Perimeter of sector is 4 times of its radius what is the radian measurre?

The equation of the circle with endpoints of a diameter at the points (3, 8) and (-5, 6) is x² + y² + 2x - 14y + 33 = 0.

These are the specified parameters:

Endpoints of a diameter at the points (3, 8) and (-5, 6).

Determine the center point of the circle (a, b).

(a, b) = ((x₁ + x₂)/2 , (y₁ + y₂)/2)

        = ((3 + (-5))/2 , (8 + 6)/2)

        = (-2/2 , 14/2)

        = (-1, 7)

The center point is (-1, 7).

Determine the radius of the circle (r).

[tex]\begin{aligned} r & = \frac{1}{2} \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} \\r & = \frac{1}{2} \sqrt{(-5-3)^2 + (6-8)^2} \\ r& = \frac{1}{2} \sqrt{(-8)^2 + (-2)^2} \\ r& = \frac{1}{2} \sqrt{64 + 4} \\ r & = \frac{1}{2} \sqrt{68} \end{aligned}[/tex]

Determine of the equation of the circle

(x - a)² + (y - b)² = r²

(x - (-1))² + (y - 7)² = (1/2 √68)²

x² + 2x + 1 + y² - 14y + 49 = 1/4 × 68

x² + y² + 2x - 14y + 50 = 17

x² + y² + 2x - 14y + 50 - 17 = 0

x² + y² + 2x - 14y + 33 = 0

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Answer:

c = s - (8×18)

Step-by-step explanation:

S = 8×18+6 = 150

c = s - (8×18)

The matrix that represents this information is

| 29  9   16 |

| 13  22   4 |

Matrices (singular matrix) are rectangular arrays or tables where numbers or elements are arranged in rows and columns

Given that:

For the month of June, they rented out 29 cars, 9 trucks, and 16 SUVs to individuals. They also rented out 13 cars, 22 trucks, and 4 SUVs

A defined above, matrices can be viewed as a table. Thus, we can write:

Cars    Trucks   SUVs

29          9           16

13          22           4

In matrice form:

| 29  9   16 |

| 13  22   4 |

Therefore, the matrix that represents this information is

| 29  9   16 |

| 13  22   4 |

Option D. is the answer

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Answer:

The two equivalent ratios of 4:5 are 8:10 and 12:15.

Step-by-step explanation:

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Answer:As hours spent studying increases, grades on the college algebra final exam increase.

Step-by-step explanation:

The probability that a student will take no more than 40 minutes to complete tee examination is 0.00.

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Given:

The length of time it takes students to complete a statistics examination is uniformly distributed and varies between 40 and 60 minutes.

We have to find the probability that a student will take no more than 40 minutes to complete the examination.

As the time required to complete the statistics examination is uniformly distributed and varies between 40 and 60 minutes so no any student will take less than 40 minutes to complete the examination.

P(X ≤ 40) = 0   where 40 ≤ x ≤ 60

Hence, the probability that a student will take no more than 40 minutes to complete tee examination is 0.00.

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Answer: Take 3326 and divide by 3

Step-by-step explanation: This will check to see if her answer is correct or not. If 3326 is divided by 3 and gets 842 then her answer is correct!

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3326 ÷ 3 = 1108.666667

Take the answer 3326, and divide it by 3, and we should get 842:

3326 ÷ 3 = 1108.666667

It does not equal 842.

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The number of ways the letters of the word DANCER can be arranged if D and A remain together is 120 ways .

In the question ,

it is given that the word is DANGER ,

the number of letters in the given word is = 6

it is given that the letters D and A are together ,

that means they are a single unit ,

So , the number of letters become = 5 letters

and  5 letters can be arranged in 5! ways ,

which can be simplified  as

5! [tex]=[/tex] 5 * 4 * 3 * 2 * 1 [tex]=[/tex] 120 ways

Therefore , the number of ways of arrangement is 120 ways .

The given question is incomplete , the complete question is

How many ways can the letters of the word DANCER be arranged in a row if D and A must remain together (in order) as a unit ?

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According to the given statement the function representing the points relation is f(x) = 32(3x - 1)

An statement, rule, or law in mathematics that establishes the link between an independent variable and a predictor variables (the dependent variable). Equations may be found all around arithmetic, and they are essential for building physical connections in the sciences. A mappings between A and B will only be a function if every member in set A only has end and only 1 photo in set B. Where A & B even be two separate sets.

Depicts a few points within the graph of the linear function f given a table.

x = -2, 1, 5, 10

f(x) = -224, 64, 448, 928

From option first,

f(x) = 32(3x - 1)

Put x = -2

= 32(-2x3-1)

= 32x(-7) = -224

Consequently, f(x) = 32 is the function used to express the points connection (3x - 1)

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Answer:

720

Step-by-step explanation:

100/5 = 20, so 20 tires made in 1 hour and 20 x 36 would be 720 so answer is 720

1) Probability that Exactly 2 have used their phones to access the Internet is; P(X = 2) = 0.2759

2) Probability that more than 2 have used their phones to access the Internet is; P(X > 2) = 0.1798

3) Probability that at least 8 have used their phones to access the Internet is; P(X ≥ 8) = 0.00001

4) Probability that no more than 5 have used their phones to access the Internet is; P(X ≤ 5) = 0.99862

The binomial probability is defined as the probability of exactly x successes on n repeated trials, with p probability.

