each element in a sequence of binary data is either 1 with probability p or 0 with probability 1 − p. a maximal subsequence of consecutive values having identical outcomes is called a run. for instance, if the outcome sequence is 1, 1, 0, 1, 1, 1, 0, the first run is of length 2, the second is of length 1, and the third is of length 3. (a) find the expected length of the first run. (b) find the expected length of the second run.

To complete the first space on the table, we need to replace g(x) by 7 and solve for x as:

g(x) = -4x - 1

7 = -4x - 1

7 + 1 = -4x - 1 + 1

8 = - 4x

8/(-4) = -4x/(-4)

-2 = x

So, the first space is -2

Then, for the second space, we need to replace x by 0 and calculate g(x) as:

g(x) = -4x - 1

g(x) = -4*0 - 1

g(x) = 0 - 1

g(x) = -1

So, the second space is -1

The third space is calculated as the first one, replacing g(x) by -13 and solving for x:

g(x) = -4x - 1

-13 = -4x - 1

-13 + 1 = -4x - 1 + 1

-12 = - 4x

-12/(-4) = -4x/(-4)

3 = x

So, the third space is 3

Finally, the fourth space is calculated as the second one, replacing x by -1, so:

g(x) = -4x - 1

g(x) = -4*(-1) - 1

g(x) = 4 - 1

g(x) = 3

So, the fourth space is 3

Answer:

x g(x)

-2 7

0 -1

3 -13

-1​ 3

Answer:

The correct answer in each case is:

Step-by-step explanation:

First, to calculate the surface area or the volume you must have all the measures in the same units, for the exercise we're gonna use centimeters and after we can replace the units in the answer if we need, then:

Now, to obtain the surface area of the triangle we're gonna use the next formula:

And we replace the values in centimeters:

To obtain this same value now in square milimeters, you must know:

Now, you must multiply:

To obtain this value now in \(m^{2}\), you must know:

You must divide:

By last, to obtain the volume of the piece of cake, you can use the next formula:

And we replace the surface area in \(cm^{2}\) because the answer must be in \(cm^{3}\):

The least expensive computer after the 20% discount would be $400.

To calculate the price of the least expensive computer after the 20% discount, we need to find 20% of the original price and subtract it from the original price.

Let's assume the original price of the least expensive computer is x. The discount of 20% can be calculated as 0.20 * x. To find the discounted price, we subtract the discount from the original price: x - 0.20 * x = 0.80 * x.

Since we know that the cost of the least expensive computer ranges from $500 to $1000, we can substitute x with $500 and calculate the discounted price: 0.80 * $500 = $400. Therefore, the least expensive computer after the 20% discount would be $400.

To learn more about discounted price, click here: brainly.com/question/14690858

#SPJ11

Answer:

\(\\\sf7x^3 - 2x^2 - 5\)

Step-by-step explanation:

\(\\\sf(6x^3 + 3x^2 - 2) + (x^3 - 5x^2 - 3)\)

Remove parenthesis.

6x^3 + 3x^2 - 2 + x^3 - 5x^2 - 3

Rearrange:

6x^3 + x^3 + 3x^2 - 5x^2 - 2 - 3

Combine like terms to get:

----------------------------------------

More on adding polynomials: https://brainly.com/question/30791478

Hope this helps! :)

Answer:

7x³ - 2x² - 5

Step-by-step explanation:

(6x³ + 3x² - 2) + (x³ - 5x² - 3)

Remove the round brackets.

= 6x³ + 3x² - 2 + x³ - 5x² - 3

Put like terms together.

= 6x³ + x³ + 3x² - 5x² - 2 - 3

Do the operations.

= 7x³ - 2x² - 5

____________

hope this helps!

Answer:

121

Step-by-step explanation:

Number of sides = n = 7

Sum of all the interior angles = (n -2)*180 = (7-2) *180

                                                = 5 *180

                                                = 900

x +  125 + 119 +117 +145 + 133 + 140 = 900

x + 779 = 900

x = 900 - 779

x = 121

Answer:

x = 121°

Step-by-step explanation:

The formula to find the sum of interior angles of a polygon is:

180 ( n - 2 )

Here,

n ⇒ number of sides ⇒ 7

First, let us find the sum of the interior angles of the polygon.

180 ( n - 2 )

180 × ( 7 - 2 )

180 × 5

900°.

