A number cube is rolled twice. what is the probability of getting a six on the first role, then a number less than 5 on the second roll?

Critical angle for the total internal reflection icrit, β =  78.28⁰

Critical angle for the total internal reflection crit, α = 17,22⁰

We have the refractive index of core, \(n_c_o_r_e\) = 1.46

We have the refractive index of clad , \(n_c_l_a_d\) = 1.4

Critical angle can be defined as the incidence angle which results in the refraction angle being equal to  at that angle of incidence.

For Total Internal Reflection to occur, the incidence angle must be greater than the critical angle.

We know that the critical angle, θ is given by:

sinθ = \(\frac{n_c_l_a_d}{n_c_o_r_e}\)

sinθ = \(\frac{1.4}{1.46}\)

sinθ = 0.959 = sin⁻¹(0.979) = 78.28⁰

β = θ = 78.28⁰

Now, for α:

\(\frac{sin(90-\alpha )}{sin\alpha } = \frac{1}{n_c_o_r_e}\)

sinα = sin(90⁰-78.28⁰) × 1.46

sinα = sin(11.72⁰) × 1.46

α = sin⁻¹(0.296)

α = 17,22⁰

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Critical angle for total internal reflection icrit β = 78.28⁰

Critical angle for total internal reflection crit, α = 17.22⁰

The refractive index of the core is ncore = 1.46.

The refractive index of clad is nclad = 1.4.

We know that the critical angle, θ is given by:

sinθ = nclad/ ncore

sinθ = 1.4/1.46

sinθ = 0.959

sin⁻¹(0.979) = 78.28⁰

β = θ = 78.28⁰

Now, for α:

sin(90- α) / sin α = 1 / ncore

sinα = sin(90⁰-78.28⁰) × 1.46

sinα = sin(11.72⁰) × 1.46

α = sin⁻¹(0.296)

α = 17.22⁰

Critical angle for icrit β = 78.28⁰

Critical angle for crit α = 17.22⁰

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Answer:

A

Step-by-step explanation:

The answer is A, because if you see the function when x is less than 1, it's the function 2x, and when x is greater than or equal to 1, it's the function 1/2*x+5/2

The probability of success, p, is the same for each trial. Each outcome is either a success (P) or a failure (Q). The correct option is A.

Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes.

You should perform x trials until you observe a success.

We have given that,

There are exactly two possible outcomes success and failure.

We have to determine the following is NOT a common characteristic of a binomial distribution.

By process of elimination:-

A binomial experiment is a statistical experiment that must meet certain requirements

All trials are independent.

There are a fixed number of n trials.

The probability of success, p, is the same for each trial.

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Option (A) Names of TV shows taped in New York are an example of qualitative data. Qualitative data is descriptive in nature and does not involve numerical values or measurements.

It deals with qualities or attributes that cannot be expressed numerically. In this case, the names of TV shows are characteristics that describe the nature of the data. Quantitative data, on the other hand, is numerical data that can be measured and expressed in numbers. A parameter is a measurable factor or variable that can be used to define a system, while statistics is a branch of mathematics that deals with data collection, analysis, and interpretation. In conclusion, since the names of TV shows are descriptive in nature and do not involve numerical values, they are an example of qualitative data.

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Answer:

18.445

Step-by-step explanation:

Multiply

The rate of change of the function is h(t)=7(t−25)

According to the question, it takes 7 joules of heat to raise the temperature of the bar 1∘C with the initial temperature of the bar is

25∘C.

Let us assume the heat

h(t) is the heat required to raise the temperature to t∘C. Then the function can be given as :

h(t)=7(t−25)

The table that shows the joules of heat would be required to raise the temperature of the gold bar to

26∘C,27∘C,28∘C,29∘C,30∘C,and  35∘C.

Temprature

degree Celcius Heat

Joules

26                               7

27                                 14

28                               21

29                               28

30                               35

35                                  70

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Answer:

Step-by-step explanation:

g(x)= x - 3

f(x - 3) = (x - 3)^2 = x^2 - 6x + 9

for the different values of x, we have found the values of the function f (x) = x² + 2 x + 1.

We are given the function:

f (x) = x² + 2 x + 1

We need to complete the given table of values for x and f (x)

For x = - 3:

f (- 3) = (- 3)² + 2 (- 3) + 1

f (- 3) = 9 - 6 + 1

f (- 3) = 4

For x = - 2:

f (- 2) = (- 2)² + 2 (- 2) + 1

f (- 2) = 4 - 4 + 1

f (- 2) = 1

For x = - 1:

f (- 1) = (- 1)² + 2 (- 1) + 1

f (- 1) = 1 - 2 + 1

f (- 1) = 0

For x = 0:

f (0) = (0)² + 2 (0) + 1

f (0) = 0 + 0 + 1

f (0) = 1

For x = 1:

f (1) = (1)² + 2 (1) + 1

f (1) = 1 + 2 + 1

f (1) = 4

For x = 2:

f (2) = (2)² + 2 (2) + 1

f (2) = 4 + 4 + 1

f (2) = 9

For x = 3:

f (3) = (3)² + 2 (3) + 1

f (3) = 9 + 6 + 1

f (2) = 16

Table:

x     - 3      - 2      - 1      0      1      2      3

y       4         1        0      1      4      9     16

Therefore, for the different values of x, we have found the values of the function f (x) = x² + 2 x + 1.

