On a shelf of a book store, there are 3 books on English, 4 books on Economics and 5 books on Business Mathematics. How many collections can be made, if each collection consists of at most 3 books on each subject?​

The volume of the cylinder is 602.88 ft³.

The surface area of the cylinder is  301.44 ft²

volume of a cylinder = πr²h

volume of a cylinder = 3.14 × 4² × 12

volume of a cylinder = 3.14 × 16 × 12

volume of a cylinder = 602.88 ft³

Surface are of a cylinder = 2πr(r + h)

Surface are of a cylinder = 2 × 3.14 × 4(4 + 8)

Surface are of a cylinder =  25.12(12)

Surface are of a cylinder = 301.44 ft²

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Option D, 4.1 is the correct answer. The mean baseball score is 4.1 given the table of values of baseball scores and score number of students. This can be obtained by using the formula for mean.

Mean can be obtained by the formula,

Mean = [tex]\frac{sum\ of\ observations}{total\ number\ of\ observations}[/tex]

Sum of basketball scores = 0×1 + 1×2 + 2×5 + 3×3 + 4×6 + 5×7 + 6×9

= 0 + 2 + 10 + 9 + 24 + 35 + 54

total number of basketball scores =  1 + 2 + 5 + 3 + 6 + 7 + 9 = 33

Mean = [tex]\frac{0+2+10+9+24+35+54}{33}[/tex] = 4.06 ≈ 4.1

Hence the mean baseball score is 4.1 given the table of values of baseball scores and score number of students. Option D, 4.1 is the correct answer.

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[tex]\\ \rm\Rrightarrow \dfrac{x^2+3x+2}{x^2-4x-5}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{x^2+2x+x+2}{x^2-5x+x-5}[/tex]

[tex]\\ \rm\Rrightarrow {(x+2)(x+1)}{(x-5)(x+1)}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{x+2}{x-5}[/tex]

And

[tex]\\ \rm\Rrightarrow \dfrac{x^2+7x+12}{x^2-3x-28}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{x^2+4x+3x+12}{x^2-7x+4x-28}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{(x+4)(x+3)}{(x-7)(x+4)}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{x+3}{x-7}[/tex]

The equation for the plane that contains the line and is perpendicular to the plane 2 · x + y - 3 · z = - 4 is - 10 · x + 17 · y - z = 76.

From the equation of the plane 2 · x + y - 3 · z = - 4 we know that its normal vector is (2, 1, - 3). Hence, we have found two direction vectors and already know a point, which are part of this parametric equation:

(x, y, z) = (- 3, 4, 5) + t · (3, 2, 4) + u · (2, 1, - 3)     (1)

The normal vector of the plane is equal to the cross product of the direction vectors of (1):

[tex]\vec n = (3, 2, 4) \,\times\,(2, 1, -3)[/tex]

[tex]\vec n = \left|\begin{array}{ccc}\hat{i}&\hat{j}&\hat{k}\\3&2&4\\2&1&-3\end{array}\right|[/tex]

[tex]\vec n = (-6-4,8+9, 3-4)[/tex]

[tex]\vec n = (-10, 17, -1)[/tex]

Since the plane contains the point (x, y, z) = (- 3, 4, 5), then we find that the independent constant of the equation of the plane is:

- 10 · x + 17 · y - z = k

- 10 · (- 3) + 17 · 4 - 5 = k

30 + 51 - 5 = k

k = 76

The equation for the plane that contains the line and is perpendicular to the plane 2 · x + y - 3 · z = - 4 is - 10 · x + 17 · y - z = 76.

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The composite function G(F(x)) = x² + 4 is formed with these following original functions:

D. F(x) = x² and G(x) = x + 4.

The composite function of f(x) and g(x) is given as follows:

[tex](f \circ g)(x) = f(g(x))[/tex]

For g of f(x), we have that:

[tex](g \circ f)(x) = g(f(x))[/tex]

For this problem, we have that:

G(F(x)) = x² + 4.

