Given the following sets, find the set (AUB)' n C.
U = {1, 2, 3,...,8}
A = {1, 2, 3, 5}
B = {1, 2, 6}
C= {1, 3, 4, 5, 6}

Therefore, the percent concentration of the first solution is 25%.

Let's call the percent concentration of the first solution x.

When we mix the two solutions, we end up with a total of 3 + 2 = 5 gallons of the new solution.

We can start by writing an equation based on the amount of pure alcohol in each solution:

[tex]3x + 2(0.65) = 5(0.41)[/tex]

The left side of the equation represents the total amount of pure alcohol in the mixture. The first term, 3x, represents the amount of pure alcohol in the 3 gallons of the first solution. The second term, 2(0.65), represents the amount of pure alcohol in the 2 gallons of the second solution.

The right side of the equation represents the total amount of pure alcohol in the final 5-gallon mixture, which is the product of the 41% concentration and the 5 gallons of the mixture.

Simplifying the equation, we get:

[tex]3x + 1.3 = 2.05[/tex]

Subtracting 1.3 from both sides, we get:

[tex]3x = 0.75[/tex]

Dividing both sides by 3, we get:

[tex]x = 0.25[/tex]

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The pre-image ABCD was translated into the picture A'B'C'D' by moving 7 units to the right. answer is option (a).

A translation transformation is one in which the pre-image's size and orientation are maintained while the position of the points on the pre-image changes.

The polygon ABCD's vertices are located at these coordinates (1, 5), (3, 1), (7, 1), (5, 5)

The polygon's vertices are located at these coordinates: (8, 5), (10, 1), (14, 1), (12, 5)

where the preimage's and image's vertices are;

A(1, 5), B(3, 1), C(7, 1), D(5, 5), and A'(8, 5), B'(10, 1), C'(14, 1), D'(12, 5),

the x and y values disagree, which shows;

A' - A = (8 - 1, 5 - 5) = (7, 0)

B' - B = (10 - 3, 1 - 1) = (7, 0)

C' - C = (14 - 7, 1 - 1) = (7, 0)

D' - D = (12 - 5, 5 - 5) = (7, 0)

In view of this, the transformation employed to produce the image A'B'C'D' from the pre-image, ABCD, is a translation, 7 units to the right.

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Answer:

7 units to the right

Step-by-step explanation:

By assuming that the farmer has goat and cows in the ratio 3:4, the  number of cows in the farm will be 32 cows.

To find out how many cows are in the farm, we need to know the total number of animals in the farm. Assuming the ratio of goats to cows is 3:4, we can write this as: [tex]3x : 4x[/tex]

Where 3x represents the number of goats, and 4x represents the number of cows. If we know that there are 24 goats, we can set up an equation to solve for x:

3x = 24

Dividing both sides by 3, we get:

x = 8

Now that we know the value of x, we can find the number of cows:

= 4x

= 4(8)

= 32

Therefore, there are 32 cows in the farm.

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Larry Mitchell invested $ [tex]7000[/tex] at  [tex]3[/tex]% annual simple interest and $[tex]13000[/tex]  at [tex]6[/tex]% annual simple interest.

Let's denote the amount Larry Mitchell invested at 3% annual simple interest as "x" (in dollars) and the amount he invested at 6% annual simple interest as  [tex]"20,000 - x"[/tex] (since he invested the rest of the advance amount).

The formula for simple interest is:

Simple Interest (SI) = Principal (P) * Rate (R) * Time (T)

Given that the total yearly interest from both accounts was $990, we can set up the following equation:

3% of x + 6% of  [tex](20,000 - x) = 990[/tex]

Converting the percentages to decimals, we get:

[tex]0.03x + 0.06(20,000 - x) = 990[/tex]

Now, we can solve for x by simplifying the equation and isolating x on one side:

[tex]0.03x + 1200 - 0.06x = 990[/tex]

[tex]-0.03x = 990 - 1200[/tex]

[tex]-0.03x = -210[/tex]

Dividing both sides by -0.03, we get:

x = (-210)/(-0.03)

[tex]x = 7000[/tex]

So, Larry Mitchell invested $7000 at 3% annual simple interest.

