Suppose at a high school with 600 students 360 students like fiction books, 210 like non-fiction books, and 70 like both fiction and non-fiction books. Which statements are correct?
A) 325 students like fiction books but not non-fiction books.
B) 140 students like non-fiction books but not fiction books.
C)70 students do not like fiction or non-fiction books.
D) The probability that a randomly selected student likes both fiction and non-fiction is 0.1167.
E)The probability that a randomly selected student likes only fiction is 0.4833​

A Negative correlation coefficient means that as one variable increases, the other decreases (i.e., an inverse relationship).

Answer:

4/10

Step-by-step explanation:

total number of fruit pieces : 10

number of apple pieces : 4

probabilty of ( picking and apple ) =  favourbale outcomes / total outcomes

= 4/10

The maximum value of z is 0, and the values of the decision variables are x1 = 0, x2 = 10, x3 = 0, x4 = 0.

maximize: z = c1x1 + c2x2 + ... + cnxn

subject to

a11x1 + a12x2 + ... + a1nxn ≤ b1

a21x1 + a22x2 + ... + a2nxn ≤ b2

am1x1 + am2x2 + ... + amnxn ≤ bmxi ≥ 0 for all i

In our case,

the given LP is:maximize: z = 36x1 + 30x2 - 3x3 - 4x

subject to:

x1 + x2 - x3 ≤ 5

6x1 + 5x2 - x4 ≤ 10

xi ≥ 0 for all i

We can rewrite the constraints as follows:

x1 + x2 - x3 + x5 = 5  (adding slack variable x5)

6x1 + 5x2 - x4 + x6 = 10  (adding slack variable x6)

Now, we introduce the non-negative variables x7, x8, x9, and x10 for the four decision variables:

x1 = x7

x2 = x8

x3 = x9

x4 = x10

The objective function becomes:

z = 36x7 + 30x8 - 3x9 - 4x10

Now we have the problem in standard form as:

maximize: z = 36x7 + 30x8 - 3x9 - 4x10

subject to:

x7 + x8 - x9 + x5 = 5

6x7 + 5x8 - x10 + x6 = 10

xi ≥ 0 for all i

To apply the simplex algorithm, we initialize the simplex tableau as follows:

  |  Cj   |   x5   |   x6   |   x7   |   x8   |   x9   |   x10  |    RHS  |

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

z |  0    |   0    |   0    |  36    |   30   |   -3   |   -4   |    0    |

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

x5|   0   |   1    |   0    |   1    |   1    |   -1   |   0    |    5    |

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

x6|   0   |   0    |   1    |   6    |   5    |   0    |   -1   |   10    |

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

Now, we can proceed with the simplex algorithm to find the optimal solution. I'll perform the iterations step by step:

Iteration 1:

1. Choose the most negative coefficient in the 'z' row, which is -4.

2. Choose the pivot column as 'x10' (corresponding to the most negative coefficient).

3. Calculate the ratios (RHS / pivot column coefficient) to find the pivot row. We select the row with the smallest non-negative ratio.

Ratios: 5/0 = undefined, 10/(-4) = -2.5

4. Pivot at the intersection of the pivot row and column. Divide the pivot row by the pivot element to make the pivot element 1.

5. Perform row operations to

make all other elements in the pivot column zero.

After performing these steps, we get the updated simplex tableau:

  |  Cj   |   x5   |   x6   |   x7   |   x8   |   x9   |   x10  |    RHS  |

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

z |  0    |   0    |  0.4   |  36    |   30   |   -3   |   0    |   12    |

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

x5|   0   |   1    |  -0.2  |   1    |   1    |   -1   |   0    |   5     |

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

x10|   0  |   0    |   0.2  |   1.2  |   1   |   0    |   1    |   2.5   |

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

Iteration 2:

1. Choose the most negative coefficient in the 'z' row, which is -3.

2. Choose the pivot column as 'x9' (corresponding to the most negative coefficient).

3. Calculate the ratios (RHS / pivot column coefficient) to find the pivot row. We select the row with the smallest non-negative ratio.

Ratios: 12/(-3) = -4, 5/(-0.2) = -25, 2.5/0.2 = 12.5

4. Pivot at the intersection of the pivot row and column. Divide the pivot row by the pivot element to make the pivot element 1.

