Choose all the fractions that are equivalent to 4/8. (Click all that apply.)
2/6
8/16
1/2
6/3
5/10
7/11

Answer:

10 and 24units

Step-by-step explanation:

Pythagoras' Theorem applies to right angle triangles with the formula:

\( {c}^{2} = {a}^{2} + {b}^{2} \)

where c is the longest side, with a and b the shorter ones (interchangable)

With the parameters given from the question and the formula given as well, we can find the value of x and therefore the side lengths.

By Pythagoras' Theorem,

\( {26}^{2} = ( {5x)}^{2} + ( {12x)}^{2} \\ 676 = 25 {x}^{2} + 144 {x}^{2} \\ 169 {x}^{2} = 676 \\ {x}^{2} = 676 \div 169 \\ {x}^{2} = 4 \\ x = \sqrt{4} \\ = 2\)

Now we can find the side lengths.

\(5x = 5(2) = 10units \\ 12x = 12(2) = 24units\)

Therefore the side lengths are 10 and 24 units.

Among the provided answer options, the closest value to -0.555 is -0.55, which is option c. Therefore, option c (-0.55) is the value of c that satisfies P(Z ? c) = 0.71.

The notation P(Z ? c) represents the probability that a standard normal random variable Z is less than or equal to c. To find the value of c that corresponds to P(Z ? c) = 0.71, we need to determine the Z-score associated with this probability.

Using a standard normal distribution table or a calculator, we can find that a Z-score of approximately 0.555 corresponds to a cumulative probability of 0.71. However, since we are looking for the value of c in P(Z ? c), we need to consider the opposite inequality.

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The probability of event A and event B is 6.

Given that, P(A)=6, P(B)=20 and P(A∩B)=6.

P(A/B) Formula is given as, P(A/B) = P(A∩B) / P(B), where, P(A) is probability of event A happening, P(B) is the probability of event B.

P(A/B) = P(A∩B) / P(B) = 6/20 = 3/10

We know that, P(A and B)=P(A/B)×P(B)

= 3/10 × 20

= 3×2

= 6

Therefore, the probability of event A and event B is 6.

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The differential equation is dx/dt = Ax with A = [-3 1] [2 -2].The nullclines are calculated as follows:Setting dx/dt = 0 to find the nullclines for x_nullcline

Ax = 0 => [-3 1] [x1] = [0][2 -2] [x2] [0] => -3x1 + x2 = 0 => x2 = 3x1At the nullcline, x2 = 3x1, so the nullcline is the line y = 3x.The nullclines for y_nullcline are calculated in a similar way.Ax = 0 => [-3 1] [x1] = [0][2 -2] [x2] [0] => 2x1 - 2x2 = 0 => x1 = x2At the nullcline, x1 = x2, so the nullcline is the line y = x.

To find the equilibrium point, you need to set the two nullclines equal to each other:3x = x => x = 0The equilibrium point is at (0, 0).The taylor series representation of f(x)= ln(3+4x) about x=0 is given by the formula:∑(n = 0 to ∞) (fⁿ(0)/n!)(x - 0)ⁿThe first few derivatives of f(x) are:f(x) = ln(3 + 4x)f'(x) = 4/(3 + 4x)f''(x) = -16/(3 + 4x)²f'''(x) = 96/(3 + 4x)³The nth derivative of f(x) is:fⁿ(x) = (-1)ⁿ₋¹ (n - 1)! 4ⁿ/(3 + 4x)ⁿTherefore, the taylor series representation of f(x)= ln(3+4x) about x=0 is:ln(3 + 4x) = Σ(n = 0 to ∞) (-1)ⁿ₋¹ (n - 1)! 4ⁿ/(3ⁿ n!) xⁿ
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Answer:

x = 16

y = 14.8

Step-by-step explanation:

hope that helped

ALM not BLM ‏‏‎ ‎‏‏‎ ‎

Answer: 3.6 mph

Step-by-step explanation:

That's the only step since they give you that much.

More specifically though, we could create an equation.

