Write each of the below number in an ascending order.
3.4 4.7 2.9 2.69

Answer:

1st graph

General Formulas and Concepts:

Algebra I

Discriminant b² - 4ac

Step-by-step explanation:

We are given that our graph will have a negative discriminant. Therefore, our graph will not touch the x-axis as it has no solutions.

Answer:

1

Step-by-step explanation:

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The value of cos2x when sine of x equals negative 15 over 17 and cos x > 0 is -161/289.

The ratio of the neighboring side's length to the longest side, or hypotenuse, in a right triangle is known as the cosine. Let's say that the hypotenuse of a triangle ABC is written as AB, and the angle between the hypotenuse and base is written as.

It's interesting to see that cos's value varies depending on the quadrant. As observed in the above table, cos 0°, 30°, etc. have positive values while cos 120°, 150°, and 180° have negative values. Cos will have a good value in the first and fourth quadrants.

Given that, sin x equals negative 15 over 17.

Using the Pythagoras theorem we have:

(17)² = (- 15)² + y²

y = 8

The value of cos x = 8/17

Then the value of cos2(x) is calculated using the formula:

cos2x = cos²x - sin²x

cos2x = (8/17)² - (15/17)²

cos2x = -161/289

Hence, the value of cos2x when sine of x equals negative 15 over 17 and cos x > 0 is -161/289.

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16.08% is the frequency of outcomes that the gambler wins on two of the dice.

The percentage of time each outcome is attained is the relative frequency. By dividing the total count for all types of outcomes by the count of a particular sort of outcome, relative frequency could be derived. The ratio of the overall trials in an actual experiment to the number of times an event occurs is used to compute relative frequency or empirical probability.

To determine the frequency of outcomes, we obtain,

On a single die, there is a 1/6 chance of winning.

P =6 ×(\(\frac{1}{6}\))² ×(\(\frac{5}{6}\))²

⇒P=\(\frac{25}{216}\)

The frequency of outcomes that the gambler wins on two of the dice=    \(\frac{25}{216}\)×100=16.08%

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Answer:

| - 16 |

Step-by-step explanation:

The absolute value function always gives a positive value, that is

| - a | = | a | = a

Then

| 6 | = 6

| - 16 | = | 16 | = 16

Thus the largest number from the list is | - 16 |

You can determine whether a system of linear equations will have one, infinite, or no solutions by using the concept of consistency and dependence of the equations.

A system of linear equations can have one solution if the equations intersect at a single point. Geometrically, this corresponds to the point where the lines intersect on a graph or the point where the planes intersect in three-dimensional space. Algebraically, this corresponds to a unique solution for the variables in the system.

A system of linear equations can have infinite solutions if the equations are dependent, meaning that they can be obtained by adding, subtracting, or multiplying one equation by a constant to obtain another equation in the system. Geometrically, this corresponds to lines that coincide or planes that are coincident or parallel. Algebraically, this corresponds to having more variables than equations in the system, which means that there are free variables that can take any value.

A system of linear equations can have no solution if the equations are inconsistent, meaning that they have no common solution. Geometrically, this corresponds to lines that are parallel or planes that do not intersect. Algebraically, this corresponds to having conflicting equations in the system, which means that there is no possible solution that satisfies all of the equations simultaneously.

To summarize, the number of solutions to a system of linear equations depends on the number of equations, the number of variables, and the consistency and dependence of the equations.

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The dimensions of the rectangular pen should be 15 by 20 feet and the maximum area is 1200 square feet.

Let the area be y .

Area = (base) × (height)

Base = 2x

Height = h

Let the area of the rectangular pens be y .

∴ y = 2xh

Perimeter of all the fencing = 4x+3h

∴ 4x+3h = 120

now we solve for h

3h = 120-4x

h = 40 - 4/3 x

Now we will substitute this value in the above first equation:

y = 2xh

or, y = 2x (40 - 4/3 x)

or, y = 80x - 8/3 x²

Now for the maximum area we have to find the first order differentiation of y

now,

dy /dx = 80 - 16/3 x

At dy/dx = 0 we get the value of x for which y is maximum.

