Sarah used 2.5 cups of cheese in a dish that serves 10 people. Many used 1.6 cups of cheese ina dish that serves 8 people. How much cheese is in one serving of Sarah's dish?

Arithmetic operations consists primarily of operations such as addition, subtraction, multiplication, and division. So the option A is correct.

The process of adding things together is known as addition. The '+' sign represents the addition process. It entails combining two or more numbers into a single expression.

The difference between two numbers is calculated using the subtraction operation. The '-' sign represents subtraction. It is nearly identical to addition, but it is the conjugate of the second term.

Multiplication is also referred to as repeated addition. It is indicated by " or '*'. It can also be combined with two or more values to produce a single value.

Division is the inverse of multiplication and is usually denoted by ". It is made up of two terms, dividend and divisor, and the dividend is divided by the divisor to yield a single term value.

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The fraction of the reading assignment done by Tuesday night is 1/2.

Given:

Let the total reading assignment be x.

Fraction of the reading assignment finished by Tori on Monday afternoon = (1/6)x

Fraction of the reading assignment finished by Tori on Tuesday afternoon = (1/3)x

The fraction of the reading assignment done by Tuesday night is,

Total - Fraction of the reading assignment completed by Tori

= \(x -(\frac{x}{6} + \frac{x}{3} )\)

= \(x -(\frac{x+ 2x}{6} )\)

= \(x - \frac{3x}{6}\)

= \(x -\frac{x}{2}\)

= \(\frac{2x-x}{2}\)

= \(\frac{x}{2}\)

So, 1/2 of the reading assignment(x) was done by Tuesday night.

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Out of the given options, the one that is not an advantage of using a sample versus a census is population size. The reason for this is that whether you use a sample or a census, the population size remains the same. However, there are several advantages to using a sample over a census.

Firstly, a sample generates a smaller dataset to analyze, which can save time and resources. Secondly, using a sample can be less expensive than conducting a census, which involves surveying every member of the population. Lastly, using a sample provides ready access to respondents, as it is often easier to reach a smaller group of people than an entire population. However, it is important to note that using a sample also has its limitations, such as the potential for sampling bias and the need to ensure that the sample is representative of the population being studied. Overall, the choice between using a sample or a census depends on the research question, available resources, and the level of accuracy and precision required.

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Answer:

It is from an actual immigrant who experienced rough treatment by the ship's workers.

Step-by-step explanation:

The text is a primary source from a slave.

Answer:

x =127

Step-by-step explanation:

Since this is a 6 sided figure, the sum of the interior angles is 720

128+133+112+x+120+100 = 720

Combine like terms

x+593=720

Subtract 593 from each side

x+593-593 = 720-593

x =127

Hint :

Sum of angles of the 6 sided figure = \( {720}^{o} \)

Answer:

\( {x}^{o} = {127}^{o} \)

Step-by-step explanation:

\( {x}^{o} + {112}^{o} + {133}^{o} + {128}^{o} + {100}^{o} + {120}^{o} = {720}^{o} \\ {x}^{o} + {593}^{o} = {720}^{o} \\ {x}^{o} = {720}^{o} - {593}^{o} \\ {x}^{o} = { 127}^{o} \)

m∠B = 10 and m∠Q = 10. Since ΔABC ≅ ΔPQR, the corresponding angles are congruent. Therefore, we can set up the following equation:

m∠B = m∠Q

Given that m∠B = 3v + 4 and m∠Q = 8v - 6, we can equate these expressions:

3v + 4 = 8v - 6

To solve for v, we can start by isolating the variable terms on one side of the equation and the constant terms on the other side:

4 + 6 = 8v - 3v

10 = 5v

Dividing both sides by 5:

v = 2

Now that we have the value of v, we can substitute it back into the expressions for m∠B and m∠Q:

m∠B = 3(2) + 4 = 10

m∠Q = 8(2) - 6 = 10

Therefore, m∠B = 10 and m∠Q = 10.

