Which list orders the numbers from least to greatest?

–5, 1, 3, –2

A number line going from negative 5 to positive 5.
1, –2, 3, –5
–2, –5, 1, 3
–5, –2, 1, 3
3, 1, –2, –5

As an estimation of the exchange rates, 16 Euros is approximately equal to 12 Pounds.

To convert Euros to Pounds, we first need to determine the conversion rate between these two currencies. From the information provided, we know that 3 Pounds is approximately equal to 4 Euros. Using this information, we can establish a conversion factor by dividing 3 Pounds by 4 Euros:

Conversion factor = 3 Pounds / 4 Euros = 0.75 Pounds per Euro

Now that we have the conversion factor, we can use it to convert 16 Euros to Pounds. To do this, we simply multiply the amount in Euros (16) by the conversion factor (0.75 Pounds per Euro):

16 Euros * 0.75 Pounds per Euro = 12 Pounds

So, as an estimation, 16 Euros is approximately equal to 12 Pounds. Keep in mind that exchange rates between currencies can fluctuate over time, so it's always a good idea to double-check the current rate before making any financial transactions.

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Complete Question:

As an estimation we are told £3 is €4.

Convert €16 to pounds.

Answer:She incorrectly factored out the value of a.

Step-by-step explanation:

In solving a quadratic equation by completing the square method, the value a is not factored out. Rather, the steps involved are:

Divide through all the terms by a

Move the term c/a to the right had side

Complete the square on both sides using the value of b/2

Obtain the values of x

Answer: B. She subtracted the wrong value to maintain balance after completing the square.

Answer:

x = 25 °

Step-by-step explanation:

First realize the opposite angles are equal , then

(4 x + 50)° = 150 °

x = 25 °

Answer:

x = 25

Step-by-step explanation:

Vertical Angles Theorem

When two straight lines intersect, the opposite vertical angles are congruent.

From inspection of the given diagram, it appears that angle 150° and angle (4x + 50)° are opposite vertical angles.

Therefore, applying the Vertical Angle Theorem:

\(\implies (4x+50)^{\circ}=150^{\circ}\)

\(\implies 4x+50=150\)

\(\implies 4x=100\)

\(\implies x=25\)

The probability that a standard normal random variable z is between -2.4 and 0.4 is approximately 0.6472.

To find the probability that a standard normal random variable z is between -2.4 and 0.4, we can follow these steps:

Step 1: Look up the cumulative probability corresponding to -2.4 in the standard normal distribution table. The cumulative probability at -2.4 is approximately 0.0082.

Step 2: Look up the cumulative probability corresponding to 0.4 in the standard normal distribution table. The cumulative probability at 0.4 is approximately 0.6554.

Step 3: Subtract the cumulative probability at -2.4 from the cumulative probability at 0.4 to find the probability between the two values:

P(-2.4 < z < 0.4) = 0.6554 - 0.0082

= 0.6472.

Therefore, The probability that z is between -2.4 and 0.4, when z is a standard normal random variable, is approximately 0.6472. This means that there is a 64.72% chance that a randomly selected value from a standard normal distribution falls within the range of -2.4 to 0.4.

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Consider a rectangular box with dimensions length (L), width (W), and height (H).The method of Lagrange multipliers can be used to find the maximum volume of a rectangular box with its diagonal length fixed at l.

Consider a rectangular box with dimensions length (L), width (W), and height (H). We want to maximize the volume of the box, V = LWH, subject to the constraint that the diagonal length is fixed at l.

To apply the method of Lagrange multipliers, we introduce a Lagrange multiplier λ and form the following function:

F(L, W, H, λ) = LWH + λ(D² - L² - W² - H²),

where D is the fixed diagonal length, and the term λ(D² - L² - W² - H²) is the constraint equation.