5. Perform row operations to make all other elements in the pivot column zero.

After performing these steps, we get the updated simplex tableau:

  |  Cj   |   x5   |   x6   |   x7   |   x8   |   x9   |   x10  |    RHS  |

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

z |  0    |   0    |  0.8   |  34    |   30   |   0    |   4    |   0     |

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

x5|   0   |   1    |  -0.4  |   0.6  |   1    |   5   |   -2   |   10    |

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

x9|   0   |   0    |   1    |   6    |   5    |   0   |   -5   |   12.5  |

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

Iteration 3:

No negative coefficients in the 'z' row, so the optimal solution has been reached.The optimal solution is:

z = 0

x1 = x7 = 0

x2 = x8 = 10

x3 = x9 = 0

x4 = x10 = 0

x5 = 10

x6 = 0

Therefore, the maximum value of z is 0, and the values of the decision variables are x1 = 0, x2 = 10, x3 = 0, x4 = 0.

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Answer: it’s 20m long

Step-by-step explanation:

I can’t explain .—.

Answer:

20 meters

multiply the length by itself then multiply the width by itself then add them together then the square root of the total is the diagonal length.

step-by-step explanation :

16 x 16 = 256

12 x 12 = 144

256 + 144 = 400 sq rt = 20

Answer. The diagonal length is 20 meters

Answer:36

Step-by-step explanation: 3X4 or 3 rectangles plus tow rectanges that = 12

Using the arrangements formula, it is found that there is a 0.0178 = 1.78% probability that all the girls are ahead of all the boys.

The number of possible arrangements of the n elements is the factorial of n, that is:

\(A_{n} = n!\)

The total number of outcomes is the arrangement of 8 elements, hence:

T = 8! = 40320

The desired number of outcomes is all-girls(5!), then all-boys(3!), hence:

D = 5! × 3! =120× 6=720

Hence, the probability is:

p = D/T =720/40320 = 0.0178

There is a 0.0178 = 1.78% probability that all the girls are ahead of all the boys.

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Answer:

I'm to cool to answer that

Step-by-step explanation:

is that a bad thing

The correct answer is (a) yes; the equilateral triangle tessellates the plane.

A tessellation is a tiling of the plane using one or more geometric shapes without any gaps or overlaps. For a regular polygon to tessellate the plane, the sum of its interior angles must be a multiple of 360 degrees.

For an equilateral triangle, each angle measures 60 degrees, so the sum of the angles in a triangle is 180 degrees. Therefore, the sum of the interior angles in a tessellation of equilateral triangles must be a multiple of 180 degrees.

Since the measure of the interior angle of an equilateral triangle is 60 degrees, we can tile the plane with equilateral triangles meeting at each vertex. At each vertex, the sum of the interior angles of the three triangles is 180 degrees, so the tessellation meets the requirement that the sum of the interior angles is a multiple of 360 degrees.

Therefore, the answer is (a) yes; the equilateral triangle tessellates the plane.

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The Values of (a+b)ab are undefined.

Given that, a = 3an and db = -2We need to find the values of (a+b)

Now, we have a = 3an... equation (1)Also, we have db = -2... equation (2)From equation (1), we get: n = 1/3... equation (3)Putting equation (3) in equation (1), we get: a = a/3a = 3... equation (4)Now, putting equation (4) in equation (1), we get: a = 3an... 3 = 3(1/3)n = 1

From equation (2), we have: db = -2=> d = -2/b... equation (5)Multiplying equation (1) and equation (2), we get: a*db = 3an * -2=> ab = -6n... equation (6)Putting values of n and a in equation (6), we get: ab = -6*1=> ab = -6... equation (7)Now, we need to find the value of (a+b).For this, we add equations (1) and (5),

we get a + d = 3an - 2/b=> a + (-2/b) = 3a(1) - 2/b=> a - 3a + 2/b = -2/b=> -2a + 2/b = -2/b=> -2a = 0=> a = 0From equation (1), we have a = 3an=> 0 = 3(1/3)n=> n = 0

Therefore, from equation (5), we have:d = -2/b=> 0 = -2/b=> b = ∞Now, we know that (a+b)ab = (0+∞)(0*∞) = undefined

Therefore, the values of (a+b)ab are undefined.

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Answer:

Step-by-step explanation:

Use formula for continuous interest:

If A = 3P, and r = 0.085 then the equation is:

The formula for compounded continuously is A = Pe^rt where A if the final amount, P is the initial value, r is the rate and t is the length of time.

E is the constant for continuous interest.

