The sum of 2 numbers is 27. One half of the first number plus one third of the
second number is 11. Find the numbers.

The correct response variable is the amount of pain relief.

Given that,

A tall glass of ice water, according to some, can help migraine sufferers find relief. Multiple migraine sufferers will be recruited by researchers to participate in a test. The individual will either take a placebo pill or a common painkiller when they get a migraine. Additionally, only half of each group will take the pill with water; the other half will sip on a small amount of water. The quantity of pain relief is then reported by participants.

To find :  What is the response variable in this experiment.

Explanation :

Response variable or study variable, in general called as dependent variable  is the variable of main focus in study. We want to study the changes in explanatory or independent variables are associated with response variable. Sometimes we want to measure the effect of predictors i.e explanatory variables on response variable.

For example in hand, we want to determine whether the drinking ice water is associated with amount of pain relief. Hence in this study, response variable is the amount of pain relief.

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Answer:2

Step-by-step explanation:

Answer:

3.7 n^2 + 4n + 2.1

Step-by-step explanation:

2.7 n^2 + n^2 = 3.7 n^2

6n - 2n = 4n

7.8 - 5.7 = 2.1

Answer:

1

5z + 6z = 11z

2

9y + -6y = 3y

3

ANSWER ( 11z + 3y)

Answer:

4x

Step-by-step explanation:

bcoz

y = 6 - 2x

6-2x = 4x

y=4x

On 6th day the Blake and Nicole will be on same page

Consider the case of Blake

The initial page number = 40

Number of pages per day = 10

Consider the B is the page number and t is the number day

Then the function will be

B = 40 + 10t

Consider the case of Nicole

The initial page number = 10

Number of pages per day = 15

Consider the N is the page number and t is the number day

Then the function will be

N = 10 + 15t

Draw the graph using the functions

Hence, on 6th day the Blake and Nicole will be on same page

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The sales tax is $1.2  and the total cost of the item is  $21.2   .

In the question,

it is given that ,

the selling price of the item is $20.

the rate of sales tax is = 6^ ,

so the sales tax can be calculated using the formula

sales tax = 6% of selling price

So , sales tax = 6% of 20

= 0.06 * 20

= 1.2

so , the sales tax is $1.2

the total cost of the item will be = selling price + sales tax

= 20 + 1.2

= 21.2

Therefore , The sales tax is $1.2  and the total cost of the item is  $21.2   .

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Answer:

===========================

Answer:

Step-by-step explanation:

Forming the equation,

→ 2x + 3 = -3x + 3

Now the value of x will be,

→ 2x + 3 = -3x + 3

→ 2x + 3x = 3 - 3

→ 5x = 0

→ x = 0/5

→ [ x = 0 ]

Then the value of y will be,

→ y = -3x + 3

→ y = -3(0) + 3

→ y = 0 + 3

→ [ y = 3 ]

Hence, the value of y is 3.

Check the picture below.

Answer:

  8.75

Step-by-step explanation:

You want the greatest possible x-coordinate of point A such that for any point B on the y-axis between (-24) and 25, the segment AB has a common point with the line segment PQ, where P(5, -12), Q(5, 9).

If we designate the points on the y-axis as X(0, -24) and Y(0, 25), we find that point A must lie in the triangle bounded by lines XY, XP, and YQ. The x-coordinate of the point of intersection of lines XP and YQ will be the greatest x-coordinate that point A can have.

The line through points (x1, y1) and (x2, y2) can be written as ...

  (y2 -y1)(x -x1) -(x2 -x1)(y -y1) = 0

This equation is readily simplified to general form ax+by+c = 0.

Line XP

  (-12-(-24))(x -0) -(5-0)(y -(-24)) = 0

  12x -5y -120 = 0

Line YQ

  (9 -25)(x -0) -(5 -0)(y -(25)) = 0

  -16x -5y +125 = 0

We want the value of x that satisfies these equations. That can be found by subtracting the second equation from the first:

  (12 -5y -120) -(-16x -5y +125) = (0) -(0)

  28x -245 = 0

  x = 245/28 = 8.75

The greatest x-coordinate is x = 8.75.

Note that because the graph is slightly deformed to the left, it is impossible to work out the exact bearing. Below, however, are steps on how to get the bearing of a map.

