what is the standard
form of a circle with a center of
(5,-2) and radius equal to 8

9514 1404 393

Answer:

Step-by-step explanation:

1. In this case, it appears that "some" means "4". The total cost of 4 place mats and 4 napkin rings is apparently ...

  $17.16 +10.36 = $27.52

Then the total cost of 1 of each is 1/4 this amount, or ...

  $27.52/4 = $6.88

__

2. The average of three numbers is their sum, divided by 3.

  (2.4 + 1.9 + 3.2)/3 = 7.5/3 = 2.5

Brian lost an average of 2.5 pounds per week.

Answer:

41.6666667 or 41 2/3 days

Step-by-step explanation:

There are 24 hours in a day. So you need to divide the hours by 24.

1000/24 is 41 and 2/3 days

Answer:

41.666667

Explanation:

Divide by 24 because 1 day is 24 hours

1000 / 24 = 41.666667

Answer:

The midpoint is ( 7,5)

Step-by-step explanation:

To find the x coordinate of the midpoint, add the x coordinate of the endpoints and divide by 2

( 4+10)/2 = 14/2 = 7

To find the y coordinate of the midpoint, add the y coordinate of the endpoints and divide by 2

(8+2)/2 = 10/2 = 5

The midpoint is ( 7,5)

The domain and range of the graph above in interval notation include the following:

Domain = [-6, 3]

Range = [-3, 3]

In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.

In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = [-6, 3] or -6 ≤ x < 3.

Range = [-3, 3] or -3 < y < 3

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Answer:

2500ml

Step-by-step explanation:

1litre=1000millilitres

2.5=?

=2.5×1000

=2500millilitres

Answer:

24

Step-by-step explanation:

subract 4 each time

As per arithmetic progression, the number comes after 28 in the given series is 24.

"An arithmetic progression is a sequence of numbers such that the difference between the consecutive terms is constant. "

The first term is = 40.

The common difference is (d) = 36 - 40 = 32 - 36 = 32 - 28 = - 4.

Here, the given series is in arithmetic progression.

Therefore, the next term after 28 is

= 28 - 4

= 24

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The two equations which can be used to represent the situation are;

r + s = 1787

4r + 3s = 5,792

The correct answer choice is option B and E

Reserved seat for basketball game = r

Students seat for basketball game = s

Cost of reserved seat tickets = $4

Cost of students tickets = $3

Total number of people who attended the basketball game= 1,787 people

Total amount earned for tickets sales= $5,792

r + s = 1787

4r + 3s = 5,792

Therefore, the basketball game situation can be represented by the equation r + s = 1787; 4r + 3s = 5,792

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The binomial expansion is solved and the error in Dakota's statement is the incorrect substitution of 36g^2h^2 for the correct expression

Given data ,

Dakota made a mistake because the third term of the expansion of (2g + 3h) should have been 36g2h2. The binomial theorem asserts that the expansion of (2g + 3h) is as follows:

( x + y )ⁿ = ⁿCₐ ( x )ⁿ⁻ᵃ ( y )ᵃ

Here, x = 2g and y = 3h. Since term numbers begin at 0, since we are seeking for the third term, r = 2.

So , on simplifying the equation , we get

= nC2 * (2g)⁽ⁿ⁻²⁾ * (3h)²

= (n! / (2! * (n - 2)!)) * (2g)⁽ⁿ⁻²⁾ * (3h)²

= ((n * (n - 1)) / 2) * (2g)⁽ⁿ⁻²⁾ * (3h)²

Hence , the correct expression for the third term of the expansion of (2g + 3h) is ((n * (n - 1)) / 2) * (2g)^(n - 2) * (3h)², where n is the exponent in the binomial expansion.

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Solution:

Given the triangle ABC as shown below:

To evaluate angle A,

Step 1: Identify the sides of the triangle ABC.

Thus, using A as the angle of focus,

Step 2: Write a trigonometric equation to measure A

Using trigonometric ratio,

Hence, the trigonometric equation is

Answer:

Step-by-step explanation:

To find the equation of a line that is perpendicular to a given line and passes through a specific point, we need to follow a few steps:

Find the slope of the provided line.

The point-slope form of a line is given by: y - y1 = m(x - x1), where (x1, y1) represents the given point.

Substituting the values, the equation of the perpendicular line becomes:

y - 5 = (-1/m)(x - 2)

Simplifying the equation further, we can rewrite it in point-slope form:

y - 5 = (-1/m)x + (2/m)

The set (A U B) n (A U C) is {2, 5, 7, 10}. A.

To find the set (A U B) n (A U C), we first need to calculate the union of sets A and B, and then calculate the union of that result with set C. Finally, we find the intersection of these two sets.

Set A U B:

The union of sets A and B, denoted as A U B, is the combination of all elements from both sets without any repetitions.

A contains the elements 2, 5, 7, and 10, while B contains the elements 1, 2, and 3.

A U B consists of the elements {1, 2, 3, 5, 7, 10}.

Set (A U B) U C:

Next, we calculate the union of the set (A U B) with set C, denoted as (A U B) U C. A U B contains the elements {1, 2, 3, 5, 7, 10} and C contains the elements {1, 2, 3, 4, 5}.

