a swimming pool is shaped like a cylinder with a radius of 15 feet and a height of 6 feet. if one cubic foot holds 7.48 gallons of the water how much gallons of water can the swimming pool hold.

Answer: a) [tex]\frac{x^{2} }{2352.25 }[/tex] + [tex]\frac{y^{2} }{529}[/tex] = 1

b) The distance of two foci is 85.4 feet

c) Area = 3502.67 square feet

Step-by-step explanation: a) An ellipse has the equation in the form of:

[tex]\frac{x^{2} }{a^{2} }[/tex]+[tex]\frac{y^{2} }{b^{2} }[/tex] = 1, where a is the horizontal axis and b is the vertical axis.

For the Statuary Hall, a = [tex]\frac{97}{2}[/tex] = 48.5 and b = [tex]\frac{46}{2}[/tex] = 23, so the equation will be

[tex]\frac{x^{2} }{2352.25 }[/tex] + [tex]\frac{y^{2} }{529}[/tex] = 1.

b) To determine the distance of the foci, we have to calculate 2c, where c is the distance between one focus and the center of the ellipse. To find c, as a, b and c create a triangle with a as hypotenuse:

[tex]a^{2}[/tex] = [tex]b^{2} + c^{2}[/tex]

[tex]c^{2} = a^{2} - b^{2}[/tex]

c = [tex]\sqrt{48.5^{2} - 23^{2} }[/tex]

c = 42.7

The distance is 2c, so 2·42.7 = 85.4 feet.

The two foci are 85.4 feet apart.

c)The area of an ellipse is given by:

A = a.b.π

A = 48.5 · 23 · 3.14

A = 3502.67 ft²

The area of the floor room is 3502.67ft².

Answer:

33 feet

Step-by-step explanation:

Use SOHCAHTOA to determine which trigonometric function to use:

sin(65)=30/x

sin(65)x=30

x=30/sin(65)

x=33.1

So the length of the ladder rounded to the nearest foot is 33 feet

The equation y = 0.75x + 2 represents the cost of going to the festival and picking x pounds of apples.

The equation provided,  y = 0.75x + 2 , follows the form  y = mx + b, where \y represents the total cost,  x represents the number of pounds of apples picked, 0.75x  represents the cost of apples at $0.75 per pound, and  2 represents the admission fee.

This equation allows you to calculate the total cost y based on the number of pounds of apples picked x , including both the admission fee and the cost per pound of apples.

Answer:

Jacob

Step-by-step explanation:

Because you can tell from the top of your head that it took Jacob 10 minutes for each mile for both days. While Otto his Wednesday time and Thursday time are not the same. Otto jogged an extra 2 minutes for his 6 miles on Thursday. So I would go with Jacob

Answer:

yggt7g7\

Step-by-step explanation:

Answer:

(a) P(X = 0) = 1/3

(b) P(X = 1) = 2/9

(c) P(X = −2) = 1/9

(d) P(X = 3) = 0

(a) P(Y = 0) = 0

(b) P(Y = 1) = 1/3

(c) P(Y = 2) = 1/3

Step-by-step explanation:

Given:

- Two 3-sided fair die.

- Random Variable X_1 denotes the number you get for rolling 1st die.

- Random Variable X_2 denotes the number you get for rolling 2nd die.

- Random Variable X = X_2 - X_1.

Solution:

- First we will develop a probability distribution of X such that it is defined by the difference of second and first roll of die.