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Answer: Option d.  0.26

Step-by-step explanation:

Since the addition of complementary angles = 90°

75° + x = 90°

x = 90° - 75 °

x = 15°  ( the complementary angle )

sine 15° = 0.25882

             = 0.26 correct to two decimal places

a. Choosing the number 9 is a dominated strategy, b. Choosing the number 37 is a dominated strategy, c. The range of numbers for which each number in the range is closer to the winning number than 30 is from 21 to 39, d. The set of best responses for Lisa if she knew that all of her classmates would submit the number 24 is an empty set.

e. The symmetric Nash equilibrium in this game is the number 25.
f. The dominated strategies are choosing the numbers 9 and 37.
g. If Lisa believes that none of her classmates will play the dominated strategies found in part f, the strategies that are never a best response for Lisa are choosing the numbers 9 and 37.
h. The rationalizable strategies in this game are choosing any number between 21 and 39.

Explanation:
a. To show that choosing the number 9 is a dominated strategy, we need to compare the payoffs of choosing 9 with the payoffs of choosing any other number. If we look at the payoff for choosing 9, it is $50 if 9 is closer to the winning number than (1/2X+10), and $0 otherwise. However, if we choose any number greater than 9, our payoff will be $50 if that number is closer to the winning number than (1/2X+10), and $0 otherwise. Therefore, choosing 9 is always dominated by choosing a number greater than 9.
b. Similarly, to show that choosing the number 37 is a dominated strategy, we compare the payoffs of choosing 37 with the payoffs of choosing any other number. The payoff for choosing 37 is $50 if 37 is closer to the winning number than (1/2X+10), and $0 otherwise. However, if we choose any number less than 37, our payoff will be $50 if that number is closer to the winning number than (1/2X+10), and $0 otherwise. Therefore, choosing 37 is always dominated by choosing a number less than 37.
c. If Lisa knows that all of her classmates would submit the number 30, she wants to choose a number that is closer to the winning number than 30. The range of numbers for which each number in the range is closer to the winning number than 30 is from 21 to 39. If Lisa chooses any number between 21 and 39, she will have a higher payoff than if she chooses 30.

d. If Lisa knows that all of her classmates would submit the number 24, there is no best response for her. Choosing any number will not give her a higher payoff than choosing 24.
e. To find a symmetric Nash equilibrium in this game, we need to find a number that is a best response to everyone else submitting that same number. The number 25 is a best response to everyone else submitting 25 because it is the closest number to (1/2X+10). Therefore, the symmetric Nash equilibrium in this game is the number 25.
f. The dominated strategies in this game are choosing the numbers 9 and 37. These strategies are dominated because there are always other numbers that will give a higher payoff.
g. If Lisa believes that none of her classmates will play the dominated strategies found in part f, the strategies that are never a best response for Lisa are choosing the numbers 9 and 37. This is because there will always be other numbers that give a higher payoff.
h. The rationalizable strategies in this game are choosing any number between 21 and 39. These strategies are rationalizable because they are best responses to the belief that all of Lisa's classmates will submit the number 30. By choosing a number in this range, Lisa ensures that she has a higher payoff than if she chooses any other number.

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The conical surface is the correct answer as it allows for slopes ranging from 20:1 to 50:1. The FAR Part 77 imaginary surface that has slopes that may range from 20:1 to 50:1 is the conical surface.

The conical surface is a three-dimensional surface defined by a combination of horizontal and inclined planes. It extends upward and outward from the end of the primary surface and has varying slope requirements. The slope of the conical surface represents the ratio of the change in elevation to the horizontal distance. A slope of 20:1 indicates that for every 20 units of horizontal distance, there is a 1-unit increase in elevation.

Similarly, a slope of 50:1 means that for every 50 units of horizontal distance, there is a 1-unit increase in elevation. Therefore, the conical surface is the correct answer as it allows for slopes ranging from 20:1 to 50:1.

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C - 1,4,4

D - 2,2,4

The product of dimensions must give 16 as a result.

Answer:

11:27 am.

Step-by-step explanation:

The time which has passed when Tom overtakes Hazel is after Hazel has walked 1 hr 15 minutes and in that time Hazel has walked

1.25 * 4.8

= 6 km.

So, Tom runs 6 km in 10:15 - 9.39 = 36 minutes

= 0.6 hrs.

So, Tom's speed is 6/0.6 = 10 km/hr.

,

and Tom will take 18/10 = 1.8 hours to finish the route,

= 1 hr 48 minutes

So he finishes the route at

9:39 + 1:48

= 11:27 am.

