What are the domain and range of ​f(x)=3(x−15)2+27​? It is a drag an drop.

Answer 1. All real numbers
Answer 2. x≥15
Answer 3. f(x)≥15
Answer 4. x≥27
Answer 5. f(x)≥27

The correct formula that defines an arithmetic sequence is option d) tn = 5n + 14.

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms remains constant. In other words, each term can be obtained by adding a fixed value (the common difference) to the previous term.

In option a) tn = 5 + 14, the term does not depend on the value of n and does not exhibit a constant difference between terms. Therefore, it does not represent an arithmetic sequence.

Option b) tn = 5n² + 14 represents a quadratic sequence, where the difference between consecutive terms increases with each term. It does not represent an arithmetic sequence.

Option c) tn = 5n(n+14) represents a sequence with a varying difference, as it depends on the value of n. It does not represent an arithmetic sequence.

Option d) tn = 5n + 14 represents an arithmetic sequence, where each term is obtained by adding a constant value of 5 to the previous term. The common difference between consecutive terms is 5, making it the correct formula for an arithmetic sequence.

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Answer:

work is shown and pictured

Answer:

910

Step-by-step explanation:

so to find 100% ( the number)

91 x 10

910 would be the number

Answer:

10

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

Let the third side be x , then

x² + 6² = (2\(\sqrt{34}\) )²

x² + 36 = 136 ( subtract 36 from both sides )

x² = 100 ( take the square root of both sides )

x = \(\sqrt{100}\) = 10

If people show up at rate of 1 person every minute , then the probability that on a random minute , at least 3 people show up is 0.084  .

The number of people showing up at bar in San Diego during any random minute is a Poisson process with an average rate of 1 person per minute.

Let X = number of people who show up during a random minute.

Then X will  follows a Poisson distribution with parameter λ = 1.

So , probability of at least 3 people showing up in a random minute is:

⇒ P(X ≥ 3) = 1 - P(X < 3)

⇒ 1 - (P(X = 0) + P(X = 1) + P(X = 2))

By using Poisson probability mass function for finding P(X = k) for k = 0,1,2   ;

⇒ P(X = k) = (\(e^{-\lambda}\))×(\(\lambda ^{k}\))/k!

Substituting in λ = 1, we get ;

⇒ P(X = 0) = (\(e^{-1}\))×(\(1 ^{0}\))/0! = 1/e  ;

⇒ P(X = 1) =  (\(e^{-1}\))×(\(1 ^{1}\))/1! =  1/e  ;

⇒  P(X = 2) =  (\(e^{-1}\))×(\(1 ^{2}\))/2! = 1/2e  ;

So, the probability of at least 3 people showing up in a random minute is:

⇒  P(X ≥ 3) = 1 - (P(X = 0) + P(X = 1) + P(X = 2))

= 1 - (1/e + 1/e + 1/2e) = 1 - (2/e + 1/2e)

= 1 - (5/2e)

= 0.083019 ≈ 0.084  .

Therefore , the required probability is 0.084  .

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The given question is incomplete , the complete question is

Your friend sings every Saturday night at your favorite bar in San Diego. During his show, people show up at the rate of 1 person every minute.

What is the probability that on a random minute, at least 3 people show up ?

Answer:

let equal side=x

unequal side=x+3

perimeter =33

x+x+x+3=33

3x=30

x=10

x+3=10+3

Answer:

Parabola

Step-by-step explanation:

This is what it looks like:

Answer:

w = (t - 3)/7

Step-by-step explanation:

..............

Answer:

sinΘ = opposite/ hypotenuse

sin (37)= CV/55

55 sin (37) = CV

CV=33.1

OAmalOHopeO

Answer:X=15d or just 15

Step-by-step explanation:Since there is an increase in manpower/hours of: [8 x 4] / [6 x 5] = 16/15, therefore, there must be decrease in days by the same pecentage. Or 16 / [16 / 15] =16 x 15/16 =15 days

Answer:

15 days

Step-by-step explanation:

Or you could just write 15 on MathsWatch

Answer:

Step-by-step explanation:

\(3x^2 + 12x + 6 = 0\\\\a=3\,,\ b=12\,,\ c=6\\\\\\ x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\ x=\dfrac{-12\pm\sqrt{12^2-4\cdot3\cdot6}}{2\cdot3}=\dfrac{-12\pm\sqrt{144-72}}{2\cdot3}=\dfrac{-12\pm\sqrt{72}}{2\cdot3}=\dfrac{-12\pm6\sqrt{2}}{6}\\\\x_1=\dfrac{6(-2+\sqrt{2})}{6}=-2+\sqrt2\\\\x_2=\dfrac{6(-2-\sqrt{2})}{6}=-2-\sqrt2\)

If derivative of \(f(x)=ln(x+4+e^{(-3x)})\), then f '(0) = -2/5.