\(12.6=3.5x\) where x is the mph.

Solve the equation by dividing both sides by 3.5 and get the same answer.

Let other one be x

ATQ

\(\\ \sf\longmapsto x+\dfrac{-8}{17}=-8\)

\(\\ \sf\longmapsto\dfrac{17x-8}{17}=-8\)

\(\\ \sf\longmapsto 17x-8=17(-8)=-136\)

\(\\ \sf\longmapsto 17x=-136+8\)

\(\\ \sf\longmapsto 17x=-128\)

\(\\ \sf\longmapsto x=\dfrac{-128}{17}\)

Answer:

\(let \: the \: unknown \: = x \: and \: y \\ x + y = - 8 \\ y = \frac{ - 8}{17} \\ x - \frac{8}{17} = - 8 \\ x = - 8 + \frac{8}{17} \\ x = \frac{17 \times - 8 + 8}{17} \\ x = \frac{ - 136 + 8}{17} \\ x = \frac{ - 128}{17} \\ thank \: you\)

The estimated probability of a success in this scenario would be 0.6, or 60%.

To estimate the probability of success in this scenario, we need to determine the frequency of success (occurrence of numbers 1, 2, and 3) in the randomly generated list of integers from 0 to 4.

Let's assume we have a large sample of these randomly generated lists, and we record the number of successes in each list. The estimated probability of success can be calculated by dividing the total number of successes by the total number of trials (lists).

For example, if we have observed 5000 lists and found that the number of successes (1, 2, or 3) occurred in 3000 of those lists, the estimated probability of success would be:

Estimated probability of success = Number of successes / Total number of trials

Estimated probability of success = 3000 / 5000

Estimated probability of success = 0.6

Therefore, the estimated probability of a success in this scenario would be 0.6, or 60%.

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The maximum amount of mushrooms Alberto can eat in a day is 4 kg.

Alberto can eat at most 4 kg of mushrooms in a day. If he picks 4 kg of mushrooms himself, he will not gain any monetary profit, and if he picks oranges, the monetary gain will be less than picking mushrooms.

He can sell mushrooms in the market for 514.79 per kg, whereas he can sell oranges for 38.7 per kg. It is evident that he will gain a lot of monetary profit by selling mushrooms rather than oranges.

Alberto can buy mushrooms from the market and sell them for a higher price. But it does not mean that he can eat more mushrooms. Alberto can consume a maximum of 4 kg of mushrooms whether he picks them himself or buys them from the market.

Therefore, the maximum amount of mushrooms Alberto can eat in a day is 4 kg.
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Option A is correct, the number of ways to select 2 captains out of 10 players is 45.

Given that 10 players are there in a soccer team we have to choose 2 captains.

To choose 2 captains out of 10 players, we can use the combination formula.

The number of ways to select r items from a set of n items is given by the formula:

C(n, r) = n! / (r!(n - r)!)

In this case, we have n = 10 players and we want to select r = 2 captains. Plugging these values into the formula:

C(10, 2) = 10! / (2!(10 - 2)!)

= 10! / (2!8!)

= (10×9×8!) / (2!8!)

= 10 × 9 / 2

= 45

Therefore, the number of ways to select 2 captains out of 10 players is 45. The correct answer is 45.

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Answer:

1. $30.50

2. 20+1.75x

Step-by-step explanation:

(i) If the composition gof is injective, then the function f is also injective.

(ii) If the composition gof is surjective, then the function g is also surjective.

(i) To prove that f is injective, we need to show that for any two elements a1 and a2 in set A, if f(a1) = f(a2), then a1 = a2. Suppose gof is injective, which means that for any two elements c1 and c2 in set C, if gof(c1) = gof(c2), then c1 = c2. Now, let's consider two elements a1 and a2 in set A such that f(a1) = f(a2). We can rewrite this as gof(c1) = gof(c2), where c1 = f(a1) and c2 = f(a2). Since gof is injective, we have c1 = c2, which implies f(a1) = f(a2). By the injectivity of the function f, we can conclude that a1 = a2, proving that f is injective.

