Graph the circle whose equation is x^2 + y^2 =16

a. What is the center of this circle? Plot and label it on the graph.

b. What is the radius of this circle?

The graph in this problem is not a function, as it contains vertically aligned points.

The domain and the range are given as follows:

A graph represents a function if it has no vertically aligned points, that is, each value of x is mapped to only one value of y. Vertically aligned points mean that a value of x is mapped to multiple values of y, that is, a single input is mapped to multiple outputs which disqualify the relation as a function.

When we trace a vertical line through the circle, it would cross the circle at two points, meaning that the graph contains vertically aligned points, and thus, is not a function.

The domain and the range are defined as follows:

More can be learned about graphs and functions at https://brainly.com/question/12463448

#SPJ1

Answer:9th term is 0.078 approx.

Step-by-step explanation: the given sequence is decreasing by a factor of 2 each time.

so we can find 4th term :-

4th term= 5/2=2.5

similarly,we can find the term 5th,6th,7th,8th terms respectively:-

5th = 2.5/2=1.25

6th=1.25/2=0.625

7th=0.625/2=0.3125

8th=0.3125/2=0.15625

so 9th term is equal to 0.078.

Answer: 50 years.

Step-by-step explanation:

We can use the formula for simple interest to solve this problem:

I = P * r * t

where I is the interest earned, P is the principal amount, r is the interest rate as a decimal, and t is the time in years.

We can rearrange this formula to solve for t:

t = I / (P * r)

Substituting the given values, we get:

t = (500 - 312.5) / (312.5 * 0.04)

t = 625 / 12.5

t = 50

Therefore, it will take 50 years for an investment of Gh312.50 at 4% simple interest to amount to Gh500.00.

The solution for the system of linear equations is: x₁ = -1, x₂ = -3, x₃ = 3 and x₄ = -2

To solve this system of linear equations, we can use the Gaussian elimination method. First, let's represent the system as an augmented matrix:

|  1  0  2  0 |  5 |

|  0  1  0 -1 | -1 |

| -1 -1  1  0 |  1 |

|  0  0  2 -1 |  4 |

Add the first row to the third row to eliminate x₁ in the third row:

|  1  0  2  0 |  5 |

|  0  1  0 -1 | -1 |

|  0 -1  3  0 |  6 |

|  0  0  2 -1 |  4 |

Add the second row to the third row to eliminate x₂ in the third row:

|  1  0  2  0 |  5 |

|  0  1  0 -1 | -1 |

|  0  0  3 -1 |  5 |

|  0  0  2 -1 |  4 |

Divide the third row by 3

|  1  0  2  0 |  5 |

|  0  1  0 -1 | -1 |

|  0  0  1 -1/3 |  5/3 |

|  0  0  2 -1 |  4 |

Subtract twice the third row from the fourth row to eliminate x₃ in the fourth row

|  1  0  2  0  |  5  |

|  0  1  0 -1  | -1  |

|  0  0  1 -1/3 |  5/3 |

|  0  0  0 -1/3 |  2/3 |

Multiply the fourth row by -3 to get x₄

|  1  0  2  0  |  5  |

|  0  1  0 -1  | -1  |

|  0  0  1 -1/3 |  5/3 |

|  0  0  0  1  | -2  |

We can use back substitution to find the values of x₁, x₂, and x₃:

x₄ = -2

x₂ - x₄ = -1 which is x₂ = -1 + (-2) = -3

x₃ - (1/3)x₄ = 5/3 therefore; x₃ = 5/3 + (1/3)(-2) = 3

x₁ + 2x₃ = 5 therefore;  x₁ = 5 - 2(3) = -1

The above answer is in response to the full question below;

Solve this system of linear equations

x₁ + 2x₃ = 5

x₂ - x₄ = -1

-x₁ - x₂ + x₃ = 1

2x₃ - x₄ = 4

Find more exercises on linear equations;

https://brainly.com/question/29739212

#SPJ1

the volume of Alice's chicken coop in cubic meters is approximately 21.46 m³.

what is volume ?

