Perform the following food service calculation. Size of juice can = 54 oz. Portions of juice served = 6 oz. Number of cases used = 2 Number of cans per case = 12 How many guests can be served? 54 216 1,944 7,776

Answer: A negative correlation

Step-by-step explanation:

If the points in the scatter plot scattered going down to the right, it shows that there are inverse relationship between the quantities.

With the increase of one quantity or variable there is decrease in the other quantity or variable.

Therefore, if in the scatter plot with points loosely scattered going down to the right , then the relationship of the data be classified as a negative correlation.

Answer:

The correct answer is f(n)=3n+38

Step-by-step explanation:

Put in y=mx+b form, so y= f(n), $3 is fee per video game rented and n is the number of video games rented, b is ($18 fixed fee for this year +$20 fee for next year). So, f(n)=3n+38.

Answer:

-6 = -11

Distributive Property

Step-by-step explanation:

A.

4x + 2(x – 3) = 4x + 2x – 11

4x + 2x - 6 = 4x + 2x - 11

6x - 6 = 6x - 11

-6 = -11

since -6 is not equal to -11, so there's no solution

B. Distributive property

The total volume of the flask will be 50.06 [tex]\rm inches ^3[/tex] and if both the sphere and the cylinder are dilated by a scale factor of 2, the resulting volume would be '8' times the original volume.

Given :

Flask can be modeled as a combination of a sphere and a cylinder.

The volume of Sphere is given by the:

[tex]V_s = \dfrac{4}{3}\pi r^3[/tex]

Given - diameter of sphere = 4.5 inches. Therefore, radius is 2.25 inches.

Now, the volume of sphere of radius 2.25 inches will be:

[tex]V_s = \dfrac{4}{3}\times \pi\times (2.25)^3[/tex]

[tex]\rm V_s = 47.71\; inches^3[/tex]

The volume of Cylinder is given by the:

[tex]V_c = \pi r^2h[/tex]

Given - diameter of cylinder = 1 inches then radius is 0.5 inches and height is 3 inches.

Now, the volume of cylinder of radius 0.5 inches and height 3 inches will be:

[tex]V_c = \pi\times (0.5)^2 \times 3[/tex]

[tex]\rm V_c = 2.35\; inches^3[/tex]

Therefore the total volume of the flask will be = 47.71 + 2.35 = 50.06 [tex]\rm inches ^3[/tex].

Now, if both the sphere and the cylinder are dilated by a scale factor of 2 than:

Radius of sphere = [tex]2.25\times 2[/tex] = 4.5 inches

Radius of cylinder = [tex]0.5\times 2[/tex] = 1 inch

Height of cylinder = [tex]3\times 2[/tex] = 6 inches

Now, the volume of sphere when radius is 4.5 inches will be:

[tex]V_s' = \dfrac{4}{3}\times \pi \times (4.5)^3[/tex]

[tex]\rm V_s' = 381.70\; inches ^3[/tex]

And the volume of cylinder when radius is 1 inch and height is 6 inches will be:

[tex]V_c' = \pi \times (1)^2\times 6[/tex]

[tex]\rm V_c'=18.85\;inches^3[/tex]

Therefore the total volume of the flask after dilation by a scale factor of 2 will be = 381.70 + 18.85 = 400.55 [tex]\rm inches ^3[/tex].

Now, divide volume with dilation by theorginal volume of the flask.

[tex]\dfrac{400.55}{50.06}=8[/tex]

Therefore, if both the sphere and the cylinder are dilated by a scale factor of 2, the resulting volume would be '8' times the original volume.

For more information, refer the link given below:

https://brainly.com/question/15861918

Hello : let  A(2,-1)    B(8,4)
the slope is :   (YB - YA)/(XB -XA)
(4+1)/(8-2)  = 5/6

Answer: Equation of line in point slope form,

[tex]y + 1 = 5 ( x - 2 )[/tex]

And, Equation of line in standard form,

[tex]5 x - 6 y = 16[/tex]

Step-by-step explanation:

Since, If a line passes through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] ,

Then the equation of line,

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)[/tex]

Here [tex]x_1 = 2[/tex], [tex]y_1=-1[/tex], [tex]x_2=8[/tex] and [tex]y_2=4[/tex]

Thus, the equation of the given line,

[tex]y-(-1)=\frac{4-(-1)}{8-2} (x-2)[/tex]

⇒ [tex]y+1=\frac{4+1}{8-2} (x-2)[/tex]

⇒ [tex]y+1=\frac{5}{6} (x-2)[/tex] -----(1)

⇒  [tex]6(y+1)= 5(x-2)[/tex]

⇒ 6 y + 6 = 5 x - 10

⇒ 6 = 5x - 6y - 10 ( By subtracting by on both sides )

⇒ 6 + 10 = 5x - 6y  ( By adding 10 on both sides )

⇒ 16 = 5x - 6y

⇒ 5 x - 6 y = 16 ------(2)

Since, in slope for of a line is, [tex]y-y_1= m (x-x_1)[/tex]

Thus, equation (1) shows the in slope form of the line.

