Express each of the following as a rational number: 7/12 - 5/6 + 1/8 - 5/8

The least number 456xy that is divisible by 20 and where x and y are different digits is 45652.

For a number to be divisible by 20, it must be divisible by both 4 and 5. Therefore, the least number 456xy that is divisible by 20 must end in a 0 and be divisible by 4.

We have:

4 + 5 + 6 + x + 2 = 17 + x

For the sum to be divisible by 4, x must be either 1 or 5.

If we choose x = 1, we get the number 45621, which is not divisible by 4.

If we choose x = 5, we get the number 45652, which is divisible by 4 and ends in 0.

Therefore, the least number 456xy that is divisible by 20 and where x and y are different digits is 45652.

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Answer:

8.4

Step-by-step explanation:

C^2-B^2=A^2

12.3^2=151.29

9^2=81

151.29-81=70.29

square root of 70.29

is 8.38

Rounded to the nearest tenth is

8.4 or B

The statement to be proved is that if (an)[infinity]n=1 is a bounded sequence and (bn)[infinity]n=1 converges to 0, then (anbn)[infinity]n=1 converges to 0 as well.

To prove this statement, we can use the squeeze theorem. Let M be a bound for the sequence (an)[infinity]n=1, i.e., |an| <= M for all n. Since (bn)[infinity]n=1 converges to 0, for any ε > 0, there exists an integer N such that |bn| < ε/M for all n ≥ N.

Now, for any n ≥ N, we have

|anbn| = |an||bn| ≤ M|bn| < ε,

where we used the fact that |an| ≤ M. This shows that (anbn)[infinity]n=1 converges to 0 as well, since the absolute value of each term is bounded by ε for n ≥ N.

In other words, we have shown that for any ε > 0, there exists an integer N such that |anbn - 0| < ε for all n ≥ N. This is the definition of convergence to 0, and so we have proven that (anbn)[infinity]n=1 converges to 0.

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Answer:

The additive inverse of A is -A. So, the additive inverse of A = [p q] is -A = [-p -q].

Here's how we can find the additive inverse of a matrix:

Find the additive inverse of each element in the matrix.

Replace each element in the matrix with its additive inverse.

For example, the additive inverse of p is -p. So, the additive inverse of the first element in A is -p.

The additive inverse of q is -q. So, the additive inverse of the second element in A is -q.

Plugging in these values, we get the following:

Additive inverse of A = [-p -q]

Step-by-step explanation:

The quadratic function is defined as follows:

p(x) = 2(x - 3)² - 1.

The quadratic function of vertex(h,k) is given by the rule presented as follows:

y = a(x - h)² + k

In which:

The vertex is the turning point of the quadratic function, where it changes from decreasing to increasing or vice-versa, hence it's coordinates are given as follows:

(3,-1).

Then:

p(x) = a(x - 3)² - 1.

When x = 0, p(x) = 17, hence the leading coefficient a is obtained as follows:

17 = 9a - 1

9a = 18

a = 2.

Hence the equation is:

p(x) = 2(x - 3)² - 1.

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Answer:

D. 42

Step-by-step explanation:

y=4x+10

substitute x=8

y=4(8)+10

y=32+10=42

Answer:

The answer is 42 cyclists

Step-by-step explanation:

y=4x+10

where,x=Temperature

y=cyclists

y=4x+10;when x=10

Y=4×8+10

y=32+10

y=42

Answer:

I believe it would be 3/10 simplified, 30/100 not simplified

Step-by-step explanation:

because it is 30%, 30% in a fraction form is 3/10, or 30/100

The value of the interquartile range (IQR) of their scores is,

Interquartile range = 25

Since, WE know that;

A box plot is the 5 -number summary of the set of data.

And, 5 -number summary is name as, the first quartile, median, third quartile, minimum, and maximum.

We have to given that;

The box pot shows the points for the Houston Rockets scored last season.

Now, From given box plot,

First Interquartile = 65

Third Interquartile = 90

Hence, The interquartile range (IQR) of their scores is, difference between Third Interquartile and first Interquartile.

So, We can formulate;

Interquartile range = Third Interquartile - First Interquartile

Substitute the given values, we get;

Interquartile range = 90 - 65

Interquartile range= 25

Therefore, We get;

The interquartile range (IQR) of their scores is,

Interquartile range= 25

Which is difference between Third Interquartile and first Interquartile.

