factor. x^2 - 11x + 30 delta math

The number of days that the second voyage last's is 480 days.

Given,

The discrepancy in the length of the two excursions, we are asked to determine how many days the second voyage lasted.

We initially assign variables in order to overcome this issue. Let the duration of the first cruise be f days and the duration of the second expedition be s days.

We are aware that the first journey lasted 43 days longer than the second.

In mathematics, f = 43 plus s. (I)

The cumulative duration of the two journeys was 1003 days. Mathematically:

f + s = 1003........(ii) (ii)

We transform I into ii

43 + s + s = 1003

43 +2s = 1003

2s = 1003 - 43

2s = 960

s = 960/2 = 480 days

That is,

The second voyage lasted about 480 days

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The researchers are investigating the perception of three-dimensional shapes on computer screens and specifically examining the components of a square figure or cube necessary for viewers to perceive details of the shape. They vary the stimuli to include fully rendered cubes, cubes with incomplete sides, and cubes with missing corner information. Four participants are recruited for an intense study, and their accuracy rates are measured across the three figure conditions. The trials are presented in different orders for each participant using a random-numbers table to determine unique sequences.

In this study, the researchers are interested in understanding how viewers perceive details of three-dimensional shapes on computer screens. They manipulate the stimuli by presenting fully rendered cubes, cubes with incomplete sides, and cubes with missing corner information. By varying these components, the researchers aim to identify which elements are necessary for viewers to accurately perceive the shape.

Four participants are recruited for an intense study, indicating a small sample size. While a larger sample size would generally be preferred for generalizability, intense studies often involve fewer participants due to the time and resource constraints associated with conducting a large number of trials. This approach allows for in-depth analysis of individual participant performance.

The participants are trained on how to detect subtle deformations in the shapes, which suggests that the study aims to assess their ability to perceive and discriminate fine details. After the training, the participants' accuracy rates are measured across the three different figure conditions, likely reported as a percentage of correctly identified shape details.

To minimize potential biases, the trials are presented in different orders for each participant, using a random-numbers table to determine unique sequences. This randomization helps control for order effects, where the order of presenting stimuli can influence participants' responses.

The researchers in this study are investigating the perception of three-dimensional shapes on computer screens. By manipulating the components of square figures or cubes, they aim to determine which elements are necessary for viewers to perceive shape details accurately. The study involves four participants, an intense study design, and measures accuracy rates across different figure conditions. The use of randomization in trial presentation helps mitigate potential order effects.

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Answer:

Step-by-step explanation: here ya go g

Yes, 10 can be replaced by a smaller number. Let's prove it first, then look for a smaller number of people.

Let us write the ages of these 10 people as a1, a2, a3, ... a10.According to the given statement,1 ≤ ai ≤ 60Thus, the age of every individual must be between 1 and 60.

Arrange these ages in a non-decreasing order.

Let's assume that no two groups can have the same sum of ages. Each group has either odd or even numbers of members. Hence, if there are an even number of members in the group, the sum of their ages will also be even. If the group has an odd number of members, the sum of their ages will also be odd.

This means that the 10 people can be divided into five groups, with the sum of the ages of each group being odd or even.

Let us consider two cases:

Case 1:

All five groups have odd sums. This implies that each group has an odd number of members, and the number of members in the group is either 1, 3, or 5. Since there are only 10 people, it is impossible to have five groups with an odd sum of ages. This is because there must be two groups that have the same sum of ages.

Case 2:

Three groups have an even sum, and two groups have an odd sum. This implies that there are two groups with an even number of members and three groups with an odd number of members. Since the ages of each individual are between 1 and 60, the sum of the ages of the members of the group with the most members must be at least 1 + 2 + 3 + 4 + 5 = 15.

Similarly, the sum of the ages of the members of the group with the least members must be at least 1 + 2 = 3. If we remove the members of the two smallest groups, we will be left with 6 members whose ages add up to at least 15 + 3 = 18, which is an even number.

This implies that the remaining three groups must have even sums, which contradicts our assumption that two groups do not have the same sum of ages. This proves that we can always find two groups of people (with no common person) the sum of whose ages is the same. The number 10 can be replaced with a smaller number, for example, 8.