What is derivative?

In calculus, the derivative of a function is a measure of how the function changes as its input changes. More specifically, the derivative of a function at a certain point is the instantaneous rate of change of the function at that point.

To find f'(0), we first need to find the derivative of f(x) with respect to x. Using the chain rule, we get:

\(f'(x) = 1 / (x+4+e^{(-3x)}) * (1 - 3e^{(-3x)})\)

Now we can find f'(0) by substituting the value x=0:

\(f'(0) = 1 / (0+4+e^{(-3(0))}) * (1 - 3e^{(-3(0))})\)

f'(0) = 1 / (4+1) * (1 - 3)

f'(0) = -2/5

Therefore, f'(0) = -2/5.

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To increase usability in a spreadsheet, you can use comments, descriptive labels, and data validation.

To increase usability in a spreadsheet, you can utilize the following techniques:

1. Comments: Comments allow you to add explanatory notes or instructions within cells. They can provide additional context or clarify the purpose of certain data or formulas. Users can view comments by hovering over the respective cell, making it helpful for collaboration and documentation.

2. Descriptive Labels: Instead of relying solely on cell references or generic labels, use descriptive labels that clearly indicate the purpose of each column, row, or range of cells. This approach enhances readability and makes it easier for users to understand the data and navigate through the spreadsheet.

3. Data Validation: Implement data validation rules to ensure the accuracy and integrity of the data entered into the spreadsheet. Data validation allows you to define constraints or conditions for input, such as numeric ranges, predefined lists, or specific text formats. It helps prevent errors and assists users in entering valid data.

4. Formatting: Properly formatting the cells, columns, and rows can greatly enhance usability. Use consistent formatting for similar types of data, apply color schemes or conditional formatting to highlight important information or trends, and adjust the column widths and row heights to optimize readability.

5. Sheet Organization: Organize the spreadsheet by using multiple sheets if needed. Group related information on separate sheets, and provide clear sheet names that reflect the content or purpose of each sheet. This helps users locate and navigate to specific sections or data within the spreadsheet.

6. Clear Instructions or Documentation: Provide clear instructions or documentation either within the spreadsheet or as separate documentation. Explain the purpose of the spreadsheet, any specific procedures or workflows, and how to interpret the data or use any embedded formulas or macros. This helps users understand the spreadsheet's functionality and ensures consistent usage.

7. Error Handling: Implement error handling mechanisms to provide informative error messages or alerts when users input incorrect or incompatible data. Clear error messages guide users in correcting their input and reduce frustration when dealing with potential errors.

By incorporating comments, descriptive labels, data validation, formatting, sheet organization, clear instructions/documentation, and error handling, you can significantly enhance the usability of your spreadsheet and make it more user-friendly for both yourself and others who interact with it.

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The median completion time for the quiz is between 20 and 30 minutes, indicating that half of the students took less than 20 minutes, while the other half took more than 30 minutes.

To calculate the c of the completion times, we first need to arrange the data in ascending order. Then we find the middle value or the average of the two middle values if the sample size is even.

Arranging the data in ascending order:

0 and less than 10: 4

10 and less than 20: 8

20 and less than 30: 13

30 and less than 40: 12

40 and less than 50: 7

50 and less than 60: 6

We have a sample size of 50, which is an even number. So, to find the median, we take the average of the 25th and 26th values, which correspond to the 13th and 14th values in the ordered data. The 13th value is in the 20 and less than 30 range, and the 14th value is also in the same range. So, the median falls within the range of 20 and less than 30. Therefore, the median completion time is between 20 and 30 minutes.

To calculate the mode, we look for the category with the highest frequency. In this case, the category with the highest frequency is the 20 and less than 30 range, which has a frequency of 13. Hence, the mode of the completion times is 20 and less than 30 minutes.

