a piece of wire 22cm long is sent into an arc of a circle of radius 4cm . what angle does the wire subtend at the centre of the circle​

Answer:

-2 1/4

The average change in the field position run was -2 1/4 yards

Answer:

B

Step-by-step explanation:

the area of the rectangle is 4x8 = 32

the area of each half of the triangle is 4x4/2 = 8.

8x2 = 16.

The triangle is 16, the rectangle is 32

3)  since we don't have the information about the interest paid (I), we cannot determine the rate of interest at this time.

(1) To find the total amount Adrian paid in 36 months, we can multiply the monthly installment by the number of installments:

Total payment A = Monthly installment * Number of installments

              = $375 * 36

              = $13,500

Therefore, Adrian paid a total of $13,500 over the course of 36 months.

(2) In the simple interest formula I = Prt, the letters used represent the following variables:

I: Interest (the amount of interest paid)

P: Principal (the initial amount, or in this case, the car worth)

r: Rate of interest (expressed as a decimal)

t: Time (in years)

(3) To find the rate of interest in percentage, we need more information. The simple interest formula can be rearranged to solve for the rate of interest:

r = (I / Pt) * 100

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Answer:

Its 70 hope that helped

Step-by-step explanation: I did this before

Answer:

Original denominator=9

Step-by-step explanation:

A student accidentally added five to both the numerator and denominator of a fraction, changing the fraction's value to 1/2. If the original numerator was a 2, what was the original denominator.

Original Numerator=2

The new numerator after the addition of 5 will be 2+5=7

New Numerator=7

New denominator=x

Value of the fraction=1/2

The Fraction is written in the form:

7/x=1/2

Cross product

7*2=1*x

14=x

x=14

Therefore, the new denominator (x)=14

Check:

7/14=1/2

Original denominator before 5 was accidentally added

=14-5

=9

Answer:

Solving for X? would be 1

Step-by-step explanation:

32x-8-12x=22x-6

20x-8=22x-6 then subtract 20x from each side and add 6 to each side

2=2x then divide by 2 and getting 1 is x

Answer:

x=-1

Step-by-step explanation:

The surface described by the equation theta = 3 can be expressed as a vertical plane that includes the z-axis and intersects the xy-plane in the line y = 0. It is important to note that while the value of theta is fixed at 3, r and z can vary. Therefore, any point that has a polar coordinate representation of (3, theta, z) will lie on this plane.
To better understand this, let us consider the polar coordinate system. It is a coordinate system in which each point is determined by a distance (r) and an angle (theta) from a fixed point (the origin). In the three-dimensional space, the polar coordinate system can be extended to include a vertical coordinate (z). In the equation theta = 3, the angle is fixed at 3. This means that any point on the surface will have the same angle of 3. However, the distance from the origin (r) and the vertical position (z) can vary independently. Therefore, the surface is a vertical plane that intersects the xy-plane in the line y = 0.To visualize this surface, one can imagine a plane that is tilted at an angle of 3 with respect to the xy-plane and passes through the origin along the z-axis. Any point that lies on this plane can be expressed in polar coordinates as (3, 3, z), where z can be any real number.

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Answer:

18 gallons containing 20% solvent and 6 gallons containing 60% solvent

Step-by-step explanation:

the painter needs 24 gallons of paint containing 30% solvent = 7.2 gallons of solvent

let a = 20% solvent paint

let b = 60% solvent paint

a + b = 24

0.2a + 0.6b = 7.2

(replace a = 24 - b in the second equation)

a + b = 24

0.2(24 - b) + 0.6b = 7.2

4.8 - 0.2b + 0.6b = 7.2

0.4b = 7.2 - 4.8 = 2.4

b = 2.4 / 0.4 = 6

a = 24 - 6 = 18

Answer:

B

Step-by-step explanation:

The equation that will satisfy the statement is

1) 2x -0.5y > 80,  (x,y < 50)

2) 4x - y > 160,  (x,y>50)

3) 8x - 2y > 320 (x,y < 50).

