A pizza shop specializes in deep-dish pizzas. They sell a 14 -inch pizza that is 3 inches deep and a 16-inch pizza that is 2 inches deep. The 14 -inch pizza is cut into 8 slices and the 16-inch pizza is cut into 7 slices, and each slice is sold for the same price. If you are purchasing one slice of pizza, which size should you choose to get the most food? Show all of your work to justify your response.

A Pizza Shop Specializes In Deep-dish Pizzas. They Sell A 14 -inch Pizza That Is 3 Inches Deep And A

Answers

Answer 1

Answer:

The 14-inch pizza cut into 8 slices.

Explanation:

The deep-dish pizza forms a cylindrical shape.

To make comparisons, we find the volume of each slice of pizza in each case.

[tex]\text{Volume of a cylinder=}\pi r^2h[/tex]

Case 1

A 14-inch pizza that is 3 inches deep.

Radius = 14/2 = 7 inches

Height = 3 inches

[tex]\begin{gathered} \text{The volume of the full pizza}=\pi\times7^2\times3 \\ =147\pi\text{ cubic inches} \end{gathered}[/tex]

Since it is cut into 8 slices:

[tex]\begin{gathered} \text{The volume of one slice=}\frac{147\pi}{8} \\ =18.375\pi\text{ cubic inches} \end{gathered}[/tex]

Case 2

A 16-inch pizza that is 2 inches deep.

Radius = 16/2 = 8 inches

Height = 2 inches

[tex]\begin{gathered} \text{The volume of the full pizza}=\pi\times8^2\times2 \\ =128\pi\text{ cubic inches} \end{gathered}[/tex]

Since it is cut into 7 slices:

[tex]\begin{gathered} \text{The volume of one slice=}\frac{128\pi}{7} \\ \approx18.285\pi\text{ cubic inches} \end{gathered}[/tex]

Conclusion

The volume of a slice of pizza in the first case (the 14 -inch pizza cut into 8 slices) is larger, therefore it should be chosen to get the most food.


Related Questions

Use the given conditions to write an equation for the line in point-slope form and general form. Passing through (8,-4) and perpendicular to the line whose equation is x-6y-5=0

Answers

Answer:

y + 4 = -6 (x - 8)

Step-by-step explanation:

Change the equation to the slope intercept form for a line

x - 6y 5 = 0  Add 5 to both sides

x - 6y = 5  Subtract x from both sides

-6y = -x + 5  Divide both sides by -6

y = [tex]\frac{1}{6}[/tex] c  - [tex]\frac{5}{-6}[/tex]  Your slope is [tex]\frac{1}{6}[/tex]

A perpendicular slope is the opposite reciprocal of [tex]\frac{1}{6}[/tex], that would be -6

y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex])  Plug is -4 for [tex]y_{1}[/tex] and 8 for [tex]y_{1}[/tex]

y - -4) -6(x-8)

y + 4= -6 (x -8)

A radar unit is used to measure speeds of a car on a motorway. Speeds are normal distributed with a mean of 90 km an hour and a standard deviation of 10 km an hour. What is the probability that a car picked at random is traveling out more than 100 km an hour

Answers

let x is the random variable that represents the speed of car.

[tex]\begin{gathered} \mu(\operatorname{mean})=90 \\ \sigma=10 \end{gathered}[/tex]

probability that x is higher than 100 :

[tex]P(x>100)[/tex]

for x=100:

[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ z=\frac{100-90}{10} \\ z=1 \end{gathered}[/tex]

so,

[tex]p(x>100)=p(z=1)[/tex]

probability =total area - area of the left of (z=1)

[tex]\begin{gathered} \text{probability}=1-0.8413 \\ p(x>100)=0.1587 \end{gathered}[/tex]

and the area of the left of z=1 is 0.8413 (from normal distribution)

The function is defined by h(x) = (4 + x)/(- 3 + 3x) Find h(4x) .

Answers

Given h(x), find h(4x) as shown below

[tex]h(4x)=\frac{4+(4x)}{-3+3(4x)}=\frac{4+4x}{-3+12x}[/tex]Thus, the expanded form of h(4x) is (4+4x)/(-3+12x)

3. An automatic machine inserts mixed vegetables into a plastic bag. Past experience revealed that some packages were underweight and some were overweight, but most of them had satisfactory weight.