Substituting the value of x back into the equation, we can find the amount he invested at 6% annual simple interest:

[tex]20,000 - x = 20,000 - 7000 = 13000[/tex]

Therefore,  Larry Mitchell invested $ [tex]7000[/tex] at  [tex]3[/tex]% annual simple interest and $[tex]13000[/tex]  at [tex]6[/tex]% annual simple interest.

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Answer:

B

Step-by-step explanation:

THE TWO SMALLER SIDES = THE LARGER SIDE HENCE ITS A TRIANGLE

The value of the logarithm expression is Logₐ(13.3)  is 2.598.

Logarithm is the exponent or power to which a base must be raised to yield a given number.

To find logₐ(13.5), we use the following techniques below

Given:

But,

Applying the law of logarithm,

Substitute the values above into equation 1

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Answer:

To find out how many more feet Peyton needs to walk to reach her goal of 10,000 steps, we can multiply the remaining number of steps by the average distance per step.

Total steps Peyton needs to reach her goal = 10,000 - 7,338 = 2,662 steps

Average distance per step = 2.5 feet

Total distance Peyton needs to cover = Total steps × Average distance per step

= 2,662 × 2.5

= 6,655 feet

Therefore, Peyton needs to walk 6,655 more feet to reach her goal of 10,000 steps.

Answer:

peyton needs to walk a total of 6655feets more

Answer:

Multiplying the first equation by 2, we get:

6x - 4y = 12

Adding the second equation, we get:

6x - 4y + x + 4y = 2 + 12

Simplifying, we get:

7x = 14

This is the same equation given in the problem statement. So any system of equations that has this equation and the second equation will also have the solution (2, 0). For example:

3x - 2y = 6

7x = 14

By using the compass to measure a distance from the original line, and then transferring that distance to another point on the line, a parallel line can be drawn.

What is the parallel lines?

Parallel lines are two lines in a plane that never intersect.

1. Orientation of Lines:

Parallel lines are lines that never intersect and remain equidistant from each other at all points.

When constructing parallel lines, the lines are drawn in the same direction and maintain the same distance between them throughout their entire length. They do not meet or cross each other.

On the other hand, perpendicular lines are lines that intersect at a right angle (90 degrees). When constructing perpendicular lines, the lines are drawn so that they intersect at a right angle, forming four right angles at the point of intersection.

2. Tools/Methods Used:

Constructing parallel lines and constructing perpendicular lines may require different tools or methods.

To construct parallel lines, one common method is to use a straightedge and a compass. A straightedge is used to draw a straight line, and a compass is used to measure and transfer distances to create additional parallel lines.

Therefore, By using the compass to measure a distance from the original line, and then transferring that distance to another point on the line, a parallel line can be drawn.

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Answer:

To approximate the location of the square root of 14 on a number line, we can first find the two integers that √14 is between. We know that:

3^2 = 9 < 14 < 16 = 4^2

So √14 is between 3 and 4. We can divide the distance between 3 and 4 into equal parts and estimate the location of √14 based on where it falls in that interval.

Dividing the interval into 10 equal parts, we get:

3.0 - 3.1 - 3.2 - 3.3 - 3.4 - 3.5 - 3.6 - 3.7 - 3.8 - 3.9 - 4.0

Since √14 is closer to 3 than to 4, we can estimate its location as being closer to 3.4 than to 3.5. Therefore, a good approximation for the location of √14 on the number line is 3.7.

The fraction of the panel left after cutting the hole is 11/12.