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Answer:

A possible solution is she should by 6 bags of popcorn and 10 drinks

Step-by-step explanation:

The price of each bag of popcorn = $7.50

The price of each drink = $4.50

The amount Sarah has to spend = $90

The number of bags of popcorn and drinks Sarah must buy = 16 bags of popcorn and drinks

Let the number of bags of popcorn purchased be represented by x and the number of drinks purchased be represented by y

Therefore, we have;

x + y ≥ 16.....(1)

x × 7.5 + y × 4.5  ≤ 90

Which gives;

7.5·x + 4.5·y ≤ 90....(2)

Rewriting the inequalities as a function of y, gives;

From inequality (1), x + y ≥ 16, we have;

y = ≥ 16 - x

From inequality (2), 7.5·x + 4.5·y ≤ 90, we have;

7.5·x + 4.5·y ≤ 90

4.5·y ≤ 90 - 7.5·x

y ≤ 90/4.5 - 7.5/4.5·x

y ≤ 20 - 5/3·x

Please find attached, the plot of the inequalities

A possible solution is given as the value of x = 6, where y = 10

Therefore, she should by 6 bags of popcorn and 10 drinks.

Answer:

x + 18 ≥ 26

Step-by-step explanation:

"greater than or equals": ≥

x + 18 ≥ 26 is your answer.

If you are trying to solve it so you isolate x, subtract 18 from both sides:

x + 18 (-18) ≥ 26 (-18)

x ≥ 26 - 18

x ≥ 8

x ≥ 8 is your answer.

~

Answer:

x+18 ≥ 26

Step-by-step explanation:

≤ is the less than or equals sign

≥ is the greater than or equals sign

x+18 ≥ 26

(This also means x must be ≥ 8)

The pattern is +1, +2, +3, …

Therefore, the next term in the sequence is 18.

Answer:

2,3,5,8,13,  21

Step-by-step explanation:

3+2=5

5+3=8

8+5=13

13+8=21

The correct option is (d) if A is divided by 2, B is divided by approximately 1.414.

Proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.

Here,
If A varies inversely as the square of B, it means that A is equal to some constant k divided by the square of B:

A = k/B²

To find the effect on B when A is multiplied by 4, we can use the inverse variation formula and substitute 4A for A,

4A = k/B^2

Simplifying this expression, we get:

B² = k/(4A)

To find the effect on B when A is multiplied by a certain factor, we can use this formula and substitute the new value of A,

a) If A is multiplied by 1.5:

1.5A = k/B²

B² = k/(1.5A)

The effect on B depends on the value of k and the original value of B, which are not given. So we cannot determine the effect on B with the information given.

b) If A is multiplied by 4:

4A = k/B²

B² = k/(4A)

Since 4A is four times the original value of A, B^2 will be divided by 4, so B will be multiplied by √4, which is 2. Therefore, when A is multiplied by 4, B is multiplied by 2.

c) If A is multiplied by 2:

2A = k/B²

B^2 = k/(2A)

Since 2A is half the original value of A, B^2 will be multiplied by 2, so B will be divided by √2, which is approximately 1.414. Therefore, when A is multiplied by 2, B is divided by approximately 1.414.

d) If A is divided by 2:

A/2 = k/B²

B² = k/(A/2)

Since A/2 is half the original value of A, B² will be multiplied by 2, so B will be divided by √2, which is approximately 1.414. Therefore, when A is divided by 2, B is divided by approximately 1.414.

Therefore, the correct option is (d) if A is divided by 2, B is divided by approximately 1.414.

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EXPLANATION:

Given;

We are given the triangle DEF on the coordinate plane. The coordinates are also given as follows;

Required;

We are required to calculate the area of triangle DEF.

Step-by-step solution;

We shall begin by drawing up the triangle with the coordinates given, on a graph page;

Observe that the points DEF has been appropriately labeled. The length of side FD is 8 units (that is, from point 0 to 8), the length of side FE is 2 units.

We now have the base (side FE) and the vertical height (side FD), we can calculate the area of the triangle using the formula;

Where the variables are;

The area therefore is;

We now have;

ANSWER:

Area = 8 square units

The first option is the correct answer

Answer: 2496in³

Step-by-step explanation:

To find volume, multiply the numbers by length, width, and height.

In this case, 24 is the length, 8 is the width, and 13 is the height.

24 × 8 × 13 = 2496 inches ³ (cubed).