Which is possible with option D, as:

[tex]G(F(x)) = G(x^2) = x^2 + 4[/tex]

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Answer:

Wolfram|Alpha is capable of solving a wide variety of systems of equations. It can solve systems of linear equations or systems involving nonlinear equations, and it can search specifically for integer solutions or solutions over another domain. Additionally, it can solve systems involving inequalities and more general constraints.

Step-by-step explanation:

Using proportions, they must win 22 games to maintain to the ratio of wins to losses.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Considering the next 28 games, we have that:

To keep the same proportion, we have that:

[tex]\frac{33}{42} = \frac{33 + x}{70}[/tex]

Applying cross multiplication:

42(33 + x) = 33 x 70

Simplifying by 14:

3(33 + x) = 33 x 5

3x = 33 x 5 - 33 x 3

3x = 33 x 2

3x = 66

x = 66/3

x = 22.

They must win 22 games to maintain to the ratio of wins to losses.

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Answer:

y = 2

Step-by-step explanation:

Algebraic Equation is an equation where alphabets are used to represent numbers.

Solving the above question,

Let the number = y

Therefore,

Sum of the number = y + 3

If it's subtracted from 10 it becomes

10 - ( y + 3 )

The result : 10 - y - 3 = 5

- y = 5 - 10 + 3

- y = -2

Therefore,

y = 2

Answer: 4.08x2

Step-by-step explanation:

Answer:

4.08x2

Step-by-step explanation:

Answer:

(a) B' U U = { f,g,h,p,q,r}

(b) B ∩ U = {g,q,r}

Step-by-step explanation:

Greetings !

(a) B/c B'= {X: X∈U and X∉B}

thus,B'= {f,h,p}

B' U U= {f,h,p} U {f,g,h,p,q,r}

= {f,g,h,p,q,r}

(b) B ∩ U= {g,q,r}

The probability that the mean fill is more than 84.8 ounces is 0.39358

From the question, the given parameters about the distribution are

The z-score of the data value is calculated using the following formula

z = (x - mean value)/standard deviation

Substitute the given parameters in the above equation

z = (84.8 - 84.5)/1.1

Evaluate the difference of 84.8 and 84.5

z = 0.3/1.1

Evaluate the quotient of 0.3 and 1.1

z = 0.27

The probability that the mean fill is more than 84.8 ounces is then calculated as:

P(x > 84.8) = P(z > 0.27)

From the z table of probabilities, we have;

P(x > 84.8) = 0.39358

Hence, the probability that the mean fill is more than 84.8 ounces is 0.39358

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Answer:

a

Step-by-step explanation:

The value of 1376 * 13 is 17888

The expression is given as:

1376 * 13

Express 1376 as 1300 + 76

(1300 + 76) * 13

Expand

1300 * 13 + 76 * 13

Evaluate the product

16900 + 988

Evaluate the sum

17888

Hence, the value of 1376 * 13 is 17888

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The output voltage of the op-amp circuit shown is -5v.

It should be noted that voltage is the electric potential difference between two points l.

In this case, the output voltage will be:

= -5 × i

where I = 1.

Voltage = -5 × 1

= -5v

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Step-by-step explanation:

when you mark such points on a coordinate grid, and mark also the coordinate differences in x and y direction as soft lines, you notice that these coordinate difference lines and the direct connection between the 2 points create a right-angled triangle.

so, Pythagoras applies :

c² = a² + b²

with c being the Hypotenuse (the baseline opposite of the 90° angle, which is the direct connection between the 2 points). a and b are the legs (coordinate differences).

so,

distance² = (8 - 6)² + (2 - 10)² = 2² + (-8)² = 4 + 64 = 68

distance = sqrt(68) = 8.246211251... ≈ 8.2

Answer:

Graph attached.