The value of the arcsin of 3 is 90 - 100.998i

From the question, we are to determine the inverse sine or arcsine of the given number

The given number is 3

All the values for the sine of angles are less than or equal to 1

That is,

Given an angle θ,

sinθ ≤ 1

From this, we can infer that the arcsine of 3 will be an imaginary number.

The arcsine of 3 is

sin⁻¹(3) = 90 - 100.998i

Hence, the value of the arcsin of 3 is 90 - 100.998i

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The improper fraction can be written as:

44/7

An improper fraction is a fraction where the numerator is larger than the denominator.

Here we want to write.

6 + 2/7 as an improper fraction, to do so, we just need to write 6 as a fraction with a denominator of 7 and then add them.

We know that:

6 = 6*(7/7) = 42/7

Then we can write:

6 + 2/7 = 42/7 + 2/7 = 44/7

That is the improper fraction.

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There are 30 adults in the swimming pool.

The ratio is a quantitative approach that shows the relation between two proportions.

From the given relation, the ratio of of the children to adults = 8 : 3

The total number of the ratio = 8 + 3 = 11

Given that there are 110 people in the population.

The number of adults that are there will be:

\(\mathbf{=\dfrac{3}{11}\times 110}\)

= 30 adults

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Answer:

4.5%

Step-by-step explanation:

Word problems

Simultaneous equation

4b + 3n = $23.50 x2

5b + 2n = $21.50 x3

We solve this equation using the elimination method. By removing necklaces, we can find the cost of a bracelet.

8b + 6n = $47 --- eqn 1

15b + 6n = $64.5 --- eqn 2

Subtract eqn 1 from eqn 2

7b = 17.5

1b = 17.5/7

1b = $2.50

Substitute the value of bracelet into eqn 1 to find the cost of 1 necklace

8(2.5) + 6n = $47

20 + 6n = $47

6n = 47 -20

6n = 27

1n = 27/6

1n = $4.5

1b + 1n = ?

2.50 + 4.50 = $7

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The Answer is

A~13057.38

The money, to the nearest cent, would be in the account after 15 years is $13060.

Due to the high frequency of compounding, daily compounded interest is larger than monthly/quarterly compounded interest since interest is accumulated on a daily basis and is determined by charging interest on principal plus interest gained on a daily basis

It is given in the question that Kennedy invested $5000

Interest rate = 6.4% compounded daily

Assuming no deposits and withdrawals

T = 15 years

The formula for amount obtained after 15 years when interest is compounded daily

\(\rm A = (P(1 + \dfrac{r}{n})^{nt})\)

\(\rm A = (5000(1 + \dfrac{6.4}{365*100})^{365*15})\)

A = 5000 * 2.612

A = $13060

Therefore , money, to the nearest cent, would be in the account after 15 years is $ 13060.

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Considering the expression of a line, the equation of the line that passes through the points (-9,-7) and (-11,-6) is the equation of the line is y= -1/2x -23/2.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m of a line can be calculated as:

m= (y₂ - y₁)÷ (x₂ -x₁)

Substituting the value of the slope m and the value of one of the points in y=mx +b, the value of the "b" can be obtained.

Being (x₁, y₁)= (-9, -7) and (x₂, y₂)= (-11, -6), the slope m can be calculated as:

m= (-6 - (-7))÷ (-11 -(-9))

m= (-6 +7)÷ (-11 +9)

m= (1)÷ (-2)

m= -1/2

Considering point 1 and the slope m, you obtain:

-7= (-1/2)×(-9) + b

-7= 9/2 +b

-7 -9/2= b

-23/2= b

Finally, the equation of the line is y= -1/2x -23/2.

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Answer:

a = -12

Remember that when a variable is times with a number, you divide the number on both sides.

When a variable is divided by a number, you multiply the number on both sides.

Hope this helps you. Thank you !!

Answer:

2.3a + 0.8a =

2.3

+ 0.8

________

3.1

________

So therefore, 2.3a + 0.8a = 3.1a

Coordinate of circumcenter of the given triangle = (3, 2)

What is circumcenter of a triangle?

Circumcenter of a triangle is the point of intersection of the perpendicular bisectors of every sides of the triangle.