Volume refers to the amount of space that an object or substance occupies in three-dimensional space. It is typically measured in cubic units, such as cubic meters (m³) or cubic feet (ft³), and is calculated by multiplying the length, width, and height of the object

In the given question,

To convert 758 cubic feet to cubic meters, we need to use the conversion factor:

1 ft³ = 0.3048³ m³

We can then multiply the volume in cubic feet by this conversion factor to get the volume in cubic meters:

758 ft³ × (0.3048 m/ft)³ = 21.46 m³ (rounded to two decimal places)

Therefore, the volume of Alice's chicken coop in cubic meters is approximately 21.46 m³.

To know more about volume , visit:

https://brainly.com/question/1578538

#SPJ1

The equation of the parabola in vertex form is y = (1/4)x² - 2.

A parabola is a symmetrical curve with a U- or smile-shaped shape. It is a particular kind of conic section, a shape created by cutting a cone with a plane.

The set of all points in a plane that are equally distant from a fixed point (referred to as the focus) and a fixed line is known as a parabola (called the directrix).

The vertex form of the equation of a parabola with vertex (h,k) is given by:

y = a(x - h)² + k

where "a" is a constant that determines whether the parabola opens up or down (if "a" is positive, the parabola opens up, and if "a" is negative, the parabola opens down).

We are given that the vertex of the parabola is (0,-2), so we have:

h = 0 and k = -2

We are also given that the parabola passes through the point (-8,14). We can use this information to find the value of "a". Substituting the coordinates of the point into the equation, we get:

14 = a(-8 - 0)² - 2

Simplifying:

14 = 64a - 2

16 = 64a

a = 16/64

a = 1/4

Now that we have found the value of "a", we can write the equation of the parabola in vertex form:

y = (1/4)x² - 2

Therefore, the equation of the parabola in vertex form is y = (1/4)x² - 2.

To know more about parabolas follow

https://brainly.com/question/13816752

#SPJ1

Answer: (D): The mean would decrease in value to about 23.3

Step-by-step explanation:

Step 1: Find the Original Mean

Mean = Sum/# of Numbers

Mean = 17 + 17 + 18 + 19 + 22 + 23 + 25 + 27 + 32 + 38/ 10 numbers

Mean = 238/10
Mean = About 23.8

Step 2: Add 18 to the original sum, divide that by 11 numbers

Mean = 238 + 18/11 numbers

Mean = 256/11

Mean = About 23.3

And so, Answer Choice (D) is correct

Answer:

Triangles in Geometry

Step-by-step explanation:

Answer: x = 2 and y = - 4 or (2,-4)

Step-by-step explanation:

Answer:

the height of the cylinder is 6 cm.

Step-by-step explanation:

Let's start by using the formulas for the volume of a cylinder and a cone:

Volume of a cylinder = πr^2h

Volume of a cone = (1/3)πr^2h

Given that the cylinder and cone have the same radius and volume, we can set their volume equations equal to each other:

πr^2h = (1/3)πr^2(18)

Simplifying this equation by canceling out πr^2 on both sides, we get:

h = (1/3) * 18

h = 6

Therefore, the height of the cylinder is 6 cm.2

Cassie has a total of 100 yellow flowers.

Given that one-fifth of the flowers are orange, a proportion can be used to find out how many flowers Cassie has in total.

Assuming x represent the total number of flowers Cassie has:

So Cassie has 125 flowers in total.

If 25 of them are orange, then the remaining flowers must be yellow:

125 - 25 = 100

Therefore, Cassie has 100 yellow flowers.

More on proportions can be found here: https://brainly.com/question/30675547

#SPJ1

Y and X can both be proportional if:

A. product is constant

B. quotient is constant

C. increase by x + 2

D. increase by 2x

Answer:

B

Step-by-step explanation:

The  fraction of prism with dimensions length=10cm , width= 5cm and height=5cm , made using two cubes of 5cm sides each filled with sand is  [tex]\frac{3}{5}[/tex]

What is a prism?

