1/3 of 36 mutlitplied by the diffrence of 15 and 2

(a) If θ(1) = 26.0 degree, the angle θ(2) of the emerging beam is 41.3 degree.

(b) The smallest incident angle θ(1) to have total internal reflection at the surface between the medium with n(4) = 1.20 and the medium with n(4) = 1.06 is 62.01.

(a) The path of a beam of light through several layers with different indices of refraction.

Using the Snell's law

n(1) sinθ(i) = n(2) sinθ(r)

The two medium's refractive indices are n(1) and n(2), and the angles of incidence and refraction are θ(i) and θ(r).

The preceding can be revised as

sinθ(r) = sinθ(i)(n(1))/(n(2))

sinθ(r) = sin 26 × 1.60/1.40

sinθ(r) = 0.50

Going from n2 to n3 .

The above calculated will become angle of incidence made with the normal at n(2) and n(3) interface.

The angle of refraction at n(3) medium

sinθ(r3) = sinθ(r) × n(2)/n(3)

sinθ(r3) = 0.50 × 1.40/1.20

sinθ(r3) = 0.58

The angle of incidence for interfaces n(3) and n(4) is now θ(r3).

sinθ(2) = (sinθ(r3) × n(3))/n(4)

sinθ(2) = (0.58 × 1.2)/1.06

sinθ(2) = 0.66

Taking square root on both side, we get

θ(2) = [tex]\sin^{-1}[/tex](0.66)

θ(2) = 41.3 degree

(b) It is possible to calculate the critical angle at the n3 to n4 interface as

θ(c) = [tex]\sin^{-1}[/tex](n(4)/n(3))

θ(c) = [tex]\sin^{-1}[/tex](1.06/1.20)

θ(c) = 62.01

The angle at which 100% internal reflection takes place is known as the critical angle.

Total internal reflection will happen if the beam is incident at an angle of 62.01 at n(3).

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The complete question is:

The figure below shows the path of a beam of light through several layers with different indices of refraction. (Assume n(4) = 1.06.)

(a) If θ(1) = 26.0 degree, what is the angle θ(2) of the emerging beam?

(b) What is the smallest incident angle θ(1) to have total internal reflection at the surface between the medium with n(4) = 1.20 and the medium with n(4) = 1.06?

Answer:

Your boss’s assistant should have multiplied 25.80 by 3.

Step-by-step explanation:

15.79 x 40 is correct but $25.80 is for every hour after 40 which is 3 so it would be $25.80 x 3

Answer:

the answer is 5.25

hopefully this will help u... ^_^

Step-by-step explanation:

2 1/4 can be written as the fraction 9/4. To get this fraction, you could divide 4 into 9. This would give you 2 1/4 as the answer.

Answer: the only clear answer i can think of would be, NO, the work she did was not clear i would say she did 4/10days she needed to work

Step-by-step explanation:

The number of selfies deleted by Alex is 52.5.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that Last week, Alex took 90 selfies and Vic took 75 selfies. Today, they each decided that some of these selfies were not very good and deleted them. Alex deleted three times as many selfies as Vic.

Alex= 90

Vic = 75

Deleted ( Alex = 3 Vic )

Alex = 1 / 2 Vic

Deleted selfies = 90 - 75 /2 = 52.5

Hence, the number of selfies deleted by Alex is 52.5.

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The angle that the vector "v = 9i + 8j - 4k" makes with the vector "u = 6i - 4j - k" is Acute Angle .

To determine the angle between two vectors, we need to find the dot product of the vectors and divide it by the product of their magnitudes.

If the result is positive, the angle between the vectors is acute, if it's negative the angle is obtuse, and if it's zero, the angle is a right angle.

In this case, the dot product of vectors "u" and "v" is:

⇒ (6i - 4j - k) . (9i + 8j - 4k) = 54 - 32 + 4 = 26  ;

The magnitude of vector "u" is = √(6² + (-4)² + (-1)²) = √(36 + 16 + 1) = √53

The magnitude of vector "v" is = √(9² + 8² + (-4)²) = √(81 + 64 + 16) = √161

So, the Cosine (Cos) of angle between two vectors "u" and "v" is:

⇒ Cos(θ) = 26/(√37 × √145) = 26/√5365  .

Since the value of Cos(θ) is positive, the angle between the vectors is acute. This means the vectors "u" and "v" are pointing in somewhat similar directions, but not exactly the same direction.

The given question is incomplete , the complete question is

Determine whether the angle vector "v" makes with vector "u" is acute, obtuse, straight, a right angle, or whether "v" is a vector in the same direction as "u" . u=6i-4j-k  and  v=9i+8j-4k .

