cm² What is the area of this shape? Give your answer in cm 3 cm 2cm 6cm 2cm Not to scale​

Answer:

Set your calculator to degree mode.

x/sin(120°) = 5/sin(23°)

x = 5sin(120°)/sin(23°) = about 11.08

11.08 belongs in the green box.

Answer:

Yes

Step-by-step explanation:

0.3983 is a number between 0 and 1, it can represent a probability.

The pattern is as follows: Start with 3, square it, subtract 10.

Looking at the given sequence: -7, 103, -997, 10003, -99997, we can observe a pattern emerging. Let's break it down:

The first number, -7, can be obtained by starting with 3, squaring it, and then subtracting 10: (-7 = 3^2 - 10).

The second number, 103, is obtained by starting with -7, adding 110, and then subtracting 10: (103 = -7 + 110 - 10).

The third number, -997, is obtained by starting with 103, subtracting 1110, and then subtracting 10: (-997 = 103 - 1110 - 10).

The fourth number, 10003, is obtained by starting with -997, adding 11110, and then subtracting 10: (10003 = -997 + 11110 - 10).

The fifth number, -99997, is obtained by starting with 10003, subtracting 111110, and then subtracting 10: (-99997 = 10003 - 111110 - 10).

From this analysis, we can see that each subsequent number in the sequence is obtained by alternately adding a positive integer (110, 1110, 11110) and subtracting 10 from the previous number. The pattern continues in this manner.

Then, alternate between adding increasingly larger positive integers and subtracting 10 to obtain subsequent numbers in the sequence.

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Answer:

20.83

Step-by-step explanation:

Certainly! Here's the math involved in calculating the infusion rate in drops per minute:

1. Convert 8 hours to minutes:

8 hours * 60 minutes/hour = 480 minutes

2. Calculate the total number of drops:

Total drops = 500 mL * 20 drops/mL

Total drops = 10,000 drops

3. Determine the infusion rate:

Infusion rate (drops per minute) = Total drops / Total time (minutes)

Infusion rate = 10,000 drops / 480 minutes

Infusion rate ≈ 20.83 drops per minute

So, the infusion rate is approximately 20.83 drops per minute.

longer explanation

To calculate the infusion rate in drops per minute, we need to determine the total number of drops in 8 hours and then divide it by the total time in minutes.

Given:

- Volume: 500 mL

- Drops per mL: 20

- Time: 8 hours

First, let's convert 8 hours into minutes:

8 hours * 60 minutes/hour = 480 minutes

Now, calculate the total number of drops:

Total drops = Volume (mL) * Drops per mL

Total drops = 500 mL * 20 drops/mL

Total drops = 10,000 drops

Finally, divide the total number of drops by the total time in minutes to find the infusion rate:

Infusion rate (drops per minute) = Total drops / Total time (minutes)

Infusion rate = 10,000 drops / 480 minutes

Infusion rate ≈ 20.83 drops per minute

Therefore, the infusion rate is approximately 20.83 drops per minute.

chatgpt

The expression (x + 1) divided by (x + 1) simplifies to just 1.

The expression that is equivalent to (x + 1) divided by (x + 1) is 1.

When we divide a number by itself, the result is always 1.

In this case, we have (x + 1) divided by (x + 1), which means we are dividing a quantity by itself. Regardless of the value of x, the numerator and denominator are the same, so the result will always be 1.

Therefore, the expression (x + 1) divided by (x + 1) simplifies to just 1.

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The expression (2.7 x 10⁴) x (9.1 x 10³) in standard form is 245700000

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

(2.7 x 10⁴) x (9.1 x 10³)

The expressions in standard form, we have

(2.7 x 10⁴) x (9.1 x 10³) = 27000  x 9100

Evaluatet the products

(2.7 x 10⁴) x (9.1 x 10³) = 245700000

Hence, the expression in standard form is 245700000

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The inverse of the given function is: f⁻¹(x) = 4x² - 3 for x ≤ 0

The inverse of a function is defined as a function that serves to undo another function. That is, if f(x) produces y, then putting y into the inverse of f' produces the output x. A function f' that has an inverse is referred to as invertible and the inverse is denoted by f⁻¹.

