Antoine manages a number of apartment buildings that use natural gas for heating, cooking, and laundry. The scatter plot shows the correlation between the outside air temperature and Antoine’s natural gas bill. Which type of correlation does the plot illustrate? A. strong negative B. strong positive C. weak negative D. weak positive Scatter plot is attached

Answer:

D

Step-by-step explanation:

Any ellipse has the following equ

ation:

[tex] \frac{ {x}^{2} }{ {a}^{2} } + \frac{ {y}^{2} }{ {b}^{2} } = 1[/tex]

where

(as in the picture)

So it should be like:

[tex] \frac{ {x}^{2} }{ { (\frac{6}{2} )}^{2} } + \frac{ {y}^{2} }{ {( \frac{4}{2} )}^{2} } = 1 \\ \frac{ {x}^{2} }{ 9} + \frac{ {y}^{2} }{ 4 } = 1[/tex]

Since it should be moved to the right and up, the answer would be:

[tex]\frac{ {(x - 5)}^{2} }{ 9} + \frac{ {(y - 1)}^{2} }{ 4 } = 1[/tex]

Option D. (x - 5)²/9 + ( y - 1 )²/4 = 1

An ellipse has the following equation:

x²/a² + y²/ b² = 1

where

2b = vertical axis length

2a = horizontal axis length

So it should be like:

x²/(6÷2)² + y²/ (4÷2)² = 1

x²/9 + y²/4 = 1

Since it should be moved to the right and up, the answer would be:

(x - 5)²/9 + ( y - 1 )²/4 = 1

Please check the attached diagram for more details.

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Answer:

A(sector) = (1 - 1/9)πr² = (17/2)π

(8/9)r² = 17/2

r = √((17/2)(9/8)) = (1/4)√153

= (3/4)√17

A(circle) = π((3/4)√17)² = 17(9/16)π

= (153/16)π

Answer

34.5 inches

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let b and s represent the weights of the big and small boxes, respectively. Then the two delivered weights can be summarized as ...

  5b +6s = 187

  3b +2s = 87

We can eliminate the "s" variable by subtracting the first equation from 3 times the second:

  3(3b +2s) -(5b +6s) = 3(87) -(187)

  4b = 74 . . . . . collect terms

  b = 18.5 . . . . . divide by 4

Using this value in the second equation, we find ...

  3(18.5) +2s = 87

  2s = 31.5 . . . . . . . . subtract 55.5

  s = 15.75 . . . . . . . . divide by 2

The large box weighs 18.5 kg; the small box weighs 15.75 kg.

Answer:

No, not a solution

Step-by-step explanation:

Step 1:  Check if solution

y = 3x + 5

-1 = 3(4) + 5

-1 = 12 + 5

-1 = 17

DOES NOT EQUAL

Answer: No, not a solution

Answer:

D) Each additional day is associated with an additional 17.5 grams of mass.

Step-by-step explanation:

Slope = 17.5

= change in mass/change in day

Which is 17.5 g increase in 1 day

Answer:

its d!

Step-by-step explanation:

Answer:

[tex]SA=54\pi\ units^2[/tex]

Step-by-step explanation:

we know that

The surface area of the cone is given by the formula

[tex]SA=\pi r^{2}+\pi rl[/tex]

where

r is the radius of the base

l is the slant height

we have

[tex]r=3\ units\\l=15\ units[/tex]

substitute

[tex]SA=\pi (3)^{2}+\pi (3)(15)[/tex]

[tex]SA=54\pi\ units^2[/tex]

[tex]\frac{9\pi }{5}[/tex] radians is equal to [tex]324[/tex]° .

Step-by-step explanation:

Degrees are a unit of angle measure. A full circle is divided into 360 degrees. For example, a right angle is 90 degrees. A degree has the symbol ° and so ninety degrees would written 90°. Another unit of angle measure is the radian.

The radian is the SI unit for measuring angles, and is the standard unit of angular measure used in many areas of mathematics. The length of an arc of a unit circle is numerically equal to the measurement in radians of the angle that it subtends; one radian is just under 57.3 degrees.

