(01.03 MC)
What is the domain of the rational function f(x)=
x²+x-20 -?
X-4x²-9x+36

The average speed of the ball which travelled 24 meters in 8 seconds is 3m/s.

Speed is simply referred to as distance traveled per unit time.

Mathematically, Speed = Distance ÷ time.

Given the data in the question;

To determine the average speed of the ball, plug the given values into the above equation and simplify.

Speed = Distance / time

Speed = 24 meters / 8 seconds

Speed = 3m/s

Therefore, the speed is 3 meters per seconds.

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Using the arithmetic operations the balance amount for 28/03/20 and incoming amount for 29/03/20 is obtained as £ 747 and £ 210 respectively.

What is arithmetic operation?

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

The statement of bank account is given.

On 25/03/20 the balance amount left in bank was £ 1200.

On 28/03/20 the outgoing amount from the bank was £ 453.

To find the balance amount for 28/03/20, use the arithmetic operation of subtraction -

Balance amount = Previous Balance - Outgoing Amount

Substitute the values in the equation -

Balance amount = 1200 - 453

Balance amount = 747

Therefore, the balance amount for 28/03/20 was £ 747.

Now, On 29/03/20 the balance amount left in bank was £ 957.

To find the incoming amount for 29/03/20, use the arithmetic operation of subtraction -

Incoming Amount = New Balance - Previous Balance

Incoming Amount = 957 - 747

Incoming Amount = 210

Therefore, the incoming amount for 29/03/20 was £ 210.

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The expected reward amount is -10$.

The product of the likelihood of each occurrence and the related reward results in the anticipated reward amount, which is equal to the expected reward value.

According to the question

We must multiply the odds of rolling an even number by the payout for rolling an even number, the odds of rolling an odd number by the payout for rolling an odd number, and then sum the results to determine the expected payoff.

P(odd) = P(1) + P(3) + P(5) = 0.1 + 0.1 + 0.1 = 0.3

P(Even) = P(2) + P(4) + P(6) = 0.3 + 0.2 + 0.2

The expected reward is calculated as follows:

(p(even) * 100 + (p(odd) * 200)) = (0.7 * 100 + (0.3 * 200)) = 70 - 60 = -10

As a result, the predicted reward is -10$.

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The image has been dragged to show where cost is proportional to area and attached

Equation y = kx can be used to define proportional functions, which are linear functions that include the origin.

While all proportional functions are linear, not all linear functions are proportional functions.

From the table the equation s calculated to be y = kx

where k = 1.25

for x = 400, y = 1.25 * 400 = 500

for x = 500, y = 1.25 * 500 = 750 and so on

this is a proportional function

For asphalt sealant the labor fee added made the function not to be a proportional function

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the measure of ∠ABE is 47°.

What is congruent of the triangle?

The shapes maintain their equality regardless of how they are turned, flipped, or rotated before being cut out and stacked. We'll see that they'll be placed entirely on top of one another and will superimpose one another. Due to their identical radius and ability to be positioned directly on top of one another, the following circles are considered to be congruent.

Any two figures can be perfectly positioned over one another to demonstrate their congruence. The relationship between two figures that are said to be congruent is described using the word "congruence."

ΔABE and ΔCEB both are congrurent trinalge.

∠ABE =∠ CEB

The ∠ CEB+ ∠CBE = 90

∠ CEB = 90-43 = 47

As ∠ABE =∠ CEB  =47°

So the measure of ∠ABE is 47°.

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The two column proof to show that ABCD is a parallelogram is as shown below

A two-column proof is defined as a geometric proof that consists of a list of statements, and the reasons that we know those statements are true.

