Work out the following sheet,please

The value of sin θ from the unit circle is sin θ = 0.9230769

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

Given data ,

The terminal side of angle θ intersects the unit circle in the first quadrant at ( 3√10/10,√10/10 )

So , the equation of circle is ( x - h )² + ( y - k )² = r²

For a unit circle , the radius r = 1

x² + y² = r²   be equation (1)

Substituting the values of x and y in the equation , we get

x = -5/13

And , y = 12/13

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

So , the value of cos θ = ( -5/13 ) and sin θ = ( 12/13 )

On simplifying the equation , we get

sin θ = ( 12/13 )

sin θ = 0.9230769

Hence , the value of sin θ = 0.9230769

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a) The continuous growth rate can be calculated using the formula:

r = (ln(B) - ln(A)) / t

where r is the continuous growth rate, A is the initial count (330), B is the count after 6 hours (1340), and t is the time elapsed (6 hours).

Substituting the values:

r = (ln(1340) - ln(330)) / 6

r = 0.3907

b) The model for the bacteria colony can be written as:

B = A * e^(rt)

where B is the number of bacteria after time t, A is the initial count (330), and e is the base of the natural logarithm.

c) To find the number of bacteria after 16 hours, substitute t = 16 and the values of A and r from above:

B = 330 * e^(0.3907 * 16)

B = 9581.57

The number of bacteria after 16 hours is approximately 9582.

The coordinate points on the graph line of the function given represent the ordered pair that satisfy the equation.

An function in mathematics defines a relationship between one variable (the independent variable, x)  and another variable (the dependent variable, y). Example -

y = f{x} = ax + b

Given is a function as -

2x - 4y = 14

The given equation is -

2x - 4y = 14

Rewriting the function, we get -

4y = 2x - 14

y = (1/2)x - (7/2)

Plot the graph of the above function. All the coordinate points on the line represent the ordered pair that satisfy the equation.

Therefore, the coordinate points on the graph line of the function given represent the ordered pair that satisfy the equation.

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The volume of the cylinder with a radius of 19 km and a height of 5 km is 5706 km³, using 3.14 for π.

What is the volume of a cylinder?

The cylinder's volume is given by the formula, πr²h, where r is the radius of the circular base and h is the height of the cylinder.

The formula for the volume of a cylinder is given by:

V = π * r²* h

Where r is the radius of the base and h is the height of the cylinder.

Given that the radius of the cylinder is 19 km and the height is 5 km, we can substitute these values into the formula:

V = π * 19² * 5

V = 3.14 * 361 * 5

V = 5706 km³

Therefore, the volume of the cylinder with a radius of 19 km and a height of 5 km is 5706 km³, using 3.14 for π.

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Answer:

The original price of the item was $9.99 and it was discounted by 70%, which means the new price is $2.99.

Step-by-step explanation:

Answer:

(2, -5)

Step-by-step explanation:

-7x=y=-19

y=7x-19

-2x+3(7x-19)=-19

-2x+21x-57=-19

19x-57=-19

19x=38

x=2

-2(2)+3y=-19

-4+3y=-19

3y=-15

y=-5

The expression from the statement is 2x - 1 = 14

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

The product of 2 and the difference between 1 is 14

Represent the variable with x

So, we have

2x and the difference between 1 is 14

When the difference is expressed as an expression, we have

2x - 1 is 14

So, we have

2x - 1 = 14

Hence, the expression is 2x - 1 = 14

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The distance between where Jenna stopped and the park is 1 1/10 miles

A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math.

The word problems are interpreted into mathematics equation.

The distance between Jena's school and the park is 1⅘ miles = 9/5 miles

He stopped after walking for 7/10 miles .

The distance left to the park from where he stopped = 9/5 - 7/10

= (18-7)/10

= 11/10 miles

= 1 1/10 miles

Therefore Jena is 1 1/10 miles away from the park when she stopped.

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-14 is less than 16. All negative numbers are less than positives!