Using the information from the problem $20 tripled would be 20x3 = $60

Now you have 60 = 20e^0.085(t)

We need to solve for t:

Divide both sides by 20:

e^0.085(t) =3

Apply the exponent rule:

0.085(t) = ln(3)

Solve for t:

T = ln(3)/0.085

T = 12.92 years. (Round off as needed)

The absolute uncertainty in A is approximately 0.022254. Rounding it to the same number of decimal places as A, we express the absolute uncertainty as 0.05995 ± 0.00008.

To calculate the absolute uncertainty in A, we need to determine the maximum and minimum values that A can take based on the uncertainties in b and c. The absolute uncertainty in A can be found by propagating the uncertainties through the equation.

Given:

b = 95.68 ± 0.05

c = 43.28 ± 0.02

To find the absolute uncertainty in A, we can use the formula for the absolute uncertainty in a function of two variables:

ΔA = |∂A/∂b| * Δb + |∂A/∂c| * Δc

First, let's calculate the partial derivatives of A with respect to b and c:

∂A/∂b = 1/π

∂A/∂c = -1/π

Substituting the given values and uncertainties, we have:

ΔA = |1/π| * Δb + |-1/π| * Δc

= (1/π) * 0.05 + (1/π) * 0.02

= 0.07/π

Since the value of π is a constant, we can approximate it to a certain number of decimal places. Let's assume π is known to 5 decimal places, which is commonly used:

π ≈ 3.14159

Substituting this value into the equation, we get:

ΔA ≈ 0.07/3.14159

≈ 0.022254

Therefore, the absolute uncertainty in A is approximately 0.022254.

To express the result in the proper format, we round the uncertainty to the same number of decimal places as the measured value. In this case, A is approximately 0.05995, so the absolute uncertainty in A can be written as:

ΔA = 0.05995 ± 0.00008

Therefore, the correct answer is option b. 0.05995 ± 0.00008.

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A bar chart is a graph that shows the differences in frequencies or percentages among categories of a nominal or an ordinal variable.

A bar chart is a commonly used graphical representation to display the distribution of data in different categories. It is particularly useful when working with nominal or ordinal variables, where the categories are distinct and unordered or have a specific order.

In a bar chart, each category is represented by a rectangular bar whose length corresponds to the frequency or percentage associated with that category. The height of the bar represents the magnitude or count of the variable in each category, allowing for easy visual comparison between the categories.

The bars in a bar chart can be arranged horizontally or vertically, depending on the preference or nature of the data. The chart may also include labels or annotations to indicate the category names or additional information.

By examining the lengths or heights of the bars in a bar chart, it becomes easy to identify the categories with the highest or lowest frequencies or percentages, as well as to compare the relative magnitudes among the different categories. This graphical representation aids in visualizing and interpreting the distribution of a nominal or an ordinal variable effectively.

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Domain of the radical function of the form f(x) = √(ax + b) + c is given by the solution of the inequality ax + b ≥ 0 and the range is the all possible values obtained by substituting the domain values in the function.

We know that the general form of a radical function is,

f(x) = √(ax + b) + c

The domain is the possible values of x for which the function f(x) is defined.

And in the other hand the range of the function is all possible values of the functions.

Here for radical function the function is defined in real field if and only if the polynomial under radical component is positive or equal to 0. Because if this is less than 0 then the radical component of the function gives a complex quantity.

ax + b ≥ 0

x ≥ - b/a

So the domain of the function is all possible real numbers which are greater than -b/a.

And range is the values which we can obtain by putting the domain values.

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The simplified radical expression by rationalizing the denominator is, \(\frac{-6}{\sqrt{5y}}\times\frac{\sqrt{5y}}{\sqrt{5y}}\) = \(\frac{-6\sqrt{5y}}{5y}$$\) = $\frac{-6\sqrt{5y}}{5y}$.

To simplify the radical expression by rationalizing the denominator, multiply both numerator and denominator by the conjugate of the denominator.

The given radical expression is \($\frac{-6}{\sqrt{5y}}$\).

Rationalizing the denominator

To rationalize the denominator, we multiply both the numerator and denominator by the conjugate of the denominator, \($\sqrt{5y}$\)

Note that multiplying the conjugate of the denominator is like squaring a binomial:

This simplifies to:

(-6√(5y))/(√(5y) * √(5y))

The denominator simplifies to:

√(5y) * √(5y) = √(5y)^2 = 5y

So, the expression becomes:

(-6√(5y))/(5y)

Therefore, the simplified expression, after rationalizing the denominator, is (-6√(5y))/(5y).