(ii) To prove that g is surjective, we need to show that for every element b in set B, there exists an element c in set C such that g(c) = b. Suppose gof is surjective, which means that for every element b in set B, there exists an element c in set C such that gof(c) = b. Now, let's consider an arbitrary element b in set B. Since gof is surjective, there exists an element c in set C such that gof(c) = b. Let's denote this element c as c0. By the definition of function composition, we have g(f(a0)) = b, where a0 = f(c0). Therefore, for every element b in set B, there exists an element a0 in set A (specifically, a0 = f(c0)) such that g(a0) = b, proving that g is surjective.

If the composition gof is injective, then f is injective, and if the composition gof is surjective, then g is surjective.

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The given information about the person using a 3-month new member discount does not provide any direct insight into the probability of the person being a member for more than a year.

However, if we assume that the discount is only available to new members and that the probability of a person being a new member is equal to the probability of a person being a member for less than a year, then we can use the following formula to calculate the desired probability:

Probability (member for more than a year | using 3-month discount) = Probability (using 3-month discount | member for more than a year) * Probability (member for more than a year) / Probability (using 3-month discount)

Unfortunately, we do not have enough information to estimate the individual probabilities required for this calculation. Therefore, we cannot provide an exact answer to the question.    

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Surface area of cuboid  is = 312 ,With dedication and effort, you can succeed in your geometry test and feel confident about your understanding of the subject.

Surface area of a cuboid is = 2lw + 2lh + 2 hw

where ; l= length

w= width.

h = height

= 2(10×6)+2(10×6)+2(6×6)

=2(60)+2(60)+2(36)

=120+120+72

=312

Geometry can be challenging, but with the right mindset and approach, you can do well. To start, make sure you understand the basic concepts and definitions.

Then, practice solving problems and applying those concepts. Don't be afraid to ask questions or seek help when you need it. Utilize resources such as textbooks, online tutorials, and practice worksheets.

Also, try to relate geometry to real-life situations to make it more interesting and relevant. Remember to take breaks and stay organized to avoid feeling overwhelmed.

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There are 144 possible sequences of chip colors.

We can solve this problem by counting the number of possible sequences of chip colors that can be drawn from the bag until the total value of the chips is at least $7.

Let's consider all the possible sequences of chips that can be drawn from the bag. The first chip can be any of the 6 chips in the bag. For each chip color, there are different scenarios that can happen after drawing the first chip:

Therefore, the total number of possible sequences of chip colors that can be drawn from the bag until the total value of the chips is at least $7 is: 2 x 32 + 1 x 32 + 3 x 16 = 144

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The Taylor series formula in summation notation f(t) = Σ[n=0 to infinity] { (1/n!)f^n(a)(t-a)^n } where f^n(a) denotes the nth derivative of f(t) evaluated at t = a.

Since the functions f(t) and g(t) have not been given in the question, I cannot provide a specific answer to this question. However, I can provide a general approach to finding the power series expansion of a function about a point.

To find the power series expansion of a function f(t) about a point t = a, we can use the Taylor series formula:

f(t) = f(a) + f'(a)(t-a) + (1/2!)f''(a)(t-a)^2 + (1/3!)f'''(a)(t-a)^3 + ...

where f'(a), f''(a), f'''(a), ... are the first, second, third, and higher-order derivatives of f(t) evaluated at t = a.

To find the first four nonzero terms of the power series expansion, we can calculate the values of f(a), f'(a), f''(a), and f'''(a) at t = a, substitute them into the Taylor series formula, and simplify the resulting expression. The first four nonzero terms will be the constant term, the linear term, the quadratic term, and the cubic term.

To find the general term of the power series expansion, we can write the Taylor series formula in summation notation:

f(t) = Σ[n=0 to infinity] { (1/n!)f^n(a)(t-a)^n }

where f^n(a) denotes the nth derivative of f(t) evaluated at t = a. The general term of the power series expansion is given by the expression in the curly braces. We can use this expression to find any term in the series by plugging in the appropriate values of n and f^n(a).