Statement 1; BD bisects AC

Reason 1; Given

Statement 2; ∠BAC ≅ ∠DCA

Reason 2; Given

Statement 3; AB║ CD

Reason 3; Properties of parallelogram

Statement 4; ∠BEA ≅ ∠CED

Reason 4; Alternate Interior angles

Statement 5: AE ≅ EC

Reason 5: Diagonals of a parallelogram bisect each other

Statement 6: ΔABE ≅ ΔCDE

Reason 6: SAS Congruency postulate

Statement 7: BA ≅ DC

Reason 7: Properties of parallelogram

Statement 8: ABCD is a parallelogram

Reason 8: Corresponding parts of congruent triangles are congruent

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For the table of values gives, the equation of line is obtained as y = 1/3x.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The coordinate points for cups of flour, x and loaves of bread y is given in the table.

The slope-intercept form of an equation is - y = mx + b

To find the slope m use the formula -

(y2 - y1)/(x2 - x1)

Substituting the values in the equation -

(3 - 2)/(9 - 6)

1/3

So, the slope point is obtained as m = 1/3.

The equation becomes - y =1/3 x + b

To find the value of b substitute the values of x and y in the equation -

2 = 1/3(6) + b

2 = 2 + b

b = 2 - 2

b = 0

So, the value for b is 0.

Now, the equation becomes -

y = 1/3x + 0

y = 1/3x

The graph is plotted for the equation.

Therefore, the equation is y = 1/3x.

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If Neely has $1.73 in coins and he gives his friend 1 quarter and 3 nickel , then the value of coins he has left is $1.65   .

the value of number of coins Neely has is = $1.73  ;

he gives his friend "1 quarter" , and the value of 1 quarter in dollar is = $0.25

the amount left with Neely is = $1.73 - $0.25 = $1.48 ;

next he gave his friend "3 nickels" , and value of 3 nickels in dollars in $0.15 ;

So , the amount left with Neely is - $1.48 - $0.15 = $1.65  .

Therefore , the Neely is left with $1.65 value of coins .

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The statement that answers the linear model possibility is NO

From the question, we have the following parameters that can be used in our computation:

Initial = 100

Year 1 = 110

year 2 = 121

year 3 = 133.10

The savings account balance is increasing at an inconsistently increasing rate, which is not linear.

The savings account starts with $100, and increases by $10 in the first year, by $11 in the second year, and by $12.10 in the third year.

This is an example of exponential growth, which cannot be modeled by a single linear equation.

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Answer:

4x-7

thats your answer

Step-by-step explanation:

:))))

The two different possible values for height h and radius r for the cones are height = 3 inches when radius = 3 inches and height = 4.5 inches when radius = 2 inches.

The volume of a cone is given by the formula [tex]V = (1/3)\pi r^2 h[/tex].

We can use this formula to find the values of h and r that will give us a cone with a volume of 9π cubic inches.

We have a volume of the cone -

(1/3)π[tex]r^2[/tex]h = 9π

solving for h, we get,

h = (3/[tex]r^2[/tex]) * 9

Now we have a formula for h in terms of r. We can substitute different values for r and see what values of h we get. Let's consider two possibilities:

                   h = (3/[tex]3^2[/tex]) * 9 = 3 inches

                   h = (3/[tex]2^2[/tex]) * 9 = 4.5 inches

So, one possible cone has a height of 3 inches and a radius of 3 inches, and another possible cone has a height of 4.5 inches and a radius of 2 inches.

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The height of the cone is about 15.9 meters.

The hypotenuse of the right triangle, which also contains the cone height as one of its legs, is formed by the radius (18 m) and slant height. You may find out the height (h) using the Pythagorean theorem.

The Pythagorean Theorem states that the squares on the hypotenuse (the side across from the right angle) of a right triangle, or, in standard algebraic notation, a2 + b2, are equal to the squares on the legs.

So,

 18² + h² = 24²

  h = √(576 -324) = √252

  h ≈ 15.9 . . . . . meters

The height of the cone is about 15.9 meters.

