draw an angle of 65° and draw an angle equal to this angle, using ruler and compass

The radius of the circle is √17.

The center of the circle is (4, 2).

A circle is a two-dimensional figure with a radius and circumference of 2πr.

The area of a circle is πr².

We have,

The equation of a circle with radius r and center (h, k) is

(x - h)² + (y - k)² = r²

Now,

x² + y² - 4 y - 8x + 3 = 0

x² - 8x + y² - 4y + 3 = 0

x² - 8x + 4² - 4² + y² - 4y + 2² - 2² + 3 = 0

(x - 4)² + (y - 2)² - 16 - 4 + 3 = 0

(x - 4)² + (y - 2)² = 16 + 4 - 3

(x - 4)² + (y - 2)² = √17

This means,

radius = √17 and center = (4, 2)

Thus,

The radius and center of the circle are √17 and (4, 2).

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Answer:

x = 3

Step-by-step explanation:

Take the first equation-  x + 2y = (-1)

Multiply both sides by 2

2(x + 2y) = 2(-1)
2x + 4y = -2

Add first and second equations

(2x + 4y = -2)

+(4x -4y = 20)
= 6x = 18

x = 18/6

x= 3

Extra info- This method is also called as Elimination method in which Elimination (whether by addition of equations or subtraction) of any variable is done.

Hope it helps

The value of a, b, and c will be 2, -1/4, and 7/3, respectively. Then the product of a, b, and c will be - 7/6.

The equivalent is the expression that is in different forms but is equal to the same value.

The meaning of straightforwardness is simplifying something to accomplish or get a handle on while likewise making it somewhat less troublesome.

The expression is given below.

[tex]\rm \rightarrow x^{-3/4 } \cdot y ^{-(-4/3)} \cdot \sqrt[4]{16x^2y^4}[/tex]

Simplify the expression, then we have

[tex]\rm \rightarrow x^{-3/4 } \cdot y ^{-(-4/3)} \cdot \sqrt[4]{16x^2y^4}\\\\\rightarrow x^{-3/4 } \cdot y ^{(4/3)} \cdot (16x^2y^4)^{1/4}\\\\\rightarrow x^{-3/4 } \cdot y ^{4/3} \cdot 2x^{1/2}y\\\\\rightarrow 2 x^{1/2 - 3/4} \cdot y^{4/3 + 1} \\\\\rightarrow 2x^{-1/4} \ \cdot y^{7/3}[/tex]

The given expression is [tex]\rm ax^by^c[/tex]. Compare the expression with given expressions, then we have

a = 2, b = - 1/4, and c = 7/3

Then the product of a, b, and c is given as,

⇒ 2 x (-1/4) x (7/3)

⇒ - 7/6

The value of a, b, and c will be 2, -1/4, and 7/3, respectively. Then the product of a, b, and c will be - 7/6.

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We can order the bonds from slowest-growing to fastest-growing as:

First bond: fixed growth rate of $50 per year

Third bond: growth rate of 4% per year, compounded continuously

Second bond: growth rate of 6% per year, compounded annually

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

To order the bonds from slowest growing to fastest growing, we need to compare their growth rates.

The first bond grows at a fixed rate of $50 per year, regardless of how long it is held.

So its growth rate is constant and does not change with time.

The second bond is worth $500 and grows at a fixed annual rate of 6%, so its value after one year will be:

Value after one year
= $500 + 0.06 x $500

= $530

After two years, its value will be:

Value after two years.

= $530 + 0.06 x $530

= $561.80

We can see that the second bond's growth rate is increasing over time since the increase in value each year is calculated as a percentage of the new value.

The third bond is worth $100 and grows at an annual rate of 4% that is applied continuously.

The formula for the value of a continuously compounded bond after t years  = $100 x e^(0.04t)

where e is the mathematical constant approximately equal to 2.718.

After one year,

The value of the third bond.

= $100 x e^(0.04 x 1) = $104.08

After two years,

Value after two years

= $100 x e^(0.04 x 2)

= $108.24

We can see that the growth rate of the third bond is also increasing over time because the interest is being compounded continuously.

Now,

We can order the bonds from slowest-growing to fastest-growing as:

First bond: fixed growth rate of $50 per year

Third bond: growth rate of 4% per year, compounded continuously

Second bond: growth rate of 6% per year, compounded annually

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The probability of spinning green and then rolling an even number is 1/36

Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.

The probability of spinning green is 1/6 because there are 6 equally likely outcomes and 1 of them is green.

The probability of rolling an even number is 3/6 because there are 6 equally likely outcomes and 3 of them are even numbers (2, 4, and 6).