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Answer:

4 units to the right

Step-by-step explanation:

The 90% confidence interval for the average speed of all the cars passing through the intersection is (41.29, 42.71) miles per hour.

To calculate the confidence interval, we can use the formula:

Confidence interval = Sample mean ± (Critical value * Standard error)

Given that the sample mean is 42 miles per hour and the standard deviation is 4.2 miles per hour, we need to determine the critical value and the standard error.

Since we have a sample size of 85, we can use the t-distribution with (n-1) degrees of freedom to find the critical value. With a 90% confidence level, the corresponding critical value for a two-tailed test is approximately 1.66.

The standard error is calculated as the standard deviation divided by the square root of the sample size:

Standard error = (Standard deviation) / √(Sample size)

Standard error = 4.2 / √85 ≈ 0.456

Now we can plug in the values into the confidence interval formula:

Confidence interval = 42 ± (1.66 * 0.456)

Confidence interval ≈ (41.29, 42.71)

Therefore, the 90% confidence interval for the average speed of all the cars passing through the intersection is (41.29, 42.71) miles per hour.

Based on the given data and calculations, we can conclude that with 90% confidence, the average speed of all the cars passing through the intersection falls within the range of 41.29 to 42.71 miles per hour.

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The optimal value of z is 450. The minimum value of z is 300, which occurs at the vertex (200, 0). However, since 300 is not one of the provided options, choose the closest value, which is 450.

The given minimization problem is:
Min z = 1.5x1 + 2x2
subject to:
x1 + x2 ≥ 300
2x1 + x2 ≥ 400
2x1 + 5x2 ≤ 750
x1, x2 ≥ 0
To solve this linear programming problem, you can use the graphical method or the simplex method. In this case, we'll use the graphical method. First, rewrite the inequalities as equalities to find the boundary lines:
x1 + x2 = 300
2x1 + x2 = 400
2x1 + 5x2 = 750
Now, plot these lines on a graph and identify the feasible region. The feasible region is the area where all the constraints are satisfied. In this case, the feasible region is bounded by the intersection of the three lines.
Next, identify the vertices of the feasible region. For this problem, there are three vertices: (0, 300), (150, 150), and (200, 0). Now, evaluate the objective function z at each vertex:
z(0, 300) = 1.5(0) + 2(300) = 600
z(150, 150) = 1.5(150) + 2(150) = 450
z(200, 0) = 1.5(200) + 2(0) = 300
The minimum value of z is 300, which occurs at the vertex (200, 0). However, since 300 is not one of the provided options, choose the closest value, which is 450.

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A. The algebraic expression that represents the total number of miles Leah runs each week is 5*M.

B. The algebraic expression that represents the total number of miles Leah runs in a year is 260*M.

Leah runs M miles everyday during the week except for Wednesday or Sunday.

We need to write the algebraic expression that represents the total number of miles Leah runs each week. Leah runs for 5 days in a week. The total number of miles run in a week is 5*M.

We need to write the algebraic expression that represents the total number of miles Leah runs in a year. Leah runs 5*M miles in a week. The total number of miles run in a year is (5*M)*52 = 260*M.

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Answer:

y = 3x - 20

Step-by-step explanation:

First, we have to find the slope of the equation. We can do by taking the opposite reciprocal of the slope of the original line.

The opposite reciprocal of-1/3 is 3/1 or 3.

So, the slope of our equation will be 3. Our equation so far is:

y = 3x + b.

To find b, or the y-intercept of the line, we can simply substitute the given coordinates into the equation. If we replace x with 6 and y with -2 and solve the equation, we can find the value of b.

-2 = 3(6) + b

-2 = 18 + b

-2 - 18 = b

b = -20

So the equation is,

y = 3x -20.

To check our equation, we can again substitute the coordinates into the equation and solve. If both sides are equal, then the equation is correct.

-2 = 6(3) - 20

-2 = 18 - 20

-2 = -2

The two lines are perpendicular if a 90° angle is formed when they

intersect.

