How to turn a number into a fraction

The domain and range of the rational function in this problem are given as follows:

The domain of a function is the set that contains all the input values that can be assumed by the function.

The function in this problem is a fraction, meaning that the denominator must assume values different of zero, hence the value outside the domain is:

x - 1 = 0 -> x = 1.

The range of a function is the set that contains all the output values that can be assumed by the function.

The function in this problem can be simplified by x - 1, hence at x = 1 it would assume a value of y = 7. However, for the range, we suppose that the function cannot be simplified, hence it is given by all real values except y = 7.

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The correct answer is 5 white triangles coincide.

3 red, 5 blue, and 8 white triangles are present on each side. The 2 pairs of red triangles are also utilized, leaving 1 red triangle, 5 blue triangles, and 8 white triangles on each half.

Additionally, there are 3 pairs of blue triangles that are used up, leaving 1 red triangle, 2 blue triangles, and 8 white triangles on each half. Additionally, we offer 2 red-white pairs. Since there is only 1 on each side, it is evident that we cannot utilize 2 red triangles on one side.

As a result, we must use 1 red and 1 white triangle per side, leaving 2 blue and 7 white triangles on each. The remaining blue triangles must be coupled with white triangles in order to create 4 blue-white pairings, one for each of the remaining blue triangles.

Blue triangles cannot be matched with other blue triangles because it would result in more than 3 worth of blue pairs. This leaves 5 white triangles per side, which must be coupled with each other to create $5 white-white pairings.

Therefore, The correct answer is 5 white triangles coincide.

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Answer:

FIRST ONE IS 7

Step-by-step explanation:

SECOUND ONE IS 12THIRD ONME IS 2

So, the variance of the number of tornadoes in a year given that at least one tornado occurs is 3.

The Poisson distribution is a discrete probability distribution that describes the number of events that occur in a fixed interval of time or space, given the average number of events per interval.

For a Poisson distribution with mean λ, the variance is equal to λ.

Given that at least one tornado occurs in a year, the mean number of tornadoes is 3. Therefore, the variance is also equal to 3.

So, the variance of the number of tornadoes in a year given that at least one tornado occurs is 3.

It's worth noting that this result is based on the assumption that the number of tornadoes follows a Poisson distribution with mean 3, which may not always be the case in real-world scenarios. The actual number of tornadoes in a given year can be influenced by various factors such as climate, weather patterns, and geography.

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if 40 makes him 30 mins late and 60 makes him 30 mins early then it only would make since that in between both 40 and 60 is 50 and that would make him go on time

mr. earl e. bird leaves his house for work at exactly 8:00 a.m. every morning

when he averages 40 miles per hour, he arrives at his workplace thirty minutes late.

when he averages 60 miles per hour, he arrives thirty minutes early.

at what average speed, in miles per hour, should mr. bird drive to arrive at his workplace precisely on time?

if 40 makes him 30 mins late and 60 makes him 30 mins early then it only would make since that in between both 40 and 60 is 50 and that would make him go on time

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There is no association between the state and the amount of median debt for graduates.

To find the association between states and the median debt, you need to find the percentage of the graduates in the state that either have a median debt of less than $ 9, 000 or at least $ 9, 000.

The percentage of California University graduates with median debt less than $ 9, 000 is:

= 130 / 575

= 23 %

The percentage of New York University graduates with median debt less than $ 9, 000 is:

= 72 / 343

= 21 %

The percentage of California University graduates with median debt at least $ 9, 000 is:

= 445 / 575

= 77 %

The percentage of New York University graduates with median debt at least $ 9, 000 is:

= 271 / 343

= 79 %

The percentages are similar to each other which shows that being from either state does not mean that there will be an association between the state and the median debt.

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Considering the expression of a line, the slope intercept form is y= -x+2.

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

where

This is known as the slope-intercept form. This form is one of the most common forms used to represent the equation of a line and can be used to find the equation of a line when given the slope of the straight line and the y-intercept (the y-coordinate of the point where the line intersects the y-axis).

In this case, the line is x+y=2. Expressed in the form y = mx + b, you get:

y= 2 -x     or     y= -x +2

Finally,  x+y=2 in slope intercept form is y= -x+2.