The probability of spinning green and then rolling an even number is the product of the probabilities of each event. To find this, we multiply the probability of spinning green (1/6) by the probability of rolling an even number (3/6):

(1/6) * (3/6) = 1/36

So, the probability of spinning green and then rolling an even number is 1/36.

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There are [tex]10^{4}[/tex] = 10,000 different possible musical entertainment lineups that can be created from a list of 10 songs.

This is computed by using the formula for combinations without repetition, which is [tex]n^{r}[/tex], where n is the number of items in the list and r is the number of items to be selected. In this case, n = 10 and r = 4, which results in [tex]10^{4}[/tex] = 10,000.

It is important to note that this calculation does not take into account any repetitions of songs, so if the same song appears more than once in the list, then the actual number of possibilities could be less. For instance, if there is a list of 10 songs, but 5 of them are the same, then the number of possible lineups would be[tex]10^{4/5}[/tex]! = 800, taking into account the repetitions.

To illustrate this further, if we were to list all the possible lineups, then we would end up with 10,000 unique combinations of 4 songs. For instance, a possible lineup could be Song 1, Song 5, Song 8, Song 10. Another possible lineup could be Song 4, Song 7, Song 9, Song 10. This process could be repeated with any combination

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Answer:

Step-by-step explanation:

Since M is the point of intersection of the diagonals of the square, it is also the midpoint of both diagonals. This means that AM is equal to half the length of a side of the square and also bisects the angle formed by the two sides that it connects.

Let's call the length of a side of the square s. Then, the distance AM can be found using the Pythagorean theorem:

AM = sqrt((5 - 2)^2 + (1 - 1)^2) = sqrt(3^2 + 0^2) = sqrt(9) = 3

So, the length of a side of the square is 2 * AM = 2 * 3 = 6.

Next, we can use the length of a side and the coordinates of A to find the coordinates of B. Since AB is a side of the square and is 6 units long, we can find B by moving 6 units to the right of A:

B = (2 + 6, 1) = (8, 1)

We can also find the coordinates of C by moving 6 units up and 6 units to the left of A:

C = (2 - 6, 1 + 6) = (-4, 7)

Finally, we can find the coordinates of D by moving 6 units down and 6 units to the right of A:

D = (2 + 6, 1 - 6) = (8, -5)

So, the coordinates of the other vertices of the square are B = (8, 1), C = (-4, 7), and D = (8, -5).

Answer:

(4-g) X 1.5

Step-by-step explanation:

Answer: B D I J M

Step-by-step explanation: you just gotta see if any of the two answers work an if they don’t it’s nethier!

Answer:

The length of each leg would be 4 units

Step-by-step explanation:

The hypotenuse of a 45-45-90 is √2 times bigger than either side length since they're the same lengths.

The probability of selecting a jury composed of 12 women from a pool of 30 people that includes 12 men and 18 women is extremely low, only 0.0657%.

The probability of an event happening is the measure of how likely that event is to occur.

In this case, we need to find the probability of selecting a jury of 12 women from a pool of 30 people. To calculate this probability, we can use the formula:

Probability = Number of favorable outcomes / Total number of outcomes

The total number of outcomes is the number of ways in which we can select 12 people from a pool of 30. We can calculate this number using the combination formula:

Total number of outcomes = C(30,12) = 30! / (12! * (30-12)!) = 28,238,760

Now, we need to calculate the number of favorable outcomes, which is the number of ways in which we can select 12 women from a pool of 18. We can calculate this number using the combination formula as well:

Number of favorable outcomes = C(18,12) = 18! / (12! * (18-12)!) = 18,564

Therefore, the probability of selecting a jury composed of 12 women is:

Probability = Number of favorable outcomes / Total number of outcomes

Probability = 18,564 / 28,238,760

Probability = 0.000657 or 0.0657%

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Coordinates of the point on the directed line segment from (1, 2) to (6,7) that partitions the segment into a ratio of 2 to 3 are (3, 4).

Using proportions, it is found that the coordinates of the desired point are (2,2).

The first point is A(1, 2)

The second point is B(6, 7)

The desired point is C(x, y)

The point C partitions the segment AB into a ratio of 3 to 2, hence:

[tex]C - A = \frac{2}{5}(B - A)[/tex]

This proportion is applied using both the x and y coordinates of the points, hence:

[tex]x - 1 = \frac{2}{5}(6 - 1)[/tex]

x - 1 = 2

x = 3

Now, [tex]y - 2 = \frac{2}{5} (7 - 2)[/tex]

y - 2 = 2

y = 4

Therefore the coordinates of the points are (3, 4).

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Answer:

Your answer is 60%.

