + log 6ˣ - log 6^ ( y )

From the properties of logarithm , we get

log A + log B = log AB

log A − log B = log A/B

log Aⁿ = n log A

B = 36 log 6 + x log 6 + y log 6

On taking the common term , we get

B = ( 36 + x + y ) ( log 6 )

c)

C = ( 1/2 )log 5ˣ

From the properties of logarithm , we get

C = ( 1/2 )x log 5

d)

D = 4 ln x - 2 ln y

From the properties of logarithm , we get

D = ln x⁴ - ln y²

On further simplification , we get

D = ln ( x⁴ / y² )

Hence , the logarithmic equations are solved

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Using the Central Limit Theorem, it is found that the sampling distribution of the sample proportion of the 50 questions on which you get the correct is approximately normal, with mean of 0.7 and standard error of 0.0648.

It states that for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1 - p)}{n}}\), as long as \(np \geq 10\) and \(n(1 - p) \geq 10\).

In this problem, we have that p = 0.7, n = 50, hence the mean and the standard deviation are given as follows:

\(\mu = p = 0.7\)

\(s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.7(0.3)}{50}} = 0.0648\)

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In the proportion (5x + 1):3 = (2x + 2):7, the value of x is -1/29.

In the proportion (6x):(4x) = 7, there is no value of x that satisfies the proportion.

To find the value of x in the given proportions, let's solve them one by one:

(5x + 1) : 3 = (2x + 2) : 7

To solve this proportion, we can cross-multiply:

7(5x + 1) = 3(2x + 2)

35x + 7 = 6x + 6

Subtracting 6x from both sides and subtracting 7 from both sides:

35x - 6x = 6 - 7

29x = -1

Dividing both sides by 29:

x = -1/29

Therefore, the value of x in the first proportion is -1/29.

(6x) : (4x) = 7

To solve this proportion, we can simplify the left side:

6x / 4x = 7

Dividing both sides by 2x:

3/2 = 7

This equation is not true, as 3/2 is not equal to 7.

Therefore, there is no value of x that satisfies the second proportion.

In summary, the value of x in the proportion (5x + 1) : 3 = (2x + 2) : 7 is -1/29, and there is no value of x that satisfies the proportion (6x) : (4x) = 7.

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Answer:

1a) 90 = 2y + 2(2x)        1b) 45 - 2x = y          

Step-by-step explanation:

1a) 90 = 2y + 2(2x)        

1b) 90 = 2y + 2(2x)           Use the equation from above and multiply

90 = 2y + 4x

-4x          - 4x               Subtract 4x from both sides

90 - 4x = 2y                 Divide both sides by 2

45 - 2x = y

The median would be 22:

Step-by-step explanation: The median is the number that is in the middle

Simply defined, the median is the number right in the middle of a set.

But before I get down to finding the median, I will order the numbers from least to greatest:

15, 17, 19, 20, 21, 22, 23

Now, the middle number is 20. So that's the median.

As for the range, it's the difference between the largest number and the smallest one:

Range = Greatest number - Smallest number

           = 23 - 15

           = 6

In summary, the median, the number in the middle, is 20, and the range, the difference between the largest number and the smallest one, is 6.

Answer:

61.15702689

Step-by-step explanation:

= 1 / 6 (49/9-14/3) + 27 / 73 / 5 × 33​

= 1/6 x 7/9 + 61.02739726

= 61.15702689 = 61.16 (2 d.p.)

Answer:

I RLY HOPE THIS IS CORRECT WISH THE BEST OF LUCK

Answer:

12.08

Step-by-step explanation:

If you order these numbers from least to greatest, you would get...

12.08, 12.087, 12.7, 12.78, 12.807

The least second it took to complete the race is 12.08

hope you have a wonderful day too! <3

5x+7x=660;

12x=660;

x=660:12;

x=55 (kg).

Then 5x=5×55=275 kg and 7x=7×55= 385 kg.

The required ratio is therefore

660= 275:385.

Answer:

V = 460.68

Step-by-step explanation:

V=(lwh)/3

Answer:

-√26, 5.15, 5.2, 16/3

Step-by-step explanation:

-√26 = -5.09

16/3 = 5.33

The standard deviation is 1.0319

x values between 10.4681 and 12.5319 are respectively ( 11 , 12 )

The probability that the number of granite specimens selected for analysis is within 1 standard deviation of its mean value is 0.6740

We are given that: a geologist has collected 14 specimens of basaltic rock and 14 specimens of granite.