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By calculating the given equations with points none of the equation represents equation of this graphed line.

What is the equation of the line?

The equation of a straight line is y=mx+c y = m x + c m is the gradient and c is the height at which the line crosses the y -axis, also known as the y-intercept.

We have given the,

y = 2x+2

y=-2x-2

y=6x+6

y=-6x-6

And, the graph.

From the line in the graph we can take the cordinate points which represents the equation of line.

point (1, 2)

By putting this point we can decide the given equation of line:

y=2(1)+2 = 4

y=-2(1)-2 = 0

y=6(1)+6 =12

y=-6(1) - 6 =-12

Hence, by calculating the given equations with points none of the equation represents equation of this graphed line.

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Answer:

the answer is 46% which is option d.

Step-by-step explanation:

To calculate Jim's DTI (debt-to-income) ratio, we need to divide his total monthly debt payments by his gross monthly income.

His total monthly debt payments are:

$2,500 (mortgage payment)

$250 (lease payment)

$500 (credit card payments)

$425 (speed boat payment)

Total Monthly Debt Payments = $2,500 + $250 + $500 + $425 = $3,675

His gross monthly income is his annual salary of $96,000 divided by 12 months which is $8,000

DTI = Total Monthly Debt Payments / Gross Monthly Income = $3,675 / $8,000 = 0.46 or 46%.

The value of Jim's DTI (debt-to-income) ratio is 40%.

Debt to income ratio is usually calculated as a percentage of the gross monthly debt payments divided by the gross monthly income.

Given that,

Annual salary = $96,000

Monthly income = 96000/12 = $8000

Total income per month = $8000 + $1,200 = $9,200

Monthly expenses = $2,500 + $250 + $500 +  $425

                               = $3675

DTI = 3675 / 9,200 = 0.399 = 39.9% ≈ 40%

Hence the DTI of Jim is 40%.

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Part A:Coefficients in  are 85 and 15.

X represents theatrical shifts, Y represents dog-walking gigs.

Part B: Two phrases, the first of which indicates the amount of money he makes from his work in the theater and the second, from dog-walking. A sum or a deduct sign is used to demarcate each phrase.

Part A: The information we don't know is contained in an expression's variable. In this instance, we don't know how many dog-walking jobs he has in addition to his theater duties. We have 2 variables—x and y—because of this. The variable is multiplied by the coefficient, which is a number. Since there are two variables in this situation, there are two coefficients: 85 and 15.

Part B: A sum or a subtract sign is used to denote the separation of each term in an equation. The terms are the numbers and variables that occur before and after the sum sign because there is only one sum in this situation. 85x and 15y are involved. He initially discloses how much money he makes for each shift at his total annual salary at the theater is determined by multiplying his hourly wage by the number of shifts he works. The second one is the sum of the money he makes from each dog-walking work multiplied by the number of jobs he completes; this is the total amount he makes from the dog-walking jobs.

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High mean with small standard deviation data outcome of the number of customers in line would best support opening another cash register.

What is standard deviation?

The standard deviation is a statistic that expresses how much variation or dispersion there is in a set of values. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the set mean.

We have to find from the given options which data outcome of the number of customers in line would best support opening another cash register.

The number of customer in the line having high mean with small standard deviation means deviation in data small and data cluster around mean. High mean I'm play high number of customer in line. This help to opening another cash register.

Hence, High mean with small standard deviation data outcome of the number of customers in line would best support opening another cash register.

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The value of the given function f(x) and g(x) is [tex]f(x) - g(x) = 4x^2 +4x+5[/tex].

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions are everywhere and are crucial for constructing physical relationships.

The given functions are:

[tex]f(x) = 5x^2 - 3 \\\\g(x) = x^2 -4x-8[/tex]

(f - g)(x) is equivalent to the following:

(f - g)(x) = f(x) - g(x)

[tex]f(x) - g(x) = 5x^2 - 3 - x^2 +4x+8\\\\f(x) - g(x) = 4x^2 +4x+5[/tex]

Hence, the value of [tex]f(x) - g(x) = 4x^2 +4x+5[/tex].