We then take partial derivatives of F with respect to L, W, H, and λ, and set them equal to zero to find critical points. Solving these equations, we obtain:

∂F/∂L = WH - 2λL = 0,

∂F/∂W = LH - 2λW = 0,

∂F/∂H = LW - 2λH = 0,

∂F/∂λ = D² - L² - W² - H² = 0.From equations (1)-(3), we find that WH = 2λL, LH = 2λW, and LW = 2λH. Dividing these equations, we get (WH)/(LW) = L/H, (LH)/(LW) = W/H, and (LW)/(LH) = W/L. Simplifying, we have L = W = H, which means the dimensions of the box are all equal.

Substituting L = W = H into equation (4), we have 3L² = D², or L = W = H = D/√3.

Therefore, the maximum volume of the rectangular box is                        (D/√3)³ = D³/√27.

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If "function-f" is defined by f(x) = √(x³+2) and "g" is an "anti-derivative" of "f" such that g(3) = 5, then g(1) = -1.585.

The "Anti-derivative" of a "function-f(x)" is a function, F(x) whose derivative is equal to f(x).

The function is defined as f(x) = √(x³+2),

The "function-g" is an anti-derivative of function-f, such that g(3) = 5 ,

Which means,

⇒ g(a) = \(\int\limits^x_0\)f(t) dt + c,

⇒ g(a) = \(\int\limits^x_0\)√(t³+2)dt + c,

⇒ 5 = \(\int\limits^x_0\)√(t³+2)dt + c,

⇒ c = 5 - \(\int\limits^x_0\)√(t³+2)dt,

So, the function g(x) = \(\int\limits^x_0\)√(t³+2)dt + 5 - \(\int\limits^3_0\)√(t³+2)dt,

⇒ g(1) =  \(\int\limits^x_0\)√(t³+2)dt + 5 - \(\int\limits^3_0\)√(t³+2)dt,

On Simplifying further ,

We get,

⇒ g(1) = 1.4971 + 5 - 8.0817,

⇒ g(1) = -1.5846 ≈ -1.585.

Therefore, the value of g(1) is -1.585.

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The given question is incomplete, the complete question is

If the function f is defined by f(x) = √(x³+2) and "g" is an antiderivative of "f" such that g(3) = 5, then g(1) = ?

Answer:

4

Step-by-step explanation:

all the details can be found in the attachment.

We are given the following equation

We are asked to solve the equation for y.

Solving for y means that we have to separate the variable y.

Step 1:

Subtract 3x from both sides of the equation

A bivariate probability distribution is a statistical distribution that describes the joint probability of two random variables. It provides the probability of each combination of values for the two variables. In simple words, it's a way to model the joint probability of two variables and the relationship between them.

A bivariate probability distribution is represented by a probability density function (pdf) or a probability mass function (pmf) depending on whether the variables are continuous or discrete. The function gives the probability of a given pair of values of the two variables. Bivariate probability distributions are useful in understanding the relationship between two variables and can be used to make predictions or draw inferences. It can be visualized using a scatter plot, a contour plot or a 3D plot. It can also be used to calculate the covariance and correlation between the two variables.

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Complete question:

Describe Bivariate Probability Distribution.

Answer: The Graph Is shifted 5 units down.

(I believe you might have forgotten to square the “(x-1)”. It should be “(x-1)^2”)

ANSWER:

13.35 hours

EXPLANATION:

Given:

Time Kristen takes to harvest = 10.2 hours

Time Kayla takes to harvest = 16. 5 hours

Let X represent the time it would take them to work together.

Here, to find the time it would take them if they worked together, let's find their mean time, using the formula below:

It would take them 13.35 hours if they worked together.

The perimeter of a rectangle is 37 units.

A rectangle is a quadrilateral. It has four angles. All the angles in a rectangle are equal. The perimeter of a rectangle is

                          p ( rectangle )   =   2 ( l + w )       →  1

where,      l  =   length of the rectangle

                w  =   width of the rectangle

As per the given question, the coordinates of a rectangle are A ( 1, 7 ), B ( 8, 7 ), C ( 8, -3 ) and D ( 1, -3 ).

To find the length and width of the rectangle i.e. the length of each side, we use the distance formula.