The formula for binomial probability distribution is;

P(X = x) = nCx * p^(x) * (1 - p)^(n - x)

Where;

P(X = x) = binomial probability

x = number of times for a specific outcome within n trials

nCx = number of combinations

p = probability of success on a single trial

q = probability of failure on a single trial

n = number of trials

1) We are given;

p = 15% = 0.15

n = 10

Thus;

P(X = 2) = 10C2 * 0.15^(2) * (1 - 0.15)^(10 - 2)

P(X = 2) = 0.2759

2) Probability that more than 2 have used their phones to access the Internet is;

P(X > 2) = P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)

Using binomial probability calculator, we have;

P(X > 2) = 0.1798

3) Probability that at least 8 have used their phones to access the Internet is;

P(X ≥ 8) = P(X = 8) + P(X = 9) + P(X = 10)

Using binomial probability calculator, we have;

P(X ≥ 8) = 0.00001

4) Probability that no more than 5 have used their phones to access the Internet is;

P(X ≤ 5) = P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

P(X ≤ 5) = 0.99862

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The answer's are A and D!

Let me know if I'm right please!

The margin of error corresponding to the 95% confidence interval for a sample mean constructed from a sample of size 53 is 7.94.

Margin of error is defined as the degree of the sampling errors in statistics. It can be calculated using the formula below.

MOE = z x (SD / √n)

where MOE = margin of error

z = found by using a z-score table

SD = sample standard deviation = 29.5

n = sample size = 53

At 95% confidence level, the area in each tail of the standard normal curve is 2.5, and the cumulative area up to the second tail is 97.5.

(100 - 95) / 2 = 2.5

100 - 2.5 = 97.5

Find 0.975 in the z-table to get the value of z.

At p = 0.975, z = 1.96

Plug in the values to the formula and solve for the margin of error.

MOE = z x (SD / √n)

MOE = 1.96 x (29.5/√53)

MOE = 7.94

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Based on the image given above, the angles that are numbered can be classified as:

∠1 and ∠2: vertical angles

∠3 and ∠4: adjacent angles

Angles that share the same vertex and also the same side, are said to be angles that lie next to each other which are called adjacent angles.

For example, the angles in the image given that are numbered as 3 and 4, share the same vertex and a common side. Therefore, they are adjacent angles.

If two angles are formed to lie directly opposite to each other when two lines intersect at a point, the angles share a common point but do not share a common side. These set of angles are called vertical angles.

For example, in the image given, angles 1 and 2 are vertical angles.

Therefore, the angles would be classified as:

Angles 1 and 2: vertical angles

Angles 3 and 4: adjacent angles

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Answer:

3 and 4 are adjacent angles, and 1 and 2 are vertical angles.

Step-by-step explanation:

vertical angles are across from each other while adjacent is next to each other. the other person's explanation is better than mine though. :')

Answer: 19/21>8/9

Step-by-step explanation:

common denominator is 63

19*3=57 so thats 57/63

8*7=56 so thats 56/63

The test for breast cancer is not effective at identifying women who have breast cancer.

What is probability?

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

It is given that, out of 2000 women, 16 are known to have breast cancer.

But, through the test, the women who do not have breast cancer are also testing positive and the women who have breast cancer are also testing negative.

So, the test for breast cancer is not effective at identifying women who have breast cancer.

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If the mean of the five values is equals to 64 then the sum of x values i.e., ∑x is 320.

Arithmetic mean:

Arithmetic mean is simply called mean or average. To calculate the arithmetic mean of a set of values, we need to add all the values and then divide the sum by the number of values in the set.

X-bar = ( a₁ + a₂ + -----+ aₙ )/n

Here, there are n items in the set, and each item is represented by one of the a's.

We have given that,

Mean of 5 values , X-bar = 64 , n = 5

we have to calculate the sum of x i.e ∑x

Using Arithmetic mean formula,

sum of x , ∑x = X-bar × n , where x is five values

so, ∑x = 64 × 5 = 320

Hence, the sum of x values is 320.

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The equation in slope-intercept form is found as; y = -x/2 + 5/2.

For the stated question.

Two point are-

(x1, y1) = (3,1)

(x2, y2) = (1,2)

Thus,

slope m = (y2 -y1)/(x2 - x1)

m = (2 - 1)/(1 - 3)

m = -1/2

Equation of line;

y - y1 = m(x - x1)

y - 1 = (-1/2)(x - 3)

y = -x/2 + 5/2

Thus, the equation in slope-intercept form is found as; y = -x/2 + 5/2.