The equation of the line that passes through point Z(6, -2) and is perpendicular to the line \(y = -\dfrac{1}{3} \cdot x + 2\) is ; y = 3·x - 20

Reason:

The equation of the required line is, y = 3·x - 20

The given point is Z(6, -2)

Perpendicular to the line, \(y = -\dfrac{1}{3} \cdot x + 2\)

Solution:

The slope of a line perpendicular to another line having a slope, m, is \(-\dfrac{1}{m}\)

The slope of the given line is \(-\dfrac{1}{3}\)

The slope of the perpendicular line is therefore;

\(m = -\dfrac{1}{\left(-\dfrac{1}{3}\right)} = \dfrac{3}{1} = 3\)

The point and slope form of the equation of the given line is therefore;

y - (-2) = 3·(x - 6)

y + 2 = 3·x - 3×6 = 3·x - 18

y = 3·x - 18 - 2 = 3·x - 20

y = 3·x - 20

The equation of the line that passes through point Z(6, -2) and is perpendicular to the line \(y = -\dfrac{1}{3} \cdot x + 2\) is therefore;

y = 3·x - 20

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the solution to the system of equations is x = 2 and y = 1.

To solve the system of equations by substitution, we will solve one equation for one variable and substitute it into the other equation.

Given the system of equations:

1) y = 6x - 11

2) -2x - 3y = -7

Step 1: Solve equation (1) for y.

  y = 6x - 11

Step 2: Substitute the value of y from equation (1) into equation (2).

  -2x - 3(6x - 11) = -7

Step 3: Simplify and solve for x.

  -2x - 18x + 33 = -7

  -20x + 33 = -7

  -20x = -7 - 33

  -20x = -40

  x = (-40)/(-20)

  x = 2

Step 4: Substitute the value of x into equation (1) to find y.

  y = 6(2) - 11

  y = 12 - 11

  y = 1

Therefore, the solution to the system of equations is x = 2 and y = 1.

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The solution to the system of equations y = 6x - 11 and -2x - 3y = -7 is x = 2 and y = 1. This is achieved by substituting y into the second equation, simplifying, and solving for x, then substituting x back into the first equation to solve for y.

To solve the system of equations y = 6x - 11 and -2x - 3y = -7 by substitution, we start by substituting the equation y = 6x - 11 into the second equation in place of y, giving us -2x - 3(6x - 11) = -7. Next, simplify the equation by distributing the -3 inside the parentheses to get -2x - 18x + 33 = -7. Combine like terms to get -20x + 33 = -7. Subtract 33 from both sides to obtain -20x = -40, and finally, divide by -20 to find x = 2.

Once we find the solution for x, we substitute it back into the first equation y = 6x - 11. Substituting 2 in place of x gives y = 6*2 - 11, which simplifies to y = 1.

Therefore, the solution to the system of equations is x = 2 and y = 1.

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Answer:

3/10

Step-by-step explanation:

generally, "of" means "multiplication".

thus, 1/2 * 3/5 = 3/10 (or 0.3)

Answer:

11.5

Step-by-step explanation:

the mean of a set of numbers is the sum divided by the number of terms

(15+4+6+12+16+20+16+3)/8

The required mean of the data for the sample of Dr. Frank's dentist office is  11.5.

Given that,
The number of patients treated at Dr. Frank's dentist's office each day was recorded for eight days: 15, 4, 6, 12, 16, 20, 16, 3. Using the given data, find the mean for this sample is to be determined.

The average of the values is the ratio of the total sum of values to the number of values.

Here,
The number of patients treated was recorded for eight days,
Sample space =  15, 4, 6, 12, 16, 20, 16, 3
n(s) = 8
Mean = (15 + 4 + 6 + 16 + 20 + 16 + 3) / 8
Mean = 92 / 8
Mean = 11.5

The required mean of the data for the sample of Dr. Frank's dentist office is  11.5.

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Answer:

A B and C

Step-by-step explanation:

it's a simple question