The correct answer choice is option C

Fraction left = (area of panel) - (area of hole) / (area of panel

Area of panel = 3 feet × 2 feet

= 6 square feet

Area of hole = 1 foot × ½ foot

= ½ square foot

So,

Fraction left = (area of panel) - (area of hole) / (area of panel

= (6) - (½) / (6)

= (5½) / (6)

= 11/2 ÷ 6

multiply by the reciprocal of 6

= 11/2 × 1/6

= 11/12

Ultimately, the fraction left is 11/12

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The data from the distribution shows a symmetric distribution.

The data from a distribution can be described as symmetric when the values of the data are evenly distributed around its center point. This mans that if the data is folded along its center point and the two halves overlap perfectly, then the distribution is said to be symmetric.

In the histogram, we see an example of symmetric data because the center value that has the frequency of 10 ahs even distribution on both sides.

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Answer:

hope this will help you...

The percent of those taking this exam had scores between 58.9 and 69.7 is 34.1%

To find the number of standard deviations 58.9 and 69.7 are above and below the mean, find the difference between these two numbers and the mean, then divide by the standard deviation 5.4:

z1 = (58.9 - 64.3) / 5.4 = -0.996

z2 = (69.7 - 64.3) / 5.4 = 1.004

Since the absolute values of the z-scores are almost equal, we can approximate the area between them as half of the total area between -1 and 1 standard deviations.

Therefore, the approximate percentage of those taking the exam with scores between 58.9 and 69.7 is:

68% / 2 = 34%

Therefore, the correct option is D 34.1%.

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Answer:

The correct function is

[tex]f(b) = {b}^{2} - 4[/tex]

Answer:

24

Step-by-step explanation:

Answer:

A. $24

Step-by-step explanation:

Given:

Solve for average tip:

Answer:

Thus, the waiter's average tip per table is $24.

The answer is A.

The area to the right of  [tex]1.42[/tex] in the standard normal distribution is approximately [tex]0.0793[/tex]  .

The region where [tex]z > 1.42[/tex]  in the standard normal distribution corresponds to the area under the curve to the right of [tex]1.42[/tex] on the z-axis.

To find this area, we can use a standard normal distribution table or a calculator with a cumulative distribution function (CDF) for the standard normal distribution.

Using a calculator with a CDF for the standard normal distribution, we can input 1.42 and calculate the area to the left of 1.42. Then, we subtract this area from 1 to get the area to the right of 1.42. Here's the calculation:

[tex]P(Z > 1.42) = 1 - P(Z < 1.42)[/tex]

Using a standard normal distribution table or a calculator, we find that  [tex]P(Z < 1.42)[/tex] is approximately 0.9207. Subtracting this value from 1, we get:

[tex]P(Z > 1.42) \approx 1 - 0.9207 \approx 0.0793[/tex]

Therefore, the area to the right of  [tex]1.42[/tex] in the standard normal distribution is approximately   [tex]0.0793[/tex].

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The equation a² + b² = c² represents the Pythagorean theorem.

This is a theorem that  states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).

The Pythagorean theorem is used to find the length of one of the sides of a right-angled triangle when the lengths of the other two sides are known.

To solve the problem, you need to have at least two side lengths given. Then, you can use the equation to find the length of the third side. For example:

If you know the lengths of sides a and b and need to find the length of the hypotenuse (c):

Plug in the known values for a and b into the equation and solve for c.

Example: If a = 3 and b = 4, then 3² + 4² = c², which gives 9 + 16 = c², so c² = 25, and c = sqrt(25) = 5.

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the area of the trapezoid is 10√3 km² (approximately 17.3 km²).To find the area of a trapezoid, we use the formula A = (1/2) * (b₁ + b₂) * h

what is trapezoid ?

A trapezoid is a quadrilateral with at least one pair of parallel sides. The parallel sides are called the bases of the trapezoid, and the other two sides are called the legs. The height (or altitude) of a trapezoid is the perpendicular distance between the two bases. The formula for the area of a trapezoid

In the given question,

To find the area of a trapezoid, we use the formula:

A = (1/2) * (b₁ + b₂) * h

where A is the area, b₁ and b₂ are the lengths of the parallel sides of the trapezoid, and h is the height (or perpendicular distance between the parallel sides).

