What happens to the surface area and volume if the lengths of the dimensions of the
prism are multiplied by a scale factor of 3?

The value of the quotient is  [tex]\frac{45\cos(\frac{\pi}{4}) i\sin(\frac{\pi}{4})}{\cos(\frac{\pi}{12}) i\sin(\frac{\pi}{12})} = 45(\cos(\frac{\pi}{6}) + i\sin(\frac{\pi}{6}))[/tex]

The expression is given as:

[tex]\frac{90\cos(\frac{\pi}{4}) i\sin(\frac{\pi}{4})}{2\cos(\frac{\pi}{12}) i\sin(\frac{\pi}{12})}[/tex]

Divide 90 by 2

[tex]\frac{45\cos(\frac{\pi}{4}) i\sin(\frac{\pi}{4})}{\cos(\frac{\pi}{12}) i\sin(\frac{\pi}{12})}[/tex]

As a general rule, we have:

[tex]\frac{\cos(\frac{\pi}{A}) i\sin(\frac{\pi}{A})}{\cos(\frac{\pi}{B}) i\sin(\frac{\pi}{B})} = \cos(\frac{\pi}{2B/A}) + i\sin(\frac{\pi}{2B/A})[/tex]

The above means that:

A = 4 and B = 12

So, we have:

2B/A = 2 * 12/4

Evaluate

2B/A = 6

So, the equation becomes

[tex]\frac{\cos(\frac{\pi}{4}) i\sin(\frac{\pi}{4})}{\cos(\frac{\pi}{12}) i\sin(\frac{\pi}{12})} = \cos(\frac{\pi}{6}) + i\sin(\frac{\pi}{6})[/tex]

Substitute [tex]\frac{\cos(\frac{\pi}{4}) i\sin(\frac{\pi}{4})}{\cos(\frac{\pi}{12}) i\sin(\frac{\pi}{12})} = \cos(\frac{\pi}{6}) + i\sin(\frac{\pi}{6})[/tex] in [tex]\frac{45\cos(\frac{\pi}{4}) i\sin(\frac{\pi}{4})}{\cos(\frac{\pi}{12}) i\sin(\frac{\pi}{12})}[/tex]

[tex]\frac{45\cos(\frac{\pi}{4}) i\sin(\frac{\pi}{4})}{\cos(\frac{\pi}{12}) i\sin(\frac{\pi}{12})} = 45(\cos(\frac{\pi}{6}) + i\sin(\frac{\pi}{6}))[/tex]

Hence, the value of the quotient is  [tex]\frac{45\cos(\frac{\pi}{4}) i\sin(\frac{\pi}{4})}{\cos(\frac{\pi}{12}) i\sin(\frac{\pi}{12})} = 45(\cos(\frac{\pi}{6}) + i\sin(\frac{\pi}{6}))[/tex]

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Complete question

What is the quotient of [tex]\frac{90\cos(\frac{\pi}{4}) i\sin(\frac{\pi}{4})}{2\cos(\frac{\pi}{12}) i\sin(\frac{\pi}{12})}[/tex]

The events are not mutually exclusive.

Two events that cannot occur at the same time are called Mutually exclusive event.

It is given that

A sample of 75 books is selected from a library.

Event A:  At least 10 of the authors are female

Event B : At least 10 of the books are fiction.

Both can happen simultaneously

Therefore the events are not mutually exclusive.

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Answer: b.) 40

Given that:

f(x) = 5 × 2ˣ

To find f(3), simplify insert [x = 3] in the given equation:

f(3) = 5 × 2³

f(3) = 5 × 2 × 2 × 2

f(3) = 40

The total time spent on his/her cell phone in a year’s time is less than the total time spent waiting in line when shopping in a lifetime.

x= 1825 hrs

z=4929.4 hrs.

This is further explained below.

let's say on average a person spends 5 hours on a mobile phone.

Individual annual mobile phone use time.

x=  5x365

x= 1825 hrs

let's consider an average every day a person, spent 5 minutes in the queue when shopping.

Take the average person. 70-year life for a person.

Hence in a year, he spent

y=365x5 mints

y=1825 min

y=30.42 hrs

Hence lifetime time spent on line

z = 70 x 30.42

z=4929.4 hrs.