Step-by-step explanation:

[tex]10 + 15=25[/tex] and [tex]\frac{15}{25}[/tex] [tex]=0.6[/tex] [tex]= 60[/tex]%

Answer:

A one-sample t-test for a population mean is the appropriate test for the researchers' hypothesis. In this case, they want to test the hypothesis that the mean battery life of their new battery is greater than a known mean battery life of their older version. The one-sample t-test allows them to compare the mean of a sample to a known population mean and determine if the difference between them is statistically significant.

Answer:

9 - y

Step-by-step explanation:

less than means Subtraction

By Using the table to work out the values of a , b , c , and d. X y = 2 x + 1 − 3 a − 2 − 3 − 1 b 0 1 1 c 2 d a = b = c = d =

Therefore, The solutions are : a = -3, b = 0, c = 6, d = 9

Equation:

In mathematics, an equation is an expression that indicates equality of two expressions by connecting them with the equal sign = . The word "equation" and related words in other languages ​​can have slightly different meanings. For example, in French an equation is defined as containing one or more variables, whereas in English a well-formed formula consisting of two expressions connected by an equal sign is an equation.

Given:

This table;

x             y = 3x+3

-3                -6

-2                 a

-1                  b

0                 3

1                  c

2                 d

To Find:

Values of a, b, c and d

Consider the 2nd row,

x = -2, y = a

Putting the values in the equation,

we get,

   a = 3(-2) + 3

⇒ a = -3

Consider the 3rd row,

x = -1, y = b

Putting the values in the equation,

we get,

   b = 3(-1) + 3

⇒ b = 0

Consider the 5th row,

x = 1, y = c

Putting the values in the equation,

   c = 3(1) + 3

⇒ c = 6

Consider the 6th row,

x = 2, y = d

   d = 3(2) + 3

⇒ d = 9

The final answer is,

a = -3, b = 0, c = 6, d = 9.

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Step-by-step explanation:

1000ml=1 litre

800 divided by(1000 multiplied by 5)=16%

Answer:

The angle is 180°

Step-by-step explanation:

[tex]{}[/tex]

Answer: look at the image for the answer and solution

Step-by-step explanation:

The probability of a college student being either female or having financial aid can be expressed as P(A ∪ B) = P(A) + P(B).

What is Probability?

Probability is a mathematical concept used to measure the likelihood of a particular event occurring. It is a way of expressing the chance or possibility of an event happening, ranging from 0 (impossible) to 1 (certain).

In probability theory, an event is a subset of the possible outcomes of an experiment or a random process. Probability can be expressed in terms of fractions, percentages, or decimals.

The symbol for the event that a college student is female is A, as given in the statement. The symbol for the event that a college student has financial aid is B, as given in the statement.

So, A={A student is female} and B={A student has financial aid}.

These events are mutually exclusive because one does not necessarily affect the other. For example, a male student can have financial aid and a female student may not have financial aid. Hence, the occurrence of one event does not influence the occurrence of the other event.

Therefore, the probability of a college student being either female or having financial aid can be represented as the union of the events A and B. It can be denoted as P(A ∪ B) and is calculated as:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Where P(A ∩ B) represents the probability of a student having both characteristics, i.e., being female and having financial aid.

However, as these events are mutually exclusive, P(A ∩ B) = 0. So the probability of a college student being either female or having financial aid is simply the sum of their individual probabilities:

P(A ∪ B) = P(A) + P(B) - 0

P(A ∪ B) = P(A) + P(B)

Hence, the probability of a college student being either female or having financial aid can be expressed as P(A ∪ B) = P(A) + P(B).

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Answer:

Three months to five years

Step-by-step explanation:

look it up

The total number of cupcakes packed is 846 cupcakes.

percentage, a relative value indicating hundredth parts of any quantity.

Let's first find out the number of boxes of each size:

40% of 60 boxes = 24 boxes are medium

35% of 60 boxes = 21 boxes are small

The remaining 60 - 24 - 21 = 15 boxes are large

Now we can calculate the total number of cupcakes packed:

24 boxes x 15 cupcakes per medium box = 360 cupcakes in medium boxes

21 boxes x 6 cupcakes per small box = 126 cupcakes in small boxes

15 boxes x 24 cupcakes per large box = 360 cupcakes in large boxes

Therefore, the total number of cupcakes packed is 360 + 126 + 360 = 846 cupcakes.