The given function is:

f(x) = -¹/₂√(x + 3)

To find the inverse of the function we replace the value of x and y and then find y in terms of x which is the inverse of the function.

Let f(x) = y

Thus:

x = -¹/₂√(y + 3)

Multiply both sides by -2 to get:

-2x = √(y + 3)

Square both sides to get:

4x² = y + 3

y = 4x² - 3

Thus, the inverse of the function is:

f⁻¹(x) = 4x² - 3 for x ≤ 0

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The solution to the given system of equations is (1,3). This is the intersection point of the two equations: y = 3x² - 8x - 2 and 2x - y = 5. Therefore, the correct answer is (1,3).

The given system of equations is: y = 3x² - 8x - 2 and 2x - y = 5

We can substitute y in the second equation with the expression obtained in the first equation.

2x - (3x² - 8x - 2) = 5 ⇒ 3x² - 10x - 7 = 0

This is a quadratic equation that can be solved using the quadratic formula.

x = (-(-10) ± sqrt((-10)² - 4(3)(-7))) / (2 * 3) ⇒ x = (10 ± sqrt(124)) / 6

Therefore, the two possible solutions for x are x = (10 + sqrt(124)) / 6 or x = (10 - sqrt(124)) / 6.

When we plug these values of x in the first equation, we can obtain the corresponding values of y. It can be observed that only one of these solutions, x = (10 - sqrt(124)) / 6 ≈ 1.166, gives a real value of y.

Therefore, the intersection point of the two equations is (1,3).

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The graphed velocity function ​v(t)=ds/dt=f'(t) and the acceleration function ​ is attached.

we start by  Plotting  the position function

Choosing a set of time values within the given interval [0, 9.5] and find the corresponding position values by substituting each time value into the position function s(t) = 152t - 16t².

We then plot the points (t, s) on a coordinate system.

We go ahead to Plot the velocity function by calculating  the derivative of the position function to obtain the velocity function v(t) = ds/dt = f'(t).

Plot the acceleration function by calculating the second derivative of the position function to obtain the acceleration function a(t) = d²s/dt² = f''(t).

We then connect the points representing the various function to create the needed graph.

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Answer: 16.26 degrees

Step-by-step explanation:

Sin^-1 (7/25)

SOH

Sin= Opposite/Hypotenuse

Answer:

Answer: 16.26 degrees

Step-by-step explanation:

Sin^-1 (7/25)

Step-by-step explanation:

The graphs that represent functions in this problem are given as follows:

Graph B and Graph D.

A graph represents a function if it has no vertically aligned points, that is, each value of x is mapped to only one value of y. Vertically aligned points mean that a value of x is mapped to multiple values of y, that is, a single input is mapped to multiple outputs which disqualify the relation as a function.

Hence the graphs that do not represent functions are given as follows:

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The APR of the credit card that has a monthly rate of 3.5% is 42%. The correct option is therefore;

B. 42%

The APR (Annual Percentage Rate) can be calculated from the monthly interest rate using the formula;

Monthly interest rate = APR/12

Therefore; APR = 12 × The monthly interest rate

The monthly interest rate charged by the credit card = 3.5%

The number of months in a year = 12

Annual percentage rate = The monthly interest rate × Number of months

Therefore, the annual percentage rate of the credit card = 3.5% × 12 = 42%

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The expression Distributive Property can be rewritten as 10t + 13t.

Distributive property with variables

Multiply, or distribute, the outer term to the inner terms.

Combine like terms.

Arrange terms so constants and variables are on opposite sides of the equals sign.

Solve the equation and simplify, if needed.

To rewrite the expression (10+13)t using the distributive property, we distribute the t to both terms inside the parentheses:

(10+13)t = 10t + 13t

Therefore, the expression Distributive Property can be rewritten as 10t + 13t.

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Here, we just need to add x and y and subtract it from 180.

x + y = 91 + 42 = 133.