In conclusion, we estimate that the typical individual will spend z=4929.4 hours waiting in line for merchandise throughout the course of their lifetime.

z=4929.4 hrs.

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Hello !

    3y + 12 =2(y + 30)

⇔ 3y + 12 = 2y + 60

⇔ y + 12 = 60

⇔ y = 60 - 12

⇔ y = 48

Answer:

y = 48

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

3y + 12 is an exterior angle of the triangle , so

3y + 12 = y + 30 + y + 30 ( base angles of an isosceles Δ are congruent )

3y + 12 = 2y + 60 ( subtract 2y from both sides )

y + 12 = 60 ( subtract 12 from both sides )

y = 48

Answer:

a. f(0) = -6

b. f(2) =10

c. f(-4) = 32

d. f(b) = 3b^2+2b-6

e. f(4a) = 48a^2+8a-6

The function values for the function f(x) = 3x² + 2x - 6, for the values are:

a. f(0) = -6

b. f(2) = 10

c. f(-4) = 34

d. f(b) = 3b² + 2b - 6

e. f(4a) = 48a² + 8a - 6

To calculate function value f(k) for a function f(x), we substitute variable x = k, in the function f(x).

In the question, we are asked to find the function value for the function f(x) = 3x² + 2x - 6 for:

a. f(0)

b. f(2)

c. f(-4)

d. f(b)

e. f(4a).

We calculate these in the following ways:-

a. f(0):

We substitute the value of x = 0 in the function f(x).

Therefore f(0) = 3(0)² + 2(0) - 6,

or, f(0) = 0 + 0 - 6 = -6.

Therefore, the function value f(0) for the function f(x) = 3x² + 2x - 6 is -6.

b. f(2):

We substitute the value of x = 2 in the function f(x).

Therefore f(2) = 3(2)² + 2(2) - 6,

or, f(2) = 12 + 4 - 6 = 10.

Therefore, the function value f(2) for the function f(x) = 3x² + 2x - 6 is 10.

c. f(-4):

We substitute the value of x = -4 in the function f(x).

Therefore f(-4) = 3(-4)² + 2(-4) - 6,

or, f(-4) = 48 - 8 - 6 = 34.

Therefore, the function value f(-4) for the function f(x) = 3x² + 2x - 6 is 34.

d. f(b):

We substitute the value of x = b in the function f(x).

Therefore f(b) = 3(b)² + 2(b) - 6,

or, f(b) = 3b² + 2b - 6.

Therefore, the function value f(b) for the function f(x) = 3x² + 2x - 6 is 3b² + 2b - 6.

e. f(4a):

We substitute the value of x = 4a in the function f(x).

Therefore f(4a) = 3(4a)² + 2(4a) - 6,

or, f(0) = 48a² + 8a - 6.

Therefore, the function value f(0) for the function f(x) = 3x² + 2x - 6 is 48a² + 8a - 6.

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The function will go somewhere between x = 4 and x = 5

The function is given as:

y = 2^x

The question implies that:

If the maximum y value on a graph is x = 20; What is the maximum x value on the graph of y = 2^x

To do this, we start by setting y to 20.

So, we have:

2^x = 20

Take the logarithm of both sides

x log(2) = log(20)

Divide by log(2)

x = 4.32

4.32 is between 4 and 5

Hence, the function will go somewhere between x = 4 and x = 5

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The equation of the parabola is y = 0.015x^2 + 0.06x + 1

A parabola is represented as:

y = ax^2 + bx + c

The points are given as:

(-4,1), (-2,0.94) and (0,1)

When these points are substituted in y = ax^2 + bx + c, we have the following linear equations

16a - 4b + c = 1

4a - 2b + c = 0.94

c = 1

In (a), we have:

16a - 4b + c = 1

4a - 2b + c = 0.94

c = 1

Remove the variables (leaving the coefficients)

a      b       c

16    -4      1        1

4      -2     1        0.94

0      0     1          1

So, the matrix representation of the system of equations is:

[tex]\left[\begin{array}{ccc}16&-4&1\\4&-2&1\\0&0&1\end{array}\right] \left[\begin{array}{c}1&0.94&1\end{array}\right][/tex]

Using a graphing calculator, we have the inverse of the coefficient matrix to be

[tex]\left[\begin{array}{ccc}0.125&-0.25&0.125\\0.25&-1&0.75\\0&0&1\end{array}\right][/tex]

Using a graphing calculator, we have the solution to the system of equations to be

a = 0.015

b = 0.06

c = 1

Recall that:

y = ax^2 + bx + c

So, we have:

y = 0.015x^2 + 0.06x + 1

Hence, the equation of the parabola is y = 0.015x^2 + 0.06x + 1

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Answer:

1/25

Step-by-step explanation:

The bag has:

The probability of picking a yellow marble is 2/10=1/5.

