Dominick is planning to take a vacation to either Orlando or Tampa Bay. He wants to go to the city that is warmer, on average. The box plot below shows the temperatures from the previous year during the time that Dominick will take his vacation: box plot labeled Orlando with min at 64.5, Q1 at 65.5, median at 67.5, Q3 at 71.5, max at 72.5. Box plot labeled Tampa Bay with min at 60, Q1 at 63.5, median at 66.25, Q3 at 72.5, max at 74 Which city should Dominick visit, and why?

Answer: a. Circle

Step-by-step explanation:

Given equation: [tex](x-8)^2+(y-12)^2=25[/tex] which is equivalent to [tex](x-8)^2+(y-12)^2=5^2[/tex]

This equation is of the form [tex](x-h)^2+(y-k)^2=r^2[/tex] which is the standard equation of a circle centered at (h,k) with radius r.

On comparing given equation to the standard equation of  circle we have, h=8 and k=12 and r =2.

Therefore, given equation represent a circle centered at (8,12) and radius=5 units.

Final answer:

Using the two given points $(82, 4)$ and $(42, 9)$, the slope is calculated to be $-1/8$. Subsequently, by using the point-slope form of the line equation and simplifying, we find that the linear relationship between price and demand is described by $y = -1/8x + 57/4$, which corresponds to choice A.

Explanation:

To determine the linear equation that best models the price-demand relationship for the mini-recorders, we are given two points. At a price of $82, the demand is 400 recorders (4 hundred), and at a price of $42, the demand is 900 recorders (9 hundred). In the mathematical representation, these points are (82, 4) and (42, 9), where x is the price and y is the demand in hundreds.

To find the slope (m) of the line, we use the slope formula:

m = (y2 - y1) / (x2 - x1), which gives us m = (9 - 4) / (42 - 82) = 5 / (-40) = -1/8.

Now, we can use the point-slope form to find the equation of the line. Let's use the point (82, 4):

y - y1 = m(x - x1)

y - 4 = (-1/8)(x - 82)

Multiplying out the right-hand side of the equation, we have:

y - 4 = (-1/8)x + (82/8)

y - 4 = (-1/8)x + 10.25

Moving 4 to the other side to get 'y' by itself, the equation becomes: y = (-1/8)x + 10.25 + 4

This simplifies to:

y = (-1/8)x + 14.25

Converting 14.25 into quarters gives us 14.25 = 57/4. Hence the equation becomes:

y = (-1/8)x + 57/4 which matches choice A.

Final answer:

The correct equation that models the price-demand relationship is y = -1/8x + 57/4, where y is the demand in hundreds and x is the price per mini-recorder.

Explanation:

To find the equation that models the price-demand relationship, we need two points to determine the line: (x1, y1) = (82, 4) and (x2, y2) = (42, 9). The demand, y, is in hundreds of recorders and x represents the price per mini-recorder. The slope (m) of the line is given by the change in demand over the change in price: m = (y2 - y1) / (x2 - x1) = (9 - 4) / (42 - 82) = 5 / (-40) = -1/8. To find the y-intercept (b), we use one of the points and the slope in the linear equation formula y = mx + b. Using the point (82, 4), we have 4 = (-1/8)(82) + b. Solving this equation gives us b = 4 + (1/8)(82) = 4 + 10.25 = 14.25. Now the linear equation is y = -1/8x + 14.25. Since y needs to be in hundreds for the units to match the point given (400, 900), we must divide b by 100, resulting in b = 14.25 / 100 = 57/4. The final price-demand relationship is y = -1/8x + 57/4.

Final answer:

Sonya's annual take-home pay, after FICA taxes of 7.65% on her annual salary of $36,590, would be $33,790.86.

Explanation:

To calculate Sonya’s annual take-home pay after FICA taxes, we first need to understand that FICA consists of two separate taxes: Social Security and Medicare. The total rate for these combined is 7.65% of the gross income. Sonya’s annual salary is $36,590.

First, we calculate the total FICA tax Sonya has to pay:

Add these two amounts to get the total FICA tax:

$2,268.58 (Social Security) + $530.56 (Medicare) = $2,799.14

Finally, subtract this total FICA tax from the annual salary to find Sonya’s take-home pay:

$36,590 (annual salary) - $2,799.14 (FICA taxes) = $33,790.86

 2 x 2 = 4 x 3 = 12

2 x 3 = 6 x 3 = 18

2 x 2 = 4 x 2 = 8 x 3 = 24 x 3 = 72

2x2 = 4 x 3 = 12 x 3 = 36

 last one is the correct answer

The variable c = 5 meaning we can replace the value of c in the equation with 5. Solve the equation now as you normally would.