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The requried, if the p-value is greater than the chosen significance level, we fail to reject the null hypothesis, meaning we don't have enough evidence to conclude that the mean height is greater than 42.5 inches.

Null Hypothesis (H0): The mean height of five-year-old children in the city is not greater than 42.5 inches.

Alternative Hypothesis (Ha): The mean height of five-year-old children in the city is greater than 42.5 inches.

We will conduct a one-sample t-test since we have the sample mean and standard deviation.

Let's calculate the t-statistic and find the corresponding p-value.

The formula for the t-statistic is:

[tex]t=\dfrac{x-\mu}{s/\sqrt n}[/tex]

Where:

x  is the sample mean (44.1 inches),

μ is the population mean under the null hypothesis (42.5 inches),

s is the sample standard deviation (3.5 inches),

n is the sample size (40).

Let's calculate the t-statistic:

[tex]t=\dfrac{44.1-42.5}{3.5/\sqrt n}\\t=2.89[/tex]

Now, we need to locate the p-value associated with this t-statistic. The p-value is the probability of observing a t-statistic as extreme as the one calculated (or even more extreme) under the assumption that the null hypothesis is true.

The p-value can be looked up using a t-distribution table or calculated with statistical software. In this matter, since the t-statistic is quite large, the p-value will be very small.

Suppose the p-value is less than the significance level (α) chosen for the test (commonly 0.05). In that case, we reject the null hypothesis in favor of the alternative hypothesis. This means there is convincing evidence that the mean height of five-year-old children in this city is greater than 42.5 inches.

Conversely, if the p-value is greater than the chosen significance level, we fail to reject the null hypothesis, meaning we don't have enough evidence to conclude that the mean height is greater than 42.5 inches.

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A function is considered a one-to-one function, also called an injective function, if it assigns a unique output value to each input value. In other words, a function is one-to-one if no two different input values have the same output value.

A function f(x) is one-to-one if and only if for any two distinct inputs x1 and x2, it holds that f(x1) ≠ f(x2).

One way to determine if a function is one-to-one is to use the horizontal line test:

if any horizontal line intersects the graph of the function at most once, then the function is one-to-one.

A one-to-one function has an inverse function. The inverse function, f^-1(x), is also a function, it assigns to each output value of f(x), an input value such that f^-1(f(x)) = x.

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The width of the rectangle is given as Area/length = 32xy³/l units.

A quadrilateral with four right angles is a rectangle. It may alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal. A square is a rectangle with four equally long sides.

Rectangles have the following basic characteristics:

The area of the rectangle is 32xy³

The length of the rectangle is l units

So, the width of the rectangle is given as Area/length = 32xy³/l units.

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In the question, diagram is not given, so that a rough diagram is given for reference.

Answer:

  33 mm

Step-by-step explanation:

Given a triangle with sides 48 mm and 55 mm, and angles x and w such that cos(x) = 4/5 and cos(w) = 1/2, you want the length of the third side (r) opposite angle x.

For sides a, b, c and angle C opposite side c, the Law of Cosines gives the relation ...

  c² = a² +b² -2ab·cos(C)

Filling in the given values, we have ...

  r² = 48² +55² -2·48·55·(4/5) = 1105

  r = √1105 ≈ 33 . . . . millimeters

The length r is about 33 mm.

__

Additional comment

Side r is irrational, so the triangle cannot have exactly the measures shown. Using other measures as true, the value of cos(w) is about 0.4994, not 1/2.

Taking cos(w) as true, side r is found using the law of cosines as 33.43717. Taking cos(x) as true, side r is found using the law of cosines as 32.24154. Taking the angle measures and 48 mm to be true, side r is found using the law of sines as 33.25538. All round to 33 mm.

The attachment shows the solution using cos(w)=1/2, or w=60°.

The price of the carpet per square meter is $32.13. It will cost $1,556.86 to carpet an area of 1475 square feet.

