Is this a function or not a function?

Answer:

B)1-x≤-1 OR 1-x≥1

\(S=\{x\in\mathbb{R}| x\le 0\quad \text{or}\quad x\ge 2 \}\)

Step-by-step explanation:

\(2|1-x|+1\geq 3\)

\(2|1-x|\geq 2\)

\(|1-x|\geq 1\)

Once we have an absolute value inequality, remember that:

For a > 0

\(\boxed{\text{If } |x|\leq a \Longleftrightarrow -a\leq x \leq a}\)

\(\boxed{\text{If } |x|\geq a \Longleftrightarrow x\leq -a \text{ or } x\geq a }\)

Therefore,

\(1-x\le -1\quad \text{or}\quad 1-x\ge 1\)

Solving

\(1-x\le -1 \Longleftrightarrow x\geq 2\)

\(1-x\ge 1 \Longleftrightarrow x\leq 0\)

We have

\(x\geq 2 \quad \cup \quad x \leq 0\)

\((-\infty, 0] \cup [2, \infty)\)

\(S=\{x\in\mathbb{R}| x\le 0\quad \text{or}\quad x\ge 2 \}\)

The process that generates more values that are more than 2 standard deviations from the mean is called a "fat-tailed" distribution.

In a fat-tailed distribution, the probability of extreme values occurring is higher compared to a normal distribution.

To understand this concept, let's consider two processes: Process A and Process B.

Process A generates a dataset with a normal distribution, while Process B generates a dataset with a fat-tailed distribution.

In a normal distribution, the majority of the data falls close to the mean, with fewer values farther away.

The probability of values more than 2 standard deviations from the mean is relatively low.

On the other hand, in a fat-tailed distribution, there is a higher likelihood of extreme values occurring.

This means that the probability of values more than 2 standard deviations from the mean is higher.

For example, let's say we have two datasets: Dataset A generated by Process A and Dataset B generated by Process B.

We calculate the mean and standard deviation for both datasets.

In Dataset A, if the mean is 50 and the standard deviation is 5, then values more than 2 standard deviations away from the mean would be greater than 60 or less than 40.

In Dataset B, if the mean is 50 and the standard deviation is also 5, then values more than 2 standard deviations away from the mean would have a wider range.

These values could be significantly higher than 60 or lower than 40, depending on the specific distribution of Dataset B.

Therefore, if Process B generates a fat-tailed distribution, it is more likely to produce values that are more than 2 standard deviations from the mean compared to Process A and its normal distribution.

In summary, the process that generates more values that are more than 2 standard deviations from the mean is a fat-tailed distribution, which has a higher likelihood of extreme values occurring.

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Answer:

2p^2-p + 5/2

Step-by-step explanation:

Here, we want to use long division method

Please check attachment for the long division process

According to the long division, the answer is

2p^2-p + 5/2

To check the answer, we multiply the binomial by the result of the division

That will be;

(2p-1)(2p^2-p + 5/2)

= 4p^3-2p^2+5p-2p^2+p-5/2

= 4p^3-2p^2-2p^2+5p+p-5/2

= 4p^3-4p^2+ 6p - 5/2

we then conclude that our answer is correct

Answer: 23 cups

Step-by-step explanation:

There were 4 groups with 5 people each and all of them ordered a cup of hot chocolate:

= 4 * 5

= 20 cups

Rebecca, Malaki, and Jeffrey each ordered an extra cup of hot chocolate so that's 3 extra cups:

= 20 + 3

= 23 cups

Answer:

this question also have same procedure.

you have to calculate x

Step-by-step explanation:

add two of them

and make equal to 4x - 11

then you will got the value of x which is x = 15

then put in 2x so EF will be 30

thanks

Answer:

The rate of change of the function = 5

Step-by-step explanation:

From the given parameters, we have;

The number of months Janenne has belonged to the book-of-the-month-club = 12

The amount Janenne has spent on the club = 70.45

The amount she paid in the first month = Monthly fee + 10.45

Let the monthly fee = x

The total amount Janenne has spent on the club  can be given by the following formula;

10.45 + 12×x = 70.45

12×x = 70.45 - 10.45 = 60

x = 60/12 = 5

The monthly due of the book club = 5

Therefore, the rate of change of the function × 5

The function of the amount spent on the club = Y = t×x

Where;

x = The rate of change of the function

t = The time in months

The rate of change of the function = 5.