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), larger than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation.

Let the number of Correct answer be x and number of incorrect answer be y.

The equation that will satisfy the statement is

1) 2x -0.5y > 80,  (x,y < 50)

2) 4x - y > 160,  (x,y>50)

3) 8x - 2y > 320 (x,y < 50)

The equations that will not satisfy the tatement are ,

1) 2x -0.5y < 80,  (x,y < 50)

2) 4x - y < 160,  (x,y>50)

3) 8x - 2y < 320 (x,y < 50)

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The equation that will satisfy the statement is
1) 2x -0.5y > 80,  (x,y < 50)
2) 4x - y > 160,  (x,y>50)
3) 8x - 2y > 320 (x,y < 50).

What is System of Equation and Inequalities?

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), larger than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation.

Let the number of Correct answer be x and number of incorrect answer be y.
The equation that will satisfy the statement is
1) 2x -0.5y > 80,  (x,y < 50)
2) 4x - y > 160,  (x,y>50)
3) 8x - 2y > 320 (x,y < 50)
The equations that will not satisfy the tatement are ,
1) 2x -0.5y < 80,  (x,y < 50)
2) 4x - y < 160,  (x,y>50)
3) 8x - 2y < 320 (x,y < 50)

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It will take Roger 2 months to save for his Deposit and finally move out.

In his current situation, Roger needs to save $2,400 to be able to move in, and he needs to pay the deposit for the apartment he wants which is the first and last month’s rent. Currently, Roger makes $2000 and his current expenses are $800 a month.

So, the money he can save per month is $2000 - $800 = $1200.

To find out how long in his current situation it will take Roger to save for his Deposit and finally move out, divide the total amount he needs to save by the money he can save per month:

$2,400 ÷ $1,200 = 2

Therefore, it will take Roger 2 months to save for his Deposit and finally move out.

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Answer:

\(w = 40m\)

Step-by-step explanation:

Given

\(Rate = 40\ words\ per\ minute\)

Required

Express as an equation

Represent the number of words with w and the minutes with m.

In 1 minute, Jordan types 40 words.

In m minutes, Jordan will type 40m words.

So, the function is:

\(w = 40m\)

The answers to the questions involving trigonometry are: 90, BC/AB ÷ BC/AB = 1, g = 6.5, <I = 62 degrees, h= 13.8, 12.0, x = 6.8, x = 66.4, 160.6, The pole = 6.7

Trigonometric ratios are special measurements of a right triangle, defined as the ratios of the sides of a right-angled triangle.  There are three common trigonometric ratios: sine, cosine, and tangent

For page 3 question 3,

a) <A + <B = 90 since <C = right angle

b) SinA = BC/AB and CosB = BC/AB

The ratio of the two angles BC/AB ÷ BC/AB = 1

I notice that the ratio of sinA and cosB gives 1

b) The ratio of CosA and SinB will give

BC/AB ÷ BC/AB

= BC/AB * AB/BC = 1

For page 5 number 3

Tan28 = g/i

g/12.2 = tan28

cross multiplying to have

g = 12.2*tan28

g = 12.2 * 0.5317

g = 6.5

b) the angle I is given as 90-28 degrees

<I = 62 degrees

To find the side h we use the Pythagoras theorem

h² = (12.2)² + (6.5)²

h² = 148.84 +42.25

h²= 191.09

h=√191.09

h= 13.8

For page 6

1) Sin42 = x/18

x=18*sin42

x = 18*0.6691

x = 12.0

2) cos28 = 6/x

xcos28 = 6

x = 6/cos28

x [= 6/0.8829

x = 6.8

3)  Tan63 = x/34

x = 34*tan63

x= 34*1.9526

x = 66.4

4) Sin50 123/x

xsin50 = 123

x = 123/sin50

x = 123/0.7660

x =160.6

5)  Sin57 = P/8

Pole = 8sin57

the pole = 8*0.8387

The pole = 6.7

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The volume of the candle is approximately 94 cubic inches.