\($(a-b)(a+b)=a^2-b^2$\)

This is what we will do to rationalize the denominator in this problem.

We will multiply the numerator and denominator by the conjugate of the denominator, which is \($\sqrt{5y}$\).

Multiplying both the numerator and denominator by \($\sqrt{5y}$\), we get \(\frac{-6}{\sqrt{5y}}\times\frac{\sqrt{5y}}{\sqrt{5y}}\) = \(\frac{-6\sqrt{5y}}{5y}$$\)

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The equation \($x^3 + y^3 + z^3 =\)k , where k ranges from 1 to 100, is a Diophantine equation that is commonly known as the "sum of three cubes" is correct.

A Diophantine equation is a polynomial equation where the coefficients and variables are integers, and the solutions are required to be integers as well.

It is named after the ancient Greek mathematician Diophantus and has applications in cryptography, coding theory, and computer science.

The problem is to find integer solutions for x, y, and z that satisfy the equation for each value of k. While there are some values of k that have known solutions, there are others that have remained unsolved for a long time.

For instance, the case k = 33 was an open problem for over 60 years until it was recently solved in 2019. The sum of three cubes problem is a well-known problem in number theory that has applications in various fields of science and engineering.

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Answer:

I believe the answer is True

Hope this Helps!

The triangles shown below must be congruent is True statement.

Two geometric figures are said to be congruent, or to be in the relationship of congruence, if one can be superimposed on the other and they correspond throughout.

As, Two triangles are congruent if their two angles and included sides are equivalent to the other triangle's two angles and included side.

Confirm that the triangles are congruent:

Both of the triangles given are right-angled triangles.

The included side between the angles 45° and 90° in both triangles is 12 units.

This is a necessary condition for the ASA congruence rule.

Thus, the given statement is True statement.

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Answer:

1/2 = D

Step-by-step explanation:

Let's look on the data we already have.

You can notice that D = 3/6 that equals 1/2

So we can defiantly say that a 1/2 equals D

Answer:

\(\huge\boxed{Answer\hookleftarrow}\)

Number of people in the U.S Army = Five hundred seventy-one thousand, one hundred eight people

Number in standard form = 571,108

Answer:

Total Cost = $72.79

Step-by-step explanation:

Tax rate: 8.75%      Tip: 18%

First, add up the cost of Mr. Rodriguez, Mrs. Rodriguez, and their 3 kids' meals.

16.25 + 19.50 + 3(6.99)    

16.25 + 19.50 + 20.97

$56.72

Next, find the cost of the tax. 8.75%

8.75% of 56.72 = 0.0875 × 56.72 = $4.963

The tip is applied after the tax so we have to add the tax first and then find 18% of the sum.

56.72 + 4.963 = 61.683

18% of 61.683 = 0.18 × 61.683 = $11.10294

Then, add to find the total cost.

56.72 + 4.963 + 11.10294  = $72.78594

I'm assuming you have to round so it's approximately $72.79

I hope its right :) good luck!

Answer:

that answer is really easy it's 72.79

The correct graph which represents the equation y = 1/2x - 1 is,

⇒ Graph of a line passing through the points negative 2 comma negative 2 and 0 comma negative 1.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The equation is,

⇒ y = 1/2x - 1

Now, After draw the equation we get;

Graph of a line passing through the points (-2, - 2) and (0, - 1).

Thus, The correct statement is,

⇒ Graph of a line passing through the points negative 2 comma negative 2 and 0 comma negative 1.

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Answer:

x = 134

Step-by-step explanation:

The mean of a data set is calculated as

mean = \(\frac{sum}{count}\)

Here mean = 113, then

\(\frac{101+119+104+111+109+x}{6}\) = 113

\(\frac{544+x}{6}\) = 113 ( multiply both sides by 6 )

544 + x = 678 ( subtract 544 from both sides )

x = 134

Answer:

ii) Over the interval [2, 4], the local minimum is at -8

iii) Over the interval [3, 5], the local minimum is at -8

iv) Over the interval [1, 4], the local maximum is at 0

Step-by-step explanation:

The graph of the function is attached below.