- Possible outcomes of X : { - 2 , -1 , 0 ,1 , 2 }

- The corresponding probabilities for each outcome are:

                  ( X = -2 ):  { X_2 = 1 , X_1 = 3 }

                  P ( X = -2 ):  P ( X_2 = 1 ) * P ( X_1 = 3 )

                                 :  ( 1 / 3 ) * ( 1 / 3 )

                                 : ( 1 / 9 )

                  ( X = -1 ):  { X_2 = 1 , X_1 = 2 } + { X_2 = 2 , X_1 = 3 }

                 P ( X = -1 ):  P ( X_2 = 1 ) * P ( X_1 = 3 ) + P ( X_2 = 2 ) * P ( X_1 = 3)

                                 :  ( 1 / 3 ) * ( 1 / 3 ) + ( 1 / 3 ) * ( 1 / 3 )

                                 : ( 2 / 9 )

       ( X = 0 ):  { X_2 = 1 , X_1 = 1 } + { X_2 = 2 , X_1 = 2 } +  { X_2 = 3 , X_1 = 3 }

       P ( X = -1 ):P ( X_2 = 1 )*P ( X_1 = 1 )+P( X_2 = 2 )*P ( X_1 = 2)+P( X_2 = 3 )*P ( X_1 = 3)

                                 :  ( 1 / 3 ) * ( 1 / 3 ) + ( 1 / 3 ) * ( 1 / 3 ) + ( 1 / 3 ) * ( 1 / 3 )

                                 : ( 3 / 9 ) = ( 1 / 3 )

                    ( X = 1 ):  { X_2 = 2 , X_1 = 1 } + { X_2 = 3 , X_1 = 2 }

                 P ( X = 1 ):  P ( X_2 = 2 ) * P ( X_1 = 1 ) + P ( X_2 = 3 ) * P ( X_1 = 2)

                                 :  ( 1 / 3 ) * ( 1 / 3 ) + ( 1 / 3 ) * ( 1 / 3 )

                                 : ( 2 / 9 )

                    ( X = 2 ):  { X_2 = 1 , X_1 = 3 }

                  P ( X = 2 ):  P ( X_2 = 3 ) * P ( X_1 = 1 )

                                    :  ( 1 / 3 ) * ( 1 / 3 )

                                    : ( 1 / 9 )                  

- The distribution Y = X_2,

                          P(Y=0) = 0

                          P(Y=1) =  1/3

                          P(Y=2) = 1/ 3

- The probability for each number of 3 sided die is same = 1 / 3.

Answer:

Step-by-step explanation:

We can use the identity:

[tex]sin^{2}A + cos^{2}A= 1[/tex]

[tex]sinA = \frac{21}{29}[/tex]

Solving we get,

cosA = 20/29

Answer:

C. 20/29

e2020

Answer:

the answer is Athens-Buford-Cu-Dacul-Athens

Step-by-step explanation:

just took the quiz

Answer:

Way 3 and 4

Step-by-step explanation:

The Algorithm of Brute Force

Let A is Athens,  

Let B is Buford,  

Let C is Cuming,

Let D is Dacula  

Use the "Brute Force" Algorithm to find the cheapest route to visit each city and return home again to Athens, we can see that there are 6 ways to visit each city and return home again to Athens.

Way 1: A→C→D→B→A = 50 + 30 + 70 + 70 = $220

Way 2: A→D→B→C→A = 60 + 70 + 25 + 50 = $205

Way 3: A→D→C→B→A = 60 + 30 + 25 + 70 = $185

Way 4: A→B→C→D→A = 70 + 25 + 30 + 60 = $185

Way 5: A→B→D→C→A = 70 + 70 + 30 + 50 = $220

Way 6: A→C→B→D→A = 50 + 25 + 70 + 60 = $205

Way 3 and 4 are the cheapest so we choose them.

6.3 many more cups of dry food will Maria's pet have eaten than Trenton's pet will have eaten over 2 seven-day weeks

Step-by-step explanation:

We have , Trenton and Maria record how much dry food their pets eat on average each day.• Trenton's pet: 4/5 cup of dry food• Maria's pet: 1.25 cups of dry food. Based on these averages . We need to find  how many more cups of dry food will Maria's pet have eaten than Trenton's pet will have eaten over 2 seven-day weeks . We need to find how much they eat for 14 days as:

Trenton's pet: 4/5 cup of dry food•

With 4/5 per day , for 14 days :

⇒ [tex]14(\frac{4}{5} )[/tex]

⇒ [tex]14(0.8 )[/tex]

⇒ [tex]11.2[/tex]

Maria's pet: 1.25 cups of dry food.