The total number of cards is 192 cards

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

Initial number of cards = 144 cards.

Nicole pays for the:

9/27 = 1/3 of the set

so she gets proportional amount of cards:

1/3*144 = 48 cards

Total number of cards Nicole has now:

144 + 48 = 192

Hence, the total number of cards is 192

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Complete question

Nicole has 144 role-playing cards and $9

to buy more cards. She and her friends buy

another set that costs $27. They evenly

split the cost and the cards in the set. How

many cards does Nicole have after she buys

part of a set with her friends?

Answer:4x - 2 = 12

Step-by-step explanation:

The number of buttons on each card from Elaine's grandmother is given as follows:

7 buttons.

The number of buttons on each card is obtained applying the proportions in the context of this problem.

Elaine sorted the buttons into 6 piles, putting 8 buttons in each pile, hence the total number is given as follows:

6 x 8 = 48.

Elaine had 6 buttons, hence the number donated is given as follows:

48 - 6 = 42.

6 cards were donated, hence the number of buttons in each card is given as follows:

42/6 = 7.

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The amount to be deposited for 10 years is $2000.

Given that,

Simple interest  is 5%

The amount to be in the account is $3000

The time period is 10 years.

The formula associated with these values is

A = P(1+rt)

where A = amount after 10 years

P = amount to be deposited in the account

r = rate of interest

t = time period

By applying the formula,

3000 = P (1+ (5% × 10))

3000 = P (1+ (0.05 × 10)

3000 = P (1 + 0.5)

3000 = P (1.5)

P = 3000/1.5

P = 2000 $

Therefore, $2000 should be deposited in an account in order to have $3000 in the account after 10 years.

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Answer:

Quadrant IV

In quadrant 4, the x-coordinate is positive, while the y-coordinate is negative.

Answer:

Circles are round shapes that doesn't have points or perhaps angles it shape is considered no a point shape thanks to it having no points ofc or can be used in measurements,yards,etc

The numbers that are exactly divisible by 7  are;

a) 525

b) 798

d) 3696

To solve this, what we will do is to quote the divisibility rule for 7 here which is that;

For a 3 digit number abc to be divisible by 7 then it means that ab - 2c must be divisible by 7. Thus;

A) 525;

52 - 2(5)

= 52 - 10

= 42

42 is divisible by 7 and as such 525 is divisible by 7

B) 798;

79 - 2(8)

= 63

63 is divisible by 7 and as such 79 is divisible by 7

C) 836;

83 - 2(6)

= 83 - 12

= 71

71 is not divisible by 7 and as such 836 is not divisible by 7

D) 3696;

369 - 2(6)

= 357

35 - 2(7)

= 21

21 is divisible by 7 and as such 3696 is divisible by 7

E) 5706;

570 - 2(6)

= 558

55 - 2(8)

= 39

It's not divisible by 7 and so  5706 is not divisible by 7

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Variables expression is done as given below.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Variables are the values for a specific item.

Example:

Apple cost = $4 per kg

Banana cost = $6 per kg

Total cost = $60

To find the number of kg for each item we have to consider x as the number of kg of apple and y as the number of kg of banana.

Here,

x and y are the variables.

Now,

The expression with the variables x and y.

4x + 6y = 60

Thus,

The expression with variables is given above.

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Every output value for g is half the output value for f.

I would describe the transformation as a vertical compression by a factor of 1/2, since every y-value was cut in half.

g(x) = 1/2 · f(x)

The linear function that predicts the number of cars that will be sold at a price of x dollars is y = -0.05x + 11580.

Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

To determine the linear function that predicts the number of cars sold we need to find the slope of the equation.