We know that 1 radian = 180°/[tex]\pi[/tex] . So [tex]\frac{9\pi }{5}[/tex] radians is equal to :

⇒ [tex]\frac{9\pi }{5}(\frac{180}{\pi } )[/tex]

⇒ [tex]\frac{9(180) }{5}[/tex]

⇒ [tex]9(36)[/tex]

⇒ [tex]324[/tex]°

Therefore , [tex]\frac{9\pi }{5}[/tex] radians is equal to [tex]324[/tex]° .

To convert 9pi/5 radians to degrees, multiply by the conversion factor of 180°/π, resulting in 324 degrees.

To convert the angle 0 = 9pi/5 radians to degrees, we need to use the relationship between radians and degrees. Recall that 360° = 2π radians. Consequently, to convert radians to degrees, we can multiply by a conversion factor of 180°/π. Using this conversion factor, the computed angle in degrees is:

9π/5 radians × (180°/π) = 9/5 × 180° = 9 × 36° = 324°

Therefore, the angle of 9π/5 radians is equivalent to 324 degrees.

Answer: 49.8 is the answer

Step-by-step explanation:

Answer:

(-4, -1)

Step-by-step explanation:

x = 4y

-4x - y = 17

Plug in 4y for x in the second equation:

-4(4y) - y = 17

Simplify. Remember to follow PEMDAS. Isolate the variable, y. Note the equal sign, what you do to one side, you do to the other.

First, multiply 4y with -4:

-4(4y) = -16y

-16y - y = 17

Simplify. Combine like terms:

-16y - y = 17

-17y = 17

Isolate the variable, y. Divide -17 from both sides:

(-17y)/-17 = (17)/-17

y = 17/-17

y = -1

Plug in -1 for y in the first equation:

x = 4y

x = 4(-1)

x = -4

x = -4, y = -1

Answer: (-4, -1)

~

Answer: 398cm²

Step-by-step explanation:

Surface area of a Rectangular Prism: 2lw+2lh+2wh

l= 5cm

w= 9cm

h= 11cm

Area= (2x5x9)+(2x5x11)+(2x9x11)

      =398cm²

Answer:

(3, -2) or (3, 2)

Step-by-step explanation:

Please see the attached pictures for full solution.

Answer:

Fourth answer choice.

Step-by-step explanation:

Start by factoring the numerator and the denominator:

(x - 1)(x + 1)

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

(x + 1)(x + 4)

Note that x can be neither -1 nor -4, since either results in an undefined quotient.  These two x-values are critical values because of this.  If we cancel the (x + 1) terms, we obtain the result

(x - 1)

--------- for x ≠ -1 and x ≠ - 4

(x + 4)

The next step is to evaluate the given quotient on the three intervals defined by {-4, -1}:  (-∞, -4), (-4, -1), (-1, ∞ ).  We choose an x-value from within each interval and evaluate the given function at each.  Suitable test values include {-10, -3, 0}:

At x = -10, the reduced given quotient (x - 1) / (x + 4) takes on the value  (-10 - 1) / (-10 + 4) = -11/(-6), which is positive.  Reject this interval, as we want and expect the quotient value to be 0 or less.

At x = -3, we get (-3 - 1) / (-3 + 4), which is negative.  The given inequality is true on the interval (-4, -1) (or -4 < x < -1).

At x = 0, we get (0 - 1) / (0 + 4), which is negative, so the inequality is true on (-1, ∞ ).

So the fourth answer choice is the correct one.

Answer:

Answer D

Step-by-step explanation:

Answer: approximately 102.8 times farther

Step-by-step explanation: If you divide the distance of Mercury to the Sun (3.6E7) from the distance of Pluto to the Sun (3.7E9) you get 102.777777. That is the approximate distance. Rounded you get 102.8

Answer: The amount of interest owed is $598.82.

Step-by-step explanation: 7.9% of $1,895 is 149.705. So, 149.705 x 4 years would be $598.82 for 4 years.

Final answer:

The total interest owed on a $1,895 loan at a 7.9% interest rate over 4 years is calculated using the formula for simple interest, resulting in a total interest amount of $598.43.

Explanation:

To find the amount of interest owed on a $1,895 loan for 4 years at a 7.9% interest rate, you can use the formula for calculating simple interest, which is Interest = Principal × Rate × Time. The principal (P) is $1,895, the rate (r) is 7.9% or 0.079 when expressed as a decimal, and the time (t) is 4 years.