Accordingly, let us make an expression to find the value of x.

145 + 133 + 140 + 125 + 119 + 117 + x = 900

Let us solve for x now.

779 + x = 900

Subtract 779 from both sides.

x = 900 - 779

x = 121

Answer:

s = -0.75

Step-by-step explanation:

Answer:

$0.65

Step-by-step explanation:

$0.40 + $0.25 = $0.65

Answer:

0.40p+0.25a=cost

Step-by-step explanation:

Considering that every apple costs 25 cents and every pear costs 40 cents, you would multiply how many apples and or pears there are by how much they are worth and then add it to get the total cost. Due to there not being a specific total or how many apples and/or pears there are, it currently can't be solved.

Answer:

The file contains the solution to the question

Answer:

equation: x/8 = 11

solution: 88

Step-by-step explanation:

Let our unknown number be the variable, x. Since we're dividing x by 8, we can rewrite it into these expressions: x/8 or x ÷ 8. Because x divided by eight equals eleven, we can translate it into this equation: x/8 = 11, or x ÷ 8 = 11.

To solve for the equation x/8 = 11, let's multiply each side by 8 so we can isolate the variable, x.

x/8 ⋅ 8 = 11 ⋅ 8

x = 88

Now that we've completed multiplying each side by 8, you can see that x = 88, meaning that the unknown number is 88.

Answer:

88

Step-by-step explanation:

Equation: 88/8

Solution: 11

The proof that ΔRST is congruent to ΔQUT is given below.

Two or more triangles are said to be congruent if and only if sides and angles of one triangle is equal to the corresponding sides and angles of another triangle.

1. It is given that ΔQRT is equilateral. So all the sides and angles are of equal measure.

2. Given ∠TQU ≅ ∠SRT

3. Given sides QU ≅ RS

4. Then since sides QT and RT are side of equilateral triangle ΔQRT, they are equal .

So sides QT ≅ RT

5. So we have, two sides and included angle of ΔRST is equal to corresponding two sides and included angle of ΔQUT.

By SAS Congruence Theorem, both the triangles ΔRST and ΔQUT are congruent to each other.

Hence completed the proof using SAS Congruence theorem.

Learn more about Congruence of Triangles here :

https://brainly.com/question/20521780

#SPJ1

The answer of the given figure is ∠B = 72° and ∠C = 108°

In geometry, corresponding angles are pairs of angles that have the same relative position and the same degree of rotation, in two different geometric figures that are being compared.

More specifically, when two lines are crossed by another line, the angles on one side of the crossing line that are in the same relative position to each other (i.e., they are on the same side of the crossing line and are either both interior angles or both exterior angles), are corresponding angles.

According to question

∠CFE = 72°

In given diagram

DC ║ EF ║ AB and CB is transversal

∴ ∠CFE + ∠BFE = 180° ( Linear pair )

72° + ∠BFE = 180°

∠BFE = 180 - 72

∠BFE = 108°

∵∠DCF = ∠BFE ( Corresponding equal angle )

∠DCF = 108°

∠C = 108°

∠CFE = ∠B (  Corresponding equal angle )

72° = ∠B

∴∠B = 72°

Hence, the ∠B = 72° and ∠C = 108°

Learn more about  Corresponding angle here

https://brainly.com/question/1597341

#SPJ1

Answer:

Its D, 15 x __ = 180

Step-by-step explanation:

Answer: Annie made a mistake in step 1 by plotting the point (1, -3) instead of (1, 0) which is the x-intercept of the given equation.

Step-by-step explanation:

She should have used the x-intercept of the equation instead of just any point.

To fix her mistake, Annie should find the x-intercept of the equation by setting y to 0, and solve for x. Then she can plot the point (1,0) and proceed with step 2 and 3.

A hypothesis is an informed prediction regarding the solution to a scientific topic that is supported by sound reasoning.

1. The 95% confidence interval for the difference in mean BPM between smokers and non-smokers based on the provided data is -3.3 BPM 10.9 BPM. The mean BPMs of smokers and non-smokers do not differ considerably, however this cannot be said with certainty because the confidence interval includes both positive and negative values.

2. It cannot be said with certainty whether group smokers or non-smokers had higher mean BPM based only on the confidence interval because it contains both positive and negative values. As a result, it is unclear whether the group's mean BPM was greater in the sample.

