A bottle of soap costs $3.45 for 64ounces. What is the cost per ounce?

There are three ways to solve systems of linear equations in two variables:

System of Linear Equations :

A system of linear equations is two or more linear equations that are being solved simultaneously.

Solution of a System :

In general, a solution of a system in two variables is an ordered pair that makes BOTH equations true. In other words, it is where the two graphs intersect, what they have in common.  So if an ordered pair is a solution to one equation, but not the other, then it is NOT a solution to the system.

A consistent system is a system that has at least one solution.

An inconsistent system is a system that has no solution.

There are three ways to solve systems of linear equations in two variables:

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If x has a percentage of 10% and that is equal to y at 100%, then x is equal to 10% of y. If x is at 100%, then the percentage of y would be 1000%.

Here's how to arrive at this answer:

First, let's set up the equation to represent the given information:

x = 10% * y

If we solve for y in this equation, we get:

y = x / (10%)

Now, if we set x equal to 100%, we get:

y = (100%) / (10%)

Simplifying this fraction gives us:

y = 10

Since y is equal to 10, the percentage of y is 1000%.

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Identifying the issue, considering potential solutions, and selecting the best course of action are the three primary components of problem-solving.

Mathematical issues can be solved in a variety of methods; however, a three-step technique is a streamlined approach that can assist anybody in solving even the most challenging problem.

Three steps is here:

1. Create a mental image of the issue

Daydreaming and the mental imagery that takes place when reading a book are two frequent instances of mental pictures. The images that athletes conjure up during practice or before a competition, describing each step they will take to achieve their objective, are another example.

2. The strategy should be used to solve the issue

A strategy is a way to manipulate numbers, use connections and interactions between numbers to solve an issue. For each procedure, there are a few key tactics. The first thing you do with the statistics is frequently used to label a technique.

3. Conclude by fixing the issue

A conclusion is a claim made after a set of premises and a set of logical principles known as syllogisms have been considered. Deduction is the process of inferring conclusions from premises and syllogisms.

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You can see that x=4 takes two different values y=7 and y=1. You should remove one of these ordered pairs (4,7) or (4,1).

What are the 4 types of function?

There are 4 types of functions:

Functions with arguments and return values. This function has arguments and returns a value: ...

Functions with arguments and without return values. ...

Functions without arguments and with return values. ...

Functions without arguments and without return values.

A function is a relation that for each input value x takes the unique value of output y.

Consider the table

x y

1 7

4 7

2 2

4 1

3 9

You can see that x=4 takes two different values y=7 and y=1. You should remove one of these ordered pairs (4,7) or (4,1).

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The system of equations has no solution because they are parallel lines.

The equation is defined as a mathematical statement that has a minimum of two terms containing variables or numbers that are equal.

In general, any equation of the form y = k, where k is a constant, represents a horizontal line that extends indefinitely in both directions.

The system of equations y=0 and y=-6 describes two lines in the coordinate plane.

The first equation, y=0, is the x-axis.

The second equation, y=-6, is a horizontal line 6 units below the x-axis.

As we know, y = 0 and y = -6 are two parallel lines.

Therefore, no solution exists.

Hence, the system of equations has no solution.

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If a statement is true, then it cannot be falsified no matter what.

A true statement will yield a true statement.

A false statement can yield a true or false statement.

The answer to your question is no, we cannot do anything to make the statement "2=2" false

We can write '8 or more' as [tex]\geq 8[/tex], using the greater-than equal to sign.  

The greater-than sign is a mathematical symbol that denotes an inequality between two values. The widely adopted form of two equal-length strokes connecting in an acute angle at the right, >, has been found in documents dated as far back as 1631. In mathematical writing, the greater-than sign is typically placed between two values being compared and signifies that the first number is greater than the second number.

Examples of typical usage include 1.5 > 1 and 1 > −2. The less-than sign and greater-than sign always "point" to the smaller number. Since the development of computer programming languages, the greater-than sign and the less-than sign have been repurposed for a range of uses and operations.

Here, we can use an alternate to the 'greater-than' symbol: a 'greater-than equal to' symbol, denoted as ≥.

Using this, we can write:

[tex]\geq[/tex] 8, denotes a number greater-than or equal to 8.

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Answer:5.6

Step-by-step explanation:

Answer: $1.40/4 = $0.35/apple

Interest earn is $6,371.45 ≅ $6,370 (round to the nearest cent)

To receive as return for effort and especially for work done or services rendered. : to bring in by way of return.