So the calculation would be:
Interest = $1,895 × 0.079 × 4

Let's perform the calculation:

Interest = $1,895 × 0.079 × 4 = $598.43

The total interest owed on the loan after 4 years would be $598.43.

Answer:

a) 8x

b)2+12y

Step-by-step explanation:

Answer:

5X+3X & 8X For the first one

and 2+12y for the second one i believe those are correct let me know in the comments below

Step-by-step explanation:

hope this helps have a great day

Answer:

b=58

Step-by-step explanation:

b-12=46

b=46+12

b=58

Answer: The equations are as follows;

5p + 4d = 43.25 ————(1) and

3p + 2d = 24.25 ————(2)

Also a bag of popcorn costs $5.25

Step-by-step explanation: We start by assigning letters to the unknown variables. Let a bag of popcorn be p and let one drink be d. The clues given in the question include the cost of buying five bags of popcorn and four drinks which is a total of $43.25. This can be expressed as

5p + 4d = 43.25 ————(1)

Another clue is that three bags of popcorn and two drinks cost $24.25. This also can be expressed as

3p + 2d = 24.25 ————(2)

Now we have a pair of simultaneous equations as follows

5p + 4d = 43.25 ————(1)

3p + 2d = 24.25 ————(2)

We shall use the elimination method since all the unknowns have coefficients greater than 1. Multiply equation one by 3, and multiply equation two by 5 (so as to eliminate ‘p’)

5p + 4d = 43.25 ——— x3

3p + 2d = 24.25 ——— x5

15p + 12d = 129.75 ———(3)

15p + 10d = 121.25 ———(4)

Subtract equation (4) from equation (3) and we have

2d = 8.5

Divide both sides of the equation by 2

d = 4.25.

That means each drink costs $4.25

We can now substitute for the value of d into equation (2)

3p + 2d = 24.25

When d = 4.25

3p + 2(4.25) = 24.25

3p + 8.5 = 24.25

Subtract 8.5 from both sides of the equation

3p = 15.75

Divide both sides of the equation by 3

p = 5.25. This means a bag of popcorn costs $5.25

Answer:

21.75

Step-by-step explanation:

i hoped this helped.  14.50 divide-by 2 = 7.25 so 14.50 + 7.25= 21.75

Answer:

Step-by-step explanation:

Answer:

80

Step-by-step explanation:

Simply radical 16 which will give you 4, then multiply 4 by 20 which equals 80

The volume of the ball is 24,400 cm³

Step-by-step explanation:

Volume of the ball = 4/3 πr³

                               = 4/3 × 3.14 × (18)³

                               = 24,416.64 cm³ ≈ 24,400 cm³ (nearest hundredth)

In physics, work is defined force that causes displacement. So this can be expressed by the following equation:

[tex]W=Fs[/tex]

Where:

[tex]F:Force \\ \\ s:Displacement[/tex]

The force can be found as:

[tex]F=ma \\ \\ F=5(10)=50N[/tex]

And for the displacement:

[tex]s=6-2=4m[/tex]

The force (weight) is down and the displacement is up, then the work must be negative. So:

[tex]W=-(50)(4) \\ \\ \boxed{W=-200J}[/tex]

Answer:

780 people

Step-by-step explanation:

65% of 1,200 is 780

Answer:

780

Step-by-step explanation:

To find the % of something simply convert 65% to a decimal > .65 then 1,200*.65=780

Answer:

900

Step-by-step explanation:

5 * 180

(5 * 100) + (5 * 80) + (5 * 0)

500 + 400 + 0

900

Answer:  900

Answer:

C) Going from A to C to D and it is shorter by 3 miles.

Step-by-step explanation:

Angles  

AB is 6 miles

BD is _12__ miles

AC is 5 miles

CD is 10 miles

First you need to find BD, so AB times CD. 6(10) = 60. then divide 60 with AC. 60/5 = 12. So  BD = 12.  

Now add  

AB and BD,  

{ 6+ 12 = 18} ABD = 18

Now add  

AC and CD

{ 5 + 10 = 15 } ACD = 15

18 - 15 = 3  

So ACD is 3 miles shorter then ABD.

Got right on the test

The shortest route is to take segment AD which is 8 miles long.

To determine the shortest route, we need to find the length of segment AD and compare it to the combined length of segments AC and CD. Since segment AD bisects LA, we can use the properties of a line segment bisector to find its length.