A circular cylinder is a three-dimensional solid object made up of two parallel and congruent circular bases and a curving surface connecting the bases.

The volume of a right circular cylinder is given by the formula:

V = πr²h

Where

Substituting the given values into the formula, we get:

V = 3.14 x 2² x 7.5

V = 3.14 x 4 x 7.5

V = 94.2

Rounding to the nearest cubic inch, we get:

V ≈ 94 cubic inches

Therefore, the volume of the candle is approximately 94 cubic inches.

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To solve this question, just divide.

49/60 = 0.81666666666

= 82%

Answer:

Crissy's percentage is 82% (81.67% rounded).

Step-by-step explanation:

1. 49 / 60 = 0.82 (0.81666 rounded)

2. 0.82 x 100

3. 82%

Finding the line that fits a set of data points the best is done using the linear regression approach. We can utilize the following procedures to apply linear regression to find an equation that would most effectively predict a fair home price depending on the square footage of the home:

Step 1 :The square footage of the house should be on the x-axis and the house's price in thousands should be on the y-axis of the graph you create in step one.

Step 2: Using the slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, determine the equation of the line of best fit.

Step 3 :Find the slope and y-intercept by substituting the comps data into the equation in step three.

Step 4: The line of best fit has the equation y = mx + b, where m is the line's slope and b is its y-intercept.

Step 5: We must use the formula m = (NΣ(xy) - (Σx)(Σy)) / (NΣ(x^2) - (Σx)^2) to determine the slope (m).

Step 6: We must apply the formula b = (y - m(x)) / N to determine the y-intercept (b).

Step 7: Using the information provided in the question, we will determine the slope and y-intercept. m = (3* (108+133+120) - (1400+1700+1500)(3)) / (3 (1400+1700+1500)(2)) = 0.09 b = (108+133+120 -0.09*(1400+1700+1500))/3 = 111.33

   Therefore, y = 0.09x + 111.33 is the equation that would most accurately forecast a reasonable property price based on the home's square footage.

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As per the question, All four students A, B, C, and D are loss-averse over money and have the same value function as below:v(x dollars)={√x     x ≥ 0   {-2√-x  x < 0They are also loss averse over mugs and have the same value function.

v(y mugs)={3y y ≥ 0
        {4y y < 0
Now, we have to find the values of a, b, c and d as below:
- Student A owns a mug and is willing to sell it for a price of a dollars or more. i.e v(a) = v(0) + v(a-A), where A is the initial endowment of A. According to the given function, v(0) = 0, v(a-A) = 3, and v(A) = 4.
So, a ≥ A+3/2
- Student B does not own a mug and is willing to pay up to b dollars for buying it. i.e v(B-b) = v(B) - v(0), where B is the initial endowment of B. According to the given function, v(0) = 0, v(B-b) = -4, and v(B) = -3.
So, b ≤ B+1/2
- Student C does not own a mug and is indifferent between getting a mug and getting c dollars. i.e v(c) = v(0) + v(c), where C is the initial endowment of C. According to the given function, v(0) = 0, v(c) = 3.
So, c = C/2
- Student D is indifferent between losing a mug and losing d dollars. i.e v(D-d) = v(D) - v(0), where D is the initial endowment of D. According to the given function, v(0) = 0, v(D-d) = -3.
So, d = D/2
2) In this case, value function for money changes to:v(x dollars)={√x     x ≥ 0
            {-√-x   x < 0
However, the value function for mugs remains the same:v(y mugs)={3y y ≥ 0
         {4y y < 0
Therefore, values for a, b, c, and d will remain the same as calculated in part (1).
3) In this case, students are not loss-averse. Value function for money:v(x dollars)={√x     x ≥ 0
            {-√-x   x < 0
Value function for mugs:v(y mugs)={3y y ≥ 0
The reference point is the status quo, i.e initial endowment. So,
- Student A owns a mug and is willing to sell it for a price of a dollars or more. The value of mug for A is 3 initially and he would sell it for 3 or more.
So, a ≥ A+3/2
- Student B does not own a mug and is willing to pay up to b dollars for buying it. The value of mug for B is 3 initially and he would buy it for 3 or less.
So, b ≤ B+3/2
- Student C does not own a mug and is indifferent between getting a mug and getting c dollars. The value of the mug for C is 3 initially.
So, c = 3
- Student D is indifferent between losing a mug and losing d dollars. The value of the mug for D is 3 initially.
So, d = 3
4) In this case, value function for money:v(x dollars)={√x     x ≥ 0
            {-√-x   x < 0
Value function for mugs: Mug will have a value of 4 for someone who owns it and 3 for someone who does not own it.
The reference point is the status quo, i.e initial endowment. So,
- Student A owns a mug and is willing to sell it for a price of a dollars or more. The value of mug for A is 4 initially and he would sell it for 4 or more.
So, a ≥ A+2
- Student B does not own a mug and is willing to pay up to b dollars for buying it. The value of mug for B is 3 initially and he would buy it for 3 or less.
So, b ≤ B+3/2
- Student C does not own a mug and is indifferent between getting a mug and getting c dollars. The value of the mug for C is 3 initially and he would like to buy it for 3.
So, c = 3
- Student D is indifferent between losing a mug and losing d dollars. The value of the mug for D is 3 initially.
So, d = 3.