Calculate the angle clockwise from north to determine a bearing. Begin with the first site by drawing a vertical line symbolizing north. Draw a line from the starting point to the ending point. Calculate the clockwise angle formed by the north line and this line.

When measuring a bearing, three principles must be followed:

Note that a bearing is an angle in degrees calculated clockwise from north in mathematics. Bearings are often specified in three figures. 30° clockwise from north, for example, is generally represented as 030°.

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Applying the inscribed angle theorem, we have:

9. B. m∠ABC = 70°

10. F. m∠Z = 54°

11. According to the two-tangent theorem, x is: D. 8 m

An inscribed angle in a circle has a measure that is half of the measure of the intercepted arc, based on the inscribed angle theorem.

The two-tangent theorem states that if two tangents are drawn from a circle to meet at a point outside the circle, the two tangents are equal to each other.

9. Measure of arc AC = 360 - 120 - 100

Measure of arc AC = 140°

m∠ABC = 1/2(measure of arc AC) [inscribed angle theorem]

m∠ABC = 1/2(140)

m∠ABC = 70° [option B]

10. Arc XYZ = 2(m∠X) [inscribed angle theorem]

Arc XYZ = 2(126) = 252°

Arc WXY = 360 - arc XYZ

Arc WXY = 360 - 252

Arc WXY = 108°

m∠Z = 1/2(arc WXY) [inscribed angle theorem]

m∠Z = 1/2(108)

m∠Z = 54° [option F]

11. x = 10 - 2 [two-tangent theorem]

x = 8 m [option D]

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Answer:

Step-by-step explanation:

2y=-3x-5

y=-3/2x-5/2

Answer:

Y= -2.5

X= -1.6

Step-by-step explanation:

2y+3x= -5

2y+3(0)= -5

2y= -5

2y÷2=y

-5÷2= -2.5

Y=-2.5

2y+3x= -5

2(0)+3x= -5

3x= -5

3x÷3=x

-5÷3= -1.6

X= -1.6

Answer:

Step-by-step explanation:

1=88

2=42

3=42+25+x=180

3=180-67

The coordinates of the points dividing the line in 5:3 is (3/2, 3)

The section formula gives the coordinates of a point which divides the line joining two points in a ratio, internally or externally.

Given a line LM, passing through points  (-1,-2) and (3,6) a point is dividing it in a ratio of 5:3

According to section formula,

(x, y) = (5*3 - 3*1)/8, (5*6 - 3*2)/8

(x, y) = (3/2, 3)

Hence, The coordinates of the points dividing the line in 5:3 is (3/2, 3)

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Answer:

x=22

Step-by-step explanation:

5x+6+3x-2=180

8x+4=180

8x=176

x=22

The amount in grams of food A and B she feeds this group of rats each day will be 2200003.84 gm and 1100006.4 gm respectively.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

Given that, she provides a certain set of lab rats with a daily meal that contains exactly 32 units of niacin and 22000 units of retinol. She uses two different brands of industrial pellet food.

If food A has 100 units of retinol and 0,12 units of niacin per gram.Niacin 0.20 units and retinol 50 units are both included in Food B per gram. The grams of each food she feeds this group A of rats each day is,

=32×0.12+22000×100

=2200003.84 gm

If food B contains 0,20 units of niacin and 50 units of retinol per gram.The grams of each food she feeds this group A of rats each day is,

=32×0.20+22000×50

=1100006.4

Thus, the amount in grams of food A and B she feeds this group of rats each day will be 2200003.84 gm and 1100006.4 gm respectively.

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well, we had a cylinder with 7mL of water, in the rock goes and kaboom the volume for the cylinder and its contents is 9 mL, well, the displaced water from the rock is equivalent to its volume, as Archimedes would properly point out, so since it was 7mL and now is 9mL well, the extra 2mL is the volume of the rock :).

sidenote:  Archimedes is Da Bomb!!!!

now, we know the rock weights 24 grams, and we also know its volume is 2mL, so its density is simply g/mL, or [tex]\cfrac{24g}{2mL}\implies 12~\frac{g}{mL}[/tex]

Answer:it will take him roughly 75 minutes or an hour and 15 minutes:)

Step-by-step explanation:

so you take 2 and multiply it by the 30 minuets and then divide 30 by 2 so it will look like this

2x30=60(1 hour)

30÷2=15

now add 60 + 15 and you get

75

Answer:

h=6+(2t)

Step-by-step explanation:

Option C is correct which is dC/dt = π (dd/dt).