Taking the union of these two sets results in {1, 2, 3, 4, 5, 7, 10}.

Finding the intersection:

Finally, we find the intersection of (A U B) U C with A U C. A U C consists of the elements {2, 5, 7, 10}.

The intersection of these two sets is the combination of common elements.

The common elements are {2, 5, 7, 10}.

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Answer: None of these answers are correct.

Step-by-step explanation:

The triangles are congruent, meaning that by CPCTC, \(\angle BAC \cong \angle DE F\).

This means that as angles in a triangle add to 180 degrees,

\(60+45+x=180\\75+x=180\\x=105\)

The solution is: Piece-wise function

f(x)=x+6 , x≤1

f(x) = x^2 + 3 , x>1, the following functions is graphed below.

Option C is correct.

Explanation:

We are given a graph of piece-wise function which break at x=1

We need to choose correct option for graph.

Function is break at x=1.

We will get two function

For x≤1 and x>1

As we can see x≤1, graph is linear and x>1 graph is parabolic.

Equation of linear graph, x≤1

Take two point of graph (0,6) and (-6,0)

Equation of line:

y-y1/y2-y1 = x-x1/x2-x1

y = x+1

f(x)=x+6 , x≤1

Equation of parabolic graph, x>1

f(x) = x^2 + 3

Piece-wise function

f(x)=x+6 , x≤1

f(x) = x^2 + 3 , x>1

Please see the attached figure.

Hence, The option C is correct.

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Using the concept of word problems and quadratic equation it will take 1 year until the sum of square of their ages be 45.

Word problems are mathematical problems that are delivered in ordinary words, instead of mathematical symbols.

Part of the problem with dealing with word problems that they first need to be translated into mathematical equations, and then the equations need to be solved.In this problem;

let x represent the number of years from now when the sum of square of their respective age will be

45.(x + 2)² + (x + 5)² = 45

Expanding the brackets;

x² + 4x + 4 + x² + 10x + 25 = 45

2x² + 14x + 29 = 45

2x² + 14x + 29 - 45 = 0

2x² + 14x - 16 = 0

Solving the quadratic equation for x;

x = 1, x = -8

Taking the positive value, the value of x is 1

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Answer:

Step-by-step explanation:

Answer:

2, 8 and 14

is this for the subject math

Answer:

then daniel has to pay $7630 dollars

Step-by-step explanation:

The value of x make the two expressions equal is -2.2

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

(x+3)(x+8)= 3/5(x+8)

Divide both sides of the equations by x + 8

So, we have the following representation

x + 3 = 3/5

Multiply through the equation by 5

So, we have

5x + 15 = 3

This gives

5x = -12

Divide both sides by 5

x = -12/5

Evaluate the quotient

x = -2.2

Hence the value of x is -2.2

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Answer:

To complete the transactions in your register:

Beginning balance on October 1: $542.89

On October 7, you pay Land Electric $43.90. This is a check transaction and the check number is 400. To record this in your register, you would subtract $43.90 from your current balance, which would bring your new balance to $498.99.

On October 23, you deposit your paycheck. To calculate your paycheck, you would multiply your hourly wage ($7.25) by the number of hours worked (40) by the number of weeks (2). This would give you a gross pay of $1140. Then, you would calculate the deductions: FICA (7.65%), federal withholding (12%), and state withholding (8.75%). To do this, you would multiply your gross pay by the percentage for each deduction and then subtract that amount from the gross pay. Your final paycheck would be $1140 - $87.41 (FICA) - $136.8 (federal withholding) - $100.65 (state withholding) = $815.34. To record this in your register, you would add $815.34 to your current balance, which would bring your new balance to $1314.33

On October 24, you buy $78.54 in clothes from FitRight and pay 6% sales tax. To calculate the sales tax, you would multiply $78.54 by 0.06 and add that amount to the total cost of the clothes. The total cost of the purchase including sales tax would be $78.54 + $4.71 = $83.25. To record this in your register, you would subtract $83.25 from your current balance, which would bring your new balance to $1231.08

The balance as of October 24 would be $1231.08

In the register

10/1 Beginning balance $542.89

10/7 Check #400 Land Electric -$43.90

10/23 Paycheck $815.34

10/24 Debit FitRight -$83.25

Ending balance $1231.08

Step-by-step explanation:

ABOVE

Answer:

Step-by-step explanation:

A heptagon is a polygon with 7 sides.

Sum of all angles of a polygon with n sides = 180(n-2) = 180 x 5 = 900°

So, the degree of each angle will be 900/7 = 128.57 or ≈129°.

Thanks

The expression that is equivalent to the expression 2ˣ⁺⁴ is 16(2ˣ)

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

2ˣ⁺⁴

The above expression is an exponential expression with the following properties

When the above expression is expanded, we have

2ˣ⁺⁴ = 2ˣ * 2⁴

Evaluate the expression 2 exponent 4

So, we have the following representation

2ˣ⁺⁴ = 2ˣ * 16

Rewrite as follows

2ˣ⁺⁴ = 16 * 2ˣ

This gives

2ˣ⁺⁴ = 16(2ˣ)

Hence, the expression that is equivalent to the expression is 16(2ˣ)

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Solution

For this case we can create the following plot:

We want to find the work so we can use this formula:

Replacing we got:

9: What is the probability of beef tips being the preferred new menu item?