3 (5) + 17 = 15 + 17 = 32

The answer is 32 and if this helps please give brainliest to help me reach expert ;)

Marie's total earnings for the two weeks were $525. She paid $262.5 to taxes and $131.25 to college tuition, leaving her with a balance of $131.25.

To find out the amount left, we need to first calculate Marie's total earnings for the two weeks by adding what she earned each week. $280 for the first week plus $245 for the second week gives her a total earnings of $525.

Marie gave half of her earnings to taxes, which is 0.5 * $525 = $262.5. After that, she spent one-fourth of her earnings on college tuition, which equals 0.25 * $525 = $131.25. Summing up both amounts, we find that she spent $262.5 + $131.25 = $393.75 on taxes and tuition.

To find out the amount Marie has left, we subtract the total expenses from her total earnings. Thus, $525 - $393.75 = $131.25 is the total amount she has left after paying her taxes and tuition.

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After calculating her total earnings, subtracting the amounts for taxes and tuition, Marie had $131.25 left. Her total earnings were $525. 1/2 went to taxes, and 1/4 went to tuition.

First, find her total earnings for the two weeks:

Total Earnings = $280 + $245 = $525

Next, calculate how much went to taxes. Since 1/2 of her total earnings went to taxes:

Taxes = 1/2 x $525 = $262.50

Then, calculate how much went to college tuition. Since 1/4 of her total earnings went to tuition:

College Tuition = 1/4 x $525 = $131.25

Finally, subtract the amounts for taxes and tuition from her total earnings to find out how much money she had left:

Money Left = $525 - $262.50 - $131.25 = $131.25

Marie had $131.25 left after paying taxes and college tuition.

To convert a fraction to a decimal, divide the numerator by the denominator. For example, 1/2 converted to a decimal is 0.5.

To convert a fraction to a decimal, you use the method defined by option B: Numerator divided by Denominator (Numerator / Denominator). This will give you the decimal equivalent of the fraction. For example, if you have the fraction 1/2, you divide the numerator (1) by the denominator (2) to get 0.5, which is the decimal equivalent of the fraction 1/2.

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The two linear equations represented in system A as :

3 x + 2 y =3   -------(1)

- 2 x - 8 y = -1  ------(2)

(1) × 2 + (2) × 3 gives

⇒ 6 x + 4 y - 6 x - 24 y = 6 -3

⇒ - 20 y = 3

⇒ y = [tex]\frac{-3}{20}[/tex]

Putting the value of y in equation (1), we get

[tex]3 x  - \frac{6}{20}=3\\\\ 3 x= \frac{66}{20} \\\\ x=\frac{11}{10}[/tex]

Two linear equation represented in system B is:

3.   -x - 14 y =1

4.   - 2 x - 8 y = -1

-2 ×Equation (3) + Equation (4)=

2 x +28 y- 2 x - 8 y= -2 -1

⇒ 20 y = -3

⇒y =[tex]\frac{-3}{20}[/tex]

Putting the value of y in equation (3),we get

[tex]-x + \frac{42}{20}=1 \\\\ x=\frac{22}{20}=\frac{11}{10}[/tex]

As Two system , that is system (A) and System (B) has same solution.

By looking at all the options , i found that Option (D) is correct. The two system will have the same solution because the first equation of System B is obtained by adding the first equation of System A to 2 times the second equation of System A.

Answer:

(D)

Step-by-step explanation:

Two linear equations by system A is given as:

[tex]3x+2y=3[/tex]           (1)

[tex]-2x-8y=-1[/tex]          (2)

Multiply equation (1) with 2 and equation (2) with 3 and then adding, we get

[tex]6x+4 y-6x-24y=6-3[/tex]

[tex]-20y=3[/tex]

[tex]y=\frac{-3}{20}[/tex]

Putting the value of y in equation (1), we get

[tex]3x-\frac{6}{20}=3[/tex]

[tex]3x=\frac{66}{20}[/tex]

[tex]x=\frac{11}{10}[/tex]

Two linear equations by system B is given as:

[tex]-x-14y=1[/tex]       (3)

[tex]-2x-8y=-1[/tex]     (4)

Multiply equation (3) with -2 and adding equation (4), we get

[tex]2x+28y-2x-8y=-2-1[/tex]

[tex]20y=-3[/tex]

[tex]y=\frac{-3}{20}[/tex]

Putting the value of y in equation (3),we get

[tex]-x+\frac{42}{20}=1[/tex]

[tex]x=\frac{11}{10}[/tex]

As Two system , that is system (A) and System (B) has same solution.