80 - 16/3 x = 0

or, - 16/3 x = -80

or, x = 15 feet

Hence height =  40 - 4/3 x = 40 - 20 = 20feet

Maximum area = 2xh = 2×15×40 = 1200 square feet

The dimensions of the rectangular pen should be 15 by 20 feet and the maximum area is 1200 square feet.

Disclaimer : The missing figure for the question is attached below.

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The absolute value of x=5 is 5.

The absolute value of a number is its positive equivalent of the number

For instance, the absolute value of -5 is 5 and the absolute value of 5 is also 5.

Generally, it is denoted by the symbol |x|.

So, we have

The absolute value of x=5

This gives

x = |5|

Evaluate

x = 5

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The dimensions of the coop are length = 12 ft and width = 9 ft

Since the coop is a rectangle, the area of the coop is A = LW where

Now, the length of the coop 3 feet longer than the width, so, L = W + 3

Now, the area of the coop A = 108 ft²

So, A = LW

A = (W + 3)W

108 = W² + 3W

Re-arranging,

W² + 3W - 108 = 0

So, we solve the equation to find the width of the coop

W² + 3W - 108 = 0

Factorizing, we have

W² + 12W - 9W - 108 = 0

W(W + 12) - 9(W + 12) = 0

(W + 12)(W - 9) = 0

W + 12 = 0 or W - 9 = 0

W = -12 or W = 9

Since W cannot be negative, W = 9

Since L = W + 3

Substituting the value of W into L, we have

L = W + 3

L = 9 + 3

L = 12 ft

So, dimensions of the coop are length = 12 ft and width = 9 ft

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The statement ''the q test is a mathematically simpler but more limited test for outliers than is the grubbs test'' is correct becauae the Q test is a simpler but less powerful test for detecting outliers compared to the Grubbs test.

The Q test and Grubbs test are statistical tests used to detect outliers in a dataset. The Q test is a simpler method that involves calculating the range of the data and comparing the distance of the suspected outlier from the mean to the range.

If the distance is greater than a certain critical value (Qcrit), the data point is considered an outlier. The Grubbs test, on the other hand, is a more powerful method that involves calculating the Z-score of the suspected outlier and comparing it to a critical value (Gcrit) based on the size of the dataset.

If the Z-score is greater than Gcrit, the data point is considered an outlier. While the Q test is easier to calculate, it is less powerful and may miss some outliers that the Grubbs test would detect.

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The homogeneous equation corresponding to W = Span(2, 1, -3) is 0.

To discover a set of one or more homogeneous equations for which the corresponding answer set is W = Span(2, 1, -three), we will use the idea of linear independence.

The set of vectors v1, v2, ..., vn is linearly unbiased if the only strategy to the equation a1v1 + a2v2 + ... + anvn = 0 (wherein a1, a2, ..., an are scalars) is a1 = a2 = ... = an = 0.

Since W = Span(2, 1, -3), any vector in W may be represented as a linear aggregate of (2, 1, -three). Let's name this vector v.

Now, to find a homogeneous equation corresponding to W, we need to discover a vector u such that u • v = 0, in which • represents the dot product.

Let's bear in mind the vector u = (1, -1, 2). To check if u • v = 0, we compute the dot product:

(1)(2) + (-1)(1) + (2)(-3) = 2 - 1 - 6 = -5.

Since u • v = -five ≠ zero, the vector u = (1, -1, 2) is not orthogonal to v = (2, 1, -3).

To discover a vector that is orthogonal to v, we can take the go product of v with any other vector. Let's pick the vector u = (1, -2, 1).

Calculating the cross product u × v, we get:

(1)(-3) - (-2)(1), (-1)(-3) - (1)(2), (2)(1) - (1)(1) = -3 + 2, 3 - 2, 2 - 1 = -1, 1, 1.