A three-dimensional solid shape or figure known as a prism has two ends that are identical or flat. Prisms are made up of equal cross-sections, flat faces, and congruent bases. The remaining faces of prism are parallelograms or rectangles. Another name for the rectangular prism is a cuboid.

Given that prism if formed using two identical cubes of side 5cm each. The prism so formed using two cubes will be a cuboid also known as rectangular prism.

Dinemsions of prism:

Length=5+5   { length of two cubes}

           =10 cm.

width= 5cm    {width of one cube}

height=5 cm   {height of one cube}

Volume of cuboid= Lengthx widthx height

                             =10 . 5 . 5

                             =250 cu. cm

Given that 150 cu. cm volume of prism is filled with sand.

Fraction of volume filled with sand =[tex]\frac{volume of sand}{total volume of prism}[/tex]

                                                         =[tex]\frac{150}{250}[/tex]

                                                         =[tex]\frac{15}{25}[/tex]

                                                         =[tex]\frac{3}{5}[/tex]

Fraction of volume filled with sand    =[tex]\frac{3}{5}[/tex]

To know more about prism, visit:

https://brainly.com/question/29722724

#SPJ1

Refer to the attachment for the complete question.

Answer:

Step-by-step explanation:

     | Male | Female | Total

------|------|--------|-------

Overweight | 15 | 36 | 51

Not Overweight | 85 | 64 | 149

------|------|--------|-------

Total | 100 | 100 | 200

Now, we can test the hypothesis that the two genders are homogeneous with respect to being overweight using a chi-square test. The null hypothesis is that there is no association between gender and overweight status.

The formula for the chi-square test is:

χ² = Σ [(O - E)² / E]

Where:

χ² = chi-square value

O = observed frequency

E = expected frequency

To calculate the expected frequency, we can use the formula:

E = (row total x column total) / grand total

Using this formula, we can calculate the expected frequencies for each cell of the contingency table:

     | Male | Female | Total

------|------|--------|-------

Overweight | 12.75 | 38.25 | 51

Not Overweight | 87.25 | 61.75 | 149

------|------|--------|-------

Total | 100 | 100 | 200

Now we can use the formula for the chi-square test to calculate the chi-square value:

χ² = [(15 - 12.75)² / 12.75] + [(36 - 38.25)² / 38.25] + [(85 - 87.25)² / 87.25] + [(64 - 61.75)² / 61.75]

χ² = 1.06 + 0.76 + 0.68 + 0.56

χ² = 3.06

Next, we need to determine the degrees of freedom (df) for our test. For a contingency table with r rows and c columns, the degrees of freedom are (r-1) x (c-1). In this case, we have 2 rows and 2 columns, so our degrees of freedom are:

df = (2-1) x (2-1) = 1

We can then use a chi-square distribution table or a statistical software program to determine the critical value of chi-square for our chosen level of significance and degrees of freedom. For a significance level of 0.05 and 1 degree of freedom, the critical value of chi-square is 3.84.

Since our calculated chi-square value of 3.06 is less than the critical value of 3.84, we fail to reject the null hypothesis. This means that there is not enough evidence to conclude that there is a significant association between gender and overweight status among diabetic patients.

the average temperature over the 8-hour period is 47°C, the minimum temperature is 32°C, and the maximum temperature is ? + 60°C

a) The average temperature can be found by integrating T(t) from 0 to 8 and dividing by the interval of integration:

Average temperature = (1/8) ∫T(t)dt from 0 to 8

= [tex](1/8) [∫(? + 4t + 32)dt from 0 to 8]= (1/8) [(?t + 2t^2 + 32t) from 0 to 8]= (1/8) [(?8 + 2(8)^2 + 32(8) - (?0 + 2(0)^2 + 32(0)))][/tex]

= (1/8) [(?8 + 128 + 256)]

= (1/8) [376]

= 47°C

Therefore, the average temperature over the 8-hour period is 47°C.

b) The minimum temperature occurs when the derivative of T(t) is equal to 0:

d/dt(T(t)) = 4

Setting this equal to 0, we find that the minimum temperature occurs at t = 0.