Thus,  Option (D) is correct. The two system will have the same solution because the first equation of System B is obtained by adding the first equation of System A to 2 times the second equation of System A.

Answer:

The total affect of the decrease in the interest rate = $29400

Step-by-step explanation:

The initial amount of money which has been deposited into the account = $30000

The rate at which the initial money was deposited = 7%

But it is given that the federal reserve decreases the reserve rate from 7% to 5%

Now, we need to find the affect of this decrease on the deposited money

The rate of change in the interest rate = 7 - 5 = 2%

So, The affect of this decrease = 2% of 30000

                                                    = $600

So, The money becomes = 30000 - 600

Therefore, The total affect of the decrease in the interest rate = $29400

The slope of the line that contains the given points T(6, 3) and V(8, 8) will be 2.5.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The slope of the line is given as,

m = (y₂ - y₁) / (x₂ - x₁)

The points are given below.

T(6, 3) and V(8, 8)

The slope is given as,

m = (8 - 3) / (8 - 6)

m = 5 / 2

m = 2.5

The slope of the line will be 2.5.

More about the linear equation link is given below.

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volume = PI x r^2 x h

using 3.14 for pi

volume = 3.14 x 2^2 x 3

volume = 37.7 cubic cm of wax needed

Round answer as needed

Answer:

12Pi cm3

Step-by-step explanation:

Answer:

The Answer Is A. edge 2020

Step-by-step explanation:

Answer:

The answer is the B)

Step-by-step explanation:

By the definition, in a function, a value in the first set of numbers only have a value in the second set of numbers, so for every pair of numbers, we have to review if the first number for this pair only appears one time in all the function.

All the set ot values agrees with this definition except the B, because the third and fourth pair have the same first value (3)

Answer:

Option a is correct.

Step-by-step explanation:

The given graph is of  the function f(x)=|x|-2

Domain are the values that x will take  in the given function x can take all the values whether fraction, integer the function will always be defined.

Hence, the domain of the function is all real numbers.

Therefore, Option a is correct.

Answer: Domain are all real number [a].

Step-by-step explanation:

Given : graph .

To find : what is the domain of the function on the graph.

Solution : We have given that a graph of function f(x) : |x| - 2.

Domain : The domain of a function is the set of its possible inputs,that is  the set of input values where for which the function is defined.

Therefore, the domain are all real number [a].

Running Speed = x
Cycling Speed = x + 9
19.5/x + 9 = 6/x
Cross multiply
19.5x = 6x + 54

19.5x - 6x = 54
13.5x = 54
x = 4
she runs 4 mph

Answer:

4 mph

Step-by-step explanation:

Final answer:

A straight line is determined by a minimum of two points. This is a fundamental concept in geometry and algebra, necessary for defining lines on any two-dimensional path or graph.

Explanation:

To determine the minimum number of points through which a straight line is drawn, we need to understand that a straight line is defined by only two points.

The minimum number of points through which a straight line is drawn is two. In geometry, a line extends infinitely in both directions but is determined by just two points. The concept of a line is fundamental in understanding various subjects such as algebra and geometry.

Answer:

The LCM of given expressions is [tex]72a^3b^2[/tex].

Step-by-step explanation:

The given expressions are

[tex]24a^3b[/tex]

[tex]36ab^2[/tex]

Find factor form of each expression.

[tex]24a^3b=2\times 2\times 2\times 3\times a\times a\times a\times b[/tex]

[tex]36ab^2=2\times 2\times 3\times 3\times a\times b\times b[/tex]

LCM is the product of all factors where common factors are considered only once.

[tex]LCM(24a^3b,36ab^2)=2\times 2\times 2\times 3\times 3\times a\times a\times a\times b\times b[/tex]

[tex]LCM(24a^3b,36ab^2)=72a^3b^2[/tex]

Therefore the LCM of given expressions is [tex]72a^3b^2[/tex].