What is the probability of selecting four packages that are underweight?

Answers

If  an automatic machine inserts mixed vegetables into a plastic bag.  the probability of selecting four packages that are underweight is: 0.000000390625

Probability

Probability can be defined as the tendency or likelihood that an event will happen.

We would be making use of multiplication rule to determine the probabiliy that four packages are underweight.

Given :

Underweight = 2.5 % or 0.025

Hence,

Now let find the probability that  P (all four underweight) :

P(all four underweight) = ( 0.025 ) ( 0.025 ) ( 0.025 ) ( 0.025 )

P(all four underweight) = 0.000000390625

Therefore we can conclude that the probability is  0.000000390625.

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Nolan is deciding between two truck rental companies. Company A charges an initialfee of $90 for the rental plus $2 per mile driven. Company B charges an initial fee of$50 for the rental plus $3 per mile driven. Let A represent the amount Company Awould charge if Nolan drives I miles, and let B represent the amount Company Bwould charge if Nolan drives a miles. Write an equation for each situation, in termsof 2, and determine the number miles driven, , that would make the cost of eachcompany the same.

Answers

first we writte the information they are giving to us:

For company A:

initial fee = $90

rent per mile = $2

For combany B:

initial fee = $50

rent per mile = $3

Now for company A the equation that represent the charge in one mile will be: (where n is the number of miles)

[tex]\begin{gathered} A=90+2(n) \\ A=90+2(1) \\ A=90 \end{gathered}[/tex]

And for company B:

[tex]\begin{gathered} B=50+3n \\ B=50+3(1) \\ B=53 \end{gathered}[/tex]

Now to determine the number miles driven, that would make the cost of each company the same, we have to make A = B

[tex]\begin{gathered} A=B \\ 90+2n=50+3n \\ \end{gathered}[/tex]

and finaly we can solve for n

[tex]\begin{gathered} 90-50=3n-2n \\ 40=n \end{gathered}[/tex]

so if they drive for 40 miles the will pay the same

The number of classified documents has increased approximately linear from 8.2 million documents in 2001 to 17. 4 million documents in 2005. let in be the number of documents in millions labeled as classified in the year that is years since 2000 find the equation of the linear model to describe the data

Answers

Knowing that

- The number of classified documents has increased linearly.

- In 2001 there were 8.2 million documents.

- In 2005 there were 17.4 million documents.

- The variable "n" represents the number of documents (in millions) labeled as classified.

- The variable "t" represents the number of years since 2000.

The Slope-Intercept Form of the equation of a line is:

[tex]y=mx+b[/tex]

Where "m" is the slope and "b" is the y-intercept.

The slope of a line can be found using this formula:

[tex]m=\frac{y_2-y_1_{}}{x_2-x_1}[/tex]

Where these two points are on the line:

[tex](x_1,y_1),(x_2,y_2)[/tex]

In this case, you know these two points:

[tex](1,8.2),(5,17.4)[/tex]

Then, you can substitute values into the formula and find the slope of the line:

[tex]m=\frac{17.4-8.2}{5-1}=\frac{9.2}{4}=2.3[/tex]

Now you know that the form of the equation is:

[tex]n=2.3t+b[/tex]

In order to find "b", you need to:

- Choose one of the points on the line:

[tex]\mleft(1,8.2\mright)[/tex]

- Identify the value of each variable. Notice that:

[tex]\begin{gathered} n=8.2 \\ t=2001 \end{gathered}[/tex]

- Substitute those values of "n" and "t", and the slope into the equation:

[tex]8.2=2.3(1)+b[/tex]

- Solve for "b":

[tex]\begin{gathered} 8.2=2.3+b \\ 8.2-2.3=b \\ b=5.9 \end{gathered}[/tex]

Therefore the equation of the Linear Model is:

[tex]n=2.3t+5.9[/tex]

Hence, the answer is: Option D.

The functions f(x) and g(x) are shown on the graph.
f(x) = |x|
What is g(x)?
10
f(x) = x
-5
107
-5
-10
g(x) = ?
~XAX
K

Answers

Answer:

what graph?

Step-by-step explanation:

By the knowledge on absolute values, functional theory and rigid transformations and given that the function f(x) = |x|, the function g(x) = f(x - 4) is equal to |x - 4|.