Therefore, the minimum temperature over the 8-hour period is T(0) = ? + 4(0) + 32 = 32°C.

c) The maximum temperature occurs when the derivative of T(t) is equal to 0:

d/dt(T(t)) = 4

Setting this equal to 0, we find that the maximum temperature occurs at t = 8.

Therefore, the maximum temperature over the 8-hour period is T(8) = ? + 4(8) + 32 = ? + 60°C.

In summary, we have found that the average temperature over the 8-hour period is 47°C, the minimum temperature is 32°C, and the maximum temperature is ? + 60°C. These results are useful in determining the overall temperature trend and can inform decisions related to temperature regulation or outdoor activities that may be influenced by the temperature.

To know more about average temperature click here:

brainly.com/question/31080273

#SPJ11

The value of x in the line segment is 6.

When lines intersects, angle relationships are formed such as vertically opposite angles, linear angles etc.

Therefore, let's find the angle x using the angle relationships formed as follows:

∠UJX + 90 + 6 = 180(sum of angles on a straight line)

∠UJX  = 180 - 96

∠UJX  = 84 degrees

Therefore,

∠UJX ≅ 14x (vertically opposite angles)

Vertically opposite angles are congruent.

Hence,

84 = 14x

divide both sides by 14

x = 84 / 14

Therefore,

x = 6

learn more on angles here: https://brainly.com/question/30114792

#SPJ1

This probability is approximately equal to [tex]1.07 * 10^-10.[/tex]

The total number of possible ways to arrange the 15 songs is 15!, which is a very large number. To find the probability that the first 3 songs in the playlist are the first 3 songs on the album in any order, we need to find the number of ways to arrange the first 3 songs on the album and divide it by the total number of possible arrangements.

Since the first 3 songs can be arranged in any order, we can use the permutation formula to find the number of ways:

P(3,3) = 3!

P(3,3) = 6

So there are 6 ways to arrange the first 3 songs on the album.

The total number of possible arrangements of all 15 songs is 15!, as mentioned earlier.

Therefore, the probability that the first 3 songs in the playlist are the first 3 songs on the album in any order is:

6 / 15!

This probability is a very small number, approximately equal to [tex]1.07 * 10^-10.[/tex]

To know more about probability visit:

https://brainly.com/question/30034780

#SPJ1

Step-by-step explanation:

4x²+32=4(x²+8)

56x³+7x²=7x²(8x-1)

6x⁴-4x²+14x=2x(3x³-2x+7)

18x³+27x-9=9(2x³+3x-1)

[tex]1.4 < \sqrt{2} < 1.5\hspace{5em}1.7 < \sqrt{3} < 1.8 \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{lllll} 1.7& < &\sqrt{3}& < &1.8\\\\ 1.7-\sqrt{2}& < &\sqrt{3}-\sqrt{2}& < &1.8-\sqrt{2}\\\\ 1.7-1.5& < &\sqrt{3}-\sqrt{2}& < &1.8-1.4\\\\ 0.2& < &\sqrt{3}-\sqrt{2}& < &0.4 \end{array}[/tex]

we're subtracting the upper-bound of √2, so is the most we can subtract from 1.7, and we're subtracting the lower-bound of √2 from 1.8, that way the resultant is within range.

Reason:

The domain is the set of allowed x inputs.

We look at the x coordinates of the endpoints.

The left-most point is when x = 2.

The right-most point is when x = 9.