When you earn interest on your interest earnings as well as the money you have saved, this is known as compound interest. A = P is the compound interest formula.

A = P[tex](1 + r/n)^{nt}[/tex]

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

$530 for 9 years at 33% interest each year using the compound interest formula, where t = number of time periods elapsed

A = P[tex](1 + r/n)^{nt}[/tex]

A= 530 (1 + 0.33/1)^9

A = $6,901.45

So to find interest I = A-P

I = $6901.45 -$530

I =  $6,371.45

Interest earn is $6,371.45 ≅ $6,370 (round to the nearest cent)

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Answer: Profit = Rs 15, Profit %= 30%

Step-by-step explanation: When S.P.( Selling Price) is greater than C.P.(Cost Price), there is a Profit.

Profit= S.P-C.P

Hence Rs 15 is the profit.

To calculate Profit %, we use the formula Profit ÷ C.P. × 100%

Hence, the Profit % is 30%.

If the two triangle are overlapping , then they are congruent.

The term congruent refers the triangles that have three sets of corresponding congruent sides and three sets of corresponding congruent angles.

Here we have to prove that the two overlapping triangles are congruent.

Here we know that the two triangle are overlappling.

Now we have to do the following process to prove that the overlapping triangles are also congruent.

As per the reflexive property of congruence, here when overlapping triangles share a common side or angle because the reflexive property of congruence states that a segment or angle is congruent to itself. Therefore, according to the geometry when two triangles share a side or angle this can be used to prove one set of congruent sides/angles.

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(i) Large Table Required are 3 and Small Table required are 8

(ii) Price of Student Ticket is $5.5 and Adult Ticket is $7.5

What is Linear Equation in Two Variable?

A linear equation in two variables is one that is stated in the form ax + by + c = 0, where a, b, and c are real integers and the coefficients of x and y, i.e. a and b, are not equal to zero.

Solution:

(i)

Seats in Large Table = 12

Cost of Large Table = $50

Seats in Small Table = 8

Cost of Small Table = $25

Let, Number of Large Tables = x

Number of Small Tables = y

According to the Question:

12x + 8y = 100

50x + 25y = 350

x = 3, y = 8 (refer graph 1)

(ii)

Cost of Student Ticket = x

Cost of Adult Ticket  = y

According to the Question:

16x + 3y = 110.5

12x + 4y = 96

x = $5.5, y = $7.5 (refer graph 2)

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The lines p and q are perpendicular in the coordinate plane.

The name of the other number line, which is a vertical one, is called the y-axis. To graph points, lines, and other objects, one can utilize the coordinate plane. A pair of numerical coordinates that uniquely identify each point in a Cartesian coordinate system in a plane are called the coordinates. These numerical coordinates are signed length measurements that represent the separations between two fixed perpendicular oriented lines and the point.

Let the equation of the line is:

y-y'=m₁(x-x')

m₁=2/6

m₁=1/3

Therefore, the equation of a line with the point (3, 4) and slope m₁=1/3

y-4=(1/3)(x-3)

y=(1/3)x-1+4

y=(1/3)x+3

And m₂= -3

The line equation that is passing through (2,7) and m₂= -3

y-7=(-3)(x-2)

y-7= -3x+6

y= -3x+13

m₁×m₂= -1

(1/3)(-3)= -1

So, the lines that are given in the coordinate plane p and q are perpendicular.

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The mean squared error is 4.67. So the option a is correct.

In the given question, demand for a product and the forecasting department's forecast for a product are given.

We have to compute the mean squared error.

Period          Actual        Forecasted      Error       Absolute      Squared

                 Demand(E)    Demand (F)     (E-F)        Error |E-F|    Error |(E-F)|^2

1                12    

2                15                12              3               3             9

3                14                15              -1                1              1

4                18                16              2                2              4

                                                                Total=6        Total=14

Now we finding the mean squared error (MAE)

Mean squared error = ∑|(E−F)|^2/n

Mean squared error = 14/3

Mean squared error = 4.67

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The equation with a solution s = 3/4 is the second option:

4s = 3

We want to see which of the given equations has a solution s = 4/3.

What you can do is take all the given equations and solve them, for example, if I solve the first one:

s - 1 = 1/4

We will get:

s = 1 + 1/4 = 5/4

So this one is not the correct one.