What is absolute value?

In mathematics, the absolute value or modulus of a real number x, denoted |x|, is the non-negative value of x without regard to its sign. Namely, {\displaystyle |x|=x} if x is a positive number, and {\displaystyle |x|=-x} if x is negative, and {\displaystyle |0|=0}.

here, we have,

According to the image attached herein,

the function f(x) is an absolute value and the function g(x) results from translating f(x) in +x direction, representing a kind of rigid transformation as Pythagorean distance at every point of the function is conserved.

There, we can define the function g(x) as follows:

g(x) = f(x - k), for k > 0     (1)

By the knowledge on absolute values, functional theory and rigid transformations

and given that

the function f(x) = |x|, the function g(x) = f(x - 4) is equal to |x - 4|.

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Find the area of

8 in
3 in
10 in
4.5

Answers

Answer:

Step-by-step explanation:

square kilometre (km 2): 1,000,000    hectare: 10,000

Unit: Area in m 2                                   square meter: SI Unit

There exist more distinctions and classifications for different types of

trapezoids, but their areas are still calculated in the same manner using the

following equation: area = b 1 + b 2 2 × h where b1 and b2 are the bases. h is the height, or perpendicular distance between the bases The Farmer and his Daughter – Ramping Endeavors

A company prices its tornado insurance using the following assumptions:
• In any calendar year, there can be at most one tornado.
• In any calendar year, the probability of a tornado is 0.09.
• The number of tornadoes in any calendar year is independent of the number of tornados in any other calendar year.
Using the company's assumptions, calculate the probability that there are fewer than 2 tornadoes in a 14-year period.Round your answer to 4 decimals.

Answers

The probability that there are fewer than 3 tornadoes in a 14-year period is 0.992333

Let x = number of tornados

n = 14

p = 0.03

There are just two outcomes that can occur in these independent, fixed trials, and the success probability is 0.03

Consequently, we may determine the probability using the binomial distribution.

Here we want to find P( X < 3) = P( X < = 3-1) = P(X <=2)

Using Excel:

P( X <=2) = "=BINOMDIST(2,14,0.03,1)" = 0.992333

Be aware that the default Excel command to find binomial probabilities that are less than or equal is  "=BINOMDIST(x, n, p, 1)"

Therefore, 0.9923333 percent of the time there won't be more than 3 tornadoes in a 14-year period.

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Victoria's speedboat can travel 105 miles upstream against a 4-mph current in the same amount of time it travels 125 miles downstream with a 4-mph current. Find the speed of Victoria's boat.

Answers

Recall that:

[tex]\text{ time }=\frac{\text{ distance}}{\text{ speed}}[/tex]

Let Victoria's speed be v.

Therefore, Victoria's resultant speed upstream is v - 4 and her resultant speed downstream is v + 4.

Hence the time of journey upstream is given by:

[tex]\frac{105}{v-4}[/tex]

And the time of journey downstream is given by:

[tex]\frac{125}{v+4}[/tex]

Since the time of journey upstream is the same as the time of journey downstream, it follows that:

[tex]\begin{gathered} \frac{105}{v-4}=\frac{125}{v+4} \\ \text{ Divide both sides by }5: \\ \frac{21}{v-4}=\frac{25}{v+4} \\ \text{ Cross-multiplying, we have:} \\ 21(v+4)=25(v-4) \\ \text{ Expanding the expressions, we have:} \\ 21v+84=25v-100 \\ 25v-21v=100+84 \\ 4v=184 \\ v=\frac{184}{4}=46 \end{gathered}[/tex]

Therefore, Victoria's speed is 46 mph

You pick a card at random, put it back, and then pick another card at random.
4 5 6 7
What is the probability of picking a 7 and then picking an odd number?
Simplify your answer and write it as a fraction or whole number.

Answers

Answer:  1/8

=======================================================

Explanation:

A = probability of picking a 7

A = 1/4 since one card is labeled "7" out of four cards total

B = probability of picking an odd number

B = 2/4 = 1/2 because there are 2 cards that are odd (5 and 7) out of 4 cards total.

C = A*B = probability events A and B happen

C = (1/4)*(1/2)

C = 1/8

This only works when we put the first card back, which means each event is independent.

