Find the size of the angle as pro-numeral in each case .

Answer:

60°

Step-by-step explanation:

Arc BC and Angle BWC are the same number of degrees.

When the vertex of an angle is at the center of a circle, its called a Central Angle. A central angle and the arc it "cuts off" have the same number of degrees.

Angle AWB and Angle BWC lay together on a straight line, so they add up to 180°.

180° - 120° is 60°

Angle BWC is 60° so Arc BC is 60°

The number of minutes spent higher than 38 meters above the ground on the Ferris wheel ride is approximately 1.0918 minutes.

To solve this problem, we need to determine the angular position of the Ferris wheel when it is 38 meters above the ground.

The Ferris wheel has a diameter of 50 meters, which means its radius is half of that, or 25 meters.

When the Ferris wheel is at its highest point, the radius and the height from the ground are aligned, forming a right triangle.

The height of this right triangle is the sum of the radius (25 meters) and the platform height (4 meters), which equals 29 meters.

To find the angle at which the Ferris wheel is 38 meters above the ground, we can use the inverse sine (arcsine) function.

The formula is:

θ = arcsin(h / r)

where θ is the angle in radians, h is the height above the ground (38 meters), and r is the radius of the Ferris wheel (25 meters).

θ = arcsin(38 / 29) ≈ 1.0918 radians

Now, we know the angle at which the Ferris wheel is 38 meters above the ground.

To calculate the time spent higher than 38 meters, we need to find the fraction of the total revolution that corresponds to this angle.

The Ferris wheel completes one full revolution in 2 minutes, which is equivalent to 2π radians.

Therefore, the fraction of the revolution corresponding to an angle of 1.0918 radians is:

Fraction = θ / (2π) ≈ 1.0918 / (2π)

Finally, we can calculate the time spent higher than 38 meters by multiplying the fraction of the revolution by the total time for one revolution:

Time = Fraction \(\times\) Total time per revolution = (1.0918 / (2π)) \(\times\) 2 minutes

Calculating this expression will give us the answer in minutes.

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Using PEMDAS and substituting 6 for x, the results of the mathematical operations are as follows:

PEMDAS is the order of mathematical operations that explains the correct sequential steps for evaluating mathematical expressions.

PEMDAS means that mathematical operations must follow the following order:

1) 9. x - 6 ( if x = 6)

= 9 x 6 - 6

= 54 - 6

= 48

2) 10. 7 + x ( if x = 6)

= 10 x 7 + 6

= 70 + 6

= 76

3) 11. 3x - 9 ( if x = 6)

= 11 x 3(6) - 9

= 11 x 18 - 9

= 198 - 9

= 189

4) 12. 63/x ( if x = 6)

= 12 x 63/6

= 126

5) 13. 5 + 5x + 10 ( if x = 6)

= 13 x 5 + 5(6) + 10

= 65 + 30 + 10

= 105

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Answer:

green line or "b"

Step-by-step explanation:

we can set this up into the slope intercept form

y=mx+b

where m is the slope and b is y intercept

12=3x+4y

-3x -3x

-3x+12=4y

/4.  /4.  /4

-3/4x+3=y

we can see the only line with a negative slope and a y intercept at 3 is the green line or "b"

hopes this helps please mark rainliest

To find the subtracted value, we need to calculate the multiplicative inverse of (4/3 - 4/9) and then subtract it from the sum of 7/12 and 7/8.

First, let's find the multiplicative inverse of (4/3 - 4/9):

Multiplicative inverse = 1 / (4/3 - 4/9)

To simplify the expression, we need a common denominator:

Multiplicative inverse = 1 / ((12/9) - (4/9))

= 1 / (8/9)

= 9/8

Now, we need to subtract the multiplicative inverse from the sum of 7/12 and 7/8:

Subtracted value = (7/12 + 7/8) - (9/8)

To perform this calculation, we need a common denominator:

Subtracted value = (7/12 * 2/2 + 7/8 * 3/3) - (9/8)

= (14/24 + 21/24) - (9/8)

= 35/24 - 9/8

To simplify further, we need a common denominator:

Subtracted value = (35/24 * 1/1) - (9/8 * 3/3)

= 35/24 - 27/24

= 8/24

= 1/3

Therefore, subtracting 1/3 from the sum of 7/12 and 7/8 will give you the multiplicative inverse of (4/3 - 4/9).