Thus total rocks = N = 14 +14 = 28

The geologist instructs a laboratory assistant to randomly select 23 of the specimens for analysis.

Thus sample size = n = 23

Part a) What is the pmf of the number of granite specimens selected for analysis?

x = the number of granite specimens selected

Thus M = Number of granite specimens = 14

Thus x can have the following values:

x n-x = 23-x

9 14

10 13

11 12

12 11

13 10

14 9

We can select a minimum 9 granite specimens, so that total becomes 9 granite specimens + 14 basaltic rock = 23

and maximum 14 granite specimens, so that total becomes 14 granite specimens + 9 basaltic rock = 23

Here x = the number of granite specimens selected follows Hypergeometric distribution with parameters N = 28 ,M=14 , n = 23 .

P(X=9) =0.02037

Similarly, we find all next probabilities:

x P(x)

9 0.0204

10 0.1426

11 0.3370

12 0.3370

13 0.1426

14 0.0204

Part b) What is the probability that all specimens of one of the two types of rock are selected for analysis?

the probability that all specimens of one of the two types of rock are selected

That is:

P( All 14 are granite specimens and rest 9 are basaltic rock OR All 14 are basaltic rock and rest 9 are granite specimens)=......?

That is:

P( 14 granite specimens , 9 basaltic rock OR 14 basaltic rock , 9 granite specimens) =......?

From above table in part a) , we have:

P( 14 granite specimens) = 0.0204 , that means

P(14 granite specimens , 9 basaltic rock) = 0.0204

and

P( 9 granite specimens)=0.0204

That is:

P( 14 basaltic rock , 9 granite specimens) = 0.0204

Thus

P( 14 granite specimens , 9 basaltic rock OR 14 basaltic rock , 9 granite specimens) =0.0204 + 0.0204

P( 14 granite specimens , 9 basaltic rock OR 14 basaltic rock , 9 granite specimens) = 0.0408

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Answer:

\(\displaystyle \int {\frac{1}{9x^2+4}} \, dx = \frac{1}{6}arctan(\frac{3x}{2}) + C\)

General Formulas and Concepts:

Algebra I

Calculus

Antiderivatives - integrals/Integration

Integration Constant C

U-Substitution

Integration Property [Multiplied Constant]:                                                                \(\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx\)

Trig Integration:                                                                                                           \(\displaystyle \int {\frac{du}{a^2 + u^2}} = \frac{1}{a}arctan(\frac{u}{a}) + C\)

Step-by-step explanation:

Step 1: Define

\(\displaystyle \int {\frac{1}{9x^2 + 4}} \, dx\)

Step 2: Integrate Pt. 1

Step 3: Identify Variables

Set up u-substitution for the arctan trig integration.

\(\displaystyle u = x \\ a = \frac{2}{3} \\ du = dx\)

Step 4: Integrate Pt. 2

Topic: AP Calculus AB

Unit: Integrals - Arctrig

Book: College Calculus 10e

We cannot make a general assumption about whether the mean is greater or less than 3.5 based solely on the fact that the median is 3.5.

The mean is a measure of central tendency that represents the average value of a set of numbers. It is also called the arithmetic mean or simply the average.

We cannot make a general assumption about whether the mean is greater or less than 3.5 based solely on the fact that the median is 3.5.

The mean and the median are two different measures of central tendency, and they can have different values depending on the distribution of the data. In general, if a data set is symmetric and bell-shaped, the mean and the median are close to each other. However, if the data set is skewed, the mean and the median may be different.

For example, consider the following two data sets:

Set 1 data: 1, 2, 3, 4, and 5.

The median is 3.

The mean is (1 + 2 + 3 + 4 + 5) / 5 = 15 / 5 = 3.

Data set 2: 1, 2, 3, 4, 10

The median is 3.

The mean is (1 + 2 + 3 + 4 + 10) / 5 = 20 / 5 = 4.

In data set 1, the mean is the same as the median. In data set 2, the mean is greater than the median because the value 10 is an outlier that pulls the mean up.

Therefore, without additional information about the distribution of the data, we cannot make a general assumption about whether the mean is greater or less than 3.5 based solely on the fact that the median is 3.5.

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