So, the vector u = (-1, 1, 1) is orthogonal to v = (2, 1, -3).

Therefore, the homogeneous equation corresponding to W = Span(2, 1, -3) is:

(-1)x + y + z = 0.

Note that this equation represents an entire answer set, now not only an unmarried solution. Any scalar more than one of the vectors (-1, 1, 1) will satisfy the equation and belong to W.

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The correct question is:

The regular expression excludes strings like "1000" or "100000" because they have an even number of 0s following the 1.

The set of all bit strings made up of a 1 followed by an odd number of 0s can be represented by the regular expression:

1(00)*

Breaking down the regular expression:

1: The string must start with a 1.

(00)*: Represents zero or more occurrences of the pattern "00". This ensures that the 1 is followed by an odd number of 0s.

Examples of valid bit strings in this set include:

10

100

10000

1000000

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Based on the calculations, the measure of angle YUV is equal to 42°.

A line segment refers to a part of a line that is bounded by two (2) distinct points and it has a fixed length.

Based on the information given, we can deduce the following:

From triangle UOV, we have:

∠OUV + ∠OUV + ∠UOV  = 180°

2OUV + 84 = 180

2OUV = 180 - 84

2OUV  = 96

OUV  = 96/2

OUV  = 48°

Now, we can determine the measure of angle YUV:

∠YUV = ∠YUO - ∠OUV

∠YUV = 90 - 48

∠YUV = 42°.

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Answer:

42

Step-by-step explanation:

The net magnetic field at point P is (6e-5 j + 0.57 k) T in 1, 1, k notation.

We can use the Biot-Savart Law to calculate the magnetic field at point P due to each wire, and then add the two contributions vectorially to obtain the net magnetic field.

The magnetic field due to a current-carrying wire can be calculated using the formula:

d = μ₀/4π * Id × /r³

where d is the magnetic field contribution at a point due to a small element of current Id, is the vector pointing from the element to the point, r is the distance between them, and μ₀ is the permeability of free space.

Let's first consider the wire carrying current I₁ (in the positive X direction). The contribution to the magnetic field at point P from an element d located at position y on the wire is:

d₁ = μ₀/4π * I₁ d × ₁ /r₁³

where ₁ is the vector pointing from the element to P, and r₁ is the distance between them. Since the wire is infinitely long, we can assume that it extends from -∞ to +∞ along the X axis, and integrate over its length to find the total magnetic field at P:

B₁ = ∫d₁ = μ₀/4π * I₁ ∫d × ₁ /r₁³

For the given setup, the integrals simplify as follows:

∫d = I₁ L, where L is the length of the wire per unit length

d × ₁ = L dy (y - 1/2 L) j - x i

r₁ = sqrt(x² + (y - 1/2 L)²)

Substituting these expressions into the integral and evaluating it, we get:

B₁ = μ₀/4π * I₁ L ∫[-∞,+∞] (L dy (y - 1/2 L) j - x i) / (x² + (y - 1/2 L)²)^(3/2)

This integral can be evaluated using the substitution u = y - 1/2 L, which transforms it into a standard form that can be looked up in a table or computed using software. The result is:

B₁ = μ₀ I₁ / 4πd * (j - 2z k)

where d = 5 mm = 5×10^-3 m is the distance between the wires, and z is the coordinate along the Z axis.

Similarly, for the wire carrying current I₂ (in the negative X direction), we have:

B₂ = μ₀ I₂ / 4πd * (-j - 2z k)

Therefore, the net magnetic field at point P is:

B = B₁ + B₂ = μ₀ / 4πd * (I₁ - I₂) j + 2μ₀I₁ / 4πd * z k

Substituting the given values, we obtain:

B = (2×10^-7 Tm/A) / (4π×5×10^-3 m) * (30A - (-30A)) j + 2(2×10^-7 Tm/A) × 30A / (4π×5×10^-3 m) * (15×10^-2 m) k

which simplifies to:

B = (6e-5 j + 0.57 k) T

Therefore, the net magnetic field at point P is (6e-5 j + 0.57 k) T in 1, 1, k notation.

