5+sin(3x)=4
solve for x on the unit circle where x is between 0 and 2pi

In summary, the redesigned equation of the path from entrance a affects the coordinates of the fountain by changing the coefficients of x and y in the equation. This change in coefficients results in a different slope for the path.

The redesigned equation of the path from entrance a affects the coordinates of the fountain by changing the values of x and y in the equation of the path.


The original equation of the path from entrance a is 3x + y = 5. To redesign the equation, we need to analyze the changes mentioned in the question: "path a ---- = path b - 2x + 5y8 wao entrance bc".

From this information, we can deduce that the new equation of the path from entrance a is given by: 3x + y = -2x + 5y + 8.

To understand how this redesigned equation affects the coordinates of the fountain, we can compare it to the original equation.

By rearranging the terms in both equations, we can see that the coefficients of x and y have changed. In the original equation, the coefficient of x is 3 and the coefficient of y is 1. However, in the redesigned equation, the coefficient of x is now -2 and the coefficient of y is 5.

These changes in the coefficients affect the slope of the path. The slope of the original equation is -3 (the coefficient of x divided by the coefficient of y), while the slope of the redesigned equation is -2/5.

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There are three areas of rhombus.

Using Diagonals A = ½ × d1 × d2

Using Base and Height A = b × h

Using Trigonometry A = b2 × Sin(a)

Here, we have only the height and base, so formula 2 can be used.

A = b x h = 21 * 19 = 399 inches.

Answer:

B

Step-by-step explanation:

v = how many students fit into a van

b = how many students fit into a bus

School A:

9v+7b=457 (1)

School B:

11v+7b=473 (2)

(1)&(2) => v=8

b=55

The expected value, mean, variance, and standard deviation are 656, 656, 63496598 and 7962.16 respectively.

To find the expected value, mean, variance, and standard deviation of a probability density function (PDF), we follow these steps:

1. Expected Value: The expected value, also known as the mean or average, is a measure of central tendency that represents the theoretical average outcome of a random variable.

It is calculated by multiplying each possible outcome by its corresponding probability and summing them up. The expected value provides a way to summarize the long-term behavior of a random variable.

2. Mean: The mean is a measure of central tendency that is often used to represent the average of a set of numbers.

It is calculated by summing up all the values in a data set and dividing the sum by the total number of values. The mean is a commonly used statistic to describe the center of a distribution.

3. Variance: The variance measures the spread or dispersion of a set of numbers around the mean. It quantifies the average squared deviation of each data point from the mean.

Mathematically, the variance is calculated by taking the average of the squared differences between each data point and the mean.

4. Standard Deviation: The standard deviation is another measure of dispersion that is closely related to the variance. It represents the square root of the variance and provides a measure of how spread out the data points are around the mean.

A smaller standard deviation indicates that the data points tend to be closer to the mean, while a larger standard deviation suggests greater variability.

Step 1: Calculate the expected value.

The expected value, denoted as E(X), is calculated by integrating the product of the random variable X and the PDF f(x) over the entire range of X. In this case, the range is [2, 6].

E(X) = ∫(2 to 6) x * f(x) dx

Since f(x) = 41, we can simplify the integral:

E(X) = ∫(2 to 6) 41x dx

     = 41 ∫(2 to 6) x dx

     = 41 [x^2/2] (from 2 to 6)

     = 41 [(6^2/2) - (2^2/2)]

     = 41 [18 - 2]

     = 41 * 16

     = 656

The expected value is 656.

Step 2: Calculate the mean.

The mean, denoted as μ (mu), is another term for the expected value.

μ = E(X) = 656

The mean is also 656.

Step 3: Calculate the variance.

The variance, denoted as Var(X), measures the spread or dispersion of the PDF. It is calculated by taking the expected value of the squared deviation from the mean.

Var(X) = E[(X - μ)^2]

      = ∫(2 to 6) (x - μ)^2 * f(x) dx

Since f(x) = 41, we can simplify the integral:

Var(X) = 41 ∫(2 to 6) (x - 656)^2 dx

Performing the integration and simplification:

Var(X) = 41 ∫(2 to 6) (x^2 - 1312x + 430336) dx

      = 41 [(x^3/3 - 1312x^2/2 + 430336x)] (from 2 to 6)

      = 41 [((6^3/3 - 1312*6^2/2 + 430336*6) - (2^3/3 - 1312*2^2/2 + 430336*2))]

      = 41 [(288 - 3936 + 2582016) - (8/3 - 5248 + 860672)]

      = 41 [2581368 - (17422/3 + 860664)]

      = 41 [2581368 - 172854 + 860664]

      = 41 [2581368 - 1032190]

      = 41 * 1549178

      = 63496598

The variance is 63496598.

Step 4: Calculate the standard deviation.