So, the answer is (1/5)² = 1/25

A correlation coefficient between number of miles driven and number of gallons of gas remaining is most likely to be 0 to -1. Then the correct option is A.

A mathematical indicator of the degree of the association seen between fluctuation of 2 factors is the correlation coefficient.

A correlation coefficient between number of miles driven and number of gallons of gas remaining is most likely to be 0 to -1.

Then the correct option is A.

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Answer:

y = (-2/3)x + 5/6

Step-by-step explanation:

The general structure of a line in slope-intercept form is:

y = mx + b

In this form, "m" represents the slope and "b" represents the y-intercept. You have been given the value of "m". To find the value of "b", you can plug the slope and the values from the point (2, -1/2) into the general equation.

m = -2/3

Point (2, -1/2):

x = 2 and y = -1/2

y = mx + b                                  <----- Slope-intercept form

y = (-2/3)x + b                            <----- Insert -2/3 in "m"

-1/2 = (-2/3)(2) + b                      <----- Insert "x" and "y" values from point

-1/2 = -4/3 + b                            <----- Multiply -2/3 and 2

-3/6 = -8/6 + b                           <----- Give the fractions common denominators

5/6 = b                                      <----- Add 8/6 to both sides

Thus, the equation of the line is:

y = (-2/3)x + 5/6

If they worked for k hours, the amount of work done would be [tex]\mathbf{ \dfrac{k(x+y)}{xy}}[/tex]hours.

Algebraic expression involves the use of variables and their arithmetic operations.

Given that:

If we have a function denoted by k (hours) indicating the work they both can do together. Then we can conclude that they can both work for:

[tex]\mathbf{=\dfrac{k}{x}+\dfrac{k}{y}}[/tex]

[tex]\mathbf{ \dfrac{k(x+y)}{xy}}[/tex]

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Answer:

  7z^2/y -8z^4y -(9/2)z^2y^4

Step-by-step explanation:

The quotient of division of a polynomial by a monomial is the sum of quotients of each of the terms divided by the monomial. "Simplify" in this context generally means that no common factors remain factored out.

The rules of exponents apply:

  (a^b)/(a^c) = a^(b-c)

  a^-b = 1/a^b

The problem is effectively three (3) division/simplification problems.

  [tex]\dfrac{-14z^4y^2+16z^6y^4+9z^4y^7}{-2z^2y^3}=\dfrac{-14z^4y^2}{-2z^2y^3}+\dfrac{16z^6y^4}{-2z^2y^3}+\dfrac{9z^4y^7}{-2z^2y^3}\\\\=7z^{4-2}y^{2-3}-8z^{6-2}y^{4-3}-\dfrac{9}{2}z^{4-2}y^{7-3}=\boxed{\dfrac{7z^2}{y}-8z^4y-\dfrac{9}{2}z^2y^4}[/tex]

__

Additional comment

We have elected to retain the original order of variables (z then y) and the original order of terms. Ordinarily, standard form would have the variables in alphabetical order (y then z) and the terms in order by decreasing degree. This order of terms also makes the leading coefficient positive. (The minus sign for a negative leading coefficient sometimes gets lost.)

Using complementary angles, it is found that a solution to the given equation is:

D. x = 16, sin 38° = cos 52°.

Two angles are called complementary if the sum of their measures is of 90º. If two angles A and B are complementary, we have that:

cos(A) = sin(B) and sin(A) = cos(B).

In this problem, the expression is:

cos(3x + 4) = sin(2x + 6).

Hence:

3x + 4 + 2x + 6 = 90

5x = 80

x = 16.

Then:

Which means that option D is correct.

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Answer:  9 eggs were left.

Step-by-step explanation:

A dozen eggs usually mean there are 12 eggs. We have two ways to solve the problems.