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The dog's running speed of 5 km/hr can be converted to approximately 3.125 mi/hr by multiplying it by the conversion factor of 1 mi/1.6 km. Rounding to the nearest thousandth, the dog can run at about 3.125 mi/hr.

To convert the dog's running speed from kilometers per hour (km/hr) to miles per hour (mi/hr), we need to use the conversion factor of 1.6 km = 1 mi.First, we can convert the dog's speed from km/hr to mi/hr by multiplying it by the conversion factor: 5 km/hr * (1 mi/1.6 km) = 3.125 mi/hr.

However, we need to round the answer to the nearest thousandth (three decimal places). Since the digit after the thousandth place is 5, we round up the thousandth place to obtain the final answer.

Therefore, the dog can run at approximately 3.125 mi/hr.

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Answer:

I think they charge a flat rate of $8 for a vehicle and $3 per person on top of that.

Step-by-step explanation:

There could be a multitude of rules, but let's try to find a simple one.

I would start by assuming that the park charges a fee for a vehicle and then for each person. Let's name those:

a - flat fee for a vehicle

b - fee per person

then a car with x people in it would be charged

a + bx

Let's see if the fees fit this assumption:

for x = 2

a + b*2 = $14

for x = 4

a + b*4 = $20

for x = 8

a + b*8 = $32

If so, we can subtract the second equation from the first and get

a + b*4 - a - b*2 = $20 - $14

b*2 = $6

b = 3$

a + b*2 = $14

a + $3*2 = a + $6 = $14

a = $8

so the first 2 equations gave us a = $8 and b = $3.

Let's see if these values fit the 3rd equation

a + b*8 = $32

$8 + $3*8 = $32

$8 + $24 = $32

$32 = $32

It fits!

That tells us that the rule is indeed very likely.

Answer: 9.75 is your answer

Step-by-step explanation:

Based on the given conditions, Jane has $31, Kevin has $25, and Hans has $50 in their wallets.

Let's solve the problem step by step.

First, let's assume that Jane has X dollars in her wallet. Since Kevin has $6 less than Jane, Kevin would have X - $6 dollars in his wallet.

Next, we're given that Hans has 2 times what Kevin has. So, Hans would have 2 * (X - $6) dollars in his wallet.

According to the information given, the total amount of money they have in their wallets is $106. We can write this as an equation:

X + (X - $6) + 2 * (X - $6) = $106

Simplifying the equation:

4X - $18 = $106

4X = $124

X = $31

Now we know that Jane has $31 in her wallet.

Substituting this value into the previous calculations, we find that Kevin has $31 - $6 = $25 and Hans has 2 * ($25) = $50.

To find the total amount they have, we sum up their individual amounts:

Jane: $31

Kevin: $25

Hans: $50

Adding these amounts together, we get $31 + $25 + $50 = $106, which matches the total amount stated in the problem.

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The complete question is:

Jane, kevin and hans have a total of $106 in their wallets. kevin has $6 less than Jane. hans has 2 times what kevin has. how much do they have in their wallets?

Around $441 million worth of food is wasted in the US each day.

According to the United States Department of Agriculture (USDA), about 30-40 percent of the food supply in the United States goes to waste. In terms of dollars, that translates to approximately $161 billion worth of food being wasted each year in the United States.

Dividing that number by 365, we can estimate that around $441 million worth of food is wasted in the US each day.

It's difficult to estimate how many people could be fed with the food that is thrown away, as food waste can take many forms, such as uneaten meals at restaurants, spoiled produce at grocery stores, and expired food in households. However, according to Feeding America, a national food bank network, approximately 42 million Americans, including 13 million children, are food insecure, which means they lack reliable access to affordable, nutritious food.