The volume of inhaled air at a maximum at t = 2, 4, 6, ...

The volume of inhaled air is at a maximum when the function V(t) is at a maximum. This occurs when the derivative of V(t) is equal to zero.

The derivative of V(t) is:

V'(t) = (3/5) pi * (pi/2) * sin(pi t/2)

Setting this equal to zero gives:

(pi/2) * sin(pi t/2) = 0

This occurs when pi t/2 is equal to a multiple of pi. This means that t/2 is equal to a multiple of 1, or t is equal to a multiple of 2. Therefore, the volume of inhaled air is at a maximum when t = 2, 4, 6, ...

The correct answer is: t = 2, 4, 6, ...

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Answer:

.20 per minute.If you dives 1 mile by 5 min u will get .20

Answer:

there aren't any options. but quadrant four would have a (x,-y) set up. positive x-values, but negative y-values.

Answer:

y = 5/ 3 x + 19/ 3

Step-by-step explanation:

Slope-intercept form,  y = m x + b .

Answer:

y=5/3x+6 1/3

Step-by-step explanation:

To get into y-intercept form you need to get y alone...

5x-3y=-19    subtract the 5x

-3y=-5x-19     divide by -3

y=5/3x+19/3    simplify

y=5/3x+6  1/3

The correct formula for the revenue generated by the item is Revenue = 200p - 5p^2.

The revenue generated by the item can be calculated by multiplying the price (p) by the unit sales (200 - 5p). Therefore, the correct formula for the revenue generated by the item is:

Revenue = Price x Unit Sales
Revenue = p(200 - 5p)
Revenue = 200p - 5p^2

The revenue generated by the item is a quadratic function of the price (p). To find the maximum revenue, we need to differentiate the function with respect to p and set it equal to zero:

dRevenue/dp = 200 - 10p = 0
10p = 200
p = 20

Therefore, the maximum revenue is generated when the price of the item is $20. Substituting p = 20 in the revenue formula, we get:

Revenue = 200(20) - 5(20^2) = $2000

Hence, the correct formula for the revenue generated by the item is Revenue = 200p - 5p^2, and the maximum revenue is achieved when the price of the item is $20, generating a revenue of $2000.

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Answer:

Step-by-step explanation:

y = -1

because if you look at the image, go on the x axis to 0, if you then look at the y coordinate to see what the value of y is, it goes to -1.  

Answer:

at x = 0, the function is undefined

Step-by-step explanation:

Solution

Answer:

n=10

Step-by-step explanation:

first distribute

-3 + 1/2 n = -1/2n + 7

next multiply both sides of the quation by 2

-6+n=-n+14

add n to both sides

-6+n+n=14

add 6 to both sides

n+n=14+6

combine like terms

2n=20

divide both sides by 2

n=10

By consistently depositing $10,000 each year for 5 years at an interest rate of 8%, you would accumulate around $48,786.15.

Over a period of 5 years, assuming an annual deposit of $10,000 at an interest rate of 8%, you would accumulate a significant amount through compound interest.

To calculate the total amount after 5 years, we can use the formula for the future value of an ordinary annuity:

\( FV = P \times \left( \frac{{(1 + r)^n - 1}}{r} \right) \)

Where:

FV = Future value

P = Annual deposit

r = Interest rate per period

n = Number of periods

In this case, the annual deposit is $10,000, the interest rate is 8% (or 0.08 as a decimal), and the number of periods is 5 years. Plugging these values into the formula:

\( FV = 10000 \times \left( \frac{{(1 + 0.08)^5 - 1}}{0.08} \right) \)

After evaluating the expression, the future value (FV) after 5 years would be approximately $48,786.15.