3. The null hypothesis can not be ruled out as per confidence interval, which contains both positive and negative numbers. According to null hypothesis, there is no discernible difference among smokers and non-smokers in terms of mean BPM. Thus, the conclusion will be that there is insufficient data to support the notion that smoking and non-smoking have significantly different mean BPMs.

4. If null hypothesis is correct,  p-value indicates likelihood of receiving a result that is as extreme to or more extreme than the observed result. The precise value of p-value can not be identified since it is not included the given information. It would be necessary to determine the p-value using the proper statistical test, such as a t-test or a z-test, in order to determine if the observed difference is statistically significant.

Read more about hypothesis on:

https://brainly.com/question/26185548

#SPJ4

Answer:

\(x = \sqrt{3 \frac{ - 1}{3} } \)

Answer:

d. solve for 'y' in the second equation

The first step is to solve for 'y' after that you will substitute it in the next step ie when using substitution method.

The exact value of secθ in simplest radical for is 1.083

Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.

We are Given θ is an angle in standard position.

Its terminal side passes through the point (12, -5).

To find the exact value of secθ in simplest radical form.

When θ is an angle in standard position and its terminal side passes through the point (x,y), then the exact value of secθ is:

So, we have x = 12 and y = -5 which is in the first quadrant.

Therefore,

r² = x² + y²

r² = ( 12 )² + ( -5 )²

r² = 144 + 25

r² = 169

r = 13

Then,

sec θ = 1/cosθ

sec θ = [ 1/(x/r) ]

sec θ = r/x

sec θ = 13/12

sec θ = 1.083

Learn more about trigonometric;

https://brainly.com/question/21286835

#SPJ1

Answer:

4 shirts and 12 pants

Step-by-step explanation:

10x + 15y = 220

x + y = 16

4 * 10 = 40

12 * 15 = 180

40 + 180 = 220

Answer:1,401.259

Step-by-step explanation:

Answer:

21881

Step-by-step explanation:

23,259-659=22600-264=22336-455=21881

Triangles are similar by SSS rule.

The triangle similarity rule states that if two triangles have corresponding angles that are congruent, then the triangles are similar. This means that their corresponding sides are proportional in length. More formally, if two triangles ABC and DEF are similar, then:

The corresponding angles are congruent: ∠A ≅ ∠D, ∠B ≅ ∠E, ∠C ≅ ∠F.

The corresponding sides are proportional: AB/DE = BC/EF = AC/DF.

Similar triangles can also be used to find the height of tall objects or the distance between two objects of known height, using the angle of elevation and the properties of similar triangles.

In the Triangle ABC and CDA;

AB=CD(Given)

BC=AD(Given)

AC=AC(sides are common)

Hence,  Triangles are similar by SSS rule.

To know more about congruent, visit:

https://brainly.com/question/12413243

#SPJ1

Answer:

−32

Step-by-step explanation:

(−2)^4(−2)

=(16)(−2)

=−32

Answer:

The answer is -32

Step-by-step explanation:

I just did it.

The magnitude of the resultant displacement vector is ________ (provide the calculated value).

The direction of the resultant displacement vector is ________ (provide the calculated direction).

To find the magnitude and direction of the resultant displacement vector using the graphical method, we can use the Pythagorean theorem and trigonometry.

Draw a scale diagram representing the initial and final positions of the pedestrian.

Measure the lengths of the east and north displacements on the diagram.

The east displacement is 6.00 units.

The north displacement is 13.0 units.

Use the Pythagorean theorem to find the magnitude of the resultant displacement vector:

Resultant displacement = √(east displacement^2 + north displacement^2)

Substitute the measured values into the equation and calculate the magnitude.

Use trigonometry to find the direction of the resultant displacement vector:

Direction = arctan(north displacement / east displacement)

Substitute the measured values into the equation and calculate the direction.

Note: Make sure to consider the appropriate quadrant for the direction.

The magnitude of the resultant displacement vector can be calculated using the Pythagorean theorem, and the direction can be found using trigonometry. By substituting the given values into the equations, we can determine the magnitude and direction of the resultant displacement vector using the graphical method.