If we assume that all the food that is currently being wasted in the US could be redistributed to those who are food insecure, it could potentially feed a significant number of people. However, in reality, the logistics of collecting, storing, and distributing food waste can be complex, and some food waste may not be safe or nutritious to eat. Additionally, addressing food waste is just one piece of the puzzle in addressing food insecurity, which is a complex issue with many underlying factors.

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we have the following:

replacing:

now,

therefore, the wide is 3.57 cm and the length is 42.86 cm

The number of bacteria that is left is 38

The half-life is the time it takes for half of the bacteria to reduce

The time is given as 1.5 hours

After 1.5 hours:

The number will have gone through 6 / 1.5 = 4 half-lives.

So, the number of bacteria cells after 6 hours will be 600 * (1/2)^4

Evaluate

600 * (1/2)^4 = 600 / 16 = 37.5

Approximate

600 * (1/2)^4 = 600 / 16 = 378

Since the number of bacteria cells is 37.

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The given data can be represented as shown in the figure below. We need to find out the distance and the direction of the plane from the airport by using the cosine and sine rules.

From the figure, we can obtain: In the triangle  ABC,AB=150 km and AC=270 km. In the triangle ACD,CD=EB-ED.

In the triangle BED, Using the cosine rule in ΔABC, we have

BC² = AB² + AC² - 2 × AB × AC × cos(C) ⇒ BC² = (150)² + (270)² - 2 × (150) × (270) × cos(42)BC = 262.78 km.

Using the sine rule in ΔABC,

we have sin(C)/AB = sin(B)/BC ⇒ sin(C) = AB × sin(B)/BC⇒ sin(C) = 150 × sin(42)/262.78sin(C)

= 0.3277cos(C) = 0.9448.

Now, in the triangle BED, we can obtain:

Using the cosine rule in ΔBED, we haveDE² = BD² + BE² - 2 × BD × BE × cos(180 - B)

⇒ DE² = (262.78)² + (270)² + 2 × (262.78) × (270) × cos(48)DE = 242.53 km.

Using the sine rule in ΔBED, we have sin(B)/BD = sin(E)/DE ⇒ sin(B) = BD × sin(E)/DE

⇒ sin(B) = 262.78 × sin(42)/242.53sin(B) = 0.7564cos(B) = 0.6549.

Therefore, The distance the crew should fly to go directly to the plane =

EC = ED + DC ⇒ EC = DE × sin(B) + DC × sin(C)⇒ EC = 242.53 × 0.7564 + 150 × 0.3277⇒ EC = 303.08 km.

Thus, the distance the crew should fly to go directly to this plane is 303.08 km.

The angle (θ) with the x-axis (east) can be obtained as follows:θ = tan^-1(EB/BC) + 42°⇒ θ = tan^-1(150/262.78) + 42°θ = 75.15°.

The direction in which the crew should fly is 75.15° with respect to the x-axis (east).

From the given data, we have to find the distance and direction of the plane from the airport by using the cosine and sine rules. In the triangle ABC, AB = 150 km and AC = 270 km.

Using the cosine rule, we can find BC: BC² = AB² + AC² - 2 × AB × AC × cos(C).

Plugging in the given values, we obtain BC = 262.78 km. Using the sine rule, we can find the angle C: sin(C)/AB = sin(B)/BC. Plugging in the given values, we obtain sin(C) = 0.3277 and cos(C) = 0.9448.

Using these values and the given data, we can determine the distance and direction of the plane from the airport. We can find the distance EC by using the formula: EC = ED + DC.

We can find ED by using the cosine rule in triangle BED: DE² = BD² + BE² - 2 × BD × BE × cos(180 - B).

Plugging in the given values, we obtain DE = 242.53 km. We can find DC by using the sine rule in triangle ABC: sin(C)/AB = sin(B)/BC.