In this case, we are not given the height, but we can still find the area if we make some assumptions. Let's assume that the trapezoid is isosceles, which means that the two non-parallel sides are equal in length. Then we can draw an altitude from one of the vertices to the opposite base, which will bisect the base and create two right triangles.

Using the Pythagorean theorem, we can find the length of the altitude:

a² + (b₁ - b₂)² = (2a)²

Simplifying and solving for a, we get:

a² + (b₁- b₂)² = 4a²

3a² = (b₁ - b₂)²

a = (1/√3) * |b₁ - b₂|

Since we know that the sum of the non-parallel sides is 10 km, we can write:

b₁ + b₂ = 10

Let's assume that b1 is the longer base, so we can write:

b₁ = 8 km

b₂ = 10 - b₁ = 2 km

Substituting these values into the formula for the altitude, we get:

a = (1/√3) * |8 - 2| = (1/√3) * 6 = 2√3 km

Now we can use the formula for the area of a trapezoid to find the area:

A = (1/2) * (b1 + b2) * h

A = (1/2) * (8 + 2) * 2√3

A = 10√3 km²

Therefore, the area of the trapezoid is 10√3 km² (approximately 17.3 km²).

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Answer:

Answer as an improper fraction: 299/32

Answer as a mixed number: 9 11/32

Step-by-step explanation:

Change 1 5/8 and 5 3/4 to improper fractions. See image. You get

13/8 × 23/4

Multiply fractions. You do this straight across: top×top and bottom×bottom

This gives you 299/32.

Simplify if possible. This is not possible to simplify. Sometimes you need to change it back to a mixed number. See image.

299/32 is 9 11/32.

see image.

Also some calculators have a D》F and F》D button. That changes decimals to fractions and fractions to decimals.

A is riskier than B in terms of pure risk. Stock B may have a lower beta than Stock A and so be less hazardous in the context of a portfolio if it has a lower correlation to the market than Stock A.

The profit or loss an investor can anticipate realising from an investment is known as the expected return. Calculating an expected return involves multiplying possible outcomes by their likelihood before adding the results. The expected return is computed by summing the results of multiplying all possible outcomes by the likelihood that each one will occur (as illustrated below).

Expeced return=Sum(probability*return)

Standard Deviation=[tex]\sqrt{sum(probability*(return-expected\ return)^2}[/tex]

Coefficient of Variation=Standard Deviation/Expected Return

1. Expected Returns:

Stock B=0.1*(-38%)+0.2*0%+0.5*21%+0.1*26%+0.1*36%=12.900%

2. Standard Deviation:

Stock A=[tex]\sqrt{(0.1*(-11\%-11.3\%)^2+0.2*(5\%-11.3\% +0.5*(13\%-11.3\%)^2+)^2 0.1*(18\%-11.3\%)^2} \\+0.1*(31\%-11.3\%)^2)[/tex]

= 10.120%

3. Coefficient of Variation:

Stock B=19.892%/12.9%=1.5420

4. Stock B may have a lower beta than Stock A and so be less hazardous in the context of a portfolio if it has a lower correlation to the market

than Stock A.

5. Sharpe Ratio:

Stock A=(11.3%-3.5%)/10.120%=0.7708

Stock B=(12.9%-3.5%)/19.892%=0.4726

6. A is riskier than B in terms of pure risk. Stock B may have a lower beta than Stock A and so be less hazardous in the context of a portfolio

if it has a lower correlation to the market than Stock A.

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yes is answer   for all option   .we can check it by rules of rounding off numbers .

what is rounding ?

Rounding is the process of approximating a number to a nearby value that is easier to work with or more appropriate for a given context. When rounding, we take a number with many decimal places or significant figures and adjust it to a simpler or more convenient value with fewer decimal places or significant figures.