Let the coordinate of circumcenter be (x , y)

Distance of Circumcenter from (4,2) =

\(\sqrt{(x - 4)^2 + (y-2)^2\)

Distance of Circumcenter from (3, 3) =

\(\sqrt{(x - 3)^2 + (y-3)^2\)

Distance of Circumcenter from (2,2) =

\(\sqrt{(x - 2)^2 + (y-2)^2\)

By the problem,

\(\sqrt{(x - 2)^2 + (y-2)^2} = \sqrt{(x - 3)^2 + (y-3)^2}\\(x - 2)^2 + (y-2)^2} = (x - 3)^2 + (y-3)^2}\\x^2 - 4x + 4 + y^2 -4y + 4 = x^2 -6x + 9 + y^2-6y + 9\\6x - 4x +6y -4y = 18-8\\2x +2y = 10\\x+ y = 5\\\)..... (1)

Again,

\(\sqrt{(x - 4)^2 + (y-2)^2} = \sqrt{(x - 3)^2 + (y-3)^2}\\(x - 4)^2 + (y-2)^2} = (x - 3)^2 + (y-3)^2}\\x^2 - 8x + 16 + y^2 -4y + 4 = x^2 -6x + 9 + y^2-6y + 9\\8x - 6x +4y -6y = 20-18\\2x -2y = 2\\x- y = 1\\\)...... (2)

Adding (1) and (2)

\(2x = 6\\x = \frac{6}{2}\\x = 3\)

Putting the value of x in (1),

3 + y = 5

y = 5 - 3

y  = 2

Coordinate of circumcenter = (3, 2)

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Answer:

0.36

Step-by-step explanation:

and I got this answer by using calculator

a) The center of G and determining the distinct conjugacy classes, we can calculate the class equation of the finite group G.

b) We have shown both implications: if a Sylow p-subgroup is normal, then it is unique, and if it is unique, then it is normal.

(a) Deriving the class equation of a finite group G involves partitioning the group into conjugacy classes. Conjugacy classes are sets of elements in the group that are related by conjugation, where two elements a and b are conjugate if there exists an element g in G such that b = gag^(-1).

To derive the class equation, we start by considering the group G and its conjugacy classes. Let [a] denote the conjugacy class containing the element a. The class equation is given by:

|G| = |Z(G)| + ∑ |[a]|

where |G| is the order of the group G, |Z(G)| is the order of the center of G (the set of elements that commute with all other elements in G), and the summation is taken over all distinct conjugacy classes [a].

The center of a group, Z(G), is the set of elements that commute with all other elements in G. It can be written as:

Z(G) = {z in G | gz = zg for all g in G}

The order of Z(G), denoted |Z(G)|, is the number of elements in the center of G.

The conjugacy classes [a] can be determined by finding representatives from each class. A representative of a conjugacy class is an element that cannot be written as a conjugate of any other element in the class. The number of distinct conjugacy classes is equal to the number of distinct representatives.

By finding the center of G and determining the distinct conjugacy classes, we can calculate the class equation of the finite group G.

(b) To prove that a Sylow p-subgroup of a finite group G is normal if and only if it is unique, we need to show two implications: if it is normal, then it is unique, and if it is unique, then it is normal.

If a Sylow p-subgroup is normal, then it is unique:

Assume that P is a normal Sylow p-subgroup of G. Let Q be another Sylow p-subgroup of G. Since P is normal, P is a subgroup of the normalizer of P in G, denoted N_G(P). Since Q is also a Sylow p-subgroup, Q is a subgroup of the normalizer of Q in G, denoted N_G(Q). Since the normalizer is a subgroup of G, we have P ⊆ N_G(P) ⊆ G and Q ⊆ N_G(Q) ⊆ G. Since P and Q are both Sylow p-subgroups, they have the same order, which implies |P| = |Q|. However, since P and Q are subgroups of G with the same order and P is normal, P = N_G(P) = Q. Hence, if a Sylow p-subgroup is normal, it is unique.

If a Sylow p-subgroup is unique, then it is normal:

Assume that P is a unique Sylow p-subgroup of G. Let Q be any Sylow p-subgroup of G. Since P is unique, P = Q. Therefore, P is equal to any Sylow p-subgroup of G, including Q. Hence, P is normal.