The standard deviation, denoted as σ (sigma), is the square root of the variance.

σ = √(Var(X))

  = √(63496598)

  ≈ 7962.16

The standard deviation is approximately 7962.16.

In summary, the expected value or mean is 656, the variance is 63496598, and the standard deviation is approximately 7962.16.

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Answer:

The Answer is: y = - 2x + 8.

the y-intersept is 8, and the slope is -2x

Answer:

B

Step-by-step explanation:

the sum of all angles in a triangle is always 180°.

the triangle RTQ is an isoceles triangle (both legs and therefore both baseline angles are equal), because we are dealing with a regular polygon.

so the angle RQT is the same as angle TRQ.

angle RQT = (180 - 108)/2 = 72/2 = 36°.

now, the polygon interior angle RQP is the supplementary angle to angle RQT (that means together they represent one side of a line like TP in this case, and therefore 180°).

angle RQP = 180 - 36 = 144°.

we know that the sum of all interior angles in a polygon is

(n - 2)×180

with n being the number of sides.

and each interior angle in a regular polygon is therefore

(n - 2)×180/n

we know that the interior angle is 144°.

so,

144 = (n - 2)×180/n

144n = (n - 2)×180 = 180n - 360

0 = 36n - 360

360 = 36n

n = 10

so, B is the right answer.

Answer:

x=6,y=0

Step-by-step explanation:

2x+y=12

3x-y=18

5x=30

x=6

6(3)-y=18

18-y=18

y=0

So, Lana gave away 26.32% of he Pokemon cards  to her little brother.

To find the percentage of cards Lana gave away, we can use the formula:(Quantity given away / Total quantity) * 100.

In this case, Lana gave away 125 cards out of her total collection of 475 cards.Plugging these values into the formula, we have:

(125 / 475) * 100 = 0.2632 * 100 = 26.32%.

Lana gave away 26.32% of her Pokemon cards to her little brother.

Alternatively, we can calculate the percentage by subtracting the remaining cards from the total and finding the ratio:

Percentage given away

= (Cards given away / Total cards) * 100

= (125 / 475) * 100

= 26.32%.

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The number of primes less than 190 using the principle of inclusion-exclusion are 42

The principle of inclusion-exclusion is known as a counting technique that computes the number of elements satisfying at least one of several properties and guaranteeing that the numbers are not counted twice.

Prime numbers are numbers only divisible by 1 and itself.

Prime numbers less than 190 are:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181

They are 42 in number

Therefore, the number of primes less than 190 using the principle of inclusion-exclusion are 42

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The volume of oil exiting the pipe is approximately 100 cu in/hr, 2,400 cu in/day, and 1.39 cu ft/day when converting cu in/day to cubic feet per day.



To calculate the volume of oil exiting the pipe every hour, you would need to know the flow rate of the oil in cubic inches per hour. Let's assume the flow rate is 100 cubic inches per hour.To find the volume of oil exiting the pipe every day, you would multiply the flow rate by the number of hours in a day. There are 24 hours in a day, so the volume of oil exiting the pipe every day would be 100 cubic inches per hour multiplied by 24 hours, which equals 2,400 cubic inches per day.

To convert the volume from cubic inches per day to cubic feet per day, you would need to divide the volume in cubic inches by the number of cubic inches in a cubic foot. There are 1,728 cubic inches in a cubic foot. So, dividing 2,400 cubic inches per day by 1,728 cubic inches per cubic foot, we get approximately 1.39 cubic feet per day.

Therefore, the volume of oil exiting the pipe is approximately 100 cubic inches per hour, 2,400 cubic inches per day, and 1.39 cubic feet per day.

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Answer:

Sam will have 4 portions. In those 4 portion will be 4 pounds per portion because 16 divide 4 Is 4

The unit vector which are in opposite direction of the u = (3,0,5) is given by option B.  -1/√34 (3,0,5) .

Vector u = ( 3, 0, 5 )

Magnitude of u is equal to

|u| = √3² + 0² + 5²

⇒ |u| = √ 9 + 25

⇒ |u| = √34

Let the required unit vector opposite in the direction of u be w

Opposite direction of u is represented by the negation of u

negation of u = ( -3 , 0 , -5 )

⇒ w = ( -3 , 0 , -5 )

Magnitude of w is equal to

|w| = √(-3)² + 0² + (-5)²

⇒|w| = √34

Unit vector w = ( 1/√34)( -3 , 0 , -5 )

Therefore, the required unit vector in the opposite direction of u is equal to option B . ( 1/√34)( -3 , 0 , -5 ).

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Recall the definition of each concept to check if it fits the figure.

A) Square: A square is a quadrilateral whose sides all have the same length.

B) Polygon: A polygon is a 2D shape formed by non-intersecting straight segments.