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9514 1404 393

Answer:

Step-by-step explanation:

Adding 10 and dividing by 4, we have ...

  4x < 28

  x < 7

The comparison does not include the "equal to" case, so the circle at x=7 is open. Values of x less than 7 are in the solution set. Those values are found to the left of 7 on the number line.

Answer:

C. The graph has an open circle at 7.

and

E.The arrow points left.

Step-by-step explanation:

i took the quiz and got it right

Answer:

16

Step-by-step explanation:

each sheep has about 6.42 pounds of wool so if you do 100/6.42 you get 15.5 but there isn't half sheeps so you round up to 16

Using a trigonometric relation we can see that:

CA = 5.03

On the image we can see a right triangle, we can see that the angle B is 40°, and the length of BC is 6 units.

We want to get CA, which is the opposite cathetus, if we use the trigonometric relation:

tan(B) = (opposite cathetus)/(adjacent cathetus)

Then we will get:

tan(40°) = CA/6

Solving for CA

CA = 6*tan(40°)

CA = 5.03

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Answer:

y ≤\(\frac{7}{4}x - 5\)

Step-by-step explanation:

We are to put the linear inequality;

7x - 4y ≥ 20

in slope intercept form.

We can rearrange the inequality as;

-4y ≥ - 7x + 20

Dividing throughout by -4 we get;

y ≤ \(\frac{7}{4} x\) - 5

Note that the inequality sign '≥' changes to '≤' since we divided all through with a negative number.

Simpson's Rule gives the exact value for the integral of a cubic function, so it will provide an accurate approximation.

First, let's divide the interval [L, L²] into n = 2 subdivisions. Since L = -2 and L² = 4, the subdivisions are [-2, 0] and [0, 4].

Using Simpson's Rule, the approximation S₂ is given by:

S₂ = (Δx/3) * [f(x₀) + 4f(x₁) + 2f(x₂) + 4f(x₃) + f(x₄)],

where Δx = (x₄ - x₀) / 2 and x₀ = -2, x₁ = -1, x₂ = 0, x₃ = 2, x₄ = 4.

Plugging in the values, we get:

Δx = (4 - (-2)) / 2 = 3,

S₂ = (3/3) * [f(-2) + 4f(-1) + 2f(0) + 4f(2) + f(4)].

Now, using the provided values for f(-2), f(0), and f(2), we can calculate the approximation S₂.

Similarly, using the Trapezoid Rule, the approximation T₂ is given by:

T₂ = (Δx/2) * [f(x₀) + 2f(x₁) + 2f(x₂) + f(x₃)].

We can calculate the approximation T₂ by plugging in the values for Δx, x₀, x₁, x₂, and x₃, and evaluating the function f at those points.