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The statement "NOT(MyAge > YourAge)" is true if MyAge is not greater than YourAge, which is not the case in this scenario because 30 is less than 40.

Therefore, option (a) is false.

The statement "MyAge >= YourAge" is also false because MyAge (30) is less than YourAge (40). Therefore, option (b) is also false.

Option (c) states that none of the above statements are true, which is also false because statement (a) is false.

Option (d) is irrelevant because it compares the values of MyAge and YourAge with string values, which is not the correct way to compare integers. Therefore, option (d) is also false.

The correct answer is (c) None of the above are a true statement.

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The required equation function j which is the transformation of [tex]f(x)= x^{1/2}[/tex] is  [tex]j(x)= (x+2)^{1/2}[/tex] .

As we can see in the graph the functions j and f are similar but the graph of j is 2 units left of f. So, function f(x) has a domain of real number greater than equal to zero, while as the function j is 2 units left of f then its equation is given as  [tex]j(x)= (x+2)^{1/2}[/tex]  where the domain of j is all real numbers greater then or equal to -2.

Thus, the equation of function j is the transformation of [tex]f(x)= x^{1/2}[/tex] is  [tex]j(x)= (x+2)^{1/2}[/tex] .

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In the question the graph is missing, a graph has been added on behalf of the incomplete question.

The point B is 27 meters east of point A.

Since we want to find the distance east, we need to consider the horizontal component of the displacement between the two points.

Using trigonometry, we can determine the eastward distance using the cosine function:

Eastward distance = 54 m x cos(061°)

Eastward distance ≈ 54 m x cos(61°)

                                ≈ 54 m * 0.500

                                ≈ 27 m

Therefore, point B is 27 meters east of point A.

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The solution of the equations is (6, 1).

An equation contains one or more terms with variables connected by an equal sign.

Example:

2x + 4y = 9 is an equation.

2x = 8 is an equation.

We have,

Using the substitution method.

We can start by setting the two expressions for Y equal to each other since they both represent the same value of Y:

-Y + 7 = (3/2)X - 3

Next, we can isolate Y on one side of the equation by subtracting 7 from both sides:

-Y = (3/2)X - 10

Then, we can multiply both sides of the equation by -1 to isolate Y and make it positive:

Y = -(3/2)X + 10

Now we have expressions for Y in terms of X for both equations. We can set them equal to each other to find the value of X that satisfies both equations:

-X + 7 = -(3/2)X + 10

To solve for X, we can start by adding (3/2)X to both sides:

(1/2)X + 7 = 10

Next, we can subtract 7 from both sides:

(1/2)X = 3

Finally, we can multiply both sides by 2 to solve for X:

X = 6

Now that we have found the value of X, we can substitute it back into one of the original equations to find the corresponding value of Y.

Let's use the first equation:

Y = -X + 7

Y = -6 + 7

Y = 1

Therefore,

The solution of the equations is (6, 1).

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It will cost approximately $1,715.20 to carpet a room with 360 square feet of floor area, assuming the carpet costs $42.88 per square yard.

To calculate the cost of carpeting a room with a floor area of 360 square feet, we need to convert the area into square yards and then multiply it by the cost per square yard.

There are 9 square feet in a square yard (1 square yard = 3 feet x 3 feet = 9 square feet). Therefore, the room's floor area in square yards is:

360 square feet / 9 = 40 square yards

Next, we multiply the area (40 square yards) by the cost per square yard ($42.88) to find the total cost of carpeting the room:

Total cost = 40 square yards * $42.88 per square yard

Calculating this gives us the final result:

Total cost = $1,715.20

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The dimension of the new picture frame is around 51.49 cm by 61.49 cm in size.

Given that,

The measure of rectangular  picture = 20 cm x 30 cm

And the resulting enclosed area = 1064 cm²

Let the length of each side = x

Therefore,

The new rectangular frame will have dimensions = 20 cm + x, 30 cm + x

The new rectangular frame's surface area is:

= (20 + x) x (30 + x).

Since area is given,

So that we can create an equation:  1064 = (20 cm + x) x (30 cm + x)

Increasing the brackets results in: 600 + 50x + x² = 1064

Organizing and making it simpler: x² + 50x - 464 = 0.

By using quadratic formula,

x = (-50 ± 174.96) / 2

Neglecting the undesirable outcome,

x = 62.98 / 2 x = 31.49

Consequently, each side length has increased by around 31.49 cm.

