find the area of the figure

Answer:

y =sin(x)

Step-by-step explanation:

small brain

Answer:

B: k pi for any integer k

Step-by-step explanation:

I took the test

Answer:

[tex]\dfrac{y^2}{9}=1-\dfrac{x^2}{25}[/tex]

Step-by-step explanation:

When converting parametric equations that involve trig functions to Cartesian equations, use trig identities to eliminate the parameter.

Given parametric equations:

[tex]x=5 \sin \theta, \quad y=3 \cos \theta, \quad 0\leq \theta\leq \pi[/tex]

Square the equation for x:

[tex]\implies x^2=(5 \sin \theta)^2=25 \sin^2 \theta[/tex]

Use the identity [tex]\sin^2 x+\cos^2x =1[/tex] to write [tex]x^2[/tex] in terms of cos:

[tex]\implies x^2=25(1-\cos^2 \theta)[/tex]

Isolate [tex]\cos^2 \theta[/tex] :

[tex]\implies \dfrac{x^2}{25}=1-\cos^2 \theta[/tex]

[tex]\implies \cos^2 \theta=1- \dfrac{x^2}{25}[/tex]

Square the equation for y:

[tex]\implies y^2=(3 \cos \theta)^2=9 \cos ^2 \theta[/tex]

Replace [tex]\cos^2 \theta[/tex] with the found equation involving [tex]x^2[/tex] :

[tex]\implies y^2=9\left(1-\dfrac{x^2}{25}\right)[/tex]

Divide both sides by 9:

[tex]\implies \dfrac{y^2}{9}=1-\dfrac{x^2}{25}, \quad \textsf{with }x\geq 0[/tex]

Answer:

49°

Step-by-step explanation:

Right angled triangle:

This is a type of triangle with one of the angle as 90°

Sum of angles in a Right angled triangle is 90°

Therefore,

y + 41° = 90°

collecting like terms

y = 90 - 41 = 49°

Therefore,

y = 49°

The equation of parabola becomes y = -2/25(x-3)^2 + 4.

According to the statement

we have given a graph and from this graph we have to find the equation of parabola in the general form.

So,

we know that the equation of parabola in general form is

y = a(x-h)^2 +k - (1)

From the graph we have:

a point on the graph is (x,y) = (-2,2)

the vertex of the graph is (h,k) = (3,4)

Now, substitute these values in the equation number (1)

Then

y = a(x-h)^2 +k

2 = a(-2-3)^2 +4

2 = a(-5)^2 +4

2 = a(25) +4

25a = -2

a = -2/25.

Now put a = -2/25 and (h,k) = (3,4) in the equation(1).

Then

the equation of parabola becomes y = -2/25(x-3)^2 + 4

So, The equation of parabola becomes y = -2/25(x-3)^2 + 4.

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The experimental probability of each event is as follows:

The experimental probability of an event is the ratio of the number of outcomes that favored the event to the total number of outcomes in the experiment.

In the question, we are given that Jake tossed a paper cup 50 times and recorded the position how it landed, which is shown in the table:

Open-sided up: 1

Closed side up 5

On the side: 44.

We are asked to determine the experimental probability of each outcome.

The number of outcomes, when the landing is open-sided up is 1.

The number of outcomes, when the landing is closed-sided up is 5.

The number of outcomes, when the landing is on the side up is 44.

The total number of times the experiment took place is 50.

Thus, the experimental probability of each event is as follows:

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Answer:

57?

Step-by-step explanation:

Answer:

(a) $1.98

(b) $6.30

Step-by-step explanation:

(a)

The new value =

1.80 + The value of the percentage increase =

1.80 + (10% × 1.80) =

1.80 + 10% × 1.80 =

(1 + 10%) × 1.80 =

(100% + 10%) × 1.80 =

110% × 1.80 =

110 ÷ 100 × 1.80 =

110 × 1.80 ÷ 100 =

198 ÷ 100 =

1.98

Calculate the actual change (the absolute difference) between the two values

The actual change =

The new value - 1.80 =

1.98 - 1.80 =

0.18

Proof of calculation.

Calculate the percentage increased value...

... and see if we get as a result...

... the actual change (the absolute difference).

Calculate the percentage increased value:

The value of the percentage increase =

10% × 1.80 =

10 ÷ 100 × 1.80 =

10 × 1.80 ÷ 100 =

18 ÷ 100 =

0.18

So we have proven that the calculations are correct.

For positive numbers

The actual change =

The value of the percentage increase

The answer:

1.80 increased by 10% = 1.98

The actual change:

1.98 - 1.80 = 0.18

(b)

Calculate the New value
The new value =

42.0 + The value of the percentage increase =

4.20 + (50% × 4.20) =

4.20 + 50% × 4.20 =

(1 + 50%) × 4.20 =

(100% + 50%) × 4.20 =

150% × 4.20 =

150 ÷ 100 × 4.20 =

150 × 4.20 ÷ 100 =

63,000 ÷ 100 =

630

(but its as a dollar so its 6.30)

Calculate the actual change (the absolute difference) between the two values

The actual change =

The new value - 4.20 =

6.30 - 4.20 =

2.10

Proof of calculation.