If f(x)=rootx-3 and g(x)=1-x^2, then what do you notice about the domaine of (f•g)(x)

Answers

The domain will be x ≥ 3 for f(x)=√x-3 and g(x)=1-x².

In case a function f gives a way to effectively create a single value y utilizing for that reason a value for x at that point that chosen x-value is said to have a place to the domain of f. there are some conditions to be checked such as denominators cannot equal 0, radicands of even roots can't have a negative value, logarithms can as it was being taken of positive values. Since we are given that f[tex]\sqrt{x-3}[/tex] and g(x)=1-x², for g(x)  since it's a polynomial function its domain had to be real numbers, whereas for f(x) is all positive and real numbers.

for the given  condition (f•g)(x)

=> (f•g)(x)= f(x)*g(x)

=> (f•g)(x) = √(x-3) * (1 - x²)

=>(f•g)(x) = √(x-3)-x²(√x-3)

So the domain for (f•g)(x) will be all positive real numbers x≥3 x ∈ [3,∞)

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y+ 4X=0 linear or nonlinear

Answers

Answer:

linear

Step-by-step explanation:

y+4x=0

-4x   -4x

=y=-4x+0

it is in the y=mx+b form so it is linear

You put together allowance money and head toward a distant planet forsome routine experiments on alien life forms. You abduct 12 aliens from thestrange planet, and you capture the internal body temperature of each(harmlessly of course). That data is presented above. Does this species ofaliens have an average internal body temperature less than that of the humanaverage of 98.6°F?

Answers

Solution

The mean of the internal body temperature of the 12 abducted aliens is given by;

[tex]\frac{96.8+98.3+97.6+98.5+97.5+97.5+98.5+65.6+95.4+98+97.4}{12}=87.14<98.6[/tex]

7.02 is what percent of 67.5?
312% of what is 39?

Answers

7.02 is 10.4% of 67.5
312% of 12.5 is 39

Explanation:
7.02/67.5 is 0.104 which is 10.4 as a percent.

100x39=3900, 3900/312 is 12.5

Hope this helped!

Simplify by finding the product of the polynomials below. Then Identify the degree of your answer. When typing your answer use the carrot key ^ (press shift and 6) to indicate an exponent. Type your terms in descending order and do not put any spaces between your characters. (8n-4)(n^2+9) This simplifies to: AnswerThe degree of our simplified answer is: Answer

Answers

Answer

[tex]\begin{gathered} \text{ Question 1:} \\ 8n^3-4n^2+72n-36 \\ \\ \text{Qusetion 2:} \\ \text{THE DEGREE OF THE POLYNOMIAL IS 3} \end{gathered}[/tex]

SOLUTION

Problem Statement

The question gives us an expression to simplify and we are to simplify by finding the product. We are also asked to find the degree of the polynomial as well

Method

We simply need to expand the bracket to solve this question. But the degree of the polynomial is gotten by assessing which term in the final expression has the highest power. If the expression has a term with its highest power being 3, then the degree of the polynomial is 3.

With this information, let us begin solving.

Implementation

1. Expanding the expression:

Expanding the polynomial, we have:

[tex]\begin{gathered} (8n-4)(n^2+9) \\ \text{ Using the FOIL method,} \\ F=8n(n^2)=8n^3 \\ O=8n(9)=72n \\ I=-4(n^2)=-4n^2 \\ L=-4(9)=-36 \\ \\ \therefore(8n-4)(n^2+9)=8n^2+72n-4n^2-36 \\ \\ \text{ Remember, we are asked to write this result in descending order of terms. Thus, we have that:} \\ 8n^3-4n^2+72n-36 \end{gathered}[/tex]

2. Degree of the polynomial:

From the above result, we can see that the highest degree of n in all the terms is 3, therefore, the degree of the polynomial is 3

Final answer

[tex]\begin{gathered} \text{ Question 1:} \\ 8n^3-4n^2+72n-36 \\ \\ \text{Qusetion 2:} \\ \text{THE DEGREE OF THE POLYNOMIAL IS 3} \end{gathered}[/tex]

Solve these problems.​

Answers

The solutions will be (x-2)(x+1), (3x+5)(5x+2) and (x+1)(x-1) respectively using factorization.

What is factorization?