The set of x values span between 2 and 9, including each endpoint. So we would say 2 ≤ x ≤ 9

[tex]\begin{array}{ccll} blueprint&actual\\ \cline{1-2} 1 & 40\\ 4& h \end{array} \implies \cfrac{1}{4}~~=~~\cfrac{40}{h} \implies h=160[/tex]

Answer:

160 inches

Step-by-step explanation:

a scale of 1:40 means that any measurement in the blue print is multiplied by 40 to find the actual measurement

so 4*40= 160 inches

Answer:

(2,3)

Step-by-step explanation:

look at where both lines intersect

2x - 1 = 5 - x

Combine like terms

2x + x = 3x

5 + 1 = 6

3x = 6

6 /3 = 2

X = 2

Put into both equation to find y and to make sure it’s true

Y =2x - 1

2(2) - 1

4 - 1 = 3

Y = 3

y = 5 - x

5 - 2 = 3

Y = 3

X=2 and y = 3

(2,3)

To solve a system of equations, we need to find the values of the variables that make both equations true simultaneously. Several methods for solving systems of equations include substitution, elimination, and graphing.

Substitution method:

Elimination method:

Graphing method:

Let's solve this using substitution and then verify with the graphing method:

To solve the system of equations y = 2x - 1 and y = 5 - x, we can substitute the expression 2x - 1 for y in the second equation and solve for x:

y = 5 - x

2x - 1 = 5 - x (substituting y = 2x - 1 for y)

3x = 6

x = 2

Now that we have found x = 2, we can substitute this value into either equation to solve for y:

y = 2x - 1

y = 2(2) - 1

y = 3

We can verify this with the graphing method by looking at where the two lines intersect. Upon inspecting the graph, the lines intersect at (2,3), verifying that the algebraic method was correct. Therefore, the solution to the system of equations is (2,3)

The $28.50 amount Jamie and Dana has to spend and the items that they bought expressed as an equation indicates;

An equation is a mathematical statement that indicates equivalence between two expression.

The amount Jamie and Dana takes to the concert = $28.50

The cost of hot dogs = $1.25

Cost of soft pretzels = $2.50

Cost of a water bottle = 50 cents
Let x represent the number of hot dogs and let y represent the number of soft pretzels Jamie and Dana bought together

The cost of the two water bottles they buy (one each) = 2 × 50 cents = $1

The equation that determines the number of hot dogs and soft pretzels they buy is therefore; 1.25·x + 2.50·y + 1 = 28.50

The graph of the equation can be found by making y the subject of the formula as follows;

1.25·x + 2.50·y = 27.50

2.50·y = 28.50 - 1 - 1.25·x

y = (27.50 - 1.25·x) ÷ 2.50 = 11 - 0.5·x

y = 11 - 0.5·x

The above equation is a linear function

The points on the graph are;

(0, 11), (2, 10), (4, 9), (6, 8), (8, 7), (10, 6), (12, 5), (14, 4), (16, 3), (18, 2), (20, 1), (22, 0)

Learn more on combinations and permutations here: https://brainly.com/question/28065038

#SPJ1

Answer:

Th expression would be 3x+4

Answer: = -26

Step-by-step explanation:

The machine has just been loaded with 850 cups. How many of these do you expect will overflow when served?

0.1587*850 = 134.857..

A vending machine automatically pours soft drinks into cups.

The amount of soft drink dispensed into a cup is normally distributed with a mean of 7.6oz and a standard deviation of 0.4oz.

Examine figure 7.- and answer the following questions.

a) estimate the probability that the machine will overflow an 8oz cup.

Procedure:

Determine the z-score for 8

z(8) = (8-7.6)/0.4 = 0.4/0.4 = 1

P(x>8) = P(z>1) = 0.1587..

-----------------------

b) Estimate the probability that the machine will not overflow an 8oz cup.

P(z<1) = 1 - 0.1587 = 0.8413..

-----------------

c) the machine has just been loaded with 850 cups. How many of these do you expect will overflow when served?

0.1587*850 = 134.857..; Rounded down you get 134 cups

Read more about probability here:

https://brainly.com/question/24756209

#SPJ1