C) Triangle: A triangle is a polygon with exactly 3 sides.

D) Polyhedron: A polyhedron is a 3D shape formed by flat polygonal shapes.

E) Pyramid: A pyramid is a polyhedron formed by a simple polygon whose lateral faces are triangles that converge in a common vertex.

F) Prism: A prism is a polyhedron formed by two parallel and equal polygonal faces, whose lateral faces are parallelograms.

The given object is a 3D shape formed by flat polygonal shapes, with a base that is a quadrilateral and whose lateral faces are triangles that converge in a common vertex.

Therefore, the only two terms that correcty describe the given object are:

D) Polyhedron

E) Pyramid

Answer:

Y=5/16x -3/4

Step-by-step explanation:

3/8 * 8/3y=(5/6x -2) *3/8

y=5/16x - 3/4

The standard form of the equation is  5x -16y = 2.

It is required to find the standard form.

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.

Given:

According to given question we have,

The least common multiple of the fraction denominators is 6. Multiplying by that gives

 16y = 5x -2

We can put this in standard form by adding 2-16y to both sides.

 5x -16y = 2

Therefore, the standard form of the equation is  5x -16y = 2.

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Answer:

(b) 91

Step-by-step explanation:

The probability of an item scanning correctly is 98.9%, so the probability of an item scanning incorrectly is 1 - 98.9% = 1.1%.

The expected number of items to buy to find one that scans incorrectly is 1 / 1.1% = 91. This means that you would expect to buy 91 items on average to find one that scans incorrectly.

Rounding up to the next integer, the answer is 92. Therefore, the correct answer is (b) 91.

Answer:

a) The hypotenuse side is BC.

b) Using the Pythagorean Theorem, we can determine the missing side: AB = √(AC² - BC²) = √(6² - 4²) = √(36 - 16) = √20 = 4.47.

c) The perimeter of the triangle is AC + BC + AB = 6 + 4 + 4.47 = 14.47.

d) The area of the triangle is ½ × AC × AB = ½ × 6 × 4.47 = 13.7.

Step-by-step explanation:

The Pythagorean Theorem states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse. So, for the triangle given, we can use this theorem to calculate the length of side AB, which is the missing side. Then, we can calculate the perimeter of the triangle by adding up all three sides and the area of the triangle by using the formula ½ × AC × AB.

A bar chart or a histogram are visual representations of data that can be used to explore a single column of data.

A bar chart is used to compare different categories of data, and a histogram is used to measure the frequency of data within a given range. Bar charts allow a user to compare the differences between the categories of data, while histograms provide a better indication of how the data is distributed within the range.

Both bar charts and histograms are useful for identifying patterns, outliers, and trends in the data. By using a bar chart or a histogram, a user can quickly and easily identify where the data is concentrated, as well as identify any outliers or trends in the data.

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Statistics computed for larger random samples tend to be less variable compared to statistics computed for smaller random samples.

This statement is based on the concept of the Central Limit Theorem (CLT) in statistics. According to the CLT, as the sample size increases, the distribution of the sample mean approaches a normal distribution regardless of the shape of the population distribution. This means that the variability of the sample mean decreases as the sample size increases.

The variability of a statistic is commonly measured by its standard deviation or variance. When working with larger random samples, the individual observations have less impact on the overall variability of the statistic. As more data points are included in the sample, the effects of outliers or extreme values tend to diminish, resulting in a more stable and less variable estimate.

In practical terms, this implies that estimates or conclusions based on larger random samples are generally considered more reliable and accurate. Researchers and statisticians often strive to obtain larger sample sizes to reduce the variability of their results and increase the precision of their statistical inferences.

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The total loan amount equal in four years when he graduates is $14,310.22.

Using this formula

A=P(1+r)^t

Where:

A= Amount=?

P=Principal=$12,000

r =interest rate=4.5%

t =Time=4 years

Let plug in the formula

Amount=12,000(1+0.045)^4

Amount=12,000(1.045)^4

Amount=12,000(1.1925)

Amount=$14,310.22

Inconclusion the total loan amount equal in four years when he graduates is $14,310.22.

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Answer: 11,500 grams

Step-by-step explanation: 920/8=115 115*100= 11,500

Answer:

x > 36

Step-by-step explanation:

158 < 2x + 2(x+7)

158 < 2x + 2x + 14

144 <4x

x > 36

Answer:

The answer is x>34

Step-by-step explanation:

I tried there way it came out wrong.

The volume of Ganymede is approximately 3.48 times the volume of the Moon, based on the given diameters of the two moons and the formula for the volume of a sphere.