The second equation is:

4s = 3

Dividing both sides by 4:

s = 3/4

So this is the correct option.

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Answer and Step-by-step explanation:

Lydia must sell at least $680 worth of tacos and burritos each day, and she only has enough supplies to make 115 tacos or burritos. If she sells each taco for $4, then she can make a maximum of 115 tacos * $4/taco = $<<115*4=460>>460 by selling tacos.

Therefore, in order to make at least $680, Lydia must sell burritos in addition to the tacos. The minimum number of burritos she must sell in order to make at least $680 is $680 - $460 = $<<680-460=220>>220.

Since Lydia sells each burrito for $6.75, she must sell at least $220 / $6.75/burrito = <<220/6.75=32.5>>32.5 burritos to make at least $680. Since she only has enough supplies to make 115 tacos or burritos, and she has already accounted for 115 tacos, she must sell a minimum of 32.5 burritos to meet the requirements.

Although it won't necessarily be harder, this will consume more of your time.

How much work performed by an element in a given timeframe, or the typical measure of work took care of by a substance at a specific moment of time. An estimate of an organization's performance and efficiency can be derived from the amount of work it handles. This term is used in computer science to describe the capacity of computer systems to handle and process work.

At the time of creation, components like databases and servers frequently receive an anticipated workload. Following that, a time-based comparison of their performance to the anticipated workload is carried out.

There is always more work to do in high school classes. You might have assignments that are more difficult, more homework, or more classes than you did in middle school. Although it won't necessarily be harder, this will consume more of your time.

Classes naturally become more challenging over time. After all, year after year, you tackle more difficult concepts. A component of education is that. Theoretically, middle school was "harder" than elementary school. There will be classes that are harder, and you might have to put in more work for some of them. But you should be able to handle these classes as long as you have a solid foundation. You can join the thousands of students who have made it this far.

Therefore, This will take up more of your time, despite the fact that it will not necessarily be harder.

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Performed at about average on spelling, but about one standard deviation below average on math.

Any test that (1) requires all test takers to answer the same questions, or a set of questions from a common bank of questions, in the same way and (2) is scored in a "standard" or consistent manner, allowing for comparison of the relative performance of individual test takers, is considered to be standardized.

Students are frequently chosen for certain programs using standardized assessments. For instance, norm-referenced examinations like the SAT (Scholastic Assessment Test) and ACT (American College Test) are used to decide whether high school students get admitted to elite institutions.

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Answer:

  75

Step-by-step explanation:

You want the remainder when n is divided by 100, where VISIONERS is the n-th word in the alphabetically-ordered list of the permutations of REVISIONS.

The letters of the word REVISIONS are, in alphabetic order, are EIINORSSV. We notice there are two each of the letters I and S.

When the permutations of the letters of REVISIONS are written in lexicographical order, the list will first have all of the permutations beginning with E, then those beginning with I, and so on until the permutations beginning with S are exhausted.

To find the rank (number n) of the first permutation beginning with V, we must count the number of permutations ahead of it in the list. This will be the sum of the numbers of permutations beginning with E, I, N, and so on through S.

The straightforward way to do this is to consider the letters individually, and the number of permutations associated with each one. For example, the letters following E will be the 8 letters IINORSSV, which have two repeat pairs. The number of permutations of these 8 letters is 8!/(2!·2!) = 10080.

The next leading letter in the list is I, which can be followed by any of the letters EINORSSV, for a total of 8!/2! = 20160 permutations.

The letter N will be the next leading letter, and it will have a number of permutations equal to the number for the letter E, 10080.

At this point, we have exhausted 4 of the 8 letters that must precede V in the ordered list, and have counted 10080 +20160 +10080 = 40320 permultations. We notice this is, in effect, 10080 permutations per letter, the number of permutations of the letters not including V.

If we were to work through the remaining letters (including the repeated S), we would find the total to be 8·10080 = 80640 permutations before any starting with V.

Effectively, our formula for the number of added permutations preceding words matching up to the k-th letter of our target word is ...

  p(9-k)!/q

where p is the number of letters in the (remaining) ordered letter list preceding the k-th letter of VISIONERS, and q is the factor that compensates for repeated letters among those remaining. "q" is the product of the factorials of the number of times a letter is repeated. For 2 letters, each repeated once, q = 2!·2! = 4.

V is the 9th letter of EIINORSSV; there are 8 letters preceding, including 2 repeated twice. k=1, so there are 8·(9-1)!/(2!·2!) = 80640 permutations preceding ones starting with V.

I is the 2nd letter of EIINORSS; there is 1 letter preceding, including 2 repeated twice. k=2, so there are 1·(9-2)!/(2!·2!) = 1260 permutations preceding ones starting with VI.

S is the 6th letter of EINORSS; there are 5 letters preceding, including 1 repeated twice. k=3, so there are 5·(9-3)!/2! = 1800 permutations preceding ones starting with VIS.

I is the 2nd letter of EINORS; there is 1 letter preceding, with no repeats. k=4, so there are 1·(9-4)! = 120 permutations preceding ones starting with VISI.

O is the 3rd letter of ENORS; there are 2 letters preceding. k=5, so there are 2·(9-5)! = 48 permutations preceding ones starting with VISIO.

N is the 2nd letter of ENRS; there is 1 letter preceding. k=6, so there are 1·(9-6)! = 6 permutations preceding ones starting with VISION.

We note that the remaining letters, ERS, are in alphabetical order, so there are no additional permutations preceding VISIONERS.

Then the number of permutations preceding VISIONERS is ...

  80640 +1260 +1800 +120 +48 +6 = 83874

and the rank of VISIONERS is 83875.

The remainder when this is divided by 100 is 75.

__

Additional comment

The usual counting method goes into more detail than the one described here. For problems of reasonable size, it is often easier to count the permutations generated ahead of the one of interest using a "next permutation" function.

In the attachment, we generated them all, and searched for the one of interest.

Answer:

you would take 249.50 and subtract 26.00 from it. then you would divide it by 3 for the initial cost of each dress

Step-by-step explanation:

249.50-26.00=223.05 then divide

223.05÷3= 74.05

hope that helped !

Answer:

If 10% of the students at Ridgewood Junior High School bring their lunch to school every day, and there are 700 students at the school, then 10% of 700 students is equal to 0.1 * 700 = <<10*.01*700=70>>70 students.

Therefore, on Thursday, 70 students brought their lunch to school.

From the concept of algebra of venn diagram we obtain that
P(A or B) = 0.75.

A set is a collection of well-defined objects.

A subset contains all the elements or few elements of the given set.

The improper subset is when it contains all the elements of the given set and the proper subset is when it doesn't contain all the elements of the given set.

From set theory, we know that N(A∪B) = N(A) + N(B) - N(A∩B).

It states that N(A) or N(B) is the sum of N(A) and N(B) minus the common intersecting region N(A∩B) as we have already considered the region in the sum of N(A) and N(B) twice.

Similarly, P(A or B) = P(A) + P(B) - P(A∩B)>

Therefore, P(A or B) = 0.50 + 0.40 - 0.15.

P(A or B) = 0.90 - 0.15.

P(A or B) = 0.75.

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The probability that exactly two of the students are juniors is given as follows:

0.270 = 27%.

The mass probability formula is presented as follows:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

The values of these parameters for this problem are given as follows:

[tex]N = 60, n = 4, k = 18[/tex]

Hence the probability that exactly two of the students are juniors is calculated as follows:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 2) = h(2,60,4,18) = \frac{C_{18,2}C_{42,2}}{C_{60,4}} = 0.270[/tex]

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The expected number of airplanes circling the airport, waiting in queue for clearance to land, if this new radar system were to be used is zero.

The new radar system is being considered as a means of reducing congestion, which implies that there is currently an issue with congestion at the airport. One way to reduce congestion is to process planes at a faster rate, which is exactly what the new radar system aims to do.

The statement "planes can be processed at a constant rate of 15 per hour (i.e., the variance is zero)" indicates that the system is able to process planes at a consistent rate of 15 per hour, with no variation in this rate. This means that there should be no planes waiting in queue for clearance to land, as they can all be processed at the constant rate of 15 per hour. Therefore, the expected number of airplanes circling the airport and waiting in queue for clearance to land is zero.

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A mode is defined as the value that has a higher frequency in a given set of values. It is the value that appears the most number of times.

In statistics, the value that consistently appears in a particular collection is referred to as the mode. The mode or modal value in a data collection is sometimes referred to as the value or number that occurs most frequently in the data set. In addition, to mean and median, it is one of the three measures of central tendency.

For example, the mode of the set {3, 7, 8, 8, 9}, is 8. Therefore, for a finite number of observations, we can easily find the mode. A set of values may have one mode or more than one mode or no mode at all.

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Rational functions can have 3 types of asymptotes:

1. Horizontal Asymptotes

2. Vertical Asymptotes

3. Oblique Asymptotes

The ratio of two polynomial functions with a non-zero denominator is known as a rational function.

1. Horizontal Asymptotes:

A graph's horizontal asymptote is a horizontal line with the equation y = b, and when the inputs get closer to 0 or 1, the graph moves toward the line. A graph's slant asymptote is a sloped line, denoted by the equation y = mx + b, where the graph slopes toward the line when the inputs approach 0 or -1.

2. Vertical Asymptotes:

Vertical asymptotes are vertical lines that represent the zeros in a rational function's numerator. Asymptotes can also occur in other situations, such as logarithms, although you'll almost probably run into them when discussing rationals for the first time.

3. Oblique Asymptotes:

These slanted asymptotes, known as oblique asymptotes, demonstrate how a function rises or falls without bound. Slant asymptotes are another name for oblique asymptotes. The slant asymptote won't be a line because the degree of the numerator is 3 and the degree of the denominator is 1, respectively.

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Angle 1 is 35°, angle 2 is 65°, angle 3 is 29°, angle 4 is 115°, angle 5 is 65°, angle 6 is 36° and finally angle 7 is 144° considering the shape triangle whenever possible.

A triangle in geometry is a three-sided polygon with three edges and three vertices. The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic. This characteristic is known as the triangle's angle sum property.

Considering the triangle that is containing angle 3 along with the angles 90° and 61° and as we know the sum of angles in a triangle = 180° so the angle 3 is 29°

As we know that opposite angles are equal we can say that angle 4 is 115°

Now considering the triangle that contain angle 3 which is 29° and angle 4 which is 115°  we can say that angle 6 is 36° by applying sum of angles in a triangle.

Considering the triangle that consists of angles 1 , 6 and 80°+ angle 3 we can say that angle 1 is 35°

now considering the trinaglewith angles 1, 2 and 80° we can say that angle 2 is  65°

As we know that opposite angles are equal we can that angle 5 is same as angle 2 which is 65°.

Finally as angle 6 + angle 7 sum = 180° as they are on the straight line

we can say that angle 7 is 144°

Angle 1 is 35°, angle 2 is 65°, angle 3 is 29°, angle 4 is 115°, angle 5 is 65°, angle 6 is 36° and finally angle 7 is 144° considering the shape triangle whenever possible.

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The required length of line segment JK would be 16 units.

The midpoint of a line segment is the point that divides the line segment into two equal parts. So, to find the length of the line segment JK, we can first find the coordinates of point J, which is the other endpoint of the line segment.

Let the coordinate of the point J would be (x, y)

Since the midpoint of the line segment is (2, -3), and point K is located at (-6, -3), we can use the midpoint formula to find the coordinates of point J:

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

4 = x - 6 ; -6 = y -3

x = 10 ; y = -3

So the coordinate of the point J :(10, -3)

Now that we have the coordinates of both endpoints of the line segment, we can use the distance formula to find the length of the line segment:

length = √((10 - (-6))² + (-3 - (-3))²)

= √((10 + 6)² + (-3 + 3)²)

= √(16² + 0)

= √(256)

= 16

Therefore, the length of line segment JK is 16 units.

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The one way of determining the factors of x³ + 4x² + 5x + 20 by grouping is (b) x²(x + 4) + 5(x + 4) .

The Grouping in a polynomial is done by the taking the GCF( greatest common factors) from the different terms .

the expression is given as : x³ + 4x² + 5x + 20 ;

in order to determine the factors by grouping ,

we first take x² common from the first two terms and 5 common from the last two terms .

we get ;

⇒ x²(x + 4) + 5(x + 4)

Therefore , the one way of determining the factors is x²(x + 4) + 5(x + 4)  .

The given question is incomplete , the complete question is

Which shows one way to determine the factors of x³ + 4x² + 5x + 20 by grouping ?

(a) x(x² + 4) + 5(x² + 4)

(b) x²(x + 4) + 5(x + 4)

(c) x²(x + 5) + 4(x + 5)

(d) x(x² + 5) + 4x(x² + 5)

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