180 - 133 = 47.

Hence, z = 47 degrees.

Answer:

Step-by-step explanation:

straight line = 180° we remove the angles x and y and find z

180 - 91 - 42 =

47°

The steps required to expand and simplify the difference between two polynomials are listed below:

Step 1: Definition of subtraction / Associative and distributive properties / (- 1) · x = - x

Step 2: Associative property

Step 3: Commutative and associative properties

Step 4: Distributive property / Definitions of addition and subtraction

Step 5: Commutative property

In this problem we must determine all steps needed to find the result of subtracting a polynomial by another polynomial. Each step is defined by a series of algebra properties:

Step 1: Definition of subtraction / Associative and distributive properties / (- 1) · x = - x

(- 3 · x³ + 5 · x² + 4 · x - 7) + (- 6 · x³ + 2 · x - 3)  

Step 2: Associative property

(- 3 · x³) + 5 · x² + 4 · x + (- 7) + (- 6 · x³) + 2 · x + (- 3)

Step 3: Commutative and associative properties

[(- 3 · x³) + (- 6 · x³)] + (4 · x + 2 · x) + [(- 7) + (- 3)] + 5 · x²

Step 4: Distributive property / Definitions of addition and subtraction

- 9 · x³ + 6 · x - 10 + 5 · x²

Step 5: Commutative property

- 9 · x³ + 5 · x² + 6 · x - 10

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The lower specification limit (LSL) of this vacuum cleaner's pivot function is 44.500 mm.

Specification limits are a set of conditions that must be met in order for a product or service to be accepted by consumers. In manufacturing, specification limits are used to determine whether a product or service meets customer or regulatory requirements, and specification limits are used as control limits to monitor the quality of manufactured products or services. Used in combination.

Related to this issue, Comfort Living Appliances has announced plans for a new flexible, lightweight vacuum cleaner. A unique component of this device is the rotating function of the handle. Plans suggest that there is still room for change within this pivot feature. The designer states that the height of this section should be 44.550 mm, but admits that anything between 44.500 and 44.645 mm is acceptable before the feature interferes with hose extension.

Therefore, the lower specification limit (LSL) is 44,500 mm.  

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The sequence of transformations that proves that the shapes are similar is given as follows:

B. a reflection across the x-axis, and then a dilation by a scale factor of 1.5

First, we have that the orientation of the figure, hence it was reflected.

The figure was reflected from the second quadrant to the third quadrant, hence the figure was reflected over the x-axis.

The base segment changes from a length of 2 units to a 3 units, hence the scale factor of the dilation is given as follows:

3/2 = 1.5.

Hence option B is the correct option for this problem.

The missing parts of the problem are given by the image presented at the end of the answer.

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The system of linear equations with infinitely many solutions is the fourth option: 11x + 12y = 13 and 22x + 24y = 26. Option D.

To determine which system of linear equations will have infinitely many solutions, we need to analyze each system and check for certain conditions.

Let's evaluate each system:

4x - 3y = -1

x - y = -2

This system consists of two linear equations. We can solve the second equation for x in terms of y: x = y - 2. Substituting this value into the first equation, we have 4(y - 2) - 3y = -1, which simplifies to y = 7. Substituting y = 7 back into the second equation, we find x = 5. Therefore, this system has a unique solution, not infinitely many solutions.

x + y = 90

y = 9x - 10

In this system, we have one equation explicitly defining y in terms of x. By substituting 9x - 10 for y in the first equation, we get x + (9x - 10) = 90, which simplifies to 10x = 100 and x = 10. Substituting x = 10 back into the second equation, we find y = 80. Thus, this system also has a unique solution.

-3x - y = 1

2x + y = -7

To solve this system, we can add the two equations together. This eliminates y and gives -x = -6, which simplifies to x = 6. Substituting x = 6 back into either equation, we find y = -19. Therefore, this system also has a unique solution.