1. To find the price of the carpet per square meter, first convert $28.99 per square yard to meters.

1 yard = 0.9144 meters

$28.99 per yard x (1 meter/ 0.9144 meters) = $32.13 per square meter

2. To find the cost of carpeting an area of 1475 square feet, first convert 1475 square feet to square yards.

1 square foot = 0.11111 square yards

1475 square feet x (1 square yard/ 0.11111 square yards) = 13,333.33 square yards

3. Multiply the cost per square yard by the number of square yards needed to carpet the area.

$28.99 per square yard x 13,333.33 square yards = $1,556.86

The complete question is:

a carpet sells for $28.99 a square yard. what is the price of the carpet per square meter? how much will it cost to carpet an area of 1475 square feet? 1 yard is equal to 0.9144 meters

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Answer:

- 8

Step-by-step explanation:

the absolute value function always gives a positive value, that is

| - a | = | a | = a

then

| - 13 | - | 21 |

= | 13 | - | 21 |

= 13 - 21

= - 8

Hope it helps.

If you have any query, feel free to ask.

The longest portion is 18 inches longer than the shortest portion.

What is algebraic equation ?

An algebraic equation is a mathematical statement that shows that two expressions are equal. It typically consists of a combination of numbers, variables and mathematical operations such as addition, subtraction, multiplication, and division.

We know that the ratio of the portions is 1:2:4, so we can use this ratio to find the length of each portion by dividing 42 inches by the sum of the ratio, 1+2+4 = 7.

So each portion is 42 inches / 7 = 6 inches.

The longest portion is 4 times the length of the shortest portion, which is 6 inches. So the longest portion is 4 * 6 inches = 24 inches.

24 - 6 = 18 inches ,

Therefore, the longest portion is 18 inches longer than the shortest portion.

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Answer:

Step-by-step explanation:

a. Possible values for m and n to achieve a total number of 46 legs are: m = 23 and n = 11; m = 22 and n = 12; m = 21 and n = 13; m = 20 and n = 14; m = 19 and n = 15; m = 18 and n = 16.

b. If the number of 2 legged animals is 2 more than the number of 4 legged animals, there must be 24 2 legged animals and 22 4 legged animals in the exhibit (24 + 22 = 46).

c. The increase in the number of legs in the exhibit might be due to the addition of a new animal to the exhibit. If the new animal has 4 legs, the total number of legs in the exhibit will increase by 4.

Answer:

a)  Possible values of m and n:

b)  9 two-legged animals and 7 four-legged animals.

c)  Either 1 four-legged animal or 2 two-legged animals have been added to the exhibit.

Step-by-step explanation:

Given expression:

2m + 4n = 46

where:

Calculate the greatest number of four-legged animals by dividing the total number of animals by 4:

[tex]\implies 46 \div 4 = 11.5[/tex]

Therefore, the greatest number of four-legged animals is 11.

When there are no four-legged animals, n = 0.

Substitute n = 0 into the given equation:

[tex]\begin{aligned}\implies 2m+4(0)&=46\\2m&=46\\ m&=23\end{aligned}[/tex]

Therefore, there are 23 two-legged animals when there are no four-legged animals.

Each time the number of four-legged animals increases by 1, the number of two-legged animals decreases by 2.

Therefore, the possible values for m and n so that the total number of legs is 46 are:

If the number of two-legged animals is 2 more than the number of four-legged animals then:

Therefore, there are 9 two-legged animals and 7 four-legged animals.

If the number of legs in the exhibit increases by 4, then either:

The value that represents the smiley face is given as follows:

402.

The first three equations compose a system of equations, and then the three solutions to this system are used to obtain the value of the smiley face.

The variables and shapes are attributed as follows:

From the third equation, the square has the value obtained as follows:

8x - 6x + 3x = 60

5x = 60

x = 60/5

x = 12.

From the second equation, the value of the star is obtained as follows:

12(12) + 5y = 234

5y = 90

y = 90/5

y = 18.

From the first equation, the value of the triangle is given as follows:

12 + 3z + 18 = 57

3z = 27

z = 9.

Considering these values, the value of the smiley face is given as follows:

Smiley = 18(9 + 18 - 12) + 12(18/9 + 9)

Smiley = 18(15) + 12(2 + 9)

Smiley = 18 x 15 + 12 x 11

Smiley = 402.

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Answer: 32

Step-By-Step Explanation: 1/8 times 32 = 4

I multiplied 8 by 4 to get 32 then checked my answer by multiplying 1/8 and 32.