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1) The system of equations to solve the given problem are:

2l-3=3b

2(l+ b)=48

2) The variables l and w stands for length and width, respectively.

3) Length l=15 and Width w=9

4) The graph of the solution is shown below:

A perimeter is a closed path that covers, surrounds, or outlines a two-dimensional shape or a one-dimensional length.

The perimeter calculation has various practical uses. A calculated perimeter is the length of fencing required to encircle a yard or garden. The circumference of a wheel/circle specifies how far it will roll in one revolution. Similarly, the amount of string coiled around a spool is proportional to the spool's perimeter; if the length of the string were precise, it would equal the perimeter.

1) The system of equations to solve the given problem are:

2l-3=3b

2(l+ b)=48

2) Here the variables are l, w

The variables l and w stands for length and width, respectively.

3) Given, perimeter of the triangle=48 inches

2l-3=3b

l=(3(b+1))/2

So, 2(l+ b)=48

3b+3+2b=48

5b=45

b=9

l=(3(10))/2

l=15

Therefore, length l=15 and width w=9

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a)The 7-year growth factor for the amount on the loan is $4285.71 b)  7-year percentage change for the amount is 6.25% c) 1-year growth factor for the amount $612.244 and d) 1-year percent change for the amount is 0.894%.

a)We know very well that growth factor is ratio of difference of principal amount and loan amount to the time taken, or

Growth factor=(Final loan amount-Initial loan amount)/Total time

=>Growth factor=(78,000-48,000)/7

=>Growth factor=30,000/7=$4285.71

b)To find the percentage change in amount, we need to use initial loan amount and the difference between two amounts, or

 percentage change=((78000-48000)/48000)×100

=>percentage change=[(30000)/48000)]×100

=>percentage change=300/48=6.25%

c)Now, we have already find the growth factor for 7 years, we need to find growth rate in 1 year. So, we use unitary method to find it

=>In 7 years growth factor is=$4285.71

  ∴In 1 years growth factor is=$4285.71/7=$612.244

d)In 7 years percentage change for the given amount is =6.25%

∴In 1 year percentage change for the given amount=6.25/7=0.894%

Hence, answers are a)$4285.71 b)6.25% c)$612.244 d)0.894%

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Answer:

The coefficient of -2 and -3 is -6.

Answer:answer will be more exact than the point you found in the first part

Step-by-step explanation:temperature in degrees Fahrenheit,

degrees Celsius

20

40

60

80 100 120 140 160 180 200 220 240

degrees Fahrenheit

a. Mark the point on the graph that shows the temperature in Celsius when it is 60

degrees Fahrenheit

b. Mark the point on the graph that shows the temperature in Fahrenheit when it

is 60 degrees Celsius.

c. Water boils at 100 degrees Celsius. Use the graph to approximate the boiling

temperature in Fahrenheit, or to confirm it, if you knew what it is.

d. The equation that converts Celsius to Fahrenheit is C = (F - 32). Use it to

calculate the temperature in Celsius when it is 60 degrees Fahrenheit. (This

answer will be more exact than the point you found in the first part

The answer to the following algebra is;

b² at b = 4 is 16

y /5 at y = 15 is 3

27/s at s = 9 is 3

q/3 + 4 at q = 3 is 5

Algebra is the system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols.

Given the following:

b² at b = 4

substitute b = 4

= 4²

= 4 × 4

= 16

y /5 at y = 15

substitute y = 15

= 15/5

= 3

27/s at s = 9

substitute s = 9

= 27/9

= 3

q/3 + 4 at q = 3

substitute q = 3

= 3/3 + 4

= 1 + 4

= 5

In conclusion, the algebraic expression is solved by substituting the value of the variables.

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The triangle has lengths of 59 feet, 66 feet, and 79 feet.

Let us represent the length of the shortest side of the triangle with x feet, and that of the other shorter side with y feet

The longest side will be (2x - 39) feet

The length of the other shorter side will give us the equation;

y + x = 2x - 39 + 46

so that by subtracting x from both sides, we have

y = 2x - x + 46 - 39

y = (x + 7) feet

From the question,

x + x + 7 + 2x - 39 = 204 feet {which is the perimeter of the triangle}

4x - 32 = 204 {collect like terms}

4x = 203 + 32

4x = 236

x = 236/4

x = 59 feet

Therefore, as the length of the shortest side of the triangle is 48 feet,

the other shorter side is;

y = 59 + 7

y = 66 feet

and the longest side is;

2(59) - 39

118 - 39

79 feet.

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Answer:

SO... y=3x+0b

Or... y = -3x+0b

Step-by-step explanation:

Answer: You can watch 14 vines.

Step-by-step explanation: 1 2/5 is equal to 1 4/10

1 4/10 is equal to 14/10

So the amount of vines you could watch is 14 in 1 minute and 24 seconds.