                  Distance = \(\sqrt{(x_{1}-x_{2})^{2} + (y_{1} - y_{2})^{2} }\)      →  2

AD   ⇒       \({(x_{1}, y_{1}) }\)   =   ( 1, 7 )   and   \({(x_{2}, y_{2}) }\)   =   ( 1, -3 )

Substitute the values in 2,

AD   =   \(\sqrt{(x_{1}-x_{2})^{2} + (y_{1} - y_{2})^{2} }\)

       =   \(\sqrt{(1-1)^{2} + (7 - (-3))^{2} }\)

       =    \(\sqrt{(0)^{2} + (10)^{2} }\)

       =    \(\sqrt{0+ (10)^{2} }\)

       =     \(\sqrt{(10)^{2} }\)

AD   =    10

∴ Width of the rectangle ( w ) = AD = BC = 10 units

AB   ⇒        \({(x_{1}, y_{1}) }\)   =    ( 1, 7 ) and   \({(x_{2}, y_{2}) }\)   =   ( 8, 7 )

Substitute the values in 2,

AB   =   \(\sqrt{(x_{1}-x_{2})^{2} + (y_{1} - y_{2})^{2} }\)

       =   \(\sqrt{(1-8)^{2} + (7 - 7)^{2} }\)

       =    \(\sqrt{(-7)^{2} + (0)^{2} }\)

       =    \(\sqrt{(7)^{2} + 0 }\)

       =     \(\sqrt{(7)^{2} }\)

AB   =    7

∴ Length of the rectangle ( l ) = AB = DC = 7 units

Substitute the values l = 10 and w = 7 in 1,

⇒  p ( rectangle )   =   2 ( l + w )

                               =   2 ( 7 + 10 )

                               =   2 ( 17 )

     p ( rectangle )   =   34

Therefore, the perimeter of the rectangle with the coordinates A ( 1, 7 ), B ( 8, 7 ), C ( 8, -3 ) and D ( 1, -3 ) is 34 units.

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Answer:

c

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

40 in 1 hour

320 in 8 hours

Step-by-step explanation:

Answer:

\(\frac{x-2}{4x+5}\)

Step-by-step explanation:

Given

\(\frac{4x^2+3x-1}{4x^2+9x+5}\) ÷ \(\frac{4x^2+7x-2}{x^2-4}\)

Factorise numerator / denominator of both fractions

= \(\frac{(4x-1)(x+1)}{(4x+5)(x+1)}\) ÷ \(\frac{(4x-1)(x+2)}{(x-2)(x+2)}\)

Cancel common factors on numerator/ denominator of both fractions

= \(\frac{4x-1}{4x+5}\) ÷ \(\frac{4x-1}{x-2}\)

Change ÷ to × and turn second fraction upside down

= \(\frac{4x-1}{4x+5}\) × \(\frac{x-2}{4x-1}\)

Cancel the common factor 4x - 1 on numerator/ denominator, leaving

\(\frac{x-2}{4x+5}\)

Answer:

-x + 2y - 36

Step-by-step explanation:

-4(x + 9) + 3(x - y) + 5y

Distribute;

-4x - 36 + 3x - 3y + 5y

Collect like terms;

-1x + 2y - 36

The Law of Cosines is a formula that relates the side lengths and angles of any triangle, expressed as c^2 = a^2 + b^2 - 2abcos(C).

The Law of Cosines is a numerical formula that relates the side lengths and points of any triangle. It expresses that the square of any side of a triangle is equivalent to the number of squares of the other different sides short two times the result of those sides and the cosine of the point between them. Numerically, the Law of Cosines can be communicated as c^2 = a^2 + b^2 - 2abcos(C), where c is the length of the side inverse to the point C, and an and b are the lengths of the other different sides.

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Answer:

80

Step-by-step explanation:

Freddie is one meter shorter than his father

His father is 180 centimeters tall

So freddie is 80 centimetres

Freddie is mother÷2

So 80=M÷2

Mother is 190 centimeters

The number of centimeters when Freddie’s mother should be tall is considered to be 90.

Since

Freddie is half as tall as his mother.