In the given question,

Yes, each number is rounded correctly to the nearest hundred thousand based on the rules of rounding.

To round to the nearest hundred thousand, we look at the digit in the hundred thousand place and the digit to its right (i.e., in the ten thousand place).

If the digit in the ten thousand place is 5 or greater, we round up the digit in the hundred thousand place by adding 1.

If the digit in the ten thousand place is less than 5, we leave the digit in the hundred thousand place as it is.

Using these rules, we can see that:

350000 rounded to the nearest hundred thousand is 400000 because the digit in the ten thousand place is 5, so we round up the digit in the hundred thousand place.

555555 rounded to the nearest hundred thousand is 560000 because the digit in the ten thousand place is 5, so we round up the digit in the hundred thousand place.

137998 rounded to the nearest hundred thousand is 200000 because the digit in the ten thousand place is 7, so we round up the digit in the hundred thousand place.

792314 rounded to the nearest hundred thousand is 800000 because the digit in the ten thousand place is 3, so we leave the digit in the hundred thousand place as it is.

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Answer:

100

Step-by-step explanation:

12x + 2y ← substitute x = 7 and y = 8 into the expression

= 12(7) + 2(8)

= 84 + 16

= 100

Answer:

14.4

Step-by-step explanation:

percentage for corn =30

total no. of acres of the land=48

=30 × 48

100

=14.4

(1) The value of X is equal to 4  (2) The mean age is 3. (3) The probability of randomly selecting  a child under the age of 9  is approximately 0.83.  

The formula for calculating the average of given numbers is equal to the sum of all values ​​divided by the total number of values. There are three main types of averages: mean, median, and mode. All of these techniques work slightly differently and often give slightly different typical values.

(i). Given that there are a total of 42 children on the birthday, finding the value of x:

2x + 3x (4x-1) + x + (x-2) + (x-3) = 42

11x - 6 = 42

11x = 48

x = 4

Therefore, the value of x is equal to 4.

(ii). To find the average age, we need to calculate the sum of all the ages and divide by the total number of children:

Average age = (7 x 2 + 8 x 3 + 9 x (4-1) +10 x 4 +11 x (4-2) 12 x (4-3)) / 42

 = (14 + 24 + 27 + 40 + 22 +12) / 42

 = 139/42

 = 3.31

Rounded to the nearest whole number, the average age is 3.  

(iii). The probability of randomly selecting  a child under 9 is obtained by adding  the number of children aged 7, 8 or 9 (because we want children under 9) and  dividing by the total number of children:

Number of children under 9 years  = 2x + 3x + (4x-1)

Number of children under 9 years  = 9x - 1

Number of children under 9  = 9(4)–1

Number of children under 9 years  = 35

Probability of choosing a child under 9  = number of children under 9  / total number of children

Probability of choosing a child under 9 = 35/42

The probability of choosing a child under 9 years old is ≈ 0.83

Thus, the probability of randomly selecting  a child under the age of 9  is approximately 0.83.

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According to the given information, the function has no cusp.

What is a function?

A function is a relation between a set of inputs and a set of possible outputs, with the property that each input is related to exactly one output.

The given piecewise function is:

c(x) = 39, when x ≤ 6

c(x) = 39 + 5(x - 6), when x > 6

A cusp is a point on the graph where the function changes direction very abruptly, like a sharp turn. This happens when the derivative of the function is not defined at that point.

The derivative of the function is:

c'(x) = 0, when x ≤ 6

c'(x) = 5, when x > 6

Since the derivative is defined and continuous at x = 6, there is no cusp at that point. Therefore, the function has no cusp.

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An equation of this line in slope-intercept form is equal to y = 2x + 7.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (7 + 1)/(0 + 4)

Slope (m) = 8/4

Slope (m) = 2

At data point (0, 7) and a slope of 2, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 7 = 2(x - 0)  

y - 7 = 2x

y = 2x + 7

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