Calculate the percentage increased value...

... and see if we get as a result...

... the actual change (the absolute difference).

Calculate the percentage increased value:

The value of the percentage increase =

50% × 4.20 =

50 ÷ 100 × 4.20 =

50 × 4.20 ÷ 100 =

21,000 ÷ 100 =

210

(but its as a dollar so its 2.10)

So we have proven that the calculations are correct.

For positive numbers

The actual change =

The value of the percentage increase

The answer:

4.20 increased by 50% = 6.30

The actual change:

6.30 - 4.20 = 2.10

The limit of f(x) as it approaches -1 is given as 3/2

In mathematics and computation, the limit can be described to be the value that a sequence is going to approach in such a way that the input would approach or tend towards a given value

The unit is used to assign values to numbers at certain points where there are no defined values.

we have 3/x-1

We have to take the value of x here to be three as the equation tends to 1.

Then we apply it in the formula

3/3-1

= 3/2

Hence the limit of f(x) is given as 3/2

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The probability that Rita will need to pick at least five beads before she picks a gray bead from her collection is approximately (C) 0.45.

What is probability?

To find the probability that Rita will need to pick at least five beads before she picks a gray bead from her collection:

Therefore, the probability that Rita will need to pick at least five beads before she picks a gray bead from her collection is approximately (C) 0.45.

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The question you are looking for is given below.

Rita is making a beaded bracelet. She has a collection of 160 blue beads, 80 gray beads, and 240 pink beads. What is the estimated probability that Rita will need to pick at least five beads before she picks a gray bead from her collection?

(A) 0.05

(B) 0.10

(C) 0.45

(D) 0.55

Answer:

1

Step-by-step explanation:

The factor (x³ - 1) is not repeated.

There are four numbers of 3-coin combinations if we can choose from nickels, dimes, quarters, and half-dollars.

The coins to select from are nickels, dimes, quarters, and half-dollars;

Thus;

Coins (n) = 4

The number of coin to select is:

Coin (r) = 3

The coin combination is then calculated using:

Combination = ⁴C₃

Apply the combination formula, we have;

Combination = 4

Thus, there are four number 3-coin combinations if we can choose from nickels, dimes, quarters, and half-dollars.

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Answer:

12

Step-by-step explanation:

took the exam

The surface area of the shape is 168 square cm

The surface area of a figure is the area of the faces of the given figure.

For the given figure, the area will be the sum of area of 2 triangles and 3 rectangles.

Area = (6*3) +(10*6)+(6+10) +(10*3)

Surface area = 18 + 120 + 30

Surface area = 168 square cm

Hence the surface area of the shape is 168 square cm

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The value of x from the given triangle is 32√3/3

In order to determine the value of x, first we need to determine the hypotenuse side of the smaller triangle.

sin 60 = 8√2/H

H = 8√2/sin60

H = 8√2 * 2/√3

H = 16√2/√3
H = 16√6/3

For the value of x, we will use the expression

sin45 = (16√6/3)/x

1/√2 = 16√6/3x
3x = 16√12
3x = 32√3

x = 32√3/3

Hence the value of x from the given triangle is 32√3/3

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The system of equation which represent the scenario is;

x + y = 42

x + y = 420.13x + 0.18y = 6.66

let

x + y = 42

x + y = 420.13x + 0.18y = 6.66

Therefore, the equation which represent the problem is;

x + y = 42

0.13x + 0.18y = 6.66

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Answer:

Your correct

Step-by-step explanation:

x = 36

x/3 = 12

x = 12(3)

x = 36

Answer:

  (C)  0

Step-by-step explanation:

As always, the first step is to read and understand the question. You are asked to find the smallest number in the set {M₁, M₂, M₃}. Each of these values is defined to be the largest number in the corresponding sets S₁, S₂, S₃.

The numbers in each set are ordered smallest to largest, so the largest number in each set is the one on the right.

The largest number in S₁ is 8, so M₁ = 8.

The largest number in S₂ is 6, so M₂ = 6.

The largest number in S₃ is 0, so M₃ = 0.

This means the set M is ...

  M = {M₁, M₂, M₃} = {8, 6, 0}

The question asks for the smallest number in set M. Clearly, it is 0.

The smallest number in the set is 0.

The length of an edge of a cube is 5 feet.

In Geometry, a Cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges.

Total surface area of a cube = 6[tex]l^{2}[/tex]

Given that,

Total surface area of a cube = 150 square feet

Total surface area of a cube = 6[tex]l^{2}[/tex]

[tex]\Rightarrow[/tex]                                  150 = 6[tex]l^{2}[/tex]

[tex]\Rightarrow[/tex]                                     [tex]l^{2}[/tex] =  [tex]\frac{150}{6}[/tex]

[tex]\Rightarrow[/tex]                                     [tex]l^{2}[/tex] = 25

[tex]\Rightarrow[/tex]                                    l [tex]=\sqrt{25}[/tex]

[tex]\Rightarrow[/tex]                                    l = 5 feet

Hence, the length of an edge of a cube is 5 feet.

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The preferred choice would be a line graph (drawn in the figure attached) for displaying the data.