The local minimum is the minimum point within a specified range while the local maximum is the maximum within a specified range.

i) We can see from the graph that within [1, 3] the local minimum is at -6, hence the first option is wrong.

ii) Over the interval [2, 4], the local minimum is at -8, hence option 2 is correct

iii) Over the interval [3, 5], the local minimum is at -8, hence option 3 is correct

iv) Over the interval [1, 4], the local maximum is at 0, hence option 3 is correct

v) Over the interval [3, 5], the local maximum is at infinity, hence option 5 is not correct

Answer:

B, C, D

Step-by-step explanation:

Hope this helps!

Answer:

3x² + 8x + 1

Step-by-step explanation:

Given

4(x² - 1) - (x² - 8x - 5) ← distribute both parenthesis

= 4x² - 4 - x² + 8x + 5 ← collect like terms

= 3x² + 8x + 1

Use statistical software or a calculator that allows for probability calculations. There are various options available such as Excel, SPSS, or online probability calculators.

To calculate the probability using technology, follow these steps:

Gather the values identified in previous steps that are required for the calculation.
Use statistical software or a calculator that allows for probability calculations. There are various options available such as Excel, SPSS, or online probability calculators.

Enter the necessary values into the software or calculator. These values will depend on the specific problem you are working on, such as the number of favourable outcomes and the total number of possible outcomes.

Follow the instructions provided by the software or calculator to compute the probability.

Most tools will have specific functions or formulas to calculate probabilities based on different scenarios (e.g., binomial, normal distribution, etc.).

Round the resulting probability to three decimal places as instructed.

By using technology and the values from previous steps, you can accurately calculate the probability by following these steps.

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Answer:

pretty sure x is 60 because 60+25 is 80 and its the same as N so 80

Step-by-step explanation:

The series Σ (from n = 1 to infinity) of 1 / (n^6 - 8) is also convergent. The subtraction of 8 from the denominator does not alter the convergence properties of the series.

To determine whether the series Σ (from n = 1 to infinity) of 1 / (n^6 - 8) is convergent or divergent, we need to analyze its behavior.

We can start by considering the power of n in the denominator, which is 6 in this case. When the power of n in the denominator is greater than 1, we typically compare the series to a p-series, which is a series of the form Σ (from n = 1 to infinity) of 1 / n^p.

For a p-series to be convergent, the value of p must be greater than 1. Conversely, if p is less than or equal to 1, the p-series is divergent.

In our case, the series has n^6 in the denominator, which means the power of n is greater than 1. Hence, we compare it to a p-series with p = 6.

Since p = 6 is greater than 1, we can conclude that the corresponding p-series, Σ (from n = 1 to infinity) of 1 / n^6, is convergent. This is a known result.

Now, let's examine the subtraction of 8 from the denominator in our given series. Subtracting a constant term from the denominator does not affect the convergence or divergence of the series. It only shifts the series horizontally along the x-axis. Therefore, the series Σ (from n = 1 to infinity) of 1 / (n^6 - 8) has the same convergence properties as the p-series Σ (from n = 1 to infinity) of 1 / n^6.

As we established earlier, the p-series with p = 6 is convergent. Therefore, the series Σ (from n = 1 to infinity) of 1 / (n^6 - 8) is also convergent.

In conclusion, the given series Σ (from n = 1 to infinity) of 1 / (n^6 - 8) is convergent. The comparison with the corresponding p-series Σ (from n = 1 to infinity) of 1 / n^6, which is convergent, allows us to determine its convergence. The subtraction of 8 from the denominator does not alter the convergence properties of the series.

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Answer:

ITS C

Step-by-step explanation:

Because since it has a one time fee of 5, the graph has to start at 5, then you narrow it down to c or d, if you look at d then you can see that the graph isnt going up 2 dollars, so then the answer is c.

The quotient and remainder when 3x^(4)-x^(2) is divided by x^(3)-x^(2)+1 is x+1 and 2x^2-3, respectively.

To find the quotient and remainder, use long division. First, divide the leading terms of both polynomials. 3x^4 divided by x^3 gives x.

Next, multiply the quotient by the divisor and subtract from the dividend. x(x^3-x^2+1) subtract from 3x^4-x^2 gives x+1.

Finally, divide the remainder by the divisor to get the remainder. x+1 divided by x^3-x^2+1 gives 2x^2-3. Therefore, the quotient and remainder when 3x^(4)-x^(2) is divided by x^(3)-x^(2)+1 is x+1 and 2x^2-3, respectively.

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