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5x+4y is the objective function's value (10,0)

The suggested LPP is: Maximize 6x+10y with restrictions 4x+6y =240, 2x+3y120

6x+3y≤240⇒2x+y≤80 x≥10 y≥0

Plot the graphs of x=10, 2x+3y=120, and x+y=80. The area of the solution that is viable is shown by the shading.

The viable region's corner points are (10, 0), (40, 0), (30, 20), and (10, 3 100).

When the objective function is examined at these values:

(x,y)

5x+4y is the objective function's value (10,0)

70 (40,0) 280 (30,20) 410 (10, 3 100  )

403.33

The figures show that 7x+10y is at its maximum when x=30 and y=20. The top number is 410.

max 5x_{1} + 4x_{2}

s.t. x_{1} + x_{2} <= 6 x_{1} - 2x_{2} <= 2 10x_{1} + 6x_{2} <= 45 x_{1} ,x 2 in mathbb Z

x_{1}, x_{2} >= 0

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By multiplying the factors, y + x = -4/5 in y-intercept form is y = -1/5(x + 4).

Multiplication is a mathematical operation that involves two numbers, known as factors, being multiplied together to produce a new number, known as the product. The equation is not in a form that can be simplified. The equation is an algebraic equation that needs to be solved using basic algebraic operations such as addition, subtraction, multiplication and division.

Generally, the factors are either whole numbers or fractions. The process of multiplication involves repeated addition of the same number multiple times, as for example, adding 5 three times results in 5 + 5 + 5 = 15.

y + x = -4/5

y = -4/5 - x

y = -1/5(4 +x)

y = -1/5(x + 4)

Thus, by multiplying the factors, y + x = -4/5 in y-intercept form is y = -1/5(x + 4).

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Complete question:

y + x = -4/5

Simplify your answer in y-intercept form

The approximate solution of the linear system represented by the graph is, (5, 6)

The equation of a straight line is a relationship between x and y coordinates, The general equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept.

Given that,

A graph in which two lines are intersecting each other,

basically solution of linear system means where both the lines will intersect,

So, in the graph it can be seen that lines are intersecting around x coordinate 5 and y coordinate 6,

Therefore, the solution is (5, 6)

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Answer:

To find the volume of a prism, use the formula V = A * h, where A is the area of the base of the prism and h is its height. For example, for the first prism, the area of the base is 8 and the height is 4, so the volume is 8 * 4 = 32. For the second prism, the area of the base is 6 and the height is 9, so the volume is 6 * 9 = 54. The first prism has a volume of 32 and the second prism has a volume of 54.

The conclusions are listed below:

In this question we find five cases related to lines, whose features can be inferred from following equation:

y = m · x + b

Where:

Please notice that line rises when m > 0, is horizontal when m = 0, falls when m < 0 and is vertical when m is undefined.

Slope can be determined by secant line formula:

m = Δy / Δx

In addition, two lines are parallel when they share the same slope.

Part 1 - The slope of the line passing through two points is:

m = (6 - 1) / (10 - 4)

m = 5 / 6

The slope of the line indicates that it rises.

Part 2 - First, write the slope of the parallel line:

m = 0

Second, calculate the y-intercept from equation of the line:

b = 7 - 0 · 4

b = 7

Third, write the equation of the parallel line:

y = 7

Part 3 - First, determine the slope of the line:

m = (4 - 0) / [0 - (-3)]

m = 4 / 3

Second, calculate the intercept of the line:

b = y - m · x

b = 4 - m · 0

b = 4

Third, write the equation of the line:

y = (4 / 3) · x + 4

Part 4 - First, write the slope of the line:

m = 12

Second, determine the y-intercept of the equation of the line:

b = y - m · x

b = 4 - 12 · 0

b = 4

Third, write the equation of the line:

y = 12 · x + 4

Part 5 - According to secant line formula, undefined slope indicates a vertical line, that is, a line parallel to y-axis.  

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(a) P(A | B) = P(A and B) / P(B) = 249 / 966 = 0.257

(b) P(A' I B) = P(B) - P(A and B) = 966 - 249 = 717

(c) P(A | B') = P(A and B') / P(B') = (4343 - 249) / (22265 - 966) = 3993 / 21399 = 0.187

(d) P(B | A) = P(A and B) / P(A) = 249 / 989 = 0.252

(a) P(A | B) = P(A and B) / P(B) = 249 / 966 represents the probability of a visit resulting in LWBS given that the visit was to hospital 4. The numerator is the number of visits to hospital 4 that resulted in LWBS, and the denominator is the total number of visits that resulted in LWBS at any hospital.

(b) P(A' I B) = P(B) - P(A and B) represents the probability of a visit resulting in LWBS given that the visit was NOT to hospital 4. The numerator is the total number of visits that resulted in LWBS at any hospital minus the number of visits to hospital 4 that resulted in LWBS, and the denominator is not needed because it is a constant (1).