Why a line graph is the preferred option here?

What is a line graph?

An individual data point is connected by a line in a line graph, sometimes referred to as a line plot or a line chart. A line graph shows numerical values over a predetermined period of time.

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Simple Random sampling

Meaning:

Simple random sampling is a type of probability sampling in which the researcher randomly selects a subset of participants from a population. Each member of the population has an equal chance of being selected.

For example, if you randomly select 1000 people from a town with a population of 100,000 residents, each person has a 1000/100000 = 0.01 probability. That's a simple calculation requiring no additional knowledge about the population's composition. Hence, simple random sampling.

Advantage:

Simple random sample advantages include ease of use and accuracy of representation. No easier method exists to extract a research sample from a larger population than simple random sampling.

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Answer:

a = (9,8)

b=(10,6)

c=(4,3)

Step-by-step explanation:

basically, you just take the original coordinates and add the translation to it.

so a was -1,6 so just at 10 to -1 as they are x coordinates nad add 2 to 6 because they are Y coordinates and you just do it for all of the points.

Using it's concept, the probability that a randomly selected student is in music/drama is: 25%.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

Hence, in this problem, the probability will be found dividing the number of students that are in music or drama by the total number of students.

These data is given in a table, which is not given in this exercise. Researching this problem on the internet, we have that there are 20 + 7 + 3 + 20 + 13 + 2 + 25 + 5 + 5 = 100 students, of which 7 + 13 + 5 = 25 are in music/drama, hence the probability is:

P = 25/100 = 25%.

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The coordinates of M' is M'(-3,-4).

According to the statement

LMNP is rotated 90 degrees clockwise about the origin.

and we have to find the coordinates of M'.

so,

when it is rotated then it take four steps to reach at the end.

So, due to its moving procedure it takes four steps to reach at end.

and due to the four step procedure it's coordinates are changes four time and that's why at the end the coordinates we have to find are become a -3 and -4. So, the coordinate we get are -3 and -4

Due to this procedure the coordinate of m' become M'(-3,-4)

So, The coordinates of M' is M'(-3,-4).

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Answer: B. M'(4, -3) Just took the test

Step-by-step explanation:

The equation computed shows that the correct options are A, B, and D.

1) The equation we want to rewrite is;

³/₅x + ²/₃ + x = ¹/₂ – ¹/₅x

(³/₅ + 1)x + ²/₃ = ¹/₂ – ¹/₅x

⁸/₅x + ²/₃ = ¹/₂ – ¹/₅x

This corresponds with the solution in Option A

2) ³/₅x + ²/₃ + x = ¹/₂ – ¹/₅x

Let us use multiplication property of equality which states that if we multiply both sides of an equation by the same quantity, then both sides remain equal.

Let's get rid of the denominators by multiplying each term by the LCM of the denominators. LCM of 2,3,5 is 30. Thus;

30(³/₅x) + 30(²/₃) + 30x = 30(¹/₂) - 30(¹/₅x)

Simplifying gives;

18x + 20 + 30x = 15 - 6x

This solution corresponds with that in option B

3) We will make use of additive property of equality which states that when we add the same number to both sides of an equation, then both sides remain equal.

Let's add 6x to both sides of 18x + 20 + 30x = 15 - 6x;

18x + 20 + 30x + 6x = 15 - 6x + 6x

⇒ 24x + 30 + 20 = 15

Using subtractive property of equality, let us subtract 20 from both sides to get;

24x + 30 + 20 - 20 = 15 - 20

This corresponds with the solution in Option D.

Complete question:

Use properties to rewrite the given equation. Which equations have the same solution as 3/5x +2/3 + x = 1/2– 1/5x? Check all that apply.

a. 8/5x+2/3=1/2-1/5x

b. 18x + 20 + 30x = 15 – 6x

c. 18x + 20 + x = 15 – 6x

d. 24x + 30x = –5

e. 12x + 30x = –5

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If Andy has 102 coins mixed with dimes and quarters and monetary value of $17.10 then he has 56 dimes and 42 quarters.

Given number of coins Andy has is 102 and montary value of all coins is $17.10.

We have to determine number of dimes and quarters.

1 dime=$0.10

1 quarter=$0.25

Suppose the number of dimes be x and number of quarters be y.

The equations are:

0.10x+0.25y=17.10------------1

x+y=102-------------2

from equation 2, y=102-x

Put the value of y=102-x in equation 1

0.10x+0.25(102-x)=17.10

0.10x+25.5-0.25x=17.10

-0.15x=17.10-25.5

-0.15x=-8.4

x=8.4/0.15

x=56

Put the value of x in y=102-x

y=102-56

y=46

Hence Andy has 56 number of dimes and 46 quarters.

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Answer:  Choice C

Reason:

The curve is below the x axis on the interval [tex]-\infty < \text{x} < 3[/tex] which shortens down to the interval notation [tex](-\infty, 3)[/tex], so this is when f(x) < 0.

Answer:

========================

Parallel lines have equal slopes, so its equation is in the form of:

Since it passes through the points (4 , - 5), find the value of the y-intercept b by substituting x- and y- coordinates into this equation:

The equation of the parallel line is: