Liza played soccer for a local league, where each team played every other team twice during the season. The function f(x)=x2−x can be used to model the total number of games played in one season of the league, where x is the number of teams.

Question
If there were 132 games played in one season, what was the total number of teams in the league that season?

Miners excavated 1000 tons of dirt, and they found 8.892 ounces of gold.

Let X stand for the random variable determining how much gold is discovered for every 1,000 tonnes of dirt dug up. After that, we learn that:

X ~ N (12, 3²)

Let K be the required amount of discovered gold. 15% of the time, less than K worth of gold is discovered. Next, we have:

P (X ≤ K) = 0.15

When we transform this into a typical normal variable, we get:

P [Z ≤ (K - 12) / 3] = 0.15

From the common normal tables, we can deduce:

P (Z ≤ -1.036) = 0.15

Comparing the two equations above, we obtain:

(K - 12) / 3 = -1.036

K = 12 - (1.036 * 3) = 12 - 3.108 = 8.892

As a result, 8.892 ounces of gold are needed.

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The True statements are

(b) h is normal if and only if every left coset ah is equal to corresponding right coset ha.

(f) h is normal if and only if it is closed under conjugation by elements of group g .

In the question ,

Part(a)

The statement given in Part(a) is False because ,

According to the definition , If H is normal then aH = Ha  ,

But , since if a is not in H then aH contains a but H does , so they can't be equal.

Part(b)

The statement in Part(b) is True because,

definition of normal subgroup is , " the subgroup h is normal if and only if every left coset ah is equal to their corresponding right coset ha ".

Part(c)

The statement in Part(c) is False because,

If H is normal then aH = Ha as sets. One Example where this is satisfied , take D₈ which contains all symmetries of a square , then the subgroup {1, r2,s,sr2} where r is a rotation by π/2 and s is a flipping along one of the diagonals, then H is normal as well as abelian. However if we take Sₙ ,which contains all permutations over n elements and take its subgroup An which contains all even permutations then Aₙ is normal in Sₙ ,however it is not abelian.

Part(d)

The statement in Part(d) is False because,

This statement is true from one side that is , if H is of index 2 then it is normal however every normal subgroup need not be of index 2.

Counter Example : Every subgroup of an abelian group is normal but every subgroup need not be of index 2.

Part(e)

The statement in Part(e) is False because,

Alternative definition of a normal subgroup is that , aHa⁻¹ = H for all a in G, which is easily implied by the definition aH = Ha, by pre and post multiplying a and a⁻¹ , respectively.

Counter Example: In D₈, take the any cyclic subgroup which is not generated by any rotation ,then it will be abelian as cyclic groups are abelian .

hence it will be closed under taking conjugation but no such subgroup is cyclic.

Part(f)

The statement in Part(f) is True because,

it is one of definitions of normal subgroups , justification is given in part (b) .

Therefore , The statements in part (b) and (f) are True , rest are False .  

The given question is incomplete , the complete question is

Let g be a group and let h be a subgroup of g. which of the following claims is true? select all that apply.

(a) h is normal if and only if every left coset ah is equal to h.

(b) h is normal if and only if every left coset ah is equal to the corresponding right coset ha.

(c) h is normal if and only if it is abelian.

(d) h is normal if and only if it has index 2.

(e) h is normal if and only if it is closed under conjugation by elements of h.

(f) h is normal if and only if it is closed under conjugation by elements of g.

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Answer:

2.3125

Step-by-step explanation:

Answer:

\(2\frac{5}{16}\)

Step-by-step explanation:

\(4\frac{5}{8}=\frac{37}{8}\)

\(\frac{37}{8}:2=\frac{37}{16} = 2\frac{5}{16}\)

Answer:

Explanation in link:

The equation has a infinite number of solutions.

Step-by-step explanation:

-6x - y = -27

18x + 3y = 81

-6x - y = 27

+6x —-+6x

-Y = 27 + 6x

Then, divide both sides by negative one to get rid of that negative y:

Y = -6x + 27

Now replace the Ys in the other equation with -6x + 27.

18x + 3(-6x + 27) = 81.

Do distribute property

18x + -18x + 81 = 81

The 18x and -18x cancel each other out.

81 = 81.

Answer:

6 and 8

Step-by-step explanation:

Answer:

6 and 8

Step-by-step explanation:

Q1: 6 and 8

Q2: 8 and 12

Q3: 12 and 15

Q4: 15 and 20

Brainlist Pls!

The solution to the equation -2 = -4m + 10 is m = 3.

Here are the solutions to the given equations:

1. -10 = 5+y

To solve for y, we need to isolate y on one side of the equation.

We can do this by adding 10 to both sides of the equation.

-10 + 10 = 5 + y + 10

Simplifying,

-0 = 5 + y

We can further simplify the equation by subtracting 5 from both sides of the equation.

-5 = y

Therefore, the solution to the equation -10 = 5+y is y = -5.2.

10x = 40

To solve for x, we need to isolate x on one side of the equation.

We can do this by dividing both sides of the equation by 10.10x/10 = 40/10

Simplifying,

x = 4

Therefore, the solution to the equation 10x = 40 is x = 4.3.

-2 = -4m + 10To solve for m, we need to isolate m on one side of the equation.

We can do this by subtracting 10 from both sides of the equation.-2 - 10 = -4m.

Simplifying,

-12 = -4mWe can further simplify the equation by dividing both sides of the equation by -4.-12/-4 = m3 = m.

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Answer:

7/8

Step-by-step explanation:

\(\frac{7}{8}=0.875\)

Answer:

its 72, 36, 144

Step-by-step explanation:

yes it is!!!

With regard to a​ regression-based forecast, the standard error of the estimate gives a measure of option (C) the variability around the regression line

The standard error of the estimate in a regression-based forecast is a measure of the variability of the actual data points around the predicted values of the regression line.

It tells us how much the actual data points are likely to deviate from the predicted values, and provides a measure of the accuracy of the forecast. It is not related to the time required to derive the forecast equation, the maximum error of the forecast, or the time period for which the forecast is valid.

Therefore, the correct option is (C) The variability around the regression line.

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The give question is incomplete, the complete question is:

With regard to a​ regression-based forecast, the standard error of the estimate gives a measure of:

A. the time required to derive the forecast equation.

B. the maximum error of the forecast.

C. the variability around the regression line.

D. the time period for which the forecast is valid.

PART A: component form of the vector is:

u = <3, 3√3>

v = <2√2, -2√2>

w = <-6√3, 6>

-7(u • v) = 42(√6 - √2)

PART B:  u and w are orthogonal

The component form of a vector is <x, y>.

PART A:

u = 6(cos 60°i + sin60°j)

x = 6(cos 60) = 6 * 1/2 = 3

y = 6(sin 60) = 6 * (√3)/2 = 3√3

In component form, u = <3, 3√3>

v = 4(cos 315°i + sin315°j)

x = 4(cos 315°) = 4 * (√2)/2 = 2√2

y = 4(sin 315°) = 4 * (-√2)/2 = -2√2

v = <2√2, -2√2>

w = −12(cos 330°i + sin330°j)

x = -12(cos 330°) = -12 * (-1/2) = -6√3

y = -12(sin 330°) = -12 * (√3)/2 = 6

w = <-6√3, 6>

The dot product of two vectors is given by:

A•B = A\(_{x}\)B\(_{x}\) + A\(_{y}\)B\(_{y}\)

−7(u • v) = -7 * [(3 * 2√2) + (3√3 * -2√2)]

            = -7 * [6√2 - 6√6]

           =  42(√6 - √2)

Part B:

The vectors will be parallel if the dot product is equal to the product of the magnitudes which means the angle between the vectors is 0 or 180.

The vectors will be orthogonal if the dot product = 0. This means the angle between them = 90.

The dot product of the vectors (u) and (w) will be as follows:

u = <3, 3√3>

w = <-6√3, 6>

u • w = (3 * -6√3) + (3√3 * 6)

        = -18√3 + 18√3

        = 0

Since the result of the dot product = 0. The vectors (u) and (w) are orthogonal.

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Answer:

D: Non-Vascular

Step-by-step explanation:

Non Vascular plants are plants without Xylem and Phloem, and instead use other simpler tissues to move water around.

Answer:

B: Nick

Step-by-step explanation:

47 is the only prime number

To graph a rational function example, start by writing the equation in the form y = (ax + b)/(cx + d).