Freddie is one metre shorter than his father.

Freddie’s father is 180 centimetres tall.

So

the Freddie is mother is

= 180 / 2

= 90

hence, The number of centimeters when Freddie’s mother should be tall is considered to be 90.

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Answer:

the value of x that makes ACDE~AFGH is 27

Therefore, The smallest set of integers guaranteed to have a difference that is a multiple of 14 is 15. This is due to the Pigeonhole Principle and the 14 possible remainders when dividing integers by 14.

The smallest set of integers for which we are guaranteed there exist two whose difference is a multiple of 14 is 15. This can be explained by considering the possible remainders when dividing integers by 14. There are 14 possible remainders (0 to 13), but if we choose 15 integers, then by the Pigeonhole Principle, at least two of them must have the same remainder when divided by 14. The difference between these two integers will be a multiple of 14, as their remainders are the same. Therefore, the smallest set of integers required is 15.
Therefore, The smallest set of integers guaranteed to have a difference that is a multiple of 14 is 15. This is due to the Pigeonhole Principle and the 14 possible remainders when dividing integers by 14.

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Answer:

13x+4

Step-by-step explanation:

Answer:

n-4=-15

Step-by-step explanation:

The person's average speed during her commute is 33.75 mph.

The speed of an object can be obtained by comparing the distance covered to the traveling time needed.

speed = distance / time

Take a look at the problem. As the information given is time in minutes and speed in miles per hour (mph), then we have to convert the time into an hour unit.

Total time = 20 minutes = 20/60 hour = 1/3 hour

Break time = 5 minutes

Commuting time = 20 - 5 = 15 minutes

                                         = 15/60 hour = 1/4 hour

Given the speed = 45 mph, then the distance covered during commuting time is:

Distance = speed x time

              = 45 x 1/4

              = 11.25 miles

Then we can calculate the average time, by comparing the distance covered to the total time:

Average speed = distance / total time

                          = 11.25 / 1/3

                          = 33.75 mph

Thus the average speed during the commute is 33.75 mph.

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(A) The graph of R(x) has a horizontal tangent line when x = 250.(B) The profit function P(x) is given by P(x) = R(x) - C(x) = (200x - 0.4x²) - (20x + 11,250).(C) The graph of P(x) has a horizontal tangent line when x = 100.(D) C(x), R(x), and P(x) can be graphed on the same coordinate system for 0 ≤ x ≤ 500. The break-even points can be found by determining the x-intercepts of the graph of P(x).

(A) To find the value of x where the graph of R(x) has a horizontal tangent line, we need to find the critical points of R(x). Taking the derivative of R(x) with respect to x, we get R'(x) = 200 - 0.8x. Setting R'(x) = 0 and solving for x, we find x = 250. Therefore, the graph of R(x) has a horizontal tangent line at x = 250.(B) The profit function P(x) represents the difference between the total revenue R(x) and the total cost C(x). Therefore, we can calculate P(x) as P(x) = R(x) - C(x). Substituting the given expressions for R(x) and C(x), we have P(x) = (200x - 0.4x²) - (20x + 11,250). Simplifying further, P(x) = -0.4x² + 180x - 11,250.

(C) To find the value of x where the graph of P(x) has a horizontal tangent line, we need to find the critical points of P(x). Taking the derivative of P(x) with respect to x, we get P'(x) = -0.8x + 180. Setting P'(x) = 0 and solving for x, we find x = 100. Therefore, the graph of P(x) has a horizontal tangent line at x = 100.(D) To graph C(x), R(x), and P(x) on the same coordinate system for 0 ≤ x ≤ 500, we plot the functions using their respective expressions. The break-even points occur when P(x) = 0, which means the x-intercepts of the graph of P(x) represent the break-even points. By solving the equation P(x) = -0.4x² + 180x - 11,250 = 0, we can find the x-values of the break-even points. Additionally, the x-intercepts of the graph of P(x) can be found by solving P(x) = 0.