Since segment AD bisects LA, we can say that AC = CD

Therefore, the shortest route is to take segment AD, which is 8 miles long, since it is equal to the combined length of segments AC and CD.

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Answer:

Slope = [tex]\frac{5}{6}[/tex]

Step-by-step explanation:

Slope = [tex]\frac{y2 - y1}{x2 - x1}[/tex]

Slope = [tex]\frac{2 - 12}{-8 - 4}[/tex]

Slope = [tex]\frac{-10}{-12}[/tex]

Slope = [tex]\frac{5}{6}[/tex]

Answer:  Slope = [tex]\frac{5}{6}[/tex]

The length of EF in the given triangle is 8.80 m.

Step-by-step explanation:

Step 1:

In the given triangle, the opposite side's length is 16.2 m, the adjacent side's length is x m while the triangle's hypotenuse measures 16.2 m units.

The angle given is 90°, this makes the triangle a right-angled triangle.

So first we calculate the angle of E and use that to find x.

Step 2:

As we have the values of the length of the opposite side and the hypotenuse, we can calculate the sine of the angle to determine the value of the angle of E.

[tex]sinE = \frac{oppositeside}{hypotenuse} =\frac{13.6}{16.2} = 0.8395.[/tex]

[tex]E = sin^{-1} (0.8395), E = 57.087.[/tex]

So the angle E of the triangle DEF is 57.087°.

Step 3:

As we have the values of the angle and the hypotenuse, we can calculate the cos of the angle to determine x.

[tex]cos E = \frac{adjacentside}{hypotenuse} = \frac{x}{16.2} .[/tex]

[tex]cos(57.087) = 0.5433, x = 16.2 (0.5433) = 8.8014.[/tex]

Rounding this off to the nearest hundredth, we get x = 8.80 m.

[tex]\bf (\stackrel{x_1}{-6}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-7}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-7}-\stackrel{y1}{8}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-6)}}}\implies \cfrac{-15}{3+6}\implies \cfrac{-15}{9}\implies -\cfrac{5}{3}[/tex]

[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{8}=\stackrel{m}{-\cfrac{5}{3}}[x-\stackrel{x_1}{(-6)}]\implies y-8=-\cfrac{5}{3}(x+6) \\\\\\ y-8=-\cfrac{5}{3}x-10\implies y = -\cfrac{5}{3}x-2[/tex]

Answer:

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

Step-by-step explanation:

Step 1: Let's find the slope between your two points.

[tex](-6,8); (3,-7)\\\\(x_{1} ,y_{1} )=(-6,8)\\\\(x_{2} ,y_{2} )=(3,-7)[/tex]

Step 2: Use the slope formula

[tex]m = \frac{y_{2} - y_{1} }{x_{2} - x_{1} }\\\\=\frac{(-7) - 8}{3- (-6)} \\\\=\frac{-15}{9}\\\\= \frac{-5}{3}[/tex]

Therefore, the equation is [tex]\frac{-5}{3}[/tex]

Answer:

Part A is Answer C

C=2pi * r

D= 2r

C= 2 * 3.14 * 31.5

C= 197.82

__________________________

Part B is 3115.67 sq cm

A = 3.14 * r*r

A= 3.14 x 31.5x31.5

A=3115.665

Rounded: 3115.67

The circumference of the circle is C = 197.82 cm

The area of the circle is A = 3,115.67 cm²

A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

The equation of circle is ( x - h )² + ( y - k )² = r²

For a unit circle , the radius r = 1

x² + y² = r² be equation (1)

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

Given data ,

Let the diameter of the circle be d = 63 cm

The circumference of a circle is given by the formula:

C = πd

where d is the diameter of the circle and π is the mathematical constant pi, approximately equal to 3.14159.

C = π(63)

C = 197.92 cm

The area of a circle is given by the formula

A = πr²

where r is the radius of the circle. Since we are given the diameter, we can find the radius by dividing the diameter by 2:

r = d/2

r = 63/2

r = 31.5 cm

Substituting the radius r = 31.5 cm into the formula for the area, we get:

A = 3.14159 x 31.5²

A = 3.14159 x 992.25

A = 3,117.15 cm²

Hence , the area of the circle is 3,117.15 cm²

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