To find the probability of a customer preferring beef tips over the other menu items, divide the quantity of customers that preferred beef tips over the total number of customers that participated in the survey:

28 / (42 + 28 + 30) = 28/100 = 28%

There is a 28% chance that beef tips is the new preferred menu item.

11: Out of a similar group of 375 customers, predict how many more customers will prefer chicken carbonara to shrimp scampi.

There are 100 customers that participated in the pre-existing survey. A grand total of 375 participants in a similar survey would mean that each food's preference would grow in a similar fashion.

100 * 3.75 = 375

You can then multiply each response group by 3.75 to find how many people prefer chicken carbonara and shrimp scampi.

42 * 3.75 = 157.5

30 * 3.75 = 112.5

Then, subtract the quantities to find out how many more people prefer chicken to shrimp.

157.5 - 112.5 = 45 people.

13: Predict the number of times that Giorgianna's name will be drawn in 32 weeks. Round to the nearest whole number.

There are five people in the group, and one is chosen as the team leader every week. 1 divided by 5 is .2, so the probability of being chosen as team leader is 20%.

You can multiply 0.2 by 32 to represent how many times the experiment will be run. The product is 6.4 times, so Giorgianna's name will likely be drawn 6 times within 32 weeks.

Answer:

9.) 7/ 25. 11). 45. 13) 6

Step-by-step explanation:

Explanation shown below;

For 13;

The probability of chosen Georgianna is 1/5

The number of times the draw would be conducted would be 32

Hence Georgianna would be chosen [ 1/5. * 32 = 6. 4 = 6[to the nearest whole]

The rectangular coordinate from the given polar coordinate is (2.73, -0.73)

To find the rectangular coordinate from the polar coordinates, we can rewrite this as;

x = r cosθ

y = r sinθ

x = r cosθ

Let's substitute the values into it;

x = (2√2)* cos(-π/12)

x =(2√2)cos(-15)

x = √3 + 1

x = 2.73

y = r sin θ

y = (2√2)sin(-π/12)

y = (2√2) * sin (-15)

y = -√3 + 1

y = -0.73

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Answer:

\(x = 31\)

Step-by-step explanation:

\(5x - 16 + x + 10 = 180\)

\(5x + x = 180 + 16 - 10\)

\(6x = 186\)

\( \frac{6x}{6} = \frac{186}{6} \)

\(x = 31\)

A randomized experiment with order, replacement, and no repetition is one in which the order of the outcomes matters, the same outcome can occur multiple times, and no outcome can occur more than once.

For example, drawing a card from a deck and then flipping a coin would be a random experiment with order, replacement, and no repetition. The order of the results is important because the outcome of the coin toss will depend on the outcome of the card draw.

The same result can occur multiple times because the same card can be drawn twice, and no result can occur more than once because the coin can only land heads or tails once.

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Random experiment with order, replacement and without repetition

The Total Probability is 4/663 and 35/2652

What is Probability?

Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. An event's probability is a number between 0 and 1.

Solution:

We know that there are 52 cards in a deck of cards.

So, probability of getting a king = 4/52 = 1/13

And probability of getting a 7 after drawing a king is 4/51,

this is because one card is drawn out from the deck and there are only 51 cards left in the deck.

Total Probability = 1*4/13*51 = 4/663

In the secon case, there are two possibilities,

It can be the kling drawn might be of spade or not

Case 1: When King drawn is of Spade

Probaility of drawing a King of Spade = 1/52

Probability of drawing a Spade after King of Spade is drawn = 11/51

Total Probaility = 1*11/52*51 = 11/2652

Case 2: When King drawn is not of Spade

Probability of drawing a King not of Spade = 2/52

Probability of drawing a Spade after drawing the King = 12/51

Total Probability = 2*12/51*52 = 24/2652

Total Probability of drawing a king and spade = 11/2652 + 24/2652 = 35/2652

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Answer:

the square root of 20 is 4.472135955

Step-by-step explanation:

The profit function is P(x) = -500.523x^2 + 600x - 200.

To find the profit function, P(x), we need to subtract the cost function, C(a), from the revenue function, R(x).

Given:

Cost function: C(a) = 500x^2 + 300

Revenue function: R(x) = -0.523x^2 + 600x - 200 + 300

Profit function, P(x), is obtained by subtracting the cost function from the revenue function:

P(x) = R(x) - C(a)

P(x) = (-0.523x^2 + 600x - 200 + 300) - (500x^2 + 300)

Simplifying the expression:

P(x) = -0.523x^2 + 600x - 200 + 300 - 500x^2 - 300

P(x) = -500x^2 - 0.523x^2 + 600x + 300 - 200 - 300

P(x) = -500x^2 - 0.523x^2 + 600x - 200

Combining like terms:

P(x) = (-500 - 0.523)x^2 + 600x - 200

Simplifying further:

P(x) = -500.523x^2 + 600x - 200

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