(c) P(A | B') = P(A and B') / P(B') represents the probability of a visit being to hospital 4 given that the visit did NOT result in LWBS. The numerator is the number of visits to hospital 4 that did NOT result in LWBS, and the denominator is the total number of visits that did NOT result in LWBS at any hospital.

(d) P(B | A) = P(A and B) / P(A) represents the probability of a visit resulting in LWBS given that the visit was to hospital 4. The numerator is the number of visits to hospital 4 that resulted in LWBS, and the denominator is the total number of visits to hospital 4.

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Answer:

yes what do you need help with

Answer:

  29.54 m

Step-by-step explanation:

You want the side opposite the 33.6° angle in a triangle that is 36 m between its 33.6° angle and its 104° angle.

In order to use the law of sines to find an unknown side opposite a given angle, we must have a known angle opposite a known side. The known side is opposite the third angle of the triangle, whose measure is ...

  180° -104° -33.6° = 42.4°

Now, we can use the law of sines:

  pole height/sin(33.6°) = (36 m)/sin(42.4°)

  pole height = (36 m)·sin(33.6°)/sin(42.4°) ≈ 29.54475 m

  pole height ≈ 29.54 m

Answer:

Step-by-step explanation:

The probability Mrs. Walker will pick all 32 of the first round games correctly is given by:

0.56^32 = 1.56789e-10

To find the probability that Mrs. Walker will pick exactly 8 games correctly in the first round, we can use the binomial formula:

P(x=8) = 32 choose 8 * 0.56^8 * (1-0.56)^(32-8)

Where 32 choose 8 is the number of ways to choose 8 games out of 32.

To find the probability that Mrs. Walker will pick exactly 28 games incorrectly in the first round, we can use the same formula as in 2:

P(x=4) = 32 choose 4 * 0.56^4 * (1-0.56)^(32-4)

Answer:um it dose not show the thing i downloded  the file if u  try again i will anser it for  tho

Step-by-step explanation:

Answer:

The area enclosed by two curves can be found by subtracting the area between one curve and the x-axis from the area between the other curve and the x-axis.

Let's call the x-value where the two curves intersect as X. At X, both y values are equal to 0. Hence, the equation for X is

-x^2 + c = x^2 - c

Solving for x, we get

2x^2 = 2c

x^2 = c

The area between y = -x^2 + c and the x-axis is equal to the area between y = x^2 - c and the x-axis, so the total area is double that, or 2c.

Setting 2c equal to 56, we have:

2c = 56

c = 28

So the value of c for which the area enclosed by the curves y = −x^2 + c and y = x^2 − c is equal to 56 is 28.

Answer:

  1/3

Step-by-step explanation:

You want to find x in a Venn diagram with regions labeled (x(x-5)), x, 2x, and 20, when the total is ε = 100. And you want to know the probability that a British stamp is from the 20th century.

The whole is the sum of the parts:

  ε = x(x-5) +x +2x +20

  100 = x² -2x +20 . . . . . . . . simplify

  81 = x² -2x +1 . . . . . . . . . subtract 19 to make a complete square

  81 = (x -1)²

  9 = x -1 . . . . . . . positive square root

  x = 10 . . . . . . . . add 1

Now we know ...

P(B) = (x +2x)/ε = 30/100 = 0.3

P(T&B) = x/ε = 10/100 = 0.1

The probability that a British stamp is from the 20th century is ...

  P(T|B) = P(T&B)/P(B) = 0.1/0.3

  P(T|B) = 1/3

Answer: A: 9 galloons and then

Step-by-step explanation:

The total surface area of the cardboard in square inches is option B. 6 × 5 × 5.

The area of a three dimensional object on it's outer surface is called the surface area of the object.

From the given figure, there are 6 squares with each square having the side length equals 5 inches.

Area of a square = a × a, where a is the length of a side.

Area of a 5 inch square = 5 × 5

There are total of 6 squares.

Total surface area = 6 × 5 × 5

Hence the total surface area of the given figure is option B. 6 × 5 × 5.

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Here, the degree of the numerator, 2, is equal to the degree of the denominator, 2, so r(x) has a nonzero horizontal asymptote

Asymptote is a line taken in relation to curve. The line is always far apart from the curve irrespective of distance. Taking the definition in sense of curve, then the curve tries to reach this line while moving towards infinity. Horizontal asymptote indicates the behaviour of function at graph edge.

The equation to be considered for formation of horizontal asymptote is y = mx + b, where u is y-axis, m is slope, x is axis and b is constant. If the two values, that are numerator and Denominator are equal, then y = b.

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Answer: P=3360+40t; 4000

Step-by-step explanation: 3560-3360 = 200, 200/5=40, 3360+40t, substitute t=16 to find out 2007 and you get 4000.