Answer:

option C 2496

Step-by-step explanation:

you multiply 13 by 24 by 8

Answer:

The answer is A. $15.00

Step-by-step explanation:

Take 25% of 60 and that is 15. Please give me brainliest

Answer:

$45.00

Step-by-step explanation:

To find percentage, most start out by dividing the percent by 100:

25 ÷ 100 = 0.25

Then, to find the percentage of 60, we multiply them.

$60 x 0.25 = $15

15 is 25% of 60. However, we're asking the sale price of the video game, not the amount it was reduced. To find this out we subtract the reduced amount from the original number:

$60 - $15 = $45

≧◡≦

Mocha here! If this answer helped you, please consider giving it brainliest because I would appreciate it greatly. Have a wonderful day!

To plot the graph of the function:

According to your graphing software, we need to find the smallest value of the function, and any point at the positive slope side of the function. Let's start with the minimum point. Let's use the general formula for an absolute value function:

The coefficients 'b' and 'c' determinates how much the function was translated from the origin. The 'b' determinates in the x-axis, and the 'c' determinates in the y-axis.

If the 'b' is positive, the function translated to the left, if it is negative the function translated to the right.

If the 'c' is positive the function went up, and if it is negative it went down.

Now let's analyze our h(x) function. Our coefficients are:

Which means our minimum point is

Now, we just need to calculate any point to the right of x = -1.

Let's calculate for x = 0.

The second point is (0,7)

Sure, here is the answer and how to solve it.

To determine the best buy, we need to calculate the price per notebook for each option.

For the 3-pack, the price per notebook is:

$3.24 ÷ 3 notebooks = $1.08 per notebook

For the 7-pack, the price per notebook is:

$6.93 ÷ 7 notebooks = $0.99 per notebook

Therefore, the 7-pack is the better buy, as it offers a lower price per notebook than the 3-pack.

Hope this helps!

~Ariana :)

The definition and explanation of an equation are given below with an example.

in mathematics, an equation is defined as an expression that expresses equality between 2 quantities or expressions. We use equations quite a lot in our daily lives whenever we have to equate two quantities and find out how they are equal. These are used in all branches of science because of the huge purpose they serve.

in simple words it tells what we have on the Left-Hand Side of the "=" sign is the same as what we have on the right-hand side of the statement. Some examples of equations are-

E²=m²c⁴+p²c²

x²+3x-1=0

70 oranges= 7 oranges × 10 oranges

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Answer:

First we need to isolate the y in the equation

-4y=16-2x (subtract the 2x)

4y=2x-16 (divide both sides by -1)

y=1/2x-4 (divide both sides by 4)

The we know the slope of this line is 1/2. I'm not sure what the choices are, but the answer would have to have a slope of 1/2. For example, y=1/2x+2 might be an answer.

Hope this helps

Step-by-step explanation:

Answer:

A. segment QR

Step-by-step explanation:

It's a little hard to explain. Sorry for the inconvenience.

Hope this helps though. Have a nice day.

Answer:

Line RS

Step-by-step explanation:

1. Find S

S is 90 because the interior angles sum is 180. 180-44-46=90

2. Find the smallest angle

Angle Q

3. Find Q's opposing side

Which is RS

Hope this helps!

The constraints as a system of linear inequalities include the following;

x + y ≤ 180

x ≥ 40

y ≥ 40

3x + 4y ≤ 640

75x + 60y ≤ 12,900

The solution set for the system of linear inequalities is shown in the coordinate plane below.

In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of SOS Smartcall produced in one day and number of SOS Basic produced in one day respectively, and then translate the word problem into algebraic equation as follows:

Based on the information provided about this cell phone company, the constraints can be written as a system of linear inequalities as follows;

x + y ≤ 180

x ≥ 40

y ≥ 40

3x + 4y ≤ 640.

75x + 60y ≤ 12,900

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The current age of Sam is 30 years and Harry is 10 years.

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. In every equation in math, we have, L.H.S = R.H.S (left hand side = right hand side). Equations can be solved to find the value of an unknown variable representing an unknown quantity. If there is no 'equal to' symbol in the statement, it means it is not an equation. It will be considered as an expression.

Let Sam's age be y years and Harry's age be x years.

Sam is currently three times harry's age.

The equation formed: y = 3x

Sam's age is also 10 more than twice harry's age.

The equation formed: y = 2x + 10

Substitute the value of y from first equation in second equation:

3x = 2x + 10

x = 10

Put the value of x in first equation:

y = 3x = 3*10 = 30

Thus, the current age of Sam is 30 years and Harry is 10 years.

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