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Answer:

hope this will help you more

Answer:

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

x = 3, x = 2

\(x^2-11x+28\)

x = 7, x = 4

Step-by-step explanation:

One is asked to solve two quadratic equations. Both of these quadratic equations are in standard form. This means that the two equations follow the following general format;

\(ax^2+bx+c\)

The quadratic formula is a method of solving a quadratic equation using the coefficients of the terms in the equation. The quadratic equation is the following,

\(\frac{-b(+-)\sqrt{b^2-4ac}}{2a}\)

Substitute in each of the terms and solve for the roots in each equation;

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

Substitute, and solve

\(\frac{-(-5)(+-)\sqrt{(-5)^2-4(1)(6)}}{2(1)}\\\\=\frac{5(+-)\sqrt{25-25}}{2}\)

\(=\frac{5+1}{2}\)          \(=\frac{5-1}{2}\)

\(=3\)               \(=2\)

\(x^2-11x+28\)

Substitute, and solve

\(\frac{-(-11)(+-)\sqrt{(-11)^2-4(1)(28)}}{2(1)}\\=\frac{11(+-)\sqrt{121-112}}{2}\)

\(=\frac{11+\sqrt{9}}{2}\)           \(=\frac{11-\sqrt{9}}{2}\)

\(=\frac{11+3}{2}\)              \(=\frac{11-3}{2}\)

\(=7\)                     \(=4\)

Given vector field, F(x, y, z) = y cos (xy) i + x cos (xy) j – sin z k To calculate the curl of F, we need to take the curl of each component and subtract as follows,∇ × F = ( ∂Q/∂y - ∂P/∂z ) i + ( ∂P/∂z - ∂R/∂x ) j + ( ∂R/∂x - ∂Q/∂y ) k...where P = y cos(xy), Q = x cos(xy), R = -sin(z)

Now we calculate the partial derivatives as follows,

∂P/∂z = 0, ∂Q/∂y = cos(xy) - xy sin(xy), ∂R/∂x = 0...

and,

∂P/∂y = cos(xy) - xy sin(xy), ∂Q/∂z = 0, ∂R/∂y = 0

Therefore,

∇ × F = (cos(xy) - xy sin(xy)) i - sin(z)j

The curl of F is given by:

(cos(xy) - xy sin(xy)) i - sin(z)j.

To state whether F is conservative, we need to determine if it is a conservative field or not. This means that the curl of F should be zero for it to be conservative. The curl of F is not equal to zero. Hence, the vector field F is not conservative. Let C be the curve joining the origin (0,1,-1) to the point with coordinates (1, 2V2,2) defined by the following parametric curve:

r(t) = n* i + t}j + tcos atk, 15t52.

The curve C is defined as follows,r(t) = ni + tj + tk cos(at), 0 ≤ t ≤ 1Given vector field, F(x, y, z) = y cos(xy) i + x cos(xy)j – sin zk Using the curve parameterization, we get the line integral as follows,∫CF.dr = ∫10 F(r(t)).r'(t)dt...where r'(t) is the derivative of r(t) with respect to t

= ∫10 [(t cos(at))(cos(n t)) i + (n cos(nt))(cos(nt)) j + (-sin(tk cos(at)))(a sin(at)) k] . [i + j + a tk sin(at)] dt

= ∫10 [(t cos(at))(cos(n t)) + (n cos(nt))(cos(nt)) + (-a t sin(at) cos(tk))(a sin(at))] dt

= ∫10 [(t cos(at))(cos(n t)) + (n cos(nt))(cos(nt)) - a^2 (t/2) (sin(2at))] dt

= [sin(at) sin(nt) - (a/2) t^2 cos(2at)]0^1

= sin(a) sin(n) - (a/2) cos(2a)

The vector field F(x, y, z) = y cos(xy) i + x cos(xy)j – sin zk is given. Firstly, we need to calculate the curl of F. This involves taking the curl of each component of F and subtracting. After calculating the partial derivatives of each component, we get the curl of F as (cos(xy) - xy sin(xy)) i - sin(z)j. Next, we need to determine whether F is conservative. A conservative field has a curl equal to zero. As the curl of F is not equal to zero, it is not a conservative field. In the second part of the problem, we have to calculate the scalar line integral of the vector field F. dr along the curve C joining the origin to the point with coordinates (1, 2V2, 2). We use the curve parameterization to calculate the line integral. After simplifying the expression, we get the answer as sin(a) sin(n) - (a/2) cos(2a).

The curl of the given vector field F(x, y, z) = y cos(xy) i + x cos(xy)j – sin zk is (cos(xy) - xy sin(xy)) i - sin(z)j. F is not conservative as its curl is not zero. The scalar line integral of the vector field F along the curve C joining the origin to the point with coordinates (1, 2V2,2) is sin(a) sin(n) - (a/2) cos(2a).

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Answer:

C.20

Step-by-step explanation:

u prob wont give me brainiest but if u would that would be great

Answer:

y=\(\sqrt[3]{x-1}\)

Step-by-step explanation:

y=x^3-1

Switch y and x

x=y^3-1

Solve for y

x-1=y^3

y=\(\sqrt[3]{x-1}\)

Answer:

12.8

Step-by-step explanation:

subtract each leg from the total distance of 37.9. 37.9 - 12.3 - 7.6 - 4.2 = 12.8

Answer:

4

Step-by-step explanation:

This expression is a difference of squares.