The two coordinated given are:

(x1, y1) = (52000, 8980)

(x2, y2) = (57000, 8730)

The slope of the equation is given by:

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

m = (8730 - 8980) / (57000 - 52000)

m = - 0.05

Substituting the value of the coordinates and slope in the point-slope form we have:

y - y1 = m (x - x1)

y - 8980 = -0.05(x - 52000)

y - 8980 = -0.05x + 2600

y = -0.05x + 11580

Hence, the linear function that predicts the number of cars that will be sold at a price of x dollars is y = -0.05x + 11580.

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Answer:Can somebody also help me with this. i'm confused please hurry!

Step-by-step explanation:

Using linear equations, the cost of each t - shirt is $8.

Consider how (0,5), (1, 4), (2, 3), etc. are all possible answers to the linear equation x + y = 5 to illustrate the infinite number of solutions to a linear equation with two variables. One solution that satisfies both solutions can exist for systems of two linear equations with two variables.

The only way to solve x + y = 5 and 2x y = 1 is to combine two equations with two variables into one equation with one variable, which is what we do when solving a system of equations. The two equations in the system can be added or subtracted to cancel out, or eliminate, one of the variables as each equation in the system has two variables.

Given,

Kathy pays 30 for 3 shirts and 2 caps.

marc pays 23 for 1 shirt and 5 caps.

Let us assume cost of t - shirt = x

cost of cap = y

⇒ 3x + 2y = 30

⇒ x + 5y = 23

on solving the equations using elimination method,

Multiply 2 equation by 3,

⇒ 3x + 2y = 30

⇒ 3x + 15y = 69

Now, subtract both equation -

⇒ - 13y = -39

⇒ y = 3

x = 30 - 2 × 3 / 3

x = 8

cost of each t - shirt = $ 8

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The measures of the interior angles of the triangle are: A=45°, B=110° and C=25°.

Triangles are geometric figures with three (3) sides. They can present different classifications regarding their sides or angles.

The sum of any triangle's angles will always be 180°, independent of its classification.

The question gives that the angles of the given  triangle are:

A=x

B= x+65°

C=25°

If A+B+C= 180° with the given values for angles B and C you can write:

x+x+65+25=180

2x+90=180

2x=180-90

x=90/2

x=45°

Thus, from the given information  you have:

A=45°

B= 45+65°=110°

C=25°

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Answer:

[tex](3+\sqrt{7},7+2\sqrt{7})[/tex]

[tex](3-\sqrt{7},7-2\sqrt{7})[/tex]

Step-by-step explanation:

Given equations:

[tex]\begin{cases}y=2x+1\\y=x^2-4x+3\end{cases}[/tex]

Substitute the second equation into the first equation:

[tex]\implies x^2-4x+3=2x+1[/tex]

Rearrange so that the terms in x are on the left side of the equation and the constants are on the right:

[tex]\implies x^2-4x-2x=1-3[/tex]

[tex]\implies x^2-6x=-2[/tex]

Add the square of half the coefficient of the term in x to both sides:

[tex]\implies x^2-6x+\left(\dfrac{-6}{2}\right)^2=-2+\left(\dfrac{-6}{2}\right)^2[/tex]

[tex]\implies x^2-6x+9=-2+9[/tex]

[tex]\implies x^2-6x+9=7[/tex]

Factor the perfect square trinomial on the left side of the equation:

[tex]\implies x^2-3x-3x+9=7[/tex]

[tex]\implies x(x-3)-3(x-3)=7[/tex]

[tex]\implies (x-3)(x-3)=7[/tex]

[tex]\implies (x-3)^2=7[/tex]

Square root both sides of the equation:

[tex]\implies x-3=\pm \sqrt{7}[/tex]

Add 3 to both sides of the equation:

[tex]\implies x=3\pm\sqrt{7}[/tex]

To find the y-values, substitute the found x-values into the first equation:

[tex]x=3+\sqrt{7}\implies y=2(3+\sqrt{7})+1=7+2\sqrt{7}[/tex]

[tex]x=3-\sqrt{7}\implies y=2(3-\sqrt{7})+1=7-2\sqrt{7}[/tex]

Therefore, the solutions to the system of equations are:

The value of the variable x when y = 6 is 2

It is important to note that a proportional relationship between variables or events means that as one increases in its value, the other also increases in the same way.