With 1.25 per day , for 14 days :

⇒ [tex]14(1.25 )[/tex]

⇒ [tex]17.5[/tex]

Subtracting Maria's - Trenton's :

⇒ [tex]17.5-11.2=6.3[/tex]

That means , 6.3 many more cups of dry food will Maria's pet have eaten than Trenton's pet will have eaten over 2 seven-day weeks

Final answer:

Over the course of two seven-day weeks, Maria's pet will have eaten 6.3 more cups of dry food than Trenton's pet.

Explanation:

To determine how much more food Maria's pet eats compared to Trenton's, we first need to calculate the daily difference in food consumption, before multiplying that by the number of days in two weeks (14 days).

Maria's pet eats 1.25 cups of dry food each day, while Trenton's pet eats 4/5 cups (which is equivalent to 1 cup). To find out how much more food Maria's pet eats per day, we subtract Trenton's pet's portion from Maria's:

1.25 cups - 0.8 cups = 0.45 cups

Now we multiply this daily difference by 14 to find the total difference over two weeks:

0.45 cups/day x 14 days = 6.3 cups

So, Maria's pet will have eaten 6.3 more cups of dry food than Trenton's pet over the course of two seven-day weeks.

Answer:

6) x = 17 ft

7) 42 in

Step-by-step explanation:

6) length of the tangents are equal.

2x - 7 = 27

2x = 34

x = 17

7) if you draw a line from T passing through the centre of the circle, it will divide the triangle into two congruent triangles

Perimeter = 2(5+7+9) = 42 in

Answer:

The random variable X follows a Binomial distribution.

[tex]E(X)=X\\SD(X)=\sqrt{\frac{X(300-X)}{300}}[/tex]

Step-by-step explanation:

The random variable X defined as the number of children who have been diagnosed with ASD.

The random sample of children selected is of size n = 300.

The probability of children diagnosed with ASD is, [tex]P(X)=p=\frac{X}{300}[/tex].

A children diagnosed with ASD is independent of all the others.

The random variable X follows a Binomial distribution.

[tex]X\sim Bin(n=300, p=\frac{X}{300})[/tex]

The expected value of X is:

[tex]E(X)=np=300\times \frac{X}{300}=X[/tex]

The standard deviation of X is:

[tex]SD(X)=\sqrt{np(1-p)}=\sqrt{300\times \frac{X}{300}[1-\frac{X}{300}]}=\sqrt{\frac{X(300-X)}{300}}[/tex]

The given statement "If you spin the spinner again and g  results, the theoretical probability will change" is false.

Option C

Step-by-step explanation:

Since there are 5 sections of equal size, the theoretical probability of landing on any one of the them is equal. The probability of landing on any one of the sections is 20%. The experimental probability is based on the results of an actual experiment, meaning spinning the spinner, and recording the results.

A. The theoretical probability of a 1 is 20%. True as explained above.

B. The experimental probability of a 2 is 25%. True. There were 4 spins. One spin resulted in a 2. The experimental probability of spinning a 1 is 1/4 or 25 (1/4) %.

C. If you spin the same spinner again and get different results, the experimental probabilities are different, but the theoretical probabilities have changed(This is the complete option). But this is false.

The theoretical probability is always 20% for any of the sections, 1, 2, 3,  4 or , 5. The experimental probability depends on the results of the actual spins that were performed.

D. All of the above is true! , is a true statement.

Answer: C. If you spin the spinner again and get different results, the theoretical probability will change

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The graph A exhibits rotational symmetry

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Answer:

subtract 2 from both sides of the equation

Step-by-step explanation:

The first step in solving the equation 5 = 2 + ? is to subtract 2 from both sides of the equation.

The first step in solving the equation 5 = 2 + ? is to subtract 2 from both sides of the equation. This helps to isolate the variable and find its value. By subtracting 2 from both sides, the equation becomes: 5 - 2 = 2 + ? - 2. Simplifying further, we get: 3 = ?.