Therefore, we have shown both implications: if a Sylow p-subgroup is normal, then it is unique, and if it is unique, then it is normal.

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On solving the provided question, we cans ay that sum of co-exterior angles are 180 so, 180-73 = x => x = 7

An angle is a form in Euclidean geometry made composed of two rays, called the angle's sides, that meet at a point in the middle known as the angle's vertex. In the plane where the rays are placed, two rays can produce an angle. An angle is also produced when two planes intersect. They're known as dihedral angles. In plane geometry, an angle is the form that two rays or lines with a common termination might take. The Latin word "angulus," which means "horn," is where the English word "angle" comes from. The two rays, also known as the sides of the angle, have a common termination known as the vertex.

here,

angle x and 73 are co-exterior angles

so, sum of co-exterior angles are 180.

so, 180-73 = x => x = 7

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Answer:

76 and 77 are the locker numbers.

Step-by-step explanation:

Let the number be x and (x + 1)

The sum of two consecutively number is 153

Now,

x + (x + 1) = 153

x + x + 1 = 153

2x + 1 = 153

Now, subtract 1 from both side we get,

2x + 1 - 1 = 153 - 1

2x = 152

Now, divide by 2 from both side we get,

2x/2 = 152/2

x = 76

Here, The value of x is 76

Now, the first number = x = 76 and the Second number = (x + 1) = 76 + 1 = 77

Thus, 76 and 77 are the locker numbers.

x + (x + 1) = 153

76 + (76 + 1) = 153

153 = 153

L.H.S = R.H.S

Hence Proved!

-TheUnknownScientist 72

The two numbers which are consecutive and have a sum of 153 are 76 and 77.

Given data:

Let's denote the two consecutive locker numbers as "x" and "x+1". According to the problem, the sum of these two numbers is 153, so we can write an equation:

x + (x+1) = 153.

Simplifying this equation, we combine the "x" terms:

2x + 1 = 153

Now, we subtract 1 from both sides of the equation:

2x = 152

To find the value of "x", we divide both sides by 2:

x = 76

So, one locker number is 76, and the consecutive locker number is 76+1 = 77.

Hence, the two locker numbers are 76 and 77, and their sum is indeed 153, as required by the problem. This solution satisfies the condition of consecutive locker numbers and their sum.

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y=4x+64

Explanation:

Two lines are perpendicular if the product of their slopes is -1.

Step 1: Find the slope of the line a

Line a passes through the points (1,-3) and (9,-5)

The slope of line a = -1/4

Step 2: Determine the slope of line b.

Let the slope of line b = k

Since the product of the two slopes is -1:

The slope of line b = 4

Step 3: Find the equation of line b.

Line b passes through the point (x1,y1)=(-8,32) and has a slope, m = 4.

Using the slope-point form of the equation of a line:

Substitute the given values

The equation of line b is y=4x+64.

Answer:

1008 \(cm^2\)

Step-by-step explanation:

Given:

Triangular prism with

Base of triangle = 5 + 9 = 14 cm

Height of triangle = 12 cm

Here, we have 3 faces of the prism as a rectangle, all have width = 20 cm

Lengths of faces = 13cm ,14cm and 15 cm respectively

To find:

Total surface area = ?

Solution:

3 faces are rectangular shape and 2 faces are triangular shape.

\(Area\ of\ rectangle = Length \times Width\)

The formula for Total Surface Area of a triangular prism is given as:

\(TSA = 2 \times \text{Area of triangular base}+{\text{Area of rectangular faces}}\\\Rightarrow TSA = 2 \times \dfrac{1}{2}\times Base \times Height+{\text{Area of rectangular faces}}\\\Rightarrow TSA = 14 \times 12 + 15 \times 20+ 13 \times 20+ 14 \times 20\\\Rightarrow TSA = 168 + 840\\\Rightarrow TSA = 1008\ cm^2\)

So, the total surface area of the given triangular prism is 1008 \(cm^2\).

Answer: See below

Step-by-step explanation:

640km/16gal

Divide both sides by 16

= 40/1

The unit rate is 40km/1gal

Answer:

Step-by-step explanation:

Solving systems of equations gives the points of intersection when the equations are graphed.

The answer is 3.