Comparing the values obtained from Simpson's Rule and the Trapezoid Rule will allow us to assess the accuracy of each method in approximating the integral.

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When y = 100, x is approximately equal to 0.04.

If y varies inversely as x^2 and y = 16 when x = 5, we can find the values of x and y when y = 100.

To solve this problem, we can use the inverse variation formula, which states that y = k/x^2, where k is the constant of variation.

Given that y = 16 when x = 5, we can substitute these values into the formula to find the value of k.

16 = k/(5^2)
16 = k/25

To find k, we can cross multiply:
16 * 25 = k
400 = k

Now that we know the value of k, we can use it to find the value of y when x = 100.

y = k/(100^2)
y = 400/(100^2)
y = 400/10000
y = 0.04

Therefore, when y = 100, x is approximately equal to 0.04.

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The gradient of the line segment AB​ is equal to 2/3.

In Mathematics and Geometry, the gradient or slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the formula for the slope of a line, we have the following;

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = 4/6

Slope (m) = 2/3.

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In terms of the sine, we can say that cos 16 can be written as:

Option B: Sine 74°

We know that all the trigonometric identities are based on the six trigonometric ratios. They are identified as sine, cosine, tangent, cosecant, secant, and cotangent

For complementary angles; or acute angles, we know that:

Sin x = Cos y,

This means that:

x + y = 90

Thus, if x = 16 then it means that:

y = 90 - 16 = 74

Hence;

Cos 16 = (sine 90-6)

Cos 16 = Sine 74

We conclude that in terms of sine; cos 16 is equal to Sine 74°

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it's 490 because when you get a zero or less it takes 10 points off your grade which leaves 490 students with good grades.

The area of the polygon is  207.06 unit².

How to find the Area of the Polygon with n-sides?

For finding the area of a polygon which is not regular or its formula is not defined, we split the figure into triangles, squares, trapezium, etc. The purpose is to visualize the given geometry as a combination of geometries for which we know how to calculate the area. We then calculate the area for each of the part and then add them up to obtain the area of the polygon.

Here, we have given a polygon in the combination of a square and a triangle.

So, to find an area of the polygon we need first to find the area of square and triangle.

Area of Polygon Formulas:

Name of the Polygon Area Formula

Triangle = 1/2 × base × height

Square = (side)²

Area of Square = (13)²

= 169 unit².

Area of Triangle = 1/2 × base × height

To find base:

(height)² + (base)² = (hypotenuse)²

(13)² = (11)² + (base)²

169 = 121 + (base)²

(base)²  = 169 - 121

base = √48 = 6.9

Area of Triangle = 1/2 × (6.92) × 11

= 38.06 unit².

Area of Polygon = Area of Square  + Area of Triangle

=  169 + 38.06

= 207.06 unit².

Therefore, the area of the polygon is  207.06 unit².

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Answer:

k = ±6

Step-by-step explanation:

guess your question is 4k²–144 = 0??

4k² = 144

k² = 36

k²–36 = 0

(k+6)(k–6) = 0

k+6 = 0 | k–6 = 0

k = –6, k = 6.

Alternatively; k = ±6.

Answer:

24 cm

Step-by-step explanation:

the perimeter is the circumference, the way to go one time fully around the object.

now think, what distances do you have to go when walking around a rectangle ?

well, there are 2 times the length and 2 times the width or breadth. that's it.

P = 2×7 + 2×5 = 14 + 10 = 24 cm

The imperial unit of length are inches, feet, miles etc, the imperial units of mass are pounds, ounces and the imperial units of capacity are pints, quarts, gallons etc

The imperial system of measurement is defined as a system of measuring quantities such as length, mass, volume, area, etc in the units that are commonly used in the UK, and other commonwealth countries. The units used in this system include inches, feet, pounds, gallons, tons, fluid ounces,

The imperial unit of length could be inches, feet, miles etc.

The imperial unit of mass is pounds, ounces

The imperial unit of capacity is pints, quarts, fluid ounces etc.

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