Answer:

[tex]\Huge \boxed{\textbf{B. \$33}}[/tex]

Step-by-step explanation:

To solve this problem, we first need to find the daily rental rate for the midsize sedans. Since the luxury sedans rent for $45 per day and their daily rate is 50% greater than the midsize sedans, we can set up the following equation:

[tex]\Large \boxed{\texttt{45 = 1.5 $\times$ Midsize daily rate}}[/tex]

Now, we can solve for the midsize daily rate:

So, the midsize sedans rent for $30 per day. There are 16 midsize sedans (20 total cars - 4 luxury sedans) and 4 luxury sedans. To find the average daily rental fee for all 20 cars, we can use the following formula:

[tex]\Large\boxed{\texttt{Average daily rental fee} = \frac{\texttt{Total rental fees}}{\texttt{Total number of cars}}}[/tex]

The total rental fees can be calculated as follows:

Now, we can find the average daily rental fee:

So, the average daily rental fee for all 20 cars at this agency is $33, which corresponds to option B.

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The equation of the parabola graphed is given as follows:

(x - 3)² = 5(y + 1)

The equation of a vertical parabola is given as follows:

(x - h)² = 4p(y - k)

In which:

The vertex is at the coordinate (3,-1), hence the parameters h and k are given as follows:

h = 3, k = -1.

The directrix is at the coordinate y = -2.25, hence the value of p is obtained as follows:

-1 - p = -2.25

p = 1.25.

Meaning that the equation of the parabola is given as follows:

(x - 3)² = 5(y + 1)

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If vector B is added to vector A and the resultant is a null vector then A and B are equal and have opposite directions

We are given two vectors, vector A and vector B.

Now, vector B is added to vector A and it is said that the resultant of this addition is a null vector. It can be written as

vector B + vector A = 0

It can also be written as

vector A = 0 - vector B

vector A =  - vector B

We can see that the magnitude of both the vectors, vector A and vector B are equal. The minus sign here represents that the direction of vector B is opposite to vector A

Hence, we can conclude that if vector B is added to vector A and the resultant is a null vector then A and B are equal and have opposite directions

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answer: b = 9metres

l = 19metres

Answer:

Dimensions are L=19, w=9, or L=9, w=19

Step-by-step explanation:

Perimeter P=2(L+W)

So,  56=2(L+W)

       28=L+W

        L=28-W

Area         A=L*W

Because A=171, so 171=L*W

Substituting the expressions: put L=28-w, to 171=L*W,

So, 171=(28-W)W

     171=28w-w²

     W²-28W+171=0

      (W-9)(W-19)=0

      W=9, or W=19

We got L=28-W before, so when w=9, put to L=28-W, so, L=19

Dimensions are L=19, w=9, or L=9, w=19

The interquartile range of the given data using R is 13.3

As per the given data,

The midterm scores of an algebra class of 20 students;

69, 84, 52, 93, 81, 74, 89, 85, 88, 63, 87, 64, 67, 72, 74, 55, 82, 91, 68, 77

We have to find the interquartile range using R.

Interquartile Range;-

The interquartile range includes the second and third quartiles or the middle half of your data set (IQR). The range gives the spread of the full data set, whereas the interquartile range gives the range of the middle half of the data set.

Interquartile range = [tex]Q_{3} -Q_{1}[/tex]

[tex]Q_{1}[/tex] is the lower quarter

[tex]Q_{3}[/tex] is the upper quarter

[tex]Q_{2}[/tex] is the median

Here,

[tex]Q_{2}[/tex] = 63 +  [tex]$\frac{87}{2}[/tex]

[tex]Q_{2}[/tex] = [tex]$\frac{150}{2}[/tex]

[tex]Q_{2}[/tex] = 75

[tex]Q_{1}[/tex] = 81 + [tex]$\frac{74}{2}[/tex]

[tex]Q_{1}[/tex] = 77.5

[tex]Q_{3}[/tex] = 74 + [tex]$\frac{55}{2}[/tex]

[tex]Q_{3}[/tex] = 64.5

Then,

Interquartile range = [tex]Q_{3} -Q_{1}[/tex] = - (64 . 5 - 77.5) = 13.3

That is,

The interquartile range for the given data set is 13.3.

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The required steps to show that circle A is similar to circle B are,
1. Dilate circle A by a scale factor of 0.5.
2. Translate circle A using the rule (x − 5, y − 5).

The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by

(x - h)² + (y - k)² = r²

where h, k is the coordinate of the center of the circle on the coordinate plane and r is the radius of the circle.

Here,
Circle A = Center of −2, −2 and a radius of 4,
Circle B = Center of 3, 3, and a radius of 2.

Steps to show circle A is similar to circle B
1. Dilate circle A by a scale factor of 0.5

2. Translate circle A using the rule (x − 5, y − 5)

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