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Answer:

[tex]p_{5} (t) = x^{5} - 5\cdot x^{4} + 3\cdot x^{3} +9\cdot x^{2}[/tex], for [tex]r_{1} = 0[/tex]

Step-by-step explanation:

The general form of quintic-order polynomial is:

[tex]p_{5}(t) = a\cdot x^{5} + b\cdot x^{4} + c\cdot x^{3} + d\cdot x^{2} + e \cdot x + f[/tex]

According to the statement of the problem, the polynomial has the following roots:

[tex]p_{5} (t) = (x - r_{1})\cdot (x-3)^{2}\cdot x^{2} \cdot (x+1)[/tex]

Then, some algebraic handling is done to expand the polynomial:

[tex]p_{5} (t) = (x - r_{1}) \cdot (x^{3}-6\cdot x^{2}+9\cdot x) \cdot (x+1)\\p_{5} (t) = (x - r_{1}) \cdot (x^{4}-5\cdot x^{3} + 3 \cdot x^{2} + 9 \cdot x)[/tex]

[tex]p_{5} (t) = x^{5} - (5+r_{1})\cdot x^{4} + (3 + 5\cdot r_{1})\cdot x^{3} +(9-3\cdot r_{1})\cdot x^{2} - 9 \cdot r_{1}\cdot x[/tex]

If [tex]r_{1} = 0[/tex], then:

[tex]p_{5} (t) = x^{5} - 5\cdot x^{4} + 3\cdot x^{3} +9\cdot x^{2}[/tex]

The polynomial P(x) given has a degree of 5, leading coefficient of 1, roots at 3, 0 (both with multiplicity 2), and -1 (with multiplicity 1). It can be written as P(x) = (x - 3)^2 * x^2 * (x + 1), according to the Fundamental Theorem of Algebra.

A polynomial P(x) of degree 5 with a leading coefficient of 1 and roots at x = 3, x = 0 with multiplicity 2, and x = -1 with multiplicity 1 can be expressed as:

P ( x ) = (x - 3)^2 * x^2 * (x + 1)

This polynomial function is derived based on the fundamental theorem of algebra that states each polynomial equation of degree 'n' has 'n' roots or zeros, considering multiplicity. Here, the factors (x-3)^2, x^2 and (x+1) correspond to the roots 3, 0 and -1 with their respective multiplicities. Multiplicity refers to the number of times a number occurs as a root in the polynomial function.

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Answer: the expression for the combined total number of miles she biked in the two days is

117 - 5x miles

Step-by-step explanation:

Let x be the number of hours she biked yesterday.

In the two days, she biked for a combined total time of 9 hours. This means that the number of hours that she biked today is (9 - x) hours.

Distance = speed × time

Yesterday, Carmen went on a bike ride. Her average speed was 8 miles per hour. This means that the distance that she covered yesterday is 8x miles

Today, she went on another ride, this time averaging 13 miles per hour. This means that the distance that she covered today is 13(9 -x) miles.

An expression for the combined total number of miles she biked in the two days is

8x + 13(9 - x)

= 8x + 117 - 13x

= 117 - 5x

Answer:

Option 4

Step-by-step explanation:

B = D = 75

A = C = 180 - 75 = 105

In a parallelogram, opposite angles are equal and consecutive angles are supplementary. Given that Angle B is 75°, the other angles are 105° (Angle A), 75° (Angle D), and 105° (Angle C).

The parking space is in the shape of a parallelogram. The properties of a parallelogram tell us that opposite angles are equal, and consecutive angles are supplementary (add up to 180 degrees). Given that the measure of Angle B is 75°, the angle opposite to it (Angle D) will also be 75° as they are opposite angles. This leaves us with Angles A and C. Since angles A and B are consecutive, Angle A is 180° - 75° = 105°. Similarly, since angles C and D are consecutive, Angle C is also 180° - 75° = 105°. Thus, the measures of the four angles in the parallelogram are 75°, 105°, 75°, and 105° respectively.