The expression that represents the magazine sale of  Graham's is 2a - 6.

Profit & Loss:

A profit and loss (P&L) statement refers to a financial statement that summarizes the revenues, costs, and expenses incurred during a specified period, usually a quarter or fiscal year. These records provide information about a company’s ability or inability to generate profit by increasing revenue, reducing costs, or both. P&L statements are often presented on a cash or accrual basis. Company managers and investors use P&L statements to analyze the financial health of a company.

The sentence "Graham sold 6 magazines less than double what Adrianne sold" can be represented by the expression 2a - 6, where a is the number of magazines Adrianne sold.

So, the expression that represents Graham's sales is 2a - 6.

Graham's magazine sales are represented by the expression 2a - 6.

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On solving the equation " [tex]2y + 3 = 13[/tex] " for y , we get the value of y is 5  .

What is an Equation ?

An Equation is defined as the mathematical statement which shows that the two mathematical expressions are equal .

the equation is given as : [tex]2y + 3 = 13[/tex] ;

In the given equation , we have to solve for y ;

Subtracting 3 from both sides ,

we get ;

⇒ [tex]2y+ 3 - 3 = 13 -3[/tex] ;

⇒ [tex]2y = 10[/tex] ;

dividing both sides by 2 ,

we get ;

⇒ [tex]y = \frac{10}{2}[/tex] ;

On simplifying ,

we get y = 5 .

Therefore , After solving for y , the value of y = 5 .

The given question is incomplete , the complete question is

How do you solve the problem 2y + 3 = 13 for y ?

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On solving the provided question, we can say that the variable x while retaining the inequality [tex]- 2 \geq 4x = > -1/2 \geq x[/tex]

An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal sign (). Different inequalities are used to contrast values, no matter how little or large. Many simple inequalities may be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.

Inequality is 2x - 6 ≥ 6(x - 2) + 8

the variable x while retaining the inequality

[tex]2x - 6 \geq 6x - 12 + 8\\-6 + 12 - 8 \geq 6x - 2x\\- 2 \geq 4x\\-1/2 ≥ x[/tex]

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The line which passes through the points (2,-1) and (4,-1) has the slope-intercept equation as y = -1.

What is the slope-intercept form?

The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation.

The line passes through point (x1,y1) = (2,-1) and (x2,y2) = (4,-1)

The formula to find slope is -

m = (y2-y1)/(x2-x1)

m = (-1+1)/(4-2)

m = 0/2

m = 0

Now use the slope and point (2,-1) to find the y-intercept.

y = mx + b

-1 = 0(2) + b

-1 = 0 + b

b = -1

Write the equation in slope-intercept form as -

y = mx + b

y = 0x + (-1)

y = -1

Therefore, the equation is obtained as y = -1.

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At 12 seconds, the cart will be moving at 24 cm per second.Rebecca is using a fan cart and measuring the rate of the cart at different times.

Rebecca is using a fan cart and measuring the rate of the cart at different times. At 10 seconds, the cart has a speed of 20 cm per second. To calculate the speed at 12 seconds, you can use the formula rate x time = distance. The rate is the speed of the cart at 10 seconds, which is 20 cm per second. The time is the difference between 10 seconds and 12 seconds, which is 2 seconds. Thus, the equation becomes 20 cm/s x 2s = 40 cm. Therefore, the speed at 12 seconds is 24 cm per second.

At 12 seconds, the cart will be moving at 24 cm per second.

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1. The  triangles, which are similar to ΔAED  are ΔAFE, ΔEFD, ΔECD, ΔABE

2.  The length of segment FA is, 32/3 units

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. Triangle resemblance is shown here by the symbol "≈"

Given that,

A rectangle ABCD having triangles in it,

1.  ΔAED is a right angle triangle,

all the triangle which are right angle triangle will be similar to  ΔAED

So,  ΔAFE, ΔEFD, ΔECD, ΔABE are similar triangles

2. Now, consider ΔEFD

EF = 8 unit

ED = 10 unit

∠CEB = 53°

∠CEF = 90°

∠DEF = 37°

∠AED = 90°

∠AEF = 53°

tan53° = FA/FE

4/3 = FA/8

FA = 32/3

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