To learn more about trigonometry, visit

brainly.com/question/13729598

#SPJ11

Answer:

The rule is. the nth term  aₙ is given by

aₙ = n² + 1

Step-by-step explanation:

The following is the summary of n, aₙ

n            aₙ      In terms of n

1             2        1² + 1

2            5        2² + 1

3            10       3² + 1

4            17        4² + 1

5            26       5² + 1

6            37       6² + 1

So the nth term is given by
n² + 1

Answer:

Step-by-step explanation:

diameter = 3.7

radius = diameter/2

=3.7/2

=1.85

area of circle = πr^2

=π*(1.85)^2

=3.4225π m^2

The travel time through the block is affected by the angle of incidence, as a slightly larger angle will increase the travel time.

(a) To find the angle of refraction, θ₁, we can use Snell's Law, which states that the ratio of the sines of the angles of incidence and refraction is equal to the ratio of the indices of refraction:

\(n_1\) * sin(θ₁) = \(n_2\) * sin(θ₂)

Plugging in the values:

1 * sin(3.25°) = 1.22 * sin(θ₂)

Solving for θ₂:

θ₂ = sin⁻¹(sin(3.25°) / 1.22)

Using a calculator, we find θ₂ ≈ 2.51° (rounded to two decimal places).

(b) Since the upper and lower surfaces of the glass are parallel, the angle of incidence at the bottom of the glass, θ₃, will be equal to the angle of refraction, θ₂:

≈ 2.51°

(c) To find the angle of refraction, θ₄, as the light ray emerges from the bottom of the glass, we can use Snell's Law again:

n₂ * sin(θ₃) = n₁ * sin(θ₄)

Plugging in the values:

1.22 * sin(2.51°) = 1 * sin(θ₄)

Solving for θ₄:

θ₄ = sin⁻¹((1.22 * sin(2.51°)) / 1)

Using a calculator, we find θ4 ≈ 3.19° (rounded to one decimal place).

(d) The distance, d, can be calculated using the formula for the shortest side of a right triangle:

Given: thickness of the glass = 2.00 cm, θ₁ = 3.25°, and θ₂ ≈ 2.51°

Plugging in the values:

d = 2.00 cm * tan(3.25° - 2.51°)

Using a calculator, we find d ≈ 0.40 cm (rounded to two decimal places).

(e) The speed of light within the glass can be calculated using the formula:

speed of light in air / speed of light in glass = \(n_2 / n_1\)

Given: speed of light in air ≈ 3.00 x 10⁸ m/s

Plugging in the values:

speed of light in glass = (3.00 x 10⁸ m/s) / 1.22

Using a calculator, we find the speed of light in glass ≈ 2.46 x 10⁸ m/s.

(f) To find the time taken by light to pass through the glass along the angled path, we need to calculate the distance traveled and then divide it by the speed of light in glass.

Given: thickness of the glass = 2.00 cm and θ₄ ≈ 3.19°

Distance traveled = thickness of the glass / cos(θ₄)

Plugging in the values:

Distance traveled = 2.00 cm / cos(3.19°)

Using a calculator, we find the distance traveled ≈ 2.01 cm.

Time taken = Distance traveled / speed of light in glass

Plugging in the values:

Time taken\(= 2.01 cm / (2.46 * 10^8 m/s)\)

Converting cm to m:

Time taken\(= (2.01 * 10^{-2} m) / (2.46 * 10^8 m/s)\)

Using a calculator, we find the time taken \(= 8.17 x 10^{-11} seconds.\)

(a) The travel time through the block is affected by the angle of incidence. A slightly larger angle will increase the travel time.

To know more about travel time,

https://brainly.com/question/20947360

#SPJ11

The minimized SOP expression for F(A,B,C,D,E) using a five-variable Karnaugh map is D'E' + BCE'. A five-variable Karnaugh map is a graphical tool used to simplify Boolean expressions.

The map consists of a grid with input variables A, B, C, D, and E as the column and row headings. The cell entries in the map correspond to the output values of the logic function for the respective input combinations.

To find the minimized SOP expression, we start by marking the cells in the Karnaugh map corresponding to the minterms given in the function: 2m(4,5,6,7,9,11,13,15,16,18,27,28,31). These cells are identified by their binary representations.

Next, we look for adjacent marked cells in groups of 1s, 2s, 4s, and 8s. These groups represent terms that can be combined to form a simplified expression. In this case, we find a group of 1s in the map that corresponds to the term D'E' and a group of 2s that corresponds to the term BCE'. Combining these groups, we obtain the expression D'E' + BCE'.