The product of the binomials (y + 3)(y - 6) gives y² - 3y - 18

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depends on other variable while a dependent variable is a variable that depends on other variable.

The product of the binomial is:

(y + 3)(y - 6)

= y(y) + y(-6) + 3(y) + 3(-6)

= y² - 3y - 18

The product of the binomials (y + 3)(y - 6) gives y² - 3y - 18

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Let's draw the figures to better understand the scenario:

The figure appears that ∠A and ∠E are pairs of corresponding angles. Since it was given that the two quadrilaterals are congruent, ∠A and ∠E must also be congruent.

With this relationship, let's first determine the value of x to be able to determine the measure of ∠A.

We get,

Let's determine the measure of ∠A.

Therefore, the measure of ∠A is 19°. The answer is letter A or the 1st option.

The area of the triangle with the given vertices is 11.5 square units.

The area of a triangle can be calculated using the coordinates of its vertices using the following formula.

To find the area of a triangle with vertices (x₁, y₁), (x₂, y₂), and (x₃, y₃), we can use the following formula:

A = (x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂))/2

Using this formula with the given vertices (0, 6), (2, −3), and (3, 4), we get:

A = (0(-3 − 4) + 2(4 − 6) + 3(6 − (-3)))/2

A = (0 - 4 + 27)/2

A = 23/2

A = 11.5

Therefore, the area of the triangle with the given vertices is 11.5 square units.

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Answer:

1,080 square inches

Step-by-step explanation:

27 inches * 40 inches = 1,080 square inches

Certainly! The problem can be solved using the Pythagorean theorem,

which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the ladder acts as the hypotenuse, and we need to find the length of the vertical side (height) it reaches up the wall.

The ladder forms the hypotenuse, and its length is given as 12 meters. The distance from the foot of the ladder to the base of the wall represents one side of the triangle, which is 4.5 meters.

By substituting the given values into the Pythagorean theorem equation: (12m)^2 = h^2 + (4.5m)^2, we can solve for the unknown height 'h'.

Squaring 12m gives us 144m^2, and squaring 4.5m yields 20.25m^2. By subtracting 20.25m^2 from both sides of the equation, we isolate 'h^2'.

We then take the square root of both sides to find 'h'. The square root of 123.75m^2 is approximately 11.12m.

Therefore, the ladder reaches a height of approximately 11.12 meters up the wall.

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Answer:

a. 1,323,002

Step-by-step explanation:

Answer:

-6x - 2y = 12

Step-by-step explanation:

Answer:

the value of m will be 20

The LCM of A = 3² × 5⁴ × 7 and B = 3⁴ × 5³ × 7 × 11 is 3898125 using Prime factorization.

Given are two numbers which are showed in the prime factorized form.

A = 3² × 5⁴ × 7

B = 3⁴ × 5³ × 7 × 11

Prime factorization is the factorization of a number in terms of prime numbers.

In order to find the LCM of these two numbers, we have to first match the common primes and write down vertically when possible and then bring down the primes in each column.

A = 3² ×         5³ × 5 × 7

B = 3² × 3² × 5³ ×       7 × 11

Bring down the primes in each column.

LCM = 3² × 3² × 5³ × 5 × 7 × 11

        = 3898125

Hence the LCM is 3898125.

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The approximate solution to the equation 1/x-1 = |x-2| after three iterations of successive approximation is x ≈ 5/2 or x ≈ 2.5.

To solve the equation 1/x-1 = |x-2| using three iterations of successive approximation, we will start with an initial guess and refine it using an iterative process.

Given that the equation involves absolute value, we will consider two cases:

Case 1: x - 2 ≥ 0

In this case, |x-2| simplifies to x-2, and the equation becomes 1/(x-1) = x-2.

Case 2: x - 2 < 0

In this case, |x-2| simplifies to -(x-2), and the equation becomes 1/(x-1) = -(x-2).

Now, let's perform the successive approximation:

Iteration 1:

Let's start with an initial guess, x = 2.

Case 1: When x - 2 ≥ 0,

1/(2-1) = 2-2,

1/1 = 0,

which is not true.

Case 2: When x - 2 < 0,

1/(2-1) = -(2-2),

1/1 = 0,

which is not true.

Since our initial guess did not satisfy the equation in either case, we need to choose a different initial guess.