Therefore, by consistently depositing $10,000 each year for 5 years at an interest rate of 8%, you would accumulate around $48,786.15. This demonstrates the power of compounding interest over time, where regular contributions can lead to significant growth in savings.

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Answer:

161

Step-by-step explanation:

145+318=463. 624-463=161

The required number that comes in place of "What" is given as 161.

Given that,
what + 145 + 318 = 624

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
What = 624 - 318 - 145
what = 161

Thus, the required number that comes in place of "What" is given as 161.

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Answer:

10

Step-by-step explanation:

a^2+b^2=c^2

9^2+3^2=c^2

81+9=c^2

100=c^2

c=10

Answer:

It will  take 18 months.

Step-by-step explanation:

y = 12.4x + 106  I am assuming that the variable x stands for the number of months.

329.20 = 12.4x + 106  Subtract 106 from both sides

329.20 - 106 = 12.4x + 106 - 106

223.20 = 12.4x  Divide both sides by 12.4

18 = x

Helping in the name of Jesus.

Answer:

80 students

Step-by-step explanation:

The line in the middle of the box is the 50% line ( the median, which is 50% above and 50% below)

Since it is at 48, there are 50% above 48 points

3/4 of the students  had less than 70 marks

3/4 s = 120

s = 4/3 * 120

The number of students = 160

We need 50 % of the students

50% of 160

.5 * 160 = 80

The  volume of the largest right circular cone that can be inscribed in a sphere of radius r is  8/27 (volume of sphere)

Let r serve as the foundation. the volume of the area, and radius x is the separation between the base and the sphere's center. Height h of the cone = R + x

∴    V= 1/3πr² h= π/ 3 (R² −x²)(R + x)

       = π/3​ (R² + R² x − Rx² −x² )

∴   dV/ dx​ = π​ /3 [R²−2Rx−3x² ]

  d²V/ dx²​ = π/3​ [−2R−6x]

For max or min V dV/dx​ =0

∴   R² −2Rx−3x² =0

⇒(R + x)(x−3x)=0    

2) x=−R, x​/3 but x = −R

When x= R/3 d² V/dx² <0  V is max only when x= R/3

​∴   Max V= 1/3π(R² − R²/9 )(R+ R/3 )

= 32πR³/81

= 8/27 ( 4/3 πR³)

= 8/27 (volume of sphere)

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In inferential statistics, the objective is to determine the probability of the alternative hypothesis being true or the null hypothesis being true.

This involves using sample data to make inferences and draw conclusions about a larger population. By analyzing the data and performing statistical tests, we assess the likelihood of the alternative hypothesis or the null hypothesis being accurate.

The alternative hypothesis represents a claim or statement that contradicts the null hypothesis and suggests that there is a significant relationship or difference between variables. To determine its probability, statistical methods such as hypothesis testing and p-values are employed. These methods evaluate the strength of evidence against the null hypothesis and support the alternative hypothesis when the evidence is substantial.

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(i) The nth partial sum of the series 2 + 2/3 + 2/9 + 2/27 + ... is given by Sn = 2(1 - (1/3)^n) / (1 - 1/3) = 3(1 - (1/3)^n). The series converges to the limit 3.

(ii) The nth partial sum of the series 5/1.2 + 5/2.3 + 5/3.4 + ... is given by Sn = 5((1/n) - (1/(n+1))). The series converges to the limit 5.