Answer:

2/6

Step-by-step explanation:

The calculation shows that 102 adults watched both programs, 416 adults watched at least one program, 314 adults watched the Big Game, and 212 adults watched the Big Game but not the New Movie.

The subject of this question is Mathematics, specifically set theory, and it is geared towards High School grade level.

Let's break this down step by step:

To find the number of adults who watched both programs, we subtract the number who watched the New Movie but not the Big Game from the total number who watch the New Movie:

285 (watched New Movie) - 183 (watched the New Movie but not the Big Game) = 102 adults watched both programs (a)

To find the number of adults who watched at least one program, we subtract the number who watched neither from the total number of adults:

644 (total number of adults) - 228 (watched neither) = 416 adults watched at least one program (b)

To find the number of adults who watched the Big Game, we add the number who watched both to those who watched only the Big Game. The later is calculated by subtracting those who watched both and those who watched neither from the total number of adults:

644 (total number of adults) - 102 (watched both) - 228 (watched neither) = 314 watched the Big Game (c)

And finally, to calculate the number of adults who watched the Big Game but not the New Movie, we subtract the ones who watched both from total Big Game watchers:

314 (watched Big Game) - 102 (watched both) = 212 watched the Big Game but not the New Movie (d)

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The four statements can be expressed in mathematical symbols using logical operators, predicates, and quantifiers. Conjunction of tautologies, existence of tautologies, negation of contradiction, and disjunction of contingencies have been expressed as mathematical propositions.

In the realm of propositional logic, each statement can be expressed using logical operators, predicates, and quantifiers:

A) ∀x∀y(T(x) ∧ T(y) → T(x ∧ y)) - This states that for any two propositions, if both are tautologies, the conjunction (AND operation) of the two is also a tautology.

B) ∃xT(x) - This implies that there exists at least one proposition that is a tautology.

C) ∀x(C(x) → T(¬x)) - This implies that for all propositions, if a proposition is a contradiction, the negation of that proposition is a tautology.

D) ∃x∃y(¬T(x) ∧ ¬C(x) ∧ ¬T(y) ∧ ¬C(y) ∧ T(x ∨ y)) - This states that there exist two propositions where neither is a tautology or a contradiction (i.e., both are contingencies), such that their disjunction (OR operation) can be a tautology.

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The logical expressions use quantifiers, predicates, and logical operators to express concepts about tautologies and contradictions, emphasizing that propositions have intrinsic logical properties based on their structure.

Logical expressions employ quantifiers, predicates, and logical operators to articulate concepts about tautologies and contradictions, highlighting the intrinsic logical properties of propositions.

A. The conjunction of two tautologies is a tautology: (∀x)(∀y)(T(x) ^ T(y) ➡ T(x ^ y))

B. Some propositions are tautologies: (∃x) T(x)

C. The negation of a contradiction is a tautology: (∀x)(C(x) ➡ T(~x))

D. The disjunction of two contingencies can be a tautology: (∃x)(∃y)(C(x) ^ C(y) ➡ T(x ∨ y))

These expressions elucidate fundamental principles governing the logical structure and interplay of propositions, enriching our understanding of logical reasoning and inference.

Answer:

The answer to your question is 17.5 units

Step-by-step explanation:

Data

A (-10, 12)

B (5, 3)

Formula

dAB = [tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2}}[/tex]

x1 = -10   y1 = 12  x2 = 5  y2 = 3

- Substitution

dAB = [tex]\sqrt{(5 + 10)^{2} + (3 - 12)^{2}}[/tex]

- Simplification

dAB = [tex]\sqrt{15^{2}+ (-9)^{2}}[/tex]

dAB = [tex]\sqrt{225 + 81}[/tex]

dAB = [tex]\sqrt{306}[/tex]

Result

dAB = 17.49 units

The answer is the first choice

Answer:

Step-by-step explanation:

The problem statement tells you each observed count is 3 times the last one.