First way:

The egg used to make breakfast: 12 x 25% = 12 x 0.25 = 3

The eggs were left: 12 - 3 = 9

Second way:

12 x (1 - 0.25)

= 12 x 0.75

= 9

Answer:

81m + 27t

Step-by-step explanation:

Using distributive property, this expression can be solved.

So 9(9m + 3t) has operations in it.

9 would be multiplied by whatever is in the parenthesis followed by the variable.

So 9 * 9 = 81.

9 * 3 = 27.

So putting it together with the variables.

It would be:

⇒ 81m + 27t  

An equation of the circle that will pass through the four (4) vertices of the square is (x + 2)² + y² = 2².

Mathematically, the general form of the equation of a circle is given by;

(x - h)² + (y - k)² = r²

Where:

Note: The center of a circle lies on the midpoint of the diagonal of a square, which is formed by joining its endpoints (opposite).

Midpoint on x-coordinate is given by:

Midpoint = (-2 - 2)/2

Midpoint = -4/2 = -2.

Midpoint on y-coordinate is given by:

Midpoint = (-2 + 2)/2

Midpoint = 0/2 = 0.

Thus, the center (h, k) = (-2, 0).

For the radius, we have:

r = √(-2)² + 0²

r = √4 = 2.

Substituting the parameters into the general equation, we have;

(x - (-2))² + (y - 0)² = 2²

(x + 2)² + y² = 2²

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The solution to the given linear equation are -4 and 2

Quadratic equations are equations that has a leading degree of 2. Given the expression below

(x-3)(x+1)=5

Expand

x^2+x - 3x - 3 = 5

x^2 - 2x - 8 =0

Factorize

x^2 + 4x - 2x - 8= 0

x(x+4)-2(x+4) = 0

x = -4 and 2

Hence the solution to the given linear equation are -4 and 2

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3x² + 6x - 24

Simplify 3.

3(x² + 6x - 8)

Think of x² +2x−8. Factor the expression by grouping. First, we need to rewrite the expression as x² + ax + bx - 8. To find a and b, set up a system to be solved.

Since ab is negative, a and b have opposite signs. Since a+b is positive, the positive number has a greater absolute value than the negative. Show all pairs of integers whose product is −8.

Calculate the sum of each pair.

The solution is the pair that gives sum 2

Rewrite x² + 2x − 8 as (x² − 2x ) + (4x − 8).

Simplify x in the first group and 4 in the second.

Simplify the common term x−2 with the distributive property.

The entire factored expression is rewritten.

3 ( x − 2 )( x + 4 ) ===> Answer

We conclude that the correct option is "B".

Answer:

y = 3x - 13

Step-by-step explanation:

We are given the points (7,8) and (3,-4)

We want to write an equation of the line that passes through those 2 points.

There are 3 ways to write the equation of the line:

Although while any one of these options work, the most common way is to use slope-intercept form, so let's do it that way.

First, we need to find the slope of the line.

The slope (m) can be found using this formula: [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] are points.

Even though we already have 2 points, let's label their values to avoid any confusion.

[tex]x_1=7\\y_1=8\\x_2=3\\y_2=-4[/tex]

Now substitute these values into the formula.

m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

m=[tex]\frac{-4-8}{3-7}[/tex]

Subtract.

m=[tex]\frac{-12}{-4}[/tex]

Divide.

m = 3

The slope of the line is 3.

Here is the equation of the line so far:

y = 3x + b

We now need to find b.

As the equation passes through  (7,8) and (3,-4), we can use either one of the points to help us solve for b.

Taking (7,8) for instance:

Substitute 7 as x and 8 as y in the equation.

8 = 3(7) + b

Multiply

8 = 21 + b

Subtract 21 from both sides

-13 = b

Substitute -13 as b in the equation.

y = 3x - 13

Topic: finding the equation of the line

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A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of the line that passes through the points (7,8) and (3,-4) is y=3x-13.

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of line is given by,

y =mx + c

where,

x is the coordinate of the x-axis,

y is the coordinate of the y-axis,

m is the slope of the line, and

c is the y-intercept.

The slope of the equation will be,

Slope, m = (-4-8)/(3-7) = -12/-4 = 3

Substitute one of the points in the equation of the line,

-4 = 3(3) + C

C = -13

Hence, the equation of the line that passes through the points (7,8) and (3,-4) is y=3x-13.