11x + 12y = 13

22x + 24y = 26

In this system, the two equations are proportional to each other. Dividing the second equation by 2 gives the first equation. This means that the two lines representing the equations are coincident and overlap. Therefore, the system has infinitely many solutions since any point on the line satisfies both equations.

In conclusion, the system of linear equations with infinitely many solutions is the fourth option: 11x + 12y = 13 and 22x + 24y = 26.

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slope 35 and 6 negative on x ies

Answer:

-2

Step-by-step explanation:

y2-y1/x2-x1

-1-3/-1+3

-4/2

-2

Answer:

$5.76

Step-by-step explanation:

There are 16 US tablespoons inside a cup.

Since there are 2 pies, each needing 1/2 a cup, we can just class this as a full cup, as it is equivalent.

Since each lemon yields 2 tablespoons, we can do the following equation:

16/2=8

This gives us 8 lemons.

8 x 0.72 = 5.76

Therefore, this should cost $5.76

Hope this helps :D

Answer:

y_1 and y_2 have one point of intersection.

Step-by-step explanation:

The point of intersection of two functions refers to the point or points on a graph where the two functions intersect or cross each other. In terms of mathematical representation, it is the solution to the system of equations formed by equating the two functions.

To find the point(s) of intersection, you need to set the two functions equal to each other and solve for the variables. The resulting values give you the x-coordinates of the intersection point(s), and by substituting these values back into either of the original functions, you can find the corresponding y-coordinates. We can also use a graphing calculator if allowed to.

It's important to note that not all pairs of functions will have points of intersection. In some cases, the functions may not intersect at all, or they may have infinitely many points of intersection if they are identical.

In our case we are asked to approximate the number of points of intersection, not what are the points of intersection. Using the graph, we can conclude that y_1 and y_2 cross each other in one spot.

A) the total number of boxes in the bottom 2 layers is 100 + 80 = 180 boxes. B) Number of boxes in each layer = W(n) * D C) the total number of boxes needed to make up the 4 layers is 280 boxes.

A) To determine the number of boxes in the bottom 2 layers:

The bottom layer has a width of 20 boxes and is 5 boxes deep.

The second layer has a width of 16 boxes and is also 5 boxes deep.

Number of boxes in the bottom layer = 20 boxes wide * 5 boxes deep = 100 boxes

Number of boxes in the second layer = 16 boxes wide * 5 boxes deep = 80 boxes

Therefore, the total number of boxes in the bottom 2 layers is 100 + 80 = 180 boxes.

B) To develop a formula to calculate the number of boxes in n layers:

Let's denote the width of each layer as W and the depth of each layer as D.

The width of each layer follows the pattern: 20, 16, 12, 8.

We can observe that the width decreases by 4 units for each consecutive layer.

The formula to calculate the width of the nth layer can be written as:

W(n) = 20 - 4 * (n - 1)

Since each layer has a depth of 5 boxes, the number of boxes in each layer can be calculated as:

Number of boxes in each layer = W(n) * D

C) To use the formula from part B to solve for the total number of boxes needed to make up the 4 layers:

We want to calculate the total number of boxes in 4 layers.

Number of boxes in 4 layers = Number of boxes in the first layer + Number of boxes in the second layer + Number of boxes in the third layer + Number of boxes in the fourth layer

= W(1) * D + W(2) * D + W(3) * D + W(4) * D

= (20 - 4 * 0) * 5 + (20 - 4 * 1) * 5 + (20 - 4 * 2) * 5 + (20 - 4 * 3) * 5

= 20 * 5 + 16 * 5 + 12 * 5 + 8 * 5

Simplifying the expression, we get:

Number of boxes in 4 layers = 100 + 80 + 60 + 40 = 280 boxes

Therefore, the total number of boxes needed to make up the 4 layers is 280 boxes.

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Answer: 40 cups of trail mix

Step-by-step explanation:

To solve the problem, we can set up a proportion. We know that Orla uses 2 cups of raisins for every 8 cups of trail mix, which can be written as:

2/8 = 10/x

Where x is the number of cups of trail mix Orla will make if she uses 10 cups of raisins.