Use this value to determine the new rectangular frame's dimensions:

Length is equal to 20 + 31.49 = 51.49 cm.

Width is equal to 30 + 31.49 = 61.49 cm.

Consequently, the new picture frame is around 51.49 cm by 61.49 cm in size.

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Approximately 32.14% of the renters do not keep a pet.

We know that there are 28 units in the apartment complex. Out of these, 19 renters keep a pet. To calculate the number of renters who do not keep a pet, we subtract the number of renters with pets (19) from the total number of renters (28):

Number of renters without pets = Total number of renters - Number of renters with pets

Number of renters without pets = 28 - 19

Number of renters without pets = 9

Now that we have the number of renters without pets (9), we can calculate the percentage of renters who do not keep a pet. To do this, we divide the number of renters without pets by the total number of renters and multiply by 100:

Percentage of renters without pets = (Number of renters without pets / Total number of renters) × 100

Percentage of renters without pets = (9 / 28) × 100

Percentage of renters without pets ≈ 32.14%

Therefore, approximately 32.14% of the renters in the apartment complex do not keep a pet.

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Answer:

 can be written as  without exponent.Given:To find:Write the given expression without exponent.Solution:Formula to be used:Step 1:Write the expanded form of given expression.Step 2:simplifyorThus, can be written as 125×y×y×y without exponent.Learn more:1) Let us simplify some more questions using the exponent rules. (i) (ii) ... brainly.in/question/196047402) find ( 46656)power of -1/6 brainly.in/question/4383230

Answer: 5y³ can be written without using exponents as 5y multiplied by itself three times:

5y × 5y × 5y

Alternatively, we can also write it as:

5 × y × y × y

One possible transformation is a reflection in the x-axis followed by a dilation centered at the origin with a scale factor of 3.

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.

Before the dilation, the figure was reflected from the first quadrant to the second quadrant, which is a lateral reflection, hence the figure was reflected over the x-axis.

The height of the blue triangle is of 1 unit, while the height of the larger triangle is of 3 units, hence the scale factor is given as follows:

k = 3/1

k = 3.

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Answer:

8 meters

Step-by-step explanation:

4(16)=64

They have the same area so the area of the square is also 64.

x^2=64

x=8

Answer: £102.60

Step-by-step explanation:

79165-78937=228

228x45=10260

10260/100=102.60

Mathis's rate of return on his investment of $1,000 in a mutual fund that sold for $1,250, including taxes, inflation, and administrative costs of $8 was 24.2%.

The rate of return represents the percentage of the net gain an investment generates.

The rate of return is determined using the quotient of the division operation between the return and the initial investment.

The return or net return is the difference between the final value and the initial value after taking into account taxes, inflation, and other administrative costs.

The initial investment = $1,000

The final sales value = $1,250

Taxes, inflation, and other costs = $8

Net sales proceeds = $1,242 ($1,250 - $8)

Returns = $242 ($1,242 - $1,000)

Rate of return = 24.2% ($242 ÷ $1,000 x 100)

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To find the point of intersection between the two lines represented by the given equations, we can solve the system of equations simultaneously.

The given equations are:

1) X + Y = 2

2) Y = (1/2)X + 5

We can solve this system by substituting the value of Y from the second equation into the first equation. Let's proceed with the substitution method:

Substitute Y = (1/2)X + 5 into the first equation:

X + (1/2)X + 5 = 2

Combine like terms:

(3/2)X + 5 = 2

Subtract 5 from both sides:

(3/2)X = -3

Multiply both sides by 2/3 to isolate X:

X = -2

Now, substitute the value of X back into the second equation to find Y:

Y = (1/2)(-2) + 5

Y = -1 + 5

Y = 4

Therefore, the lines represented by the given equations intersect at the point (-2, 4).

The coordinates of the point on the graph are (0, -7).

We have,

The concept being used here is the Cartesian coordinate system, which is a system for representing points in a two-dimensional space.

In this system, each point is described by an ordered pair (x, y), where x represents the position along the horizontal x-axis, and y represents the position along the vertical y-axis.

The coordinates are always in an ordered pair.

i.e

(x, y)

Where x is the value of the x-axis and y is the value of the y-axis.

We see that,

The point lies in (0, -7)

Thus,

The coordinates of the point on the graph are (0, -7).

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when k = 4, the function x + k/x will have a relative maximum at x = -2.

To find the value of k that will make x+k/x have a relative maximum at x=-2, we can use the first derivative test.