Iteration 2:

Let's try x = 3.

Case 1: When x - 2 ≥ 0,

1/(3-1) = 3-2,

1/2 = 1,

which is not true.

Case 2: When x - 2 < 0,

1/(3-1) = -(3-2),

1/2 = -1,

which is not true.

Again, our guess did not satisfy the equation in either case.

Iteration 3:

Let's try x = 2.5.

Case 1: When x - 2 ≥ 0,

1/(2.5-1) = 2.5-2,

1/1.5 = 0.5,

which is true.

Case 2: When x - 2 < 0,

1/(2.5-1) = -(2.5-2),

1/1.5 = -0.5,

which is not true.

Our guess of x = 2.5 satisfies the equation in Case 1.

Therefore, the approximate solution to the equation 1/x-1 = |x-2| after three iterations of successive approximation is x ≈ 5/2 or x ≈ 2.5.

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Answer:

The combined amount of chocolate and regular milk sold was 52 cartons.

Step-by-step explanation:

1. Divide

36 ÷ 9 = 4

(This means that the ratio has a unit rate of 4. That means):

2. Second ratio rate

4 x 4 = 16

(Because the unit rate is 4).

3. Add

(Now, we add the original 36 cartons with the 16 cartons we found because the first step was just for finding the unit rate).

36 + 16 = 52 cartons.

May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 3 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!

Given the following five-number summary: 2.9, 5.7, 10.0, 13.2, 21.1, so Q₁ = 5.7. This can be solved using the concept of quartile.

A kind of percentile is a quartile. The first quartile (Q₁, or the lowest quartile), which corresponds to the 25th percentile of the data, is below which 25% of the data are found. The second quartile (Q₂, or the median), which represents the 50th percentile, indicates that 50% of the data are below this quartile.

There are 5 data points, and the middle value of the lower half of the data set will represent the first quartile. So the second data value is the first quartile. So, Q₁ = 5.7

There are 5 data points, and the middle value of the upper half of the data set will represent the third quartile. The fourth data value is the third quartile. So,

Q₃ = 13.2

SO IQR will be:

= Q₃ - Q₁

= 13.7 - 5.1

= 7.5

Thus, Q₁ = 5.7

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Given

mean = 9.4 ppm

standard deviation = 1.7 ppm

40 randomly selected large cities are studied.

Find

a) What is the distribution of X?

b) What is the distribution of ¯x?

c) What is the probability that one randomly selected city's waterway will have less than 9.1 ppm pollutants?

d) For the 40 cities, find the probability that the average amount of pollutants is less than 9.1 ppm.

e) For part d), is the assumption that the distribution is normal necessary?

f) Find the IQR for the average of 40 cities.

Q1 , Q3 , IQR:

Explanation

a) distribution of X = X ~ N(9.4 ,1.7)

b) distribution of ¯x

so , distribution of ¯x =

c)

Answer:

540 megabytes

Step-by-step explanation:

We will first need to find out how much space a singular song will take up. We will do this by the storage taken up (884) by the number of songs she has:

884 / 221 = 4 mb taken up per song

Then we want to find out how many megabytes 135 of these songs take up, so we will multiply the mb taken up per song (4) by the number of songs we want to find (135):

4 x 135 = 540 megabytes

Edit: made a mistake in my original answer, apologies!

The largest possible area will be 14400 meters², the pen's length should be 120 meters, and the width should be 120 meters.

The perimeter of a rectangle is defined as the addition of the lengths of the rectangle's four sides.

Let's assume that the length of the pen would be x.

We have been given the perimeter as 480 meters.

Let w be the width of the rectangle  and l be the length of the rectangle

The perimeter of a rectangle = 2(l+w)

So, 480= 2(x + w)

240 = x + w

w = 240 - x

Length = x and width = (240 – x)

Area = x(240 - x) = 240x - x²

To get the maximum area, we equate the first derivative of the area to zero.

A = 240x - x²dA/dx = 240 - 2x = 0

2x = 240

x = 120

So, width = 240 – x = 240 – 120 = 120.

Maximum area = length × width

Maximum area = 120 × 120 = 14400 meters²

Thus, the pen should be 120 meters long and 120 meters wide, with a maximum possible area of 14400 meters².

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Answer:

can i have a photo, please?