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Answer:

Period is [tex]\mbox{\huge {\boxed{\pi }}}[/tex]

Step-by-step explanation:

Each gridline marker on the horizontal axis is π/4

The period of this function is the horizontal displacement at which the function starts to repeat itself

Looking at the function we see that the minimum value of the function is 1 and occurs first at -π/4 and then at 3π/4

So the period is 3π/4 - (-π/4) = 3π/4 + π/4 = (3/4 + 1/4)π = π

We could also double check this using another point of reference

let's take the peaks of the function
The first peak visible is at -3π/4 and the next peak at π/4

So the period = π/4 - (-3π/4) = π/4 + 3π/4 = π

The equation of the line that is parallel to the line x = -2 and passes through the point (-5, 4) is x = -5.

A mathematical statement that equates two algebraic expressions is known as an equation. The equal to (=) sign appears between the expression and an equation.

Parallel lines are straight lines in the same plane that never cross each other.

The parallel lines have the same slope.

Given that,

Equation of the given line is x = -2

Any line parallel to this line will be in the form x = K, where K is a constant.

The line will pass through ( -5 , 4).

The line x = K will satisfy the point ( -5 , 4)

-5 = K

x = -5

Hence, the equation of the line that is parallel to the line x = -2 and passes through the point (-5, 4) is x = -5.

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Answer:

=q > - 1

Step-by-step explanation:

8q > - 8

= 8q/8 > -8/8

=q > - 1.

Answer: Yes, No, No, Yes, No

Step-by-step explanation:

I think Graphing is the best way to tackle this. But I prefer algebra:

A) 2(-8) + 6(7) = 26

-16 + 42 = 26

26 = 26

The answer for A is Yes. I wont show work for the others, i think its pretty intuitive, (just substitute the coordinates for x and y, and check if the resulting statement is true)

B. No

C. No

D. Yes

E. No

The value of (f - g)(-1) is 5.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = -5x³ - 8x² - 4x + 3

g(x) = 3x³ - 2x² - 8x - 4

Now,

(f - g)(x)

= f(x) - g(x)

= -5x³ - 8x² - 4x + 3 - (3x³ - 2x² - 8x - 4)

= -5x³ - 8x² - 4x + 3 - 3x³ + 2x² + 8x + 4

= -8x³ - 6x² + 4x + 7

Now,

(f - g) (-1)

Substitute x = -1.

= -8(-1)³ - 6(-1)² + 4(-1) + 7

= -8 x -1 - 6 - 4 + 7

= 8 - 6 - 4 + 7

= 8 - 10 + 7

= 15 - 10

= 5

Thus,

(f - g)(-1) = 5

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The required Jodi will consume 180 calories if she eats 5 chocolates.

When two quantities are directly proportional, it indicates that if one increases by a specific percentage, the other also increases by the same percentage. As gas costs increase, the cost of food may as well as well.

We can use proportionality to solve this problem. Since the number of calories consumed varies directly with the number of chocolates eaten, we can write:

calories consumed / chocolates eaten = constant

Let's call this constant k. We can solve for k using the information given:

72 calories / 2 chocolates = k

k = 36 calories/chocolate

Now we can use this constant to find the number of calories Jodi will consume if she eats 5 chocolates:

calories consumed / chocolates eaten = k

calories consumed / 5 chocolates = 36 calories/chocolate

calories consumed = 5 chocolates * 36 calories/chocolate

calories consumed = 180 calories

Therefore, Jodi will consume 180 calories if she eats 5 chocolates.

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Answer:

2

Step-by-step explanation:

Amy +3

Ray -4

Kim -2

Jammel +5

So,

3 - 4 - 2 +5 = ?

Answer is 2 points.

Answer:

firstly, I would fill up the 10-oz glass with juice and use it to fill the 6-oz glass. This would leave me with 4 oz left in the 10-oz glass

Step-by-step explanation:

On solving the provided question we can say that by bodmas ((4 / 3) / (1/4)) + ((2 / 5) / (1/4)) + ((4 / 15) / (1/4)) =8

The acronym BODMAS helps children learn the hierarchy of math operations (the correct order for solving math problems). The acronym BODMAS is made up of the following terms:

B Bracket, O Degrees (Power/Exponent or Square Root), D Division, M Multiplication, A Addition, and S Subtraction. BODMAS is also known as PDMAS in some areas. It symbolizes exponents, division, multiplication, addition and subtraction. It also represents brackets. The BODMAS rule states that parentheses must be handled first, then powers or roots (that is, of), division, multiplication, addition, and finally subtraction. Known as BODMAS in India and the UK, PEMDAS is primarily used in the US. However, they are identical to each other. The parentheses, order, and order of addition, subtraction, multiplication, and division are the same for the two rules.  

by bodmas

((4 / 3) / (1/4)) + ((2 / 5) / (1/4)) + ((4 / 15) / (1/4)) =8

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