A number or other mathematical object is factorized or factored in mathematics by writing it as the product of numerous factors, typically smaller or simpler things of the same kind.

18) 8x³-8x²-16x = 0

Taking 8x common we get,

8x(x²-x-2) = 0

x²-x-2 = 0×8x

x²-(2-1)x-2 = 0

x²-2x+x-2 = 0

x(x-2)+1(x-2) = 0

(x-2)(x+1) = 0

Hence, the factors are (x-2)(x+1).

19) 15x³+31x²+10x = 0

Taking x as common as we get,

x(15x²+31x+10) = 0

Factorize 15x²+31x+10=0

15x²+(25+6)x+10=0

15x²+25x+6x+10=0

5x(3x+5)+2(3x+5)=0

(3x+5)(5x+2)=0

Hence the factors are (3x+5)(5x+2).

20) x³-x=0

Taking x as common as we get,

x(x²-1)=0

x²-1=0

(x+1)(x-1)=0

Hence the factors are (x+1)(x-1).

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This graph shows the height in inches, `h`, of a bamboo plant `t` months after it has been planted.
Write an equation that describes the relationship between `t` and `h`.
Drag the movable point to trace along the line if that helps you with your thinking.

Answers

The graph that shows the relationship between the height of the bamboo and months planted is given as h = 5t + 10

How to solve an equation?

Given that the graph shows the relationship between the height (h) of a bamboo plant after months it has been planted.

Let us assume that h is plotted on the vertical axis and months (t) is planted on the horizontal axis.

If the graph passes through the points (0, 0) and (2, 10), hence:

h - 10 = [(10 - 0)/(2 - 0)](t - 0)

h - 10 = 5(t)

h = 5t + 10

The graph is given as h = 5t + 10

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Given the Frequency Distribution: (SHOW WORK)
Find the:
(A) Range
(B) Mean
(C) Mode
(D) Median
(E) Variance
(F) Standard Deviation of This Sample

Answers

The measures of the frequency distribution is;

(A) Range = 7

(B) Mean = 29

(C) Mode = 12

(D) Median = 29

(E) Variance = 7.612

(F) Standard Deviation = 2.759

How to solve frequency distribution?

A) The range of a frequency distribution is;

Range = Highest Value - Lowest Value

Thus;

Range = 32 - 25

Range = 7

B) Mean is expressed as;

x' = ∑fx/∑f

x' = [(25 * 4) + (26 * 6) + (28 * 6) + (30 * 4) + (32 * 12)]

x' = 928/32

x' = 29

C) Mode is the value with the highest frequency and so in this case;

Mode = 12

D) Median is the middle term when arranged from lowest to highest. In this case, it is the 16.5th term. Thus; Median = (28 + 30)/2 = 29

E) Variance = 7.612

F) The standard deviation is;

σ = √Variance

σ = 2.759

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Tell how many tens & onesWrite the number and the word name

Answers

Every column have 7 bricks

There are 8 columns,

Then there are

8x7 = 56 bricks + another 7 bricks = 63 bricks

Divide now 63 between 10

63/10 = 6 tens + 3 ones

ANSWER IS

6 TENS 3 ONES

Kylie shoots an arrow during an archery lesson at camp. The height of the arrow can be modeled by the equation ℎ = −8t(2t−6), where ℎ is the height in feet of the arrow and t is the time in seconds. How long is the arrow in the air?

Answers

The arrow will be in the air for 3 seconds after 3 seconds the arrow hit the target.

What is a quadratic equation?

Any equation of the form [tex]\rm ax^2+bx+c=0[/tex]  where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

The equation:

h = −8t(2t−6)

To find the total number of seconds the arrow will be in the air:

Plug h = 0

−8t(2t−6) = 0

t(2t−6) = 0

t = 0   or    t = 6/2

t = 0  or   t = 3 seconds

Thus, the arrow will be in the air for 3 seconds after 3 seconds the arrow hit the target.

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What is the product of
(5+2i) and (-3 - 4i)?

Answers

Answer:

-7 - 26i

Step-by-step explanation:

(5+2i)(-3 - 4i)

take this and distribute them to each other

-15 -20i -6i -8i^2

then combine like terms

-15-26i-8i^2

i^2 is always equal to -1, so replace i^2 with -1 in the problem

-15-26i-8(-1)

now solve

-15-26i+8

now combine like terms and you have your answer

-7-26i

Use the graph of the function to estimate the intervals on which the function is increasing or decreasing. (Enter your answers using interval notation.)