And, standard form of the line is ax + by = c where a, b and c are the integers.

Thus, equation (2) shows the standard form of the given line.

The roots of the equation [tex]y=4x^2+2x-30[/tex] are x = -3 and x = 5/2

The given quadratic equation is:

[tex]y=4x^2+2x-30[/tex]

Set y = 0

[tex]4x^2+2x-30=0[/tex]

Factor the trinomial completely

[tex]4x^2-10x+12x-30=0\\\\2x(2x-5)+6(2x-5)=0\\\\(2x-5)(2x+6)=0[/tex]

Set each factor to zero and solve

2x  -  5  =  0

2x  =  5

x  =  5/2

2x  +  6  =  0

2x  =  -6

x  =  -6/2

x  =  -3

The roots of the equation [tex]y=4x^2+2x-30[/tex] are x = -3 and x = 5/2

Learn more on roots of a quadratic equation here: https://brainly.com/question/776122

Answer:

97.

For finding f(g(x)) we will plugin value of g(x) in place of x in f(x).

99.

Step-by-step explanation:

Answer:

[tex]\frac{1}{12}[/tex].

Step-by-step explanation:

Given : Two 6-sided dice are rolled.

To find : what is the probability the sum of the two numbers on the die will be 4.

Solution : We have given

Two 6-sided dice are rolled.

Dice have number { 1,2,3,4,5,6}  { 1,2,3,4,5,6} .

[tex]Probability =\frac{outcome\ happn}{total\ outcome}[/tex].

sum of the two numbers on the die will be 4.

Case (1) : first dice rolled 3 and second dice rolled 1.

{3,1}

3 +1 = 4 .

Case (2) : first dice rolled 1 and second dice rolled 3 .

{1,3}

1 + 3 = 4 .

Case (3) : first dice rolled 2 and second dice rolled 2.

{2,2}

2 + 2 = 4.

Then there are 3 possible outcomes where the sum of the two dice is equal to 4.

The number of total possible outcomes = 36.

[tex]Probability =\frac{3}{36}[/tex].

[tex]Probability =\frac{1}{12}[/tex].

Probability of getting sum of two dice is [tex]\frac{1}{12}[/tex].

Therefore,  [tex]\frac{1}{12}[/tex].

Answer:

The answer is 3 for A P E X

Step-by-step explanation:

Answer:

Perpendicular lines.

Step-by-step explanation:

We have been given that line BC has an equation of a line [tex]y=2x+3[/tex] and line EF has an equation of a line [tex]y=-\frac{1}{2}x+4[/tex]. We are asked to determine what these both equations represent.

We know that slope of two perpendicular lines is negative reciprocal of each other. This means the product of slope of both lines is equal to [tex]-1[/tex].

Let us find the product of slopes of both lines.

[tex]2\times \frac{-1}{2}[/tex]

Upon cancelling 2 with 2 we will get,

[tex]=-1[/tex]

Therefore, the given two equations represent equations of two perpendicular lines.

From the information, A is a right angle, B is an acute triangle and C is an acute angle.

It will be a right triangle if a² + b² = c². It will be аcute if a² + b² > c² and it'll be obtuse if a² + b² < c².

For the first one,

a² + b² = 3² + 4² = 9 + 16 = 25 and c² = 5² = 25

25 = 25

This is a right triangle.

For the second one,

a² + b² = 5² + 6²

= 25 + 36 = 61

c² = 7² = 49

61 > 49 = аcute triangle.

For the third one,

a² + b² = 8² + 9²

= 64 + 81 = 145

c² = 12² = 144

145 > 144 = аcute triangle.

Learn more about triangles on:

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Squaring both sides of an inequality can be valid if you know both sides are non-negative, but it can introduce extraneous solutions. Therefore, it's important to check any solutions against the original inequality to ensure their validity, especially in cases involving negative numbers or functions with restricted domains.

When you're working with inequalities, you have to be careful when performing operations like squaring both sides. Unlike equalities, where multiplication or division by the same number on both sides does not change equality, with inequalities, the effect can be more complex due to the direction of the inequality sign and the possibility of dealing with negative numbers.

For instance, squaring both sides of an inequality is not always a valid operation because if one or both sides of the inequality are negative, squaring could lead to incorrect results. When you square a negative number, it becomes positive, which could potentially reverse the inequality's direction. However, if you know that both sides of the inequality are non-negative, then squaring both sides is permissible. This concept is similar to solving quadratic constraints without introducing square roots, using identities like |(1 + ix)²|² = ([1 + ix|²)².

To avoid introducing solutions that were not there originally (extraneous solutions), it is important to check the solutions obtained after squaring against the original inequality. An example where squaring both sides might be questioned is when solving trigonometric inequalities, where a common mistake is to square both sides without considering the domain of the original function.

divide total miles by speed

125/65 = 1.923 hours

there are 60 minutes per hour

multiply 1.923*60 = 115.384 minutes

 rounded off to nearest whole number = 115 minutes