From the information given, we have that;

The variable y and x is proportional

This is represented as;

y ∝ x

Find the constant value

k = y/x

Substitute the values

k = 12/4

k = 3

Then when y = 6, we get;

x = y/k

x = 6/3

x = 2

Hence, the value is 2

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Answer:

Step-by-step explanation:

The equation of the line with the given points is y = 6x - 4. This can be derived by calculating the slope of the line, which is 6, and then using the point-slope form of the equation of a line, y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. In this case, the given points are (x1, y1) = (1, 10), so the equation of the line is y - 10 = 6(x - 1) or y = 6x - 4.

Answer y == 3

+7

Step-by-step explanation:

The graph of a linear relationship contains the points (1, 10) and (3, 16).

Write the equation of the line in slope-intercept fo

Step-by-step explanation:

the general slope-intercept form is

y = ax + b

a is the slope, which is the ratio of "y coordinate change / x coordinate change" when going from one point to another on the line.

b is the y-intercept - the y value when x = 0.

for the slope we see

x changes by +2 (from 1 to 3)

y changes by +6 (from 10 to 16)

so, the slope a is +6/+2 = 3

and the semi-ready equation is

y = 3x + b.

now we use one of the points in the equation to solve for b. I picked (1, 10) :

10 = 3×1 + b = 3 + b

b = 7

so, the full equation is

y = 3x + 7

The percent of the total calories in each brownie comes from fat is 34%

Percentage is described as a number or ratio expressed as a fraction of 100.

It is often represented with the percent sign, "%"

Abbreviations like "pct" and "pc" are used to denoted it.

Percentage is a dimensionless number, that is, it has no unit of measurement.

From the information given, we have that;

207 calories of fat/606 calories in a brownie × 100/1

Divide the values, we get;

0. 34 × 100/1

Multiply the values

34%

Hence, the value is 34%

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The slope-intercept form of the function described by this table?

x 0 1 2 3

y 3 8 13 18. is y = 5x + 3

The slope-intercept form of a linear equation is given by y = mx + b, where m is the slope of the line and b is the y-intercept. To find the equation that fits the table, we can use the two points (0, 3) and (1, 8) to calculate the slope and y-intercept.

First, calculate the slope:

m = (8 - 3) / (1 - 0) = 5

Next, use the point-slope form of a line to find the y-intercept:

y - 3 = 5(x - 0)

Expanding the right-hand side:

y - 3 = 5x

Adding 3 to both sides:

y = 5x + 3

So, the slope-intercept form of the function described by the table is:

y = 5x + 3

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Answer:

a) GH¢15x

b) GH¢15

Step-by-step explanation:

a) To find the cost function, C(x), given that it is linear, we need to find the slope and y-intercept of the line that represents the cost to produce x units of the product. We can use the point-slope form of a line to find the cost function: C(x) = mx + b, where m is the slope and b is the y-intercept.

We have two points: (100, GH¢1,500) and (0, GH¢0), which represents the cost to produce 100 units and 0 units, respectively. The slope can be found by dividing the change in y by the change in x:

m = (GH¢1,500 - GH¢0) / (100 - 0) = GH¢15

The y-intercept can be found by plugging in one of the points and solving for b:

GH¢1,500 = (GH¢15)(100) + b

GH¢1,500 = GH¢1,500 + b

b = GH¢0

So the cost function is C(x) = GH¢15x + GH¢0.

b) To find the average cost per item to produce 50 units and 300 units, we need to divide the total cost by the number of units produced.

For 50 units:

C(50) = GH¢15 * 50 + GH¢0 = GH¢750

Average cost = C(50) / 50 = GH¢15

For 300 units:

C(300) = GH¢15 * 300 + GH¢0 = GH¢4,500

Average cost = C(300) / 300 = GH¢15