The volume of a sphere is the amount of space occupied by the sphere in three-dimensional space. It can be calculated using the formula V = (4/3)πr³, where V is the volume of the sphere, r is the radius of the sphere, and π (pi) is a mathematical constant approximately equal to 3.14159. This formula states that the volume of a sphere is four-thirds of the product of pi and the cube of the sphere's radius.

In the given question,

The volume of a sphere can be calculated using the formula V = (4/3)πr³, where r is the radius of the sphere. Since we are given the diameters of the two moons, we can calculate their radii by dividing the diameters by 2. Therefore, the radius of Ganymede is 3,388/2 = 1,694 km, and the radius of the Moon is 1,245/2 = 622.5 km.

Now, we can calculate the volumes of the two moons:

V_Ganymede = (4/3)π(1694)³ ≈ 7.66 x 10^10 km³

V_Moon = (4/3)π(622.5)³ ≈ 2.2 x 10^10 km³

To find how many times larger Ganymede's volume is compared to the Moon's volume, we can divide the volume of Ganymede by the volume of the Moon:

V_Ganymede / V_Moon ≈ (7.66 x 10¹⁰) / (2.2 x 10¹⁰) ≈ 3.48

Therefore, the volume of Ganymede is approximately 3.48 times the volume of the Moon.

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Answer:

-7 and -5

Step-by-step explanation:

It is where the parabola intercepts the x axis which is -7 and -5

Therefore , the solution of the given problem of ratio comes out to be Colin thus receives £29.40 more than Paul.

The simple formula "a / b," where "b" may be variable greater than zero, can be used to define a set of numbers "a" and "b" that are equal. Two ratios are combined to form a ratio. If there was only one man and three ladies, the equation ratio would be 1:3. In the group, there are 3/4 females and 1/4 men. Parts can be a division between various items, a figure, or a specific amount of a component's volume.

Here,

The total amount of components in the ratio 2:5:1 must first be determined.

2 + 5 + 1 = 8

As a result, there will be 8 proportionate portions of the tips. By dividing the total recommendations by 8, we can determine the value of each component:

78.40 ÷ 8 = 9.80

Thus, each component is valued £9.80.

We can now calculate the ratio to determine how much each server will receive:

=> Paul: 2 parts × £9.80/part = £19.60

=> Colin: 5 parts × £9.80/part = £49.00

=> Brian: 1 part × £9.80/part = £9.80

Paul's income can be subtracted from Colin's income to determine how much more Colin earns than he does for Paul:

=> £49.00 - £19.60 = £29.40

Colin thus receives £29.40 more than Paul.

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Answer:

a) There are 9 outcomes.

b) **i have attached the tree diagram**

c) 1/9

d) 1/9

Step-by-step explanation:

Both events (choosing a shirt and choosing pants) are not mutually exclusive (disjoint). Meaning that both events can occur at the same time.

a) For a sequence of two events in which the first event can occur m ways and the second event can occur n ways, the events together can occur a total of m • n ways. So for this problem, you would do 3 • 3 which equals 9.

b) **tree diagram is attached**

c) Because there are two different events occurring (choosing a shirt and choosing pants) you need to multiply using the Multiplication Rule for Independent Events : P(A and B) = P(A) * P(B)

The probability of event A occurring (choosing a red shirt) is 1/3 and the probability of event B occurring (choosing brown pants) is also 1/3.

1/3 * 1/3 = 1/9

d) You would do the same thing here as part c.

The probability of event A occurring (choosing a blue shirt) is 1/3 and the probability of event B occurring (choosing blue pants) is again 1/3.

1/3 * 1/3 = 1/9

I hope this was helpful!! :)

Answer:

46°

Step-by-step explanation:

from large triangle:

let the third unknown angle be 'a'

then,

a+x+7+85=180

a=88-x

now,from small triangle,

let the third unknown angle be 'b'

then,

b+x+2x=180

b=180-3x

b=a (vertically opposite angles)

then,

180-3x=88-x

2x=92

x=46

The answer is (D) 39 cm²

What is the formula of a trapezoid?

The formula Area of trapezoid = 1/2 (a + b) h is used to determine the area of a trapezoid, where a and b are the bases (parallel sides) and h is the perpendicular height.

According to figure,

The portion of the base from the perpendicular to the right vertex is 6.2 cm, so we can label the remaining side as 3 + 6.2 = 9.2 cm.

shape is actually a trapezoid, with bases of 9.2 cm and 6.2 cm, and a height of 5 cm. The area of a trapezoid is given by the formula:

Area = (base1 + base2) * height / 2

Substituting the given values, we get:

Area = (9.2 + 6.2) * 5 / 2

Area = 15.4 * 5 / 2

Area = 38.5 cm²

Rounding to the nearest whole number, we get an area of 39 cm². Therefore, the answer is (D) 39 cm².

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Answer:

A. T=3

B. A=5

C. M=2

D. C=7

E. F =4