Then, plot the points where the denominator equals zero (when x = -d/c). These points are called vertical asymptotes.Next, plot the points where the numerator equals zero (when x = -b/a). These are called horizontal asymptotes.Finally, plot points between the vertical and horizontal asymptotes to graph the rational function.Plotting the points between the vertical and horizontal asymptotes will allow you to see the shape of the graph. Start by plotting points on either side of the vertical and horizontal asymptotes. Then, plot points at evenly spaced x-values between the vertical and horizontal asymptotes. For example, if the vertical asymptote is at x=-d/c, and the horizontal asymptote is at x=-b/a, you can plot points at x=-1.5d/c, x=-0.5d/c, x=-1.5b/a, and x=-0.5b/a. By plotting these points and connecting them with a smooth curve, you can graph the rational function.

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The shortest length possible in the given question is 4.0×\(10^{-10}\) cm .

Distance is measured by length. The quantity of length has the dimension of distance in the International System of Quantities. Most measurement systems choose a base unit for length from which all other units are derived. The metre serves as the fundamental unit of length in the International System of Units.

Most people interpret length to mean an object's longest dimension. Nevertheless, depending on the object's position, this is not always the case.

There are several terms for the length of a fixed object, including height, which is also known as vertical length or vertical extent, and width, breadth, or depth. When a base exists from which vertical measurements can be taken, height is used.

Nanometer(nm)- In the International System of Units (SI), a nanometer (American spelling) is a unit of length that is equal to 1000 picometres and one billionth (short scale) of a meter (0.000000001 m).

now , for find the shortest length we can covert all the given units into centimeter,

1 pm = \((10)^{-10}\) cm

1 nm = \((10)^{-7}\) cm

1 m =  100 cm

we have , 400 pm = 4× \((10)^{-8}\) cm

                4.0 nm  =  4 × \((10)^{-7}\) cm

      4.0 x \((10)^{-4}\)m = 4 × \((10)^{-2}\) cm

and   4.0 x \((10)^{-10}\) cm

hence , clearly it is shown that shortest length is 4.0 x \((10)^{-10}\) cm .

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The dimensions of the rectangle is 25m × 25m.

Two dimensions make up a rectangle: the length and, perpendicular to that, the breadth.

The three dimensions of a three-dimensional shape are length, width, and depth.

It is given that

Perimeter of the rectangle = 100m

Area is as large as possible if both the values are the same number.

The measurements must be equivalent for the rectangle to attain its maximum area.

Consider the dimensions as x

So perimeter can be written as

2 (x + x) = 100

2 (2x) = 100

By additional computation

4x = 100

Divide both sides by 4

x = 25

Therefore, the dimensions of a rectangle is 25m × 25m.

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Answer:

3/ax-4=20

first add 4 to both sides

3/ax=20+4

multiply by a/3

24a/3

so x=8a

Answer: 1/8a

Step-by-step explanation: add 4 to both sides first, which will give you 3/ax = 24. Now multiply both sides by ax/3 to get rid of the 3/ax, which will then give you 1 = 24 * ax/3, which equals to 1 = 24ax/3. This can be simplified further and you'll get 1 = 8ax. now divide both sides by 8a to isolate x, you will end up with 1/8a = x.

The result of the following questions are

\((x)(x^{7})(7x^{3})=7x^{11} \\(15x^{6}y^{2})(\frac{1}{5}x^{3}y^{3})=3x^{9}y^{5}\\\frac{2c^{2}d^{3} }{3c^{-2}d^{-4} }=\frac{2}{3}c^{4}d^{7}\)

Given,

We have to solve the questions using exponent rules

Part 1

\((x)(x^{7})(7x^{3})=7x^{1+7+3}\\=7x^{11}\)

Part 2

\((15x^{6}y^{2})(\frac{1}{5}x^{3}y^{3} )=\frac{15}{5} (x^{6+3}y^{2+3})\\ =3(x^{9}y^{5})\)

Part 3

\(\frac{2c^{2}d^{3} }{3c^{-2}d^{-4} }=\frac{2}{3}{c^{2--2}d^{3--4}\\=\frac{2}{3}c^{4}d^{7}\)

Hence, the result of the following questions are

\((x)(x^{7})(7x^{3})=7x^{11} \\(15x^{6}y^{2})(\frac{1}{5}x^{3}y^{3})=3x^{9}y^{5}\\\frac{2c^{2}d^{3} }{3c^{-2}d^{-4} }=\frac{2}{3}c^{4}d^{7}\)

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Answer:

def drugPotency(loss,expire):

   m=0

   effectiveness=100

   print('Month:',m,'\t','effectiveness:',effectiveness)

   while effectiveness>=expire:

       effectiveness=effectiveness*(1-loss/100)

       m+=1

       if effectiveness>=expire:

           print('Month:',m,'\t','effectiveness:',effectiveness)

       else:

           print('Month:',m,'\t','effectiveness:',effectiveness,'DISCARDED')

drugPotency(4.0,50.0)    

Step-by-step explanation:

Box B has the smaller range of masses, with a range of 49 grams, compared to Box A's range of 97,649 grams.