__

Expressed as an exponential function with an initial value of 50 and a growth factor of 3, the formula is ...

  y = (initial value)×(growth factor)^x

  y = 50·3^x

The question asks about a mold growth experiment which demonstrates exponential growth, where the number of mold cells triples with each measurement. Starting with 50 cells, the cell count increases to 150, 450, and so on.

The situation described in your question is an example of exponential growth, a mathematical concept often used in biology to describe how populations like your mold cells multiply over time, trebling with each measurement. Considering your initial mold count was 50, each subsequent measurement or observation will be 3 times the previous count:

And so on. The pattern continues, with each period's mold cell count being three times that of the previous period.

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Answer:

Step-by-step explanation:

The equation of a straight line can be represented in the slope intercept form as

y = mx + c

Where

c represents the y intercept

m represents the slope of the line.

The equation of the given line is

y = - 2x + 3

Comparing with the slope intercept form, slope = - 2

If two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line.

Therefore, the slope of the line passing through (4, - 3) is 1/2

To determine the y intercept, we would substitute m = 1/2, x = 4 and y = -3 into y = mx + c. It becomes

- 3 = 1/2 × 4 + c

- 3 = 2 + c

c = - 3 - 2

c = - 5

The equation becomes

y = x/2 - 5

Multiplying through by 2, it becomes

2y = x - 5

x - 2y - 5 = 0

Therefore

A = 1

B = - 2

C = - 5

Answer:

The third fret is 64.390mm from the first fret

Step-by-step explanation:

Distance between first and second fret is 33.641mm

Distance between second and third fret is 31.749mm

Hence distance between third and first fret will be = 33.641 + 31.749 = 64.390mm

Answer65.

Step-by-step explanation:

In this question, we are asked to state the distance between third and first frets.

Now, to consider this distance, just visualize. From the particulars in the question we can see that to get the distance, we need to add the two numbers together.

Mathematically, to calculate the distance, we need to make addition. This is represented by 31.749 + 33.641 = 65.39mm

The distance between the first fret and the second fret is 65.39mm

Answer:

The value of interest charged after 4 years = $ 960

Step-by-step explanation:

Principal amount P = $ 8000

Rate of interest R = 3 %

Time = 4 year

Simple interest = [tex]\frac{P R T}{100}[/tex]

⇒ S.I. = 8000 × 4 × [tex]\frac{3}{100}[/tex]

⇒ S.I. = $ 960

This is the value of interest  after 4 years.

Answer:

the volume of the box increases 48 times compared to the 1st one.

Step-by-step explanation:

Volume of the box (1) = LWH

=> The new volume of the box = 4L * 4W * 3H = 48LWH  

So the volume of the box increases 48 times compared to the 1st one.

Answer:

Step-by-step explanation:

Hello!

The variable of interest is

X: number of 18-20-year-olds that consume alcoholic beverages in a sample of 50.

The proportion of underage people that drinks are known to be p= 0.697

This variable is discrete. This experiment has two possible outcomes success or failure, we will call "success" each time we encounter an underage individual that consumes alcohol and "failure" will be counting an underage that does not consume alcohol. The number of repetitions of the trial is fixed n= 50. All randomly selected underage individuals are independent and the probability of success is constant trough the whole experiment p=0.697.

Then we can say that this variable has a binomial distribution and we will use that distribution to do the calculations.

a. Under a binomial distribution, the expected value is calculated as:

E(X)= n*p= 50*0.697= 34.85.

The variance of a binomial distribution is:

V(X)= n*p*(1-p)= 50*0.697*0.303= 10.55955

And the standard deviation is the square root of the variance:

√V(X)= 3.2495 ≅ 3.25

b. To know how rare the value 45, you have to see how distant it is concerning the expected value. For this you have to subtract the expected value and divide it by the standard deviation:

[X-E(X)]/√V(X)

(45-34.85)/3.25= 3.12

The value X=45 is 3.12 standard deviations above the mean, which means that it would be rare to find 45 people or more than consumed alcohol.

c. P(X≥45) = 1 - P(X<45)= 1 - P(X≤44)= 1 - 0.9994= 0.0006

I hope it helps!