Step-by-step explanation:

Given equation:

[tex]y=\dfrac{1}{3}x+5[/tex]

The given equation is a linear equation in slope-intercept form, where 1/3 is the slope and 5 is the y-intercept.

To graph the equation, find and plot at least two points, then draw a straight line through them.

To find the points on the line, input values of x into the equation:

[tex]x = 0 \implies y=\dfrac{1}{3}(0)+5 \implies (0,5)[/tex]

[tex]x=3 \implies y=\dfrac{1}{3}(3)+5 \implies (3,6)[/tex]

[tex]x=6 \implies y=\dfrac{1}{3}(6)+5 \implies (6,7)[/tex]

See attachment for the graph of the given equation.

Find some points

x=0

x=3

x=-3

Graph attached

The value of the ratio based on the angle illustrated is 1:12.

From the information given, it should be noted that the angle in a circle is 360°. Therefore, the value of theta will be:

= 360° - 330°

= 30°

The equivalent expression based on the angle will be:

= 30/360

= 1/12

= 1:12

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If one of the roots is [tex]w=B+2i[/tex], then the other root is its conjugate [tex]\bar w=B-2i[/tex]. So we can factorize the quadratic to

[tex]z^2 + 4z + 20 + iz (A+1) = (z-(B+2i)) (z-(B-2i))[/tex]

Expand the right side and collect all the coefficients.

[tex]z^2 + (4+(A+1)i) z + 20 = z^2 - 2B z + B^2+4[/tex]

From the [tex]z[/tex] and constant terms, we have

[tex]\begin{cases}4 + (A+1)i = -2B \\ 20 = B^2 + 4 \end{cases}[/tex]

From the second equation we get

[tex]B^2 = 16 \implies B = \pm4[/tex]

Then

[tex]4+(A+1)i = \pm8[/tex]

[tex](A+1)i = 4 \text{ or } (A+1)i = -12[/tex]

Since [tex]\frac1i=-i[/tex], we have

[tex]-\dfrac{A+1}i = 4 \text{ or } -\dfrac{A+1}i = -12[/tex]

[tex]A+1 = -4i \text{ or } A+1 = 12i[/tex]

[tex]\boxed{A = -1 - 4i \text{ or } A = -1 + 12i}[/tex]

The 80% confidence interval for the number of chocolate chips per cookie for Big Chip cookies is (12.4,13.3).

Given that a sample of 101 cookies and per cookie in the sample has a mean of 12.9 and a standard deviation of 3.2.

From the given information,

Let n=101 represents the size of the sample.

Let [tex]\bar{x}[/tex]= 12.9 represents the mean of the sample.

Let s= 3.2 represents the standard deviation of the sample.

Degrees of freedom:

df = n-1

df= 101-1

df= 100

The critical value of t at 0.2 level of significance with 100 degrees of freedom is,

[tex]\begin{aligned}t_{cric}&=t_{(\frac{\alpha}{2}, n-1)}\\ &=t_{(0.2,100)}\\ &=1.2900\end[/tex]

The 80% confidence interval for the number of chocolate chips per cookie for Big chip cookies is computed as follows:

[tex]\begin{aligned}CI_{80\%}&=\bar{x}\pm t_{(\frac{\alpha}{2},n-1)}\left(\frac{s}{\sqrt{n}}\right)\\ &=12.9\pm 1.2900\left(\frac{3.2}{\sqrt{101}}\right)\\ &=12.9\pm 1.2900\times 0.3184\\ &=12.9\pm 0.410736\\ &=12.489264,13.310736\end[/tex]

Hence, the 80% confidence interval for the number of chocolate chips per cookie for Big Chip cookies when the mean is 12.9 and standard deviation is 3.2 is (12.4,13.3).

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A logarithmic function is the inverse of an exponential function.

A logarithmic function is the inverse of an exponential function.

Now we have the function;

f(x) = log(x) and the translated function f(x) = log (x-h) + k.