According to the question,

We know that the diameter of the circle is half the radius of the circle.

d = r/2

By transferring r to the left-hand side and d to the right-hand side

r = d/2

We also know that circumference of the circle is

C=2πr

C=2πd/2

C=πd

Now we will differentiate on both the side with respect to t and we will get,

dC/dt = π (dd/dt)

Differentiation is a technique for tracking down the subordinate of a capability. Differentiation is a process, where we find the momentary rate of change in capability in light of one of its variables. We usually differentiate with respect to time which is represented as ds/dt.

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The value of the variable m in the rectangle is given as follows:

m = 12.5.

The segments from the rectangle, and their lengths, are given as follows:

They are opposite vertices of the rectangle, as they do not have any common vertex.

Since they are opposite vertex, it doesn't matter if these segments are bases, heights or diagonals, they will have the same length.

Thus the numeric value of variable m is obtained as follows:

WY = XZ

(as they have the same length).

Replacing the measures of each of these segments:

12m + 7 = 16m - 43

12m - 16m = -43 -7

-4m = -50

4m = 50 (multiplication by -1).

m = 50/4

m = 12.5.

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To calculate the distance between two points, we have to:

[tex]\large\displaystyle\text{$\begin{gathered}\sf The \ points\ are \left \{ {{A=(x_1,y_1)} \atop {B=(x_2,y_2)}} -\to\boldsymbol{\sf{m=\frac{\Delta y}{\Delta x }\iff \ m=\frac{y_2-y_1}{x_2-x_1} }} \right. \end{gathered}$}[/tex]

We have that the points to calculate the slope are:  (x₁ = -4, y₁ = 4) and (x₂ = -15, y₂ = 2)

Add the data in the formula:              

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{m=\frac{y_2-y_1}{x_2-x_1} } \end{gathered}$}} \\ \\ \boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{m=\frac{2-4}{-5-(-4) } } \end{gathered}$}} \\ \\ \boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{m=\frac{-2}{-11} } \end{gathered}$} }}[/tex]

The statement of Gabriella, “The graph will not have an inverse function.” is incorrect. Option B is correct.

Let us understand about the given graph:

The given graph is a graph of a cube root function.

So, the statement of Noelle, “The graph represents the function [tex]f(x)=\sqrt[3]{x}[/tex]." is correct.

So, option A is not correct.

The inverse of a cube root function is a cubic function.

So, the statement of Gabriella, “The graph will not have an inverse function.” is incorrect.

So, option B is correct.

The domain and range of the cube root function are all real numbers.

So, the statement of Julian, “The domain and range of the function is all real numbers.” is correct.

So, option C is not correct.

From the graph, we can see f(-1) = -1.

So, the statement of Yemen, “The value of f(-1) = -1.” is correct.

So, option D is not correct.

Thus, the statement of Gabriella, “The graph will not have an inverse function.” is incorrect. Option B is correct.

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Answer:

  P'(-16, 0)

Step-by-step explanation:

You want the coordinates of the image of P(-4, 0) when the figure is dilated by a factor of 4 about the origin.

Dilation about the origin multiplies each coordinate by the dilation factor:

  P' = 4P

  P' = 4(-4, 0) = (-16, 0)

The coordinate of the image point are (-16, 0).

The words that describe the pattern that can be used to complete the table is that the number of lines is double the number of figures, which indicates that the correct option is option A

A. The total number of lines y is two times the figure number x

An equation is a mathematical statement that connects two expression with an equals sign.

The pattern that can be used to complete the table is therefore;

The number of lines, y, is twice the number of figures, x

The relationship expressed mathematically as an equation is presented as follows;

y = 2·x

The completed table is presented as follows;

Figure Number, x   [tex]{}[/tex] Total Lines, y                        [tex]{}[/tex] Ordered pair

1                         [tex]{}[/tex]            2                                          (1, 2)

2                         [tex]{}[/tex]           4                                          (2, 4)

3                         [tex]{}[/tex]           6                                          (3, 6)

4                         [tex]{}[/tex]           8                                          (4, 8)

5                         [tex]{}[/tex]           10                                        (10, 5)

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