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Answer:294,25$

Step-by-step explanation:

you make 7% of 100 multiply by $275 and the price that gives you you make more $275 and that gives you your results

The vector joining the ship to the rock is t= 5i+5 j

A vector is a quantity or phenomenon that has two independent properties: magnitude and direction, a quantity that has both magnitude and direction but not position.

The direction is 0.9505 radians east of north.

The position vector of the ship: r= 1i+0j

The position vector of the ship: s= 4i+5j

The vector joining the ship to the rock is: t=r+s

t=(1 i + 0 j) + (4i + 5 j)

t=5i+5j

Θ=π/2-arctan(5/7)

Θ=0.9505 radians

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the values of m in the equation m^2 = 36 , is m= ±6.

A square root of a number is a value that, when multiplied by itself, gives the number. In mathematics, a square root of a number x is a number y such that y² = x; in other words, a number y whose square is x.

here, we  have,

given that,

the equation m^2 = 36.

taking root on both side, we get,

m= ±6.

Hence, the values of m in the equation m^2 = 36 , is m= ±6.

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They will vote for in the upcoming School actions maybe they have to choose example should to best represent the entire population is they have to ask to every tenth student in the cafeteria.

Every Nth name from the list of target population members is chosen in systematic sampling. For instance, every tenth member on the list will be included in the sample. Thus, the 10th, 20th, 30th, and so forth will be chosen to make up the sample group.

According to this, they must consult a student in the tenth grade because he is the most knowledgeable about school and has the most experience of anybody.

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Answer:

x = -1

Step-by-step explanation:

Since a triangle's angles all add up to 180 based on this formula: 180(n-2) (n being the # of sides of the shape you're solving for, and the total being the interior), we can set up this equation:

46 + (x+62) + 73 = 180

Now, we can solve for x:

x = 180-73-62-46

x = -1

The perimeter of triangle XYZ is 38.95 inches

Consider the following figure.

The area of rectangle WXYZ is 115. 5 in.²

From given figure we can observe that PQ = 4 in.

So, XW = YZ = 2 × PQ

XW = YZ = 2 × 4

XW = YZ = 8 inches

This means, the width of rectangle WXYZ is  8 inches

We know that the area of the reactngle is given by the formula,

A = length × width

here, A = 115.5 in.² and width = 8  in.

115.5 = length × 8

length = 115.5 / 8

length = 14.44 in.

So, XY = WZ =  14.44 in.

For right triangle XYZ using Pythagoras theorem,

XZ² = XY² + YZ²

XZ² = 14.44² + 8²

XZ² = XY² + YZ²

XZ² = 272.51

XZ = 16.51 in.

So, the perimeter of triangle XYZ would be,

P = XY + YZ + XZ

P = 14.44 + 8 + 16.51

P = 38.95 inches

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The Probability that the next pair Michael takes out is black = 8 / 19

What is Probability?

Probability is deals with "occurrence of Random event. The value is expressed from 0 to 1".

According to the question,

Total number of pairs of socks = 8 + 12 =20

Probability of taking pairs of black socks,  P(B )= 8 / 20

Probability of taking pairs of white socks,  P(W) = 12 / 20

But after taking Black pair socks the total number socks = 19.

Hence, the Probability of taking Black pair socks from drawer is 8 / 19 .

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let the number be x and y

x + y = 30 -----(1)

x = y + 15 -----(2)

y + y + 15 = 30

2y = 15

y = 7.5

x = 7.5 + 15 = 22.5

x= 22.5 , y = 7.5

After 45 seconds they blink together again.

Least Common Multiple is a mathematical term. The smallest number that is a multiple of both of two numbers is called the least common multiple.

For example, L.C.M of 16 and 20 will be 2 x 2 x 2 x 2 x 5 = 80, where 80 is the smallest common multiple for numbers 16 and 20.

Given:

One sign blinks every 9 seconds. The other sign blinks every 15 seconds.

Now, to find they blink together again we have to find the LCM of 9 and 15.