Answers

The intervals on which the graph is increasing at (-∞, 0) U (3.5, ∞). On the other hand, the graph is decreasing at (0, 3.5)

What is the graph?

A graph can be defined as a pictorial representation or a diagram that represents data or values.

Increased or decreased functions are two categories of functions. Consequently, a function increases when the y-values grow, while a function decreases when the y-values decrease.

The graph indicates the y-values increase in the x-intervals from -∞  to 0 and from 3.5 to ∞. You can express that a function is increasing in the following ways using interval notation:  (-∞, 0) U (3.5, ∞).

The graph, on the other hand, is decreasing: (0, 3.5)

Hence, the intervals on which the graph is increasing at (-∞, 0) U (3.5, ∞). On the other hand, the graph is decreasing at (0, 3.5)

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Describe two different ways to translate a figure that result in the same image. Justify your answer.

Answers

The ways to translate the figure include:

It doesn't change its orientation.

It also doesn't change its size or shape.

How to illustrate the information?

When a geometric figure glides up, down, left, or right on the coordinate plane, this is referred to as translation. The figure changes its location but not its orientation. It also retains its size and shape. When you translate a figure, you slide it left or right, up or down.

When you translate a figure, you slide it left or right, up or down. This indicates that the coordinates for the figure's vertices will vary on the coordinate plane. To graph a, make the same modification at each point. The variations in coordinates of a reflection can be used to identify it.

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What is the equation of the line that passes through the point (5, 0) and has a slope of 6/5?​

Answers

Answer:

[tex]y=\frac{6}{5}(x-5)[/tex]

Step-by-step explanation:

Use point-slope form.

Describe a series of transformations Matt can perform to device if the two windows are congruent

Answers

Answer:

the transformation matt can from A

Express Your Answer As A Polynomial In Standard Form.
f(x)= x-7
g(x)= 3x^2-7x-10

Find (f o g)(x)

Look at photo

Answers

According to the solving the  Polynomial  Standard Form of the given equation is :

3x^2-7x-17.

What is Polynomial  Standard Form?

When expressing a polynomial in its standard form, the greatest degree of terms are written first, followed by the next degree, and so on. When x is the variable and ai are coefficients, the polynomial has the conventional form f(x) = anxn + an-1xn-1 + an-2xn-2 +... + a1x + a0.

According to the given data:

f(x)= x-7

g(x)= 3x^2-7x-10

f(x)= x-7 by substituting in the value of  g into f.

f(3x^2-7x-10) =  (3x^2-7x-10)-7

                     = 3x^2-7x-17

According to the solving the slandered form of the given equation is :

3x^2-7x-17

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Simplify these thing below please. I am stuck again... Thank you

Answers

[tex]9\sqrt{56 x^7 y^{12}}\qquad \begin{cases} 56=7\cdot 2\cdot 2\cdot 2\\ \qquad 7\cdot 2^2 \cdot 2\\ \qquad 2^2\cdot 14\\ x^7=x^{(3)(2)+1}\\ \qquad (x^3)^2\cdot x^1\\ y^{12}=y^{(6)(2)}\\ \qquad (y^6)^2 \end{cases}\hspace{5em} \begin{array}{llll} 9\sqrt{2^2(14)(x^3)^2 x (y^6)^2} \\\\\\ 9(2)(x^3)(y^6)\sqrt{14x} \\\\\\ {\Large \begin{array}{llll} 18x^3y^6\sqrt{14x} \end{array}} \end{array}[/tex]

Answer:

[tex]\textsf{1.} \quad 18\;x^3\;y^{6}\sqrt{14x}[/tex]

[tex]\textsf{2.} \quad -8\sqrt{2}[/tex]

 

Step-by-step explanation:

Question 1

Given expression:

[tex]9\sqrt{56x^7y^{12}}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]

[tex]\implies 9\sqrt{56}\sqrt{x^7}\sqrt{y^{12}}[/tex]

Rewrite 56 as 4·14:

[tex]\implies 9\sqrt{4 \cdot 14}\sqrt{x^7}\sqrt{y^{12}}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]