Similarly;

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Missing parts;

Use the graphing calculator to graph the parent function.

f(x) = log(x)

Add the translated function.

f(x) = log (x-h) + k

Plug in different values of h and k to answer the following questions.

What happens when h is positive?

What happens when h is negative?

What happens when k is positive?

What happens when k is negative?

Answer:

When h is positive: horizontal shift to the right

When h is negative: horizontal shift to the left

When k is positive: vertical shift up

When k is negative: vertical shift down

Step-by-step explanation:

got it right on Edge

Answer:

(4, 7/2)

Step-by-step explanation:

midpoint = x values/2, y values/2

The set of all three-digit binary numbers as required in the task content includes; 100,101,110,111.

A binary number by definition is one which is made of a combination of numbers 0 and 1.

On this note, it follows that the three digits binary numbers in discuss include; 100,101,110,111.

Binary numbers are most often used in computer programs to represent data.

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The preparation of the Cash Flow Statement for Nikea Inc. for the year ended December 31, 2013, is as follows:

Direct Method:

Nikea Inc.

Cash received from customers  $600,000

Cash paid to suppliers of goods (400,000)

Cash paid to vendors of servides (30,000)

Cash from operating activities    $170,000

Indirect Method:

Nikea Inc.

For the year ended December 31, 2013

Net income                                $150,000

Add non-cash expenses:

Depreciation                                 20,000

Cash from operating activities $170,000

The direct method of preparing the Cash Flow Statement starts with the operating income and adds the non-cash expenses to obtain the cash flow from operating activities.

On the other hand, the indirect method reconciles the accounts receivable and payable to extract the exact cash flows received from customers or paid to suppliers of goods and services.

Both methods of determining the cash flow from operating activities yield the same result.

Nikea’s income statement for the year 2013

Sales                          $600,000

Cost of Goods Sold   (400,000)

Gross Profit                 200,000

Operating Expenses   (30,000)

Deprecation                (20,000)

Net Income                 150,000

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Answer:

the difference between them is zero cause on first year simple interest and compound interest are equal

Answer:

A = 228 tickets

Step-by-step explanation:

We need to set up a system of equation to find the number of adult tickets sold, where A represents the adult tickets and S represents the student tickets.

Because the number of adult and student tickets together equals 506, we have A + S = 506.

Because there are 56 more student tickets than adult tickets we have A + 56 = S

And the way the system is already set up allows us to use substitution.

Thus, we have:

[tex]A + S=506\\A+56 = S\\\\A+A+56 =506\\2A+56=506\\2A=456\\\\A=228\\228+56=S\\278=S[/tex]

The number of student tickets was not necessary to find in this problem, but I found anyway just in case you wanted check the work or wanted to prove the validity of the values.

Answer:

x = 30 degrees

Step-by-step explanation:

angles MNO, LNM, and KNL make a straight line: 105+45+y = 180 --> y = 30 degrees

KNL = 30 degrees

angle KLN is 90 degrees, a triangle is equal to 180 degrees

2x+30+90 = 180

2x = 60

x = 30 degrees

Answer:

Answer:the answer is zero

Answer:the answer is zero Step-by-step explanation:

Answer:the answer is zero Step-by-step explanation:when we add -42 and -54 the answer we get is -96. -96and +96 cut each other and then the answer is zero

[tex] - 42 - 54 + 96 = 0[/tex]

The correct product of (6x - 2)(6 x + 2) is 36x^2 - 4

The expression is given as:

(6x - 2)(6 x + 2).

The above expression is a difference of two squares.

And this is represented as

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

So, we have

(6x - 2)(6 x + 2) = (6x)^2 - 2^2

Evaluate

(6x - 2)(6 x + 2) = 36x^2 - 4

Hence, the correct product of (6x - 2)(6 x + 2) is 36x^2 - 4

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Answer:

from looking at this we can see

1*4=4

2*4=8

3*4=12

6*4=24

a

Hope This Helps!!!