For 9 the lights will blink at seconds: 0, 9, 18, 27, 36, 45, 54, 63,

and, For 15 the lights will blink at seconds: 0, 15, 30, 45, 60, 75

Hence, they blink together at 45 seconds.

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Equation with inversely proportional relation gives answer of the following questions :

1.  a.  w = k₁ / f                                b. f =60 ⇒ w = 8

2. a. B = k₂/ y                                  b. y = 5 ⇒ B = 2.08

1. Representation of the formula connecting :

w is inversely proportional to the variable f

a . w ∝ ( 1 / f )

⇒ w = k₁ / f  

where k₁ is the constant of proportionality.

When w = 40 , f = 12

40 = k₁ / 12

⇒ k₁ = (40)(12)

⇒ k₁ = 480

b . f = 60

Value of 'w' is equal to :

⇒ w= 480 / 60

⇒ w = 8

2. B is inversely proportional to the variable y

a . B ∝ ( 1 / y )

⇒B = k₂ / y

where k₂ is the constant of proportionality.

When B = 0.8 , y = 13

0.8 = k₂ / 13

⇒ k₂ = (0.8)(13)

⇒ k₂ = 10.4

b . y = 5

⇒ B= 10.4 / 5

⇒ B = 2.08

Therefore, the required values and formula to represents the inversely proportional relation are:

The above question is incomplete, the complete question is :

1. W is inversely proportional to f , When f = 12, w = 40

(a) Find a formula connecting w and f .

(b) Find the value of w when f = 60.

2. B is inversely proportional to y , When B = 0. 8, y = 13

(a) Find an equation for B in terms of y.

(b) Work out the value of B when y = 5

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Answer:

.375 as a decimal

Step-by-step explanation:

Range provides a precise measurement of variability for both sets of data because it compares the greatest and lowest values in a dataset.

It is a helpful measure of variability for comparing the constancy of temperature between Desert Landing and Flower Town because it is unaffected by skewness or symmetry.

A histogram is a graph that shows how a dataset is distributed. In a dataset, it is a way to show the frequency of various values or ranges of values.

In a histogram, the y-axis normally indicates the frequency or count of the values, and the x-axis typically shows the values or ranges of values.

Each bin in the data is represented by a bar whose height is equal to the number of observations in that bin. The data is divided into bins. The distribution of data is visualized using histograms, which are also used to spot anomalies and spot patterns or trends in the data.

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The probability that the mean loss from f-i-re is larger than $300 for an S-R-S of 1000 home owners is 0.3085.

This problem can be solved using the Central Limit Theorem, which states that the sampling distribution of the mean of any independent, random variable will be normal or nearly normal if the sample size is large enough (typically if n > 30).

Since the population is strongly right-skewed and the sample size is large (n = 1000), we can assume that the sampling distribution of the mean loss from fi-re will be approximately normal.

The mean of the sampling distribution is equal to the population mean, and a standard deviation equal to the population standard deviation divided by the square root of the sample size. In this case, we have:

Populatio mean (μ) = $250

Population standard deviation (σ) = $5000

Sample size (n) = 1000

Sample mean = $300

Probability of sample mean > $300 = ?

Now, standard deviation of sample mean = σ / sqrt(n) = $5000 / sqrt(1000) = $158.11

Now, we need to standardize the sample mean using the z-score formula:

z = (sample mean- population mean) / (σ / sqrt(n)) = (300 - 250) / 158.11 = 0.316

Using a standard normal distribution table or calculator, we can find the probability of a z-score greater than 0.316 to be approximately 0.3765 or about 37.65%.

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The total wage can only be an integer multiple of the wage per person.

The number of people working in the factory on a particular day can be calculated by dividing the total wage by the wage per person. This can be expressed mathematically as:

Number of People = Total Wage ÷ Wage per Person

For the given scenario, the number of people working on the day when the factory paid 9225 can be calculated as:

Number of People = 9225 ÷ 7175

Number of People = 1.287

Since the number of people has to be a whole number, this means that there were 1 people working in the factory on the day when the factory paid 9225. This is because when the wage per person is the same for everyone, the total wage can only be an integer multiple of the wage per person.