[tex]\implies 9\sqrt{4}\sqrt{14}\sqrt{x^7}\sqrt{y^{12}}[/tex]

Rewrite 4 as 2²:

[tex]\implies 9\sqrt{2^2}\sqrt{14}\sqrt{x^7}\sqrt{y^{12}}[/tex]

Simplify:

[tex]\implies 9\cdot 2\sqrt{14}\sqrt{x^7}\sqrt{y^{12}}[/tex]

[tex]\implies 18\sqrt{14}\sqrt{x^7}\sqrt{y^{12}}[/tex]

[tex]\textsf{Apply exponent rule} \quad \sqrt{a}=a^{\frac{1}{2}}:[/tex]

[tex]\implies 18\sqrt{14}\;(x^7)^{\frac{1}{2}}\;(y^{12})^{\frac{1}{2}}[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies 18\sqrt{14}\;x^{\frac{7}{2}}\;y^{\frac{12}{2}}[/tex]

[tex]\implies 18\sqrt{14}\;x^{\frac{7}{2}}\;y^6[/tex]

Rewrite ⁷/₂ as 3 + ¹/₂

[tex]\implies 18\sqrt{14}\;x^{(3+\frac{1}{2})}\;y^{6}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{b+c}= a^b \cdot a^c:[/tex]

[tex]\implies 18\sqrt{14}\;x^3 \; x^{\frac{1}{2}}\;y^{6}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{\frac{1}{2}}=\sqrt{a}:[/tex]

[tex]\implies 18\sqrt{14}\;x^3 \; \sqrt{x}\;y^{6}[/tex]

Rearrange:

[tex]\implies 18\;x^3\;y^{6}\sqrt{14x}[/tex]

Question 2

Given expression:

[tex]7\sqrt{32}-6\sqrt{72}[/tex]

Rewrite 32 as 16·2 and 72 as 36·2:

[tex]\implies 7\sqrt{16 \cdot 2}-6\sqrt{36 \cdot 2}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]

[tex]\implies 7\sqrt{16}\sqrt{2}-6\sqrt{36}\sqrt{2}[/tex]

Rewrite 16 as 4² and 36 as 6²:

[tex]\implies 7\sqrt{4^2}\sqrt{2}-6\sqrt{6^2}\sqrt{2}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{a^2}=a, \quad a \geq 0:[/tex]

[tex]\implies 7 \cdot 4\sqrt{2}-6\cdot 6\sqrt{2}[/tex]

Simplify:

[tex]\implies 28\sqrt{2}-36\sqrt{2}[/tex]

[tex]\implies -8\sqrt{2}[/tex]

Yvonne wants to use a dissection argument to justify the formula for the area of a circle. She dissects the circle into congruent sectors and reassembles the sectors as a parallelogram-like figure. The diagram below shows the arrangement for a circle dissected into 8 sectors. M Height Base Yvonne knows that as the number of sectors of the circle increases, the reassembled figure becomes closer and closer to an actual parallelogram so that it can be used to determine the area of the circle. Determine the value of each characteristic of the parallelogram in the table below. Select the best value for each characteristic.base of the parallelogram height of the parallelogram area of the parallelogram

Answers

Each sector is formed like a triangle with a circle base. The sum of all the bases should be equal to half the length of the circle's circumference, this is calculated with the following expression:

[tex]\text{base}=\frac{2\pi r}{2}=\pi r[/tex]

This is the base of the parallelogram.

The height of each triangle is the radius of the circle, therefore:

[tex]\text{height}=r[/tex]

The area of the parallelogram is the product of the base and the height.

[tex]\text{Area =}\pi r^2[/tex]

So the base is pi*r;

The height is r;

The area is pi*r².

What’s the correct answer answer asap for brainlist

Answers

Answer:

B. radio stations stopped advertising

Answer:

As televisions became more affordable and advertisers flocked to the new medium, radio stations had to quickly adapt to the changing field. Stations stopped using live in-studio performances, instead playing less expensive recordings.

Step-by-step explanation:

In the 1950s, television surpassed radio as the most popular broadcast medium, and commercial radio programming shifted to narrower formats of news, talk, sports and music. Religious broadcasters, listener-supported public radio and college stations provide their own distinctive formats.

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