The question asks which of the boxes has the smaller range of masses and what is the value of this range in grams (g).
To find the range, we need to subtract the smallest value from the largest value in each box.
In Box A, the smallest value is 4 and the largest value is 97653. So, the range in Box A is 97653 - 4 = 97649 g.
In Box B, the smallest value is 2 and the largest value is 8762. However, we are given that key 35 represents a mass of 53 g and key 51 represents a mass of 51 g. So, the actual largest value in Box B is 51. Therefore, the range in Box B is 51 - 2 = 49 g.
Comparing the ranges, we can see that the range in Box B (49 g) is smaller than the range in Box A (97649 g).

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Answer:

x= 9, x= 2

Step-by-step explanation:

x^2- 2x- 9x+ 18= 0

x (x-2) -9 (x-2)

(x-9) (x-2)

x-9= 0, x-2= 0

Therefore, x= 9, x= 2

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Answer: \(136\)

Step-by-step explanation: \(5x7=35\) \(5x7=35\) \(6x4/2=12\) \(6x4/2=12\) \(7x6=42\) \(35+35+12+12+42=136\)

The indefinite integral is: (t^2)i + (t)j + (3t)k + C

To find the indefinite integral of the given vector function (2ti + j + 3k) with respect to t, we need to integrate each component separately.

Step 1: Integrate the i-component with respect to t:
∫(2t) dt = t^2 + C1

Step 2: Integrate the j-component with respect to t:
∫(1) dt = t + C2

Step 3: Integrate the k-component with respect to t:
∫(3) dt = 3t + C3

Now, combine the integrated components and the constants of integration (C1, C2, C3) to form the final result:

Your answer: (t^2)i + (t)j + (3t)k + C

Here, C = (C1)i + (C2)j + (C3)k is the constant of integration in vector form.

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Given:

2.2 pounds = 1 kilogram

Weight of Mary = 120 pounds.

To find:

The weight of Marry in kilograms.

Solution:

We have,

2.2 pounds = 1 kilogram

Using this conversion, we get

1 pound = \(\dfrac{1}{2.2}\) kilogram

120 pound = \(\dfrac{1}{2.2}\times 120\) kilogram

                  = \(\dfrac{120}{2.2}\) kilogram

                  \(\approx 54.54\) kilogram

Therefore, the weight of Mary is about 54.54 kilograms.

n=4 is the degree maclurins polynomial is required so that the error in the approximation is less than 0.001.

Given that,

The expression is

e⁰⁵=1+0.5+0.5²/2!+0.5³/3!+.....

We have to find what degree maclurins polynomial is required so that the error in the approximation is less than 0.001.

We know that,

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

√e=1.64872

Pₙ( x)= e⁰⁵=1+0.5+0.5²/2!+0.5³/3!+.....

P₂=1+0.5+0.5²/2!=1.625

P₃= P₂+0.5³/3!=1.6458

P₄= P₃+0.5⁴/4!=1.648404

√e - P₄ = -0.0003158

Therefore, n=4 is the degree maclurins polynomial is required so that the error in the approximation is less than 0.001.

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Answer:

77.77

Step-by-step explanation:

100% × 77 = 77.

Adding an extra 1%,

101% × 77 = 77.77

Where 100% = 1 and

101% = 1.01

Answer:

200 in²

Step-by-step explanation:

To find the area, you need to split it into two squares. The upper square would be 10 inches times 10 inches which would give you 100 inches squared. Since both are the same size, you can add both square areas together to give you 200 inches squared.

The center and shape of the distribution are respectively:

9.6

Skewed left

The center of a distribution is a found using a statistics such as mean, median, or mode, and then provides a single value that is representative of the data. The spread is one that describes how close the data values are to each other using the range or standard deviation. The shape is one that describes how the data looks on a graph.

From the bar graph, we see that the center of the distribution is at 9.6.

Similarly, we also see that it is skewed left because it is longer on the left side of its peak than on its right.

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