Step-by-step explanation:

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

Work Shown:

A = P*e^(r*t)

A = 47000*e^(0.0526*17)

A = 114,932.799077198

A = 114,932.80

Notes:

Mark's account balance after 17 years would be $114,932.8

\(A=Pe^{rt}\)

where,

A = Accrued amount

P = Principal amount

r = interest rate as a decimal

R = interest rate as a percent

r = R/100

t = time in years

For given question,

P = $47000, t = 17 years

R = 5.26%

\(\Rightarrow r =\frac{5.26}{100}\\\\\Rightarrow r = 0.0526\)

Using the Continuous Compounding Formula,

\(\Rightarrow A=Pe^{rt}\\\\\Rightarrow A=47000\times e^{0.0526\times 17}\\\\\Rightarrow A=114932.8\)

Therefore, Mark's account balance after 17 years would be $114,932.8

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Answer:

b.2

Step-by-step explanation:

thats ur answer

Answer:

B. 2

Step-by-step explanation:

Javon will have 1 and 1/3 yards (or 4 feet) of trim leftover.

To answer this question, we need to convert the length of the trim from feet to yards. Since there are 3 feet in 1 yard, we can divide 16 by 3 to get 5 and 1/3 yards.

Next, we need to determine how many pieces of trim Javon can cut that are 1 yard long. Since there are 3 feet in 1 yard, each piece of trim will be 3 feet long. We can divide 5 and 1/3 yards by 1 yard to get 5 pieces of trim.

Finally, we need to find out how much of a yard Javon will have left over. We can multiply the leftover distance in yards by 3 to convert it back to feet. The leftover distance is 1 and 1/3 yards, so multiplying by 3 gives us 4 feet.

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Answer:

Dollars per passenger would be $252.
The maximum revenue is $63,404.

Step-by-step explanation:

Let's define the number of passengers above 212 as x.

The revenue function is given by R(x) = (212 + x)(292 - x).

We can expand and simplify the revenue function:

\(R(x) = 212 * 292 + 212 * (-x) + x * 292 + x * (-x)\)

= \(61804 - 212x + 292x - x^2\)

= \(-x^2 + 80x + 61804\)

The revenue function is a quadratic function in the form\(R(x) = -x^2 + 80x + 61804\), representing a downward-opening parabola.

To find the x-coordinate of the vertex (which gives the number of passengers for maximum revenue), use the formula \(x = -b/2a\), where \(a = -1\) and \(b = 80\).

\(x=\frac{-80}{2*(-1)}\)

\(= \frac{80}{2}\)

\(= 40\)

Therefore, the number of passengers above 212 for maximum revenue is 40.

Substitute x = 40 into the revenue function to find the maximum revenue:

\(R(x) = -(40)^2 + 80(40) + 61804\)

\(= -1600 + 3200 + 61804\)

\(= 61804 + 1600\)

\(= 63404\)

Hence, the maximum revenue is $63,404.

To determine the fare per passenger, subtract x from the base fare of $292:

Fare per passenger = Base fare - x

\(= 292 - 40\)

\(= 252\) Dollars per passenger.

Answer:

300

Step-by-step explanation:

I think it will be 300 because

People High-Fives

2. 1

3. 3

4. 6

5. 10

6. 15

7. 21

8. 28

9. 36

10. 45.

There fore 10 people's high five will be 45 keep repeating and finding out the high fives I got 300 but I'm not sure if it's correct

The required number of high fives is 300.

Given that,
There are 25 students and one teacher in the class. After an exam, everyone high-fives everyone else to celebrate how well they did. How many high-fives were there is to be determined.

In arithmetic, combination and permutation are two different ways of grouping elements of a set into subsets. In a combination, the components of the subset can be recorded in any order. In a permutation, the components of the subset are listed in a distinctive order.

Here,
There are 25 students
n = 25
For each high five, there would be at least 2 students,
r = 2

The number of high five is given by combination,
= 25 C 2
= 25 * 24 / 2
= 600 / 2
= 300

Thus, the required number of high fives is 300.

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Answer:

Following are the solution to this question:

Step-by-step explanation:

C'(t) was its time, in years, or t shift of cash per unit. That C'(1980) meaning, therefore, becomes the change of cashier's population to t = 1980.  