Plugging in the given values, we obtain sin(B) = 0.7564 and cos(B) = 0.6549. Finally, we can find the angle θ with the x-axis by using the formula: θ = tan^-1(EB/BC) + 42°.

Plugging in the given values, we obtain θ = 75.15°.Therefore, the distance the crew should fly to go directly to this plane is 303.08 km. The direction in which the crew should fly is 75.15° with respect to the x-axis (east).

Therefore, the distance the crew should fly to go directly to this plane is 303.08 km and the direction in which the crew should fly is 75.15° with respect to the x-axis (east).

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Answer: it's not clear so i can't tell you the equation as it requires the slope but i can tell you the y-intercept is 4

Step-by-step explanation:

Answer:

\(2 \div 3 \\ \frac{2}{3} \)

There are 360 different codes that can be made, and the probability that the code is between 2000 and 3000 is P = 1/6.

There are 6 different digits, and we know that the digits can't be repeated, then for each one of the 4 digits we will have 6 options, 5, 4, 3 respectively.

Then the total number of codes will be:

C = 6*5*4*3 = 360

360 different codes.

b) Now we want to find the probability that the code is between 2000 and 3000, then we only look at the number of codes that start with the 2.

Then for the second digit we have 5 options (2 is already taken)

for the second we have 4 options

for the last one we have 3 options.

So the number of codes that start with 2 are:

C' = 5*4*3 = 60

Then the probability that a random code starts with 2 is:

P = 60/360 = 1/6

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The number of 4-letter words that can be formed without any condition imposed is 8,064.

To determine the number of 4-letter words that can be formed without any conditions, we can use the concept of permutations. Since we have 8 options (a, b, c, d, e, f, g) for each letter position, we can multiply the number of options for each position to find the total number of possibilities.

For the first letter position, we have 8 options to choose from. Similarly, for the second, third, and fourth positions, we also have 8 options each. Therefore, the total number of possibilities is:

8 options for the first position × 8 options for the second position × 8 options for the third position × 8 options for the fourth position = 8 × 8 × 8 × 8 = 8,064.

Hence, there are 8,064 possible 4-letter words that can be formed without any conditions imposed.

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Answer:

let the number be x then

(x+7)8-4

Answer:

b

Step-by-step explanation:

The best instrument to determine the predictive validity of a metric scale would be a correlation-coefficient.

This measure assesses the strength of the relationship between two variables, in this case, the metric scale scores and the predicted outcome. A high correlation would indicate that the metric scale is a good predictor of the outcome, whereas a low correlation would indicate that the metric scale is not a reliable predictor.

Cronbach's alpha is a measure of internal consistency and would not be appropriate for determining predictive validity. Fisher's r-to-z test is used to compare the strength of two correlations and is not necessary in this scenario. Therefore, the answer is B, a correlation-coefficient.

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Answer:

Step-by-step explanation:

24(mx+n)=3x+17

24(14x+13)=3x+17

336x+312=3x+17

336x-3x=17-312

333x=-295

X=16.063

The required solution has one solution at x = 0.886 and Equation have infinitely many solution when n = -15.41 .

What is a linear equation ?

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

Given:

The given equation is

24(mx+n)=3x+17,

where m and n are real numbers.

According to given question we have

By put the value of m=14 and n=13, in given equation we have

24(mx +n)=3x+17

24(14x+13)=3x+17

336x+312=3x+17

336x-3x=17-312

333x=-295

X=-0.885

Thus x = 0.886 we can say that the equation having one solution .

;  if m = 18 then find n .

put m = 18 in the given equation

= 24(18.(0.886) + n ) = 3(0.886) + 17

= 24(15.94) + 24n = 2.658 + 17

= 382.56 + 24n = 19.658

= 24n = 19.658 - 382.56

= n = -362.902/24

n = -15.12

The equation have infinitely many solution when n = -15.41.

Therefore, the required solution has one solution at x = 0.886 and

Equation have infinitely many solution when n = -15.41 .

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