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Answer:

D. c/6 - x

Step-by-step explanation:

Rearranging with subject '6y':

6y = c - 6x

Dividing the above equation by 6 to get subject 'y':

y = c/6 - x

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Extract the common factor 6.

[tex]\bf{6(x+y)=c }[/tex]

Divide both sides by 6.

[tex]\bf{x+y=\dfrac{c}{6} }[/tex]

Subtract x from both sides.

[tex]\bf{y=\dfrac{c}{6}-x \ \ \to \ \ \ Answer }[/tex]

Therefore, the correct option is "D".

The  last day for taking the cash discount is May 5  and discount is taken is: $12,398.6.

Since the invoice was dated April 12, the last day for taking the cash discount is May 5.

Cash discount

Using this formula

Amount paid =Invoice amount × (1-rate)

Let plug in the formula

Amount paid=$13,190 ×(1-6%)

Amount paid=$13,190×0.94

Amount paid=$12,398.6

Therefore the  last day for taking the cash discount is May 5 and the amount to be paid is: $12,398.6.

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a. The department that accounts for approximately one-fifth of the annual budget, based on the pie chart, is the Research Department.

b. The percentage of the annual budget used by the Marketing and Sales departments combined is 30%.

c. If 18% of the annual budget is used for Research, approximately the percentage used for Marketing is 9%.

A pie chart is a graphical representation of data in a circle.  In this pie chart, the area or percentage of the whole circle is 100%

Thus, we can obtain the values of the different groups represented in the pie chart by systematically dividing the circle accordingly.

The rule to follow is that vertical angles are always congruent (equal) as they have two lines that intersect to form opposite angles.

Research, Sales, and Marketing = 50% of the budget (half of the pie chart)

Research = 18%

Sales and Marketing = 32% (50% - 18%)

Research equals Media and Support and Media and Support are equal.

Therefore, Media is 9% (18%/2) and Support is also 9%.

Since opposite angles are always equal, Engineering (opposite to Sales and Marketing combined) is 32%.

This results in a total of 100% (18% + 32% + 9% + 9% +32%)

The pie chart attached shows how the annual budget for Equipment Producers Incorporated is divided by department. Use this chart to answer the questions below.

c) If 18% of the annual budget is used for Research, approximately what percentage is used for Marketing?

Thus, the department that accounts for approximately one-fifth of the annual budget, based on the pie chart, is the Research Department.

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Answer:

Shown in the attachment.

Step-by-step explanation:

Shown in the attachment.

Answer:

$4020.52

Step-by-step explanation:

The future value is the principal multiplied by the amount $1.00 is worth in the future.

$4,000 × 1.00513 = $4020.52

Answer:

1.33 repeating

Step-by-step explanation:

you just do 4 divided by 3.

Please mark as brianliest if i got it right

When x = 64 and y = 3, we will have:

z = 3,313.21

First, we know that z varies directly with x and inversely with y², then we can write:

z = k*x/y^2

Where k is a constant.

We know that z = 182 when x = 25 and y = 8, replacing that we can find the value of k.

182 = k*25/(8²)

k = 182*8²/25 = 465.92

Now, we just need to evaluate the function in x = 64 and y = 3.

z = (465.92)*64/3² = 3,313.21

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The student, who suggests that if we do half and half of each bag, we will be giving them at least 60%, is correct.

The phrase "at least" means the minimum that is true or possible.

Mathematically, by "at least," we mean 'equal to or greater than.'

Since each bag of nuts contain 16 ounces,

The 1st bag contains x/2 ounces (50%) of plain nuts and x/2 ounces (50%) of chocolate-covered nuts.

The 2nd bag contains x/5 ounces (20%)of plain nuts and 4x/5 ounces (80%) of chocolate-covered nuts.

If half of the 1st bag is mixed with half of the 2nd bag, each bag will contain only 65% (that is, 25% (50%/2) from the 1st bag and 40% (80%/2) from the 2nd bag).

Thus, the student, who suggests that if we do half and half of each bag, we will be giving them at least 60%, is correct since they will not be given less than 60% of chocolate-covered nuts inside.

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Answer:

$12.03

Step-by-step explanation:

I = prt

I = (875)(0.055)(3/12)

I = 12.03

Answer: $12.03