The final step is to check for any remaining cells that are not covered by the combined terms. In this case, there are no remaining cells. Therefore, the minimized SOP expression for the given logic function F(A,B,C,D,E) is D'E' + BCE'.

Learn more about combinations here: https://brainly.com/question/29595163

#SPJ11

Answer:

The price decreased by 12.5%

Step-by-step explanation:

150/120 = 1.25

1.25 x 10 = 12.5

Based on the results of the t-test, we can draw a conclusion regarding the validity of the dean's claim.

To find the probability that 25 randomly selected graduates have an average daily income of less than 550 pesos, we need to use the Central Limit Theorem (CLT) since we are dealing with sample means.

The CLT states that the distribution of sample means tends to follow a normal distribution as the sample size increases, regardless of the shape of the original distribution, under certain conditions. One of these conditions is that the sample size is sufficiently large (usually considered as n ≥ 30).

Given:

Population mean (μ) = 600 pesos (according to the dean's claim)

Standard deviation of the population (σ) = 100 pesos (given)

Sample size (n) = 25

To calculate the probability, we need to standardize the average daily income using the formula for the standard error of the mean:

Standard Error (SE) = σ / sqrt(n)

SE = 100 / sqrt(25)

SE = 100 / 5

SE = 20

Now, we can calculate the z-score, which represents how many standard errors the desired value is away from the mean:

z = (x - μ) / SE

z = (550 - 600) / 20

z = -50 / 20

z = -2.5

Using a standard normal distribution table or a calculator, we can find the probability associated with the z-score of -2.5. The probability is the area to the left of the z-score.

P(Z < -2.5) ≈ 0.0062

Therefore, the probability that 25 randomly selected graduates have an average daily income of less than 550 pesos is approximately 0.0062 or 0.62%.

If random samples of 25 graduates had an average daily income of 550 pesos, we can compare it to the dean's claim of an average daily income of 600 pesos.

In this case, we can use hypothesis testing to assess the validity of the dean's claim. We can set up the null hypothesis (H0) as the dean's claim being true (μ = 600 pesos) and the alternative hypothesis (Ha) as the dean's claim being false (μ ≠ 600 pesos).

We can then conduct a t-test using the given sample mean, the population standard deviation (100 pesos), the sample size (n = 25), and the significance level (usually α = 0.05).

If the t-test results in a p-value that is smaller than the significance level (α), we reject the null hypothesis and conclude that there is evidence to suggest that the dean's claim is not valid.

However, if the p-value is greater than α, we fail to reject the null hypothesis, and we do not have enough evidence to conclude that the dean's claim is incorrect.

Therefore, based on the results of the t-test, we can draw a conclusion regarding the validity of the dean's claim.

Learn more about probability here:

https://brainly.com/question/32004014

#SPJ11

(a) The values of f(0) = 3 and g(2) = 2.

(b) The values of x for which f(x) = g(x) are -2, 2.

(c) The solutions of the equation f(x) = −1 are x = -3, 4.

(d) The interval on which f is decreasing is [0, 4].

(e) The domain and range of f are:

domain = [-4, 4].

range = [-2, 3].

(f) The domain and range of g are:

domain = [-4, 3].

range = [-0.5, 4].

In Mathematics and Geometry, a function is an equation which defines and represents the relationship that exist between two or more variables.

Part a.

By critically observing the graph of f(x) and g(x) shown in the image attached below, the corresponding output values are as follows:

f(0) = 3.

g(2) = 2.

Part b.

The values of x for which f(x) is equal to g(x) are x = -2 and x = 2;

f(-2) = g(-2) = 1.

f(2) = g(2) = 2.

Part c.

The estimated solutions of the equation f(x) = −1 are as follows;

f(-3) = -1

f(4) = -1

Therefore, x = -3, 4.

Part d.

The function f(x) is decreasing over this interval [0, 4].

Part e.

By critically observing the graph of f(x) shown in the image attached below, we can logically deduce the following domain and range:

domain = [-4, 4].

range = [-2, 3].

Part f.

By critically observing the graph of g(x) shown in the image attached below, we can logically deduce the following domain and range:

domain = [-4, 3].

range = [-0.5, 4].

Read more on domain here: brainly.com/question/9765637

#SPJ4

Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

A.

E.

F.

Step-by-step explanation:

Those are the three points connected on the triangle.

Answer:D. LMD

Step-by-step explanation: