Brine is a solution of salt and water. If a tub contains 50 gallons of a 5% solution of brine, how much water must evaporate to change it to an 8% solution? 81.25 gallons 62.50 gallons 18.75 gallons

a1=1/2d

r=1/2

sup it needs twenty character apparently

The [tex]a_{1} =\frac{d}{2}[/tex]  and [tex]r=\frac{1 }{2 }[/tex] are for the infinite Geometric sequence.

Geometric sequence a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

i.e. [tex]a+ar+ar^2+ar^3+......[/tex]

Here, [tex]a=[/tex] First term and [tex]r=[/tex] common ratio

Next term formula, [tex]a_{n} =a_{1}\ *\ r^{n-1}[/tex]

We have,

[tex]d=[/tex] distance to her destination,

Now,

According to the question;

Zeno has to travel half that distance i.e. [tex]\frac{d}{2}[/tex],

Then half of half of distance i.e. [tex]\frac{d}{4}[/tex],

Then half of [tex]\frac{d}{4}[/tex] distance i.e. [tex]\frac{d}{8}[/tex]  and so on.

So,

Here, we have,

[tex]\frac{d}{2},\frac{d}{4},\frac{d}{8}, .........[/tex]

So,

We have Geometric Sequence,

Here,

[tex]a_{1} =\frac{d}{2}[/tex] and

Now,

[tex]r=[/tex] common ratio,

[tex]r=\frac{a_{2} }{a_{1} }[/tex]

[tex]r=\frac{\frac{d}{4} }{\frac{d}{2} }[/tex]

We get,

[tex]r=\frac{1 }{2 }[/tex]

So, These are [tex]a_{1} =\frac{d}{2}[/tex]  and [tex]r=\frac{1 }{2 }[/tex] of the Geometric sequence.

Hence, we can say that he [tex]a_{1} =\frac{d}{2}[/tex]  and [tex]r=\frac{1 }{2 }[/tex] are for the infinite Geometric sequence.

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Answer:

Matrix addition is commutative.

Step-by-step explanation:

We know that if there are two matrices X and Y of same order(i.e. same number of the rows and columns) then the addition between the two matrix is commutative i.e.

X+Y=Y+X.

While in case of multiplication of two matrices commutativity may or may not hold true.

Answer:

This year 1,023 books were sold.

Step-by-step explanation:

Last year the number of yearbooks were sold = 465

This year sales are increased 120% over last years sales.

this year sale = 465 + (120% of 465)

                      = 465 + ([tex]\frac{120}{100}[/tex] × 465)

                     = 465 + (1.2 × 465)

                     = 465 + 558

                     = 1,023 books

This year 1,023 books were sold.

Each point on the coordinate plane has an address, called the coordinates.

The coordinate plane is a two-dimension surface formed by two number lines. One number line is horizontal and is called the x-axis. The other number line is vertical number line and is called the y-axis.

The coordinate plane is a two-dimension surface formed by two number lines.

A coordinate plane, also known as a rectangular coordinate plane grid, is a two-dimensional plane formed by the intersection of a vertical line called the Y-axis and a horizontal line called the X-axis.

One number line is horizontal and is called the x-axis.

The other number line is vertical number line and is called the y-axis.

The two axes meet at a point called the origin.

Hence, Each point on the coordinate plane has an address, called the coordinates.

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The function y = f(-x) has the points (-3,-6).

When we substitute -x into a function f(x) to get f(-x), we are essentially reflecting the graph of f(x) across the y-axis. This is because replacing x with -x negates the x-values, effectively flipping the function horizontally.

Given that (3, 6) is a point on the graph of y = f(x), if we substitute -3 for x in f(-x), we get:

[tex]\[ f(-(-3)) = f(3) \][/tex]

So, the corresponding point on the graph of [tex]\(y = f(-x)\)[/tex] is [tex]\((3, 6)\)[/tex] since the function values stay the same when we reflect across the y-axis. Therefore, the point [tex](-3, -6)\)[/tex] is on the graph of [tex]\(y = f(-x)\)[/tex].

This problem can be directly solved by using a conversion factor. Simple research will tell us that 1 gallon contains about 3.78 Liter. Therefore the volume in Liter is:

volume = 75 gallons * (3.78 Liter / gallon)

volume = 283.5 Liters

The type of reasoning demonstrated in the scenario is deductive reasoning.

Deductive reasoning starts with a general premise or statement and applies it to a specific case to reach a logical conclusion. In this case, the premise is that white chickens lay white eggs and colored chickens lay brown eggs. Therefore, when encountering a white chicken, the conclusion is drawn that it will lay white eggs.

To understand deductive reasoning, let's break it down:

Premise:

White chickens lay white eggs.

Colored chickens lay brown eggs.

Observation:

Encounter a white chicken.

Conclusion:

Therefore, the white chicken will lay white eggs.

This conclusion is based on the general premise about the egg-laying behavior of white and colored chickens. Deductive reasoning allows us to draw specific conclusions from general principles, assuming the premises are true.

To find the maximum and minimum values of the function f(x, y) = x + y + 4 on the circular disk x^2 + y^2 ≤ 1, evaluate the function at the boundary of the disk.

To find the maximum and minimum values of the function f(x, y) = x + y + 4 on the circular disk x^2 + y^2 ≤ 1, we can use the method of level curves and gradients.

In this case, since the function f(x, y) = x + y + 4 is linear, it does not have any critical points. Therefore, the maximum and minimum values of the function on the circular disk x^2 + y^2 ≤ 1 are obtained by evaluating the function at the boundary of the disk.

When x^2 + y^2 = 1, the function value is largest at the point (x, y) = (-1, 0), giving a maximum value of -1 + 0 + 4 = 3. The function value is smallest at the point (x, y) = (1, 0), giving a minimum value of 1 + 0 + 4 = 5.

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Answer:

The first pan has to be divided into 4 equal parts.

The second pan has to be divided into 3 equal parts.

Step-by-step explanation:

The first step to solve this problem is finding the least common multiple of 6 and 8.

The multiples of 6 are {0,6,12,18,24,30,36,42,...}

The multiples of 8 are {0,8,16,24,32,...}

The least common multiple of 6 and 8 is 24.

So both kinds of pasta have to be baked so after the second step they have 24 equal parts.

So:

First pan:

The first pan was sliced into 6 equal parts.

24/6 = 4.

So each of the 6 parts have to be divided into 4 equal parts.

After the second step, they have 6*4 = 24 equal parts.

Second pan:

The second pan was sliced into 8 equal parts

24/8 = 3

So each of the 8 parts have to be divided into 3 equal parts.

After the second step, they have 8*3 = 24 equal parts.

Answer:

A. 78 + 10 + 23 + 52

Step-by-step explanation:

We can solve the problem by using the commutative property: "in an addition, changing the order of the operands does not change the result.

The original addition is 52 + 23 + 10 + 78. We see that option A is exactly the same addition, only the order of the numbers has been changed:

78 + 10 + 23 + 52

Therefore, the two additions are equivalent.

Answer: 3, 11

Step-by-step explanation:

As u see in this screen shot there is wrongs and rights

The original price of the ticket is $42.

Let the original cost of the ticket be represented by x

Based on the information given, the equation to solve the question will be:

x + (7% × x) = $44.94

x + (7/100 × x) = $44.94

x + (0.07 × x) = $44.94

x + 0.07x = $44.94

1.07x = $44.94

Divide both side by 1.07

1.07x/1.07 = $44.94/1.07

x = $42

Therefore, the original price of the ticket is $42.

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The original price of the ticket was $42.

To find the original price of the ticket, we need to subtract the extra fees from the total amount Charlotte paid.

Let x be the original price of the ticket.

The extra fees would be 7% of x, which is 0.07x. Since the total paid is $44.94, we can set up the equation:

x + 0.07x = 44.94

Combining like terms on the left side gives us 1.07x = 44.94.

Next, we divide both sides by 1.07 to isolate x:

x = 44.94 / 1.07 = $42

Therefore, the original price of the ticket was $42.

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1. Add Deposits

2. Bank Errors

3. Outstanding Checks

4. Check Register Reconciliation

5. Interest Earned

6. Check Register Errors

7. Compare Both Statements

Final answer:

The probability that the sample mean of SAT scores will be larger than 1224 is 0.008. This is calculated using the z-score, which in this case is 2.4 after determining the standard error of the sampling distribution.

Explanation:

To find the probability that the sample mean will be larger than 1224, we will use the concept of the sampling distribution of the sample mean. Given the population mean (μ) is 1200 and standard deviation (σ) is 60, and that the sample size (n) is 36, the standard deviation of the sampling distribution, known as the standard error (SE), is

σ/√n = 60/√36 = 10.

We calculate the z-score for the sample mean of 1224 using the formula

z = (X - μ)/SE = (1224 - 1200)/10 = 2.4

A z-score of 2.4 indicates that the sample mean is 2.4 standard errors above the population mean.

To find the probability associated with this z-score, we refer to the normal distribution table or use a calculator. The probability to the left of z = 2.4 is 0.9918. Therefore, the probability that the sample mean is greater than 1224 is

1 - 0.9918 = 0.0082

which can be rounded to three decimal places as 0.008.