They could either use t = 1970 or t = 1990 to approximate the C'(1980) price. When using t = 1970:

\(C'(1980) = \frac{[C(1980) - C(1970)]}{[1980 - 1970]}\\\\\)

              \(= \frac{(571 - 265)}{10}\\\\ = \$ \ 30.6 \\\)

t = 1990:

\(C'(1980) = \frac{[C(1980) - C(1990)]}{[1980 - 1990]}\)

              \(= \frac{(571 - 1063)}{ -10} \\\\= \$ \ 49.2\)

\(▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)

The equation of line that passes through (-2,2) and perpendicular to y=1/2x-3 is :

\(y = - 2x - 2\)

\( \large \boxed{ \mathfrak{Explanation}}\)

The equation of given line is :

here, we can infer that slope of the given line is \(\dfrac{1}{2}\) by comparing it with the general equation of line.

Let the slope of line perpendicular to it be m, now as we know if the lines are perpendicular then the product of their slopes will be equal to -1,

that is :

let's solve for m (slope of perpendicular line) ~

now, let's find the equation of line perpendicular to y=1/2x-3 using the point - slope form, ( by using point (-2 , 2) and slope (-2))

hence, the required equation is :

\(\mathrm{✌TeeNForeveR✌}\)

Answer:

\( I = \dfrac{1}{3}sin(3x) - 3cos(x) + C\)

Step-by-step explanation:

We need to integrate the given expression. Let I be the answer .

\(\implies\displaystyle\sf I = \int (cos(3x) + 3sin(x) )dx \\\\\implies\displaystyle I = \int cos(3x) + \int sin(x)\ dx \)

\(\implies\displaystyle\sf I = \int cos\ u \dfrac{1}{3}du + \int 3sin \ x \ dx \\\\\implies\displaystyle \sf I = \int \dfrac{cos\ u}{3} du + \int 3sin\ x \ dx \\\\\implies\displaystyle\sf I = \dfrac{1}{3}\int \dfrac{cos(u)}{3} + \int 3sin(x) dx \\\\\implies\displaystyle\sf I = \dfrac{1}{3} sin(u) + C +\int 3sin(x) dx \\\\\implies\displaystyle \sf I = \dfrac{1}{3}sin(u) + C + 3\int sin(x) \ dx \\\\\implies\displaystyle\sf I = \dfrac{1}{3}sin(u) + C + 3(-cos(x)+C) \\\\\implies \underset{\blue{\sf Required\ Answer }}{\underbrace{\boxed{\boxed{\displaystyle\red{\sf I = \dfrac{1}{3}sin(3x) - 3cos(x) + C }}}}}\)

Answer:

\(\displaystyle \large{\frac{\sin 3x}{3} - 3\cos x + C}\)

Step-by-step explanation:

We are given the indefinite integral:—

\(\displaystyle \large{\int (\cos 3x + 3\sin x) \ dx}\)

Important Formulas

\(\displaystyle \large{\int f(ax+b) \ dx = \frac{1}{a} F(ax+b) + C}\\\displaystyle \large{\int \cos(ax) \ dx = \frac{1}{a} \sin (ax) + C \ \ \tt{(a \ \ is \ \ a \ \ constant.)}}\\\displaystyle \large{\int \sin x \ dx = - \cos x + C}\\\displaystyle \large{\int [f(x) \pm g(x)] \ dx = \int f(x) \ dx \pm \int g(x) \ dx}\\\displaystyle \large{\int kf(x) \ dx = k \int f(x) \ dx \ \ (\tt{k \ \ is \ \ a \ \ constant.})}\)

Therefore, from the integral, apply the properties above:—

\(\displaystyle \large{\int (\cos 3x + 3\sin x) \ dx = \int \cos 3x \ dx + \int 3 \sin x \ dx}\\\displaystyle \large{\int (\cos 3x + 3\sin x) \ dx = \int \cos 3x \ dx + 3 \int \sin x \ dx}\\\displaystyle \large{\int (\cos 3x + 3\sin x) \ dx = \frac{1}{3} \sin 3x + 3\cdot -\cos x + C}\\\displaystyle \large{\int (\cos 3x + 3\sin x) \ dx = \frac{\sin 3x}{3} - 3\cos x + C}\)

Hence, the solution is:—

\(\displaystyle \large \boxed{\frac{\sin 3x}{3} - 3\cos x + C}\)