First, we find the derivative of x+k/x with respect to x:

f'(x) = 1 - k/x^2

Next, we set x = -2 and solve for k to make f'(-2) = 0:

f'(-2) = 1 - k/(-2)^2 = 1 - k/4

1 - k/4 = 0

k = 4

what is derivative?

A derivative is a mathematical concept that represents the rate at which a function changes over time or space. It is the slope of a tangent line to a curve at a particular point.

In other words, the derivative of a function f(x) at a point x=a is defined as the limit of the difference quotient as h approaches zero:

f'(a) = lim[h→0] [f(a+h) - f(a)]/h

The derivative gives us information about how quickly the function is changing at a specific point.

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Answer:

1111 in binary is 10001010111. Unlike the decimal number system where we use the digits 0 to 9 to represent a number, in a binary system, we use only 2 digits that are 0 and 1 (bits).

The domain to plot the growth function is 0 ≤ x < 7

Given that

f(d) = 11(1.01)ᵇ

When the radius is approximately 1179 mm

We have

11(1.01)ᵇ = 11.79

Divide

(1.01)ᵇ = 1.072

Take the logarithm

d = log(1.072)/log(1.01)

Evaluate

d = 6.99

So, the reasonable domain is 0 ≤ x < 7

Here, we have

f(d) = 11(1.01)ᵇ

The y-intercept is 11

This means tha the initial radius of the algae is 11 mm

For the average rate, we have

f(7) = 11(1.01)⁷ = 11.79

f(2) = 11(1.01)² = 11.22

So, we have

Rate  = (11.22 - 11.79)/(2 - 7)

Evaluate

Rate  = 0.114

So, the average rate of change from day 2 to day 7 is 0.114 mm per day

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Answer:

Let's start by assigning variables to the unknown ages:Trisha's age = TAge of Trisha's first brother = T + 3Age of Trisha's second brother = T - 3Age of Trisha's third brother = T/3Age of Trisha's father = 3TWe know that the sum of all their ages is 95:T + (T + 3) + (T - 3) + T/3 + 3T = 95Combining like terms, we can simplify this equation:8T + T/3 = 92Multiplying both sides by 3 to get rid of the fraction:24T + T = 276Simplifying again:25T = 276Dividing both sides by 25:T = 11.04So Trisha is 11.04 years old.We can check our answer by plugging it back into the original equation and verifying that the sum of all their ages is indeed 95:T + (T + 3) + (T - 3) + T/3 + 3T = 95

11.04 + (11.04 + 3) + (11.04 - 3) + 11.04/3 + 3(11.04) = 95

95 = 95The sum of their ages is 95, so our answer is correct. Therefore, Trisha is 11.04 years old.

Step-by-step explanation:

The probability of selecting a checkered fabric sample is determined by dividing the number of checkered fabric samples by the total number of fabric samples. In this case, Lacey has 10 fabric samples and 4 of them are checkered. Therefore, the probability of selecting a checkered fabric sample is 4/10 or 0.4.

In other words, there is a 40% chance that Lacey will choose a checkered fabric sample for her bedroom. It is important to note that probability is always expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

In conclusion, the probability of selecting a checkered fabric sample from Lacey's options is 0.4 or 40%.
Hi! The probability of Lacey selecting a checkered fabric sample can be calculated using the formula: probability = number of successful outcomes / total number of outcomes. In this case, there are 4 checkered fabric samples and a total of 10 fabric samples. So, the probability of selecting a checkered fabric is:

Probability = 4 (checkered samples) / 10 (total samples) = 2/5 or 0.4.

Therefore, the probability that a randomly selected fabric sample will be checkered is 0.4 or 40%.

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The method used to determine the probability that a football team will win the next game is subjective.

The subjective method involves relying on personal judgment, experience, or expert opinion to estimate the probability of an event. In this case, the sports analyst has assessed various factors such as team performance, player injuries, historical data, and other relevant information to form their subjective opinion that the team's probability of winning is 0.37.

This method is based on the analyst's subjective assessment and may vary from one analyst to another. It does not involve any formal calculations or statistical techniques. The probability estimate is derived from the individual's knowledge, expertise, and perception of the situation.

It's important to note that subjective probabilities can be influenced by biases or personal opinions, and they may not always accurately reflect the true probability of an event. However, they can provide valuable insights and serve as a useful starting point for decision-making or further analysis.

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