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Answer:

la respuesta es 28 porque 32 dividido por 112 es 28

In a Venn diagram, we illustrate the relationships between sets a, b, and c, specifically the relationships a ⊂ b (a is a subset of b) and a ⊂ c (a is a subset of c).

A Venn diagram is a visual representation of sets using overlapping circles. In this case, we have three sets: a, b, and c. To illustrate the relationship a ⊂ b, we draw a circle representing set b and a smaller circle inside it representing set a. This indicates that every element in a is also an element of b, but b may contain additional elements that are not in a. The subset a is completely contained within set b. Similarly, to represent the relationship a ⊂ c, we draw a circle representing set c and a smaller circle inside it representing set a. This indicates that every element in a is also an element of c, but c may contain additional elements that are not in a. The subset a is completely contained within set c. By using the Venn diagram, we visually demonstrate the relationships between sets a, b, and c. The diagram clearly shows that a is a subset of both b and c, indicating that all elements of a are also elements of b and c. However, b and c may have additional elements that are not in a.

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Elena's yearly cash inflows from the project after the payback period is $15,000. A correct answer is an option (b).

The payback period is the time it takes for the project's cash inflows to equal the initial investment. In this case, the payback period is 6 years, meaning that after 6 years, Elena will have received enough cash inflows to recover her initial investment of $150,000.

Since the project pays Elena an even amount per year for 10 years, and the payback period is 6 years, she will receive cash inflows for an additional 4 years after the payback period. Therefore, to calculate Elena's yearly cash inflows, we divide the remaining cash inflows by the number of years remaining:

Remaining cash inflows = $150,000 (initial investment) - cash inflows received during the payback period

= $150,000 - ($15,000 x 6)

= $60,000

Yearly cash inflows = Remaining cash inflows/number of years remaining

= $60,000 / 4

= $15,000

Hence, B is the correct option.

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That a full cut round brilliant diamond with a 6.50 mm girdle diameter typically weighs around 1.00 carat.

carat weight is determined by a combination of a diamond's size and density. A diamond's size is measured by its diameter, which is the distance across the widest part of the diamond, known as the girdle. Therefore, a diamond with a larger girdle diameter will generally weigh more than a diamond with a smaller diameter, assuming all other factors are equal.

the weight of a diamond can be estimated based on its girdle diameter, and a full-cut round brilliant diamond with a 6.50 mm girdle diameter typically weighs around 1.00 carat. However, it's important to note that other factors, such as depth, cut, and clarity, can also affect a diamond's weight and value.

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Answer:

The answer is below

Step-by-step explanation:

The scale for the drawing is 1 inch = 40 feet.

The right angled triangle has legs of 3 inches and 4 inches. Using the scale, the length of the legs is:

3 inches = 3 inch * 40 feet / inch = 120 feet and 40 inches =  4 inch * 40 feet / inch = 160 feet.

The area of a right angled triangle is half the product of the two legs. Hence:

Area of right angled triangle = 1/2 * 120 feet * 160 feet = 9600 ft²

The rectangle with dimensions of 1.5 inches and 2.5 inches. Using the scale, the length of the sides is:

1.5 inches = 1.5 inch * 40 feet / inch = 60 feet and 2.5 inches =  2.5 inch * 40 feet / inch = 90 feet.

The area of a rectangle is the product of the two sides. Hence:

Area of rectangle = 60 feet * 90 feet = 5400 ft²

Answer:

i think it's true

Step-by-step explanation:

Answer:

with a line accross the points

Solution:

Note that:

Divide the length of the court by 2x to find the width of the court.

\(\\ \rm\hookrightarrow 6x^2+20x=2x\)

\(\\ \rm\hookrightarrow 6x^2=-18x\)

\(\\ \rm\hookrightarrow x^2=-3x\)

\(\\ \rm\hookrightarrow x=-3\)

Answer:

B, C, E

Step-by-step explanation:

The solution of the inequality is x ≤ -7

The graph would have a closed circle because it's less than or equal to

-7 is a part of the solution because it's less than or equal to -7

Answer:

Step-by-step explanation:

Subtract 22 from both sides to get \(x\leq -7\). So the 2nd one is correct

The sign is less than or equal to, so the graph does indeed have a closed circle. So the 3rd one is also correct

The answer is x is less than or EQUAL to -7, so -7 is included in the asnwer. So the 5th one is also correct

Answer:

x = 25

y = 6

Step-by-step explanation:

In a parallelogram, opposite angles are equal.