To solve for x, we can cross-multiply:

2x = 8 * 10

2x = 80

Then divide by 2:

x = 40

Therefore, if Orla uses 10 cups of raisins, she will make 40 cups of trail mix.

The value of tan(60) in the right triangle is √3.

The figure in the image is a right triangle, having one of its interior angles at 90 degrees.

To determine the value of tan( 60° ), we first need to find the measure of length side opposite to angle 60 degrees.

Using trigonometric ratio:

tanθ = opposite/adjacent

Plug in: opposite = x and adjacent = 5

tan(60) = x / 5

x =  tan(60) × 5

x = 5√3

Now, we find tan( 60° ):

Using trigonometric ratio: tanθ = opposite/adjacent

tan( 60° ) = [tex]\frac{5\sqrt{3} }{5}[/tex]

Simplify:

tan( 60° ) = √3

Therefore, the value of tan( 60° ) is √3.

Option C)√3 is the correct answer.

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Answer:

412.92

Step-by-step explanation:

[tex]A = P(1+\frac{r}{n} )^{nt}[/tex]

A: Amount, P: Principal, r: interest, n: no.of times compounded yearly and t: time in years

We have P = 300

r = 4% = 0.04

n = 12 (compounded monthly)

t = 8

[tex]A = 300(1+\frac{0.04}{12} )^{12*8}\\\\300(\frac{12.04}{12} )^{96}\\\\= 412.92[/tex]

Answer:

Using the Pythagorean Theorem, we know x^2 + 46^2 is equal to 65^2. With that in mind, it is important to note:

65^2 = 4,225

46^2 = 2,116

To find the missing angle, we must subtract 2,116 from 4,225 and then identify the difference’s square root.

4,225 - 2,116 = 2,109

√2,109 ≈ 45

Hence, x ≈ 45.

Step-by-step explanation:

        Hence, AGNES's ANNUAL TAXABLE INCOME is:   346560

MAKE A PLAN:

Calculate AGNES's Total Monthly Income, Subtract her Deductions and Personal Relief, and Then Find Her Annual Taxable Income:

1) - Calculate AGNES's Total Monthly Income:

     20000  +  15000  =  35000

2) - Calculate AGNES's  Total Monthly Deductions:

      960  +   3500  +  400  =  4860

3) - Calculate AGNES's MONTHLY TAXABLE INCOME:

     35000  -   4860  -  1260  =  28880

4) - Calculate AGNES's ANNUAL TAXABLE INCOME:

     28880  *   12   =    346560

       Hence, AGNES's ANNUAL TAXABLE INCOME is:   346560

       I hope this helps you!

The solution of the inequality equation is x > -π/2 or x > 3π/2.

The value of x in the inequality is calculated by applying the following formula as follows;

Given 0 ≤ x < 2π,

tan (x/2) > - 1

To determine the value of x take the arc tan of (-1) as follows;

x/2 > arc tan (-1)

x/2 > -π/4

x > -π/2

In the interval π/2 ≤ x < π:

x/2 > arc tan (-1)

x/2 > 3π/4

x > 3π/2

Thus, the solution of the inequality equation is x > -π/2 or x > 3π/2.

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The graph that shows a direct variation is the one in which a straight line passes through the origin, with the equation y = kx and the slope equal to k.

The graph that shows a direct variation is the one in which a straight line passes through the origin.

A direct variation is a type of relationship between two variables in which their ratio is constant.

It means that as one variable increases, the other variable increases proportionally, and as one variable decreases, the other variable decreases proportionally.
In a direct variation, the equation is usually in the form y = kx, where k is the constant of proportionality. The graph of a direct variation is a straight line that passes through the origin, or (0,0). This means that when x = 0, y = 0. The slope of the line is equal to k.
For example, if we have a direct variation between the number of miles driven and the amount of gas used, the equation would be y = kx, where y is the amount of gas used, x is the number of miles driven, and k is the constant of proportionality, which represents the gas mileage of the car.

The graph of this direct variation would be a straight line passing through the origin.

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