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A rotation of the 270º will map the blade formed by triangle CBD onto the blade formed by triangle EDF.

The rotations are defined as clockwise or counterclockwise as follows:

The entire circumference formed by the image has an angle measure given as follows:

360º.

Triangle EDF is 3/4 of the circumference away from triangle CBD, hence the angle measure of the counterclockwise rotation is given as follows:

3/4 x 360º = 0.75 x 360º = 270º.

Which is the angle measure used to complete the blank in this problem.

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The inequality 14.5v ≥ 235 can be used to determine the minimum number of visits Brianna needs to earn her first free movie ticket.

The inequality 14.5v ≥ 235 can be used to determine the minimum number of visits Brianna needs to earn her first free movie ticket.14.5v ≥ 235

To figure out how many visits Brianna needs to earn her first free movie ticket, we can set up an inequality. We'll set the left side of the equation equal to the total points needed for a free movie ticket (235 points). We'll set the right side of the equation equal to the points earned per visit (14.5 points) multiplied by the number of visits (v).

14.5v ≥ 235

The inequality 14.5v ≥ 235 can be used to determine the minimum number of visits Brianna needs to earn her first free movie ticket.

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The Area of the base of the basket is 10 ft².

Given,

Volume of basket = 15 cubic feet

h = 1.5 ft

V = πr²h

15 = πr² (1.5)

πr² = 15/1.5

πr² = 10 ft²

Area of base of the basket = 10 ft²

(or)

15 = πr² (1.5)

r = √15/π(1.5)

Simplifying the values, we can get radius of basket = 1.78

Then, area of base of basket = πr²

Substituting the values of π = 3.14 and r = 1.78 in above formula, we get,

Area of base of the basket ≈ 9.95 ft²

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A cylinder can be measured in two separate ways: volume and area. As area gauges an object's two-dimensional surface, volume gauges how much space an object takes up.

If the cylinder's height and base area are known, the cylinder's volume may be determined by multiplying the base area by the cylinder's height. By dividing the base's circumference by its height, one may get the cylinder's area.

Given,

Volume of basket = 15 cubic feet

h = 1.5 ft

V = πr²h

15 = πr² (1.5)

πr² = 15/1.5

πr² = 10 ft²

Area of base of the basket = 10 ft²

(or)

15 = πr² (1.5)

r = √15/π(1.5)

We may obtain radius of basket = 1.78 by simplifying the numbers.

Then, area of base of basket = πr²

By replacing the values of 3.14 and 1.78 in the formula above, we obtain,

Area of base of the basket ≈ 9.95 ft²

Therefore, The Area of the base of the basket is 10 ft².

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Answer:

To estimate the total weight of the pet food Adam buys, we can use benchmark fractions to compare the weight of the dog food (7/8 pound) and the weight of the cat food (1 3/4 pounds) to a benchmark fraction that we are familiar with.

We know that 1 whole pound is equal to 16 ounces. So, we can use this as a benchmark to estimate the weight of the dog food and cat food.

First, we'll convert 7/8 pound to ounces. 7/8 pound is equal to 7/8 * 16 = 14 ounces

Next, we'll convert 1 3/4 pound to ounces. 1 3/4 pound is equal to 1 * 16 + 3/4 * 16 = 16 + 12 = 28 ounces.

Now we can add the weight of the dog food and the cat food to get the total weight of the pet food Adam buys.

14 ounces + 28 ounces = 42 ounces

So, the total weight of the pet food Adam buys is approximately 42 ounces, which is roughly 2.6 pounds.

The estimate was made with benchmark fractions, which allows us to make a rough estimation of the weight of the pet food, but it's not as precise as the exact weight in pound or ounces.