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Answer:

Step-by-step explanation:

assuming you meant -4(-3x-3y)=15, it can be simplified by multiplying -4 with the inside of the parenthesis, 12x+12y=15, divide by 12 and x+y=15/12 or 1.25, x+y=1.25

Among the given options, the set (b) {(x, y, z) ∈ ℝ³ | y = x + =} is not a subspace of ℝ³.  among the given options, the set (b) {(x, y, z) ∈ ℝ³ | y = x + =} is not a subspace of ℝ³ because it does not contain the zero vector.

To determine if a set is a subspace of ℝ³, it must satisfy three conditions:

   The set must contain the zero vector (0, 0, 0).

   The set must be closed under vector addition.

   The set must be closed under scalar multiplication.

Let's evaluate each option:

a) {(x, y, z) ∈ ℝ³ | 3x + y + 2z = 0}:

This set is a plane passing through the origin and contains the zero vector. It is closed under vector addition and scalar multiplication, satisfying all three conditions. Therefore, option (a) is a subspace of ℝ³.

b) {(x, y, z) ∈ ℝ³ | y = x + =}:

This set represents a plane in ℝ³ defined by the equation y = x + =. However, it does not contain the zero vector since when x = y = z = 0, the equation does not hold. Therefore, option (b) is not a subspace of ℝ³.

c) {(x, y, z) ∈ ℝ³ | 4x = 3y = 2z = }:

This set has a typo in its definition, as the equation contains multiple equal signs. Assuming it should be written as 4x = 3y = 2z = 0, it still does not contain the zero vector. Therefore, option (c) is not a subspace of ℝ³.

d) {(x, y, z) ∈ ℝ³ | x + y + z = 1}:

This set represents a plane passing through the point (1, 0, 0), (0, 1, 0), and (0, 0, 1). It contains the zero vector (0, 0, 0), as it satisfies the equation x + y + z = 1 when x = y = z = 0. It is also closed under vector addition and scalar multiplication. Therefore, option (d) is a subspace of ℝ³.

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The coordinate of the centroid of the given triangle will be at (-2.33,5).

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The given triangle with vertices has been drawn.

The midpoint of H( – 6, 3) and F(1, 5) will be as,

x = (-6 + 1)/2 = -2.5

y = (3 + 5)/2 = 4 so D(-2.5,4)

The coordinate of the centroid will intersect 2:1 of the median from the vertex side.

Thus by intercept formula,

x = (2 × -2.5 + 1 × -2)/(2 + 1) and y = (2 × 4 + 1 × 7)/(2 + 1)

x = -2.33 and y = 5

So the coordinate of vertices will be (-2.33,5).

Hence "The specified triangle's centroid's coordinate will be at (-2.33,5)".

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The limit as x approaches 5 of |x - 5| / (x - 5) does not exist. There is a discontinuity at x = 5, which prevents the existence of the limit at that point.

To determine the existence of the limit, we evaluate the left-sided and right-sided limits separately.

Left-sided limit:

As x approaches 5 from the left side (x < 5), the expression |x - 5| / (x - 5) simplifies to (-x + 5) / (x - 5). Taking the limit as x approaches 5 from the left side, we substitute x = 5 into the expression and get (-5 + 5) / (5 - 5), which is 0 / 0, an indeterminate form. This indicates that the left-sided limit does not exist.

Right-sided limit:

As x approaches 5 from the right side (x > 5), the expression |x - 5| / (x - 5) simplifies to (x - 5) / (x - 5). Taking the limit as x approaches 5 from the right side, we substitute x = 5 into the expression and get (5 - 5) / (5 - 5), which is 0 / 0, also an indeterminate form. This indicates that the right-sided limit does not exist.

Since the left-sided limit and the right-sided limit do not agree, the overall limit as x approaches 5 does not exist.

Geometrically, if we sketch the graph of the function y = |x - 5| / (x - 5), we would observe a vertical asymptote at x = 5, indicating that the function approaches positive and negative infinity as x approaches 5 from different sides. There is a discontinuity at x = 5, which prevents the existence of the limit at that point.

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