(√3 + i)(√3 - i) = (√3)²-(i)², which is

3 - (-1)

= 3 + 1

= 4

The area of the given figure is 12 square meters

The given figure is a parallelogram

Parallelogram is a geometric figure that has both pair of opposites parallel sides and opposite sides are equal . Number of vertices and edges are four

The height of the parallelogram = 2 meters

The base length of the parallelogram = 6 meters

The area of the parallelogram = The height of the parallelogram × The base length of the parallelogram

Substitute the values in the equation

The area of the parallelogram = 2 × 6

Multiply the numbers

= 12 square meters

Therefore, the area is 12 square meters

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I have solved the question in general , as the given question is incomplete

The complete question is :

What is the area of the figure ?

Yes, there are experts here in data forecasting methods who can help you with the topics you've mentioned including time series (holts, holts winter), naive method, regression, acf, pacf, arima, stl method and multivariate time series.

Below are brief explanations of each of these terms:

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The slope of the given graph is determined as 1/3.

The slope of a line is a measure of its steepness of the graph. Mathematically, slope is calculated as rise over run or  change in y divided by change in x.

The formula is given as;

slope = Δy / Δx

where;

The slope of the given graph is calculated as follows;

choose the following coordinate points;

( x₁, y₁) = (-6, 0 )

( x₂, y₂) = ( 6 , 4 )

The slope = ( y₂ - y₁ ) / ( x₂ - x₁)

slope = ( 4 - 0 ) / ( 6 - - 6)

slope = ( 4 ) / ( 12)

slope = 1 / 3

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AS per the permutation concept, the number of ways can Alice win or draw exactly three times is 240

Permutation:

In probability, permutation refers the arrangement of objects in a definite order.

Given,

Alice and Bob are playing a game in which there are several rounds and each round can be a win, a loss, or a draw for Alice.

Here we need to find the number of ways can Alice win or draw exactly three times, if they play 6 rounds.

While we looking into the given question, we know that,

Total number of games = 6

Possible values = 3 ( win, loss, or draw)

Here we need to find the probability of winning 3 times, it can be calculated by using the permutation as,

=> 6! / (6 - 3)!

=> 6! / 3!

=> 120

Similarly, the the probability of draw 3 times, it can be calculated by using the permutation as,

=> 6!/ (6 - 3)!

=> 120

So, the number of ways can Alice win or draw exactly three times is

=> 120 + 120 =  240

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Answer:

y-1=-3(x+2)

Step-by-step explanation:

136.5 percent chance.

91 percent in one hour

how much percent in 1.5 hour?

we need to find how much percentage is in 0.5 hour

91 divided by 2 = 45.5

91 + 45.5 = 136.5

Am i bad? pls tell

Answer:

v×9=99

Step-by-step explanation:

HOPE THAT THIS IS HELPFUL

HAVE A GREAT DAY

Answer:

h=43

Step-by-step explanation:

t=35

35/5 =7

50-7 =43

The standard equation of the circle will be (x+5)²+(y+5)²= 145

The center of the circle, which is the midpoint between those two locations, may be found first since you know the diameter endpoints.

formula for the midpoint

= ((x1+x2)/2, (y1+y2)/2)

Given points are - (3, 4), (−13, −14)

The circle's center is at (-5,-5)

Therefore, the circle's equation will take the form (x+5)²+(y+5)²=R², where R is the circle's radius.

The distance between a point on the circle and the circle's center in order to get the radius.

Therefore, let's calculate the distance between (-5, -5) and (-13,-14)

Radius R = √((-13+5)²+(-14+5)²) using the distance formula.

= 12.04

equation will be -

(x+5)²+(y+5)²= 145

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There were 312 pieces of paper on the bulletin board by the end of the school year.

To find the number of pieces of paper on the bulletin board, we need to calculate the total area covered by the book titles and then divide it by the area of each piece of paper.

Area of the bulletin board: 34 2/3 square feet.

Let's first convert the area of the bulletin board to a fraction:

Area of bulletin board = 34 2/3 = (3 * 34 + 2)/3 = 104/3 square feet.

Next, we find the area of each piece of paper:

Area of each piece of paper = (1/3) ft * (1/3) ft = 1/9 square feet.

Now, we can find the number of pieces of paper on the bulletin board by dividing the total area covered by the area of each piece of paper:

Number of pieces of paper = Area of bulletin board / Area of each piece of paper

Number of pieces of paper = (104/3) / (1/9)

Number of pieces of paper = (104/3) * (9/1)

Number of pieces of paper = 936/3

Number of pieces of paper = 312

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Answer:

the actual length is 15 yards

Answer:

7

Step-by-step explanation:

\(\sqrt{49}\) means x*x = 49

x * x = 49

x= 7

\(\sqrt{49} =7\)

Hope this helps :)

Have a great day!