2x and 50 are opposite angles,

2x = 50

Divide 2 on both sides,

x = 50 / 2

x = 25

In a parallelogram opposite sides are equal.

y + 5 and 11 are opposite sides,

y + 5 = 11

y = 11 - 5

y = 6

Answer:

x=25

y=6

Step-by-step explanation:

from the diagram,

2x= 50(opposite angles of a parallelogram)

2x= 50

dividing bothsides by 2

2x/2=50/2

x= 25

then,

y+5=11(opposite sides of a parallelogram)

y= 11-5

y= 6

You have to do 10.98+4.06

i would split this into 2 parts so i would get 10+4 and 0.98+0.06

10+4=14

0.98+0.06= 1.04

then we add 14 to 1.04

14+1.04=15.04

So your answer would that Emilys journey is 15.04km in total

Answer:

To complete the square for the equation -5x² + 10x = -315, we can follow these steps:

Move the constant term (-315) to the right side of the equation:

-5x² + 10x + 315 = 0

Divide both sides of the equation by the coefficient of the x^2 term (-5) to get a coefficient of -1 for the x^2 term:

x² - 2x - 63 = 0

Add the square of half the coefficient of the x term to both sides of the equation:

x² - 2x + 1 - 1 - 63 = 0 + 1

Simplify the left side of the equation by factoring the quadratic trinomial and combining like terms:

(x - 1)² - 64 = 1

Add 64 to both sides of the equation:

(x - 1)² = 65

So the intermediate step in completing the square for -5x² + 10x = -315 is:

(x - 1)² - 64 = 1

This is the result of adding the square of half the coefficient of the x term (-1) to both sides of the equation and simplifying.

well, since the y-intercept is at -5, or namely when the line hits the y-axis is at -5, that's when x = 0, so the point is really (0 , -5), and we also know another point on the line, that is (-1 ,6), to get the equation of any straight line, we simply need two points off of it, so let's use those two

\(\stackrel{y-intercept}{(\stackrel{x_1}{0}~,~\stackrel{y_1}{-5})}\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{6}-\stackrel{y1}{(-5)}}}{\underset{run} {\underset{x_2}{-1}-\underset{x_1}{0}}} \implies \cfrac{6 +5}{-1} \implies \cfrac{ 11 }{ -1 } \implies - 11\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-5)}=\stackrel{m}{- 11}(x-\stackrel{x_1}{0}) \implies y +5 = - 11 ( x -0) \\\\\\ y+5=-11x\implies {\Large \begin{array}{llll} y=-11x-5 \end{array}}\)

Answer:

42.50 = 8.50p

Solution of the equation : p = 5

The can buy 5 pizza.

Step-by-step explanation:

Given;

Total cost allocated for buying pizza C = $42.50

Cost of one pizza c = $8.50

Number of pizza they can buy = p

This can be expressed in an equation as;

Total cost = cost per pizza × number of pizza

C = pc

Substituting the values of C and c;

42.50 = 8.50p

We can solve the derived equation for p;

p = 42.50/8.50

p = 5

Answer:

AAS

Step-by-step explanation:

\(\overline{PR} \cong \overline{PR}\) by the reflexive property.

Answer:

439.8 ft²

Step-by-step explanation:

Answer:

Okay! So for this we need to realize a few things!

First the triangle CDE is an Isosceles triangle, thus two of the side angles (the non \(x\)) are the same value! That means that angle:

\(<ECD = <CED = 36\)°

Which means that:

\(x = (180-2*36)=108\)°

Now that we know what angle ECD is, we know that angle BCE is equal to:\(180-<ECD = 180-36=144\)°

Lastly we know that angle \(<ABF = <BCE\) are similar due to parallel lines, thus:

\(<ABF = <BCE = 144\)°.

Therefore:

\(x=108\)°

\(y=144\)°

Answer:

EZ. Btw you kinda already did it. 2/7 is a division problem. Another way is 2 divided by 7

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given the inequality expression |x| < a. The two cases for solving the expression are x<a and -x < a (or x>-a)

Note that the absolute value of a number will return both its positive and negative value. That's why the value of x i.e |x| returns both x and -x in the expression above.

The connecting word of the expression is that 'the absolute value of variable x is less than a' where a can take any value.

Answer:

p = 9

Step-by-step explanation:

\(\frac{3}{4}\) (p - 1) = p - 3 ( multiply both sides by 4 to clear the fraction )

3(p - 1) = 4p - 12 ← distribute left side

3p - 3 = 4p - 12 ( subtract 3p from both sides )

- 3 = p - 12 ( add 12 to both sides )

9 = p