The required values are:

a) Expect to have consumed alcoholic beverages[tex]=np=34.85[/tex]

and, Standard Deviation [tex]\sigma =3.25[/tex]

b) yes, 45 is more than two standard deviations above the expected value(mean)

C) Probability[tex]=0.0015[/tex]

a)

[tex]n=50\\p=0.6970[/tex]

They expect to have consumed alcoholic beverages,

[tex]=n \times p\\=50 \times 0.6970\\=34.85[/tex]

Standard Deviation,

[tex]\sigma =\sqrt{\left ( np\left ( 1-p \right ) \right )} \\ =\sqrt{\left (34.85 \right )(1-0.6970)} \\ =3.25[/tex]

b) Yes, 45 is more than 2 standard deviations above the expected value (mean)

C) Probability,

[tex]P=\left ( x > 44.5 \right ) \\ P=\frac{( Z > 44.5-34.85)}{3.25} \\ P=\left ( Z > 2.97 \right ) \\ P=1-P\left ( Z < 2.97 \right ) \\ P=1-0.9985 \\ P=0.0015[/tex]

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Answer:

[tex] x^{\frac{3}{5}} [/tex]

Step-by-step explanation:

[tex] \dfrac{\sqrt[3]{x^3}}{\sqrt[5]{x^2}} = [/tex]

[tex] = \dfrac{x^\frac{3}{3}}{x^\frac{2}{5}} [/tex]

[tex] = \dfrac{x^1}{x^\frac{2}{5}} [/tex]

[tex] = x^{\frac{1}{1} - \frac{2}{5}} [/tex]

[tex] = x^{\frac{5}{5} - \frac{2}{5}} [/tex]

[tex] = x^{\frac{3}{5}} [/tex]

Answer:

7.54 sq. inches

Step-by-step explanation:

The cake with the cut portion has been shown in the figure below.

For calculating the area of cut part we first need to calculate the area of whole cake.

Diameter of the cake is given in the question as 12 inches.

So the area of the cake = [tex]\pi \frac{Diameter^2}{4}[/tex] = [tex]3.14 \times \frac{12\times12}{4} = 113.04[/tex] [tex]inches^2[/tex]

Since when the central angle is 360°, the area is 113.04 square inches

So when the central angle is 24°, the area of the section will be

[tex]\frac{113.04\times 24}{360} =7.54[/tex]

Thus area of the slice cut by Nestor is 7.54 sq. inches.

Fraction = [tex]\frac{7.54}{113.04} = 0.07[/tex]

Answer:

cluster sampling

Step-by-step explanation:

In cluster sampling, the population is divided into groups or clusters (in this case, students divided in the 20 classes), the researcher then randomly selects a subset of clusters and samples the individuals within those clusters. In this example, since students from 5 out of 20 classes are sampled, the sampling process can be characterized as cluster sampling.

Answer:

5 cents.

Step-by-step explanation:

We have been George has $2.00 to spend at a store. He buys 3 cans of soda. Each can of soda costs 65 cents.

First of all George should calculate the total cost of 3 cans of soda by multiplying 3 by $0.65.

[tex]\text{Cost of 3 cans of soda}=\$0.65\times 3[/tex]

[tex]\text{Cost of 3 cans of soda}=\$1.95[/tex]

Now, George should subtract $1.95 from $2.00 to find the amount of change as:

[tex]\text{Amount of change that George will receive}=\$2.00-\$1.95[/tex]

[tex]\text{Amount of change that George will receive}=\$0.05[/tex]

Therefore, George will receive 5 cents in change.

Answer:

0.05 cents

Step-by-step explanation:

Given that George has $2.00 to spend at a store. He buys 3 cans of soda. Each can of soda costs 65 cents.

George has to use both multiplication and subtraction to find out the change

Spending at a store ...  2.00$

Cost of each can ... 0.65$

cost of 3 cans      ...  3*0.65 = 1.95$

Change he receives   ... 2-1.95 =0.05 cents