The expression which is equivalent to  \(\frac{\sqrt[7]{x^{2} } }{\sqrt[5]{y^{3} } }\) is \((x^{\frac{2}{7} } })({x^{-\frac{3}{5} } } )\). The 1st option is the answer

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we substitute the same value(s) for the variable(s)

Since \(\frac{\sqrt[7]{x^{2} } }{\sqrt[5]{y^{3} } }\)

In indices, ∛(x) = x^(1/3). Also,  ∛(x)² =  x^(2/3). Thus, the given expression can be written as:

\(\frac{\sqrt[7]{x^{2} } }{\sqrt[5]{y^{3} } } = \frac{x^{\frac{2}{7} } }{x^{\frac{3}{5} } } = (x^{\frac{2}{7} } })({x^{-\frac{3}{5} } } )\)

Note: the sign changed to negative because division changed to multiplication

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Answer:

As a relation between height and hypotenuse in right triangle GHJ, we have:

HK^2 = KG x KJ

=> HK = sqrt(KG x KJ) = sqrt(2 x 8) = sqrt(16) = 4

Hope this helps!

:)

the critical z-value for a one-tailed test is approximately 2.326.

To compare the percent of senior citizens who attend a play at least once per year with the percent of people in their twenties, we can perform a hypothesis test for the difference in proportions.

First, let's define the parameters and hypotheses:

Parameter 1: p₁ = Proportion of senior citizens who attend a play at least once per year

Parameter 2: p₂ = Proportion of people in their twenties who attend a play at least once per year

Null Hypothesis: H₀: p₁ - p₂ = 0 (There is no difference between the proportions)

Alternative Hypothesis: H₁: p₁ - p₂ > 0 (The proportion of senior citizens who attend a play at least once per year is greater than the proportion of people in their twenties)

Next, let's check the conditions for both populations:

Condition 1: Random Sample

The samples of 100 senior citizens and 100 people in their twenties were randomly selected, so this condition is met.

Condition 2: Independent Samples

We assume that the samples are independent, meaning that the responses of one person do not influence the responses of others in the same sample. As long as the samples were selected randomly, this condition is typically satisfied.

Condition 3: Normal Condition

To check the normal condition, we need to verify that the number of successes and failures in each sample is at least 10. In this case, both samples have more than 10 successes and 10 failures (86 and 76 successes, and 14 and 24 failures), so this condition is met.

Now, we can perform the hypothesis test and calculate the p-value:

We can use a z-test for the difference in proportions since the sample sizes are large and the conditions are met. The test statistic is calculated as:

z = \((\hat{p}_1 - \hat{p}_2) / sqrt((\hat{p}_1(1 - \hat{p}_1) / n_1) + (\hat{p}_2(1 -\hat{p}_1) / n_2))\)

where:

\(\hat{p}_1\) = 0.86 (proportion of senior citizens who attended a play at least once per year)

\(\hat{p}_1\) = 0.76 (proportion of people in their twenties who attended a play at least once per year)

n₁ = 100 (sample size of senior citizens)

n₂ = 100 (sample size of people in their twenties)

Calculating the test statistic:

z = (0.86 - 0.76) / sqrt((0.86 * 0.14 / 100) + (0.76 * 0.24 / 100))

z = 0.1 / sqrt(0.001204 + 0.001824)

z = 0.1 / sqrt(0.003028)

z ≈ 1.760

The p-value can be found using the z-table or statistical software. With a significance level of α = 0.01, the critical z-value for a one-tailed test is approximately 2.326. Since 1.760 < 2.326, the p-value is greater than 0.01.

Conclusion:

Since the p-value is greater than the significance level (p > α), we fail to reject the null hypothesis. There is not enough evidence to conclude that the proportion of senior citizens who attend a play at least once per year is significantly greater than the proportion of people in their twenties.

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Answer:

Hold on i got it

Step-by-step explanation:

Answer:

26

Step-by-step explanation:

26/2=13

13+7=20

The vertex of V' had a preimage of V(0, 3) as V' has a dilation of 3.

Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.

Dilation: The preimage is scaled up or down to create the image.

Reflection: The picture is a preimage that has been reversed.

Rotation: Around a given point, the preimage is rotated to create the final image.

Translation: The image is translated and moved a fixed amount from the preimage.

Given, On a coordinate plane, polygon S'T'U'V' has points (- 2, 4), (- 4, 1),

(- 2, - 2), and (0, 1) with a dilation rule  DO,1/3 (x, y) to [(1/3)x, (1/3)y].

Therefore, The coordinates of the vertex V had a preimage of,

3(V'), which is 3(0, 1) = (0, 3).

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