(i) For the series 2 + 2/3 + 2/9 + 2/27 + ..., notice that each term can be expressed as 2/3^n. The nth partial sum, Sn, can be obtained by summing up the terms from the first term to the nth term. This can be calculated using the formula for the sum of a geometric series: Sn = a(1 - r^n) / (1 - r), where a is the first term and r is the common ratio. In this case, a = 2 and r = 1/3. Simplifying the formula gives Sn = 2(1 - (1/3)^n) / (1 - 1/3) = 3(1 - (1/3)^n). As n approaches infinity, (1/3)^n approaches 0, so the series converges to the limit 3.

(ii) For the series 5/1.2 + 5/2.3 + 5/3.4 + ..., each term can be expressed as 5/(n(n+1)). The nth partial sum, Sn, can be obtained by summing up the terms from the first term to the nth term. In this case, we don't have a geometric series, but we can still find a formula for Sn. By observing the pattern, we can rewrite each term as 5((1/n) - (1/(n+1))). Summing up these terms, we find that Sn = 5((1/1) - (1/2)) + ((1/2) - (1/3)) + ... + ((1/n) - (1/(n+1))). Notice that many terms cancel out, leaving only the first and last terms. Simplifying, we have Sn = 5((1/1) - (1/(n+1))) = 5(1 - 1/(n+1)). As n approaches infinity, 1/(n+1) approaches 0, so the series converges to the limit 5.

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Answer:

Yes

Step-by-step explanation:

Because it’s a trapezoid and those can be trapezoid because they have one pair of parallel sides and a parallelogram has two pairs of parallel sides so a parallelogram is also a trapezoid.

The correct answer is (D) The full length to which it can be extended.

The size classification of an extension ladder indicates the full length to which it can be extended.
An extension ladder's size classification indicates the total length the ladder can reach when its fly section is fully extended.

This helps users determine if the ladder will be long enough for their specific needs when working at height.

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Answer: There will be 30 tiles in each row.

Step-by-step explanation:

To find the number of tiles in each row, we need to determine the room's dimensions and the size of each tile. Given that the area of the square room is 225 square feet, we know that the room is a perfect square. Let's denote the length of one side of the square as "x" feet.

We can calculate the length of one side of the square by taking the square root of the area:

x = √225 = 15 feet

Since each tile is 6 inches by 6 inches, we need to convert the measurements to feet: 6 inches = 6/12 = 0.5 feet

To determine the number of tiles in each row, we divide the length of the side of the room by the length of each tile:

Number of tiles in each row = (Side length of the room) / (Length of each tile)

Number of tiles in each row = 15 feet / 0.5 feet = 30 tiles

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Answer:

ABD = CDB

AB is parallel to DC

Step-by-step explanation:

angle a and c are right angles so they are equal and angle b and d are equal because they have a line that touch both letters

AB and DC are parellel because they are the same looking lines just on oppisite sides

As per the ASA congruence theorem, the triangles ΔABD and ΔCDB are congruent.

When two parallel lines are intersected by a transversal, alternate external angles are created.

Given that, m∠A = m∠C = 90° and AB║DC.

In triangles ΔABD and ΔCDB,

m∠A = m∠C = 90°

m∠ABD = m∠BDC (Alternate interior angles)

BD = DB (Common side)

Hence, as per the ASA congruence theorem, the triangles ΔABD and ΔCDB are congruent.

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Heya !! here's your solution :

\( \hookrightarrow \: ( {x}^{2} + 2x) \times (x - 1)\)

\( \hookrightarrow \: \: {x}^{3} - {x}^{2} + 2 {x}^{2} - 2x\)

\( \hookrightarrow \: {x}^{3} + {x}^{2} - 2x\)

therefore , the correct Option is D

Answer:

470

Step-by-step explanation:

1323 rounds to 1320

443 rounds to 440

409 rounds to 410

1320 - (440 + 410) =

1320 - 850 =

470 <=== malcolm has about 470 miles left to go

Answer:

9/4

Step-by-step explanation:

you can use photomath for questions like these :P

Answer:

2 1/4

Step-by-step explanation:

3/4 x 3 = 9/4 = 2 1/4

Hope that helps!